coe

📁 Source: MathlibTest/coe.lean

Statistics

Metric	Count
Definitions coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe, coe	52
Theorems coe, coe, coe, coe, coe, coe	6
Total	58

AbstractCompletion

Definitions

Name	Category	Theorems
coe 📖	CompOp	17 math math: mapEquiv_coe, dense, compare_coe, continuous_coe, closure_range, uniformContinuous_coe, extend_def, extend_coe, map_coe, extend_comp_coe, extension₂_coe_coe, inseparable_extend_coe, LaurentSeries.valuation_LaurentSeries_equal_extension, LaurentSeries.LaurentSeries_coe, map₂_coe_coe, isUniformInducing, isDenseInducing

CategoryTheory.Idempotents.Karoubi

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

CategoryTheory.Subgroupoid

Definitions

Name	Category	Theorems
coe 📖	CompOp	10 math math: inclusion_inj_on_objects, inclusion_refl, coe_comp_coe, hom.faithful, coe_inv_coe', coe_inv_coe, inclusion_trans, hom.inj_on_objects, inclusion_faithful, inclusion_comp_embedding

ClopenUpperSet.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Complex.UnitDisc

Definitions

Name	Category	Theorems
coe 📖	CompOp	23 math math: coe_eq_zero, normSq_lt_one, coe_neg, coe_smul_circle, coe_conj, coe_pow, isEmbedding_coe, coe_mk, coe_closedBall_smul, instCanLiftCoeLtRealNormOfNat, re_coe, coe_mul, coe_smul_closedBall, coe_injective, continuous_coe, im_coe, coe_zero, norm_lt_one, coe_injective_iff, coe_star, coe_inj, coe_circle_smul, sq_norm_lt_one

ContDiffMapSupportedIn.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousAffineEquiv

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousAffineEquiv.ContinuousAffineMap

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousAlgEquiv

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousAlgHom.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousLinearEquiv.ContinuousLinearMap

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousLinearMap.LinearMap

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ContinuousLinearMap.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

DFunLike

Definitions

Name	Category	Theorems
coe 📖	CompOp	37214 math, 4 bridge math: AddGroupNorm.add_apply, ContinuousMap.dense_setOf_contDiff, CircleDeg1Lift.mono, AdicCompletion.of_surjective_iff, Equiv.Perm.decomposeFin_symm_of_refl, Orthonormal.exists_orthonormalBasis_extension_of_card_eq, MultilinearMap.map_piecewise_smul, Prod.Lex.toLex_lt_toLex', TopCat.isInducing_pullback_to_prod, ArithmeticFunction.vonMangoldt.residueClass_eq, TopologicalSpace.OpenNhds.coe_id, Finsupp.coe_neg, FirstOrder.Language.PartialEquiv.toEmbedding_apply, QuadraticMap.polar_zero_left, Equiv.sumEmpty_symm_apply, IsLocalization.algebraMap_apply_eq_map_map_submonoid, AffineSubspace.wOppSide_lineMap_right, normalize_one, SSet.OneTruncation₂.nerveEquiv_apply, AffineMap.coe_comp, MonoidHom.map_exists_left_inv, SchwartzMap.norm_toLp_le_seminorm, WeierstrassCurve.Jacobian.map_addX, Polynomial.fderiv, MeasurableEquiv.injective, Matrix.l2_opNorm_toEuclideanCLM, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, IsLocalMaxOn.fderivWithin_nonpos, ContinuousMapZero.coe_star, Polynomial.mul_div_eq_iff_isRoot, CliffordAlgebra.unop_reverseOp, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂, AddMonoid.Coprod.swap_surjective, ContDiffMapSupportedIn.coe_toBoundedContinuousFunction, val_toAddUnits_apply, OrthonormalBasis.singleton_repr, DirectSum.decompose_sub, Pi.comul_eq_adjoint, DFinsupp.coprodMap_apply, FiniteField.Extension.frob_apply, MvPolynomial.pUnitAlgEquiv_symm_monomial, Complex.norm_conj, Algebra.PreSubmersivePresentation.jacobian_ofAlgEquiv, CircleDeg1Lift.units_inv_apply_apply, ContinuousAlternatingMap.cons_add, MvPowerSeries.coeff_zero_eq_constantCoeff_apply, LinearMap.det_toContinuousLinearMap, OrderDual.isBounded_preimage_toDual, DirectSum.IsInternal.ofBijective_coeLinearMap_same, SymAlg.unsym_comp_sym, LinearEquiv.multilinearMapCongrLeft_symm_apply, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, Behrend.roth_lower_bound, QuotientAddGroup.kerLift_mk, MvPolynomial.funext_iff, OrderRingHom.coe_orderAddMonoidHom_apply, ValueDistribution.logCounting_zero, ContinuousLinearEquiv.preimage_symm_preimage, Polynomial.rightInverse_ofMultiset_roots, MeasureTheory.exists_pos_preimage_ball, MvPolynomial.eval_indicator_apply_eq_one, Polynomial.support_monomial, ProbabilityTheory.Kernel.restrict_apply', MultilinearMap.domDomCongrLinearEquiv'_symm_apply, MeasureTheory.Measure.prod_apply_symm, continuous_decomposeProdAdjoint, TensorProduct.finsuppRight_apply, LieModule.shiftedGenWeightSpace.shift_apply, hasFDerivAt_iff_hasDerivAt, LieEquiv.bijective, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, Homeomorph.isClosed_preimage, Quaternion.normSq_eq_zero, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv, IsAlgebraic.exists_nonzero_dvd, AlgebraicGeometry.Scheme.toSpecΓ_apply, partialSups_apply, ContinuousLinearEquiv.antilipschitz, CuspFormClass.qExpansion_isBigO, AddCircle.measure_univ, LieModuleHom.map_sub, UniformConvergenceCLM.isEmbedding_coeFn, SkewMonoidAlgebra.mapDomain_smul, LatticeHom.toFun_eq_coe, DFinsupp.comul_single, VectorBundleCore.toFiberBundleCore_coordChange, upperBounds_supClosure, MonoidAlgebra.mapDomainRingEquiv_single, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, AddMonoidAlgebra.modOf_apply_add_self, HurwitzZeta.hasSum_int_hurwitzZetaOdd, IsometryClass.diam_image, geometric_hahn_banach_open, MeasureTheory.SimpleFunc.coe_range, MvPolynomial.join₁_rename, SSet.op_δ, AddUnits.orderEmbeddingVal_apply, DistribMulAction.toModuleAut_apply, TensorProduct.mapInclIsometry_apply, IsSymmetricAlgebra.lift_eq, ContinuousOn.clm_apply, Set.chainHeight_eq_of_relEmbedding, MvPowerSeries.hasSubst_def, ModularForm.coe_mul, InitialSeg.trans_apply, LinearMap.IsSymmetric.clm_adjoint_eq, MeasureTheory.Measure.MeasureDense.approx, AddMonoidAlgebra.singleHom_apply, Pi.nonUnitalRingHom_apply, MeasureTheory.Integrable.measure_norm_gt_lt_top_enorm, AddUnits.map_mk, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply', FreeAddMonoid.lift_symm_apply, Polynomial.Gal.galActionHom_restrict, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, AffineEquiv.coe_symm_toEquiv, BoundingSieve.nu_lt_one_of_dvd_prodPrimes, Ideal.toCotangent_to_quotient_square, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, AddSubgroup.centerToAddOpposite_apply_coe, pow_ofDual, SemiNormedGrp₁.comp_apply, Sequential.homeoOfIso_apply, isCompl_toDual_iff, LinearMap.comp_toSpanSingleton, Derivation.map_natCast, AddSubmonoid.LocalizationMap.mk'_spec, ContinuousMap.toLp_inj, LieHom.coe_zero, nndist_ofMul, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, LieAlgebra.Extension.incl_apply_mem_ker, Finsupp.snd_sumFinsuppLEquivProdFinsupp, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, WeierstrassCurve.Projective.map_dblZ, TopCat.binaryCofan_isColimit_iff, OrderIso.sumAssoc_apply_inl_inl, KaehlerDifferential.kerCotangentToTensor_toCotangent, Rep.resCoindHomEquiv_symm_apply_hom, Monoid.Coprod.inl_injective, RCLike.conj_re, ContinuousMultilinearMap.map_piecewise_smul, NumberField.basisMatrix_eq_embeddingsMatrixReindex, QuadraticMap.Isometry.ext_iff, Polynomial.isUnit_C_add_X_mul_iff, MonoidHom.CompTriple.comp_apply, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, OrderMonoidIso.apply_symm_apply, LinearEquiv.coe_toEquiv, CategoryTheory.Functor.functorHomEquiv_apply_app, CoalgEquiv.coe_toCoalgHom, MulAction.compHom_smul_def, QuadraticMap.not_anisotropic_iff_exists, Representation.repOfTprodIso_inv_apply, LinearIsometryEquiv.strictConvex_preimage, Quaternion.star_mul_self, CoalgHom.ext_of_ring_iff, Finset.weightedVSub_sdiff, Rep.resCoindHomEquiv_apply_hom, Polynomial.degree_normalize, MeasureTheory.tendsto_integral_thickenedIndicator_of_isClosed, MvPolynomial.aeval_sum, DomMulAct.smul_monoidHom_apply, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', ContinuousLinearMap.sum_comp_single, Finsupp.sum_toMultiset, WithBot.coe_toDualTopEquiv_eq, ContinuousMap.ext_iff, Polynomial.isMonicOfDegree_X_add_one, Cardinal.aleph_le_beth, RootPairing.InvariantForm.apply_reflection_reflection, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, CategoryTheory.Quiv.equivOfIso_symm_apply, CategoryTheory.PreZeroHypercover.isoMk_hom_h₀, AffineIsometryEquiv.coe_constVSub, Polynomial.natDegree_mul_leadingCoeff_inv, MvPolynomial.dvd_monomial_one_iff_exists, Finsupp.range_subset_insert_frange, GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset, Quaternion.coe_normSq_add, PiLp.continuousLinearEquiv_symm_apply, minpoly_sub_algebraMap_splits, WittVector.bind₁_frobeniusPoly_wittPolynomial, Homeomorph.isInducing, WithBot.ofDual_map, Submodule.toAddSubgroup_toZModSubmodule, AlgCat.hom_inv_apply, AbsoluteValue.map_neg, Fin.sign_cycleIcc_of_eq, Cardinal.toNat_ofENat, WithZero.logOrderIso_apply, ContinuousMap.isUniformInducing_equivBoundedOfCompact, CliffordAlgebra.contractRight_algebraMap_mul, Equiv.Perm.SameCycle.exists_pow_eq_of_mem_support, CategoryTheory.Functor.map_homCongr, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr, Finsupp.fst_sumFinsuppLEquivProdFinsupp, CategoryTheory.nerve.edgeMk_edge, Complex.log_conj_eq_ite, LinearMap.restrictScalars_toMatrix, IsometryEquiv.image_sphere, MeasureTheory.SimpleFunc.exists_forall_le, smoothSheafCommRing.ι_forgetStalk_inv, Submodule.starProjection_apply_eq_isComplProjection, Matrix.comp_diagonal_diagonal, AddMonoidHom.coe_rangeRestrict, Lagrange.interpolate_one, RingEquiv.piCongrRight_apply, MeasureTheory.Lp.toTemperedDistributionCLM_apply, LSeries.convolution_one_eq_convolution_zeta, SupBotHom.dual_comp, StarModule.decomposeProdAdjointL_symm_apply, CategoryTheory.GrothendieckTopology.Plus.toPlus_mk, Filter.map_mul, MeasureTheory.StronglyMeasurable.integral_kernel_prod_right'', fderiv_iteratedFDeriv, RCLike.sqrt_eq_ite, ContinuousAlgHom.coe_mk', Trivialization.pullback_linear, Finsupp.finite_of_degree_le, ContinuousMap.HomotopyRel.prod_apply, WithTop.map_ofDual, Equiv.sumAssoc_symm_apply_inl, Algebra.normalizedTrace_map, ContinuousLinearMap.inner_map_map_of_mem_unitary, ContinuousLinearEquiv.symm_preimage_preimage, InitialSeg.inj, sign_intCast, AffineIsometryEquiv.pointReflection_apply, Ideal.Quotient.exists_algHom_fixedPoint_quotient_under, OrderIso.isLUB_image, Cardinal.natCast_lt_toENat_iff, RootPairing.rootForm_self_smul_coroot, CategoryTheory.uliftCoyonedaEquiv_apply, Cardinal.toNat_surjective, CliffordAlgebra.toBaseChange_reverse, FormalMultilinearSeries.comp_rightInv_aux1, Submodule.toAddSubmonoid_toNatSubmodule, Circle.periodic_exp, CompleteLatticeHom.range_coe, Equiv.extendSubtype_mem, MeasureTheory.LpToLpRestrictCLM_coeFn, StarModule.selfAdjointPart_add_skewAdjointPart, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, ContinuousLinearMap.hasFPowerSeriesOnBall, SimpleGraph.UnitDistEmbedding.iso_p_apply, Polynomial.taylor_eval, Affine.Simplex.affineCombination_mem_closedInterior_iff, AdjoinRoot.algEquivOfAssociated_apply_root, AlgHom.coe_toLinearMap, MeasureTheory.Measure.bind_apply, map_comp_one, MeasurableEquiv.piCurry_apply, Set.IsPWO.exists_monotone_subseq, FirstOrder.Language.Embedding.map_rel, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, hasSum_mellin_pi_mul_sq', PrincipalSeg.trans_apply, Ordinal.toNimber_eq_zero, FirstOrder.Language.ElementaryEmbedding.map_rel, DFinsupp.liftAddHom_apply, RatFunc.laurent_injective, DilationEquiv.toPerm_apply, AddMonoidHom.coe_ker, unitsEquivNeZero_symm_apply, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, Equiv.prodSumDistrib_apply_left, TensorAlgebra.ofDirectSum_of_tprod, Matrix.natCast_kronecker, SemidirectProduct.rightHom_inl, AlgHom.mem_range_self, Bialgebra.comulAlgHom_apply, map_symmDiff', cfcₙ_def, Affine.Simplex.altitudeFoot_restrict, AddMagmaCat.coe_id, Submonoid.mem_map_equiv, Subalgebra.inclusion_right, TensorProduct.forall_vanishesTrivially_iff_forall_fg_rTensor_injective, AddCircle.coe_equivIco_mk_apply, AffineMap.lineMap_apply_module, NNReal.orderIsoIccZeroCoe_apply_coe_coe, LieDerivation.IsKilling.ad_mem_ker_killingForm_ad_range_of_mem_orthogonal, AlgebraicGeometry.QuasiCompact.isCompact_preimage_singleton, LinearMap.apply_symm_toPerfPair_self, LinearMap.SeparatingRight.toMatrix₂', ContinuousLinearMap.rightInverse_of_comp, MulHom.coe_snd, FreeMonoid.map_apply_map_symm_eq, ZeroHom.zsmul_apply, LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, KaehlerDifferential.mvPolynomialBasis_apply, PowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, MeasurableEquiv.surjective, Submodule.rTensorOne_symm_apply, Finset.Colex.toColex_le_singleton, Finsupp.mulHom_ext'_iff, DistLat.hom_inv_apply, iSupIndep.linearEquiv_symm_apply, Equiv.invFun_as_coe, MvPowerSeries.WithPiTopology.tendsto_trunc_atTop, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, Matrix.toLinAlgEquiv_one, LinearIsometryEquiv.hasStrictFDerivAt, AlgebraicGeometry.Scheme.fromSpecStalk_closedPoint, AlgebraicGeometry.SurjectiveOnStalks.eq_stalkwise, Bialgebra.comul_natCast, CategoryTheory.ComposableArrows.opEquivalence_counitIso_inv_app_app, Finsupp.linearCombination_apply_of_mem_supported, CategoryTheory.mateEquiv_counit_symm, PMF.tsum_coe, DirectSum.mulHom_of_of, MeasureTheory.mulEquivHaarChar_smul_integral_map, IsUpperSet.ofDual, ContinuousLinearMap.derivWithin_of_bilinear, HahnModule.support_smul_subset_vadd_support', LinearMap.inl_map_mul, BoolAlg.coe_id, VitaliFamily.FineSubfamilyOn.measure_diff_biUnion, PEquiv.vecMul_toMatrix_toPEquiv, AddMonoidAlgebra.mul_single_apply, LinearMap.IsProj.map_mem, PowerSeries.hasSum_aeval, AlgebraicGeometry.Proj.fromOfGlobalSections_resLE, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, MonoidWithZeroHom.comp_apply, Polynomial.rootSet_mapsTo, Homeomorph.smulOfNeZero_symm_apply, affineHomeomorph_image_Ioc, AddCon.sSup_eq_addConGen, Language.map_kstar, HasStrictFDerivAt.isLittleOTVS, ConjAct.smul_def, ValuationRing.mem_integer_iff, minpoly.ToAdjoin.injective, RootPairing.RootPositiveForm.algebraMap_rootLength, AlternatingMap.sub_apply, Finset.weightedVSubOfPoint_map, Filter.Germ.coe_coeMulHom, FirstOrder.Language.Equiv.map_fun, Equiv.Perm.sameCycle_conj, Algebra.SubmersivePresentation.cotangentComplexAux_injective, Valued.isOpen_closedball, SemimoduleCat.Hom.hom₂_apply, Equiv.right_vsub_pointReflection, Matrix.GeneralLinearGroup.det_scalar, Bundle.ContMDiffRiemannianMetric.isVonNBounded, IsLocalization.surjective_quotientMap_of_maximal_of_localization, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_apply, MeasureTheory.OuterMeasure.map_iInf, ContinuousLinearEquiv.equivOfInverse'_apply, SimpleGraph.Iso.map_adj_iff, AddSubmonoid.LocalizationMap.mk'_eq_iff_eq_add, Ordinal.principal_add_omega, LinearMap.baseChange_eq_ltensor, LaurentPolynomial.degree_C_mul_T_ite, MeasureTheory.lpNorm_conj, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, CategoryTheory.Functor.natTransEquiv_apply_app, RingTheory.Sequence.isWeaklyRegular_map_algebraMap_iff, Module.Flat.iff_lTensor_exact', NonUnitalAlgHom.map_smul, CategoryTheory.Pseudofunctor.DescentData.subtypeCompatibleHomEquiv_toCompatible_presheafHomObjHomEquiv, WeierstrassCurve.Projective.map_neg, Module.Basis.det_comp_basis, Module.Basis.equivFun_self, Polynomial.X_pow_mul_assoc_C, MeasureTheory.vaddInvariantMeasure_iff, Polynomial.mem_aroots', Equicontinuous.inducing_uniformFun_iff_pi, ClosureOperator.setOf_isClosed_eq_range_closure, CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_desc, CategoryTheory.coyonedaEquiv_symm_app_apply, TensorProduct.enorm_lid, CommAlgCat.comp_apply, AlgebraicGeometry.Scheme.bot_mem_grothendieckTopology, Module.Basis.coe_map, WittVector.ghostMap.bijective_of_invertible, HahnSeries.SummableFamily.zero_apply, Submodule.topEquiv_symm_apply_coe, LinearMap.charpoly_def, OrderIso.map_radical, Polynomial.separable_X_add_C, SetTheory.PGame.default_nim_one_rightMoves_eq, Lagrange.eval_iterate_derivative_eq_sum, DirichletCharacter.changeLevel_injective, Field.Emb.Cardinal.equivLim_coherence, Cardinal.toNat_ofNat, Polynomial.map_dickson, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff, SubMulAction.ofStabilizer.conjMap_comp_apply, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerLeft, Polynomial.mahlerMeasure_const, Algebra.RingHom.adjoin_algebraMap_apply, AddGroupNorm.coe_le_coe, TrivSqZeroExt.fstCLM_apply, BoundedLatticeHom.coe_toLatticeHom, ProbabilityTheory.Kernel.prod_apply', Ideal.Filtration.submodule_closure_single, WithOne.coeMulHom_apply, MonomialOrder.sPolynomial_leadingTerm_mul', TopCat.PrelocalPredicate.res, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, MeasureTheory.SignedMeasure.toMeasureOfZeroLE_apply, ProbabilityTheory.Kernel.tendsto_m_density, exists_continuous_sum_one_of_isOpen_isCompact, iSupIndep.dfinsupp_lsum_injective, MulChar.equivToUnitHom_mul_apply, LinearMap.BilinForm.dualSubmoduleParing_spec, Polynomial.eraseLead_monomial, CategoryTheory.PreGaloisCategory.mulAction_def, SymmetricAlgebra.lift_ι_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, isSublattice_preimage_ofDual, CommRingCat.KaehlerDifferential.map_d, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm, continuous_cfcₙHomSuperset_left, MeasureTheory.condExpInd_of_measurable, Fin.valOrderEmb_apply, SubAddAction.map_ofFixingAddSubgroupUnion_bijective, Submodule.FG.rTensor.directedSystem, MulHom.id_apply, OreLocalization.numeratorHom_surjective_of_finite, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, Fin.univ_map_def, ProbabilityTheory.absolutelyContinuous_posterior_iff, Matrix.vecMulVec_empty, IsAddIndecomposable.image_baseOf_neg_comp_eq, SpectrumRestricts.nnreal_of_nonneg, AddHom.coe_prodMap, cfcₙL_integral, AddEquiv.coprodComm_apply, toLex_sub, Diffeomorph.coe_refl, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left_symm, TopologicalSpace.Opens.id_apply, Matrix.replicateCol_cons, MvPolynomial.coe_C, FreeMonoid.freeMonoidCongr_of, Derivation.apply_eval_eq, Algebra.PreSubmersivePresentation.jacobiMatrix_naive, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm', DFinsupp.single_eq_same, LatticeHom.withTopWithBot_apply, ProbabilityTheory.Kernel.sectR_apply, IsDiscreteValuationRing.addVal_zero, OneHom.withTopMap_apply, Topology.lawsonClosed_of_lowerClosed, ContinuousLinearMap.le_of_opNorm_le_of_le, FirstOrder.Language.LEquiv.onTerm_symm_apply, LieDerivation.coe_smul, InfHom.top_apply, LieDerivation.lie_der_ad_eq_ad_der, ModuleCat.MonoidalCategory.braiding_hom_apply, orderOf_map_dvd, AddValuation.map_sub_swap, PiTensorProduct.lift_reindex, OrderRingIso.ext_iff, StieltjesFunction.measure_univ_of_tendsto_atBot_atBot, SupHom.subtypeVal_coe, OrderIsoClass.map_le_map_iff, Rep.coe_linearization_obj_ρ, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, MeasureTheory.Measure.restrict_singleton, AddSubgroup.quotientEquivProdOfLE_symm_apply, Finsupp.mapRange_apply, reindex_mem_doublyStochastic, RCLike.one_re, IsometryEquiv.image_emetric_closedBall, Finsupp.coe_sumElim, MvPowerSeries.coeff_zero_eq_constantCoeff, LinearMap.BilinForm.zero_right, MeasureTheory.IsZeroOrProbabilityMeasure.measure_univ, ContMDiffMap.coeFnMonoidHom_apply, dot_self_cross, CategoryTheory.Functor.homObjEquiv_apply_app, Finset.affineCombination_vsub, SubMulAction.ofFixingSubgroup_insert_map_apply, MeasurableEquiv.preimage_symm, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three_assoc, CliffordAlgebra.contractRight_algebraMap, RatFunc.liftMonoidWithZeroHom_apply, CategoryTheory.CoreSmallCategoryOfSet.functor_obj, LocallyConstant.congrRight_apply, coe_iterateFrobenius_mul, PerfectionMap.lift_symm_apply, NonUnitalAlgHom.congr_fun, AddMonoidAlgebra.lift_apply', continuousOn_stereoToFun, addMonoidAlgebraEquivDirectSum_apply, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, ofBoolRing_one, Order.IsSuccPrelimit.dual, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, ModularForm.smul_slash, MvPolynomial.algHom_ext_iff, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_apply_coe, OrderEmbedding.supIrredLowerSet_apply, LinearIsometryEquiv.comp_fderiv, AffineMap.lineMap_vsub_left, DFinsupp.lsum_lsingle, WeierstrassCurve.map_a₂, AddMonoidAlgebra.mapDomainRingEquiv_apply, MvPolynomial.map_bind₁, MonoidAlgebra.liftMagma_apply_apply, ProbabilityTheory.Kernel.coe_nsmul, jacobiTheta₂_conj, AddChar.toMonoidHomEquiv_zero, TwoSidedIdeal.orderIsoRingCon_symm_apply, RingEquiv.apply_symm_apply, GaussianInt.toComplex_mul, OrderEmbedding.sorted_ge_listMap, Coalgebra.Repr.induced_ι, OrderIso.map_csInf, AffineIsometry.image_intrinsicClosure, Matrix.toLin_kronecker, DFinsupp.toMultiset_sup, ContinuousLinearMap.isBigO_comp, Lagrange.interpolate_eq_of_values_eq_on, Trivialization.pullback_source, LieModuleHom.mem_range, negAddMonoidHom_apply, ContinuousMulEquiv.coe_refl, QuaternionAlgebra.coe_linearEquivTuple_symm, CliffordAlgebra.involute_eq_of_mem_odd, ContinuousLinearEquiv.unitsEquiv_apply, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_assoc, AlternatingMap.domCoprod.summand_mk'', IsometryEquiv.dimH_preimage, WithCStarModule.equiv_add, rothNumberNat_spec, Orthonormal.inner_left_finsupp, ModuleCat.restrictScalars.map_apply, RightOrdContinuous.coe_toOrderEmbedding, Unitary.conjStarAlgAut_trans_conjStarAlgAut, Valuation.IsTrivialOn.valuation_algebraMap_le_one, MvPolynomial.totalDegree_monomial, ContinuousMap.addEquivBoundedOfCompact_apply, AlgEquiv.moduleEndSelfOp_apply_apply, HahnSeries.orderTop_single_le, Polynomial.derivative_X_sq, Monoid.Coprod.fst_apply_inl, Matrix.SeparatingLeft.toBilin', ProbabilityTheory.isGaussian_iff_gaussian_charFun, GroupSeminorm.apply_one, ArchimedeanClass.FiniteResidueField.mk_ratCast, Algebra.Generators.aeval_val_surjective, Irreducible.maximalIdeal_eq_setOf_le_v_coe, cfc_le_algebraMap_iff, ofDual_toAdd_zero, convexIndependent_set_iff_inter_convexHull_subset, LinearMap.detAux_def'', MulActionHom.prod_apply, MeasureTheory.Measure.sum_apply_eq_zero', BoxIntegral.BoxAdditiveMap.map_split_add, IncidenceAlgebra.prod_mk, ProbabilityTheory.Kernel.iIndepSet_iff_meas_biInter, Polynomial.coe_normUnit_of_ne_zero, PowerSeries.constantCoeff_expand, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, GrpWithZero.forget_map, Nucleus.coe_toInfHom, iterate_map_one, DomAddAct.mk_vadd_indicatorConstLp, RootPairing.posRootForm_posForm_apply_apply, Ideal.selfBasis_def, Equiv.sigmaAssocProd_apply_fst, Subsemiring.coe_subtype, Ideal.Filtration.submodule_eq_span_le_iff_stable_ge, TensorProduct.LieModule.liftLie_apply, IsTopologicalAddGroup.isInducing_iff_nhds_zero, Polynomial.separable_X_pow_sub_C_unit, LinearEquiv.multilinearMapCongrRight_apply, PowerSeries.coeff_mul_one_sub_of_lt_order, List.Nodup.getEquiv_apply_coe, norm_cfcₙHom, AddCon.eq, CategoryTheory.GrothendieckTopology.mem_toPretopology, CategoryTheory.opHom_apply, Module.Basis.mem_submodule_iff, WeierstrassCurve.Projective.Equation.baseChange, IsCompactOperator.clm_comp, NonemptyInterval.dual_map, CommSemiRingCat.hom_inv_apply, MeasureTheory.lintegral_def, Nat.divModEquiv_apply, OmegaCompletePartialOrder.le_ωSup, LinearMap.BilinForm.dualSubmoduleToDual_apply_apply, HasFDerivWithinAt.continuousMultilinearMap_apply, BoundedContinuousFunction.forall_coe_zero_iff_zero, LowerSet.map_Iio, ConjAct.toConjAct_inv, MeasureTheory.VectorMeasure.coeFnAddMonoidHom_apply, IsLocalizedModule.liftOfLE_apply, FreeAddMonoid.toList_sum, MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalInterior, Matrix.transposeInvertibleEquivInvertible_symm_apply, Polynomial.smeval_monomial_mul, PiTensorProduct.lift.tprod, IntermediateField.aeval_gen_minpoly, Seminorm.mem_ball_zero, RCLike.map_apply, exists_contMDiffMap_zero_one_of_isClosed, LinearMap.toAddMonoidHom_coe, Monovary.sum_mul_comp_perm_eq_sum_mul_iff, LinearMap.iterateRange_succ, IsUltrametricDist.isNonarchimedean_invariantExtension, TopCat.pullbackIsoProdSubtype_hom_fst, CompleteLatticeHom.coe_toBoundedLatticeHom, Coalgebra.lTensor_counit_comul, LieSubmodule.coe_map, Equiv.subtypeUnivEquiv_apply, Polynomial.splits_iff_exists_multiset, CategoryTheory.Arrow.equivSigma_symm_apply_left, ArithmeticFunction.sigma_pos, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg, Matrix.det_apply, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, DFA.reindex_apply_accept, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd, CliffordAlgebra.contractRight_eq, OrthonormalBasis.orthogonalProjection_eq_sum, cfcₙHom_mono, DirectSum.bracket_apply, MonoidHom.coe_mrange, Path.subpath_self, OrderDual.ofDual_le_ofDual, CategoryTheory.conjugateEquiv_iso, Equiv.prodCongrLeft_apply_snd, IsIntegrallyClosed.exists_algebraMap_eq_of_isIntegral_pow, LinearIsometryEquiv.coe_symm_toIsometryEquiv, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, ContinuousLinearEquiv.coe_toHomeomorph, ContinuousLinearMap.analyticWithinAt_bilinear, LinearMap.toMatrixAlgEquiv'_mul, MeasureTheory.aestronglyMeasurable_condExpInd, sInfHomClass.map_sInf, Fin.coe_succEmb, Metric.Snowflaking.uniformContinuous_ofSnowflaking, LieDerivation.ad_apply_lieDerivation, Diffeomorph.contMDiffWithinAt, TopologicalSpace.Opens.inclusion'_hom_apply, BoundedContinuousMapClass.map_bounded, ValuationSubring.mem_comap, WithBot.lt_ofDual_iff, OrderMonoidIso.val_inv_unitsWithZero_symm_apply, InfHom.comp_apply, Finset.geomSum_lt_geomSum_iff_toColex_lt_toColex, ContinuousAffineEquiv.image_symm_eq_preimage, Algebra.norm_algebraMap_of_basis, exists_continuous_forall_mem_convex_of_local, StarAlgHom.mem_equalizer, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, SSet.stdSimplex.mem_nonDegenerate_iff_strictMono, AddMonoidAlgebra.domCongr_comp_lsingle, Equiv.coe_vaddConst, HasCompactSupport.convolution_integrand_bound_left, ofAdd_multiset_prod, LinearMap.BilinForm.toMatrix_toBilin, Module.Relations.Solution.ofπ'_var, SSet.stdSimplex.coe_triangle_down_toOrderHom, derivationToSquareZeroOfLift_apply, polynomialFunctions.eq_adjoin_X, SimplexCategory.eq_const_of_zero, QuadraticMap.Isometry.inl_apply, AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_comp, WithZero.val_expOrderIso_apply, ContinuousLinearMap.compSL_apply, IsPathConnected.exists_path_through_family', InfTopHom.symm_dual_id, Fin.cycleRange_succAbove, Complex.sinh_conj, ProbabilityTheory.lintegral_condCDF, Finsupp.degree_eq_sum, ContinuousLinearMap.continuous₂, Module.Basis.end_repr_apply, LinearMap.IsSymmetric.inner_map_polarization, Homeomorph.finTwoArrow_apply, RCLike.geometric_hahn_banach_point_open, AddMonoidAlgebra.mul_apply, Monoid.PushoutI.NormalWord.base_smul_def, DirectSum.Decomposition.decompose'_eq, Complex.coe_realPart, Polynomial.ofFn_zero, Algebra.Presentation.differentials.comm₁₂_single, Polynomial.toLaurent_eq_zero, wittPolynomial_zmod_self, ValuationSubring.coe_mem_principalUnitGroup_iff, CategoryTheory.Functor.mapExtLinearMap_toAddMonoidHom, AddMonoidHom.isOfFinAddOrder, Finset.sum_map', Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_apply, IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, SchwartzMap.neg_apply, LieDerivation.iterate_apply_lie, Homeomorph.coe_mulRight₀, Polynomial.roots_normalize, isLeftRegular_ofColex, NonUnitalStarSubalgebra.mem_map, fderivWithin_comp_derivWithin_of_eq, Equiv.Perm.SameCycle.exists_pow_eq, ContinuousAffineEquiv.prodComm_apply, Pretrivialization.linearEquivAt_symm_apply, ContinuousLinearEquiv.differentiable, Submodule.linearProjOfIsCompl_apply_left, Subgroup.IsComplement.equiv_fst_eq_iff_leftCosetEquivalence, IsSelfAdjoint.quasispectrumRestricts, Finsupp.embDomain_apply, AlgEquiv.leftInverse_symm, Nat.Prime.exists_orderOf_eq_pow_factorization_exponent, IncidenceAlgebra.constSMul_apply, ContinuousMap.continuous, Module.exists_basis_of_span_of_flat, AddSubmonoid.LocalizationMap.symm_comp_ofAddEquivOfLocalizations_apply, ValuationSubring.valuation_lt_one_iff, MvPowerSeries.coeff_zero, MvPolynomial.map_mapRange_eq_iff, ULift.orderIso_symm_apply_down, Valuation.leSubmodule_v_le_of_mem, WithConv.addEquiv_symm_apply_ofConv, IsLocalRing.ResidueField.algebraMap_residue, TopCat.presheafToType_map, LinearMap.coe_toSeminorm, MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates, Filter.map_add, HeytingHomClass.map_himp, ContinuousLinearMap.integral_compLp, FormalMultilinearSeries.comp_partialSum, MvPowerSeries.weightedOrder_monomial, Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval, Similar.comp_right, Equiv.ulift_apply, OmegaCompletePartialOrder.ContinuousHom.const_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add, exists_isIdempotentElem_eq_of_ker_isNilpotent, YoungDiagram.transposeOrderIso_symm_apply, Language.reverseIso_apply, IndexedPartition.proj_fiber, RelIso.one_apply, CuspFormClass.holo, AdicCompletion.mk_zero_of, MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum, OrderIso.pnatIsoNat_symm_apply, LinearMap.adjoint_adjoint, Finsupp.embDomain_some_some, TestFunction.ext_iff, DirectSum.finite_support, BumpCovering.eventuallyEq_one, Polynomial.roots_expand, MonoidHom.coprod_apply, Dilation.tendsto_nhds_iff, DoubleCentralizer.star_snd, bernsteinApproximation.apply_zero, AffineEquiv.coe_toEquiv, MeasureTheory.SimpleFunc.sum_measure_preimage_singleton, ContinuousAlgHom.toAlgHomMonoidHom_apply, Matrix.SeparatingRight.toLinearMap₂, TopologicalSpace.Opens.map_coe, quadraticChar_card_sqrts, Equiv.plift_apply, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk, LinearIsometry.coe_toLinearMap, MvPowerSeries.eq_iff_frequently_trunc'_eq, Pi.constAlgHom_apply, PowerSeries.coeff_mul_of_lt_order, Matrix.entryAddHom_apply, LinearMap.IsReflective.regular, Affine.Simplex.orthogonalProjectionSpan_map, RootPairing.linearIndepOn_root_baseOf', taylorWithin_succ, LinearMap.BilinForm.symmCompOfNondegenerate_left_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, MvPolynomial.pUnitAlgEquiv_apply, CategoryTheory.Abelian.Ext.homLinearEquiv_apply, Fin.cycleIcc.trans_right_one, RingEquiv.toOpposite_symm_apply, MeasureTheory.iInf_mul_le_lintegral, AddGrpCat.forget₂_map, AlgebraicGeometry.Scheme.Cover.LocallyDirected.directed, Localization.one_rel, FirstOrder.Language.Equiv.bijective, map_multiset_sum, PolyEquivTensor.toFunBilinear_apply_eq_sum, Complex.UnitDisc.normSq_lt_one, LinearMap.BilinForm.dualSubmoduleToDual_injective, FractionalIdeal.mapEquiv_apply, Rep.MonoidalClosed.linearHomEquiv_symm_hom, List.equivSigmaTuple_symm_apply, MeasureTheory.Measure.addHaar_image_continuousLinearMap, Valuation.FiniteField.algebraMap_le_one, sInfHom.le_apply_bliminf, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Polynomial.algEquivCMulXAddC_apply, ContDiffMapSupportedIn.coe_add, Polynomial.mul_divByMonic_eq_iff_isRoot, ExteriorAlgebra.GradedAlgebra.liftι_eq, MeasureTheory.withDensity_apply_le, Matrix.IsHermitian.isClosedEmbedding_cfcAux, AffineEquiv.sOppSide_map_iff, IntermediateField.algHomEquivAlgHomOfSplits_symm_apply, sigmaFinsuppEquivDFinsupp_support, SlashInvariantForm.coe_prodEqualWeights, Action.leftRegularTensorIso_inv_hom, PresentedAddMonoid.ext_iff, Nat.Primes.prodNatEquiv_symm_apply, BoundedContinuousFunction.dist_eq_iSup, Nat.multiplicity_eq_factorization, Equiv.image_swap_of_mem_of_notMem, IsUltrametricDist.algNormOfAlgEquiv_extends, groupCohomology.isoCocycles₁_hom_comp_i_apply, Monoid.Coprod.swap_inr, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, RCLike.ofRealCLM_apply, Valuation.FiniteField.algebraMap_eq_one, RCLike.normSq_to_real, ZMod.χ₈'_int_eq_if_mod_eight, DFinsupp.lsingle_apply, SchwartzMap.integral_sesq_fourier_fourier, MultilinearMap.fromDFinsuppEquiv_apply, Polynomial.cardPowDegree_zero, AffineIsometryEquiv.pointReflection_involutive, AlgEquiv.coe_adjoinSingletonEquivAdjoinRootMinpoly_symm, OrderMonoidHom.inl_mul_inr_eq_mk, ProbabilityTheory.condDistrib_apply_of_ne_zero, galRestrict_symm_algebraMap_apply, Equiv.Perm.exists_fixed_point_of_prime, LinearIsometryEquiv.surjective, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso, NumberField.InfinitePlace.norm_embedding_of_isReal, ContinuousAlgHom.map_smul_of_tower, AddMonoid.Coprod.swap_inj, AddMonoid.End.natCast_apply, BoundedContinuousFunction.coe_zsmul, Module.Presentation.cokernelSolution_var, DFinsupp.filter_apply_neg, Subgroup.quotientEquivOfEq_mk, DirectSum.Gmodule.smulAddMonoidHom_apply_of_of, HahnSeries.map_single, MeasureTheory.forall_measure_preimage_add_iff, PMF.toMeasure_pure_apply, ProbabilityTheory.condDistrib_ae_eq_condExp, Finset.affineCombination_affineCombinationSingleWeights, ModularFormClass.differentiableAt_comp_ofComplex, LinearMap.exists_monic_and_aeval_eq_zero, ContinuousMap.HomotopyRel.fst_eq_snd, MeasureTheory.coe_measureUnivNNReal, Polynomial.monic_X_sub_C, Equiv.uniqueProd_symm_apply, NormedAddGroupHom.completion_def, PadicInt.lift_sub_val_mem_span, AddMonoid.Coprod.toProd_apply_inr, IsLinearMap.image_convexHull, MeasurableEquiv.smul_apply, UniformEquiv.funUnique_apply, MvPolynomial.eval₂Hom_X, Polynomial.monomial_eq_monomial_iff, CategoryTheory.Iso.eHomCongr_inv_comp_assoc, AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply_mk, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Nat.factorization_eq_zero_of_not_dvd, AlgEquiv.opOp_apply, Matrix.SpecialLinearGroup.map_mapGL, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_map, AddMonoidHom.exact_of_comp_of_mem_range, ProbabilityTheory.Kernel.lintegral_swapRight, RatFunc.num_div, Algebra.algebraMap_self_apply, Subring.coe_subtype, CompactlySupportedContinuousMap.coe_sub, AddCommGrpCat.biproductIsoPi_inv_comp_π_apply, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, LinearMap.inr_apply, ContinuousLinearMap.coe_comp', RootPairing.Polarization_apply, MonoidHom.CompTriple.instRootCompTriple, AddCommGrpCat.comp_apply, Subgroup.equivSMul_apply_coe, LinearEquiv.extendScalarsOfIsLocalizationEquiv_symm_apply, affineHomeomorph_image_Ico, Submonoid.equivOp_symm_apply_coe, LinearIsometryEquiv.analyticOnNhd, PolynomialModule.comp_single, QuadraticMap.lineDeriv, MvPolynomial.exists_finset_rename, geometric_hahn_banach_point_point, LinearEquiv.flip_apply, MonomialOrder.monic_X_sub_C, AlternatingMap.add_apply, MvPolynomial.hom_C, PolynomialModule.map_lsingle, Ideal.finite_setOf_absNorm_le₀, HilbertBasis.coe_mk, CategoryTheory.GrothendieckTopology.ext_iff, ContinuousAlternatingMap.uniformContinuous_eval_const, Bornology.IsBounded.image, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval_apply, ContinuousLinearEquiv.image_closure, LieSubalgebra.inclusion_apply, IsPrimePow.exists_ordCompl_eq_one, nndist_ofAdd, Complex.linearEquiv_det_conjLIE, EuclideanGeometry.reflection_orthogonal_vadd, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_same, IncidenceAlgebra.coe_constSMul, LeftInvariantDerivation.leibniz, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, FreeMonoid.toList_prod, OneHomClass.map_one, Ideal.toCharacterSpace_apply_eq_zero_of_mem, Valuation.HasExtension.val_map_le_iff, Representation.IntertwiningMap.mul_apply, LinearEquiv.restrictScalars_apply, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, MeasureTheory.convolution_eq_right', Polynomial.coeff_derivative, Module.Basis.tensorProduct_apply, LinearMap.funLeft_id, MeasureTheory.Measure.le_comap_apply, EisensteinSeries.hasSum_e2Summand_symmetricIcc, quasispectrum.algebraMap_mem, Complex.normSq_pos, OrderIso.map_covBy, hasFDerivAt_iff_hasGradientAt, QuotientGroup.kerLift_mk, BialgHom.coe_fn_inj, TensorProduct.AlgebraTensorModule.rid_symm_apply, AddGrpCat.id_apply, LinearIsometryEquiv.coe_ofLinearIsometry_symm, NonUnitalIsometricContinuousFunctionalCalculus.isometric, OrderEmbedding.birkhoffFinset_inf, IntermediateField.LinearDisjoint.linearIndependent_right', PowerSeries.coeff_of_lt_order_toNat, groupCohomology.mem_cocycles₂_def, ContinuousMap.constPi_apply, MeasureTheory.Measure.addHaar_sphere, HahnSeries.SummableFamily.embDomain_apply, RootPairing.root'In_corootSpanMem_eq_pairingIn, IsAdicComplete.StrictMono.mk_liftRingHom, RCLike.reCLM_apply, AlgebraicGeometry.QuasiCompact.isCompact_preimage, HVertexOperator.coeff_add, Pi.constMonoidHom_apply, PowerSeries.constantCoeff_subst, LieHom.ext_iff, ContinuousAffineMap.lineMap_apply', MulEquiv.map_eq_one_iff, Valuation.isEquiv_iff_val_sub_one_lt_one, ExteriorAlgebra.ι_eq_algebraMap_iff, MulAut.one_apply, smooth_barycentric_coord, CircleDeg1Lift.translate_inv_apply, AffineMap.coe_smul, Algebra.TensorProduct.prodRight_tmul_fst, SchwartzMap.coe_zero, unitInterval.symmHomeomorph_apply, Equiv.inv_def, cfcₙHom_apply_mem_elemental, QuotientGroup.lift_mk, ContinuousMultilinearMap.cpolynomialOn, PowerSeries.WithPiTopology.continuous_coeff, MeasureTheory.hausdorffMeasure_segment, Matrix.scalar_inj, nhds_ofMul, DFinsupp.lex_lt_iff_of_unique, Submodule.algebraMap_mem, ClassGroup.mk0_integralRep, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, Lat.ext_iff, MulChar.eq_iff, ConjAct.toConjAct_mul, FreeMonoid.ofList_smul, IsHilbertSum.surjective_isometry, IsLocalization.algEquiv_symm_mk', Polynomial.homogenize_map, Submonoid.LocalizationMap.injective_iff, MvPowerSeries.trunc'_trunc', CircleDeg1Lift.map_sub_int, AnalyticOn.aeval_polynomial, TopCat.GlueData.preimage_image_eq_image, SimpleGraph.lapMatrix_toLinearMap₂', Subring.coe_comap, Quiver.SingleObj.pathEquivList_nil, InnerProductSpace.volume_closedBall_of_dim_even, Valuation.one_apply_lt_one_iff, MeasureTheory.L1.setToL1_indicatorConstLp, FormalMultilinearSeries.ofScalars_apply_eq', FreeGroupBasis.repr_apply_coe, RCLike.div_re_ofReal, toLex_mul, LinearMap.coe_compAlternatingMap, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, Quaternion.snd_imJ_dualNumberEquiv_symm, FreeAddMonoid.lift_ofList, AddConstMapClass.map_sub_nsmul, UniformEquiv.refl_apply, CompactExhaustion.isClosed, AddDissociated.randomisation, AlgebraicGeometry.RingedSpace.basicOpen_res, Real.fourierCoeff_tsum_comp_add, LieHom.zero_apply, PowerBasis.exists_eq_aeval, NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply, sign_mul_self, UnitAddTorus.coe_mFourierBasis, Localization.algebraMap_injective_of_span_eq_top, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, FundamentalGroupoid.equiv_symm_apply_as, LowerSet.compl_map, MeasureTheory.lintegral_const, Orientation.inner_rotation_pi_div_two_right_smul, Complex.lim_conj, MultilinearMap.map_update_smul, StarSubalgebra.inclusion_apply, PowerSeries.coeff_mul_C, ModularFormClass.hasFPowerSeries_cuspFunction, ContinuousAlgEquiv.map_nhds_eq, MulHom.coe_srange, CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ω₀, extDeriv_constOfIsEmpty, AlgebraicGeometry.Scheme.Hom.denseRange, Equiv.toPEquiv_apply, Ordinal.typein_le_typein, Module.FaithfullyFlat.iff_exact_iff_lTensor_exact, RCLike.separate_convex_open_set, Orientation.oangle_add_left_smul_rotation_pi_div_two, SimpleGraph.incidenceSetEquivNeighborSet_apply_coe, Topology.IsClosedEmbedding.continuousOn_comap_finiteMeasure, Convex.norm_image_sub_le_of_norm_fderivWithin_le', LocalSubring.range_toSubring, thickenedIndicator_mono_infEDist, Monoid.Coprod.lift_apply_inr, Dilation.mapsTo_eball, RootPairing.coroot_eq_polarizationEquiv_apply_root, Finset.prod_map', ZMod.unitsMap_surjective, Real.fourierIntegral_comp_linearIsometry, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, Ideal.exists_comap_galRestrict_eq, IsGroupLikeElem.comul_eq_tmul_self, MonoidHom.map_finprod_mem', Trivialization.preimageHomeomorph_symm_apply, MvPolynomial.support_finSuccEquiv, NumberField.canonicalEmbedding.mem_span_latticeBasis, LinearMap.compAlternatingMap_apply, MeasureTheory.measure_sdiff_inv_smul, WithTop.toDualBotEquiv_coe, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_eq, Polynomial.algebraMap_pi_eq_aeval, Finset.map_filter', Submodule.orthogonalDecomposition_symm_apply, AffineEquiv.pointReflection_fixed_iff_of_injective_two_nsmul, Set.map_finite_iInf, DistribMulActionHom.one_apply, MeasurableEquiv.coe_smul₀, MulEquivClass.map_finprod, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, IsometryEquiv.preimage_sphere, LocallyConstant.apply_eq_of_isPreconnected, val_inv_unitsEquivProdSubtype_symm_apply, CategoryTheory.Limits.IsLimit.equivIsoLimit_apply, LieDerivation.zero_apply, ContinuousMultilinearMap.map_smul_univ, RatFunc.coe_mapAlgHom_eq_coe_map, Polynomial.Sequence.basis_natDegree_strictMono, normalize_dvd_iff, image_smul_setₛₗ, LieHom.congr_fun, groupCohomology.d₂₃_hom_apply, OrthogonalFamily.linearIsometry_apply_single, NumberField.integralBasis_apply, IsLocalization.Away.algebraMap_isUnit_iff, Algebra.PreSubmersivePresentation.cotangentComplexAux_apply, ContinuousLinearMapWOT.neg_apply, SimpleGraph.map_singletonSubgraph, MeasureTheory.ComplexMeasure.equivSignedMeasure_symm_apply, MvPolynomial.rTensor_apply_tmul_apply, InnerProductSpace.rankOne_one_left_eq_innerSL, OrderIso.image_Icc, Set.toENat_cardinalMk_subtype, MvPolynomial.degrees_monomial, IsLowerSet.ofDual, Function.ExtendByOne.hom_apply, Polynomial.ker_evalRingHom, MeasureTheory.Integrable.measure_enorm_ge_lt_top, MeasureTheory.Measure.haar_singleton, Subalgebra.toSubmodule_injective, convexHull_insert, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, Set.dual_ordConnectedComponent, ContinuousMulEquiv.surjective, AddSubmonoid.LocalizationMap.surj₂, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, Equiv.Set.union_symm_apply_left, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, Monoid.Coprod.map_apply_inl, Nat.Prime.factorization_pos_of_dvd, StandardEtalePair.inv_aeval_X_g, FreeAddGroup.map.id', AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, OrderIso.isMin_apply, AlternatingMap.constLinearEquivOfIsEmpty_symm_apply, SetTheory.PGame.exists_leftMoves_neg, Polynomial.eval₂_intCastRingHom_X, Seminorm.le_finset_sup_apply, MulEquiv.coe_trans, unitInterval.volume_Ioo, IsIntegrallyClosedIn.isIntegral_iff, reindex_mem_doublyStochastic_iff, MeasurableEquiv.measurableEmbedding, exteriorPower.basis_apply, AddEquiv.addMonoidHomCongrLeftEquiv_apply, TopCat.GlueData.π_surjective, ContinuousMap.compMonoidHom'_apply, PrincipalSeg.map_pred, ValuationSubring.integralClosure_algebraMap_injective, Additive.toMul_mono, Ideal.mem_span_iff_exists_isHomogeneous, UniformSpaceCat.completionHom_val, ContMDiffMap.coeFnAlgHom_apply, Function.FactorizedRational.divisor, AddGroupNorm.ext_iff, Topology.IsGeneratedBy.homeomorph_symm_coe, AffineIsometryEquiv.coe_symm_toAffineEquiv, OrderIso.continuous, LinearMap.Nondegenerate.congr, MeasureTheory.SimpleFunc.coe_zpow, IsPurelyInseparable.minpoly_eq', SimpleGraph.isVertexCover_preimage_iso, unitInterval.volume_Iic, LightCondensed.ihomPoints_apply, SetTheory.PGame.Domineering.shiftUp_apply, MeasureTheory.AEStronglyMeasurable.integral_condDistrib_map, CommRingCat.closure_range_union_range_eq_top_of_isPushout, Subgroup.centerCongr_symm_apply_coe, zpowersMulHom_symm_apply, Equiv.sumCompl_symm_apply_pos, CategoryTheory.shrinkYonedaEquiv_comp, IntermediateField.algebraMap_mem, MDifferentiableAt.clm_bundle_apply, Cardinal.toENat_eq_natCast_iff, CliffordAlgebraQuaternion.j_quaternionBasis, Matrix.GeneralLinearGroup.map_det, LaurentPolynomial.mk'_mul_T, LatticeHom.fst_apply, UniformOnFun.gen_eq_preimage_restrict, Finset.map_zero, Ordinal.mem_range_typein_iff, GroupSeminorm.coe_sup, Finsupp.sumElim_inr, Polynomial.expand_eq_sum, ContinuousMap.hasBasis_nhds, NormedSpace.expSeries_summable_of_mem_ball, Equiv.optionIsSomeEquiv_symm_apply_coe, SkewMonoidAlgebra.toFinsupp_apply, Polynomial.Gal.galActionHom_bijective_of_prime_degree', PiTensorProduct.tmulEquiv_symm_apply, Equiv.coe_constVSub_symm, Finsupp.sub_apply, ContinuousMap.HomotopyWith.coe_toContinuousMap, ExteriorAlgebra.ι_inj, WittVector.aeval_verschiebung_poly', Polynomial.root_X_sub_C, FreeAddMonoid.count_apply, NumberField.Units.logEmbedding_fundSystem, subset_closedConvexHull, NonemptyInterval.map_pure, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, Ideal.exists_smith_normal_form, Seminorm.norm_sub_map_le_sub, toColex_ofColex, NonUnitalStarAlgHom.inl_apply, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', MultilinearMap.map_update_add, ContinuousAffineMap.fderiv, Lex.forall, dotProductEquiv_symm_apply, Matrix.abs_det_reindex, ofBoolRing_sub, groupHomology.d₁₀_single_one, nsmul_finEquivZMultiples_symm_apply, PowerSeries.heval_C, Algebra.Norm.Transitivity.polyToMatrix_cornerAddX, LinearEquiv.piCongrRight_apply, Equiv.piComm_apply, MulEquiv.monoidHomCongrLeft_apply, addMonoidHomLequivNat_symm_apply, polynomial_smul_apply', IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, RingHomInvPair.comp_apply_eq₂, LinearIsometry.lipschitz, AddMonoidHom.coe_mk, DirectSum.component.of, MonomialOrder.degree_add_of_ne, monoidHomOfForallMemZpowers_apply_gen, Finset.singletonAddMonoidHom_apply, LinearMap.IsProj.codRestrict_apply_cod, Polynomial.hasseDeriv_zero', LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, DeltaGenerated.topToDeltaGenerated_map_hom_hom_apply, Matrix.scalar_comm, Matrix.separatingRight_toLinearMap₂'_iff, CuspForm.toFun_eq_coe, Polynomial.continuous_aeval, SchwartzMap.norm_le_seminorm, BiheytingHomClass.map_sdiff, frobeniusEquiv_apply, AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints, Geometry.SimplicialComplex.vertex_mem_convexHull_iff, ZSpan.volume_real_fundamentalDomain, MvPolynomial.rTensorAlgEquiv_apply, CategoryTheory.Iso.conjAut_apply, realPart_idem, HNNExtension.NormalWord.prod_group_smul, BitVec.equivFin_symm_apply_toFin, NumberField.mixedEmbedding.convexBodyLT'_mem, MvPolynomial.one_def, ClassGroup.mk0_eq_mk0_iff, PiTensorProduct.mapLMonoidHom_apply, Algebra.Generators.H1Cotangent.δAux_mul, Complex.kahler, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_ι_presheafHom, TopCat.isOpenEmbedding_iff_comp_isIso, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', NonUnitalAlgHom.one_apply, ContinuousMap.integral_apply, CliffordAlgebra.mul_ι_mul_ι_of_isOrtho, MvPowerSeries.coeff_mul_monomial, ContinuousLinearMap.map_add_add, X_pow_sub_C_splits_of_isPrimitiveRoot, quadraticChar_card_card, UniformFun.ofFun_one, PiTensorProduct.isEmptyEquiv_apply_tprod, partialSups_const_add, AddEquiv.toMultiplicative_apply_symm_apply, LinearIsometry.diam_image, PartENat.withTopEquiv_symm_apply, Finsupp.restrictDom_apply, AddMonoidHom.toMultiplicative_add, MeasureTheory.Measure.swap_comp, ContinuousLinearMap.sSup_unit_ball_eq_norm, SimpleGraph.Walk.IsHamiltonian.getVertEquiv_apply, Rack.toEnvelGroup.univ_uniq, Multiset.toFinsupp_add, closedConvexHull_min, AddAut.apply_inv_self, RootPairing.Base.span_coroot_support, Lagrange.eval_interpolate_not_at_node', CategoryTheory.Functor.curryingEquiv_symm_apply_obj_obj, Valuation.mem_maximalIdeal_iff, Complex.areaForm, NNReal.rpowMonoidHom_apply, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, Complex.re_eq_add_conj, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, Order.height_ofDual, Differential.implicitDeriv_C, QuadraticMap.sum_polar_sub_repr_sq, ContinuousAlgEquiv.symm_apply_eq, Finsupp.curryEquiv_apply, CategoryTheory.Bicategory.conjugateEquiv_whiskerRight, LinOrd.ofHom_apply, AddMonoid.Coprod.mk_of_inr, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, Dilation.mapsTo_closedEBall, Derivation.coe_add, Diffeomorph.contMDiffOn_comp_diffeomorph_iff, CliffordAlgebraComplex.ofComplex_conj, OrderIso.map_bot', Finsupp.card_Ioc, HomologicalComplex.Hom.comm_from_apply, AlgHom.coe_toRingHom, Matrix.det_smul_inv_mulVec_eq_cramer, ContinuousMap.dist_lt_iff, Metric.exists_continuous_real_forall_closedEBall_subset, Pi.algebraMap_apply, WittVector.coeff_truncate, LinearMap.map_add, LinearMap.zero_apply, Matrix.SpecialLinearGroup.continuous_toGL, GaussianInt.intCast_im, BoundedContinuousFunction.coe_one, Matrix.pow_eq_aeval_mod_charpoly, MonoidHom.transferSylow_eq_pow, LieModule.Weight.exists_ne_zero, WeierstrassCurve.VariableChange.map_s, IntermediateField.algHomEquivAlgHomOfSplits_apply_apply, GroupNorm.le_def, Unitization.inrNonUnitalAlgHom_toFun, Ideal.toCotangent_eq, MvPolynomial.mem_image_support_coeff_finSuccEquiv, AddMonoid.Coprod.snd_apply_inr, SkewMonoidAlgebra.erase_apply_toFinsupp, MonoidHom.map_exists_right_inv, finSumFinEquiv_apply_left, RingHom.IsIntegralElem.map, AlgebraicGeometry.coprodSpec_apply, WeierstrassCurve.Affine.CoordinateRing.smul, Polynomial.resultant_X_add_C_right, Finsupp.equivCongrLeft_apply, ContDiffMapSupportedInClass.map_contDiff, Polynomial.pow_rootMultiplicity_dvd, Function.Embedding.coeWithTop_apply, AlternatingMap.map_vecCons_smul, MulMemClass.subtype_apply, CStarModule.innerₛₗ_apply, NonUnitalSubalgebraClass.coe_subtype, Module.Flat.toAlgebra_injective, SetTheory.PGame.relabel_moveLeft', Submodule.mulMap_tmul, CategoryTheory.iterated_mateEquiv_conjugateEquiv, strictAntiOn_toDual_comp_iff, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, AlgebraicGeometry.morphismRestrict_base_coe, BoundedOrderHomClass.map_top, Filter.Tendsto.lineMap, Ideal.absNorm_span_insert, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, ProbabilityTheory.lintegral_toKernel_univ, MulSemiringAction.toRingHom_apply, NonarchAddGroupSeminorm.coe_iSup_apply, convexHull_multiset_sum, FirstOrder.Language.DirectLimit.of_f, Polynomial.Gal.smul_def, OrderMonoidWithZeroHom.coe_orderMonoidHom, AlgebraicGeometry.surjectiveOnStalks_iff, WeierstrassCurve.Jacobian.baseChange_add, Nucleus.monotone, Homeomorph.isPathConnected_preimage, partialSups_succ', Polynomial.derivWithin_aeval, UniformOnFun.toFun_one, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, Module.End.smul_def, Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.analyticWithinAt, MultilinearMap.mkPiAlgebra_apply, AdjoinRoot.minpoly_root, Valuation.mem_leSubmodule_iff, ContinuousAffineMap.differentiableWithinAt, MulActionHom.coe_smul, FreeAddMonoid.toPiTensorProduct, Finset.weightedVSubOfPoint_apply, MultilinearMap.dfinsuppFamily_single, NonUnitalSubsemiringClass.subtype_apply, PowerSeries.coeff_rescale, HahnSeries.cardSupp_single_of_ne, RootPairing.chainTopCoeff_reflectionPerm_right, Fin.natAddEmb_apply, X_pow_sub_C_eq_prod, Finsupp.toMultiset_strictMono, Profinite.NobelingProof.injective_πs', summable_riemannZetaSummand, MeasureTheory.measure_congr, AddMonCat.comp_apply, Complex.normSq_natCast, Function.Embedding.coe_refl, MulEquivClass.map_mul, MvPolynomial.scalarRTensor_apply_monomial_tmul, Geometry.SimplicialComplex.convexHull_subset_space, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, MeasureTheory.eLpNorm'_const', ArithmeticFunction.cardFactors_pow, MvPolynomial.comapEquiv_symm_coe, FirstOrder.Language.ElementarySubstructure.subtype_apply, ofDual_max, List.form_perm_zpow_apply_mem_imp_mem, MvPolynomial.homogeneousComponent_eq_zero', QuadraticMap.canLift, Polynomial.derivative_intCast_mul, PositiveLinearMap.apply_le_of_isSelfAdjoint, LinearMap.injective_iff_surjective_of_finrank_eq_finrank, ContinuousMap.HomotopyEquiv.refl_symm_apply, CircleDeg1Lift.map_add_nat, SimpleGraph.isClique_map_image_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite, LieModule.toEnd_pow_apply_map, Polynomial.toMatrix_sylvesterMap', LaurentPolynomial.comul_T, Module.basisUnique_repr_eq_zero_iff, WeierstrassCurve.Projective.eval_polynomial, ContinuousMap.Homotopy.extend_apply_of_one_le, Finset.affineCombination_apply_eq_lineMap_sum, EmbeddingLike.injective', Homeomorph.piCongr_apply, IntermediateField.coe_algebraMap_over_bot, Valuation.mem_supp_iff, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, MulChar.toUnitHom_eq, volume_iUnion_setOf_liouvilleWith, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, isMin_toDual_iff, Polynomial.rootMultiplicity_eq_rootMultiplicity, AbstractCompletion.mapEquiv_coe, Real.ringHom_apply, LeftOrdContinuous.rightOrdContinuous_dual, AddMonoidHom.restrictHom_apply, DirectSum.coe_toModule_eq_coe_toAddMonoid, ContinuousMultilinearMap.le_mul_prod_of_opNorm_le_of_le, OrderIso.arrowCongr_apply, Matrix.toLinearMapRight'_mul, RCLike.ofRealLI_apply, RingTheory.Sequence.isWeaklyRegular_cons_iff', toColex_sub, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Hamming.toHamming_sub, qExpansion_eq_zero_iff, DFinsupp.piecewise_single_erase, WithBot.orderIsoPUnitSumLex_symm_inl, eval_minpolyDiv_self, Algebra.normalizedTrace_surjective, TopCat.Presheaf.locally_surjective_iff_surjective_on_stalks, MonotoneOn.dual_left, OrderIso.isGLB_preimage', Nat.ordCompl_le, LinearMap.IsPositive.ne_zero_iff, Quiver.starEquivCostar_symm_apply_fst, GroupNorm.toGroupSeminorm_eq_coe, MvPolynomial.eval₂_expand, FreeMonoid.hom_eq_iff, WittVector.mapFun.zero, Finset.product_self_eq_disjiUnion_perm_aux, OrderIso.symm_trans_apply, NonUnitalRingHom.mem_range, SchwartzMap.add_apply, ModularForm.mul_slash, Finset.centroid_eq_affineCombination_fintype, OrderedFinpartition.extendEquiv_apply, SubMulAction.subtype_eq_val, MvPolynomial.weightedDegree_eq_zero_iff, Height.mulHeight₁_eq, MonoidHom.map_mul₂, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, QuotientGroup.coe_mk', Submodule.exists_fg_le_eq_rTensor_inclusion, WithAbs.algebraMap_left_apply, finsuppTensorFinsupp_apply, deriv_abs, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection, Homeomorph.finTwoArrow_symm_apply, OrderIso.sumCongr_apply, CongruenceSubgroup.Gamma_mem', IsAddFoelner.eventually_meas_ne_top, Finsupp.onFinset_apply, map_finset_sum, iterateFrobeniusEquiv_symm_add_apply, Equiv.Perm.smul_def, DirectSum.decompose_of_mem_same, curveIntegrable_segment, SSet.ι₀_snd_assoc, MonoidHom.toAdditive_apply_apply, ZMod.LFunction_stdAddChar_eq_expZeta, WithZero.map'_zero, Polynomial.disjoint_ker_aeval_of_isCoprime, Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular, Equiv.Perm.Basis.injective, BoxIntegral.TaggedPrepartition.tag_mem_Icc, Nucleus.himp_apply, TensorPower.cast_cast, Fintype.coe_finsetEquivSet, MvPolynomial.universalFactorizationMap_comp_map, StieltjesFunction.measure_botSet, OrderIso.coe_dualDual_symm, Additive.ofMul_eq_top, RootPairing.Base.algebraMap_cartanMatrixIn_apply, MvPolynomial.aeval_algebraMap_eq_zero_iff, intervalIntegral.tsum_intervalIntegral_eq_of_summable_norm, Representation.ofMulActionSelfAsModuleEquiv_symm_apply, Module.Basis.equivFun_symm_apply, Equiv.symm_preimage_preimage, IsometryEquiv.range_eq_univ, NumberField.FinitePlace.mk_apply, RestrictedProduct.image_coe_preimage_inclusion_subset, WithLp.prod_nndist_eq_of_L2, FreeGroup.prod.of, SkewPolynomial.monomial_add, LinearMap.isPositive_adjoint_comp_self, ProbabilityTheory.covarianceBilinDual_apply', Manifold.IsImmersionAt.map_target_subset_target, MonoidHom.preimage_smul_setₛₗ, FreeAddMonoid.lift_apply, BoundedContinuousFunction.algebraMap_apply, CoxeterMatrix.reindex_relationsSet, LieEquiv.injective, Circle.exp_arg, Combinatorics.Subspace.IsMono.reindex, LinearMap.BilinForm.IsAlt.neg_eq, CategoryTheory.ReflQuiv.adj.homEquiv_symm_apply, Rep.diagonalSuccIsoFree_inv_hom_single, Set.Ioi_ofDual, MvPowerSeries.support_expand, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, Algebra.norm_eq_zero_iff_of_basis, AddSubgroup.closure_preimage_eq_top, Subgroup.MapSubtype.orderIso_apply_coe, LinearMap.BilinMap.polar_toQuadraticMap, OrderIso.withTopCongr_apply, ContinuousAffineEquiv.injective, coe_frobeniusEquiv_symm_comp_coe_frobenius, PolynomialModule.smul_def, CategoryTheory.Iso.isoCongr_symm_apply, Equiv.Perm.SameCycle.exists_nat_pow_eq, InfTopHom.inf_apply, AlgEquiv.one_apply, spectrumRestricts_iff, GaussianInt.toComplex_def', DirichletCharacter.Odd.eval_neg, Submonoid.coe_invOrderIso_apply, RingEquiv.coe_prodComm_symm, Equiv.Perm.Basis.toCentralizer_equivariant, CoalgHom.coe_addMonoidHom_injective, MeasureTheory.SimpleFunc.coe_lt_coe, Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoin, ContinuousLinearMap.smul_apply, CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq, StrictAntiOn.dual_left, RCLike.re_add_im, ContinuousAffineMap.ext_iff, Ideal.relNorm_smul, LinearMap.isAdjointPair_iff_comp_eq_compl₂, RingEquiv.surjective, HahnSeries.C_injective, Ideal.map_ofList, LinearMap.IsPerfPair.bijective_left, hasFTaylorSeriesUpToOn_top_iff_right, IsLocalization.mk'_spec_mk, MeasureTheory.charFunDual_apply, DirichletCharacter.LSeries_eulerProduct_tprod, OmegaCompletePartialOrder.ContinuousHom.ωSup_apply, TensorProduct.congr_congr, MonoidHom.restrictHomKerEquiv_apply_coe, InnerProductSpace.Core.inner_mul_inner_self_le, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, MonomialOrder.degree_monomial, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, CategoryTheory.Limits.IsLimit.liftConeMorphism_eq_isTerminal_from, CategoryTheory.Functor.coe_mapLinearMap, IsCoveringMap.comp_homeomorph_iff, IsLocalization.AtPrime.coe_orderIsoOfPrime_apply_coe, RingEquiv.ofHomInv'_apply, SchwartzMap.sub_apply, WithTop.toDual_top, Additive.ofMul_bot, Frm.coe_comp, LinearIsometry.map_smul, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, AddChar.map_nsmul_eq_pow, ClassGroup.mk_eq_mk_of_coe_ideal, IsCoveringMapOn.homeomorph_comp_iff, RootPairing.reflectionPerm_eq_iff_smul_root, ContinuousMap.coeFn_toAEEqFun, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, RingCon.ker_apply, RingHom.star_apply, BoundedOrderHomClass.map_bot, Module.Basis.range_ofVectorSpace, AddHom.coeFn_apply, ContinuousMap.exists_finite_approximation_of_mem_nhds_diagonal, FractionalIdeal.coeIdealHom_apply, BotHom.bot_apply, MeasureTheory.Lp.simpleFunc.toSimpleFunc_indicatorConst, qExpansionRingHom_apply, LinearMap.exact_zero_iff_surjective, IsPrimePow.minFac_pow_factorization_eq, AddCommGrpCat.asHom_hom_apply, Matrix.separatingRight_toLinearMap₂_iff, Matrix.cramer_transpose_row_self, IncidenceAlgebra.zeta_mul_kappa, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, MeasureTheory.Measure.hausdorffMeasure_zero_singleton, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_apply_val, Complex.ofRealLI_apply, MulChar.exists_apply_eq_pow, CompactlySupportedContinuousMap.coe_inf, AdicCompletion.map_val_apply, CuspFormClass.zero_at_infty_comp_ofComplex, Matrix.SpecialLinearGroup.coeToGL_det, CharacterModule.int.divByNat_self, PowerSeries.coeff_expand_mul, Affine.Simplex.circumcenter_map, conformalAt_iff, Module.End.HasUnifEigenvector.pow_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, LinearIsometry.isComplete_image_iff', Finsupp.coe_le_coe, HasFPowerSeriesWithinOnBall.hasSum_sub, Representation.repOfTprodIso_apply, AddGroupExtension.Equiv.refl_apply, RingEquiv.op_apply_apply, LocallyBoundedMap.coe_id, AlgebraicGeometry.Scheme.affineBasisCover_is_basis, Ideal.isHomogeneous_iff_subset_iInter, prevD_comp_left, MonoidHom.toMulHom_coe, AddEquiv.addSubgroupMap_symm_apply, right_lt_lineMap_iff_one_lt, NumberField.Units.fun_eq_repr, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, SSet.Subcomplex.Pairing.IsProper.isUniquelyCodimOneFace, LinearMap.coe_semilinearMap, Finset.mem_dfinsupp_iff_of_support_subset, LieSubmodule.Quotient.mk_eq_zero, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, Polynomial.derivative_C_mul, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, ModuleCat.freeHomEquiv_apply, Algebra.algebraMap_ofSubsemiring_apply, isLeftRegular_toLex, Bifunctor.mapEquiv_apply, Matrix.compAlgEquiv_apply, ClosureOperator.ofCompletePred_apply, ZeroHom.neg_apply, AntilipschitzWith.hausdorffMeasure_preimage_le, AffineSubspace.map_pointwise_vadd, Matrix.spectrum_toEuclideanLin, Cardinal.aleph_succ, Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval, eval₂_minpolyDiv_self, UpperHalfPlane.normSq_pos, NumberField.canonicalEmbedding.latticeBasis_apply, Finsupp.singleAddHom_apply, Polynomial.support_trinomial, supClosed_preimage_ofDual, Ideal.quotientEquiv_symm_apply, WittVector.constantCoeff_surjective, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, AddEquiv.piAdditive_apply, NumberField.IsCMField.unitsComplexConj_torsion, ConjAct.stabilizer_eq_centralizer, LinearMap.rTensor_comm, ProbabilityTheory.Kernel.borelMarkovFromReal_apply', RingEquiv.idealComapOrderIso_apply, MvPolynomial.expand_X, WittVector.teichmuller_mul_pow_coeff_of_ne, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, Poly.const_apply, PerfectClosure.mk_mul_mk, MeasureTheory.norm_condExpL2_le, ProbabilityTheory.Kernel.iIndep.meas_biInter, RatFunc.num_div_dvd, IsLocalMaxOn.hasFDerivWithinAt_nonpos, MulEquiv.inv'_apply, Multiset.equivDFinsupp_symm_apply, CategoryTheory.CountableCategory.instObjAsType, CompactlyGenerated.homeoOfIso_apply, MeasureTheory.VectorMeasure.equivMeasure_apply, Finset.uIcc_toDual, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, TensorProduct.equivFinsuppOfBasisLeft_symm_apply, ProbabilityTheory.IsGaussian.integrable_dual, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm, RootPairing.Hom.root_weightMap, ContinuousLinearEquiv.contDiff_comp_iff, addMonoidHomLequivInt_apply, StarSubalgebra.coe_map, OrthonormalBasis.nnnorm_eq_one, AlgebraicGeometry.range_eq_range_of_surjective, MeasurableEquiv.bijective, FractionalIdeal.coeIdeal_span_singleton, mem_subalgebraEquivIntermediateField, Complex.norm_mul_self_eq_normSq, RelHomClass.directed, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, contDiff_prodAssoc_symm, ProbabilityTheory.IsRatCondKernelCDF.iInf_rat_gt_eq, MeasureTheory.integral_domSMul, SemilinearIsometryClass.ediam_image, PrincipalSeg.map_succ, InnerProductSpace.isIdempotentElem_rankOne_self, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, MeasureTheory.MemLp.exists_simpleFunc_eLpNorm_sub_lt, ProbabilityTheory.Kernel.density_fst_univ, OrderEmbedding.mulRight_apply, ProbabilityTheory.Kernel.setIntegral_deterministic', Equiv.Perm.card_support_swap_mul, IsAddQuotientCoveringMap.homeomorph_comp, SupBotHom.symm_dual_comp, DFinsupp.liftAddHom_apply_single, BumpCovering.toPartitionOfUnity_apply, Submodule.tensorEquivSpan_apply_tmul, ContDiffMapSupportedIn.iteratedFDerivLM_apply, MonoidAlgebra.mapRangeRingHom_single, Matrix.cstar_nnnorm_def, DilationEquiv.coe_toHomeomorph, isCompact_setOf_finiteMeasure_le_of_isCompact, Polynomial.iterate_derivative_zero, IsBaseChange.basis_repr_comp_apply, minpoly.algEquiv_apply, IsUnit.unit_inv_map, SupHom.bot_apply, ClosureOperator.closure_iSup₂_closure, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGlued, CompleteLatticeHom.coe_tosSupHom, finEquivZPowers_symm_apply, MeasureTheory.weightedSMul_apply, ContinuousMultilinearMap.norm_map_snoc_le, supClosure_eq_self, MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply, NumberField.InfinitePlace.le_iff_le, MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure, WithLp.addEquiv_apply, MeasureTheory.Measure.ext_iff, TopCat.coe_of_of, PiTensorProduct.ofDirectSumEquiv_tprod_lof, MeasureTheory.measurePreserving_funUnique, Finset.image_neg, RootPairing.two_nsmul_reflection_eq_of_perm_eq, TopCat.Presheaf.stalkSpecializes_stalkPushforward, ContinuousLinearMap.comp_condExp_comm, Submodule.linearMap_eq_zero_iff_of_eq_span, OrderIso.lt_iff_lt, PreTilt.valAux_eq, Ordinal.isInitialIso_apply, Padic.withValUniformEquiv_norm_le_one_iff, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, Module.DualBases.basis_repr_symm_apply, Trivialization.continuousLinearMapAt_apply, Module.Basis.toDual_linearCombination_left, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, WittVector.verschiebung_zmod, RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, PowerSeries.catalanSeries_coeff, MvPolynomial.IsSymmetric.map, AlgHom.coe_addMonoidHom_injective, Nat.divisorsHom_apply, CategoryTheory.NatTrans.naturality_apply, Polynomial.Chebyshev.algebraMap_eval_U, AddMonoidHom.map_zero, IsLocalization.Away.algebraMap_pow_isUnit, WithZero.withZeroUnitsEquiv_symm_apply_coe, AlgebraicGeometry.Scheme.mem_grothendieckTopology_iff, NumberField.norm_norm_le_norm_mul_house_pow, TopHom.symm_dual_id, Multiplicative.ofAdd_eq_top, Valued.toNormedField.norm_le_one_iff, Polynomial.rootMultiplicity_eq_natTrailingDegree, ArchimedeanOrder.le_def, Polynomial.aeval_algebraMap_eq_zero_iff, ProbabilityTheory.setLIntegral_preCDF_fst, Module.Basis.constr_comp, Polynomial.card_rootSet_le_derivative, TestFunction.coe_neg, AddMonoidHom.toMultiplicativeRight_apply_apply, AddCircle.homeomorphCircle'_apply_mk, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal, Nucleus.map_himp_apply, PowerSeries.coeff_X_mul_largeSchroderSeries, VitaliFamily.withDensity_le_mul, Equiv.neg_def, MeasureTheory.pdf.uniformPDF_ite, Rat.padicValuation_cast, Ideal.algebraMap_quotient_injective, FreeAbelianGroup.toFinsupp_toFreeAbelianGroup, realPart_ofReal, Module.Basis.constr_symm_apply, Codisjoint.map, Geometry.SimplicialComplex.mem_space_iff, LinearMap.mapMatrixLinear_apply, mulEquivOfOrderOfEq_symm_apply_gen, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_x, Cardinal.extend_function_finite, Multiset.coe_consEquiv_of_eq_of_eq, TopCat.GlueData.open_image_open, finSuccAboveOrderIso_symm_apply_last, LightCondensed.forget_obj_val_map, PMF.toOuterMeasure_mono, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, AddHom.coe_srangeRestrict, Finset.image_orderEmbOfFin_univ, OrderIso.isCoatom_iff, map_iInf₂, ProbabilityTheory.Kernel.partialTraj_succ_of_le, HahnSeries.SummableFamily.coe_neg, ConjRootClass.aeval_minpoly_iff, Submodule.coe_mapAlgEquiv_symm_apply, Matrix.GeneralLinearGroup.map_comp_apply, HahnSeries.SummableFamily.mul_toFun, Homeomorph.vadd_symm_apply, geometric_hahn_banach_open_point, LinearMap.BilinForm.toMatrixAux_eq, IsPerfectClosure.equiv_comp_equiv_apply_eq_self, LocallyConstant.comapMonoidHom_apply, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, Polynomial.Gal.restrict_smul, PowerSeries.expand_subst, Orientation.linearEquiv_det_rotation, Matrix.mul_mul_left, AddMonoidHom.noncommPiCoprod_apply, MeasureTheory.MeasuredSets.sub_le_edist, PowerSeries.coeff_trunc, AffineEquiv.constVAdd_apply, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousAddMonoidHom.coe_id, SubMulAction.ofFixingSubgroup_equivariantMap_injective, Algebra.Extension.H1Cotangent.equiv_apply, Finsupp.sumFinsuppLEquivProdFinsupp_apply, ContinuousLinearMap.isBigOWith_sub, ArithmeticFunction.carmichael_pow_of_prime_ne_two, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, OrderAddMonoidIso.symm_comp_self, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, CategoryTheory.Bicategory.mateEquiv_comp_id_right, MeasureTheory.Measure.measure_mono_both, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, Algebra.algebraMap_eq_smul_one', ClosedSubmodule.mem_comap, PowerSeries.expand_apply, Subgroup.transferTransversal_apply, PolynomialModule.eval_map, Valued.extension_extends, PresentedGroup.ext_iff, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Polynomial.contract_expand, MeasureTheory.Measure.lintegral_rnDeriv, ModularForm.constℝ_apply, GroupExtension.Section.mul_inv_mem_range_inl, MulEquiv.prodProdProdComm_apply, MonCat.forget_map, IsChain.preimage_iso_iff, ProbabilityTheory.Kernel.map_apply, LieModule.trace_toEnd_eq_zero_of_mem_lcs, Matrix.det_det, ContinuousLinearEquiv.coe_prodAssoc, GroupSeminorm.coe_iSup_apply, Monoid.Foldl.ofFreeMonoid_apply, LinearMap.IsProj.mem_iff_map_id, ContDiffMapSupportedIn.coe_of_support_subset, lt_map_inv_iff, Algebra.Generators.cotangentSpaceBasis_apply, CliffordAlgebra.involute_prod_map_ι, IsLocalization.coeSubmodule_span, Polynomial.derivative_mul, IsAdjoinRootMonic.coeff_apply, OrderEmbedding.sorted_lt_listMap, Equiv.Perm.IsCycle.exists_pow_eq, Module.Basis.mem_span, MultilinearMap.map_insertNth_add, PowerSeries.trunc_mul_trunc, ContinuousMap.attachBound_apply_coe, Unitary.conjStarAlgAut_symm, Module.Relations.Solution.surjective_π_iff_span_eq_top, AddAutAdditive_apply_symm_apply, StarAlgEquiv.norm_map, Equiv.isHomeomorph_of_discrete, MulAut.inv_apply, InfHom.bot_apply, Matrix.toLinearMap₂'_comp, SkewMonoidAlgebra.lift_apply', RCLike.star_def, OrthonormalBasis.sum_inner_mul_inner, LieHom.surjective_rangeRestrict, Matrix.adjugate_fin_two, Topology.WithUpper.continuous_toUpper, Valued.valuedCompletion_surjective_iff, Finsupp.supportedEquivFinsupp_symm_single, map_ratCast_smul, AffineMap.pi_lineMap_apply, Differentiable.continuousMultilinear_apply_const, groupHomology.d₃₂_single, FormalMultilinearSeries.changeOriginSeriesTerm_apply, PiTensorProduct.lift_reindex_symm, Complex.equivRealProdAddHom_symm_apply, Matrix.l2_opNorm_mulVec, DirectLimit.Module.of_f, SupClosed.image, RingEquiv.asBoolRingAsBoolAlg_apply, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, IsometryEquiv.apply_symm_apply, Finset.weightedVSubOfPoint_insert, AffineBasis.tot, ComplexShape.Embedding.AreComplementary.desc'_inl, Matrix.diagonal_vec3, orderOf_ofAdd_eq_addOrderOf, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_eq_iff', Polynomial.div_def, finSumEquivOfFinset_inr, Equiv.apply_swap_eq_self, Multiset.toDFinsupp_support, MeasureTheory.OuterMeasure.comap_map, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U, RingHom.rangeRestrict_surjective, Module.FaithfullyFlat.lTensor_injective_iff_injective, Finset.add_sum_eq_sum_insertNone, TopModuleCat.hom_zero_apply, ContDiffAt.clm_apply, MulChar.map_one, kroneckerTMulAlgEquiv_symm_single_tmul, Multiset.cast_symm_apply_fst, LieModuleHom.zsmul_apply, MeasureTheory.measure_compl_sigmaFiniteSet, MvPolynomial.IsWeightedHomogeneous.pderiv, sSupHom.symm_dual_id, Cubic.of_a_eq_zero', ModuleCat.mkOfSMul'_smul, MeasureTheory.ae_le_const_iff_forall_gt_measure_zero, LinearIsometry.coe_toLinearIsometryEquiv, OrderEmbedding.monotone, BialgEquiv.coe_toBialgHom, Seminorm.finset_sup_apply, ExteriorAlgebra.lift_symm_apply, Rep.coindToInd_of_support_subset_orbit, ContinuousLinearEquiv.map_sub, PiTensorProduct.map_reindex_symm, ContinuousLinearMap.hasDerivAtFilter, RelIso.sumLexComplRight_apply, DFinsupp.equivFunOnFintype_symm_coe, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, MeasureTheory.Content.sup_le, WithLp.coe_linearEquiv, finrank_quotient_span_eq_natDegree_norm, MeasureTheory.OuterMeasure.le_boundedBy', ValuativeRel.valuation_eq_zero_iff, Function.Embedding.sigmaMk_apply, AddHom.subsemigroupMap_apply_coe, AffineIsometryEquiv.coe_refl, WittVector.mapFun.nsmul, ContinuousMultilinearMap.alternatization_apply_apply, Action.ofMulAction_apply, Real.fourierIntegral_eq, OrderMonoidWithZeroHom.toFun_eq_coe, RelIso.smul_def, CategoryTheory.FunctorToTypes.shrinkMap_app, RootPairing.root_coroot_two, Cardinal.aleph_pos, Representation.finsupp_apply, GrpCat.surjective_of_epi, Hamming.ofHamming_zero, ModuleCat.extendScalarsId_hom_app_one_tmul, isAddRightRegular_ofMul, Polynomial.C_inj, CategoryTheory.eHomEquiv_id, MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt, PeriodPair.basis_one, OrderIso.mulRight₀_symm_apply, MvPolynomial.X_pow_eq_monomial, normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity, ContinuousAffineMap.comp_apply, List.sortedGT_map_ofDual, OrderIso.smulRight_apply, Ordinal.liftInitialSeg_coe, MvPolynomial.isEmptyRingEquiv_apply, Set.smul_graphOn_univ, LinearMap.toMatrix_apply', WittVector.ghostComponent_apply, InfClosed.image, ContinuousMultilinearMap.map_update_sub, Path.extend_extends, Polynomial.opRingEquiv_op_monomial, MvPowerSeries.rescaleUnit, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, Polynomial.natDegree_monomial_le, MeasureTheory.setLIntegral_le_iSup_mul, MeasureTheory.Measure.InnerRegular.map, AddConstMapClass.map_add_nsmul, Submonoid.mul_leftInvEquiv, ContinuousMap.sup_apply, Finsupp.card_Ico, CategoryTheory.Quiv.homEquivOfIso_symm_apply, Finset.Colex.toColex_univ, HahnModule.coeff_single_smul_vadd, ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, Module.Flat.iff_rTensor_preserves_injective_linearMap, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point, AlgebraicGeometry.ValuativeCriterion.Existence.specializingMap, Module.Presentation.directSum_var, measure_le_lintegral_thickenedIndicatorAux, FreeAddMonoid.toList_comp_ofList, InfHom.symm_dual_comp, Polynomial.prod_X_sub_C_nextCoeff, Submodule.re_inner_starProjection_eq_normSq, CategoryTheory.InducedCategory.endEquiv_symm_apply_hom, WeakSpace.map_apply, InverseSystem.piEquivSucc_self, Ordinal.iSup_typein_succ, LinearMap.llcomp_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, NormedAddGroupHom.coe_toAddMonoidHom, Function.Embedding.coe_smul, Algebra.IsPushout.equiv_symm_algebraMap_left, Finsupp.toColex_monotone, Affine.Simplex.sign_excenterWeights_singleton_pos, DFinsupp.mapRange_def, Polynomial.mem_roots_sub_C', Finsupp.filter_apply_neg, GenLoop.fromLoop_apply, Matrix.one_kronecker, PMF.toOuterMeasure_pure_apply, LinearMap.toMatrix₂_mul, Equiv.boolArrowEquivProd_symm_apply, FormalMultilinearSeries.congr, VitaliFamily.le_mul_withDensity, aeval_wittPolynomial, LieSubmodule.mem_comap, AffineEquiv.coe_homothetyUnitsMulHom_eq_homothetyHom_coe, WittVector.ghostComponent_verschiebungFun, NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply', OrderIso.toFun_eq_coe, LinearEquiv.det_trans, StrictMono.orderIsoOfSurjective_symm_apply_self, OnePoint.isBoundedAt_iff_exists_SL2Z, StarMulEquiv.coe_mk, LieEquiv.map_lie, WithBot.subtypeOrderIso_symm_apply, LinearMap.BilinForm.smul_left_of_tower, SubAddAction.subtype_apply, Flag.coe_map, groupHomology.mapCycles₁_comp_apply, Polynomial.Monic.leadingCoeff_C_mul, toDegLex_inj, DirectSum.decomposeAlgEquiv_symm_apply, Matrix.BlockTriangular.map, Orientation.kahler_comp_rightAngleRotation', Matrix.lieConj_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, dist_sq_lineMap_lineMap_of_inner_eq_zero, SemiNormedGrp₁.coe_id, Homeomorph.image_interior, DFinsupp.equivProdDFinsupp_smul, Rep.leftRegularHom_hom, CompleteLatticeHom.dual_symm_apply_toFun, AddMonCat.zeroHom_apply, ContinuousMultilinearMap.coe_coe, SemiRingCat.inv_hom_apply, Affine.Simplex.restrict_reindex, RatFunc.laurent_X, CategoryTheory.InducedCategory.endEquiv_apply, Topology.WithLawson.ofLawson_toLawson, Ideal.mem_leadingCoeffNth_zero, VectorField.fderiv_apply_lieBracket, ZMod.LFunction_one_sub, Equiv.piCongrLeft_apply, MulAut.conjNormal_symm_apply, SimpleGraph.Walk.map_copy, Polynomial.leadingCoeff_quadratic, MeasureTheory.Measure.outerMeasure_le_iff, Finset.map_filter, SchwartzMap.coeFn_zero, PrimeSpectrum.primeSpectrumProd_symm_inl, PrincipalSeg.isLowerSet_range, AddUnits.embedProduct_injective, TopologicalSpace.Closeds.complOrderIso_symm_apply, EquicontinuousOn.tendsto_uniformOnFun_iff_pi', PMF.toMeasure_bind_apply, InfTopHom.coe_toInfHom, MeasureTheory.inner_condExpL2_left_eq_right, ArithmeticFunction.cardFactors_multiset_prod, Orientation.rotation_eq_self_iff, ValuationSubring.valuation_le_iff, SubMulAction.fixingSubgroup_smul_eq_fixingSubgroup_map_conj, AddConstEquiv.trans_apply, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, AddMagma.FreeAddSemigroup.lift_symm_apply, Equiv.Perm.apply_inv_self, Cardinal.toNat_eq_iff, IsometryEquiv.withLpUniqueProd_symm_apply, RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, ContinuousMap.toLp_denseRange, OrderHom.le_map_sup_fixedPoints, Multiset.prod_X_sub_X_eq_sum_esymm, map_equiv_removeNone, IsLocalization.bijective_lift_piRingHom_algebraMap_comp_piEvalRingHom, ContinuousLinearMap.toContinuousAddMonoidHom_add, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, CircleDeg1Lift.commute_nat_add, Monoid.End.coe_one, AnalyticOnNhd.compContinuousLinearMap, AddMonoidAlgebra.comul_single, ClassGroup.Quot_mk_eq_mk, MeasureTheory.sum_addContent_le_of_subset, Module.Basis.dualBasis_coord_toDualEquiv_apply, PowerSeries.trunc_X_pow_self_mul, Matrix.repr_toLin, thickenedIndicator_one_of_mem_closure, SimpleGraph.leftInverse_comap_map, LieAlgebra.Orthogonal.soIndefiniteEquiv_apply, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae, IsChain.image_iso, UniformFun.edist_eval_le, isSublattice_latticeClosure, WeakDual.isClosed_image_polar_of_mem_nhds, ProbabilityTheory.Kernel.condExp_traj', Set.preimage_div_preimage_subset, PrimeSpectrum.equivSubtype_apply_coe, Polynomial.coeffList_C_mul, AlternatingMap.map_perm, AdicCompletion.of_ofAlgEquiv_symm, Polynomial.support_C_mul_X, IsIntegrallyClosed.isIntegral_iff, Polynomial.exists_partition_polynomial, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, AddActionHom.id_apply, CompleteLatticeHom.coe_comp, WeierstrassCurve.Projective.baseChange_negDblY, ZLattice.covolume_eq_det_inv, AlgebraicGeometry.SheafedSpace.colimit_exists_rep, SimpleGraph.homOfConnectedComponents_apply, EmbeddingLike.pairwise_comp, Set.ordConnected_preimage, PadicComplex.valuation_extends, ContinuousLinearMap.integral_apply, RCLike.algebraMap_eq_ofReal, Affine.Simplex.faceOppositeCentroid_restrict, OrderHom.dual_id, NumberField.IsCMField.equivInfinitePlace_symm_apply, SemiRingCat.comp_apply, Submonoid.LocalizationMap.mul_mk'_eq_mk'_of_mul, WType.equivSigma_apply, Function.Embedding.smul_apply, ODE.FunSpace.isUniformInducing_toContinuousMap, Lagrange.derivative_nodal, ContinuousAffineMap.prodMap_apply, Module.Basis.constrL_basis, Polynomial.nnqsmul_eq_C_mul, CliffordAlgebra.even.lift.aux_mul, WithZero.map'_coe, Wbtw.map, Unitary.toUnits_injective, LocalizedModule.restrictScalars_map_eq, Representation.Coinvariants.mk_inv_tmul, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, Subgroup.equivOp_symm_apply_coe, Matrix.SpecialLinearGroup.toGLPos_injective, Submodule.reflection_orthogonal_apply, PolynomialModule.map_smul, Polynomial.leadingCoeff_C_mul_of_isUnit, Equiv.Perm.sign_of_cycleType, Submodule.linearProjOfIsCompl_apply_right, MvPowerSeries.coeff_pow, FreeMagma.lift_of, isBot_ofDual_iff, PolynomialModule.add_apply, Module.forall_dual_apply_eq_zero_iff, CFC.exists_pos_algebraMap_le_iff, toDual_pow, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, CategoryTheory.Bicategory.Adjunction.homEquiv₂_symm_apply, RCLike.inner_apply', LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, SSet.ofSimplex_le_skeleton, MeasureTheory.Measure.AbsolutelyContinuous.kernel_of_compProd, AddSubmonoid.addUnitsTypeEquivIsAddUnitAddSubmonoid_apply_coe, Quaternion.imK_equivProd_symm_apply, AlgebraicGeometry.isIso_SpecMap_iff, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_π, Convex.lineMap_mem, CartanMatrix.C_two, IsLocalization.to_map_eq_zero_iff, MulHom.coe_fst, Polynomial.aroots_X_sub_C, Polynomial.Gal.galActionHom_injective, ProbabilityTheory.iIndepFun_iff, KaehlerDifferential.mvPolynomialBasis_repr_D_X, RestrictedProduct.continuous_rng_of_principal, ContinuousAddMonoidHom.snd_toFun, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, PrincipalSeg.isMin_apply_iff, Complex.conj_inv, Finset.exists_equiv_extend_of_card_eq, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, LinearEquiv.algEquivOfRing_apply, Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero, AlgebraicGeometry.Scheme.Hom.range_fiberι, SemistandardYoungTableau.to_fun_eq_coe, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_one_of_monotone, ContinuousLinearMap.comp_memLp, AddEquiv.invFun_eq_symm, exteriorPower.coe_basis, Localization.AtPrime.mapPiEvalRingHom_bijective, NNReal.coe_toRealHom, Submonoid.fg_iff_add_fg, TopologicalSpace.Opens.coe_inclusion', Module.DirectLimit.map_apply_of, PMF.toMeasure_ofFinset_apply, RingEquiv.toOpposite_apply, MvPolynomial.optionEquivLeft_C, AlternatingMap.constLinearEquivOfIsEmpty_apply, SemistandardYoungTableau.ext_iff, CentroidHom.star_centerToCentroidCenter, Polynomial.taylor_mul, AddMonoidHom.toAddEquiv_symm_apply, SubMulAction.ofStabilizer.conjMap_comp_inv_apply, RootPairing.Equiv.id_coweightMap_apply, MvPolynomial.rename_rename, Sublattice.map_equiv_eq_comap_symm, Cardinal.toNat_congr, ModuleCat.ι_coprodIsoDirectSum_hom_apply, ContinuousAffineMap.coe_mk, CategoryTheory.ConcreteCategory.surjective_of_epi_of_preservesPushout, AddSubgroup.coe_addSubgroupOf, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero, Monoid.End.coe_pow, Subring.addEquivOp_apply_coe, Lex.exists, Finsupp.linearCombination_id_surjective, Real.fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.tensorKer_tmul, Matrix.det_permute, CircleDeg1Lift.iterate_pos_le_iff, NumberField.InfinitePlace.isometry_embedding, FreeMagma.toFreeSemigroup_of, OrderEmbedding.le_map_sup, AlgEquiv.toOpposite_apply, WithZero.coe_unitsWithZeroEquiv_eq_units_val, LinearMap.toMatrixAlgEquiv_comp, Polynomial.degree_quadratic_lt, OrderEmbedding.image_Ioc, OrderIso.sumLexIicIoi_symm_apply_of_lt, MeasureTheory.Measure.InnerRegular.map_iff, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearIsometryEquiv.comp_fderivWithin, Matrix.isParabolic_iff_exists, MeasureTheory.measure_eq_top_of_subset_compl_sigmaFiniteSetWRT'_of_measurableSet, LinearMap.det_mulLeft, OrderIso.tendsto_atTop_iff, Ordinal.omega_lt_omega, TensorProduct.sum_tmul_basis_right_injective, TopologicalSpace.OpenNhds.inclusionMapIso_hom, IntermediateField.coe_bot, Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_mem, CategoryTheory.Functor.CorepresentableBy.equivOfIsoObj_symm_apply, MulChar.toMonoidWithZeroHom_apply, EuclideanGeometry.orthogonalProjection_congr, ModuleCat.restrictScalarsComp'App_hom_apply, Ordinal.omega0_lt_omega_one, FintypeCat.uSwitch_map_uSwitch_map, Subspace.dualLift_of_subtype, ZeroAtInftyContinuousMap.add_apply, LinearMap.IsPositive.re_inner_nonneg_right, OrderIso.range_eq, Con.liftOnUnits_mk, Ideal.map_pi, Part.Fix.exists_fix_le_approx, AlgebraicGeometry.Scheme.Cover.iUnion_range, val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe, WeierstrassCurve.Projective.comp_equiv_comp, MulChar.apply_mem_algebraAdjoin_of_pow_eq_one, OneHom.inv_apply, Algebra.TensorProduct.congr_symm_apply, stdSimplexHomeomorphUnitInterval_symm_apply_coe, Real.fourier_continuousLinearMap_apply, ZMod.dft_even_iff, PiTensorProduct.reindex_reindex, DirectSum.of_smul, RootPairing.Hom.comp_coweightMap_apply, PresheafOfModules.epi_iff_surjective, Submonoid.leftInvEquiv_symm_mul, WeierstrassCurve.Affine.CoordinateRing.basis_one, Subgroup.coe_inclusion, CategoryTheory.Sieve.overEquiv_pullback, ValuativeExtension.srel_iff_srel, RootPairing.reflectionPerm_involutive, Submodule.mulMap_one_right_eq, IsUniformGroup.uniformContinuous_iff_isOpen_ker, OrdinalApprox.gfp_mem_range_gfpApprox, StieltjesFunction.measure_Ioi_of_tendsto_atTop_atTop, Finsupp.mem_frange_of_mem, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_φ, ContinuousMap.congr_arg, RootPairing.EmbeddedG2.shortAddLongRoot_shortRoot, RingEquiv.map_sub, pow_toColex, ProbabilityTheory.iIndep.meas_biInter, Polynomial.sum_bernoulli, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, Finset.affineCombination_sdiff_sub, Matrix.abs_det_submatrix_equiv_equiv, TopologicalSpace.Opens.comap_mono, AlgebraicGeometry.Scheme.mem_basicOpen', CommAlgCat.inv_hom_apply, Padic.complete', Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly, AddEquiv.prodUnique_apply, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, CategoryTheory.Adjunction.homEquiv_naturality_left_square, StarMulEquiv.symm_apply_apply, Algebra.norm_eq_matrix_det, MvPolynomial.iterToSum_sumToIter, Equiv.piOptionEquivProd_symm_apply, LinearMap.compRight_apply, Cardinal.mk_preimage_equiv_lift, LightCondensed.ihomPoints_symm_comp, AddMonoidHom.coe_prodMap, FirstOrder.Language.Embedding.equivRange_toEquiv_apply, RootPairing.Base.sub_notMem_range_coroot, Cardinal.toENat_ofENat, toWeakSpaceCLM_bijective, WithZero.lift'_symm_apply_apply, ZMod.invDFT_apply, CompleteLatticeHom.apply_limsup_iterate, LinearEquiv.mapMatrix_apply, AlternatingMap.map_linearDependent, Finsupp.sumElim_apply, Subsemigroup.centerToMulOpposite_apply_coe, PiTensorProduct.subsingletonEquiv_symm_apply, Representation.asAlgebraHom_single, AddConstMapClass.map_add_one, AddSubsemigroup.coe_toSubsemigroup_symm_apply, AffineIsometryEquiv.ofTop_apply, Finset.orderEmbOfFin_unique, Trivialization.linearMapAt_symmₗ, Function.Embedding.subtype_injective, Polynomial.C_mul_X_eq_monomial, AddValuation.map_pow, MeasureTheory.measure_eq_top_iff_of_symmDiff, OrderAddMonoidIso.symm_comp_eq, NumberField.mixedEmbedding.normAtAllPlaces_apply, Subalgebra.comap_map_eq, Set.principalSegIioIicOfLE_toRelEmbedding, Function.fromTypes_cons_equiv_symm_apply, Matrix.liftLinear_single, HasFDerivWithinAt.clm_apply, MulOpposite.coe_opLinearEquiv_symm, Algebra.Generators.toAlgHom_ofComp_localizationAway, LieAlgebra.finrank_engel, Submonoid.LocalizationMap.map_id, sInfHom.dual_id, Polynomial.sylvester_comm, skewAdjointLieSubalgebraEquiv_apply, CliffordAlgebraQuaternion.toQuaternion_star, SmoothPartitionOfUnity.contMDiffAt_finsum, ContinuousAffineMap.neg_apply, LinearMap.IsSymmetric.im_inner_self_apply, signHom_apply, image_vadd_setₛₗ, LinearIsometryEquiv.antilipschitz, MeasureTheory.Measure.measure_isMulLeftInvariant_eq_smul_of_ne_top, imaginaryPart_I_smul, Finset.Ioi_toDual, ContinuousMap.le_def, MeasureTheory.Measure.count_injective_image', LinearEquiv.coe_mk, eval_det_add_X_smul, AntivaryOn.dual, DFinsupp.zero_apply, PresentedGroup.mk_eq_mk_of_mul_inv_mem, HasFPowerSeriesOnBall.unshift, Continuous.convolution_integrand_fst, Pi.toColex_monotone, DirectSum.fromAddMonoid_of_apply, PadicComplex.coe_eq, Pi.counit_coe_dFinsupp, Equiv.apply_symm_apply, Ordinal.toNatOrdinal_eq_one, toLex_inj, OrderMonoidHom.one_apply, AlgebraicGeometry.Scheme.Hom.mem_opensRange, ContinuousAlternatingMap.vecCons_smul, Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq, WellFoundedGT.monotone_chain_condition, RootPairing.Equiv.coweightEquiv_symm_coweightMap, AffineIsometry.coeFn_injective, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, AddMonoidAlgebra.mapRangeAlgHom_single, idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, upperClosure_image, TensorProduct.toIntegralClosure_bijective_of_isLocalization, AddGroupExtension.Section.exists_eq_inl_add, MeasureTheory.measure_inv_null, PowerSeries.derivative_exp, ContinuousAffineMap.toFun_eq_coe, MeasureTheory.SimpleFunc.forall_mem_range, DilationEquiv.smulTorsor_symm_apply, TensorProduct.piScalarRight_symm_algebraMap, OrderAddMonoidHom.inl_apply, ContDiffMapSupportedIn.structureMapCLM_apply, RCLike.sub_conj, iteratedFDerivWithin_succ_eq_comp_right, mem_derangements_iff_fixedPoints_eq_empty, PresentedAddMonoid.surjective_mk, ofColex_one, LinearPMap.mk_apply, Equiv.piSplitAt_symm_apply, RCLike.re_sqrt_ofReal, AddSubgroup.mem_toSubgroup', Convex.convex_remove_iff_notMem_convexHull_remove, Topology.WithUpperSet.toUpperSet_inj, MeasureTheory.measure_biUnion, Finsupp.sum_zsmul, SSet.stdSimplex.obj₀Equiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', Prod.Lex.lt_iff', upperSetIsoLowerSet_apply, AffineIsometry.nndist_map, MeasureTheory.setLIntegral_pos_iff, MeasureTheory.Measure.comp_apply_univ, NumberField.mem_maximalRealSubfield_iff, RingHom.rangeS_eq_top, Circle.exp_natCast_mul, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, FirstOrder.Language.Equiv.symm_apply_apply, RelEmbedding.coe_one, Pi.colex_asc, Algebra.trace_eq_of_ringEquiv, IsometryEquiv.subLeft_symm_apply, Matrix.reindex_mem_colStochastic_iff, ProbabilityTheory.Kernel.swapRight_apply', AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen, CategoryTheory.PreGaloisCategory.autEmbedding_injective, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, tangentMap_snd, iteratedDerivWithin_vcomp_two, Monoid.CoprodI.NeWord.mulHead_prod, LaurentSeries.LaurentSeriesRingEquiv_def, SimpleGraph.Coloring.mem_colorClass, Field.Emb.Cardinal.directed_filtration, Sequential.homeoOfIso_symm_apply, tangentMap_chart, SchwartzMap.lineDerivOp_fourier_eq, Polynomial.logMahlerMeasure_C_mul, ProbabilityTheory.condExp_ae_eq_integral_condDistrib_id, NonUnitalAlgHom.fst_toFun, WittVector.mapFun.add, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, PowerSeries.coeff_of_lt_order, Algebra.TensorProduct.mapOfCompatibleSMul_surjective, Set.FiniteExhaustion.instFiniteElemCoeNat, FreeMonoid.lift_restrict, BoxIntegral.Box.upper_mem_Icc, MvPowerSeries.constantCoeff_subst, Path.Homotopic.map_lift, Orientation.areaForm_le, StarSubalgebra.range_le, ContinuousMap.coe_addRight, Seminorm.ext_iff, RCLike.pos_iff, LinearMap.BilinForm.congr_apply, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, Polynomial.C_1, DirectSum.lie_module_bracket_apply, AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_apply, SSet.OneTruncation₂.nerveHomEquiv_id, DomMulAct.symm_mk_pow, AddMonoid.Coprod.fst_swap, Measurable.lintegral_kernel_prod_left', Rep.indToCoindAux_self, Polynomial.aeval_map_algebraMap, CategoryTheory.ShortComplex.ShortExact.ab_surjective_g, CategoryTheory.Iso.commGroupIsoToMulEquiv_symm_apply, Seminorm.uniformContinuous_of_forall, LocallyConstant.congrLeftRingEquiv_apply_apply, LinearMap.id'_coe, SupHom.dual_id, isClosedEmbedding_cfcₙAux, UniformEquiv.self_comp_symm, Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar, TensorAlgebra.toTrivSqZeroExt_ι, Representation.asGroupHom_apply, Finsupp.sumFinsuppAddEquivProdFinsupp_symm_inl, Order.succ_toAdd, AlgebraicGeometry.isCompact_iff_exists, AddChar.wInner_cWeight_self, LieModule.traceForm_eq_sum_finrank_nsmul', Set.up_union, MeasureTheory.Measure.measure_subtype_coe_le_comap, MeasureTheory.ProbabilityMeasure.toMeasure_add_pos_gt_mem_nhds, DomMulAct.smul_linearMap_apply, Multiset.coe_subsingletonEquiv, MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving, ciSup_partialSups_eq', LinearMap.mul_apply_apply, eval₂_minpolyDiv_of_eval₂_eq_zero, Multiplicative.toAdd_image_setMul, MvPolynomial.divMonomial_add_modMonomial, Set.coe_singletonZeroHom, CommRingCat.id_apply, Filter.HasBasis.notMem_measureSupport, LinearIsometry.norm_map, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, Metric.Snowflaking.preimage_ofSnowflaking_closedBall, Ring.ordFrac_eq_div, Equiv.restrictPreimageFinset_symm_apply_coe, LeftInvariantDerivation.coe_derivation, RootPairing.coreflection_image_eq, LinearMap.BilinForm.toMatrix_compRight, MeasureTheory.Measure.comp_add, isTop_toDual_iff, MeasureTheory.smul_le_stoppedValue_hittingBtwn, TensorProduct.enorm_comm, RingHom.Bijective.respectsIso, HahnSeries.SummableFamily.ext_iff, LinearMap.det_pi, CircleDeg1Lift.iterate_pos_lt_iff, QuadraticMap.map_add_self, CategoryTheory.Bicategory.mateEquiv_vcomp, AddCon.sup_def, MeasureTheory.piContent_tendsto_zero, LocallyConstant.coe_smul, innerSL_apply_apply, MeasureTheory.Lp.coeFn_const, AbsoluteValue.map_units_intCast, CategoryTheory.Abelian.Ext.precomp_mk₀_injective_of_epi, DirichletCharacter.LSeries_modOne_eq, CategoryTheory.InducedCategory.homLinearEquiv_apply, ContinuousMapZero.id_toFun, coe_factor_orderIso_map_eq_one_iff, SpecialLinearGroup.coe_zpow, NonUnitalSubringClass.coe_subtype, ModuleCat.AlternatingMap.postcomp_apply, MeasureTheory.Measure.measure_toMeasurable_add_inter_right, IsLocalization.map_mk', ContinuousLinearMap.IsInvertible.surjective, AlgEquiv.isTranscendenceBasis_iff, OrderMonoidIso.withZero_symm_apply_symm_apply, PowerSeries.algebraMap_apply'', AddMonoidAlgebra.mapRangeAddEquiv_apply, minpoly_algebraMap_add_splits, MeasureTheory.measure_le_setLAverage_pos, SimpleGraph.walkLengthTwoEquivCommonNeighbors_symm_apply_coe, SmoothPartitionOfUnity.locallyFinite, ArithmeticFunction.zeta_apply, Finsupp.erase_same, WittVector.eq_iterate_verschiebung, IsCyclic.val_mulAutMulEquiv_apply, CategoryTheory.ShrinkHoms.id_def, RingHom.map_neg, inf_mem_infClosure, smulMulHom_apply, convexHull_eq_iInter, equivShrink_symm_div, LinearMap.ext_ring_op_iff, MvPowerSeries.trunc'_expand_trunc', Submodule.mapQ_apply, Complex.star_def, MulAut.conjNormal_val, Ideal.intNorm_mem_spanNorm, LinearEquiv.restrictScalars_symm_apply, BotHom.coe_comp, SeminormFamily.filter_eq_iInf, gcd_mul_left, AddSubmonoidClass.coe_subtype, MeasureTheory.Integrable.norm_integral_condExpKernel, WeierstrassCurve.ψ₂_sq, toMul_uzpow, CategoryTheory.conjugateEquiv_symm_id, ZeroAtInftyContinuousMap.coe_smul, Homeomorph.coe_uniqueProd, SkewMonoidAlgebra.coeff_erase_same, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, MeasureTheory.measure_preimage_mul, LinearIsometryEquiv.fderivWithin, BoxIntegral.Box.measurableSet_Icc, Affine.Simplex.incenter_map, even_ofMul_iff, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerₛₗ_apply, dist_toDual, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, exists_smooth_one_nhds_of_subset_interior, AddEquiv.coprodPUnit_symm_apply, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, OrderAddMonoidIso.strictMono_symm, IsLocalization.map_comp_map, Algebra.lmul_algebraMap, EuclideanSpace.inner_single_left, HasFTaylorSeriesUpTo.hasFDerivAt, TensorProduct.AlgebraTensorModule.rid_tmul, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, List.SortedLT.coe_getIso_symm_apply, ContinuousAlternatingMap.tsum_eval, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, AddMonoidHom.coe_prod, norm_iteratedFDerivWithin_clm_apply, MulHom.subsemigroupComap_apply_coe, Polynomial.hasseDeriv_one', CongruenceSubgroup.exists_Gamma_le_conj', SpecialLinearGroup.toLinearEquiv_symm_to_linearMap, OrderDual.instNeBotNhdsWithinIio, Polynomial.derivative_comp_one_sub_X, IsometryClass.lipschitz, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, MeasureTheory.Measure.toSphere_apply_aux, MvPolynomial.optionEquivLeft_X_some, Orientation.neg_rotation, AlternatingMap.congr_fun, ProbabilityTheory.Kernel.coe_add, Equiv.piCongrSigmaFiber_symm_apply, MeasureTheory.Measure.pi'_pi, OrderMonoidIso.withZero_symm_apply_apply, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Submodule.dualQuotEquivDualAnnihilator_apply, AddSubgroup.IsComplement.quotientAddGroupMk_leftQuotientEquiv, PolynomialModule.comp_smul, Unitization.splitMul_apply, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, HahnSeries.addOppositeEquiv_symm_support, AList.lookupFinsupp_eq_zero_iff, DomAddAct.map_mk_symm_nhds, CoheytingHom.id_apply, Polynomial.monic_X_pow_add_C, unitsNonZeroDivisorsEquiv_apply, OrderEmbedding.infIrredUpperSet_surjective, MeasureTheory.measure_diff_le_iff_le_add, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit, MeasureTheory.Measure.measure_inter_eq_of_ae, Cardinal.ord.orderEmbedding_coe, AddAut.mulRight_symm_apply, TensorAlgebra.ι_comp_lift, LinearEquiv.domMulActCongrRight_symm_apply, Polynomial.monic_multisetProd_X_sub_C, sum_hom_units, ContinuousLinearMap.toBilinForm_apply, WittVector.IsocrystalHom.frob_equivariant, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, MvPolynomial.eval₂Hom_monomial, CategoryTheory.nerve.functorOfNerveMap_map, MeasureTheory.Integrable.measure_norm_ge_lt_top, ProbabilityTheory.Kernel.trajContent_cylinder, isSquare_toMul_iff, Measurable.apply_continuousLinearMap, AddChar.doubleDualEmb_injective, Summable.mapL, LieSubalgebra.equivOfLe_apply, ProbabilityTheory.covarianceBilin_apply_eq_cov, Matrix.charpoly_map, OrderIso.toRelIsoLT_apply, IsOpen.measure_eq_iSup_isClosed, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, LocallyConstant.charFn_eq_one, StandardEtalePair.homEquiv_symm_apply, ProbabilityTheory.covarianceBilin_self, LinearEquiv.conj_apply_apply, SSet.opFunctorCompOpFunctorIso_inv_app_app, Valuation.IsTrivialOn.eq_one, Coalgebra.sum_map_tmul_counit_eq, equivEquivIso_hom, DoubleCentralizer.nnnorm_def', Ordinal.omega0_lt_preOmega_iff, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, Algebra.IsPushout.cancelBaseChange_tmul, MeasureTheory.tendsto_measure_iUnion_atBot, IsArtinianRing.localization_surjective, CategoryTheory.Functor.toOrderHom_coe, Polynomial.derivative_pow_eq_zero, MeasureTheory.Measure.ae_mem_finset_iff, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, Matrix.diagonal_fin_two, Ideal.instCanLiftTwoSidedIdealCoeOrderHomAsIdealIsTwoSided, LinearMap.adjoint_eq_toCLM_adjoint, LinearMap.BilinForm.IsNonneg.nonneg, AbsoluteValue.coe_mk, AddMonoidHom.map_dfinsuppSumAddHom, Quaternion.normSq_natCast, LinearEquiv.skewSwap_symm_apply, minpoly.eq_iff_aeval_eq_zero, Disjoint.dual, RingCon.coe_inj, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, strictAntiOn_comp_ofDual_iff, Subalgebra.equivOfEq_apply, SimplexCategory.toTopObj_one_coe_add_coe_eq_one, AddValuation.top_iff, ContinuousMultilinearMap.mkPiAlgebra_apply, UniformOnFun.uniformContinuous_ofUniformFun, TensorProduct.tensorTensorTensorComm_tmul, latticeClosure_univ, IsCyclotomicExtension.discr_odd_prime, AddMonoidHom.inl_strictMono, Seminorm.bddAbove_range_iff, frobenius_one, MvPolynomial.homogeneousComponent_of_mem, Equiv.refl_apply, ContinuousLinearMap.map_zero, MulEquiv.toAdditive_apply_apply, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, ZeroHom.coe_comp, AddMonoidAlgebra.mapDomainAddEquiv_single, finEquivPowers_apply, LieModuleHom.ker_eq_bot, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, PowerSeries.coeff_succ_mul_X, ProbabilityTheory.cond_apply, WeierstrassCurve.Jacobian.map_dblX, Complex.lipschitz_equivRealProd, Prod.Lex.compare_def, AlgebraicGeometry.HasRingHomProperty.stalkMap, ContinuousAffineEquiv.symm_symm_apply, Module.exists_dual_forall_apply_eq_one, Equiv.Perm.subtypePerm_ofSubtype, OnePoint.equivOfIsEmbeddingOfRangeEq_apply_infty, BoxIntegral.IntegrationParams.tendsto_embedBox_toFilteriUnion_top, DirichletCharacter.changeLevel_def, PolyEquivTensor.right_inv, LinearIndependent.linearCombination_repr, Topology.WithLawson.isOpen_preimage_ofLawson, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, BoundedContinuousFunction.dist_le, Function.Embedding.setValue_eq, CommGrpCat.epi_iff_surjective, Equiv.piCongr_apply_apply, congr_fun, Diffeomorph.uniqueMDiffOn_preimage, SkewMonoidAlgebra.mapDomain_one, ModuleCat.linearIndependent_shortExact, exteriorPower.basis_repr_ne, TensorProduct.gradedComm_tmul_one, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Real.tsum_eq_tsum_fourierIntegral_of_rpow_decay_of_summable, ContinuousAffineEquiv.coe_toContinuousAffineMap, Submodule.orthogonalProjection_mem_subspace_eq_self, Set.ordConnected_range, Action.diagonalSuccIsoTensorDiagonal_inv_hom, MvPolynomial.aeval_X_left_apply, RestrictedProduct.one_apply, AddMonoidAlgebra.mapDomainNonUnitalAlgHom_apply, gcd_greatest, CategoryTheory.GrothendieckTopology.OneHypercover.mem₀, Polynomial.toPowerSeries_toMvPowerSeries, PolynomialModule.aeval_equivPolynomial, ContinuousOn.eval_const, FreeAddSemigroup.lift_comp_of, ContinuousAddMonoidHom.prodMap_toFun, Profinite.NobelingProof.coe_πs, Equiv.sumAssoc_apply_inr, PseudoMetric.refl, Module.length_of_free, ContinuousLinearMap.IsPositive.inner_nonneg_right, AbsoluteValue.IsEuclidean.sub_mod_lt, MeasureTheory.meas_le_lintegral₀, Rep.coe_res_obj_ρ, finCongr_apply, SmoothPartitionOfUnity.nonneg, Finsupp.if_mem_support, ContinuousMap.Homotopy.apply_zero_path, TensorAlgebra.adjoin_range_ι, IsNilpotent.map_exp, CategoryTheory.Abelian.Ext.mk₀_addEquiv₀_apply, WithLp.prod_norm_eq_idemFst_of_L1, HahnSeries.coeff_single_mul_add, Subgroup.conj_smul_subgroupOf, PowerSeries.order_expand, LeftInvariantDerivation.left_invariant', ContinuousLinearEquiv.map_tsum, selfAdjoint.expUnitaryPathToOne_apply, LinearEquiv.coe_withLpCongr, TensorProduct.AlgebraTensorModule.congr_symm_tmul, Finsupp.filter_apply_pos, FirstOrder.Language.ElementaryEmbedding.ext_iff, Polynomial.leadingCoeff_det_X_one_add_C, MeasureTheory.Measure.haarMeasure_closure_self, Coalgebra.sum_tmul_counit_eq, Equiv.arrowCongr'_apply, MulEquiv.symm_comp_self, MeasureTheory.OuterMeasure.mono'', ProbabilityTheory.iIndepFun_iff_measure_inter_preimage_eq_mul, AddEquiv.toMultiplicativeRight_apply_apply, RootPairing.Base.root_mem_span_int, PrincipalSeg.mem_range_iff_rel, SubAddAction.ofStabilizer.conjMap_comp, WittVector.frobeniusEquiv_symm_apply, Orientation.eq_rotation_self_iff_angle_eq_zero, RingEquiv.prodProdProdComm_apply, MvPolynomial.homogeneousComponent_mem, DFinsupp.subtypeDomainLinearMap_apply, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, AddCommute.map, MvPolynomial.pUnitAlgEquiv_symm_apply, Submodule.factor_mk, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, eventually_homothety_image_subset_of_finite_subset_interior, Submonoid.fromLeftInv_leftInvEquiv_symm, strictMono_dual_iff, sbtw_iff_mem_image_Ioo_and_ne, SubAddAction.ofFixingAddSubgroup_of_inclusion_injective, MvPowerSeries.coeff_monomial_mul, QuasispectrumRestricts.nnreal_iff, PrimeSpectrum.equivSubtype_symm_apply_asIdeal, LinearMap.det_zero, ProbabilityTheory.sum_prob_mem_Ioc_le, hasSum_one_div_nat_pow_mul_fourier, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, NumberField.mixedEmbedding.norm_unit_smul, CompactlySupportedContinuousMap.coe_mul, FreeAddMonoid.count_of, LinearEquiv.conjAlgEquiv_symm_apply_apply, Matrix.toLinearMap₂_toMatrix₂, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, Fin.orderHom_injective_iff, Equiv.Perm.Basis.toCentralizer_apply, LinearMap.toMatrix_one, Complex.nndist_self_conj, Equiv.sigmaSigmaSubtypeEq_apply, Submonoid.coe_map, ContinuousAddEquiv.eq_comp_symm, faithfulSMul_iff_algebraMap_injective, Equiv.swap_apply_apply, MonCat.ext_iff, SkewMonoidAlgebra.smul_of, Equiv.Perm.notMem_support, Traversable.foldMap_hom_free, Finsupp.weight_single_one_apply, MvPolynomial.expand_eq_zero, Field.Emb.Cardinal.filtration_succ, CFC.nnnorm_sqrt, CochainComplex.HomComplex.Cocycle.toCochainAddMonoidHom_apply, PreQuasiregular.equiv_symm_apply, ModuleCat.monoidalClosed_uncurry, Equiv.subtypeEquivRight_apply_coe, MulAction.stabilizerEquivStabilizer_symm_apply, OrderDual.ofDual_bot, AlgEquiv.toOpposite_symm_apply, Algebra.FormallyUnramified.lmul_elem, DualNumber.range_lift, Measurable.add_simpleFunc, ContinuousMapZero.instCanLift, AffineIsometryEquiv.range_eq_univ, ContinuousMap.dist_le_two_norm, QuaternionAlgebra.imIₗ_apply, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, NumberField.mixedEmbedding.norm_eq_norm, LinearMap.IsReflective.smul_coroot, RingCon.rel_mk, MeasureTheory.Measure.measurable_measure, CategoryTheory.Limits.biproduct.whiskerEquiv_inv, ContinuousMap.isOpen_setOf_mapsTo, MvPowerSeries.exists_finsupp_eq_lexOrder_of_ne_zero, QuotSMulTop.equivTensorQuot_naturality, DirectSum.sub_apply, IsMaxChain.image, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, TopCommRingCat.instReflectsIsomorphismsTopCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier, ContinuousLinearEquiv.hasSum', IsometryEquiv.toRealLinearIsometryEquiv_apply, SimpleGraph.TripartiteFromTriangles.toTriangle_surjOn, DoubleQuot.coe_quotQuotMkₐ, Ideal.isHomogeneous_iff_forall_subset, LieAlgebra.IsKilling.rootSystem_coroot_apply, Module.Basis.mk_repr, Set.image_pow_of_ne_zero, AddMonoid.End.ofNat_apply, SSet.Subcomplex.range_eq_ofSimplex, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, MeasureTheory.measure_preimage_fst_singleton_eq_tsum, MulHom.op_symm_apply_apply, MeasureTheory.SimpleFunc.coe_sup, Polynomial.roots_monomial, MeasureTheory.Measure.isTopologicalBasis_isOpen_lt_top, pow_toLex, AddMonoid.Coprod.map_map, Polynomial.coeff_zero_of_isScalarTower, isConjRoot_of_algEquiv, AddAut.mul_apply, SimpleGraph.Path.mapEmbedding_coe, AddEquiv.additiveMultiplicative_apply, LieModuleEquiv.injective, Finsupp.mapDomain_comapDomain_nat_add_one, ProbabilityTheory.boolKernel_comp_measure, X_pow_sub_C_irreducible_iff_of_odd, MvPowerSeries.coeff_X_pow, Valuation.mem_ltIdeal_iff, ArithmeticFunction.cardDistinctFactors_apply, LinearMap.submoduleComap_apply_coe, ContinuousMap.norm_le, LinearMap.compl₂_apply, Subring.coe_inclusion, LieModuleEquiv.toEquiv_mk, WeierstrassCurve.Jacobian.baseChange_polynomialZ, CentroidHom.starCenterIsoCentroid_symm_apply_coe, Unitary.mapEquiv_symm_apply, starLinearEquiv_symm_apply, SimplexCategory.const_comp, FreeAlgebra.lift_comp_ι, OrderRingIso.apply_symm_apply, Valuation.toFun_eq_coe, NNReal.sqrt_le_iff_le_sq, AlgEquiv.coe_ringEquiv', Polynomial.zero_notMem_multiset_map_X_sub_C, Polynomial.card_roots_sub_C', AlgHom.rangeRestrict_surjective, Valuation.val_le_one_or_val_inv_lt_one, ContinuousLinearMap.id_apply, MeasureTheory.Measure.haarMeasure_apply, Matrix.toSquareBlock_def, MvPolynomial.support_monomial, HasFDerivWithinAt.hasLineDerivWithinAt, LinearIsometryEquiv.range_eq_univ, SlashInvariantForm.quotientFunc_mk, RingEquiv.map_list_sum, Irreducible.natSepDegree_eq_one_iff_of_monic', IsMinFilter.dual, CliffordAlgebraDualNumber.equiv_symm_eps, Monovary.sum_smul_comp_perm_le_sum_smul, SubAddAction.subtype_eq_val, LinearMap.IsReflective.apply_self_mul_coroot_apply, IsLocalization.surj, DirichletCharacter.LSeriesSummable_of_one_lt_re, MeasureTheory.OuterMeasure.restrict_trim, TensorAlgebra.toDirectSum_tensorPower_tprod, Submonoid.mem_map, MonoidAlgebra.tensorEquiv.invFun_tmul, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_φ, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, Equiv.Perm.ofFn_comp_perm, ProbabilityTheory.uncenteredCovarianceBilin_apply, NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass, Finset.weightedVSubOfPoint_congr, Polynomial.rootMultiplicity_expand_pow, ExteriorAlgebra.ιMulti_span_fixedDegree, Algebra.Presentation.localizationAway_relation, MonoidAlgebra.antipode_single, TemperedDistribution.lineDerivOp_fourier_eq, CofiniteTopology.continuous_of, sigmaFinsuppAddEquivDFinsupp_apply, toBoolRing_inf, MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top, Wbtw.right_mem_image_Ici_of_left_ne, Polynomial.coeff_map, Module.End.independent_genEigenspace, Equiv.mulLeft₀_apply, MeasureTheory.measure_biUnion_le, Polynomial.aeval_iterate_derivative_of_ge, MeasureTheory.charFun_neg, AddSubgroup.coe_comap, Module.Flat.ker_lTensor_eq, ModularForm.SL_slash, le_addRothNumber_product, Set.dual_ordConnectedSection, MvPolynomial.monomial_finsupp_sum_index, OrderIso.isBoundedUnder_ge_comp, KaehlerDifferential.cotangentComplexBaseChange_tmul, TopCat.uliftFunctorObjHomeo_symm_naturality_apply, Polynomial.eq_C_of_degree_eq_zero, CongruenceSubgroup.conjGL_coe, QuadraticAlgebra.algebraMap_inj, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, AddSubmonoid.fromLeftNeg_leftNegEquiv_symm, NumberField.FinitePlace.norm_def', ArithmeticFunction.sum_Ioc_mul_zeta_eq_sum, Function.Embedding.embFinTwo_apply_zero, AddCommMonCat.coe_id, MeasureTheory.measure_eq_measure_of_levyProkhorovEDist_eq_zero_of_isClosed, SpecialLinearGroup.mem_center_iff_spec, IsPRadical.pow_mem, WithLp.coe_congr, Equiv.comp_swap_eq_update, OrderIso.map_csInf', Rep.diagonalHomEquiv_symm_apply, Module.Basis.ofZLatticeBasis_apply, quasispectrumRestricts_iff, SupIrred.ofDual, Homeomorph.induced_eq, Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span, cross_cross, MeasureTheory.IsFundamentalDomain.measure_set_eq, Matrix.submatrix_vecMul_equiv, TwoSidedIdeal.orderIsoRingCon_apply, MulEquiv.map_one, ContinuousAlternatingMap.map_insertNth, Matrix.separatingRight_toBilin_iff, ContinuousAddEquiv.symm_comp_eq, AddConstEquiv.refl_apply, BoundedLatticeHom.coe_comp_sup_hom', Polynomial.derivative_expand, OrderIso.monotone, associatesEquivOfUniqueUnits_symm_apply, MeasurableEquiv.map_apply, MulSemiringActionHom.instMulSemiringActionSemiHomClassCoeMonoidHom, HahnSeries.orderTop_sub_pos, OpenPartialHomeomorph.transHomeomorph_symm_apply, FormalMultilinearSeries.derivSeries_coeff_one, MeasureTheory.Measure.ae_ae_of_ae_compProd, Polynomial.derivative_sum, SemidirectProduct.inl_aut, Isometry.coe_affineIsometryOfStrictConvexSpace, ProbabilityTheory.Kernel.IndepSets.indep_aux, TwoSidedIdeal.equivMatrix_symm_apply_ringCon, Polynomial.isCoveringMapOn_eval, Homeomorph.vaddConst_apply, AddChar.sum_mulShift, IsBaseChange.of_fintype_basis_eq, Behrend.roth_lower_bound_explicit, Submodule.starProjection_add_starProjection_orthogonal, DFA.comap_reindex, ContinuousAlternatingMap.le_mul_prod_of_opNorm_le_of_le, MvPolynomial.mul_def, Cardinal.lift_eq_aleph_one, MulAlgebraNorm.extends_norm', Matrix.spectrum_toLpLin, Homeomorph.homeomorph_mk_coe, RelIso.relHomCongr_symm_apply, QuasispectrumRestricts.rightInvOn, ExteriorAlgebra.ι_eq_zero_iff, MulEquiv.piMultiplicative_apply, MeasureTheory.Measure.OuterRegular.comap, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe, Filter.Tendsto.partialSups_apply, MeasureTheory.lintegral_indicator_one_le, OrderIso.image_Ico, SemiNormedGrp.explicitCokernelπ_desc_apply, IsAdjoinRoot.algEquiv_algEquiv, Polynomial.nextCoeffUp_C_eq_zero, CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply, Finsupp.linearEquivFunOnFinite_symm_coe, Path.range_subpath_of_ge, Set.Ioc_ofDual, X_pow_sub_C_irreducible_of_odd, Polynomial.aeval_fn_apply, Complex.reLm_coe, Polynomial.derivative_pow_succ, MulChar.map_ringChar, AddEquiv.neg_apply, AddChar.coe_mul, ContinuousLinearMap.opNorm_lsmul_apply_le, Polynomial.Sequence.basis_eq_self, MeasureTheory.Measure.measure_univ_pos, StarAlgebra.elemental.characterSpaceToSpectrum_coe, RingEquiv.map_neg, Subsemigroup.centerCongr_symm_apply_coe, RootPairing.zero_notMem_range_root, Module.Basis.repr_isUnitSMul, Equiv.sigmaCongrLeft_apply, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, BumpCovering.point_finite, rotation_injective, IsLocalization.algEquivOfAlgEquiv_eq, CategoryTheory.Presheaf.imageSieve_app, MvPolynomial.natDegree_finSuccEquiv, ContinuousAffineMap.coe_sub, Circle.ofConjDivSelf_coe, Equiv.divRight_symm_apply, LieModuleHom.coe_mk, CoxeterSystem.lift_apply_simple, AffineBasis.coe_smul, LatticeHom.comp_apply, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, ContinuousMap.norm_coe_le_norm, ContinuousMultilinearMap.uniformContinuous_eval_const, Finsupp.prod_toMultiset, IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow, Ideal.finite_setOf_absNorm_eq, OrderIso.invENNReal_symm_apply, MulOpposite.opAddEquiv_apply, Function.Embedding.sumSet_apply, AffineMap.lineMap_rev_mem_affineSpan_pair, BoxIntegral.BoxAdditiveMap.zero_apply, ZeroAtInftyContinuousMap.smul_apply, pow_image_of_prime_by_factor_orderIso_dvd, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, NumberField.mixedEmbedding.mem_idealLattice, smoothSheafCommRing.ι_evalHom_apply, RootPairing.InvariantForm.pairing_mul_eq_pairing_mul_swap, SemidirectProduct.inr_injective, Set.FiniteExhaustion.mono, StandardEtalePresentation.toPresentation_algebra_smul, ZeroHom.nsmul_apply, iSupIndep.dfinsuppSumAddHom_injective, fderiv_clm_comp, IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, IsSymmetricAlgebra.equiv_apply, sum_smul_minpolyDiv_eq_X_pow, Polynomial.derivative_ofNat, SetTheory.PGame.grundyValue_eq_iff_equiv_nim, Equiv.swap_apply_self, cyclotomicCharacter.toZModPow, IsFractionRing.fieldEquivOfAlgEquivHom_apply, NonUnitalSubsemiring.coe_map, UpperHalfPlane.im_smul_eq_div_normSq, OrderMonoidIso.val_unitsCongr_symm_apply, BoxIntegral.unitPartition.mem_smul_span_iff, TopCat.Presheaf.germ_exist_of_isBasis, smulMonoidWithZeroHom_apply, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, MeasureTheory.eLpNorm_const_lt_top_iff_enorm, Submodule.quotDualCoannihilatorToDual_apply, deltaGenerated_eq_coinduced, DomMulAct.coe_mkHomeomorph_symm, GroupExtension.Section.mul_inv_mul_mul_mem_range_inl, InnerProductSpace.Core.inner_smul_left, supIrred_ofDual, AddConstMapClass.map_const, OrderAddMonoidHom.coe_orderHom, SchwartzMap.bilinLeftCLM_apply, ContinuousLinearMap.intCast_apply, RingAut.smul_def, AlternatingMap.smulRight_apply, CategoryTheory.Functor.OneHypercoverDenseData.mem₁, LinearIndependent.of_isLocalizedModule_of_isRegular, ODE.FunSpace.range_toContinuousMap, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, Submodule.injective_inclusionSpan, FunctionField.inftyValuation.X_inv, fderiv_continuousAlternatingMap_apply_const, DirichletCharacter.conductor_le_conductor_mem_conductorSet, CategoryTheory.SingleObj.mapHom_id, Prod.Lex.monotone_fst, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, Sublattice.coe_map, ProbabilityTheory.Kernel.setIntegral_restrict, RootPairing.root_sub_root_mem_of_pairingIn_pos, Matrix.charmatrix_reindex, LieHom.mem_idealRange, Multiset.mapAddMonoidHom_apply, Equiv.Perm.subtypeCongrHom_injective, Finset.forall_mem_map, LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank, NNReal.sqrt_mul_lt_half_add_of_ne, Equiv.Perm.cycleOf_self_apply_zpow, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, NumberField.Units.regOfFamily_eq_det, Submonoid.LocalizationMap.mulEquivOfLocalizations_apply, WeakDual.CharacterSpace.apply_mem_spectrum, FirstOrder.Language.Embedding.ext_iff, CocompactMapClass.norm_le, Disjoint.map, ofDual_inf, MulEquiv.eq_symm_apply, FiniteField.frobeniusAlgEquivOfAlgebraic_apply, ContinuousLinearMap.nhds_zero_eq_of_basis, Polynomial.monomial_one_one_eq_X, MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, ContinuousLinearMap.coprodEquiv_apply, ContinuousMulEquiv.coe_trans, QuotientGroup.rangeKerLift_injective, Homeomorph.coe_addLeft, MeasureTheory.ProbabilityMeasure.prod_prod, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, Equiv.prod_assoc_image, CartanMatrix.D_four, RingCat.Colimits.cocone_naturality_components, Ideal.quotient_map_C_eq_zero, Finsupp.toMultiset_zero, LinearMap.toAddMonoidHom_mulLeft, cfc_apply_one, CategoryTheory.Linear.comp_apply, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, LinearEquiv.map_mem_invtSubmodule_conj_iff, Coalgebra.coassoc_symm_apply, Equiv.Perm.iterate_eq_pow, MeasureTheory.measure_setOf_frequently_eq_zero, HahnSeries.single_zero_natCast, Module.End.isFinitelySemisimple_sub_algebraMap_iff, Ordinal.card_le_aleph, ContinuousLinearMap.cpolynomialAt, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_same_orientation, equivShrink_symm_sub, Complex.equivRealProd_apply, Matrix.cramer_row_self, InfiniteGalois.normalAutEquivQuotient_apply, WithTop.lt_toDual_iff, Span.repr_def, CompHausLike.coe_id, CategoryTheory.ShiftedHom.opEquiv_symm_add, Equiv.sigmaPreimageEquiv_symm_apply_snd_coe, Int.padicValuation_lt_one_iff, LinearMap.mem_isPairSelfAdjointSubmodule, Polynomial.natDegree_X_pow_sub_C, UpperHalfPlane.specialLinearGroup_apply, AffineMap.hasDerivWithinAt, Polynomial.Splits.eval_derivative, HahnSeries.single_zero_ofScientific, CategoryTheory.Limits.kernelSubobject_arrow'_apply, Submodule.dualPairing_apply, Submodule.starProjection_singleton, RCLike.conj_nat_cast, MeasureTheory.VectorMeasure.mapₗ_apply, ContinuousMap.coe_intCast, HasFPowerSeriesAt.eventually_hasSum, HasDerivAt.clm_apply, Equiv.Perm.next_toList_eq_apply, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', Finsupp.degree_add, MeasureTheory.measure_union_null_iff, IsLocalization.algEquiv_apply, SemilinearMapClass.toMulActionSemiHomClass, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal, NonUnitalAlgHom.coe_lmul_eq_mul, SlashInvariantForm.coe_constℝ, RatFunc.map_apply_ofFractionRing_mk, LeftInvariantDerivation.left_invariant, ContinuousMap.dist_le, mfderiv_comp_apply_of_eq, CentroidHom.zero_apply, PowerSeries.degree_weierstrassMod_lt, ContinuousLinearMap.comp_condExp_add_const_comm, OrderIso.divRight_symm_apply, Submodule.mem_iSup_iff_exists_finsupp, Matrix.toLin_mul_apply, IncidenceAlgebra.moebius_inversion_top, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C, Monoid.Coprod.fst_toProd, SmoothPartitionOfUnity.locallyFinite', ofBoolAlg_inj, LinearMap.prodMap_apply, ProbabilityTheory.integrable_toReal_condExpKernel, EuclideanSpace.basisFun_apply, MeasureTheory.volume_measurePreserving_piCongrLeft, DilationEquiv.map_cobounded, isCompl_ofDual_iff, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_le_one, Polynomial.derivative_smul, LinearMap.tensorEqLocusEquiv_apply, Finsupp.single_eq_same, toMatrix_distrib_mul_action_toLinearMap, Composition.embedding_comp_inv, MeasurableEquiv.image_preimage, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, MonoidHom.map_mulIndicator, MvPolynomial.eval₂_zero'_apply, groupCohomology.coe_mapCocycles₁, LinearMap.domRestrict'_apply, Polynomial.eval₂_hom, ProbabilityTheory.Kernel.sectR_prodMkRight, Bundle.RiemannianMetric.isVonNBounded, Dilation.coe_mk, MeasureTheory.tilted_neg_same', PowerSeries.gaussNorm_monomial, Equiv.Perm.SameCycle.apply_left, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Ordinal.omega_zero, ArithmeticFunction.moebius_eq_or, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, AddSubgroup.coe_subtype, LocallyConstant.range_finite, BoundedContinuousFunction.indicator_apply, finSuccEquiv_zero, Con.sup_eq_conGen, IsLocalHomeomorph.Homeomorph.isLocalHomeomorph, FirstOrder.Language.Equiv.coe_toElementaryEmbedding, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', AddMonoid.Coprod.swap_bijective, OrderIso.isGLB_image', MeasureTheory.le_eLpNorm_of_bddBelow, NumberField.FinitePlace.mulSupport_finite, MonoidHom.map_div₂, AlgHom.coe_mapIntegralClosure, Convex.affine_image, Complex.convexHull_reProdIm, NumberField.FinitePlace.embedding_apply, SlashInvariantForm.smul_applyℝ, groupHomology.mem_cycles₂_iff, UniformConvergenceCLM.smul_apply, Subgroup.IsComplement.equiv_snd_eq_self_iff_mem, exist_norm_eq, LocallyConstant.coe_comap_apply, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, Sylow.coe_smul, RingHom.mapMatrix_apply, LinearIsometryEquiv.ext_iff, Equiv.Perm.disjoint_ofSubtype_noncommPiCoprod, ModuleCat.Iso.homCongr_eq_arrowCongr, MvPowerSeries.X_pow_eq, Complex.conjLIE_apply, OrderIso.neg_apply, UniformOnFun.ofFun_sum, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, Finsupp.coe_ceilDiv_def, Nat.orderEmbeddingOfSet_apply, ProbabilityTheory.sum_meas_smul_cond_fiber, DFinsupp.coe_mono, DFinsupp.tsub_apply, pinGroup.val_inv_toUnits_apply, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, LatticeHom.coe_withTopWithBot, WithOne.lift_coe, ContinuousLinearMap.measurable, Polynomial.Splits.monomial, LinearIsometryEquiv.coe_symm_toHomeomorph, RestrictedProduct.continuous_coe, toMul_ofMul, QuadraticMap.neg_apply, Seminorm.continuous_of_forall', AlgebraicIndependent.polynomial_aeval_of_transcendental, AbsoluteValue.eq_zero, HahnSeries.SummableFamily.binomialFamily_orderTop_pos, toLex_ofNat, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, Polynomial.roots_C_mul_X_pow, ContDiffWithinAt.clm_apply, Circle.starRingEnd_addChar, AlgEquiv.linearEquivConj_mulLeft, RingCon.sSup_def, TopologicalSpace.OpenNhds.comp_apply, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_f, Function.Embedding.image_apply, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_μ, MvPolynomial.degreeOf_C, AddSubmonoid.val_neg_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, CategoryTheory.Functor.FullyFaithful.homMulEquiv_apply, CircleDeg1Lift.isUnit_iff_bijective, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mk, Valuation.Integers.isPrincipal_iff_exists_isGreatest, Algebra.TensorProduct.prodRight_symm_tmul, Path.Homotopy.map_apply, MeasureTheory.Integrable.simpleFunc_mul', AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_inv_app, MaximalSpectrum.toPiLocalization_apply_apply, WeakDual.CharacterSpace.ext_iff, AddCommMonCat.ofHom_apply, QuadraticAlgebra.norm_algebraMap, MvPowerSeries.mapAlgHom_apply, PrincipalSeg.transInitial_apply, WeierstrassCurve.Projective.polynomial_relation, IsLocalization.mk'_tmul, Matrix.GeneralLinearGroup.map_inv_mul_map, PiToModule.fromEnd_apply, CategoryTheory.Limits.Types.isColimit_iff_coconeTypesIsColimit, InitialSeg.toOrderEmbedding_apply, RootPairing.span_orbit_eq_top, AddMonoidHom.toFun_eq_coe, ProbabilityTheory.IsRatCondKernelCDFAux.bddBelow_range, ContinuousLinearMap.coe_smul', DomMulAct.smul_mulDistribActionHom_apply, IndexedPartition.equivQuotient_symm_proj_apply, RingHom.surjective_of_tmul_eq_tmul_of_finite, MeasureTheory.Measure.domSMul_apply, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, ModuleCat.CoextendScalars.smul_apply', norm_ofAdd, Path.pi_coe, MultilinearMap.add_apply, Multiplicative.ofAdd_le, RCLike.ofReal_re, Finsupp.le_weight_of_ne_zero', RelHom.swap_apply, WeierstrassCurve.Jacobian.map_negDblY, ENNReal.mulRightOrderIso_symm_apply, DirectSum.toAddMonoid.unique, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_symm_apply_snd_coe, Polynomial.toContinuousMap_apply, ProbabilityTheory.iIndepFun.measure_inter_preimage_eq_mul, Algebra.coe_algebraMap_ofSubring, Finsupp.filter_eq_indicator, Localization.algEquiv_apply, StarAlgEquiv.mul_apply, Specialization.ofEquiv_toEquiv, IsCoveringMap.comp_homeomorph, HahnSeries.cardSupp_single_le, AddConstMap.coe_addLeftHom_apply, UniformOnFun.uniformContinuous_eval, ContinuousAffineMap.differentiable, NonUnitalSubsemiring.mem_map_equiv, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, ContinuousAffineMap.smul_apply, MeasureTheory.charFun_toDual_symm_eq_charFunDual, OrderEmbedding.maximal_mem_image, Module.Basis.isUnit_det, MvPolynomial.algHom_ext'_iff, MonoidHom.finset_prod_apply, Equiv.coe_fn_symm_mk, CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_true, WithLp.sndL_apply, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, TensorPower.gMul_eq_coe_linearMap, PEquiv.mem_iff_mem, AddMonoidHom.coe_flip_mul, hasStrictFDerivAt_iff_isLittleOTVS, CStarMatrix.mapₗ_reindexₐ, LieSubalgebra.toEnd_eq, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, IntermediateField.mem_adjoin_iff, Equiv.sumIsRight_apply, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, LinearAlgebra.FreeProduct.mul_injections, FunctorToFintypeCat.naturality, Complex.cosh_conj, RatFunc.laurent_algebraMap, AddMonoidHom.coe_id, ContinuousAlternatingMap.smul_apply, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff', AlgebraicGeometry.SpecMap_preimage_basicOpen, Polynomial.iterate_derivative_eq_factorial_smul_sum, Nat.coe_orderEmbeddingOfSet, unitInterval.coe_symmMeasurableEquiv, OrderIso.sortedGT_listMap, isConjRoot_iff_exists_algEquiv, ContinuousAlternatingMap.compContinuousLinearMapₗ_apply, MeasureTheory.condLExp_bot', MeasureTheory.AddContent.measure_eq, OpenPartialHomeomorph.transHomeomorph_target, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, Localization.algEquiv_mk', LinearMap.lTensor_id_apply, HahnSeries.ofPowerSeries_X_pow, OrderHom.id_coe, genericPoints.equiv_symm_apply, BoundedLatticeHom.dual_id, DomAddAct.isOpenEmbedding_mk, OrderIso.isNormal, IsFoelner.eventually_meas_ne_zero, ArithmeticFunction.cardFactors_apply, LinearMap.BilinForm.toMatrix'_apply, ContinuousMap.specializes_coe, DifferentiableOn.clm_apply, CommRingCat.mkUnder_ext_iff, ContMDiff.clm_apply, NumberField.FinitePlace.prod_eq_inv_abs_norm, AlgHom.IsArithFrobAt.mk_apply, OrthogonalFamily.orthonormal_sigma_orthonormal, Localization.localRingHom_mk', ContinuousLinearMap.coe_restrictScalarsₗ, Set.unitEquivUnitsInteger_symm_apply_coe, Polynomial.iterate_derivative_X_add_pow, Function.Embedding.sectR_apply, OrderHom.piIso_symm_apply, PiTensorProduct.lifts_smul, Quiver.SingleObj.toPrefunctor_symm_id, Finsupp.sum_smul_index_linearMap', BoundedOrderHom.symm_dual_id, CircleDeg1Lift.commute_iff_commute, SSet.S.equivElements_symm_apply_dim, MvPolynomial.mem_range_map_iff_coeffs_subset, PEquiv.toMatrix_toPEquiv_mulVec, exposed_point_def, Sym.coe_equivNatSumOfFintype_apply_apply, PowerBasis.quotientEquivQuotientMinpolyMap_apply, Equiv.Perm.val_equivUnitsEnd_apply, LinearMap.BilinMap.toQuadraticMapAddMonoidHom_apply, IsChain.preimage_embedding, InnerProductSpace.canonicalCovariantTensor_eq_sum, CategoryTheory.PreGaloisCategory.toAutMulEquiv_isHomeomorph, DoubleQuot.coe_quotLeftToQuotSupₐ, NonUnitalStarRingHom.coe_zero, RCLike.re_add_im_ax, CommGrpCat.forget_map, linearIndependent_iff_injective_finsuppLinearCombination, toDegLex_injective, MeasureTheory.SimpleFunc.tendsto_approxOn_range_L1_enorm, ContinuousAlternatingMap.piLIE_apply_apply, GroupExtension.rightHom_inl, groupCohomology.d₁₂_hom_apply, QuadraticMap.Isometry.single_apply, isGLB_infClosure, PreInnerProductSpace.Core.smul_left, WeierstrassCurve.Projective.map_negAddY, Nucleus.coe_inf, DFinsupp.equivFunOnFintype_single, BoundedContinuousFunction.coe_neg, PartENat.withTopEquiv_one, CategoryTheory.Functor.functorPushforward_imageSieve_mem, toColex_vadd, StieltjesFunction.measure_Ici_of_tendsto_atTop_atTop, BialgEquiv.congr_fun, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, IsAntichain.image_relIso_iff, Finsupp.equivFunOnFinite_apply, Differentiable.fderiv_norm_rpow, Module.FaithfullyFlat.lTensor_exact_iff_exact, AffineIsometryEquiv.coe_symm_trans, NatOrdinal.toOrdinal_min, fderivWithin_fderivWithin, Localization.mulEquivOfQuotient_symm_monoidOf, Matrix.map_swap, MonoidHom.map_list_prod, Poly.coe_zero, Complex.oangle, LaurentSeries.valuation_single_zpow, MvPolynomial.aeval_X, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, MvPolynomial.comapEquiv_coe, Pi.constMulHom_apply, NumberField.InfiniteAdeleRing.algebraMap_apply, RCLike.normSq_neg, IncidenceAlgebra.coe_sub, Ordinal.enum_symm_apply_coe, MeasureTheory.Measure.coe_nnreal_smul_apply, ContinuousLinearMap.isBigOWith_id, Function.Embedding.sumSet_range, rothNumberNat_le, UnitAddTorus.mFourierSubalgebra_coe, GroupExtension.Splitting.rightInverse_rightHom, StrictAntiOn.dual, AddSubgroup.noncommPiCoprod_single, LinearMap.BilinForm.SeparatingRight.toMatrix, Homeomorph.shearAddRight_symm_coe, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, mulRight_bound, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_symm_apply_val, Equiv.sigmaAssocProd_apply_snd_snd, Equiv.Perm.subtypeCongr.apply, AdicCompletion.incl_apply, IntermediateField.algHomEquivAlgHomOfSplits_apply, LinearIsometry.map_add, CategoryTheory.Iso.refl_conj, OrderMonoidHom.mul_apply, AdicCompletion.map_ext'_iff, HahnSeries.single_pow, SubMulAction.ofFixingSubgroup_of_inclusion_injective, Algebra.injective_of_transcendental, UniformOnFun.ofFun_toFun, HomologicalComplex.Hom.comm_to_apply, Real.volume_closedEBall, Homeomorph.piCongrLeft_symm_apply, map_inv, IntermediateField.botEquiv_symm, NonUnitalRingHom.map_closure, Ideal.quotientInfToPiQuotient_inj, Bundle.TotalSpace.toProd_apply, AlgebraicGeometry.Scheme.stalkMap_congr_assoc, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, MvPolynomial.exists_dvd_map_of_isAlgebraic, Cubic.disc_eq_prod_three_roots, Path.ofLine_extend, NumberField.Units.dirichletUnitTheorem.seq_decreasing, ProfiniteAddGrp.ofHom_apply, val_unitarySubgroupUnitsEquiv_symm_apply_coe, smoothSheafCommRing.eval_germ, AdicCompletion.ofTensorProduct_surjective_of_finite, PrincipalSeg.transRelIso_top, Matrix.kroneckerMap_reindex_right, MeasureTheory.Measure.comapₗ_eq_comap, RootPairing.Hom.root_weightMap_apply, AddMonoidAlgebra.mapDomainAddEquiv_apply, LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero', Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_str, unitInterval.volume_Ico, partialSups_eq_sup'_range, Polynomial.pUnitAlgEquiv_symm_toPowerSeries, AlgEquiv.op_apply_apply, MvPolynomial.scalarRTensor_apply_X_tmul_apply, Equiv.permCongr_symm_apply, Polynomial.degree_C_mul_of_isUnit, Nat.factorization_eq_of_coprime_right, ContinuousLinearEquiv.coe_toDiffeomorph_symm, meas_essSup_lt, UpperHalfPlane.σ_sq, Equiv.vanishesTrivially_comp, Ordinal.toGame_lt_iff, frobenius_natCast, toDual_vadd', AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, AffineSubspace.coe_subtypeA, MulEquiv.comapSubgroup_symm_apply, MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, CategoryTheory.Functor.FullyFaithful.homEquiv_apply, LinearEquiv.congrRight₂_apply, SubAddAction.ofFixingAddSubgroup_of_singleton_bijective, WittVector.map_teichmuller, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', map_sub, PresheafOfModules.pushforward_map_app_apply, AlgebraicGeometry.instIsGermInjectiveAtCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfIsOpenImmersion, Nat.factorization_mul_apply_of_coprime, MeasureTheory.measure_eq_top_of_setLIntegral_ne_top, AbsoluteValue.abs_abv_sub_le_abv_sub, ofLex_add, ZMod.dft_mul_const, Pi.single_comp_equiv, MeasureTheory.Measure.pi_map_piCongrLeft, Shrink.linearEquiv_symm_apply, PrincipalSeg.mem_range_iff_rel', MultilinearMap.coe_restrictScalars, ContinuousSemilinearEquivClass.map_continuous, FormalMultilinearSeries.hasSum_of_finite, MultilinearMap.domDomCongrEquiv_symm_apply, CoalgHom.map_smul_of_tower, ContinuousLinearMap.comp_inl_add_comp_inr, signedDist_right_congr, LightCondensed.finYoneda_map, LieDerivation.IsKilling.exists_eq_ad, LieModule.Weight.coe_zero, ULift.moduleEquiv_symm_apply, finsum_comp_equiv, cross_self, padicNormE.nonarchimedean', Module.Basis.mk_coord_apply_eq, PreTilt.coeff_pow_p, isRightRegular_ofLex, WithTop.le_toDual_iff, SimpleGraph.map_edgeFinset_induce_of_support_subset, SemilinearIsometryClass.ediam_range, LieAlgebra.lieCharacterEquivLinearDual_apply, DFinsupp.toLex_monotone, LieDerivation.coe_add, Polynomial.derivative_X, LieAlgebra.of_smul, WithCStarModule.equiv_symm_snd, SetTheory.PGame.grundyValue_nim_add_nim, ProbabilityTheory.Kernel.integral_deterministic', RootPairing.invtRootSubmodule.eq_top_iff, lineMap_le_map_iff_slope_le_slope_right, fderiv_comp_deriv, ContinuousMultilinearMap.contDiffAt, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, CliffordAlgebra.contractRight_mul_ι, FreeGroup.ext_hom_iff, toLex_eq_one, groupCohomology.coboundariesToCocycles₁_apply, SpecialLinearGroup.mem_center_iff, Equiv.exists_congr_right, Polynomial.sumIDeriv_map, Submodule.LinearDisjoint.op, AddSubmonoid.LocalizationMap.addEquivOfLocalizations_symm_apply, CategoryTheory.tensorRightHomEquiv_symm_naturality, Finset.map_truncatedInf, MeasureTheory.measure_compl, ContMDiffSection.coe_injective, Nimber.succ_def, WittVector.verschiebung_coeff_succ, MvPowerSeries.ext_trunc', Module.FaithfullyFlat.lTensor_bijective_iff_bijective, toColex_inv, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, AdicCompletion.val_smul_eq_evalₐ_smul, RestrictScalars.ringEquiv_algebraMap, Matrix.blockDiagonal'RingHom_apply, Matrix.Nondegenerate.toLinearMap₂, rTensor_injective_iff_lcomp_surjective, MvPolynomial.smul_monomial, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, MonoidWithZeroHom.one_apply_zero, RCLike.is_real_TFAE, Cardinal.toNat_mul, isUpperSet_preimage_toDual_iff, MeasureTheory.Measure.comp_compProd_comm, SetTheory.PGame.add_moveLeft_inl, ULift.algEquiv_apply, Polynomial.degree_mul_leadingCoeff_inv, Representation.directSum_apply, Seminorm.continuous', Algebra.Extension.h1Cotangentι_injective, TensorProduct.gradedMul_assoc, LocallyBoundedMap.ext_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul, MonoidAlgebra.opRingEquiv_single, CliffordAlgebra.op_reverse, BoolAlg.ext_iff, BoundedContinuousFunction.coe_normComp, AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, AffineIsometryEquiv.edist_map, OrderHom.lfp_le_gfp, PerfectClosure.frobenius_mk, ContinuousMap.toNNReal_neg_algebraMap, Submodule.quotientPi_aux.map_smul, RingHom.mem_fieldRange_self, ContinuousAlgEquiv.continuousOn, Part.toUnitMono_coe, Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff, AddMonoidHom.map_zsmul, QuadraticMap.map_smul_of_tower, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply, Finset.image_smul_distrib, LinearMap.inl_injective, ContinuousAlgHom.coe_mul, Path.ext_iff, Module.Basis.prod_repr_inl, ContDiffOn.clm_apply, MeasureTheory.measure_compl_sigmaFiniteSetWRT, CompactExhaustion.exists_mem, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff, Lagrange.eval_interpolate_not_at_node, WithLp.prodContinuousLinearEquiv_symm_apply, MeasureTheory.Measure.haarMeasure_unique, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, PrimeSpectrum.primeSpectrumProd_symm_inr_asIdeal, Polynomial.eq_prod_roots_of_splits, FiniteField.frobeniusAlgHom_apply, ContinuousMap.HomotopyLike.map_zero_left, Traversable.foldlm.ofFreeMonoid_comp_of, ContinuousLinearMap.opNNNorm_le_iff, Polynomial.map_injective_iff, ContinuousLinearMap.isometry_mul_flip, Polynomial.eq_prod_roots_of_monic_of_splits_id, ContinuousMap.Homotopy.evalAt_eq, IsChain.image_embedding_iff, PNat.coeAddHom_apply, Quaternion.snd_re_dualNumberEquiv_symm, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, Ideal.torsionMapQuot_apply, ModularForm.coe_constℝ, Matrix.kroneckerTMul_assoc', Ordinal.enum_zero_le, LinearEquiv.cast_symm_apply, MonomialOrder.degree_sub_le, AlgebraicGeometry.Scheme.hom_inv_apply, Isometry.hausdorffMeasure_image, OrderIso.preimage_Ioc, ZSpan.smul, Module.Basis.flag_le_ker_dual, SSet.horn.yonedaEquiv_ι, IsArtinian.eventuallyConst_of_isArtinian, Multiset.coeEquiv_apply_coe, Submonoid.coe_invOrderIso_symm_apply, Polynomial.mirror_monomial, Valuation.IsEquiv.orderRingIso_apply, Codisjoint.dual, BoundedContinuousFunction.evalCLM_apply, ContinuousMultilinearMap.piLinearEquiv_symm_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.invApp_app_apply, Antitone.dual_right, AffineSubspace.subtype_apply, AlgebraicGeometry.Scheme.Hom.range_asFiberHom, ProbabilityTheory.compProd_posterior_eq_map_swap, Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff, AnalyticOnNhd.eval_linearMap', Homeomorph.toOpenPartialHomeomorph_apply, CliffordAlgebra.reverse_involute_commute, MulDistribMulAction.toMulEquiv_apply, LinearMap.compPMap_apply, Module.AEval.of_symm_smul, Algebra.adjoin_singleton_algebraMap, Nat.ordCompl_dvd_ordCompl_iff_dvd, Equiv.Perm.eq_on_support_mem_disjoint, inner_gradientWithin_right, NormedAddCommGroup.norm_toCompl, MeasureTheory.OuterMeasure.coe_iSup, Locale.localePointOfSpacePoint_toFun, EuclideanGeometry.reflection_map, QuotientAddGroup.mk'_eq_mk', ZeroAtInftyContinuousMap.coe_mk, lowerClosure_image, CompactlySupportedContinuousMap.hasCompactSupport, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same, Matrix.intrinsicStar_toLin', LieModule.isNilpotent_toEnd_genWeightSpace_zero, Finset.coeMonoidHom_apply, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, DomMulAct.mem_stabilizer_iff, LinearMap.le_rank_iff_exists_linearIndependent, Module.Basis.ofZLatticeComap_apply, RelIso.map_rel_iff', Polynomial.UniversalCoprimeFactorizationRing.exists_liesOver_residueFieldMap_bijective, ValuationSubring.valuation_unit, AddChar.prod_apply, RelEmbedding.smul_def, Monoid.CoprodI.lift_of, AffineEquiv.coe_mul, AffineEquiv.continuous_of_finiteDimensional, CategoryTheory.conjugateEquiv_symm_comp_assoc, Algebra.TensorProduct.algebraMap_apply, Polynomial.dvd_iterate_derivative_pow, QuaternionAlgebra.imKₗ_apply, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, IsLocalization.Away.sec_spec, map_comp_pow, VitaliFamily.mul_measure_le_of_subset_lt_limRatioMeas, Delone.DeloneSet.mapIsometry_trans, Sym.coe_equivNatSum_apply_apply, ProbabilityTheory.Kernel.apply_eq_measure_condKernel_of_compProd_eq, Ideal.Quotient.algEquivOfEqMap_apply, Monoid.Coprod.swap_surjective, IsLocalizedModule.liftOfLE_mk', Composition.blocksFun_sigmaCompositionAux, PresheafOfModules.sections_property, HasStrictFDerivAt.comp_hasStrictDerivAt, ContinuousLinearMap.adjoint_id, Submodule.FG.lTensor.directedSystem, InnerProductSpace.smul_left, ContinuousAlternatingMap.coe_pi, TopologicalSpace.Opens.map_obj, isMinOn_dual_iff, MvPowerSeries.map_algebraMap_eq_subst_X, Polynomial.coeffs_monomial, Specialization.isOpen_toEquiv_preimage, lp.coeFnAddMonoidHom_apply, LinearMap.coe_toContinuousLinearMap', Equiv.withBotCongr_apply, CompleteLatticeHom.coe_id, MeasurableEquiv.preimage_image, CategoryTheory.Subfunctor.ofSection_eq_range, OrderHom.monotone, Ideal.Quotient.factor_mk, HasFDerivWithinAt.linear_multilinear_comp, KaehlerDifferential.polynomialEquiv_D, Equiv.symm_comp_self, Equiv.ofLeftInverse_apply_coe, IsLocalization.mem_span_map, MvPolynomial.optionEquivLeft_apply, Con.ker_rel, SemimoduleCat.Iso.homCongr_eq_arrowCongr, iteratedFDerivWithin_succ_eq_comp_left, Sequential.isoEquivHomeo_apply, UpperHalfPlane.moebius_im, SimpleGraph.Iso.connectedComponentEquiv_symm_apply, Equiv.exists_congr_left, List.SortedLT.of_map_ofDual, EmbeddingLike.map_eq_one_iff, CentroidHom.coe_toAddMonoidHom, minpoly_algHom_toLinearMap, OrderIso.map_pred, TopologicalSpace.Opens.comp_apply, RCLike.abs_im_div_norm_le_one, AddSubgroupClass.inclusion_self, ModularForm.prod_slash, DirichletCharacter.changeLevel_trans, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, Polynomial.ofFn_eq_sum_monomial, MeasurableEquiv.finTwoArrow_apply, AlgCat.inv_hom_apply, toMul_neg, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, WithBot.ofDual_le_iff, CharacterModule.smul_apply, Set.algebraMap_mem_centralizer, ofLex_ratCast, Equiv.Perm.IsCycleOn.exists_pow_eq', BialgEquiv.coe_toEquiv, MeasureTheory.Measure.count_apply, Module.Basis.coe_mkFinConsOfLE, Matrix.coe_mulVecLin, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, ProbabilityTheory.Kernel.integral_restrict, DFinsupp.prod_eq_zero_iff, CommRing.Pic.mul_eq_tensor, ArchimedeanClass.FiniteResidueField.mk_eq_zero, affineIndependent_equiv, norm_sub_mul_self, CentroidHom.natCast_apply, Seminorm.coe_le_coe, MvPolynomial.totalDegree_coeff_finSuccEquiv_add_le, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, ContinuousMapZero.coe_mul, Finsupp.sigmaFinsuppAddEquivPiFinsupp_apply, Equiv.finsuppUnique_symm_apply_support_val, ContinuousMap.val_unitsLift_apply_apply, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂, TwoSidedIdeal.instIsTwoSidedCoeOrderHomIdealAsIdeal, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Polynomial.prime_C_iff, Multiset.Icc_eq, AddEquivClass.apply_coe_symm_apply, convexJoin_segments, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.coe_dualBasis, Equiv.semiconj_conj, Matrix.mulVecLin_apply, OrderIso.bddAbove_image, OnePoint.equivOfIsEmbeddingOfRangeEq_apply_coe, Ideal.algebraMap_quotient_residueField_mk, Equiv.divLeft_involutive, zpowersHom_symm_apply, AdjoinRoot.mk_surjective, Finset.map_ofDual_max, toColex_add, LieAlgebra.IsKilling.corootSpace_eq_bot_iff, PowerSeries.coeff_ne_zero_C, Cardinal.mk_preimage_equiv, Field.localization_map_bijective, RelIso.sumLexComplLeft_symm_apply, SchwartzMap.laplacianCLM_eq, AlgebraicGeometry.Scheme.Hom.tendsto_cofinite_cofinite, AddSubmonoid.add_leftNegEquiv_symm, CStarModule.innerSL_apply, PrincipalSeg.isSuccLimit_apply_iff, IsLocalizedModule.iso_symm_apply, SimpleGraph.Embedding.apply_mem_neighborSet_iff, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, AddChar.add_apply, QuadraticMap.toBilinHom_apply, SemidirectProduct.inr_inj, IsometryClass.antilipschitz, ZeroAtInftyContinuousMap.coe_comp_to_continuous_fun, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_apply, LTSeries.exists_relSeries_covBy_and_head_eq_bot_and_last_eq_bot, Finset.Colex.toColex_lt_toColex_iff_max'_mem, UniformOnFun.isometry_restrict, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, continuous_equivFun_basis, WittVector.map_coeff, ExteriorAlgebra.liftAlternating_ι_mul, RestrictedProduct.sub_apply, ArithmeticFunction.moebius_ne_zero_iff_eq_or, Algebra.smul_leftMulMatrix, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity, TensorProduct.AlgebraTensorModule.rightComm_symm_tmul, DirichletCharacter.LSeries_twist_vonMangoldt_eq, Con.conGen_idem, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, LinearMap.tensorKer_coe, Derivation.mapCoeffs_X, LinearIsometryEquiv.conjStarAlgEquiv_apply, MultilinearMap.smul_apply, StieltjesFunction.measure_Ioo, Matrix.mem_range_scalar_iff_commute_transvectionStruct, Sequential.isoEquivHomeo_symm_apply, Fin.orderIsoTriple_zero, Module.Relations.Solution.surjective_fromQuotient_iff_surjective_π, MvPolynomial.ACounit_X, EReal.sign_eq_and_abs_eq_iff_eq, Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff, StarAlgEquiv.restrictScalars_symm_apply, optionProdEquiv_symm_inr, Real.vector_fourierIntegral_eq_integral_exp_smul, SemiconjBy.tprod, map_ratCast, ContinuousLinearMap.isCompact_image_coe_of_bounded_of_closed_image, IsChain.preimage_iso, TensorProduct.map_map, Equiv.Perm.set_support_zpow_subset, MvPolynomial.prime_rename_iff, OrderIso.equivalence_functor, PadicInt.mahlerTerm_apply, Nat.ordProj_of_not_prime, AddEquiv.map_zero, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, Equiv.Perm.IsCycle.pow_eq_one_iff', IsLocalization.isUnit_comp, MeasureTheory.Measure.measure_toMeasurable_add_inter_left, Pi.ofLex_apply, Equiv.Set.rangeInl_symm_apply_coe, multiplesAddHom_apply, MeasureTheory.Measure.measure_preimage_neg, FractionalIdeal.coe_extendedHomₐ_eq_span, RootPairing.Hom.id_coweightMap_apply, IsIntegralClosure.algebraMap_lift, MeasureTheory.measure_support_eapprox_lt_top, HomogeneousLocalization.range_awayMapAux_subset, rootsOfUnity.integer_power_of_ringEquiv, Algebra.IsPushout.cancelBaseChange_symm_tmul, ContinuousAffineMap.coe_to_continuousMap, RootPairing.coPolarization_apply_eq_zero_iff, PresheafOfModules.toSheafify_app_apply', Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap, IsCyclotomicExtension.isCyclotomicExtension_zero_iff, ProbabilityTheory.bayesRisk_of_subsingleton', Module.Basis.coe_extendLe, Valuation.Compatible.srel_iff_lt, Equiv.embeddingEquivOfFinite_apply, LinearMap.toMatrixOrthonormal_reindex, PiTensorProduct.projectiveSeminormAux_smul, bind₁_xInTermsOfW_wittPolynomial, Polynomial.abc, AlternatingMap.map_update_smul, Ideal.relNorm_mono, LinearMap.toMatrixAlgEquiv_toLinAlgEquiv, Ordinal.omega_le_omega, AddSubmonoid.LocalizationMap.eq_iff_exists, conjneg_conj, Function.Embedding.exists_of_card_le_finset, IsQuasiregular.map, ContinuousMap.coeNNRealReal_apply, AlgEquiv.coe_inv, ContinuousLinearEquiv.apply_symm_apply, MeasureTheory.ConvolutionExistsAt.integrable, Fintype.linearIndependent_iff', FractionalIdeal.absNorm_eq', Matrix.IsHermitian.eigenvalues_eq, OrderIso.isLUB_image', AffineSubspace.sOppSide_lineMap_left, AlgebraicGeometry.Scheme.Hom.coe_resLE_base, InitialSeg.acc, CategoryTheory.ForgetEnrichment.equivFunctor_map, Finset.image_univ_equiv, Lat.dual_map, AlgebraicGeometry.IsAffineOpen.fromSpecStalk_closedPoint, ofDual_iInf, HahnSeries.embDomainLinearMap_apply, LieIdeal.incl_injective, TopologicalSpace.OpenNhds.val_apply, Equiv.boolNot_apply, ArithmeticFunction.cardDistinctFactors_apply_prime_pow, Function.sSup_div_semiconj, Algebra.TensorProduct.piRightHom_mul, Module.le_rank_iff_exists_linearMap, HVertexOperator.coeff_isPWOsupport, InfiniteGalois.mem_bot_iff_fixed, StarAlgHom.prodEquiv_apply, MvPowerSeries.substAlgHom_X, Equiv.Perm.set_support_mul_subset, Polynomial.cyclotomic_expand_eq_cyclotomic_mul, Matrix.permanent_permute_rows, WeierstrassCurve.Jacobian.eval_polynomialY, ModularGroup.one_lt_normSq_T_zpow_smul, Ideal.quotientInfToPiQuotient_surj, IsChain.image_relIso, Sum.Lex.inr_le_inr_iff, congr, Finsupp.linearCombination_zero_apply, RingHom.id_apply, contMDiff_equivTangentBundleProd_symm, finSuccEquiv_symm_none, AddChar.directSum_apply, Frm.Iso.mk_hom, QuadraticMap.associated_eq_self_apply, AddCircle.homeomorphAddCircle_apply_mk, WeierstrassCurve.Affine.CoordinateRing.coe_basis, LieDerivation.apply_lie_eq_add, FreeGroup.lift_of_eq_id, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, QuadraticMap.toMatrix'_comp, LinearMap.trace_mul_cycle, SemilinearMapClass.distribMulActionSemiHomClass, InfTopHom.symm_dual_comp, Dilation.mapsTo_sphere, Tropical.tropOrderIso_symm_coe_fn, MonoidHom.coe_comp, FreeMonoid.countP_of, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, Submodule.map_span_le, Polynomial.natSepDegree_X_sub_C_pow, PMF.binomial_apply_zero, CentroidHom.starCenterIsoCentroid_apply, AddMonoidHom.map_finsum, CategoryTheory.extensiveTopology.mem_sieves_iff_contains_colimit_cofan, inner_smul_left_eq_star_smul, ProbabilityTheory.covarianceOperator_apply, SheafOfModules.unitHomEquiv_symm_comp, ContinuousMultilinearMap.mkPiRing_apply_one_eq_self, LinearEquiv.piFinTwo_symm_apply, BoundedContinuousFunction.toContinuousMapLinearMap_apply, Matrix.mul_val_succ, Finset.card_insertNone, IsLocalization.algEquivOfAlgEquiv_apply, RCLike.mul_conj, Polynomial.isMonicOfDegree_two_iff', RootPairing.coxeterWeightIn_eq_four_iff_not_linearIndependent, Module.exists_smul_eq_zero_and_mk_eq, Polynomial.leadingCoeff_opRingEquiv, Fin.insertNthEquiv_apply, Ordinal.enum_lt_enum, Polynomial.not_isRoot_C, algebraMapCLM_coe, Finset.mem_finsuppAntidiag, Submodule.val_mulMap'_tmul, RCLike.norm_conj, CategoryTheory.yonedaEquiv_apply, Set.powersetCard.mem_mulActionHom_compl, ContDiffAt.laplacian_CLM_comp_left, finSuccEquiv_succ, Localization.localRingHom_to_map, Matrix.GeneralLinearGroup.coe_toLin, ContinuousMap.coe_inf', HahnSeries.SummableFamily.coe_add, MvPolynomial.constantCoeff_rename, NonUnitalSubalgebra.inclusion_mk, BoundedContinuousFunction.nsmul_apply, NNReal.orderIsoRpow_apply, QuadraticMap.polar_prod, TopCat.isOpenEmbedding_iff, WellFoundedGT.iSup_eq_monotonicSequenceLimit, HahnSeries.SummableFamily.add_apply, Multiset.prod_X_add_C_coeff, equivShrink_top, ContinuousAddEquiv.coe_refl, Subgroup.IsComplement.equiv_one, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, WithBot.orderIsoPUnitSumLex_symm_inr, AddMonoidHom.coe_of_map_add_neg, MonoidAlgebra.single_one_mul_apply, MeasureTheory.Measure.haar.addHaarContent_apply, Ideal.map_spanIntNorm, ofAdd_toAdd, AlgEquiv.symm_apply_eq, ContinuousMultilinearMap.mkPiRing_apply, ContinuousOpenMap.id_apply, Matrix.kroneckerMap_assoc₁, lineMap_inv_two, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_measure_eq_zero, MvPowerSeries.continuous_aeval, OmegaCompletePartialOrder.ContinuousHom.ωSup_apply_ωSup, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, OrderEmbedding.preimage_uIoc, Finset.weightedVSub_apply_const, ProbabilityTheory.uniformOn_inter, OmegaCompletePartialOrder.OrderHom.ωSup_coe, CompactlySupportedContinuousMap.toBoundedContinuousFunction_apply, CliffordAlgebra.equivBaseChange_symm_apply, sSupHomClass.map_sSup, Module.End.genEigenspace_directed, AddEquiv.val_neg_piAddUnits_apply, Valuation.isEquiv_iff_val_lt_val, LinearMap.fst_surjective, ProfiniteGrp.coe_id, AlgebraicGeometry.IsClosedImmersion.base_closed, OrderDual.toDual_le_toDual, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, uliftMultiplesHom_symm_apply, AddMonoidHom.coe_smul', NNReal.agmSequences_zero, ContinuousAlternatingMap.toAlternatingMapLinear_apply, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, Module.Basis.repr_self_apply, NonUnitalSubring.closure_preimage_le, Algebra.PreSubmersivePresentation.jacobiMatrix_reindex, MeasureTheory.Measure.sum_smul_dirac, AddCircle.homeomorphCircle'_symm_apply, TestFunction.continuous_iff_continuous_comp, InitialSeg.leAdd_apply, Polynomial.exists_partition_polynomial_aux, MvPolynomial.map_bind₂, MeasureTheory.measure_eq_top_of_subset_compl_sigmaFiniteSetWRT', CategoryTheory.Localization.LeftBousfield.galoisConnection, RootPairing.coroot'In_rootSpanMem_eq_pairingIn, Polynomial.natDegree_C_add, Algebra.map_leftMulMatrix_localization, AddEquiv.funUnique_symm_apply, Ordinal.isInitialIso_symm_apply_coe, MeasureTheory.Measure.ae_mem_finset_iff_map_eq_sum_dirac, Finsupp.mem_range_mapDomain_iff, OrderRingIso.coe_toOrderRingHom, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, MonoidHom.coe_toMultiplicative_range, LinearMap.ker_localizedMap_eq_localized'_ker, AlgebraicGeometry.quasiCompact_iff, CategoryTheory.FreeGroupoid.functorEquiv_apply, SimpleGraph.Iso.reachable_iff, Field.isSeparable_algebraMap, Polynomial.Splits.eval_root_derivative, Ring.map_multichoose, Cubic.c_eq_three_roots, PMF.toMeasure_apply_singleton, ContinuousLinearMap.coe_zero', Complex.normSq_ratCast, Profinite.effectiveEpi_tfae, CategoryTheory.ForgetEnrichment.equivInverse_map, exteriorPower.alternatingMapLinearEquiv_ιMulti, Directed.measure_iUnion, PowerSeries.mapAlgHom_apply, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, ContinuousLinearMap.opNorm_mul_flip_apply, MeasurableEquiv.trans_apply, IsometryEquiv.withLpProdUnique_apply, PresheafOfModules.Derivation.d_map, OrderIso.image_symm_image, TensorProduct.directSum_lof_tmul_lof, ConvexOn.univ_sSup_of_countable_affine_eq, LinearEquiv.coe_inv, IsLocalizedModule.iso_apply_mk, SlashInvariantForm.add_apply, Polynomial.C_mul', Polynomial.eraseLead_add_C_mul_X_pow, OrderIso.subLeft_apply, KaehlerDifferential.kerToTensor_apply, FractionalIdeal.count_finsuppProd, isConjRoot_algHom_iff, RootPairing.Base.cartanMatrix_apply_eq_zero_iff, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, AddHom.withTopMap_apply, matPolyEquiv_map_smul, Action.rightDual_ρ, Quaternion.imJ_fst_dualNumberEquiv, quadraticChar_two, Algebra.discr_eq_discr, ContinuousLinearMap.ebound, IsSublattice.latticeClosure_eq, AlgHom.coe_coe, FirstOrder.Language.Term.constantsVarsEquiv_symm_apply, RatFunc.laurent_div, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, unitInterval.volume_apply, LinearIsometry.isEmbedding, Submodule.coe_subtypeL', TopologicalSpace.OpenNhds.inclusionMapIso_inv, CFC.negPart_algebraMap, InnerProductSpace.inner_left_rankOne_apply, Finsupp.mem_span_iff_linearCombination, DirectSum.lequivCongrLeft_apply, LinearEquiv.bijective, AffineEquiv.prodComm_apply, LocallyBoundedMap.coe_comp, MeasureTheory.SimpleFunc.nearestPtInd_succ, MvPolynomial.iterToSum_C_X, star_dotProduct_toMatrix₂_mulVec, ContDiffMapSupportedIn.contDiff, CircleDeg1Lift.dist_map_zero_translationNumber_le, norm_iteratedFDeriv_clm_apply, AddCon.liftOnAddUnits_mk, TestFunction.toBoundedContinuousFunctionCLM_apply, isStablyFiniteRing_iff_injective_of_surjective, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, FractionalIdeal.coe_mem_one, LieEquiv.one_apply, RootPairing.root_coroot_eq_pairing, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, Submodule.spanRank_toENat_eq_iInf_encard, RCLike.continuous_normSq, Subsemigroup.opEquiv_symm_apply, LinearIsometryEquiv.norm_map, LocallyConstant.congrRightₗ_symm_apply_apply, AddHom.toAddEquiv_apply, Equiv.comp_surjective, Subgroup.apply_coe_mem_map, CliffordAlgebraQuaternion.toQuaternion_ofQuaternion, MvPolynomial.map_eval₂, TopCat.Presheaf.germ_stalkSpecializes_apply, Homeomorph.funSplitAt_symm_apply, Topology.WithLowerSet.ofLowerSet_inj, Nat.pow_succ_factorization_not_dvd, StarAlgEquiv.coe_toAlgEquiv, MvPolynomial.eval_map, IsLocalFrameOn.coeff_apply_of_mem, SSet.prodStdSimplex.orderHomOfSimplex_coe, LieHom.coe_id, SpecialLinearGroup.coe_one, IsBaseChange.linearMapLeftRightHom_comp_apply, CuspForm.zero_apply, AlternatingMap.congr_arg, TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange, ContinuousLinearEquiv.hasTemperateGrowth, LatticeHom.coe_comp, Polynomial.isMonicOfDegree_X_sub_one, IsometryEquiv.neg_apply, toDual_sInf, AddEquiv.coe_prodComm_symm, StarRingEquiv.trans_apply, RelIso.preimage_eq_image_symm, SymOptionSuccEquiv.decode_inr, NonUnitalStarSubalgebra.mem_comap, ContinuousLinearMap.HasLeftInverse.leftInverse_leftInverse, Homeomorph.shearMulRight_coe, Equiv.prodPiEquivSumPi_apply, ProbabilityTheory.uniformOn_of_univ, CategoryTheory.Functor.Final.colimitCoconeOfComp_isColimit, Sym2.lift_comp_map, WittVector.mapFun.one, CommRingCat.free_map_coe, LinearIsometryEquiv.map_zero, AffineMap.slope_comp, OrderIso.essSup_apply, AlternatingMap.smul_apply, DirichletCharacter.LFunction_eq_LSeries, SchwartzMap.fderivCLM_apply, CategoryTheory.Functor.equivCatHom_symm_apply, MeasureTheory.exists_measurable_superset₂, Polynomial.degreeLT.basis_val, MultilinearMap.congr_fun, AffineIsometryEquiv.coe_constVAdd, Ordinal.isInitial_preOmega, RestrictedProduct.single_mul, Subring.centerCongr_apply_coe, sign_nonneg_iff, NonUnitalStarAlgHom.prodEquiv_symm_apply, contDiff_prodAssoc, MeasureTheory.Measure.le_sum_apply, Polynomial.map_mem_nthRootsFinset, Subspace.dualAnnihilator_dualAnnihilator_eq, Finset.weightedVSubOfPoint_indicator_subset, MultilinearMap.currySumEquiv_apply, SimpleGraph.Embedding.sumInr_apply, TwoSidedIdeal.mem_mk, OrderHom.antisymmetrization_apply, setBasisOfLinearIndependentOfCardEqFinrank_repr_apply, MulChar.apply_mem_algebraAdjoin, AddMonoid.End.mulRight_apply_apply, TopCat.range_prod_map, map_dvd_iff_dvd_symm, DomMulAct.smul_addMonoidHom_apply, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, FreeMonoid.ofList_append, Orientation.map_of_isEmpty, UpperSet.mem_map, MvPowerSeries.monomial_mem_nonzeroDivisors, SimpleGraph.EdgeLabeling.get_pullback, Finsupp.equivMapDomain_single, LocallyConstant.toContinuousMapLinearMap_apply, UniformConvergenceCLM.coe_zero, SymAlg.sym_bijective, Algebra.Presentation.differentials.hom₁_single, ProbabilityTheory.Kernel.compProd_null, Real.volume_closedBall, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, CategoryTheory.InducedCategory.homEquiv_apply, CategoryTheory.Functor.functorPushforward_mem_iff, AddMonoidAlgebra.mapDomain_one, LinOrd.dual_map, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, RingEquiv.mopMatrix_symm_apply, ProbabilityTheory.tilted_mul_apply_cgf, CategoryTheory.Bicategory.Adjunction.homEquiv₁_apply, Module.End.intCast_apply, PowerSeries.derivative_inv', Besicovitch.exists_closedBall_covering_tsum_measure_le, IsCompact.measure_closure, AddAction.stabilizer_vadd_eq_stabilizer_map_conj, AddEquiv.symm_comp_eq, SetSemiring.up_lt_up, FirstOrder.Language.Embedding.coe_injective, Profinite.NobelingProof.Products.max_eq_eval, LinearIsometryEquiv.apply_symm_apply, groupCohomology.isMulCoboundary₁_of_mem_coboundaries₁, Submodule.norm_starProjection_apply_le, Homeomorph.toEquiv_piCongr, LocalizedModule.divBy_apply, ProbabilityTheory.Kernel.lintegral_id_prod, ContinuousLinearMap.contMDiff, TensorProduct.AlgebraTensorModule.lTensor_id, ContinuousLinearMap.mdifferentiable, Module.Basis.toMatrix_smul, OrderIso.sumLexIioIci_symm_apply_Ici, BialgHom.ext_iff, SeparationQuotient.mkAddMonoidHom_apply, StarMonoidHom.coe_toMonoidHom, SymAlg.sym_neg, Monoid.Coprod.toProd_surjective, Matrix.diagonal_vec1, CategoryTheory.Limits.WidePullbackCone.reindex_pt, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, OrderMonoidIso.trans_apply, OrderEmbedding.preimage_Ici, ModularForm.norm_eq_zero_iff, MeasureTheory.setLIntegral_eq_const, Int.divModEquiv_apply, WeierstrassCurve.Affine.Point.toClass_zero, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, Algebra.Generators.defaultHom_val, Finset.ofDual_inf, Seminorm.continuousAt_zero_of_forall', MvPolynomial.map_eval₂Hom, IsOpen.measure_zero_iff_eq_empty, HasFDerivAt.norm_sq, TensorProduct.quotientTensorQuotientEquiv_symm_apply_mk_tmul, Equiv.Perm.Basis.sameCycle, AddHom.toAddEquiv_symm_apply, MvPolynomial.supportedEquivMvPolynomial_symm_X, MulEquiv.toSingleObjEquiv_inverse_map, VectorBundleCore.coordChange_self, biUnion_range_succ_disjointed, Ideal.relNorm_relNorm, OrderIso.dualAntisymmetrization_symm_apply, skewAdjointLieSubalgebraEquiv_symm_apply, CircleDeg1Lift.map_lt_add_floor_translationNumber_add_one, AddMonCat.ext_iff, Algebra.Generators.exists_presentation_of_basis_cotangent, Circle.isAddQuotientCoveringMap_exp, Finsupp.Lex.single_strictAnti, RootPairing.Hom.comp_indexEquiv_symm_apply, map_birkhoffAverage, Valuation.isNontrivial_iff_exists_lt_one, LieModule.Weight.ext_iff, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, LinearIsometry.map_starProjection', Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, NonUnitalSubsemiring.centerCongr_symm_apply_coe, Bialgebra.counitBialgHom_apply, RCLike.ofNat_re, zero_prodMap_dualTensorHom, MeasureTheory.mulEquivHaarChar_eq, ContinuousLinearEquiv.isOpenMap, LinearMap.sum_repr_mul_repr_mulₛₗ, OrderIso.strictMono, cfcHom_continuous, IsScalarTower.coe_toAlgHom', SymAlg.sym_zero, CircleDeg1Lift.tendsto_atBot, Finsupp.single_smul, AddCommGrpCat.isColimit_iff_bijective_desc, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, MeasureTheory.prob_compl_eq_one_iff₀, OrderAddMonoidIso.eq_symm_comp, FreeAddSemigroup.lift_symm_apply, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, Multiplicative.toAdd_mono, MeasureTheory.Measure.measurable_coe, Polynomial.derivative_monomial, cfcL_apply, ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_comp_trim, TensorProduct.AlgebraTensorModule.rTensor_one, groupCohomology.mem_cocycles₁_of_addMonoidHom, OrderHom.map_lfp, Algebra.TensorProduct.basis_apply, QuotientAddGroup.coe_mk', ConjRootClass.minpoly.map_eq_prod, NumberField.mixedEmbedding.commMap_apply_of_isComplex, Valuation.Integers.valuation_irreducible_lt_one, innerₛₗ_apply_apply, Equiv.Perm.OnCycleFactors.kerParam_range_card, TruncatedWittVector.truncate_wittVector_truncate, MonoidWithZeroHom.map_eq_zero_iff, RelEmbedding.sumLiftRelInr_apply, UpperSet.map_map, MonoidWithZeroHom.one_apply_eq_zero_iff, MeasureTheory.Measure.restrict_apply_self, Equiv.coe_toEmbedding, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, LinearMap.ringLmapEquivSelf_symm_apply, groupCohomology.cocycles₂.d₂₃_apply, SSet.Subcomplex.Pairing.dim_p, norm_ofMul, CocompactMap.isCompact_preimage_of_isClosed, TensorAlgebra.ι_def, Module.Basis.equiv_apply, Matrix.adjp_apply, CategoryTheory.GrothendieckTopology.trivial_covering, Equiv.piCongrSet_apply, CentroidHom.smul_def, TopologicalSpace.Opens.infLELeft_apply_mk, MvPolynomial.pderiv_one, LinearIsometryEquiv.coe_toAffineIsometryEquiv, NumberField.Units.pos_at_place, LinearMap.lTensor_surj_iff_rTensor_surj, LinearMap.liftBaseChange_one_tmul, LinearIsometry.coe_toContinuousLinearMap, groupCohomology.d₀₁_hom_apply, Affine.Simplex.excenterWeightsUnnorm_reindex, AddValuation.map_add', IncidenceAlgebra.one_apply, MvPowerSeries.coe_substAlgHom, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_hom, AffineEquiv.span_eq_top_iff, LieModuleHom.coe_id, MvPolynomial.mkDerivation_X, BumpCovering.support_toPOUFun_subset, ProbabilityTheory.Kernel.nsmul_apply, Equiv.Perm.cycleOf_eq_one_iff, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, PointwiseConvergenceCLM.tendsto_nhds, MvPolynomial.pderiv_mul, Con.mk'_surjective, FiniteDimensional.basisSingleton_apply, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, Equiv.toPartialEquiv_apply, RingHom.map_rat_algebraMap, Fin.consEquiv_apply, ProbabilityTheory.setLIntegral_condKernel_univ_right, Ideal.absNorm_pos_iff_mem_nonZeroDivisors, Algebra.lmul_injective, algebraMap_le_of_le_spectrum, ExteriorAlgebra.algebraMap_inj, QuadraticMap.associated_rightInverse, GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity, WeierstrassCurve.Projective.baseChange_negAddY, FintypeCat.equivEquivIso_apply_hom, SpectrumRestricts.nnreal_iff, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image, GroupSeminorm.lt_def, Polynomial.aeval_sumIDeriv, Finset.inf_map, Representation.ofMulAction_apply, ContinuousAffineMap.coe_lineMap_eq, padicNormE.image', MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero, geometric_hahn_banach_compact_closed, Equiv.piSplitAt_apply, AddCon.mk'_surjective, ProbabilityTheory.condExpKernel_comp_trim, OrderIso.apply_symm_apply, Set.opEquiv_apply, OrderIso.isGLB_image, DirectSum.lmap_apply, PowerSeries.rescale_X, Rep.linearization_single, SemiNormedGrp.coe_comp, AddEquiv.coe_comapAddSubgroup, IsometryEquiv.preimage_emetric_closedBall, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, ProbabilityTheory.IsCondKernelCDF.integral, LinearMap.spectrum_toMatrix', map_preNormEDS, Profinite.NobelingProof.Products.eval_πs, AddEquiv.addSubgroupCongr_apply, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd, LieModule.trace_toEnd_genWeightSpace, Seminorm.mem_closedBall_zero, Bialgebra.counitAlgHom_apply, CategoryTheory.InjectiveResolution.of_def, OrthogonalFamily.norm_sq_diff_sum, MeasureTheory.SimpleFunc.const_apply, Polynomial.sumIDeriv_C, DistLat.dual_map, Set.conj_mem_fixingAddSubgroup, Polynomial.Chebyshev.T_derivative_eq_U, MeasureTheory.mul_meas_ge_le_pow_eLpNorm', ContinuousAlternatingMap.map_coord_zero, Subalgebra.aeval_coe, Real.smul_map_diagonal_volume_pi, Equiv.Set.image_apply, DirichletCharacter.norm_LSeries_product_ge_one, SupHom.coe_bot, Algebra.traceMatrix_apply, ArithmeticFunction.pmul_apply, iterateFrobeniusEquiv_def, AddMonoidHom.restrict_eq_zero_iff, MeasureTheory.Measure.haar.addHaarContent_outerMeasure_self_pos, Set.Definable.image_comp_embedding, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, SkewMonoidAlgebra.coeff_erase_ne, Lat.coe_id, ContinuousLinearEquiv.comp_hasFDerivAt_iff, QuotientAddGroup.equivIocMod_zero, FreeAbelianGroup.lift_add, matPolyEquiv_diagonal_X, Additive.ofMul_top, ContinuousLinearMap.eq_adjoint_iff, ContinuousLinearMap.hasFDerivAt, AddEquiv.piUnique_apply, QuadraticMap.sum_apply, Polynomial.coeff_taylor_natDegree, MeasureTheory.Measure.map_fst_prod, Matrix.uniqueAddEquiv_apply, Equiv.piCongrRight_symm_apply, char_dvd_card_solutions_of_add_lt, Equiv.Perm.disjoint_ofSubtype_of_memFixedPoints_self, CategoryTheory.Coyoneda.objOpOp_inv_app, groupHomology.d₃₂_single_one_thd, CategoryTheory.GradedObject.comapEquiv_counitIso, normalize_eq_normalize, SimpleGraph.Subgraph.spanningHom_injective, StarAlgHom.snd_apply, Multiset.coe_sumAddMonoidHom, OrderEmbedding.preimage_Icc, NumberField.InfinitePlace.comap_apply, MvPolynomial.comp_eval₂Hom, SheafOfModules.freeHomEquiv_freeMap, CliffordAlgebraComplex.ofComplex_toComplex, Submodule.starProjection_tendsto_self, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add, NonUnitalSubalgebra.inclusion_right, Module.End.maxGenEigenspace_eq, Orientation.volumeForm_map, ContMDiffVectorBundle.pullback, MeasureTheory.inducedOuterMeasure_caratheodory, ArithmeticFunction.LSeries_zeta_mul_Lseries_moebius, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom_assoc, MvPolynomial.ACounit_surjective, Fin.cycleRange_apply, rotation_apply, toMatrix_rotation, WCovBy.toDual, IsBot.toDual, Polynomial.roots_C_mul, Set.image_finset_sum, Matrix.blockTriangular_transvection', ProbabilityTheory.Kernel.traj_map_updateFinset, LinearIsometryEquiv.piLpCongrRight_apply, Finset.Colex.le_iff_max'_mem, AffineBasis.coord_apply_ne, RingEquiv.piOptionEquivProd_apply, CategoryTheory.Iso.homCongr_trans, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RingEquiv.op_apply_symm_apply, HahnSeries.SummableFamily.support_hsum_subset, RCLike.nonpos_iff, MeasureTheory.exists_null_pairwise_disjoint_diff, Complex.normSq_mk, LinearMap.BilinForm.sum_right, MeasureTheory.Measure.addHaar_ball_of_pos, CategoryTheory.Subobject.wideCospan_map_term, convexHull_union_neg_eq_absConvexHull, RingCon.comapQuotientEquivRange_symm_mk, Subalgebra.mulMap_toLinearMap, CategoryTheory.FunctorToTypes.binaryProductEquiv_apply, map_compl', RCLike.smul_re, Algebra.TensorProduct.piScalarRight_tmul, FourierTransform.fourierEquiv_apply, BotHom.dual_apply_apply, Ideal.Filtration.mem_submodule, MulChar.inv_apply_eq_inv, Algebra.mem_adjoin_iff, AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap, Diffeomorph.apply_symm_apply, RingEquiv.piCongrLeft_symm_apply, ofMul_list_prod, CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists, IsFractionRing.mk'_eq_div, NNReal.sqrt_sq, SchwartzMap.toLpCLM_apply, ProbabilityTheory.Kernel.swapRight_apply, Homeomorph.toEquiv_piCongrLeft, Matrix.SpecialLinearGroup.map_intCast_injective, ContinuousLinearMap.single_apply, AddConstMapClass.map_add_const, Polynomial.coeff_divByMonic_X_sub_C_rec, LinearMap.separatingRight_congr_iff, ProbabilityTheory.Kernel.lintegral_fst, ofLex_sub, Equiv.traverse_def, UniformFun.uniformSpace_eq_iInf_precomp_of_cover, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub, RestrictedProduct.inclusion_apply, Equiv.Perm.permCongr_eq_mul, ContinuousLinearMap.toSpanSingleton_apply, LinearMap.IsSymmetric.directSum_decompose_apply, GaussianInt.toComplex_def₂, OrthonormalBasis.sum_sq_inner_right, QuotientGroup.kerLift_mk', Real.volume_val, CategoryTheory.Limits.IsColimit.equivIsoColimit_apply, FreeNonUnitalNonAssocAlgebra.of_comp_lift, SSet.opFunctorCompOpFunctorIso_hom_app_app, ContinuousLinearMap.sum_apply, LinearMap.rTensor_id_apply, Monovary.sum_comp_perm_mul_le_sum_mul, MulHom.coe_srangeRestrict, ZMod.stdAddChar_coe, AddAutAdditive_apply_apply, MeasureTheory.volume_pi_pi, BoxIntegral.Box.Ioo_subset_coe, Equiv.Perm.OnCycleFactors.kerParam_injective, Homeomorph.piCurry_apply, WeierstrassCurve.Projective.baseChange_negY, MulHom.coe_prodMap, finTwoArrowEquiv'_apply, SlashInvariantFormClass.eq_cuspFunction, Module.eval_apply_injective, CategoryTheory.Functor.FullyFaithful.isoEquiv_apply, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_apply_coe, Matrix.lift_cRank_submatrix, Derivation.linearEquiv_coe_to_linearMap_comp, Seminorm.lt_def, NonemptyInterval.toLex_strictMono, cfcHom_nonneg_iff, UniversalEnvelopingAlgebra.lift_unique, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Int.padicValuation_eq_one_iff, AddOpposite.opMulEquiv_symm_apply, IsSelfAdjoint.selfAdjointPart_apply, MeasureTheory.lintegral_singleton, le_comap_range_lTensor, RCLike.realRingEquiv_symm_apply, HasFDerivAt.continuousMultilinear_apply_const, RingQuot.mkAlgHom_surjective, AffineIndependent.affineCombination_eq_iff_eq, Equiv.Perm.mem_support_iff_of_commute, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap, Homeomorph.contDiff_unitBall, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, OneHom.id_apply, HasFDerivWithinAt.continuousAlternatingMap_apply, InnerProductSpace.rankOne_apply, AlgEquiv.isSeparable_iff, BoundedContinuousFunction.coe_mul, HahnSeries.single.addMonoidHom_apply_coeff, RelIso.mul_apply, RestrictedProduct.coe_comp_structureMap, Homeomorph.isEmbedding, Equiv.trans_apply, Finset.Colex.cons_lt_cons, AnalyticOn.iteratedFDerivWithin_comp_perm, SubMulAction.ofStabilizer.inv_conjMap_comp_apply, EuclideanSpace.nndist_eq, Matrix.diagLinearMap_apply, LinearMap.polar_singleton, CategoryTheory.CommSq.instHasLift, ValuationSubring.mapOfLE_valuation_apply, Orthonormal.exists_hilbertBasis_extension, MeasureTheory.Measure.haarMeasure_self, Matrix.diagonalLinearMap_apply, Dilation.antilipschitz, PrincipalSeg.exists_eq_iff_rel, ContinuousMap.exists_finite_sum_mul_approximation_of_mem_uniformity, AddHom.coe_prod, AffineIsometryEquiv.comp_continuous_iff, AlgebraicGeometry.Scheme.Pullback.Triplet.isPullback_SpecMap_tensor, AlgebraicGeometry.Scheme.forget_map, LieModule.shiftedGenWeightSpace.toEnd_eq, SetSemiring.imageHom_def, Unitary.coe_linearIsometryEquiv_apply, LieModule.iSup_genWeightSpace_eq_top', Finset.Nat.antidiagonalEquivFin_symm_apply_coe, Order.succ_ofAdd, ProbabilityTheory.Kernel.coeAddHom_apply, SimpleGraph.Copy.topEmbedding_apply, ContinuousLinearEquiv.ext_iff, DirectSum.coeAddMonoidHom_eq_dfinsuppSum, SemilinearIsometryEquivClass.norm_map, AlgHom.le_equalizer, TopCat.GlueData.isOpen_iff, ModularForm.prod_slash_sum_weights, AffineIsometryEquiv.coe_trans, PMF.toMeasure_ofFintype_apply, AlgebraicGeometry.sigmaMk_mk, Localization.localRingHom_injective_of_primesOver_eq_singleton, Ideal.finsuppTotal_apply_eq_of_fintype, NNReal.sqrt_pos, Finset.Colex.toColex_sdiff_le_toColex_sdiff', IncidenceAlgebra.zeta_of_le, MeasureTheory.Conservative.frequently_measure_inter_ne_zero, Equiv.subtypeEquivCodomain_symm_apply, ConcaveOn.comp_linearMap, NumberField.prod_abs_eq_one, Matrix.sum_sum_single, AddMonoidHom.toZeroHom_coe, AddMonoid.Coprod.neg_def, Equiv.left_inv', Complex.isCauSeq_conj, Opposite.equivToOpposite_coe, ContinuousLinearEquiv.map_smul, gelfandStarTransform_apply_apply, groupHomology.isoCycles₁_inv_comp_iCycles_apply, FinBddDistLat.ofHom_apply, Ring.DirectLimit.congr_symm_apply_of, MeasureTheory.lintegral_countable, MultilinearMap.map_sum, PowerSeries.coe_add, NormalizedGCDMonoid.normalize_lcm, ArithmeticFunction.neg_apply, WittVector.factorPowSucc_fontaineThetaModPPow_eq, MeasureTheory.Measure.mkMetric_apply, DirectSum.fromAddMonoid_of, Fin.snocEquiv_apply, Submodule.reflection_singleton_apply, ProbabilityTheory.Kernel.IsCondKernel.isProbabilityMeasure_ae, Trivialization.pullback_target, Metric.PiNatEmbed.toPiNatEquiv_apply_ofPiNat, LocallyConstant.zero_apply, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_snd, Cardinal.isNormal_preAleph, Equiv.sumSigmaDistrib_symm_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, TopologicalSpace.Fiber.sigmaIsoHom_inj, StarModule.decomposeProdAdjointL_apply, HasDerivAt.hasGradientAt, OrderIso.sumLexAssoc_symm_apply_inr_inr, MonoidHom.toHomPerm_apply_symm_apply, AddGroupNorm.coe_add, HasFTaylorSeriesUpToOn.zero_eq', Equiv.sigmaPUnit_symm_apply_snd, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, DFinsupp.sumAddHom_single, Finsupp.erase_ne, MeasureTheory.measure_liminf_cofinite_eq_zero, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_symm_apply_fst, DFinsupp.subtypeSupportEqEquiv_apply_coe, MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates_aux, BoxIntegral.Box.le_iff_Icc, Subgroup.quotientEquivProdOfLE_apply, MeasureTheory.Measure.count_singleton', InitialSeg.monotone, RingCat.forget₂_map, Equiv.optionEquivSumPUnit_symm_inr, strongRankCondition_iff_forall_not_injective, MulSemiringActionHom.map_smulₛₗ, Ideal.Quotient.factor_comp_apply, MeasureTheory.Measure.map_comp, TensorProduct.liftAux_tmul, MultilinearMap.map_insertNth_smul, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, RootPairing.RootPositiveForm.zero_lt_posForm_iff, MvPolynomial.aeval_eq_eval, QuotSMulTop.equivTensorQuot_naturality_mk, CategoryTheory.Pi.equivalenceOfEquiv_unitIso, MvPolynomial.supDegree_esymmAlgHomMonomial, RootPairing.toLinearMap_apply_CoPolarization, partialSups_add_one', SchwartzMap.compCLMOfContinuousLinearEquiv_apply, LinearMap.BilinForm.ext_iff_of_isSymm, MultilinearMap.map_update, PowerSeries.catalanSeries_constantCoeff, LieDerivation.inner_apply_apply, AffineIsometryEquiv.pointReflection_midpoint_left, FractionalIdeal.extendedHomₐ_coeIdeal_eq_map, HarmonicAt.analyticAt_complex_partial, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atTop, AddEquivClass.apply_mem_center, Submodule.IsCompl.projection_apply_left, MeasureTheory.SimpleFunc.setToSimpleFunc_const, CommBialgCat.id_apply, comap_inv_leftUniformSpace, OrderHom.top_def, GaussianInt.normSq_le_normSq_of_re_le_of_im_le, FormalMultilinearSeries.ofScalars_apply_eq, ofDual_min, NonUnitalStarAlgHom.coe_comp, Real.volume_pi_ball, CategoryTheory.Limits.kernel.condition_apply, MulEquiv.coe_refl, MeasureTheory.Measure.const_comp, PrincipalSeg.map_bot, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, RootPairing.Base.linearIndependent_pair_of_ne, dot_cross_self, Preord.coe_id, interior_convexHull_nonempty_iff_affineSpan_eq_top, LieEquiv.coe_injective, Coalgebra.Repr.induced_index, MeasureTheory.Measure.iInf_IicSnd_gt, MonoidAlgebra.mem_adjoin_support, MvPolynomial.schwartz_zippel_totalDegree, cfc_apply_mkD, IsLocalization.smul_mk'_self, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, Polynomial.leadingCoeff_X_pow_add_C, OrderAddMonoidHom.add_apply, Equiv.eq_symm_comp, TopologicalSpace.Opens.complOrderIso_apply, Colex.forall, surjective_of_nonzero_of_finrank_eq_one, Convex.mapsTo_lineMap, AbsoluteValue.eq_on_nat_iff_eq_on_int, Behrend.bound_aux', ContinuousLinearMap.toSpanSingleton_apply_one, AffineIsometry.coe_comp, AddChar.zero_apply, MeasureTheory.biSup_measure_Iic, Equiv.piCongrLeft_preimage_univ_pi, OrderHom.gfp_const_inf_le, groupCohomology.map_H0Iso_hom_f_apply, AffineMap.homothety_continuous, monotoneOn_comp_ofDual_iff, Ring.ordFrac_eq_ord, NormedSpace.Dual.toWeakDual_continuous, MeasureTheory.Lp.compMeasurePreservingₗ_apply, ArithmeticFunction.sigma_apply, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point_assoc, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, MeasureTheory.measurable_measure_add_right, PowerSeries.coeff_heval, LieModule.Cohomology.twoCochain_alt, HahnSeries.coeff_single_same, Polynomial.eval_C, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, AmpleSet.preimage_iff, StarAlgHom.coe_prod, groupCohomology.d₁₂_comp_d₂₃_apply, Module.endTensorEndAlgHom_apply, IsometryEquiv.coe_toHomeomorph, Cardinal.toENat_eq_zero, BoundedContinuousFunction.toContinuousMapMonoidHom_apply, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_mk', PointedCone.coe_map, RelIso.eq_iff_eq, Affine.Simplex.sign_touchpointWeights_empty, Matrix.toLpLin_mul_same, ConjAct.forall, Matrix.charmatrix_apply_eq, groupCohomology.H0IsoOfIsTrivial_inv_apply, CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply, OrderAddMonoidIso.equivLike_neg_eq_symm, MvPolynomial.aeval_ite_mem_eq_self, LieDerivation.commutator_apply, NonarchAddGroupSeminorm.coe_sup, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, Polynomial.toFinsupp_monomial, Monoid.Coprod.map_map, IsGalois.mem_range_algebraMap_iff_fixed, Finsupp.eq_single_iff, AdjoinRoot.algEquivOfAssociated_root, LinearMap.mem_skewAdjointSubmodule, Homeomorph.opensCongr_apply, MeasureTheory.Measure.sum_apply_of_countable, MeasureTheory.weightedSMul_nonneg, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, NumberField.mixedEmbedding.convexBodyLT_volume, CliffordAlgebra.toProd_ι_tmul_one, signedDist_left_congr, OrderIso.inv_symm_apply, cfcₙ_eq_cfcₙL_mkD, Lagrange.nodal_insert_eq_nodal, Finset.imageMonoidHom_apply, Algebra.SubmersivePresentation.map_jacobianOfHasCoeffs, MvPolynomial.le_weightedTotalDegree, SimpleGraph.card_le_chromaticNumber_iff_forall_surjective, OneHom.map_one, AlgHom.coe_fn_inj, MeasureTheory.measure_integral_le_pos, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_symm_apply, PresheafOfModules.congr_map_apply, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, TopHom.coe_top, OrderIso.addRight_apply, Function.locallyFinsuppWithin.restrict_apply, StrictMono.orderIsoOfSurjective_self_symm_apply, FormalMultilinearSeries.id_apply_one', RingEquiv.ext_iff, Localization.mk_algebraMap, Polynomial.mapAlgHom_eq_eval₂AlgHom'_CAlgHom, RingEquiv.piCongrLeft'_apply, Polynomial.coe_monomial, Equiv.ofFiberEquiv_map, MeasureTheory.AEStronglyMeasurable.integral_condExpKernel, FreeMonoid.toList_mul, stdSimplexHomeomorphUnitInterval_zero, AddHom.srangeRestrict_surjective, tensorIteratedFDerivTwo_eq_iteratedFDeriv, CompleteLatticeHom.dual_id, TensorProduct.coe_directSumRight', toDual_smul', Subsemigroup.equivOp_symm_apply_coe, Algebra.TensorProduct.comm_comp_map_apply, MeasureTheory.measure_pos_iff_nonempty_of_isAddLeftInvariant, Function.locallyFinsuppWithin.logCounting_nonneg, MvPolynomial.eval₂Hom_C_id_eq_join₁, MeasurableEquiv.piFinTwo_symm_apply, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity, AffineMap.congr_arg, ContinuousLinearEquiv.contDiffAt_comp_iff, Affine.Simplex.ExcenterExists.touchpoint_map, Algebra.dvd_algebraMap_intNorm_self, Nucleus.coe_mk, NonemptyInterval.coe_dual, map_complEDS', Submodule.quotEquivOfEqBot_symm_apply, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective, Module.DualBases.coe_dualBasis, ContinuousLinearMap.precompL_apply, CliffordAlgebra.changeForm_self_apply, MeasureTheory.Content.le_outerMeasure_compacts, Orientation.inner_rightAngleRotation_swap', Polynomial.count_map_roots, ArithmeticFunction.abscissaOfAbsConv_zeta, NNReal.le_sqrt_iff_sq_le, WeierstrassCurve.map_c₆, PowerSeries.aeval_eq_sum, MeasureTheory.withDensity_apply_eq_zero, AddMonoidHom.coe_toMultiplicativeRight, Metric.Snowflaking.toSnowflaking.sizeOf_spec, CategoryTheory.Pi.equivalenceOfEquiv_counitIso, HahnSeries.single_zero_nnratCast, PresheafOfModules.freeYonedaEquiv_symm_app, IsometryEquiv.inv_apply_self, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom, IsSelfAdjoint.adjoint_eq, spectralAlgNorm_def, Representation.apply_sub_id_partialSum_eq, Rep.finsuppToCoinvariantsTensorFree_single, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, Submodule.mem_dualAnnihilator, HNNExtension.equiv_eq_conj, Submonoid.topOrderMonoidIso_symm_apply_coe, AddUnits.coeHom_apply, HahnSeries.SummableFamily.binomialFamily_apply_of_orderTop_nonpos, ContinuousLinearEquiv.isBigO_comp, DFinsupp.coeFnAddMonoidHom_apply, CategoryTheory.Limits.biproduct.matrixEquiv_symm_apply, PolyEquivTensor.toFunAlgHom_apply_tmul, NNReal.sqrt_eq_rpow, Equiv.bijective, MeasureTheory.Measure.addHaar_preimage_smul, Finsupp.toMultiset_toFinsupp, ofLex_intCast, Submonoid.adjoin_eq_span_of_eq_span, groupCohomology.eq_d₂₃_comp_inv_apply, InitialSeg.map_pred, PiTensorProduct.mul_assoc, QuadraticAlgebra.linearEquivTuple_apply, MvPolynomial.eval_mem, RootPairing.Base.linearIndepOn_coroot, OrderRingHom.apply_eq_self, MeasureTheory.measure_spanningSets_lt_top, PolynomialLaw.exists_lift', HahnSeries.SummableFamily.lsum_apply, ofBoolAlg_inf, LinearMap.toMatrix_baseChange, OrthonormalBasis.measurePreserving_repr, PMF.toMeasure_apply, groupCohomology.eq_d₁₂_comp_inv_apply, Equiv.piCongrLeft_symm_apply, Submodule.reflection_apply, Prod.Lex.monotone_fst_ofLex, Sym2.sortEquiv_apply_coe, Finset.orderIsoOfFin_symm_apply, Metric.exists_continuous_nnreal_forall_closedBall_subset, MeasureTheory.laverage_eq', Algebra.Generators.algebraMap_surjective, RCLike.abs_re_le_norm, DirectSum.mk_smul, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, curveIntegralFun_segment, ZMod.completedLFunction_def_even, HasDerivWithinAt.clm_apply, Multiplicative.ofAdd_lt, Behrend.map_mod, SchwartzMap.integral_fourierInv_smul_eq, TwoSidedIdeal.bot_asIdeal, AddSubmonoid.coe_toSubmonoid_apply, ZeroHom.withTopMap_apply, Tuple.sort_perm, Coalgebra.sum_counit_tmul_eq, Finset.weightedVSub_map, Cardinal.toENat_eq_ofNat, RootPairing.coroot_eq_smul_coroot_iff, Representation.asAlgebraHom_def, mem_absConvexHull_iff, Module.Basis.ofSpan_subset, AddEquivClass.coe_symm_apply_apply, AlgEquiv.restrictNormalHom_surjective, PMF.toMeasure_ofMultiset_apply, Set.image_sub, MvPolynomial.pow_idealOfVars, DomMulAct.continuous_mk, LocallyConstant.comapRingHom_apply_apply, PresheafOfModules.restrictScalarsObj_map, FreeLieAlgebra.of_comp_lift, Ordinal.one_toPGame_leftMoves_default_eq, WittVector.teichmuller_zero, Circle.exp_eq_exp, CategoryTheory.GrothendieckTopology.intersection_covering_iff, AlgebraicGeometry.IsPreimmersion.isEmbedding, MvPolynomial.idealOfVars_eq_restrictSupportIdeal, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, Complex.volume_sum_rpow_le, PolynomialLaw.toFun_eq_rTensor_φ_toFun', QuadraticMap.linMulLin_apply, AddCommGrpCat.neg_hom_apply, Multiplicative.ofAdd_image_setAdd, AddGroupExtension.Equiv.map_inl, RCLike.geometric_hahn_banach_closed_point, GenLoop.homotopyTo_apply, CategoryTheory.tensorLeftHomEquiv_naturality, Homeomorph.coe_symm_toEquiv, RootPairing.toPerfPair_comp_root, isRegular_toLex, signedDist_triangle, IsometryEquiv.piCongrLeft'_apply, RingCon.coe_comapQuotientEquivRangeₐ_mk, sphere_subset_range_iff_surjective, IsAntichain.image_relEmbedding, MeasureTheory.ae_measure_preimage_mul_right_lt_top, Matrix.eRank_submatrix, groupHomology.chains₁ToCoinvariantsKer_surjective, Set.image_smul_distrib, HahnSeries.SummableFamily.coeff_hsum_mul, CStarMatrix.ofMatrix_apply, ofAdd_zero, TensorProduct.adjoint_map, QuadraticAlgebra.norm_zero, MulChar.one_apply_coe, Filter.pureAddMonoidHom_apply, IsUltrametricDist.invariantExtension_apply, MeasureTheory.OuterMeasure.comap_iInf, MeasureTheory.volume_preserving_piFinsetUnion, Equiv.Perm.sign_trans_trans_symm, AddChar.IsPrimitive.zmod_char_eq_one_iff, CategoryTheory.FinCategory.categoryAsType_comp, MonoidHom.subgroupOf_range_eq_of_le, Sum.Lex.inr_strictMono, IsLocalization.Away.algebraMap_surjective_of_isIdempotentElem, Ordinal.toGame_one, MeasureTheory.SimpleFunc.measurable_bind, SSet.Subcomplex.Pairing.isUniquelyCodimOneFace, AEMeasurable.im, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, DFinsupp.equivFunOnFintype_apply, MeasureTheory.Measure.addHaar_sphere_of_ne_zero, NonUnitalSubring.centerCongr_apply_coe, SetTheory.PGame.relabel_moveRight, Polynomial.eval_divByMonic_eq_trailingCoeff_comp, AddMonoidAlgebra.divOfHom_apply_apply, FirstOrder.Language.Hom.domRestrict_toFun, Polynomial.algebraMap_apply, FirstOrder.Language.Term.constantsVarsEquivLeft_apply, UniformOnFun.toFun_ofFun, LinearMap.GeneralLinearGroup.generalLinearEquiv_to_linearMap, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, ProbabilityTheory.Kernel.ae_compProd_iff, SkewMonoidAlgebra.mapDomain_single, TopCat.coequalizer_isOpen_iff, LinearMap.IsContPerfPair.bijective_left, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, AlgebraicGeometry.Scheme.mem_jointlySurjectiveTopology_iff_jointlySurjectivePretopology, SchwartzMap.inner_toL2_toL2_eq, LinearEquiv.conj_comp, Valuation.Integers.map_le_one, CentroidHom.coe_add, RootPairing.Equiv.id_indexEquiv_apply, toBoolRing_ofBoolRing, Preord.ext_iff, DFinsupp.smul_apply, IncidenceAlgebra.zeta_mul_zeta, MeasureTheory.SimpleFunc.memLp_zero, Algebra.isInvariant_iff, SymAlg.unsym_mul, RingCat.inv_hom_apply, Algebra.trace_eq_of_algEquiv, MvPolynomial.eval_rename_prod_mk, PartitionOfUnity.locallyFinite, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, FreeMagma.hom_ext_iff, ArithmeticFunction.cardDistinctFactors_apply_prime, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, DistribMulAction.toAddMonoidHom_apply, AdjoinRoot.algHom_ext_iff, TwoSidedIdeal.equivMatrix_apply, CategoryTheory.Bicategory.conjugateEquiv_symm_id, jacobiTheta₂'_conj, uliftZPowersHom_symm_apply, LinearEquiv.domMulActCongrRight_apply, Rep.coinvariantsTensorFreeLEquiv_symm_apply, PowerBasis.equivAdjoinSimple_symm_aeval, PMF.uniformOfFinset_apply_of_mem, Equiv.divLeft_symm_apply, LinearEquiv.piCurry_apply, CliffordAlgebra.contractRight_comm, Finsupp.coeFnAddHom_apply, RingEquiv.ofHomInv_symm_apply, Behrend.map_succ, BotHom.id_apply, Nucleus.restrict_toFun, InnerProductSpace.gramSchmidt_def, AffineIsometryEquiv.continuousAt, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, LinearMap.submoduleMap_coe_apply, Orientation.map_eq_neg_iff_det_neg, MulSemiringActionHom.coe_fn_coe', TrivSqZeroExt.map_inr, ofColex_div, UniformFun.toFun_sub, Unitization.starLift_symm_apply_apply, Matrix.coe_vecMulLinear, Maximal.dual, SimpleGraph.Iso.sumComm_apply, nnnorm_toMul, Fin.appendHomeomorph_apply, RingHom.map_matrix_mul, Ideal.absNorm_eq_pow_inertiaDeg', Homeomorph.coe_prodCongr, TopCat.GlueData.ι_fromOpenSubsetsGlue_apply, MeasureTheory.MeasurePreserving.measure_preimage_emb, PiLp.nnnorm_eq_of_L2, Module.End.mem_invtSubmodule_iff_mapsTo, UniformOnFun.toFun_neg, DirectSum.mk_injective, MvPolynomial.optionEquivRight_C, Valuation.HasExtension.val_map_eq_iff, AddCon.coe_inj, Pi.evalRingHom_apply, Finsupp.mapRange.addEquiv_apply, UniformEquiv.coe_toEquiv, Cardinal.preAleph_nat, CliffordAlgebra.EquivEven.reverse_e0, Behrend.map_le_of_mem_box, Equiv.ofBijective_apply_symm_apply, RingEquiv.mopMatrix_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, MulEquiv.map_div, Matrix.kroneckerMap_reindex, Complex.coe_orthonormalBasisOneI, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, CStarMatrix.toCLM_injective, CommGrpCat.ext_iff, Nat.pairEquiv_apply, WeierstrassCurve.Affine.map_addY, CategoryTheory.Limits.Bicone.whisker_pt, ContinuousMap.mem_idealOfSet, WithZero.coe_expEquiv_apply, SlashInvariantForm.constℝ_toFun, OrderEmbedding.preimage_Iic, MeasureTheory.meas_eLpNormEssSup_lt, OrderHom.coe_antisymmetrization, MeasurableSet.exists_isCompact_isClosed_diff_lt, Part.Fix.approx_mem_approxChain, ContinuousLinearMap.isPositive_self_comp_adjoint, MvPolynomial.monomial_zero, Filter.map_inv', RingCon.unop_iff, ExteriorAlgebra.algebraMap_eq_one_iff, AddGroupSeminorm.ext_iff, toAdd_mul, MvPolynomial.map_mvPolynomial_eq_eval₂, CategoryTheory.Bicategory.conjugateEquiv_apply, Polynomial.monomial_mul_C, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField_assoc, ProbabilityTheory.cond_apply_self, PEquiv.single_apply_of_ne, ContinuousLinearMap.hasFPowerSeriesAt, LinearMap.trace_eq_matrix_trace_of_finset, Unitization.starLift_apply_apply, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, ModularGroup.sl_moeb, CategoryTheory.Adjunction.eq_homEquiv_apply, LinearMap.adjoint_toContinuousLinearMap, Polynomial.X_pow_eq_monomial, Finset.affineCombination_apply_const, Finsupp.curryLinearEquiv_symm_apply_apply, ContinuousMapZero.coe_add, Topology.WithLower.toLower_inj, MeasureTheory.MemLp.meas_ge_lt_top, BialgHom.coe_coe, Matrix.SeparatingLeft.toLinearMap₂', MeasureTheory.SimpleFunc.apply_mk, DirectSum.decompose_eq_mul_idempotent, WeierstrassCurve.integralModel_Δ_eq, AddAutAdditive_symm_apply_symm_apply, Homeomorph.isPreconnected_preimage, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, FreeMonoid.toList_nil, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, OrderIso.bijective, Cardinal.toNat_apply_of_aleph0_le, MonomialOrder.degree_reduce_lt, LinearIsometryEquiv.coe_neg, Path.extend_symm_apply, MvPolynomial.eval_eval₂, LinearMap.rTensor_comp_flip_mk, MulActionHom.map_smul, IsLocalization.mk'_mul_cancel_left, ClassGroup.mk0_eq_one_iff, TensorProduct.dualDistrib_apply_comm, CategoryTheory.Iso.conj_pow, Affine.Simplex.orthogonalProjectionSpan_eq_point, Polynomial.trunc_toLaurent, LinearMap.BilinForm.IsAlt.eq_of_add_add_eq_zero, MeasureTheory.FinStronglyMeasurable.tendsto_approx, TopologicalSpace.Opens.comap_comap, Padic.addValuation.apply, Archimedean.embedReal_apply, AddOpposite.opAddEquiv_apply, Polynomial.toAddCircle_X_pow_eq_fourier, Matroid.Indep.exists_eq_image_of_mapSetEmbedding, Homeomorph.sumArrowHomeomorphProdArrow_apply, Algebra.traceMatrix_localizationLocalization, Subalgebra.val_apply, Finsupp.llift_apply, StarMulEquiv.ofStarMonoidHom_symm_apply, SSet.prodStdSimplex.objEquiv_apply_fst, DirichletCharacter.LFunction_changeLevel, AddSubmonoid.LocalizationMap.injective_iff, MvPolynomial.totalDegree_eq, ExteriorAlgebra.liftAlternating_comp, NumberField.InfinitePlace.smul_apply, Algebra.algebraMap_intNorm, MeasureTheory.Integrable.simpleFunc_mul, isRight_finSumNatEquiv_symm_apply, ZeroHom.coe_sub, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, RingHom.rangeSRestrict_surjective, Subsemiring.centerCongr_symm_apply_coe, Unitary.linearIsometryEquiv_coe_apply, MonoidHom.fiberEquivKer_symm_apply, ArithmeticFunction.sigma_one_apply_prime_pow, WittVector.iterate_verschiebung_mul, LaurentSeries.ofPowerSeries_powerSeriesPart, MeasureTheory.isFiniteMeasure_iff, Representation.Coinvariants.mk_tmul_inv, ofDual_ofNat, MvPolynomial.rename_msymm, LinearIsometryEquiv.image_eq_preimage_symm, ContinuousMap.mem_nhds_iff, Cardinal.mk_image_embedding, InitialSeg.map_succ, AddMonoidHom.ker_eq_bot_iff, Homeomorph.residual_map_eq, Matrix.IsHermitian.eigenvectorUnitary_col_eq, Equiv.arrowCongr_apply, ClosureOperator.conjBy_apply, LinearEquiv.coe_symm_toEquiv, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, CategoryTheory.Equivalence.toOrderIso_apply, Algebra.isIntegral_trace, LieHom.quotKerEquivRange_toFun, AddChar.sum_eq_ite, LDL.lowerInv_eq_gramSchmidtBasis, AddSubmonoid.LocalizationMap.mk'_spec', wbtw_lineMap_iff, MvPolynomial.eval₂_id, iSup_partialSups_eq, SeparatingDual.exists_eq_one, LinearEquiv.conj_refl, CharacterModule.curry_apply_apply, AlternatingMap.neg_apply, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, CategoryTheory.MonObj.ofRepresentableBy_one, ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq, IsometryEquiv.constVSub_symm_apply, Quiver.starEquivCostar_apply_fst, AddSubmonoid.LocalizationMap.ofAddEquivOfLocalizations_eq_iff_eq, Ideal.quotientEquivAlg_mk, Ordinal.toNimber_min, AlgHom.apply_mem_spectrum, MeasureTheory.Measure.hausdorffMeasure_le_liminf_sum, AddMonoidAlgebra.single_apply, LinearMap.map_sub₂, Finset.singletonMonoidHom_apply, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_snd, Polynomial.scaleRoots_eval₂_mul, ZeroHom.comp_apply, mulRothNumber_map_mul_left, fderiv_eq_deriv_mul, Path.Homotopy.target, MeasureTheory.measure_inter_add_diff₀, BialgHom.coe_fn_injective, CuspFormClass.zero_at_cusps, AlgHom.coe_range, CategoryTheory.Iso.conjAut_mul, RingHom.toRatAlgHom_apply, HahnSeries.SummableFamily.sub_apply, AddSubsemigroup.mem_map_equiv, ProbabilityTheory.Kernel.swap_apply, Polynomial.le_gaussNorm, CategoryTheory.ConcreteCategory.comp_apply, IsAlgebraic.algHom, Submodule.starProjection_inner_eq_zero, nndist_right_lineMap, Prod.Lex.toLexOrderHom_coe, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, RCLike.norm_sq_eq_def_ax, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, UniformOnFun.lipschitzWith_one_ofFun_toFun, Polynomial.as_sum_range_C_mul_X_pow', AlgebraicGeometry.Scheme.exists_germ_injective, MeasureTheory.Measure.haar.addHaarContent_outerMeasure_closure_pos, OrderHom.prodIso_apply, Matrix.sum_cramer, Module.Basis.det_isUnitSMul, LaurentSeries.single_order_mul_powerSeriesPart, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, LocallyConstant.eval_apply, ProbabilityTheory.Kernel.measurable_densityProcess_countableFiltration_aux, FreeGroup.lift_apply_of, ContinuousOpenMap.comp_apply, Orientation.abs_volumeForm_apply_of_orthonormal, AddMonoidHom.addSubgroupOf_range_eq_of_le, Preord.inv_hom_apply, SemidirectProduct.inl_left_mul_inr_right, ContinuousLinearMap.toSesqForm_apply_coe, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefree, coe_algebraMapCLM, CommGrpCat.coe_comp, signedDist_linear_apply_apply, Nat.factorization_factorial, AddAction.map_stabilizer_le, Algebra.TensorProduct.assoc_tmul, MulAut.smul_def, Homeomorph.continuous, mem_vectorSpan_iff_eq_weightedVSub, SlashInvariantForm.one_coe_eq_one, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, UniformFun.toFun_ofFun, RootPairing.mapsTo_reflection_root, CategoryTheory.Limits.Concrete.productEquiv_symm_apply_π, ContinuousMultilinearMap.curry0_apply, MulHom.coe_prod, Prod.Lex.toLex_le_toLex', ProbabilityTheory.Kernel.deterministic_prod_apply', Function.FromTypes.curry_two_eq_curry, SpecialLinearGroup.mem_range_toGeneralLinearGroup_iff, Module.Basis.toDualEquiv_apply, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_pointReflection_center_right, Complex.cos_conj, Module.End.mapsTo_genEigenspace_of_comm, CliffordAlgebra.changeFormAux_changeFormAux, HahnSeries.support_abs, CategoryTheory.Functor.CorepresentableBy.equivOfIsoObj_apply, Function.Exact.iff_of_ladder_linearEquiv, Fintype.bilinearCombination_apply_single, MonoidWithZeroHom.fst_mono, ofColex_add, ProbabilityTheory.Kernel.coe_zero, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, LinearMap.BilinForm.nondegenerate_toMatrix_iff, Matrix.derivative_det_one_add_X_smul, Nucleus.map_himp_le, LinearMap.coe_inr, Polynomial.integralNormalization_C, MeasureTheory.measure_smul_eq_zero_iff, exteriorPower.ιMulti_span_of_span, SimpleGraph.card_edgeFinset_map, DirectSum.IsInternal.collectedBasis_mem, LieModuleEquiv.refl_apply, SemilatSupCat.Iso.mk_inv_toFun, LieHom.one_apply, Circle.exp_two_pi_mul_int, OrderAddMonoidHom.addCommute_inlₗ_inrₗ, Matrix.SpecialLinearGroup.coe_int_neg, CategoryTheory.FinCategory.asTypeToObjAsType_map, NormedAddGroupHom.smul_apply, MeasureTheory.FiniteMeasure.restrict_apply_measure, IsGroupLikeElem.antipode_antipode, AddSubsemigroup.coe_toSubsemigroup_apply, PMF.toOuterMeasure_ofFinset_apply, LinearMap.coe_smul, PiLp.coe_continuousLinearEquiv, Con.mkMulHom_apply, LieAlgebra.IsKilling.apply_coroot_eq_cast', Polynomial.rootMultiplicity_X_sub_C_pow, Ideal.range_mul', EMetric.exists_continuous_nnreal_forall_closedBall_subset, AddLocalization.mkOrderEmbedding_apply, IsometryEquiv.image_emetric_ball, PositiveLinearMap.coe_toLinearMap, Module.Basis.eq_of_apply_eq_iff, AlgebraicGeometry.IsOpenImmersion.iff_isIso_stalkMap, QuadraticAlgebra.algebraMap_re, HasFDerivAt.multilinear_comp, Homotopy.prevD_succ_cochainComplex, RelHom.one_apply, Polynomial.resultant_X_sub_C_right, CliffordAlgebra.ι_mul_ι_comm, MonoidAlgebra.opRingEquiv_symm_apply, ContinuousMultilinearMap.linearDeriv_apply, MonoidAlgebra.of_mem_span_of_iff, gelfandTransform_bijective, AlgHom.coe_id, Polynomial.differentiableOn_aeval, Monovary.dual_left, AddEquiv.comp_symm_eq, NormedSpace.expSeries_apply_eq_div', SchwartzMap.integral_bilin_fourierIntegral_eq, LinearEquiv.map_zero, IsLocalRing.residue_eq_zero_iff, PowerSeries.binomialSeries_coeff, Equiv.Perm.IsThreeCycle.support_eq_iff_mem_support, Equiv.Perm.viaFintypeEmbedding_sign, MeasureTheory.tendsto_measure_biInter_gt, LocallyConstant.coe_zero, Finset.Colex.lt_iff_exists_forall_lt, DegLex.forall_iff, sbtw_iff_left_ne_and_right_mem_image_Ioi, MeasureTheory.Measure.comap_preimage, Geometry.SimplicialComplex.convexHull_inter_convexHull, Matrix.updateCol_reindex, IsometryClass.ediam_range, RootPairing.root'_coroot_eq_pairing, StrictMono.orderIso_apply, dotProductEquiv_apply_apply, AlgebraicGeometry.Scheme.Cover.instIsIsoCommRingCatStalkMapFromGlued, Finsupp.erase_apply, Real.fourierIntegral_continuousMultilinearMap_apply, BialgEquiv.congr_arg, AddGroupNorm.coe_sup, AddHom.subsemigroupMap_surjective, MeasureTheory.Measure.pi_hyperplane, MvPolynomial.degreeOf_coeff_finSuccEquiv, NNReal.sqrt_zero, MvPowerSeries.isUnit_iff_constantCoeff, MeasureTheory.inducedOuterMeasure_eq', DirectSum.decompose_of_mem, LinearMap.rank_diagonal, MultilinearMap.map_piecewise_sub_map_piecewise, LinearPMap.adjointAux_unique, Finsupp.mapRange.addMonoidHom_apply, Multiset.toFinsupp_sum_eq, Affine.Simplex.ExcenterExists.excenter_map, Con.refl, LinearMap.ker_localizedMap_eq_localized₀_ker, QuotSMulTop.map_comp_mkQ, SupBotHom.coe_toBotHom, ContinuousAffineMap.decomp, Polynomial.derivative_rootMultiplicity_of_root, NumberField.RingOfIntegers.withValEquiv_symm_apply, RootPairing.injOn_dualMap_subtype_span_root_coroot, CategoryTheory.PreGaloisCategory.autMapHom_apply, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Equiv.pprodEquivProd_apply, NumberField.mixedEmbedding.polarSpaceCoord_target, AddCircle.scaled_exp_map_periodic, AffineMap.comp_apply, DomMulAct.map_mk_symm_nhds, ContinuousMap.concatCM_left, OnePoint.isZeroAt_iff_exists_SL2Z, AlgEquiv.coe_refl, LinearIsometryEquiv.adjoint_eq_symm, Equiv.transPartialEquiv_symm_apply, LightProfinite.proj_comp_transitionMapLE', FundamentalGroupoid.equiv_apply, MvPolynomial.mem_pow_idealOfVars_iff, Matrix.comp_single_single, SemistandardYoungTableau.zeros, NumberField.mixedEmbedding.negAt_apply_snd, Int.normalize_of_nonneg, Semigrp.hom_inv_apply, TopologicalSpace.IsOpenCover.comap, RatFunc.liftMonoidWithZeroHom_apply_div', DomMulAct.comap_mk_nhds, Equiv.mapMatrix_apply, transcendental_iff_injective, TensorProduct.directLimitRight_tmul_of, TopCat.Presheaf.germ_res_apply, ContinuousMapZero.ext_iff, MeasureTheory.ProbabilityMeasure.continuous_lintegral_boundedContinuousFunction, AffineEquiv.apply_lineMap, GaussianInt.toComplex_div_re, VertexOperator.ncoeff_smul, LinearMap.sub_mem_ker_iff, MulEquiv.coe_submonoidMap_apply, MeasureTheory.SimpleFunc.piecewise_apply, MeasureTheory.measure_lt_one_eq_integral_div_gamma, Algebra.TensorProduct.map_tmul, Ideal.finsuppTotal_apply, bijective_iterateFrobenius, zmultiples_equiv_zmultiples_apply, WittVector.verschiebung_nonzero, ContinuousAlternatingMap.toAlternatingMap_curryLeft, AddCircle.equivIco_coe_eq, MulEquiv.prodMultiplicative_symm_apply, ProbabilityTheory.cond_pos_of_inter_ne_zero, Multiset.toDFinsupp_apply, CategoryTheory.Iso.homFromEquiv_symm_apply, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, ContinuousMap.tprod_apply, MulEquiv.val_piUnits_symm_apply, LinearMap.smul_apply, AlgHom.op_apply_apply, MeasureTheory.meas_le_ae_eq_meas_lt, LinearMap.rTensor_tmul, nndist_toMul, MeasureTheory.Measure.forall_measure_inter_spanningSets_eq_zero, nnnorm_algebraMap_nnreal, Finsupp.ext_iff', ContinuousAffineEquiv.symm_apply_apply, ContinuousOrderHom.coe_comp, NonUnitalStarAlgHom.nnnorm_apply_le, AlternatingMap.map_basis_eq_zero_iff, Orientation.neg_rotation_neg_pi_div_two, LinearMap.separatingRight_toMatrix₂'_iff, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply, Complex.conj_rootsOfUnity, FreeAddMonoid.vadd_def, Matrix.toEuclideanLin_apply, MeasureTheory.Measure.toENNRealVectorMeasure_apply, SlashInvariantForm.smul_apply, TwoSidedIdeal.orderIsoMatrix_apply_ringCon_r, BoundedContinuousFunction.isEmbedding_coeFn, DFinsupp.lt_def, Equiv.prodUnique_symm_apply, Valuation.ext_iff, LieSubmodule.Quotient.toEnd_comp_mk', IsLeast.dual, Equiv.Perm.sameCycle_inv_apply_left, CategoryTheory.TwoSquare.equivNatTrans_apply, EquicontinuousOn.tendsto_uniformOnFun_iff_pi, AlgEquiv.toAlgHom_op, algebraMap_pos, Bornology.IsVonNBounded.image_multilinear', OrderMonoidWithZeroHom.comp_apply, Submodule.biSup_eq_range_dfinsupp_lsum, Quaternion.imI_fst_dualNumberEquiv, CompactlySupportedContinuousMap.star_apply, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, Rep.resCoindAdjunction_unit_app_hom_hom, Equiv.Perm.ofSubtype_apply_mem_iff_mem, ContinuousAffineMap.zero_apply, Polynomial.taylor_injective, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, AffineBasis.convexHull_eq_nonneg_coord, iteratedDerivWithin_eq_iteratedFDerivWithin, Equiv.instIdempotentOpCoeForallForallArrowCongr, CategoryTheory.coyonedaEquiv_comp, CategoryTheory.uliftYonedaEquiv_symm_apply_app, ContinuousLinearMap.toLinearMap₁₂_apply, FiniteField.coe_frobeniusAlgEquivOfAlgebraic, WithAbs.equiv_algebraMap_apply, AffineIsometry.id_apply, AddMonoidHom.fiberEquiv_symm_apply, partialSups_const_mul, groupCohomology.mem_cocycles₁_def, Equiv.ofLeftInverse_symm_apply, LatticeHom.subtypeVal_coe, Equiv.symm_apply_apply, TensorProduct.toIntegralClosure_bijective_of_smooth, Polynomial.iterate_derivative_mul_X, LocallyConstant.evalRingHom_apply, WittVector.mapFun.sub, ContinuousAlternatingMap.piEquiv_apply, MvPolynomial.rename_id_apply, MeasureTheory.measure_neg_vadd_inter, Algebra.toMatrix_lmul_eq, OrderIso.prodAssoc_apply, ContinuousLinearMap.sSup_sphere_eq_nnnorm, OrderHom.snd_coe, RootPairing.Equiv.weightHom_toLinearMap, val_unitsCentralizerEquiv_apply_coe, SymAlg.unsym_zero, Filter.tendsto_prodAssoc_symm, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, Equiv.Perm.sign_symm, VectorFourier.fourierPowSMulRight_eq_comp, SlashInvariantForm.coe_smulℝ, RCLike.intCast_re, PEquiv.trans_symm_eq_iff_forall_isSome, Complex.measurableEquivPi_apply, Matrix.permMatrixHom_apply, MeasureTheory.measure_univ_le_add_compl, ContinuousAlternatingMap.le_opNNNorm, Matrix.addMonoidHomMulLeft_apply, ProbabilityTheory.Kernel.isIrreducible_iff, monotone_dual_iff, MeasureTheory.Measure.addHaarMeasure_closure_self, ContinuousLinearEquiv.symm_trans_apply, CategoryTheory.Presheaf.isLocallyInjective_iff_equalizerSieve_mem_imp, AddChar.sub_apply, MeasureTheory.charFunDual_eq_charFun_map_one, Fin.orderIsoSingleton_apply, DirectSum.coe_of_mul_apply_aux, NonUnitalRingHom.coe_prodMap, Polynomial.update_eq_add_sub_coeff, RootPairing.restrictScalars_pairing, AddMonoidHom.rangeRestrict_surjective, Polynomial.monic_finprod_X_sub_C, Polynomial.degree_C_mul_of_mul_ne_zero, Ordinal.range_omega, EuclideanGeometry.orthogonalProjection_map, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_eq_iff, MeasureTheory.SimpleFunc.iSup_coe_eapprox, WithSeminorms.tendsto_nhds', LinearMap.toMatrixAlgEquiv'_id, RCLike.im_eq_zero_iff_isSelfAdjoint, isAdjointPair_toLinearMap₂, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Cubic.discr_eq_prod_three_roots, HahnSeries.single.linearMap_apply, ContinuousMultilinearMap.le_of_opNNNorm_le, MvPolynomial.constantCoeff_C, OrderDual.isBounded_preimage_ofDual, MvPowerSeries.monomial_mem_nonzeroDivisorsLeft, AddConstMapClass.map_nat, Condensed.epi_iff_surjective_on_stonean, IsCyclotomicExtension.aeval_zeta, LinearEquiv.congrLeft_symm_apply, Equiv.emptySum_apply_inr, NonUnitalRingHom.mem_srange, MvPowerSeries.expand_mul, MvPowerSeries.smul_eq_C_mul, LinearEquiv.conjAlgEquiv_apply, SpecialLinearGroup.centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq, AlgebraicGeometry.Scheme.Hom.toImage_app_injective, ContinuousMap.piEquiv_symm_apply, CliffordAlgebra.ι_sq_scalar, cfcHom_isClosedEmbedding, HeytAlg.Iso.mk_inv, AlgebraNormClass.map_smul_eq_mul, LieModule.Cohomology.d₂₃_apply, MeasureTheory.SimpleFunc.restrict_lintegral, Equiv.altCongrHom_apply_coe, CategoryTheory.conjugateEquiv_symm_apply_app, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, Representation.Coinvariants.le_comap_ker, Seminorm.pullback_apply, PrincipalSeg.le_iff_le, InitialSeg.isNormal, Matrix.uniqueRingEquiv_apply, MulAction.toPerm_apply, unitInterval.symmMeasurableEquiv_apply, LinearMap.id_apply, CommGrpCat.hom_inv_apply, mfderivWithin_projIcc_one, StieltjesFunction.measure_singleton, RootPairing.zero_notMem_range_coroot, MeasureTheory.tendsto_measure_iUnion_atTop, Ideal.mem_map_of_mem, RingEquiv.coe_toMulEquiv, ext'_iff, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, CompletelyPositiveMapClass.map_cstarMatrix_nonneg', NumberField.Units.dirichletUnitTheorem.seq_next, ModuleCat.endRingEquiv_symm_apply_hom, LinearMap.BilinForm.sub_left, Fin.cycleIcc_of_last, CuspForm.coe_trace, Quaternion.algebraMap_def, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, Monoid.CoprodI.inv_def, ContinuousAlternatingMap.hasSum_eval, Algebra.intTrace_eq_of_isLocalization, intervalIntegral.integral_pos_iff_support_of_nonneg_ae', TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply, Real.Polynomial.isRoot_cos_pi_div_five, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, Equiv.prodPUnit_apply, Polynomial.coe_C, RingHom.mem_range, BddOrd.coe_id, ContinuousMap.continuous_iff_continuous_uniformOnFun, MvPowerSeries.trunc_C, Finsupp.notMem_support_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, MulHom.mul_apply, RingEquiv.map_mul, addRightEmbedding_apply, SimpleGraph.Iso.sumBoxProdDistrib_apply, AddCon.coe_iInf, Multiset.map_noncommProd_aux, DFinsupp.subtypeDomain_def, Diffeomorph.coe_coe, Equiv.Perm.congr_arg, NumberField.mixedEmbedding.convexBodyLT_mem, TensorProduct.leftComm_tmul, FreeAddMonoid.mem_map, Zsqrtd.hom_ext_iff, exteriorPower.alternatingMapLinearEquiv_symm_map, NumberField.InfinitePlace.coe_apply, TopCat.pullback_topology, Fin.cycleIcc_of_gt, WeierstrassCurve.Affine.C_addPolynomial, GroupExtension.Equiv.symm_symm_apply, SetSemiring.down_one, inner_mul_inner_self_le, Ideal.relNorm_top, MeasureTheory.Measure.setIntegral_condKernel, ArithmeticFunction.moebius_sq, LinearEquiv.symm_apply_eq, PowerSeries.coeff_subst, Polynomial.sumIDeriv_eq_self_add, toDual_zero, MulRingSeminorm.apply_one, Ideal.Quotient.factorₐ_apply_mk, MvPolynomial.map_map, Con.ker_apply, Submodule.span_range_inclusion_restrictScalars_eq_top, coe_equiv_lpPiLp_symm, Algebra.IsAlgebraic.algHom_bijective, OrderRingHom.coe_coe_ringHom, MeasureTheory.union_ae_eq_right, ContinuousMap.comp_const, TopCat.Presheaf.germ_stalkPullbackInv_assoc, Matrix.vandermonde_succ, TensorProduct.comm_comm, MeasurableEquiv.self_comp_symm, MeasureTheory.SimpleFunc.integral_eq_sum_filter, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, SimpleGraph.Iso.symm_apply_reachable, Finsupp.sumFinsuppAddEquivProdFinsupp_symm_apply, Rat.padicValuation_self, AddUnits.coe_unop_opEquiv, LinearMap.restrictScalars_apply, Algebra.trace_algebraMap, Polynomial.self_sub_monomial_natDegree_leadingCoeff, Abelianization.mk_eq_of, AffineMap.map_vadd', OrderIso.infIrredUpperSet_symm_apply, OrderHom.iInf_apply, commute_lmul_rmul, Polynomial.bernoulli_generating_function, NumberField.Units.coe_mul, AlgHom.ext_iff, Abelianization.map_map_apply, PEquiv.map_toMatrix, NonemptyInterval.dual_top, Filter.pureMonoidHom_apply, LinearMap.det_baseChange, BoxIntegral.Prepartition.card_filter_mem_Icc_le, BoundedOrderHom.comp_apply, IsCusp.of_isFiniteRelIndex_conj, CategoryTheory.nerve.homEquiv_apply, Polynomial.natDegree_finset_prod_X_sub_C_eq_card, ConjAct.toConjAct_zero, BoundedLatticeHom.symm_dual_comp, AddChar.map_neg_eq_inv, RCLike.conjCLE_apply, Polynomial.support_C_mul_X', Valuation.ltIdeal_v_le_of_mem, LinearIsometry.preimage_closedBall, UniformOnFun.isEmbedding_toFun_finite, Preord.hom_inv_apply, OrderIso.map_inf, Rep.homEquiv_apply_hom, AddChar.map_zsmul_eq_zpow, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, Magma.AssocQuotient.lift_comp_of', SchwartzMap.eLpNorm_lt_top, Finsupp.mapRange_neg', QuadraticForm.tmul_tensorMap_apply, Affine.Simplex.circumradius_restrict, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, HahnEmbedding.Partial.truncLT_mem_range_extendFun, MulAutMultiplicative_symm_apply_apply, RingHom.congr_fun, ProbabilityTheory.integral_stieltjesOfMeasurableRat, PointwiseConvergenceCLM.postcomp_apply, dite_comp_equiv_update, List.SortedLT.coe_getIso_apply, QuadraticMap.polar_neg_left, segment_subset_convexHull, Semigrp.inv_hom_apply, MulAut.mul_apply, MvPolynomial.degrees_def, ContMDiffAt.mfderiv_apply, MeasureTheory.MemLp.exists_boundedContinuous_integral_rpow_sub_le, toDegLex_ofDegLex, MeasurableSet.measure_eq_iSup_isCompact_of_ne_top, PseudoMetric.IsUltra.isTransitiveRel_closedBall, finCongr_symm_apply_coe, DirichletCharacter.zetaMul_prime_pow_nonneg, Polynomial.iterate_derivative_X, ModN.basis_apply_eq_mkQ, CategoryTheory.conjugateEquiv_apply_app, UniformEquiv.continuous_symm, TopologicalSpace.Opens.complOrderIso_symm_apply, Equiv.Perm.SameCycle.symm_apply_right, ProbabilityTheory.condExp_ae_eq_integral_condDistrib, Part.Fix.approx_le_fix, isExtrFilter_dual_iff, MvPolynomial.nonempty_support_finSuccEquiv, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, HahnSeries.single_zero_intCast, ValuationSubring.subtype_injective, ContinuousLinearMap.map_sub, Algebra.TensorProduct.algEquivIncludeRange_symm_tmul, map_dvd_iff, MulEquiv.opOp_symm_apply, FirstOrder.Language.Substructure.coe_comap, OrderIso.map_csSup_of_directedOn, antivaryOn_toDual_left, OrderIso.image_setOf_maximal, Module.Flat.out, ContinuousAlgHom.map_smul, Unitization.nnnorm_def, RelHom.coeFn_mk, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp, HasStrictFDerivAt.abs, MeasureTheory.Measure.nullMeasurableSet_prod, RatFunc.coe_X, MonoidAlgebra.lift_symm_apply, ExteriorAlgebra.ιMulti_succ_apply, FirstOrder.Language.DirectLimit.lift_unique, NumberField.InfinitePlace.comp_of_comap_eq, AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset, ContinuousLinearMap.exists_lt_apply_of_lt_opNNNorm, MeasureTheory.measurePreserving_finTwoArrow_vec, ProbabilityTheory.Kernel.map_apply', IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two, HahnSeries.single_mul_single, Equiv.equivCongr_refl_left, AddMonoidAlgebra.uniqueRingEquiv_apply, IsPurelyInseparable.iterateFrobenius_algebraMap, AddSubgroup.mem_iff_toAddUnits_mem_addUnits, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, nndist_left_lineMap, PrincipalSeg.mem_range_of_rel_top, Finsupp.fun_support_eq, Matrix.liftLinear_singleLinearMap, ContinuousLinearMap.le_opNorm, IsUltrametricDist.invariantExtension_extends, CFC.rpow_algebraMap, LieModule.Cohomology.d₁₂_apply_apply, RCLike.mul_im_ax, Affine.Simplex.medial_restrict, convexHull_toCone_eq_sInf, Function.locallyFinsuppWithin.logCounting_eval_zero, Finset.Ioc_ofDual, Polynomial.eval₂_ofFinsupp, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, SimpleGraph.Subgraph.comap_verts, WittVector.frobenius_isPoly, DFinsupp.notMem_support_iff, Polynomial.eval₂_monomial, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, AddActionSemiHomClass.map_vaddₛₗ, Multiset.consEquiv_symm_some, AddMonoidHom.map_trace, LinearMap.smulRight_apply, LocallyConstant.evalMonoidHom_apply, Ideal.toTwoSided_asIdeal, BialgEquiv.refl_symm_apply, LatticeHom.subtypeVal_apply, Module.AEval'.X_smul_of, Finsupp.univ_sum_single_apply', Fin.consEquivL_apply, AdjoinRoot.smul_mk, ContinuousMulEquiv.eq_comp_symm, Module.Relations.Solution.directSumEquiv_apply_var, AffineIsometry.coe_mul, LinearMap.isUnit_iff_isUnit_det, SupBotHomClass.map_bot, Function.HasTemperateGrowth.toTemperedDistribution_apply, Euclidean.closedBall_eq_image, List.getEquivOfForallCountEqOne_apply, PowerSeries.map_cos, GroupExtension.Equiv.map_inl, MeasureTheory.Measure.setLIntegral_rnDeriv, DifferentiableAt.continuousAlternatingMap_apply_const, Ordinal.cof_preOmega, ContinuousLinearMap.flipMultilinear_apply_apply, Submodule.equivSubtypeMap_symm_apply, DirectSum.decompose_symm_sub, DomAddAct.isOpenEmbedding_mk_symm, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, CircleDeg1Lift.strictMono_iff_injective, OrderIso.refl_apply, Order.pred_ofAdd, ContinuousMultilinearMap.uncurrySum_apply, AddCommGrpCat.coe_comp, ContinuousMultilinearMap.map_sum, AlgebraicGeometry.AffineSpace.homOverEquiv_symm_apply_coe, Filter.Tendsto.coeFun, NumberField.FinitePlace.prod_eq_inv_abs_norm_int, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, Matrix.submatrix_single_equiv, Orthonormal.inner_left_fintype, SubMulAction.map_ofFixingSubgroupUnion_def, MvPolynomial.pderiv_rename, NumberField.mixedEmbedding.negAt_preimage, AdjoinRoot.algHom_ext'_iff, PowerSeries.coeff_coe, Valued.isClopen_ball, Submodule.botEquivPUnit_apply, InnerProductSpace.Core.norm_eq_sqrt_re_inner, IsIntegrallyClosedIn.exists_algebraMap_eq_of_pow_mem_subalgebra, MeasureTheory.piContent_cylinder, LieSubmodule.incl_apply, CochainComplex.fromSingle₀Equiv_apply_coe, NonUnitalRingHom.mem_srange_self, LieModule.mem_posFittingCompOf, sigmaFinsuppAddEquivDFinsupp_symm_apply, Polynomial.coe_compRingHom_apply, MulEquiv.monoidHomCongrLeftEquiv_apply, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, Balanced.convexHull, Algebra.Presentation.comp_relation_inr, MonoidHom.map_frobeniusEquiv_symm, MonoidHom.map_iterate_frobenius, OrderEmbedding.preimage_Ioc, Finset.Colex.toColex_strictMono, Topology.WithLawson.toLawson_inj, IsometryEquiv.divLeft_apply, FunctionField.inftyValuation.polynomial, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, MeasureTheory.Measure.map_apply, ContinuousMap.coev_apply, DirectSum.Gmodule.of_smul_of, AdjoinRoot.liftAlgHom_of, CongruenceSubgroup.exists_Gamma_le_conj, Matrix.liftLinear_comp_singleLinearMap, InfTopHom.dual_id, AffineBasis.coord_apply, Polynomial.pow_rootMultiplicity_not_dvd, MonoidAlgebra.uniqueRingEquiv_apply, Quaternion.normSq_smul, LatticeHom.id_apply, ofDual_hnot, Algebra.TensorProduct.leftComm_tmul, TotallyDisconnectedSpace.continuousMapEquivOfConnectedSpace_symm_apply_apply, LinearMap.ofIsComplProd_apply, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, LinearMap.mul_apply', SemimoduleCat.MonoidalCategory.tensorHom_tmul, Ideal.relNorm_eq_pow_of_isPrime_isGalois, LocalizedModule.divBy_mul_by, IsFractionRing.algHom_commutes, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, Finsupp.basis_repr, exists_continuous_zero_one_of_isClosed, ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_apply, Matrix.toBilin_apply, IsLocalRing.basisQuotient_repr, FormalMultilinearSeries.comp_coeff_zero, LieHom.mem_range_self, AdjoinRoot.evalEval_apply, MeasureTheory.addContent_diff_of_ne_top, Ideal.absNorm_eq_pow_inertiaDeg_of_liesOver, MeasureTheory.SimpleFunc.mem_range, CategoryTheory.frobeniusMorphism_mate, LinearMap.toMatrix₂'_compl₁₂, QuadraticAlgebra.omega_mul_coe_mul_mk, Equiv.optionSubtype_symm_apply_apply_coe, DilationEquiv.coe_one, FirstOrder.Language.Formula.equivSentence_not, groupCohomology.mapCocycles₂_comp_i_apply, NonemptyFinLinOrd.epi_iff_surjective, Function.update_updateFinset, AddMonoidAlgebra.opRingEquiv_symm_single, Chebyshev.psi_sub_theta_eq_sum_not_prime, ValuativeRel.ValueGroupWithZero.embed_strictMono, exists_continuous_forall_mem_convex_of_local_const, ModularForm.coe_neg, CommAlgCat.ofHom_apply, CuspForm.coeHom_apply, Valuation.IsEquiv.pos_iff, Homeomorph.measurableEmbedding, PowerSeries.constantCoeff_X, Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac_assoc, SchwartzMap.integral_sesq_fourier_eq, Module.Relations.surjective_toQuotient, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MvPolynomial.monomial_eq_monomial_iff, LinearEquiv.det_baseChange, CompactlySupportedContinuousMap.sub_apply, Metric.Snowflaking.ofSnowflaking_comp_toSnowflaking, zmultiplesAddHom_symm_apply, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, NormedAddGroupHom.add_apply, DFinsupp.equivProdDFinsupp_apply, BoundedContinuousFunction.coe_toContinuousMapStarₐ, MonoidAlgebra.support_gen_of_gen', MeasureTheory.aestronglyMeasurable_condExpL2, DualNumber.lift_apply_eps, gaussSum_mul, cfcL_integrable, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, modularCyclotomicCharacter.spec, algebraicIndependent_empty_iff, Ideal.absNorm_mem, LocallyConstant.coe_sub, subset_absConvexHull, Polynomial.derivative'_apply, AdjoinRoot.Minpoly.toAdjoin.surjective, ContinuousMap.HomotopyWith.apply_one, BialgEquiv.ext_iff, DoubleCentralizer.norm_def', Additive.toMul_le, AlternatingMap.ext_ring_iff, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, AddEquiv.finsuppUnique_symm, ContinuousLinearMap.adjointAux_norm, Module.End.ringHomEndFinsupp_apply_apply, MeasureTheory.L1.setToL1_smul_left, ContinuousWithinAt.clm_apply_of_inCoordinates, LinearMap.prodEquiv_apply, RingCon.comapQuotientEquivOfSurj_symm_mk', Equiv.congr_fun, Representation.smul_ofModule_asModule, CStarMatrix.norm_def', isSquare_ofAdd_iff, coe_basisOfOrthonormalOfCardEqFinrank, Polynomial.constantCoeff_apply, Algebra.TensorProduct.includeRight_apply, QuadraticAlgebra.algebraMap_dvd_iff, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Subalgebra.LinearDisjoint.linearIndependent_left_op_of_flat, RCLike.abs_re_div_norm_le_one, SchwartzMap.memLp, Profinite.NobelingProof.Products.eval_πs', Polynomial.mem_support_derivative, MonomialOrder.toSyn_strictMono, Polynomial.aeval_X_pow, SetTheory.PGame.add_moveRight_inr, algebra_compatible_smul, MvPowerSeries.coeff_X, LinearMap.ker_eq_bot, Module.Relations.Solution.IsPresentation.linearMapEquiv_apply, IsChain.image_relEmbedding, ArithmeticFunction.moebius_apply_one, CommMonCat.coe_comp, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MDifferentiable.clm_bundle_apply₂, Equiv.sigmaAssocProd_apply_snd_fst, ContinuousLinearMap.fderiv, RestrictedProduct.mapAlong_apply, Quaternion.re_equivProd_symm_apply, MulEquiv.comp_symm_eq, Polynomial.map_mem_nthRootsFinset_one, PowerSeries.eq_shift_mul_X_pow_add_trunc, Equiv.setSubtypeComm_apply, IsometryEquiv.subRight_apply, MeasureTheory.Measure.addHaar_ball_mul, List.toFinsupp_apply_fin, Polynomial.monomial_pow, Representation.ofMulAction_single, AlgHom.commutes', RelEmbedding.preimage_apply, AddMonoidHom.addSubmonoidComap_apply_coe, AlgebraicGeometry.IsOpenImmersion.isOpen_range, NormedAddGroupHom.toFun_eq_coe, AddConstMap.toEnd_apply, SimpleGraph.hasseDualIso_apply, norm_sub_sq, Algebra.compHom_algebraMap_apply, AlgebraicGeometry.Scheme.affineOpenCover_idx, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, Module.Basis.toLin_toMatrix, CategoryTheory.Limits.Pi.reindex_hom_π_assoc, Fin.sign_cycleRange, LinearIsometryEquiv.inner_map_eq_flip, Module.Basis.mulOpposite_apply, Submodule.linearProjOfIsCompl_apply_right', ValueDistribution.logCounting_top, Finsupp.sum_equivMapDomain, ModuleCat.MonoidalCategory.associator_hom_apply, WithConv.symm_linearEquiv_apply, WeierstrassCurve.Projective.Point.toAffineAddEquiv_apply, toDual_sSup, AddMonoidAlgebra.opRingEquiv_symm_apply, MeasurableEquiv.comap_apply, MeasureTheory.Integrable.measure_ge_lt_top, groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂, ContinuousLinearEquiv.continuousAlternatingMapCongrLeftEquiv_apply, ContinuousAddMonoidHom.coe_comp, Equiv.Perm.sign_eq_prod_prod_Ioi, span_eq_top_localization_localization, IsFractionRing.injective, MeasureTheory.L1.setToL1_zero_left, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, Quaternion.linearIsometryEquivTuple_symm_apply, OrderMonoidIso.invFun_eq_symm, SetSemiring.down_mul, StarRingEquiv.leftInverse_symm, MvPolynomial.eval₂_mul_monomial, AlgEquiv.prodCongr_apply, CommBialgCat.isoEquivBialgEquiv_apply, padicNormE.eq_padic_norm', EuclideanGeometry.angle_orthogonalProjection_self, ContinuousLinearMap.toContinuousAffineMap_map_zero, Equiv.Perm.coe_mul, MvPolynomial.weightedHomogeneousComponent_zero, MultilinearMap.dfinsuppFamily_apply_toFun, LinearMap.flip_injective_iff₁, LieAlgebra.Extension.toKer_bracket, NormedAddGroupHom.extension_coe_to_fun, Matrix.toLinearEquivRight'OfInv_symm_apply, Polynomial.coeff_ofFinsupp, LocallyConstant.continuous, LieHom.map_add, RootPairing.Hom.id_weightMap_apply, WithCStarModule.equiv_symm_neg, QuasilinearOn.dual, Function.Embedding.arrowCongrLeft_apply, ContinuousAffineMap.coe_mk_contLinear_eq_linear, LatticeHom.dual_symm_apply_toFun, Equiv.Set.insert_symm_apply_inr, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, Complex.isometry_conj, StrictMono.dual_right, Polynomial.Bivariate.aveal_eq_map_swap, EuclideanGeometry.orthogonalProjection_apply_mem, ProbabilityTheory.Kernel.instNeZeroMeasureCoeSectROfProdMk, Equiv.pnatEquivNat_apply, ExteriorAlgebra.ιMulti_span, MultilinearMap.dfinsuppFamily_apply_support', ContinuousMap.norm_le_of_nonempty, SModEq.map, Polynomial.le_trailingDegree_C, MulEquiv.mapSubgroup_apply, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Localization.SmallShiftedHom.equiv_comp, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso, Derivation.add_apply, Pi.counit_eq_adjoint, CompleteLatticeHom.toFun_eq_coe, AddChar.neg_apply, ConvexCone.coe_map, WithLp.unitization_algebraMap, ArithmeticFunction.not_LSeriesSummable_moebius_at_one, Polynomial.eval_natCast_map, Module.FaithfullyFlat.lTensor_surjective_iff_surjective, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, Fintype.card_range, Rep.norm_comm_apply, LinearMap.BilinForm.coeFnAddMonoidHom_apply, CategoryTheory.Linear.leftComp_apply, PartialEquiv.transEquiv_symm_apply, Metric.Snowflaking.image_toSnowflaking_emetricClosedBall, MulEquiv.op_apply_symm_apply, AffineBasis.toMatrix_mul_toMatrix, ProbabilityTheory.covarianceBilin_apply_basisFun_self, PseudoMetric.IsUltra.isTrans_closedBall, FormalMultilinearSeries.ofScalars_apply_zero, HahnSeries.SummableFamily.hsum_smul_module, AlgebraicGeometry.LocallyRingedSpace.iso_inv_base_hom_base_apply, LinearMap.toMatrixOrthonormal_apply_apply, SlashInvariantForm.const_toFun, NumberField.mixedEmbedding.normAtPlace_apply_of_isReal, MulEquiv.map_finprod, RCLike.I_re_ax, Equiv.Perm.decomposeFin_symm_apply_one, MeasureTheory.condExpInd_nonneg, IsLocalizedModule.map_linearMap_of_isLocalization, DirectSum.sum_univ_of, RatFunc.coe_mapRingHom_eq_coe_map, RootPairing.Equiv.toEndUnit_inv, balancedHull_subset_convexHull_union_neg, AddHom.compLeft_apply, RootPairing.reflectionPerm_self, Submodule.coe_isComplEquivProj_symm_apply, Equiv.Perm.prod_Ioi_comp_eq_sign_mul_prod, UniformOnFun.toFun_div, CategoryTheory.Limits.Pi.reindex_hom_π, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, MonomialOrder.div_single, MvPolynomial.esymmAlgHomMonomial_single, AlgebraicGeometry.Scheme.Pullback.Triplet.snd_SpecTensorTo_apply, LinearEquiv.eq_symm_apply, MvPolynomial.homogeneousComponent_C_mul, ContinuousLinearMap.fpowerSeries_apply_zero, SupHom.id_apply, CliffordAlgebra.EquivEven.ι_eq_v_add_smul_e0, AlgEquiv.quotientBot_mk, AdicCompletion.pi_apply_coe, isAddRightRegular_toColex, Matrix.toLin'_mul_apply, LaurentPolynomial.eval₂_C_mul_T, MultilinearMap.fromDirectSumEquiv_symm_apply, LinOrd.hom_inv_apply, PositiveLinearMap.nsmul_apply, MultilinearMap.coe_inj, LaurentSeries.coe_algebraMap, Subsemigroup.mem_map, Orientation.areaForm_to_volumeForm, ProbabilityTheory.posterior_boolKernel_apply_true, UniformEquiv.trans_apply, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, DFinsupp.zipWith_def, affineHomeomorph_symm_apply, MvPowerSeries.expand_substAlgHom, MeasureTheory.isProbabilityMeasureSMul, MeasureTheory.measure_eq_top_of_subset_compl_sigmaFiniteSetWRT, Subsemiring.addEquivOp_apply_coe, VectorPrebundle.mk_contMDiffCoordChange, IsCompact.exists_open_superset_measure_lt_top', MulSemiringAction.toRingEquiv_apply, ContinuousLinearMap.mul_apply, Diffeomorph.mdifferentiableOn, SetTheory.PGame.mul_moveRight_inl, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, Equiv.toFun_as_coe, Polynomial.toLaurent_C_mul_T, AddChar.sum_apply, Topology.WithUpper.toUpper_ofUpper, LowerSet.coe_map, Monoid.Coprod.swap_injective, sSupHom.coe_bot, MeasureTheory.Measure.measure_toMeasurable_inter, Matrix.det_eval_matrixOfPolynomials_eq_det_vandermonde, DirectSum.lie_of_of_ne, MeasureTheory.OuterMeasure.map_apply, Nimber.toOrdinal_max, BddDistLat.coe_id, Homeomorph.coe_neg, IntermediateField.coe_inclusion, MeasurableEquiv.toLp_symm_apply, Polynomial.card_roots_le_derivative, PiTensorProduct.projectiveSeminorm_apply, extDerivWithin_constOfIsEmpty, AddCommGrpCat.forget₂_map, PadicInt.algebraMap_apply, Matrix.toLinearMapₛₗ₂'_single, MeasureTheory.SimpleFunc.coe_add, Multiset.lcm_singleton, LieAlgebra.bracket_ofTwoCocycle, CliffordAlgebra.ofBaseChange_toBaseChange, Complex.summable_conj, LinearMap.exact_subtype_mkQ, Representation.ofDistribMulAction_apply_apply, SheafOfModules.GeneratingSections.epi, UpperHalfPlane.denom_cocycle_σ, ProbabilityTheory.Kernel.parallelComp_apply_prod, Fin.orderIsoPair_zero, SeparationQuotient.liftNormedAddGroupHomEquiv_apply, ContinuousAffineMap.norm_def, LieSubmodule.toSubmodule_orderEmbedding_apply, MeasureTheory.OuterMeasure.le_pi, MvPolynomial.IsHomogeneous.map, FirstOrder.Language.Hom.ext_iff, Antivary.sum_mul_le_sum_comp_perm_mul, Specialization.toEquiv_inj, Convex.closure_subset_interior_image_homothety_of_one_lt, PowerSeries.support_expand_subset, Valued.exists_coe_eq_v, Polynomial.aevalTower_algebraMap, toLex_vadd', SymAlg.unsym_add, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, signedDist_le_dist, Algebra.span_le_adjoin, UniformEquiv.uniformContinuous_symm, AffineSubspace.coe_subtypeₐᵢ, Algebra.Extension.Cotangent.val_mk, Matrix.nondegenerate_toBilin'_iff, Finsupp.liftAddHom_comp_single, Polynomial.rootsExpandPowEquivRoots_apply, MvPolynomial.map_expand, Finset.coe_coeMonoidHom, Matrix.vec_of, Equiv.mulLeft₀_symm_apply, Ideal.Quotient.stabilizerHom_surjective, Representation.coinvariantsFinsuppLEquiv_apply, Algebra.Norm.Transitivity.comp_det_mul_pow, ContinuousLinearMap.IsInvertible.bijective, NNReal.algebraMap_eq_coe, NonUnitalSubsemiring.centerToMulOpposite_symm_apply_coe, ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, Finsupp.card_toMultiset, FirstOrder.Language.Substructure.subtype_apply, finSuccEquiv'_eq_some, ZMod.χ₄_int_mod_four, Homeomorph.piCongrLeft_apply_apply, Finset.Colex.mem_initSeg, AffineBasis.coe_vadd, Complex.log_inv_eq_ite, MeasureTheory.measure_lt_top, LieAlgebra.rank_le_natTrailingDegree_charpoly_ad, RCLike.re_nonneg_of_nonneg, Algebra.traceMatrix_of_matrix_vecMul, ContinuousLinearEquiv.coeFn_ofBijective, isConjRoot_of_algEquiv₂, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, RootPairing.Base.exists_root_eq_sum_nat_or_neg, HahnSeries.single_zero_mul_eq_smul, modularCyclotomicCharacter.toFun_spec', LinearMap.id_coe, Homeomorph.comap_cocompact, ValuativeRel.ValueGroupWithZero.mk_eq_div, RingEquiv.quotientBot_symm_mk, CategoryTheory.hom_id, HomogeneousLocalization.awayMap_mk, DilationEquiv.coe_symm_toHomeomorph, MonoidHom.toAdditive_symm_apply_apply, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, Convex.convexHull_union, Polynomial.Bivariate.swap_apply, PeriodPair.latticeBasis_zero, TopCat.pullbackFst_apply, Matrix.SpecialLinearGroup.isClosedEmbedding_toGL, DifferentialAlgebra.deriv_algebraMap, GroupSeminormClass.map_one_eq_zero, ContinuousOpenMap.toFun_eq_coe, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm_assoc, Finsupp.update_self, closedConvexHull_eq_closure_convexHull, MeasureTheory.Egorov.measure_inter_notConvergentSeq_eq_zero, Diffeomorph.coe_prodCongr, IncidenceAlgebra.neg_apply, Submodule.linearDisjoint_iff, NormedAddGroupHom.IsQuotient.norm_le, OrderIso.map_wcovBy, AddSubmonoid.LocalizationMap.mk'_eq_iff_eq', nndist_toDual, LinearMap.BilinForm.congr_comp, LinearMap.toMatrixAlgEquiv_apply, MvPolynomial.map_aeval, Matrix.updateRow_submatrix_equiv, TopologicalSpace.Opens.mem_comap, CentroidHom.centroid_eq_centralizer_mulLeftRight, Finset.mem_convexHull', InitialSeg.map_rel_iff, StarAlgHom.comp_apply, FreeMonoid.toList_ofList, Module.Basis.maximal, AddGroupNorm.le_def, StarConvex.affine_image, ZMod.LFunction_def_odd, LinearMap.IsSymmetric.coe_re_inner_self_apply, MulChar.star_apply, Lagrange.eq_interpolate_iff, LocallyConstant.congrRightₐ_apply_apply, Module.Basis.mem_center_iff, SkewMonoidAlgebra.comapSMul_def, TwoP.swapEquiv_functor_map_hom_toFun, cfcₙ_apply_mkD, PartialFun.Iso.mk_inv, Matrix.center_eq_range, CategoryTheory.Sieve.overEquiv_le_overEquiv_iff, MeasureTheory.IsFundamentalDomain.covolume_eq_volume, exists_hilbertBasis, HNNExtension.NormalWord.prod_cons, LinearIsometry.coe_one, Fin.cycleIcc.trans_left_one, RatFunc.coe_coe, Polynomial.derivative_eval, MonoidHom.isOfFinOrder, AddConstMapClass.map_sub_nat', AddChar.coe_compAddMonoidHom, OrderIso.mulRight₀_apply, Dilation.ediam_range, Pi.compRightL_apply, subset_convexHull, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, AddAction.orbitZMultiplesEquiv_symm_apply', ContinuousLinearMap.comp_memLp', Algebra.coe_algebraMap_ofSubsemiring, AddSemigrp.coe_id, SSet.iSup_skeleton, Ideal.quotEquivOfEq_mk, FreeNonUnitalNonAssocAlgebra.lift_unique, Algebra.traceForm_apply, PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, ContinuousLinearMap.map_smul_of_tower, SchwartzMap.fourier_lineDerivOp_eq, Valuation.unit_map_eq, QuadraticMap.ofPolar_apply, Finset.orderEmbOfFin_eq_orderEmbOfFin_iff, AddMonoidHom.id_apply, Complex.equivRealProd_symm_apply, WeierstrassCurve.Jacobian.map_negY, GradedTensorProduct.auxEquiv_one, Manifold.IsImmersionAtOfComplement.map_target_subset_target, Equiv.toOrderIsoSet_symm_apply, Algebra.TensorProduct.basis_repr_tmul, ContinuousMulEquiv.symm_apply_eq, IsAntichain.preimage_iso_iff, RingHom.rangeS_toSubmonoid, Lat.forget_map, cfcₙHom_id, LinearMap.BilinForm.apply_dualBasis_left, AddChar.wInner_cWeight_eq_zero_iff_ne, Sym.coe_equivNatSum_symm_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap, sigmaAntidiagonalEquivProd_symm_apply_snd, ContinuousLinearMapWOT.inducingFn_apply, DFinsupp.injective_pi_lapply, tangentBundle_model_space_coe_chartAt, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', ProbabilityTheory.avgRisk_le_mul', MvPolynomial.map_frobenius_expand, LindemannWeierstrass.exp_polynomial_approx, DirichletCharacter.norm_le_one, linearIndependent_monoidHom, alternatingGroup.normalClosure_swap_mul_swap_five, norm_iteratedFDerivWithin_clm_apply_const, IsometryEquiv.image_closedEBall, SubgroupClass.subtype_injective, Subgroup.coe_map, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, AffineEquiv.prodAssoc_symm_apply, IsometryEquiv.symm_apply_apply, CStarMatrix.inner_toCLM_conjTranspose_left, CircleDeg1Lift.floor_sub_le_translationNumber, QuadraticMap.ext_iff, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, RootPairing.reflection_apply_root', finprod_emb_domain, StandardEtalePair.homEquiv_apply_coe, Valuation.Integers.le_of_dvd, Module.exists_finite_presentation, toDual_eq_zero, LinearMap.toMatrix'_toLin', BoundedContinuousFunction.coe_nsmulRec, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atBot_zero, affineSpan_eq_affineSpan_lineMap_units, NumberField.FinitePlace.norm_embedding_eq, MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint, ModuleCat.MonoidalCategory.tensorHom_tmul, DFinsupp.le_iff', Polynomial.map_expand, PolynomialModule.monomial_smul_single, Convex.convexHull_subset_iff, Set.image_infs, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, Complex.normSq_mul, DFinsupp.coe_tsub, Derivation.leibniz_div, WittVector.mapFun.pow, ContinuousAlgEquiv.continuous, RootPairing.flipEquiv_apply, MultilinearMap.curryRight_apply, Cardinal.preAleph_le_aleph, lineMap_mono_endpoints, Ideal.injective_quotient_le_comap_map, ProbabilityTheory.Kernel.restrict_apply, Multiset.addHom_ext_iff, OrderEmbedding.coe_ofStrictMono, Polynomial.C_eq_zero, GrpWithZero.coe_id, AffineBasis.interior_convexHull, MeasureTheory.Measure.add_comp, Equiv.sumPiEquivProdPi_symm_apply, Fin.natAdd_castLEEmb_apply_val, Polynomial.dvd_comp_X_add_C_iff, IntermediateField.LinearDisjoint.trace_algebraMap, SimpleGraph.Embedding.map_adj_iff, MonoidAlgebra.mapDomainAddEquiv_single, groupHomology.d₂₁_single_inv_mul_ρ_add_single, Sum.Lex.inl_bot, Equiv.leftInverse_symm, LieModuleHom.mem_ker, Submodule.toLocalized₀_apply_coe, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_inv_apply, Polynomial.separable_X_pow_sub_C, Int.coe_castRingHom, QuadraticAlgebra.C_eq_algebraMap, SSet.nonDegenerateEquivOfIso_symm_apply_coe, MvPolynomial.weightedDecomposition.decompose'_apply, LightCondSet.topCatAdjunctionUnit_val_app_apply, Set.PartiallyWellOrderedOn.exists_monotone_subseq, LinearMap.add_apply, SymAlg.sym_add, AffineIndependent.comp_embedding, partialSups_add_one, FirstOrder.Language.Substructure.coe_inclusion, NonUnitalSubalgebra.iSupLift_of_mem, Equiv.Perm.support_swap_mul_eq, Subgroup.quotientCentralizerEmbedding_apply, RelIso.cast_apply, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, ValuativeExtension.mapValueGroupWithZero_mk, Module.mapEvalEquiv_apply, FinBddDistLat.hom_inv_apply, LinearMap.range_toAddSubmonoid, CategoryTheory.Subobject.symm_apply_mem_iff_mem_image, Finset.insertNone_eraseNone, OrderAddMonoidIso.coe_toEquiv_symm, ContinuousMultilinearMap.ext_ring_iff, OrderEmbedding.toOrderHom_coe, Polynomial.dvd_comp_C_mul_X_add_C_iff, Module.Basis.extendLe_subset, DirichletCharacter.mul_delta, Polynomial.mapEquiv_symm_apply, LieSubmodule.orderIsoMapComap_apply, MeasurableEquiv.funUnique_symm_apply, NormedAddGroupHom.neg_apply, Polynomial.valuation_of_mk, MeasureTheory.lintegral_indicator_const_comp, NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, AlgCat.forget_map, FundamentalGroup.map_apply, ContinuousAlgHom.coe_toContinuousLinearMap, Module.Basis.mulOpposite_is_orthonormal_iff, PowerSeries.isUnit_iff_constantCoeff, ProbabilityTheory.Kernel.iIndepSet.meas_biInter, TensorProduct.toMatrix_assoc, MonoidHom.inr_apply, TopCat.colimit_topology, LinearMap.applyₗ'_apply_apply, MonoidAlgebra.mapRangeRingEquiv_single, Module.Basis.mk_range_eq_rank, HahnSeries.SummableFamily.smul_apply', Module.Basis.prod_apply_inr_fst, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, MonoidWithZeroHom.coe_mk, SemilinearIsometryClass.continuous, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, MonoidHom.inr_mono, Ideal.Quotient.algebraMap_quotient_map_quotient, CategoryTheory.nerve.edgeMk_id, Function.emptyHom_toFun, FirstOrder.Ring.lift_genericPolyMap, multiplesAddHom_symm_apply, Submodule.mem_map, CategoryTheory.nerve.right_edge, MeasureTheory.OuterMeasure.isCaratheodory_iff_le', postcomp_extClass_surjective_of_projective_X₂, Subring.mopRingEquivOp_apply_coe, WittVector.truncate_surjective, Trivialization.continuousLinearEquivAt_apply, MeasureTheory.Measure.comp_eq_sum_of_countable, WithBot.map_ofDual, Cardinal.liftInitialSeg_toFun, AddSubmonoid.centerCongr_symm_apply_coe, Set.Finite.infClosure, Matrix.toLinearMap₂'_apply', PresheafOfModules.Derivation.postcomp_d_apply, Nat.ordCompl_dvd_ordCompl_of_dvd, Field.Emb.Cardinal.two_le_deg, SimpleGraph.induceUnivIso_apply, Profinite.epi_iff_surjective, ContinuousLinearMap.pi_apply, Homeomorph.map_punctured_nhds_eq, MeasureTheory.SimpleFunc.memLp_iff_integrable, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_φ, Sym.cast_rfl, AlgebraicGeometry.Scheme.presieve₀_mem_precoverage_iff, SimplexCategory.mkOfSucc_homToOrderHom_one, TemperedDistribution.fourierInv_lineDerivOp_eq, Fin.coe_cycleRange_of_lt, RingCat.forget_map_apply, LieSubmodule.lie_top_eq_of_span_sup_eq_top, Con.kerLift_mk, OrthonormalBasis.coe_reindex, Complex.mul_conj', SubAddAction.ofStabilizer.conjMap_comp_neg_apply, MeasureTheory.measure_biUnion_toMeasurable, MeasureTheory.OuterMeasure.iInf_apply', Orientation.reindex_neg, Finset.geomSum_le_geomSum_iff_toColex_le_toColex, ofDual_preimage_latticeClosure, norm_algebraMap_nnreal, ContinuousMap.coeFnAddMonoidHom_apply, SimpleGraph.Iso.map_symm_apply, MeasureTheory.condExpL2_indicator_ae_eq_smul, Affine.Simplex.excenter_eq_affineCombination, exteriorPower.ιMultiDual_apply_diag, MulEquiv.apply_eq_iff_eq, AbsoluteValue.isEquiv_iff_lt_one_iff, SkewPolynomial.φ_iterate_apply, ContinuousLinearMap.exists_lt_apply_of_lt_opNorm, mfderivWithin_comp_projIcc_one, Module.DualBases.eval_of_ne, AddAction.orbitZMultiplesEquiv_symm_apply, TopologicalSpace.Opens.isOpenEmbedding_obj_top, MeasureTheory.Measure.setIntegral_condKernel_univ_left, AddSubmonoid.closure_image_isAddIndecomposable_baseOf, Equiv.equivCongr_apply_apply, AddMonoidHom.mulRight_apply, MvPolynomial.expand_monomial, IsOrderRightAdjoint.comp_orderIso, Equiv.injective_pointReflection_left_of_injective_two_nsmul, IsMIntegralCurveOn.hasDerivWithinAt, SetTheory.PGame.mulOption_neg_neg, Algebra.mem_bot, MvPowerSeries.substAlgHom_eq_aeval, DirectSum.gMulHom_apply_apply, PartitionOfUnity.sum_eq_one', Function.Embedding.vadd_apply, LinearMap.sumOfConjugatesEquivariant_apply, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, Diffeomorph.contMDiff_comp_diffeomorph_iff, Algebra.SubmersivePresentation.basisKaehlerOfIsCompl_apply, BoundedContinuousFunction.restrict_apply, Polynomial.X_pow_smul_rTensor_monomial, MeasureTheory.StronglyMeasurable.integral_kernel_prod_right, ZMod.AddAutEquivUnits_symm_apply, PresheafOfModules.Derivation.d_one, norm_toAdd, Polynomial.X_pow_sub_one_splits, Derivation.bracket_eq_fun, injective_frobenius, AlgEquiv.arrowCongr_apply, Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, VitaliFamily.FineSubfamilyOn.measure_le_tsum, Finset.weightedVSubOfPoint_vadd, Sublattice.inclusion_apply, Module.Basis.le_span, Equiv.Perm.zpow_apply_mem_support_of_mem_cycleFactorsFinset_iff, Finsupp.LinearEquiv.finsuppUnique_symm_apply, SubMulAction.subtype_injective, BiheytingHom.toFun_eq_coe_aux, MonCat.oneHom_apply, CategoryTheory.Idempotents.Karoubi.inclusionHom_apply, StrictMonoOn.dual_left, PiToModule.fromEnd_injective, MultilinearMap.domDomCongrLinearEquiv_symm_apply, isCompactOperator_iff_isCompact_closure_image_ball, MvPolynomial.expand_char, CircleDeg1Lift.map_one_add, IncidenceAlgebra.mul_apply, Polynomial.coeff_C_ne_zero, starMulAut_apply, Set.Finite.preimage_embedding, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, Valuation.val_lt_one_iff, ofDual_smul, Polynomial.isMonicOfDegree_add_add_two, Quaternion.normSq_le_zero, RingCon.eq, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub, Set.initialSegIic_toFun, LinearMap.coe_lTensorHom, AntivaryOn.dual_right, Algebra.right_comm, FreeAddGroup.lift_mk, Module.Basis.mk_coord_apply_ne, KaehlerDifferential.mapBaseChange_tmul, groupCohomology.cocycles₂_map_one_fst, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, Polynomial.degree_X_pow_add_C, ExteriorAlgebra.algebraMap_eq_zero_iff, Module.DirectLimit.quotMk_of, SkewPolynomial.monomial_def, MvPolynomial.monomial_mul_mem_coeffsIn, Matrix.det_one_add_smul, Valuation.IsUniformizer.zpowers_eq_valueGroup, minpoly_algebraMap_sub_splits, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, PresheafOfModules.sectionsMap_coe, MvPowerSeries.coeff_monomial_same, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq, Equiv.sigmaSumDistrib_symm_apply, HahnSeries.SummableFamily.Equiv_toFun, OrderIso.smulRightDual_apply, LinearMap.toMatrix_id, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, ContinuousMap.HomotopyRel.refl_apply, PreTilt.mk_comp_untilt_eq_coeff_zero, Homeomorph.isLocalHomeomorph, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, MeasureTheory.Measure.prod_prod_le, PowerSeries.WithPiTopology.continuous_constantCoeff, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, AlgEquiv.isTranscendenceBasis, MvPolynomial.eval₂Hom_congr, Polynomial.smul_monomial, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, HNNExtension.inv_t_mul_of, IsCyclotomicExtension.Rat.discr_prime_pow', Polynomial.Monic.comp_X_sub_C, Rat.coe_castHom, RelEmbedding.sumLexMap_apply, SmoothPartitionOfUnity.sum_finsupport', Finpartition.parts_map, unitsEquivProdSubtype_apply_coe, OmegaCompletePartialOrder.Chain.zip_coe, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_apply, ZMod.ringHom_rightInverse, CompletelyPositiveMap.map_cstarMatrix_nonneg, DirectSum.IsInternal.collectedBasis_coe, Fintype.finsetEquivSet_apply, OpenPartialHomeomorph.toHomeomorphOfSourceEqUnivTargetEqUniv_symm_apply, InnerProductSpace.toDualMap_apply_apply, Fin.revOrderIso_apply, RootPairing.IsOrthogonal.reflection_apply_left, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply_self, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, MeasurableEquiv.coe_toEquiv, NNRealRMK.lintegral_rieszMeasure, TwoSidedIdeal.ker_ringCon, AddMonCat.FilteredColimits.colimit_add_mk_eq, MultilinearMap.currySum_apply', MonoidHom.compLeft_apply, Finsupp.cons_succ, DirichletCharacter.eval_modulus_sub, CategoryTheory.ShortComplex.abToCycles_apply_coe, MeasureTheory.Integrable.measure_lt_lt_top, MvPolynomial.map_rename, PrimeSpectrum.toPiLocalization_surjective_of_discreteTopology, Valuation.val_le_one_or_val_inv_le_one, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_pow_ne_two, ExteriorAlgebra.ιMulti_zero_apply, groupHomology.d₁₀_comp_coinvariantsMk_apply, LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec, ProbabilityTheory.Kernel.mutuallySingular_singularPart, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_apply_fst, val_unitsCenterToCenterUnits_apply_coe, Orientation.kahler_eq_zero_iff, AffineBasis.coord_reindex, AddChar.sum_apply_eq_ite, CochainComplex.HomComplex.leftHomologyData_π_hom_apply, ArithmeticFunction.moebius_apply_prime_pow, Polynomial.hom_eval₂, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, LinearEquiv.coe_curry, zpowersHom_apply, KaehlerDifferential.kerTotal_eq, IsFractionRing.surjective_iff_isField, ContinuousLinearEquiv.unitsEquivAut_apply, PositiveLinearMap.preGNS_norm_def, MeasurableEquiv.coe_sumPiEquivProdPi, Finset.Colex.erase_lt_erase, LinearMap.eq_adjoint_iff_basis_left, Set.coe_biUnionEqSigmaOfDisjoint_symm_apply, powersHom_symm_apply, IsFreeGroupoid.SpanningTree.functorOfMonoidHom_map, LinearMap.BilinForm.isNonneg_def, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, PositiveLinearMap.leftMulMapPreGNS_apply, RootPairing.pairing_one_four_iff', MeasureTheory.addEquivAddHaarChar_smul_preimage, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub, ProbabilityTheory.iIndepSets.meas_iInter, AlgebraicGeometry.isIso_iff_isIso_stalkMap, ContinuousLinearEquiv.comp_differentiableOn_iff, MvPowerSeries.hasSum_aeval, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, TestFunction.contDiff, Rep.ρ_hom, Monoid.Coprod.closure_range_inl_union_inr, Matrix.mul_reindexLinearEquiv_one, Ordinal.typein_top, AbsoluteValue.map_sub_eq_zero_iff, isAddLeftRegular_ofDual, Equiv.Set.univ_symm_apply, thickenedIndicator_zero, dist_left_pointReflection, Module.Basis.mk_apply, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom, IsUnit.unit_map, BoundedContinuousFunction.integral_const_sub, RingEquiv.asBoolRingAsBoolAlg_symm_apply, LinearEquiv.image_symm_eq_preimage, ContinuousMap.continuous_compactOpen, Monoid.CoprodI.mrange_eq_iSup, OrderAddMonoidIso.symm_apply_eq, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', Valuation.map_add_of_distinct_val, MvPolynomial.killCompl_C, Algebra.Presentation.quotientEquiv_symm, FractionalIdeal.mem_coeSubmodule, AddMonoidAlgebra.singleZeroRingHom_apply, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', LaurentPolynomial.algebraMap_apply, Rep.diagonalSuccIsoFree_inv_hom_single_single, BialgHom.id_apply, ContinuousMap.Homotopy.ulift_apply, Finset.Colex.erase_le_erase, MvPolynomial.eval₂_const_pUnitAlgEquiv_symm, MonoidHom.coe_snd, DoubleQuot.quotQuotEquivComm_quotQuotMk, OneHom.ext_iff, TopHom.coe_inf, SetTheory.PGame.mul_moveRight_inr, AlgebraicGeometry.StructureSheaf.comap_const, Fin.appendIsometry_symm_apply, LieModuleHom.map_neg, Representation.IntertwiningMap.coe_zero, Quaternion.inv_def, frobenius_mul, CongruenceSubgroup.Gamma1_mem', ProperCone.mem_dual, RestrictedProduct.zsmul_apply, InnerProductSpace.HarmonicOnNhd.comp_CLM, strictMonoOn_dual_iff, MulEquiv.eq_symm_comp, BddOrd.ext_iff, TopCat.isOpenEmbedding_iff_isIso_comp', Prod.Lex.prodLexAssoc_symm_apply, MeasureTheory.continuous_diracProbaEquiv, ProbabilityTheory.stronglyMeasurable_integral_condDistrib, MvPowerSeries.weightedOrder_monomial_of_ne_zero, Homeomorph.isClosed_image, MeasureTheory.LevyProkhorov.toMeasureEquiv_symm_apply_toMeasure, TensorPower.algebraMap₀_mul, groupCohomology.H1IsoOfIsTrivial_inv_apply, Algebra.Generators.H1Cotangent.δAux_C, Polynomial.degree_X_sub_C, Module.Basis.prod_apply_inl_snd, Polynomial.iterate_derivative_X_sub_pow, Nimber.toOrdinal_min, MvPolynomial.support_finSuccEquiv_nonempty, EquivLike.injective_comp, AddEquiv.symmEquiv_symm_apply_symm_apply, signedDist_apply_apply, Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply, algebraMap_strictMono, AddChar.toMonoidHomEquiv_symm_apply, ContinuousMap.piMap_apply, SimpleGraph.Copy.toHom_apply, NonUnitalAlgHom.prod_apply, Polynomial.support_trinomial', AddMonoidAlgebra.divOf_apply, ZSpan.quotientEquiv_apply_mk, AddSubsemigroup.toSubsemigroup'_closure, Equiv.Set.insert_apply_left, QuadraticMap.associated_prod, LieModuleHom.map_smul, Pretrivialization.coe_linearMapAt, SupHom.symm_dual_comp, SSet.stdSimplex.ext_iff, AddGrpCat.FilteredColimits.colimit_add_mk_eq, Complex.liftAux_apply, WithConv.equiv_apply, AddConstMapClass.map_add_nat, OrderIso.setIsotypicComponents_apply, GenLoop.loopHomeo_apply, isAddLeftRegular_ofColex, ConvexCone.coe_comap, LinearIndependent.repr_eq_single, WithZero.expOrderIso_symm_apply, PowerSeries.support_expand, SchwartzMap.integral_norm_sq_fourier, IncidenceAlgebra.coe_zero, DirectSum.lie_of, AddCon.addConGen_idem, OrderIso.comap_atTop, Finset.image_vadd_distrib, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, MeasureTheory.AddContent.extend_eq, AddMonoidHom.rangeRestrict_injective_iff, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_fst, MonoidWithZeroHom.map_one, SemimoduleCat.ofHom₂_hom_apply_hom, StarAlgEquiv.coe_refl, CliffordAlgebra.star_def', Function.Embedding.sigmaSet_apply, ContMDiffSection.coe_nsmul, LieModuleHom.coe_toLinearMap, TensorProduct.gradedComm_algebraMap_tmul, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_map_app, PowerSeries.coeff_inv_aux, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', RingCon.sup_def, OrderIso.dualDual_apply, HahnSeries.toMvPowerSeries_symm_apply_coeff, CocompactMap.comp_apply, Field.Emb.Cardinal.isLeast_leastExt, Diffeomorph.contMDiff_toFun, MvPowerSeries.X_pow_dvd_iff, Equiv.coe_ofInjective_symm, PresheafOfModules.map_comp_apply, CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker_aux, SemiNormedGrp.ext_iff, Polynomial.C_0, MeasureTheory.OuterMeasure.restrict_iInf, MeasureTheory.OuterMeasure.comap_apply, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_apply_coe_asIdeal, LaurentSeries.inducing_coe, CategoryTheory.HomOrthogonal.matrixDecomposition_id, WittVector.mk_pow_fontaineTheta, SeparatingDual.exists_continuousLinearEquiv_apply_eq, UnitAddTorus.mFourierCoeff_toLp, MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero, ProbabilityTheory.gaussianReal_map_continuousLinearMap, PowerSeries.degree_trunc_lt, ContinuousMap.coe_homeoFnOfDiscrete, NonUnitalSubalgebra.unitization_injective, CategoryTheory.PreZeroHypercover.interLift_h₀, FirstOrder.Ring.realize_termOfFreeCommRing, MeasureTheory.Measure.pi_pi_aux, quadraticChar_dichotomy, IsAdjoinRootMonic.basis_repr, OpenPartialHomeomorph.homeomorphOfImageSubsetSource_symm_apply, InitialSeg.exists_eq_iff_rel, Manifold.pathELength_def, MeasureTheory.Lp.simpleFunc.stronglyMeasurable, StieltjesFunction.measure_univ, AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPoint, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, MulAutMultiplicative_apply_apply, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, Module.Baer.ExtensionOf.is_extension, MeasureTheory.integrableOn_const_iff, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, Localization.mkOrderEmbedding_apply, LinearMap.toMatrix_transpose, WeakDual.toStrongDual_inj, Representation.leftRegular_norm_eq_zero_iff, AddChar.ext_iff, LieAlgebra.Orthogonal.indefiniteDiagonal_assoc, Equiv.toPartialEquiv_symm_apply, isAddRegular_toAdd, Polynomial.expand_eq_comp_X_pow, QuadraticMap.zero_apply, TrivSqZeroExt.fst_expSeries, ofBoolAlg_bot, LinearIsometry.ext_iff, EuclideanSpace.volume_closedBall_fin_three, IsometryEquiv.diam_image, ContinuousMultilinearMap.mkPiAlgebraFin_apply, FirstOrder.Field.lift_genericMonicPoly, BoxIntegral.Box.isCompact_Icc, NumberField.exists_conjugate_one_le_norm, LinearMap.toMatrix₂_toLinearMapₛₗ₂, Polynomial.exists_finset_of_splits, MeasureTheory.VectorMeasure.restrictₗ_apply, Set.coe_singletonOneHom, Multiplicative.ofAdd_eq_bot, isLowerSet_preimage_toDual_iff, CategoryTheory.Functor.representableByUliftFunctorEquiv_symm_apply_homEquiv, ModuleCat.biprodIsoProd_inv_comp_snd_apply, PMF.toOuterMeasure_apply_eq_of_inter_support_eq, TensorProduct.finsuppLeft_smul', map_preNormEDS', Algebra.QuasiFiniteAt.exists_fg_and_exists_notMem_and_awayMap_bijective, InitialSeg.map_bot, TensorAlgebra.toDirectSum_ofDirectSum, InverseSystem.globalEquiv_compatibility, Equiv.asEmbedding_apply, ContinuousLinearMap.mulLeftRight_apply, equivTangentBundleProd_apply, NumberField.InfinitePlace.norm_embedding_eq, Finset.piCongrLeft_comp_restrict, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, Function.piCongrLeft'_symm_update, Ordinal.enum_le_enum', AddMagma.FreeAddSemigroup.lift_comp_of, Multiset.coeEmbedding_apply, PreQuasiregular.equiv_apply_val, AddSubmonoid.LocalizationMap.mk'_zero, MeasureTheory.measure_inter_lt_top_of_right_ne_top, Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd, SchwartzMap.differentiable, PresheafOfModules.pushforward_map_app_apply', Matrix.hadamard_of_one, PowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto, Equiv.symm_symm_apply, PowerSeries.coe_smul, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, isSeparable_algebraMap, OrderHom.sSup_apply, Valuation.map_add, starL_apply, MvPolynomial.aevalTower_toAlgHom, LinearMap.extendTo𝕜'_apply, MeasurableEquiv.piEquivPiSubtypeProd_apply, HasOuterApproxClosed.tendsto_apprSeq, MonoidHom.compHom_apply_apply, LieIdeal.mem_killingCompl, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, PreTilt.coeff_frobeniusEquiv_symm, SemistandardYoungTableau.col_strict, IntermediateField.aeval_coe, AffineMap.lineMap_injective, Equiv.Perm.sign_of_cycleType_eq_replicate, FreeAbelianGroup.liftMonoid_coe_addMonoidHom, LinearIsometryEquiv.fderiv, Equiv.boolArrowEquivProd_apply, Module.DirectedSystem.map_map, Algebra.Generators.ofComp_val, DilationClass.edist_eq', coe_eq_coe_fn, Orientation.areaForm_swap, Subalgebra.mem_toSubmodule, OrderHom.Subtype.val_coe, SimplexCategory.Hom.mk_toOrderHom_apply, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, MeasureTheory.Content.le_innerContent, ZeroAtInftyContinuousMapClass.norm_le, AddEquiv.withZeroCongr_apply, ProbabilityTheory.measurable_condDistrib, ContinuousLinearMap.holderₗ_apply_apply, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, Units.coe_map, MeasureTheory.Measure.discard_comp, Subgroup.Normal.conj_smul_eq_self, Fin.insertNthOrderIso_symm_apply, AddChar.sum_eq_zero_iff_ne_zero, MeasureTheory.exists_isSigmaFiniteSet_measure_ge, HopfAlgebra.sum_mul_antipode_eq_smul, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective, CategoryTheory.Discrete.equivalence_unitIso, Algebra.Extension.subsingleton_h1Cotangent, MeasureTheory.measure_preimage_vadd_of_nullMeasurableSet, Monoid.PushoutI.NormalWord.base_smul_eq_smul, ContinuousMultilinearMap.unit_le_opNorm, UniformSpaceCat.hom_ext_iff, Cardinal.mk_image_embedding_lift, Algebra.Presentation.map_relationOfHasCoeffs, Finsupp.finite_support, LaurentSeries.continuous_coe, ext_inner_map, NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero, MeasureTheory.measurable_measure_mul_right, Fin.castLEquiv_symm_apply, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage_singleton, Coalgebra.sum_map_tmul_tmul_eq, LinearMap.trace_smulRight, Submonoid.LocalizationMap.ofMulEquivOfDom_comp_symm, Algebra.TensorProduct.basisAux_map_smul, Units.map_mk, Matrix.coe_ofAddEquiv_symm, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₁₃_eq_conjugateEquiv_symm, Matrix.charpoly_of_upperTriangular, Pi.basis_repr_single, algebraMap_apply, Geometry.SimplicialComplex.inter_subset_convexHull, EquicontinuousOn.inducing_uniformOnFun_iff_pi', convexJoin_segment_singleton, pinGroup.val_toUnits_apply, Finset.lcm_singleton, Finset.Colex.toColex_le_toColex_iff_max'_mem, Bundle.ContinuousRiemannianMetric.symm, Real.volume_preimage_mul_left, Equiv.add_def, MeasureTheory.IsAddFundamentalDomain.measure_eq, LinearMap.convOne_apply, AdicCompletion.factor_eval_eq_evalₐ, DividedPowers.ofRingEquiv_dpow, DividedPowers.equiv_apply, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, Equiv.piCongrLeft_preimage_pi, Module.Relations.Solution.fromQuotient_toQuotient, PiTensorProduct.reindex_comp_tprod, Hamming.nndist_eq_hammingDist, ContinuousLinearMap.analyticOn_bilinear, MeasureTheory.memLp_const_iff, AddMonoidAlgebra.counit_single, Matrix.IsHermitian.eigenvectorUnitary_mulVec, ContinuousLinearEquiv.piUnique_symm_apply, Valuation.HasExtension.val_map_lt_iff, AddMonoidHom.coe_dfinsuppSumAddHom, TopCat.pullbackSnd_apply, MonoidAlgebra.coe_algebraMap, LinearIsometryEquiv.measurePreserving, equivShrink_symm_bot, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, ProfiniteGrp.toLimit_surjective, Function.OfArity.curryEquiv_symm_apply, FreeAlgebra.star_algebraMap, QuadraticAlgebra.norm_eq_one_iff_mem_unitary, Finsupp.eq_option_embedding_update_none_iff, MeasureTheory.Measure.infinitePi_map_piCongrLeft, Polynomial.Monic.normalize_eq_self, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, gcd_eq_normalize, Algebra.traceMatrix_reindex, LinearIsometryEquiv.coe_toLinearEquiv, Equiv.sum_comp, Function.locallyFinsuppWithin.logCounting_eventually_le, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', SSet.opFunctor_map, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, pow_finEquivZPowers_symm_apply, Function.locallyFinsuppWithin.apply_eq_zero_of_notMem, MvPolynomial.eval₂_map, LinearMap.isIdempotentElem_map_one_iff, Algebra.Generators.exists_presentation_of_free_cotangent, MeasureTheory.Measure.restrict_eq_zero, AddMonoidAlgebra.mapRangeRingHom_single, MeasureTheory.hausdorffMeasure_measurePreserving_piFinTwo, CircleDeg1Lift.map_le_of_map_zero, supPrime_toDual, Subalgebra.range_isScalarTower_toAlgHom, Polynomial.irreducible_mul_leadingCoeff_inv, PresheafOfModules.Derivation.d_mul, ContinuousAffineEquiv.image_preimage, LightProfinite.isClosedMap, dist_ofDual, iterateFrobenius_one_apply, TensorProduct.equivFinsuppOfBasisRight_apply_tmul, RingCon.comapQuotientEquivRangeS_symm_mk, MvPolynomial.X_mul_pderiv_monomial, GaussianInt.toComplex_injective, AddSubgroup.index_eq_natAbs_det, ContinuousLinearMap.deriv, Matrix.diagonal_vec2, AffineIsometryEquiv.dist_pointReflection_fixed, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, WittVector.verschiebung_injective, MvPowerSeries.lexOrder_def_of_ne_zero, MonomialOrder.degree_add_le, Submodule.coe_prodEquivOfIsCompl', MulAut.inv_apply_self, Module.Basis.ofEquivFun_repr_apply, MulOpposite.algebraMap_apply, IsSepClosed.roots_eq_zero_iff, NonemptyInterval.toDualProdHom_apply, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, Real.volume_pi_Ico, QuadraticMap.map_smul, Valued.is_topological_valuation, Matrix.toLinAlgEquiv_mul, Finset.toDual_min', ClosureOperator.le_closure_iff, GradeMinOrder.exists_nat_orderEmbedding_of_forall_covby_finite, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr, Ordinal.bfamilyOfFamily'_typein, Finsupp.mapRange_sub', MvPolynomial.degree_optionEquivLeft, NonUnitalAlgHom.zero_apply, toAdd_multiset_sum, toDual_compares_toDual, MeasureTheory.Integrable.integral_norm_condDistrib_map, exists_birkhoff_representation, QuadraticAlgebra.imₗ_apply, fderiv_continuousAlternatingMap_apply, CircleDeg1Lift.le_map_of_map_zero, SemilinearIsometryClass.lipschitz, Normal.algHomEquivAut_symm_apply, AddSubsemigroup.topEquiv_apply, SlashInvariantForm.coe_translate, ArchimedeanClass.FiniteElement.val_add, MulRingNorm.ext_iff, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, Finset.Ioo_orderDual_def, IsIntegrallyClosedIn.exists_algebraMap_eq_of_isIntegral_pow, Pi.toLex_update_le_self_iff, HahnEmbedding.Seed.strictMono_coeff, LinearMap.det_mulRight, apply_wcovBy_apply_iff, FreeAbelianGroup.map_of_apply, MeasureTheory.Measure.mkMetric_le_liminf_tsum, ContinuousAlgHom.comp_apply, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, Algebra.Generators.naive_val, uniformContinuous_toMul, MvPowerSeries.coeff_index_single_X, PowerSeries.WithPiTopology.uniformContinuous_coeff, FractionalIdeal.mem_map, Ideal.Quotient.factorₐ_apply, BoundedContinuousFunction.coe_smul, Complex.measurableEquivRealProd_apply, Cardinal.aleph_one_le_continuum, Path.truncate_self, MeasureTheory.OuterMeasure.restrict_ofFunction, SetTheory.PGame.mul_moveLeft_inl, Module.one_le_rank_iff, Polynomial.aeval_one, ofColex_vadd', CompactlySupportedContinuousMap.coe_star, IsLocalizedModule.fromLocalizedModule.bij, Equiv.Perm.VectorsProdEqOne.vectorEquiv_apply_coe, gal_X_pow_sub_C_isSolvable, MDifferentiable.clm_bundle_apply, CategoryTheory.GrothendieckTopology.OneHypercover.mem_sieve₁', MeasureTheory.measure_mul_right_null, Lagrange.interpolate_eq_sum, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, UniformOnFun.ofFun_div, MonoidAlgebra.mapDomain_algebraMap, StarSubalgebra.mem_bot, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, MeasureTheory.Measure.hausdorffMeasure_mono, AddEquiv.prodProdProdComm_apply, Module.Basis.sumQuot_repr_left, Module.AEval.C_smul, Algebra.Extension.CotangentSpace.map_tmul, Metric.measure_closedBall_pos_iff, RootPairing.IsReduced.linearIndependent_iff, LinearEquiv.ofSubmodules_apply, Submodule.quotientQuotientEquivQuotientAux_mk, Orientation.kahler_swap, coe_innerSL_apply, MulChar.ringHomComp_apply, DomMulAct.map_mk_nhds, Matrix.toLinearMap₂'Aux_single, Polynomial.sum_C_index, DistribMulActionHom.congr_fun, groupCohomology.H2π_comp_map_apply, edist_ofDual, ProfiniteAddGrp.hom_neg_apply, Submonoid.topEquiv_symm_apply_coe, Matrix.vecMulBilin_apply, IsValuativeTopology.isOpen_ball, element_smul_restrictScalars, ContinuousAlternatingMap.ofSubsingleton_apply_toContinuousMultilinearMap, ArithmeticFunction.moebius_eq_zero_of_not_squarefree, cfcHom_le_iff, Matrix.frobenius_nnnorm_one, Orientation.det_rotation, MeasureTheory.Measure.infinitePi_map_piCurry, NatOrdinal.succ_def, Matrix.charmatrix_apply_ne, CommSemiRingCat.ofHom_apply, Polynomial.aeval_eq_zero_of_mem_rootSet, Finsupp.embDomain_single, OrderIso.dual_apply, Submodule.topEquiv_apply, Homeomorph.continuousMapCongr_symm_apply, IsLocalization.surj'', Orientation.rotation_pi_apply, MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc, MvPowerSeries.LinearTopology.mem_basis_iff, PiTensorProduct.tprod_prod, OrderHom.coe_le_coe, HahnSeries.cardSupp_truncLT_le, Coalgebra.comm_comul, Module.Relations.Solution.IsPresentation.linearEquiv_apply, MvPowerSeries.subst_monomial, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_symm_apply, gc_upperPolar_lowerPolar, ContinuousLinearEquiv.uniqueProd_symm_apply, LinearMap.IsSymmetric.inner_map_self_eq_zero, volume_setOf_liouville, AddSubgroup.noncommPiCoprod_apply, RatFunc.map_apply, SSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff, DirectSum.support_of, MonoidWithZero.coe_inverse, Unitization.lift_symm_apply_apply, RingHom.coe_coe, Finsupp.sum_ite_eq, cfcHom_id, AddEquiv.toMultiplicativeLeft_apply_symm_apply, cross_anticomm, ContinuousLinearMap.isCompact_image_coe_closedBall, AlgebraicGeometry.Scheme.Hom.coe_resLE_apply, Sum.Lex.toLex_lt_toLex, OrthonormalBasis.prod_apply, OmegaCompletePartialOrder.ωSup_le_iff, Ordinal.CNF.coeff_zero_apply, Polynomial.le_rootMultiplicity_map, CategoryTheory.Coyoneda.objOpOp_hom_app, RingEquiv.moduleEndSelf_symm_apply, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_symm_τr, exists_contMDiffSection_forall_mem_convex_of_local, CircleDeg1Lift.ext_iff, MeasureTheory.measure_sigmaFiniteSetGE_le, PartOrd.coe_id, RegularNormedAlgebra.isometry_mul', RingHom.coe_rangeSRestrict, Polynomial.degreeLT.addLinearEquiv_castAdd, Finset.inf'_map, convexJoin_singleton_segment, SlashInvariantForm.ext_iff, Orientation.rotation_rotation, AffineSubspace.map_mk', Finsupp.indicator_of_notMem, ContinuousMap.HomotopyRel.trans_apply, cauchyPowerSeries_apply, KaehlerDifferential.polynomialEquiv_comp_D, convexHull_diam, Multiset.equivDFinsupp_apply, MeasureTheory.Measure.mem_cofinite, MvPolynomial.coeff_expand_smul, MvPowerSeries.le_weightedOrder_map, Invertible.mulRight_apply, PerfectRing.liftEquiv_comp_apply, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, Submodule.subtype_apply, DistribMulAction.toAddMonoidEnd_apply, TopologicalSpace.Opens.frameHom_toFun, KaehlerDifferential.span_range_map_derivation_of_isLocalization, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, thickenedIndicator_le_one, MeasureTheory.projectiveFamilyContent_eq, Pi.constNonUnitalRingHom_apply, Finsupp.optionElim_some, ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero, map_lt_lineMap_iff_slope_lt_slope_right, DFinsupp.coe_mk', Ideal.powQuotSuccInclusion_apply_coe, LaurentPolynomial.antipode_T, le_emultiplicity_map, Algebra.Generators.algebraMap_apply, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, IsLocalization.map_eq_zero_iff, BialgHom.comp_apply, Subalgebra.algebraMap_mk, LinearIsometryEquiv.coe_toHomeomorph, AddEquiv.self_comp_symm, Order.height_orderIso, disjoint_toDual_iff, powCoprime_symm_apply, FractionalIdeal.extendedHom_apply, inner_re_zero_right, MulHom.mclosure_preimage_le, ContinuousLinearMap.isClosed_image_coe_closedBall, ZMod.χ₈'_nat_eq_if_mod_eight, SSet.Subcomplex.ofSimplexProd_eq_range, Finsupp.sum_fintype, MulSemiringActionHom.id_apply, NNReal.count_const_le_le_of_tsum_le, RingHom.toIntAlgHom_apply, CategoryTheory.nerve.homEquiv_edgeMk, DoubleCentralizer.central, Rep.ihom_ev_app_hom, ContinuousLinearMap.coe_neg', Preord.ofHom_apply, ProbabilityTheory.Kernel.fst_real_apply, LieModule.coe_chainTop, MeasureTheory.projectiveFamilyContent_diff, LinearEquiv.toSpanNonzeroSingleton_homothety, ModularFormClass.levelOne_neg_weight_eq_zero, FreeMonoid.lift_of_comp_eq_map, SemimoduleCat.MonoidalCategory.whiskerRight_apply, Matrix.GeneralLinearGroup.upperRightHom_apply, ContinuousMap.coe_vadd, ModularFormClass.continuous, two_nsmul_lie_lmul_lmul_add_add_eq_zero, Equiv.uniqueSigma_apply, MeasureTheory.integral_condExpL2_eq, AffineIsometryEquiv.continuousWithinAt, LieModuleHom.comp_apply, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, IsBaseChange.endHom_toMatrix, StrictMono.coe_orderIsoOfSurjective, Finsupp.mapRange.equiv_refl, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, MeasureTheory.Measure.toOuterMeasure_apply, ContinuousMap.inf_apply, Representation.Coinvariants.sub_mem_ker, HasFPowerSeriesOnBall.coeff_zero, ProbabilityTheory.setBernoulli_singleton, Matrix.transposeRingEquiv_symm_apply, MeasureTheory.OuterMeasure.map_iInf_comap, FirstOrder.Language.Hom.mem_range, Pi.toLex_update_lt_self_iff, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, Valuation.map_div, List.sum_hom_nonempty, Ideal.range_mul, Action.FunctorCategoryEquivalence.functor_map_app, OrderIso.sumLexIicIoi_symm_apply_of_le, VectorBundleCore.localTriv_symm_fst, MvPolynomial.map_esymm, BoundedOrderHom.dual_apply_toOrderHom, DistribMulAction.toLinearEquiv_symm_apply, LocalizedModule.equivTensorProduct_apply_mk, Algebra.TensorProduct.lid_tmul, ContinuousMap.dist_apply_le_dist, Field.Emb.Cardinal.succEquiv_coherence, ModuleCat.homLinearEquiv_symm_apply, Equiv.Perm.coe_support_eq_set_support, ProbabilityTheory.Kernel.piecewise_apply', cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, affineCombination_mem_affineSpan_pair, Set.map_finite_iSup, MDifferentiableWithinAt.clm_bundle_apply₂, ComplexShape.TensorSigns.ε'_succ, Set.Countable.exists_cycleOn, AddMonoid.Coprod.prod_mk_fst_snd, MulActionHom.prodMap_apply, Equiv.bijective_comp, MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq_of_subset, Topology.WithUpper.ofUpper_lt_ofUpper, Hamming.ofHamming_smul, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub, RelEmbedding.sumLexInl_apply, WeierstrassCurve.Affine.map_linePolynomial, Finsupp.mem_rangeSingleton_apply_iff, Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply, MeasurableEquiv.map_symm_map, AddSubgroupClass.subtype_apply, IsAdicComplete.of_liftRingHom, StarSubalgebra.mem_comap, Algebra.discr_powerBasis_eq_norm, LinearMap.BilinForm.sum_left, FreeMonoid.lift_ofList, AddMonCat.equivalence_inverse_map, Pi.evalMonoidHom_apply, Equiv.prodAssoc_apply, LinearMap.surjective_iff_ne_zero, MeasureTheory.integrable_thickenedIndicator, GradedTensorProduct.mul_def, Polynomial.natTrailingDegree_C, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Module.Flat.iff_lTensor_preserves_injective_linearMap, CompactlySupportedContinuousMapClass.hasCompactSupport, Homeomorph.isProperMap, QuaternionAlgebra.Basis.j_compHom, Complex.UnitDisc.coe_conj, Polynomial.X_mul_C, MonoidWithZeroHom.one_apply_val_unit, Module.IsTorsionBySet.mk_smul, VectorField.pullbackWithin_eq_of_fderivWithin_eq, spinGroup.val_inv_toUnits_apply, MeasureTheory.OuterMeasure.isCaratheodory_iff, Metric.Snowflaking.mk_eq_toSnowflaking, CategoryTheory.congr_arg, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul, hasDerivWithinAt_abs, Path.continuous_extend, Algebra.toSubmodule_bot, IsLocalization.mapFrameHom_apply, OrderIso.map_sInf_eq_sInf_symm_preimage, ContinuousLinearEquiv.finTwoArrow_symm_apply, CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_fst, ContinuousLinearEquiv.isAddHaarMeasure_map, Derivation.mapCoeffs_C, MeasureTheory.Measure.snd_compProd, WithZero.lt_ofAdd_iff, MvPolynomial.weightedHomogeneousComponent_eq_zero', IsAddUnit.preimage_vadd_setₛₗ, hasFDerivAtFilter_iff_isLittleO, InitialSeg.eq_relIso, PowerSeries.coeff_zero_one, CategoryTheory.Pretopology.mem_toGrothendieck, Module.Basis.toMatrix_map, AddSubmonoid.coe_map, map_finset_sup', CategoryTheory.Functor.homObjEquiv_symm_apply_app, Ordinal.card_le_preAleph, PiTensorProduct.ofFinsuppEquiv'_tprod_single, prod_mem_ideal_map_of_mem_conductor, TensorProduct.lidIsometry_apply, HasFDerivAt.clm_apply, Metric.Snowflaking.val_eq_ofSnowflaking, finSigmaFinEquiv_apply, MeasureTheory.Measure.AbsolutelyContinuous.comp_right, ContDiffMapSupportedIn.seminorm_le_iff, FinBddDistLat.ext_iff, PartitionOfUnity.exists_finset_nhds, LieModule.isNilpotent_toEnd_of_isNilpotent, MeasurableSet.exists_isCompact_lt_add, MeasureTheory.Measure.restrict_apply_superset, NumberField.InfinitePlace.mkReal_coe, MeasureTheory.FiniteMeasure.tendsto_measure_iUnion_accumulate, StarRingEquiv.rightInverse_symm, Nat.factorization_eq_card_pow_dvd_of_lt, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, HahnSeries.SummableFamily.smul_apply, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, AddMonoidHom.map_finsum_plift, AddConstMapClass.map_add_zsmul, AddMonoidAlgebra.toDirectSum_single, MeasureTheory.tendsto_measure_of_tendsto_indicator, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, AlgebraicGeometry.StructureSheaf.comap_apply, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, AddMonoidHom.eval_apply_apply, subset_closedAbsConvexHull, Cardinal.aleph_mul_aleph0, Finset.weightedVSubOfPoint_filter_of_ne, orzechProperty_iff, CommMonCat.coyoneda_obj_map, MultilinearMap.curryFinFinset_apply, MeasureTheory.SimpleFunc.const_lintegral_restrict, CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback, gc_upperBounds_lowerBounds, SignType.map_cast, MonoidAlgebra.single_mul_apply, MonoidHom.closure_preimage_le, Path.extend_trans_of_le_half, ContinuousLinearMap.hasDerivAt, norm_map', Affine.Simplex.ninePointCircle_restrict, ContinuousMonoidHom.swap_toFun, Function.Embedding.setValue_eq_iff, Polynomial.coeff_C_mul_X, starRingAut_apply, RootPairing.toLinearMap_apply_apply_Polarization, ContinuousLinearEquiv.compContinuousAlternatingMap_coe, Module.DirectedSystem.map_self, ProbabilityTheory.Kernel.indepSet_iff_measure_inter_eq_mul, Polynomial.leadingCoeff_cubic, ProbabilityTheory.Kernel.compProd_deterministic_apply, Valuation.one_lt_val_iff, MeasureTheory.SimpleFunc.tendsto_eapprox, BooleanSubalgebra.mem_comap, Finset.centroid_map, StrongDual.toWeakDual_inj, FirstOrder.Language.LEquiv.onFormula_apply, ContinuousAffineEquiv.prodCongr_apply, qExpansion_of_mul, IsTopologicalGroup.isOpenMap_iff_nhds_one, RootPairing.exist_set_root_not_disjoint_and_le_ker_coroot'_of_invtSubmodule, SSet.stdSimplex.obj₀Equiv_apply, Subgroup.IsComplement.equiv_mul_left_of_mem, ArithmeticFunction.sigma_zero_apply, Orientation.map_eq_iff_det_pos, CircleDeg1Lift.dist_map_map_zero_lt, AffineEquiv.sSameSide_map_iff, coe_basisOfPiSpaceOfLinearIndependent, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_mem, LinearMap.BilinForm.Nondegenerate.congr, Subgroup.smul_leftQuotientEquiv, groupCohomology.isMulCoboundary₂_of_mem_coboundaries₂, Rep.MonoidalClosed.linearHomEquivComm_hom, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Homeomorph.image_closure, AddMonoidHom.flip_apply, MeasureTheory.tendstoInMeasure_iff_norm, LatticeHom.withTopWithBot'_toFun, TopCat.isIso_iff_isHomeomorph, AddSubgroup.mem_map_of_mem, Polynomial.map_monomial, Quiver.SingleObj.toPrefunctor_apply_map, OpenPartialHomeomorph.toHomeomorphSourceTarget_apply_coe, rieszContentAux_image_nonempty, MeasureTheory.FiniteMeasure.normalize_eq_of_nonzero, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, Polynomial.expand_one, MeasureTheory.Content.measure_eq_content_of_regular, DFinsupp.toMultiset_single, Polynomial.revAt_zero, Polynomial.resultant_C_zero_right, IsPrimitiveRoot.norm_eq_neg_one_pow, Algebra.TensorProduct.tensorTensorTensorComm_symm_tmul, PiLp.sumPiLpEquivProdLpPiLp_symm_apply_ofLp, Polynomial.natDegree_eq_one, isGroupLikeElem_iff, MvPolynomial.expand_C, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sq, CochainComplex.HomComplex.leftHomologyData_i_hom_apply, PadicInt.fwdDiff_tendsto_zero, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, RootPairing.Base.coroot_mem_span_int, Continuous.pathExtend, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, MvPowerSeries.trunc'_trunc'_pow, intervalIntegral.hasSum_intervalIntegral_of_summable_norm, SemimoduleCat.homLinearEquiv_apply, MeasureTheory.SimpleFunc.finite_range, Lat.comp_apply, MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, PEquiv.toMatrix_toPEquiv_eq, MeasureTheory.volume_preserving_prodAssoc, ContinuousAlgHom.coe_id', ModuleCat.smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, continuous_toAdd, TensorProduct.equivFinsuppOfBasisLeft_symm, Finset.centerMass_id_mem_convexHull, LocallyBoundedMap.coe_ofMapBounded, LocallyConstant.ext_iff, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, Homeomorph.divRight_apply, WeierstrassCurve.Affine.baseChange_negY, Equiv.Set.congr_symm_apply, MeasureTheory.Measure.count_apply_eq_top, LinearMap.isClosedEmbedding_of_injective, Algebra.directSumGAlgebra_toFun_apply, ProbabilityTheory.Kernel.Invariant.def, CovBy.image, SimpleGraph.Hom.coe_id, LinearMap.IsProj.eq_conj_prodMap, LinearMap.flip_surjective_iff₁, LinearMap.tensorEqLocus_coe, map_finsuppProd, Quaternion.normSq_nonneg, TensorAlgebra.toExterior_ι, LaurentPolynomial.smeval_C_mul, OrderMonoidIso.val_unitsCongr_apply, SupBotHom.subtypeVal_coe, Equiv.permCongrHom_coe, DirichletCharacter.unit_norm_eq_one, NNReal.strictConcaveOn_sqrt, Padic.norm_eq_zpow_log_mulValuation, coe_galRestrict_apply, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, VitaliFamily.measure_limRatioMeas_zero, RingCon.inf_iff_and, MeasureTheory.ofReal_setAverage, AlgebraicGeometry.Scheme.range_fromSpecStalk, PadicInt.ext_of_toZModPow, AlternatingMap.alternatizeUncurryFin_apply, MonomialOrder.eq_C_of_degree_eq_zero, LinearMap.span_preimage_le, Polynomial.aeval_subalgebra_coe, minpoly.sub_algebraMap, CategoryTheory.Functor.equivCatHom_apply, Submodule.mem_comap, ofBoolRing_add, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two, addEquivOfAddOrderOfEq_apply_gen, infClosed_preimage_toDual, WeierstrassCurve.φ_three, Matrix.uniqueEquiv_symm_apply, CoheytingHom.toFun_eq_coe_aux, HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_symm_mk, AddHom.ENatMap_apply, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, LinearMap.dfinsuppSum_apply, LinearMap.IsPositive.inner_nonneg_left, SSet.skeleton_le_skeletonOfMono, LinearMap.toAddMonoidHom'_apply, ValuationSubring.valuation_lt_one_or_eq_one, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, ContinuousMap.norm_eq_iSup_norm, Polynomial.separable_or, MonoidHom.transferSylow_restrict_eq_pow, Dilation.comp_apply, AdjoinRoot.mk_eq_mk, Matrix.piRingEquiv_apply, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, SSet.prodStdSimplex.objEquiv_δ_apply, TopCat.prod_topology, RelEmbedding.injective, SetTheory.PGame.toRightMovesNim_one_symm, Derivation.toFun_eq_coe, MeasureTheory.ProbabilityMeasure.coeFn_comp_toFiniteMeasure_eq_coeFn, RootPairing.IsOrthogonal.coreflection_apply_right, Equicontinuous.tendsto_uniformFun_iff_pi, Finset.card_eraseNone_le, LinearIsometry.enorm_map, ContinuousOrderHom.id_apply, Matrix.toLinearMap₂'_apply, HasFDerivAt.continuousAlternatingMap_apply, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, Profinite.NobelingProof.GoodProducts.smaller_factorization, PositiveLinearMap.map_nonneg, Finset.coe_coeAddMonoidHom, MeasureTheory.convolution_precompR_apply, NonUnitalSubring.topEquiv_symm_apply_coe, AlgebraNorm.ext_iff, Algebra.TensorProduct.includeLeft_apply, AddMonCat.equivalence_counitIso, PolynomialModule.single_smul, toDual_sdiff, AdjoinRoot.algHomOfDvd_root, matPolyEquiv_coeff_apply_aux_1, Matrix.uniqueAddEquiv_symm_apply, Polynomial.leadingCoeffHom_apply, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, LinearIsometry.map_sub, Affine.Simplex.affineCombination_mem_interior_face_iff_mem_Ioo, ProbabilityTheory.Kernel.rnDeriv_singularPart, map_eq_zero_iff_eq_one, LinearIsometryEquiv.map_add, LinearMap.funLeft_surjective_of_injective, DirichletCharacter.Odd.to_fun, latticeClosure_mono, LinearMap.mem_submoduleImage_of_le, SimpleGraph.edgeFinset_map, ProbabilityTheory.Indep_iff, Equiv.divRight₀_symm_apply, Set.Finite.isCompact_convexHull, IncidenceAlgebra.moebius_inversion_bot, MvPolynomial.coeffs_C, Polynomial.degreeLT.addLinearEquiv_apply_fst, UniformSpace.Completion.map_smul_eq_mul_coe, PowerSeries.intValuation_eq_of_coe, Submodule.mulLeftMap_apply, ZMod.χ₈'_int_eq_χ₄_mul_χ₈, OrderIso.map_iSup, AddMonoidAlgebra.neg_apply, Submonoid.toAddSubmonoid_closure, CompactlySupportedContinuousMap.mul_apply, image_latticeClosure', lTensorHomEquivHomLTensor_apply, SkewMonoidAlgebra.addHom_ext_iff, LinearMap.BilinForm.separatingLeft_toMatrix'_iff, Topology.WithUpper.ofUpper_le_ofUpper, isCusp_SL2Z_iff', RootPairing.neg_mem_range_coroot_iff, midpoint_pointReflection_left, Equiv.Perm.SameCycle.zpow_right, MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc, TensorProduct.finsuppScalarRight_apply, Algebra.FormallySmooth.iff_injective_lTensor_residueField, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, ContinuousAddMonoidHom.nsmul_apply, Valuation.one_apply_of_ne_zero, ModularGroup.lcRow0Extend_symm_apply, Real.volume_Icc_pi, FirstOrder.Language.Hom.mem_range_self, AffineIsometryEquiv.map_vsub, Subgroup.pointwise_smul_def, Finset.centerMass_id_mem_convexHull_of_nonpos, RootPairing.reflection_same, Valued.continuous_valuation, LinearMap.extendScalarsOfIsLocalizationEquiv_apply, Polynomial.C_eq_natCast, Finsupp.zipWith_apply, WithZeroMulInt.toNNReal_pos, FractionalIdeal.dual_eq_dual_mul_dual, ofLex_vadd, AdicCompletion.sumInv_apply, ContinuousMap.Homotopy.cast_apply, FiberBundle.pullback_trivializationAt', Ideal.Fiber.lift_residueField_surjective, ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self, Algebra.leftMulMatrix_injective, LocallyFiniteOrder.orderAddMonoidHom_bijective, Sublattice.subtype_apply, LinearMap.compMultilinearMap_alternatization, LocallyConstant.congrRightₐ_symm_apply_apply, ContinuousLinearEquiv.coe_toContinuousAffineEquiv, ContinuousCohomology.I_obj_ρ_apply, isConjRoot_iff_aeval_eq_zero, Subgroup.conjAct_pointwise_smul_iff, MulEquiv.coprodPUnit_symm_apply, MeasureTheory.setIntegral_condExpL2_indicator, NNReal.sqrt_le_sqrt, Equiv.Perm.decomposeFin.symm_sign, ContinuousMap.toNNReal_algebraMap, MulAction.stabilizerEquivStabilizer_compTriple, Path.toHomotopyConst_apply, CompleteLatticeHom.setPreimage_apply, MeasurableEquiv.quasiMeasurePreserving_symm, MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd, CuspForm.holo', MeasureTheory.Measure.infinitePi_pi, AddChar.sum_eq_card_of_eq_one, InnerProductSpace.nnnorm_rankOne, ArithmeticFunction.smul_apply, HeytAlg.coe_comp, LinearEquiv.skewSwap_apply, Polynomial.derivative_X_sub_C_sq, FreeMonoid.mem_map, AlgebraicGeometry.stalkToFiberRingHom_homogeneousLocalizationToStalk, CondensedSet.topCatAdjunctionCounit_bijective, Matrix.charpoly_sub_scalar, IsPrimitiveRoot.autToPow_eq_modularCyclotomicCharacter, CircleDeg1Lift.inf_apply, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, AlgEquiv.default_apply, WeierstrassCurve.Jacobian.comp_equiv_comp, Frm.ext_iff, antilipschitzWith_iff_exists_mul_le_norm', FreeLieAlgebra.liftAux_map_smul, ContinuousMultilinearMap.norm_image_sub_le, MvPolynomial.optionEquivRight_X_none, MonovaryOn.dual_left, Polynomial.aeval_X_left_apply, GrpWithZero.coe_comp, Seminorm.closedBall_zero_eq_preimage_closedBall, MvPolynomial.homogeneousComponent_isHomogeneous, CategoryTheory.Iso.eHomCongr_comp_assoc, PreInnerProductSpace.Core.conj_inner_symm, Polynomial.smul_eq_C_mul, MonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, MvPolynomial.rename_psum, convexHull_add, RootPairing.Hom.comp_indexEquiv_apply, DirichletCharacter.sum_characters_eq, BoundedContinuousFunction.lintegral_nnnorm_le, CategoryTheory.Adjunction.homEquiv_unit, CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply, Sym.coe_equivNatSumOfFintype_symm_apply, Module.Relations.Solution.ofQuotient_var, ContinuousAffineEquiv.refl_apply, CategoryTheory.Under.postAdjunctionRight_unit_app_right, Subgroup.quotientSubgroupOfEmbeddingOfLE_apply_mk, CategoryTheory.Limits.WidePullbackCone.reindex_base, MeasurableEquiv.ofInvolutive_apply, Finset.affineCombination_congr, LinearMap.trace_mul_comm, spectrum.gelfandTransform_eq, HahnSeries.single_sub, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, ContinuousMonoidHom.coe_id, IsChain.image_relEmbedding_iff, OrthonormalBasis.orthogonalProjection_apply_eq_sum, CategoryTheory.Iso.toIsometryEquiv_toFun, MulEquiv.invFun_eq_symm, ModularGroup.denom_apply, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, Finsupp.toMultiset_apply, Orientation.kahler_comp_rightAngleRotation, LinearMap.toKerLocalized_isLocalizedModule, EsakiaHom.comp_apply, SimpleGraph.Embedding.sumInl_apply, ContinuousLinearEquiv.arrowCongr_apply, AddMonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, Equiv.Perm.mem_support_cycle_of_cycle, NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst, IsometryEquiv.edist_eq, IndexedPartition.proj_out, FiniteField.algebraMap_trace_eq_sum_pow, AddMonoidHom.addSubgroupMap_apply_coe, CoxeterSystem.getElem_succ_leftInvSeq_alternatingWord, HahnSeries.addOppositeEquiv_support, Affine.Simplex.face_restrict, IsFoelner.tendsto_meas_smul_symmDiff, EReal.abs_mul_sign, pow_ofColex, Polynomial.revAt_eq_self_of_lt, AddSubmonoid.centerToAddOpposite_symm_apply_coe, ModuleCat.CoextendScalars.smul_apply, ContinuousAlgHom.uniformContinuous, CategoryTheory.conjugateEquiv_leftUnitor_hom, Module.Basis.reindexRange_apply, unop_map_list_prod, Homeomorph.continuousMapCongr_apply, CliffordAlgebra.changeFormAux_apply_apply, Submodule.isOpenQuotientMap_mkQ, LeftInvariantDerivation.comp_L, CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₀, SetSemiring.zero_def, OrderMonoidIso.coe_mulEquiv, OrderEmbedding.coe_birkhoffFinset, MeasureTheory.measure_mul_measure_eq, Equiv.Perm.sameCycle_apply_right, InfHom.coe_comp, Algebra.coe_bot, ArithmeticFunction.cardDistinctFactors_eq_zero, Finset.eraseNone_union, Polynomial.opRingEquiv_op_C, ArithmeticFunction.vonMangoldt.residueClass_apply, ProfiniteAddGrp.neg_hom_apply, SkewMonoidAlgebra.lift_of, OreLocalization.numeratorHom_inj, LocalizedModule.equivTensorProduct_symm_apply_tmul, RatFunc.mk_def, OrderMonoidIso.symm_apply_apply, Ideal.relNorm_singleton, Real.sinhHomeomorph_symm_apply, DistribMulActionHom.coe_zero, AffineMap.differentiableWithinAt, Complex.lift_apply, Submodule.factor_eq_factor, ProbabilityTheory.indepSets_singleton_iff, DirectSum.coeLinearMap_of, Subgroup.range_zpowersHom, AlgebraicGeometry.coprodMk_inl, AdicCompletion.sum_lof, LinearEquiv.arrowCongr_symm_apply, TensorProduct.finsuppScalarRight_apply_tmul, PartOrd.dual_map, Submonoid.inclusion_inj, Polynomial.C_eq_intCast, image_gaugeRescaleHomeomorph_interior, Perfection.coeff_map, MeasureTheory.IsProbabilityMeasure_comap_equiv, RestrictedProduct.mul_single, Subalgebra.mopAlgEquivOp_symm_apply, Representation.single_smul, SkewMonoidAlgebra.lift_single, Polynomial.smeval.linearMap_apply, PartOrdEmb.comp_apply, Polynomial.degree_C_lt_degree_C_mul_X, Module.Basis.matrix_apply, Polynomial.aroots_C_mul, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, MeasureTheory.addMeasure_map_restrict_apply, VectorField.fderivWithin_pullbackWithin, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, WeierstrassCurve.Jacobian.polynomialY_eq, SSet.op_σ, Polynomial.eval_derivative_of_splits, Polygon.edgeSet_eq_image_edgePath, Polynomial.isUnit_iff, MvPolynomial.sum_homogeneousComponent, ContinuousLinearMap.toUniformConvergenceCLM_apply, TemperedDistribution.delta_apply, Module.Relations.Solution.IsPresentation.linearMapEquiv_symm_apply, DFinsupp.lex_lt_iff, DirectSum.coeLinearMap_eq_dfinsuppSum, CategoryTheory.Aut.toEnd_apply, AffineEquiv.linear_equivUnitsAffineMap_symm_apply, ContinuousAlternatingMap.curryLeft_apply_apply, CategoryTheory.uliftYonedaEquiv_apply, HahnEmbedding.Partial.orderTop_eq_iff, RingTheory.Sequence.IsWeaklyRegular.of_flat, BoundedContinuousFunction.coe_intCast, multiplesEquivMultiples_apply, WeierstrassCurve.Jacobian.map_dblZ, ContinuousLinearMap.contDiffPointwiseHolderAt, ofDual_himp, ContinuousAffineEquiv.symm_apply_eq, LieSubmodule.coe_map_toEnd_le, Module.FinitePresentation.linearEquivMap_symm_apply, CondensedSet.topCatAdjunctionCounit_hom_apply, Subalgebra.inclusion_inclusion, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, norm_ofDual, exists_basis_of_pairing_ne_zero, CategoryTheory.Iso.homCongr_comp, RootPairing.polarizationIn_Injective, IsApproximateSubgroup.image, LinearIsometryEquiv.coe_ofEq_apply, ContDiffMapSupportedIn.coe_smul, MeasureTheory.SimpleFunc.coe_piecewise, ContinuousMap.spectrum_eq_preimage_range, OrderAddMonoidHom.coe_addMonoidHom, PadicInt.mahlerSeries_apply, HahnSeries.SummableFamily.coe_powers, Path.extend_apply, Con.coe_inf, Algebra.IsEpi.injective_lift_mul, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_apply, ContinuousLinearEquiv.isBigO_sub, AlgebraicGeometry.Scheme.Pullback.Triplet.hy, LinearMap.restrictScalarsₗ_apply, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_assoc, AlgCat.id_apply, MonoidAlgebra.mapRangeAlgHom_single, LinearIsometry.edist_map, Polynomial.roots_X_pow_char_pow_sub_C_pow, LieModuleHom.coe_smul, OrderIso.map_ciInf_of_directed, MeasureTheory.Measure.instIsProbabilityMeasureBindCoeKernelOfIsMarkovKernel, sSupHom.bot_apply, Equiv.pointReflection_vsub_right, BoundedContinuousFunction.coe_posPart, SimpleGraph.Embedding.mapNeighborSet_apply_coe, Matrix.cRank_toNat_eq_rank, uniformContinuous_ofMul, Submonoid.LocalizationMap.lift_localizationMap_mk', AddSubmonoid.toNatSubmodule_toAddSubmonoid, Module.Basis.localizationLocalization_apply, AffineMap.homothety_neg_one_apply, SummationFilter.support_map, SeparationQuotient.outCLM_uniformContinuous, LinearMap.exists_antilipschitzWith, HahnSeries.SummableFamily.isPWO_iUnion_support, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, Matrix.conjTransposeLinearEquiv_apply, Finsupp.coe_pointwise_smul, InnerProductSpace.isSymmetricProjection_rankOne_self, ProbabilityTheory.Kernel.compProd_eq_tsum_compProd, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, VitaliFamily.ae_tendsto_lintegral_div, mulRothNumber_spec, AddSubsemigroup.centerToAddOpposite_symm_apply_coe, AlternatingMap.zero_apply, SchwartzMap.continuous, uliftPowersHom_symm_apply, UniformOnFun.postcomp_uniformContinuous, MulEquiv.coprodAssoc_symm_apply_inr_inr, NumberField.mulHeight_eq, Affine.Simplex.interior_restrict, CategoryTheory.Arrow.equivSigma_apply_snd_snd, Algebra.TensorProduct.right_algebraMap_apply, AddMonoidHom.mrange_eq_top, Localization.map_isUnit_of_le, Matrix.isNilpotent_toLin'_iff, CategoryTheory.bijection_natural, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, Finset.affineCombination_eq_linear_combination, Polynomial.coeff_mapAlgHom_apply, CategoryTheory.Functor.Initial.limitConeComp_isLimit, FreeCommRing.lift_of, VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSet, Multiset.prod_X_sub_C_dvd_iff_le_roots, TopCat.sigmaIsoSigma_inv_apply, divRadical_dvd_derivative, Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRing, Ideal.map_relNorm, Coalgebra.TensorProduct.lid_tmul, Polynomial.aeval_prod_apply, Polynomial.leadingCoeff_mul_prod_normalizedFactors, Orientation.volumeForm_zero_pos, ModuleCat.exteriorPower.desc_mk, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', ChainComplex.toSingle₀Equiv_apply_coe, iterateFrobeniusEquiv_add_apply, MvPolynomial.coe_monomial, ofLex_pow, Ordinal.CNF.coeff_of_not_mem_CNF, AffineMap.toFun_eq_coe, ContinuousMap.Homotopy.pathExtend_evalAt, LinearMap.trace_one, RatFunc.mk_eq_div', CategoryTheory.Limits.Pi.reindex_inv_π_assoc, SetTheory.PGame.Domineering.shiftRight_apply, AddMonoidHom.toAddHom_coe, Module.Basis.constrL_apply, PresheafOfModules.unit_map_one, OrderDual.toDual_inj, SkewMonoidAlgebra.lift_apply, LinearMap.span_inl_union_inr, Module.AEval'.of_symm_X_smul, MeasureTheory.VectorMeasure.restrictGm_apply, Equiv.algEquiv_apply, ArithmeticFunction.IsMultiplicative.multiplicative_factorization, CircleDeg1Lift.lt_map_of_nat_lt_translationNumber, CliffordAlgebra.reverse_involute, TensorAlgebra.equivFreeAlgebra_symm_ι, selfAdjoint.imaginaryPart_coe, Module.Basis.reindexFinsetRange_apply, ofMul_multiset_prod, homTensorHomEquiv_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, MeasureTheory.Measure.smul_measure_isAddInvariant_le_of_isCompact_closure, NonUnitalRingHom.coe_snd, ConvexIndependent.comp_embedding, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero, Equiv.Perm.cycleType_ofSubtype, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, QuadraticMap.associated_apply, AddSubgroup.tendsto_zmultiples_subtype_cofinite, CategoryTheory.Functor.FullyFaithful.homEquiv_symm_apply, LieModule.mem_genWeightSpace, CompHausLike.homeoOfIso_symm_apply, Equiv.equivPUnit_symm_apply, WeierstrassCurve.Jacobian.eval_polynomialX, ProbabilityTheory.Kernel.prodMkLeft_apply, Finset.eraseNone_none, Subgroup.centerCongr_apply_coe, Polynomial.aeval_add_of_sq_eq_zero, monomial_mem_adjoin_monomial, MvPowerSeries.X_def, MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasure_of_mem, Matrix.IsHermitian.charpoly_cfc_eq, Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero, Polynomial.derivativeFinsupp_apply_toFun, Equiv.pointReflection_midpoint_right, MvPolynomial.totalDegree_rename_le, IsometryEquiv.hausdorffMeasure_image, NormedSpace.norm_expSeries_summable, WithVal.apply_symm_equiv, MeasureTheory.measure_inv_smul_sdiff, Polynomial.Chebyshev.aeval_T, Valuation.val_eq_one_iff, ExteriorAlgebra.GradedAlgebra.ι_sq_zero, ContinuousLinearEquiv.hasMFDerivAt, Polynomial.aeval_comp, OrderIso.supIrredLowerSet_symm_apply, ProbabilityTheory.Kernel.lintegral_withDensity, MeasureTheory.ConvolutionExistsAt.integrable_swap, Condensed.finYoneda_map, Monoid.Coprod.con_inv_mul_cancel, Equiv.equivCongr_refl_right, ProbabilityTheory.Kernel.rnDeriv_eq_rnDeriv_measure, MvPolynomial.C_apply, AddValuation.map_add_of_distinct_val, Equiv.Perm.subtypeCongr.right_apply_subtype, Finset.sum_map, MeasureTheory.measure_neg_null, RootPairing.linearIndependent_iff_coxeterWeightIn_ne_four, DirectSum.coe_of_mul_apply_add, AddChar.coe_toMonoidHomEquiv, OrderIso.ofRelIsoLT_apply, SchwartzMap.laplacianCLM_eq', Equiv.subtypeSubtypeEquivSubtype_apply_coe, Polynomial.deriv_aeval, ContinuousWithinAt.eval, CircleDeg1Lift.coe_toOrderIso_symm, VectorBundleCore.trivializationAt_coordChange_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_fst, CategoryTheory.CartesianClosed.homEquiv_apply_eq, CategoryTheory.Classifier.SubobjectRepresentableBy.homEquiv_eq, RootPairing.pairing_reflectionPerm_self_left, IsModuleTopology.continuous_bilinear_of_pi_fintype, DoubleCentralizer.nnnorm_def, ContMDiffMap.coe_nsmul, MvPolynomial.coe_mapEquivMonic_comp', TensorProduct.mk_apply, MeasureTheory.Measure.comapₗ_apply, AlgEquiv.ext_iff, ofColex_smul', Bialgebra.algebraMap_injective, IsLocalization.mk'_eq_mul_mk'_one, Equiv.Perm.mem_list_cycles_iff, RCLike.re_monotone, Monoid.IsTorsion.torsionMulEquiv_apply, AddSubmonoid.toNatSubmodule_closure, DFinsupp.mapRange.addEquiv_apply, MulEquiv.prodMultiplicative_apply, pow_toDual, Subgroup.mem_map_equiv, QuadraticMap.IsometryEquiv.toIsometry_apply, IsLocalization.ringEquivOfRingEquiv_symm_apply, IsLocalizedModule.finsetIntegerMultiple_image, RootPairing.weylGroup_apply_root, MonCat.FilteredColimits.M.map_mk, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, image_openSegment, Rack.envelAction_prop, MeasureTheory.measure_eq_zero_or_top_of_subset_compl_sigmaFiniteSet, LinearMap.BilinForm.dualSubmodule_span_of_basis, RingCon.ofMatrix_rel, Polynomial.exists_eq_gaussNorm, CliffordAlgebra.star_def, AffineEquiv.pointReflection_fixed_iff_of_module, PrincipalSeg.isSuccPrelimit_apply_iff, monovary_toDual_right, MvPowerSeries.map_subst, StieltjesFunction.measure_Iic_of_tendsto_atBot_atBot, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, HahnSeries.map_C, CuspFormClass.petersson_bounded_left, AddMonCat.forget_map, DirectSum.IsInternal.subordinateOrthonormalBasis_subordinate, DiscreteQuotient.map_comp_proj, Algebra.sInf_toSubmodule, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, CategoryTheory.Bicategory.mateEquiv_symm_apply', CircleDeg1Lift.translate_iterate, MeasurableEquiv.coe_IicProdIoc_symm, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_symm_apply, QuadraticMap.map_zero, RingEquiv.symm_apply_apply, Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero, unitarySubgroupUnitsEquiv_apply_coe, Equiv.sumAssoc_apply_inl_inl, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, Homeomorph.continuousMapOfUnique_apply, MeasureTheory.Content.lt_top, ContinuousAlternatingMap.coe_smul, ExteriorAlgebra.lift_comp_ι, Profinite.NobelingProof.πs'_apply_apply, DifferentiableAt.fderiv_norm_self, ProbabilityTheory.Kernel.integrable_densityProcess, Filter.map_sub, Polynomial.nextCoeff_C_mul_X_add_C, Diffeomorph.image_eq_preimage_symm, exists_increasing_or_nonincreasing_subseq, RelEmbedding.coe_toEmbedding, AddMonoidAlgebra.decomposeAux_coe, Polynomial.monic_mapAlg_iff, Order.pred_toMul, BoundedContinuousFunction.lintegral_lt_top_of_nnreal, AffineMap.apply_lineMap, WithBot.ofDual_apply_coe, MeasureTheory.OuterMeasure.map_comap_le, Cardinal.toENat_lt_natCast_iff, matPolyEquiv_symm_apply_coeff, AddAut.conj_symm_apply, CommAlgCat.algEquivOfIso_apply, Matrix.adjugate_fin_three, RCLike.im_ofReal_pow, Polynomial.ofFinsupp_single, Matrix.natCast_fin_three, Finsupp.DegLex.single_lt_iff, NumberField.Units.span_basisOfIsMaxRank, Submonoid.centerToMulOpposite_apply_coe, CategoryTheory.Localization.homEquiv_eq, Dilation.coe_mkOfNNDistEq, PartOrdEmb.hom_inv_apply, MeasureTheory.SimpleFunc.coe_star, Matrix.toLinearEquiv'_symm_apply, MvPowerSeries.ext_iff, LinearMap.BilinForm.IsSymm.eq, GroupExtension.Section.exists_mul_eq_mul_mul_inl, AffineMap.linear_injective_iff, StarAlgEquiv.one_apply, CommRing.Pic.mapRingHom_id_apply, LinearIsometryEquiv.smul_apply, Polynomial.toLaurent_injective, PiTensorProduct.subsingletonEquiv_apply_tprod, ProbabilityTheory.uniformOn_empty, LaurentSeries.val_le_one_iff_eq_coe, stdSimplex.eq_one_of_unique, WeierstrassCurve.Projective.eval_polynomialX, LinearEquiv.uniqueProd_apply, PowerSeries.constantCoeff_invUnitsSub, DFinsupp.sigmaCurryLEquiv_apply, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_apply, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, Equiv.Perm.cycleOf_apply_apply_pow_self, Equiv.hasSum_iff, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc, Equiv.punitProd_symm_apply, PiTensorProduct.constantBaseRingEquiv_symm, Polynomial.scaleRoots_eval₂_eq_zero, DistLat.ext_iff, FirstOrder.Language.DirectedSystem.map_self, LinearMap.hasStrictDerivAt, AddMonoidAlgebra.lsingle_apply, AddEquiv.toMultiplicativeRight_apply_symm_apply, LinearIsometryEquiv.coe_injective, LinearIsometryEquiv.contDiff, LinearMap.BilinForm.mul_toMatrix'_mul, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, WeierstrassCurve.Projective.baseChange_polynomial, continuous_algebraMap, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, FreeGroup.map.mk, ContDiff.continuous_fderiv_apply, Sym2.mkEmbedding_apply, Matrix.GeneralLinearGroup.continuous_det, Poly.neg_apply, TensorProduct.mapOfCompatibleSMul_surjective, AffineMap.hasDerivAt_lineMap, PrimeSpectrum.isIdempotentElemEquivClopens_symm_bot, DistLat.Iso.mk_inv, LinearMap.toMatrixAlgEquiv_id, ProbabilityTheory.Kernel.martingale_densityProcess, EisensteinSeries.gammaSetDivGcdSigmaEquiv_symm_eq, OrderAddMonoidHom.addCommute_inl_inr, MeasureTheory.FiniteMeasure.tendsto_iff_forall_lintegral_tendsto, Trivialization.linearEquivAt_apply, AddEquiv.uniqueProd_symm_apply, Polynomial.le_trailingDegree_monomial, Algebra.algebraMap_intNorm_fractionRing, QuaternionAlgebra.algebraMap_injective, DirectSum.ofPow, normHom_apply, IsSublattice.of_dual, fderivWithin_continuousAlternatingMap_apply_const_apply, Finset.Colex.singleton_le_toColex, AddHom.op_apply_apply, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois_finite_family, Polynomial.prod_multiset_root_eq_finset_root, Polynomial.dvd_C_mul, ContinuousLinearEquiv.piUnique_apply, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality', ContinuousMulEquiv.symm_comp_self, Equiv.Perm.inv_eq_iff_eq, RelIso.emptySumLex_apply, UniformOnFun.ofFun_inv, Complex.equivRealProdCLM_symm_apply, Polynomial.iterate_derivative_derivative_mul_X_sq, HahnSeries.single_eq_zero_iff, Nat.ordProj_dvd_ordProj_iff_dvd, Tropical.tropEquiv_coe_fn, StarAlgHom.coe_mk', ContinuousMulEquiv.eq_symm_apply, AddMonoidAlgebra.of_apply, FirstOrder.Language.Equiv.refl_apply, CartanMatrix.D_three, AddMonoidHom.isClosed_range_coe, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, Seminorm.convexOn, OrderIso.divRight₀_symm_apply, UniqueFactorizationMonoid.normalize_normalized_factor, Matrix.toMvPolynomial_map, ContinuousMultilinearMap.map_update_add, MvPolynomial.single_eq_monomial, CategoryTheory.Bicategory.Adjunction.homEquiv₂_apply, Equiv.Perm.extendDomain_apply_subtype, IsFractionRing.self_iff_surjective, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, AddMonoidAlgebra.gradeBy.isInternal, AlgEquiv.equivCongr_apply, Equiv.sigmaSigmaSubtype_symm_apply, Associates.out_mk, AlgebraicGeometry.Scheme.preimage_basicOpen_top, MvPowerSeries.trunc_one, IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_apply, finsuppTensorFinsupp'_single_tmul_single, spectrum.algebraMap_mem_iff, LinearMap.det_eq_one_of_not_module_finite, DirectSum.of_zero_smul, CompHausLike.isClosedMap, CircleDeg1Lift.map_int_of_map_zero, Finsupp.mapDomain.coe_linearEquiv, ZFSet.coeEquiv_apply_coe, IsometryEquiv.ediam_preimage, FiberBundle.pullback_trivializationAtlas', MultilinearMap.coe_sum, CStarAlgebra.nnnorm_le_iff_of_nonneg, Matrix.SpecialLinearGroup.map_apply_coe, PEquiv.mul_toMatrix_apply, UniversalEnvelopingAlgebra.ι_comp_lift, AlgHom.opComm_symm_apply_apply, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, Finsupp.single_eq_of_ne, Homeomorph.sumProdDistrib_symm_apply, MonomialOrder.le_degree, Finset.weightedVSub_empty, SubAddAction.conjMap_ofFixingAddSubgroup_bijective, MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder_of_subset, LocallyConstant.congrRightₗ_apply_apply, Derivation.comp_aeval_eq, Algebra.Extension.Cotangent.val_smul''', AddCommGrpCat.ext_iff, ContinuousLinearMap.const_apply_apply, Polynomial.X_pow_sub_C_separable_iff, CFC.spectrum_algebraMap_eq, Polynomial.aeval_homogenize_X_one, ContinuousAt.clm_apply, Module.Basis.orientation_eq_iff_det_pos, CliffordAlgebraQuaternion.k_quaternionBasis, PreErgodic.measure_self_or_compl_eq_zero, CategoryTheory.PreGaloisCategory.toAut_hom_app_apply, OrderIso.to_galoisConnection, Diffeomorph.sumAssoc_coe, AddValuation.toValuation_ofValuation, DomMulAct.isInducing_mk_symm, QuaternionAlgebra.equivTuple_symm_apply, MulHom.map_multiset_ne_zero_prod, map_complEDS₂, RingCon.op_iff, MeasureTheory.Measure.mapₗ_congr, RingAut.one_apply, IsPrimitiveRoot.coe_autToPow_apply, IntermediateField.restrictRestrictAlgEquivMapHom_apply, Ideal.kerLiftAlg_injective, WeakDual.CharacterSpace.continuousMapEval_bijective, OneHom.coe_mk, NumberField.Units.logEmbeddingQuot_apply, IsClosed.measure_eq_one_iff_eq_univ, DFinsupp.lex_def, Algebra.norm_eq_prod_embeddings, OrderIso.mulLeft₀_apply, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_naturality_apply, affineSpan_convexHull, MulHom.comp_apply, NumberField.InfinitePlace.pos_iff, ArithmeticFunction.coe_mul, zpowersMulHom_apply, equicontinuousWithinAt_iff_continuousWithinAt, Module.Flat.iff_rTensor_injective, HahnEmbedding.Partial.coeff_eq_of_mem, LinOrd.inv_hom_apply, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_def, LieModule.Weight.coe_coe, StarRingEquiv.symm_apply_apply, AlgebraicGeometry.PresheafedSpace.GlueData.pullback_base, Representation.prod_apply_apply, CompactlySupportedContinuousMap.coe_toRealLinearMap, IsPurelyInseparable.minpoly_eq, Matrix.coe_detMonoidHom, LowerSemicontinuousOn.isClosed_re_epigraph, SeparatingDual.dualMap_surjective_iff, LinearIsometry.id_apply, NumberField.canonicalEmbedding.integralBasis_repr_apply, RingHom.mem_range_self, Ordinal.liftPrincipalSeg_coe, CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, Representation.tprod_apply, OmegaCompletePartialOrder.ContinuousHom.ωScottContinuous, ContinuousAffineEquiv.prodComm_symm_apply, InnerProductGeometry.norm_toLp_symm_crossProduct, Module.Invertible.algEquivOfRing_apply, MeasureTheory.measure_le_inter_add_diff, mem_closure_isSwap, Delone.DeloneSet.mapIsometry_symm_apply_carrier, Polynomial.nextCoeff_mul_C, AddCommMonCat.equivalence_functor_map, Polynomial.coeff_X_sub_C_mul, WeierstrassCurve.Affine.CoordinateRing.mk_ψ, CategoryTheory.Functor.map_isoCongr, sigmaFinsuppEquivDFinsupp_add, MeasureTheory.IsSetSemiring.isSetRing_supClosure, Matrix.neg_of, dualTensorHom_apply, MvPolynomial.coeff_C, IsNoetherian.range_finsetBasis, Subsemigroup.topEquiv_symm_apply_coe, Cubic.of_a_eq_zero, invMonoidHom_apply, Finset.Colex.toColex_image_lt_toColex_image, BilinForm.mul_toMatrix_mul, Polynomial.comp_C_mul_X_eq_zero_iff, ZSpan.measureReal_fundamentalDomain, InfHom.dual_apply_toFun, EuclideanGeometry.orthogonalProjection_apply', IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, MeasureTheory.condExpIndSMul_empty, CategoryTheory.Functor.coconeTypesEquiv_apply_pt, Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed, AddConstMapClass.semiconj, Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero, AffineBasis.coe_reindex, ContinuousAddMonoidHom.inl_toFun, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, NonUnitalStarSubalgebra.val_inclusion, OrderAddMonoidHom.ext_iff, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, SmoothPartitionOfUnity.contDiffAt_finsum, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.liftHom_fac, MeasureTheory.measure_vadd, Topology.WithScott.toScott_ofScott, MeasureTheory.prob_le_one, AddSubgroup.toZModSubmodule_toAddSubgroup, CliffordAlgebra.involute_mem_evenOdd_iff, Nucleus.mem_toSublocale, CentroidHom.neg_apply, MeasureTheory.SimpleFunc.coe_le, IsGalois.intermediateFieldEquivSubgroup_apply, SymAlg.unsym_inv, fourier_one, MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, ContinuousMap.coeFnAlgHom_apply, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, AddMonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app, LieRingModule.toEnd_apply_apply, FreeLieAlgebra.lift_comp_of, FintypeCat.toProfinite_map_hom_hom_apply, gal_X_pow_sub_C_isSolvable_aux, PrincipalSeg.apply_covBy_apply_iff, MvPolynomial.bind₂_map, Equiv.sub_def, RingHom.Bijective.isStableUnderBaseChange, MeasureTheory.measure_union_lt_top_iff, FunOnFinite.continuous_linearMap, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, isQuasiregular_iff', QuadraticForm.tensorRId_symm_apply, Polynomial.ofReal_eval, Equiv.forall_congr_left, Equiv.funSplitAt_symm_apply, HasFPowerSeriesOnBall.fderiv_eq, Finsupp.weight_single, val_toUnits_apply, Polynomial.degree_quadratic, WittVector.frobenius_bijective, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, MeasureTheory.OuterMeasure.coe_add, SSet.prodStdSimplex.objEquiv_naturality, Seminorm.coe_restrictScalars, RootPairing.pairing_reflectionPerm_self_right, Equiv.prodSumDistrib_apply_right, OrderAddMonoidHom.coe_zero, NumberField.Units.basisOfIsMaxRank_apply, TopCat.pullbackIsoProdSubtype_inv_fst_assoc, CoalgEquiv.refl_apply, coe_normGroupNorm, Finset.sum_apply', DFinsupp.sumZeroHom_apply, OrderIso.isCompl, Nat.exists_factorization_lt_of_lt, Module.Invertible.rTensorEquiv_apply_apply, AddMonoidHom.toMultiplicativeRight_symm_apply_apply, Ideal.relNorm_le_comap, Fin.succAboveEmb_apply, SpectrumRestricts.algebraMap_image, PowerSeries.rescale_rescale, ContinuousMap.coeFnRingHom_apply, Rep.coindVEquiv_symm_apply_coe, LinearMap.localized'_range_eq_range_localizedMap, AlgebraicGeometry.Scheme.Pullback.range_fst_comp, WithOne.mapMulHom_coe, BoundedContinuousFunction.isBounded_range, exists_extension_of_le_sublinear, CategoryTheory.Coverage.mem_toGrothendieck_sieves_of_superset, CategoryTheory.ComposableArrows.opEquivalence_unitIso_inv_app, SubsemiringClass.subtype_injective, AlternatingMap.map_congr_perm, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, ArithmeticFunction.moebius_apply_of_squarefree, LinearEquiv.lTensor_tmul, instFullFunctor, Monoid.Coprod.map_apply_inr, RingEquiv.map_neg_one, PseudoMetric.IsUltra.le_sup', Ideal.algebraMap_residueField_surjective, ZeroAtInftyContinuousMap.coe_zero, Finset.sum_smul_const_vsub_eq_vsub_affineCombination, Associates.mkMonoidHom_apply, Equiv.Perm.prodExtendRight_apply_ne, MeasureTheory.Measure.coeAddHom_apply, PowerBasis.map_gen, BoxIntegral.BoxAdditiveMap.coe_injective, Quaternion.fst_imK_dualNumberEquiv_symm, DirectSum.coe_congr_addEquiv, TopologicalSpace.OpenNhds.op_map_id_obj, Cardinal.cast_toNat_eq_iff_lt_aleph0, MeasureTheory.OuterMeasure.map_le_restrict_range, Unitary.map_coe, DirectSum.coe_decompose_mul_add_of_left_mem, AddMonoid.Coprod.inl_injective, AbsoluteValue.apply_nat_le_self, AddMonoidHom.map_add_neg, Submonoid.LocalizationMap.mk'_one, FinBddDistLat.coe_id, LinearIsometryEquiv.coe_trans, PowerSeries.trunc_trunc_mul_trunc, CategoryTheory.Limits.Concrete.prodEquiv_apply_fst, inner_self_im, CategoryTheory.nerve.nonempty_compStruct_iff, MeasureTheory.Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, SubAddAction.ofFixingAddSubgroup.append_left, RingHomIsometric.enorm_map, WithBot.coe_addHom, LocallyConstant.map_apply, MvPolynomial.transcendental_polynomial_aeval_X_iff, PadicAlgCl.norm_extends, Monoid.PushoutI.NormalWord.prod_cons, Equiv.Finset.union_inl, CategoryTheory.Limits.kernel.lift_ι_apply, Module.Basis.linearMap_apply, FreeMonoid.lift_comp_of, RootPairing.Equiv.root_indexEquiv_eq_smul, MeasureTheory.Measure.integral_condKernel, RingHom.coe_rangeRestrictField, Polynomial.monic_X_pow_sub_C, AdicCompletion.mkₐ_apply_coe, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, ContinuousAlgEquiv.symm_trans_apply, normalize_eq_normalize_iff, OrderHom.withBotMap_coe, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_snd_coe, MeasureTheory.SimpleFunc.nnnorm_approxOn_le, GenLoop.mk_apply, AlgebraicGeometry.Scheme.germToFunctionField_injective, AddEquiv.map_dfinsuppSumAddHom, Subalgebra.centralizer_coe_image_includeRight_eq_center_tensorProduct, DirichletCharacter.LSeriesSummable_mul, ProbabilityTheory.variance_map_equiv, AddMonoid.End.intCast_apply, RelIso.bijective, CoalgEquiv.coe_toLinearEquiv, InnerProductSpace.gramSchmidtOrthonormalBasis_apply, ContinuousLinearMap.uniformContinuous, NonarchAddGroupSeminorm.coe_zero, QuadraticMap.map_finsuppSum, Cardinal.aleph_add_aleph, Monoid.Coprod.prod_mk_fst_snd, Complex.sq_norm, Matrix.eta_fin_three, lipschitzOnWith_cfc_fun_of_subset, Dilation.isClosedEmbedding, AffineMap.left_vsub_lineMap, ContinuousMonoidHom.snd_toFun, Polynomial.rootsExpandEquivRoots_apply, Metric.Snowflaking.image_ofSnowflaking_eball, Set.singletonAddMonoidHom_apply, MeasureTheory.SimpleFunc.exists_forall_norm_le, Real.volume_singleton, PowerSeries.coeff_invOfUnit, ProfiniteGrp.denseRange_toLimit, Fin.natAddOrderEmb_apply, smul_preimage_set_subset, LieAlgebra.Extension.incl_injective, PiTensorProduct.projectiveSeminorm_tprod_le, Matrix.toLinearMap₂_compl₁₂, Affine.Simplex.affineCombination_mem_closedInterior_face_iff_nonneg, CompactlySupportedContinuousMap.smul_apply, MeasureTheory.Measure.restrict_apply, AddMonoidHom.zero_apply, LieModule.Weight.IsZero.eq, Matrix.eRank_reindex, MeasureTheory.measure_lintegral_le_pos, ModularForm.coe_natCast, LinearAlgebra.FreeProduct.ι_apply, QuaternionAlgebra.imK_swapEquiv_symm_apply, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', Field.primitive_element_iff_algHom_eq_of_eval', CategoryTheory.Limits.Types.Small.productIso_inv_comp_π, Complex.Gamma_conj, LinearEquiv.coe_neg, UpperHalfPlane.σ_mul, RingHom.compLeft_apply, Units.map_neg, Derivation.neg_apply, ValuativeExtension.mapValueGroupWithZero_strictMono, Polynomial.leadingCoeff_linear, LocallyConstant.congrLeftₐ_apply_apply, multiplicity_addValuation_apply, MeasureTheory.Measure.mutuallySingular_of_mutuallySingular_compProd, ContinuousLinearMap.proj_apply, AdjoinRoot.coe_mapAlgHom, CategoryTheory.Limits.FintypeCat.productEquiv_apply, RingOfIntegers.isUnit_norm_of_isGalois, NonUnitalAlgHom.map_mul, Finset.image_pow_of_ne_zero, GroupExtension.Equiv.refl_apply, nsmulAddMonoidHom_apply, MulAut.coe_inv, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, NonarchAddGroupSeminormClass.map_neg_eq_map', AffineMap.hasDerivWithinAt_lineMap, PeriodPair.basis_zero, CategoryTheory.uliftYonedaEquiv_symm_map, Polynomial.rootMultiplicity_eq_natFind_of_ne_zero, AddSubsemigroup.mem_map_of_mem, Finsupp.lcoeFun_apply, UniformFun.postcomp_isUniformInducing, Module.Finite.exists_nat_not_surjective, TensorProduct.quotientTensorEquiv_symm_apply_mk_tmul, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, ProbabilityTheory.Kernel.trajContent_tendsto_zero, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, Polynomial.isMonicOfDegree_two_iff, MeasureTheory.Integrable.norm_integral_condDistrib, DomAddAct.isInducing_mk, LinearIsometryEquiv.piLpCongrLeft_apply, AlgebraicGeometry.Scheme.Modules.germ_restrictStalkNatIso_hom_app, NonUnitalSubsemiring.unitization_apply, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_pos_eq_zero_of_hasSubGaussianMGF_zero, coe_basisOfTopLeSpanOfCardEqFinrank, PowerBasis.leftMulMatrix, AddMonoidHom.map_finsum_mem', BoxIntegral.Box.measure_coe_lt_top, AffineMap.pi_apply, ModuleCat.imageIsoRange_inv_image_ι_apply, ProbabilityTheory.iIndepFun.meas_biInter, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π, NumberField.ComplexEmbedding.IsConj.eq, CategoryTheory.GrothendieckTopology.top_mem, TopHom.dual_symm_apply_apply, MeasurableEquiv.symm_preimage_preimage, Polynomial.C_mul_X_pow_eq_monomial, AlgEquiv.coe_pow, MonoidAlgebra.domCongr_single, FreeAbelianGroup.liftAddEquiv_symm_apply, CategoryTheory.Functor.IsLocallyFull.functorPushforward_imageSieve_mem, ContinuousLinearMap.fderiv_of_bilinear, TestFunction.coe_smul, has_fderiv_at_filter_real_equiv, PiTensorProduct.ofDirectSumEquiv_symm_lof_tprod, toBoolAlg_zero, basisOfLinearIndependentOfCardEqFinrank_repr_apply, Polynomial.nextCoeff_X_add_C, ExteriorAlgebra.liftAlternating_ιMulti, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, AddSubmonoid.LocalizationMap.of_addEquivOfAddEquiv_apply, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, Homeomorph.map_nhds_eq, MonomialOrder.leadingTerm_monomial, PrimeSpectrum.toPiLocalization_not_surjective_of_infinite, NumberField.Units.regulator_eq_det, IsDedekindDomain.primesOverEquivPrimesOver_inertiagDeg_eq, MvPowerSeries.WithPiTopology.continuous_coeff, Ordinal.toNatOrdinal_min, orthonormalBasis_one_dim, finPiFinEquiv_apply, DFinsupp.mem_singleton_apply_iff, Height.AdmissibleAbsValues.isNonarchimedean, CategoryTheory.Iso.toAlgEquiv_symm_apply, ThreeAPFree.addRothNumber_eq, Matroid.mapEmbedding_isBase_iff, PrimeSpectrum.preimage_comap_zeroLocus, NonemptyInterval.dual_pure, MvPolynomial.support_rename_of_injective, PowerSeries.coe_mul, cfcₙHom_integral, EuclideanGeometry.orthogonalProjection_orthogonalProjection_of_le, unitary.linearIsometryEquiv_coe_symm_apply, ContinuousMultilinearMap.neg_apply, PiTensorProduct.tprodL_toFun, LieModuleHom.coe_zsmul, OrthogonalIdempotents.equiv, SSet.stdSimplex.spineId_arrow_apply_zero, MeasureTheory.setIntegral_condExpInd, IncidenceAlgebra.apply_eq_zero_of_not_le, StieltjesFunction.measure_univ_of_tendsto_atTop_atTop, MulEquiv.withZero_apply_symm_apply, Matrix.replicateRow_empty, WithBot.Ico_bot_coe, SimpleGraph.Copy.comp_apply, AdicCompletion.map_comp_apply, IsIntegralClosure.isIntegral_iff, ContinuousMap.Homotopy.compContinuousMap_apply, AddCircle.add_projection_respects_measure, MeasureTheory.Measure.map_piSingleton, PowerSeries.trunc_mul_C, MvPolynomial.eval_ofNat, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, LieModuleHom.coe_injective, ContinuousMap.dist_lt_of_dist_lt_modulus, DifferentiableWithinAt.continuousAlternatingMap_apply_const, Metric.Snowflaking.preimage_toSnowflaking_emetricClosedBall, continuousOn_cfc_setProd, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, NonUnitalStarAlgHom.comp_apply, CompactExhaustion.mem_find, HahnSeries.order_single_mul_of_isRegular, Representation.IntertwiningMap.isIntertwiningMap_of_mem_center, FintypeCat.comp_apply, MeasureTheory.ae_eq_set, ContinuousLinearEquiv.hasMFDerivWithinAt, Cardinal.preAleph_omega0, iteratedFDerivWithin_succ_apply_right, PiTensorProduct.ofFinsuppEquiv_tprod_single, MonoidHom.smulOneHom_apply, Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalence, NonUnitalStarRingHom.one_apply, MeasureTheory.Content.innerContent_exists_compact, MeasureTheory.Measure.InnerRegular.comap, CliffordAlgebra.changeForm_ι_mul, PresheafOfModules.map_smul, Path.cast_coe, ProbabilityTheory.condDistrib_ae_eq_iff_measure_eq_compProd, LieModule.traceForm_lieSubalgebra_mk_right, MonoidAlgebra.scalarTensorEquiv_tmul, Matrix.of_add_of, PMF.ext_iff, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, Matrix.cramer_apply, Abelianization.map_of, MeasureTheory.Measure.MeasureDense.fin_meas_approx, tendsto_integral_exp_smul_cocompact, RingEquiv.cast_apply, AlternatingMap.map_update_add, OrderMonoidIso.symm_comp_self, mem_affineSpan_iff_eq_affineCombination, Matroid.Indep.mapEmbedding, IsometryEquiv.preimage_emetric_ball, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, Diffeomorph.sumCongr_inl, ContinuousMap.Homotopy.comp_apply, LinearMap.lsum_apply, OrderIso.coe_symm_toEquiv, Finsupp.toFreeAbelianGroup_comp_singleAddHom, AddMonoidHom.coe_coe, xInTermsOfW_eq, FGModuleCat.FGModuleCatEvaluation_apply, Polynomial.eq_X_add_C_of_degree_le_one, IsometryEquiv.comp_continuousOn_iff, ModuleCat.epi_iff_surjective, HeytingHom.coe_comp, AddEquiv.addMonoidHomCongrLeft_apply, Complex.dist_self_conj, LinearEquiv.funUnique_symm_apply, CategoryTheory.Abelian.subobjectIsoSubobjectOp_apply, SchwartzMap.toBoundedContinuousFunctionCLM_apply, Hamming.nnnorm_eq_hammingNorm, Cardinal.toENat_lift, ZeroAtInftyContinuousMap.ContinuousMap.liftZeroAtInfty_apply_toFun, AffineIsometryEquiv.continuousOn, Finset.Ioo_ofDual, RelHom.mul_apply, OrderIso.map_ciSup, RCLike.conj_ofReal, Module.Basis.forall_coord_eq_zero_iff, Cardinal.mk_subtype_of_equiv, StarAlgHom.realContinuousMapOfNNReal_apply, LinearMap.localized'_ker_eq_ker_localizedMap, OrderIso.coe_dualDual, MeasureTheory.SimpleFunc.pair_preimage_singleton, AddCommGrpCat.free_map_coe, Equiv.extendSubtype_not_mem, ArithmeticFunction.IsMultiplicative.map_gcd, extDeriv_apply_vectorField, AddMonoidHom.compl₂_apply, Set.preimage_sub_preimage_subset, curveIntegral_segment, Matrix.cRank_toNat_eq_finrank, toDual_wcovBy_toDual_iff, AddMonoidHom.mulOp_apply_apply, Equiv.Perm.image_inv, Module.Ray.linearEquiv_smul_eq_map, DFinsupp.erase_same, TestFunction.postcompCLM_apply, MvPolynomial.eval_eq_eval_mv_eval', Nat.factorization_eq_one_of_squarefree, Finsupp.unique_single, DFinsupp.sum_eq_sum_fintype, MulAut.coe_one, ProfiniteGrp.comp_apply, Path.ofLine_mem, FintypeCat.uSwitchEquiv_naturality, RootPairing.exists_value, AlgebraicGeometry.morphismRestrict_base, Equiv.Perm.fixed_point_card_lt_of_ne_one, MulEquiv.subgroupCongr_apply, PerfectRing.comp_lift_apply, map_comp_div, CentroidHom.sub_apply, AffineIsometry.lipschitz, finRotate_succ_eq_decomposeFin, sign_zero, MvPolynomial.ACounit_C, MeasureTheory.lintegral_le_iSup_mul, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, ProbabilityTheory.Kernel.boolKernel_apply, SimpleGraph.Embedding.map_mem_edgeSet_iff, MeasureTheory.Integrable.measure_gt_lt_top, MeasureTheory.addEquivAddHaarChar_eq, StarMulEquiv.apply_symm_apply, AddSubmonoid.LocalizationMap.symm_comp_ofAddEquivOfLocalizations_apply', Equiv.iSup_comp, UniformOnFun.tendsto_iff_tendstoUniformlyOn, disjoint_partialSups_right, Derivation.leibniz_inv, IsValuativeTopology.isClopen_sphere, Monoid.fg_iff_exists_freeMonoid_hom_surjective, ProbabilityTheory.stronglyMeasurable_condExpKernel, Real.fourierIntegral_continuousLinearMap_apply, OrthonormalBasis.coe_ofRepr, Module.Relations.Solution.postcomp_var, SemidirectProduct.congr'_apply_right, AddSubgroup.mem_ofAddUnits_iff_toAddUnits_mem, IsCoveringMap.injective_path_homotopic_map, LinearMap.mk₂_apply, CategoryTheory.Limits.Sigma.whiskerEquiv_hom, PowerSeries.IsWeierstrassDivisionAt.degree_lt, BooleanSubalgebra.coe_map, LinearMap.iterateFrobenius_def, OrderIso.finsetSetFinite_symm_apply, subtypeOrEquiv_symm_inl, Equiv.withBotSubtypeNe_symm_apply_coe, ProbabilityTheory.setBernoulli_apply', Monoid.CoprodI.mclosure_iUnion_range_of, infPrime_ofDual, Polynomial.expand_C, CategoryTheory.ShortComplex.ShortExact.ab_injective_f, groupCohomology.coboundaries₂.val_eq_coe, CircleDeg1Lift.coe_toOrderIso_inv, Finsupp.le_def, isAddRegular_ofColex, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, MonoidHom.map_finprod_of_preimage_one, Homeomorph.coe_unitBall_apply_zero, Homeomorph.isBigOWith_congr, Antivary.sum_mul_le_sum_mul_comp_perm, Nucleus.ext_iff, Con.mem_subgroup_iff, RootPairing.PolarizationIn_eq, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, Metric.Snowflaking.isBounded_preimage_ofSnowflaking_iff, Submodule.adjoint_subtypeL, Polynomial.logMahlerMeasure_X_sub_C, CompHausLike.isoEquivHomeo_symm_apply, RootPairing.RootPositiveForm.exists_eq, RelIso.coe_toEmbedding, LieModule.Weight.zero_apply, ProbabilityTheory.iIndepSets_iff, Subgroup.subtype_apply, Equiv.Perm.SameCycle.exists_pow_eq', AddOpposite.opHomeomorph_apply, GaloisConnection.dual, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, NumberField.AdeleRing.algebraMap_snd_apply, LinearMap.toLinearMap_toContPerfPair, DFinsupp.coe_sup, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, inner_re_zero_left, TensorProduct.AlgebraTensorModule.rTensor_comp, AlgEquiv.sumArrowEquivProdArrow_symm_apply_inr, IsSelfAdjoint.neg_algebraMap_norm_le_self, PresheafOfModules.Monoidal.tensorObj_map_tmul, DFinsupp.update_eq_sub_add_single, CommAlgCat.algEquivOfIso_symm_apply, Homeomorph.smul_symm_apply, LinearMap.coe_restrictScalars, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, OrderIso.map_atBot, Polynomial.C_mem_lifts, fixingAddSubmonoid_fixedPoints_gc, Pi.basis_apply, Polynomial.aevalTower_toAlgHom, PowerSeries.hasSum_of_monomials_self, FreeAddMagma.toFreeAddSemigroup_comp_of, Polynomial.monomial_eq_zero_iff, Subsemigroup.mem_map_of_mem, Matrix.comp_transpose, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, Equiv.optionSubtypeNe_symm_of_ne, OrderHom.comp_const, coevaluation_apply_one, AddEquiv.symm_apply_apply, MeasureTheory.Measure.sum_comp_equiv, CliffordAlgebraQuaternion.i_quaternionBasis, Bundle.TotalSpace.toProd_symm_apply_proj, Nat.factorization_choose_prime_pow_add_factorization, AlgHom.comp_apply, MeasureTheory.Measure.mutuallySingular_compProd_right_iff, MatrixEquivTensor.toFunBilinear_apply, Equiv.pprodProd_apply, LatticeHom.dual_apply_toFun, continuous_decomposeProdAdjoint_symm, MonoidAlgebra.basis_apply, LinearMap.isSymmetric_adjoint_mul_self, HahnSeries.coeff_single_zero_mul, CentroidHom.star_apply, AddSubgroup.addSubgroupOfEquivOfLe_apply_coe, MeasureTheory.SimpleFunc.preimage_eq_empty_iff, OrderMonoidIso.val_inv_unitsCongr_symm_apply, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, ModularForm.coe_prodEqualWeights, ContinuousLinearMap.opNorm_mul_apply, Order.isPredPrelimit_toDual_iff, ModuleCat.exteriorPower.map_mk, AffineBasis.toMatrix_apply, gelfandStarTransform_symm_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, Matrix.reindex_mem_rowStochastic_iff, MeasureTheory.exists_pos_measure_of_cover, ContinuousLinearMap.norm_smulRightL, Matrix.piRingEquiv_symm_apply, SMulCommClass.toDistribMulActionHom_toFun, ZeroAtInftyContinuousMap.zero_apply, WittVector.frobenius_frobeniusRotation, TensorPower.mul_assoc, RelHomClass.directedOn, AffineIsometry.comp_continuous_iff, SimpleGraph.Copy.injective, MeasureTheory.AddContent.supClosure_apply_finpartition, Convex.radon_partition, toDual_vadd, MvPolynomial.optionEquivLeft_X_none, FirstOrder.Language.Substructure.coe_subtype, HomogeneousLocalization.val_awayMap, PowerSeries.rescale_zero_apply, FintypeCat.equivEquivIso_symm_apply_symm_apply, Real.volume_pi_Ioc, ContinuousLinearEquiv.uniqueDiffOn_image, inner_self_ofReal_re, Units.orderEmbeddingVal_apply, AddCon.addConGen_of_addCon, IsAdjoinRootMonic.map_modByMonic, isLeftRegular_toMul, AddChar.map_add_eq_mul, CategoryTheory.FinCategory.categoryAsType_id, AffineMap.decomp', LieAlgebra.Extension.lie_incl_mem_ker, IsBaseChange.transvection, AddActionHom.snd_apply, CategoryTheory.PreGaloisCategory.evaluation_injective_of_isConnected, LinearIsometry.equivRange_apply_coe, Metric.Snowflaking.image_toSnowflaking_eball, prevD_eq_toPrev_dTo, CategoryTheory.Limits.IsColimit.homEquiv_apply, LieSubalgebra.toEnd_mk, ProbabilityTheory.Kernel.ae_lt_top_of_comp_ne_top, MvPolynomial.algebraicIndependent_polynomial_aeval_X, Pi.lex_eq_dfinsupp_lex, FreeAddGroup.lift_apply_of, groupCohomology.isMulCocycle₁_of_mem_cocycles₁, Submonoid.closure_singleton_eq, ofDual_pow, LocallyConstant.coeFnMonoidHom_apply, RCLike.conjLIE_apply, commute_lmul_sq_rmul, PowerSeries.substAlgHom_X, DilationEquiv.trans_apply, unitSphereToUnits_apply_coe, MvPowerSeries.le_lexOrder_iff, MonoidHom.apply_mnat, ContinuousAlternatingMap.coe_sub, Submodule.reflection_orthogonalComplement_singleton_eq_neg, LinearMap.toBilin'Aux_toMatrixAux, finSumNatEquiv_symm_apply_fin, PadicInt.coe_addChar_of_value_at_one, MonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, LieAlgebra.coe_rootSpaceWeightSpaceProduct_tmul, ofMul_vadd, FinBddDistLat.inv_hom_apply, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, Subgroup.coe_subtype, RootPairing.Equiv.weightMap_weightEquiv_symm, StarRingEquiv.apply_symm_apply, lipschitzGroup.conjAct_smul_ι_mem_range_ι, Subalgebra.finrank_toSubmodule, FreeGroupBasis.lift_apply_apply, IsTensorProduct.map_map, InverseSystem.PEquivOn.compat, Pi.le_toLex_update_self_iff, AddConstMap.coe_smul, Derivation.map_one_eq_zero, LightProfinite.effectiveEpi_iff_surjective, ContinuousLinearEquiv.comp_fderiv, Finset.weightedVSub_weightedVSubVSubWeights, LaurentPolynomial.degree_C_mul_T, Subalgebra.algebraMap_def, InfHom.dual_id, MvPowerSeries.expand_one_apply, WithTop.ofDual_apply_top, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, CategoryTheory.Functor.Final.colimitCoconeComp_isColimit, BoxIntegral.Box.measure_Icc_lt_top, Equiv.coe_subtypeEquivCodomain_symm, IsLocalRing.map_tensorProduct_mk_eq_top, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_open, ArithmeticFunction.one_apply_ne, Subgroup.centerToMulOpposite_apply_coe, Polynomial.natDegree_mul_leadingCoeff_self_inv, AffineMap.lineMap_vsub_right, Localization.awayMap_surjective_iff, Complex.orthonormalBasisOneI_repr_apply, Finsupp.floorDiv_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, Module.End.intCast_def, Module.Dual.eval_apply, OrderMonoidIso.withZeroUnits_symm_apply, ContinuousLinearMap.isBigO_id, DFinsupp.single_le_iff, Equiv.Perm.sameCycle_symm_apply_right, IsLocalRing.residue_def, ContinuousMapZero.integral_apply, SimplexCategory.toTop_map, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, RCLike.conj_mul, TwoSidedIdeal.orderIsoIsTwoSided_symm_apply, MeasureTheory.L1.setToL1_eq_setToL1SCLM, Representation.coinvariantsTprodLeftRegularLEquiv_apply, Matrix.piLinearEquiv_apply, PadicInt.mahlerSeries_apply_nat, ModuleCat.id_apply, Polynomial.CAlgHom_apply, AddAut.coe_inv, PerfectRing.bijective_frobenius, ZMod.dft_comp_unitMul, Real.volume_emetric_closedBall, MvPolynomial.degreeOf_rename_of_injective, WeierstrassCurve.coe_map_Δ', AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, LinearMap.toMatrix₂_compl₂, Finsupp.sum_ite_eq', GradedTensorProduct.includeLeft_apply, MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure, Equiv.Perm.sign_prodExtendRight, Affine.Triangle.dist_circumcenter_reflection_orthocenter, Polynomial.trailingDegree_C_mul_X_pow, AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_comp_iff_of_isOpenImmersion, MeasureTheory.FiniteMeasure.self_eq_mass_mul_normalize, ArchimedeanClass.orderHom_zero, Polynomial.Monic.quotient_isIntegralElem, MeasureTheory.norm_condExpL2_coe_le, Ordinal.mem_range_omega_iff, Subring.comap_map_eq, FunctionField.valuedFqtInfty.def, Module.End.isUnit_inv_apply_apply_of_isUnit, Pretrivialization.continuousLinearMapCoordChange_apply, PowerSeries.IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, dist_ofAdd, Seminorm.ball_zero_eq_preimage_ball, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, Bundle.Trivial.isInducing_toProd, RingCon.comapQuotientEquivRange_mk, ProbabilityTheory.Kernel.indepFun_iff_measure_inter_preimage_eq_mul, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, finsuppTensorFinsuppLid_symm_single_smul, SameRay.map, Finset.weightedVSubOfPoint_sdiff, NormedAlgebra.exists_isMinOn_norm_sub_smul, WeierstrassCurve.Projective.baseChange_dblXYZ, Polynomial.X_pow_sub_one_eq_prod, Polynomial.toAddCircle.integrable, NonUnitalAlgHom.mem_range, LieHom.ker_eq_bot, DFinsupp.sum_mapRange_index.linearMap, ContinuousMap.smul_apply, DomAddAct.continuous_mk_symm, DirectSum.one_def, TopologicalSpace.Opens.inclusion'_top_functor, AddOreLocalization.numerator_isAddUnit, MeasureTheory.prob_compl_eq_one_sub₀, MvPolynomial.exists_rename_eq_of_vars_subset_range, ProbabilityTheory.Kernel.prod_apply, ContinuousMap.coe_comp, Polynomial.prod_multiset_X_sub_C_dvd, ArchimedeanClass.map_mk_le, Besicovitch.ae_tendsto_rnDeriv, fourier_zero, InnerProductSpace.trace_rankOne, PiTensorProduct.congr_symm_tprod, MonomialOrder.span_leadingTerm_eq_span_monomial, WeierstrassCurve.map_b₈, Ideal.pi_mkQ_surjective, MvPolynomial.optionEquivRight_symm_apply, Nat.factorization_prod_apply, Ergodic.iff_mem_extremePoints_measure_univ_eq, coe_toPrincipalIdeal, Finset.image_nsmul_of_ne_zero, MonoidWithZeroHom.inl_strictMono, Polynomial.degree_cubic_lt, PowerSeries.heval_apply, Cardinal.toNat_monotoneOn, AdjoinRoot.mul_div_root_cancel, rTensorHomEquivHomRTensor_apply, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, BoxIntegral.Integrable.toBoxAdditive_apply, NumberField.Units.coe_coe, MeasureTheory.Measure.addHaarMeasure_eq_iff, Complex.normSq_I, LinearMap.trace_eq_contract_apply, PiTensorProduct.constantBaseRingEquiv_tprod, Polynomial.eq_X_add_C_of_natDegree_le_one, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, TensorPower.algebraMap₀_one, ExteriorAlgebra.liftAlternatingEquiv_apply, RCLike.imLm_coe, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, ProbabilityTheory.avgRisk_le_iSup_risk, AlgebraicGeometry.Scheme.Cover.isOpenEmbedding_fromGlued, FreeAlgebra.liftAux_eq, LinearIsometryEquiv.coe_toContinuousLinearEquiv, GradedRing.projZeroRingHom'_apply_coe, LatticeHom.withTop_apply, AlgebraicGeometry.Scheme.Hom.app_surjective, RootPairing.Equiv.coweightHom_injective, Polynomial.leadingCoeff_normalize, CategoryTheory.opEquiv_apply, map_nonpos, TrivSqZeroExt.algebraMap_eq_inl', dualTensorHomEquivOfBasis_symm_cancel_right, BoundedContinuousFunction.bddAbove_range_norm_comp, ContinuousMap.pow_apply, fourier_neg', ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd, MeasureTheory.pdf.IsUniform.measure_preimage, RingEquiv.symm_apply_eq, FunctionField.algebraMap_injective, MvPowerSeries.LinearTopology.isTopologicallyNilpotent_iff_constantCoeff, SubAddAction.conjMap_ofFixingAddSubgroup_coe_apply, NormedSpace.normalize_smul, MeasureTheory.Measure.count_eq_zero_iff, Equiv.Perm.cycleOf_pow_apply_self, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, MonoidHom.toOneHom_coe, MvPolynomial.eval₂Hom_zero_apply, Multiset.toFinsupp_union, LinearMap.toPMap_apply, MonomialOrder.span_leadingTerm_eq_span_monomial₀, sign_mul_abs, SemiNormedGrp.zero_apply, ContinuousLinearMap.isClosed_image_coe_of_bounded_of_weak_closed, AlgebraicGeometry.coe_opensRestrict_symm_apply, groupCohomology.d₁₂_apply_mem_cocycles₂, OrderEmbedding.withTopCoe_apply, AddMonCat.coe_comp, HahnSeries.addVal_le_of_coeff_ne_zero, LocallyConstant.coeFnAddMonoidHom_apply, LinearEquiv.coe_pow, finCongr_apply_mk, NormedSpace.eq_iff_forall_dual_eq, Sym2.lift₂_mk, Matrix.toLpLin_symm_pow, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_apply_inv, Polynomial.degree_C, Module.Invertible.embAlgebra_injective, FreeCommRing.hom_ext_iff, Cubic.of_b_eq_zero, NonUnitalSubalgebra.mem_map, MeasureTheory.FiniteMeasure.pi_pi, MulActionHom.fst_apply, MonoidHom.submonoidMap_apply_coe, ModuleCat.hom_inv_apply, Polynomial.mkDerivation_one_eq_derivative', ContinuousLinearEquiv.integral_comp_comm, Algebra.IsCentral.baseField_essentially_unique, Real.fourierIntegralInv_comp_linearIsometry, Diffeomorph.range_comp, Real.nnabs_of_nonneg, PseudoMetric.isSymm_closedBall, PowerSeries.coe_sub, spinGroup.units_involute_act_eq_conjAct, ContinuousLinearMap.summable, MvPolynomial.scalarRTensor_apply_tmul, Algebra.map_intNormAux, MvPolynomial.degrees_C, TensorProduct.prodLeft_tmul, Matrix.smul_of, le_map_div_add_map_div, ProfiniteAddGrp.comp_apply, Real.coe_expOrderIso_apply, SimpleGraph.Walk.darts_map, ContinuousMultilinearMap.le_opNorm, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, IsAdicComplete.of_lift, AbsoluteValue.IsEquiv.le_one_iff, Polynomial.derivative_X_add_C, FreeAddMonoid.ofList_append, Matrix.replicateRow_cons, ContinuousMonoidHom.mul_toFun, PartitionOfUnity.coe_finsupport, IsLocalization.tensorProduct_isLocalizedModule, smoothSheafCommRing.forgetStalk_inv_comp_eval_assoc, Subgroup.subtype_injective, Interval.coe_dual, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, RingCon.comap_rel, MeasureTheory.prob_compl_eq_one_iff, WithZeroMulInt.toNNReal_lt_one_iff, map_ofNat, Finsupp.update_apply, AffineMap.lineMap_continuous, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', ContinuousMap.coe_sub, AddEquiv.toAdditive_toMultiplicative_symm_apply, NonemptyInterval.fst_dual, AffineMap.ext_iff, Submodule.coe_linearProjOfIsCompl_apply, Monoid.PushoutI.of_apply_eq_base, MvPowerSeries.constantCoeff_invOfUnit, Algebra.norm_localization, Submodule.inclusion_apply, MonoidHom.inv_apply, Finsupp.prod_zpow, TensorAlgebra.lift_symm_apply, MonoidHom.mrange_eq_top, SchwartzMap.delta_apply, CategoryTheory.Quiv.homEquivOfIso_apply, ConvexOn.bddAbove_convexHull, PrimeSpectrum.isIdempotentElemEquivClopens_one_sub, RootPairing.rootForm_root_self, UniformFun.toFun_zero, MeasureTheory.SimpleFunc.measurable, Dilation.nndist_eq, MeasureTheory.IsSetSemiring.mem_supClosure_iff, Algebra.mul_sub_algebraMap_commutes, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, Primrec.of_equiv_symm_iff, Finsupp.rangeIcc_toFun, MultilinearMap.domCoprodDep_apply, Submonoid.LocalizationMap.top_injective_iff, DirichletCharacter.LSeries_changeLevel, ContinuousLinearEquiv.comp_right_fderiv, AlgEquiv.op_apply_symm_apply, MvPowerSeries.monomial_mem_nonzeroDivisorsRight, ModuleCat.monoidalClosed_curry, LocallyConstant.indicator_of_notMem, LatticeHom.symm_dual_id, ProbabilityTheory.Kernel.setIntegral_const, ContinuousAlgEquiv.symm_map_nhds_eq, Polynomial.hermite_succ, Orientation.rotation_map, AddMonoidHom.fiberEquivKer_apply, MeasureTheory.ProbabilityMeasure.pi_pi, Set.powersetCard.addActionHom_of_embedding_surjective, Subalgebra.isIdempotentElem_toSubmodule, WeierstrassCurve.Jacobian.polynomial_relation, MulArchimedeanClass.liftOrderHom_mk, NucleusClass.idempotent, groupCohomology.d₀₁_apply_mem_cocycles₁, RCLike.div_im, SymAlg.sym_sub, Valuation.coe_coe, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, FirstOrder.Language.Equiv.ext_iff, AddMonoidAlgebra.tensorEquiv.invFun_tmul, PowerSeries.expand_one_apply, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_le, Orientation.oangle_rotation_left, SupClosed.infClosure, AddGroupNormClass.toNormedAddGroup_norm_eq, AbstractCompletion.uniformContinuous_compareEquiv, hasFDerivAt_norm_rpow, LinearMap.proj_apply, PrimeSpectrum.basicOpen_le_basicOpen_iff_algebraMap_isUnit, MeasureTheory.measure_univ_of_isMulLeftInvariant, CategoryTheory.Equivalence.inverseFunctor_map, AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singleton, finsuppTensorFinsupp'_symm_single_mul, Setoid.quotientKerEquivOfRightInverse_apply, ContinuousMulEquiv.eq_symm_comp, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_apply_hom, IsGaloisGroup.mulEquivCongr_apply_smul, IsBaseChange.det_endHom, AddMonoid.Coprod.map_apply_inr, WithVal.apply_equiv, Dilation.coe_comp, ContinuousLinearMap.toLinearMapRingHom_apply, List.formPerm_apply_mem_of_mem, ContinuousLinearMap.compL_apply, IsLocalization.injective, OrderMonoidIso.withZeroUnits_apply, DirectSum.decompose_symm_neg, isOpenMap_toWeakSpace_symm, Finset.affineCombination_of_eq_one_of_eq_zero, ContinuousLinearMap.lsmul_flip_inj, AlgEquiv.commutes, LinearMap.polyCharpolyAux_map_eval, IsSquare.map, SpecialLinearGroup.coe_inv, Topology.WithUpperSet.toUpperSet_specializes_toUpperSet, ContDiffMapSupportedIn.hasCompactSupport, AlternatingMap.curryLeft_apply_apply, FreeAbelianGroup.liftAddGroupHom_apply, Real.volume_ball, affineCombination_mem_affineSpan, Matrix.toLinearMapₛₗ₂'_aux_eq, ContinuousAlternatingMap.map_piecewise_smul, Function.locallyFinsuppWithin.eq_zero_codiscreteWithin, powCoprime_inv, ContinuousAffineEquiv.preimage_symm, MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul, Cardinal.toENat_le_ofNat, AddMagmaCat.forget_map, IsLocalizedModule.mapExtendScalars_apply_apply, Con.comapQuotientEquivOfSurj_symm_mk', CommRing.Pic.inv_eq_dual, Fin.coe_cycleRange_of_le, ZSpan.repr_ceil_apply, stdSimplex.map_coe, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, AddMonoidAlgebra.mapRangeRingHom_apply, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, AddMonoidHom.mem_graph, MonoidAlgebra.singleAddHom_apply, IsometryEquiv.image_eball, MvPolynomial.eval_prod, RootPairing.EmbeddedG2.indexEquivAllRoots_symm_apply, Path.Homotopy.hcomp_half, Algebra.coe_norm_int, BoxIntegral.Box.iUnion_Ioo_of_tendsto, Monoid.PushoutI.lift_base, RingCon.mk'_surjective, finSumNatEquiv_apply_left, Real.volume_Icc_pi_toReal, toColex_eq_zero, Cardinal.lt_omega_iff_card_lt, MvPolynomial.C_mul_X_eq_monomial, LinearIsometry.inner_map_map, MatrixEquivTensor.invFun_algebraMap, Algebra.Generators.Hom.aeval_val, FinEnum.equiv_up, BddOrd.dual_map, Profinite.NobelingProof.Products.eval_eq, AddChar.pow_apply, TwoSidedIdeal.opOrderIso_symm_apply, AlgEquiv.mopMatrix_apply, AddMonoidHom.withTopMap_apply, NonUnitalSubring.unitization_apply, Finsupp.add_apply, Algebra.TensorProduct.productMap_left_apply, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, WithTop.orderIsoSumLexPUnit_toLex, Affine.Simplex.excenterWeights_reindex, ContinuousAffineMap.coe_add, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, LinearEquiv.det_symm_mul_det, PowerSeries.coeff_derivativeFun, MeasureTheory.mulEquivHaarChar_smul_map, RingHom.mem_ker, AddSubmonoid.leftNegEquiv_add, OrderIso.preimage_Ioo, SupBotHom.bot_apply, Homeomorph.Set.univ_symm_apply_coe, KaehlerDifferential.linearMapEquivDerivation_apply_apply, ZLattice.comap_equiv_apply, Submodule.surjective_tensorToSpan, RingHom.ext_iff, AddMonoidHom.coe_mker, Equiv.Perm.subtypeEquivSubtypePerm_apply_coe, Subalgebra.lTensorBot_one_tmul, MeromorphicOn.divisor_sub_const_self, PolyEquivTensor.toFunLinear_mul_tmul_mul, ArithmeticFunction.two_mul_carmichael_two_pow_of_three_le_eq_totient, MeasureTheory.Content.outerMeasure_interior_compacts, UniformSpace.Completion.mapEquiv_coe, Unitization.cobounded_eq_aux, Metric.exists_smooth_forall_closedBall_subset, ContinuousLinearMap.analyticAt, Representation.Coinvariants.mk_self_apply, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, Polynomial.hermite_eq_iterate, InfTopHomClass.map_top, Polynomial.ofFinsupp_algebraMap, finSumNatEquiv_symm_apply_add_left, OrderHom.prodMap_coe, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, CategoryTheory.Limits.IsInitial.to_eq_descCoconeMorphism, RingQuot.idealQuotientToRingQuot_apply, Polynomial.aeval_pi_apply, Set.Iio_toDual, spectrum.resolvent_eq, LaurentSeries.algebraMap_apply, AffineMap.continuous_iff, Subgroup.fg_iff_add_fg, MulActionHom.coe_zero, IsAdjoinRoot.map_repr, ZMod.toAddCircle_inj, ofAdd_bot, Valuation.IsEquiv.one_lt_iff_one_lt, ContinuousWithinAt.partialSups_apply, Metric.Snowflaking.ediam_image_ofSnowflaking, addRothNumber_union_le, GroupSeminorm.ext_iff, Set.PartiallyWellOrderedOn.imageProdLex, Equiv.piCongrLeft_symm_preimage_univ_pi, Rep.indToCoindAux_fst_mul_inv, Submodule.orthogonalProjection_mem_subspace_orthogonalComplement_eq_zero, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_map_tensor_isPullback, BoundedContinuousFunction.sub_apply, IsFoelner.eventually_meas_ne_top, SSet.Subcomplex.PairingCore.pairing_p_equivII, Path.Homotopy.hcomp_apply, UniformFun.isometry_ofFun_continuousMap, FreeAddGroup.map.comp, DirectSum.addEquivProdDirectSum_symm_apply_toFun, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial, quadraticChar_sum_zero, MvPowerSeries.coeff_index_single_self_X, RelEmbedding.one_apply, dist_affineCombination_lt_of_strictConvexSpace, AddSubmonoid.equivOp_apply_coe, OrderIso.divLeft_apply, lt_finRotate_iff_ne_last, HasFPowerSeriesWithinAt.fderivWithin_eq, AlgHom.prodEquiv_symm_apply, NumberField.Units.finrank_mul_regOfFamily_eq_det, CategoryTheory.Iso.addCommGroupIsoToAddEquiv_symm_apply, TensorAlgebra.equivDirectSum_apply, AddEquiv.map_eq_zero_iff, Algebra.Presentation.comp_aeval_relation_inl, AdjoinRoot.aeval_eq_of_algebra, MeasureTheory.ProbabilityMeasure.apply_mono, QuadraticMap.comp_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', Matrix.linfty_opNNNorm_toMatrix, OmegaCompletePartialOrder.ContinuousHom.apply_mono, Homotopy.dNext_zero_chainComplex, dist_lineMap_left, PartitionOfUnity.exists_finset_nhds_support_subset, AddHom.srange_eq_top_iff_surjective, Finset.mem_finsupp_iff, MvPowerSeries.WithPiTopology.as_tsum, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, Equiv.Perm.sign_abs, MeasureTheory.OuterMeasure.isometry_comap_mkMetric, MeasureTheory.Measure.prod_apply_le, Finsupp.indicator_apply, RatFunc.laurent_at_zero, DirectSum.of_mul_of, QuadraticAlgebra.equivProd_symm_apply, inCoordinates_apply_eq₂, Algebra.commutes', ZMod.completedLFunction_def_odd, CategoryTheory.Sheaf.ΓHomEquiv_naturality_left, ProbabilityTheory.Kernel.le_compProd_apply, OrthonormalBasis.norm_eq_one, Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, MvPolynomial.degreeOf_le_iff, AddConstEquiv.ext_iff, Module.Basis.end_apply_apply, KaehlerDifferential.tensorKaehlerEquivBase_tmul, ContinuousAlternatingMap.map_update_sub, NormedAddGroupHom.completion_coe, RCLike.im_to_real, Equiv.toHomeomorph_refl, RestrictedProduct.smul_apply, CategoryTheory.Limits.biproduct.matrixEquiv_apply, coe_addEquiv_lpPiLp_symm, MvPolynomial.C_0, Real.fourier_real_eq, Function.update_comp_equiv, CentroidHom.smul_apply, Module.Basis.coe_constrL, WittVector.mulN_coeff, ContinuousAlternatingMap.le_opNorm, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul, ModuleCat.exteriorPower.iso₀_hom_apply, MeasureTheory.OuterMeasure.map_comap, FintypeCat.hom_ext_iff, Subgroup.Commensurable.commensurator_mem_iff, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, Matrix.isRepresentation.toEnd_represents, ofMul_zpow, Cardinal.mk_toNat_eq_card, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, ContinuousAffineEquiv.coe_toEquiv, MvPowerSeries.constantCoeff_inv, LieModule.Weight.ext_iff', MulActionHom.ofEq_apply, Seminorm.rescale_to_shell_zpow, Equiv.Perm.SameCycle.exists_fin_pow_eq, CompleteSublattice.mem_subtype, BoundedContinuousFunction.nndist_set_exists, Rep.applyAsHom_comm_apply, Algebra.GrothendieckGroup.lift_symm_apply, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, StarMulEquiv.leftInverse_symm, FourierTransform.fourierInvCLM_apply, span_coeff_minpolyDiv, MulSemiringActionHom.map_neg, Homeomorph.piSplitAt_symm_apply, AddMonoidHom.mclosure_preimage_le, Fin.sign_cycleIcc_of_ge, UpperHalfPlane.norm_σ, IsPrimitiveRoot.sub_one_norm_isPrimePow, FreeRing.map_of, DilationEquiv.bijective, Valuation.mem_unitGroup_iff, MeasureTheory.Measure.dirac_apply', LaurentPolynomial.smeval_C, GroupExtension.Section.inv_mul_mem_range_inl, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, MulOpposite.isometry_opLinearEquiv, HahnSeries.coe_truncLTLinearMap, Polynomial.support_binomial', MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion₀, map_continuousWithinAt, Path.Homotopy.symm_apply, NormedSpace.expSeries_hasSum_exp, ContinuousAlgEquiv.toContinuousLinearEquiv_apply, isConjRoot_iff_eq_algebraMap, MeasureTheory.Measure.coe_toOuterMeasure, FirstOrder.Language.LEquiv.onSentence_apply, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, MeasureTheory.distribHaarChar_apply, AddSubgroup.IsComplement.mk''_rightQuotientEquiv, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, Topology.isGeneratedBy_iff, AddGroupExtension.rightHom_inl, LinearEquiv.comp_symm_eq, MonoidHom.transfer_def, MeasureTheory.L1.integral_def, AlgebraicGeometry.Scheme.Cover.covers, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, MulEquiv.prime_iff, MeasureTheory.volume_sum_rpow_lt, CategoryTheory.ConcreteCategory.epi_iff_surjective_of_preservesPushout, ArchimedeanOrder.val_of, ContinuousMultilinearMap.range_toUniformOnFun, Quotient.outRelEmbedding_apply, Submodule.botEquivPUnit_symm_apply, PowerBasis.coe_basis, Equiv.Perm.subtypeCongr.left_apply_subtype, groupHomology.chainsMap_f_single, QuadraticMap.toQuadraticMap_associated, IsLocalization.mk'_spec', FormalMultilinearSeries.hasSum, ContinuousLinearMap.IsPositive.conj_adjoint, CategoryTheory.yonedaMon_naturality_assoc, Congruent.comp_dilation, ContinuousLinearMap.flip_apply, TensorProduct.map_map_assoc_symm, MvPolynomial.bind₂_monomial, IsLocalizedModule.fromLocalizedModule.inj, tangentMapWithin_snd, algebraMap_galRestrict_apply, IsAntichain.image_iso, FirstOrder.Language.ElementaryEmbedding.map_constants, Matrix.toEuclideanCLM_toLp, PiTensorProduct.liftAux.smul, Module.Invertible.bijective_curry, ContinuousAlternatingMap.map_update_add, Algebra.traceForm_toMatrix, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, powMonoidWithZeroHom_apply, IsLocalization.map_map, Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots, AddMonoid.End.smul_apply, CategoryTheory.Oplax.StrongTrans.Modification.equivOplax_symm_apply, signedDist_eq_zero_of_orthogonal, antitone_toDual_comp_iff, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq, NonUnitalStarRingHom.coe_mk, IsometryClass.diam_range, Valued.isOpen_sphere, Interval.subset_coe_map, NormedAddGroupHom.isometry_id, DualNumber.lift_inlAlgHom_eps, ModuleCat.restrictScalarsId'App_hom_apply, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, groupCohomology.subtype_comp_d₀₁_apply, GrpCat.SurjectiveOfEpiAuxs.g_apply_infinity, ContinuousAlternatingMap.piEquiv_symm_apply, GrpCat.toAddGrp_map, unitInterval.volume_uIcc, FreeAddMonoid.ofList_vadd, MvPolynomial.monomialOneHom_apply, Cardinal.le_preAleph_ord, Finset.Colex.toColex_sdiff_lt_toColex_sdiff, Module.Basis.coe_sumCoords_of_fintype, ContinuousCohomology.Iobj_ρ_apply, SymmetricPower.span_tprod_eq_top, Finsupp.sumFinsuppLEquivProdFinsupp_symm_apply, LinearMap.coprod_apply, realPart.norm_le, OrderIso.coe_toRelIsoLT, HahnSeries.SummableFamily.coe_smul', LieHom.map_sub, LinearMap.BilinForm.dualSubmodule_dualSubmodule_flip_of_basis, DFinsupp.prod_eq_prod_fintype, Fin.accumulate_invAccumulate, SheafOfModules.pushforwardComp_inv_app_val_app, ZeroHom.coe_smul, ZSpan.volume_fundamentalDomain, PseudoEpimorphism.coe_id, Submodule.span_range_inclusion_eq_top, Cardinal.aleph1_le_lift, ContinuousAt.clm_apply_of_inCoordinates, Affine.Simplex.median_reindex, Complex.tendsto_normSq_cocompact_atTop, Localization.mk_one_eq_monoidOf_mk, MeasureTheory.tendsto_measure_of_ae_tendsto_indicator_of_isFiniteMeasure, Sum.Lex.inl_mono, CFC.posPart_algebraMap_nnreal, SemistandardYoungTableau.row_weak_of_le, NumberField.mixedEmbedding.convexBodySumFun_apply, IsDedekindDomain.HeightOneSpectrum.valuation_def, WeierstrassCurve.Projective.map_negDblY, Set.ncard_map, PrincipalSeg.monotone, finsum_emb_domain, DyckWord.equivTreesOfNumNodesEq_symm_apply_coe, PartialEquiv.transEquiv_target, MonoidHom.coeFn_apply, HasFDerivAt.comp_hasDerivAt, StandardEtalePair.HasMap.map, OrderMonoidIso.equivLike_inv_eq_symm, contDiffOn_stereoToFun, val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe, Polynomial.X_add_C_scaleRoots, basis_toMatrix_basisFun_mul, cross_anticomm', Ordinal.typein_lt_type, ProbabilityTheory.Kernel.fst_apply, ContinuousMap.coe_const', Matrix.det_reindexAlgEquiv, Fin.coe_of_injective_castSucc_symm, MvPolynomial.leadingCoeff_esymmAlgHomMonomial, spinGroup.conjAct_smul_ι_mem_range_ι, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, Matrix.toLin_scalar, Polynomial.resultant_C_right, RelIso.coe_one, SimpleGraph.Walk.map_nil, InfPrime.dual, Pi.ofColex_apply, Matrix.submatrix_id_mul_right, Prod.Lex.sumLexProdLexDistrib_symm_apply, TensorProduct.instDirectedSystemCoeLinearMapIdRTensor, Polynomial.splits_C, unitInterval.volume_Ici, MulChar.equivToUnitHom_symm_coe, Submodule.image_span_subset_span, Rat.AbsoluteValue.exists_nat_rpow_iff_isEquiv, exteriorPower.presentation.relationsSolutionEquiv_symm_apply_var, IsometryEquiv.ext_iff, MeasureTheory.measure_iUnion_null_iff, RCLike.ext_iff, BialgHom.coe_toAlgHom, Polynomial.Splits.comp_X_sub_C, Equiv.Perm.SameCycle.pow_right, LeftInvariantDerivation.evalAt_coe, Homotopy.prevD_chainComplex, WithZero.lift'_coe, StarRingEquiv.coe_refl, Unitary.coe_symm_linearIsometryEquiv_apply, Polynomial.iterate_derivative_natCast_mul, LocallyConstant.indicator_apply, fderiv_inverse, Subgroup.mem_map_of_mem, Nat.factorization_one_right, Affine.Simplex.altitudeFoot_map, lineMap_lt_right_iff_lt_one, MonoidAlgebra.mem_span_support, WeierstrassCurve.Ψ_ofNat, LinearIsometryEquiv.diam_image, GradedTensorProduct.auxEquiv_symm_one, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_point_assoc, Finset.coe_singletonAddMonoidHom, FractionalIdeal.count_ne_zero, AddMagmaCat.ofHom_apply, groupCohomology.H2π_eq_iff, Function.Embedding.optionEmbeddingEquiv_apply_snd_coe, Function.fromTypes_nil_equiv_apply, MeasureTheory.measure_singleton_lt_top, Sum.Lex.toLexRelIsoLE_coe, DirectSum.sigmaLcurry_apply, lipschitzWith_thickenedIndicator, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, Finsupp.finite_range, RCLike.conj_conj, QuadraticMap.isOrtho_def, ContMDiffMap.coe_sub, Finsupp.lex_iff_of_unique, MeasureTheory.Measure.setIntegral_compProd, MeasureTheory.SimpleFunc.restrict_const_lintegral, SkewMonoidAlgebra.of_apply, ProbabilityTheory.Kernel.deterministic_apply, WithBot.toDual_map, TopologicalSpace.Opens.map_functor_eq, LinearMap.adjoint_rTensor, toBilin'Aux_toMatrixAux, MeasureTheory.OuterMeasure.trim_eq_iInf', NumberField.det_basisOfFractionalIdeal_eq_absNorm, IsSimpleModule.toSpanSingleton_surjective, map_pow_le_pow, AddGroupExtension.Section.exists_add_eq_inl_add_add, Matroid.closure_eq_subtypeClosure, ProbabilityTheory.Kernel.iIndepSets.meas_biInter, ValuationClass.map_add_le_max, MeasureTheory.measure_pos_iff_nonempty_of_vaddInvariant, Real.Angle.coe_coeHom, GradedTensorProduct.auxEquiv_comm, QuadraticAlgebra.lift_apply_apply, ZSpan.measure_fundamentalDomain, MeasureTheory.FiniteMeasure.map_fst_prod, Units.coe_map_inv, MvPolynomial.pderiv_sumToIter, StarMonoidHom.ext_iff, TopCommRingCat.forgetToTopCatTopologicalRing, Hamming.ofHamming_sub, QuadraticMap.polar_add_left, Equiv.image_eq_iff_eq, BoundedContinuousFunction.toLp_inj, Nat.castOrderEmbedding_apply, Path.Homotopy.eval_apply, Matrix.reindex_apply, CircleDeg1Lift.units_apply_inv_apply, RingEquiv.piEquivPiSubtypeProd_symm_apply, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image, RCLike.normSq_inv, MvPolynomial.coeff_homogeneousComponent, FreeAddMonoid.ofList_map, sign_pos, ContinuousMultilinearMap.restrictScalarsLinear_apply, CategoryTheory.uliftYonedaEquiv_naturality, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, Equiv.symmEquiv_apply_apply, MvPolynomial.support_expand_subset, BoundedContinuousFunction.coe_natCast, Function.fromTypes_zero_equiv_symm_apply, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, QuaternionAlgebra.Basis.k_compHom, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, ofLex_eq_one, ProbabilityTheory.setLIntegral_condKernel, ProbabilityTheory.condExpKernel_ae_eq_condExp', OmegaCompletePartialOrder.Chain.pair_zero, TensorProduct.finsuppLeft_symm_apply_single, ValuationSubring.valuation_le_one, MeasureTheory.hahn_decomposition, Finsupp.linearEquivFunOnFinite_symm_apply, dotProduct_comp_equiv_symm, CategoryTheory.Sieve.overEquiv_symm_iff, PowerSeries.le_order_map, RestrictedProduct.nsmul_apply, IntermediateField.AdjoinSimple.norm_gen_eq_one, Rat.AbsoluteValue.equiv_on_nat_iff_equiv, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff, OmegaCompletePartialOrder.ContinuousHom.bind_apply, toDual_max, ProbabilityTheory.lintegral_condKernel, Pi.coe_evalLatticeHom, ContinuousLinearMap.toSpanSingleton_apply_map_one, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Height.mulHeight_comp_equiv, LieModuleEquiv.apply_eq_iff_eq_symm_apply, LieModule.coe_genWeightSpaceOf_zero, Polynomial.aevalTower_X, OrderMonoidIso.val_unitsWithZero_symm_apply, ofMul_pow, NumberField.InfinitePlace.orbitRelEquiv_apply_mk'', DFinsupp.filter_def, DFinsupp.eraseAddHom_apply, RootPairing.root_add_root_mem_of_pairingIn_neg, LinearEquiv.mul_apply, LinearMap.adjoint_inner_right, AddMonoidAlgebra.commAlgEquiv_single_single, padicNormE.defn, Homeomorph.subLeft_symm_apply, TensorAlgebra.equivFreeAlgebra_ι_apply, Algebra.TensorProduct.productMap_apply_tmul, BoundedContinuousFunction.toContinuousMapAddMonoidHom_apply, lineMap_le_lineMap_iff_of_lt', MeasureTheory.ProbabilityMeasure.eq_of_forall_toMeasure_apply_eq_iff, BoundedLatticeHom.coe_comp_lattice_hom', BilinForm.dotProduct_toMatrix_mulVec, LinearEquiv.multilinearMapCongrRight_symm_apply, MeasureTheory.FiniteMeasure.eq_of_forall_toMeasure_apply_eq_iff, AddMonoid.Coprod.snd_toProd, DirectSum.coe_decompose_mul_of_left_mem_of_le, InnerProductSpace.adjoint_rankOne, Finsupp.toDFinsupp_coe, Equiv.Perm.Basis.card_ofPermHom_support, DihedralGroup.oddCommuteEquiv_symm_apply, ContinuousLinearMap.compFormalMultilinearSeries_apply', Homeomorph.smulOfNeZero_apply, MeasureTheory.Integrable.condKernel_ae, LinearMap.BilinForm.tensorDistrib_tmul, ContinuousAt.eval, RelIso.coe_mul, CategoryTheory.Iso.trans_conjAut, LinearEquiv.piUnique_symm_apply, AdjoinRoot.mk_leftInverse, map_nnrat_smul, ContinuousAddEquiv.surjective, algebraMap.coe_deriv, CliffordAlgebra.coe_toEven_reverse_involute, DirectSum.coe_mul_of_apply_of_not_le, CategoryTheory.Subfunctor.Subpresheaf.IsGeneratedBy.of_equiv, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, OrderEmbedding.image_Ioo, MvPolynomial.totalDegree_C, MonoidHom.fiberEquiv_symm_apply, LocallyConstant.constAddMonoidHom_apply, OrderIso.subRight_symm_apply, PerfectRing.lift_lift_apply, LowerSet.coe_iicsInfHom, RelIso.ext_iff, OrderMonoidHom.commute_inl_inr, MultilinearMap.coe_currySumEquiv_symm, equivShrink_symm_zero, CompactlySupportedContinuousMap.coe_smul, CategoryTheory.conjugateEquiv_counit_symm, Polynomial.natDegree_C_mul_X, AlgebraicGeometry.Scheme.stalkMap_congr_point_assoc, Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, TensorProduct.AlgebraTensorModule.mk_apply, RingEquiv.quotientBot_mk, List.formPerm_apply_getElem_zero, MonoidHom.coe_of_map_div, CircleDeg1Lift.map_map_zero_lt, IsBot.ofDual, ProbabilityTheory.condDistrib_comp_map, QuadraticForm.baseChange_tmul, Submonoid.leftInvEquiv_apply, CategoryTheory.Sieve.functorPushforward_over_map, norm_map, ContinuousMap.homeoFnOfDiscrete_symm_apply, DFinsupp.extendWith_some, QuadraticMap.proj_apply, LinearMap.trace_transpose', ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup, RingCon.coe_inf, Manifold.IsImmersionAt.writtenInCharts, smoothSheafCommRing.forgetStalk_inv_comp_eval, InnerProductSpace.rankOne_eq_zero, ContinuousLinearMap.lipschitz, AlgebraicGeometry.Scheme.GlueData.isOpen_iff, Polynomial.differentiable_aeval, ProbabilityTheory.isGaussian_map_equiv_iff, ContinuousMap.coe_restrict, OrderEmbedding.minimal_mem_image, Ideal.image_subset_nonunits_valuationSubring, Polynomial.natTrailingDegree_monomial, Equiv.Perm.sumCongr_apply, MeasureTheory.eLpNorm_one_le_of_le', Circle.exp_two_pi, IsSemilinearSet.image, map_mem_perfectClosure_iff, EquivLike.surjective_comp, Homeomorph.sumArrowHomeomorphProdArrow_symm_apply, ContinuousAddMonoidHom.range_toContinuousMap, MvPowerSeries.WithPiTopology.uniformContinuous_coeff, AddMonoidHom.coe_graph, FractionalIdeal.absNorm_bot, ContMDiffSection.coe_zero, DirectSum.decompose_symm_one, Real.fourierIntegral_convergent_iff', lineMap_strict_mono_endpoints, IsCoveringMapOn.comp_homeomorph_iff, WeierstrassCurve.Projective.polynomialZ_eq, ProbabilityTheory.aestronglyMeasurable_integral_condDistrib, LinearEquiv.eq_symm_comp, isMax_ofDual_iff, fderivWithin_continuousMultilinear_apply_const_apply, Polynomial.comp_C, BoolAlg.hasForgetToHeytAlg_forget₂_map, ContinuousAffineMap.coe_linear_eq_coe_contLinear, DirichletCharacter.changeLevel_one, LinearMap.comp_apply, CommRing.Pic.mk_eq_iff, WeierstrassCurve.map_a₄, Algebra.norm_eq_of_equiv_equiv, BoundedContinuousFunction.toLp_injective, LieModuleHom.smul_apply, IsTensorProduct.equiv_symm_apply, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, MeasureTheory.Measure.addHaar_ball_center, Polynomial.coeff_mul_X_sub_C, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, Projectivization.cross_mk_of_cross_ne_zero, LieModuleHom.nsmul_apply, infClosed_infClosure, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_assoc, NormedAddCommGroup.denseRange_toCompl, OrderIso.image_Iio, MeasureTheory.integrable_map_equiv, MeasureTheory.Measure.ae_eq_or_eq_iff_map_eq_dirac_add_dirac, SimpleGraph.Hom.map_adj, MonomialOrder.lex_lt_iff_of_unique, MulSemiringActionHom.map_sub, ZeroHom.ext_iff, Module.Basis.range_extendLe, SubsemiringClass.coe_subtype, TopCat.Sheaf.extend_hom_app, padicNormE.add_eq_max_of_ne', IsChain.image_relIso_iff, CategoryTheory.Functor.mapBicone_whisker, OrderIso.withBotCongr_symm_apply, Finset.Colex.toColex_sdiff_le_toColex_sdiff, toDual_inv, Seminorm.continuous, Matrix.toLpLin_one, ofMul_inv, PowerSeries.rescale_mk, RingEquiv.prodZeroRing_symm_apply, Convex.toWeakSpace_closure, FractionalIdeal.mem_one_iff, lp.singleAddMonoidHom_apply, Module.Basis.trace_mul_traceDual, Seminorm.coe_smul, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, LinearIsometry.lTensor_apply, OmegaCompletePartialOrder.ContinuousHom.seq_apply, Subsemiring.opEquiv_apply, AddChar.expect_apply_eq_zero_iff_ne_zero, CliffordAlgebra.ι_mul_ι_mul_ι, QuadraticAlgebra.norm_eq_one, AddMonoidHom.sub_apply, Complex.normSq_add, sInfHom.continuous, Algebra.smul_def', MeasurableSet.exists_isCompact_diff_lt, MulEquiv.toMonoidWithZeroHom_apply, minpoly.frobenius_of_isSeparable, finsuppTensorFinsupp'_apply_apply, MeasureTheory.ae_restrict_eq_bot, OrderAddMonoidHom.zero_apply, Polynomial.eval_monomial_one_add_sub, Equiv.sumIsLeft_symm_apply_coe, RatFunc.numDenom_div, Pi.mulSingle_comp_equiv, ContinuousMap.isUnit_iff_forall_isUnit, IsPathConnected.exists_path_through_family, ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_map_map, ContinuousMap.Homotopy.apply_one_path, Homeomorph.isSimplyConnected_image, MeasureTheory.tendstoInMeasure_iff_dist, groupCohomology.cocycles₂_map_one_snd, MeasureTheory.FiniteMeasure.testAgainstNN_coe_eq, Con.rel_mk, Equiv.sumProdDistrib_symm_apply_right, ContinuousAlgHom.map_sum, ContinuousOn.lineMap, BoundedContinuousFunction.comp_apply, AddActionHom.ext_iff, MeasureTheory.Measure.measure_toMeasurable_inter_of_sFinite, PartOrdEmb.Limits.CoconePt.fac_apply, Equiv.sumArrowEquivProdArrow_symm_apply_inr, Module.End.HasEigenvector.apply_eq_smul, Finsupp.finset_sum_apply, IsEvenlyCovered.homeomorph_comp, Monoid.PushoutI.NormalWord.prod_summand_smul, CompactExhaustion.subset, AddSubmonoid.mem_map, SkewMonoidAlgebra.toFinsuppAddEquiv_apply, tsum_pow_div_one_sub_eq_tsum_sigma, MeasureTheory.Measure.toSphere_apply_univ, Polynomial.roots_expand_map_frobenius, NormedAddGroupHom.le_of_opNorm_le, MvPolynomial.coeff_rename_embDomain, DFinsupp.colex_lt_iff_of_unique, CStarMatrix.algebraMap_apply, Submodule.norm_sq_eq_add_norm_sq_starProjection, RCLike.re_eq_norm_of_mul_conj, inner_map_polarization', Fin.appendIsometryOfEq_apply, PartitionOfUnity.sum_le_one', AddMonoidHom.coe_finset_sum, DirectedSystem.map_self', MultilinearMap.curryFinFinset_symm_apply_piecewise_const, Submonoid.mem_comap, map_hnot, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isCompact, Bundle.ContMDiffRiemannianMetric.symm, SimpleGraph.Copy.ext_iff, LinearMap.mul'_apply, Matrix.natCast_fin_two, LinearIsometryEquiv.ofTop_symm_apply_coe, LinearMap.map_neg, IsIntegralClosure.algebraMap_injective, MulAutMultiplicative_symm_apply_symm_apply, le_partialSups_of_le, OrderIso.trans_apply, MeasurableSet.measure_eq_iSup_isCompact, RootPairing.InvariantForm.exists_apply_eq_or, upperSetIsoLowerSet_symm_apply, OmegaCompletePartialOrder.Chain.mem_map, MulAction.toFun_apply, InnerProductSpace.inner_right_rankOne_apply, ContinuousMap.one_apply, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, FreeAbelianGroup.equivFinsupp_symm_apply, HilbertBasis.hasSum_repr, ModuleCat.homAddEquiv_symm_apply_hom, Rep.coinvariantsTensorFreeLEquiv_apply, VectorField.fderiv_pullback, PowerSeries.constantCoeff_surj, strictMono_iff_map_pos, Finsupp.uncurry_apply, PiTensorProduct.ofFinsuppEquiv_symm_single_tprod, bddBelow_preimage_toDual, Algebra.top_toSubmodule, map_inv_le_iff, comp_partialSups, IsLocalization.Away.map_injective_iff, AbsoluteValue.coe_toMonoidHom, HasFDerivWithinAt.hasGradientWithinAt, AlgHom.coe_tensorEqualizer, HeytAlg.id_apply, SchwartzMap.pairing_apply, MeasureTheory.Content.mono, OmegaCompletePartialOrder.ContinuousHom.ωScottContinuous_apply, ContinuousMap.inseparable_coe, MvPolynomial.monomial_left_inj, Polynomial.natDegree_X_add_C, lcm_mul_left, charpoly_leftMulMatrix, Finsupp.leftInverse_lcomapDomain_mapDomain, MulEquiv.strictMono_subsemigroupCongr, Module.Dual.transpose_apply, Module.Basis.reindexRange_repr_self, Finset.map_one, QuadraticMap.polar_smul_left_of_tower, Sbtw.right_mem_image_Ioi, ENNReal.orderIsoIicOneBirational_apply_coe, UniformFun.tendsto_iff_tendstoUniformly, Real.fourier_comp_linearIsometry, FreeGroupBasis.injective, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, ContinuousLinearMapWOT.smul_apply, CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles, LinearMap.det_prodMap, MulArchimedeanClass.map_mk_le, DirectSum.coe_decompose_mul_of_left_mem, MeasureTheory.Lp.coeFn_compMeasurePreserving, MeasureTheory.measure_symmDiff_le, AddCommGrpCat.biprodIsoProd_inv_comp_snd_apply, MeasureTheory.SimpleFunc.coe_zero, Set.Ici_ofDual, unitInterval.volume_uIoo, Polynomial.map_taylor, fderivWithin_comp_derivWithin, LinearMap.isPosSemidef_iff_posSemidef_toMatrix, MvPolynomial.X_dvd_monomial, UniformOnFun.one_apply, WeierstrassCurve.Jacobian.baseChange_addX, ContinuousAlternatingMap.apply_apply, RootPairing.zero_le_rootForm, UnitAddTorus.mFourier_add, HasFPowerSeriesWithinOnBall.unshift, Dioph.inject_dummies_lem, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, MonomialOrder.degLex_le_iff, ConvexIndependent.mem_convexHull_iff, FirstOrder.Language.ElementaryEmbedding.map_fun, MonoidHom.noncommPiCoprod_apply, finCycle_eq_finRotate_iterate, BoundedContinuousFunction.integrable, powCoprime_one, LinearEquiv.ofSubmodule'_symm_apply, MeasureTheory.laverage_eq, NumberField.RingOfIntegers.coe_eq_zero_iff, ContinuousAffineMap.coe_toAffineMap, Equiv.mulEquiv_apply, DFinsupp.lex_lt_of_lt_of_preorder, groupHomology.toCycles_comp_isoCycles₁_hom_apply, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, GroupNorm.coe_sup, ArithmeticFunction.sigma_apply_prime_pow, subset_tangentConeAt_prod_right, PositiveLinearMap.preGNS_inner_def, BoundedContinuousFunction.pow_apply, comap_neg_leftUniformSpace, continuous_ofDual, Set.singletonMonoidHom_apply, MeasureTheory.SimpleFunc.memLp_iff_finMeasSupp, LaurentPolynomial.degree_C, TensorProduct.toIntegralClosure_mvPolynomial_bijective, image_smul_set, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, Finset.card_eraseNone_of_not_mem, fderivWithin_inv', MeasureTheory.Measure.haar.addHaarContent_self, MvPolynomial.finSuccEquiv_coeff_coeff, PositiveLinearMap.ext_iff, spectralAlgNorm_mul, AddConstMapClass.map_nat_add', ofAdd_list_prod, TannakaDuality.FiniteGroup.sumSMulInv_apply, SubgroupClass.subtype_apply, CategoryTheory.Functor.natTransEquiv_symm_apply_app, Matrix.inv_reindex, DFinsupp.erase_add_single, MvPowerSeries.constantCoeff_C, Ordinal.CNF.coeff_of_mem_CNF, TensorProduct.AlgebraTensorModule.rTensor_tmul, AddCommMonCat.comp_apply, SubalgebraClass.coe_val, RingEquiv.zeroRingProd_symm_apply, ContinuousAddEquiv.symm_apply_eq, AddEquiv.coe_prodAssoc, spectralNorm_eq_invariantExtension, not_disjoint_segment_convexHull_triple, IntermediateField.extendScalars.orderIso_apply, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_symm_apply, Tuple.graphEquiv₂_apply, AlgEquiv.smul_def, RootPairing.Equiv.comp_coweightMap_apply, Behrend.map_injOn, AddEquiv.coprodAssoc_apply_inr, LinearEquiv.surjective, Representation.mem_invariants_iff_of_forall_mem_zpowers, AddActionHom.ofEq_apply, right_lt_lineMap_iff_lt, Finsupp.single_eq_of_ne', Equiv.eq_preimage_iff_image_eq, Matrix.det_map, MeasureTheory.Measure.hausdorffMeasure_smul₀, Equiv.subtypeEquivRight_apply, NonUnitalRingHom.compLeft_apply, EmbeddingLike.comp_injective, Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, WithTop.orderIsoSumLexPUnit_symm_inl, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_fst, Polynomial.support_C, spinGroup.involute_act_ι_mem_range_ι, CategoryTheory.Functor.mapExtLinearMap_coe, CategoryTheory.PreZeroHypercover.reindex_f, PowerSeries.substAlgHom_comp_substAlgHom, Derivation.mapCoeffs_monomial, MeasureTheory.ae_ae_add_linearMap_mem_iff, Dilation.ratioHom_apply, MeasureTheory.volume_preserving_piFinSuccAbove, AddMonoidHom.mem_eqLocusM, Algebra.PreSubmersivePresentation.jacobiMatrix_apply, FinBddDistLat.forget_map, Subalgebra.valA_apply, Poly.proj_apply, Equiv.Perm.Basis.ofPermHom_apply, AddSubmonoid.mem_map_of_mem, PrincipalSeg.apply_wCovBy_apply_iff, RelIso.symm_apply_eq, map_finprod, StarAlgEquiv.rightInverse_symm, TensorProduct.prodLeft_symm_tmul, RootPairing.chainBotCoeff_reflectionPerm_right, Equiv.Perm.IsCycleOn.exists_pow_eq, Affine.Simplex.altitude_restrict_eq_comap_subtype, UniformOnFun.edist_eval_le, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, OrderIso.withZeroUnits_symm_apply, ShelfHom.map_act, RootPairing.Equiv.weightEquiv_apply, MeasureTheory.lintegral_nnnorm_condExpL2_le, optionProdEquiv_mk_some, CommMonCat.val_units_map_hom_apply, CommRingCat.HomTopology.precompHomeomorph_apply, Module.FaithfullyFlat.rTensor_exact_iff_exact, CategoryTheory.Functor.OneHypercoverDenseData.mem₁₀, DilationEquiv.coe_toEquiv, Module.Basis.subset_extendLe, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C', SmoothPartitionOfUnity.le_one, CategoryTheory.PreZeroHypercover.isoMk_hom_s₀, IsLocalizedModule.map_comp', CategoryTheory.ShortComplex.exact_iff_of_hasForget, MvPowerSeries.monomial_zero_eq_C, MvPowerSeries.coeff_inv, FintypeCat.id_apply, RingCon.coe_ofMatrix_eq_relationMap, RCLike.conj_eq_iff_re, AddMonoidHom.map_nsmul, LieHom.map_lie, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, DFinsupp.sigmaUncurry_apply, MeasurableEquiv.restrict_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, MvPolynomial.coeff_C_mul, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, SkewMonoidAlgebra.lift_unique, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, Complex.re_sq_le_normSq, AffineEquiv.pointReflection_involutive, ContinuousMonoidHom.ext_iff, MvPolynomial.rename_esymm, LaurentPolynomial.eval₂_T, SymAlg.sym_injective, CircleDeg1Lift.le_floor_map_map_zero, StrongDual.toLp_of_not_memLp, Polynomial.roots_expand_image_frobenius, LinearEquiv.rTensor_refl_apply, Equiv.tsum_eq, PolynomialModule.single_apply, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, ContinuousLinearMap.fderivWithin_of_bilinear, LaurentSeries.derivative_iterate_coeff, Module.Basis.smul_det, MeasureTheory.Lp.compMeasurePreservingₗᵢ_apply_coe, MvPolynomial.quotient_map_C_eq_zero, Finset.coe_orderIsoOfFin_apply, Finsupp.single_apply_left, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap_apply, QuadraticMap.toBilin_apply, UniformOnFun.postcomp_isUniformInducing, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff, Diffeomorph.coeFn_injective, ofBoolRing_toBoolRing, Finsupp.linearCombination_linear_comp, ContinuousMap.lt_def, Topology.WithLowerSet.isLowerSet_toLowerSet_preimage, OrderMonoidIso.coe_mk, SimplexCategory.toTop₀_map, Iio_orderDual_def, AlgHom.coe_prod, NonarchAddGroupSeminorm.coe_smul, Algebra.TensorProduct.lmul'_apply_tmul, Quaternion.expSeries_odd_of_imaginary, IsometryEquiv.divRight_apply, ProbabilityTheory.IsCondKernelCDF.setIntegral, CircleDeg1Lift.coe_mk, toAdd_zpow, MvPolynomial.iterToSum_X, Module.End.isNilpotent_iff_of_finite, AffineSubspace.signedInfDist_eq_signedDist_of_mem, AlgebraicGeometry.Scheme.Hom.mem_preimage, NonUnitalAlgHom.restrictScalars_apply, ProbabilityTheory.Kernel.withDensity_absolutelyContinuous, AlgebraicGeometry.Scheme.Spec_map_stalkMap_fromSpecStalk_assoc, TensorAlgebra.lift_ι_apply, Matrix.singleLinearMap_apply, FreeAddMagma.lift_comp_of, MeasureTheory.L1.setToFun_eq_setToL1, AddMonoidHom.noncommCoprod_unique, MeasureTheory.OuterMeasure.restrict_univ, Module.Basis.repr_eq_iff, lineMap_mem_openSegment, NonUnitalRingHom.comp_apply, MulHom.restrict_apply, CommBialgCat.bialgEquivOfIso_apply, Polynomial.degreeLT.addLinearEquiv_apply_snd, IsLocalization.mk'_mem_iff, BumpCovering.le_one, KaehlerDifferential.linearMapEquivDerivation_symm_apply, Complex.div_im, Polynomial.natSepDegree_C_mul_X_sub_C_pow, MultilinearMap.domCoprod_alternization_coe, unitSphereToUnits_injective, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_eq_map_apply, AffineEquiv.prodAssoc_apply, HahnSeries.SummableFamily.single_toFun, Function.Injective.map_swap, Finset.coe_singletonMulHom, NNReal.sqrt_eq_iff_eq_sq, SSet.prodStdSimplex.objEquiv_apply_snd, map_eq_top_iff, Submodule.span_singleton_algebraMap_of_isUnit, MvPolynomial.C_mul_monomial, Set.injOn_iff_map_eq_zero, RingEquiv.map_one, Invertible.mulLeft_apply, HasFPowerSeriesWithinAt.coeff_zero, SlashInvariantForm.sub_apply, Finsupp.le_iff, starL'_apply, PowerSeries.exp_mul_exp_neg_eq_one, LinearMap.neg_apply, Algebra.normalizedTrace_intermediateField, AlgebraicGeometry.Scheme.Hom.isConstructible_preimage, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, LinearMap.BilinForm.smul_right_of_tower, Homeomorph.funUnique_apply, ArithmeticFunction.one_eq_delta, TensorProduct.inner_lid_lid, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendsto, ContinuousMultilinearMap.cons_smul, Matrix.SpecialLinearGroup.mapGL_injective, EuclideanSpace.volume_closedBall_fin_two, Submonoid.LocalizationMap.mk'_eq_iff_eq, PiTensorProduct.reindex_trans, WithCStarModule.equiv_neg, Submonoid.val_inv_unitsTypeEquivIsUnitSubmonoid_symm_apply, LinearMap.BilinForm.tensorDistribEquiv_apply, Behrend.map_apply, ClassGroup.mkMMem_surjective, MvPowerSeries.HasSubst.comp, OrderMonoidIso.eq_symm_apply, AddMonoidAlgebra.lift_apply, Finsupp.mem_submodule_iff, Finset.attach_affineCombination_coe, ContDiffMapSupportedIn.uniformSpace_eq_iInf, ContinuousAlternatingMap.add_apply, Representation.ofQuotient_coe_apply, KaehlerDifferential.span_range_derivation, convexHull_vadd, MeasureTheory.Measure.setIntegral_condKernel_univ_right, RingEquiv.injective, Localization.algEquiv_mk, Matrix.eta_fin_two, Dilation.toContinuous, addMonoidAlgebraEquivDirectSum_symm_apply, DomMulAct.coe_smul_addMonoidHom, SeparationQuotient.outCLM_isUniformEmbedding, ContinuousMap.equivFnOfDiscrete_apply, Algebra.Generators.H1Cotangent.exact_map_δ, NonUnitalAlgHom.mem_range_self, Algebra.Extension.algebraMap_surjective, RatFunc.num_C, AlgebraicGeometry.IsImmersion.isLocallyClosed_range, ContinuousMap.HomotopyRel.compContinuousMap_apply, Pi.orthonormalBasis_apply, Function.locallyFinsuppWithin.logCounting_eventuallyLE, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, Finsupp.comp_liftAddHom, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, MeasureTheory.enorm_indicatorConstLp_le, eq_affineCombination_of_mem_affineSpan_image, LinearMap.finrank_genEigenspace_le, ContinuousAffineEquiv.apply_symm_apply, MulEquiv.coprodPUnit_apply, cfcₙAux_id, Nonneg.val_unitsEquivPos_symm_apply_coe, Algebra.Generators.H1Cotangent.δAux_monomial, LinearMap.coe_fst, SemiNormedGrp.id_apply, LinearMap.BilinForm.toMatrix_apply, Equiv.biSup_comp, Module.Basis.sumQuot_repr_inl, RootPairing.Hom.coweightHom_injective, MvPolynomial.vars_monomial, LinearMap.IsSymmetric.diagonalization_symm_apply, SSet.hoFunctor.unitHomEquiv_eq, Polynomial.modByMonicHom_apply, minpoly.dvd_iff, Equiv.toEmbedding_apply, AddEquiv.piUnique_symm_apply, Finsupp.sigmaFinsuppEquivPiFinsupp_apply, ProbabilityTheory.tsum_prob_mem_Ioi_lt_top, PiTensorProduct.liftIsometry_tprodL, Algebra.trace_isNilpotent_of_isNilpotent, WeierstrassCurve.Jacobian.map_add, TopologicalSpace.Closeds.complOrderIso_apply, MonoidAlgebra.coe_mapRangeRingHom, midpoint_pointReflection_right, maximal_orthonormal_iff_basis_of_finiteDimensional, Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic, LinearEquiv.piUnique_apply, LinearEquiv.sumPiEquivProdPi_apply, CompHausLike.finiteCoproduct.isOpenEmbedding_ι, ContinuousAlternatingMap.map_sum, partialSups_eq_sup_range, quadraticChar_eq_zero_iff, exists_spanning_measurableSet_le, IsCoveringMap.injective_path_homotopic_mapFn, Homeomorph.comp_continuousWithinAt_iff, RingEquiv.map_eq_zero_iff, AdjoinRoot.coe_injective, MvPolynomial.pow_idealOfVars_eq_span, MulHom.srange_eq_top_iff_surjective, ProbabilityTheory.condExp_ae_eq_trim_integral_condExpKernel_of_stronglyMeasurable, OnePoint.map_smul, TensorProduct.norm_comm, Set.preimage_mul_preimage_subset, LieAlgebra.killingForm_apply_eq_zero_of_mem_rootSpace_of_add_ne_zero, Cardinal.le_aleph_ord, RootPairing.reflectionPerm_coroot, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, ContinuousMap.coe_mulRight, ContinuousMultilinearMap.ofSubsingleton_symm_apply_apply, NumberField.Units.complexEmbedding_injective, TensorProduct.map₂_apply_tmul, CliffordAlgebra.adjoin_range_ι, RatFunc.smul_eq_C_mul, LinearEquiv.invFun_eq_symm, essSup_eq_sInf, LieSubmodule.traceForm_eq_zero_of_isTrivial, CliffordAlgebra.changeFormEquiv_apply, Profinite.NobelingProof.Products.evalFacProps, QuadraticAlgebra.norm_neg, PiTensorProduct.one_def, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, Polynomial.roots_C_mul_X_sub_C_of_IsUnit, AddLocalization.r_of_eq, MulHom.toFun_eq_coe, AddMonoidHom.map_mclosure, SetTheory.PGame.mul_moveLeft_inr, LinearMap.dualProd_apply_apply, Real.volume_pi_Ioc_toReal, prevD_nat, Nat.ordProj_mul_ordCompl_eq_self, AnalyticOnNhd.eval_linearMap, Order.succ_ofMul, LinearIsometryEquiv.coe_toMeasurableEquiv, isStrictlyPositive_algebraMap, lieEquivMatrix'_apply, ContinuousMap.compactOpen_eq, Module.Basis.algebraMap_injective, PresheafOfModules.mono_iff_surjective, MeasureTheory.FiniteMeasure.coeFn_def, Algebra.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap, RingTheory.Sequence.IsRegular.of_faithfullyFlat, curveIntegral_segment_const, MeasureTheory.Content.outerMeasure_eq_iInf, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, PowerSeries.trunc_X_of, LinearMap.map_zero, TensorProduct.dualDistribEquivOfBasis_symm_apply, BilinForm.toMatrix_toBilin, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, AlgHom.toLinearMap_apply, SimplexCategory.congr_toOrderHom_apply, Continuous.exists_contMDiff_approx, PerfectClosure.mk_add_mk, Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeff, OrderEmbedding.sortedLT_listMap, CommRing.Pic.mk_eq_self, Equiv.transPartialEquiv_source, Nat.pairwise_coprime_pow_primeFactors_factorization, LaurentPolynomial.C_apply, SemimoduleCat.MonoidalCategory.tensorLift_tmul, CategoryTheory.ShortComplex.ab_exact_iff_function_exact, galLift_algebraMap_apply, LinearMap.toFun_eq_coe, VectorBundleCore.localTriv_symm_apply, StarSubalgebra.subtype_apply, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, FreeAddSemigroup.lift_of, HahnSeries.SummableFamily.smul_hsum, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, HasFDerivAt.abs, Antivary.dual_left, tendsto_measure_cthickening, WeakDual.isCompact_closedBall, IncidenceAlgebra.add_apply, ContinuousLinearEquiv.bijective, MeasureTheory.L1.integral_eq_setToL1, IsLocalizedModule.linearEquiv_apply, LinearIsometryEquiv.image_sphere, Polynomial.derivative_X_pow_succ, Function.Embedding.coe_subtype, CategoryTheory.PreGaloisCategory.continuous_mapAut_whiskeringRight, Convex.second_derivative_within_at_symmetric, ArchimedeanClass.stdPart_eq_sInf, AffineMap.proj_apply, CompHausLike.Sigma.isOpenEmbedding_ι, ProbabilityTheory.Kernel.ae_kernel_lt_top, AffineMap.id_apply, LieModule.weight_vector_multiplication, NumberField.InfinitePlace.map_ratCast, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, NumberField.Units.norm, SkewPolynomial.φ_def, MeasureTheory.exists_simpleFunc_forall_lintegral_sub_lt_of_pos, Affine.Simplex.signedInfDist_apply_self, BoxIntegral.BoxAdditiveMap.volume_apply, quadraticChar_zero, LinearMap.isSymm_def, MeasureTheory.Measure.absolutelyContinuous_comp_of_countable, Algebra.Generators.toAlgHom_ofComp_surjective, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, Finset.geomSum_ofColex_strictMono, CircleDeg1Lift.mul_apply, IsPrimitiveRoot.norm_eq_one, spinGroup.conjAct_smul_range_ι, AddEquiv.funUnique_apply, Localization.mkHom_surjective, AddSubmonoid.mk_add_mk_neg_eq_zero, Finsupp.coe_neLocus, Matrix.toPerfectPairing_apply_apply, AbsoluteValue.abs_apply, Matrix.updateRow_reindex, LocallyConstant.ofIsClopen_fiber_zero, TangentBundle.trivializationAt_apply, CliffordAlgebra.EquivEven.neg_e0_mul_v, ContinuousWithinAt.eval_const, FreeAddMonoid.map_surjective, Path.Homotopic.map, strictMono_comp_ofDual_iff, Sublattice.apply_coe_mem_map, Topology.IsGeneratedBy.continuous_equiv_symm, ConvexOn.sSup_of_countable_affine_eq, TestFunction.coe_ofSupportedInCLM, Representation.mem_invariants, Equiv.right_inv', Homeomorph.smul_apply, exists_contMDiffMap_zero_one_nhds_of_isClosed, LinearMap.quotientInfEquivSupQuotient_apply_mk, VitaliFamily.ae_tendsto_limRatio, Circle.exp_sub, KaehlerDifferential.kerTotal_mkQ_single_add, MeasureTheory.measure_sdiff_neg_vadd, PointedContMDiffMap.smul_def, IsBaseChange.of_basis, MvPolynomial.bind₁_comp_bind₁, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, lp.singleContinuousAddMonoidHom_apply, Homeomorph.isPathConnected_image, Function.locallyFinsuppWithin.le_def, Semigrp.id_apply, SpecialLinearGroup.congr_linearEquiv_coe_apply, Metric.Snowflaking.image_ofSnowflaking_ball, IsMax.toDual, CategoryTheory.nerve.homEquiv_comp, FunOnFinite.linearMap_apply_apply, MulAlgebraNorm.toFun_eq_coe, HasFDerivWithinAt.abs, ProbabilityTheory.condExp_ae_eq_trim_integral_condExpKernel, Polynomial.eq_C_of_natDegree_le_zero, NatOrdinal.toOrdinal_max, ContinuousMultilinearMap.map_piecewise_add, ModularForm.zero_apply, MvPolynomial.commAlgEquiv_C, LinearIsometryEquiv.nnnorm_map, MvPolynomial.coeff_zero_C, MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported, MeasureTheory.measure_compl_le_add_iff, ProbabilityTheory.gaussianReal_map_linearMap, ConjAct.ofConjAct_zero, Polynomial.monic_X_add_C, OrderEmbedding.birkhoffSet_inf, IsOpen.measure_pos, Finset.map_affineCombination, Differential.coeff_mapCoeffs, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, realPart_add_I_smul_imaginaryPart, AffineBasis.ind, Ordinal.typein_lt_typein, DistLat.forget_map, FirstOrder.Language.DirectLimit.partialEquivLimit_comp_inclusion, ArithmeticFunction.LSeries_zeta_eq, Finset.coe_singletonOneHom, Rep.indToCoindAux_comm, MeasureTheory.Measure.map_def, Module.End.iSup_genEigenspace_eq, CategoryTheory.nerve.left_edge, Algebra.Generators.Hom.algebraMap_toAlgHom', MulSemiringAction.toAlgEquiv_symm_apply, MeasurableEquiv.measurableSet_image, RCLike.ofNat_mul_re, Polynomial.logMahlerMeasure_X_add_C, ContinuousLinearMap.toContinuousAddMonoidHom_zero, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, AddChar.doubleDualEmb_apply, Homeomorph.comp_isOpenMap_iff, IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra, OrthonormalBasis.tensorProduct_repr_tmul_apply', MonoidHom.restrictHomKerEquiv_symm_coe_apply, Subalgebra.iSupLift_mk, ContDiffMapSupportedIn.continuous_iff_comp_withOrder, MeasureTheory.Measure.condKernel_apply_of_ne_zero, Set.exists_isOpen_lt_add, smoothSheafCommRing.forgetStalk_inv_comp_eval_apply, ContinuousLinearMap.leftInverse_of_comp, SimpleGraph.Walk.map_map, QuadraticMap.evalAddMonoidHom_apply, MeasureTheory.withDensity_apply_eq_zero', CategoryTheory.nerve.mk₁_homEquiv_apply, Matrix.SpecialLinearGroup.mapGL_inj, IntermediateField.mem_fixedField_iff, SemilinearMapClass.map_smul_inv, ProbabilityTheory.Kernel.copy_apply, QuadraticMap.polar_self, ContinuousLinearMap.norm_map_of_mem_unitary, Equiv.swap_comp_apply, exists_increasing_or_nonincreasing_subseq', Module.DirectLimit.congr_symm_apply_of, ProbabilityTheory.Kernel.rnDeriv_ne_top, monoidEndToAdditive_apply_apply, finRotate_of_lt, Pi.mulSingle_multiplicativeOfAdd_eq, LieDerivation.exp_map_apply, MulEquiv.eq_comp_symm, subset_tangentConeAt_prod_left, AddMonoid.Coprod.swap_injective, IsLocalization.finsetIntegerMultiple_image, Finset.map_toDual_max, NumberField.IsCMField.complexConj_apply_apply, LocallyConstant.mapₐ_apply_apply, ContinuousLinearMap.derivWithin, SubAddAction.ofFixingAddSubgroup_of_eq_bijective, TopCat.range_pullback_map, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_left, Function.locallyFinsuppWithin.coe_sub, LinearEquiv.sumArrowLequivProdArrow_symm_apply_inr, MonoidHom.pow_apply, CategoryTheory.yonedaMon_naturality, finSuccEquiv'_symm_coe_above, Algebra.Generators.cotangentSpaceBasis_repr_tmul, Metric.Snowflaking.isBounded_image_ofSnowflaking_iff, Algebra.norm_eq_iff, MonomialOrder.monic_X_add_C, right_le_lineMap_iff_le, LieDerivation.ext_iff, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, LinearEquiv.funCongrLeft_apply, RestrictedProduct.mulSingle_eq_of_ne', OrderHom.le_def, Path.mul_apply, Polynomial.aevalTower_C, ContinuousAffineMap.coe_injective, CategoryTheory.Limits.FintypeCat.productEquiv_symm_comp_π_apply, Dilation.edist_eq, FreeAddMonoid.toList_of, tendsto_measure_Icc, RatFunc.laurent_laurent, LieModuleHom.coe_neg, IncidenceAlgebra.mu_apply, exists_mem_interior_convexHull_affineBasis, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, Submodule.localized'_span, Equiv.optionSubtype_apply_symm_apply, Equiv.Set.union_apply_left, LinearMap.compr₂_apply, ContinuousLinearMap.precompR_apply, LieAlgebra.cartan_sup_iSup_rootSpace_eq_top, HahnSeries.SummableFamily.smul_support_subset_prod, isRegular_ofAdd, GroupExtension.Section.exists_eq_inl_mul, HarmonicAt.differentiableAt_complex_partial, LaurentSeries.exists_ratFunc_val_lt, AffineIsometry.image_intrinsicInterior, PowerSeries.constantCoeff_one, addOrderOf_ofMul_eq_orderOf, PointwiseConvergenceCLM.isEmbedding_coeFn, ArchimedeanClass.FiniteElement.val_mul, MeasureTheory.SimpleFunc.lintegral_restrict, AlgebraicGeometry.Scheme.Cover.exists_lift_trans_eq, ArithmeticFunction.IsMultiplicative.map_prod_of_prime, RootPairing.corootSpanMem_reflectionPerm_self, RelIso.relHomCongr_apply, MvPolynomial.aevalTower_X, QuadraticMap.Isometry.snd_apply, cardinalInterFilter_aleph_one_iff, CategoryTheory.Functor.is_cover_of_isCoverDense, QuadraticMap.prod_apply, Topology.WithLowerSet.toLowerSet_ofLowerSet, WeierstrassCurve.Affine.addPolynomial_slope, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, Finset.equivBitIndices_apply, AddChar.forall_apply_eq_zero, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, NonUnitalAlgHom.toAlgHom_zero, WithBot.le_toDual_iff, Complex.equivRealProd_apply_le', Int.toAdd_pow, LinearMap.minpoly_toMatrix', cfc_map_polynomial, IsPrimitiveRoot.autToPow_injective, Polynomial.coeff_C_mul, antitone_iff_map_nonpos, Ideal.Quotient.eq_zero_iff_dvd, Equiv.cast_eq_iff_heq, MonoidHom.map_cyclic, LieSubalgebra.coe_ad_pow, NormedSpace.exp_continuousMap_eq, RatFunc.num_algebraMap, Ideal.mem_of_liesOver, LinearIsometry.isComplete_image_iff, map_birkhoffSum, AddSubmonoid.closure_singleton_eq, RingEquiv.map_zero, FirstOrder.Language.Equiv.map_constants, OrderIso.ofHomInv_apply, AddEquiv.coe_addSubmonoidMap_apply, finsuppEquivDFinsupp_apply, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, MeasureTheory.measure_union_add_inter, FractionalIdeal.extendedHomₐ_injective, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', MvPolynomial.bind₂_monomial_one, Finset.image_pow, Set.prod_self_eq_iUnion_perm, Function.Embedding.arrowCongrRight_apply, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two, OrderAddMonoidIso.eq_comp_symm, Finset.card_eraseNone_of_mem, InfHom.id_apply, Homeomorph.prodPUnit_apply, StarAlgHom.ext_iff, BoxIntegral.Box.coe_ae_eq_Icc, AlgebraicGeometry.Spec_map_localization_isIso, OrderIso.isGLB_preimage, QuotientGroup.quotientQuotientEquivQuotientAux_mk, MonoidWithZeroHom.valueGroup_eq_range, RingHom.map_one, MeasureTheory.Measure.prod_apply, Derivation.leibniz', MeasureTheory.Measure.compProd_assoc', AlternatingMap.constOfIsEmpty_apply, Real.fourierInv_comp_linearIsometry, Derivation.leibniz_zpow, LinOrd.id_apply, ordinaryHypergeometricSeries_apply_eq', MvPolynomial.mem_support_notMem_vars_zero, Equiv.Perm.sign_trans, IncidenceAlgebra.mu_ofDual, MulAction.toPerm_symm_apply, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, MonoidHom.iterate_map_frobenius, DFinsupp.Lex.le_iff_of_unique, AlgebraicGeometry.Scheme.stalkClosedPointTo_fromSpecStalk, ContinuousLinearEquiv.differentiableAt, Polynomial.degree_monomial_le, OrderEmbedding.strictMono, Function.Embedding.optionMap_apply, BddDistLat.coe_comp, NumberField.InfinitePlace.ext_iff, FreeAlgebra.lift_ι_apply, MvPolynomial.commAlgEquiv_X, ProbabilityTheory.IsGaussian.charFun_eq', IsFreeGroup.lift_of, Interval.dual_top, AlgHom.coe_toMonoidHom, MeasureTheory.measure_laverage_le_pos, Module.End.genEigenspace_inf_le_add, ProbabilityTheory.covarianceBilinDual_eq_covariance, PowerSeries.map_sin, AddMonoidAlgebra.mapDomainNonUnitalRingHom_apply, Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd, ContMDiffSection.coe_smul, DFinsupp.sumAddHom_comm, DomMulAct.mk_smul_toLp, Subgroup.noncommPiCoprod_apply, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, IntermediateField.adjoin_map, InnerProductSpace.Core.inner_im_symm, OrthonormalBasis.sum_sq_norm_inner_right, FiniteArchimedeanClass.liftOrderHom_mk, LinearMap.liftBaseChangeEquiv_symm_apply, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, AffineEquiv.coe_homothetyUnitsMulHom_apply_symm, signedDist_zero, MeasureTheory.condExpL1CLM_indicatorConstLp, DirichletCharacter.Even.toUnitHom_eval_neg_one, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, List.prod_hom_nonempty, AddMonoidAlgebra.modOf_apply_of_not_exists_add, ArithmeticFunction.pow_carmichael, InfHom.dual_symm_apply_toFun, HahnSeries.embDomainOrderEmbedding_apply, TopHom.sup_apply, Real.volume_Iio, OrderEmbedding.infIrredUpperSet_apply, partialSups_monotone, Polynomial.rootMultiplicity_eq_nat_find_of_nonzero, Multiset.map_noncommProd, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero, Equiv.Perm.perm_mapsTo_inl_iff_mapsTo_inr, AddConstMapClass.map_sub_const, IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le, MonoidWithZeroHom.toZeroHom_coe, TwoSidedIdeal.ker_eq_bot, CommAlgCat.lift_unop_hom, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, ContinuousLinearMap.ratio_le_opNorm, CategoryTheory.Localization.Preadditive.homEquiv_apply, ArchimedeanClass.mk_map_nonneg_of_archimedean, InfHom.const_apply, AddHom.toFun_eq_coe, MvPolynomial.mapEquiv_apply, iteratedFDerivWithin_eq_equiv_comp, QuadraticForm.dualProd_apply, spectralMulAlgNorm_def, qExpansion_one, cmp_toDual, RootPairing.RootPositiveForm.isOrthogonal_reflection, List.getEquivOfForallCountEqOne_symm_apply_val, UniformEquiv.image_preimage, WithTop.ofDual_lt_ofDual_iff, MeasureTheory.Measure.InnerRegularWRT.of_sigmaFinite, UnitAddCircle.measure_univ, Fintype.bilinearCombination_apply, FreeAddMonoid.toList_zero, ProbabilityTheory.Kernel.parallelComp_def, AddCommGrpCat.homAddEquiv_symm_apply_hom, dist_center_homothety, MvPolynomial.eval₂Hom_congr', Polynomial.coeff_monomial_of_ne, Algebra.TensorProduct.equivFinsuppOfBasis_apply, StarAlgHom.coe_coe, CompactlySupportedContinuousMap.toRealLinearMap_apply, LinearMap.compQuadraticMap_polar, Polynomial.derivative_X_sub_C_pow, LinearMap.toMatrix₂_comp, AddSubgroup.addCommute_subtype_of_addCommute, InformationTheory.klDiv_zero_left, Ideal.map_span, CategoryTheory.Arrow.equivSigma_apply_fst, MeasureTheory.measure_biUnion_eq_iSup, AddMonoidHom.map_closure, CompactExhaustion.exists_mem_nhds, CategoryTheory.Functor.map_conj, dist_toAdd, exteriorPower.map_apply_ιMulti_family, AddGroupSeminorm.toFun_eq_coe, Module.End.eigenspace_le_genEigenspace, Matrix.l2_opNNNorm_mulVec, AddSubgroup.toIntSubmodule_symm, MeasureTheory.measure_neg_vadd_symmDiff, AffineMap.lineMap_lineMap_right, MeasureTheory.integrable_comp, IsGreatest.dual, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, LocallyFiniteOrder.orderAddMonoidHom_strictMono, PrincipalSeg.lt_top, FirstOrder.Language.LHom.coe_substructureReduct, RingCon.kerLiftₐ_mk, LinearIsometryEquiv.map_eq_iff, PartitionOfUnity.sum_eq_one, MulEquiv.withZero_apply_apply, addLeftEmbedding_apply, AlgHom.map_adjugate, Complex.normSq_eq_norm_sq, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, CategoryTheory.InducedCategory.homEquiv_symm_apply_hom, Lagrange.degree_interpolate_erase_lt, Matrix.charpoly.univ_coeff_eval₂Hom, ArithmeticFunction.cardFactors_pos_iff_one_lt, Equiv.image_subset, LinearEquiv.conj_exact_iff_exact, AddMonoidHom.toMultiplicative_symm_apply_apply, exists_bounded_zero_one_of_closed, Module.Quotient.mk_smul_mk, map_mem_separableClosure_iff, DyckWord.equivTreesOfNumNodesEq_apply_coe, HasStrictFDerivAt.isLittleO, FreeAddMonoid.ofList_cons, supClosure_empty, Multiset.toFinsupp_inter, Equiv.mulRight₀_apply, MvPolynomial.optionEquivRight_X_some, MeasureTheory.Measure.addHaarMeasure_unique, Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl, AffineEquiv.coe_constVSub, Algebra.isNilpotent_trace_of_isNilpotent, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_f, isometry_cfcₙHom, NormedAddGroupHom.mem_ker, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, MulChar.pow_apply_coe, MeasureTheory.limsup_measure_closed_le_iff_liminf_measure_open_ge, Equiv.Perm.sameCycle_zpow_right, MeasureTheory.Measure.compProd_apply_univ, ExteriorAlgebra.ιMulti_range, Valued.hasBasis_nhds_zero, IsPurelyInseparable.surjective_algebraMap_of_isSeparable, PerfectRing.liftEquiv_id_apply, Polynomial.natDegree_C_mul_eq_of_mul_eq_one, Lat.Iso.mk_inv, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod, RingHom.Bijective.ofLocalizationSpan, ContDiffMapSupportedIn.structureMapCLM_zero_apply, LieSubmodule.orderIsoMapComap_symm_apply, isClosedMap_ofAdd, CategoryTheory.Limits.Types.isLimitEquivSections_apply, PrimeSpectrum.mem_image_comap_basicOpen, rothNumberNat_zero, Polynomial.eraseLead_C_mul_X, CategoryTheory.GrothendieckTopology.mem_over_iff, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_pt, AlgebraicGeometry.Scheme.stalkMap_hom_inv_assoc, ZeroHom.sub_apply, MonomialOrder.degree_le_iff, CuspForm.coe_smul, MeasureTheory.ProbabilityMeasure.toNNReal_measureReal_eq_coeFn, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff, TrivSqZeroExt.sndCLM_apply, PowerSeries.derivativeFun_C, MvPolynomial.aeval_expand, mul_gaussSum_inv_eq_gaussSum, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, WithAbs.algebraMap_right_apply, RestrictedProduct.continuous_rng_of_top, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, Polynomial.natDegree_C, TensorProduct.gradedComm_algebraMap, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, MeasureTheory.Measure.pi_ball, AddGrpCat.zero_apply, CategoryTheory.Limits.WalkingPair.swap_apply_right, NonUnitalRingHom.mem_range_self, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup, SimpleGraph.Iso.map_mem_edgeSet_iff, IsLocalization.isUnit_piRingHom_algebraMap_comp_piEvalRingHom, AffineEquiv.map_vadd, LinearMap.lsmul_flip_apply, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_mul, SchwartzMap.norm_iteratedFDeriv_le_seminorm, groupHomology.cyclesIso₀_comp_H0π_apply, ContinuousMultilinearMap.prodEquiv_symm_apply_fst, Complex.inv_cpow_eq_ite', Algebra.TensorProduct.opAlgEquiv_apply, EuclideanGeometry.reflection_reflection, AlgHom.norm_apply_le_self, Representation.IsIrreducible.bijective_or_eq_zero, MeasureTheory.L1.setToL1_add_left', Submodule.norm_orthogonalProjection_apply_le, DistribMulActionHom.coe_fn_coe', OrderIso.map_succ, ProbabilityTheory.IsRatCondKernelCDFAux.mono, ContinuousAffineMap.coe_mk_const_linear_eq_linear, MeasurableEmbedding.equivRange_apply, MulChar.coe_mk, antitoneOn_toDual_comp_iff, MeasureTheory.Measure.le_iff', liftOfDerivationToSquareZero_mk_apply, Bialgebra.counit_surjective, RealRMK.integral_rieszMeasure, Matrix.addMonoidHomMulRight_apply, Complex.antilipschitz_equivRealProd, isLocalizedModule_iff, PartENat.withTopEquiv_ofNat, LinearMap.deriv, AlgebraicIndependent.lift_reprField, IsometryEquiv.divLeft_symm_apply, BialgEquiv.apply_symm_apply, AddMonoidHom.coe_toMultiplicativeLeft, ValuativeExtension.vlt_iff_vlt, RCLike.conj_I_ax, Matrix.SeparatingRight.toLinearMap₂', LocallyConstant.mulIndicator_apply, InitialSeg.map_isMin, BoundedContinuousFunction.memLp_top, Algebra.Extension.Hom.sub_one_tmul, WithBot.toDual_bot, MeasurableSet.exists_isClosed_lt_add, Besicovitch.exist_finset_disjoint_balls_large_measure, MeasureTheory.measurePreserving_piCongrLeft, killingForm_eq_zero_of_mem_zeroRoot_mem_posFitting, Matroid.mapEmbedding_ground_eq, MeasureTheory.Measure.mem_support_iff, MeasureTheory.measure_le_measure_union_left, map_intCast, StarAlgEquiv.leftInverse_symm, Representation.asModuleEquiv_symm_map_smul, bernstein.variance, FirstOrder.Language.ElementaryEmbedding.injective, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, CompositionAsSet.blocks_partial_sum, GradedAlgebra.proj_recompose, CoheytingHomClass.map_top, X_pow_sub_C_irreducible_iff_of_prime_pow, Real.continuous_probChar, LeftInvariantDerivation.map_zero, RegularWreathProduct.left_inl, Monoid.CoprodI.lift_mrange_le, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, AlgEquiv.eq_symm_apply, CommMonCat.val_inv_units_map_hom_apply, TensorProduct.norm_assoc, AddMonoidAlgebra.domCongr_single, OrderIso.sumLexIioIci_symm_apply_Iio, CategoryTheory.ProjectiveResolution.extMk_hom, FirstOrder.Language.PartialEquiv.le_iff, StarSubalgebra.isClosedEmbedding_inclusion, AddSubsemigroup.opEquiv_symm_apply, DualNumber.lift_smul, MeasureTheory.OuterMeasure.mkMetric'.tendsto_pre, Module.Basis.repr_linearCombination, groupHomology.eq_d₃₂_comp_inv_apply, Module.Basis.dualBasis_apply_self, Finset.gcd_mul_left, MonoidHom.mem_eqLocusM, Submodule.apply_coe_mem_map, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, SpecialLinearGroup.det_eq_one, AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeι, PowerSeries.constantCoeff_invOfUnit, MvPolynomial.aeval_algebraMap_apply, UniformConvergenceCLM.add_apply, PowerSeries.order_monomial, ContinuousMultilinearMap.sum_apply, DihedralGroup.oddCommuteEquiv_apply, MulHom.mem_eqLocus, Coalgebra.sum_counit_smul, LinearMap.isClosed_range_coe, LieAlgebra.lieCharacterEquivLinearDual_symm_apply, CategoryTheory.Functor.map_conjAut, exteriorPower.presentation.relationsSolutionEquiv_apply_apply, ContMDiffAt.clm_apply_of_inCoordinates, TensorProduct.lift.tmul', Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, BoxIntegral.Box.Ioo_ae_eq_Icc, Function.Embedding.sumSet_preimage_inr, AddCon.ker_rel, LaurentPolynomial.T_apply, RCLike.I_eq_zero_or_im_I_eq_one, CompleteLatticeHom.ext_iff, AffineMap.homothety_apply_same, Module.DirectLimit.of_f, SkewMonoidAlgebra.coeff_equivMapDomain, IsLocalization.Away.awayToAwayLeft_eq, TensorProduct.assoc_tmul, Equiv.symm_comp_eq, SMulCommClass.toMulActionHom_apply, DilationEquiv.ext_iff, Equiv.sigmaEquivProd_symm_apply, Finsupp.ceilDiv_apply, Polynomial.constantCoeff_coe, bernstein_apply, CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpi, MvPolynomial.C_1, Equiv.arrowProdEquivProdArrow_apply, Prod.Lex.le_iff, Equiv.embeddingFinSucc_snd, PointedCone.mem_dual, WittVector.IsocrystalEquiv.frob_equivariant, PiTensorProduct.reindex_tprod, LinearMapClass.map_smul_of_tower, Submodule.mem_iSup_iff_exists_dfinsupp, Fin.addRothNumber_eq_rothNumberNat, MvPolynomial.eval₂Hom_X', Subsemiring.centerCongr_apply_coe, Quaternion.imK_fst_dualNumberEquiv, IsAdjoinRoot.map_X, TopologicalSpace.productOfMemOpens_isEmbedding, infIccOrderIsoIccSup_apply_coe, MulEquiv.coe_prodAssoc, PMF.toMeasure_apply_eq_toOuterMeasure_apply, DomAddAct.symm_mk_neg, ProbabilityTheory.Kernel.setIntegral_deterministic, CategoryTheory.conjugateEquiv_symm_iso, mem_subalgebraEquivIntermediateField_symm, AddSubgroup.toSubgroup_closure, Algebra.TensorProduct.equivFinsuppOfBasis_symm_apply, QuadraticForm.tensorRId_apply, Equiv.Perm.OnCycleFactors.mem_range_toPermHom'_iff, Sublattice.coe_comap, RingEquiv.map_eq_one_iff, Equiv.Perm.extendDomain_apply_image, InnerProductSpace.toDualMap_apply, List.coe_toFinsupp, gelfandTransform_map_star, BoundedOrderHom.dual_id, geometric_hahn_banach_point_closed, MvPolynomial.rTensor_apply_X_tmul, CondensedMod.epi_iff_surjective_on_stonean, DomMulAct.continuous_mk_symm, Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs, Ideal.quotientEquiv_symm_mk, IsDiscreteValuationRing.addVal_def', NonUnitalAlgHom.map_adjoin, RelIso.sumLexEmpty_symm_apply, Algebra.SubmersivePresentation.linearIndependent_aeval_val_pderiv_relation, MulMemClass.coe_subtype, HahnSeries.of_symm_smul_of_eq_mul, PEquiv.trans_eq_some, wittPolynomial_one, Polynomial.toLaurent_comp_C, IsSelfAdjoint.skewAdjointPart_apply, polynomialFunctions.starClosure_eq_adjoin_X, MvPolynomial.pderiv_X, IsField.localization_map_bijective, List.sortedGE_map_ofDual, MeasureTheory.Measure.compProd_apply, AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eq, UniformEquiv.piCongrLeft_symm_apply, MvPowerSeries.coeff_homogeneousComponent, CategoryTheory.Equivalence.symmEquivFunctor_map, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, RCLike.normSq_nonneg, Polynomial.IsRoot.mul_div_eq, contraction_of_isPowMul, compl_image_latticeClosure, ContinuousAlgEquiv.ext_iff, IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, mulRightEmbedding_apply, Finset.image_mul, KaehlerDifferential.exact_mapBaseChange_map, MeasureTheory.IsProjectiveLimit.measure_univ_eq, Finset.normalize_lcm, CategoryTheory.GrothendieckTopology.coversTop_iff_of_isTerminal, Polynomial.sum_C_mul_X_pow_eq, PowerSeries.monomial_mul_monomial, ProbabilityTheory.Kernel.eq_boolKernel, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, LinearEquiv.isAdjointPair_symm_iff, Topology.WithScott.ofScott_inj, LinearMap.pow_eq_aeval_mod_charpoly, closedAbsConvexHull_min, AddHom.mulOp_apply_apply, MonoidHom.toAdditiveLeft_apply_apply, toBoolAlg_add, IsValuativeTopology.continuous_valuation, NumberField.IsCMField.coe_ringOfIntegersComplexConj, LinearMap.prodEquiv_symm_apply, DifferentiableAt.conj_conj, MonoidAlgebra.mapRangeAlgHom_apply, AffineIsometryEquiv.ofTop_symm_apply_coe, NonUnitalSubalgebra.inclusion_injective, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg, MvPolynomial.eval_eq', Filter.Eventually.volume_pos_of_nhds_real, InfiniteGalois.mulEquivToLimit_symm_continuous, Padic.mulValuation_toFun, AddMonoid.Coprod.snd_surjective, LinearMap.BilinForm.add_left, LocallyConstant.coe_comap, PiLp.basisFun_repr, AddGroupExtension.Equiv.trans_apply, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp, HahnSeries.SummableFamily.smul_toFun, modularCyclotomicCharacter.toFun_spec, MeasureTheory.Measure.lintegral_rnDeriv_le, LinearMap.toSpanSingleton_apply_one, AlgebraicGeometry.PresheafedSpace.stalkMap.congr, LinearMap.tensorProductEnd_apply, Path.Homotopic.map_trans_evalAt, ContinuousLinearMap.adjoint_inner_left, AddChar.sum_apply_eq_zero_iff_ne_zero, minpoly.algEquiv_eq, Bialgebra.TensorProduct.assoc_tmul, AlgebraicGeometry.Scheme.Hom.isClosedMap, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, PseudoMetric.coe_le_coe, IsMulFreimanHom.mulRothNumber_mono, ClosureOperator.ofPred_apply, OrderRingHom.coe_comp, PointwiseConvergenceCLM.isInducing_inducingFn, NormedAddGroupHom.coe_comp, Matrix.toLpLin_pow, AddGroupExtension.Equiv.refl_symm_apply, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, PowerBasis.liftEquiv_symm_apply, KaehlerDifferential.tensorKaehlerEquiv_tmul, Matrix.transpose_empty_cols, AlgebraicGeometry.Scheme.Hom.isLocallyClosed_range, DomMulAct.coe_smul_linearMap, CartanMatrix.D_three', TensorProduct.inner_mapIncl_mapIncl, AddSubsemigroup.topEquiv_symm_apply_coe, Orientation.oangle_rotation_oangle_right, CongruenceSubgroup.IsArithmetic.conj, WithTop.toDualBotEquiv_symm_top, isTranscendenceBasis_equiv, Nonneg.val_unitsHomeomorphPos_symm_apply_coe, MonoidHom.noncommPiCoprod_mulSingle, Module.AEval'.X_pow_smul_of, Bornology.IsVonNBounded.image_multilinear, Set.uIoo_toDual, IsSelfAdjoint.map, Homeomorph.isCompact_preimage, isStronglyTranscendental_mk_radical_conductor, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, Finsupp.degree_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, AddEquiv.op_symm_apply_symm_apply, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable, RootPairing.toLinearMap_apply_PolarizationIn, LieRinehartAlgebra.Hom.map_smul_apply', Finsupp.domCongr_apply, MeasureTheory.Lp.simpleFunc.add_toSimpleFunc, Rep.toAdditive_symm_apply, Continuous.clm_bundle_apply, Algebra.Generators.H1Cotangent.δAux_toAlgHom, Field.DirectLimit.nontrivial, RootPairing.InvariantForm.isOrthogonal_reflection, IncidenceAlgebra.smul_apply, Matrix.kroneckerAlgEquiv_apply, DirichletCharacter.toUnitHom_eq_char', Polynomial.as_sum_support_C_mul_X_pow, ProbabilityTheory.Kernel.setLIntegral_restrict, IsCyclic.val_inv_mulAutMulEquiv_apply, AddHom.mulLeft_apply, ofColex_mul, Real.abs_mulExpNegMulSq_comp_le_norm, Equiv.sigmaFiberEquiv_apply, NormedAddGroupHom.le_opNorm_of_le, LinearIsometryEquiv.coe_prodAssoc_symm, Finsupp.linearCombination_single_index, TopCat.uliftFunctorObjHomeo_naturality_apply, finSumFinEquiv_apply_right, Polynomial.derivWithin, PseudoMetric.isSymm_ball, ContinuousLinearMap.isBoundedBilinearMap, AlgHom.opComm_apply_apply, CategoryTheory.GlueData.glue_condition_apply, Algebra.Generators.comp_val, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, Finsupp.prod_unique, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, DirectSum.algebraMap_apply, nnnorm_algebraMap, ArchimedeanClass.stdPart_map_real, TopCat.homeoOfIso_apply, fdifferential_apply, PrincipalSeg.apply_subrelIso, FiberwiseLinear.trans_openPartialHomeomorph_apply, ContinuousMultilinearMap.hasBasis_nhds_zero, KaehlerDifferential.D_apply, DomMulAct.isClosedEmbedding_mk, CompactlySupportedContinuousMap.integrable, MeasureTheory.OuterMeasure.map_iInf_le, CliffordAlgebra.EquivEven.e0_mul_v_mul_e0, RCLike.le_iff_re_im, CategoryTheory.Subfunctor.ofSection_eq_range', Homeomorph.isClosed_setOf_iff, AlgebraicGeometry.morphismRestrict_appLE, Equiv.pointReflection_involutive, MeasureTheory.ProbabilityMeasure.coeFn_empty, AddChar.coe_toAddMonoidHom, Equiv.Perm.IsCycle.pow_eq_one_iff, CliffordAlgebraComplex.ofComplex_I, InnerProductSpace.AlgebraOfCoalgebra.mul_def, Algebra.adjoin_eq_ring_closure, ProbabilityTheory.Kernel.partialTraj_compProd_traj, LinearMap.BilinForm.separatingRight_toMatrix'_iff, LinearMap.extendTo𝕜_apply, Matrix.isUnit_toLin'_iff, Real.coe_nnabs, Equiv.Perm.sign_sumCongr, AddAut.coe_mul, ProbabilityTheory.Kernel.lintegral_prodMkRight, AffineIsometryEquiv.coe_inv, RelIso.subrelUnivIso_symm_apply, ProbabilityTheory.condDistrib_apply_ae_eq_condExpKernel_map, cfcHom_integral, RingCon.sSup_eq_ringConGen, AddHom.prod_apply, MulChar.apply_mem_rootsOfUnity_of_pow_eq_one, NumberField.Units.fundSystem_mk, IsValuativeTopology.mem_nhds_iff', AffineMap.const_apply, UnitAddTorus.coeFn_mFourierLp, Stonean.epi_iff_surjective, MvPolynomial.eval₂_C, coe_ringEquiv_lpBCF, Dilation.mapsTo_closedBall, Equiv.bijOn_symm_image, MeasureTheory.Integrable.integral_norm_condExpKernel, HahnEmbedding.IsPartial.truncLT_mem_range, DividedPowers.isDPMorphism_iff, MeasureTheory.StronglyMeasurable.integral_kernel_prod_right', AddSubgroup.centerCongr_apply_coe, RatFunc.liftMonoidWithZeroHom_apply_div, MeasureTheory.setIntegral_map_equiv, PrimitiveSpectrum.gc_closureOperator, AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersion, Module.piEquiv_apply_apply, DirichletCharacter.changeLevel_toUnitHom, HahnSeries.SummableFamily.smul_support_finite, RelIso.coe_fn_injective, Submodule.span_algebraMap_image, CategoryTheory.Limits.Pi.whiskerEquiv_inv, HVertexOperator.coeff_smul, Equiv.Perm.sign_eq_prod_prod_Iio, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T, Abelianization.coe_lift_symm, RootPairing.EmbeddedG2.long_eq_three_mul_short, LinearMap.BilinForm.smul_left, Polynomial.degree_quadratic_le, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, Polynomial.eq_quadratic_of_degree_le_two, OrderAddMonoidIso.coe_addEquiv, OneHom.coe_comp, AbsoluteValue.le_sub, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, CircleDeg1Lift.transnumAuxSeq_zero, compContinuousLinearMap_zero, finSuccEquivLast_castSucc, Finsupp.lift_apply, AddCircle.volume_of_add_preimage_eq, PMF.toOuterMeasure_apply_le_toMeasure_apply, PrimeSpectrum.isIdempotentElemEquivClopens_symm_inf, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, SupHom.coe_top, MeromorphicOn.divisor_sub_const_of_ne, AlgHom.IsArithFrobAt.localize_algebraMap, Affine.Simplex.orthogonalProjectionSpan_congr, WeierstrassCurve.φ_one, Module.End.pow_apply, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, LinearIndependent.linearCombinationEquiv_apply_coe, AlgEquiv.ofAlgHom_symm_apply, Subalgebra.mvPolynomial_aeval_coe, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two', LinearIsometryEquiv.preimage_ball, Function.Embedding.swap_apply, DomMulAct.smul_mulActionHom_apply, MulEquiv.arrowCongr_apply, IsAdjoinRoot.adjoinRootAlgEquiv_apply_root, Nat.factorization_choose_le_one, MeasureTheory.le_inducedOuterMeasure, CircleDeg1Lift.lt_map_of_int_lt_translationNumber, Polynomial.exists_iterate_derivative_eq_factorial_smul, FormalMultilinearSeries.apply_eq_pow_smul_coeff, Subgroup.IsComplement.leftCosetEquivalence_equiv_fst, Equiv.Perm.sameCycle_inv_apply_right, NonUnitalAlgHom.prodEquiv_apply, ProbabilityTheory.IsZeroOrMarkovKernel.isZeroOrProbabilityMeasure, RatFunc.num_dvd, AddEquiv.subsemigroupMap_apply_coe, CircleDeg1Lift.iterate_mono, MeasureTheory.SimpleFunc.norm_approxOn_y₀_le, Function.locallyFinsuppWithin.ext_iff, LocallyConstant.one_apply, MeasureTheory.Measure.sum_apply, AffineMap.lineMap_mem, Polynomial.divX_eq_zero_iff, innerₗ_apply, fderivWithin_continuousMultilinear_apply_const, GenLoop.ext_iff, RelEmbedding.ofMonotone_coe, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, Polynomial.rootsExpandPowToRoots_apply, BialgEquiv.invFun_eq_symm, map_inv₀, OrderIso.coe_toOrderEmbedding, TensorProduct.AlgebraTensorModule.leftComm_tmul, MeasureTheory.OuterMeasure.add_apply, HahnSeries.truncLT_add, CircleDeg1Lift.tendsto_translation_number', continuousMultilinearCurryFin0_symm_apply, WeierstrassCurve.Projective.baseChange_addXYZ, minpoly.isIntegrallyClosed_eq_field_fractions, IsLocalization.algebraMap_mem_map_algebraMap_iff, ContinuousLinearEquiv.integrable_comp_iff, PrincipalSeg.cocone_ι_app, CategoryTheory.Limits.biproduct.reindex_inv, Finset.weightedVSub_smul, WithZero.withZeroUnitsEquiv_symm_strictMono, totallyBounded_absConvexHull, map_zero, CoheytingHomClass.map_sdiff, Ideal.Quotient.mk_singleton_self, Function.Embedding.coe_sigmaSet, TensorAlgebra.toClifford_ι, RootPairing.GeckConstruction.trace_toEnd_eq_zero, NonUnitalSubring.topEquiv_apply, continuousMul_induced, MulSemiringAction.charpoly_eq_prod_smul, PEquiv.ofSet_eq_some_iff, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, Polynomial.monomial_injective, RestrictedProduct.ext_iff, OrderIso.map_sSup_eq_sSup_symm_preimage, SpectralMap.coe_comp, ContinuousMap.dist_lt_iff_of_nonempty, Matrix.toLin'_mul, Polynomial.taylor_eq_zero, SemistandardYoungTableau.highestWeight_apply, AdjoinRoot.mk_eq_zero, ModularForm.toSlashInvariantForm_coe, MonoidAlgebra.lsingle_apply, PowerBasis.equivOfMinpoly_gen, Poly.sumsq_nonneg, Matrix.of_one_hadamard, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, AddGroupSeminorm.coe_lt_coe, InverseSystem.invLimEquiv_apply_coe, OrderHom.symm_dual_id, HilbertBasis.coe_mkOfOrthogonalEqBot, SupClosed.dual, MeasureTheory.Measure.ext_prod₃_iff', FiniteField.frobeniusAlgEquiv_symm_apply, Submodule.toSubalgebra_toSubmodule, AdjoinRoot.Minpoly.coe_toAdjoin, toLex_ofLex, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff, DFinsupp.coe_neg, MeasureTheory.OuterMeasure.boundedBy_eq, WithLp.prod_norm_eq_idemFst_sup_idemSnd, CategoryTheory.Functor.CorepresentableBy.homEquiv_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, LieEquiv.ext_iff, Cardinal.extend_function_of_lt, MeasureTheory.Integrable.exists_boundedContinuous_lintegral_sub_le, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, Unitary.conjStarAlgAut_ext_iff', ContinuousMap.uncurry_apply, exists_continuous_one_zero_of_isCompact, Submodule.iSup_eq_range_dfinsupp_lsum, ModularGroup.lcRow0Extend_apply, isOfFinOrder_ofAdd_iff, PowerSeries.expand_smul, AlgebraicGeometry.Scheme.Hom.apply_mem_image_iff, MeasurableEquiv.neg_apply, Equiv.pprodEquivProdPLift_apply, AlgebraicGeometry.Scheme.Hom.asFiberHom_apply, AffineMap.lineMap_mono, MeasureTheory.Measure.add_comp', TensorProduct.gradedComm_tmul_of_zero, LinearMap.isNilpotent_toMatrix_iff, MulEquiv.coprodAssoc_apply_inl_inl, Monoid.CoprodI.range_eq_iSup, GroupLike.valMonoidHom_apply, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral, AddMonoidAlgebra.mapDomainBialgHom_apply, Metric.Snowflaking.image_ofSnowflaking_eq_preimage, ClosureOperator.ext_iff, Polynomial.card_support_eq, Composition.index_embedding, Module.Basis.span_apply, cfcₙHom_predicate, FirstOrder.Language.Hom.id_apply, ContinuousLinearEquiv.symm_smul_apply, LieModule.Cohomology.twoCochain_skew, Irreducible.addVal_pow, Circle.exp_neg, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, SupHom.dual_comp, Equiv.sumCompl_apply_inl, MeasureTheory.lintegral_rpow_eq_lintegral_meas_lt_mul, CategoryTheory.Limits.Concrete.isColimit_exists_rep, ProbabilityTheory.IsCondKernelCDF.setLIntegral, Module.Relations.Solution.directSum_var, TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply, Polynomial.reflect_monomial, VectorField.lieBracketWithin_smul_left, LocallyConstant.congr_arg, AddMonoidHom.addSubmonoidMap_surjective, LocallyConstant.evalₗ_apply, SlashInvariantForm.coe_mk, LinearMap.BilinForm.dotProduct_toMatrix_mulVec, Lagrange.degree_interpolate_lt, Seminorm.coe_sup, CliffordAlgebraQuaternion.equiv_apply, MeasureTheory.measure_le_laverage_pos, supIrred_toDual, BumpCovering.toPartitionOfUnity_eq_mul_prod, AffineMap.right_vsub_lineMap, IsLocalization.Away.tensorRight, MeasureTheory.indicatorConstLp_univ, DFinsupp.le_def, Monoid.PushoutI.NormalWord.cons_head, Submonoid.leftInvEquiv_mul, infClosure_singleton, ProbabilityTheory.Kernel.condKernelCountable_apply, Quaternion.re_fst_dualNumberEquiv, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ModuleCat.inv_hom_apply, List.Sorted.coe_getIso_symm_apply, Module.End.rTensorAlgHom_apply_apply, Set.up_mul, LinearMap.det_eq_det_toMatrix_of_finset, frobenius_sub, LieModule.traceForm_comm, FiniteField.norm_surjective, Similar.comp_right_iff, AddMonoidAlgebra.coe_algebraMap, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, Homeomorph.piEquivPiSubtypeProd_apply, WeierstrassCurve.Jacobian.baseChange_addXYZ, PseudoEpimorphism.toFun_eq_coe, ContinuousAffineEquiv.apply_eq_iff_eq, ArithmeticFunction.zeta_pos, ContinuousAlgEquiv.continuousWithinAt, ContinuousAlternatingMap.map_sum_finset, MulEquiv.restrictRootsOfUnity_coe_apply, SemiNormedGrp.completion.norm_incl_eq, FormalMultilinearSeries.compAlongComposition_bound, AddCon.inf_iff_and, ArchimedeanClass.lt_of_pos_of_archimedean, Polynomial.leadingCoeff_pow_X_add_C, MeasureTheory.OuterMeasure.trim_le_trim_iff, Algebra.linearMap_apply, OrthonormalBasis.singleton_apply, Fin.accumulate_rec, ProfiniteGrp.inv_hom_apply, NonUnitalSubalgebra.iSupLift_mk, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, MeasureTheory.Measure.lt_iff', groupCohomology.cocycles₂.coe_mk, AffineMap.coe_id, RingHom.isIntegralElem_map, MulSemiringActionHom.map_smul, LinearMap.toMatrix_reindexRange, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, LinearMap.IsProj.map_id, SSet.horn_obj, MeasurableEquiv.measurable_toFun, MvPolynomial.C_add, ContinuousAffineEquiv.apply_eq_iff_eq_symm_apply, StrictMono.orderIsoOfRightInverse_symm_apply, PiTensorProduct.tprodMonoidHom_apply, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg, AbsoluteValue.IsEquiv.lt_iff_lt, ExteriorAlgebra.liftAlternating_apply_ιMulti, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom, BoundedLatticeHom.coe_comp_sup_hom, ContinuousLinearMap.hasSum, NNRat.coe_castHom, ContinuousLinearMap.coe_smulRightₗ, Equiv.symm_apply_eq, FractionalIdeal.canonicalEquiv_mk0, AddMagma.FreeAddSemigroup.lift_comp_of', Cardinal.aleph_le_aleph, ContinuousLinearMap.lipschitz_apply, LocallyConstant.constₐ_apply_apply, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, List.formPerm_apply_getElem, PowerBasis.equivAdjoinSimple_aeval, MonoidHom.map_finprod_mem, Module.Flat.iff_lTensor_exact, AddChar.neg_apply', Polynomial.coeff_map_eq_comp, PolynomialLaw.exists_lift, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app, even_toAdd_iff, Abelianization.lift_apply_of, WeierstrassCurve.Jacobian.map_addZ, PowerSeries.C_injective, IsometryEquiv.preimage_closedEBall, CategoryTheory.Limits.idZeroEquivIsoZero_apply_inv, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, FreeMonoid.map_surjective, MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict, QuadraticAlgebra.reₗ_apply, LaurentSeries.derivative_apply, absConvexHull_nonempty, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn_real, RootPairing.algebraMap_coxeterWeightIn, Multiset.toFinsupp_apply, toMul_zero, IsDedekindDomain.primesOverEquivPrimesOver_apply, CoalgEquiv.trans_apply, ContinuousMap.HomotopyWith.coeFn_injective, Matrix.isUnit_submatrix_equiv, IsCoveringMapOn.comp_homeomorph, CategoryTheory.PreGaloisCategory.toAutHomeo_apply, ProfiniteAddGrp.id_apply, CategoryTheory.Functor.functorPushforward_equalizer_mem, MonoidHom.toFun_eq_coe, MulEquiv.prodUnique_symm_apply, algebraMap_monotone, groupHomology.mapCycles₁_id_comp_apply, Wbtw.left_mem_image_Ici_of_right_ne, Diffeomorph.sumComm_coe, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, PEquiv.trans_eq_none, AddEquiv.neg'_apply, Polynomial.cauchyBound_C, LinearMap.ker_toAddSubmonoid, LowerSet.iicsInfHom_apply, MonoidAlgebra.single_mul_apply_aux, PMF.toOuterMeasure_apply_singleton, LieModule.isFaithful_iff, ContinuousMultilinearMap.constOfIsEmpty_apply, MeasureTheory.projectiveFamilyContent_cylinder, AddMonoidHom.inl_apply, Equiv.subtypePreimage_apply, Matrix.submatrix_updateCol_equiv, OrderIso.sumDualDistrib_symm_inl, AddConstMapClass.map_nat_add, ContinuousLinearMap.lsmul_apply, CStarMatrix.of_sub_of, exteriorPower.ιMulti_span_fixedDegree_of_span_eq_top, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, MeasureTheory.IsAddFundamentalDomain.measure_set_eq, Valuation.map_sub_swap, Valuation.isEquiv_iff_val_le_one, Finsupp.toFreeAbelianGroup_single, finSuccAboveEquiv_symm_apply_ne_last, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, CommAlgCat.isoEquivAlgEquiv_apply, Normal.algHomEquivAut_apply, MeasureTheory.SimpleFunc.eapprox_comp, ContinuousAlgEquiv.isOpenMap, extDerivWithin_apply_vectorField_of_pairwise_commute, Diffeomorph.coe_trans, AddMonoidHom.associator_apply, Antitone.measure_iUnion, Finsupp.degree_zero, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, CommRing.Pic.mapAlgebra_apply, LinearMap.vecCons_apply, Real.log_of_pos, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, Quiver.SingleObj.toPrefunctor_comp, LinearMap.IsReflective.reflective_reflection, DifferentiableAt.comp_ringHom, Path.truncate_zero_zero, NonUnitalAlgHom.prodEquiv_symm_apply, CategoryTheory.PreZeroHypercover.reindex_X, Bundle.ContMDiffRiemannianMetric.pos, MvPolynomial.isHomogeneous_C_mul_X, NormedAddGroupHom.coe_nsmul, RatFunc.laurentAux_div, finRotate_apply_zero, Matrix.ofLp_toLpLin, traceForm_dualSubmodule_adjoin, disjointed_add_one, Localization.mulEquivOfQuotient_mk, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf', Pi.single_additiveOfMul_eq, AffineIsometryEquiv.continuous, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, TensorPower.galgebra_toFun_def, Nucleus.comp_eq_right_iff_le, CategoryTheory.Adjunction.homAddEquiv_sub, ContinuousAt.coeFun, WittVector.mul_polyOfInterest_aux4, Matrix.det_permutation, AddSubmonoid.LocalizationMap.isAddUnit_comp, SimpleGraph.boxProdComm_symm_apply, signedDist_triangle_left, InfTopHom.id_apply, FreeGroup.injective_lift_of_ping_pong, AddCommGrpCat.Colimits.quotUliftToQuot_ι, CategoryTheory.tensorLeftHomEquiv_tensor, CoheytingHom.coe_id, Real.tsum_eq_tsum_fourier_of_rpow_decay_of_summable, OrderMonoidIso.withZero_apply_symm_apply, ProbabilityTheory.Kernel.finset_sum_apply', Action.tensorUnit_ρ, LinearIsometryEquiv.congr_arg, FractionalIdeal.adjoinIntegral_coe, Module.range_piEquiv, DirectSum.lof_eq_of, MeasureTheory.StronglyMeasurable.integral_condExpKernel, OrderIso.bddBelow_preimage, LinearEquiv.cast_apply, Equiv.finsuppUnique_apply, AlgebraicGeometry.genericPoint_eq_of_isOpenImmersion, Submonoid.LocalizationMap.eq_iff_exists, Multiset.cardHom_apply, SSet.skeleton_obj_eq_top, SSet.Subcomplex.yonedaEquiv_coe, finAddFlip_apply_mk_right, polyEquivTensor_symm_apply_tmul, Polynomial.roots_C_mul_X_add_C, ContinuousMonoidHom.inv_toFun, DistribMulActionHom.id_apply, Polynomial.natDegree_C_mul_le, NormedAddGroupHom.extension_coe, map_vadd, AlgebraicGeometry.Scheme.homeoOfIso_apply, ProbabilityTheory.Kernel.lintegral_map, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, MeasureTheory.measurePreserving_arrowProdEquivProdArrow, Polynomial.divX_hom_toFun, CategoryTheory.Functor.IsDenseSubsite.equalizer_mem, ProbabilityTheory.Kernel.pow_add_apply_eq_lintegral, LinearMap.IsSymmetric.continuous, ContinuousLinearMap.toContinuousAddMonoidHom_comp, affineHomeomorph_image_I, ContinuousMap.restrictPreimage_apply, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, MeasureTheory.measure_le_lintegral_pos, IsContMDiffRiemannianBundle.exists_contMDiff, Set.principalSegIio_toRelEmbedding, Ideal.quotientToQuotientRangePowQuotSucc_mk, ConcaveOn.comp_affineMap, MvPowerSeries.weightedHomogeneousComponent_of_lt_weightedOrder_eq_zero, Ideal.mem_map_of_equiv, Equiv.pnatEquivNat_symm_apply, SignType.castHom_apply, CommRing.Pic.ext_iff, MulSemiringActionHom.comp_apply, FreeAddMonoid.toList_add, List.formPerm_apply_getElem_length, CommGrpCat.mono_iff_injective, MvPolynomial.rename_eval₂, StarModule.decomposeProdAdjoint_symm_apply, Module.Basis.dualBasis_equivFun, AffineEquiv.map_midpoint, PresheafOfModules.presheaf_map_apply_coe, MulAction.stabilizerEquivStabilizer_apply, LinearMap.charpoly_eq_X_pow_iff, controlled_sum_of_mem_closure_range, MeasureTheory.Lp.norm_const_le, Equiv.zero_def, AddCircle.equivAddCircle_apply_mk, AddHom.isClosed_range_coe, MulEquiv.coe_prodComm_symm, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac, MonoidHom.eq_iff_eq_on_generator, Seminorm.coe_add, BooleanSubalgebra.subtype_injective, absConvexHull_empty, MeasureTheory.volume_sum_rpow_le, MeasureTheory.Measure.pi_map_eval, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, Subalgebra.mul_toSubmodule, MvPowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, ProbabilityTheory.IsMarkovKernel.isProbabilityMeasure, MulEquiv.toMonoidWithZeroHom_injective, ofDual_compares_ofDual, partialSups_mul_const, isAddRightRegular_ofDual, ZeroAtInftyContinuousMap.toBCF_apply, AlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, Monoid.Coprod.toProd_apply_inr, PiTensorProduct.piTensorHomMap_tprod_tprod, Subgroup.IsComplement.equiv_fst_eq_self_of_mem_of_one_mem, DirichletCharacter.LSeries.mul_mu_eq_one, Finsupp.single_eq_update, WithTop.toDual_lt_iff, CategoryTheory.Abelian.Ext.homEquiv_chgUniv, Preord.id_apply, PadicInt.toZModPow_ofIntSeq_of_pow_dvd_sub, ModularGroup.coe_T_inv, integral_conj, Unitization.starLift_range, Polynomial.leadingCoeff_X_pow_sub_C, PowerSeries.eq_X_mul_shift_add_const, ofBoolAlg_sup, MeasureTheory.SimpleFunc.nearestPtInd_le, LaurentPolynomial.mk'_eq, Finsupp.optionElim_eq_elim', MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul', CuspFormClass.zero_at_infty, CommRingCat.forget_map, associatesNonZeroDivisorsEquiv_mk_mk, MeasureTheory.ProbabilityMeasure.coeFn_def, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, CuspForm.coe_neg, Submodule.coe_inclusion, ContDiffMapSupportedIn.zero_on_compl, OrderDual.ext_iff, precomp_extClass_surjective_of_projective_X₂, LinearIsometry.extend_apply, Matroid.mapEmbedding_indep_iff, BoundedContinuousFunction.norm_le, AffineSubspace.wOppSide_lineMap_left, NumberField.FinitePlace.norm_lt_one_iff_mem, AddMonoidHom.single_apply, MvPowerSeries.coeff_subst, MultilinearMap.map_update_smul_left, OrderIso.setCongr_symm_apply, RingEquiv.moduleEndSelfOp_apply, CoalgHomClass.counit_comp_apply, AlternatingMap.map_update_zero, MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec, AlgHom.IsArithFrobAt.apply_of_pow_eq_one, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbv, IsPrimitiveRoot.primitiveRootsPowEquiv_symm_apply_coe, Rep.ofMulDistribMulAction_ρ_apply_apply, Algebra.adjoin_nonUnitalSubalgebra_eq_span, Basis.ofRankEqZero_apply, SSet.OneTruncation₂.ofNerve₂.natIso_hom_app_obj, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, mulMonoidWithZeroHom_apply, LocallyConstant.comapAddMonoidHom_apply, Finsupp.apply_surjective, LatticeHom.withTop_toFun, IncidenceAlgebra.coe_inj, DirectSum.map_injective, MvPowerSeries.expand_eq_expand, WithOne.mapMulHom_mapMulHom, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, ContinuousLinearMap.iteratedFDerivWithin_comp_left, StarMonoidHom.one_apply, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, MeasureTheory.SimpleFunc.map_lintegral, MulHomClass.map_mul, WithZeroMulInt.toNNReal_neg_apply, InnerProductSpace.rank_rankOne, OrderIso.smulRight_symm_apply, WeierstrassCurve.map_a₆, map_comp_sub, MonoidHom.map_one₂, Set.Finite.equiv_image_eq_iff_subset, MeasureTheory.OuterMeasure.comap_top, AlgebraicGeometry.formallySmooth_stalkMap_iff, IsIntegrallyClosedIn.algebraMap_eq_of_integral, Algebra.Generators.localizationAway_σ, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, LinearMap.toMatrix_smulBasis_left, AdjoinRoot.quotEquivQuotMap_apply, CategoryTheory.enrichedFunctorTypeEquivFunctor_symm_apply_obj, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, AddCon.quot_mk_eq_coe, DomAddAct.symm_mk_add, PrincipalSeg.transRelIso_apply, MulEquiv.coe_comapSubgroup, MvPowerSeries.substAlgHom_comp_substAlgHom_apply, AddSubgroup.quotientiInfEmbedding_apply_mk, MeasureTheory.SimpleFunc.coe_mul, IsAdjoinRootMonic.modByMonicHom_map, QuotientAddGroup.lift_mk', ContinuousLinearMap.HasRightInverse.rightInverse_rightInverse, toMul_add, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, StarHomClass.map_star, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_fst, NonUnitalAlgHom.coe_coe, AddChar.zsmul_apply, ContinuousAddEquiv.eq_symm_comp, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, isClosedMap_toDual, CompactExhaustion.iUnion_eq, IsAddUnit.preimage_vadd_set, MvPowerSeries.constantCoeff_smul, CategoryTheory.FinCategory.asTypeToObjAsType_obj, sigmaFinsuppEquivDFinsupp_symm_apply, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, OrderMonoidIso.symm_comp_eq, TopCat.nonempty_isLimit_iff_eq_induced, SetTheory.Game.birthday_ordinalToGame, toMul_sum, CategoryTheory.Sieve.overEquiv_top, AffineEquiv.coeFn_inj, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, FreeAddGroup.map.id, DirectSum.of_zero_mul, VertexOperator.ncoeff_apply, Valuation.IsUniformizer.val, Module.Dual.transpose_comp, IsLocalization.Away.awayToAwayRight_eq, TensorProduct.congr_tmul, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, UnitAddTorus.mFourier_neg, NonUnitalStarRingHom.coe_id, ContMDiffAt.clm_bundle_apply, Polynomial.derivativeFinsupp_apply_apply, CategoryTheory.Limits.CofanTypes.equivOfIsColimit_symm_apply, AlgebraicGeometry.isIso_stalkMap_coprodSpec, MeasureTheory.Measure.notMem_support_iff, ContinuousMap.addUnitsLift_apply_neg_apply, FreeAddMagma.map_of, EquivLike.apply_eq_iff_eq, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, LinearIndependent.localization_localization, IsAzumaya.mulLeftRight_comp_congr, ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq, MeasureTheory.SimpleFunc.memLp_approxOn_range, NumberField.IsCMField.equivInfinitePlace_apply, LinearMap.BilinForm.isSymm_iff_flip, AddMonoidHom.compr₂_apply, HahnSeries.order_abs, OrderAddMonoidIso.coe_mk, FreeMonoid.ofList_toList, RatFunc.mk_eq_div, PartOrdEmb.ofHom_apply, Convex.taylor_approx_two_segment, LieAlgebra.Extension.ringModuleOf_bracket, MvPolynomial.mapAlgEquiv_apply, optionProdEquiv_symm_inl, IsAdjoinRoot.lift_root, Polynomial.Bivariate.equivMvPolynomial_symm_X_0, Set.opEquiv_self_symm_apply_coe, MeasureTheory.measure_le_setAverage_pos, absConvexHull_eq_self, Polynomial.sup_aeval_range_eq_top_of_isCoprime, RingHom.toMonoidWithZeroHom_eq_coe, AddMonoidAlgebra.mapRangeAlgEquiv_apply, Equiv.Perm.viaFintypeEmbedding_apply_image, Module.Basis.prod_apply, MulAction.IsBlock.preimage, MulChar.sum_one_eq_card_units, Nat.dvd_ordCompl_of_dvd_not_dvd, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem, ArithmeticFunction.sigma_eq_zero, Subgroup.mem_toAddSubgroup', Algebra.adjoin_insert_algebraMap, Diffeomorph.isLocalDiffeomorph, MonoidHom.coe_prodMap, Valuation.HasExtension.val_map_le_one_iff, RootPairing.corootForm_apply_apply, LinearMap.flip_bijective_iff₁, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, isClosedMap_ofMul, Delone.DeloneSet.mapIsometry_symm_apply_coveringRadius, smoothSheafCommRing.evalHom_germ, CircleDeg1Lift.map_nat_add, Sublattice.mem_map, RelIso.compl_apply, LatticeCon.ker_r, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, Derivation.coeFnAddMonoidHom_apply, DilationEquiv.mulRight_symm_apply, MeasureTheory.OuterMeasure.iInf_apply, Polynomial.taylor_apply, CompleteLatticeHom.comp_apply, Submodule.comap_coe, InnerProductSpace.toDual_apply_apply, SimplexCategory.toTopObj_one_add_eq_one, LinearMap.flip_bijective_iff₂, AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue, AlgEquiv.cast_symm_apply, Matrix.TransvectionStruct.toMatrix_reindexEquiv, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, ofColex_eq_zero, LieSubalgebra.coe_inclusion, exists_continuous_nonneg_pos, OrderMonoidIso.coe_orderIso, Valuation.map_sub, ContinuousOpenMap.ext_iff, WittVector.frobeniusPoly_zmod, AddEquiv.finsuppUnique_apply, InitialSeg.image_Iio, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, Ideal.Quotient.stabilizerHom_surjective_of_profinite, Algebra.Extension.Cotangent.mk_eq_zero_iff, BialgEquiv.coe_toAlgEquiv, Polynomial.natDegree_C_mul_of_mul_ne_zero, HahnSeries.support_truncLT, ContinuousAlternatingMap.map_zero, Rat.valuation_le_one_iff_den, MonoidAlgebra.ofMagma_apply, WeakDual.CharacterSpace.coe_coe, CompactlySupportedContinuousMap.smulc_apply, ContinuousLinearMap.adjointAux_apply, MulAlgebraNorm.ext_iff, PresheafOfModules.Derivation.congr_d, Finsupp.finite_of_nat_weight_le, MultilinearMap.fromDFinsuppEquiv_single, ContinuousFunctionalCalculus.exists_cfc_of_predicate, isHomeomorph_iff_exists_homeomorph, MulHom.coe_ofDense, MulHom.coe_coe, MulEquiv.map_inv, SheafOfModules.freeHomEquiv_symm_comp, Orientation.inner_rotation_pi_div_two_right, BoundedLatticeHom.coe_toSupBotHom, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, WeierstrassCurve.Affine.C_addPolynomial_slope, DirichletCharacter.sum_char_inv_mul_char_eq, infIooOrderIsoIooSup_symm_apply_coe, MvPolynomial.eval_neg, LinearMap.BilinForm.mem_dualSubmodule, Algebra.FiniteType.iff_quotient_mvPolynomial', coe_lpBCFₗᵢ, le_map_add_map_div', IsLocalization.map_eq, commute_lmul_rmul_sq, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, LinearMap.det_toLin', AddMonoidHom.withBotMap_apply, Complex.normSq_sub, MonoidHom.coe_of_map_mul_inv, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, AddSubsemigroup.centerCongr_apply_coe, Set.preimage_pow_subset, ArithmeticFunction.coe_mk, MulEquiv.isUnit_map, EReal.sign_mul, RCLike.measurable_re, Submodule.linearEquiv_det_reflection, CategoryTheory.CosimplicialObject.cechConerveEquiv_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', SetTheory.PGame.relabel_moveLeft, FreeGroup.map.id', WithZero.unitsWithZeroEquiv_symm_apply, NormedAddGroupHom.zero_apply, ContinuousMap.periodic_tsum_comp_add_zsmul, Equiv.symm_trans_apply, Real.volume_Ico, DFinsupp.card_Iic, map_nnratCast, Polynomial.iterate_derivative_comp_one_sub_X, Profinite.IndexFunctor.surjective_π_app, Monoid.CoprodI.Word.mem_smul_iff_of_ne, LinearMap.mapMatrixModule_apply, Algebra.Presentation.differentials.surjective_hom₁, Trivialization.symmL_continuousLinearMapAt, CategoryTheory.Iso.homCongr_refl, OrderIso.equivClosureOperator_apply, Valuation.mem_valuationSubring_iff, MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zero, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, ProbabilityTheory.IsGaussianProcess.comp_left, DirectSum.lmap_eq_map, GaussianInt.toComplex_im_div, Module.Basis.coe_smul, ValuationSubring.coe_unitGroupMulEquiv_apply, ContinuousMap.evalCLM_apply, LinearPMap.apply_comp_inclusion, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, AddHomClass.map_add, ProperCone.innerDual_singleton, MeasureTheory.SimpleFunc.memLp_iff, DFinsupp.filterLinearMap_apply, ProbabilityTheory.Kernel.aemeasurable, HahnSeries.embDomain_single, CircleDeg1Lift.commute_add_int, Polynomial.Splits.eq_prod_roots, algebraMap_isometry, OrderMonoidHom.toFun_eq_coe, SetTheory.Game.le_birthday, real_inner_eq_re_inner, frobenius_zero, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, CategoryTheory.GrothendieckTopology.coe_copy, RCLike.add_conj, DirectSum.coe_congr_linearEquiv, Polynomial.evalEvalRingHom_apply, ZeroAtInftyContinuousMap.neg_apply, Nat.Prime.dvd_iff_one_le_factorization, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, minimal_toDual, EuclideanGeometry.reflection_eq_self_iff, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply, TensorAlgebra.lift_comp_ι, RingEquiv.congr_arg, RCLike.ofReal_re_ax, Matrix.submatrix_mulVec_equiv, LinearIsometryEquiv.comp_differentiableOn_iff, RingOfIntegers.norm_algebraMap, ProbabilityTheory.IndepSet_iff, GroupExtension.Section.rightHom_section, LieSubmodule.toEnd_comp_subtype_mem, LinearIsometryEquiv.comp_differentiableAt_iff, BialgHom.congr_arg, MeasureTheory.IsProbabilityMeasure.measure_univ, disjoint_ofDual_iff, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, LeftInvariantDerivation.coe_sub, RingHom.map_iterate_frobenius, FreeGroup.map.comp, IsWellFounded.rank_eq_typein, ProbabilityTheory.Kernel.condKernel_apply_eq_condKernel, ContinuousMap.val_unitsLift_symm_apply_apply, NonUnitalStarAlgHom.prod_apply, CategoryTheory.Subobject.mapIsoToOrderIso_apply, CategoryTheory.Functor.RepresentableBy.equivOfIsoObj_symm_apply, coe_toLexLinearEquiv, MvPowerSeries.HasSubst.const_coeff, MeasureTheory.Measure.restrict_apply_eq_zero, MvPolynomial.tensorEquivSum_one_tmul_C, OrderHom.isLeast_lfp, PowerSeries.exp_mul_exp_eq_exp_add, Nat.ofAdd_mul, Nat.Primes.prodNatEquiv_apply, CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois, Monoid.CoprodI.Word.of_smul_def, BooleanSubalgebra.apply_coe_mem_map, Submodule.mk_mem_projectivization_iff, ofAdd_image_zmultiples_eq_zpowers_ofAdd, Representation.norm_ofMulDistribMulAction_eq, ContinuousAddEquiv.symm_comp_self, Matrix.kroneckerMapBilinear_apply_apply, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, MvPolynomial.eq_modMonomial_single_iff, LaurentSeries.powerSeriesPart_coeff, Multiset.sum_hom_ne_zero, ContDiffWithinAt.continuousLinearMap_comp, NumberField.InfinitePlace.smul_coe_apply, Finset.orderEmbOfFin_zero, toLex_add, SubAddAction.SMulMemClass.coe_subtype, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, CategoryTheory.HomOrthogonal.equiv_of_iso, AffineIsometryEquiv.pointReflection_fixed_iff, Subgroup.smul_apply_eq_smul_apply_inv_smul, ArithmeticFunction.carmichael_two_pow_of_le_two, AddSubmonoid.toSubmonoid_closure, Poly.ext_iff, Continuous.clm_apply, MeasurableEquiv.map_apply_eq_iff_map_symm_apply_eq, CategoryTheory.FunctorToTypes.binaryProductEquiv_symm_apply, PowerBasis.trace_gen_eq_nextCoeff_minpoly, MultilinearMap.constOfIsEmpty_apply, RCLike.im_eq_conj_sub, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, map_add, LinearMap.SeparatingRight.congr, monotone_iff_map_nonneg, LinearEquiv.symm_apply_apply, Equiv.psigmaCongrRight_apply, Ideal.pi_tensorProductMk_quotient_surjective, Fin.Embedding.coe_tail, Matrix.rank_eq_finrank_range_toLin, ValuationRing.isFractionRing_iff, SimpleGraph.Hom.mapEdgeSet_coe, MvPolynomial.rTensor_apply_tmul, AffineIsometry.diam_image, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, MeasureTheory.eLpNorm'_le_eLpNorm'_mul_rpow_measure_univ, OrthonormalBasis.volume_parallelepiped, Equiv.Perm.closure_cycle_coprime_swap, ContinuousAlternatingMap.norm_ofSubsingleton, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, MonoidWithZeroHom.one_apply_def, RingEquiv.symm_toRingHom_apply_toRingHom_apply, MulChar.eq_one_iff, toDual_intCast, Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, WittVector.pow_dvd_ghostComponent_of_dvd_coeff, SimpleGraph.comap_symm, CliffordAlgebra.invOf_ι_mul_ι_mul_ι, Matrix.toLinearMapRight'_mul_apply, StarAlgHom.coe_toAlgHom, MeasureTheory.FiniteMeasure.coeFn_zero, RootPairing.Equiv.comp_indexEquiv_apply, Subgroup.subgroupOfEquivOfLe_symm_apply_coe_coe, latticeClosure_prod, AddMonoidHom.neg_apply, MeasurableEquiv.coe_toLp, ContinuousOrderHom.coe_toOrderHom, Complex.inv_re, CategoryTheory.GradedObject.comapEquiv_unitIso, InnerProductSpace.rankOne_def, WeierstrassCurve.Affine.Point.map_injective, CliffordAlgebraQuaternion.equiv_symm_apply, AlgHom.map_det, Affine.Simplex.ExcenterExists.touchpointWeights_restrict, PerfectRing.liftEquiv_apply, Polynomial.degree_derivative_lt, Equiv.Perm.Disjoint.mul_apply_eq_iff, Diffeomorph.mfderivToContinuousLinearEquiv_coe, BilinForm.toMatrix_comp, Matrix.GeneralLinearGroup.map_inv, ProbabilityTheory.Kernel.partialTraj_le_def, CommRing.Pic.instFreeAsModuleOfNat, TensorProduct.nnnorm_map, AlgebraicGeometry.Scheme.instIsIsoCommRingCatResidueFieldMapOfIsOpenImmersion, Polynomial.div_wf_lemma, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_ne, Module.Basis.ofZLatticeBasis_span, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, IsLocalMinOn.hasFDerivWithinAt_nonneg, BoundedContinuousFunction.mkOfCompact_apply, Homeomorph.comp_continuous_iff', Matrix.charmatrix_fromBlocks, NonarchAddGroupSeminorm.lt_def, Orientation.oangle_rotation, CharacterModule.intSpanEquivQuotAddOrderOf_apply, WeierstrassCurve.Jacobian.baseChange_dblX, ContinuousLinearEquiv.injective, MeasureTheory.laverage_mul_measure_univ, isRightRegular_toColex, Matrix.reindexLinearEquiv_one, PowerBasis.exists_smodEq, Frm.Iso.mk_inv, ProbabilityTheory.Kernel.meas_countablePartitionSet_le_of_fst_le, Equiv.Perm.prodExtendRight_apply_eq, LieAlgebra.ad_nilpotent_of_nilpotent, Subring.centerToMulOpposite_symm_apply_coe, OreLocalization.numeratorRingHom_apply, Set.powersetCard.coe_ofFinEmb, Set.mulIndicator_ae_eq_one, AlgebraicGeometry.Scheme.instIsOverMapResidueFieldMapOverInferInstanceOverClass, CliffordAlgebra.EvenHom.contract, RCLike.conj_im_ax, AddCircle.volume_closedBall, Valuation.ofAddValuation_apply, HahnSeries.SummableFamily.coe_injective, Polynomial.derivative_natCast_mul, ContinuousLinearMap.coe_flipₗᵢ', AddMonoidHom.finsuppSum_apply, MeasureTheory.OuterMeasure.exists_measurable_superset_forall_eq_trim, MDifferentiableAt.clm_bundle_apply₂, MeasureTheory.OuterMeasure.dirac_apply, AddLocalization.mk_zero_eq_addMonoidOf_mk, Valuation.Integers.isIntegral_iff_v_le_one, AlgHom.mulLeftRight_apply, WeierstrassCurve.Jacobian.baseChange_negDblY, Complex.preimage_equivRealProd_prod, SimpleGraph.Walk.IsHamiltonian.getVertEquiv_symm_apply, SchwartzMap.integral_mul_laplacian_right_eq_left, CategoryTheory.congr_fun, MonoidHom.coe_toHomUnits, ContinuousAffineMap.coe_comp, ModuleCat.mono_iff_injective, Module.Relations.Solution.directSumEquiv_symm_apply_var, FreeGroup.lift_symm_apply, Algebra.TensorProduct.commRight_tmul, MeasureTheory.tendsto_measure_vadd_diff_isCompact_isClosed, AddSubgroup.range_zmultiplesHom, Module.Basis.linearCombination_dualBasis, Finsupp.prod_of_support_subset, Equiv.permCongr_trans, Polynomial.eq_X_add_C_of_degree_eq_one, Ideal.mapCotangent_toCotangent, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul, DilationEquiv.symm_apply_apply, CategoryTheory.Presheaf.app_localPreimage, PiTensorProduct.norm_eval_le_injectiveSeminorm, Algebra.discr_eq_discr_of_algEquiv, CompleteLatticeHom.apply_liminf_iterate, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, ContinuousLinearMap.coe_coe, FiniteDimensional.basisSingleton_repr_apply, SchwartzMap.convolution_apply, ZeroAtInftyContinuousMap.sub_apply, Filter.map_neg', IsFractionRing.mk'_num_den', MulHom.coe_mk, partialSups_succ, Multiset.map_noncommSum_aux, Diffeomorph.sumComm_inr, NumberField.mixedEmbedding.realSpace.volume_eq_zero, SimpleGraph.Iso.apply_mem_neighborSet_iff, MeasureTheory.tendsto_setToFun_approxOn_of_measurable_of_range_subset, Function.locallyFinsuppWithin.restrict_eqOn_compl, Submodule.sub_starProjection_mem_orthogonal, sbtw_iff_right_ne_and_left_mem_image_Ioi, Module.Flat.iff_lTensor_preserves_injective_linearMap', ArchimedeanClass.mk_sub_stdPart_pos, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk₀_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, MeasureTheory.Measure.MeasureDense.indicatorConstLp_subset_closure, HahnSeries.SummableFamily.const_toFun, Algebra.Generators.Cotangent.surjective_map_ofComp, PointwiseConvergenceCLM.equivWeakDual_apply, WeierstrassCurve.Jacobian.baseChange_polynomialY, Subalgebra.linearEquivOp_apply_coe, PrimeSpectrum.preimage_specComap_zeroLocus, Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero, PowerSeries.evalNegHom_X, IsLocalization.Away.commutes, Polynomial.fderiv_aeval, ValuativeExtension.mapValueGroupWithZero_valuation, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, CoalgHom.mul_apply, ConjAct.units_smul_def, AddConstEquiv.coe_symm_toEquiv, MvPolynomial.map_ofNat, Valuation.isEquiv_iff_val_eq_one, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one, Subsemiring.mem_map_equiv, transpose_dualTensorHom, AffineMap.linearMap_vsub, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, AffineEquiv.val_equivUnitsAffineMap_apply, inner_self_conj, Char.card_pow_card, HeytAlg.hom_inv_apply, ContinuousMap.Homotopy.extend_apply_coe, BoundedOrderHom.symm_dual_comp, MvPolynomial.coeff_monomial_mul, MeasureTheory.SimpleFunc.edist_approxOn_y0_le, Equiv.piCongrLeft_symm_preimage_pi, AlgebraNorm.toFun_eq_coe, LinearMap.coe_proj, toMul_sub, SupBotHom.comp_apply, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, AddMonoid.End.mulLeft_apply_apply, FreeAddGroup.closure_eq_range, Matrix.toLin_mul, Finset.mapRange_finsuppAntidiag_eq, ConvexOn.real_univ_sSup_of_countable_affine_eq, TensorProduct.AlgebraTensorModule.assoc_tmul, MeasureTheory.memLp_const_iff_enorm, Set.graphOn_prod_graphOn, MonoidHom.toMulEquiv_symm_apply, Set.dual_ordConnected, Matrix.of_zero, Set.image_list_prod, CategoryTheory.PreGaloisCategory.toAutMulEquiv_apply, Rep.indResAdjunction_counit_app_hom_hom, ProbabilityTheory.Kernel.discard_apply, QuaternionAlgebra.coe_addEquivProd, RestrictedProduct.coe_single_apply, NumberField.mixedEmbedding.mem_span_latticeBasis, FDRep.hom_hom_action_ρ, CategoryTheory.Functor.mapAction_obj_ρ_apply, NonUnitalAlgHom.map_zero, ContinuousLinearMap.add_apply, IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one, Ideal.exists_relNorm_eq_pow_of_isPrime, Polynomial.mahlerMeasure_C_mul_X_add_C, CliffordAlgebra.map_apply_ι, exteriorPower.ιMulti_apply_coe, toDual_mul, Action.FintypeCat.toEndHom_apply, AddSubmonoid.coe_negOrderIso_symm_apply, RingEquiv.coe_toAddEquiv, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, AddGroupSeminorm.add_bddBelow_range_add, QuotientGroup.mk'_apply, ContinuousAlternatingMap.sub_apply, zmultiplesHom_ker_eq, ContinuousOpenMap.coe_id, WeierstrassCurve.isGoodReduction_iff, InfClosed.infClosure_eq, AddAction.stabilizerEquivStabilizer_symm_apply, MeasureTheory.Measure.map_eq_sum, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, MvPolynomial.eval₂Hom_rename, Algebra.bijective_algebraMap_iff, LocallyConstant.add_apply, IsAlgebraic.exists_nonzero_coeff_and_aeval_eq_zero, Real.sinhEquiv_symm_apply, HasSum.mapL, MulOpposite.coe_symm_opMulEquiv, Matrix.toLin_pow, MeasureTheory.volume_preserving_pi_empty, ContinuousMap.Homotopy.evalAt_apply, Finsupp.le_degree, Submodule.coe_tensorSpanEquivSpan_apply_tmul, Module.Basis.equivFunL_symm_apply_repr, SetTheory.PGame.moveRight_nim, Algebra.TensorProduct.lmul'_comp_map, Finset.map_insert, Subalgebra.topEquiv_apply, LieSubmodule.mem_baseChange_iff, associatesNonZeroDivisorsEquiv_symm_mk_mk, Module.End.aeval_apply_of_hasEigenvector, CircleDeg1Lift.continuous_iff_surjective, Profinite.NobelingProof.iso_map_bijective, Perfection.coeff_mk, AffineIsometry.coe_toAffineMap, MvPolynomial.degree_degLexDegree, DilationEquiv.mulLeft_symm_apply, Rack.act'_apply, Subring.subtype_injective, BoundedContinuousFunction.innerProbChar_apply, IsometryEquiv.mulLeft_apply, Finsupp.prod_equivMapDomain, QuadraticMap.associated_tmul, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, Submodule.FG.lTensor.directLimit_apply', PowerBasis.mem_span_pow', IsAzumaya.bij, TensorProduct.directSumLeft_tmul_lof, MeasureTheory.integral_pos_iff_support_of_nonneg_ae, ProbabilityTheory.IsSFiniteKernel.sFinite, CartanMatrix.B_two, IsometryEquiv.map_midpoint, Algebra.Generators.H1Cotangent.exact_δ_map, OrthonormalBasis.repr_apply_apply, WittVector.mapFun.mul, lineMap_le_left_iff_nonpos, IsGalois.normalAutEquivQuotient_apply, Subgroup.IsComplement.equiv_fst_eq_one_of_mem_of_one_mem, Ideal.Quotient.mk_bijective_iff_eq_bot, AddEquivClass.map_eq_zero_iff, PowerSeries.coeff_invUnitsSub, PowerBasis.repr_gen_pow_isIntegral, AddCon.comap_conGen_equiv, SemimoduleCat.hom_inv_apply, CategoryTheory.SingleObj.functor_map, MeasureTheory.tendsto_measure_Iic_atTop, IsGalois.normalBasis_apply, IsometryEquiv.addLeft_apply, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm, DFinsupp.lex_lt_of_lt, HahnSeries.lt_orderTop_single, ProbabilityTheory.Kernel.HasSubgaussianMGF.add, FreeMonoid.toList_of, QuotientGroup.rangeKerLift_surjective, Matroid.mapSetEmbedding_indep_iff', Module.Basis.det_reindex_symm, Dilation.isUniformEmbedding, LinearEquiv.trans_apply, SkewPolynomial.monomial_zero_one, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow', Subring.mem_map, Finsupp.card_Icc, Sequential.isoOfHomeo_inv, Ring.DirectLimit.congr_apply_of, CategoryTheory.pullbackShiftFunctorZero'_hom_app, ContinuousMap.HomotopyEquiv.trans_apply, MeasureTheory.exists_mem_forall_mem_nhdsWithin_pos_measure, WithLp.prod_nnnorm_eq_of_L2, ProbabilityTheory.covarianceBilin_comm, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, sSupHom.dual_symm_apply_toFun, Derivation.liftKaehlerDifferential_comp, Representation.FiniteCyclicGroup.coinvariantsKer_eq_range, Matrix.toLin_self, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, Rep.coindToInd_apply, EReal.sign_coe, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, isAddLeftRegular_toLex, AddCircle.continuous_equivIoc_symm, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, Orientation.inner_rotation_pi_div_two_left, Circle.coe_inv_eq_conj, UpperSet.coe_iciSupHom, AddGroup.preimage_vadd_set, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, MeasureTheory.ProbabilityMeasure.toFiniteMeasure_apply, ContinuousMap.toLp_def, Finsupp.equivFunOnFinite_symm_apply_support, Polynomial.eq_C_of_natDegree_eq_zero, MeasureTheory.measure_limsup_cofinite_eq_zero, groupHomology.mapCycles₁_comp_i_apply, CliffordAlgebra.ι_mul_ι_add_swap, ENNReal.orderIsoIicCoe_symm_apply_coe, Ordinal.toNatOrdinal_one, kroneckerTMulLinearEquiv_one, CategoryTheory.uliftYonedaEquiv_comp, AffineIsometryEquiv.apply_symm_apply, AmpleSet.preimage, Matrix.singleAddMonoidHom_apply, cmpLE_ofDual, IsLocalization.AtPrime.to_map_mem_maximal_iff, NumberField.IsCMField.complexConj_apply_eq_self, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, Quiver.SingleObj.pathEquivList_symm_cons, DirectSum.lieAlgebraComponent_apply, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_symm_apply, AlternatingMap.ofSubsingleton_apply_apply, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, MagmaCat.coe_comp, SimpleGraph.Hom.map_mem_edgeSet, SSet.stdSimplex.face_obj, MeasureTheory.Measure.countable_meas_level_set_pos, MulHom.subsemigroupMap_surjective, VectorField.lieBracket_fmul_left, LieEquiv.ofEq_apply, MultilinearMap.domCoprod_alternization_eq, Affine.Simplex.sign_excenterWeights_singleton_neg, TensorProduct.AlgebraTensorModule.leftComm_symm_tmul, AffineMap.vadd_lineMap, DomAddAct.mk_zsmul, MeasureTheory.SimpleFunc.coe_map, SheafOfModules.pushforwardCongr_hom_app_val_app, Subsemigroup.toAddSubsemigroup_closure, RootPairing.Hom.comp_weightMap_apply, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_lintegral, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, Module.Basis.SmithNormalForm.snf, mem_affineSpan_pair_iff_exists_lineMap_rev_eq, Polynomial.sum_monomial_index, ZMod.ringEquivCongr_refl_apply, Module.DirectLimit.linearEquiv_of, Finsupp.sum_unique, RootPairing.pairing_neg_one_neg_four_iff, Polynomial.derivativeFinsupp_derivative, BoundedContinuousFunction.neg_norm_le_apply, CentroidHom.coe_intCast, NonUnitalAlgHom.coe_inr, Valuation.RankOne.strictMono, Equiv.Set.univPi_symm_apply_coe, finCongr_apply_coe, SchwartzMap.integral_bilin_fourier_eq, fwdDiff_aux.shiftₗ_pow_apply, monotone_toDual_comp_iff, MonoidHom.mem_mker, Complex.det_conjAe, OrderMonoidHom.inrₗ_apply, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, HasFDerivWithinAt.lim, ofLex_neg, Polynomial.smeval_C, Orientation.oangle_rotation_self_left, Complex.sub_conj, CategoryTheory.Functor.sectionsEquivHom_naturality, Finsupp.lsum_single, Measurable.lintegral_kernel_prod_right'', CocompactMap.ext_iff, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, KaehlerDifferential.ker_map, SchwartzMap.zero_apply, MvPolynomial.dvd_monomial_iff_exists, ContinuousLinearEquiv.contDiffPointwiseHolderAt, ProbabilityTheory.Kernel.id_prod_apply', CompactlySupportedContinuousMapClass.uniformContinuous, OrderIso.map_iInf, Set.Finite.subtypeEquivToFinset_apply_coe, ContinuousMultilinearMap.analyticAt, DividedPowers.DPMorphism.dpow_comp, LinearMap.BilinForm.neg_left, CategoryTheory.evalEquiv_apply, ModuleCat.comp_apply, Algebra.FormallySmooth.mk_lift, WeierstrassCurve.Projective.baseChange_polynomialY, MulActionSemiHomClass.map_smulₛₗ, MeasureTheory.Measure.IsFiniteMeasureOnCompacts.comap, mem_span_C_coeff, AlgebraicIndependent.aeval_of_algebraicIndependent, AddGroupSeminormClass.map_neg_eq_map, ClosedSubmodule.orthogonal_eq_inter, AffineEquiv.apply_symm_apply, PiTensorProduct.tprodCoeff_eq_smul_tprod, ZMod.χ₈'_eq_χ₄_mul_χ₈, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, PositiveLinearMap.toPreGNS_ofPreGNS, MeasureTheory.diracProba_comp_diracProbaEquiv_symm_eq_val, TopCat.id_app, ArithmeticFunction.sigma_one_apply, AlgHom.toKerIsLocalization_apply, MulEquiv.val_inv_piUnits_apply, SetLike.GradeZero.algebraMap_apply, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, ContinuousMultilinearMap.prodL_apply, LinearMap.BilinForm.sum_repr_mul_repr_mul, Finsupp.linearEquivFunOnFinite_single, Module.Basis.mulOpposite_repr_op, Orientation.kahler_neg_orientation, MvPolynomial.aeval_bind₁, AddMonCat.coe_id, PMF.ofFinset_apply, TensorProduct.AlgebraTensorModule.rightComm_tmul, OrderHom.pi_coe, QuadraticForm.dualProdIsometry_invFun, PowerSeries.prod_monomial, PMF.uniformOfFintype_apply, IsFractionRing.to_map_eq_zero_iff, Homeomorph.comp_continuousAt_iff', ModuleCat.restrictScalarsCongr_hom_app, Finset.none_mem_insertNone, CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, AdicCompletion.coe_eval, CompactlySupportedContinuousMap.sup_apply, Set.vadd_graphOn_univ, strictAnti_toDual_comp_iff, AffineBasis.basisOf_reindex, Polynomial.isCoprime_expand, hasFDerivWithinAt_iff_hasDerivWithinAt, Subgroup.HasDetOne.det_eq, Polynomial.X_mul_divX_add, ProperCone.coe_comap, Real.sinhEquiv_apply, FintypeCat.equivEquivIso_apply_inv, IsFractionRing.div_surjective, Complex.conj_im, finSumFinEquiv_symm_apply_castAdd, LinearMap.separatingLeft_toMatrix₂'_iff, LatticeHom.withBot_toFun, cfc_add_const, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, MeasureTheory.Measure.pi_singleton, Module.Basis.smulTower'_repr_mk, sInfHom.dual_apply_toFun, hasFTaylorSeriesUpToOn_succ_iff_right, AddMonoidHom.mem_mker, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd, StarAlgHom.restrictScalars_apply, ContinuousOn.clm_bundle_apply₂, EisensteinSeries.hasSum_e2Summand_symmetricIco, RingHom.isometry, partialSups_le, Equiv.sigmaUnique_apply, ContinuousMap.Homotopy.symm_apply, ContinuousMulEquiv.symm_trans_apply, conj_trivial, ContinuousLinearMap.coe_flipMultilinearEquiv, Matrix.GeneralLinearGroup.fixpointPolynomial_eq_zero_iff, CliffordAlgebraQuaternion.ofQuaternion_star, Finset.image_some_eraseNone, ProbabilityTheory.Kernel.condDistrib_trajMeasure, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, unitInterval.volume_Icc, Monoid.Coprod.lift_apply_inl, MeasureTheory.tsum_measure_le_measure_univ, MonoidAlgebra.lift_unique, ContinuousMap.prodMap_apply, RelEmbedding.coe_fn_injective, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, derangements.Equiv.RemoveNone.mem_fiber, MonoidHom.coe_toAdditive_map, CategoryTheory.PreGaloisCategory.toAut_isHomeomorph, ArithmeticFunction.convolution_vonMangoldt_const_one, Seminorm.bddAbove_iff, SimpleGraph.cliqueFinset_map_of_equiv, Algebra.norm_inv, ContinuousAlgEquiv.comp_continuous_iff, LaurentSeries.exists_Polynomial_intValuation_lt, DirectSum.coe_mul_apply, DirectLimit.exists_eq_one, MeasureTheory.tendsto_measure_of_tendsto_indicator_of_isFiniteMeasure, HomologicalComplex.alternatingConst_iCycles_even_comp_apply, Polynomial.card_support_binomial, DirectSum.mk_apply_of_notMem, NonUnitalAlgHom.coe_Lmul, AlternatingMap.map_eq_zero_of_not_injective, AffineIsometryEquiv.dist_pointReflection_self, AlgEquiv.opComm_apply_apply, PowerSeries.coeff_succ_C, Polynomial.sum_monomial_eq, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, IsPGroup.powEquiv_apply, TannakaDuality.FiniteGroup.leftRegular_apply, IsCoveringMap.monodromy_map, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C', HomogeneousLocalization.awayMapₐ_apply, ContinuousMultilinearMap.norm_map_init_le, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, HahnSeries.coeff_truncLT, IsLocalization.mk'_algebraMap_eq_mk', Equiv.plift_symm_apply, ContinuousMap.coeFnLinearMap_apply, LinearEquiv.map_smulₛₗ, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, Finsupp.rangeIcc_apply, Fin.snoc_eq_cons_rotate, SSet.stdSimplex.map_apply, Equiv.Perm.cycleOf_apply_apply_self, MulActionHom.coe_sub, ofLex_natCast, QuaternionAlgebra.lift_apply, MulEquiv.apply_eq_iff_symm_apply, DFA.reindex_refl, Valued.continuous_extensionValuation, preimage_smul_setₛₗ_of_isUnit_isUnit, MonomialOrder.degree_sum_le, LeftInvariantDerivation.left_invariant'', groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, ordinaryHypergeometricSeries_apply_zero, CliffordAlgebra.contractLeft_contractLeft, MulOpposite.opContinuousLinearEquiv_symm_apply, TensorProduct.AlgebraTensorModule.assoc_symm_tmul, SchwartzMap.compCLMOfAntilipschitz_apply, NonUnitalAlgHom.coe_one, ContinuousAlternatingMap.hasStrictFDerivAt, ContinuousAffineMap.hasStrictFDerivAt, LinearMap.pi_apply, Filter.coe_pureZeroHom, MeasureTheory.projectiveFamilyContent_congr, SchwartzMap.tsupport_lineDerivOp_subset, AddCommMonCat.neg_hom_apply, Subring.topEquiv_apply, IsLocalization.toLocalizationMap_apply, AffineIsometryEquiv.dist_pointReflection_self_real, TensorProduct.algebraMap_gradedMul, AddLocalization.addEquivOfQuotient_mk', IncidenceAlgebra.coe_add, RingEquiv.subsemiringMap_apply_coe, ProbabilityTheory.Kernel.singularPart_eq_zero_iff_apply_eq_zero, SimpleGraph.map_adj, MeasureTheory.measure_add_diff, MeasureTheory.SimpleFunc.edist_approxOn_mono, FiniteField.algebraMap_norm_eq_pow, SchwartzMap.fourierInv_apply_eq, DFinsupp.single_eq_of_ne, toAdd_pow, trace_eq_finrank_mul_minpoly_nextCoeff, Multiset.gcd_singleton, PowerSeries.trunc_trunc_mul, Matrix.comp_toSquareBlock, NonUnitalStarAlgHom.inr_apply, Interval.dual_bot, SchwartzMap.smulRightCLM_apply_apply, IsUnifLocDoublingMeasure.measure_mul_le_scalingConstantOf_mul, AddEquiv.symmEquiv_apply_symm_apply, Finsupp.prod_embDomain, MulChar.val_neg_one_eq_one_of_odd_order, Equiv.Perm.cycleOf_self_apply_pow, hasEigenvector_toLin'_diagonal, PerfectClosure.of_apply, AddCon.rel_mk, Pi.lex_desc, MonoidAlgebra.tensorEquiv_symm_single, MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sum, CategoryTheory.SingleObj.toEnd_def, LinearOrderedField.inducedOrderRingHom_toFun, NormedSpace.norm_expSeries_summable_of_mem_ball, Submonoid.mk_mul_mk_inv_eq_one, ValuationSubring.valuation_le_one_iff, AddChar.map_zero_eq_one, LinearMap.lcomp_apply, volume_regionBetween_eq_lintegral', Matrix.GeneralLinearGroup.toLin'_apply, CovBy.toDual, LinearMap.mapMatrixModule_id_apply, OrderIso.isAtom_iff, Representation.apply_bijective, Equiv.Perm.viaEmbeddingHom_apply, MvPolynomial.algebraMap_apply, MeasurableEquiv.ext_iff, SlashInvariantForm.exists_one_half_le_im_and_norm_le, AlgebraicGeometry.isCompl_range_inl_inr, Derivation.restrictScalars_apply, List.prod_map_hom, toColex_one, CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space, AddMonoid.End.smul_def, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, ClosureOperator.le_closure, MvPolynomial.mkDerivationₗ_monomial, Dilation.mapsTo_emetric_closedBall, hasStrictFDerivAt_iff_hasStrictDerivAt, LinearIsometryEquiv.coe_toIsometryEquiv, MeasureTheory.Integrable.norm_integral_condKernel, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, Ideal.mem_quotient_iff_mem, WithLp.prod_norm_eq_add_idemFst, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, MeasureTheory.piContent_eq_measure_pi, CategoryTheory.conjugateEquiv_whiskerRight, ValuationSubring.mem_unitGroup_iff, MeasureTheory.Measure.restrict_iUnion_apply, Finsupp.le_weight, LightCondensed.isoFinYonedaComponents_inv_comp, LinearMap.toMatrixAlgEquiv'_apply, LieAlgebra.ad_pow_lie, DomMulAct.smul_aeeqFun_aeeq, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, NonemptyInterval.dual_map₂, mulRight_continuous, IsDiscreteValuationRing.addVal_uniformizer, IsFreeGroup.toFreeGroup_symm_apply, CongruenceSubgroup.isArithmetic_conj_SL2Z, Finset.mul_prod_eq_prod_insertNone, FreeAddGroup.ext_hom_iff, Submodule.FG.rTensor.directLimit_apply, UniformEquiv.coe_prodComm, ContinuousAlternatingMap.map_update_smul, ofColex_inv, CoheytingHom.comp_apply, Equiv.sumIsLeft_apply, MeasureTheory.Measure.restrict_apply_le, DifferentiableAt.continuousAlternatingMap_apply, binomialSeries_apply, MeasureTheory.L1.setToL1_smul_left', MeasureTheory.exists_null_frontier_thickening, VectorField.mpullback_apply, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, MeasureTheory.integral_map_equiv, SubMulAction.algebraMap_mem, MvPolynomial.exists_fin_rename, ThreeGPFree.le_mulRothNumber, LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, IsLocalization.Away.map_surjective_iff, TensorProduct.directLimitLeft_rTensor_of, Equiv.swap_apply_def, Equiv.Perm.cycleOf_apply_apply_zpow_self, OrderAddMonoidIso.self_comp_symm, NonUnitalRingHom.op_symm_apply_apply, LinearMap.IsSymmetric.toSelfAdjoint_apply, TensorProduct.finsuppScalarRight_smul, LatticeHom.withTop'_toFun, RatFunc.liftOn_div, LieHom.comp_apply, InfHom.dual_comp, Polynomial.Splits.comp_X_add_C, AddMonoid.Coprod.fst_toProd, RCLike.conj_div, MeasureTheory.Lp.constₗ_apply, SimpleGraph.comap_surjective, DFinsupp.Colex.le_iff_of_unique, Submonoid.mk_inv_mul_mk_eq_one, Function.locallyFinsuppWithin.coe_zsmul, WeierstrassCurve.map_b₆, QuotientRing.isOpenMap_coe, InnerProductSpace.volume_ball, RingEquiv.coe_mk, CategoryTheory.bijection_symm_apply_id, EuclideanGeometry.orthogonalProjection_subtype, SSet.Truncated.spine_map_vertex, nhds_toAdd, Antivary.sum_smul_lt_sum_comp_perm_smul_iff, AlgHom.mem_range, galLiftEquiv_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, RelEmbedding.coe_toRelHom, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, LinearMap.toMvPolynomial_baseChange, AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSections_mem_grothendieckTopology, IncidenceAlgebra.prod_apply, HNNExtension.NormalWord.unitsSMulGroup_snd, AList.lookupFinsupp_eq_iff_of_ne_zero, LinearMap.BilinForm.IsAlt.self_eq_zero, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, TensorPower.tprod_mul_tprod, RingHomIsometric.nnnorm_map, LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_sup, Polynomial.degree_derivative_eq, ofDual_sInf, Equiv.Set.rangeInr_apply_inr, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, ContinuousMulEquiv.invFun_eq_symm, Polynomial.C_mul_monomial, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, BoundedContinuousFunction.coe_sum, Sum.Lex.toLex_le_toLex, Matrix.reindexLinearEquiv_comp, RCLike.im_mul_ofReal, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, Submonoid.unitsTypeEquivIsUnitSubmonoid_apply_coe, Fin.valEmbedding_apply, VectorField.lieBracket_eq, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app, lipschitzWith_circleMap, Finset.mem_finsupp_iff_of_support_subset, Orientation.map_eq_det_inv_smul, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, AdicCompletion.factorₐ_evalₐ_one, ProbabilityTheory.Kernel.prodAssoc_symm_prod, Seminorm.continuousAt_zero', HasDerivAtFilter.hasGradientAtFilter, ContinuousLinearMap.coe_restrict_scalarsL', Equiv.instAssociativeCoeForallForallArrowCongr, Polynomial.natDegree_hasseDeriv_le, ModuleCat.FilteredColimits.M.mk_map, ContinuousLinearMapWOT.isInducing_inducingFn, SlashInvariantFormClass.periodic_comp_ofComplex, MonoidWithZeroHom.range_nontrivial, sInfHom.toFun_eq_coe, TensorProduct.lid_symm_apply, AlternatingMap.coe_mk, Specialization.toEquiv_le_toEquiv, groupCohomology.π_comp_H0Iso_hom_apply, MeasureTheory.ProbabilityMeasure.map_apply_of_aemeasurable, RootPairing.algebraMap_pairingIn, BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact, cfc_def, Metric.Snowflaking.image_ofSnowflaking_closedEBall, Unitization.inrNonUnitalStarAlgHom_apply, MvPolynomial.optionEquivLeft_coeff_coeff, CommMonCat.forget_map, SimpleGraph.TripartiteFromTriangles.is3Clique_iff, AddSubmonoid.LocalizationMap.sec_spec', CompactlySupportedContinuousMap.toReal_apply, SSet.ι₀_snd, Order.exists_orderEmbedding_insert, Path.Homotopic.Quotient.mk_map, PositiveLinearMap.exists_norm_apply_le, HahnSeries.algebraMap_apply, ProbabilityTheory.Kernel.ae_comp_iff, IsFractionRing.ringEquivOfRingEquiv_algebraMap, ComplexShape.symmetryEquiv_apply_coe, AddMonCat.FilteredColimits.M.map_mk, IsTensorProduct.equiv_apply, AddChar.zmodChar_apply', MeasureTheory.Measure.bind_apply_le, Unitary.mapEquiv_apply, Matrix.vecMulLinear_apply, DoubleCentralizer.star_fst, Matrix.toLinearMapₛₗ₂'_toMatrix', LinearMap.continuous_of_isContPerfPair, Homeomorph.coe_inv, Affine.Simplex.affineCombination_mem_setInterior_face_iff_mem, ConvexCone.mem_map, ArithmeticFunction.moebius_apply_prime, BialgEquiv.trans_apply, Bialgebra.comul_algebraMap, ZMod.castHom_apply, LieEquiv.trans_apply, LinearMap.toMatrix'_algebraMap, WithZero.toMulBot_lt, ComplexShape.symmetryEquiv_symm_apply_coe, Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one, MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv, Algebra.FiniteType.iff_quotient_freeAlgebra, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, Submodule.orderIsoMapComap_apply', QuotientRing.isQuotientMap_coe_coe, MeasureTheory.forall_measure_preimage_mul_iff, fourier_coe_apply, Polynomial.separable_X_pow_sub_C', HahnSeries.embDomain_coeff, RestrictedProduct.comp_single, Matrix.charpoly.optionEquivLeft_symm_univ_isHomogeneous, LinearMap.ext_iff, Matrix.cramer_reindex, Algebra.IsAlgebraic.algHomEquivAlgHomOfSplits_apply_apply, Submodule.inclusionSpan_apply_coe, Module.End.coe_pow, algebraMap_smul, Subgroup.IsComplement.equiv_snd_eq_self_of_mem_of_one_mem, Sym.equivCongr_apply, Rep.resIndAdjunction_homEquiv_symm_apply, groupHomology.coe_mapCycles₂, Equiv.Perm.ext_iff, Finset.toDual_inf', finsuppTensorFinsupp_single, ContinuousMap.coe_zero, DirectSum.decompose_mul_add_left, TensorProduct.counit_tmul, PiTensorProduct.liftEquiv_symm_apply, AddUnits.addRight_apply, dist_right_pointReflection, PiToModule.fromMatrix_apply_single_one, LocalizedModule.coe_map_eq, RestrictedProduct.isEmbedding_coe_of_principal, CategoryTheory.Localization.homEquiv_comp, LinearIsometryEquiv.piLpCurry_apply, RCLike.summable_conj, Representation.linHom_apply, ArithmeticFunction.cardFactors_eq_sum_factorization, MeasureTheory.Integrable.exists_boundedContinuous_integral_sub_le, IsLocalization.localization_localization_surj, FractionalIdeal.isFractional_adjoin_integral, MvPolynomial.sum_weightedHomogeneousComponent, MvPolynomial.exists_degree_lt, MeasureTheory.SimpleFunc.approxOn_mem, RCLike.geometric_hahn_banach_point_point, ProfiniteAddGrp.coe_id, Associates.normalize_out, Quaternion.normSq_inv, Cardinal.ord_aleph, Con.orderIsoOp_symm_apply, AlgHom.mapMatrix_apply, Equiv.piFinsetUnion_right, Set.image_nsmul_of_ne_zero, ContinuousMultilinearMap.cons_add, TestFunction.coe_ofSupportedInLM, CircleDeg1Lift.iterate_monotone, MeasureTheory.ae_eq_empty, Metric.Snowflaking.preimage_toSnowflaking_closedBall, IsLocalization.algEquiv_comp_algebraMap_apply, TopCat.piIsoPi_inv_π_apply, Subgroup.quotientEquivProdOfLE_symm_apply, ContinuousMultilinearMap.map_add_univ, Fin.accumulate_apply, QuadraticMap.associated_toQuadraticMap, Composition.boundary_zero, OrderIso.conj_apply, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, RingCon.lift_surjective_iff, DomMulAct.isQuotientMap_mk_symm, transcendental_aeval_iff, MonoidWithZeroHom.one_apply_of_ne_zero, PrincipalSeg.strictMono, FreeMonoid.map_map, MeasureTheory.Measure.eventually_cofinite, GrpCat.SurjectiveOfEpiAuxs.agree, Function.Embedding.trans_apply, MonoidHom.noncommCoprod_unique, MvPolynomial.C_surjective, RootPairing.pairingIn_reflectionPerm_self_left, HNNExtension.NormalWord.unitsSMul_one_group_smul, LocallyConstant.toContinuousMapMonoidHom_apply, Homeomorph.preimage_symm, Unitization.starMap_inl, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, DilationEquiv.mulLeft_apply, MvPowerSeries.HasSubst.coeff_zero, LinearMap.dualMap_injective_iff, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, QuadraticMap.IsometryEquiv.map_app, Finsupp.card_uIcc, AlgebraicGeometry.Scheme.Pullback.range_map, CategoryTheory.ShortComplex.Homotopy.equivSubZero_symm_apply, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, RootPairing.bijOn_reflection_root, MulAction.stabilizer_smul_eq_stabilizer_map_conj, Nucleus.coe_toSublocale, FreeLieAlgebra.liftAux_map_add, ContinuousLinearEquiv.prodComm_apply, Monoid.PushoutI.NormalWord.prod_base_smul, Polynomial.Splits.aeval_eq_prod_aroots, eventually_homothety_mem_of_mem_interior, CocompactMap.coe_id, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, MeasureTheory.addContent_sUnion, ProbabilityTheory.posterior_prod_id_comp, Poly.isPoly, IsPrimitiveRoot.associated_sub_one_map_sub_one, OrdinalApprox.lfpApprox_ord_eq_lfp, DistLat.id_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, NonarchAddGroupSeminorm.coe_lt_coe, CategoryTheory.ConcreteCategory.injective_of_mono_of_preservesPullback, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, HasOuterApproxClosed.measure_le_lintegral, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, MvPolynomial.isEmptyRingEquiv_symm_apply, MeasureTheory.OuterMeasure.map_map, TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage, AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullback, AlternatingMap.curryLeft_apply_toMultilinearMap, Equiv.punitProd_apply, LieModule.isNilpotent_toEnd_of_isNilpotent₂, MeasureTheory.OuterMeasure.biInf_apply, Polynomial.as_sum_range, MonoidAlgebra.lift_apply', unitary.toUnits_injective, AddGroupNormClass.toNormedAddCommGroup_norm_eq, ArithmeticFunction.convolution_vonMangoldt_zeta, LinearIsometryEquiv.coe_ofLinearIsometry, toLex_pow, classifyingSpaceUniversalCover_map, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, iteratedFDerivWithin_one_apply, FirstOrder.Language.ElementaryEmbedding.map_boundedFormula, RingHom.functions_ext_iff, Polynomial.toLaurent_apply, RingQuot.eq_lift_comp_mkRingHom, SkewPolynomial.monomial_zero_right, SymAlg.sym_inv, DFinsupp.toMultiset_le_toMultiset, Matrix.adjugate_fin_three_of, QuadraticAlgebra.coe_dvd_iff_dvd, NonUnitalAlgHom.coe_comp, Antivary.sum_smul_le_sum_smul_comp_perm, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_inv, PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map, LinearMap.IsReflective.isOrthogonal_reflection, MulChar.coe_toMonoidHom, normedAddGroupHomCompletionHom_apply, MeasureTheory.SignedMeasure.re_toComplexMeasure, Finsupp.card_Ioo, isConjRoot_of_algEquiv', CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, Subring.mopRingEquivOp_symm_apply, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, Diffeomorph.uniqueMDiffOn_image, MeasurableEquiv.comap_symm, equicontinuousOn_iff_continuousOn, LieModule.Weight.coe_eq_zero_iff, Representation.IntertwiningMap.algebraMap_apply, groupHomology.H1π_comp_map_apply, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, SSet.StrictSegal.spineInjective, OrderHom.gfp_le, IsCoercive.bounded_below, Matrix.mem_range_scalar_iff_commute_single, CoalgHom.coe_mk, AddEquiv.map_finsum_mem, ContinuousMap.sigmaEquiv_symm_apply, MeasureTheory.VectorMeasure.ennrealToMeasure_apply, QuadraticMap.coeFn_add, UniqueFactorizationMonoid.radical_of_prime, Module.Basis.repr_reindex, AddCon.le_def, MultilinearMap.map_update_neg, MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant, BilinearForm.toMatrixAux_eq, ModularGroup.denom_S, CliffordAlgebra.contractLeft_ι_mul, QuadraticMap.two_nsmul_associated, IsLocalFrameOn.toBasisAt_coe, AddMonoid.IsTorsion.torsionAddEquiv_symm_apply_coe, coe_ofLexMulEquiv, MeasureTheory.SimpleFunc.sum_eapproxDiff, LinearMap.BilinForm.exists_orthogonal_basis, Polynomial.expand_inj, NumberField.mixedEmbedding.covolume_idealLattice, CommMonCat.comp_apply, Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux, stdSimplex.vertex_coe, SymAlg.sym_unsym, AddEquiv.add_submonoid_map_symm_apply, TensorProduct.lid_tmul, Affine.Simplex.ExcenterExists.excenter_restrict, Commute.cfcₙHom, Abelianization.lift_of_comp, LinearMap.mem_eqLocus, RootPairing.rootForm_reflection_reflection_apply, Submodule.IsPrincipal.generator_submoduleImage_dvd_of_mem, indicator_le_thickenedIndicator, LieHom.lie_apply, PreTilt.coeff_frobenius, AddConstMapClass.map_sub_zsmul, MvPolynomial.renameEquiv_apply, toDual_compl, ProbabilityTheory.bayesRisk_const_of_nonempty, AlgebraicGeometry.Scheme.Hom.isSpectralMap, AddMemClass.subtype_apply, MonoidHom.div_apply, QuadraticAlgebra.mul_star, CategoryTheory.ProjectiveResolution.of_def, Polynomial.opRingEquiv_op_X, ArchimedeanClass.FiniteElement.val_sub, MonoidHom.fiberEquivKer_apply, PerfectRing.lift_comp_lift_apply, TopologicalSpace.productOfMemOpens_injective, LinearMap.isAdjointPair_one, RootPairing.chainTopCoeff_eq_zero_iff, Finsupp.DegLex.single_antitone, Subsemiring.centerToMulOpposite_symm_apply_coe, NumberField.place_apply, OrderRingIso.trans_apply, MeasureTheory.SimpleFunc.support_indicator, MeasureTheory.SimpleFunc.coe_pow, Finsupp.Lex.single_lt_iff, Finsupp.support_sum, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, convexHull_add_subset, Set.image_vadd_distrib, AddMagmaCat.coe_comp, RootPairing.isValuedIn_iff_mem_range, Nimber.add_nat, CliffordAlgebra.comp_ι_sq_scalar, AlgebraicGeometry.mem_range_iff_of_surjective, MeasureTheory.Measure.add_apply, IncidenceAlgebra.coe_neg, PerfectRing.liftEquiv_symm_apply, RootPairing.posRootForm_posForm_pos_of_ne_zero, MultilinearMap.compMultilinearMap_apply, AddMonoidHom.range_eq_top, ContinuousMap.nnnorm_lt_iff, Primrec.of_equiv, MeasureTheory.setLAverage_eq', AffineMap.congr_fun, LieDerivation.map_sub, Polynomial.natDegree_mul_C_eq_of_mul_eq_one, Matrix.SeparatingLeft.toBilin, Ideal.Quotient.mk_span_range, MeasureTheory.dirac_eq_zero_iff_not_mem, NumberField.mixedEmbedding.volume_preserving_negAt, WithCStarModule.equiv_symm_smul, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, FreeNonUnitalNonAssocAlgebra.lift_symm_apply, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, PEquiv.coe_mk, FreeSemigroup.lift_symm_apply, UniformEquiv.apply_symm_apply, Matrix.charpoly_toLin, Module.subsingletonEquiv_symm_apply, LinearMap.inr_injective, AddConstMapClass.map_sub_ofNat', CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_apply_homEquiv, Equiv.pow_def, TopologicalSpace.OpenNhds.id_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, Set.image_multiset_prod, PseudoEpimorphism.comp_apply, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_assoc, HahnSeries.SummableFamily.coeff_support, NumberField.mixedEmbedding.normAtPlace_add_le, IsometryEquiv.coe_withLpProdUnique, Module.Basis.coe_sumCoords_eq_finsum, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, UniformOnFun.lipschitzWith_iff, LinearMap.toMatrixOrthonormal_symm_apply, LinearMap.map_dfinsuppSumAddHom, Finsupp.mk_mem_graph_iff, CondensedSet.topCatAdjunctionUnit_val_app_apply, LinearEquiv.extendScalarsOfIsLocalization_symm_apply, legendreSym.at_two, Equiv.prodCongr_apply, ContinuousLinearMap.map_tsum, Derivation.compAlgebraMapL_apply_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, mem_integralClosure_iff_mem_fg, DFinsupp.le_iff, MeasureTheory.IsSetSemiring.diff_mem_supClosure, LinearEquiv.congrLeft_apply, isLocalization_iff, OrderIso.sumAssoc_apply_inr, OrderDual.toDual_lt_toDual, Subrepresentation.submoduleSubrepresentationOrderIso_apply, IsUltrametricDist.norm_fwdDiff_iter_apply_le, CategoryTheory.GrothendieckTopology.le_def, IsLocalizedModule.map_linearCombination, CircleDeg1Lift.commute_sub_int, Equiv.Perm.preimage_inv, QuadraticMap.map_sub, Polynomial.content_C_mul, hasSum_cauchyPowerSeries_integral, LocallyConstant.charFn_eq_zero, OrderIso.symm_apply_eq, SchwartzMap.coeFn_toLp, toBoolAlg_add_add_mul, addRothNumber_spec, ContinuousLinearMap.aestronglyMeasurable_comp₂, AddHom.op_symm_apply_apply, Equiv.Perm.sameCycle_apply_left, LinearMap.BilinMap.baseChange_tmul, Homeomorph.divRight_symm_apply, Polynomial.Splits.eq_X_sub_C_of_single_root, IsBaseChange.of_fintype_basis, ofMul_image_powers_eq_multiples_ofMul, ProbabilityTheory.cond_inter_self, RelIso.symm_apply_apply, MeasureTheory.lintegral_deriv_eq_volume_image_of_antitoneOn, Module.Flat.eqLocus_lTensor_eq, TruncatedWittVector.commutes_symm', Subspace.dualRestrict_leftInverse, QuadraticForm.tmul_tensorAssoc_apply, FiniteField.algebraMap_norm_eq_prod_pow, CategoryTheory.mateEquiv_hcomp, TruncatedWittVector.truncate_truncate, RingNorm.apply_one, Equiv.image_compl, MvPolynomial.aeval_eq_zero, DirichletCharacter.zetaMul_nonneg, Polynomial.coeff_det_X_add_C_card, TwoP.swap_map, ContinuousAlgEquiv.image_closure, WittVector.mapFun.zsmul, eventually_nhdsWithin_sign_eq_of_deriv_neg, MeasureTheory.SimpleFunc.coe_natCast, Set.FiniteExhaustion.subset_succ, Topology.WithUpperSet.isUpperSet_toUpperSet_preimage, MvPolynomial.eval₂_cast_comp, Valuation.toAddValuation_apply, RingEquiv.invFun_eq_symm, Shrink.ext_iff, AddMonoidHom.ext_nat_iff, SpectralMapClass.map_spectral, StrongDual.dualPairing_apply, GroupSeminorm.inf_apply, ContinuousMap.map_specializes, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, Equiv.subtypeEquivRight_symm_apply, SimpleGraph.boxProdAssoc_apply, AddOreLocalization.numeratorHom_surjective_of_finite, CategoryTheory.Functor.curryingEquiv_apply_obj, CategoryTheory.Sieve.overEquiv_symm_pullback, TopCat.GlueData.f_open, InitialSeg.eq_principalSeg, LinearIsometry.ediam_image, IsLocalMinOn.hasFDerivWithinAt_eq_zero, SmoothPartitionOfUnity.sum_eq_one', HopfAlgebra.sum_antipode_mul_eq_smul, OrthonormalBasis.sum_sq_inner_left, Circle.exp_inj, OrderIso.map_cofinal, LinearEquiv.piRing_symm_apply, CoalgHom.coe_id, Module.DirectLimit.congr_apply_of, MeasureTheory.OuterMeasure.restrict_empty, AddCon.mem_addSubgroup_iff, DomAddAct.comap_mk.symm_nhds, NonUnitalRingHom.map_sclosure, PEquiv.toMatrix_toPEquiv_mul, MvPowerSeries.constantCoeff_zero, MeasureTheory.Measure.count_apply_lt_top, addMonoidAlgebraAlgEquivDirectSum_symm_apply, Fin.orderIsoTriple_one, BoundedContinuousFunction.uniformContinuous_coe, MeasureTheory.setToFun_indicator_const, trace_eq_trace_adjoin, DistribMulAction.toModuleEnd_apply, MeasureTheory.Measure.restrict_apply_univ, MeasureTheory.OuterMeasure.mkMetric'.tendsto_pre_nat, FreeAddGroup.lift_of_eq_id, CategoryTheory.yonedaEquiv_yoneda_map, CliffordAlgebra.even.lift_ι, MeasureTheory.sum_addContent_eq_of_sUnion_eq, Matrix.reindex_isTotallyUnimodular, OrthonormalBasis.reindex_apply, Fin.insertNthEquiv_symm_apply, AddLocalization.r_iff_exists, Polynomial.eval_homogenize, Polynomial.quotientSpanXSubCAlgEquiv_mk, LinearMap.toMatrix_mulVec_repr, Valued.isClosed_ball, AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_image, MulAction.IsBlock.of_subgroup_of_conjugate, LinearMap.BilinForm.zero_left, Module.Basis.range_extend, BumpCovering.locallyFinite, Submodule.IsCompl.projection_eq_self_iff, GroupExtension.Section.mul_mul_mul_inv_mem_range_inl, Finsupp.sum_filter_index, MeasureTheory.Measure.compProd_id_eq_copy_comp, FrameHom.coe_toLatticeHom, BddDistLat.forget_map, LinearMap.toMatrix_innerₛₗ_apply, TensorProduct.piRight_symm_apply, OmegaCompletePartialOrder.ωScottContinuous_iff_map_ωSup_of_orderHom, AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen, AddMonCat.neg_hom_apply, Algebra.embeddingsMatrixReindex_eq_vandermonde, ENNReal.mulRightOrderIso_apply, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem_ne, MeasureTheory.Measure.finset_sum_apply, ContinuousMapZero.toContinuousMapCLM_apply, Tuple.self_comp_sort, Equiv.Perm.cycleOf_apply_of_not_sameCycle, Module.Basis.ofIsLocalizedModule_apply, ContMDiffMap.contMDiff, Cubic.of_c_eq_zero', CompleteOrthogonalIdempotents.equiv, Quaternion.equivProd_apply, Valuation.zero_iff, MonoidAlgebra.mapDomainBialgHom_apply, OrderMonoidHom.inlₗ_mul_inrₗ_eq_toLex, QuadraticMap.associated_left_inverse', HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, CentroidHom.coe_sub, isClosedMap_toAdd, RelIso.rel_symm_apply, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Matrix.uniqueAlgEquiv_apply, MeasureTheory.Measure.infinitePiNat_map_piCongrLeft, Complex.continuous_conj, AddMonoidAlgebra.apply_add_of_supDegree_le, Pi.addHom_apply, MeasureTheory.Lp.norm_const', LieModule.Cohomology.mem_twoCochain_iff, Function.locallyFinsuppWithin.toClosedBall_divisor, toLex_ratCast, RingEquiv.piEquivPiSubtypeProd_apply, NNReal.sqrt_mul, Equiv.mul_swap_eq_swap_mul, Submodule.mkQ_apply, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, MeasureTheory.Content.outerMeasure_le, SchwartzMap.coeHom_injective, Zsqrtd.lift_symm_apply_coe, PointwiseConvergenceCLM.equivWeakDual_symm_apply, Submodule.toIntSubmodule_toAddSubgroup, Localization.mapPiEvalRingHom_bijective, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, Algebra.adjoin_range_eq_range_freeAlgebra_lift, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, exists_orderEmbedding_covby_of_forall_covby_finite, InfTopHom.coe_id, NumberField.IsCMField.unitsMulComplexConjInv_apply_torsion, InfHom.withBot_toFun, Orientation.rightAngleRotation_map', TensorProduct.gradedComm_one, NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm, FirstOrder.Language.HomClass.map_constants, AddSubmonoid.val_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, ProperCone.hyperplane_separation_point, AlgEquiv.restrictScalars_symm_apply, PadicInt.Coe.ringHom_apply, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, Finsupp.single_eq_set_indicator, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, CompleteSublattice.mem_map, NonUnitalSubalgebra.iSupLift_inclusion, AdjoinRoot.coe_injective', SemilatSupCat.dual_map, Monoid.CoprodI.Word.cons_eq_smul, MulEquiv.self_comp_symm, Finsupp.filter_eq_sum, iterateFrobenius_inj, RingEquiv.map_add, Unitization.starMap_inr, LinearMap.funLeft_injective_of_surjective, NumberField.mixedEmbedding.negAt_apply_isComplex, disjoint_map_orderIso_iff, TensorProduct.lift.tmul, AddGrpCat.ext_iff, WeierstrassCurve.Jacobian.baseChange_dblY, SchwartzMap.norm_toLp, Finsupp.snd_sumFinsuppAddEquivProdFinsupp, IsUniformAddGroup.uniformContinuous_iff_isOpen_ker, CategoryTheory.Functor.IsWellOrderContinuous.nonempty_isColimit, Equiv.Finset.union_symm_left, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, AffineMap.hasDerivAt, SSet.mem_skeleton_obj_iff_of_nonDegenerate, Matrix.toLin_apply_eq_zero_iff, LinearIsometry.coe_pow, MvPolynomial.modMonomial_add_divMonomial, DFinsupp.update_self, RegularWreathProduct.toPermInj, MeasureTheory.measure_empty, LinearIsometry.dist_map, TwoSidedIdeal.asIdeal_jacobson, WithZero.lift_coe, Matrix.kroneckerMap_reindex_left, ContinuousMap.prodSwap_apply, StarConvex.linear_image, Submodule.setLike.coe_galgebra_toFun, Orientation.inner_rotation_pi_div_two_left_smul, infClosure_eq_self, FrameHom.coe_comp, Finsupp.erase_eq_sub_single, AddSemigrp.comp_apply, Polynomial.aeval_X_left_eq_map, AddMonoidAlgebra.modOf_apply_of_exists_add, Finset.Colex.ofColex_top, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, MulEquiv.coprodAssoc_apply_inl_inr, MonomialOrder.span_leadingTerm_eq_span_monomial', Submodule.norm_sq_eq_add_norm_sq_projection, Lagrange.X_sub_C_dvd_nodal, RootPairing.flipEquiv_symm_apply, Algebra.Extension.Hom.toRingHom_algebraMap, AddMonoidHom.mulLeft₃_apply, ContinuousAffineMap.contDiff, WeakDual.CharacterSpace.coe_toNonUnitalAlgHom, Finsupp.mem_toMultiset, TensorProduct.lTensorHomToHomLTensor_apply, GroupSeminorm.coe_comp, LinearMap.extendTo𝕜'_apply_re, NonUnitalAlgHom.coe_prod, AddMonoidHom.snd_mono, IsAbsoluteValue.toAbsoluteValue_apply, MeasureTheory.measure_iInter_eq_iInf_measure_iInter_le, closedConvexHull_closure_eq_closedConvexHull, ArithmeticFunction.sigma_pos_iff, IsLocalizedModule.mapEquiv_apply, IsLocalization.algebraMap_isUnit_iff, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, MonoidWithZeroHom.one_apply_apply_eq, genericPoints.equiv_apply, Algebra.PreSubmersivePresentation.jacobian_eq_det_aevalDifferential, Finset.orderEmbOfFin_last, vadd_preimage_set_subset, tangentCoordChange_comp, Equiv.prodComm_apply, SemidirectProduct.congr'_apply_left, Submodule.span_image_linearEquiv, lipschitzOnWith_cfc_fun, MeasureTheory.measurePreserving_piFinTwo, MvPolynomial.bind₁_C_right, AddEquiv.mapAddSubgroup_symm_apply, ProbabilityTheory.Kernel.singularPart_eq_zero_iff_measure_eq_zero, IsArtinian.monotone_stabilizes, CategoryTheory.unit_conjugateEquiv_symm, UpperHalfPlane.σ_num, MeasurableEquiv.curry_symm_apply, MvPolynomial.coe_coeffs_map, Nat.castEmbedding_apply, Polynomial.det_taylorLinearEquiv_toLinearMap, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, Subring.coe_map, Additive.toMul_lt, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, Complex.conj_cpow, Matrix.nondegenerate_toBilin_iff, LinearIsometry.norm_iteratedFDeriv_comp_left, TrivSqZeroExt.inlHom_apply, LinearEquiv.det_symm, AddSubmonoid.mem_bsupr_iff_exists_dfinsupp, AddMonoidHom.addSubgroupComap_apply_coe, ManyOneEquiv.of_equiv, CategoryTheory.PreGaloisCategory.evaluation_aut_bijective_of_isGalois, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, Coalgebra.sum_counit_tmul_map_eq, OrderHom.prod_coe, Equiv.addRight_symm_apply, Subgroup.coe_toAddSubgroup_symm_apply, AddConstMapClass.map_add_int, Equiv.Set.sumCompl_symm_apply_of_mem, fourierIntegral_eq_half_sub_half_period_translate, CategoryTheory.Pretriangulated.preadditiveYoneda_homologySequenceδ_apply, Equiv.Perm.Basis.ofPermHom_mem_centralizer, OmegaCompletePartialOrder.ContinuousHom.coe_toOrderHom, RCLike.re_to_real, IncidenceAlgebra.sum_Icc_mu_left, Polynomial.roots_X_sub_C, LinearMap.range_toContinuousLinearMap, ProbabilityTheory.tilted_mul_apply_mgf', CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, AffineMap.vsub_lineMap, AdicCompletion.mk_ofAlgEquiv_symm, Submodule.traceDual_le_span_map_traceDual, linearDepOn_iff, Ideal.exact_mulQuot_quotOfMul, AddMonoidAlgebra.coe_add, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, MvPolynomial.decompose'_apply, Complex.algHom_ext_iff, Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe, WithCStarModule.linearEquiv_apply, OrderHomClass.to_lattice_hom_apply, Fin.castOrderIso_apply, AffineMap.vsub_apply, ZMod.lift_castAddHom, Polynomial.mkDerivationEquiv_symm_apply, Finset.ofDual_sup', Path.uniformContinuous, AdicCompletion.mk_smul_mk, MonoidAlgebra.opRingEquiv_symm_single, Monoid.Coprod.fst_apply_inr, Equiv.subtypeQuotientEquivQuotientSubtype_mk, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux2, Fin.cons_apply_cycleRange, lineMap_le_right_iff_le, ProbabilityTheory.Kernel.setLIntegral_deterministic, Polynomial.isUnit_C, LinearIsometryEquiv.image_ball, coe_basisOfLinearIndependentOfCardEqFinrank, Path.extend_of_one_le, ContinuousLinearEquiv.dimH_image, Finsupp.sum_embDomain, CoalgEquiv.coe_coe, EuclideanGeometry.orthogonalProjection_vadd_eq_self, dist_lineMap_right, OmegaCompletePartialOrder.ContinuousHom.coe_mk, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, CoxeterSystem.rightInvSeq_concat, AddSubgroup.injective_noncommPiCoprod_of_iSupIndep, Nat.divModEquiv_symm_apply, PseudoMetric.IsUltra.isTransitiveRel_ball, MulActionHom.coe_one, AddChar.div_apply, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, Matrix.toLin'_reindex, HahnModule.coeff_smul_order_add_order, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, Valuation.Integers.hom_inj, OneHom.coe_mul, ContinuousMultilinearMap.coe_continuous, HahnModule.of_symm_smul, IsFractionRing.stabilizerHom_surjective, ContinuousMap.coe_addLeft, AffineMap.differentiableAt, Complex.equivRealProdAddHom_symm_apply_re, AffineIsometry.coe_id, CategoryTheory.Discrete.equivalence_functor, Quaternion.algebraMap_injective, BoundingSieve.nu_lt_one_of_prime, Valuation.srel_iff_lt, MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable, prevD_eq, LinearMap.transvection.apply, DFinsupp.toFinsupp_coe, abs_mul_sign, RCLike.neg_iff, InfiniteGalois.proj_adjoin_singleton_val, ContinuousAddMonoidHom.zero_toFun, Localization.r_of_eq, PowerSeries.IsRestricted.isRestricted_iff, PowerSeries.exp_pow_sum, Pi.evalNonUnitalRingHom_apply, MeasureTheory.tendsto_measure_iInter_le, ProbabilityTheory.Kernel.prodAssoc_prod, LinearMap.BilinForm.toDual_def, MulEquiv.symm_apply_eq, tendsto_measure_thickening, CliffordAlgebra.contractRight_mul_algebraMap, Module.Relations.Solution.IsPresentation.uniq_var, MeasureTheory.OuterMeasure.map_ofFunction, ContinuousLinearMap.hasFDerivAtFilter, Polynomial.expand_expand, TwoSidedIdeal.mem_fromIdeal, Submodule.IsLocalizedModule.localized₀FrameHom_apply, IsMaxOn.dual, WeierstrassCurve.C_Ψ₂Sq, HasFPowerSeriesOnBall.hasSum, ArithmeticFunction.sigma_one, CommRingCat.HomTopology.precompHomeomorph_symm_apply, Subgroup.IsComplement.equiv_snd_eq_one_of_mem_of_one_mem, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, WithLp.prodContinuousLinearEquiv_symm_apply_ofLp, AlgebraicGeometry.Scheme.stalkMap_congr_hom_assoc, LieAlgebra.IsKilling.coroot_mem_corootSpace, MulAut.coe_mul, ProbabilityTheory.bayesRisk_le_mul', AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, AffineBasis.toMatrix_vecMul_coords, MonoidWithZeroHom.map_zero, ContinuousLinearEquiv.finTwoArrow_apply, CategoryTheory.unit_conjugateEquiv, ArithmeticFunction.IsMultiplicative.prod_primeFactors, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_lintegral, quadraticChar_exists_neg_one', MeasureTheory.Measure.comap_apply, Polynomial.Chebyshev.algebraMap_eval_C, Circle.exp_add_two_pi, ContinuousMap.HomotopyWith.trans_apply, AdjoinRoot.smul_of, IncidenceAlgebra.zero_apply, Matrix.PosSemidef.toLinearMap₂'_zero_iff, MultilinearMap.domDomCongrLinearEquiv_apply, sSupHom.dual_apply_toFun, Polynomial.natDegree_quadratic_le, Polynomial.Bivariate.swap_Y, compl_image_latticeClosure_eq_of_compl_image_eq_self, Poly.coe_mul, Subalgebra.mulMap'_surjective, RCLike.sqrt_eq_real_add_ite, PartOrd.coe_comp, Polynomial.rootSet_C_mul_X_pow, groupHomology.π_comp_H0Iso_hom_apply, LinearMap.BilinForm.toMatrix'_compLeft, PreTilt.coeff_iterate_frobeniusEquiv_symm, Matrix.toLinearMapₛₗ₂_apply, AddMonoid.Coprod.toProd_apply_inl, Submodule.starProjection_apply, Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, EquivLike.coe_symm_apply_apply, ContinuousMap.abs_apply, ModularForm.one_coe_eq_one, Matrix.mul_mul_right, Path.image_extend_of_subset, partialSups_eq_sUnion_image, ContinuousLinearMap.eventually_nhds_zero_mapsTo, cfc_apply_zero, isClosedMap_ofDual, IsLocalizedModule.fromLocalizedModule_mk, Polynomial.monomial_mul_X, AddEquiv.arrowCongr_apply, MeasureTheory.OuterMeasure.map_comap_of_surjective, MultilinearMap.freeDFinsuppEquiv_single, Module.Basis.isUnitSMul_apply, Finsupp.lcomapDomain_apply, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_apply, MeasureTheory.Measure.addHaar_parallelepiped, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, MeasureTheory.lintegral_indicator_const_le, Polynomial.rootSet_derivative_subset_convexHull_rootSet, LineDeriv.laplacianCLM_eq_sum, DomAddAct.symm_mk_zsmul, IsLocalRing.ResidueField.mapEquiv_apply, Monoid.PushoutI.homEquiv_symm_apply, ProbabilityTheory.Kernel.ae_eq_of_compProd_eq, IsPrimitiveRoot.associated_map_sub_one_map_sub_one, PNat.equivNonZeroDivisorsNat_symm_apply_coe, TopHom.ext_iff, SmoothPartitionOfUnity.mem_finsupport, PMF.filter_apply_eq_zero_iff, Polynomial.mapAlgHom_monomial, AlgHom.IsArithFrobAt.restrict_injective, WittVector.bind₁_wittMulN_wittPolynomial, Sum.Lex.toLexRelIsoLE_symm_coe, equivShrink_symm_top, RCLike.inv_im, Equiv.Set.sumCompl_symm_apply, ProbabilityTheory.inter_pos_of_cond_ne_zero, LieEquiv.ofSubalgebras_apply, groupCohomology.eq_d₀₁_comp_inv_apply, MeasureTheory.SimpleFunc.exists_range_iff, WeakDual.isSeqCompact_closedBall, MultilinearMap.map_zero, LinearMap.BilinForm.dualBasis_repr_apply, NonUnitalStarSubalgebra.inclusion_mk, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, SummationFilter.comap_filter, ContinuousAffineEquiv.ext_iff, MultilinearMap.map_add_sub_map_add_sub_linearDeriv, MeasureTheory.smulInvariantMeasure_iff, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PiTensorProduct.liftEquiv_apply, MvPowerSeries.coeff_one, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, map_list_prod, PositiveLinearMap.zero_apply, LinearMap.smul_lTensor, DomMulAct.mk_smul_indicatorConstLp, Polynomial.iterate_derivative_X_pow_eq_natCast_mul, PowerSeries.one_le_order_iff_constCoeff_eq_zero, WeierstrassCurve.Jacobian.map_dblXYZ, DoubleQuot.coe_quotQuotEquivQuotSupₐ, CentroidHom.coe_one, QuadraticMap.Isometry.comp_apply, RelHom.coe_fn_injective, OmegaCompletePartialOrder.Chain.range_pair, LinearMap.lsmul_injective, ModuleCat.MonoidalCategory.tensorLift_tmul, CategoryTheory.Groupoid.isoEquivHom_apply, MeasureTheory.norm_condExpInd_apply_le, Profinite.NobelingProof.Products.eval_πs_image', has_antideriv_at_fourier_neg, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, NonUnitalAlgHom.coe_restrictScalars', RelHom.coe_fn_toFun, LineDeriv.iteratedLineDerivOpCLM_apply, ContinuousMap.tsum_apply, FirstOrder.Language.Substructure.skolem₁_reduct_isElementary, Equiv.addEquiv_apply, AnalyticWithinAt.aeval_polynomial, DFinsupp.Colex.lt_iff, Ideal.quotientMulEquivQuotientProd_snd, AddEquiv.coprodPUnit_apply, latticeClosure_singleton, QuadraticMap.Isometry.map_app, MulAction.toPermHom_apply, NormedSpace.expSeries_apply_eq, toLex_intCast, Module.IsReflexive.bijective_dual_eval', NormedAddGroupHom.uniformContinuous, MvPowerSeries.C_inv, MeasureTheory.Measure.setLIntegral_rnDeriv', PartENat.withTopEquiv_symm_ofNat, PiLp.basisFun_apply, CategoryTheory.Groupoid.isoEquivHom_symm_apply_hom, MulEquiv.withOneCongr_apply, fderivWithin_iteratedFDerivWithin, UniformOnFun.continuous_rng_iff, Unitization.algebraMap_eq_inl, Diffeomorph.contMDiffAt_diffeomorph_comp_iff, ProbabilityTheory.iIndepSet.meas_biInter, Convex.isLittleO_alternate_sum_square, ProbabilityTheory.uniformOn_eq_zero_iff, CompleteLatticeHom.coe_mk, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, Polynomial.le_rootMultiplicity_iff, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, OrderIso.sumLexIicIoi_symm_apply_Iic, Finsupp.support_subset_singleton, AddMonoidAlgebra.commRingEquiv_single_single, UniformSpaceCat.completionFunctor_map, Polynomial.natDegree_taylor, MeasureTheory.Content.toFun_eq_toNNReal_apply, Unitization.sndHom_apply, WittVector.fromPadicInt_comp_toPadicInt_ext, AlgebraicGeometry.Scheme.mem_overGrothendieckTopology, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, ContinuousMultilinearMap.contDiff, ProbabilityTheory.Kernel.measurable_kernel_prodMk_left', Polynomial.degree_taylor, Topology.WithScott.isOpen_iff_isUpperSet_and_scottHausdorff_open', RingCon.ringConGen_of_ringCon, MeasureTheory.SimpleFunc.lintegral_eq_of_subset', Monoid.Coprod.swap_map, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, span_range_eq_top_iff_surjective_fintypeLinearCombination, hasFDerivAt_iff_tendsto, Complex.equivRealProdAddHom_symm_apply_im, Orientation.eq_rotation_self_iff, ofDegLex_inj, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, GenLoop.toLoop_apply, HasCompactMulSupport.comp_homeomorph, CategoryTheory.GrothendieckTopology.Cover.Arrow.hf, RelEmbedding.pairwise_swap_listMap, MulEquiv.coe_toMonoidHom, CategoryTheory.Preadditive.epi_iff_surjective, Finsupp.filter_eq_zero_iff, AddCommMonCat.ext_iff, HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', ContinuousMultilinearMap.piLinearEquiv_apply, Subalgebra.mem_map, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, Affine.Simplex.face_points, FreeAddMonoid.ofList_nil, Prod.Lex.sumLexProdLexDistrib_apply, ExteriorAlgebra.liftAlternating_one, Subsemiring.addEquivOp_symm_apply_coe, PolynormableSpace.induced, MeasureTheory.OuterMeasure.boundedBy_le, AddGroupSeminorm.coe_add, Complex.selfAdjointEquiv_apply, Subspace.flip_quotDualCoannihilatorToDual_bijective, Valued.isClopen_sphere, ContinuousMap.exists_finite_sum_const_indicator_approximation_of_mem_nhds_diagonal, CategoryTheory.FunctorToTypes.shrink_map, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_φ, CategoryTheory.LocallyDiscrete.locallyDiscreteEquiv_symm_apply_as, LinearMap.isSelfAdjoint_iff', CommGrpCat.ofHom_apply, Matrix.ofNat_fin_three, Matrix.GeneralLinearGroup.continuous_upperRightHom, PiTensorProduct.liftAux_tprodCoeff, BoundedContinuousFunction.nnrealPart_coeFn_eq, PolynomialModule.zero_apply, PadicAlgCl.valuation_p, LinearIsometryEquiv.piLpCongrRight_single, OrderIso.arrowCongr_symm_apply, MonomialOrder.degree_X_sub_C, Int.normalize_coe_nat, FreeAddMonoid.toList_map, closure_convexHull_extremePoints, finSuccEquiv'_at, Finset.range_orderEmbOfFin, NumberField.IsCMField.complexEmbedding_complexConj, Equiv.sumPiEquivProdPi_symm_preimage_univ_pi, ContinuousLinearMap.deriv_of_bilinear, sum_embeddings_eq_finrank_mul, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet, Submodule.apply_mem_map₂, NonUnitalRingHom.srangeRestrict_surjective, map_lt_lineMap_iff_slope_lt_slope_left, Orientation.areaForm'_apply, MvPolynomial.monomial_one_mul_cancel_left_iff, ZeroHom.coe_id, Padic.padicNormE.is_norm, Function.Embedding.congr_apply, Finsupp.mapRange.linearMap_apply, VectorBundleCore.coe_coordChange, AddHom.id_apply, Matrix.comp_apply, WithOne.lift_one, TensorProduct.LieModule.map_tmul, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_id, pinGroup.conjAct_smul_ι_mem_range_ι, IsTopologicalAddGroup.isOpenMap_iff_nhds_zero, hasFDerivAtFilter_iff_hasDerivAtFilter, Monotone.dual_left, Equiv.psigmaEquivSigma_apply, Subfield.coe_comap, DirectSum.linearEquivFunOnFintype_lof, Set.coe_singletonAddHom, CategoryTheory.Localization.homEquiv_symm_apply, SimpleGraph.incidenceSetEquivNeighborSet_symm_apply_coe, normalize_eq_zero, CategoryTheory.ObjectProperty.galoisConnection_isColocal, MeasureTheory.hausdorffMeasure_lineMap_image, FiniteMulArchimedeanClass.liftOrderHom_mk, AddMonoidHom.map_exists_left_neg, TopologicalSpace.OpenNhds.map_id_obj_unop, ZMod.lift_comp_coe, groupCohomology.cocycles₁_map_inv, UpperHalfPlane.normSq_denom_pos, Module.Basis.sumQuot_repr_inl_of_mem, Module.Basis.end_apply, Rep.freeLiftLEquiv_apply, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors, lcm_mul_right, MeasureTheory.Measure.lintegral_condKernel, SSet.stdSimplex.mem_face_iff, PadicComplex.valuation_p, MvPolynomial.aevalTower_C, DirectSum.coeAlgHom_of, innerSLFlip_apply_apply, Equiv.Perm.subtypeEquivSubtypePerm_apply_of_mem, AlgEquiv.apply_symm_apply, TensorPower.algebraMap₀_eq_smul_one, Set.powersetCard.coe_map, CentroidHomClass.map_mul_left, Submonoid.coe_subtype, ContinuousLinearEquiv.mdifferentiableOn, Module.End.ringEquivEndFinsupp_apply_apply_apply, TensorProduct.rTensor_injective_of_forall_vanishesTrivially, CategoryTheory.Groupoid.invEquiv_apply, LieDerivation.lie_lieDerivation_apply, PowerSeries.coeff_mk, NonUnitalSubalgebraClass.subtype_injective, LieModuleHom.coe_restrictLie, Submodule.set_smul_eq_map, AddMonoidHom.mem_mrange, OrderIso.image_Iic, IsFractionRing.closure_range_algebraMap, MonoidAlgebra.mapRangeAlgEquiv_apply, CategoryTheory.Precoverage.mem_toGrothendieck_iff, MulArchimedeanOrder.lt_def, AffineMap.lipschitzWith_of_finiteDimensional, MvPolynomial.expand_one_apply, ENat.toENNRealOrderEmbedding_apply, MeasureTheory.ProbabilityMeasure.tendsto_measure_iUnion_accumulate, Affine.Triangle.dist_orthocenter_reflection_circumcenter, CommRingCat.HomTopology.isClosedEmbedding_hom, finSuccEquiv'_ne_last_apply, RingEquiv.map_list_prod, OrthogonalFamily.hasSum_linearIsometry, Matrix.permanent_permute_cols, MvPolynomial.coe_basisMonomials, ODE.FunSpace.toContinuousMap_apply_eq_apply, MeasureTheory.Measure.OuterRegular.map, Nat.exponent_eq_exponent_mul_factorization_of_prime_pow_eq_base_pow, Polynomial.support_C_subset, Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, algebraMap_lt_algebraMap, Polynomial.hasFDerivAt, Matrix.adjugate_reindex, UniformConvergenceCLM.topologicalSpace_eq, NormedAddGroupHom.IsQuotient.norm_lift, Submonoid.LocalizationMap.mk'_mul_cancel_left, Complex.inv_cpow_eq_ite, TestFunctionClass.map_hasCompactSupport, ArithmeticFunction.log_apply, MultilinearMap.curryMid_apply_apply, ofAdd_smul, Complex.liftAux_apply_I, MeasureTheory.Measure.haar.haarContent_apply, AlternatingMap.map_update_sum, CategoryTheory.CountableCategory.instLocallySmallObjAsType, Subring.mem_map_equiv, isAddRightRegular_toLex, MeasureTheory.Measure.pi_univ, LieHom.toNonUnitalAlgHom_toFun, PMF.toOuterMeasure_ofMultiset_apply, FractionalIdeal.canonicalEquiv_spanSingleton, PresheafOfModules.surjective_of_epi, Ideal.symm_apply_mem_of_equiv_iff, IsAntichain.image_relIso, OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge, Cubic.of_b_eq_zero', IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff, MeasureTheory.FiniteMeasure.limsup_measure_closed_le_of_tendsto, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, MeasureTheory.dirac_eq_one_iff_mem, signedDist_smul_of_pos, CategoryTheory.GlueData.t_inv_apply, Pi.constRingHom_apply, MeasureTheory.le_measure_symmDiff, Distribution.mapCLM_apply, SemidirectProduct.congr'_symm_apply_right, IncidenceAlgebra.zeta_prod_apply, Subalgebra.adjoin_eq_span_basis, WeierstrassCurve.Affine.derivative_addPolynomial_slope, MvPolynomial.map_expand_pow_char, Matrix.compRingEquiv_symm_apply, Polynomial.support_C_mul_X_pow', Multiplicative.ofAdd_strictMono, FourierTransform.fourierCLE_apply, equivShrink_div, Module.End.isSemisimple_sub_algebraMap_iff, CategoryTheory.unitCompPartialBijective_natural, AddGroupExtension.Equiv.symm_symm_apply, PowerBasis.equivAdjoinSimple_gen, OrderRingHom.ext_iff, xInTermsOfW_aux, RootPairing.isReduced_iff', MonoidHom.mem_ker, MulEquiv.AddMonoid.End_apply, Quaternion.normSq_eq_norm_mul_self, MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, MeasureTheory.Measure.restrict_congr_meas, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, RatFunc.ofFractionRing_comp_algebraMap, Polynomial.aeval_apply_smul_mem_of_le_comap, RingHom.toKerIsLocalization_apply, Pi.algHom_apply, Matrix.Nondegenerate.toBilin, Finsupp.sumFinsuppEquivProdFinsupp_symm_inr, CategoryTheory.SimplicialThickening.functor_map, Polynomial.eq_C_content_mul_primPart, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, WeakDual.CharacterSpace.toAlgHom_apply, PowerSeries.sub_const_eq_X_mul_shift, ContinuousMap.hasSum_apply, BoundedContinuousFunction.continuous, BoundedLatticeHom.dual_symm_apply_toFun, LinearMap.coe_range, TensorProduct.finsuppScalarRight_apply_tmul_apply, SemimoduleCat.MonoidalCategory.tensorμ_apply, LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, map_eq_zero, sSupHom.comp_apply, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, MulActionHom.congr_fun, Ideal.ResidueField.map_algebraMap, EuclideanGeometry.oangle_orthogonalProjection_self, MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero, Sublattice.prodEquiv_apply, Homeomorph.toCocompactMap_toFun, ofLex_toLex, AddSubsemigroup.coe_map, Finsupp.coe_curryAddEquiv, algebraMap_mk, Derivation.coe_comp, Affine.Simplex.map_altitude_restrict, AlgEquiv.coe_symm_toLinearEquiv, CommBialgCat.inv_hom_apply, AddSubmonoid.LocalizationMap.ofAddEquivOfDom_apply, ClosureOperator.closure_sup_closure_right, Bundle.Trivial.homeomorphProd_symm_apply_snd, ProbabilityTheory.Kernel.partialTraj_map_frestrictLe₂_apply, MvPolynomial.mapRange_eq_map, Equiv.Perm.coe_one, UniformFun.isometry_ofFun_boundedContinuousFunction, RestrictedProduct.evalRingHom_apply, Ordinal.isNormal_preOmega, Field.Emb.Cardinal.equivSucc_coherence, ContinuousLinearMap.bilinear_hasTemperateGrowth, LinearMap.toMatrix'_apply, finCycle_symm_apply, GrpCat.hom_inv_apply, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, SupHom.coe_comp, LinearMap.mem_span_iff_continuous_of_finite, MeasureTheory.measure_compl_sigmaFiniteSet_eq_zero_iff_sigmaFinite, Polynomial.rootMultiplicity_mul_X_sub_C_pow, IsContinuousRiemannianBundle.exists_continuous, antitone_iff_map_nonneg, ContinuousMap.comp_apply, Set.OrdConnected.null_frontier, MeasureTheory.Measure.sum_apply₀, LinearEquiv.baseChange_tmul, MvPolynomial.monomial_mem_pow_idealOfVars_iff, MeasureTheory.restrict_compl_sigmaFiniteSet_eq_zero_or_top, InnerProductSpaceable.inner_.norm_sq, PiTensorProduct.ofDFinsuppEquiv_tprod_apply, MulSemiringAction.toRingAut_apply, ProbabilityTheory.gaussianReal_apply, WittVector.ghostComponent_frobeniusFun, DomMulAct.symm_mk_one, CategoryTheory.FinCategory.objAsTypeToAsType_map, RatFunc.algebraMap_X, RingCon.opOrderIso_apply, Ideal.Quotient.stabilizerHom_apply, LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ, UniformConvergenceCLM.sub_apply, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_apply, AlternatingMap.coe_inj, MonoidHom.coe_coe, WithBot.toDual_apply_bot, QuadraticForm.tmul_tensorComm_apply, WithTop.orderIsoSumLexPUnit_top, Valued.isClosed_sphere, SubMulAction.inclusion_injective, WithTop.subtypeOrderIso_symm_apply, AddMonoidAlgebra.mul_single_zero_apply, SSet.stdSimplex.coe_edge_down_toOrderHom, Module.Basis.repr_symm_single, Matrix.toLpLin_toLp, NumberField.CMExtension.equivMaximalRealSubfield_apply, CategoryTheory.Preadditive.mono_iff_injective, PowerSeries.coeff_largeSchroderSeries, RelEmbedding.prodLexMkRight_apply, Representation.finsuppToCoinvariants_single_mk, ArithmeticFunction.vonMangoldt_pos_iff, UniformFun.toFun_smul, Affine.Simplex.faceOpposite_restrict, ModularFormClass.exp_decay_sub_atImInfty, Function.fromTypes_succ_equiv_symm_apply, RingEquiv.moduleEndSelf_apply, FirstOrder.Language.DirectLimit.liftInclusion_of, CategoryTheory.Localization.SmallHom.equiv_mk, Equiv.hasProd_iff, ConvexOn.sSup_of_nat_affine_eq, TopologicalSpace.productOfMemOpens_isInducing, IsLocalization.Away.isUnit_of_dvd, ofMul_image_zpowers_eq_zmultiples_ofMul, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app', apply_eq_dotProduct_toMatrix₂_mulVec, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', Monoid.End.coe_mul, ContinuousLinearMap.postcomp_apply, Polynomial.degreeLT.addLinearEquiv_apply, Equiv.subtypeEquivCodomain_apply, ProbabilityTheory.Kernel.densityProcess_fst_univ_ae, PowerSeries.constantCoeff_C, SchwartzMap.fourierTransformCLE_apply, CategoryTheory.ComposableArrows.opEquivalence_inverse_obj, CategoryTheory.enrichedFunctorTypeEquivFunctor_apply_map, CategoryTheory.Functor.flippingEquiv_symm_apply_map_app, Submodule.fst_orthogonalDecomposition_apply, OrderMonoidIso.unitsWithZero_apply, kroneckerLinearEquiv_symm_kronecker, Submodule.quotEquivOfEqBot_apply_mk, IsValuativeTopology.isClosed_closedBall, CoalgHom.coe_fn_inj, DFinsupp.coe_add, MeasureTheory.Measure.addHaarMeasure_apply, LinearMap.coe_toContinuousLinearMap, Set.uIcc_ofDual, MonomialOrder.degree_smul_le, CentroidHom.coe_neg, ContinuousLinearMap.prodMapL_apply, Equiv.Perm.set_support_inv_eq, CategoryTheory.MorphismProperty.gc_llp_rlp, DFinsupp.card_Ioo, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, Rep.indToCoindAux_mul_fst, LinearEquiv.coe_toContinuousLinearEquiv', OrderIso.preimage_Iio, NNReal.sqrt_eq_zero, MulEquiv.coe_mapSubgroup, CategoryTheory.GrothendieckTopology.mem_sInf, Finpartition.exists_enumeration, Profinite.NobelingProof.factors_prod_eq_basis_of_ne, RightOrdContinuous.orderDual, LinearMap.BilinForm.separatingRight_toMatrix_iff, MeasureTheory.Measure.prod_prod, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, AffineMap.lineMap_apply_module', LinearMap.flip_apply, CommRingCat.hom_inv_apply, RingCon.factorₐ_mk, MultilinearMap.freeDFinsuppEquiv_def, LinearMap.mulLeft_apply, ENat.toENNRealRingHom_apply, TensorProduct.finsuppLeft_apply, CircleDeg1Lift.commute_add_nat, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, Polynomial.Chebyshev.aeval_S, AddChar.coe_pow, ContinuousLinearMap.toSpanSingletonLE_apply, ModularForm.sub_apply, Finset.Colex.lt_iff_exists_filter_lt, LinearMap.ext_ring_iff, RingCon.refl, MvPolynomial.irreducible_sumSMulX, AnalyticOnNhd.aeval_mvPolynomial, ContinuousAffineMap.apply_lineMap', MeasureTheory.FiniteMeasure.apply_mono, RatFunc.intDegree_C, HomogeneousLocalization.awayMap_fromZeroRingHom, AddMonoidHom.coe_of_map_sub, ContinuousAt.pathExtend, MeasureTheory.tilted_apply_eq_ofReal_integral, AntitoneOn.dual_right, SupBotHom.id_toFun, LinearMap.BilinForm.SeparatingLeft.toMatrix', RootPairing.Equiv.comp_weightMap_apply, toAdd_eq_zero, FreeMonoid.ofList_nil, DirectedSystem.map_map', UniformFun.ofFun_zero, Polynomial.normalize_content, Odd.map, IsIntegralClosure.algebraMap_injective', CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, TopCat.isOpenEmbedding_iff_comp_isIso', Polynomial.algebraMap_pi_self_eq_eval, MvPolynomial.totalDegree_eq_zero_iff_eq_C, Set.Finite.isClosed_convexHull, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, MeasureTheory.measure_lt_top_of_subset, WithZeroMulInt.toNNReal_le_one_iff, TensorProduct.mapBilinear_apply, Ordinal.preOmega_ofNat, ModularFormClass.exists_petersson_le, Polynomial.eval₂_at_natCast, CentroidHom.coe_id, UniformEquiv.coe_symm_toEquiv, MonoidHom.restrict_apply, Lagrange.eq_interpolate, Submodule.smul_starProjection_singleton, NumberField.Units.mem_torsion, DFinsupp.lex_iff_of_unique, Polynomial.mem_annIdeal_iff_aeval_eq_zero, AlgebraicIndependent.algebraMap_injective, MeasureTheory.Measure.MeasureDense.fin_meas, CompactlyGenerated.isoOfHomeo_hom, finsuppTensorFinsuppRid_symm_single_smul, CoxeterSystem.lengthParity_comp_simple, Subalgebra.LinearDisjoint.trace_algebraMap, ProbabilityTheory.setLIntegral_condKernel_univ_left, LightCondensed.forget_map_val_app, MeasureTheory.ProbabilityMeasure.le_liminf_measure_open_of_tendsto, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_symm_apply, ContinuousLinearMap.map_smulₛₗ, StieltjesFunction.measure_Ici, smoothRightMul_one, Circle.invOn_arg_exp, ArithmeticFunction.carmichael_two_pow_of_le_two_eq_totient, Homeomorph.image_compl, LinearEquiv.prodComm_apply, TensorProduct.prodRight_symm_tmul, LinearIsometryEquiv.dist_map, Polynomial.card_support_eq', SetTheory.PGame.default_nim_one_leftMoves_eq, MvPowerSeries.coeff_expand_smul, OrthonormalBasis.coe_mk, BoxIntegral.Box.lower_mem_Icc, ProbabilityTheory.cond_eq_inv_mul_cond_mul, ProbabilityTheory.Kernel.boolKernel_false, RCLike.one_im, Multiplicative.toAdd_eq_top, ArchimedeanClass.lt_of_lt_stdPart, UpperHalfPlane.coe_smul, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_hom_φ, Function.FromTypes.curryEquiv_symm_apply, finsetBasisOfTopLeSpanOfCardEqFinrank_repr_apply, AddGroupExtension.Splitting.rightHom_splitting, LinearEquiv.conj_apply, SheafOfModules.freeHomEquiv_comp_apply, AffineIsometryEquiv.coe_vaddConst, DFinsupp.mapRange.linearEquiv_apply, ContinuousMap.coe_injective, NormedAddGroupHom.sub_apply, TopCat.isOpenEmbedding_f_zeroHypercover, Action.FunctorCategoryEquivalence.inverse_obj_ρ_apply, Finset.orderEmbOfFin_singleton, LinearEquiv.ofSubmodules_symm_apply, TopologicalSpace.Compacts.equiv_symm_apply, isLowerSet_preimage_ofDual_iff, MeasureTheory.lintegral_eq_lintegral_meas_le, Complex.inv_def, WithZero.val_inv_expOrderIso_apply, Complex.equivRealProdLm_apply, Orientation.inner_comp_rightAngleRotation, NonUnitalStarAlgebra.range_eq_top, AddMonoid.Coprod.lift_apply_inl, HomogeneousIdeal.mem_irrelevant_iff, PiTensorProduct.dualDistribInvOfBasis_apply, AffineSubspace.wSameSide_lineMap_left, CategoryTheory.shrinkYonedaEquiv_naturality, Ideal.homogeneousHull_eq_iSup, IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le, Matrix.isRepresentation.toEnd_exists_mem_ideal, OrderIso.compl_symm_apply, AffineEquiv.list_wbtw_map_iff, LinearMap.kerComplementEquivRange_apply_coe, UniformFun.ofFun_div, LinearIsometryEquiv.continuousWithinAt, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, Ioi_orderDual_def, Rack.invAct_apply, Representation.asAlgebraHom_single_one, MeasureTheory.measure_iUnion₀, RingEquiv.ofHomInv_apply, Algebra.Generators.Hom.toAlgHom_X, CStarAlgebra.linear_combination_nonneg, MvPolynomial.weightedTotalDegree_eq_zero_iff, ZMod.ringEquivCongr_ringEquivCongr_apply, Equiv.Perm.inv_apply_self, TopologicalSpace.Opens.isOpenEmbedding, AlgebraicGeometry.Scheme.zeroLocus_map, RCLike.natCast_re, OrderIso.prodAssoc_symm_apply, OrderIso.le_iff_le, MvPolynomial.bind₁_rename, ContinuousMap.equivBoundedOfCompact_apply, Quiver.Hom.opEquiv_apply, Equiv.sumCompl_apply_inr, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, LinearMap.isUnit_det, ProbabilityTheory.Kernel.lintegral_traj, Ordinal.preOmega_le_omega, MeasureTheory.measure_symmDiff_inv_smul, RegularWreathProduct.fun_id, Equiv.withTopSubtypeNe_symm_apply_coe, Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, convexHull_empty, ContinuousWithinAt.lineMap, Subgroup.IsComplement.equiv_fst_mul_equiv_snd, Polynomial.C_eq_algebraMap, NonUnitalStarSubalgebra.unitization_injective, Submodule.restrictScalarsEquiv_symm_apply, PowerSeries.constantCoeff_inv, Subgroup.quotientEquivProdOfLE'_symm_apply, TwoSidedIdeal.opOrderIso_apply, map_rootsOfUnity_eq_pow_self, Polynomial.map_roots_le, Subalgebra.coe_algebraMap, SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_map, val_unitsNonZeroDivisorsEquiv_symm_apply_coe, MeasureTheory.measure_vadd_eq_zero_iff, MDifferentiableWithinAt.clm_apply_of_inCoordinates, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, LieAlgebra.IsKilling.apply_coroot_eq_cast, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, Function.Embedding.sym2Map_apply, MeasureTheory.inducedOuterMeasure_exists_set, ZMod.invDFT_def', NumberField.discr_eq_discr, AlgEquiv.coe_apply_coe_coe_symm_apply, LinearMap.quotientInfEquivSupQuotient_injective, linearIndependent_inl_union_inr', Polynomial.mapAlg_eq_map, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_zeroLocus, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc, MonovaryOn.dual_right, signedDist_lineMap_lineMap, Module.toCentroidHom_apply_toFun, Complex.ofRealCLM_apply, RelHom.toOrderHom_coe, HahnSeries.leadingCoeff_pos_iff, ModuleCat.piIsoPi_inv_kernel_ι_apply, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, UniformEquiv.finTwoArrow_apply, MonoidAlgebra.ringHom_ext_iff, addRothNumber_le_ruzsaSzemerediNumber, List.sum_map_hom, Submodule.map₂_eq_span_image2, Polynomial.separable_def', NonUnitalStarSubalgebra.unitization_apply, MeasurableSet.exists_isOpen_diff_lt, Matrix.projVandermonde_map, ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, Fin.sign_cycleIcc_of_le, wittStructureRat_prop, Finsupp.inf_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Int.coe_castAddHom, Sublattice.subtype_injective, MeasureTheory.Integrable.integral_condExpKernel, AddConstMapClass.map_one_add, map_finset_inf', MeasureTheory.SimpleFunc.FinMeasSupp.integrable, IsPrimitiveRoot.minpoly_dvd_expand, MeasureTheory.Measure.m_iUnion, CategoryTheory.Presheaf.imageSieve_apply, Rep.ihom_obj_ρ_apply, Module.Basis.restrictScalars_repr_apply, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, absConvexHull_add_subset, Algebra.TensorProduct.congr_apply, InnerProductSpace.Core.inner_self_nonneg, Orthonormal.inner_finsupp_eq_sum_right, AffineBasis.sum_coord_apply_eq_one, TopCat.GlueData.range_fromOpenSubsetsGlue, AddEquiv.bijective, IsLocalization.sec_spec', BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding, PartitionOfUnity.finsum_smul_mem_convex, Matrix.ker_toLin_eq_bot, Polynomial.eval_unique, FreeAddMonoid.freeAddMonoidCongr_of, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, NonUnitalSubring.centerCongr_symm_apply_coe, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, MvPolynomial.degrees_rename, exists_continuous_zero_one_of_isCompact', CategoryTheory.GrothendieckTopology.OneHypercover.IsPreservedBy.mem₁, TopCat.coe_id, MeasureTheory.Measure.WeaklyRegular.innerRegular_measurable, CategoryTheory.yonedaEquiv_naturality', sInfHom.coe_comp, Finset.centerMass_mem_convexHull, FourierTransform.fourierInvₗ_apply, FreeMonoid.count_of, AddEquiv.mulOp_symm_apply, Polynomial.derivative_of_natDegree_zero, Real.volume_pi_le_prod_diam, Algebra.Presentation.comp_relation, MeasureTheory.ProbabilityMeasure.apply_le_one, SpecialLinearGroup.det_coe, TensorProduct.AlgebraTensorModule.dualDistrib_apply, AlgebraicGeometry.Scheme.GlueData.ι_eq_iff, monovaryOn_toDual_right, Finset.prod_X_add_C_coeff, legendreSym.hom_apply, NNReal.mul_self_sqrt, inner_re_symm, Representation.finsupp_single, AddCon.comap_eq, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left, ofBoolRing_le_ofBoolRing_iff, ContinuousLinearMap.toLinearMap_innerSL_apply, IsChain.preimage_relIso, Polynomial.Gal.restrictComp_surjective, Polynomial.Bivariate.equivMvPolynomial_symm_C, IsCyclotomicExtension.Rat.discr_prime_pow_ne_two', Matrix.reindexAlgEquiv_mul, IsLocalization.map_smul, Finset.eraseNone_map_some, RootPairing.Hom.coroot_coweightMap, Valuation.one_apply_eq_zero_iff, Seminorm.iSup_apply, Subsemiring.centerToMulOpposite_apply_coe, CliffordAlgebra.GradedAlgebra.ι_apply, MonoidHom.map_inv₂, Topology.WithUpper.isOpen_preimage_ofUpper, HasFPowerSeriesAt.hasStrictDerivAt, FreeAbelianGroup.map_id_apply, StarRingEquiv.invFun_eq_symm, Equiv.prodPProd_apply, EuclideanGeometry.dist_orthogonalProjection_eq_dist_iff_eq_of_mem, antivary_toDual_right, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, SchwartzMap.pderivCLM_apply, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, Module.End.isUnit_iff, AddConstEquiv.toAddConstMapHom_apply, LinearMapClass.ker_eq_bot, AddSubmonoid.add_leftNegEquiv, NumberField.Units.regOfFamily_of_isMaxRank, Polynomial.divX_mul_X_add, SubAddAction.ofFixingAddSubgroup_insert_map_bijective, AlgebraicGeometry.AffineSpace.comp_homOfVector, ofBoolAlg_mul_ofBoolAlg_eq_left_iff, DistribMulActionHom.comp_apply, Subfield.subtype_apply, CondensedMod.hom_naturality_apply, LieSubalgebra.coe_incl', Topology.WithLower.isOpen_def, MvPowerSeries.aeval_coe, ArithmeticFunction.vonMangoldt_sum, Ordinal.type_subrel, BoundedOrderHom.coe_comp, AddAut.conj_inv_apply, NormalizedGCDMonoid.normalize_gcd, FintypeCat.toLightProfinite_map_hom_hom_apply, Polynomial.Splits.roots_map, AddIrreducible.map, Polynomial.aeval_eq_smeval, MaximalSpectrum.equivSubtype_symm_apply_asIdeal, MeasureTheory.meas_ge_le_lintegral_div, Polynomial.toFinsuppIsoLinear_symm_apply_toFinsupp, Module.Basis.equivFunL_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, CategoryTheory.Localization.SmallShiftedHom.equiv_mk, SymAlg.invOf_sym, CompactlyGenerated.isoOfHomeo_inv, SemidirectProduct.mul_def, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, NonUnitalNonAssocCommSemiring.mem_center_iff, RootPairing.isValuedIn_iff, CategoryTheory.Limits.Types.Small.productIso_inv_comp_π_apply, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', Nat.factorization_centralBinom_eq_zero_of_two_mul_lt, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, WithSeminorms.tendsto_nhds, QuotientAddGroup.equivIcoMod_symm_apply, Finsupp.prod_eq_zero_iff, toDual_min, star_mul_self_add_self_mul_star, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, Complex.arg_conj, LieModule.genWeightSpace_chainBotCoeff_sub_one_zsmul_sub, inner_map_complex, EquicontinuousOn.isClosed_range_uniformOnFun_iff_pi, LieModuleEquiv.symm_apply_apply, Polynomial.natSepDegree_X_pow_char_pow_sub_C, ProbabilityTheory.Kernel.setLIntegral_compProd_univ_left, Multiset.coe_countPAddMonoidHom, CompleteLatticeHom.symm_dual_id, StarMulEquiv.ext_iff, SSet.ι₁_snd_assoc, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, Homeomorph.map_cocompact, Module.Basis.injective, LaurentPolynomial.algebraMap_X_pow, finTwoArrowEquiv_symm_apply, GradedTensorProduct.auxEquiv_mul, ModularForm.ext_iff, ContinuousMultilinearMap.apply_apply, MeasureTheory.OuterMeasure.sup_apply, map_neg, Prod.Lex.uniqueProd_apply, FiniteAddGrp.ofHom_apply, BoundedContinuousFunction.coe_ofNormedAddCommGroupDiscrete, Rat.AbsoluteValue.padic_eq_padicNorm, Fintype.linearIndependent_iff'ₛ, Equiv.withTopCongr_apply, QuadraticForm.tmul_tensorRId_apply, ProbabilityTheory.Kernel.measurable_lintegral_indicator_const, MulEquiv.prodUnique_apply, LinearMap.IsSymmetric.adjoint_eq, Trivialization.continuousLinearEquivAt_apply', Matrix.ofNat_fin_two, IsCoveringMap.homeomorph_comp_iff, FreeMonoid.toList_cons, BoundedContinuousFunction.norm_le_of_nonempty, AddChar.mulShift_apply, MeasureTheory.Measure.ae_eq_or_eq_iff_eq_dirac_add_dirac, ArithmeticFunction.zeta_apply_ne, ContinuousMultilinearMap.flipLinear_apply_apply, MonoidHom.coe_finsuppProd, tendsto_integral_mul_one_add_inv_smul_sq_pow, NormedAddGroupHom.Equalizer.liftEquiv_apply, ZMod.AddAutEquivUnits_apply, WittVector.IsPoly.poly, MvPolynomial.map_hsymm, ProbabilityTheory.Kernel.comp_apply, AddValuation.map_zero, ContMDiffMap.coe_mul, Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe, Squarefree.natFactorization_le_one, AddChar.coe_toAddMonoidHomEquiv, AddMonoidHom.mul_apply, WeakDual.CharacterSpace.coe_toCLM, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, FractionalIdeal.extendedHomₐ_eq_zero_iff, MvPolynomial.monomial_le_degreeOf, RelIso.apply_eq_iff_eq, normalize_gcd, SymmetricAlgebra.algebraMap_eq_zero_iff, HahnSeries.ofPowerSeries_apply_coeff, RelIso.inv_apply_self, HasGradientAt.hasFDerivAt, TensorProduct.piRight_symm_single, toLex_zero, Submodule.lTensorOne'_tmul, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_apply_asIdeal, NonUnitalRingHom.range_eq_top, ENat.coe_toNatHom, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, eq_intCast, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, CategoryTheory.Functor.flippingEquiv_symm_apply_obj_obj, RCLike.norm_le_re_iff_eq_norm, SimpleGraph.map_neighborFinset_induce_of_neighborSet_subset, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply', ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, Multiset.toDFinsupp_replicate, RootPairing.CoPolarizationIn_eq, Module.FinitePresentation.linearEquivMap_apply, ContinuousMap.coe_smul', QuotientGroup.mk'_eq_mk', Derivation.map_zero, OrderIso.map_csSup', MeasureTheory.Measure.parallelComp_comp_compProd, UniformSpace.Completion.continuous_coeRingHom, Submodule.equivOpposite_apply, RelEmbedding.pairwise_listMap, LinearMap.hasDerivWithinAt, AlgebraicGeometry.AffineSpace.isOpenMap_over, MvPowerSeries.homogeneousComponent_of_lt_order_eq_zero, finEquivMultiples_symm_apply, Cardinal.isRegular_aleph_succ, AlgebraicGeometry.surjective_iff, GaussianInt.toComplex_add, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, CStarMatrix.toCLM_apply_single, Ideal.mul_homogeneous_element_mem_of_mem, Affine.Simplex.exradius_restrict, Equiv.Perm.support_ofSubtype, Module.Relations.map_single, SimpleGraph.degree_induce_support, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, ModuleCat.lof_coprodIsoDirectSum_inv_apply, Sequential.isoOfHomeo_hom, QuotientGroup.map_mk', RingCon.quotientQuotientEquivQuotient_coe_coe, convexHull_pair, Submodule.span_preimage_eq, FourierTransform.fourierEquiv_symm_apply, Polynomial.coeffList_C, BoundedContinuousFunction.norm_integral_le_norm, LinearIsometry.continuous, Set.Finite.measure_zero, IsLocalization.mk'_add_eq_iff_add_mul_eq_mul, Polynomial.Splits.taylor, TopologicalSpace.Fiber.sigmaIsoHom_apply, SemidirectProduct.rightHom_surjective, NonUnitalSubsemiringClass.coe_subtype, LinearMap.BilinMap.isSymm_iff_eq_flip, Polynomial.eval_intCast_map, MonoidAlgebra.curryRingEquiv_symm_single, Matrix.entryAddMonoidHom_apply, AddMonoid.Coprod.mk_surjective, Finset.Colex.toColex_le_toColex, MeasureTheory.Measure.haar.haarContent_self, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isOpen, AddMonoidHom.coe_snd, PrincipalSeg.ext_iff, ContinuousLinearMap.lipschitzWith_of_opNorm_le, ContinuousAffineEquiv.trans_apply, Equiv.graph_inv, Finset.equivBitIndices_symm_apply, t1Space_TFAE, ContinuousMultilinearMap.hasStrictFDerivAt, Submodule.rTensorOne'_tmul_one, AlgEquiv.coe_mapIntegralClosure, Submodule.inner_orthogonalProjection_eq_of_mem_right, OrderIso.image_setOf_minimal, MeasureTheory.Measure.measure_eq_zero_of_subset_diff_everywherePosSubset, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul', Submodule.reflection_reflection, IsIntegralClosure.algebraMap_equiv, QuadraticAlgebra.norm_natCast, Equiv.piCongr'_symm_apply_symm_apply, DirectSum.decompose_symm_algebraMap, OrderIso.sumLexCongr_apply, MulEquiv.coprodCongr_apply, ZeroAtInftyContinuousMap.isBounded_image, AddMonoid.End.coe_mul, Matrix.det_one_add_X_smul, SimpleGraph.UnitDistEmbedding.unit_dist, Finset.affineCombination_map, ProbabilityTheory.condDistrib_comp, RingEquiv.ofRingHom_symm_apply, ProbabilityTheory.Kernel.setIntegral_density_of_measurableSet, map_pow, WithVal.lt_def, Algebra.adjoin_mem_exists_aeval, AlgHom.fst_apply, Equiv.eq_comp_symm, Topology.WithLawson.isOpen_def, RingHom.coe_fst, QuaternionAlgebra.Basis.liftHom_apply, Monoid.IsTorsion.torsionMulEquiv_symm_apply_coe, Set.powersetCard.mem_ofFinEmb_iff_mem_range, CategoryTheory.Functor.curryingFlipEquiv_apply_obj, wittStructureRat_rec, Algebra.compHom_smul_def, FreeAddMonoid.ofList_toList, Complex.normSq_ofNat, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, InitialSeg.lt_apply_iff, OrderHomClass.mono, coe_polyEquivTensor'_symm, MulHom.toMulEquiv_symm_apply, Finset.coe_coeEmb, FirstOrder.Language.Embedding.substructureEquivMap_apply, AddEquiv.toMultiplicativeLeft_symm_apply_symm_apply, AlgebraicGeometry.germ_injective_of_isIntegral, Poly.coe_sub, baseChange_ext_iff, CategoryTheory.Iso.toEquiv_fun, RootPairing.IsG2.span_eq_rootSpan_int, FirstOrder.Language.Equiv.apply_symm_apply, LinearMap.llcomp_apply', Equiv.injective_comp, Homeomorph.comap_nhds_eq, StrictAnti.dual_left, Ideal.Quotient.torsionBy_eq_span_singleton, WithCStarModule.equiv_zero, jacobiSym.at_neg_two, imaginaryPart.norm_le, ContinuousMultilinearMap.pi_apply, AffineBasis.det_smul_coords_eq_cramer_coords, hasFTaylorSeriesUpTo_succ_nat_iff_right, Submonoid.centerToMulOpposite_symm_apply_coe, PowerBasis.equivAdjoinSimple_symm_gen, LieModule.exists_forall_pow_toEnd_eq_zero, HeytAlg.inv_hom_apply, edist_toAdd, SimpleGraph.Hom.mapDart_apply, LinearIndependent.map', Seminorm.preimage_metric_closedBall, Real.sinOrderIso_apply, HSpace.hmul_e_e, Finset.Icc_orderDual_def, ModuleCat.Derivation.desc_d, OrderIso.supIrredLowerSet_apply, CategoryTheory.Abelian.Ext.bilinearComp_apply_apply, LinearMap.BilinForm.zero_apply, Equiv.Finset.union_symm_right, Prod.comul_apply, CategoryTheory.generate_discretePresieve_mem, Measurable.setLIntegral_kernel_prod_left, MonoidAlgebra.mapRangeAddEquiv_apply, reesAlgebra.monomial_mem, AlgEquiv.funUnique_apply, AddSubmonoid.IsLocalizationMap.addEquiv_comp, ContinuousAlgEquiv.cast_symm_apply, Finset.sup'_comp_eq_map, FreeLieAlgebra.liftAux_map_mul, LinearIsometryEquiv.coe_symm_toLinearEquiv, AddSubmonoid.LocalizationMap.add_mk'_zero_eq_mk', DirectSum.lieAlgebraOf_apply, RingHom.pi_bijective_of_isIdempotentElem, AddMonoid.Coprod.mk_of_neg_add, Finset.Ioo_toDual, DirectSum.map_of, Fin.cycleRange_symm_zero, ZeroAtInftyContinuousMap.uniformContinuous, MeasureTheory.FiniteMeasure.restrict_eq_zero_iff, TannakaDuality.FiniteGroup.equivApp_inv, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative, Algebra.Extension.CotangentSpace.map_cotangentComplex, AddEquiv.coprodAssoc_symm_apply_inr_inr, AddGroupSeminorm.coe_iSup_apply, WeierstrassCurve.Jacobian.map_addY, HasFDerivWithinAt.norm_sq, CFC.abs_algebraMap, Concept.swapEquiv_apply, tsum_riemannZetaSummand, MvPolynomial.coeff_sumSMulX, AddEquiv.mapMatrix_apply, mulAutArrow_apply_apply, AlternatingMap.map_update_update, IntermediateField.coe_val, Set.Ico_toDual, Finset.map_toDual_min, MvPolynomial.expand_eq_C, PresheafOfModules.injective_of_mono, Equiv.Perm.mem_alternatingGroup, lp.singleContinuousLinearMap_apply, LieDerivation.IsKilling.ad_mem_orthogonal_of_mem_orthogonal, Finsupp.multinomial_eq_of_support_subset, Polynomial.roots_expand_image_frobenius_subset, ContinuousLinearMapWOT.isEmbedding_inducingFn, PartitionOfUnity.nonneg, MonoidAlgebra.commAlgEquiv_single_single, LinearMap.linearIndependent_iff, Equiv.Perm.SameCycle.apply_right, SlashInvariantForm.coe_sub, Matroid.mapEquiv_dep_iff, QuotSMulTop.equivQuotTensor_naturality, AlgEquiv.toRingEquiv_unop, AddMonoidHom.coe_toNatLinearMap, LinearMap.smulRightₗ_apply, MeasureTheory.Measure.coe_add, ProbabilityTheory.meas_ge_le_variance_div_sq, Set.powersetCard.ofFinEmbEquiv_symm_apply, WithBot.toDualTopEquiv_coe, MeasureTheory.SimpleFunc.pair_preimage, CategoryTheory.Functor.FullyFaithful.mulEquivEnd_symm_apply, Submodule.rTensorOne'_tmul, Ideal.relNorm_algebraMap', PowerSeries.derivativeFun_coe, GroupSeminorm.smul_apply, JacobsonNoether.exist_pow_eq_zero_of_le, LinearEquiv.coe_toAffineEquiv, RingCon.lift_bijective_iff, Matrix.det_reindex, CliffordAlgebra.reverse.map_mul, SSet.OneTruncation₂.nerveEquiv_symm_apply_map, IsLocalizedModule.mapEquiv_symm_apply, MeasureTheory.lintegral_indicator_one₀, IsValuativeTopology.mem_nhds_zero_iff, AlgebraicGeometry.IsOpenImmersion.opensEquiv_apply_coe, DFinsupp.comapDomain'_apply, AlgebraicGeometry.isClosedImmersion_iff_isAffineHom, LatticeHom.ext_iff, ofBoolRing_zero, Polynomial.comp_eq_zero_iff, normalize_apply, SupBotHom.subtypeVal_apply, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, BoundedContinuousFunction.apply_le_norm, ArithmeticFunction.carmichael_dvd, AddMonoidHom.map_inv₂, Diffeomorph.sumCongr_coe, ofDual_eq_one, hasDerivAt_fourier_neg, OrthonormalBasis.coe_of_orthogonal_eq_bot_mk, QuotientAddGroup.sound, MvPowerSeries.le_weightedOrder_subst, TwoSidedIdeal.mem_comap, ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors, Pi.constAddMonoidHom_apply, Semigrp.ext_iff, MeasureTheory.Measure.count_singleton, Subsemiring.isHomogeneous_iff_subset_iInter, ofDual_compl, ModuleCat.free_ε_one, Profinite.exists_isClopen_of_cofiltered, Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub, Module.End.IsSemisimple.aeval, Finsupp.mapDomainEmbedding_apply, Polynomial.coeff_monomial, RatFunc.smul_eq_C_smul, Multiset.uIcc_eq, EquivLike.range_eq_univ, MvPowerSeries.trunc'_expand, multiplesHom_symm_apply, eq_affineCombination_of_mem_affineSpan_of_fintype, Subgroup.orderIsoCon_apply, FiniteDimensional.range_basisSingleton, ProbabilityTheory.HasGaussianLaw.map, MvPolynomial.universalFactorizationMapPresentation_map, EuclideanGeometry.reflection_apply_of_mem, ProbabilityTheory.condExp_ae_eq_integral_condExpKernel, OrderIso.ofUnique_symm_apply, isLeft_finSumNatEquiv_symm_apply, ContinuousMultilinearMap.toContinuousLinearMap_apply, Subgroup.injective_noncommPiCoprod_of_iSupIndep, IsTop.ofDual, isOpenMap_toAdd, AddHom.coe_id, Set.image_mul, Equiv.ulift_symm_apply, Cardinal.toNat_rightInverse, PowerSeries.invUnitsSub_mul_sub, Module.Invertible.rTensor_injective_iff, NumberField.FinitePlace.add_le, ContinuousLinearMap.one_apply, MeasureTheory.setAverage_eq', SimpleGraph.Walk.IsSubwalk.map, SetSemiring.add_def, BoundedContinuousFunction.add_apply, ContinuousMap.unitsLift_apply_inv_apply, DirectSum.decompose_symm_add, AnalyticAt.harmonicAt_conj, AffineBasis.coord_apply_combination_of_notMem, IsAddFoelner.eventually_meas_ne_zero, ProperCone.dual_singleton, Ordinal.principal_mul_omega, MvPolynomial.coeff_rename_mapDomain, RCLike.ofReal_im, Set.embeddingOfSubset_apply_coe, ContinuousLinearMap.uncurryBilinear_apply, Nat.factorization_choose_of_lt_three_mul, codisjoint_ofDual_iff, exists_root_adjoin_eq_top_of_isCyclic, PEquiv.symm_trans_self, CliffordAlgebra.EquivEven.Q'_apply, Set.Icc_ofDual, NonUnitalStarSubalgebraClass.coe_subtype, Additive.ofMul_strictMono, LinearMap.injective_of_comp_eq_id, existsUnique_isIdempotentElem_eq_of_ker_isNilpotent, CircleDeg1Lift.semiconj_of_isUnit_of_translationNumber_eq, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', AdicCompletion.of_bijective_iff, StandardEtalePair.lift_X, BoundedContinuousFunction.coe_add, Module.Basis.coe_singleton, Algebra.TensorProduct.basisAux_tmul, AlgebraicGeometry.AffineSpace.hom_ext_iff, map_comp_nsmul, groupCohomology.norm_ofAlgebraAutOnUnits_eq, ofDual_neg, MeasureTheory.measure_sigmaFiniteSetWRT', Algebra.lsmul_injective, LocallyConstant.coeFnAlgHom_apply, prevD_eq_zero, UniformSpaceCat.coe_comp, Matrix.reindexLieEquiv_apply, FreeGroup.range_lift_eq_closure, Finsupp.multinomial_update, iccHomeoI_apply_coe, DividedPowers.IsDPMorphism.map_dpow, MvPowerSeries.monomial_zero_eq_C_apply, MonomialOrder.degree_mul_le, ValuativeExtension.vle_iff_vle, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_apply_asIdeal, ZSpan.coe_floor_self, Metric.exists_continuous_real_forall_closedBall_subset, Additive.ofMul_mono, SSet.stdSimplex.isoNerve_hom_app_apply, MeasureTheory.VectorMeasure.equivMeasure_symm_apply, Module.Basis.singleton_repr, MeasureTheory.Measure.comp_eq_comp_const_apply, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc, ContinuousLinearMap.mfderiv_eq, RootPairing.algebraMap_rootFormIn, MeasureTheory.exists_lt_lintegral_simpleFunc_of_lt_lintegral, KaehlerDifferential.derivationQuotKerTotal_apply, ModP.preVal_mk, InnerProductGeometry.norm_ofLp_crossProduct, Valuation.apply_posSubmonoid_pos, Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le, MeasureTheory.integral_posConvolution, NonUnitalAlgHom.quasispectrum_apply_subset, RelIso.apply_eq_iff_eq_symm_apply, AddChar.toMonoidHom_apply, Finsupp.count_toMultiset, Cardinal.aleph1_lt_lift, hasStrictDerivAt_abs, Orthonormal.linearIsometryEquiv_symm_apply_single_one, TensorProduct.AlgebraTensorModule.uncurry_apply, TensorProduct.map_comm, TwoSidedIdeal.mem_asIdealOpposite, Module.DirectLimit.exists_of, fourier_eval_zero, MonoidAlgebra.coe_add, UniformFun.edist_le, WithLp.equiv_symm_apply, Equiv.Perm.sign_of_pow_two_eq_one, Submodule.map_subtype_embedding_eq, MulEquivClass.apply_mem_center, LinearEquiv.coe_toContinuousLinearEquiv_symm', MvPolynomial.algebraTensorAlgEquiv_symm_X, LinearMap.coe_sum, finCycle_apply, Pretrivialization.linearMapAt_apply, InnerProductSpace.volume_ball_of_dim_odd, SimpleGraph.Subgraph.edgeSet_map, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_map_term, Valuation.one_srel_iff, MulActionHom.comp_apply, PresentedGroup.mk_eq_one_iff, QuadraticAlgebra.norm_coe, DFinsupp.coe_orderEmbeddingToFun, ArchimedeanOrder.of_val, FirstOrder.Language.BoundedFormula.IsAtomic.realize_comp, RingHom.map_closureS, Matrix.IsHermitian.cfcAux_apply, Localization.localAlgHom_apply, SchwartzMap.fourierInv_lineDerivOp_eq, RatFunc.valuation_eq_LaurentSeries_valuation, Affine.Simplex.touchpointWeights_reindex, Multiplicative.toAdd_image_nsmul, FractionalIdeal.extendedHomₐ_eq_one_iff, AffineEquiv.wSameSide_map_iff, Differential.mapCoeffs_monomial, GaussianInt.toComplex_sub, RCLike.abs_im_le_norm, MvPolynomial.expand_injective, gaussSum_mulShift_of_isPrimitive, Fin.coe_of_injective_castLE_symm, DomMulAct.isClosedEmbedding_mk_symm, CoalgHom.id_apply, MeasureTheory.StronglyMeasurable.exists_spanning_measurableSet_norm_le, Polynomial.integralNormalization_eval₂_eq_zero, ProbabilityTheory.Kernel.comp_discard', CategoryTheory.PreGaloisCategory.toAut_surjective_of_isPretransitive, ContDiffMapSupportedIn.tsupport_subset, AlternatingMap.domCoprod'_apply, isMax_toDual_iff, InnerProductSpace.harmonicAt_comp_CLE_iff, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen, Perfection.coeff_iterate_frobenius, InnerProductSpace.coe_gramSchmidtBasis, Set.powersetCard.mem_compl, smoothingFun_le, Bundle.RiemannianMetric.symm, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, Semigrp.comp_apply, ModularForm.const_toFun, NonUnitalRingHom.sclosure_preimage_le, QuadraticMap.sub_apply, MvPolynomial.mem_restrictDegree, AddMonoidHom.map_neg, closedBall_subset_range_iff_surjective, MvPolynomial.support_coeff_finSuccEquiv, ModP.v_p_lt_preVal, MeasureTheory.SimpleFunc.coe_toLargerSpace_eq, Module.AEval.X_pow_smul_of, dist_homothety_self, ExteriorAlgebra.ι_sq_zero, bijective_algebraMap_of_linearEquiv, minpoly.aeval, AddMonoidHom.compHom_apply_apply, BoundedContinuousFunction.dist_coe_le_dist, Antivary.sum_mul_eq_sum_mul_comp_perm_iff, Polynomial.degree_X_pow_sub_C, SkewMonoidAlgebra.coe_algebraMap, AlgebraicGeometry.Scheme.singleton_mem_precoverage_iff, Submonoid.LocalizationMap.map_eq_zero_iff, Polynomial.taylor_coeff_zero, AddMonoidHom.toMultiplicative_id, ProbabilityTheory.Kernel.integral_const, MonomialOrder.monic_monomial, Algebra.Presentation.aeval_val_relation, IsometryEquiv.map_hausdorffMeasure, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, Additive.toMul_strictMono, PowerSeries.monomial_zero_eq_C, Cardinal.toNat_strictMonoOn, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero, AlgHom.equalizer_toSubsemiring, IsCompact.measure_eq_iInf_isOpen, Subalgebra.mul_toSubmodule_le, LieHom.rangeRestrict_apply, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, isIntegral_algebraMap, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, MultilinearMap.coe_mk, iteratedFDeriv_eq_equiv_comp, Condensed.epi_iff_locallySurjective_on_compHaus, Equiv.coe_addRight, groupCohomology.mem_cocycles₂_iff, Localization.mulEquivOfQuotient_mk', NumberField.Units.coe_neg_one, Function.locallyFinsuppWithin.mk_of_mem_toFun, LinearMap.polyCharpolyAux_map_eq_charpoly, ProbabilityTheory.Kernel.add_apply, FractionalIdeal.mem_coeIdeal, AddSubmonoid.fromCommLeftNeg_apply, Valuation.IsRankOneDiscrete.generator_zpowers_eq_range, Matrix.SpecialLinearGroup.scalar_eq_coe_self_center, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, AddSemiconjBy.map, ofAdd_sum, AddMonoidHom.inr_mono, linear_isometry_complex, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, RelEmbedding.sumLexInr_apply, NonUnitalStarAlgHom.restrictScalars_apply, AddMonoid.Coprod.lift_apply_inr, Submodule.LinearDisjoint.injective, Set.preimage_add_preimage_subset, DirectSum.lmap_surjective, PrimeSpectrum.toPiLocalization_bijective, GroupExtension.rightHom_surjective, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, Submodule.baseChange_eq_span, MulEquiv.toMultiplicative_toAdditive_symm_apply, UniformOnFun.topologicalSpace_eq, SimpleGraph.map_adj_apply, linearMap_toMatrix_mul_basis_toMatrix, FreeMonoid.comp_lift, Path.extend_range, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Real.Angle.toCircle_coe, TrivSqZeroExt.liftEquiv_apply, CliffordAlgebra.isUnit_ι_iff, Ordinal.le_enum_succ, MDifferentiableOn.clm_bundle_apply, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, QuaternionAlgebra.Basis.i_compHom, MeasureTheory.measure_add_measure_compl, QuotientGroup.map_mk, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, LinearMap.mem_submoduleImage, AddActionHom.map_mem_fixedBy, Unitization.norm_eq_sup, ZMod.χ₈_int_mod_eight, AddGroup.preimage_vadd_setₛₗ, AddChar.toAddMonoidHomEquiv_symm_zero, MeasureTheory.SimpleFunc.vadd_apply, IncidenceAlgebra.sum_Icc_mu_right, Equiv.coe_vaddConst_symm, Submodule.dualCopairing_apply, RCLike.nonneg_iff, Homeomorph.continuous_symm, isAtom_dual_iff_isCoatom, Algebra.discr_of_matrix_mulVec, MeasureTheory.Measure.addHaarMeasure_self, Module.Basis.coe_reindex, LieRingModule.compLieHom_apply, ContinuousWithinAt.clm_apply, Subsemigroup.strictMono_topEquiv, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, FreeAbelianGroup.toFinsupp_of, LinearEquiv.toSpanNonzeroSingleton_apply, AlgebraicGeometry.Scheme.Hom.isOpenMap, CategoryTheory.Adjunction.instMonoCoeEquivHomObjHomEquivOfReflectsMonomorphisms, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_apply_snd, MeasureTheory.measure_inter_inv_smul, AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero, ProbabilityTheory.isGaussian_map, instIsZLatticeRealSpan, AddSubmonoid.leftNegEquiv_symm_add, Affine.Simplex.orthogonalProjection_circumcenter, Sym.cast_cast, Homeomorph.ext_iff, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.InducedCategory.homAddEquiv_symm_apply_hom, MeasureTheory.OuterMeasure.ofFunction_eq_iInf_mem, Matrix.kroneckerTMulAlgEquiv_symm_apply, OrderMonoidHom.ext_iff, AddChar.sum_eq_zero_of_ne_one, Module.dualPairing_apply, ContinuousAlgEquiv.isClosed_image, LinearMap.iterateKer_coe, Polynomial.mul_eq_sum_sum, Irreducible.map, MeasureTheory.FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasure, ContinuousLinearEquiv.coe_toLinearEquiv, PowerSeries.monomial_pow, MvPolynomial.degrees_map_le, ext_iff, LocallyConstant.toContinuousMapAddMonoidHom_apply, RatFunc.liftRingHom_apply, Matrix.ofLp_toEuclideanCLM, QuotientGroup.quotientMapSubgroupOfOfLe_mk, Quaternion.expSeries_even_of_imaginary, MeasurableEquiv.measurable_invFun, AddConstMap.pow_apply, Polynomial.mkDerivationEquiv_apply, hasFTaylorSeriesUpToOn_succ_nat_iff_right, addRothNumber_empty, Derivation.liftKaehlerDifferential_comp_D, ContinuousMap.sigma_apply, ProbabilityTheory.Kernel.HasSubgaussianMGF.isFiniteMeasure, Equiv.sumAssoc_apply_inl_inr, Equiv.Perm.SameCycle.zpow_left, coe_polyEquivTensor', QuadraticMap.smul_apply, QuadraticAlgebra.isUnit_iff_norm_isUnit, Ideal.Quotient.exists_algEquiv_fixedPoint_quotient_under, Module.Flat.instSubalgebraToSubmodule, unitsCenterToCenterUnits_injective, MulChar.pow_apply', MeasureTheory.measure_union₀_aux, MvPolynomial.esymmAlgHom_fin_surjective, DomMulAct.mk_smul_mulActionHom_apply, ContinuousLinearMap.coe_add', measure_le_lintegral_thickenedIndicator, infClosure_univ, Diffeomorph.symm_apply_apply, coe_invMonoidHom, MvPolynomial.expand_inj, Set.Ioo_ofDual, CategoryTheory.antitone_chain_condition_of_isArtinianObject, CategoryTheory.LocalizerMorphism.equiv_smallHomMap', LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, AddEquiv.coe_refl, ContinuousAlgEquiv.symm_comp_self, HNNExtension.of_mul_t, Fin.cycleRange_of_eq, Rep.resIndAdjunction_homEquiv_apply, equivShrink_mul, AlgEquiv.toUnder_inv_right_apply, ArithmeticFunction.cardDistinctFactors_prod, IsMulIndecomposable.image_baseOf_inv_comp_eq, Module.End.disjoint_genEigenspace, CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom, groupCohomology.isMulCocycle₂_of_mem_cocycles₂, Perfection.map_apply_coe, Irreducible.natSepDegree_eq_one_iff_of_monic, MvPolynomial.supDegree_esymm, GroupSeminorm.zero_apply, Polynomial.natDegree_X_pow_add_C, CStarMatrix.toCLM_apply_eq_sum, Matrix.scalar_commute, TensorProduct.AlgebraTensorModule.coe_lTensor, CategoryTheory.coyonedaEquiv_naturality, Matrix.cons_transpose, AddHom.ext_iff, Submodule.span_algebraMap_image_of_tower, LinearMap.exact_smul_id_smul_top_mkQ, mahler_natCast_eq, Submonoid.apply_coe_mem_map, ContMDiffMap.coe_add, Ideal.mk_mem_cotangentIdeal, AffineMap.lineMap_vsub, RootPairing.toPerfPair_flip_comp_coroot, Rep.toAdditive_apply, Coalgebra.rTensor_counit_comp_comul, ContinuousLinearMap.le_of_opNorm_le, ContinuousMapZero.coe_neg, FiniteField.two_pow_card, BoxIntegral.Box.volume_apply', MulHom.prod_apply, Equiv.Perm.Basis.mem_support_self, LightCondensed.isLocallySurjective_iff_locallySurjective_on_lightProfinite, SSet.skeleton_succ, Nat.factorization_lt, LocallyConstant.coe_mul, DFinsupp.linearEquivFunOnFintype_symm_apply, Equiv.Perm.decomposeOption_symm_of_none_apply, LinearMap.toMatrix_transpose_apply, Finset.map_toFinset, AlgHom.mul_apply, ProbabilityTheory.Kernel.compProd_eq_zero_iff, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, AffineIsometry.map_vsub, ContinuousAddMonoidHom.ext_iff, DirectSum.coe_decompose_mul_of_right_mem_of_not_le, RatFunc.map_apply_div, Submodule.coe_mapAlgEquiv_apply, Cardinal.preAleph_limit, PadicInt.coe_adicCompletionIntegersEquiv_apply, AlgebraicGeometry.Scheme.basicOpen_res_eq, MeasureTheory.measurePreserving_prodAssoc, DomAddAct.mk_add, Ideal.relNorm_int, CircleDeg1Lift.le_map_map_zero, CircleDeg1Lift.map_sub_nat, ZMod.toAddCircle_natCast, Equiv.invOn, Cardinal.toNat_le_toNat, Order.IsSuccLimit.dual, GaussianInt.toComplex_star, AffineIsometryEquiv.diam_image, Polynomial.divX_C_mul, OrderEmbedding.maximal_mem_image_iff, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj, isCompactOperator_iff_image_closedBall_subset_compact, DirectSum.coe_decompose_mul_of_left_mem_of_not_le, Circle.star_addChar, Pi.basis_repr, FreeCommRing.lift_comp_of, DFinsupp.equivCongrLeft_apply, CategoryTheory.coyonedaEquiv_apply, BooleanSubalgebra.coe_inclusion, BoundedContinuousFunction.coe_sup, PowerSeries.eq_X_pow_mul_shift_add_trunc, MultilinearMap.map_sum_finset_aux, Matrix.kroneckerTMulStarAlgEquiv_apply, MeasureTheory.SimpleFunc.FinMeasSupp.meas_preimage_singleton_ne_zero, UniformFun.toFun_one, LieSubmodule.toEnd_restrict_eq_toEnd, Matrix.transposeRingEquiv_apply, MulEquiv.congr_fun, AffineMap.map_vectorSpan, ENNReal.mulLeftOrderIso_symm_apply, PresheafOfModules.pushforward_obj_map_apply, Topology.WithUpper.ofUpper_toUpper, Polynomial.iterate_derivative_C, OrderIso.symm_preimage_preimage, StandardEtalePresentation.equivRing_x, Metric.Snowflaking.toSnowflaking_ofSnowflaking, AddEquiv.eq_comp_symm, ProbabilityTheory.Kernel.ext_iff, MeasureTheory.measure_inter_lt_top_of_left_ne_top, ComplexShape.Embedding.AreComplementary.equiv_inl, StarSubalgebra.coe_subtype, SkewMonoidAlgebra.liftNC_one, RCLike.continuous_re, Subgroup.topEquiv_symm_apply_coe, AlgEquiv.piCongrLeft'_apply, Finsupp.cons_tail, SupBotHom.coe_sup, Topology.WithUpper.toUpper_lt_toUpper, Equiv.Perm.IsCycleOn.pow_card_apply, WeierstrassCurve.Affine.map_slope, NormedSpace.algebraMap_exp_comm, AlgebraicGeometry.Scheme.Pullback.Triplet.hx, Unitary.linearIsometryEquiv_coe_symm_apply, quadraticChar_neg_two, ContinuousMap.div_apply, HasCompactSupport.comp_homeomorph, MeasureTheory.measure_neg_vadd_sdiff, Subgroup.normalizerMonoidHom_apply_apply_coe, toMatrix_dualTensorHom, MvPolynomial.eval_eq, Subgroup.IsComplement.equiv_symm_apply, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, TopHom.inf_apply, Equiv.pprodCongr_symm_apply, LieIdeal.coe_inclusion, MeasureTheory.exists_ne_forall_mem_nhds_pos_measure_preimage, MulEquiv.congr_arg, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, CategoryTheory.Limits.kernelOrderHom_coe, ProbabilityTheory.Kernel.piecewise_apply, Set.wellFoundedOn_iff_no_descending_seq, NormedAddGroupHom.ratio_le_opNorm, SemimoduleCat.homAddEquiv_apply, FirstOrder.Language.HomClass.monotone, UniversalEnvelopingAlgebra.lift_ι_apply, FreeRing.hom_ext_iff, cfc_le_algebraMap, OrderRingHom.coe_coe_orderMonoidWithZeroHom, SSet.ι₁_snd, MeasurableEquiv.memLp_map_measure_iff, NormedSpace.expSeries_apply_eq_div, Polynomial.degree_mul_leadingCoeff_self_inv, Ideal.absNorm_dvd_absNorm_of_le, subset_latticeClosure, ProbabilityTheory.Kernel.lintegral_compProd', Submodule.eq_starProjection_of_mem_of_inner_eq_zero, PowerSeries.trunc_trunc_of_le, rothNumberNat_def, OrderMonoidIso.strictMono_symm, IsLocalization.algEquivOfAlgEquiv_mk', ContDiff.comp_continuousLinearMap, MeasureTheory.Measure.map_conv_continuousLinearMap, Cardinal.isNormal_aleph, Polynomial.mahlerMeasure_X_add_C, PolynomialModule.comp_apply, LinearEquiv.arrowCongr_apply, exists_dual_vector, ContinuousMap.vadd_apply, nndist_center_homothety, IsDedekindDomain.primesOverEquivPrimesOver_ramificationIdx_eq, TopCat.GlueData.MkCore.t_inv, LieHom.coe_range, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DFinsupp.coe_piecewise, FreeLieAlgebra.lift_unique, AlgebraicGeometry.Scheme.Hom.stalkFunctor_toImage_injective, MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul, AlgebraicGeometry.isOpenImmersion_iff_stalk, AlgEquiv.piCongrLeft_apply, Fin.snocOrderIso_apply, MeasureTheory.mem_map_restrict_ae_iff, ContinuousMultilinearMap.tsum_eval, MulOpposite.coe_opLinearEquiv_toLinearMap, Rack.toEnvelGroup.univ, MonomialOrder.sPolynomial_def, SupHom.coe_const, OmegaCompletePartialOrder.Chain.directed, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Homeomorph.comp_continuous_iff, ofDegLex_toDegLex, Complex.conjAe_coe, RingHomInvPair.comp_apply_eq, Equiv.semiconj₂_conj, MulChar.IsQuadratic.gaussSum_frob_iter, one_le_thickenedIndicator_apply', MeasureTheory.SimpleFunc.memLp_top, ContinuousLinearMap.coeLM_apply, SSet.Truncated.StrictSegal.spineInjective, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, comap_subtype_coe_apply, AlgebraicGeometry.Scheme.image_basicOpen, RingHom.map_sub, groupHomology.d₂₁_comp_d₁₀_apply, HahnSeries.unit_aux, fourierCoeff_toLp, Orientation.oangle_rotation_oangle_left, DirectSum.lmap_lof, IsLocalizedModule.mk'_cancel', DyckWord.equivTree_symm_apply, UniformEquiv.symm_comp_self, CentroidHom.ext_iff, IntermediateField.restrictRestrictAlgEquivMapHom_injective, ContinuousAlternatingMap.toContinuousMultilinearMapLinear_apply, EmbeddingLike.apply_eq_iff_eq, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, Nat.not_dvd_ordCompl, Equiv.conj_comp, exteriorPower.alternatingMapLinearEquiv_apply_ιMulti, DFinsupp.sup_apply, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, OrthonormalBasis.det_to_matrix_orthonormalBasis, Algebra.Generators.H1Cotangent.δAux_ofComp, BoundedLatticeHom.ext_iff, IsLocalRing.ResidueField.map_map, SimpleGraph.incMatrix_mul_transpose, CategoryTheory.regularTopology.isLocallySurjective_iff, AlgEquiv.symm_trans_apply, RingOfIntegers.norm_norm, Polynomial.taylor_X_pow, CircleDeg1Lift.transnumAuxSeq_def, AffineMap.coe_const, MeasureTheory.SimpleFunc.coe_vadd, LieDerivation.coe_neg, Monoid.PushoutI.ofCoprodI_of, GaussianInt.toComplex_def, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, convexJoin_subset_convexHull, CliffordAlgebra.changeForm_ι_mul_ι, RingEquiv.prodCongr_apply, SupHom.withTop'_toFun, RelIso.symm_apply_rel, SubMulAction.subtype_apply, InfClosed.preimage, groupHomology.mapCycles₂_comp_apply, Module.Relations.Quotient.linearMap_ext_iff, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, RingSeminorm.eq_zero_iff, FreeAddGroup.map_eq_lift, Polynomial.reflect_support, TensorProduct.AlgebraTensorModule.homTensorHomMap_apply, ProbabilityTheory.condKernel_compProd, Algebra.adjoin_toSubmodule_le, Homeomorph.piCongrLeft_apply, OmegaCompletePartialOrder.Chain.ext_iff, strictAnti_iff_map_neg, dimH_eq_iInf, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, RootPairing.reflectionPerm_root, Equiv.Perm.IsCycle.pow_eq_pow_iff, QuaternionAlgebra.lift_symm_apply, Homeomorph.comap_coclosedCompact, Finset.affineCombination_indicator_subset, LinearMap.isPositive_toContinuousLinearMap_iff, Prod.Lex.toLex_lt_toLex, TrivSqZeroExt.inlAlgHom_apply, OrthogonalFamily.summable_of_lp, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, Equiv.piCongrSigmaFiber_apply, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_assoc, addRothNumber_lt_of_forall_not_threeAPFree, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, ProbabilityTheory.IsGaussian.charFunDual_eq, IsLocalRing.exists_surjective_of_not_isLocalRing, Matrix.range_toLin', IsLocalization.map_integerMultiple, AddCommMonCat.coe_comp, LinearIsometryEquiv.analyticWithinAt, coe_fourierBasis, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, HasFPowerSeriesAt.apply_eq_zero, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, tendsto_measure_Icc_nhdsWithin_right, LinearIsometryEquiv.toSpanUnitSingleton_apply, ContinuousMultilinearMap.prodEquiv_symm_apply, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, subset_infClosure, AddChar.inv_apply, MonoidHom.map_neg, FormalMultilinearSeries.comp_coeff_one, UpperSet.map_Ici, LaurentPolynomial.algebraMap_eq_toLaurent, AddChar.doubleDualEmb_bijective, ContinuousMapZero.nonUnitalStarAlgHom_precomp_apply, LinearMap.prodMapLinear_apply, MonoidWithZeroHom.one_apply_eq_one_iff, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', LieModule.IsFaithful.injective_toEnd, Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero, MulActionHom.coe_mul, MeasureTheory.Measure.sInf_apply, PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, Continuous.homeoOfEquivCompactToT2.t1_counterexample, AddChar.wInner_cWeight_eq_one_iff_eq, AddSubgroup.IsComplement.rightQuotientEquiv_apply, ProbabilityTheory.Kernel.prodMkRight_apply, map_inv_natCast_smul, LinearIndependent.span_repr_eq, PowerSeries.map_eq_zero, ContinuousLinearMap.le_opNorm_of_le, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Multiset.map_univ_val_equiv, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, Valuation.mem_leAddSubgroup_iff, AddMonoidHom.op_symm_apply_apply, IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, MeasureTheory.OuterMeasure.map_iSup, AlgEquivClass.commutes, AddCon.coe_mk', convexHull_eq_empty, Differential.mapCoeffs_C, AffineMap.lineMap_eq_lineMap_iff, OrderIso.tendsto_atTop, Submodule.map₂_span_singleton_eq_map_flip, LinearEquiv.finTwoArrow_apply, InitialSeg.map_isSuccPrelimit, MeasureTheory.Measure.fst_apply, LinearMap.pi_apply_eq_sum_univ, LocallyConstant.mapMonoidHom_apply, DirectSum.addEquivProdDirectSum_apply, OrderRingIso.coe_mk, spectrum.preimage_algebraMap, DilationEquiv.smulTorsor_apply, RootPairing.rootForm_self_eq_zero_iff, LocallyConstant.congrLeftRingEquiv_symm_apply_apply, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, QuaternionAlgebra.re_swapEquiv_symm_apply, LinearMap.linearIndependent_iff_of_disjoint, PerfectRing.lift_id_apply, ContinuousLinearEquiv.lipschitz, frobeniusEquiv_symm_pow, iteratedDeriv_vcomp_three, Specialization.ofEquiv_inj, VectorField.fderivWithin_apply_lieBracket_of_isSymmSndFDerivWithinAt, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, SubgroupClass.inclusion_mk, Tropical.tropEquiv_symm_coe_fn, BddOrd.forget_map, ModularFormClass.qExpansion_coeff, Submodule.prodEquivOfIsCompl_symm_apply, AddEquiv.comapAddSubgroup_apply, ZMod.dft_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, PiTensorProduct.piTensorHomMap_tprod_eq_map, QuadraticMap.PosDef.nonneg, sigmaFinsuppEquivDFinsupp_smul, Module.End.coe_mul, CuspForm.coe_translate, Rep.ofDistribMulAction_ρ_apply_apply, Diffeomorph.coe_prodComm, Quaternion.fst_imJ_dualNumberEquiv_symm, OrderMonoidIso.val_inv_unitsCongr_apply, Equiv.Perm.sign_refl, MonomialOrder.le_add_right, LinearEquiv.skewProd_symm_apply, AlgHom.one_apply, Homeomorph.image_symm, CommMonCat.inv_hom_apply, CuspFormClass.petersson_bounded_right, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, Submodule.injective_tensorToSpan, DFinsupp.erase_eq_sub_single, IsCyclotomicExtension.discr_prime_pow_ne_two, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure, MvPolynomial.as_sum, MeasureTheory.integrable_of_summable_norm_restrict, FreeAddMonoid.toList_of_add, Polynomial.comp_C_mul_X_coeff, PiTensorProduct.singleAlgHom_apply, Equiv.ofLeftInverseOfCardLE_apply, LinearMap.dualMap_apply', Ordinal.enum_typein, Submodule.Quotient.restrictScalarsEquiv_symm_mk, Measurable.setLIntegral_kernel, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, HNNExtension.of_mul_inv_t, RelEmbedding.sumLiftRelMap_apply, iteratedFDerivWithin_two_apply', AddMonoid.Coprod.swap_eq_zero, Units.isEmbedding_embedProduct, smul_algebraMap, MeasureTheory.Measure.haar.is_left_invariant_haarContent, AddCommGrpCat.Colimits.quotToQuotUlift_ι, le_map_div_mul_map_div, ModularFormClass.bdd_at_infty, starRingEnd_apply, AddChar.val_mem_rootsOfUnity, MeasureTheory.Integrable.to_average, LinearMap.mul_toMatrix', Seminorm.add_apply, signedDist_vadd_right, AddEquiv.mulOp_apply, FinBddDistLat.comp_apply, Matrix.liftLinear_apply, MvPolynomial.isUnit_iff_eq_C_of_isReduced, Rep.linearization_η_hom_apply, toAdd_ofAdd, Monoid.CoprodI.Word.equivPair_symm, NumberField.Ideal.tendsto_norm_le_div_atTop₀, FiniteField.coe_frobeniusAlgEquivOfAlgebraic_iterate, SkewMonoidAlgebra.update_eq_erase_add_single, Complex.conj_mul', GroupNorm.coe_le_coe, ContinuousAlgEquiv.image_eq_preimage_symm, RelIso.injective, Set.up_empty, LinearMap.det_eq_zero_iff_ker_ne_bot, AddEquiv.toMultiplicativeRight_symm_apply_apply, AddMonoidHom.nsmul_apply, Polynomial.int_eval₂_eq, RCLike.zero_re, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, MonomialOrder.leadingCoeff_monomial, Set.isPWO_iff_exists_monotone_subseq, Quaternion.equivTuple_apply, RelHomClass.map_inf, AddSubmonoid.LocalizationMap.ofAddEquivOfLocalizations_apply, Algebra.Presentation.differentials.comm₂₃', Dilation.coe_one, gal_C_isSolvable, MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit, ProbabilityTheory.IsRatCondKernelCDFAux.mono', Set.Countable.measure_zero, Polynomial.coeff_reflect, LieSubalgebra.mem_comap, Module.Basis.restrictScalars_apply, RootPairing.invtRootSubmodule.eq_bot_iff, NonUnitalSubsemiringClass.subtype_injective, Submodule.toAddSubgroup_toIntSubmodule, ContinuousMap.val_addUnitsLift_apply_apply, unitInterval.symmMeasurableEquiv_symm_apply, AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv, strictMonoOn_toDual_comp_iff, AddEquiv.coe_trans, AffineIsometry.coe_toAffineIsometryEquiv, AffineSubspace.mem_map, Archimedean.embedReal_injective, CentroidHom.comp_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, Coalgebra.TensorProduct.map_tmul, Module.Basis.flag_succ, SimpleGraph.le_chromaticNumber_iff_forall_surjective, Polynomial.resultant_X_sub_C_pow_left, InnerProductSpace.Core.inner_re_symm, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, Set.chainHeight_eq_of_relIso, AdjoinRoot.liftAlgHom_eq_algHom, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, AddMonoidHom.coe_mgraph, OrderMonoidIso.withZero_apply_apply, MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero, Equiv.optionSubtypeNe_symm_apply, ModuleCat.smulNatTrans_apply_app, CategoryTheory.PreOneHypercover.inter_p₂, CommBialgCat.hom_inv_apply, rotationOf_rotation, bijective_rootsOfUnityAddChar, Matrix.of_apply, exteriorPower.ιMultiDual_apply_ιMulti, Homeomorph.continuous_sumAssoc, InnerProductSpace.gramSchmidt_triangular, Matrix.diagonal_kroneckerTMul, MvPolynomial.monomial_add_single, edist_toMul, Set.ordConnected_image, finSuccEquiv'_below, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none, Algebra.normalizedTrace_algebraMap_apply_eq_self, UniformFun.lipschitzWith_ofFun_iff, PiTensorProduct.lift_comp_reindex, TopCat.isClosed_iff_of_isColimit, LinearMap.ext_iff₂, NormedSpace.equicontinuous_TFAE, ContinuousLinearMap.differentiable, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, isRightRegular_toDual, FreeGroupBasis.reindex_apply, Fin.succAbove_cycleRange, OrderRingIso.symm_apply_apply, algebraMap_le_cfc, QuadraticAlgebra.basis_repr_apply, DomMulAct.isEmbedding_mk, Subalgebra.algebraMap_mem', Submodule.starProjection_map_apply, AddSubgroup.addSubgroupOfEquivOfLe_symm_apply_coe_coe, MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_ne_zero, Function.Embedding.coeWithBot_apply, FirstOrder.Language.Formula.equivSentence_inf, RCLike.smul_im, CliffordAlgebra.EquivEven.neg_v_mul_e0, HahnSeries.ofPowerSeries_X, AddCommGroup.DirectLimit.of_f, Submodule.natAbs_det_equiv, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, LieIdeal.inclusion_injective, LinearMap.coe_prod, LinearMap.dualMap_bijective_iff, ProbabilityTheory.Kernel.rnDerivAux_le_one, HomotopicalAlgebra.AttachCells.reindex_π, TensorPower.multilinearMapToDual_apply_tprod, CategoryTheory.Sheaf.ΓObjEquivSections_naturality_symm, exists_contMDiffOn_forall_mem_convex_of_local, Valuation.vle_iff_le, PartOrd.comp_apply, HVertexOperator.of_coeff_coeff, Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le, Equiv.coe_mulLeft, Cardinal.toNat_lt_iff_lt_of_lt_aleph0, UniformEquiv.image_symm, PiTensorProduct.map₂_tprod_tprod, LinearMap.star_eq_adjoint, Module.Basis.mem_submodule_iff', skewAdjoint.negISMul_apply_coe, ProbabilityTheory.Kernel.comp_const, Polynomial.toFn_zero, SimpleGraph.Subgraph.map_verts, ContinuousMapZero.coe_smul, IsOpen.measure_eq_iSup_isCompact, IsLocalizedModule.mk'_one, Submodule.smithNormalFormBotBasis_def, nnnorm_ofAdd, RelIso.symm_comp_self, MulEquiv.surjective, Module.Basis.sum_dual_apply_smul_coord, Equiv.prodCongrLeft_apply_fst, MeasureTheory.lintegral_countable', PMF.integral_eq_tsum, Polynomial.toLaurent_X_pow, LinearMap.compMultilinearMapₗ_apply, DFinsupp.Icc_eq, SpectrumRestricts.real_iff, Matrix.vecMul_permMatrix, dist_self_homothety, Finset.Colex.toColex_lt_singleton, Polynomial.ofFn_zero', TrivSqZeroExt.inrCLM_apply, Sublattice.mem_subtype, OrderIso.divRight₀_apply, MulHom.compLeft_apply, MeasureTheory.tilted_const', StarSubalgebra.coe_bot, Complex.sin_conj, Matrix.mul_adjugate_apply, OrderIso.sumLexIicIoi_symm_apply_Ioi, MonomialOrder.degree_pow_le, AddEquiv.piAdditive_symm_apply, GaussianInt.to_real_re, PrimeSpectrum.primeSpectrumProd_symm_inr, Polynomial.derivative_C_mul_X, AddOpposite.opEquiv_apply, RingEquiv.map_det, Con.coe_iInf, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, IsLocalFrameOn.eventually_eq_sum_coeff_smul, CommRingCat.toAlgHom_apply, Ideal.quotientMap_mk, Polynomial.Bivariate.swap_X, MvPolynomial.eval_add, WeierstrassCurve.Projective.map_polynomialX, ContinuousMap.homeoFnOfDiscrete_apply, LatticeHom.coe_withTop, LinearEquiv.conjRingEquiv_apply_apply, List.formPerm_pow_apply_head, RatFunc.liftRingHom_apply_div', AdjoinRoot.lift_mk, LinearMap.toMatrix_smulBasis_right, MeasurableEquiv.curry_apply, Matrix.toLpLin_symm_id, lineMap_lt_left_iff_lt, UniformSpaceCat.coe_mk, Polynomial.eval_iterate_derivative_rootMultiplicity, MeasureTheory.SimpleFunc.integrable_iff, List.SortedGT.of_map_ofDual, Polynomial.lcoeff_apply, LieEquiv.lieSubalgebraMap_apply, Fin.cycleRange_of_le, Polynomial.iterate_derivative_derivative_mul_X, Module.Basis.toDual_eq_repr, IsGLB.dual, AlgEquiv.toLieEquiv_symm_apply, AddSemigrp.neg_hom_apply, AddSubsemigroup.strictMono_topEquiv, Polynomial.Chebyshev.add_one_mul_self_mul_T_eq_poly_in_T, Matrix.range_toLin_eq_top, Set.val_unitEquivUnitsInteger_apply_coe, MeasureTheory.Measure.fst_univ, Monotone.measure_iInter, PMF.seq_apply, Trivialization.coe_linearMapAt, ValuationSubring.monotone_mapOfLE, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, NonUnitalStarSubalgebra.iSupLift_inclusion, AddSubmonoid.LocalizationMap.surj, Algebra.SubmersivePresentation.map_jacobianRelationsOfHasCoeffs, List.exists_map_eq_of_sorted_iff_sbtw, LinearMap.coe_toAffineMap, toMul_zsmul, Unitization.inrHom_apply, ModularFormClass.exists_bound, Equiv.funUnique_apply, WeierstrassCurve.Jacobian.baseChange_dblU, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, AddHom.coe_comp, MeasureTheory.tendsto_measure_Ioc_atBot, WeierstrassCurve.Affine.CoordinateRing.map_mk, ModularForm.neg_apply, Subrel.relEmbedding_apply, Finsupp.prod_hom_add_index, MonoidAlgebra.exists_finset_adjoin_eq_top, WithZero.toMulBot_coe_ofAdd, Module.Basis.baseChange_end, Submonoid.LocalizationMap.ofMulEquivOfDom_comp, ContinuousAddMonoidHom.prod_toFun, MonCat.comp_apply, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, LinearIsometryEquiv.coe_coe, Polynomial.Splits.X_add_C, convexHull_singleton, LocallyConstant.mapRingHom_apply_apply, AddConstMap.ext_iff, LinearAlgebra.FreeProduct.identify_one, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, CategoryTheory.Sheaf.isLocallyInjective_iff_injective, TensorProduct.lid'_apply_tmul, IsLocalRing.ResidueField.map_residue, SubMulAction.ofFixingSubgroup_of_eq_apply, Algebra.TensorProduct.liftEquiv_apply, MeasureTheory.Measure.inf_apply, LinearIsometry.preimage_ball, Matrix.toLin_finTwoProd_apply, Valued.toNormedField.norm_le_iff, Metric.Snowflaking.ediam_preimage_ofSnowflaking, MulOpposite.opMulEquiv_apply, Submodule.mapQ_eq_factor, StarAlgEquiv.apply_symm_apply, Valuation.map_add', AddConstMapClass.antitone_iff_Icc, Homeomorph.continuousMapOfUnique_symm_apply, FreeLieAlgebra.universalEnvelopingEquivFreeAlgebra_apply, LatticeHom.dual_id, exists_integral_inj_algHom_of_quotient, Measurable.lintegral_kernel, CategoryTheory.Limits.imageSubobject_arrow_comp_apply, CliffordAlgebra.reverse_prod_map_ι, Rep.leftRegularHomEquiv_symm_apply, TannakaDuality.FiniteGroup.equivApp_hom, tendsto_integral_mulExpNegMulSq_comp, ContinuousLinearMap.sSup_sphere_eq_norm, MeasureTheory.OuterMeasure.restrict_iSup, FormalMultilinearSeries.applyComposition_single, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, PrincipalSeg.trans_top, TopCat.pullbackIsoProdSubtype_inv_snd_apply, CategoryTheory.Limits.Types.limitEquivSections_symm_apply, MeasureTheory.tilted_apply, RingEquiv.subsemiringMap_symm_apply_coe, DirectSum.coe_of_mul_apply_of_not_le, Localization.mkAddMonoidHom_apply, MvPowerSeries.trunc_map, Submonoid.LocalizationMap.isUnit_comp, ContinuousInv.induced, Finsupp.weight_single_index, RingHom.isIntegralElem_leadingCoeff_mul, SimpleGraph.Subgraph.spanningCoeEquivCoeOfSpanning_apply_coe, RingCon.comapQuotientEquivRangeS_mk, coe_finRotate, CategoryTheory.Adjunction.homAddEquiv_add, Antitone.dual, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, Polynomial.degree_C_lt, NonUnitalSubalgebra.mem_comap, algebraMap_comp_intCast, measurable_measure_prodMk_left_finite, Measurable.lintegral_kernel_prod_left, PowerSeries.coeff_exp, HVertexOperator.coeff_inj_iff, Complex.conj_eq_iff_re, HasFPowerSeriesAt.fderiv_eq, MeasureTheory.Integrable.integral_condDistrib_map, LinearPMap.adjointDomainMkCLM_apply, map_pos_of_ne_zero, Module.Basis.sum_repr_mul_repr, Orientation.oangle_sign_smul_left, NumberField.Units.dirichletUnitTheorem.seq_norm_le, IsSelfAdjoint.algebraMap, MeasureTheory.Measure.infinitePi_singleton_of_fintype, LinearMap.BilinForm.dualBasis_eq_iff, map_le_lineMap_iff_slope_le_slope_right, CategoryTheory.ComposableArrows.opEquivalence_unitIso_hom_app, Equiv.Perm.perm_symm_mapsTo_iff_mapsTo, MeromorphicOn.divisor_apply, Matrix.isPositive_toEuclideanLin_iff, ContDiffPointwiseHolderAt.continuousLinearMap_comp, isExtrOn_dual_iff, MeasureTheory.SMulInvariantMeasure.measure_preimage_smul, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, unitary.val_toUnits_apply, MeasureTheory.OuterMeasure.isCaratheodory_iff_le, AddSubgroup.orderIsoAddCon_symm_apply_coe, FreeMonoid.lift_eval_of, RootPairing.coreflection_apply_self, padic_polynomial_dist, ContinuousLinearMap.coe_restrictScalarsIsometry, InfIrred.dual, MonoidHom.div_mem_ker_iff, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, AbsoluteValue.pos, Con.eq, AddMonoid.Coprod.snd_apply_inl, Localization.mapToFractionRing_apply, Finsupp.linearCombination_apply, QuadraticMap.coeFnAddMonoidHom_apply, SimplexCategory.II.castSucc_mem_finset_iff, PointedCone.mem_map, ZeroAtInftyContinuousMapClass.zero_at_infty, toDual_hnot, MulEquiv.cast_symm_apply, Matrix.diagonal_fin_one, SemiNormedGrp.inv_hom_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.isIso, RingEquiv.trans_apply, coe_frobeniusEquiv, ContinuousLinearMap.memLp_of_bilin, MeasureTheory.SimpleFunc.neg_apply, WittVector.iterate_verschiebung_coeff_eq_zero, Function.Embedding.setValue_right_apply_eq, addMonoidEndRingEquivInt_apply, PartitionOfUnity.locallyFinite', ContinuousMap.coe_neg, TensorAlgebra.ofDirectSum_toDirectSum, StarMulEquiv.toStarMonoidHom_coe, CategoryTheory.Functor.mapExtAddHom_apply, MonoidAlgebra.smul_of, Polynomial.aeval_conj, MonoidHom.transfer_center_eq_pow, DFinsupp.sum_apply, StarAlgHom.ofId_apply, BddDistLat.dual_map, TopologicalSpace.Opens.coe_id, Finsupp.prod_filter_index, MeasureTheory.toOuterMeasure_eq_inducedOuterMeasure, Polynomial.nextCoeff_C_eq_zero, AddHom.coe_fst, ProbabilityTheory.Kernel.partialTraj_succ_self, LinearEquiv.symm_trans_apply, DFA.reindex_apply_start, Module.Basis.baseChange_apply, FreeAlgebra.toTensor_ι, Pi.ωScottContinuous_uncurry, Nucleus.coe_lt_coe, IsCyclotomicExtension.Rat.galEquivZMod_apply_of_pow_eq, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, Polynomial.iterate_derivative_eq_zero, TopCat.presheafToTypes_map, CommRingCat.HomTopology.isEmbedding_hom, FourierTransform.fourierₗ_apply, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, ModularForm.eq_const_of_weight_zero, SkewMonoidAlgebra.mapDomain_id, RingEquiv.mapTwoSidedIdeal_apply, ContinuousMap.coe_nsmul, AffineMap.map_vadd, LinearMap.uncurryMid_apply, RootPairing.polarizationEquiv_apply, MeasureTheory.smul_le_stoppedValue_hitting, CategoryTheory.Iso.toAlgEquiv_apply, ContinuousMulEquiv.symm_apply_apply, SupHom.withTop_toFun, CategoryTheory.Limits.colimit.w_apply, AddChar.one_apply, Finset.Colex.singleton_lt_singleton, AddMonoidHom.ENatMap_apply, PerfectRing.liftAux_id_apply, Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent, CliffordAlgebra.reverseOpEquiv_opComm, AbsoluteValue.IsEquiv.lt_one_iff, iInter_halfSpaces_eq, Polynomial.hasseDeriv_coeff, CStarMatrix.reindexₐ_apply, RCLike.re_eq_add_conj, ContinuousAlgEquiv.coe_toAlgEquiv, ContinuousLinearEquiv.refl_apply, ofDual_ratCast, Cardinal.card_typein_lt, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor, OrderIso.lt_symm_apply, PMF.toMeasure_uniformOfFintype_apply, NumberField.integralBasis_repr_apply, Equiv.sigmaUnique_symm_apply, Matrix.toBilin'Aux_single, ZSpan.isAddFundamentalDomain', Matrix.scalarAlgHom_apply, ContinuousLinearMap.differentiableWithinAt, MeasureTheory.Measure.integrable_compProd_iff, AddGrpCat.toGrp_map, continuousMultilinearCurryFin0_apply, exists_finite_inj_algHom_of_fg, AlgHom.default_apply, CStarMatrix.ofMatrix_eq_ofMatrixL, Matrix.rank_submatrix, EquivLike.comp_injective, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, Polynomial.degree_C_mul_X_pow_le, Prod.Lex.covBy_iff, MonoidHom.mrangeRestrict_surjective, geometric_hahn_banach_closed_compact, Polynomial.separable_prod_X_sub_C_iff', EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, toAdd_one, RingCon.coe_algebraMap, map_sum, DivisibleHull.coeAddMonoidHom_apply, MulOpposite.opEquiv_apply, OrderHom.lfp_lfp, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_bijective, CategoryTheory.yonedaGrp_naturality_assoc, AddCommMonCat.coyoneda_map_app, IsLocalizedModule.map_mk', AddSubmonoid.leftNegEquiv_symm_fromLeftNeg, Multiplicative.toAdd_eq_bot, Polynomial.le_trailingDegree_C_mul_X_pow, ite_apply, LieModuleHom.coe_range, exteriorPower.pairingDual_ιMulti_ιMulti, Polynomial.map_mapRingHom_evalEval, UniformFun.toFun_prod, RootPairing.linearIndepOn_root_baseOf, unitInterval.symmHomeomorph_symm_apply, QuotientGroup.lift_mk', Polynomial.algEquivAevalNegX_symm_apply, NonUnitalSubalgebra.inclusion_inclusion, partialSups_eq_biSup, MagmaCat.id_apply, NonUnitalStarAlgHom.coe_toNonUnitalAlgHom, NonUnitalStarAlgHom.coe_restrictScalars', Polynomial.revAt_le, MeasurableEquiv.apply_symm_apply, Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors, LinearEquiv.isUnit_det', FreeMonoid.toList_of_mul, AdjoinRoot.root_isInv, Polynomial.monomial_zero_one, TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding, MvPolynomial.eval₂_eq', Equiv.Set.sumDiffSubset_symm_apply_of_notMem, Homeomorph.image_apply_coe, LieDerivation.coeFnAddMonoidHom_apply, Filter.Tendsto.eval_const, MonoidHomClass.isometry_iff_norm, ProbabilityTheory.Kernel.continuous_integral_integral, Polynomial.hasseDeriv_mul, InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv, MonoidHom.mulSingle_apply, Path.range_subpath, Pi.lt_toColex_update_self_iff, AffineMap.coe_fst, ExteriorAlgebra.map_apply_ι, LinearMap.mul_toMatrix₂, homeomorphUnitSphereProd_symm_apply_coe, PointwiseConvergenceCLM.coeLMₛₗ_apply, ContinuousLinearMap.postcompCompactConvergenceCLM_apply, Equiv.ofBijective_symm_apply_apply, Submonoid.subtype_injective, ProbabilityTheory.covarianceBilin_self_nonneg, Module.algebraMap_end_eq_smul_id, Shrink.algEquiv_apply, Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_apply, supsSupHom_apply, LocallyConstant.constRingHom_apply, Orientation.rightAngleRotation_rightAngleRotation, WittVector.dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeff, CategoryTheory.Bicategory.conjugateEquiv_symm_comm, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, PowerSeries.trunc_one_left, Cardinal.card_typein_toType_lt, FrameHom.coe_id, groupHomology.H2π_eq_iff, MonomialOrder.monic_monomial_one, DirectSum.addEquivProdDirectSum_symm_apply_support', MvPowerSeries.isHomogeneous_iff_eq_homogeneousComponent, controlled_prod_of_mem_closure_range, SchwartzMap.toBoundedContinuousFunction_apply, SemidirectProduct.left_inl, LaurentSeries.coe_X_compare, Algebra.TensorProduct.basis_repr_symm_apply', Frm.id_apply, AffineMap.image_uIcc, AddSemigrp.hom_neg_apply, Set.uIcc_toDual, Even.map, Metric.exists_continuous_nnreal_forall_closedEBall_subset, commute_lmul_lmul_sq, ExteriorAlgebra.ι_leftInverse, ProbabilityTheory.integral_linearMap_gaussianReal, Localization.algEquiv_symm_mk', AlgebraicGeometry.Scheme.IdealSheafData.support_comap, IsSelfAdjoint.conj_adjoint, ContinuousLinearMap.compLeftContinuous_apply, MeasureTheory.measure_pos_of_superset, WeierstrassCurve.Jacobian.baseChange_polynomial, TensorProduct.inner_assoc_assoc, TopologicalSpace.Opens.set_range_inclusion', ContinuousMultilinearMap.curryMidEquiv_apply, NormedAddGroupHom.completion_coe_to_fun, IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map, AddSubmonoid.leftNegEquiv_apply, SimplexCategory.mono_iff_injective, MvPolynomial.aeval_def, AddCommGrpCat.zero_apply, RingCon.congrₐ_mk, MeasureTheory.SimpleFunc.tendsto_approxOn, LinearMap.mem_range_self, MeasureTheory.Integrable.condDistrib_ae, AlgebraicGeometry.Scheme.stalkMap_congr_hom, SemiNormedGrp₁.iso_isometry, RootPairing.linearIndependent_iff_coxeterWeight_ne_four, Matrix.lieConj_symm_apply, NonUnitalRingHom.srange_eq_top_iff_surjective, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, Real.fourier_eq, MeasureTheory.measure_eq_div_smul, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, AffineEquiv.injective_pointReflection_left_of_injective_two_nsmul, SimpleGraph.TripartiteFromTriangles.cliqueSet_eq_image, Setoid.prodQuotientEquiv_symm_apply, PMF.toOuterMeasure_ofFintype_apply, AddSubgroup.vadd_leftQuotientEquiv, ApproximatesLinearOn.lipschitz_sub, CategoryTheory.Groupoid.CategoryTheory.Functor.mapVertexGroup_apply, Subgroup.noncommPiCoprod_mulSingle, EquivLike.comp_bijective, Matrix.val_planeConformalMatrix, ContinuousMultilinearMap.iteratedFDeriv_eq, AntilipschitzWith.le_hausdorffMeasure_image, kroneckerTMulLinearEquiv_mul, RingHom.codomain_trivial_iff_map_one_eq_zero, Homeomorph.vaddConst_symm_apply, CategoryTheory.Bicategory.mateEquiv_symm_apply, OrderEmbedding.withTopMap_apply, CategoryTheory.Functor.Elements.initialOfCorepresentableBy_snd, Real.volume_Iic, WittVector.IsPoly.map, FractionalIdeal.canonicalEquiv_coeIdeal, QuadraticMap.discr_comp, finTwoArrowEquiv_apply, Equiv.iInf_comp, ContinuousMap.nnnorm_lt_iff_of_nonempty, Finsupp.fst_sumFinsuppEquivProdFinsupp, Module.Basis.linearMap_repr_apply, Polynomial.coeff_mul_C, Ordinal.blsub_type, Equiv.ofBijective_apply, MulEquiv.trans_apply, AffineMap.lineMap_vadd_apply, Path.symm_apply, PrincipalSeg.coe_coe_fn', Affine.Simplex.affineCombination_mem_interior_iff, exteriorPower.alternatingMapLinearEquiv_comp_ιMulti, MvPolynomial.monomial_eq_zero, ZSpan.norm_fract_le, mulAutArrow_apply_symm_apply, StrictMono.dual_left, LinearMap.coe_dfinsuppSum, ContinuousAddMonoidHom.coprod_toFun, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, AlgEquiv.cast_apply, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, FirstOrder.Language.StrongHomClass.map_rel, HasStrictFDerivAt.continuousMultilinear_apply_const, AlgEquiv.toLinearMapHom_apply_apply, Cardinal.lift_eq_aleph1, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, toColex_neg, LinearMap.lsmul_eq_DistribMulAction_toLinearMap, Nucleus.range_subset_range, groupHomology.H1AddEquivOfIsTrivial_single, Module.eval_apply_eq_zero_iff, Pi.monoidHom_apply, MeasureTheory.addContent_mono, RatFunc.liftRingHom_ofFractionRing_algebraMap, Subgroup.map_centralizer_le_centralizer_image, Int.absNorm_under_mem, AlgebraicGeometry.Scheme.Pullback.range_snd_comp, MvPolynomial.eval_monomial, SymAlg.sym_eq_one_iff, LaurentSeries.hasseDeriv_comp_coeff, AddGrpCat.mono_iff_injective, PresheafOfModules.homEquivOfIsLocallyBijective_apply, CategoryTheory.Limits.kernelSubobject_arrow_comp_apply, WithTop.ofDual_apply_coe, NonUnitalStarAlgHom.snd_apply, GroupExtension.Section.exists_mul_eq_inl_mul_mul, Finsupp.degree_preimage_add, kroneckerTMulLinearEquiv_symm_kroneckerTMul, MvPolynomial.coeff_coe, Units.coe_unop_opEquiv, LinearMap.coeFn_sum, Module.Basis.det_reindex, OrderIso.toInitialSeg_toFun, LinearEquiv.zero_apply, MultilinearMap.curryFinFinset_apply_const, DirectSum.mk_apply_of_mem, AdicCompletion.map_mk, MeasureTheory.Measure.hausdorffMeasure_zero_or_top, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, RootPairing.bijOn_coreflection_coroot, ContinuousLinearMap.analyticOnNhd_bilinear, Polynomial.hermite_eq_deriv_gaussian', CategoryTheory.Limits.Concrete.prodEquiv_symm_apply_snd, ProbabilityTheory.Kernel.measurableSet_mutuallySingular, Relation.cutExpand_le_invImage_lex, AddCommGrpCat.id_apply, groupCohomology.mem_cocycles₁_iff, Set.opEquiv_self_apply_coe, Polynomial.Splits.image_rootSet, ContinuousLinearEquiv.hasSum, MultilinearMap.freeFinsuppEquiv_def, ContinuousLinearMap.reApplyInnerSelf_apply, Set.Ioc_toDual, MonomialOrder.degree_C, Fin.coe_castSuccEmb, imaginaryPart_realPart, AbsoluteValue.nonneg, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Monoid.CoprodI.of_apply, AddAction.compHom_vadd_def, MultilinearMap.map_update_sub, RingCat.ofHom_apply, Orientation.oangle_sign_smul_add_smul_smul_add_smul, MulEquiv.mapSubgroup_symm_apply, Ideal.quotientToQuotientRangePowQuotSucc_surjective, ValuativeRel.RankLeOneStruct.strictMono, ProbabilityTheory.setLIntegral_toKernel_univ, IsModuleTopology.continuous_bilinear_of_finite_left, WithZero.lift'_unique, smoothSheafCommRing.ι_forgetStalk_inv_apply, Finsupp.liftAddHom_apply, LinearMap.lsum_single, DoubleCentralizer.algebraMap_snd, MvPolynomial.coeff_monomial_mul', UniformOnFun.uniformSpace_eq_iInf_precomp_of_cover, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, equicontinuous_iff_continuous, NormedSpace.expSeries_apply_zero, injective_iff_map_eq_zero', MeasurableEquiv.sigmaFinite_map, Polynomial.aeval_smul, SimpleGraph.Embedding.coe_comp, WithZero.mapAddHom_coe, Equiv.optionSubtype_symm_apply_apply_none, Finsupp.smul_apply, PresheafOfModules.unitHomEquiv_apply_coe, Complex.normSq_zero, HahnSeries.coeff_single_of_ne, Polynomial.rootMultiplicity_C, Algebra.Generators.cotangentCompAwaySec_apply, LieModule.trace_comp_toEnd_genWeightSpace_eq, Equiv.optionEquivSumPUnit_none, MonoidHom.coe_mker, MvPolynomial.monomial_mem_coeffsIn, SimpleGraph.ConnectedComponent.toSimpleGraph_hom_apply, MonomialOrder.toSyn_monotone, ContinuousLinearMap.differentiableAt, ContinuousLinearMap.sub_apply, BoundedContinuousFunction.neg_apply, RelIso.symm_symm_apply, PrincipalSeg.transInitial_top, ArithmeticFunction.sigma_eq_prod_primeFactors_sum_range_factorization_pow_mul, eventually_nhdsWithin_sign_eq_of_deriv_pos, LinearMap.nondegenerate_congr_iff, SimpleGraph.Hom.comap_apply, PresentedGroup.mk_eq_mk_of_inv_mul_mem, Polynomial.eq_prod_roots_of_splits_id, RCLike.wInner_const_left, Valuation.Integers.dvdNotUnit_iff_lt, Rep.coindResAdjunction_homEquiv_apply, RelHomClass.map_sup, AbsoluteValue.pos_iff, ContinuousMap.continuous_iff_continuous_uniformFun, CliffordAlgebra.involute_eq_of_mem_even, Matrix.sum_cramer_apply, TensorProduct.gradedMul_one, SimpleGraph.Walk.IsHamiltonian.supportGetEquiv_apply, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_apply, ProbabilityTheory.covarianceBilinDual_self_eq_variance, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_obj_some, PartOrdEmb.coe_comp, Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff, RatFunc.laurentAux_algebraMap, AlgebraicGeometry.LocallyRingedSpace.GlueData.ι_jointly_surjective, RCLike.wInner_cWeight_const_left, EsakiaHom.coe_id, MvPolynomial.coe_eval₂Hom, Matroid.mapEquiv_ground_eq, MvPowerSeries.coeff_trunc', LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply, CliffordAlgebra.contractLeft_comm, DirectSum.ext_component_iff, MonoidHom.coe_comp_rangeRestrict, BialgHom.ofAlgHom_apply, SimpleGraph.cliqueFinset_map, CompactlySupportedContinuousMap.integralLinearMap_apply, AddMonoidAlgebra.lift_single, UniformEquiv.finTwoArrow_symm_apply, HeytAlg.comp_apply, MulEquiv.ext_iff, Finsupp.Colex.le_iff_of_unique, MvPolynomial.vars_C_mul, ModuleCat.FreeMonoidal.εIso_inv_freeMk, Polynomial.coeff_C, Equiv.Perm.IsCycleOn.range_pow, PowerSeries.sub_const_eq_shift_mul_X, Module.End.smulLeft_apply, tangentBundle_model_space_coe_chartAt_symm, Padic.valuation_p_lt_one, CategoryTheory.PreZeroHypercover.interSnd_h₀, Circle.exp_add, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Path.Homotopy.trans_apply, Equiv.coe_piCongr', Finsupp.Lex.le_iff_of_unique, Topology.WithUpperSet.ofUpperSet_le_iff, ProbabilityTheory.uniformOn_eq_one_of, geometric_hahn_banach_open_open, SemidirectProduct.inl_aut_inv, Finsupp.coe_update, CategoryTheory.conjugateEquiv_symm_comp, ZMod.invDFT_apply', iteratedFDerivWithin_succ_apply_left, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, CircleDeg1Lift.coe_mul, AdjoinRoot.modByMonicHom_mk, MeasureTheory.eLpNorm_indicator_const_le, inner_self_eq_norm_mul_norm, Affine.Simplex.range_faceOpposite_reindex, WithTop.toDual_apply_top, coe_equiv_lpPiLp, hasStrictFDerivAt_norm_sq, Ideal.Filtration.submodule_span_single, EquivLike.inv_apply_eq, AddSubgroupClass.inclusion_mk, QuadraticAlgebra.coe_norm_eq_mul_star, Matrix.traceLinearMap_apply, OrderMonoidWithZeroHom.ext_iff, ProbabilityTheory.condExpKernel_singleton_ae_eq_cond, SpecialLinearGroup.coe_mul, FractionalIdeal.mem_dual, Submodule.starProjection_unit_singleton, Affine.Simplex.altitudeFoot_reindex, BooleanSubalgebra.latticeClosure_subset_closure, Matrix.dualNumberEquiv_symm_apply, AddSubmonoid.inclusion_inj, Monoid.Coprod.snd_swap, Subsemigroup.coe_comap, Finset.weightedVSub_const_smul, LinearMap.toMatrix'_mul, SmoothPartitionOfUnity.coe_finsupport, qExpansion_sub, SchwartzMap.fourier_evalCLM_eq, DFinsupp.erase_def, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, MeasureTheory.SimpleFunc.inv_apply, AddSubgroup.toZModSubmodule_symm, finSumFinEquiv_symm_last, LinearIsometryEquiv.ofTop_apply, isFoelner_iff, SlashInvariantForm.coe_prod, GradedTensorProduct.includeRight_apply, RingNorm.toFun_eq_coe, LieHom.range_eq_top, LinearIsometryEquiv.comp_differentiableWithinAt_iff, MvPowerSeries.coeff_zero_mul_X, groupHomology.isoCycles₂_hom_comp_i_apply, Con.rel_eq_coe, PrincipalSeg.relIsoTrans_apply, PowerSeries.coe_divXPowOrderHom, tangentBundleModelSpaceHomeomorph_coe, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv, map_comp_add, FreeMonoid.ofList_cons, Subgroup.mem_ofUnits_iff_toUnits_mem, LinearMap.coe_compMultilinearMap, Algebra.trace_self_apply, NonUnitalAlgHom.inl_apply, infsInfHom_apply, IsometryEquiv.bijective, Matrix.cons_mul, Algebra.intNorm_eq_of_isLocalization, LinearMap.adjoint_toSpanSingleton, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀, MulOpposite.opEquiv_symm_apply, Module.End.lie_apply, LinearMap.lcomp_apply', CliffordAlgebra.ofBaseChange_tmul_ι, mul_basis_toMatrix, UniformFun.toFun_div, MeasureTheory.Measure.measure_toMeasurable_inter_of_cover, Algebra.Generators.toAlgHom_ofComp_rename, RingCon.ofMatrix_rel', AddCommGrpCat.int_hom_ext_iff, DirectSum.decompose_algebraMap, Valuation.Integers.valuation_unit, OrthonormalBasis.coe_toBasis, DifferentiableOn.continuousMultilinear_apply_const, NNReal.agm_eq_agm_gm_am, Polynomial.natDegree_X_sub_C, AddMonoidAlgebra.mapDomainAlgHom_apply, MonCat.coe_comp, convex_convexHull, SlashInvariantForm.coe_natCast, Monoid.CoprodI.Word.mem_equivPair_tail_iff, Iic_orderDual_def, SupHom.symm_dual_id, ofBoolAlg_symmDiff, MeasureTheory.prob_compl_eq_zero_iff, IsLocalization.localization_localization_map_units, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, LinearMap.GeneralLinearGroup.congrLinearEquiv_apply, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, IsLocalization.Away.mul_invSelf, WeierstrassCurve.Affine.CoordinateRing.mk_φ, ContinuousAlgEquiv.trans_apply, Behrend.map_succ', UniformOnFun.ofFun_sub, Affine.Simplex.affineCombination_eq_touchpoint_iff, Emetric.exists_contMDiffMap_forall_closedBall_subset, SubAddAction.ofFixingAddSubgroup_of_eq_apply, Finsupp.linearCombination_embDomain, Valuation.IsEquiv.lt_iff_lt, starL_symm_apply, BoundedContinuousFunction.coeFnAddMonoidHom_apply, SchwartzMap.contDiffAt, MulEquiv.inv'_symm_apply, AddMonoidHom.coe_toMultiplicative', LieEquiv.apply_symm_apply, Equiv.image_eq_preimage, LinearEquiv.image_eq_preimage_symm, wittStructureRat_rec_aux, Polynomial.Bivariate.equivMvPolynomial_symm_X_1, GroupSeminorm.coe_zero, AddSubgroup.apply_coe_mem_map, LinearMap.BilinForm.dualSubmodule_dualSubmodule_of_basis, CategoryTheory.Sheaf.ΓObjEquivHom_naturality_symm, CliffordAlgebra.reverse_reverse, RootPairing.IsRootSystem.span_root_eq_top, AddSubmonoid.LocalizationMap.add_mk'_eq_mk'_of_add, Poly.coe_add, ProbabilityTheory.Kernel.coe_mk, Equiv.subLeft_symm_apply, WittVector.fontaineThetaModPPow_teichmuller, MeasureTheory.exists_pos_ball, RingEquiv.ofNonUnitalRingHom_apply, Polynomial.iterate_derivative_X_pow_eq_smul, Valuation.map_mul, AddEquiv.coprodAssoc_apply_inl_inr, TopCat.Presheaf.isLocallySurjective_iff, AbsoluteValue.IsEquiv.le_iff_le, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, Subring.topEquiv_symm_apply_coe, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, starMulEquiv_apply, MonoidHom.op_symm_apply_apply, SetSemiring.one_def, Units.toAut_hom, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto', Module.dualProdDualEquivDual_apply_apply, ContinuousMap.sigmaMk_apply, OrderHom.le_lfp, RootPairing.Equiv.comp_indexEquiv_symm_apply, WeierstrassCurve.Projective.eval_polynomialZ, MvPowerSeries.coeff_inv_aux, AddEquiv.coprodCongr_apply, OrderIso.surjective, trace_eq_sum_roots, Matrix.matPolyEquiv_charmatrix, DilationEquiv.mulRight_apply, map_isIntegral_int, IndexedPartition.equivQuotient_index_apply, DFinsupp.zsmul_apply, Equiv.ofInjective_symm_apply, AlgebraicGeometry.range_eq_univ, Algebra.TensorProduct.rid_tmul, Equiv.subtypeEquivRight_symm_apply_coe, WittVector.verschiebung_coeff_zero, RootPairing.zero_le_posForm, AddCommGrpCat.Colimits.Quot.desc_toCocone_desc_app, LinearMap.injective_iff_surjective, Cardinal.toNat_lift, WeierstrassCurve.Jacobian.Point.toAffineAddEquiv_apply, Polynomial.natDegree_C_mul, DFinsupp.toMultiset_toDFinsupp, Submodule.quotientPi_apply, OneHom.one_apply, HahnSeries.cardSupp_mul_single_le, NumberField.canonicalEmbedding.nnnorm_eq, GrpCat.coe_comp, CompactExhaustion.isCompact, CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero, MeasureTheory.measure_union_add_inter₀', PowerBasis.mem_span_pow, Equiv.Perm.zpow_apply_mem_support, Additive.ofMul_le, Submodule.rTensorOne_tmul, iterate_map_add, Algebra.Generators.ker_localizationAway, Polynomial.card_support_eq_three, Polynomial.linearIndependent_powers_iff_aeval, Polynomial.aeval_def, Subgroup.mem_comap, RatFunc.algebraMap_apply_div, CommMonCat.coe_id, nnnorm_toDual, CategoryTheory.Subfunctor.orderIsoSubobject_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, Polynomial.Chebyshev.derivative_U_eval_one, SimpleGraph.map_symm, algebraMap_memℓp_infty, Function.piCongrLeft'_update, NumberField.FinitePlace.mulSupport_finite_int, MeasureTheory.mem_ae_iff_prob_eq_one, ContMDiffMap.coe_pow, galLiftEquiv_symm_apply, FractionalIdeal.mem_coeIdeal_of_mem, BiheytingHom.coe_id, Finsupp.DegLex.lt_iff, convexHull_sum, CategoryTheory.tensorRightHomEquiv_naturality, ContinuousMap.tendsto_iff_tendstoUniformly, spectrum.mem_resolventSet_iff, LinearMap.BilinForm.sub_apply, IsLocalizedModule.rTensor, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, LinearIsometryEquiv.withLpProdCongr_symm_apply, Equiv.piCongrLeft_sumInl, AlgebraicGeometry.Scheme.Hom.comp_apply, equivTangentBundleProd_symm_apply_snd, ContinuousLinearEquiv.analyticOn, RatFunc.div_smul, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, CircleDeg1Lift.translate_apply, Valuation.ofAddValuation_toAddValuation, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, SchwartzMap.hasFDerivAt, Traversable.foldl.unop_ofFreeMonoid, LinearEquiv.conj_symm_conj, ProbabilityTheory.Kernel.iIndepFun.measure_inter_preimage_eq_mul, ENat.toNatHom_apply, LinearMap.toSpanSingleton_apply, MonomialOrder.degLex_single_le_iff, MvPolynomial.constantCoeff_smul, Function.updateFinset_updateFinset, ContinuousLinearMap.map_sub₂, QuasispectrumRestricts.real_iff, CommRing.Pic.mapAlgebra_self_apply, Polynomial.aeval_mul, BiheytingHom.toFun_eq_coe, HahnSeries.C_zero, exists_orthonormalBasis, ContinuousLinearMap.bilinearComp_apply, MeasureTheory.measure_mul_laverage, MvPolynomial.totalDegree_expand, SheafOfModules.pushforwardCongr_inv_app_val_app, RingCon.coe_comapQuotientEquivRange_mk, MulEquiv.equivLike_inv_eq_symm, AlgHom.map_adjoin, IntermediateField.algebraMap_apply, killingForm_apply_apply, CocompactMap.coe_toContinuousMap, MeasureTheory.sum_measure_preimage_singleton, HahnSeries.addVal_apply_of_ne, SemiNormedGrp₁.mkHom_apply, MvPolynomial.algHom_C, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Equiv.option_symm_apply_none_iff, Submodule.reflection_sub, AddSubgroup.topEquiv_symm_apply_coe, Matrix.SpecialLinearGroup.toGL_injective, CategoryTheory.Groupoid.vertexGroupIsomOfMap_apply, LieDerivation.lie_apply, LinearMap.trace_id, LinearMap.toMatrix_algebraMap, SpectralMap.ext_iff, Frm.coe_id, MeasureTheory.Measure.toSphere_apply', IsAlgClosure.equivOfEquiv_symm_algebraMap, AlgEquiv.coe_ringEquiv, LinearEquiv.coe_curry_symm, ContinuousMap.exists_mem_subalgebra_near_continuous_of_isCompact_of_separatesPoints, Algebra.trace_trace, LinearMap.spectrum_toMatrix, AdicCompletion.ofAlgEquiv_apply, CategoryTheory.Abelian.Ext.homAddEquiv_apply, MvPolynomial.leadingCoeff_toLex_C, MeasureTheory.Measure.comap_apply₀, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, IsConjRoot.exists_algEquiv, sSupHom.coe_id, Polynomial.monomial_one_eq_iff, LaurentPolynomial.leval_apply, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, NonUnitalSubring.mem_map, AddLocalization.zero_rel, Equiv.smul_def, Ideal.Quotient.factor_surjective, AddMonoidAlgebra.lift_symm_apply, MulAut.conj_apply, MeasureTheory.ae_eq_univ_iff_measure_eq, Nonneg.unitsHomeomorphPos_apply_coe, AddMonoid.Coprod.swap_map, Polynomial.resultant_X_sub_C_pow_right, Dilation.isUniformInducing, RCLike.inner_apply, IsSelfAdjoint.conj_eq, StandardEtalePresentation.toSubmersivePresentation_jacobian, MeasureTheory.Measure.volume_subtype_coe_le_volume, SchwartzMap.evalCLM_apply_apply, Real.volume_Icc, AffineIsometry.map_eq_iff, LieSubalgebra.mem_engel_iff, WittVector.iterate_frobenius_coeff, CategoryTheory.Discrete.monoidalFunctor_ε, ProbabilityTheory.Kernel.lintegral_prod, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, Polynomial.smeval_C_mul, CategoryTheory.coherentTopology.mem_sieves_iff_hasEffectiveEpiFamily, IsBaseChange.equiv_symm_apply, Algebra.norm_eq_norm_adjoin, Algebra.IsAlgebraic.algHom_bijective₂, Function.Exact.inr_fst, Finsupp.comapDomain_apply, ArchimedeanClass.map_mk_eq, RootPairing.coroot_eq_neg_iff, TensorProduct.congr_symm_tmul, Ideal.idealProdEquiv_symm_apply, Complex.conj_cpow_eq_ite, toColex_smul, LinearIsometry.injective, wittStructureInt_prop, Fin.orderIsoSubtype_apply, Orientation.rotation_eq_self_iff_angle_eq_zero, SkewMonoidAlgebra.toFinsuppAddEquiv_symm_apply, LinearMap.SeparatingRight.toMatrix₂, OrdinalApprox.gfpApprox_ord_eq_gfp, OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective, Matrix.one_submatrix_mul, PerfectionMap.map_map, MvPowerSeries.coeff_weightedHomogeneousComponent, Polynomial.X_sub_C_dvd_sub_C_eval, FinPartOrd.dual_map, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ContinuousMap.coe_equivFnOfDiscrete, Dilation.toFun_eq_coe, AbsoluteValue.IsEquiv.log_div_log_pos, UpperSet.coe_icisSupHom, ContinuousLinearMap.coe_pow, AlgebraicGeometry.Scheme.Hom.isOpenEmbedding, NonUnitalRingHom.coe_range, LightProfinite.surjective_transitionMapLE, Polynomial.expand_eq_zero, Matrix.map_single, TopCat.pullbackIsoProdSubtype_inv_fst, OrderHom.canLift, Finsupp.support_eq_singleton, Set.preimage_nsmul_subset, SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_image, IsSelfAdjoint.sq_spectrumRestricts, MvPolynomial.eval_pow, Height.mulHeight_eq, CompleteLat.dual_map, WithBot.map_add, Matrix.isUnit_toLin_iff, Polynomial.degreeLT.addLinearEquiv_apply', MvPowerSeries.order_le, OrderRingHom.toFun_eq_coe, AddChar.expect_eq_zero_iff_ne_zero, ProbabilityTheory.IdentDistrib.measure_preimage_eq, QuadraticAlgebra.algebraMap_eq, RootPairing.InvariantForm.apply_weylGroup_smul, Algebra.discr_of_matrix_vecMul, Algebra.TensorProduct.cancelBaseChange_tmul, Equiv.Perm.coe_inv, Convex.linear_image, MeasureTheory.Measure.compl_support_eq_sUnion, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, ContMDiffWithinAt.clm_bundle_apply₂, NumberField.FinitePlace.coe_apply, Finsupp.mul_apply, RingCon.coe_quotientKerEquivRangeS_mk, SimpleGraph.Walk.IsHamiltonian.supportGetEquiv_symm_apply_val, Matrix.uniqueLinearEquiv_apply, MeasureTheory.StronglyMeasurable.integral_condExpKernel', Representation.ofMulActionSelfAsModuleEquiv_apply, WeierstrassCurve.Ψ_three, Submodule.singleton_smul, Polynomial.differentiableAt_aeval, toColex_vadd', ProbabilityTheory.condDistrib_snd_prod, StarMonoidHom.comp_apply, IsFoelner.tendsto_meas_smul_symmDiff_smul, AddEquiv.apply_symm_apply, Subspace.quotAnnihilatorEquiv_apply, MulEquiv.op_apply_apply, RootPairing.IsReduced.linearIndependent, LinearMap.conjugate_apply, Equiv.Perm.Basis.toPermHom_apply_toCentralizer, circleEquivGen_symm_apply, Equiv.Perm.apply_pow_apply_eq_iff, NonUnitalAlgHom.ext_iff, PowerSeries.derivative_invOf, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, isBounded_convexHull, MeasureTheory.Measure.toTemperedDistribution_apply, Finsupp.mapDomain_apply, Quiver.Hom.opEquiv_symm_apply, InfHom.withTop_toFun, Unitary.conjStarAlgAut_apply, Matrix.reindex_updateRow, ContMDiffMap.mdifferentiable', IsPrimitiveRoot.norm_toInteger_sub_one_eq_one, NNReal.le_gm_and_am_le, Subsemiring.comap_toSubmonoid, Polynomial.prime_X_sub_C, SimpleGraph.isVertexCover_image_iso, MonoidHom.restrict_eq_one_iff, InfTopHom.dual_comp, ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply, WeakDual.CharacterSpace.compContinuousMap_apply, Submodule.unitsToPic_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, PowerSeries.HasSubst.monomial', map_prod, CategoryTheory.tensorRightHomEquiv_tensor, ContinuousAlgHom.continuous, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, lipschitzOnWith_cfcₙ_fun, maximal_toDual, LocallyConstant.evalAddMonoidHom_apply, CircleDeg1Lift.translationNumber_le_ceil_sub, Submodule.orderIsoMapComap_symm_apply', LocallyConstant.apply_eq_of_preconnectedSpace, ProbabilityTheory.Kernel.setIntegral_densityProcess, BoxIntegral.Box.Icc_def, RestrictedProduct.topologicalSpace_eq_of_principal, ContinuousMultilinearMap.compContinuousLinearMap_apply, AddOreLocalization.numeratorHom_apply, Affine.Simplex.circumcenter_restrict, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, iterateFrobeniusEquiv_one_apply, Matrix.Module.scalar_smul, Ideal.spanNorm_eq, Matrix.diagonal_toLin', LinearMap.re_inner_adjoint_mul_self_nonneg, RootPairing.root_eq_neg_iff, ContMDiffMap.coe_zero, PointwiseConvergenceCLM.coeLM_apply, Subgroup.quotientiInfSubgroupOfEmbedding_apply_mk, TensorPower.mul_one, NNReal.continuous_sqrt, DomAddAct.vadd_aeeqFun_aeeq, ContinuousAlternatingMap.prod_apply, Diffeomorph.contDiff, NonUnitalSubalgebra.coe_comap, Hamming.toHamming_smul, IntermediateField.LinearDisjoint.norm_algebraMap, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, NatOrdinal.toOrdinal_natCast, RelEmbedding.coe_trans, SimplexCategory.II.map'_eq_last_iff, PMF.pure_apply_of_ne, CategoryTheory.ConcreteCategory.congr_arg, CategoryTheory.Localization.SmallShiftedHom.equiv_chgUniv, MvPolynomial.eval₂Hom_zero'_apply, CStarMatrix.toCLM_apply, CentroidHom.add_apply, MonoidAlgebra.liftNC_single, DirichletCharacter.modOne_eq_one, Representation.IsIrreducible.injective_or_eq_zero, Polynomial.coeff_monomial_zero_mul, DirichletCharacter.convolution_twist_vonMangoldt, CoalgEquiv.ext_iff, CategoryTheory.Subfunctor.range_eq_ofSection', PowerSeries.coe_zero, FractionalIdeal.exists_mem_algebraMap_eq, AddEquiv.symm_map_add, ContinuousAlternatingMap.pi_apply, ContinuousLinearEquiv.hasFDerivWithinAt, Module.End.mem_genEigenspace_top, Submodule.coe_mulMap_comp_eq, FractionalIdeal.absNorm_eq, Orientation.oangle_rotation_right, Polynomial.eval₂_def, Affine.Simplex.height_restrict, Valued.closure_coe_completion_v_lt, EquivLike.inv_apply_apply, QuadraticMap.map_finsuppSum', AddLocalization.addEquivOfQuotient_apply, rothNumberNat_isLittleO_id, Con.sSup_eq_conGen, QuotientGroup.kerLift_injective, Bialgebra.counit_natCast, exists_bounded_mem_Icc_of_closed_of_le, Action.leftRegularTensorIso_hom_hom, Equiv.Perm.IsCycle.cycleOf, DoubleCentralizer.algebraMap_toProd, QuotientAddGroup.quotientAddEquivOfEq_mk, SimpleGraph.Coloring.injective_comp_of_pairwise_adj, CompleteSublattice.subtype_injective, MeasureTheory.Integrable.re_im_iff, image_vadd_set, BotHom.coe_bot, exteriorPower.oneEquiv_symm_apply, CategoryTheory.Limits.WalkingPair.swap_symm_apply_tt, SeparationQuotient.mk_outCLM, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, TensorProduct.AlgebraTensorModule.curry_apply, ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib, NonUnitalStarAlgHom.coe_zero, RootPairing.Base.linearIndepOn_root, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, RCLike.normSq_mul, LinearMap.isPositive_self_comp_adjoint, Hamming.toHamming_add, NonUnitalStarAlgHom.prodEquiv_apply, QuadraticForm.tensorLId_symm_apply, IsUniformGroup.comap, smoothLeftMul_one, AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjective, CoalgHom.coe_coe, AlgebraicGeometry.Spec.map_apply, RatFunc.eval_C, Algebra.TensorProduct.mul_one, RingEquiv.idealComapOrderIso_symm_apply, isIntegral_algEquiv, DistribMulActionHom.coe_one, sign_mul, RingTheory.Sequence.isWeaklyRegular_append_iff', MulHom.isClosed_range_coe, IsAdjoinRootMonic.ext_elem_iff, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, Matrix.charpoly_toLin', ArithmeticFunction.IsMultiplicative.map_one, FreeAddMagma.lift_comp_of', Quaternion.fst_imI_dualNumberEquiv_symm, RCLike.hasSum_conj, IsometryEquiv.piFinTwo_symm_apply, BoundedLatticeHom.symm_dual_id, CategoryTheory.Subfunctor.IsGeneratedBy.of_equiv, Finsupp.degLex_def, Valued.valuation_isClosedMap, RestrictedProduct.vadd_apply, uliftMultiplesHom_apply_apply, Path.inv_apply, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, Multiset.cast_apply_fst, QuadraticMap.sq_apply, NonUnitalRingHom.zero_apply, LinearIsometry.map_neg, Lagrange.iterate_derivative_interpolate, PowerSeries.map_X, starₗᵢ_apply, Module.End.injOn_genEigenspace, FirstOrder.Language.ElementaryEmbedding.coe_injective, FormalMultilinearSeries.id_comp, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, Finset.mem_convexHull, CategoryTheory.Functor.RepresentableBy.equivOfIsoObj_apply, RingHom.injective, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_add, LieSubmodule.coe_inclusion, Polynomial.taylorAlgHom_apply, OrderEmbedding.preimage_uIcc, ContinuousLinearMap.norm_map_tail_le, Codisjoint.map_orderIso, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, MulEquiv.toFun_eq_coe, WeierstrassCurve.Projective.map_addY, CommRingCat.Colimits.cocone_naturality_components, NonarchAddGroupNorm.le_def, IsDiscreteValuationRing.addVal_mul, AlgebraicGeometry.pointOfClosedPoint_apply, MulEquiv.uniqueProd_symm_apply, Finsupp.univ_sum_single_apply, Representation.norm_comp_self, Matrix.toLinearMap₂'_toMatrix', SheafOfModules.conjugateEquiv_pullbackComp_inv, isSMulRegular_algebraMap_iff, Polynomial.pow_sub_dvd_iterate_derivative_pow, RootPairing.Base.toCoweightBasis_apply, MonoidHom.ext_iff, ProbabilityTheory.condExp_ae_eq_integral_condExpKernel', OrderHom.isFixedPt_lfp, IsDiscreteValuationRing.addVal_add, MeasureTheory.OuterMeasure.coe_fn_injective, iterateFrobenius_def, AddSubmonoid.mem_subPairs, MulEquiv.multiplicativeAdditive_apply, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two', PiTensorProduct.ofFinsuppEquiv_apply, OpenPartialHomeomorph.toHomeomorphOfSourceEqUnivTargetEqUniv_apply, Subalgebra.inclusion_mk, Submonoid.centerCongr_symm_apply_coe, ProbabilityTheory.IndepFun.meas_inter, AffineSubspace.WSameSide.map, Fin.snocOrderIso_symm_apply, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, ArithmeticFunction.sum_Ioc_zeta, ContinuousMulEquiv.apply_symm_apply, MeasureTheory.measure_le_measure_closure_of_levyProkhorovEDist_eq_zero, SemilinearIsometryClass.antilipschitz, AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding, Filter.Germ.coe_coeAddHom, Metric.exists_contMDiffMap_forall_closedBall_subset, SetTheory.PGame.equiv_nim_grundyValue, ContinuousAffineMap.map_vadd, RingCon.kerLiftₐ_injective, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, summable_dirichletSummand, ContinuousMap.compAddMonoidHom'_apply, Additive.toMul_bot, Finsupp.equivFunOnFinite_symm_coe, CentroidHom.id_apply, MeasureTheory.StronglyMeasurable.integral_condDistrib, AddEquiv.addMonoidHomCongrRightEquiv_symm_apply, ContinuousMultilinearMap.map_coord_zero, Continuous.coeFun, finSumFinEquiv_symm_apply_natAdd, Metric.Snowflaking.ofSnowflaking_toSnowflaking, Delone.DeloneSet.mapIsometry_refl, Cardinal.toNat_eq_one, Submodule.isIdempotentElemEquiv_apply_coe, MulHom.mem_srange, powCoprime_apply, MeasureTheory.boundedBy_measure, Equiv.Perm.IsCycleOn.apply_mem_iff, LinearEquiv.piCongrLeft'_symm_apply, NumberField.mixedEmbedding.norm_nonneg, BooleanSubalgebra.closure_latticeClosure, UniformSpace.Completion.algebraMap_def, CocompactMapClass.cocompact_tendsto, parallelepiped_basis_eq, nndist_lineMap_right, Matrix.toLinearMapₛₗ₂'_apply, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, monotone_iff_map_nonpos, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, CommAlgCat.hom_inv_apply, InfHom.coe_mk, Polynomial.hasFDerivAt_aeval, CategoryTheory.Functor.coe_mapAddHom, OrderIso.coe_prodComm, continuous_cfcHomSuperset_left, PrimeSpectrum.isIdempotentElemEquivClopens_symm_sup, ContinuousLinearEquiv.comp_continuousOn_iff, OrderHomClass.monotone, convexHull_neg, TensorProduct.finsuppScalarRight_symm_apply_single, IntermediateField.adjoin.range_algebraMap_subset, ArithmeticFunction.sum_Ioc_mul_eq_sum_prod_filter, ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smul, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, ContinuousMap.sum_apply, List.sortedLE_map_toDual, ContinuousMap.Homotopy.trans_apply, PolynomialModule.eval_lsingle, AddChar.toAddMonoidHomEquiv_symm_apply, MulEquiv.monoidHomCongrRightEquiv_apply, IsAdjoinRoot.lift_map, multiplicity_map_eq, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, SymAlg.unsym_smul, ArithmeticFunction.one_one, PMF.toOuterMeasure_uniformOfFinset_apply, Ideal.relNorm_algebraMap, OrderHom.coe_mk, Finsupp.lt_def, EisensteinSeries.vecMul_SL2_mem_gammaSet, MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint, AddHom.comp_apply, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply, Equiv.Perm.ofSubtype_apply_of_mem, IsLocalizedModule.map_apply, Polynomial.C_sub, Subalgebra.inclusion_injective, Homeomorph.onePointCongr_symm_apply, sSupHom.continuous, DFinsupp.coe_smul, CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, ContinuousLinearMap.compContinuousAlternatingMap_coe, LinearEquiv.submoduleMap_apply, AbsoluteValue.map_units_int_smul, ContinuousMap.HomotopyRel.symm_apply, Equiv.preimage_subset, ContinuousLinearMap.compContinuousMultilinearMap_coe, Module.End.genEigenspace_one, ContinuousLinearEquiv.ofSubmodule'_apply, MeasureTheory.AEEqFun.toGermMonoidHom_apply, exists_dual_vector'', AffineEquiv.equivUnitsAffineMap_symm_apply_apply, HasFDerivAt.continuousAlternatingMap_apply_const, RelEmbedding.map_rel_iff, Submodule.spanSingleton_apply, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, AlgebraicGeometry.Scheme.Hom.isEmbedding, ModuleCat.free_η_freeMk, FirstOrder.Language.BoundedFormula.realize_relabelEquiv, Int.padicValuation_self, Matrix.BlockTriangular.comp, Module.Flat.iff_lTensor_injective, AlgebraicGeometry.sigmaι_eq_iff, Equiv.finsuppUnique_symm_apply_apply, Matrix.toLin'_pow, BoundedContinuousFunction.continuous_coe, RootPairing.IsOrthogonal.reflection_apply_right, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, LinearMap.pi_ext_iff, DFinsupp.coe_neLocus, ProbabilityTheory.Kernel.ext_iff', MeasureTheory.inducedOuterMeasure_eq_iInf, LaurentPolynomial.single_eq_C, PiTensorProduct.injectiveSeminorm_apply, Homeomorph.unitBall_apply_coe, FirstOrder.Language.Substructure.reduct_withConstants, convexIndependent_set_iff_notMem_convexHull_diff, OrthogonalIdempotents.surjective_pi, Polynomial.algEquivOfCompEqX_symm_apply, PartitionOfUnity.sum_finsupport_smul_eq_finsum, Polynomial.roots_X_pow_char_sub_C_pow, Function.FromTypes.uncurry_two_eq_uncurry, LinearMap.range_eq_top, OrderHom.gfp_gfp, FormalMultilinearSeries.compContinuousLinearMap_applyComposition, CategoryTheory.discreteEquiv_symm_apply_as, LeftInvariantDerivation.map_add, AddCommGrpCat.epi_iff_surjective, MeasureTheory.Measure.setLIntegral_condKernel, StieltjesFunction.measure_Ioi, IsNilpotent.map, Module.Basis.mem_span_image, Finsupp.mapRange_add', AddEquiv.toMultiplicative_apply_apply, RingHom.mem_rangeS, IsSymmetricAlgebra.equiv_symm_apply, Order.IsPredLimit.dual, Valued.closure_coe_completion_v_mul_v_lt, LinearIsometryEquiv.toLinearEquiv_smul, MeasureTheory.MemLp.continuousLinearMap_comp, OrderIso.divRight_apply, ContinuousOn.coeFun, Sym.mem_cast, PrimeSpectrum.discreteTopology_iff_toPiLocalization_surjective, ProbabilityTheory.IsGaussian.memLp_dual, MeasureTheory.Measure.coe_smul, RingHom.rangeS_top_iff_surjective, Encodable.decode_ofEquiv, RingHom.SurjectiveOnStalks.residueFieldMap_bijective, LieModule.Cohomology.mem_twoCocycle_iff, Metric.Snowflaking.image_toSnowflaking_eq_preimage, normalize_coe_units, WeierstrassCurve.Affine.Point.map_baseChange, Topology.IsGeneratedBy.equiv_symm_comp_continuous_iff, Complex.normSq_conj, IsometryEquiv.hausdorffMeasure_preimage, CliffordAlgebra.ofBaseChangeAux_ι, Ideal.ker_tensorProductMk_quotient, Path.refl_apply, MeasureTheory.Measure.compProd_eq_comp_prod, MvPowerSeries.coeff_apply, Unitary.toAlgEquiv_conjStarAlgAut, Finsupp.sumFinsuppAddEquivProdFinsupp_apply, MonoidHom.coe_ofClosureMEqTopLeft, Valuation.HasExtension.val_algebraMap, WeierstrassCurve.VariableChange.map_t, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_of_eq, Unitization.lift_range, LieModuleEquiv.trans_apply, Finset.affineCombination_apply, Equiv.Perm.sign_mul, thickenedIndicator_tendsto_indicator_closure, NonemptyInterval.map_snd, StarMulEquiv.ofStarMonoidHom_apply, DividedPowers.DPMorphism.toRingHom_apply, Subfield.coe_subtype, Complex.continuous_normSq, DomAddAct.vadd_Lp_ae_eq, ContinuousAffineEquiv.coe_refl, FintypeCat.equivEquivIso_symm_apply_apply, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Sym2.coe_lift_symm_apply, LinearMap.BilinForm.SeparatingLeft.toMatrix, BoundedContinuousFunction.const_apply', LinearEquiv.rTensor_symm_tmul, Polynomial.aeval_eq_prod_aroots_sub_of_monic_of_splits, Algebra.inf_toSubmodule, AddAction.IsBlock.of_addSubgroup_of_conjugate, OmegaCompletePartialOrder.ContinuousHom.ofFun_apply, Bialgebra.comul_mul, Derivation.liftKaehlerDifferential_unique_iff, Finset.mapRange_finsuppAntidiag_subset, MeasureTheory.ProbabilityMeasure.continuous_lintegral_continuousMap, MvPolynomial.derivation_C, ProbabilityTheory.covarianceBilinDual_self_nonneg, AddEquiv.equivLike_neg_eq_symm, stdSimplex.ext_iff, AlgebraicGeometry.IsOpenImmersion.opensEquiv_symm_apply, MeasureTheory.measurePreserving_piFinSuccAbove, Valued.valuedCompletion_apply, conformalFactorAt_inner_eq_mul_inner', InfiniteGalois.limitToAlgEquiv_apply, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, MvPolynomial.mem_support_coeff_optionEquivLeft, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, BoxIntegral.Box.isBounded_Icc, HahnSeries.coeff_truncLT_of_le, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, Function.Embedding.refl_apply, AlgHom.compLeft_apply, RootPairing.Hom.indexEquiv_mul, PowerSeries.constantCoeff_divXPowOrder, MeasureTheory.measure_iUnion, HahnSeries.toPowerSeriesAlg_apply, PrincipalSeg.cocone_pt, AffineMap.linear_surjective_iff, AffineEquiv.coe_one, Path.range_segment, MeasureTheory.AEDisjoint.eq, Finsupp.lex_lt_iff_of_unique, LinearIsometryEquiv.analyticOn, MeasureTheory.measure_compl₀, MultilinearMap.cons_add, Polynomial.Bivariate.swap_C_C, Module.Basis.localizationLocalization_repr_algebraMap, LocallyConstant.comapₗ_apply_apply, Ideal.Quotient.eq_zero_iff_mem, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, SimpleGraph.TripartiteFromTriangles.toTriangle_is3Clique, CStarMatrix.smul_of, RatFunc.liftRingHom_apply_div, AffineSubspace.subtype_injective, TensorProduct.AlgebraTensorModule.mapBilinear_apply, LieHom.coe_comp, RelIso.IsWellOrder.preimage, ValuationSubring.algebraMap_apply, LinearMap.BilinMap.toQuadraticMapLinearMap_apply, MeasureTheory.FiniteMeasure.prod_apply, TemperedDistribution.fourier_lineDerivOp_eq, LinearIsometryEquiv.analyticAt, AdjoinRoot.liftAlgHom_mk, convexHull_sphere_eq_closedBall, SemimoduleCat.MonoidalCategory.braiding_hom_apply, Matrix.toLinAlgEquiv'_apply, groupHomology.inhomogeneousChains.d_single, IsometryEquiv.sumArrowIsometryEquivProdArrow_symm_apply, PowerSeries.monomial_eq_mk, IsLocalRing.ResidueField.map_id_apply, ModularForm.coe_eq_zero_iff, Complex.equivRealProdLm_symm_apply, ContDiffPointwiseHolderAt.clm_apply, Matrix.l2_opNNNorm_def, Polynomial.natDegree_derivative_le, ContinuousAffineEquiv.surjective, RestrictedProduct.inv_apply, norm_lt_iff_of_compactlySupported, PMF.apply_lt_top, ContinuousLinearEquiv.strictConvex_image, GroupExtension.Equiv.rightHom_comm, isOpen_deltaGenerated_iff, TensorProduct.piRightHom_tmul, cfcₙHom_isClosedEmbedding, map_lt_map_iff, Subsemiring.opEquiv_symm_apply, NonarchAddGroupSeminorm.smul_apply, UniformFun.dist_le, ProbabilityTheory.Kernel.integral_densityProcess, RelHom.coe_one, MeasureTheory.charFunDual_map_const_add, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, LinearMap.lTensor_comm, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure, CategoryTheory.Equivalence.induced_inverse_map, RootPairing.rootForm_apply_apply, LatticeHom.coe_mk, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, MvPolynomial.dvd_smul_X_iff_exists, MeasurableEmbedding.gaussianReal_comap_apply, PowerSeries.inv_eq_zero, Equiv.existsUnique_congr_left, LinearEquiv.det_conj, ThreeAPFree.le_rothNumberNat, ContinuousMap.zpow_apply, Module.Basis.dualBasis_apply, Ideal.basisSpanSingleton_apply, LinearMap.apply_toPerfPair_flip, TensorProduct.quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, CompHausLike.mono_iff_injective, MeasureTheory.L1.SimpleFunc.setToL1S_const, SmoothPartitionOfUnity.finsum_smul_mem_convex, MeasureTheory.Measure.finiteAt_principal, AddSubmonoid.toNatSubmodule_symm, MeasureTheory.charFunDual_map_add_const, FreeGroup.closure_eq_range, CategoryTheory.Precoverage.generate_mem_toGrothendieck, Module.Basis.sum_toMatrix_smul_self, RootPairing.Equiv.weightHom_apply, MvPowerSeries.coeff_trunc, SupBotHom.dual_id, AddEquiv.strictMono_subsemigroupCongr, ContinuousLinearMap.integrable_comp, ModuleCat.exteriorPower.iso₁_hom_apply, MeasureTheory.Measure.sum_apply_eq_zero, CategoryTheory.nerve.homEquiv_id, sInfHom.coe_id, AlgebraicGeometry.Scheme.stalkMap_comp, CentroidHom.coe_comp, ContinuousLinearMap.adjointAux_adjointAux, AddChar.toMonoidHomEquiv_symm_one, Measurable.im, WithCStarModule.linearEquiv_symm_apply, IsMulIndecomposable.baseOf_subset_one_lt, Complex.equivRealProdLm_symm_apply_im, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, ContinuousMap.notMem_setOfIdeal, AlgHom.snd_apply, OrderAddMonoidHom.coe_add, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_ι, MeasurableEquiv.piUnique_symm_apply, IsAntichain.preimage_iso, Module.Basis.addHaar_eq_iff, gc_Ici_sInf, FormalMultilinearSeries.changeOriginIndexEquiv_apply_fst, apply_eq_star_dotProduct_toMatrix₂_mulVec, tensorKaehlerQuotKerSqEquiv_tmul_D, MvPolynomial.mkDerivation_monomial, smoothSheafCommRing.eval_surjective, PowerBasis.basis_eq_pow, Complex.add_conj, WeierstrassCurve.Projective.map_dblY, SetTheory.PGame.moveRight_neg, LinearMap.aeval_eq_aeval_mod_charpoly, Matroid.IsBasis.mapEmbedding, Submonoid.LocalizationMap.ext_iff, CategoryTheory.id_apply, AlgHom.range_eq_top, LinearMap.toMatrix_mul, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, BialgHom.coe_toLinearMap, IsMin.ofDual, MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc, Subrepresentation.apply_mem_toSubmodule, Complex.coe_basisOneI_repr, Localization.algEquiv_symm_mk, OrderIso.image_Ici, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, Finsupp.linearCombination_single, realPart_I_smul, Matrix.submatrix_updateRow_equiv, LinearMap.polar_gc, LinearMap.det_map, ProbabilityTheory.Kernel.IndepFun.meas_inter, Monovary.sum_mul_comp_perm_le_sum_mul, Zsqrtd.lift_apply_apply, Equiv.induced_symm, Set.indicator_ae_eq_zero, AddMonoidHom.addSubgroupMap_surjective, mulLeft_continuous, val_unitsEquivProdSubtype_symm_apply, Module.Presentation.CokernelData.π_lift, ProbabilityTheory.IsRatCondKernelCDFAux.le_one', TwoSidedIdeal.subtype_injective, DividedPowers.equiv_apply', TopModuleCat.freeMap_map, Equiv.Set.image_symm_preimage, Quaternion.normSq_add, VitaliFamily.ae_tendsto_div, Finsupp.embDomain_apply_self, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, Subgroup.quotientEquivSigmaZMod_apply, ZSpan.span_top, AddCommGroup.ModEq.map, CategoryTheory.Functor.isIso_ranAdjunction_homEquiv_iff, LinearMap.toMatrix₂_compl₁₂, TensorProduct.tensorQuotientEquiv_apply_mk_tmul, Valued.cauchy_iff, RootPairing.Equiv.bijective_weightMap, MeasureTheory.exists_measure_pos_of_not_measure_iUnion_null, RCLike.norm_im_le_norm, Seminorm.exists_apply_eq_finset_sup, toAdd_vadd, SimpleGraph.Copy.injective', ModularForm.coeHom_apply, LE.le.dual, NormedAddGroupHom.coe_neg, DFinsupp.notMem_neLocus, HahnSeries.cardSupp_single_mul_le, LinearMap.hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, MeasureTheory.measure_mono_ae, TwoSidedIdeal.coe_equivMatrix_symm_apply, Complex.tanh_conj, VitaliFamily.ae_tendsto_measure_inter_div, Fin.consEquiv_symm_apply, Subring.centerToMulOpposite_apply_coe, SemimoduleCat.MonoidalCategory.braiding_inv_apply, Matrix.minpoly_toLin', BoxIntegral.BoxAdditiveMap.coe_mk, addRothNumber_singleton, AlgebraicGeometry.Scheme.residue_surjective, Finsupp.ofSupportFinite_fin_two_eq, MvPolynomial.schwartz_zippel_sup_sum, LeftInvariantDerivation.coe_add, FreeMonoid.toList_map, Equiv.sumCompl_apply_symm_of_neg, PolynomialModule.smul_apply, Module.Basis.reindexFinsetRange_repr_self, QuadraticForm.tensorDistrib_tmul, AddMonoidAlgebra.mul_apply_left, affineCombination_mem_affineSpan_image, mem_compactlySupported, MeasureTheory.measure_preimage_snd_singleton_eq_sum, signedDist_lineMap_left, Algebra.adjoin_eq_span_of_subset, Equiv.cast_apply, ContinuousLinearEquiv.coe_prodProdProdComm, MeasureTheory.SimpleFunc.const_lintegral, selfAdjoint.realPart_unitarySelfAddISMul, SupHom.subtypeVal_apply, Equiv.sumCongr_apply, RootPairing.Base.span_int_root_support, ContinuousAffineMap.coe_const, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, MeasureTheory.measure_lintegral_div_measure, LinearEquiv.symm_comp_eq, IsLocalizedModule.linearEquiv_symm_apply, MeasureTheory.condExpL2_indicator_of_measurable, Polynomial.algEquivAevalXAddC_symm_apply, ExteriorAlgebra.ι_add_mul_swap, LinearMap.equivProdOfSurjectiveOfIsCompl_apply, MonoidHom.submonoidComap_apply_coe, BoundedOrderHom.dual_comp, AffineMap.lineMap_apply_zero, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, MultilinearMap.coe_smul, MvPolynomial.rename_monomial, AlternatingMap.map_eq_zero_of_eq, Set.image_finset_prod, Nonneg.unitsEquivPos_apply_coe, Representation.coind'_apply_apply, LieModule.toModuleHom_apply, ModularGroup.tendsto_normSq_coprime_pair, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, MvPolynomial.aeval_toMvPolynomial, ProbabilityTheory.covarianceBilin_real_self, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, Valuation.one_apply_le_one, LinearMap.eq_adjoint_iff, Finsupp.orderEmbeddingToFun_apply, FractionalIdeal.coeSubmoduleHom_apply, ZeroAtInftyContinuousMap.coe_mul, MeasureTheory.Measure.IicSnd_apply, Preord.forget_map, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, Equiv.subtypeEquivCodomain_symm_apply_eq, Finset.sum_insertNone, Equiv.swap_mul_eq_mul_swap, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, AffineBasis.exists_affineBasis, MvPolynomial.prime_C_iff, WittVector.exists_frobenius_solution_fractionRing, derivationToSquareZeroEquivLift_symm_apply_apply_coe, sSupHom.toFun_eq_coe, Delone.DeloneSet.mapIsometry_symm_apply_packingRadius, EReal.sign_bot, NumberField.mixedEmbedding.norm_smul, GradedTensorProduct.mulHom_apply, WittVector.ghostComponentModPPow_teichmuller_coeff, PositiveLinearMap.gnsStarAlgHom_apply, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, LieModule.toEnd_eq_iff, BilinForm.toMatrix_compRight, MonoidHom.map_closure, ContDiffOn.continuousOn_fderivWithin_apply, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, Continuous.eval_const, Polynomial.nextCoeff_X_sub_C, Algebra.discr_mul_isIntegral_mem_adjoin, map_zpow, RingOfIntegers.isUnit_norm, SchwartzMap.tsupport_iteratedLineDerivOp_subset, MulSemiringAction.toRingEquiv_symm_apply, Complex.normSq_intCast, MeasureTheory.addContent_union', LinearMap.BilinForm.nondegenerate_toMatrix'_iff, LaurentSeries.exists_powerSeries_of_memIntegers, Con.coe_inj, sbtw_pointReflection_of_ne, Polynomial.natDegree_C_mul_X_pow, Homeomorph.preimage_interior, MvPolynomial.eval_mul, AddMonoidHom.compHom'_apply_apply, Finset.affineCombination_affineCombinationLineMapWeights, Polynomial.wronskianBilin_apply, AdjoinRoot.coe_mkₐ, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Module.DirectLimit.linearEquiv_symm_mk, bernsteinApproximation.apply_one, CompactExhaustion.subset_interior, Algebra.smulTower_leftMulMatrix, MonoidHom.coe_toAdditiveLeft, LinearMap.toMatrix₂_toLinearMap₂, FirstOrder.Language.Equiv.surjective, MeasureTheory.condExp_ae_eq_condExpL1CLM, OrderRingHom.coe_id, MeasureTheory.Content.mk_apply, Set.Finite.supClosure, Ideal.Quotient.algEquivOfEqComap_apply, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePos, LinearMap.detAux_def', CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_map, Orthonormal.inner_right_finsupp, TensorAlgebra.algebraMap_eq_one_iff, MultilinearMap.fromDirectSumEquiv_lof, CategoryTheory.Functor.LocallyCoverDense.functorPushforward_functorPullback_mem, TensorProduct.directSumRight_tmul_lof, LinearMap.toMatrix_transpose_apply', MvPowerSeries.eq_zero_iff_forall_coeff_eq_zero_and, Submodule.IsPrincipal.generator_map_dvd_of_mem, Denumerable.ofEquiv_ofNat, WittVector.iterate_verschiebung_iterate_frobenius, ConvexOn.convex_re_epigraph, Finsupp.piecewise_apply, GaussianInt.to_real_im, OrderIso.coe_refl, BooleanSubalgebra.mem_map_of_mem, ValuationSubring.valuation_eq_iff, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, MeasurableEquiv.piUnique_apply, CliffordAlgebra.changeForm_one, FirstOrder.Language.Term.constantsVarsEquivLeft_symm_apply, surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar, MonoidHom.inl_mono, ContinuousAffineMap.coe_zero, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, LieHom.id_apply, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_left, Cardinal.toNat_toENat, ordinaryHypergeometricSeries_apply_eq, AffineIsometry.norm_map, LinearMap.norm_extendTo𝕜'_apply_sq, SpecialLinearGroup.coe_pow, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, DirectLimit.Ring.of_f, AddMonoidHom.coe_comp_rangeRestrict, ValuativeRel.one_apply_posSubmonoid, CliffordAlgebra.lift_symm_apply, SmoothPartitionOfUnity.sum_le_one', ZMod.χ₄_nat_one_mod_four, SemiNormedGrp.explicitCokernelπ_apply_dom_eq_zero, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, Int.tendsto_zmultiplesHom_cofinite, Subgroup.IsComplement.rightCosetEquivalence_equiv_snd, Equiv.inducedStructure_funMap, AdjoinRoot.algEquivOfEq_root, OrthonormalBasis.tensorProduct_apply', ValueDistribution.characteristic_sub_characteristic_inv, MeasurableEquiv.piCongrLeft_apply_apply, ContinuousAddEquiv.self_comp_symm, ENNReal.coe_ofNNRealHom, WithSeminorms.equicontinuous_TFAE, LieIdeal.topEquiv_apply, EuclideanSpace.basisFun_repr, RCLike.sqrt_of_nonneg, Module.Invertible.rTensor_bijective_iff, MvPowerSeries.expand_subst, Module.Basis.repr_symm_single_one, CategoryTheory.CoreSmallCategoryOfSet.functor_map, LinearMap.eqOn_span_iff, NumberField.mixedEmbedding.span_latticeBasis, FreeAbelianGroup.notMem_support_iff, ContinuousLinearMap.integral_comp_id_comm', MeasureTheory.Measure.measure_compl_support, Height.AdmissibleAbsValues.mulSupport_finite, Cardinal.aleph_max, CategoryTheory.Discrete.addMonoidalFunctor_obj, Matrix.submatrix_id_mul_left, Ideal.quotEquivOfEq_eq_factor, Equiv.sigmaAssocProd_symm_apply_snd, OrderMonoidWithZeroHom.coe_comp, TopCat.coinduced_of_isColimit, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, Polynomial.dvd_mul_leadingCoeff_inv, Equiv.Perm.Basis.ofPermHom_support, WithBot.toDual_le_iff, ContinuousLinearMap.coprodEquivL_apply_apply, HasFTaylorSeriesUpToOn.hasFDerivAt, Nat.image_piFinTwoEquiv_finMulAntidiag, map_units_inv, Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero, Equiv.swap_apply_of_ne_of_ne, Ideal.relNorm_eq_bot_iff, CategoryTheory.Functor.pushforward_cover_iff_cover_pullback, StarMonoidHom.ofClass_coe, LinearMap.toMatrix'_intrinsicStar, LocallyConstant.coe_mk, Module.Finite.exists_free_surjective, MultilinearMap.domCoprod'_apply, RCLike.realLinearIsometryEquiv_symm_apply, Lat.ofHom_apply, Convex.exists_subset_interior_convexHull_finset_of_isCompact, finEquivZMultiples_apply, AlgEquiv.spectrum_eq, ProbabilityTheory.iIndepSets.meas_biInter, PrincipalSeg.orderIsoIio_apply_coe, galRestrictHom_symm_algebraMap_apply, LinearMap.BilinForm.congr_congr, RatFunc.algebraMap_C, SimplexCategory.rev_map_apply, BoundedContinuousFunction.coeFn_toLp, Polynomial.C_mul_X_pow_eq_self, Fin.consOrderIso_apply, ContinuousLinearMap.isBigOWith_comp, FreeAddGroup.freeAddGroupCongr_apply, Submodule.linearMap_eq_iff_of_span_eq_top, AddConstMapClass.map_add_int', AddMonoidAlgebra.GradesBy.decompose_single, Equiv.Set.rangeSplittingImageEquiv_symm_apply_coe, MeasurableEquiv.coe_IicProdIoc, ZeroAtInftyContinuousMap.ContinuousMap.liftZeroAtInfty_symm_apply, ProbabilityTheory.Kernel.isProjectiveLimit_trajFun, ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd_of_measurable, map_list_sum, MvPolynomial.universalFactorizationMapPresentation_relation, QuadraticMap.polar_smul_left, AffineMap.fst_lineMap, HahnSeries.coeff_ofFinsupp, IntermediateField.adjoinRootEquivAdjoin_apply_root, Nat.pairEquiv_symm_apply, TrivSqZeroExt.inrHom_apply, MeasureTheory.map_eq_setLIntegral_pdf, Equiv.comp_bijective, Circle.leftInverse_exp_arg, continuous_clm_apply, List.Sorted.coe_getIso_apply, AnalyticAt.aeval_polynomial, Matrix.compLinearEquiv_symm_apply, IntermediateField.normalClosureOperator_apply, AddEquiv.prodAdditive_apply, ContinuousLinearEquiv.skewProd_apply, freeGroupEquivCoprodI_symm_apply, coe_frobenius_comp_coe_frobeniusEquiv_symm, ContinuousLinearMap.hasTemperateGrowth, Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_support, InnerProductSpace.gramSchmidtOrthonormalBasis_det, Dilation.comp_continuousOn_iff, MonoidWithZeroHom.coe_coe, WithBot.ofDual_lt_iff, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, ContinuousMultilinearMap.hasSum_eval, OneHom.mul_apply, Polynomial.degree_X_sub_C_le, LinearMap.map_rTensor, TestFunction.coe_add, Seminorm.uniformContinuous, QuadraticForm.tensorComm_apply, Finsupp.coe_onFinset, AffineSubspace.topEquiv_symm_apply_coe, MeasureTheory.SimpleFunc.ext_iff, Filter.Realizer.ofEquiv_F, UniformOnFun.lipschitzWith_eval, Submodule.coe_isComplEquivProj_apply, jacobiSym.neg, PowerSeries.trunc_C, MvPolynomial.monic_esymm, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, AddMonoidHom.toAddEquiv_apply, Polynomial.eval₂_at_intCast, AffineSubspace.isometryEquivMap.coe_apply, CategoryTheory.mateEquiv_symm_apply, MeasureTheory.eLpNorm_le_of_ae_enorm_bound, PEquiv.coe_mk_apply, SemiNormedGrp₁.coe_comp, QuadraticAlgebra.lift_symm_apply_coe, ContinuousAlternatingMap.hasBasis_nhds_zero, Matrix.mem_range_scalar_iff_commute_single', Equiv.ofFiberEquiv_apply, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, Orientation.oangle_sub_right_smul_rotation_pi_div_two, AlgEquiv.op_symm_apply_symm_apply, MeasureTheory.Measure.nnreal_smul_coe_apply, ProbabilityTheory.lintegral_toKernel_mem, FrameHom.coe_toInfTopHom, FractionalIdeal.coeFun_mapEquiv, CategoryTheory.comp_apply', Polynomial.Monic.mem_rootSet, OrthonormalBasis.sum_sq_norm_inner_left, QuadraticMap.pi_apply_single, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, ArchimedeanClass.FiniteResidueField.mk_eq_mk, Submonoid.coe_comap, AddCon.kerLift_mk, Submodule.prodEquivOfIsCompl_symm_apply_left, map_finset_inf, Equiv.Perm.getElem_toList, MvPolynomial.eval₂_zero_apply, ProbabilityTheory.Kernel.coe_finset_sum, OrderHom.bot_def, PrincipalSeg.lt_apply_iff, AbsoluteValue.ext_iff, CategoryTheory.Limits.IsColimit.descCoconeMorphism_eq_isInitial_to, Ordinal.toNimber_one, Antivary.sum_smul_lt_sum_smul_comp_perm_iff, Path.prod_coe, Algebra.PreSubmersivePresentation.aevalDifferential_single, CompactlySupportedContinuousMap.le_def, Polynomial.cardPowDegree_apply, PrincipalSeg.ofElement_apply, cross_apply, LinearMap.isPositive_iff_complex, ofLex_one, GaussianInt.toComplex_re_div, AlgebraicIndependent.algebraMap_aevalEquiv, spectrum.map_polynomial_aeval_of_nonempty, cfcₙHom_le_iff, AddChar.inv_apply', LinearEquiv.lieConj_apply, Valued.norm_def, Cardinal.ord_preAleph, Valuation.comap_apply, ProbabilityTheory.measure_eq_zero_or_one_or_top_of_indepSet_self, bernstein_nonneg, SSet.orderEmbeddingN_apply, Interval.dual_pure, IsBaseChange.toDual_comp_apply, VectorFourier.fourierSMulRight_apply, AddCon.coe_sInf, LieModule.isNilpotent_toEnd_of_mem_rootSpace, CategoryTheory.Functor.IsDenseSubsite.functorPushforward_mem_iff, AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, inner_self_eq_norm_sq, RingHom.toFun_eq_coe, IsBaseChange.linearMapLeftRightHom_toMatrix, UniversalEnvelopingAlgebra.lift_symm_apply, Module.Basis.extend_apply_self, Action.FintypeCat.quotientToEndHom_mk, ContinuousLinearEquiv.isBigO_sub_rev, AdjoinRoot.Minpoly.coe_toAdjoin_mk_X, IsLocalization.mk'_eq_iff_eq, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_assoc, convexHull_mono, Polynomial.sumIDeriv_apply, Finset.Ico_ofDual, NonUnitalAlgHom.coe_range, map_div_le_add, Real.volume_pi_Ioo, Derivation.leibniz, ContinuousLinearMap.isSelfAdjoint_iff', SupBotHom.coe_comp, ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq, MvPolynomial.aeval_id_rename, Topology.WithLowerSet.toLowerSet_inj, LinearIsometry.map_smulₛₗ, AffineSubspace.map_span, OrthonormalBasis.equiv_apply_euclideanSpace, RootPairing.PolarizationIn_apply, Submodule.injective_subtype, MaximalSpectrum.equivSubtype_apply_coe, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, measurable_fderiv_apply_const, LatticeHom.coe_toSupHom, AlternatingMap.eq_smul_basis_det, Field.Emb.Cardinal.eq_bot_of_not_nonempty, OnePoint.equivProjectivization_symm_apply_mk, LinearMap.BilinForm.toMatrixAux_apply, SupBotHom.coe_toSupHom, Polynomial.sylvesterDeriv_updateRow, translate_eq_domAddActMk_vadd, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, PEquiv.refl_apply, Algebra.algebraMap_eq_smul_one, Submodule.linearProjOfIsCompl_isCompl_projection, MeasureTheory.OuterMeasure.comap_mono, CategoryTheory.extensiveTopology.isLocallySurjective_iff, ContinuousLinearEquiv.isUniformEmbedding, PiTensorProduct.mapMultilinear_apply, LinearMap.mem_ker, ProbabilityTheory.Kernel.measurableSet_absolutelyContinuous, GroupExtension.Equiv.inl_comm, Module.Flat.iff_rTensor_exact', Finset.affineCombination_filter_of_ne, RootPairing.pairingIn_reflectionPerm_self_right, DFinsupp.nsmul_apply, DividedPowers.Quotient.OfSurjective.dpow_apply', IsConjRoot.add_algebraMap, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, MeasureTheory.Measure.addHaar_image_linearMap, List.formPerm_pow_apply_getElem, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, Metric.Snowflaking.preimage_toSnowflaking_eball, LinearMap.liftQ₂_mk, MeasureTheory.measure_univ_of_isAddLeftInvariant, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, Submodule.quotientEquivOfIsCompl_apply_mk_coe, IsLocalFrameOn.coeff_apply_of_notMem, ContinuousLinearMap.toContinuousAddMonoidHom_injective, Fin.cycleIcc_of_ge_of_lt, Subalgebra.linearDisjoint_iff, InfHom.withTop'_toFun, Finsupp.equivMapDomain_eq_mapDomain, LieHom.range_coe, smoothSheafCommRing.forgetStalk_hom_comp_evalHom, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, RingEquiv.coe_toEquiv, Additive.ext_iff, Polynomial.degree_C_mul_X_le, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Monoid.CoprodI.Word.equivPair_tail, VectorBundleCore.localTriv_coordChange_eq, WithBot.toDual_apply_coe, RCLike.lipschitzWith_re, Finset.toDual_inf, SemiNormedGrp.explicitCokernelπ_surjective, groupCohomology.coboundaries₂.coe_mk, AddEquiv.coe_addSubgroupMap_apply, BoundedLatticeHom.subtypeVal_coe, LinearMap.BilinForm.isAdjointPair_iff_eq_of_nondegenerate, ContinuousMultilinearMap.uncurryRight_apply, CategoryTheory.Functor.curryingEquiv_symm_apply_map_app, Finsupp.sum_nsmul, Module.isTorsionFree_iff_algebraMap_injective, ContinuousMap.toUniformOnFun_toFun, AddValuation.ofValuation_toValuation, TestFunction.coe_zero, NonarchAddGroupSeminorm.ext_iff, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem, LieDerivation.neg_apply, Polynomial.dvd_derivative_iff, Finsupp.toMultiset_add, HahnSeries.SummableFamily.coe_mk, MeasureTheory.FiniteMeasure.coeFn_smul, Polynomial.coeff_mul_monomial_zero, isAddRegular_toLex, coe_finRotate_symm_of_ne_zero, PartitionOfUnity.locallyFinite_tsupport, SetTheory.PGame.forall_rightMoves_neg, Nat.primeFactorsList_count_eq, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow, AddSemigrp.ofHom_apply, Polynomial.roots_ofMultiset, convex_absConvexHull, Ordinal.omega0_lt_omega1, PMF.coe_le_one, LinearMap.coe_domRestrict, Measurable.re, MeasureTheory.L1.tendsto_setToL1, ContMDiffSection.coe_sub, MeasureTheory.eLpNorm_const', Set.powersetCard.mulActionHom_compl_bijective, Multiset.toFinsupp_singleton, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq_on, ContinuousLinearMap.isVonNBounded_iff, MeasureTheory.condExpL1CLM_indicatorConst, ConjAct.toConjAct_smul, Ordinal.bfamilyOfFamily_typein, ULift.orderIso_apply, Topology.WithUpperSet.toUpperSet_le_iff, Finset.Ioc_orderDual_def, AlternatingMap.coe_injective, NumberField.FinitePlace.norm_def_int, GroupExtension.Equiv.refl_symm_apply, LowerSet.iicInfHom_apply, NormedAddGroupHom.bound, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, Submodule.localized'_eq_span, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_fst, IsAdjoinRoot.lift_algebraMap, Module.Invertible.toModuleEnd_bijective, Finsupp.coe_basis, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, UpperHalfPlane.J_smul, OrderIso.equivalence_counitIso, SSet.Subcomplex.PairingCore.equivI_apply_coe, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, WittVector.verschiebung_mul_frobenius, SetTheory.PGame.forall_leftMoves_neg, Valuation.leIdeal_v_le_of_mem, MvPolynomial.eq_C_of_isEmpty, QuotientGroup.quotientQuotientEquivQuotientAux_mk_mk, Quiver.SingleObj.toHom_apply, DifferentiableOn.continuousAlternatingMap_apply, AddConstMapClass.monotone_iff_Icc, AdicCompletion.of_surjective, AddChar.val_isUnit, iterate_map_zero, Finset.toDual_max', CategoryTheory.TransfiniteCompositionOfShape.iic_F, Polynomial.expand_zero, MeasureTheory.measure_lt_top_of_isCompact_of_isAddLeftInvariant, PiTensorProduct.dualDistrib_apply, OrderMonoidHom.comp_apply, DFinsupp.lsum_single, Complex.orthonormalBasisOneI_repr_symm_apply, SlashInvariantForm.slash_action_eqn'', Finset.Colex.insert_le_insert, IsLocalization.injectiveₛ, Order.PFilter.sInf_gc, LinearEquiv.uniqueProd_symm_apply, CliffordAlgebraQuaternion.ofQuaternion_mk, OrderEmbedding.supIrredLowerSet_surjective, SmoothPartitionOfUnity.sum_nonneg, PartOrdEmb.inv_hom_apply, Ordinal.typein_enum, ProbabilityTheory.cond_iInter, Algebra.Generators.Cotangent.exact, CategoryTheory.Bicategory.conjugateEquiv_symm_comp, Valuation.veq_iff_eq, CompactlySupportedContinuousMap.ext_iff, WeierstrassCurve.Projective.baseChange_dblZ, Matrix.conjTransposeAddEquiv_apply, MeasureTheory.L1.SimpleFunc.integrable, Polynomial.eraseLead_C_mul_X_pow, PerfectRing.lift_comp_lift_apply_eq_self, subtypeOrLeftEmbedding_apply_left, IsAddQuotientCoveringMap.homeomorph_comp_iff, self_mul_sign, AlternatingMap.domDomCongrEquiv_apply, MonoidHom.map_div, Ordinal.mk_toPGame, ProbabilityTheory.Kernel.parallelComp_apply', Matrix.toLinOfInv_symm_apply, ContDiffWithinAt.laplacianWithin_CLM_comp_left, Manifold.riemannianEDist_def, ContinuousLinearEquiv.coe_neg, Polynomial.roots_expand_pow_map_iterateFrobenius_le, Seminorm.coe_bot, WittVector.coeff_frobenius_charP, zpowGroupHom_apply, LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv', LinearIsometry.norm_iteratedFDerivWithin_comp_left, CommBialgCat.isoEquivBialgEquiv_symm_apply, HasFDerivAtFilter.isLittleO, LinearMap.toMatrix_smulRight, MonoidHom.compHom'_apply_apply, HahnModule.ext_iff, Finsupp.single_apply_eq_zero, convexHullAddMonoidHom_apply, ModularFormClass.qExpansion_coeff_zero, SimpleGraph.induceHomOfLE_apply, ContinuousLinearMap.range_coeFn_eq, Multiplicative.ofAdd_bot, IsometryEquiv.withLpProdCongr_apply, Homeomorph.isHomeomorph, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, Polynomial.Monic.natSepDegree_eq_one_iff, BoundedContinuousFunction.prod_apply, EuclideanGeometry.oangle_homothety, midpoint_eq_iff', Polynomial.resultant_taylor, Polynomial.trailingDegree_C, Set.coe_snd_unionEqSigmaOfDisjoint, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, GaussianInt.toComplex_re, CategoryTheory.Limits.Types.Small.limitCone_pt_ext_iff, AddGroupExtension.Equiv.rightHom_comm, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, Finsupp.subtypeDomain_apply, PEquiv.ofSet_eq_some_self_iff, AlgEquiv.coe_restrictScalars', CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction, WeierstrassCurve.Projective.polynomialX_eq, AddMonoidAlgebra.singleAddHom_apply, ZeroHom.coe_mk, ContinuousMap.inv_apply, QuotientGroup.congr_apply, Subsemiring.mem_comap, kroneckerTMulLinearEquiv_tmul, LinearEquiv.alternatingMapCongrRight_apply_apply, CategoryTheory.CommSq.right_adjoint_hasLift_iff, MeasureTheory.levyProkhorovEDist_le_max_measure_univ, Submodule.comapMkQOrderEmbedding_eq, LinearMap.toMatrix₂Aux_eq, PowerSeries.WithPiTopology.continuous_C, Matrix.diagonalAddMonoidHom_apply, ProbabilityTheory.uniformOn_self, Representation.averageMap_invariant, RingEquiv.sumArrowEquivProdArrow_symm_apply, MulHom.toMulEquiv_apply, Matrix.represents_iff, MeasureTheory.SimpleFunc.coe_le_coe, DFinsupp.mapRange_apply, Filter.comap_mul_comap_le, AddSubgroup.opEquiv_symm_apply, ArithmeticFunction.mul_apply_one, WithBot.toDual_lt_toDual_iff, FreeAddMonoid.lift_comp_of, ContinuousMap.coe_zsmul, signedDist_anticomm, absConvexHull_mono, Prime.dvd_finsuppProd_iff, Ring.DirectLimit.ringEquiv_of, Quiver.starEquivCostar_apply_snd, Multiset.toFinsupp_symm_apply, ArchimedeanClass.lt_of_stdPart_lt, CategoryTheory.Limits.Types.Small.limitCone_π_app, ofBoolAlg_sdiff, imaginaryPart_apply_coe, BumpCovering.locallyFinite_tsupport, ZSpan.map, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, ContinuousLinearMap.isVonNBounded_image2_apply, IsOpen.measure_eq_biSup_integral_continuous, ofColex_inj, MonoidWithZeroHom.inr_mono, MulSemiringActionHom.map_one', MulSemiringActionHom.coe_fn_coe, biUnion_Iic_disjointed, Module.End.natCast_def, List.sortedLT_map_ofDual, Homeomorph.comp_continuousOn_iff, IsModuleTopology.continuous_of_linearMap, IsValuativeTopology.hasBasis_nhds_zero', MvPolynomial.monomial_zero', PartitionOfUnity.continuous_finsum_smul, MeasureTheory.measure_map_restrict_apply, LinearEquiv.extendScalarsOfIsLocalizationEquiv_apply, Valuation.extendToLocalization_mk', X_pow_sub_C_irreducible_of_prime, MultilinearMap.curryLeft_apply, LinearIsometryEquiv.symm_comp_self, Nat.setOf_pow_dvd_eq_Icc_factorization, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, Polynomial.roots_multiset_prod_X_sub_C, UniformOnFun.uniformContinuous_toFun, Subsemigroup.mem_comap, Subsemigroup.centerToMulOpposite_symm_apply_coe, PowerSeries.coe_C, AddChar.mulShift_spec', iteratedDeriv_eq_equiv_comp, CartanMatrix.A_three, CategoryTheory.Bicategory.mateEquiv_hcomp, TopCat.Presheaf.stalkFunctor_map_germ_apply, FreeAbelianGroup.equivFinsupp_apply, IsMulFreimanIso.mulRothNumber_congr, Finset.convexHull_eq, PowerBasis.equivOfMinpoly_aeval, CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_fst, MeasureTheory.Measure.mem_support_iff_forall, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl, MeasureTheory.weightedSMul_smul, pinGroup.conjAct_smul_range_ι, TopCat.Presheaf.germ_res_apply', MvPowerSeries.coeff_truncFun', LinearMap.lsmul_apply, Equiv.Perm.card_fixedPoints, Topology.image_snd_preimageImageRestrict, FreeCommRing.of_cons, Finsupp.sumFinsuppEquivProdFinsupp_symm_apply, MeasureTheory.integral_continuousLinearMap_prod, Submodule.coe_subtypeₗᵢ, Subalgebra.rTensorBot_tmul_one, ZMod.ringHom_map_cast, EisensteinSeries.eisensteinSeries_SIF_apply, CategoryTheory.Iso.homCongr_apply, OrderIso.map_csInf_of_directedOn, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis, Ordinal.preOmega_zero, LieModule.Weight.coe_weight_mk, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, Submodule.IsCompl.projection_add_projection_eq_self, LieDerivation.toLinearMapLieHom_injective, OrderIso.ofUnique_apply, ContinuousAlternatingMap.uniformContinuous_coe_fun, ContinuousMap.inf'_apply, Equiv.natSumNatEquivNat_symm_apply, Equiv.Perm.toList_pow_apply_eq_rotate, QuotientAddGroup.lift_mk, Ideal.card_norm_le_eq_card_norm_le_add_one, OrthonormalBasis.inner_eq_zero, Homeomorph.mulLeft₀_symm_apply, FreeLieAlgebra.liftAux_spec, ContinuousMultilinearMap.cpolynomialAt, PrincipalSeg.subrelIso_symm_apply, Finsupp.counit_single, MvPolynomial.weightedHomogeneousComponent_directSum, CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderComposition, MeasureTheory.Lp.norm_const, ContinuousLinearMap.NonlinearRightInverse.right_inv, FirstOrder.Language.Equiv.injective, OrderIso.dualAntisymmetrization_apply, Diffeomorph.symm_image_image, HasFTaylorSeriesUpToOn.shift_of_succ, Equiv.permCongr_apply, Fintype.coe_finsetOrderIsoSet_symm, TemperedDistribution.laplacian_eq_sum, Polynomial.natDegree_hasseDeriv, vecMulVecBilin_apply_apply, curveIntegralFun_def', OrderAddMonoidIso.apply_symm_apply, SimplexCategory.mkOfSucc_homToOrderHom_zero, LocallyConstant.congrLeftₐ_symm_apply_apply, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, Algebra.Generators.aeval_val_σ, Topology.IsGeneratedBy.isOpen_iff, Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx, Polynomial.eval_one_map, MagmaCat.coe_id, isAdjointPair_toLinearMap₂', Orientation.areaForm_comp_rightAngleRotation, DFinsupp.ext_iff, NumberField.mixedEmbedding.continuous_norm, Matrix.cRank_reindex, RootPairing.Equiv.coweightMap_coweightEquiv_symm, Real.sinhOrderIso_apply, Module.Dual.baseChange_apply_tmul, Associates.mk_normalize, antitoneOn_comp_ofDual_iff, Matrix.col_eq_transpose, Matrix.toLin'_apply', CategoryTheory.monotone_chain_condition_of_isNoetherianObject, Finsupp.lex_lt_of_lt, AddEquiv.cast_apply, IsometryEquiv.piCongrLeft_symm_apply, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_apply, CharacterModule.ext_iff, Set.up_image, totallyBounded_convexHull, LinearMap.rTensor_baseChange, CuspForm.coe_sub, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, SimpleGraph.Hom.coe_comp, IntermediateField.adjoin.algebraMap_mem, Representation.asModuleEquiv_symm_map_rho, PrincipalSeg.map_isSuccPrelimit, AffineSubspace.mem_comap, aeSeq.measure_compl_aeSeqSet_eq_zero, apply_covBy_apply_iff, SimpleGraph.Subgraph.map_adj, RootPairing.Base.toCoweightBasis_repr_coroot, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, ContinuousMultilinearMap.prodEquiv_apply, LinearMap.isPairSelfAdjoint_equiv, MeasureTheory.IsFiniteMeasure.average, LieEquiv.surjective, RingHom.prod_bijective_of_isIdempotentElem, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, Set.exists_equiv_range_eq_graphOn_univ, Polynomial.homogenize_C_mul, BddDistLat.inv_hom_apply, Finsupp.single_swap, MeasureTheory.measure_union_eq_top_iff, Nat.Subtype.orderIsoOfNat_apply, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, FirstOrder.Language.Term.realize_constantsVarsEquivLeft, AdjoinRoot.powerBasisAux'_repr_symm_apply, Polynomial.Bivariate.swap_monomial_monomial, MvPowerSeries.coeff_prod, SkewMonoidAlgebra.map_sum, OrderDual.toDual_le, IsometryEquiv.ediam_image, ZSpan.exist_unique_vadd_mem_fundamentalDomain, ArithmeticFunction.ppow_apply, ContinuousMultilinearMap.ratio_le_opNorm, spectrum.add_singleton_eq, AddSubmonoid.topEquiv_symm_apply_coe, ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, CategoryTheory.ReflQuiv.adj.homEquiv_naturality_left_symm, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, Matrix.Represents.congr_fun, CategoryTheory.conjugateEquiv_counit, ZSpan.fundamentalDomain_subset_parallelepiped, MvPowerSeries.exists_coeff_ne_zero_and_order, MeasureTheory.Measure.restrict_iUnion_apply_eq_iSup, Finsupp.coe_finset_sum, NonUnitalSubalgebra.coe_map, RootPairing.reflectionPerm_eq_reflectionPerm_iff_of_span, LinearMap.congr_fun₂, MeasureTheory.Measure.FiniteSpanningSetsIn.finite, MvPowerSeries.map_eq_zero, Condensed.isoFinYonedaComponents_inv_comp, PositiveLinearMap.map_smul_of_tower, ContinuousLinearMap.norm_extendTo𝕜'_bound, groupHomology.π_comp_H1Iso_hom_apply, TensorPower.toTensorAlgebra_gMul, Homeomorph.continuous_sumAssoc_symm, Tactic.NormNum.isNNRat_nnrealSqrt_of_isNNRat, GradedRing.mem_support_iff, RegularWreathProduct.right_inl, Set.Nonempty.absConvexHull, ZMod.dft_comp_neg, DirectSum.coeAddMonoidHom_of, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, MvPolynomial.mem_zeroLocus_iff, TensorProduct.directSumLeft_symm_lof_tmul, MeasureTheory.hausdorffMeasure_homothety_image, Matrix.ker_toLin'_eq_bot_iff, Polynomial.rootMultiplicity_expand, LinearMap.isIdempotentElem_apply_one_iff, Matrix.algebraMap_eq_diagonal, Ordinal.typein_surj, WCovBy.ofDual, Quaternion.normSq_exp, AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr, Finset.orderEmbOfCardLe_mem, MeasureTheory.AEStronglyMeasurable.re, HasFDerivWithinAt.hasDerivWithinAt, Fin.castAddEmb_apply, Localization.mk_one_eq_algebraMap, Nat.factorization_choose', AddLocalization.addEquivOfQuotient_mk, Polynomial.contract_C, ContinuousMultilinearMap.integral_apply, Representation.ofModule_asModule_act, NonUnitalSubalgebra.unitization_apply, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, Equiv.Perm.IsCycle.exists_zpow_eq, Polynomial.sylvester_map_map, LinearMap.vecCons₂_apply, ContinuousAffineMap.add_apply, NonUnitalRingHom.ext_iff, AddMonoidAlgebra.coeff_smul, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, eq_lineMap_of_dist_eq_mul_of_dist_eq_mul, Equiv.Perm.Basis.ofPermHomFun_commute_zpow_apply, AddChar.zmodChar_apply, codisjoint_toDual_iff, AlgHom.tensorEqualizerEquiv_apply, DualNumber.lift_apply_apply, CommGrpCat.inv_hom_apply, AdicCompletion.Ideal.mk_eq_mk, LieHom.map_neg, Topology.WithUpper.ofUpper_inj, Finsupp.lsum_apply, CategoryTheory.Functor.flippingEquiv_symm_apply_obj_map, Matrix.charpoly_fin_two, ContinuousMap.exists_finite_sum_const_mulIndicator_approximation_of_mem_nhds_diagonal, WithBot.ofDual_lt_ofDual_iff, continuousSMul_induced, LinearMap.eval_charpoly, WithCStarModule.norm_single, LinearMap.SeparatingLeft.toMatrix₂, TopCat.pullbackIsoProdSubtype_hom_snd, AddMonCat.id_apply, ContMDiffSection.coe_add, MultilinearMap.map_update_zero, OrderHom.coe_iInf, Equiv.Perm.subtypeEquivSubtypePerm_apply_of_not_mem, LieModuleHom.zero_apply, DistLat.ofHom_apply, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, LinearMap.toMatrix'_toLinearMap₂', AddCon.ker_apply, Algebra.mul_sub_algebraMap_pow_commutes, Nucleus.coe_bot, TensorPower.toTensorAlgebra_gOne, AffineEquiv.pointReflection_apply_eq_equivPointReflection_apply, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, Derivation.llcomp_apply, ProbabilityTheory.Kernel.setLIntegral_density, Subtype.impEmbedding_apply_coe, WithTop.ofDual_le_ofDual_iff, EquivFunctor.mapEquiv_apply, MultilinearMap.iteratedFDeriv_aux, StarAlgEquiv.coe_pow, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, RCLike.conj_tsum, HasGradientWithinAt.fderivWithin_apply, RingHom.coe_one, Matrix.rank_reindex, Padic.complete'', Topology.IsEmbedding.toHomeomorph_apply_coe, HahnModule.of_symm_add, ContMDiffOn.clm_apply, ZMod.ringHom_surjective, CategoryTheory.unopHom_apply, AlgebraicGeometry.Scheme.Hom.map_mem_image_iff, Topology.WithLowerSet.ofLowerSet_le_iff, AddChar.starComp_apply, Isometry.isometryEquivOnRange_apply, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, PiTensorProduct.tprod_eq_tprodCoeff_one, MeasureTheory.integral_comp, map_finset_prod, Equiv.Perm.SameCycle.apply_eq_self_iff, Algebra.adjoin_inl_union_inr_eq_prod, Basis.multilinearMap_apply_apply, Finset.sum_eraseNone, CoalgEquiv.invFun_eq_symm, MulSemiringActionHom.map_zero, RCLike.I_im, LinearMap.BilinForm.toLin'Flip_apply, DFinsupp.toMultiset_inf, IntermediateField.relfinrank_eq_toNat_relrank, MeasureTheory.integral_pos_iff_support_of_nonneg, Set.image_multiset_sum, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, Polynomial.separable_prod_X_sub_C_iff, Equiv.finsetCongr_apply, MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le, Nat.factorization_choose_le_log, LinearMap.reduceModIdeal_apply, CategoryTheory.Limits.isLimitConeOfAdj_lift, Polynomial.resultant_C_left, ContinuousWithinAt.partialSups, LieModule.genWeightSpace_chainTopCoeff_add_one_zsmul_add, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, HahnSeries.single_neg, Finset.weightedVSubOfPoint_smul, OrderIso.sumAssoc_symm_apply_inr_inl, AddGroupSeminorm.sup_apply, CategoryTheory.InducedCategory.homAddEquiv_apply, LinearMap.charpoly_constantCoeff_eq_zero_iff, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, Algebra.ofId_apply, PadicInt.continuous_addChar_of_value_at_one, groupCohomology.map_id_comp_H0Iso_hom_apply, cfc_eq_cfcL_mkD, PolynomialModule.equivPolynomial_single, groupCohomology.cocycles₁_map_mul_of_isTrivial, MvPolynomial.homogeneousComponent_apply, AddMonoidHom.op_apply_apply, AddSubmonoid.LocalizationMap.eq', Polynomial.natDegree_mul_C_of_isUnit, MeasureTheory.Measure.ae_comp_iff, Equiv.optionCongr_apply, Topology.WithUpper.toUpper_inj, Polynomial.dickson_add_two, NumberField.ComplexEmbedding.isConj_apply_apply, WeierstrassCurve.Affine.baseChange_addPolynomial, BilinForm.toMatrix_mul_basis_toMatrix, LinearMap.convexOn, OrderIso.sumLexIicIoi_apply_inr, iteratedFDeriv_zero_apply, DFinsupp.subtypeSupportEqEquiv_symm_apply_coe, Polynomial.toFn_comp_ofFn_eq_id, Subgroup.conj_smul_le_of_le, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, Complex.div_re, NonUnitalAlgHom.addHomMk_coe, AlgEquiv.arrowCongr_comp, Nat.Primes.coe_prodNatEquiv_apply, MultilinearMap.dfinsuppFamilyₗ_apply, FreeRing.lift_comp_of, MulChar.mul_apply, AdjoinRoot.quotEquivQuotMap_apply_mk, AddEquiv.congr_arg, WeakDual.isClosed_closedBall, Nat.factorization_eq_zero_of_not_prime, MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, AffineMap.derivWithin, antitone_dual_iff, UniformEquiv.comap_eq, contDiff_succ_iff_fderiv_apply, map_finsum, LatticeHom.withTopWithBot_toFun, Ordinal.coe_preOmega, WeierstrassCurve.Projective.map_dblU, Matrix.piAddEquiv_symm_apply, SubmonoidClass.coe_subtype, hasDerivAt_fourier, ContinuousAlgHom.mul_apply, UniformOnFun.continuousOn_eval₂, Monoid.foldlM.ofFreeMonoid_apply, Unitization.lift_symm_apply, Rep.standardComplex.d_of, coe_lpPiLpₗᵢ, FractionalIdeal.absNorm_span_singleton, PowerSeries.coe_neg, BooleanSubalgebra.subtype_apply, MeasureTheory.setLIntegral_one, Derivation.map_neg, AntitoneOn.dual_left, HahnSeries.SummableFamily.coeff_smul, NonUnitalStarAlgHom.coe_one, CuspForm.neg_apply, Module.Flat.tensorProduct_mapIncl_injective_of_left, AddGroupSeminorm.coe_le_coe, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Topology.WithUpperSet.ofUpperSet_toUpperSet, DirectSum.GAlgebra.map_mul, SemimoduleCat.id_apply, MeasureTheory.withDensity_apply₀, Matrix.lift_cRank_reindex, Submodule.Quotient.equiv_symm_apply, VitaliFamily.ae_eventually_measure_zero_of_singular, ofDual_one, AddChar.mul_apply, ContinuousLinearEquiv.smulLeft_apply_apply, iSupIndep.linearEquiv_apply, Derivation.map_algebraMap, MulDistribMulAction.toMulEquiv_symm_apply, stdSimplexHomeomorphUnitInterval_apply_coe, MvPolynomial.eval_indicator_apply_eq_zero, AddGroupSeminorm.coe_sSup_apply, VectorBundleCore.localTriv_apply, Equiv.permCongr_mul, NumberField.RingOfIntegers.withValEquiv_apply, Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, FirstOrder.Language.ElementaryEmbedding.refl_apply, divMonoidHom_apply, Multiplicative.mem_toSubgroup, Multiset.replicateAddMonoidHom_apply, QuadraticMap.half_moduleEnd_apply_eq_half_smul, OrderHom.apply_coe, Cardinal.preAleph_max, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Module.Basis.coe_finTwoProd_repr, AddChar.coe_zero, Equiv.Set.univ_apply, LinearMap.coe_snd, LinearIsometry.inr_apply, Polynomial.supNorm_monomial, Polynomial.Bivariate.swap_map_C, MvPolynomial.sumToIter_iterToSum, MeasureTheory.Lp.simpleFunc.memLp, Besicovitch.ae_tendsto_measure_inter_div, QuadraticForm.dualProdIsometry_toFun, Valuation.map_one, Set.map_finite_biSup, Polynomial.derivative_comp, OrderIso.subRight_apply, Polynomial.Monic.eq_X_add_C, IsometryEquiv.measurePreserving_hausdorffMeasure, iterate_map_mul, LinearMap.BilinForm.mul_toMatrix', WithCStarModule.equiv_symm_sub, OrderMonoidWithZeroHom.coe_mk, ArithmeticFunction.carmichael_finset_lcm, CategoryTheory.Adjunction.homAddEquiv_symm_zero, MvPowerSeries.coeff_C_mul, Complex.volume_preserving_equiv_real_prod, MvPolynomial.divMonomial_mul_monomial, Perfection.ext_iff, AddEquiv.addMonoidHomCongrLeftEquiv_symm_apply, IsGroupLikeElem.antipode, MvPolynomial.map_surjective_iff, Localization.mulEquivOfQuotient_symm_mk, MulArchimedeanClass.map_mk_eq, CategoryTheory.ConcreteCategory.forget₂_comp_apply, LieModule.toEnd_lie, ContinuousAffineMap.coe_id, AddMonoidHom.ext_iff, AddUnits.coeHom_injective, OrderIso.map_ciSup', Homeomorph.Set.prod_apply, Monoid.PushoutI.homEquiv_apply_coe, PseudoEpimorphism.coe_comp, QuadraticForm.tensorAssoc_symm_apply, Homeomorph.isBigO_congr, LaurentPolynomial.eval₂_C_mul_T_neg_n, HahnSeries.SummableFamily.coe_sub, AffineMap.lineMap_apply, Equiv.Perm.sameCycle_pow_right, MulEquivClass.apply_mem_center_iff, LinearIsometryEquiv.coe_coe'', emultiplicity_map_eq, MonoidAlgebra.tensorEquiv_tmul, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, ArithmeticFunction.cardDistinctFactors_zero, constantCoeff_wittPolynomial, Set.PartiallyWellOrderedOn.fiberProdLex, HomotopicalAlgebra.AttachCells.reindex_cofan₂, Finsupp.linearCombination_unique, Ordinal.typein_injective, PiTensorProduct.isEmptyEquiv_symm_apply, PresheafOfModules.toPresheaf_map_app_apply, MeasureTheory.NoAtoms.measure_singleton, topologicalAddGroup_induced, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, Finset.Ioc_toDual, AffineBasis.coord_apply_eq, WeierstrassCurve.Affine.CoordinateRing.mk_Ψ_sq, DistribMulAction.toLinearEquiv_apply, RingHom.surjective_iff_epi_and_finite, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, Equiv.Perm.decomposeFin_symm_apply_succ, LinearEquiv.map_add, CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom, CliffordAlgebra.reverse.commutes, ProbabilityTheory.Kernel.lintegral_snd, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, LinearMap.map_mul_iff, PiTensorProduct.subsingletonEquiv_symm_apply', AddValuation.map_mul, HahnSeries.addOppositeEquiv_orderTop, AffineBasis.coord_apply_centroid, AlgebraicGeometry.Scheme.map_basicOpen, BoundedContinuousFunction.nndist_coe_le_nndist, extDerivWithin_apply_vectorField, WeierstrassCurve.Projective.polynomialY_eq, ProbabilityTheory.Kernel.integrable_density, MvPolynomial.aeval_eq_constantCoeff_of_vars, PowerSeries.X_eq, val_unitsCentralizerEquiv_symm_apply_coe, Polynomial.eq_C_of_degree_le_zero, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, ContinuousLinearMap.measurable_comp, AddMonoidHom.inl_mono, toLex_natCast, Equiv.Perm.sign_symm_trans_trans, Finset.coe_eraseNone, CategoryTheory.conjugateEquiv_rightUnitor_hom, ZMod.LFunction_def_even, Real.fourier_bilin_convolution_eq, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_apply_coe_coe, Topology.IsGeneratedBy.homeomorph_coe, MeasureTheory.OuterMeasure.boundedBy_eq_self, MeasureTheory.Measure.one_le_hausdorffMeasure_zero_of_nonempty, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, MeasureTheory.IsSetRing.partialSups_mem, BoxIntegral.BoxAdditiveMap.toSMul_apply, ProbabilityTheory.IsGaussian.map_rotation_eq_self, AddGroupSeminormClass.toSeminormedAddGroup_norm_eq, Finsupp.coe_lsum, LinearMap.toSpanSingleton_homothety, sup_mem_supClosure, Set.Iic_toDual, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, AddSubmonoid.subtype_injective, ProbabilityTheory.hasFiniteIntegral_prodMk_left, LocallyConstant.vadd_apply, ContinuousLinearMap.hasFDerivWithinAt, CategoryTheory.SmallObject.restrictionLE_map, WittVector.liftEquiv_apply, TopologicalSpace.Opens.adjunction_counit_map_functor, AlgebraicGeometry.coprodSpec_coprodMk, fdifferential_comp, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, ContDiffMapSupportedIn.ext_iff, CStarMatrix.mul_entry_mul_eq_inner_toCLM, WittVector.ghostMap_apply, MvPolynomial.weightedHomogeneousComponent_finsupp, Dilation.coe_mul, RingCon.congr_mk, Real.volume_pi_Ioo_toReal, MonoidWithZeroHom.toMonoidHom_coe, LinearIsometry.orthonormal_comp_iff, MonoidHom.mulExact_of_comp_of_mem_range, Matrix.kronecker_assoc, ZMod.lift_comp_castAddHom, IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two, LaurentSeries.hasseDeriv_coeff, MeasureTheory.Measure.coe_finset_sum, homeomorphSphereProd_symm_apply_coe, ContinuousMap.HomotopyWith.extendProp, Matrix.trace_fin_one_of, GaussianInt.toComplex_inj, AddMonoidAlgebra.lift_of, nsmulCoprime_neg, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, RelIso.sumLexComplRight_symm_apply, AddCommGrpCat.mono_iff_injective, ModularFormClass.differentiableAt_cuspFunction, MeasureTheory.Measure.smul_measure_isMulInvariant_le_of_isCompact_closure, ContinuousLinearEquiv.prodUnique_symm_apply, Polynomial.gaussNorm_monomial, PMF.toOuterMeasure_bindOnSupport_apply, fourier_apply, ExteriorAlgebra.toTrivSqZeroExt_ι, WeierstrassCurve.Projective.negDblY_eq, Diffeomorph.uniqueDiffOn_image, ContinuousLinearMap.le_opNorm₂, AddMonoidHom.coe_toRatLinearMap, OrderIso.preimage_Icc, ContinuousAlgEquiv.symm_symm_apply, ContinuousLinearEquiv.coe_mk, ProbabilityTheory.Kernel.lintegral_const, left_le_lineMap_iff_le, quotient_norm_mk_eq, NNReal.sqrt_eq_one, Algebra.norm_eq_prod_automorphisms, ContinuousLinearMap.lpPairing_eq_integral, LinearMap.norm_map_iff_inner_map_map, Polynomial.expand_X, powersHom_apply, CoxeterMatrix.reindexGroupEquiv_apply_simple, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, Module.Flat.iff_lTensor_injectiveₛ, ArithmeticFunction.sigma_zero_apply_prime_pow, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, PresheafOfModules.Derivation'.d_app, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, ClosureOperator.closure_sup_closure_left, Seminorm.continuous_iff, QuaternionAlgebra.coe_starAe, List.zipWith_swap_prod_support', lowerBounds_infClosure, ofAdd_add, Finsupp.linearCombination_mapDomain, LowerSet.mem_map, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, gcd_same, ProbabilityTheory.Kernel.instNeZeroMeasureCoeSectLOfProdMk, MulChar.starComp_apply, Submodule.unitsQuotEquivRelPic_symm_apply, WithTop.toDual_lt_toDual_iff, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, QuaternionAlgebra.imI_swapEquiv_symm_apply, Submodule.torsionBy.mk_ideal_smul, Span.finsupp_linearCombination_repr, OrderHom.apply_mono, MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc, FirstOrder.Language.DirectLimit.equiv_iff, RCLike.wInner_const_right, ProbabilityTheory.covarianceOperator_inner, ProbabilityTheory.cond_add_cond_compl_eq, SymmetricAlgebra.equivMvPolynomial_symm_X, Finset.mem_map_equiv, SetLike.algebraMap_mem_graded, CongruenceSubgroup.finiteIndex_conjGL, CategoryTheory.ConcreteCategory.hom_ext_iff, Matrix.sub_scalar_sq_eq_disc, AddMonoidAlgebra.coe_mapRangeRingHom, Subalgebra.map_toSubmodule, le_mulRothNumber_product, Polynomial.contentIdeal_C, sign_apply, NNReal.sqrt_pos_of_pos, LinearMap.sumOfConjugates_apply, InnerProductSpace.rankOne_def', ofDual_iSup, CommRing.Pic.mapRingHom_mapRingHom, ContDiff.fderiv_apply, HahnSeries.embDomainOrderAddMonoidHom_injective, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, SchwartzMap.tendsto_cocompact, MulEquiv.symm_map_mul, Polynomial.taylor_taylor, ContinuousAlternatingMap.sum_apply, LeftInvariantDerivation.coe_injective, Affine.Simplex.incenter_restrict, BooleanSubalgebra.inclusion_injective, MeasureTheory.measure_diff_add_inter, MeasureTheory.OuterMeasure.le_comap_map, RootPairing.Equiv.bijective_coweightMap, Polynomial.exists_approx_polynomial, AddMonCat.ofHom_apply, Set.dual_ordSeparatingSet, FractionalIdeal.canonicalEquiv_canonicalEquiv, ContinuousMap.Homotopy.curry_apply, OrderHom.equivalenceFunctor_functor_obj_obj, MeasureTheory.pdf.IsUniform.pdf_eq, Polynomial.eval_C_X_eval₂_map_C_X, MvPolynomial.expand_bind₁, MeasureTheory.NullMeasurable.measure_preimage_eq_measure_restrict_preimage_of_ae_compl_eq_const, MvPolynomial.map_injective_iff, DirectSum.component.lof_self, LinearMap.toMatrixRight'_id, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_symm_apply_val, DeltaGeneratedSpace.isOpen_iff, HilbertBasis.orthonormal, RelEmbedding.inj, Similar.comp_left_iff, CliffordAlgebra.toBaseChange_ofBaseChange, leibniz_cross, MulEquiv.coprodAssoc_apply_inr, Diffeomorph.sumCongr_inr, AddMonoid.End.coe_pow, CategoryTheory.Iso.hom_inv_id_apply, PMF.apply_eq_zero_iff, AddMonoidHom.coe_toMultiplicative, IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic, Orientation.inner_rightAngleRotation_left, minpoly.isIntegrallyClosed_dvd_iff, HasFDerivAt.comp_hasDerivWithinAt, PowerSeries.gaussNorm_C, AlgebraicGeometry.Scheme.Hom.injective, SkewMonoidAlgebra.lift_unique', ContinuousMap.tendsto_iff_forall_isCompact_tendstoUniformlyOn, ConvexOn.dual, MulAction.orbitZPowersEquiv_symm_apply, WithSeminorms.continuous_seminorm, SetLike.GradeZero.coe_algebraMap, HasFDerivWithinAt.multilinear_comp, Ordinal.toZFSetIso_apply, Nimber.toOrdinal_eq_one, lp.lsingle_apply, CategoryTheory.Functor.RepresentableBy.isRepresentedBy, MonoidHom.range_eq_top, CliffordAlgebraComplex.equiv_symm_apply, Polynomial.expand_monomial, MeasureTheory.Integrable.measure_norm_gt_lt_top, Matrix.IsHermitian.eigenvectorUnitary_apply, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, Tuple.comp_sort_eq_comp_iff_monotone, cfcHomSuperset_apply, HVertexOperator.coeff_inj, RelEmbedding.eq_preimage, PolynomialModule.smul_single_apply, AddCommGrpCat.Colimits.Quot.ι_desc, OrderHom.dual_comp, absConvex_convexClosedHull, Topology.WithScott.toScott_inj, MeasureTheory.Measure.lintegral_condKernel_mem, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, MvPolynomial.prod_X_pow_eq_monomial, AddSubgroup.quotientiInfEmbedding_apply, AddMonoid.End.natCast_def, fderiv_apply_one_eq_deriv, RelEmbedding.refl_apply, TensorProduct.rid_tmul, AffineMap.isOpenMap_linear_iff, CategoryTheory.Linear.homCongr_apply, Polynomial.supNorm_C, WeakDual.coeFn_continuous, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, MDifferentiableAt.clm_apply_of_inCoordinates, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isEverywherePos, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, OrderIso.comap_atBot, IsPrimitiveRoot.primitiveRootsPowEquivOfCoprime_apply_coe, Submodule.coe_torsionBySet, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul, Submodule.mem_dualCoannihilator, isUnit_map_iff, SetSemiring.down_imageHom, ArithmeticFunction.zero_apply, fwdDiff_aux.fwdDiffₗ_apply, Sum.Lex.inl_strictMono, AffineMap.map_midpoint, OrthogonalIdempotents.lift_of_isNilpotent_ker, BialgHom.coe_toCoalgHom, LinearMap.minpoly_toMatrix, Complex.cot_conj, RelIso.pairwise_swap_listMap, HasFTaylorSeriesUpToOn.compContinuousLinearMap, Equiv.toIso_hom, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_w_apply, MeasureTheory.measure_toMeasurable, LinearMap.det_dualMap, MeasurableEquiv.coe_piCongrLeft, RingEquiv.map_prod, RingHom.Bijective.containsIdentities, Function.Embedding.right_inv_of_invOfMemRange, PiToModule.fromEnd_apply_single_one, IsUltrametricDist.algNormOfAlgEquiv_apply, Equiv.Perm.mem_ofSign, RingHom.FaithfullyFlat.codescendsAlong_surjective, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, Homeomorph.sumProdDistrib_apply, map_multiset_prod, MulChar.ofUnitHom_eq, DirectSum.of_injective, MvPowerSeries.weightedHomogeneousComponent_mul_of_le_weightedOrder, PartENat.withTopEquiv_symm_one, Con.sup_def, Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one, Set.vadd_graphOn, Sym2.sortEquiv_symm_apply, Fin.coe_orderIso_apply, matrixEquivTensor_apply_single, Rep.indToCoindAux_mul_snd, stdSimplex.sum_eq_one, SchwartzMap.integral_sesq_fourierIntegral_eq, Submodule.norm_orthogonalProjection_apply, AddEquiv.coprodAssoc_symm_apply_inl, Subfield.relfinrank_eq_toNat_relrank, Submodule.orderIsoMapComap_symm_apply, CategoryTheory.GrothendieckTopology.Cover.condition, CharacterModule.homEquiv_symm_apply_apply_apply, QuadraticMap.PosDef.le_zero_iff, Matrix.SpecialLinearGroup.range_toGL, ContinuousOn.partialSups, ClosureOperator.closure_sup_closure, Matrix.diagAddMonoidHom_apply, CStarMatrix.ofMatrix_symm_apply, ContinuousLinearMap.IsPositive.inner_nonneg_left, AddOpposite.coe_opAddEquiv, AddGroupSeminorm.apply_one, Finset.Colex.toColex_mono, LinearIsometryEquiv.coe_toLinearIsometry, ProbabilityTheory.Kernel.setLIntegral_deterministic', MvPolynomial.constantCoeff_monomial, RootPairing.coroot_root_two, ContinuousLinearMap.map_add, ModuleCat.homEquiv_extendScalarsComp, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, AddEquiv.punitCoprod_symm_apply, AffineEquiv.linearHom_apply, toENat_rank_span_set, DirectSum.coe_decompose_mul_of_right_mem, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_snd, dNext_comp_left, CategoryTheory.CommSq.left_adjoint_hasLift_iff, WithBot.ofDual_symm_apply, UniformConvergenceCLM.isVonNBounded_image2_apply, CliffordAlgebra.reverse_mem_evenOdd_iff, MvPolynomial.smul_eval, Equiv.asEmbedding_range, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, ContinuousMapZero.map_zero', HNNExtension.t_mul_of, CategoryTheory.Limits.Pi.reindex_inv_π, Finsupp.multinomial_eq, WithAbs.norm_eq_abv, CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit, Ordinal.omega0_le_omega, AlgebraicGeometry.StructureSheaf.const_algebraMap, Subsemiring.inclusion_injective, AlgEquiv.restrictScalars_apply, AddEquiv.symmEquiv_symm_apply_apply, LinearMap.adjoint_lTensor, LieModule.Cohomology.add_apply_apply, ArithmeticFunction.add_apply, Matrix.conjTransposeRingEquiv_symm_apply, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, MonoidHom.finsuppProd_apply, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', MeasureTheory.Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_top, MvPowerSeries.substAlgHom_coe, DirichletCharacter.LSeriesSummable_iff, ContinuousAffineEquiv.coe_trans, Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, continuousAdd_induced, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, AddMonoidHom.addSubmonoidMap_apply_coe, NormedAddGroupHom.incl_apply, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, Summable.toCompl_tsum, Equiv.sigmaSigmaSubtype_apply, LinearEquiv.smulOfNeZero_apply, PseudoMetric.triangle, HasOuterApproxClosed.apprSeq_apply_eq_one, fderiv_continuousMultilinear_apply_const_apply, Ideal.Quotient.mk_surjective, LinearMap.slope_comp, MeasurableEquiv.funUnique_apply, MultilinearMap.map_add_eq_map_add_linearDeriv_add, Seminorm.le_def, RingCon.quotientQuotientEquivQuotientₐ_mk_mk, TopCat.pullbackIsoProdSubtype_inv_snd, IsometryEquiv.funUnique_apply, InfHom.inf_apply, Set.coe_singletonMonoidHom, Homeomorph.isDenseEmbedding, RCLike.conj_eq_iff_real, multilinearCurryLeftEquiv_apply, MeasureTheory.AEStronglyMeasurable.ae_of_compProd, DividedPowers.isDPMorphism_def, ContinuousAlternatingMap.map_add_univ, LinearIsometryEquiv.coe_withLpProdUnique, LieModuleHom.neg_apply, IsFreeGroup.lift_symm_apply, AddSubmonoid.LocalizationMap.addEquivOfLocalizations_right_inv_apply, Equiv.prodProdProdComm_apply, FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence, MeasureTheory.Integrable.convolution_integrand, SchwartzMap.fourierTransformCLE_symm_apply, LieModule.exists_forall_lie_eq_smul, Monoid.CoprodI.NeWord.prod_singleton, Set.powersetCard.addActionHom_singleton_bijective, Algebra.TensorProduct.cancelBaseChange_symm_tmul, PartENat.withTopEquiv_natCast, Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe, AddCommGrpCat.Colimits.Quot.map_ι, matPolyEquiv_map_C, QuaternionAlgebra.re_equivProd_symm_apply, WittVector.ghostComponent_verschiebung, starL'_symm_apply, OrthonormalBasis.map_apply, MulHom.map_mclosure, RCLike.ofNat_mul_im, Matrix.SpecialLinearGroup.isEmbedding_toGL, CliffordAlgebra.evenToNeg_ι, ModuleCat.ExtendScalars.map_tmul, LinearMap.toMatrixOrthonormal_apply, PowerSeries.map_subst, IsLocalization.algEquiv_mk', MvPolynomial.C_eq_zero, ofColex_smul, DivisibleHull.qsmul_def, AddMagmaCat.ext_iff, MonoidAlgebra.mapRangeRingEquiv_apply, gcd_zero_right, convexHull_eq_singleton, MeasureTheory.condExpL1CLM_lpMeas, MvPolynomial.supDegree_toLex_C, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, convexHull_eq_zero, Module.Basis.coe_parallelepiped, ContinuousLinearEquiv.unitsEquivAut_symm_apply, MvPolynomial.coeff_rTensorAlgHom_tmul, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, ClosureOperator.closure_iSup_closure, smoothSheafCommRing.ι_forgetStalk_inv_assoc, PiTensorProduct.tmulEquivDep_symm_apply, fwdDiff_aux.shiftₗ_apply, Homeomorph.piCongrRight_apply, FiniteGaloisIntermediateField.adjoin_map, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, Submodule.rTensorOne_tmul_one, OrderAddMonoidIso.comp_symm_eq, Polynomial.card_roots_X_pow_sub_C, NumberField.InfinitePlace.embedding_of_isReal_apply, Sym.cons_equiv_eq_equiv_cons, Representation.asAlgebraHom_of, ProbabilityTheory.HasGaussianLaw.map_fun, ContMDiffWithinAt.clm_bundle_apply, Matrix.replicateRow_mul_replicateCol, Submodule.eq_starProjection_of_mem_orthogonal, AddSubgroup.centerCongr_symm_apply_coe, Fin.revPerm_apply, MvPolynomial.aeval_zero, MeasureTheory.Measure.count_apply_finset', Ideal.Quotient.eq, MeasurableEquiv.refl_apply, MonoidWithZeroHom.snd_inr, Ideal.quotientEquivAlgOfEq_mk, LinearIsometryEquiv.trans_apply, Differentiable.clm_apply, ContinuousMultilinearMap.add_apply, AddSubgroup.mem_comap, OrderMonoidIso.self_comp_symm, cfcₙHom_eq_cfcₙ_extend, MonoidWithZeroHom.snd_inl_apply_of_ne_zero, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, ContinuousLinearMap.mdifferentiableWithinAt, AddEquiv.prodAdditive_symm_apply, Equiv.sumProdDistrib_apply_left, LieAlgebra.of_zero, NonUnitalStarRingHom.coe_comp, SimpleGraph.Walk.reverse_map, ContMDiff.clm_bundle_apply, OrthogonalFamily.inner_sum, Invertible.mulLeft_symm_apply, sign_one, MeasureTheory.Measure.exists_sum_smul_dirac, Algebra.leftMulMatrix_complex, NormedAddGroupHom.id_apply, QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_measurableSet, Poly.one_apply, Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff, MultilinearMap.piFamily_apply, PartOrd.inv_hom_apply, Valuation.one_vlt_iff, RingHom.equivRatAlgHom_apply, ProbabilityTheory.covarianceBilin_apply_pi, RingHom.sclosure_preimage_le, PresheafOfModules.map_comp, LieAlgebra.IsKilling.biSup_corootSpace_eq_top, Equiv.mul_def, PeriodPair.latticeBasis_one, PartOrdEmb.id_apply, ContinuousMultilinearMap.prodEquiv_symm_apply_snd, IsScalarTower.algebraMap_smul, DFinsupp.card_uIcc, CategoryTheory.conjugateEquiv_mateEquiv_vcomp, PiTensorProduct.liftAux_tprod, IsValuativeTopology.isClopen_ball, MvPolynomial.killCompl_rename_app, IsLocalization.mk'_eq_iff_eq_mul, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι, isRightRegular_toLex, AddMonoid.Coprod.inr_injective, AddAction.toFun_apply, Algebra.Norm.Transitivity.eval_zero_comp_det, AbsoluteValue.trivial_apply, PrimeSpectrum.comapEquiv_apply, IsValuativeTopology.hasBasis_nhds, Nat.coe_castAddMonoidHom, MeasureTheory.SimpleFunc.measurableSet_support, Monotone.dual_right, SchwartzMap.integral_bilinear_laplacian_right_eq_left, diffToIdealOfQuotientCompEq_apply, NormedRing.algEquivComplexOfComplete_symm_apply, LinearMap.lTensor_comp_mk, SimpleGraph.ConnectedComponent.iso_image_comp_eq_map_iff_eq_comp, AddMonoidHom.map_mul₂, Module.Basis.toDual_injective, zsmulAddGroupHom_apply, MvPowerSeries.algebraMap_apply'', ContinuousLinearMap.natCast_apply, IsAdjoinRootMonic.coeff_apply_lt, DomMulAct.mk_smul_mulDistribActionHom_apply, MultilinearMap.constLinearEquivOfIsEmpty_apply, SupHom.const_apply, HasFDerivAt.lim, MeasureTheory.FiniteMeasure.restrict_apply, mem_affineSpan_pair_iff_exists_lineMap_eq, MulEquiv.symmEquiv_apply_apply, AbsoluteValue.IsAdmissible.exists_approx, LinearEquiv.finTwoArrow_symm_apply, IsLocalization.coe_toLocalizationMap, Nat.Icc_factorization_eq_pow_dvd, Seminorm.comp_apply, WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv, LieModule.traceForm_eq_zero_if_mem_lcs_of_mem_ucs, ZLattice.covolume_eq_det_mul_measureReal, IsPrimitiveRoot.primitiveRootsPowEquiv_apply_coe, openSegment_eq_image_lineMap, Equiv.Perm.sigmaCongrRightHom_injective, CategoryTheory.Limits.WidePullbackCone.reindex_π, LinearMap.map_mul_algebraMap, AffineEquiv.pointReflection_midpoint_right, Equiv.existsUnique_congr_right, ContinuousLinearMap.isometry_mul, MulAut.conj_inv_apply, Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, AlgEquiv.algHomUnitsEquiv_apply_symm_apply, NonarchAddGroupSeminorm.apply_one, AddCommMonCat.hom_neg_apply, Homeomorph.trans_apply, SimpleGraph.IsAcyclic.of_comap, Finset.Icc_toDual, Finsupp.mem_rangeIcc_apply_iff, LinearMap.detAux_comp, AddCircle.measurePreserving_equivIoc, powersMulHom_apply, Rat.castOrderEmbedding_apply, CategoryTheory.Functor.inducedTopology_sieves, BoxIntegral.Box.mapsTo_insertNth_face_Icc, TopCat.Presheaf.germ_exist, BoolAlg.dual_map, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, Circle.argEquiv_symm_apply, RingHom.surjectiveOnStalks_iff_forall_maximal', ContinuousLinearMap.isOpen_injective, MeasureTheory.measurePreserving_piUnique, ContinuousLinearEquiv.coe_symm_toHomeomorph, Nat.ordCompl_pos, qExpansion_add, Ordinal.toGame_zero, IsFractionRing.mk'_mk_eq_div, FirstOrder.Language.BoundedFormula.IsQF.realize_embedding, RingEquiv.cast_symm_apply, MeasureTheory.Integrable.norm_integral_condDistrib_map, UniformFun.ofFun_smul, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, AddConstEquiv.coe_val_inv_equivUnits_apply, Matroid.mapSetEmbedding_indep_iff, OneHom.coe_div, MvPolynomial.comp_aeval, NumberField.RingOfIntegers.coe_injective, LinearEquiv.map_dfinsuppSumAddHom, ProbabilityTheory.condExpKernel_ae_eq_condExp, Language.map_map, LieHom.toFun_eq_coe, Equiv.neg_apply, ZMod.χ₈_nat_mod_eight, RingEquiv.map_pow, AddCircle.toCircle_apply_mk, RingEquiv.prodZeroRing_apply, OrthonormalBasis.sum_repr_symm, groupCohomology.cocyclesOfIsMulCocycle₂_coe, homeomorphUnitSphereProd_apply_fst_coe, RCLike.isCauSeq_im, MeasureTheory.one_le_prob_iff, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, Subgroup.toAddSubgroup_closure, DirectSum.IsInternal.collectedBasis_repr_of_mem_ne, Module.dualProdDualEquivDual_apply, HahnSeries.single_injective, MvPolynomial.constantCoeff_X, Polynomial.image_rootSet, MvPolynomial.divMonomial_monomial, MvPolynomial.frobenius_zmod, Module.Basis.toMatrix_apply, InnerProductSpace.norm_sq_eq_re_inner, RootPairing.RootPositiveForm.rootLength_reflectionPerm_self, LeftInvariantDerivation.coe_neg, Cardinal.mk_toNat_of_infinite, FirstOrder.Language.Term.constantsVarsEquiv_apply, LinearMap.surjective_of_comp_eq_id, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, LinearIsometry.coe_injective, MultilinearMap.cons_smul, CategoryTheory.ofGrothendieck_iff, Function.Embedding.toFun_eq_coe, ContinuousAlternatingMap.ext_iff, Diffeomorph.contMDiffOn_diffeomorph_comp_iff, AffineEquiv.injective_pointReflection_left_of_module, Equiv.sigmaAssocProd_symm_apply_fst, realPart_surjective, StrongDual.toLpₗ_apply, Orientation.kahler_apply_self, AddConstMap.coe_replaceConsts, MagmaCat.ofHom_apply, MeasureTheory.L1.setToL1_apply_coeToLp, VitaliFamily.ae_tendsto_lintegral_div', Equiv.sumProdDistrib_apply_right, wbtw_iff_right_eq_or_left_mem_image_Ici, Equiv.divRight_apply, PowerSeries.expand_C, Homeomorph.prodUnique_symm_apply_snd, AddConstMapClass.map_nat', Module.Invertible.rTensorInv_leftInverse, BoundedContinuousFunction.nndist_eq_iSup, RootPairing.Hom.weight_coweight_transpose_apply, Polynomial.derivative_sq, Hamming.ofHamming_add, AddHom.coe_add, MultilinearMap.curryFinFinset_symm_apply_const, IsAntichain.preimage_embedding, KaehlerDifferential.mvPolynomialBasis_repr_apply, MulEquiv.funUnique_symm_apply, TopCat.GlueData.fromOpenSubsetsGlue_injective, Polynomial.leadingCoeff_C_mul_X_pow, AddEquiv.coe_mapAddSubgroup, WittVector.frobeniusPolyAux_eq, SimpleGraph.colorable_iff_exists_bdd_nat_coloring, LinearMap.prodMapAlgHom_apply_apply, signedDist_triangle_right, Polynomial.mem_roots_sub_C, RingInvo.involution, MulEquiv.uniqueProd_apply, ofDegLex_injective, Polynomial.hermite_eq_deriv_gaussian, MeasureTheory.Measure.MutuallySingular.measure_nullSet, Differential.mapCoeffs_X, MulEquiv.comapSubgroup_apply, isCompact_closedAbsConvexHull_of_totallyBounded, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, AddSubgroup.MapSubtype.orderIso_apply_coe, FreeAddSemigroup.length_map, sSupHom.dual_comp, IntermediateField.AdjoinSimple.trace_gen_eq_zero, HasStrictFDerivAt.continuousAlternatingMap_apply, ProbabilityTheory.Kernel.lintegral_prod_symm, MeasureTheory.Measure.infinitePi_map_curry_symm, ModuleCat.free_μ_freeMk_tmul_freeMk, Orthonormal.inner_left_sum, ciSup_partialSups_eq, Matrix.isHermitian_submatrix_equiv, algebraMap_le_iff_le_spectrum, Module.DualBases.eval_same, Orientation.inner_smul_rotation_pi_div_two_right, Set.powersetCard.coe_compl, ProbabilityTheory.hasFiniteIntegral_comp_iff, ZSpan.instDiscreteTopologySubtypeMemSubmoduleIntSpanRangeCoeBasisRealOfFinite, WellQuasiOrdered.exists_monotone_subseq, Matrix.SpecialLinearGroup.coe_GLPos_neg, ContinuousLinearEquiv.map_neg, MvPolynomial.optionEquivLeft_coeff_some_coeff_none, PowerSeries.map_algebraMap_eq_subst_X, NonarchAddGroupSeminorm.zero_apply, MvPowerSeries.coeff_zero_one, ContinuousLinearMap.continuous_uncurry_of_multilinear, TensorProduct.forall_vanishesTrivially_iff_forall_rTensor_injective, MeasureTheory.SimpleFunc.memLp_approxOn, Finsupp.sigmaFinsuppLEquivPiFinsupp_apply, DFinsupp.equivProdDFinsupp_add, Equiv.coe_prodComm, preimage_vadd_setₛₗ', IntermediateField.mem_adjoin_range_iff, Monovary.dual_right, ArchimedeanClass.FiniteElement.val_zero, Equiv.set_forall_iff, QuadraticForm.toDualProd_apply, RatFunc.liftAlgHom_apply_div, Poly.sumsq_eq_zero, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, Nat.ordCompl_mul, tendsto_iff_forall_eval_tendsto_topDualPairing, Path.Homotopy.cast_apply, AlgEquiv.coe_coe_symm_apply_coe_apply, CategoryTheory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.CommSq.LiftStruct.opEquiv_symm_apply, Subring.closure_preimage_le, RatFunc.liftRingHom_C, MonoidHom.mem_range, LinearIsometry.map_starProjection, CategoryTheory.Iso.toLinearEquiv_apply, IsLocalFrameOn.coeff_apply_zero_at, Diffeomorph.contMDiffAt_comp_diffeomorph_iff, CyclotomicRing.adjoin_algebra_injective, LinearMap.IsNonneg.nonneg, DFinsupp.coe_update, MeasureTheory.hausdorffMeasure_vadd, SymmetricAlgebra.lift_comp_ι, Orientation.inner_mul_areaForm_sub', LieHom.isIdealMorphism_iff, Frm.inv_hom_apply, AddChar.eq_zero_iff, TopologicalSpace.Opens.adjunction_counit_app_self, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, ContMDiffSection.coeAddHom_apply, WithZero.toMulBot_zero, RootPairing.CoPolarization_apply, SchwartzMap.ext_iff, ContinuousLinearMap.inr_apply, InfPrime.ofDual, Module.End.one_apply, LinearMap.det_id, Polynomial.not_isUnit_X_add_C, Fin.castLEquiv_apply, AlgebraicGeometry.LocallyOfFiniteType.stalkMap, Trivialization.proj_clift, RootPairing.chainTopCoeff_reflectionPerm_left, CategoryTheory.Bicategory.mateEquiv_eq_iff, LinearMap.compLeft_apply, MeasureTheory.dist_convolution_le', DomMulAct.stabilizer_card', Profinite.IndexFunctor.map_comp_π_app, ContinuousLinearEquiv.uniqueProd_apply, finsuppTensorFinsuppRid_single_tmul_single, OrderIso.withBotCongr_apply, TopologicalSpace.Opens.mem_map, AdicCompletion.sum_of, toLex_inv, WittVector.coeff_frobeniusFun, MeasureTheory.OuterMeasure.sSup_apply, CategoryTheory.Arrow.equivSigma_symm_apply_hom, Dilation.mapsTo_ball, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, LinearIndependent.linearCombinationEquiv_symm_apply, Polynomial.degree_cubic, WithZero.lift_zero, Locale.PT.isOpen_iff, Submodule.equivSubtypeMap_apply, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_deriv_mul, eq_affineCombination_of_mem_affineSpan, AlternatingMap.curryLeftLinearMap_apply, Nat.ordProj_le, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, ModuleCat.Derivation.d_map, MonoidHom.inl_apply, AlgEquiv.val_algHomUnitsEquiv_symm_apply, ProbabilityTheory.aestronglyMeasurable_trim_condExpKernel, SimpleGraph.UnitDistEmbedding.embed_p_apply, MeasureTheory.Measure.InnerRegularCompactLTTop.innerRegular, SymmetricAlgebra.lift_ι, OrderMonoidHom.inlₗ_apply, MeasureTheory.OuterMeasure.mkMetric'.pre_le, Polynomial.natSepDegree_C_mul, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, Algebra.adjoin_eq_exists_aeval, ContinuousMultilinearMap.piEquiv_apply, absConvexHull_subset_closedAbsConvexHull, lcm_one_left, ZSpan.isAddFundamentalDomain, CircleDeg1Lift.coe_toOrderIso, AddMonoidHom.coe_toHomAddUnits, Module.DualBases.basis_repr_apply, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, IsLocalRing.split_injective_iff_lTensor_residueField_injective, UpperHalfPlane.petersson_symm, AbsoluteValue.IsEuclidean.map_lt_map_iff', Algebra.Extension.Hom.mapKer_apply_coe, MvPolynomial.totalDegree_renameEquiv, SymAlg.unsym_injective, AlternatingMap.map_update_neg, AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singleton, Module.preReflection_apply, CircleDeg1Lift.translate_zpow, StarSubalgebra.algebraMap_mem, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, QuaternionAlgebra.hom_ext_iff, Equiv.preimage_symm_preimage, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff, SpecialLinearGroup.congr_linearEquiv_apply_apply, Algebra.toMatrix_lmul', ContinuousMap.Homotopy.extend_apply_of_mem_I, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, CategoryTheory.forget₂_comp_apply, RingSeminorm.toFun_eq_coe, Submodule.isIdempotentElemEquiv_symm_apply_coe, dist_homothety_center, InitialSeg.lt_iff_lt, LinearMap.continuous_of_nonzero_on_open, AddSubgroup.coe_toZModSubmodule, Derivation.smul_apply, LieAlgebra.ad_apply, MvPolynomial.expand_mul, AffineEquiv.prodCongr_apply, List.formPerm_mem_iff_mem, DFinsupp.sigmaCurryLEquiv_symm_apply, SSet.stdSimplex.monotone_apply, NormedAddGroupHom.coe_sum, sum_hom_units_eq_zero, FreeAlgebra.algebraMap_inj, AddMonoid.End.coe_one, Homeomorph.shearMulRight_symm_coe, Polynomial.hasseDeriv_monomial, FirstOrder.Language.Formula.realize_equivSentence_symm_con, ConvexOn.real_univ_sSup_affine_eq, LieAlgebra.toEnd_pow_apply_mem, LaurentPolynomial.C_eq_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, Multiplicative.toAdd_lt, AddMonoidAlgebra.single_mul_apply, MonoidHom.toAdditiveRight_symm_apply_apply, Subsemiring.mopRingEquivOp_apply_coe, PowerSeries.trunc_trunc_pow, Localization.monoidOf_eq_algebraMap, ArithmeticFunction.id_apply, PolynomialLaw.isCompat, FirstOrder.Language.PartialEquiv.toEquiv_inclusion_apply, Equiv.symm_trans_swap_trans, PowerSeries.coeff_mul, abs_signedDist_eq_dist_iff_vsub_mem_span, PowerSeries.constantCoeff_largeSchroderSeries, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, Equiv.optionIsSomeEquiv_apply, Valuation.one_vle_iff, Matrix.blockDiagonal'AddMonoidHom_apply, TopologicalSpace.IrreducibleCloseds.equivSubtype_apply, ProbabilityTheory.IsFiniteKernel.isFiniteMeasure, isRightRegular_toMul, Profinite.NobelingProof.πs_apply_apply, IsLocalization.toInvSubmonoid_mul, AddMonoidHom.toMultiplicativeLeft_symm_apply_apply, WeierstrassCurve.Projective.baseChange_polynomialX, Fin.succFunEquiv_symm_apply, ExteriorAlgebra.isUnit_algebraMap, Nat.factorization_le_factorization_choose_add, ContinuousOrderHom.comp_apply, ArithmeticFunction.LSeries_vonMangoldt_eq, Module.Invertible.leftInverse_iff_rightInverse, Homeomorph.nhds_eq_comap, LinearIsometry.coe_id, Affine.Simplex.affineCombination_mem_interior_face_iff_pos, LinearIsometryEquiv.strictConvex_image, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, ContinuousLinearMap.toSpanSingleton_one, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, Module.DualBases.dual_lc, BumpCovering.toFun_eq_coe, CategoryTheory.GrothendieckTopology.dense_covering, linearIndependent_equiv, wbtw_iff_left_eq_or_right_mem_image_Ici, CategoryTheory.extensiveTopology.presheafIsLocallySurjective_iff, MeasureTheory.Measure.deterministic_comp_eq_map, SchwartzMap.le_seminorm, groupCohomology.coboundariesOfIsMulCoboundary₁_coe, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, toWeakSpace_closedConvexHull_eq, MeasureTheory.OuterMeasure.ext_iff, FirstOrder.Language.Hom.map_fun, ExteriorAlgebra.map_injective_field, BoundedLatticeHom.toFun_eq_coe, LinearMap.apply_single, WithCStarModule.inner_single_right, CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply, IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow, MonoidWithZeroHom.inl_injective, FreeAddMonoid.freeAddMonoidCongr_symm_of, Matrix.cRank_submatrix, List.formPerm_apply_mem_eq_self_iff, Quiver.SingleObj.toPrefunctor_id, CommRingCat.ofHom_apply, abs_sub_map_le_div, Algebra.Extension.contangentEquiv_tmul, GradedTensorProduct.algebraMap_def', Unitization.norm_def, BoundedContinuousFunction.coe_ofNat, ContMDiff.clm_bundle_apply₂, Representation.IntertwiningMap.toLinearMap_apply, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, SheafOfModules.pushforwardComp_hom_app_val_app, DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSum, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul, convexHull_pi, AddConstMapClass.map_sub_int', Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, CategoryTheory.Discrete.equivOfEquivalence_apply, Unitary.conjStarAlgAut_symm_apply, IsPerfectClosure.equiv_self_apply, ArithmeticFunction.prodPrimeFactors_apply, toColex_inj, AffineEquiv.ext_iff, isAddRightRegular_toDual, DirectSum.mulHom_apply, LieModuleEquiv.coe_toLinearEquiv, ArithmeticFunction.sigma_eq_one_iff, DirectSum.coe_mul_of_apply_of_mem_zero, ThreeAPFree.le_addRothNumber, MeasureTheory.projectiveFamilyContent_diff_of_subset, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_ne, Polynomial.derivativeFinsupp_map, WithLp.equiv_apply, GenLoop.toLoop_apply_coe, Ideal.quotOfMul_surjective, CategoryTheory.isNoetherianObject_iff_monotone_chain_condition, AddEquiv.coe_prodComm, AddEquiv.coe_toEquiv_symm, Cardinal.toENat_strictMonoOn, Ordinal.typein_apply, HahnModule.coeff_smul, MvPolynomial.C_mul', UniformFun.precomp_uniformContinuous, ProbabilityTheory.measurableSet_integrable, AmpleSet.image_iff, map_natCast_smul, Submodule.map₂_span_span, InfHom.ext_iff, SchwartzMap.eLpNorm_le_seminorm, MulHom.coeFn_apply, finSuccAboveOrderIso_apply, Trivialization.pullback_apply, MeasureTheory.L1.setToL1_congr_left', ContinuousMapZero.mkD_eq_self, MeasureTheory.Content.outerMeasure_exists_open, CochainComplex.HomComplex.δ_hom_apply, WithBot.toDualTopEquiv_symm_bot, Polynomial.cyclotomic.eval_apply, Equiv.Perm.extendDomain_apply_not_subtype, Polynomial.mem_roots_iff_aeval_eq_zero, Equiv.Perm.ofSubtype_apply_coe, LieModule.coe_genWeightSpace_of_top, frobenius_neg, Pretrivialization.linearMapAt_symmₗ, PerfectionMap.comp_equiv, AddHom.coe_coe, MvPolynomial.isEmptyAlgEquiv_apply, Module.Basis.coe_ofVectorSpace, LieAlgebra.lieCharacter_apply_of_mem_derived, AffineBasis.ext_iff, MulEquiv.eq_iff_eq_on_generator, Submodule.det_reflection, ClassGroup.mk_mk0, parallelepiped_comp_equiv, LinearMap.BilinForm.ext_iff, OrderMonoidIso.apply_eq_iff_symm_apply, BddDistLat.ofHom_apply, MvPolynomial.bind₂_X_right, RingEquiv.piUnique_symm_apply, ContinuousLinearMap.measurable_apply, IsLocalization.scaleRoots_commonDenom_mem_lifts, map_mul, Function.Embedding.sigmaSet_range, SSet.S.equivElements_apply_fst, Finsupp.llift_symm_apply, Int.ofAdd_mul, WeakDual.CharacterSpace.eq_set_map_one_map_mul, IsLocalizedModule.map_id, Finsupp.Colex.lt_iff, finAddFlip_apply_mk_left, LinearIsometry.preimage_sphere, Orientation.kahler_rotation_left', DirectSum.of_eq_same, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, CategoryTheory.codiscreteEquiv_apply, lineMap_lt_map_iff_slope_lt_slope, MeasureTheory.Measure.addHaar_affineSubspace, IsSepClosed.algebraMap_surjective, Nat.equivProdNatSmoothNumbers_apply', measure_Icc_lt_top, hasFDerivAtFilter_iff_isLittleOTVS, AffineMap.toConstProdLinearMap_apply, PowerSeries.C_eq_algebraMap, ContinuousMonoidHom.id_toFun, LinearMap.quotKerEquivRange_apply_mk, BddOrd.id_apply, CategoryTheory.Limits.Concrete.prodEquiv_symm_apply_fst, CategoryTheory.ObjectProperty.isLocal.homEquiv_apply, TensorProduct.finsuppScalarLeft_apply_tmul_apply, RCLike.hasSum_re, AddEquiv.surjective, Equiv.mulLeft_symm_apply, Matrix.ker_diagonal_toLin', AddMonoidAlgebra.modOf_apply_self_add, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, LocallyConstant.constMonoidHom_apply, left_lt_lineMap_iff_lt, second_derivative_symmetric, Equiv.ofRightInverseOfCardLE_apply, Polynomial.monomial_add, Algebra.Generators.cMulXSubOneCotangent_eq, LightCondSet.topCatAdjunctionCounit_bijective, LatticeHom.symm_dual_comp, Filter.Tendsto.eval, ContinuousAlternatingMap.curryLeft_same, CompactlyGenerated.homeoOfIso_symm_apply, MvPolynomial.map_C, Real.volume_Ioc, FreeAlgebra.ι_comp_lift, Set.Finite.fin_embedding, NonUnitalStarSubalgebra.coe_map, Polynomial.eval₂_at_one, map_abs, spectrum.singleton_add_eq, Finsupp.apply_single', ProbabilityTheory.Kernel.integral_density, ContinuousMultilinearMap.curryRight_apply, TensorProduct.inner_comm_comm, CliffordAlgebraComplex.toComplex_ι, UpperHalfPlane.σ_ofReal, Rep.linearization_obj_ρ, MeasureTheory.Measure.dirac_apply_ne_zero_iff_eq_one, AdicCompletion.AdicCauchySequence.map_apply_coe, Equiv.divLeft_apply, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, MeasureTheory.measure_liminf_atTop_eq_zero, TruncatedWittVector.truncate_surjective, Metric.measure_closedEBall_pos, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, AffineBasis.toMatrix_inv_vecMul_toMatrix, RootPairing.RootPositiveForm.two_mul_apply_root_root, FreeAbelianGroup.lift_comp_apply, NormedSpace.expSeries_apply_eq', Ideal.pointwise_smul_eq_comap, PEquiv.ext_iff, ContinuousMap.curry_apply, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd, AlgebraicGeometry.isOpenImmersion_eq_inf, LieModuleHom.range_eq_top, AddLocalization.mk_eq_mk_iff, Equiv.coe_addLeft, CpltSepUniformSpace.hom_comp, AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_base_fst, ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_mutuallySingularSetSlice, gc_upperClosure_coe, Finsupp.equivMapDomain_symm_apply, Ideal.toCotangent_apply, Submodule.inner_orthogonalProjection_eq_of_mem_left, AlgebraicGeometry.compactSpace_iff_exists, AddMonoidHom.map_zmultiples, Polynomial.resultant_X_add_C_left, WeierstrassCurve.Jacobian.baseChange_neg, MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac, gal_X_sub_C_isSolvable, SimplexCategory.II.map'_eq_castSucc_iff, finSuccEquiv_symm_some, Real.integrable_of_summable_norm_Icc, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, Sym2.coe_lift₂_symm_apply, map_dfinsuppSum, ContinuousAlgEquiv.symm_apply_apply, ContinuousMap.comp_one, MonoidAlgebra.smul_apply, NormedAddGroupHom.le_opNorm, Finsupp.prod_pow, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap, MonoidAlgebra.singleHom_apply, MeasureTheory.OuterMeasure.measure_inter_union, Polynomial.Bivariate.equivMvPolynomial_X, Module.End.mem_iInf_maxGenEigenspace_iff, AddCommGrpCat.injective_of_mono, Polynomial.hasDerivWithinAt_aeval, Multiset.coe_consEquiv_of_eq_of_lt, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, PrimeSpectrum.piLocalizationToMaximal_surjective, Ordinal.ToType.mk_symm_apply_coe, InitialSeg.transPrincipal_apply, image_segment, CategoryTheory.ShortComplex.ShortExact.injective_f, ProbabilityTheory.IndepFun.measure_inter_preimage_eq_mul, groupHomology.isoCycles₁_hom_comp_i_apply, MulEquiv.submonoidMap_symm_apply, OrderHom.curry_apply, LinearMap.coe_rTensorHom, IsometryEquiv.coe_withLpUniqueProd, GrpCat.forget₂_map, Unitary.toRingEquiv_conjStarAlgAut, RingEquiv.mapMatrix_apply, AddMonoidHom.coe_smul, LinearMap.isLinearMap_of_compatibleSMul, MvPolynomial.C_dvd_iff_dvd_coeff, Algebra.IsInvariant.isInvariant, SimpleGraph.Iso.mapNeighborSet_apply_coe, FirstOrder.Language.Hom.mem_eqLocus, Matrix.kronecker_assoc', RingHom.iterate_map_frobenius, UniformOnFun.edist_def', Equiv.Perm.zpow_eq_zpow_on_iff, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Module.Basis.map_apply, CoalgHom.congr_fun, Finsupp.mk_mem_graph, HahnSeries.coeff_toPowerSeries, InfTopHom.subtypeVal_coe, AddMonoidHom.restrict_apply, Finsupp.coe_add, isIntegrallyClosedIn_iff, Finsupp.nsmul_apply, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, ContinuousLinearMap.extendTo𝕜_apply, MvPolynomial.pderiv_C_mul, Measurable.simpleFunc_add, Filter.Germ.coe_coeRingHom, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, Nat.card_divisors, Module.Basis.det_comp, TwoSidedIdeal.comap_comap, Module.Basis.symmetricAlgebra_repr_apply, OreLocalization.numeratorHom_apply, Monoid.CoprodI.lift_of', LinearEquiv.prodProdProdComm_apply, rotation_trans, RingHom.map_iterate_frobeniusEquiv_symm, Valued.toNormedField.one_lt_norm_iff, DirectSum.single_eq_lof, NumberField.absNorm_differentIdeal, Unitary.val_toUnits_apply, DirichletCharacter.changeLevel_factorsThrough, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, LinOrd.forget_map, RingCon.coe_comapQuotientEquivRangeₐ_symm_mk, Algebra.TensorProduct.assoc_symm_tmul, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁, Subgroup.coe_toAddSubgroup_apply, Algebra.TensorProduct.opAlgEquiv_symm_apply, Cubic.equiv_symm_apply_b, PowerSeries.coeff_smul, MeasureTheory.SimpleFunc.setToSimpleFunc_indicator, FirstOrder.Language.HomClass.realize_term, DomAddAct.continuous_mk, Polynomial.coeff_monomial_same, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap_1, NormedAddGroupHom.comp_apply, ContinuousAlgHom.ext_ring_iff, MeasureTheory.OuterMeasure.coeFnAddMonoidHom_apply, Module.AEval.of_symm_X_smul, LinearEquiv.sumPiEquivProdPi_symm_apply, MeasureTheory.tendsto_measure_sigmaFiniteSetGE, HasFDerivAt.comp_hasDerivWithinAt_of_eq, EuclideanSpace.volume_ball_fin_three, Polynomial.aeval_coe_eq_smeval, MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply, PiLp.projₗ_apply, AddEquiv.coe_prodAssoc_symm, AffineMap.restrict.surjective, ArithmeticFunction.ext_iff, NonUnitalStarAlgHom.map_adjoin_singleton, MonoidAlgebra.mapDomainNonUnitalRingHom_apply, Affine.Simplex.inradius_restrict, OrderAddMonoidIso.coe_trans, isAddLeftRegular_toAdd, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, Field.Emb.Cardinal.filtration_apply, Derivation.leibniz_of_mul_eq_one, Quotient.mkRelHom_apply, ProbabilityTheory.IsGaussian.integral_dual, WithTop.toDual_symm_apply, AbsoluteValue.IsEquiv.eq_iff_eq, SheafOfModules.Presentation.map_relations_I, Equiv.Set.rangeSplittingImageEquiv_apply_coe_coe, FGModuleCat.Iso.conj_eq_conj, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, matrixEquivTensor_apply_symm, MeasureTheory.Measure.integral_compProd, NonUnitalStarAlgHom.fst_apply, Polynomial.IsMonicOfDegree.aeval_add, BialgHom.coe_comp, Finsupp.supportedEquivFinsupp_symm_apply_coe_support_val, Convex.addHaar_frontier, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', WithTop.ofDual_map, SupBotHom.sup_apply, ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring, Polynomial.natDegree_multiset_prod_X_sub_C_eq_card, AddLocalization.addEquivOfQuotient_symm_mk', Bialgebra.counit_mul, AddConstMap.coe_comp, Nat.nth_apply_eq_orderIsoOfNat, RingCon.coe_iInf, AffineIsometryEquiv.symm_apply_apply, Cardinal.preAleph_le_of_isSuccPrelimit, Complex.linearEquiv_det_conjAe, Submodule.orderIsoMapComap_apply, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, Orientation.abs_areaForm_le, Metric.Snowflaking.preimage_toSnowflaking_closedEBall, DomMulAct.comap_mk.symm_nhds, SlashInvariantForm.toFun_eq_coe, Affine.Simplex.ExcenterExists.sign_touchpointWeights, MeasureTheory.AddSubgroup.index_mul_measure, ProbabilityTheory.Kernel.compProd_apply_univ_le, ZeroHom.smul_apply, Set.conj_mem_fixingSubgroup, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, ZLattice.exists_forall_abs_repr_le_norm, LinearEquiv.symmEquiv_apply_apply, intervalIntegrable_const_iff, ContDiffWithinAt.laplacianWithin_CLM_comp_left_nhds, le_monotonicSequenceLimit, Equicontinuous.isUniformInducing_uniformFun_iff_pi, Cardinal.range_aleph, Matrix.toBilin'_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, mulMonoidHom_apply, groupHomology.lsingle_comp_chainsMap_f, ContinuousLinearEquiv.neg_apply, AffineMap.restrict.coe_apply, NumberField.RingOfIntegers.isIntegral_coe, MultilinearMap.dfinsuppFamily_single_left_apply, AlgEquiv.symm_apply_apply, sInfHom.dual_comp, Matrix.toMvPolynomial_eval_eq_apply, Polynomial.C_dvd_iff_dvd_coeff, IsAdjoinRoot.lift_self_apply, CompactlySupportedContinuousMap.finsetInf'_apply, MultilinearMap.domDomCongrLinearEquiv'_apply, BotHomClass.map_bot, Pretrivialization.symmₗ_apply, WithTop.map_toDual, LinearMap.det_restrictScalars, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, MulActionHom.map_mem_fixedPoints, OneHom.coe_mulSingle, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, EuclideanGeometry.angle_homothety, Submodule.linearMap_eq_iff_of_eq_span, Finset.image_nsmul, Nat.Prime.factorization_self, CliffordAlgebra.changeForm_ι, MeasureTheory.FiniteMeasure.restrict_mass, LinearIsometryEquiv.edist_map, ContinuousAddEquiv.isAddHaarMeasure_map, Polynomial.hasStrictDerivAt_aeval, finEquivZMultiples_symm_apply, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, AnalyticOn.iteratedFDeriv_comp_perm, Diffeomorph.mdifferentiable, LieAlgebra.conj_ad_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, LocallyConstant.coe_const, Function.Embedding.piCongrRight_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, AffineIsometryEquiv.map_eq_iff, AddEquiv.addDissociated_preimage, MonoidHom.map_sub_swap, Mathlib.Tactic.Elementwise.hom_elementwise, IsValuativeTopology.hasBasis_nhds_zero, Submonoid.LocalizationMap.mulEquivOfLocalizations_symm_apply, LinearMap.flip_injective_iff₂, Valuation.IsEquiv.eq_zero, Equiv.Perm.IsCycle.zpowersEquivSupport_apply, VectorPrebundle.exists_coordChange, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_lintegral, Algebra.embeddingsMatrix_apply, BoolAlg.coe_comp, AffineMap.lineMap_anti, CategoryTheory.Localization.homEquiv_apply, MvPowerSeries.coeff_add_mul_monomial, AddMonoidAlgebra.single_mul_apply_of_not_exists_add, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, ContinuousLinearMap.continuous, Quotient.finChoiceEquiv_apply, AddMonoid.Coprod.fst_apply_inl, RestrictScalars.ringEquiv_map_smul, ComplexShape.Embedding.homEquiv_symm_apply, Equiv.prodSumDistrib_symm_apply_right, Matrix.adjugate_def, Equiv.permCongr_refl, Bialgebra.TensorProduct.map_tmul, AddChar.toMonoidHomEquiv_apply, Metric.Snowflaking.preimage_ofSnowflaking_ball, MDifferentiableOn.clm_apply, monoidEndToAdditive_symm_apply_apply, MeasureTheory.SimpleFunc.coe_smul, RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, SSet.prodStdSimplex.objEquiv_map_apply, MeasureTheory.Measure.hausdorffMeasure_le_liminf_tsum, Equiv.tprod_eq, MeasureTheory.setLAverage_eq, AddAut.coe_one, ZMod.χ₄_int_three_mod_four, Equiv.left_vsub_pointReflection, MvPolynomial.natDegree_optionEquivLeft, MeasureTheory.piPremeasure_pi', LieAlgebra.Extension.ofTwoCocycle_proj_apply, AlgebraicGeometry.Scheme.stalkMap_congr_point, frobeniusEquiv_def, AddCon.rel_eq_coe, RestrictScalars.lsmul_apply_apply, Equiv.trans_swap_trans_symm, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, LaurentPolynomial.single_eq_C_mul_T, AddCon.sSup_def, MonoidHom.apply_mint, SubAddAction.ofStabilizer.snoc_last, Fin.predAboveOrderHom_coe, SemidirectProduct.mulEquivProd_symm_apply_left, CategoryTheory.GrothendieckTopology.OneHypercover.IsPreservedBy.mem₀, Subalgebra.coe_val, Finsupp.card_pi, AlgHom.toUnder_right, AddSubmonoid.mem_closure_image_pos_iff, AddMonoidAlgebra.mapDomain_algebraMap, ContinuousMultilinearMap.domDomCongr_apply, ContMDiffMap.mdifferentiable, LinearMap.compQuadraticMap_apply, ContinuousMapZero.toContinuousMapHom_toNNReal, ContinuousAddMonoidHom.coe_zero, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, Valuation.IsNontrivial_iff_exists_one_lt, ModularForm.SL_slash_def, MeasureTheory.Measure.le_map_apply, LinearMap.toMatrix_prodMap, SimpleGraph.coe_recolorOfEmbedding, AddChar.norm_apply, HahnModule.coeff_single_zero_smul, Path.Homotopy.coeFn_injective, StarAlgHom.coe_comp, Matrix.toLin_apply, SimpleGraph.Iso.comap_apply, PseudoMetric.IsUltra.le_sup, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_x, Polynomial.Splits.C_mul_X_pow, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, Ideal.absNorm_top, Path.range_reparam, Equiv.optionSubtype_apply_apply, WittVector.constantCoeff_wittMul, ProbabilityTheory.Kernel.lintegral_density, bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero, AlgHom.liftNormal_commutes, AddSubmonoid.isLocalizationMap_iff_bijective, spectrum.singleton_sub_eq, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, groupCohomology.H1π_eq_zero_iff, Matrix.toLin'_one, NonUnitalAlgHom.map_add, groupHomology.H1AddEquivOfIsTrivial_symm_apply, ExteriorAlgebra.map_injective, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, Matrix.submatrix_diagonal_equiv, LinOrd.ext_iff, LinearIsometry.coe_toAffineIsometry, PiTensorProduct.tmulEquivDep_apply, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset', ArithmeticFunction.sigma_mono, Polynomial.iterate_derivative_eq_zero_of_degree_lt, Ideal.absNorm_apply, ContinuousLinearEquiv.unitsEquivAut_apply_symm, CategoryTheory.Functor.OneHypercoverDenseData.sieve_mem, MvPolynomial.totalDegree_eq_zero_iff, AdicCompletion.mk_surjective, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply, Affine.Simplex.sign_touchpointWeights_singleton_pos, Polynomial.toFinsuppIsoLinear_apply, Affine.Simplex.altitude_reindex, CategoryTheory.conjugateEquiv_comm, SpectralMap.coe_comp_continuousMap, Homeomorph.divLeft_apply, MeasureTheory.FiniteMeasure.coeFn_add, MvPowerSeries.monomial_pow, QuaternionAlgebra.equivTuple_apply, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, MeasureTheory.Integrable.integral_norm_condDistrib, AddEquiv.toMultiplicativeRight_symm_apply_symm_apply, ContDiffMapSupportedIn.postcompCLM_apply, LinearIsometry.comp_continuous_iff, AddMonoidHom.dfinsuppSum_apply, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, AlgebraicGeometry.instIsZariskiLocalAtTargetStalkwiseBijectiveCoeRingHom, NonUnitalStarSubalgebra.iSupLift_of_mem, isLeftRegular_ofDual, ContinuousAt.partialSups, DoubleCentralizer.coeHom_apply, TopCat.range_pullback_to_prod, RingHom.map_mulVec, IsAdicComplete.mk_liftAlgHom, RingHom.op_symm_apply_apply, Ideal.absNorm_pos_of_nonZeroDivisors, signedDist_neg, IsContDiffImplicitAt.bijective, AddMonoidHom.mapMatrix_apply, ClosureOperator.closure_min, CStarAlgebra.mul_star_le_algebraMap_norm_sq, LinearAlgebra.FreeProduct.lift_unique, RelIso.refl_apply, Submodule.eq_starProjection_of_mem_orthogonal', ProbabilityTheory.covarianceBilin_apply_basisFun, finSuccEquiv'_symm_some_below, RelIso.apply_symm_apply, DirichletCharacter.absicssaOfAbsConv_eq_one, MvPowerSeries.expand_comp_substAlgHom, DualNumber.coe_lift_symm_apply, MeasureTheory.Measure.notMem_support_iff_exists, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, Polynomial.exists_eq_X_add_C_of_natDegree_le_one, DirectSum.sigmaCurry_apply, supClosure_singleton, Algebra.Generators.self_algebra_smul, MvPowerSeries.map_map, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, StarAlgEquiv.coe_symm_toAlgEquiv, Algebra.TensorProduct.linearEquivIncludeRange_symm_tmul, MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant, Matrix.charpoly_coeff_eq_prod_coeff_of_le, Ideal.coe_comap, Homeomorph.isSigmaCompact_image, SimpleGraph.Path.mapEmbedding_injective, Function.locallyFinsuppWithin.restrict_eqOn, ContinuousAlternatingMap.restrictScalarsLI_apply, MultilinearMap.freeFinsuppEquiv_apply, MultilinearMap.map_piecewise_add, MonoidAlgebra.domCongr_comp_lsingle, MeasureTheory.lintegral_finset, Algebra.TensorProduct.algEquivIncludeRange_tmul, Orientation.oangle_sign_smul_right, PowerSeries.subst_coe, MatrixEquivTensor.left_inv, Ideal.quotientEquiv_apply, AddMonoidAlgebra.apply_eq_zero_of_not_le_supDegree, ClassGroup.mk_eq_one_iff, Finset.sigmaAntidiagonalEquivProd_symm_apply_snd_coe, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, Orientation.normSq_kahler, Finsupp.filter_apply, Ideal.quotientInfEquivQuotientProd_snd, Ideal.toCotangent_eq_zero, AlgEquiv.linearEquivConj_mulLeftRight, Complex.volume_closedBall, AddGroupSeminorm.coe_sSup_apply', Cardinal.aleph0_le_preAleph, ProbabilityTheory.IsCondKernelCDF.integrable, IntermediateField.AdjoinPair.algebraMap_gen₁, Module.Basis.constr_apply_fintype, ContinuousLinearEquiv.comp_right_differentiableOn_iff, IsCompl.map, OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective, UniformSpace.Completion.coe_toComplₗᵢ, OrderHom.mono, hasGradientAt_iff_hasFDerivAt, AlgebraicGeometry.IsAffineOpen.comap_primeIdealOf_appLE, TopCat.GlueData.ι_isOpenEmbedding, DFinsupp.coprodMap_apply_single, LinearMap.IsSymmetric.invariant_orthogonalComplement_eigenspace, MultilinearMap.alternatization_apply, RatFunc.denom_div, CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff, LinearEquiv.symm_conj_apply, algebraMapCLM_apply, WeierstrassCurve.coe_inv_map_Δ', AddMonoidAlgebra.liftMagma_apply_apply, Cardinal.preAleph_succ, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, Polynomial.opRingEquiv_symm_C_mul_X_pow, TensorProduct.LieModule.lift_apply, Matrix.cramer_submatrix_equiv, Nat.ordProj_dvd_ordProj_of_dvd, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_symm_apply_fst, AlgebraicGeometry.Scheme.stalkMap_hom_inv, TopCat.subpresheafToTypes_map_coe, BotHom.sup_apply, ContinuousLinearEquiv.symm_comp_self, RingEquiv.coe_prodComm, Poly.add_apply, Polynomial.eval_map_apply, Homeomorph.image_symm_apply_coe, CoalgEquiv.refl_symm_apply, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, MvPolynomial.decomposition.decompose'_apply, BoundedContinuousFunction.coe_abs, MultilinearMap.ofSubsingletonₗ_apply, MeasureTheory.hausdorffMeasure_measurePreserving_funUnique, PowerSeries.invOfUnit_eq, Finsupp.coe_smul, List.SortedLE.of_map_ofDual, pinGroup.toUnits_injective, Profinite.NobelingProof.GoodProducts.square_commutes, Frm.hom_inv_apply, Complex.normSq_inv, CliffordAlgebra.ι_mul_ι_add_swap_of_isOrtho, groupCohomology.cochainsMap_f, ContinuousAlternatingMap.cons_smul, groupCohomology.coboundaries₁.val_eq_coe, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, Equiv.prod_comp, strictAnti_iff_map_pos, groupHomology.d₃₂_single_one_fst, Valuation.mem_ltAddSubgroup_iff, ENNReal.orderIsoUnitIntervalBirational_apply_coe, DirectSum.coeRingHom_of, Matrix.mulVecLin_submatrix, IsIntegralClosure.algebraMap_mk', WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, BoundedLatticeHom.asBoolRing_apply, inhomogeneousCochains.d_hom_apply, Isometry.inl, Algebra.Generators.toKaehler_tmul_D, DFinsupp.lsum_symm_apply, ProbabilityTheory.cond_mul_eq_inter', ContinuousMap.image_coev, Diffeomorph.sumEmpty_apply_inl, Finset.sup_map, QuaternionAlgebra.imK_equivProd_symm_apply, MeasureTheory.measure_inter_add_diff, Subalgebra.iSupLift_of_mem, MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt, MvPolynomial.mem_support_finSuccEquiv, FirstOrder.Language.Embedding.map_constants, PrimeSpectrum.preimage_comap_zeroLocus_aux, ZMod.dft_dft, LinearMap.finsupp_sum_apply, List.SortedGT.of_map_toDual, Quaternion.imJ_snd_dualNumberEquiv, MeasureTheory.nnnorm_indicatorConstLp_le, coe_finRotate_of_ne_last, ContinuousOpenMap.coe_toContinuousMap, locallyFinsuppWithin.logCounting_divisor, AbsoluteValue.nonpos_iff, MulEquiv.symm_trans_apply, iteratedFDeriv_one_apply, Algebra.smulTower_leftMulMatrix_algebraMap_ne, PresentedGroup.mk_surjective, Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity, ContinuousLinearEquiv.iteratedFDeriv_comp_left, WithConv.linearEquiv_apply, piFinTwoEquiv_apply, Equiv.piEquivPiSubtypeProd_symm_apply, PerfectRing.liftAux_id, minpoly.aeval_algHom, AlgEquiv.coe_toLinearEquiv, cfcₙHom_map_quasispectrum, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality, IsDiscreteValuationRing.addVal_pow, AddAut.mulRight_apply, RingCon.le_def, image_latticeClosure, PowerSeries.coeff_monomial_same, Submodule.mulRightMap_apply, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, IsApproximateAddSubgroup.image, CategoryTheory.Limits.colimit.ι_desc_apply, AddMonoid.Coprod.map_mk_ofList, LinearEquiv.conjAlgEquiv_apply_apply, Ordinal.enum_succ_eq_top, DFinsupp.Lex.lt_iff_of_unique, LocallyConstant.coe_neg, Localization.r_iff_exists, Algebra.adjoin_image, quasispectrum.algebraMap_mem_iff, List.SortedLT.of_map_toDual, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, Finset.singletonAddHom_apply, MultilinearMap.piFamilyₗ_apply, OrderIso.coe_symm_toRelIsoGT, AlgHom.coe_comp, InverseSystem.piSplitLE_eq, finRotate_succ_symm_apply, FrameHomClass.map_sSup, partialSups_zero, MultilinearMap.fromDirectSumEquiv_apply, TrivSqZeroExt.liftEquivOfComm_apply, ComplexShape.Embedding.homEquiv_apply_coe, ContinuousAlternatingMap.vecCons_add, Nimber.toOrdinal_one, Subalgebra.coe_map, TensorProduct.isBaseChange, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, DFinsupp.filter_apply, MonoidHom.rangeRestrict_surjective, HahnSeries.single_add, Rep.coind'_ext_iff, HasFPowerSeriesOnBall.factorial_smul, LatticeHom.coe_snd, AlgebraicGeometry.isImmersion_iff, Polynomial.monic_expand_iff, Polynomial.iterate_derivative_prod_X_sub_C, Cardinal.cast_toNat_of_aleph0_le, Matrix.BlockTriangular.transpose, HasFDerivAt.hasLineDerivAt, WeierstrassCurve.Affine.Point.map_map, Equiv.sigmaSubtype_symm_apply_coe_snd, doublyStochastic_eq_convexHull_permMatrix, Pi.toColex_apply, LinearEquiv.algEquivOfRing_symm_apply, AlternatingMap.map_vecCons_add, IsHomeomorphicTrivialFiberBundle.proj_eq, EmbeddingLike.injective, CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker, ContinuousAlternatingMap.norm_image_sub_le', AbsoluteValue.le_add, MeasureTheory.ae_iff, Filter.pureOneHom_apply, MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous, Homotopy.dNext_succ_chainComplex, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd, wellFoundedGT_iff_monotone_chain_condition, AddMonoid.Coprod.mk_eq_mk, AffineSubspace.sSameSide_lineMap_right, Polynomial.signVariations_eraseLead_mul_X_sub_C, Finset.some_mem_insertNone, RelIso.compl_symm_apply, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, Finsupp.comapSMul_apply, Valuation.HasExtension.algebraMap_mem_valuationSubring, Function.Embedding.coe_quotientOut, latticeClosure_eq_self, InfHomClass.map_inf, MonoidHom.coe_graph, LaurentSeries.valuation_LaurentSeries_equal_extension, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, MeasureTheory.L1.setToL1_congr_left, IsGalois.intermediateFieldEquivSubgroup_symm_apply, MulAction.map_stabilizer_le, ContMDiffMap.coe_smul, ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_compl_mutuallySingularSetSlice, AddActionHom.map_vadd, OrderIso.sumLexAssoc_symm_apply_inr_inl, eval_det, Matrix.reindexLinearEquiv_mul, LinearMap.concaveOn, MulSemiringActionHom.map_mul', AddMonoid.Coprod.toProd_surjective, Homeomorph.piUnique_apply, Polynomial.dvd_content_iff_C_dvd, Submodule.map₂_le, Algebra.iInf_toSubmodule, Polynomial.natSepDegree_expand, CommGrpCat.coe_id, OrderMonoidIso.comp_symm_eq, AddChar.coe_doubleDualEquiv, PrimeSpectrum.nhdsOrderEmbedding_apply, NoZeroSMulDivisors.iff_algebraMap_injective, MeasureTheory.SimpleFunc.bind_apply, UpperSet.icisSupHom_apply, homothety_invOf_two, iteratedFDeriv_succ_apply_right, cfc_const, CategoryTheory.CommSq.right_adjoint, RestrictedProduct.range_coe_principal, LaurentPolynomial.comul_C, DomMulAct.mk_zpow, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, FormalMultilinearSeries.leftInv_coeff_one, Polynomial.coeff_C_succ, algebraMap_injective_of_field_isFractionRing, LaurentSeries.hasseDeriv_single_add, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac', ProbabilityTheory.Kernel.measurable_densityProcess_aux, AddConstMapClass.map_ofNat', Finsupp.coe_orderIsoMultiset_symm, MeasureTheory.Measure.measure_preimage_of_map_eq_self, Nat.Partition.ofSym_map, IsPrimitiveRoot.norm_eq_one_of_linearly_ordered, MeasureTheory.Measure.dirac_apply_eq_zero_or_one, ContinuousMap.comp_zero, AddGroupNorm.apply_one, Submodule.isOpenMap_mkQ, MvPolynomial.funext_set_iff, MeasureTheory.Measure.mapₗ_apply_of_measurable, Subsemiring.isHomogeneous_iff_forall_subset, Matrix.comp_symm_diagonal, map_compl, CommGrpCat.id_apply, Derivation.coeFn_coe, MultilinearMap.smulRight_apply, OrderIso.bddAbove_preimage, PiTensorProduct.mul_def, RootPairing.rootForm_self_sum_of_squares, RingHom.map_adjugate, finsuppLEquivDirectSum_single, LinearMap.map_zero₂, HilbertBasis.repr_symm_single, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, UniformConvergenceCLM.isUniformInducing_coeFn, TopCat.pullback_fst_image_snd_preimage, HilbertBasis.repr_apply_apply, Polynomial.opRingEquiv_symm_monomial, ContinuousMulEquiv.coe_mk, MeasureTheory.Measure.pi_closedBall, CategoryTheory.Functor.OneHypercoverDenseData.mem₀, LocallyConstant.coe_one, ContinuousLinearMap.hasMFDerivAt, SetTheory.PGame.relabel_moveRight', RingCon.quotientQuotientEquivQuotient_mk_mk, PartENat.withTopEquiv_top, IsLocalization.algEquivOfAlgEquiv_symm_apply, CircleDeg1Lift.map_add_int, MulEquiv.punitCoprod_symm_apply, absConvexHull_eq_iInter, Polynomial.toAddCircle_monomial_eq_smul_fourier, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, TensorProduct.assocIsometry_apply, Algebra.commute_algebraMap_left, OrderEmbedding.sortedGE_listMap, MeasureTheory.toMeasurable_def, mulRothNumber_empty, Complex.inner, Matrix.toLin_conjTranspose, mulRightLinearMap_apply, WittVector.map_verschiebung, imaginaryPart_surjective, LieEquiv.symm_apply_apply, Polynomial.separable_C, MulEquiv.coprodComm_symm_apply, Submodule.linearDisjoint_op, PiTensorProduct.mem_lifts_iff, coe_iterateFrobenius, CliffordAlgebra.toBaseChange_comp_reverseOp, StarAlgEquiv.symm_apply_apply, Equiv.preimage_eq_iff_eq_image, WittVector.verschiebung_frobenius, ContinuousOn.continuous_restrict_iff_continuous_uniformOnFun, FixedPoints.toAlgAut_surjective, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Orthonormal.inner_finsupp_eq_sum_left, Subgroup.transferTransversal_apply', Sylow.card_eq_multiplicity, Submodule.quotientEquivOfIsCompl_symm_apply, MonoidHom.coe_mulSingle, ProfiniteGrp.hom_inv_apply, MvPolynomial.map_monomial, QuasispectrumRestricts.algebraMap_image, PresheafOfModules.Elements.fromFreeYoneda_app_apply, fderiv_deriv, Padic.exi_rat_seq_conv, NormedAddGroupHom.SurjectiveOnWith.surjOn, GenLoop.loopHomeo_symm_apply, Finsupp.comul_single, HopfAlgebra.mul_antipode_rTensor_comul_apply, Module.Basis.coe_mk, Submodule.spanRank_toENat_eq_iInf_finset_card, MeasureTheory.addContent_union, CategoryTheory.Functor.IsLocallyFaithful.functorPushforward_equalizer_mem, AddMonoidHom.preimage_vadd_setₛₗ, Matrix.IsHermitian.spectral_theorem, Module.Relations.Solution.IsPresentation.uniq_symm_var, AddMonoidAlgebra.liftNC_smul, CategoryTheory.Equivalence.congrLeftFunctor_map, Submodule.exists_smith_normal_form_of_rank_eq, MvPolynomial.monomial_mem_restrictSupport, WithLp.unitizationAlgEquiv_symm_apply_ofLp, Metric.Snowflaking.continuous_toSnowflaking, BialgEquiv.coe_toCoalgEquiv, AffineIsometryEquiv.dist_map, algebraicIndependent_iff_injective_aeval, MvPowerSeries.rescale_rescale, Ring.DirectLimit.quotientMk_of, LinearIsometryEquiv.injective, OrderMonoidHom.coe_mul, SimpleGraph.map_neighborFinset_induce, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, IsInvariantSubring.coe_subtypeHom', CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff_of_small, DirectedSystem.lTensor, AddCommGroup.DirectLimit.congr_apply_of, AlgEquiv.toUnder_hom_right_apply, OrderEmbedding.preimage_Iio, LieAlgebra.Extension.bracket, MeasureTheory.integral_le_measure, MvPolynomial.aeval_map_algebraMap, ContinuousLinearEquiv.coe_apply, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq, Ordinal.typein_surjOn, AddConstMap.coe_mul, MeasureTheory.addEquivAddHaarChar_smul_map, NNReal.sum_mul_le_sqrt_mul_sqrt, Algebra.Generators.Hom.toAlgHom_C, LinearEquiv.conj_conj_symm, SubAddAction.ofStabilizer.conjMap_bijective, Submonoid.LocalizationMap.mk'_eq_iff_eq', Bifunctor.mapEquiv_symm_apply, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, CategoryTheory.Adjunction.homAddEquiv_symm_neg, NumberField.RingOfIntegers.mapRingHom_apply, ContinuousMap.zero_apply, HasOuterApproxClosed.tendsto_lintegral_apprSeq, ModuleCat.HasColimit.coconePointSMul_apply, RatFunc.intDegree_polynomial, Int.normalize_of_nonpos, Algebra.Extension.Cotangent.map_toInfinitesimal_bijective, QuadraticMap.canLift', toPrincipalIdeal_eq_iff, GradedTensorProduct.auxEquiv_tmul, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, MulOpposite.opLinearIsometryEquiv_symm_apply, ContinuousLinearEquiv.image_eq_preimage_symm, Finsupp.subtypeDomain_eq_zero_iff', LinearIndependent.finsuppLinearCombination_injective, latticeClosure_empty, Ideal.cotangentEquivIdeal_apply, LaurentPolynomial.eval₂_C, LieSubalgebra.inclusion_injective, TopologicalGroup.isOpenMap_iff_nhds_one, Complex.expMonoidHom_apply, SemistandardYoungTableau.col_weak, AlgHom.coe_fieldRange, Complex.coe_imAddGroupHom, TestFunction.tsupport_subset, OrderIso.conj_symm_apply, LinearMap.det_eq_sign_charpoly_coeff, InitialSeg.apply_wCovBy_apply_iff, CircleDeg1Lift.le_ceil_map_map_zero, MeasureTheory.IsAddFundamentalDomain.measure_eq_card_smul_of_vadd_ae_eq_self, Derivation.map_one_eq_zero', Sum.Lex.inl_lt_inl_iff, Subalgebra.LinearDisjoint.linearIndependent_right_of_flat, MulChar.star_apply', FirstOrder.Language.Substructure.coe_map, cfc_eval_C, CompactlySupportedContinuousMap.inf_apply, AddCon.comap_rel, VitaliFamily.covering, TwoSidedIdeal.rel_iff, IsometryEquiv.dimH_image, Matrix.diagonalAlgHom_apply, LinearIsometryEquiv.hasFDerivAt, LieModuleHom.coe_add, IsPerfectClosure.equiv_comp_equiv_apply, ContinuousLinearEquiv.surjective, Metric.exists_continuous_ennreal_forall_closedEBall_subset, OrderIso.sumLexAssoc_apply_inl_inl, Equiv.coe_constVSub, Finsupp.lapply_apply, CoalgEquiv.coe_symm_toEquiv, Subgroup.subgroupOfContinuousMulEquivOfLe_apply, Polynomial.mahlerMeasure_X_sub_C, RCLike.mul_im_I_ax, Subalgebra.lTensorBot_symm_apply, SlashInvariantForm.coe_zero, monotone_stabilizes_iff_noetherian, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum, UniformFun.ofFun_prod, Module.Basis.smulTower'_apply, LinearIsometry.isometry, BoxIntegral.Box.Ioo_subset_Icc, RCLike.continuous_conj, RatFunc.v_def, OrderEmbedding.withBotCoe_apply, Algebra.GrothendieckAddGroup.of_injective, RingOfIntegers.coe_norm, OrderEmbedding.image_setOf_maximal, EMetric.exists_continuous_real_forall_closedBall_subset, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, CircleDeg1Lift.coe_one, BoundedContinuousFunction.lintegral_of_real_lt_top, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, SimpleGraph.Walk.length_map, minpoly.add_algebraMap, MvPowerSeries.coeff_zero_X_mul, AdicCompletion.congr_symm_apply, FirstOrder.Language.LEquiv.onBoundedFormula_symm_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, Equiv.swap_apply_eq_iff, CategoryTheory.ReflQuiv.adj.homEquiv_apply, MeasureTheory.measure_preimage_smul_of_nullMeasurableSet, NumberField.mixedEmbedding.polarCoord_symm_eq, MeasureTheory.Measure.sub_apply, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, HasFDerivAt.lim_real, Function.MulExact.iff_monoidHom_rangeRestrict, QuadraticMap.Isometry.proj_apply, MonoidHom.mclosure_preimage_le, iterate_frobenius, Nucleus.inf_apply, Finset.Ioi_ofDual, TopCat.continuous_iff_of_isColimit, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, Submonoid.LocalizationMap.sec_spec', EuclideanGeometry.dist_reflection_eq_of_mem, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, NonUnitalAlgHom.quasispectrum_apply_subset', LinearEquiv.ofSubsingleton_apply, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, PointwiseConvergenceCLM.precomp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp, ArchimedeanClass.FiniteResidueField.mk_ne_zero, CategoryTheory.ShortComplex.ab_exact_iff, exists_homeomorph_image_eq, PowerSeries.map_invUnitsSub, AbsoluteValue.coe_toMulHom, SimpleGraph.Subgraph.hom_injective, IsLocalization.lift_id, continuous_barycentric_coord, UniformEquiv.injective, signedDist_vsub_self_rev, emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso, Algebra.smul_units_def, BumpCovering.ind_apply, SemidirectProduct.right_inr, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, Matrix.GeneralLinearGroup.mem_center_iff_val_eq_scalar, Real.probChar_apply', Diffeomorph.contMDiff_invFun, LinearIsometryEquiv.rTensor_apply, CommRingCat.HomTopology.continuous_apply, Polynomial.div_eq_quo_add_rem_div, BoxIntegral.BoxAdditiveMap.sum_partition_boxes, InitialSeg.apply_covBy_apply_iff, LinearIsometryEquiv.inner_map_map, norm_algebraMap, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, WithCStarModule.equiv_smul, LinearMap.map_span, UpperHalfPlane.coe_J_smul, MulAction.orbitEquivQuotientStabilizer_symm_apply, map_pos_of_ne_one, ContinuousLinearEquiv.self_comp_symm, BiheytingHom.ext_iff, ContinuousLinearMap.toContinuousAddMonoidHom_inj, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, Orientation.neg_rotation_pi_div_two, AddEquiv.addOrderOf_eq, PolynomialModule.equivPolynomialSelf_apply_eq, unitary.coe_map, Finset.image_infs, GrpCat.SurjectiveOfEpiAuxs.h_apply_infinity, Cardinal.aleph_one_le_lift, NumberField.Units.coe_pow, Finsupp.fst_sumFinsuppAddEquivProdFinsupp, CategoryTheory.Bicategory.toNatTrans_mateEquiv, OrderIso.sumComm_apply, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_hom, AffineMap.lineMap_same_apply, IsPurelyInseparable.algebraMap_elemReduct_eq', Subspace.dualLift_of_mem, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.fac'_assoc, InnerProductSpace.isStarProjection_rankOne_self, ExteriorAlgebra.ιMulti_apply, SymAlg.sym_surjective, QuadraticMap.Isometry.fst_apply, BoundedContinuousFunction.dist_le_iff_of_nonempty, LinearEquiv.coe_ofEq_apply, Polynomial.degreeLT.addLinearEquiv_symm_apply, Rat.padicValuation_eq_zero_iff, SeparationQuotient.mk_comp_outCLM, MulSemiringAction.charpoly_eq, RootPairing.algebraMap_posRootForm_posForm, LinearEquiv.eq_comp_symm, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, MvPolynomial.esymmAlgHom_zero, Trivialization.apply_eq_prod_continuousLinearEquivAt, CliffordAlgebra.EquivEven.v_sq_scalar, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, DirectSum.IsInternal.collectedOrthonormalBasis_mem, ContinuousAlternatingMap.piLIE_symm_apply_apply, IsAdjoinRootMonic.coeff_injective, HeytingHom.toFun_eq_coe_aux, CharacterModule.dual_bijective_iff_bijective, MeasureTheory.lintegral_singleton', ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, IsometryEquiv.diam_preimage, AlgHom.congr_arg, NonUnitalRingHom.coe_one, ContinuousLinearMapWOT.ext_dual_iff, toLex_vadd, NonemptyFinLinOrd.dual_map, PMF.binomial_apply, DomMulAct.mk_smul_linearMap_apply, endVecAlgEquivMatrixEnd_apply_apply, LinearIsometry.integral_comp_comm, ContinuousAffineMap.coe_smul, MeasureTheory.integrableOn_map_equiv, Complex.normSq_div, IsAddUnit.addUnit_map, SupHom.withBot_toFun, RelIso.symm_trans_apply, Ideal.apply_mem_of_equiv_iff, ContinuousAddEquiv.apply_eq_iff_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Partition.partscopyEquiv_symm_apply_coe, MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN, Submodule.coe_torsionBy, ModularForm.IsGLPos.coe_smul, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, Quaternion.snd_imK_dualNumberEquiv_symm, LaurentSeries.LaurentSeries_coe, MvPolynomial.homogeneousComponent_eq_zero, contDiff_clm_apply_iff, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, BoxIntegral.Box.exists_seq_mono_tendsto, HasFPowerSeriesAt.hasFDerivAt, AddGroupSeminorm.comp_apply, MeasureTheory.OuterMeasure.coe_zero, Submodule.dualAnnihilator_gc, StrictConvex.linearIsometry_preimage, OrthonormalBasis.measurePreserving_repr_symm, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Nat.factorization_centralBinom_of_two_mul_self_lt_three_mul, ContinuousAlgHom.map_add, AddMonoidAlgebra.liftNC_single, OrderRingHom.coe_coe_orderAddMonoidHom, Homeomorph.Set.prod_symm_apply_coe, MeasureTheory.measure_add_measure_eq, EsakiaHom.coe_comp, Basis.mem_ideal_iff', Topology.WithLowerSet.toLowerSet_le_iff, ContinuousAlgEquiv.symm_image_image, Polynomial.coe_basisMonomials, MvPowerSeries.map_monomial, FormalMultilinearSeries.comp_coeff_zero', Finsupp.zero_apply, QuadraticMap.map_add_add_add_map, Equiv.Perm.decomposeOption_symm_sign, PowerSeries.trunc_apply, MvPolynomial.coeToMvPowerSeries.algHom_apply, MeasureTheory.measure_iUnion_le, Ideal.quotientToQuotientRangePowQuotSucc_injective, CompletelyRegularSpace.exists_BCNN, Seminorm.cont_withSeminorms_normedSpace, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope, Topology.WithGeneratedByTopology.continuous_from_iff, ContinuousMap.HomotopyWith.ext_iff, Finsupp.DegLex.single_le_iff, Finset.centroid_mem_convexHull, groupCohomology.cocyclesMk₁_eq, IsDedekindDomain.FiniteAdeleRing.ext_iff, Units.mulLeft_apply, Valuation.map_inv, Equiv.ofInjective_apply, AffineMap.toConstProdLinearMap_symm_apply, ContinuousMultilinearMap.smul_apply, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal', IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk, Nucleus.sInf_apply, PiTensorProduct.ofDFinsuppEquiv_tprod_single, Equiv.locallyFinite_comp_iff, IsometryEquiv.toDilationEquiv_toDilation, DirectLimit.exists_eq_zero, spec_cfcₙAux, CategoryTheory.Localization.SmallHom.equiv_chgUniv, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Polynomial.isMonicOfDegree_one_iff, RingCon.coe_mk, map_mabs, lightProfiniteToLightCondSetIsoTopCatToLightCondSet_hom_app_val_app_apply, ShelfHom.comp_apply, RelEmbedding.sumLiftRelInl_apply, AddUnits.embedProduct_apply, root_X_pow_sub_C_pow, LinearEquiv.smul_apply, instInvertibleReprₛ, Finset.sup'_map, MvPolynomial.degreeOf_eq_sup, HahnSeries.archimedeanClassOrderIsoWithTop_apply, SSet.stdSimplex.const_down_toOrderHom, supClosure_mono, Booleanisation.liftLatticeHom_injective, AlgebraicIndependent.liftAlgHom_comp_reprField, Order.succ_toMul, ContinuousOrderHom.coe_id, map_dvd, TensorProduct.SMul.aux_of, SetTheory.PGame.Domineering.shiftRight_symm_apply, DirectSum.decomposeLinearEquiv_apply, RingHom.mem_rangeS_self, QuadraticMap.lineDifferentiableAt, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Polynomial.support_opRingEquiv, ContinuousMap.norm_lt_iff, Real.volume_eball, Subalgebra.finiteDimensional_toSubmodule, prodEquivPiFinTwo_apply, EuclideanSpace.piLpCongrLeft_single, AffineEquiv.equivUnitsAffineMap_symm_apply_symm_apply, MulChar.one_apply, Order.isPredLimit_toDual_iff, BoundedContinuousFunction.coe_mk, ProbabilityTheory.iIndep_iff, MvPolynomial.rename_rightInverse, Action.ρ_self_inv_apply, SubMulAction.ofStabilizer.snoc_last, Equiv.Perm.mem_cycleFactorsFinset_support, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, PrimeMultiset.coe_coePNatMonoidHom, EquivLike.range_comp, bddBelow_preimage_ofDual, HasFPowerSeriesOnBall.eventually_hasSum, Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply, CategoryTheory.Limits.limit.lift_π_apply, CategoryTheory.Limits.Bicone.whisker_π, isSemilinearSet_image_iff, MeasureTheory.lintegral_unique, PerfectionMap.comp_symm_equiv, BddBelow.dual, Pi.evalMulActionHom_apply, Submonoid.equivOp_apply_coe, DirectSum.ext_iff, OmegaCompletePartialOrder.ContinuousHom.id_apply, ContinuousLinearMap.hasStrictFDerivAt, MeasureTheory.VectorMeasure.mapGm_apply, MeasureTheory.SimpleFunc.sup_apply, Ideal.associatesEquivIsPrincipal_symm_apply, RingCon.mkₐ_apply, ContinuousMap.norm_lt_iff_of_nonempty, LinearMap.BilinForm.nondegenerate_congr_iff, Matrix.transposeAddEquiv_apply, MeasureTheory.Measure.dirac_apply_ne_one_iff_eq_zero, iterate_map_neg, AddCommGrpCat.coe_id, LowerAdjoint.closureOperator_apply, OrthonormalBasis.enorm_eq_one, CategoryTheory.equivYoneda_hom_app, BoundedContinuousFunction.forall_coe_one_iff_one, EuclideanGeometry.dist_reflection, NumberField.conj_basisMatrix, ZMod.χ₄_nat_three_mod_four, ContinuousMap.coe_add, Monoid.Coprod.mk_of_inr, LinearMap.aeval_self_charpoly, AbsoluteValue.IsAdmissible.exists_partition, MultilinearMap.sub_apply, char_dvd_card_solutions, WeierstrassCurve.Projective.baseChange_add, Topology.WithUpperSet.ofUpperSet_le_ofUpperSet, Complex.normSq_ofReal, RingHom.coe_fieldRange, Monoid.PushoutI.Reduced.exists_normalWord_prod_eq, CommSemiRingCat.comp_apply, exteriorPower.alternatingMapLinearEquiv_comp, AddMemClass.coe_subtype, Matrix.GeneralLinearGroup.map_swap, CommGrpCat.comp_apply, Matrix.trace_toLin'_eq, signedDist_linear_apply, PreInnerProductSpace.Core.re_inner_nonneg, Finset.weightedVSub_filter_of_ne, TensorProduct.gradedComm_of_zero_tmul, Trivialization.pullback_symm_apply_snd, Finset.map_truncatedSup, DirichletCharacter.sum_characters_eq_zero, Homeomorph.injective, Heyting.Regular.coe_toRegular, NumberField.IsCMField.unitsMulComplexConjInv_apply, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, CategoryTheory.Limits.Pi.whiskerEquiv_hom, coe_addEquiv_lpBCF_symm, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Finsupp.ofSupportFinite_coe, MeasureTheory.Measure.inv_apply, LocallyConstant.congrLeftₗ_symm_apply_apply, AddConstEquiv.toPerm_apply, AlgebraicGeometry.Scheme.basicOpen_appLE, AffineIsometry.isometry, OrderIso.neg_symm_apply, Matrix.submatrix_one_equiv, LeftInvariantDerivation.map_smul, Matrix.toLin'OfInv_symm_apply, Orientation.rotation_eq_matrix_toLin, CategoryTheory.unit_mateEquiv_symm, MonotoneOn.dual, oneTangentSpaceIcc_def, OrderAddMonoidHom.inlₗ_apply, MeasurableEquiv.piEquivPiSubtypeProd_symm_apply, Pi.monotoneUncurry_coe, Mathlib.Tactic.ComputeDegree.natDegree_C_le, ArithmeticFunction.map_zero, Quaternion.sq_eq_neg_normSq, AffineMap.lineMap_apply_ring, LinearMap.BilinForm.flip_apply, TrivSqZeroExt.inlCLM_apply, Set.unit_valuation_eq_one, AffineSubspace.sOppSide_lineMap_right, Ordinal.isInitial_omega, toDual_sub, ProbabilityTheory.Kernel.prodComm_prod, HasDerivAt.hasFDerivAt_equiv, Polynomial.rootSet_maps_to', Submodule.mem_projectivization_iff_submodule_le, MeasureTheory.OuterMeasure.pi_pi_le, AddEquiv.toMultiplicative_symm_apply_apply, PiTensorProduct.map_tprod, OrderMonoidHom.fstₗ_apply, Representation.isTrivial_def, preimage_vadd_setₛₗ_of_isAddUnit_isAddUnit, ContinuousMap.coe_id, NonUnitalAlgHom.toFun_eq_coe, cfcHom_eq_cfc_extend, IsSymmSndFDerivAt.iteratedFDeriv_cons, Filter.tendsto_prodAssoc, WeierstrassCurve.Jacobian.polynomialZ_eq, Matrix.mul_submatrix_one, ProbabilityTheory.IsRatCondKernelCDFAux.iInf_rat_gt_eq, Bornology.IsBounded.measure_lt_top, CompactlySupportedContinuousMap.add_apply, WithSeminorms.congr_equiv, Behrend.card_sphere_le_rothNumberNat, Orientation.inner_rightAngleRotation_swap, CategoryTheory.Iso.homToEquiv_apply, MeasureTheory.OuterMeasure.measureOf_eq_coe, Module.Basis.sumQuot_repr_inr_of_mem, MulRingNorm.toFun_eq_coe, HeytAlg.ofHom_apply, NumberField.Units.abs_det_eq_abs_det, ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib₀, RingHom.rangeRestrictFieldEquiv_apply_symm_apply, MonomialOrder.sPolynomial_monomial_mul, UniformEquiv.piCongrLeft_toEquiv, ProbabilityTheory.Kernel.prodMkLeft_apply', GroupSeminormClass.map_inv_eq_map, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Path.continuous, unitsEquivNeZero_apply_coe, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, IsGroupLikeElem.antipode_mul_cancel, Topology.WithLower.ofLower_le_ofLower, AlgHom.coe_restrictScalars', Real.volume_le_diam, infClosed_preimage_ofDual, Compactum.continuous_of_hom, MvPolynomial.eval₂Hom_map_hom, AffineIsometryEquiv.ext_iff, MeasureTheory.le_toMeasure_apply, RingCon.comapQuotientEquivRangeₐ_mk, MultilinearMap.piFamily_single_left_apply, LieSubmodule.Quotient.surjective_mk', Finsupp.coe_basisSingleOne, Equiv.Perm.subtypeCongrHom_apply, LaurentPolynomial.eval₂_toLaurent, continuous_toDual, IsPurelyInseparable.algebraMap_iterateFrobenius, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply, Finsupp.coe_lmapDomain, Fintype.coe_finsetOrderIsoSet, ProbabilityTheory.Kernel.lintegral_comap, Module.Basis.sumCoords_self_apply, AbsoluteValue.not_isNontrivial_iff, map_iInf, VertexOperator.ext_iff, CategoryTheory.Functor.curryingEquiv_apply_map, Polynomial.coe_mapRingHom, RCLike.normSq_eq_def', CommSemiRingCat.id_apply, Polynomial.C_mul_dvd, ContinuousLinearMap.comp_analyticOn, Path.continuous_uncurry_extend_of_continuous_family, MeasurableEmbedding.comap_apply, PartOrdEmb.forget_map, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', OrderEmbedding.addRight_apply, Algebra.trace_localization, MonoidHom.coe_compAddChar, IsSimpleOrder.equivBool_symm_apply, LinearIsometryEquiv.piLpCurry_symm_apply, AffineEquiv.symm_apply_apply, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, BoundedContinuousFunction.norm_lt_iff_of_compact, IndexedPartition.out_proj, IsLocalization.toInvSubmonoid_surjective, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv, AffineEquiv.coe_trans, AddConstMapClass.strictAnti_iff_Icc, DistribMulAction.toAddEquiv_apply, Finset.weightedVSub_vadd, ModuleCat.MonoidalCategory.tensorμ_apply, EuclideanGeometry.Sphere.IsTangent.eq_orthRadius_or_eq_orthRadius_pointReflection_of_parallel_orthRadius, LeftOrdContinuous.coe_toOrderEmbedding, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two, LinearMap.isNilpotent_trace_of_isNilpotent, AffineEquiv.ofLinearEquiv_apply, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, DivisibleHull.coeOrderAddMonoidHom_apply, WithBot.lt_toDual_iff, Monotone.dual, MeasureTheory.measure_add_closure_zero, MvPolynomial.finSuccEquiv_eq, QuadraticAlgebra.norm_intCast, char_dvd_card_solutions_of_sum_lt, CircleDeg1Lift.commute_int_add, List.toFinsupp_apply_le, Derivation.coe_smul, LinearMap.BilinForm.compRight_apply, AffineEquiv.coe_refl, RatFunc.liftAlgHom_apply_ofFractionRing_mk, NonUnitalStarAlgHom.mem_range_self, Equiv.finsetSubtypeComm_symm_apply, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, Algebra.adjoin_eq_adjoin_union, SymmetricAlgebra.equivMvPolynomial_ι_apply, Part.fix_eq_ωSup, ContinuousLinearEquiv.image_symm_eq_preimage, Nat.ordCompl_self_pow_mul, CommRingCat.forget_map_apply, BoolAlg.hom_inv_apply, emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso, MeasureTheory.ofReal_setIntegral_one, AlgEquiv.coe_algHom, TopCat.pullbackIsoProdSubtype_inv_fst_apply, FreeMonoid.mrange_lift, BoundedLatticeHom.dual_apply_toFun, LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank, InfHom.withBot'_toFun, QuadraticAlgebra.linearEquivTuple_symm_apply, ContinuousLinearMap.coeFn_compLpL, WithAbs.equivWithAbs_equiv_symm_apply, BddDistLat.id_apply, NormedAddGroupHom.Equalizer.lift_apply_coe, Module.algebraMap_end_apply, Equiv.image_eq_preimage_symm, rotationOf_coe, topologicalGroup_induced, Ideal.norm_mem_spanNorm, Real.nndist_eq, LinearIsometryEquiv.coe_inv, NonUnitalSubsemiring.mem_map, AddMonoidAlgebra.lift_unique', AddCommGroup.DirectLimit.directedSystem, MulEquiv.toAdditive_symm_apply_apply, InitialSeg.map_isSuccLimit, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, MulActionHom.toQuotient_apply, Subalgebra.toSubmodule_toSubalgebra, Equiv.sumProdDistrib_symm_apply_left, Module.FinitePresentation.linearEquivMapExtendScalars_apply, Polynomial.isNilpotent_monomial_iff, IsLocalizedModule.iso_symm_apply_aux, IsPrimitiveRoot.norm_pow_sub_one_two, Polynomial.as_sum_range', AbsConvex.absConvexHull_subset_iff, ContinuousLinearMap.sub_apply', IsBaseChange.endHom_apply, Algebra.norm_complex_apply, Antitone.dual_left, LinearIndependent.fintypeLinearCombination_injective, NumberField.mixedEmbedding.volume_negAt_plusPart, ZMod.lift_coe, UpperSet.iciSupHom_apply, NumberField.mixedEmbedding.convexBodyLT'_volume, RootPairing.Equiv.indexHom_apply, NonUnitalStarAlgHom.coe_coe, MvPowerSeries.isUnit_constantCoeff, MonoidAlgebra.mul_single_apply_of_not_exists_mul, LipschitzWith.coe_toLocallyBoundedMap, CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, GroupLike.val_toUnits_apply, stdSimplex.zero_le, AdicCompletion.AdicCauchySequence.map_comp_apply, MeasureTheory.sum_measure_le_measure_univ, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, PowerSeries.constantCoeff_divXPowOrder_eq_zero_iff, MvPolynomial.homogeneousComponent_zero, Path.source_mem_range, FractionalIdeal.exists_ne_zero_mem_isInteger, ContinuousLinearMap.coeFn_injective, MeasureTheory.mem_ae_iff_prob_eq_one₀, Ordinal.iSup_typein_limit, MeasureTheory.addContent_biUnion_eq, Orientation.oangle_sub_left_smul_rotation_pi_div_two, Set.singletonMulHom_apply, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, ContinuousLinearEquiv.prodAssoc_apply, AffineEquiv.affineIndependent_set_of_eq_iff, map_partialSups, uliftPowersHom_apply_apply, AddCon.lift_mk', AffineIsometryEquiv.coe_vaddConst_symm, thickenedIndicator_subset, AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization, Homeomorph.isConnected_preimage, PowerSeries.coeff_monomial, FractionalIdeal.canonicalEquiv_flip, Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem, AbsoluteValue.hasBasis_uniformity, Topology.WithLawson.ofLawson_inj, rothNumberNat_le_ruzsaSzemerediNumberNat, LinearMap.mul''_apply, CartanMatrix.A_two, Module.Basis.parallelepiped_eq_map, Polynomial.natDegree_monomial, IsometryClass.dist_eq, selfAdjoint.realPart_coe, Function.Exact.iff_of_ladder_addEquiv, ContinuousMap.HomotopyLike.map_one_left, RingCon.factorₐ_apply, Equiv.swap_eq_update, Subgroup.index_toAddSubgroup, AddChar.toMonoidHomEquiv_add, Algebra.discr_powerBasis_eq_prod, IsDedekindDomain.HeightOneSpectrum.intAdicAbv_eq_one_iff, Module.Invertible.rTensorInv_injective, ProbabilityTheory.IsRatCondKernelCDFAux.le_one, TensorProduct.AlgebraTensorModule.lTensor_mul, AddMonoidHom.coe_toIntLinearMap_ker, ContDiffMapSupportedIn.norm_apply_le_seminorm, iterate_map_pow, Complex.norm_def, FreeAddMonoid.lift_eval_of, TensorProduct.piScalarRight_symm_single, finSuccEquiv'_above, LinearMap.bijective_or_eq_zero, contDiffOn_clm_apply, OrderIso.infIrredUpperSet_apply, ContinuousLinearMap.le_opNNNorm, associated_norm_prod_smith, spectrum.subset_polynomial_aeval, PowerSeries.expand_mul, RCLike.re_mul_ofReal, Path.neg_apply, SmoothPartitionOfUnity.sum_eq_one, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, IsValuativeTopology.isOpen_closedBall, LinearEquiv.map_eq_zero_iff, DirectSum.coe_decompose_mul_add_of_right_mem, QuadraticMap.coeFn_sub, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, PEquiv.mem_trans, iterate_map_nsmul, Matrix.mem_range_scalar_of_commute_single, NumberField.InfinitePlace.isometry_embedding_of_isReal, TestFunction.coe_sub, Polynomial.factorial_mul_shiftedLegendre_eq, AlternatingMap.coe_alternatization, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_right, ContinuousMap.star_apply, CompHausLike.const_comp, ContinuousAlternatingMap.piLinearEquiv_symm_apply, Path.target_mem_range, fderiv_continuousAlternatingMap_apply_apply, Equiv.Perm.pow_apply_mem_support, Matrix.scalar_comm_iff, DirectSum.coe_mul_of_apply_aux, FormalMultilinearSeries.id_apply_zero, SchwartzMap.hasDerivAt, measurable_equivCurry_symm, Finset.fold_map, SubMulAction.ofStabilizer.snoc_castSucc, MvPolynomial.monomial_left_injective, UniformFun.postcomp_uniformContinuous, AddValuation.map_neg, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T, Polynomial.C_comp, Module.End.mem_eigenspace_iff, MulEquiv.multiplicativeAdditive_symm_apply, Equiv.uniqueSigma_symm_apply, Algebra.TensorProduct.one_mul, Finset.gcd_singleton, ProbabilityTheory.uniformOn_add_compl_eq, ContinuousAlgEquiv.eq_symm_apply, ENNReal.count_const_le_le_of_tsum_le, exists_continuous_zero_one_of_isCompact, GroupNorm.coe_add, TensorPower.algebraMap₀_mul_algebraMap₀, Seminorm.inf_apply, MvPolynomial.coeff_map, Ideal.constr_basisSpanSingleton, IsAdjoinRootMonic.map_modByMonicHom, ClassGroup.mk_eq_mk, LinearIsometry.antilipschitz, PiTensorProduct.mapLMultilinear_apply_apply, TensorPower.gMul_def, NonUnitalStarRingHom.zero_apply, Diffeomorph.contMDiffWithinAt_comp_diffeomorph_iff, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, IsFreeGroup.toFreeGroup_apply, MeasureTheory.Measure.dirac_apply_of_mem, MeasureTheory.Measure.map_toOuterMeasure, SymAlg.sym_mul_self, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, Subgroup.quotientiInfEmbedding_apply_mk, Function.Exact.iff_linearMap_rangeRestrict, LieAlgebra.of_add, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, Module.Flat.iff_rTensor_exact, Affine.Simplex.incenter_eq_affineCombination, CategoryTheory.ActionCategory.curry_apply_left, MultilinearMap.domDomRestrict_apply, AddSubmonoid.mk_neg_add_mk_eq_zero, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, RelEmbedding.ofMapRelIff_coe, OrthogonalIdempotents.map, MulEquiv.piUnique_apply, HasFDerivWithinAt.clm_comp, FreeAddGroup.sum_mk, LinearMap.mem_polar_singleton, ContinuousAffineMap.congr_fun, MvPolynomial.monomial_sum_index, SetTheory.PGame.moveLeft_neg_toLeftMovesNeg, MeasureTheory.IsProjectiveLimit.measure_cylinder, CategoryTheory.WithTerminal.widePullbackShapeEquiv_inverse_obj, Function.Involutive.toPerm_involutive, ContinuousLinearMap.uncurryMid_apply, DirichletCharacter.mul_convolution_distrib, LinearEquiv.isUnit_det, UniformFun.edist_def, AddCon.sup_eq_addConGen, AddMonoidAlgebra.opRingEquiv_single, MonoidWithZeroHom.apply_one_apply_eq, addEquivOfAddOrderOfEq_symm_apply_gen, Polynomial.div_C, signedDist_self, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right_symm, LinearMap.IsSymm.eq, CategoryTheory.Sieve.overEquiv_symm_generate, FirstOrder.Language.StrongHomClass.realize_formula, TopCat.piIsoPi_hom_apply, SemimoduleCat.MonoidalCategory.associator_inv_apply, SubAddAction.ofFixingAddSubgroup_insert_map_apply, MeasureTheory.condLExp_bot_ae_eq, Ideal.apply_coe_mem_map, normalize_lcm, Tuple.eq_sort_iff, exists_smooth_section_forall_mem_convex_of_local, NNReal.one_le_sqrt, jacobiSum_nontrivial_inv, spectralNorm_extends, FreeAddMonoid.mrange_lift, isBoundedBilinearMap_apply, AEMeasurable.apply_continuousLinearMap, MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq, HasFPowerSeriesWithinOnBall.coeff_zero, Action.ρ_one, RootPairing.restrictScalars_coe_root, OrderMonoidIso.symm_apply_eq, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', OrderHom.ext_iff, CuspFormClass.exists_bound, sign_neg, InfiniteGalois.mem_range_algebraMap_iff_fixed, MeasureTheory.diracProba_toMeasure_apply', GrpCat.ofHom_apply, BotHom.ext_iff, SSet.stdSimplex.obj₀Equiv_symm_mem_face_iff, AbsoluteValue.exists_one_lt_lt_one_of_not_isEquiv, Unitary.val_inv_toUnits_apply, Polynomial.separable_def, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_f, Algebra.Smooth.exists_finiteType, ContinuousLinearEquiv.map_smulₛₗ, Ring.DirectLimit.map_id, Sym.append_comm, CliffordAlgebra.contractLeft_ι, ContMDiffMap.coe_neg, CategoryTheory.Equivalence.induced_unitIso, Algebra.adjoin_union_coe_submodule, AddMonoidAlgebra.ofMagma_apply, LinearMap.polyCharpolyAux_map_aeval, AffineMap.coe_prodMap, Matrix.mvPolynomialX_mapMatrix_eval, CartanMatrix.D_two, MeasureTheory.diff_ae_eq_self, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, BoxIntegral.BoxAdditiveMap.map_apply, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero, MvPolynomial.monic_monomial_eq, MvPowerSeries.coeff_zero_iff, AffineEquiv.pointReflection_apply, InfTopHom.comp_apply, map_div₀, RingCon.opOrderIso_symm_apply, WithZero.le_ofAdd_iff, KaehlerDifferential.map_surjective, OrderIso.sumLexEmpty_apply_inl, Cardinal.continuum_toENat, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, sInfHom.dual_symm_apply_toFun, Homeomorph.vadd_apply, NonarchAddGroupSeminorm.add_bddBelow_range_add, Matrix.blockDiag'AddMonoidHom_apply, Filter.coe_pureMulHom, Trivialization.coe_symmₗ, Pi.counit_coe_finsupp, Polynomial.comp_one, SupClosed.supClosure_eq, essInf_eq_sSup, UniformFun.ofFun_neg, TensorProduct.directSumLeft_tmul, IsLocalization.mem_localizationLocalizationSubmodule, Dilation.comap_cobounded, Poly.coe_one, IsUniformAddGroup.comap, MvPolynomial.image_support_finSuccEquiv, Polynomial.iterate_derivative_smul, Matrix.IsHermitian.eigenvectorUnitary_coe, ContDiffMapSupportedIn.coe_sub, HVertexOperator.ext_iff, Finset.weightedVSubOfPoint_apply_const, WithBot.toDualTopEquiv_symm_coe, WithLp.sndₗ_apply, Isometry.hausdorffMeasure_preimage, CategoryTheory.Functor.instIsWellOrderContinuousCompFunctor, RingHomIsometric.norm_map, ContinuousMap.piEquiv_apply, OrderIso.sumLexIicIoi_apply_inl, Nat.equivProdNatFactoredNumbers_apply, ContinuousAffineMap.hasFDerivAtFilter, hasStrictFDerivAt_ringInverse, PowerSeries.coeff_X, HahnSeries.coeff_single, KaehlerDifferential.map_compDer, AddUnits.coe_map_neg, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, MvPolynomial.pderiv_monomial_single, Algebra.TensorProduct.piRightHom_one, Algebra.trace_eq_matrix_trace, Homeomorph.homeomorphOfUnique_symm_apply, MeasureTheory.toMeasure_apply₀, AddMonoidAlgebra.mul_single_apply_aux, LE.le.ofDual, Sbtw.left_mem_image_Ioi, OrderIso.sumDualDistrib_inl, ProbabilityTheory.Kernel.isProper_iff_inter_eq_indicator_mul, signedDist_vsub_self, IsConjRoot.aeval_eq_zero, Matrix.blockTriangular_transpose_iff, CategoryTheory.GrothendieckTopology.bot_covering, Set.FiniteExhaustion.finite, Finset.Ici_toDual, LinearMap.liftBaseChange_tmul, ContinuousLinearMap.mul_apply', spectralAlgNorm_one, CategoryTheory.PreGaloisCategory.fiber_in_connected_component, RestrictedProduct.continuous_rng_of_principal_iff_forall, AddSubmonoid.surjOn_iff_le_map, LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ, Function.Embedding.sumSet_preimage_inl, ProbabilityTheory.Kernel.withDensity_rnDeriv_le, SupHom.withBot'_toFun, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, Submodule.mulMap_one_left_eq, MonoidHom.commute_inl_inr, Equiv.embeddingEquivOfFinite_symm_apply, Polynomial.sumIDeriv_X, GroupExtension.Section.exists_eq_mul_inl, CategoryTheory.GradedObject.comapEquiv_inverse, EuclideanGeometry.inversion_mul, Algebra.traceMatrix_of_basis, Polynomial.Bivariate.aevalAeval_swap, Field.Emb.Cardinal.deg_lt_aleph0, groupHomology.d₂₁_apply_mem_cycles₁, WeierstrassCurve.Δ_integral_of_isIntegral, MvPolynomial.eval₂_rename, ContDiffOn.continuousLinearMap_comp, AlgebraicIndependent.aeval_repr, CentroidHom.toFun_eq_coe, RingHom.map_zero, MeasureTheory.AddContent.inducedOuterMeasure_eq, MeasureTheory.lintegral_eq_lintegral_meas_lt, LinearEquiv.prodUnique_symm_apply, PathConnectedSpace.exists_path_through_family, OrderAddMonoidIso.apply_eq_iff_symm_apply, TensorProduct.quotTensorEquivQuotSMul_symm_mk, OrderAddMonoidIso.coe_refl, MvPolynomial.support_expand, Subalgebra.algEquivOpMop_apply, OrderHom.map_gfp, Algebra.trace_algebraMap_of_basis, DomAddAct.isQuotientMap_mk_symm, OrderDual.toDual_top, Cardinal.toNat_inj_of_lt_aleph0, CategoryTheory.ShortComplex.ShortExact.surjective_g, Dilation.comp_continuous_iff, Sum.Lex.lt_def, MeromorphicNFOn.zero_set_eq_divisor_support, Unitary.norm_map, ContinuousMap.realToNNReal_apply, Equiv.pprodProd_symm_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, isAddRightRegular_ofLex, SSet.stdSimplex.objEquiv_symm_comp, WittVector.fontaineTheta_teichmuller, AdjoinRoot.liftHom_eq_algHom, nsmulCoprime_symm_apply, finProdFinEquiv_symm_apply, AdicCompletion.of_ofLinearEquiv_symm, MulSemiringActionHom.coe_polynomial, AddGroupExtension.Section.add_add_add_neg_mem_range_inl, Algebra.IsPushout.equiv_tmul, Trivialization.coordChangeL_symm_apply, MeasureTheory.le_trim, LieModule.traceForm_lieSubalgebra_mk_left, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, MeasureTheory.inducedOuterMeasure_eq_extend, SpecialLinearGroup.toLinearEquiv_symm_apply, MeasurableEquiv.map_map_symm, Topology.lawsonClosed_of_scottClosed, Submodule.starProjection_apply_mem, Equiv.symmEquiv_symm_apply_apply, MeasureTheory.hausdorffMeasure_smul_right_image, AddEquiv.addSubmonoidMap_symm_apply, TopologicalSpace.Fiber.instFiniteFiberCoeLocallyConstant, NumberField.inverse_basisMatrix_mulVec_eq_repr, IsometryEquiv.apply_inv_self, OrderMonoidHom.coe_comp, signedDist_smul, MonoidAlgebra.liftMagma_symm_apply, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LieModule.Cohomology.smul_apply_apply, MeasureTheory.SimpleFunc.measure_support_lt_top_of_lintegral_ne_top, CStarAlgebra.norm_le_iff_le_algebraMap, Polynomial.contentIdeal_monomial, ContinuousAlternatingMap.le_of_opNorm_le, AddMonoid.Coprod.fst_apply_inr, AddMonoidAlgebra.liftMagma_symm_apply, CategoryTheory.ConcreteCategory.isIso_iff_bijective, groupCohomology.coboundariesToCocycles₂_apply, LinearIsometryEquiv.map_sub, IsAddUnit.map, linearIndependent_iff_injective_fintypeLinearCombination, ProbabilityTheory.Kernel.rnDeriv_lt_top, HahnSeries.coeff_toPowerSeries_symm, WithBot.ofDual_bot, CategoryTheory.ShortComplex.Homotopy.equivSubZero_apply, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, AddSubmonoid.topEquiv_apply, Finsupp.toFreeAbelianGroup_toFinsupp, Polynomial.dvd_C_mul_X_sub_one_pow_add_one, Sym2.lift_smul_lift, CategoryTheory.PresheafOfGroups.OneCochain.ev_precomp, RCLike.im_tsum, AddMonoid.Coprod.swap_swap, Affine.Simplex.faceOppositeCentroid_reindex, RatFunc.denom_div_dvd, GrpCat.mono_iff_injective, AddConstEquiv.equivUnits_symm_apply_apply, MeasureTheory.Measure.compProd_apply_prod, InnerProductSpace.rankOne_comp_rankOne, ProbabilityTheory.Kernel.lintegral_piecewise, TemperedDistribution.fourierTransform_apply, SemidirectProduct.equivProd_apply, smulAddHom_apply, CategoryTheory.comp_apply, Orientation.oangle_add_right_smul_rotation_pi_div_two, MonomialOrder.degree_eq_zero_iff, Finsupp.sum_update_add, MeasureTheory.Measure.count_apply_infinite, Polynomial.rootSet_C, Equiv.Perm.viaEmbedding_apply, AddMonoidAlgebra.tensorEquiv_tmul, Polynomial.injective_ofFn, FirstOrder.Language.Equiv.map_rel, FirstOrder.Language.Embedding.map_fun, MeromorphicOn.circleAverage_log_norm, EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq, ProbabilityTheory.Kernel.continuous_integral_integral_comp, SimpleGraph.UnitDistEmbedding.subsingleton_p_apply, matPolyEquiv_symm_C, Equiv.piCongrFiberwise_apply, FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion, MultilinearMap.mkPiAlgebraFin_apply, ProbabilityTheory.parallelProd_posterior_comp_copy_comp, OrderIso.image_Ioi, LinearIsometryEquiv.symm_apply_apply, Valuation.integer.v_irreducible_pos, MeasureTheory.Measure.compl_mem_cofinite, UniformEquiv.continuous, Polynomial.eval₂_at_zero, Matrix.spectrum_toLin, AddMonoidAlgebra.gradeBy.gradedMonoid, ZMod.χ₄_apply, TensorAlgebra.ι_leftInverse, StieltjesFunction.measure_Icc, Equiv.permCongr_def, Polynomial.toFinsupp_algebraMap, CompactlySupportedContinuousMap.coe_zero, RingHom.injective_respectsIso, ModuleCat.ihom_map_apply, ProbabilityTheory.Kernel.fst_apply', Algebra.FiniteType.iff_quotient_freeAlgebra', CategoryTheory.GrothendieckTopology.mem_sieves_iff_coe, AlgEquiv.opComm_apply_symm_apply, PowerSeries.constantCoeff_zero, IsTranscendenceBasis.comp_equiv, geometric_hahn_banach_point_open, TestFunction.mkCLM_apply, Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_mem, Complex.equivRealProdAddHom_apply, CategoryTheory.Equivalence.induced_inverse_obj, Submodule.quotDualCoannihilatorToDual_injective, Module.Basis.eval_injective, MulEquiv.coe_prodAssoc_symm, Polynomial.Bivariate.equivMvPolynomial_C_X, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Polynomial.lifts_iff_coeff_lifts, ContinuousMultilinearMap.norm_iteratedFDeriv_le, PowerSeries.IsWeierstrassDivisorAt.coeff_div, Affine.Simplex.centroid_restrict, CategoryTheory.ShortComplex.zero_apply, Locale.openOfElementHom_toFun, PolyEquivTensor.toFunBilinear_apply_apply, Unitization.starLift_apply, Fin.succFunEquiv_apply, lcm_same, finSuccEquiv_eq_some, Monovary.sum_comp_perm_mul_eq_sum_mul_iff, Prod.algebraMap_apply, Polynomial.natDegree_mul_C_eq_of_mul_ne_zero, StarSubalgebra.range_subset, LinearMap.toMatrix'_comp, Matrix.toLinearEquiv'_apply, Polynomial.coe_compRingHom, Fin.castLEOrderIso_symm_apply, LinearMap.isUnit_toMatrix'_iff, Orientation.inner_smul_rotation_pi_div_two_left, Fin.consOrderIso_symm_apply, MvPolynomial.IsSymmetric.rename, Submodule.quotientPi_symm_apply, MeasureTheory.isProbabilityMeasure_iff, AddMonoidHom.mclosure_range, MvPolynomial.IsHomogeneous.aeval, NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iff, CategoryTheory.Sheaf.ΓObjEquivHom_naturality, SimpleGraph.coe_recolorOfEquiv, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, RatFunc.laurent_C, IsHomeomorph.homeomorph_symm_apply, Action.ρAut_apply_hom, PrimitiveSpectrum.closedsGC_closureOperator, MeasureTheory.trim_measurableSet_eq, LinearMap.BilinForm.add_right, AddMonoidHom.map_list_sum, CategoryTheory.HomOrthogonal.matrixDecomposition_apply, AddSubmonoid.LocalizationMap.mk'_add_eq_mk'_of_add, Polynomial.ofMultiset_apply, DirectSum.lie_of_same, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, Matrix.toBilin_toMatrix, IsBaseChange.toDual_apply, Equiv.Perm.fst_prodExtendRight, BoxIntegral.hasIntegral_const, ZLattice.volume_image_eq_volume_div_covolume, CategoryTheory.NatTrans.appHom_apply, RestrictedProduct.range_coe, Subgroup.quotientiInfEmbedding_apply, Delone.DeloneSet.mapIsometry_apply_packingRadius, Int.absNorm_under_dvd_absNorm, CompactlySupportedContinuousMap.coe_sup, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, MeasurableEquiv.symm_apply_apply, BiheytingHom.id_apply, measurable_measure_prodMk_left, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, MeasureTheory.SimpleFunc.coe_mk, ofMul_one, RootPairing.reflection_apply_self, CategoryTheory.Functor.IsRepresentedBy.uliftYonedaIso_hom, AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff, Finset.imageAddHom_apply, ContinuousAlternatingMap.range_toAlternatingMap, LinearIsometryEquiv.isometry, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_hom, Module.AEval.mem_mapSubmodule_symm_apply, CompHausLike.finiteCoproduct.ι_injective, Real.map_linearMap_volume_pi_eq_smul_volume_pi, PolyEquivTensor.toFunLinear_tmul_apply, RingHom.toNatAlgHom_coe, MeasureTheory.IsFundamentalDomain.measure_eq_tsum', SemimoduleCat.MonoidalCategory.whiskerLeft_apply, OrderIso.invENNReal_apply, OrderMonoidHom.commute_inlₗ_inrₗ, RingHom.kerLift_injective, SetTheory.PGame.Domineering.shiftUp_symm_apply, ContinuousMap.toLp_injective, Subsemigroup.opEquiv_apply, Subsemigroup.mem_map_equiv, Sublattice.comap_equiv_eq_map_symm, Circle.exp_zero, OmegaCompletePartialOrder.ContinuousHom.congr_fun, Finsupp.bilinearCombination_apply, MeasureTheory.setLIntegral_const, OmegaCompletePartialOrder.ContinuousHom.Prod.apply_apply, DirectSum.decompose_zero, StandardEtalePresentation.lift_bijective, groupHomology.toCycles_comp_isoCycles₂_hom_apply, PMF.uniformOfFinset_apply_of_notMem, groupCohomology.cocyclesOfIsMulCocycle₁_coe, ArithmeticFunction.coe_zeta_smul_apply, DifferentiableAt.comp_semilinear₁, OrderEmbedding.maximal_apply_mem_inter_range_iff, isBot_toDual_iff, StarAlgEquiv.coe_trans, ContinuousAlternatingMap.compContinuousLinearMap_apply, RCLike.norm_re_le_norm, CoxeterSystem.lengthParity_simple, Cardinal.lift_le_aleph1, MonomialOrder.leadingTerm_C, WithAbs.equiv_equivWithAbs_symm_apply, ContinuousLinearMap.comp_smulₛₗ, BoxIntegral.Box.diam_Icc_le_of_distortion_le, NumberField.Units.coe_injective, groupCohomology.H2π_eq_zero_iff, ContinuousMulEquiv.self_comp_symm, MvPolynomial.DirectSum.coeLinearMap_eq_finsum, Finsupp.coe_nsmul, CategoryTheory.Limits.biproduct.whiskerEquiv_hom, Finsupp.embSigma_apply_of_ne, absConvex_absConvexHull, CFC.log_smul', Submonoid.LocalizationMap.mk'_mul_eq_mk'_of_mul, ModularForm.IsGLPos.smul_apply, FunctionField.inftyValuation.X_zpow, UniformEquiv.funUnique_symm_apply, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_hom, BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm, Matrix.nondegenerate_toLinearMap₂_iff, TensorPower.list_prod_gradedMonoid_mk_single, SlashInvariantForm.coe_trace, UniversalEnvelopingAlgebra.ι_apply, Polynomial.coeff_iterate_derivative, LinearMap.fst_apply, GroupNorm.apply_one, ContinuousMap.multipliable_apply, SimpleGraph.Iso.boxProdSumDistrib_symm_apply, MonoidHom.coe_mk, AddAction.toPermHom_apply_symm_apply, LieHom.coe_toLinearMap, LaurentSeries.hasseDeriv_comp, MeasureTheory.FiniteMeasure.map_apply, IsUnit.preimage_smul_set, MeasureTheory.Measure.measure_toMeasurable_inter_of_sum, Finsupp.apply_linearCombination, StrongDual.toLpₗ_of_not_memLp, DividedPowers.ofRingEquiv_dpow_apply, IsStarNormal.map, infIooOrderIsoIooSup_apply_coe, AddGroupExtension.inl_injective, AddMonoidHom.apply_nat, CategoryTheory.MonObj.ofRepresentableBy_mul, MonoidAlgebra.support_gen_of_gen, PiTensorProduct.mapL_apply, edist_ofAdd, Submodule.liftQ_apply, LinearIsometryEquiv.submoduleMap_symm_apply_coe, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, Matrix.reindexLinearEquiv_apply, LinearMap.BilinForm.comp_congr, Module.Relations.Solution.IsPresentation.surjective_π, LinearMap.disjoint_ker_iff_injOn, ofLex_inj, Matrix.cramer_subsingleton_apply, Finsupp.erase_add_single, Cubic.prod_X_sub_C_eq, AffineMap.coe_lineMap, OpenPartialHomeomorph.homeomorphOfImageSubsetSource_apply, Euclidean.closedBall_eq_preimage, Matrix.toBilin'_comp, MeasureTheory.OuterMeasure.sInf_apply, MonoidHom.coe_id, MonoidAlgebra.mul_single_one_apply, PMF.binomial_apply_self, Matrix.isHermitian_iff_isSymmetric, CategoryTheory.Limits.Concrete.productEquiv_apply_apply, MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasure, CategoryTheory.Localization.homEquiv_refl, MvPolynomial.support_monomial_subset, CategoryTheory.Presheaf.IsLocallySurjective.imageSieve_mem, ContinuousMap.sigmaEquiv_apply, MagmaCat.hom_inv_apply, AddGroupExtension.Section.rightHom_comp_section, Subspace.dualRestrict_surjective, cfcₙHomSuperset_id, re_inner_self_pos, MvPolynomial.monomial_mul, HahnSeries.support_single_of_ne, MonomialOrder.toSyn_eq_zero_iff, FirstOrder.Language.Substructure.subtype_injective, OrderIso.isLUB_preimage, LieModule.toEnd_pow_lie, Trivialization.pullback_baseSet, MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse, MeasureTheory.volume_preserving_piFinTwo, Order.PFilter.mem_mk, ContinuousAffineMap.hasFDerivAt, AddAut.conj_apply, GroupNorm.add_apply, Fintype.map_balance, OrderAddMonoidIso.toFun_eq_coe, Equiv.Perm.OnCycleFactors.coe_toPermHom, RingEquivClass.map_add, Polynomial.algHom_ext_iff, Module.compHom.toLinearMap_apply, RelHom.preimage_apply, RootPairing.InvariantForm.apply_eq_or_aux, KaehlerDifferential.kerTotal_mkQ_single_mul, Antisymmetrization.prodEquiv_symm_apply_mk, Tuple.antitone_pair_of_not_sorted', RestrictedProduct.eventually, Polynomial.coeToPowerSeries.algHom_apply, IsBaseChange.endHom_one, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Poly.zero_apply, LaurentPolynomial.ext_iff, Finset.supIndep_map, SimplexCategoryGenRel.simplicialEvalσ_of_isAdmissible, Equiv.coe_constVAdd, Quaternion.sq_eq_normSq, ofLex_inv, Equiv.Set.Equiv.strictMono_setCongr, AlgebraicGeometry.isDominant_iff, OrderIso.apply_eq_iff_eq_symm_apply, SemidirectProduct.rightHom_eq_right, AlgebraicGeometry.Flat.generalizingMap, MulAlgebraNormClass.map_smul_eq_mul, DirectedSystem.rTensor, AdicCompletion.evalOneₐ_of, groupCohomology.cocycles₁.val_eq_coe, TwoSidedIdeal.coe_mk, MagmaCat.ext_iff, MeasureTheory.Measure.comap_apply_le, DifferentiableAt.continuousMultilinear_apply_const, HomotopicalAlgebra.AttachCells.reindex_cofan₁, MulActionHom.coe_neg, MulHom.coe_mul, Polynomial.rootMultiplicity_eq_multiplicity, CategoryTheory.Localization.homEquiv_trans, NumberField.mixedEmbedding.logMap_unit_smul, NumberField.Units.coe_one, PointedCone.mem_span_set, CentroidHom.comp_mul_comm, WittVector.truncate_lift, spectralAlgNorm_extends, AlgebraicGeometry.Scheme.Hom.fiberι_asFiber, SemiNormedGrp₁.ext_iff, AddMonoidHom.zsmul_apply, CompactlySupportedContinuousMap.zero_apply, CommSemiRingCat.forget_map, Representation.norm_ofDistribMulAction_eq, UniformOnFun.lipschitzOnWith_iff, Module.End.HasUnifEigenvector.apply_eq_smul, AddSubgroup.coe_toIntSubmodule, WithZero.logEquiv_apply, Algebra.IsCentral.mem_center_iff, MultilinearMap.freeFinsuppEquiv_single, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_inv, AddOpposite.coe_symm_opAddEquiv, OrderEmbedding.birkhoffSet_sup, Algebra.Generators.H1Cotangent.exact_map_δ', ContinuousMapZero.evalCLM_apply, WeakBilin.coeFn_continuous, Dilation.coe_id, DistribMulActionHom.instDistribMulActionSemiHomClassCoeMonoidHom, PowerBasis.equivOfMinpoly_apply, Lagrange.degree_interpolate_le, Equiv.Perm.IsThreeCycle.nodup_iff_mem_support, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', OneHom.mulSingle_apply, Matrix.compAlgEquiv_symm_apply, Polynomial.bernoulli_def, LinearMap.kerComplementEquivRange_symm_apply, CommAlgCat.forget_map, SemilatInfCat.Iso.mk_inv_toFun, TannakaDuality.FiniteGroup.sumSMulInv_single_id, BoundedContinuousFunction.nnnorm_coe_le_nnnorm, Additive.toMul_top, CategoryTheory.SingleObj.mapHom_comp, MeasureTheory.Content.outerMeasure_caratheodory, thickenedIndicator_apply, TopCat.GlueData.MkCore.t_id, Module.AEval.X_smul_of, Set.coe_singletonMulHom, Equiv.prodCongrRight_apply_snd, AlgHom.eqOn_adjoin_iff, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, Submodule.map₂_span_singleton_eq_map, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, DFinsupp.card_pi, BooleanSubalgebra.mem_map, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal, MonoidHom.transferCenterPow_apply, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, MeasureTheory.OuterMeasure.le_trim_iff, Subring.mem_closure_image_of, TensorProduct.eq_repr_basis_left, ValuativeRel.exists_valuation_div_valuation_eq, Polynomial.derivative_eval₂_C, map_natCast, InnerProductSpace.rankOne_comp, StarMonoidHom.coe_mk, LaurentSeries.powerSeriesRingEquiv_coe_apply, Trivialization.mk_coordChangeL, MvPowerSeries.weightedOrder_eq_nat, QuotientAddGroup.quotientBot_apply, Equiv.Perm.sign_permCongr, SmoothBumpCovering.embeddingPiTangent_injOn, Ideal.Quotient.mk_out, ContinuousAlternatingMap.coe_mk, Polynomial.multiset_prod_X_sub_C_nextCoeff, OrderIso.injective, StarAlgEquiv.restrictScalars_apply, Representation.averageMap_id, ArithmeticFunction.carmichael_dvd_totient, frobenius_def, Polynomial.C_div, Complex.measurableEquivPi_symm_apply, Subring.integralClosure_le_iff, LieModule.chainTopCoeff_add_one, IsLocalization'.toIsLocalizationMap, groupCohomology.H1π_comp_map_apply, ContinuousAffineMap.norm_image_zero_le, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, StrongDual.mem_polarSubmodule, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_root, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.c_iso, Equiv.Set.sumDiffSubset_apply_inr, exists_dual_vector', lineMap_le_map_iff_slope_le_slope, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, Composition.mem_range_embedding, MulChar.inv_apply_eq_inv', CategoryTheory.SimplicialObject.cechNerveEquiv_symm_apply, SupPrime.dual, FormalMultilinearSeries.apply_eq_prod_smul_coeff, OrderRingIso.lt_symm_apply, AbsoluteValue.IsAdmissible.exists_partition', EuclideanSpace.basisFun_inner, Equiv.embeddingCongr_apply, AffineEquiv.coe_constVSub_symm, MeasureTheory.SimpleFunc.coe_neg, ClassGroup.equivPic_symm_apply, MvPowerSeries.totalDegree_trunc', OmegaCompletePartialOrder.ContinuousHom.flip_apply, PrimeSpectrum.isIdempotentElemEquivClopens_apply_toOpens, PowerSeries.as_tsum, PrimeSpectrum.basicOpen_isIdempotentElemEquivClopens_symm, CliffordAlgebra.invOf_ι, LinearMap.lTensor_bij_iff_rTensor_bij, QuotientAddGroup.equivIocMod_symm_apply, Orientation.kahler_rightAngleRotation_left, dist_toMul, HeytingHomClass.map_bot, Rep.leftRegularHom_hom_single, SlashInvariantForm.coe_neg, groupCohomology.cocycles₁_map_one, AlgHom.map_smul_of_tower, Matrix.isUnit_comp_iff, CochainComplex.HomComplex.CohomologyClass.mkAddMonoidHom_apply, Ordinal.toGame_nmul, MeasureTheory.measure_eq_zero_iff_eq_empty_of_smulInvariant, AddSubsemigroup.mem_comap, CliffordAlgebra.prodEquiv_symm_apply, AffineMap.lineMap_eq_right_iff, Cardinal.toNat_injOn, MeasureTheory.measure_inv_smul_symmDiff, Equiv.Perm.IsCycleOn.pow_apply_eq_pow_apply, fg_adjoin_of_finite, MulEquiv.irreducible_iff, infClosed_range, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv_symm, IsometryEquiv.coe_eq_toEquiv, CategoryTheory.conjugateEquiv_comp_assoc, UniformOnFun.uniformContinuous_restrict, MeasureTheory.measure_biUnion_finset_le, AddSubsemigroup.centerCongr_symm_apply_coe, tangentMap_chart_symm, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, isCompactOperator_iff_isCompact_closure_image_closedBall, Finset.map_cons, LinearMap.separatingLeft_congr_iff, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, MeasureTheory.Content.outerMeasure_exists_compact, Module.Basis.end_repr_symm_apply, MvPowerSeries.expand_monomial, TensorAlgebra.GradedAlgebra.ι_apply, AddEquiv.symm_trans_apply, ProbabilityTheory.Kernel.singularPart_eq_singularPart_measure, AlgebraicGeometry.IsOpenImmersion.instIsIsoCommRingCatStalkMap, AddSubsemigroup.mem_map, LinearMap.GeneralLinearGroup.coe_ofLinearEquiv, LieSubmodule.coe_toEnd, ArithmeticFunction.cardDistinctFactors_eq_one_iff, AffineSubspace.comap_span, FirstOrder.Ring.MvPolynomialSupportLEEquiv_symm_apply_coeff, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, MvPolynomial.aeval_bind₂, NumberField.IsCMField.mem_realUnits_iff, OrderEmbedding.image_setOf_minimal, Equiv.polishSpace_induced, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, LinearMap.continuous_of_finiteDimensional, ProbabilityTheory.Kernel.withDensity_apply, StarMonoidHom.coe_id, Module.evalEquiv_apply, Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex, Function.Embedding.invFun_restrict, Polynomial.normalize_eq_self_iff_monic, CentroidHom.toEndRingHom_apply, GroupNorm.ext_iff, AlgebraicGeometry.isPreimmersion_iff, Polynomial.Chebyshev.algebraMap_eval_T, SchwartzMap.tsupport_smulLeftCLM_subset, HahnEmbedding.Partial.coeff_eq_zero_of_mem, ProbabilityTheory.IsMarkovKernel.is_probability_measure', HurwitzZeta.hasSum_nat_hurwitzZetaOdd, AlgebraicGeometry.Scheme.AffineCover.covers, PadicInt.hasSum_mahler, DistribMulActionHom.coe_toLinearMap, Lagrange.nodal_eq_mul_nodal_erase, ProbabilityTheory.Kernel.iIndep.meas_iInter, CategoryTheory.coyonedaEquiv_coyoneda_map, Module.Basis.range_ofSpan, MvPolynomial.rename_bind₁, LinearMap.IsReflective.dvd_two_mul, IntermediateField.extendScalars.orderIso_symm_apply_coe, Diffeomorph.coe_toEquiv, CliffordAlgebra.contractRight_contractRight, InnerProductSpace.toMatrix_rankOne, MeasureTheory.measure_zero_iff_ae_notMem, isOfFinAddOrder_ofMul_iff, Matrix.uniqueRingEquiv_symm_apply, HasFDerivWithinAt.continuousMultilinear_apply_const, RingHom.map_iterateFrobenius, RingHom.map_det, SubMulAction.ofFixingSubgroup.append_left, Set.Iic_ofDual, List.support_formPerm_le', LinearMap.equivariantProjection_apply, QuadraticForm.tmul_tensorLId_apply, RingCon.matrix_apply_single, Affine.Simplex.affineCombination_mem_affineSpan_faceOpposite_iff, OrderHom.toFun_eq_coe, separate_convex_open_set, AddEquiv.mapAddSubgroup_apply, WithOne.map_map, LieAlgebra.InvariantForm.mem_orthogonal, FirstOrder.Language.Theory.CompleteType.formula_mem_typeOf, IncidenceAlgebra.mu_eq_neg_sum_Ioc_of_ne, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, OrderIso.mulLeft₀_symm_apply, MeasureTheory.Measure.measure_isAddLeftInvariant_eq_vadd_of_ne_top, Equiv.bijOn_swap, Coalgebra.Repr.convMul_apply, ContinuousOrderHom.toFun_eq_coe, ofColex_vadd, Finmap.keysLookupEquiv_apply_coe_snd, AffineEquiv.apply_eq_iff_eq_symm_apply, ProbabilityTheory.Kernel.ext_fun_iff, BoundedContinuousFunction.coe_restrict, PeriodPair.latticeEquiv_symm_apply, CFC.abs_algebraMap_nnreal, MvPolynomial.rTensor_symm_apply_single, finTwoArrowEquiv'_symm_apply, PowerSeries.derivative_coe, nhds_ofDual, AddCon.mkAddHom_apply, WittVector.ghostComponent_zero_verschiebung, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_apply, MeasureTheory.mul_meas_ge_le_lintegral₀, Complex.equivRealProdLm_symm_apply_re, MulHom.ext_iff, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, ContinuousAffineMap.apply_lineMap, PartENat.withTopEquiv_le, MvPolynomial.pderiv_X_of_ne, Diffeomorph.uniqueMDiffOn_image_aux, Polynomial.divX_C_mul_X_pow, AffineIsometryEquiv.coe_toIsometryEquiv, Module.Basis.toMatrix_mul_toMatrix_flip, ProbabilityTheory.posterior_boolKernel_apply_false, LieModule.toEnd_apply_apply, LieAlgebra.Extension.ofTwoCocycle_incl_apply, MvPolynomial.prod_X_add_C_coeff, RingCon.mkₐ_surjective, MvPolynomial.renameSymmetricSubalgebra_symm_apply_coe, Finsupp.update_eq_sub_add_single, MeasureTheory.ComplexMeasure.im_apply, ProbabilityTheory.covariance_map_equiv, CategoryTheory.ConcreteCategory.coe_id, LinearMap.IsPerfPair.bijective_right, StandardEtalePair.hom_ext_iff, Algebra.Generators.Hom.toAlgHom_comp_apply, PowerSeries.coeff_zero_eq_constantCoeff_apply, Order.IsPredPrelimit.dual, TopHomClass.map_top, Submodule.IsLocalizedModule.localized'FrameHom_apply, RingQuot.mkRingHom_surjective, CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_apply, SeparationQuotient.mk_algebraMap, PiTensorProduct.liftIsometry_comp_mapL, CStarMatrix.reindexₗ_apply, MvPolynomial.degree_finSuccEquiv, CliffordAlgebra.star_ι, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, MvPowerSeries.inv_eq_zero, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_indicator_mul_lintegral, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Polynomial.X_pow_mul_monomial, Ordinal.le_preOmega_self, Polynomial.roots_expand_pow_map_iterateFrobenius, ProbabilityTheory.Kernel.singularPart_of_subset_compl_mutuallySingularSetSlice, CategoryTheory.Limits.coneOfSectionCompYoneda_π, QuadraticForm.tensorLId_apply, OrderAddMonoidIso.ext_iff, AddAction.toPerm_symm_apply, Equiv.Perm.cycleOf_self_apply, dist_pointReflection_right, MeasureTheory.Measure.addHaar_smul_of_nonneg, MeasureTheory.condExpIndL1Fin_disjoint_union, Seminorm.continuous_from_bounded, AddMonoidAlgebra.mul_apply_add_eq_mul_of_uniqueAdd, OrderRingIso.apply_eq_self, MvPowerSeries.order_expand, Surreal.nat_toGame, Unitary.coe_map_star, ContinuousMap.isHomeomorph_coe, ContinuousLinearMap.opNorm_le_iff, LaurentPolynomial.toLaurent_support, Representation.free_single_single, Submodule.isQuotientEquivQuotientPrime_iff, RCLike.geometric_hahn_banach_open, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two, NumberField.mixedEmbedding.normAtPlace_neg, LinearMap.mul_toMatrix₂_mul, MeasureTheory.Measure.measure_neg, ContinuousLinearMap.completion_apply_coe, toMul_nsmul, Polynomial.aeval_derivative_of_splits, EuclideanGeometry.orthogonalProjection_mem, Set.Subsingleton.measure_zero, RootPairing.pairingIn_one_four_iff, MvPolynomial.nonempty_support_optionEquivLeft, span_eq_top_of_isLocalizedModule, AddSubmonoid.mem_comap, Function.locallyFinsuppWithin.coe_nsmul, Dilation.tendsto_cobounded, LinearEquiv.coord_self, RCLike.conj_wInner_symm, InnerProductSpace.isSymmetric_rankOne_self, Sum.Lex.toLexRelIsoLT_coe, LieHom.coe_injective, IsIntegral.map, AlgEquiv.subalgebraMap_apply_coe, MeasurableEquiv.image_symm, MonoidHom.coe_rangeRestrict, MulSemiringActionHom.map_one, coe_ofLexAddEquiv, MeasureTheory.OuterMeasure.isometryEquiv_map_mkMetric, SSet.skeletonOfMono_zero, sInfHom.id_apply, Polynomial.map_expand_pow_char, QuadraticMap.map_sum', ContinuousAlgHom.coe_fst', DFinsupp.mem_pi, MvPolynomial.pderiv_monomial, Algebra.trace_quotient_mk, PrincipalSeg.isNormal, IsLocalization.bijective_linearMap_mul', CategoryTheory.Limits.Concrete.widePushout_exists_rep', Finsupp.lcongr_symm_single, IsSMulRegular.of_flat_of_isBaseChange, Complex.coe_algebraMap, CategoryTheory.Iso.isoCongr_apply, ContinuousMap.coe_toLp, Real.fourierIntegral_convergent_iff, SkewMonoidAlgebra.sum_mapDomain_index, Equiv.Perm.cycleOf_apply, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Commute.cfcHom, LinearMap.lTensor_comp_apply, smoothingFun_le_self, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField_assoc, Module.Basis.apply_eq_iff, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', UniformEquiv.uniformContinuous, WithTop.toDual_le_toDual_iff, Representation.IntertwiningMap.isIntertwining', Finset.le_card_quotient_mul_sq_inter_subgroup, Module.Flat.iff_forall_exists_factorization, CuspForm.ext_iff, skewAdjointPart_apply_coe, AffineIsometryEquiv.pointReflection_self, Orientation.map_neg, WeierstrassCurve.ψ_three, CliffordAlgebra.involute_ι, AlgebraicGeometry.IsFinite.finite_preimage_singleton, OmegaCompletePartialOrder.ωScottContinuous.isLUB, LinearMap.image_convexHull, CStarMatrix.ofMatrix_eq_ofMatrixStarAlgEquiv, continuousMultilinearCurryLeftEquiv_apply, BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact, ProbabilityTheory.HasGaussianLaw.map_equiv, RestrictedProduct.structureMap_apply, Set.coe_unionEqSigmaOfDisjoint_symm_apply, Orientation.abs_areaForm_of_orthogonal, UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv_symm, Prefunctor.costar_conj_star, Isometry.affineIsometryOfStrictConvexSpace_apply, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, SubAddAction.image_inclusion, LeftInvariantDerivation.coe_smul, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, surjective_frobenius, exteriorPower.alternatingMapToDual_apply_ιMulti, BoundedContinuousFunction.nnnorm_le, Finsupp.coe_sym2Mul, Module.Basis.mk_coord_apply, continuous_selfAdjointPart, HasFPowerSeriesAt.deriv, GradedTensorProduct.includeLeftRingHom_apply, IsCoprime.map, Polynomial.lsum_apply, LinearMap.exact_of_comp_eq_zero_of_ker_le_range, sigmaFinsuppLequivDFinsupp_symm_apply, YoungDiagram.equivListRowLens_apply_coe, SubMulAction.ofStabilizer.conjMap_comp, OneHom.pow_apply, ArchimedeanClass.FiniteResidueField.mk_le_mk, LinearMap.exact_zero_iff_injective, RingCon.coe_sInf, AddUnits.coe_map, DilationEquiv.injective, Ordinal.toGame_lf_iff, SlashInvariantForm.slash_action_eqn_SL'', Equiv.surjective_comp, ProbabilityTheory.setLIntegral_toKernel_prod, sigmaFinsuppEquivDFinsupp_single, CoalgHom.coe_toLinearMap, AffineBasis.coords_apply, LinearMap.BilinForm.tensorDistribEquiv_tmul, Nat.prod_pow_primeFactors_factorization, Order.isSuccLimit_toDual_iff, innerₗ_apply_apply, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, Composition.invEmbedding_comp, TopCat.Presheaf.germ_stalkPullbackInv, InfTopHom.coe_comp, InfTopHom.dual_apply_toFun, Algebra.trace_surjective, HahnSeries.ofPowerSeriesAlg_apply_coeff, ContinuousAlternatingMap.ofSubsingleton_apply_apply, Module.Dual.lie_apply, ZMod.χ₄_int_one_mod_four, Affine.Simplex.sign_touchpointWeights_singleton_neg, Algebra.surjective_algebraMap_iff, ProbabilityTheory.Kernel.lintegral_deterministic_prod, Equiv.ofPreimageEquiv_map, SetSemiring.up_le_up, Action.Hom.comm_assoc, Affine.Simplex.orthogonalProjectionSpan_restrict, QuasiconvexOn.dual, isAddRightRegular_ofColex, RingHom.injective_iff_ker_eq_bot, MeasureTheory.piPremeasure_pi, LinearMap.coe_inl, coe_powMonoidWithZeroHom, RingCon.ext_iff, SimpleGraph.Reachable.map, Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk, LinearMap.trace_tensorProduct', Monoid.PushoutI.NormalWord.summand_smul_def', MeasureTheory.AEStronglyMeasurable.integral_condKernel, LaurentSeries.powerSeriesEquivSubring_apply, CategoryTheory.forgetAdjToOver.homEquiv_symm, Algebra.Generators.toComp_toAlgHom_monomial, FinEnum.down_equiv_symm, Homeomorph.uniqueProd_symm_apply_snd, MonoidAlgebra.GroupSMul.linearMap_apply, DFinsupp.lex_le_iff_of_unique, Ordinal.enum_le_enum, LinearMap.polar_eq_biInter_preimage, MvPolynomial.counit_surjective, Equiv.self_comp_symm, ContinuousAffineEquiv.continuous, ProbabilityTheory.HasSubgaussianMGF.add, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, Module.Finite.exists_comp_eq_id_of_projective, LinearMap.IsReflective.coroot_apply_self, DFinsupp.inf_apply, Cardinal.preAleph_zero, Polynomial.coeff_expand_mul, Set.Ioo_toDual, Representation.Coinvariants.mk_eq_zero, MeasurableEquiv.piMeasurableEquivTProd_apply, MvPowerSeries.map_iterateFrobenius_expand, ConjAct.ofConjAct_toConjAct, Seminorm.coe_sSup_eq, AddEquiv.symm_comp_self, RingCon.quotientQuotientEquivQuotientₐ_symm_mk, OrderMonoidIso.toFun_eq_coe, Polynomial.eval_zero_map, Homeomorph.isPreconnected_image, precomp_compactConvergenceCLM_apply, HNNExtension.hom_ext_iff, MeasureTheory.SimpleFunc.integrable_approxOn_range, TensorProduct.leftComm_symm_tmul, LieModule.commute_toEnd_of_mem_center_right, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, Finsupp.equivMapDomain_apply, MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero_aux, uliftZMultiplesHom_apply_apply, KaehlerDifferential.D_tensorProductTo, Finset.measure_zero, unitary.norm_map, DFinsupp.toMultiset_injective, addRothNumber_map_add_left, MeasurableEmbedding.map_apply, MvPolynomial.rename_injective, MeasureTheory.Measure.snd_univ, Multiset.toFinsupp_zero, ofDual_natCast, HahnSeries.single_zero_one, DFinsupp.comapDomain_apply, NumberField.mixedEmbedding.unitSMul_smul, MeasureTheory.SimpleFunc.exists_le_lowerSemicontinuous_lintegral_ge, AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows, ContinuousLinearEquiv.fderiv, FreeAddMonoid.lift_restrict, RingCon.kerLift_injective, QuotientGroup.congr_mk', fourierCoeff_eq_intervalIntegral, IntermediateField.inclusion_injective, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi, Subring.mem_comap, Filter.EventuallyEq.measure_eq, ArchimedeanClass.FiniteElement.val_one, Seminorm.bddBelow_range_add, Polynomial.nextCoeff_map_eq, PartENat.withTopEquiv_lt, Polynomial.derivative_pow, ContinuousAlternatingMap.restrictScalarsCLM_apply, Valuation.IsNontrivial.exists_one_lt, GrpCat.FilteredColimits.colimit_mul_mk_eq, RingEquiv.piCongrLeft_apply, DMatrix.map_add, Algebra.adjoin_eq_span, AlgebraicGeometry.Proj.fromOfGlobalSections_morphismRestrict, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, ChainComplex.fromSingle₀Equiv_symm_apply_f_zero, ContMDiffWithinAt.mfderivWithin_apply, IsAtom.dual, IsDedekindDomain.HeightOneSpectrum.intValuation_def, Finset.le_card_quotient_add_sq_inter_addSubgroup, AddMonoidAlgebra.le_infDegree_mul, NumberField.mixedEmbedding.continuous_normAtPlace, AlgebraicIndependent.sumElim_comp, iterate_frobeniusEquiv_symm_pow_p_pow, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, SchwartzMap.tsupport_fderivCLM_subset, OrderIso.pnatIsoNat_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, Trivialization.symmₗ_linearMapAt, ContinuousLinearMap.isBigOTVS_comp, ofDual_intCast, Homeomorph.coe_prodComm, PadicAlgCl.valuation_def, Continuous.exists_contMDiff_approx_and_eqOn, ContinuousMap.evalStarAlgHom_apply, Subalgebra.mem_comap, DFinsupp.coeFnLinearMap_apply, Matrix.stdBasis_eq_single, Algebra.Extension.toKaehler_surjective, ContinuousLinearEquiv.mdifferentiableWithinAt, TopHom.coe_sup, LinearMap.det_eq_one_of_finrank_eq_zero, DFinsupp.sumZeroHom_piSingle, IsometryEquiv.addRight_apply, Polynomial.C_ofNat, CategoryTheory.OverPresheafAux.MakesOverArrow.app, Polynomial.reverse_add_C, ProbabilityTheory.Kernel.isProjectiveMeasureFamily_partialTraj, ContinuousMap.piComparison_fac, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp_app_apply, SpectralMap.toFun_eq_coe, SkewMonoidAlgebra.toFinsupp_mapDomain, LinearMap.congr_fun, IsMaxAntichain.image, AddSubsemigroup.equivOp_symm_apply_coe, OrderDual.exists, NonUnitalStarRingHom.map_le_map_of_map_star, TensorAlgebra.range_lift, AlgebraicGeometry.stalkMap_toStalk_apply, PartENat.withTopEquiv_apply, MeasureTheory.laverage_union, ContinuousLinearMap.NonlinearRightInverse.right_inv', AlgebraicGeometry.IsAffineOpen.primeIdealOf_eq_map_closedPoint, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, Module.Basis.abs_det_adjustToOrientation, Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree, WeierstrassCurve.Projective.negDblY_eq', Homeomorph.piFinTwo_apply, Irreducible.normalizedFactors_pow, ContinuousLinearEquiv.mdifferentiable, PiTensorProduct.one_mul, IsometryEquiv.comp_continuous_iff', CoalgEquiv.coe_toEquiv, Submodule.IsCompl.projection_apply_eq_zero_iff, MvPolynomial.quotient_mk_comp_C_injective, VitaliFamily.measure_le_mul_of_subset_limRatioMeas_lt, QuotSMulTop.equivQuotTensor_naturality_mk, Submonoid.LocalizationMap.map_zero, SymAlg.unsym_bijective, Finset.weightedVSubOfPoint_eq_of_weights_eq, AdjoinRoot.algEquivOfEq_apply_root, LieHom.coe_one, MonoidHom.coe_toAdditive_range, AddEquiv.opOp_symm_apply, DFinsupp.add_apply, SymmetricAlgebra.algebraMap_eq_one_iff, MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree, OrderIso.upperBounds_image, RingHom.injective_nat, QuadraticMap.map_neg, MeasureTheory.ae_measure_preimage_add_right_lt_top_of_ne_zero, MulHom.coe_comp, DirectSum.decomposeLinearEquiv_symm_apply, ContinuousLinearMap.integral_comp_L1_comm, Algebra.SubmersivePresentation.aeval_jacobianOfHasCoeffs, ArithmeticFunction.moebius_sq_eq_one_of_squarefree, ContinuousMap.canLift, TopologicalSpace.Opens.leSupr_apply_mk, PMF.toOuterMeasure_apply_inter_support, MultilinearMap.map_coord_zero, CategoryTheory.Bicategory.mateEquiv_square, Module.Flat.iff_lTensor_preserves_injective_linearMapₛ, Submodule.linearMap_eq_zero_iff_of_span_eq_top, CompactlySupportedContinuousMap.toNNRealLinear_apply, Polynomial.derivative_prod, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, Finset.Colex.le_def, ContinuousMultilinearMap.alternatization_apply_toContinuousMultilinearMap, Equiv.sumAssoc_symm_apply_inr_inl, DFinsupp.mapRange.addMonoidHom_apply, FreeMonoid.ofList_singleton, Affine.Simplex.touchpoint_reindex, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, PMF.apply_eq_one_iff, Finsupp.single_add_erase, Int.natAbsHom_apply, rothNumberNat_add_le, AddHom.mulOp_symm_apply_apply, WType.NatαEquivPUnitSumPUnit_apply, Polynomial.isSplittingField_C, ProbabilityTheory.Kernel.setLIntegral_compProd, LinearMap.toMatrix'_id, Module.Basis.det_self, FunctionField.inftyValuation.X, CliffordAlgebra.even_toSubmodule, CategoryTheory.Discrete.equivalence_counitIso, Real.hasDerivAt_fourierChar, Multiset.toFinsupp_toMultiset, setBasisOfTopLeSpanOfCardEqFinrank_repr_apply, ContinuousLinearMap.intervalIntegral_apply, quadraticChar_eq_one_of_char_two, LinearMap.polyCharpolyAux_coeff_eval, ZMod.unitsMap_val, AddAction.orbitEquivQuotientStabilizer_symm_apply, AlgebraicGeometry.Scheme.IsLocallyDirected.glueDataι_naturality, isAddLeftRegular_toDual, Equiv.Perm.coe_subsingleton, MeasureTheory.tendsto_measure_iInter_atTop, RingEquiv.toSemilinearEquiv_symm_apply, AddSubgroup.surjective_normedMk, Module.Invertible.lTensor_injective_iff, Preord.dual_map, AddMonoidAlgebra.tensorEquiv_symm_single, SimpleGraph.Copy.coe_id, IsIntegral.map_of_comp_eq, not_irreducible_expand, AlgebraicClosure.Monics.map_eq_prod, RingHom.coe_snd, AddMonoidAlgebra.lift_of', MeasureTheory.tendsto_measure_Ici_atBot, Equiv.Perm.SameCycle.conj, LieModule.toEnd_baseChange, AffineEquiv.equivUnitsAffineMap_symm_apply_toFun, DFinsupp.erase_apply, selfAdjointPartL_apply_coe, Matrix.submatrix_one_embedding, HasFDerivWithinAt.comp_hasDerivWithinAt, PMF.integral_eq_sum, RootPairing.Equiv.coweightHom_op, NonUnitalSubring.mem_comap, weightedVSub_mem_vectorSpan, LinearMap.coe_comp, liftOfDerivationToSquareZero_apply, LocalizedModule.mul_by_divBy, CentroidHom.coe_zero, SkewMonoidAlgebra.update_zero_eq_erase, Equiv.withBotSubtypeNe_apply, EuclideanGeometry.inner_weightedVSub, MonomialOrder.degree_prod_le, ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_comp, AffineMap.lineMap_apply_one, CategoryTheory.PreGaloisCategory.exists_hom_from_galois_of_fiber, Module.End.genEigenspace_zero_nat, AlgHomClass.commutes, CategoryTheory.OverPresheafAux.OverArrows.app_val, Orientation.kahler_rotation_left, Algebra.toSubmodule_eq_top, Representation.le_comap_invariants, strictAnti_dual_iff, LinearMap.exact_map_mkQ_range, MeasureTheory.lintegral_indicator_const, MeasureTheory.Measure.ext_prod₃_iff, LindemannWeierstrass.integral_exp_mul_eval, minpoly.dvd_map_of_isScalarTower', AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, GromovHausdorff.HD_below_aux2, OrderIso.coe_toRelIsoGT, Homeomorph.onePointCongr_apply, Ring.DirectLimit.map_comp, CategoryTheory.Functor.coconeTypesEquiv_apply_ι_app, Set.Iio_ofDual, Ideal.associatesEquivIsPrincipal_apply, PiTensorProduct.liftIsometry_symm_apply, Homeomorph.piCurry_symm_apply, InfHom.coe_const, AddSubmonoid.LocalizationMap.eq_mk'_iff_add_eq, Homeomorph.image_eq_preimage_symm, FreeLieAlgebra.hom_ext_iff, LinearEquiv.symmEquiv_symm_apply_apply, Derivation.tensorProductTo_mul, nnnorm_cfcₙHom, Con.comap_eq, SemiRingCat.ofHom_apply, ModularFormClass.hasSum_qExpansion_of_abs_lt, fderivWithin_continuousAlternatingMap_apply_apply, ClosureOperator.IsClosed.closure_le_iff, Composition.mem_range_embedding_iff', PowerSeries.coeff_map, equivShrink_lt_equivShrink, IsPGroup.powEquiv_symm_apply, StarAlgEquiv.symm_trans_apply, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist', SpectralMap.comp_apply, MeasureTheory.Measure.Subtype.volume_univ, contractLeft_apply, IsometryEquiv.piCongrLeft_apply, HahnSeries.SummableFamily.smulFamily_toFun, HomeomorphClass.map_continuous, LatticeHom.snd_apply, WithCStarModule.norm_equiv_le_norm_prod, Algebra.Extension.Cotangent.mk_surjective, ContinuousMultilinearMap.iteratedFDerivComponent_apply, NonUnitalSubring.centerToMulOpposite_symm_apply_coe, AddLocalization.mkHom_apply, Besicovitch.exists_disjoint_closedBall_covering_ae, Matrix.diagonal_kronecker, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add, AlgebraicGeometry.PresheafedSpace.GlueData.opensImagePreimageMap_app_assoc, MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ, AlgHom.fieldRange_eq_top, ProbabilityTheory.Kernel.snd_apply', AffineMap.lineMap_apply', map_indicator, Equiv.Perm.sumCongrHom_injective, SemimoduleCat.Iso.conj_eq_conj, CategoryTheory.Subfunctor.range_eq_ofSection, GaussianInt.intCast_real_norm, IsometryEquiv.coe_toEquiv, LSeries_one_mul_Lseries_moebius, RootPairing.pairingIn_neg_one_neg_four_iff, ContinuousLinearEquiv.comp_differentiableAt_iff, HahnSeries.leadingCoeff_nonneg_iff, CategoryTheory.orderDualEquivalence_counitIso, LinearMap.BilinMap.tensorDistrib_tmul, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, SemiRingCat.hom_inv_apply, Rat.AbsoluteValue.padic_le_one, Affine.Simplex.setInterior_restrict, CategoryTheory.ConcreteCategory.id_apply, Quaternion.self_mul_star, Finsupp.coe_eq_zero, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, ArithmeticFunction.vonMangoldt.residueClass_le, Metric.Snowflaking.toSnowflaking_comp_ofSnowflaking, Projectivization.cross_mk, RestrictScalars.addEquiv_symm_map_smul_smul, PowerSeries.eval₂_C, ContinuousLinearMap.toContinuousAddMonoidHom_neg, Polynomial.expand_mul, WeierstrassCurve.Affine.map_negAddY, OrderIso.sumDualDistrib_symm_inr, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, LinearMap.BilinForm.mul_toMatrix_mul, Polynomial.eval_sumIDeriv_of_pos, Multiset.map_noncommSum, RootPairing.neg_root_mem, LieAlgebra.IsKilling.root_apply_coroot, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, RingHom.surjective_of_epi_of_finite, MeasureTheory.SimpleFunc.div_apply, associatesEquivOfUniqueUnits_apply, LieDerivation.coe_injective, PowerSeries.constantCoeff_smul, AffineMap.vadd_apply, List.formPerm_apply_of_notMem, MvPolynomial.dvd_monomial_mul_iff_exists, OrthonormalBasis.orthonormal_adjustToOrientation, TwoSidedIdeal.top_asIdeal, MeasureTheory.isTightMeasureSet_iff_exists_isCompact_measure_compl_le, MeasureTheory.measure_eq_iInf', StarRingEquivClass.map_star, DirichletCharacter.LSeries_eulerProduct_hasProd, ContinuousMap.coe_apply, EquivLike.apply_coe_symm_apply, MeasureTheory.FiniteMeasure.smul_apply, NumberField.AdeleRing.algebraMap_injective, MvPolynomial.killCompl_map, Trivialization.coe_linearMapAt_of_mem, Equiv.inv_apply, CategoryTheory.Coverage.mem_toGrothendieck, Algebra.IsAlgebraic.bijective_of_isScalarTower', equivShrink_add, MeasureTheory.volume_pi_ball, FreeAbelianGroup.mul_def, ContMDiffMap.coeFnAddMonoidHom_apply, Ideal.quotientMap_injective', Matrix.traceAddMonoidHom_apply, MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnion₀, MeasureTheory.aestronglyMeasurable_condExpL1CLM, Matrix.updateCol_submatrix_equiv, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Polynomial.aeval_continuousMap_apply, map_one, Finset.map_eq_image, IsFractionRing.algEquivOfAlgEquiv_algebraMap, Hamming.norm_eq_hammingNorm, IsAlgClosed.algebraMap_bijective_of_isIntegral, Equiv.ulift_symm_down, IsLocalization.Away.tensor, BialgHom.toCoalgHom_apply, ProbabilityTheory.Kernel.snd_apply, Polynomial.mkDerivation_X, IsLocalization.orderIsoOfPrime_symm_apply_coe, Ordinal.card_omega, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, Valuation.toMonoidWithZeroHom_coe_eq_coe, AddLocalization.mkHom_surjective, Polynomial.coe_aeval_mk_apply, MeasureTheory.ProbabilityMeasure.apply_union_le, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_unit_f_aux, iteratedFDeriv_succ_eq_comp_right, MulAction.zpowersQuotientStabilizerEquiv_symm_apply, AlgHom.spectrum_apply_subset, Complex.hasSum_conj, CategoryTheory.Limits.Cocone.w_apply, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, MeasureTheory.FiniteMeasure.measureReal_eq_coe_coeFn, PowerSeries.heval_X, L_apply, LineDeriv.tensorLineDerivTwo_eq_lineDerivOp_lineDerivOp, ContinuousLinearEquiv.comp_hasFDerivAt_iff', DirectSum.toAddMonoidAlgebra_of, MonoidHom.mk'_apply, Representation.invariants_eq_inter, NormedRing.algEquivComplexOfComplete_apply, Polynomial.dickson_one_one_eq_chebyshev_T, Algebra.FiniteType.iff_quotient_mvPolynomial, RingAut.inv_apply, AdjoinRoot.coe_liftAlgHom, Finset.Icc_ofDual, Set.ordConnected_dual, CategoryTheory.Discrete.addMonoidalFunctor_δ, Pi.toLex_apply, IsLocalization.sec_spec, Finset.coeAddMonoidHom_apply, map_sub_rev, CFilter.ofEquiv_val, TwoSidedIdeal.mem_asIdeal, Polynomial.leadingCoeff_mul_C_of_isUnit, ContinuousMapZero.le_def, SimpleGraph.isClique_map_iff_of_nontrivial, convexHull_univ, Finsupp.rangeSingleton_apply, ContinuousLinearMap.ofNat_apply, RootPairing.RootPositiveForm.isSymm_posForm, IsometryClass.nndist_eq, Setoid.piQuotientEquiv_symm_apply, BoundedOrderHom.coe_id, FunctionField.ringOfIntegers.algebraMap_injective, TrivSqZeroExt.algebraMap_eq_inl, ContDiffMapSupportedIn.seminorm_apply, IsBaseChange.endHom_comp_apply, AddMonoidHom.smul_apply, LinearMap.BilinForm.toMatrix_mul_basis_toMatrix, inner_map_self_eq_zero, AffineEquiv.injective, MeasureTheory.SimpleFunc.coe_sub, LinearMap.coe_single, IsDiscreteValuationRing.addVal_eq_zero_iff, FirstOrder.Language.Hom.comp_apply, RingEquiv.op_symm_apply_symm_apply, OrthogonalFamily.eq_ite, exists_contMDiffMap_forall_mem_convex_of_local, Abelianization.equivOfComm_apply, Subfield.extendScalars.orderIso_apply, Equiv.subtypeSubtypeEquivSubtypeExists_apply_coe, List.formPerm_apply_head, WithConv.addEquiv_apply, convexHull_ediam, BoundedContinuousFunction.coeFnMonoidHom_apply, LinearAlgebra.FreeProduct.rel_id, MeasureTheory.addContent_eq_add_disjointOfDiffUnion_of_subset, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_apply, infPrime_toDual, FreeAlgebra.lift_unique, Matrix.toLinAlgEquiv_apply, AffineMap.linearHom_apply, WithSeminorms.tendsto_nhds_atTop, measure_eq_measure_preimage_add_measure_tsum_Ico_zpow, DomAddAct.mk_nsmul, ContinuousLinearEquiv.map_eq_zero_iff, Submonoid.LocalizationMap.of_mulEquivOfMulEquiv_apply, MeasureTheory.Measure.count_apply_finset, Ordinal.card_typein, OrderIso.funUnique_apply, NumberField.IsCMField.unitsComplexConj_eq_self_iff, Module.Basis.coe_ofRepr, AlgEquiv.toRingEquiv_op, MultilinearMap.mkPiRing_apply_one_eq_self, EReal.sign_top, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, DistribMulActionHom.map_zero', ArithmeticFunction.toArithmeticFunction_eq_self, RingEquiv.nonUnitalSubsemiringMap_symm_apply_coe, LinearMap.nondegenerate_toMatrix₂'_iff, Orientation.inner_sq_add_areaForm_sq, Monovary.sum_smul_comp_perm_lt_sum_smul_iff, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, QuadraticMap.weightedSumSquares_apply, TensorProduct.range_map_eq_span_tmul, ContinuousMultilinearMap.hasFDerivAt, BotHom.dual_symm_apply_apply, cfc_apply, signedDist_smul_of_neg, ContinuousMap.prod_apply, AlgHom.subalgebraMap_coe_apply, AddMonoidAlgebra.curryRingEquiv_symm_single, MeasureTheory.inv_measure_univ_smul_eq_self, RingEquiv.image_eq_preimage, LinearMap.BilinForm.toMatrix'_comp, DirectSum.decomposeAlgEquiv_apply, TopCat.GlueData.preimage_range, Algebra.norm_eq_one_of_not_exists_basis, coe_fn_eq, IsCompact.measure_lt_top, MulLEAddHomClass.map_mul_le_add, Valuation.srel_one_iff, Ordinal.lift_typein_top, AddSubgroup.mem_map_equiv, VectorField.lieBracket_smul_left, LinearMap.mapMatrix_apply, ContinuousLinearMap.rotation_apply, Equiv.funSplitAt_apply, RelEmbedding.prodLexMap_apply, AddGroupNorm.sup_apply, AddMonoidAlgebra.opRingEquiv_apply, AddMonoid.Coprod.swap_inl, Function.Embedding.coe_trans, ContinuousAddMonoidHom.neg_toFun, ProbabilityTheory.Kernel.sum_apply, FintypeCat.hom_apply, OrderAddMonoidHom.inlₗ_add_inrₗ_eq_toLex, IsAdicComplete.mk_liftRingHom, WeierstrassCurve.Jacobian.baseChange_dblXYZ, HNNExtension.toSubgroupEquiv_neg_apply, LieModule.exists_nontrivial_weightSpace_of_isSolvable, ContinuousMap.mkD_apply_of_continuousOn, ContinuousLinearMap.coe_sum', PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, finSuccEquiv'_last_apply, Algebra.Generators.CotangentSpace.exact, Traversable.foldr.ofFreeMonoid_comp_of, Polynomial.coeff_zero_eq_aeval_zero, AlgebraicGeometry.IsOpenImmersion.range_pullback_to_base_of_right, Fin.castOrderIso_symm_apply, Algebra.Generators.H1Cotangent.δAux_X, OrderHom.equivFunctor_apply, Algebra.TensorProduct.comm_symm_tmul, map_mem_nonunits_iff, DoubleCentralizer.algebraMap_fst, MonomialOrder.div_set, CliffordAlgebra.prodEquiv_apply, Fin.cycleRange_of_lt, SemidirectProduct.congr'_symm_apply_left, RCLike.re_le_re, AddMonoidAlgebra.grade.decompose_single, Polynomial.derivation_ext_iff, RCLike.reLm_coe, DFinsupp.neg_apply, ValuationSubring.surjective_unitGroupToResidueFieldUnits, MvPolynomial.support_optionEquivLeft, LocallyConstant.neg_apply, MvPowerSeries.coeff_rescale, Ordinal.typein_ordinal, spectrum.mem_iff, Cardinal.toNat_le_iff_le_of_lt_aleph0, Module.Basis.linearIndependent, SetSemiring.down_add, NumberField.mixedEmbedding.indexEquiv_apply_isReal, MonoidHom.isClosed_range_coe, OrderRingHom.coe_ringHom_apply, MonoidHom.toAdditive_id, EisensteinSeries.q_expansion_bernoulli, FreeGroup.prod_mk, Submodule.exists_injOn_mkQ_image_span_eq_of_span_eq_map_mkQ_of_le_jacobson_bot, TopCat.isOpenEmbedding_iff_isIso_comp, DFinsupp.lmk_apply, NNReal.orderIsoIccZeroCoe_symm_apply_coe, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_π, AddMonoidHom.sub_mem_ker_iff, SchwartzMap.convolution_continuous_left, Submodule.IsCompl.projection_apply, ContinuousLinearMap.adjoint_toSpanSingleton, isLeftRegular_ofAdd, gaussSum_mul_gaussSum_pow_orderOf_sub_one, Equiv.curry_apply, Quiver.starEquivCostar_symm_apply, Equiv.prodPiEquivSumPi_symm_apply, MeasureTheory.SimpleFunc.coe_restrict, CategoryTheory.coherentTopology.mem_sieves_of_hasEffectiveEpiFamily, MulEquiv.symmEquiv_symm_apply_apply, TensorProduct.equivFinsuppOfBasisRight_apply, LSeries.one_convolution_eq_zeta_convolution, ContinuousAddMonoidHom.coe_coe, Algebra.norm_eq_of_algEquiv, Equiv.ofUnique_apply, ContinuousAlternatingMap.coe_zero, mulLinearMap_apply_apply, right_le_lineMap_iff_one_le, MonoidWithZeroHom.snd_mono, CategoryTheory.ShortComplex.moduleCat_exact_iff, Module.Basis.self_mem_flag_iff, ContinuousLinearMap.ext_iff, Finset.eraseNone_eq_biUnion, rootOfSplitsXPowSubC_pow, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, UpperHalfPlane.coe_specialLinearGroup_apply, lineMap_le_lineMap_iff_of_lt, MeasureTheory.measure_if, ContinuousMonoidHom.coe_one, OrderIso.preimage_Ici, LinearIsometryEquiv.coe_one, OrthonormalBasis.orthonormal, TopCat.Presheaf.map_restrict, CategoryTheory.Limits.Bicone.whisker_ι, MultilinearMap.ext_ring_iff, Ordinal.type_lift_preimage, ContinuousLinearMap.mfderivWithin_eq, ContinuousMultilinearMap.nnnorm_ofSubsingleton, ZMod.χ₄_eq_neg_one_pow, UniformOnFun.edist_eq_pi_restrict, Polynomial.not_isUnit_X_sub_C, UniqueFactorizationMonoid.normalizedFactors_irreducible, SemilatSupCat.Iso.mk_hom_toFun, OrthogonalIdempotents.embedding, Function.Embedding.coe_vadd, Metric.Snowflaking.preimage_toSnowflaking_ball, CliffordAlgebra.changeForm_contractLeft, IsExposed.eq_inter_halfSpace, RingCon.coe_bot, map_div_rev, AddMonoidAlgebra.mapDomainRingEquiv_single, GroupLike.val_inv, Ideal.ResidueField.lift_algebraMap, AddMonoidHom.toMultiplicative_apply_apply, Module.End.genEigenspace_top, DistribMulActionHom.map_add', infClosure_min, Int.abs_eq_normalize, absConvexHull_min, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, ContinuousMap.coe_sup', Cardinal.lift_aleph, MvPolynomial.dvd_X_iff_exists, RCLike.natCast_im, IsLocalization.surj_of_gcd_domain, IsLocalization.map_eq_toLinearMap_mapₐ, Ordinal.toNatOrdinal_zero, GrpCat.inv_hom_apply, tsum_prod_pow_eq_tsum_sigma, BoundedLatticeHomClass.map_top, Equiv.emptySum_symm_apply, AddGroupExtension.Section.rightHom_section, AddMonoidHom.map_finsum_Prop, MvPowerSeries.WithPiTopology.hasSum_of_monomials_self, AddOpposite.opEquiv_symm_apply, Real.coe_comp_expOrderIso, AddSubmonoid.LocalizationMap.toAddMonoidHom_apply, MvPolynomial.finSuccEquiv_X_succ, MonoidAlgebra.curryRingEquiv_single, ArithmeticFunction.abs_moebius_eq_one_of_squarefree, PadicAlgCl.valuation_coe, MonoidAlgebra.scalarTensorEquiv_symm_single, WittVector.StandardOneDimIsocrystal.frobenius_apply, Polynomial.card_support_eq_two, CategoryTheory.orderDualEquivalence_functor_obj, OmegaCompletePartialOrder.ContinuousHom.monotone, PresentedGroup.one_of_mem, triple_product_eq_det, MulEquiv.toMultiplicative_toAdditive_apply, DFinsupp.erase_ne, List.Wbtw.map, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Valuation.IsUniformizer.val_pos, MvPolynomial.aeval_ofNat, CompHaus.effectiveEpi_tfae, LinearEquiv.dualMap_apply, Finset.orderEmbOfFin_apply, AbsoluteValue.sum_le, AddGroupExtension.Section.exists_add_eq_add_add_inl, GroupExtension.inl_conjAct_comm, ProbabilityTheory.measurable_condExpKernel, AddConstMapClass.map_int_add, Subring.centerCongr_symm_apply_coe, MeasureTheory.Integrable.integral_condDistrib, AffineIsometry.diam_range, MeasureTheory.integrable_condExpL2_indicator, TensorAlgebra.algebraMap_inj, AdicCompletion.factor_eval_liftRingHom, QuadraticMap.coe_associatedHom, MvPowerSeries.constantCoeff_one, CategoryTheory.isoOpEquiv_symm_apply, CliffordAlgebra.involute_involute, Algebra.smulTower_leftMulMatrix_algebraMap, Fin.revOrderIso_symm_apply, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, CStarAlgebra.star_mul_le_algebraMap_norm_sq, Con.orderIsoOp_apply, LinearMap.mem_selfAdjointSubmodule, CategoryTheory.unit_mateEquiv, Homeomorph.sigmaProdDistrib_symm_apply, groupHomology.isoCycles₂_inv_comp_iCycles_apply, Poly.map_apply, DistribMulActionHom.zero_apply, Con.conGen_of_con, CategoryTheory.conjugateEquiv_associator_hom, SeminormClass.map_smul_eq_mul, Con.le_def, tangentCoordChange_self, CategoryTheory.PreGaloisCategory.surjective_on_fiber_of_epi, Equiv.subtypePreimage_symm_apply_coe_pos, WeierstrassCurve.Affine.Point.toClass_some, QuadraticMap.polar_comp, Algebra.TensorProduct.tmul_one_eq_one_tmul, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, List.exists_map_eq_of_sorted_iff_wbtw, ProbabilityTheory.swap_compProd_posterior, GroupSeminorm.coe_sSup_apply', LinearIndependent.inl_union_inr, CategoryTheory.Bicategory.conjugateEquiv_apply', SSet.spine_map_vertex, fderiv_norm_smul, ContinuousMap.summable_apply, Fin.appendIsometryOfEq_symm_apply, Set.coe_snd_biUnionEqSigmaOfDisjoint, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, WithTop.le_ofDual_iff, Part.ωScottContinuous_toUnitMono, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, Finset.Iio_toDual, Function.fromTypes_succ_equiv_apply, Affine.Simplex.excenterWeights_restrict, Equiv.prodCongrLeft_apply, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, Ideal.asIdeal_toTwoSided, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, Metric.PiNatEmbed.toPiNatHomeo_apply_ofPiNat, uniformEquicontinuousOn_iff_uniformContinuousOn, MulRingNorm.isPowMul, CompactExhaustion.subset_succ, iterate_map_div, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, ContinuousLinearMap.exists_mul_lt_apply_of_lt_opNNNorm, isUpperSet_preimage_ofDual_iff, Metric.Snowflaking.edist_toSnowflaking_toSnowflaking, Algebra.Presentation.aeval_val_relationOfHasCoeffs, MeasureTheory.MemLp.re, Finsupp.le_iff', ModuleCat.mkOfSMul_smul, HasFDerivAt.hasFDerivAt_norm_smul, EMetric.measure_ball_pos, Module.Basis.det_basis, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, LinearEquiv.funUnique_apply, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, CategoryTheory.Functor.RepresentableBy.ext_iff, NatOrdinal.toOrdinal_eq_zero, TensorProduct.directSum_symm_lof_tmul, CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp, LinearEquiv.sumArrowLequivProdArrow_apply_fst, RCLike.nnnorm_conj, MeasureTheory.Measure.map_apply_of_aemeasurable, Equiv.Perm.OnCycleFactors.Subgroup.Centralizer.toConjAct_smul_mem_cycleFactorsFinset, RootPairing.GeckConstruction.ωConj_toFun, cfc_polynomial, AddMonoidHom.fiberEquiv_apply, map_mul_inv, Ordinal.omega0_le_preOmega_iff, MvPolynomial.eval₂Hom_eq_zero, Matrix.piEquiv_symm_apply, MeasurableEquiv.vadd_apply, AddConstMapClass.map_one, toDual_neg, GradedTensorProduct.algebraMap_def, MulEquiv.toMonoidWithZeroHom_bijective, SchwartzMap.integral_fourier_mul_eq, ContinuousEvalConst.continuous_eval_const, RCLike.ratCast_re, Homeomorph.comp_isOpenMap_iff', MeasureTheory.AEStronglyMeasurable.im, ProbabilityTheory.avgRisk_const_left, HahnSeries.addOppositeEquiv_symm_orderTop, Module.bijective_dual_eval, LinearMap.isLinear, CochainComplex.toSingle₀Equiv_symm_apply_f_succ, ContinuousMap.continuous_uncurry_of_continuous, PowerSeries.coeff_one, RCLike.ofReal_eq_re_of_isSelfAdjoint, Nat.ordProj_self_pow, BoolAlg.comp_apply, DFinsupp.comp_liftAddHom, AffineMap.prod_apply, Representation.norm_self_apply, MeasureTheory.measure_smul, PseudoMetric.coe_mk, UniformOnFun.edist_def, injective_iff_map_eq_zero, Finsupp.univ_sum_single, IsLocalization.map_units_map_submonoid, IsometryEquiv.image_closedBall, PositiveLinearMap.add_apply, Equiv.coinduced_symm, HahnSeries.iterateEquiv_apply, polynomial_expand_eq, Polynomial.eq_mul_leadingCoeff_of_monic_of_dvd_of_natDegree_le, Rep.coindResAdjunction_homEquiv_symm_apply, ValuationSubring.principalUnitGroupEquiv_apply, AlgEquiv.autCongr_apply, Module.End.eigenspace_div, CompleteLat.Iso.mk_hom, Affine.Simplex.sOppSide_affineSpan_faceOpposite_of_pos_of_neg, Complex.normSq_nonneg, Matrix.IsHermitian.coe_re_apply_self, MvPolynomial.expand_comp_bind₁, HopfAlgebra.counit_antipode, Submodule.toLocalizedQuotient'_mk, MonomialOrder.leadingCoeff_C, Finset.UV.toColex_compress_lt_toColex, ContMDiffMap.coe_div, MeasureTheory.ae_mem_iff_measure_eq, continuous_ofMul, OrderIso.essInf_apply, PowerSeries.constantCoeff_mk, MeasureTheory.FiniteMeasure.mk_apply, MeasureTheory.Measure.iInf_rat_gt_prod_Iic, coe_lpBCFₗᵢ_symm, SetSemiring.down_ssubset_down, AlternatingMap.map_update_sub, MeasureTheory.Integrable.re, ProbabilityTheory.condDistrib_self, TopologicalSpace.Opens.functor_map_eq_inf, Dilation.congr_fun, LieHom.toNonUnitalAlgHom_apply, TwoSidedIdeal.orderIsoMatrix_symm_apply_ringCon_r, AddValuation.of_apply, Submodule.image_span_subset, toColex_mul, Algebra.SubmersivePresentation.aeval_invJacobianOfHasCoeffs, exists_ordCompl_eq_one_iff_isPrimePow, PowerSeries.eq_shift_mul_X_add_const, Monoid.CoprodI.Word.equivPair_head_smul_equivPair_tail, Complex.volume_preserving_equiv_pi, LocallyConstant.congrLeft_symm_apply, ContinuousMap.Homotopy.extend_of_mem_I, LinearEquiv.coe_zero, AddEquiv.symm_apply_eq, iterateFrobeniusEquiv_apply, Algebra.Extension.Hom.subToKer_apply_coe, CategoryTheory.Adjunction.homAddEquiv_zero, coe_lpPiLpₗᵢ_symm, spectrum.add_mem_add_iff, IsBoundedBilinearMap.toContinuousLinearMap_apply, Equiv.smulRight_symm_apply, InfTopHom.coe_mk, monotoneOn_toDual_comp_iff, RelIso.map_rel_iff, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Matrix.toLinearMapRight'_apply, ContinuousMap.HomotopyEquiv.coe_invFun, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply, Finsupp.degree_preimage_nsmul, DirectSum.decompose_of_mem_ne, map_inv_lt_iff, SupHom.sup_apply, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, Equiv.coe_refl, MeasureTheory.OuterMeasure.boundedBy_apply, WithBot.le_ofDual_iff, SimpleGraph.Hom.mapNeighborSet_coe, LinearMap.BilinForm.toMatrix_mul, BoundedContinuousFunction.coe_zsmulRec, toAdd_prod, Differentiable.continuousAlternatingMap_apply_const, Pi.lt_toLex_update_self_iff, SupBotHom.symm_dual_id, Polynomial.chebyshev_T_eq_dickson_one_one, ModuleCat.restrictScalars.smul_def, CategoryTheory.GrothendieckTopology.Cover.ext_iff, AddGroup.fg_iff_exists_freeAddGroup_hom_surjective, Subgroup.equivOp_apply_coe, FirstOrder.Language.BoundedFormula.mapTermRelEquiv_apply, MvPolynomial.aeval_injective_iff_of_isEmpty, AlgebraicGeometry.StructureSheaf.comapₗ_const, Finset.ofDual_min', ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, Polynomial.resultant_map_map, MeasureTheory.tendsto_lintegral_thickenedIndicator_of_isClosed, MonCat.val_units_map_hom_apply, WithLp.idemSnd_apply, ofBoolRing_inj, FunctionField.inftyValuedFqt.def, PowerSeries.coeff_prod, Submodule.reflection_eq_self_iff, Equiv.ext_iff, WittVector.constantCoeff_wittAdd, HasFPowerSeriesWithinOnBall.fderivWithin_eq, jacobson_density, AffineIsometryEquiv.surjective, CategoryTheory.Localization.SmallShiftedHom.postcompEquiv_symm_apply, Module.FaithfullyFlat.tensorProduct_mk_injective, FreeAddSemigroup.map_of, galRestrict_apply, MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, MultilinearMap.domCoprod_apply, TestFunction.coe_ofSupportedIn, TopCat.Presheaf.restrictOpenCommRingCat_apply, finSumFinEquiv_symm_apply_castSucc, ContinuousMultilinearMap.piₗᵢ_symm_apply, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, integral_coe_re_add_coe_im, NonUnitalRingHom.op_apply_apply, ZMod.toAddCircle_intCast, FreeAddMagma.toFreeAddSemigroup_of, RCLike.wInner_one_const_right, Polynomial.toFinsuppIsoAlg_symm_apply_toFinsupp, Algebra.Generators.ofComp_kerCompPreimage, MeasureTheory.not_isFiniteMeasure_iff, NonemptyFinLinOrd.id_apply, IntermediateField.LinearDisjoint.linearIndependent_right, CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_false, GaussianInt.toComplex_im, MulAut.conj_symm_apply, Unitization.fstHom_apply, CategoryTheory.ReflQuiv.adj.homEquiv_naturality_right, Matrix.diagonalRingHom_apply, LinearIsometry.coe_comp, RCLike.lt_iff_re_im, ContinuousMap.val_addUnitsLift_symm_apply_apply, Finset.weightedVSub_congr, AlgHom.coe_toContinuousLinearMap, QuadraticMap.pi_apply, LocallyConstant.coe_inj, Algebra.SubmersivePresentation.basisCotangent_localizationAway_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, FaithfulSMul.algebraMap_injective, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, MulAction.orbitZPowersEquiv_symm_apply', PMF.toMeasure_apply_eq_one_iff, Similar.comp_left, hahnEmbedding_isOrderedModule_rat, Finsupp.lcongr_single, AddEquiv.map_add, GaussianInt.im_toComplex, ContinuousMap.coe_zpow, Affine.Simplex.reindex_points, Subalgebra.pi_toSubsemiring, MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder, AddEquiv.ext_iff, HomogeneousLocalization.val_awayMap_eq_aux, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, LieModuleEquiv.ofTop_apply, Polynomial.iterate_derivative_C_mul, Nat.prod_factorization_eq_prod_primeFactors, AddValuation.map_sub, SimpleGraph.degree_induce_of_neighborSet_subset, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, FreeRing.lift_of, MvPolynomial.eval_sub, AddConstMapClass.map_sub_one, Sym.equivCongr_symm_apply, LinearEquiv.submoduleMap_symm_apply, Submodule.IsHomogeneous.mem_iff, Polynomial.reflect_C_mul_X_pow, FreeMagma.lift_symm_apply, MonoidAlgebra.of_commute, Algebra.commute_algebraMap_right, Polynomial.card_support_eq_one, Subgroup.HasDetPlusMinusOne.det_eq, ProbabilityTheory.uniformOn_inter_self, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Nat.factorization_eq_zero_iff_remainder, MeasureTheory.measure_inv_smul_union, SheafOfModules.unitHomEquiv_comp_apply, AddGroupSeminorm.coe_smul, MonoidHom.map_iterateFrobenius, PiTensorProduct.tprod_noncommProd, NonUnitalSubring.mem_map_equiv, CliffordAlgebra.involuteEquiv_apply, Continuous.matrix_cramer, Valuation.RankOne.strictMono', CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, MonoidAlgebra.comul_single, ProbabilityTheory.Kernel.compProd_preimage_fst, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_f, PowerSeries.coeff_mul_X_pow', MvPolynomial.esymmAlgHom_fin_injective, LinearMap.GeneralLinearGroup.coe_toLinearEquiv, LieModuleHom.coe_comp, Matrix.GeneralLinearGroup.map_mul_map_inv, List.toFinsupp_apply_lt, Quaternion.normSq_def', SimpleGraph.Iso.boxProdSumDistrib_apply, SchwartzMap.pairing_continuous_left, AlgebraicGeometry.Scheme.Pullback.Triplet.fst_SpecTensorTo_apply, ConvexOn.univ_sSup_affine_eq, PolyEquivTensor.invFun_monomial, LieAlgebra.SpecialLinear.val_single, AddMonoid.Coprod.snd_swap, ContinuousLinearEquiv.map_add, ContinuousMap.toNNReal_apply, Matrix.ofLp_toEuclideanLin_apply, Polynomial.coe_expand, CompactlySupportedContinuousMap.coe_toContinuousMap, ContinuousLinearMap.smulRight_comp_smulRight, WithBot.orderIsoPUnitSumLex_toLex, lipschitzOnWith_cfcₙ_fun_of_subset, spectralNorm.eq_of_normalClosure', AddSubgroup.opEquiv_apply, signedDist_vadd_right_swap, Subgroup.opEquiv_symm_apply, OrderDual.forall, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, StrictAnti.dual, Matrix.det_reindex_self, Matrix.toLinearMap₂_apply, CategoryTheory.ConcreteCategory.mono_iff_injective_of_preservesPullback, CategoryTheory.ShiftedHom.opEquiv'_symm_add, StieltjesFunction.outer_le_length, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, tsum_dirichletSummand, LieModuleEquiv.coe_mk, ContinuousAffineMap.fderivWithin, AdicCompletion.of_inj, Module.Basis.det_inv, Finsupp.linearEquivFunOnFinite_apply, MvPolynomial.aeval_comp_bind₁, SubgroupClass.inclusion_inclusion, Equiv.coe_inj, BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq, NumberField.exists_ideal_in_class_of_norm_le, MeasureTheory.LevyProkhorov.toMeasureEquiv_apply, AddCommGroup.DirectLimit.congr_symm_apply_of, AffineIndependent.convexHull_inter', NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, QuadraticMap.coeFn_neg, CompactlySupportedContinuousMap.coe_smulc, WeierstrassCurve.Projective.baseChange_addX, NumberField.mixedEmbedding.normAtPlace_apply, SchwartzMap.integralCLM_apply, ofBoolRing_mul, Nat.Prime.pow_dvd_iff_dvd_ordProj, TopHom.top_apply, NonUnitalStarSubalgebra.inclusion_right, Submonoid.LocalizationMap.eq', linearEquiv_det_rotation, LieModule.isNilpotent_iff_forall, AddCircle.continuous_mk', ExteriorAlgebra.map_surjective_iff, AffineSubspace.sOppSide_pointReflection, measure_zero_of_dimH_lt, AddMonoidHom.fiberEquivKer_symm_apply, ZLattice.abs_repr_lt_of_norm_lt, Matrix.swap_mulVec, Matrix.IsTotallyUnimodular.reindex, polynomialFunctions_coe, Polynomial.aroots_C_mul_X_pow, Polynomial.mkDerivation_one_eq_derivative, Complex.coe_selfAdjointEquiv, ContinuousLinearEquiv.symm_symm_apply, Matrix.GeneralLinearGroup.val_inv_det_apply, map_continuousAt, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, GroupNorm.lt_def, LinearMap.vecEmpty_apply, PolynormableSpace.withSeminorms', EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, DistribSMul.toAddMonoidHom_apply, map_comp_zsmul, SemidirectProduct.rightHom_inr, MeasureTheory.Measure.mem_support_restrict, Ideal.quotientMulEquivQuotientProd_fst, midpoint_eq_iff, ContinuousMap.neg_norm_le_apply, SpecialLinearGroup.toGeneralLinearGroup_injective, map_eq_bot_iff, Matrix.charpoly_sub_diagonal_degree_lt, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, NonarchAddGroupSeminorm.toZeroHom_eq_coe, MeasureTheory.Measure.comp_assoc, MultilinearMap.freeDFinsuppEquiv_apply, MeasureTheory.OuterMeasure.restrict_biInf, CliffordAlgebra.forall_mul_self_eq_iff, LinearMap.mem_range, LinearMap.IsSymmetric.apply_eigenvectorBasis, MeasureTheory.SimpleFunc.seq_apply, IsAddUnit.addUnit_neg_map, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_apply, ModularFormClass.levelOne_weight_zero_const, Complex.dist_conj_conj, HasStrictFDerivAt.hasStrictDerivAt, CliffordAlgebra.even.lift_symm_apply_bilin, ProbabilityTheory.condExp_ae_eq_integral_condDistrib', LieModuleEquiv.ext_iff, ArithmeticFunction.LSeries_zeta_eq_riemannZeta, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, Magma.AssocQuotient.lift_comp_of, groupHomology.cyclesMk₂_eq, AffineMap.decomp, t1Space_iff_continuous_cofinite_of, AlgEquiv.coe_toEquiv, IsAlgClosure.equivOfEquiv_algebraMap, RootPairing.coroot_root_eq_pairing, CliffordAlgebra.evenEquivEvenNeg_apply, NormedAddGroupHom.coe_sub, ZeroHom.single_apply, ProbabilityTheory.Kernel.condExp_densityProcess, CircleDeg1Lift.lt_iterate_pos_iff, EuclideanSpace.volume_ball_fin_two, AlgebraicGeometry.StructureSheaf.res_apply, ContinuousAddEquiv.invFun_eq_symm, Rep.coindVEquiv_apply_hom, LinearMap.compl₁₂_apply, IsLUB.dual, BotHom.coe_id, Finsupp.optionElim_apply_some, Polynomial.fourierCoeff_toAddCircle_natCast, Subring.subtype_apply, Polynomial.leadingCoeff_C_mul_X, Ordinal.lift_preOmega, Monoid.CoprodI.Word.equivPair_smul_same, Dilation.coe_mkOfDistEq, LinearMap.leftInverse_apply_of_inj, Equiv.ofRightInverseOfCardLE_symm_apply, ContinuousLinearEquiv.comp_right_differentiableAt_iff, Subalgebra.linearDisjoint_iff_injective, ArithmeticFunction.coe_inj, Polynomial.map_smul, FreeAddMagma.toFreeAddSemigroup_map, nnnorm_algebraMap', LieModule.isNilpotent_toEnd_sub_algebraMap, FreeAddGroup.map.mk, MeasureTheory.MeasurePreserving.measure_preimage_le, ConvexOn.real_univ_sSup_of_nat_affine_eq, NonUnitalStarSubalgebraClass.subtype_injective, Finsupp.prod_option_index, MeasureTheory.SimpleFunc.mem_restrict_range, RootPairing.IsValuedIn.exists_value, norm_add_sq, ArithmeticFunction.IsMultiplicative.eq_iff_eq_on_prime_powers, AdicCompletion.ofTensorProduct_tmul, isOpenMap_ofMul, MulEquiv.orderOf_eq, continuous_algebraMap_iff_smul, ContinuousAddMonoidHom.fst_toFun, isClosedEmbedding_cfcₙHom_of_cfcHom, QuadraticAlgebra.algHom_ext_iff, Valuation.vle_one_iff, tsupport_comp_eq_preimage, Polynomial.degreeLT.addLinearEquiv_symm_apply', sign_nonpos_iff, SubMulAction.ofFixingSubgroup.append_right, LinearIsometry.diam_range, ContinuousMap.coe_inf, RingCon.quot_mk_eq_coe, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, RCLike.norm_sq_re_conj_add, Cardinal.aleph0_le_aleph, spectrum.map_polynomial_aeval_of_degree_pos, Derivation.coe_restrictScalars, IsLocalization.toInvSubmonoid_eq_mk', Complex.conjCLE_apply, ContinuousMap.spectrum_eq_range, UniformFun.lipschitzWith_iff, LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.LocallyDiscrete.locallyDiscreteEquiv_apply, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, DomAddAct.mk_vadd_toLp, ContinuousLinearMap.neg_apply, Equiv.summable_iff, AffineEquiv.refl_apply, AffineMap.homothety_isOpenMap, disjoint_partialSups_left, MeasureTheory.Measure.instIsFiniteMeasureBindCoeKernelOfIsFiniteKernel, Polynomial.constantCoeff_surjective, EuclideanSpace.inner_basisFun_real, LatticeHom.withBot'_toFun, Cardinal.toENat_le_iff_of_le_aleph0, Submonoid.mem_divPairs, UniformOnFun.ofFun_prod, AddMonoidAlgebra.domCongr_support, Finmap.keysLookupEquiv_symm_apply_keys, MonoidAlgebra.mem_ideal_span_of_image, KaehlerDifferential.kerTotal_mkQ_single_smul, Module.Basis.self_mem_span_image, Finset.intervalGapsWithin_snd_of_lt, MultilinearMap.uncurryRight_apply, SeparationQuotient.mkMonoidHom_apply, LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero, innerSLFlip_apply, Polynomial.eraseLead_C, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension, LinearIsometryEquiv.prodComm_symm_apply, PEquiv.mem_ofSet_self_iff, Polynomial.Splits.X_sub_C, ContinuousLinearEquiv.differentiableOn, PresheafOfModules.Derivation.d_app, Additive.ofMul_eq_bot, MvPolynomial.rTensor_apply_monomial_tmul, Set.singletonAddHom_apply, ContinuousAt.clm_bundle_apply₂, Polynomial.isUnit_primPart_C, Valuation.IsEquiv.val_sub_one_lt_one_iff, LatticeHom.coe_toInfHom, Homeomorph.preimage_frontier, sigmaAntidiagonalEquivProd_symm_apply_fst, ContinuousLinearEquiv.hasStrictFDerivAt, CoalgEquiv.coe_symm_toLinearEquiv, CommBialgCat.comp_apply, Equiv.optionEquivSumPUnit_symm_inl, UniformEquiv.preimage_symm, MonoidHom.fst_mono, Preord.coe_comp, AlgHom.mem_fieldRange, AddGrpCat.neg_hom_apply, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, jacobiSym.at_two, coe_addEquiv_lpBCF, Polynomial.iterate_derivative_mul_X_pow, RestrictedProduct.comp_mulSingle, HahnSeries.SummableFamily.binomialFamily_apply, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, iterate_map_inv, Matrix.mulVecBilin_apply, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, MvPolynomial.eval₂_const_pUnitAlgEquiv, ContinuousAlternatingMap.map_vecCons_sub, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, fderivWithin_derivWithin, PowerSeries.coeff_zero_C, Matrix.mul_empty, sign_pow, Function.Embedding.toEquivRange_eq_ofInjective, ZMod.map_smul, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow', NonemptyInterval.coe_coeHom, RestrictedProduct.coe_mulSingle_apply, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, Complex.arg_conj_coe_angle, SetTheory.PGame.add_moveRight_inl, EquivLike.coe_apply, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, AddSubgroup.MapSubtype.orderIso_symm_apply, MonoidHom.prod_apply, Algebra.Generators.repr_CotangentSpaceMap, DirectSum.toModule_lof, MonoidAlgebra.lift_apply, CircleDeg1Lift.tendsto_translation_number₀, ContinuousLinearEquiv.mfderiv_eq, LinearEquiv.congrQuadraticMap_symm_apply, Module.Basis.dualBasis_repr, ClosureOperator.mk'_apply, fourierCoeffOn_of_hasDerivAt_Ioo, groupHomology.H1π_eq_zero_iff, ContinuousLinearMap.toContinuousAddMonoidHom_restrictScalars, SubgroupClass.coe_subtype, Trivialization.coe_continuousLinearEquivAt_eq, NumberField.mixedEmbedding.volume_eq_zero, Algebra.intNorm_zero, Algebra.normalizedTrace_minpoly, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, SemiNormedGrp.ofHom_apply, IsAdjoinRootMonic.modByMonicHom_root_pow, PiTensorProduct.mul_one, AddChar.compAddMonoidHom_apply, Algebra.Generators.reindex_val, MeasureTheory.locallyIntegrable_map_homeomorph, ZMod.toAddCircle_apply, CategoryTheory.Abelian.Ext.bilinearCompOfLinear_apply_apply, CategoryTheory.Localization.SmallShiftedHom.precompEquiv_symm_apply, unitary.coe_map_star, ContinuousMulEquiv.apply_eq_iff_eq, MulEquiv.cast_apply, PiTensorProduct.tmulEquiv_apply, BialgEquiv.trans_symm_apply, lieEquivMatrix'_symm_apply, Finset.Iic_ofDual, HomogeneousLocalization.val_awayMap_mk, TwoSidedIdeal.mem_iff, Complex.nndist_conj_self, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, ProbabilityTheory.Kernel.sectL_prodMkLeft, IsPrimitiveRoot.card_quotient_toInteger_sub_one, ProbabilityTheory.covarianceBilin_real, MvPowerSeries.eq_zero_iff_forall_coeff_zero, ProbabilityTheory.Kernel.traj_apply, Hamming.ofHamming_inj, Polynomial.annIdealGenerator_aeval_eq_zero, OmegaCompletePartialOrder.ContinuousHom.comp_apply, Cardinal.preAleph_le_preAleph, Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C, OrderIso.coe_symm_toRelIsoLT, DistribMulActionHom.ext_iff, Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr, MonomialOrder.degLex_lt_iff, LinearMap.compQuadraticMap'_apply, InfiniteGalois.toAlgEquivAux_eq_liftNormal, DilationEquivClass.edist_eq', MeasureTheory.Measure.count_univ, IsSMulRegular.of_isLocalization, PrimeSpectrum.comap_basicOpen, Projectivization.smul_def, TopologicalSpace.OpenNhds.isOpenEmbedding, Matrix.proj_diagonal, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', imaginaryPart_ofReal, IsLocalization.eq_iff_eq, MeasureTheory.eLpNorm_one_le_of_le, AddGroupExtension.Section.equivComp_apply, QuadraticMap.Isometry.map_app', Module.Dual.baseChange_baseChange, Bundle.TotalSpace.toProd_symm_apply_snd, CategoryTheory.CommSq.left_adjoint, IsValuativeTopology.hasBasis_nhds', ContinuousMulEquiv.ext_iff, separatingDual_iff_injective, Cycle.formPerm_apply_mem_eq_next, Matrix.adjugate_submatrix_equiv_self, Affine.Simplex.median_restrict, LightCondMod.hom_naturality_apply, MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder, minpoly.eq_X_sub_C', MeasureTheory.Measure.compProd_assoc, Module.Relations.Solution.IsPresentation.bijective, TensorProduct.dualDistribInvOfBasis_apply, DistribMulActionHom.map_neg, Matrix.permMatrix_mulVec, CategoryTheory.Iso.symm_self_conj, Equiv.Set.insert_symm_apply_inl, Pi.comul_coe_finsupp, RCLike.normSq_pos, Polynomial.taylor_coeff_one, MeasureTheory.SimpleFunc.eLpNorm'_eq, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, MeasureTheory.measure_union₀', latticeClosure_idem, Finsupp.sum_hom_add_index, ChainComplex.toSingle₀Equiv_symm_apply_f_zero, isVisible_iff_lineMap, MonoidAlgebra.lift_mapRangeRingHom_algebraMap, lcm_units_coe_left, Set.algebraMap_mem_center, ModularGroup.im_smul_eq_div_normSq, isNilpotent_tensor_residueField_iff, LinearEquiv.isSMulRegular_congr', ClosureOperator.closure_top, Homeomorph.preimage_image, MvPolynomial.pderiv_pow, SchwartzMap.fourier_coe, SSet.mem_skeleton, Polynomial.toContinuousMapAlgHom_apply, MeasureTheory.Measure.le_iff, CentroidHom.mul_apply, DFinsupp.equivProdDFinsupp_symm_apply, Derivation.map_smul_of_tower, SymAlg.unsym_surjective, GroupSeminorm.toFun_eq_coe, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, constantCoeff_wittStructureRat_zero, Module.Basis.smulTower_apply, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', ContinuousMap.tendsto_iff_tendstoLocallyUniformly, LinearMap.map_smul₂, RestrictedProduct.single_eq_of_ne, groupHomology.d₂₁_single_one_fst, Finset.imageMulHom_apply, IsSelfAdjoint.commute_cfcₙHom, Rat.ringOfIntegersEquiv_apply_coe, convexHull_zero, ContinuousLinearMap.measurable_coe, PowerSeries.forall_coeff_eq_zero, finSuccEquivLast_last, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, RatFunc.liftRingHom_apply_ofFractionRing_mk, AffineMap.homothety_apply, Polynomial.algebraMap_hahnSeries_apply, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, Euclidean.ball_eq_preimage, ContinuousMultilinearMap.uniformContinuous_coe_fun, HahnModule.orderTop_vAdd_le_orderTop_smul, NonUnitalRingHom.id_apply, MeasureTheory.Measure.exists_regular_eq_of_compactSpace, Polynomial.sup_ker_aeval_le_ker_aeval_mul, ContinuousLinearMap.analyticOn, Con.coe_mk', Polynomial.fderivWithin_aeval, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, ContinuousLinearMap.nndist_le_opNNNorm, OneHom.coe_inv, WeierstrassCurve.Jacobian.map_polynomialZ, le_map_add_map_sub', ContinuousMonoidHom.mul_apply, Matrix.eval_charpoly, AddGroupSeminorm.add_apply, sInfHom.coe_top, WeierstrassCurve.Projective.map_addXYZ, IsIntegrallyClosed.algebraMap_eq_of_integral, MagmaCat.forget_map, Monoid.CoprodI.Word.prod_cons, RingHom.injective_stableUnderComposition, dualTensorHom_prodMap_zero, MeasureTheory.SimpleFunc.measurableSet_preimage, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, Equiv.Perm.pow_mod_card_support_cycleOf_self_apply, Ordinal.omega_strictMono, MvPolynomial.aeval_esymm_eq_multiset_esymm, MvPowerSeries.coeff_truncFun, ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, AlgebraicGeometry.IsClosedImmersion.isClosedEmbedding, PolyEquivTensor.toFunLinear_one_tmul_one, finCongr_symm_apply, MeasureTheory.SimpleFunc.const_algebraMap, Cardinal.toENat_eq_top, LinearEquiv.prodCongr_apply, Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint, NumberField.Ideal.tendsto_norm_le_div_atTop, Matrix.SpecialLinearGroup.coe_GL_coe_matrix, UpperHalfPlane.cosh_half_dist, lineMap_lt_map_iff_slope_lt_slope_left, CategoryTheory.GrothendieckTopology.mem_toPrecoverage_iff, Unitization.starMap_apply, Seminorm.zero_or_exists_apply_eq_finset_sup, norm_add_mul_self, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, OrderIso.sortedLT_listMap, SetTheory.PGame.add_moveLeft_inr, Valuation.Integers.valuation_pos_iff_ne_zero, SchwartzMap.lineDerivOp_fourierInv_eq, OrderedFinpartition.compAlongOrderFinpartition_apply, Subring.ringEquivOpMop_symm_apply_coe, MultilinearMap.domCoprod_alternization, Trivialization.continuousLinearEquivAt_symm_apply, CompactlySupportedContinuousMap.sum_apply, ofLex_ofNat, CliffordAlgebraComplex.equiv_apply, LocallyConstant.congrRightRingEquiv_apply_apply, FreeAddGroup.range_lift_le, MonoidHom.restrictHom_apply, AddEquiv.addMonoidHomCongrRightEquiv_apply, Trivialization.coordChangeHomeomorph_coe, MeasureTheory.measure_le_eq_lt, hasDerivAt_abs, PEquiv.eq_some_iff, MvPolynomial.bind₂_C_right, NumberField.mixedEmbedding.stdBasis_apply_isReal, Finsupp.coe_rangeIcc, DirichletCharacter.LSeries_eulerProduct_exp_log, RCLike.conj_im, Valued.isOpen_closedBall, Polynomial.fderivWithin, LinearMap.IsContPerfPair.bijective_right, Finset.toDual_sup, ClosureOperator.isClosed_iff_closure_le, MvPowerSeries.algebraMap_apply', PowerSeries.coeff_C, LinearIsometryEquiv.coe_symm_toContinuousLinearEquiv, Submonoid.opEquiv_apply, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, MvPolynomial.constantCoeff_eq, OrderHom.coe_inf, LinearMap.toMvPolynomial_constantCoeff, Monovary.sum_comp_perm_mul_lt_sum_mul_iff, lineMap_le_right_iff_le_one, Diffeomorph.continuous, LocallyBoundedMap.id_apply, FreeGroup.map.of, ProbabilityTheory.tilted_mul_apply_mgf, Path.truncate_zero_one, Cubic.equiv_symm_apply_c, Equiv.embeddingFinSucc_fst, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, HahnSeries.coeff_toMvPowerSeries_symm, SSet.iSup_skeletonOfMono, ZMod.completedLFunction_one_sub_odd, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, ProbabilityTheory.Kernel.prodMkRight_apply', Ideal.Quotient.mkₐ_eq_mk, MonoidAlgebra.uniqueRingEquiv_symm_apply, Polynomial.monomial_neg, WeierstrassCurve.Projective.map_polynomialZ, CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq, RootPairing.rootSpanMem_reflectionPerm_self, Trivialization.coordChangeL_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Affine.Simplex.sign_excenterWeights_empty, LinearMap.isUnit_toMatrix_iff, QuaternionAlgebra.coe_symm_addEquivProd, ContDiffAt.iteratedFDeriv_comp_perm, FaithfulSMul.algebraMap_eq_one_iff, QuadraticMap.polar_neg_right, StarRingEquiv.symm_trans_apply, LinearMap.det_smul, Polynomial.hasDerivAt, CompHausLike.homeoOfIso_apply, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, WeierstrassCurve.Affine.Point.toClass_injective, PiTensorProduct.map_comp_reindex_symm, ContinuousAffineMap.sub_apply, Finset.intervalGapsWithin_succ_fst_of_lt, AddUnits.range_embedProduct, MeasurableEquiv.piCurry_symm_apply, MonoidAlgebra.of_injective, MonoidWithZeroHom.fst_apply_coe, MvPolynomial.eval_rename, VectorPrebundle.mk_coordChange, Ideal.rootsOfUnityMapQuot_apply, LinearMapClass.map_smul, Polynomial.Monic.comp_X_add_C, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Module.Basis.linearCombination_repr, Pi.monotoneCurry_coe, Field.Emb.Cardinal.strictMono_filtration, MvPolynomial.mkDerivationₗ_C, convexHull_eq_union_convexHull_finite_subsets, EuclideanSpace.volume_ball, MonoidWithZeroHom.fst_inl, QuadraticMap.polar_sub_right, ProbabilityTheory.bayesRisk_le_iInf', Mathlib.Tactic.Elementwise.forget_hom_Type, quadraticChar_sq_one, TensorProduct.enorm_assoc, MonoidWithZeroHom.fst_surjective, Submonoid.IsLocalizationMap.mulEquiv_comp, UniformEquiv.piCongr_toEquiv, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, injective_iff_map_eq_one', CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, SpectralMap.coe_id, LocalizedModule.map_id, ContinuousMultilinearMap.ofSubsingleton_apply_toMultilinearMap, RCLike.conj_I, MvPowerSeries.isWeightedHomogeneous_weightedHomogeneousComponent, BumpCovering.sum_toPartitionOfUnity_eq, union_support_maximal_linearIndependent_eq_range_basis, Equiv.Perm.pow_apply_mem_toList_iff_mem_support, Seminorm.ball_comp, Polynomial.divX_C, OrthonormalBasis.repr_symm_single, groupCohomology.cocycles₂.val_eq_coe, RingInvo.coe_ringEquiv, Cardinal.toNat_eq_one_iff_unique, Real.fourierChar_apply, coeff_minpolyDiv, ContinuousMulEquiv.isHaarMeasure_map, IsLocalization.tmul_mk', AlgEquiv.mul_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, NumberField.canonicalEmbedding.norm_le_iff, TensorProduct.AlgebraTensorModule.rTensor_mul, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.curryMidLinearEquiv_apply, RelEmbedding.coe_natLT, StandardEtalePresentation.toPresentation_σ', LinearMap.BilinForm.toMatrix_compLeft, CategoryTheory.Iso.eHomCongr_comp, Polynomial.monomial_zero_right, MeasureTheory.Measure.real_def, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_mutuallySingular, Part.Fix.le_f_of_mem_approx, Path.extend_one, LinearMap.trace_eq_matrix_trace, Submodule.mem_one, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, TensorProduct.quotientTensorEquiv_apply_tmul_mk, AddGrpCat.hom_neg_apply, RootPairing.polarizationEquiv_symm_apply_coroot, ofBoolAlg_top, Filter.prod_assoc, BoundedContinuousFunction.edist_eq_iSup, SimplexCategory.II.mem_finset_iff, SimpleGraph.isClique_range_copy_top, Nat.factorization_eq_primeFactorsList_multiset, RootPairing.Base.exists_root_eq_sum_int, BilinForm.toMatrix_apply, Equiv.Perm.sigmaCongrRightHom_apply, MonoidHom.ext_mint_iff, WeakDual.CharacterSpace.norm_le_norm_one, UniformFun.mem_gen, AddEquiv.opOp_apply, DFinsupp.finset_sum_apply, ContinuousLinearEquiv.continuous, RootPairing.pairingIn_reflectionPerm, MulEquiv.mulDissociated_preimage, thickenedIndicator_mono_infEdist, SchwartzMap.sum_apply, Pretrivialization.linearEquivAt_apply, MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero, Representation.IntertwiningMap.coe_add, PolynomialModule.lsingle_apply, CategoryTheory.PreGaloisCategory.endEquivAutGalois_mul, NonUnitalAlgHom.snd_apply, Algebra.SubmersivePresentation.cotangentComplexAux_surjective, MulSemiringAction.toAlgEquiv_apply, Fin.cycleRange_symm_succ, ContinuousMap.sigmaCodHomeomorph_symm_apply, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, LinearMap.continuous_on_pi, Matrix.linfty_opNorm_toMatrix, OrderHomClass.coe_to_lattice_hom, ConvexOn.real_sSup_of_countable_affine_eq, AddSubmonoid.LocalizationMap.ext_iff, HasFPowerSeriesAt.eventually_hasSum_of_comp, Representation.self_inv_apply, unitInterval.volume_Ioc, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.stalk_iso, cfcL_integral, exteriorPower.zeroEquiv_ιMulti, witt_structure_prop, OrderMonoidHom.snd_apply, MonoidHom.eq_iff, RingHom.toSemilinearMap_apply, Subsemiring.map_toSubmonoid, ContinuousMap.coe_mk, Algebra.TensorProduct.piRight_tmul, RelEmbedding.acc_iff_isEmpty_subtype_mem_range, ContinuousAlgEquiv.refl_apply, Equiv.image_symm_image, RingHom.smul_def, Polynomial.Monic.C_dvd_iff_isUnit, Polynomial.iterate_derivative_sub, bijective_frobenius, Additive.forall, ContinuousMap.coeFn_toLp, MeasureTheory.L1.norm_setToL1_le_mul_norm', Equiv.Set.rangeInl_apply_inl, Equiv.piCongrLeft_apply_eq_cast, Seminorm.rescale_to_shell, LinearIsometryEquiv.withLpProdCongr_apply, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, IsometryEquiv.dist_eq, MvPowerSeries.weightedOrder_le, Prefunctor.symmetrifyStar, RingHom.rangeRestrictField_bijective, map_nonunit, Matrix.toBilin'_apply', FirstOrder.Language.Embedding.coe_toHom, ProbabilityTheory.Kernel.withDensity_rnDeriv_eq_zero_iff_apply_eq_zero, Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one, Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, RingHom.surjective_stableUnderComposition, coe_starₗᵢ, Equiv.Set.rangeInr_symm_apply_coe, OrderEmbedding.minimal_mem_image_iff, Algebra.Presentation.coeffs_subset_range, map_mulIndicator, SupHom.coe_sup, AdjoinRoot.map_root, PartitionOfUnity.sum_le_one, Module.Basis.linearCombination_coord, Valuation.IsEquiv.one_le_iff_one_le, IsometryEquiv.vaddConst_apply, LinearMap.BilinForm.IsSymm.polarization, Polynomial.signVariations_monomial, MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq, RootPairing.linearIndepOn_coroot_iff, Real.nnabs_coe, DFinsupp.toFun_eq_coe, innerSL_apply_norm, Polynomial.nextCoeff_map_of_leadingCoeff_ne_zero, CategoryTheory.Oplax.StrongTrans.Modification.equivOplax_apply, MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zero, CategoryTheory.Functor.mapEnd_apply, Finsupp.sup_apply, BoxIntegral.Box.splitCenterBoxEmb_apply, AffineIsometryEquiv.coe_one, Nucleus.mem_range, Equiv.Perm.IsCycleOn.range_zpow, Polynomial.natSepDegree_C, Function.locallyFinsuppWithin.posPart_apply, Interval.map_pure, Submonoid.LocalizationMap.mk'_mul_cancel_right, LinearMap.exact_subtype_ker_map, CategoryTheory.Limits.Concrete.widePushout_exists_rep, LieModule.coe_chainBot, IsIntegrallyClosed.eq_map_mul_C_of_dvd, Sublattice.mem_map_of_mem, Finsupp.coe_floorDiv, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, Equiv.Set.congr_apply, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, AffineIsometry.toAffineIsometryEquiv_apply, Derivation.map_aeval, IsSelfAdjoint.coe_selfAdjointPart_apply, Finsupp.cons_zero, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, Matrix.toLinearMap₂'_single, ContinuousMultilinearMap.sub_apply, MeasureTheory.setLIntegral_pdf_le_map, AffineEquiv.coe_toAffineMap, Pi.toColex_strictMono, GroupSeminorm.comp_apply, ExteriorAlgebra.liftAlternating_comp_ιMulti, MeasureTheory.SimpleFunc.tendsto_nearestPt, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_symm_apply, WeierstrassCurve.Jacobian.Equation.baseChange, CategoryTheory.Functor.representableByUliftFunctorEquiv_apply_homEquiv, ContinuousWithinAt.clm_bundle_apply₂, matPolyEquiv_eval_eq_map, Finset.sumEquiv_apply_snd, Submonoid.LocalizationMap.mk'_spec', CliffordAlgebra.toEven_ι, Polynomial.monic_mul_leadingCoeff_inv, Valuation.ltSubmodule_v_le_of_mem, WittVector.iterate_verschiebung_mul_coeff, OrderHom.isGreatest_gfp_le, WType.equivSigma_symm_apply, BddAbove.dual, SchwartzMap.fourierInv_coe, CategoryTheory.ShiftedHom.homEquiv_apply, Algebra.Extension.H1Cotangent.map_apply_coe, Polynomial.eq_X_sub_C_of_splits_of_single_root, NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate, InnerProductSpace.Core.inner_self_ofReal_re, NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex, FirstOrder.Language.Hom.toFun_eq_coe, Metric.measure_eball_pos, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero', Algebra.TensorProduct.mul_assoc, AddSubmonoid.LocalizationMap.addEquivOfLocalizations_left_neg_apply, Polynomial.Splits.aeval_eq_prod_aroots_of_monic, LinearMap.adjoint_inner_left, Topology.WithScott.ofScott_toScott, CongruenceSubgroup.mem_conjGL, ContinuousLinearMap.fderivWithin, MeasureTheory.measure_preimage_smul_le, RingEquiv.symm_trans_apply, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, WittVector.constantCoeff_wittNSMul, UniformOnFun.toFun_sum, Polynomial.card_support_C_mul_X_pow_le_one, AddMonoidHom.map_indicator, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_surjective, LinearEquiv.piCurry_symm_apply, LightCondensed.ihomPoints_symm_apply, CircleDeg1Lift.tendsto_atTop, PolyEquivTensor.left_inv, UniformEquiv.ext_iff, AlgebraicGeometry.Spec_zeroLocus, LocallyConstant.mapₗ_apply_apply, List.SortedGE.of_map_ofDual, CliffordAlgebra.equivBaseChange_apply, Circle.exp_int_mul_two_pi, Polynomial.eval_eq_sum_degreeLTEquiv, Submodule.mulMap'_surjective, ofColex_pow, OrderMonoidHom.inl_apply, Polynomial.monomial_mul_X_pow, LinearIsometry.map_eq_iff, finSuccEquiv_eq_none, LinearMap.toMvPolynomial_comp, MeasureTheory.Measure.measure_mono_left, RingEquiv.congr_fun, AlgHom.coe_toLieHom, Module.Basis.toDual_apply, Submodule.subtypeL_apply, ContinuousAffineMap.coe_contLinear, PowerSeries.coeff_inv, AddMonoidHom.coe_toIntLinearMap_map, WeierstrassCurve.Jacobian.baseChange_dblZ, AlgEquiv.restrictNormal_commutes, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_apply_coe, stdSimplexHomeomorphUnitInterval_one, Traversable.foldrm.ofFreeMonoid_comp_of, Complex.lift_symm_apply_coe, ContinuousMultilinearMap.coe_pi, matPolyEquiv_coeff_apply, LinearMap.BilinForm.mul_toMatrix, ValuationSubring.coe_comap, FractionalIdeal.absNorm_nonneg, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_apply, NonarchAddGroupNorm.coe_le_coe, MeasureTheory.measure_lintegral_sub_measure, Seminorm.continuousAt_zero_of_forall, RCLike.hasSum_iff, Matrix.piAlgEquiv_symm_apply, MeasureTheory.mulEquivHaarChar_smul_preimage, gcd_zero_left, Homeomorph.subRight_symm_apply, ContinuousMap.congr_fun, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, ProbabilityTheory.Kernel.singularPart_eq_zero_iff_absolutelyContinuous, PerfectClosure.mk_eq_iff, Module.Basis.tensorAlgebra_repr_apply, Polynomial.discr_C, FreeAlgebra.lift_symm_apply, UniformOnFun.uniformContinuous_restrict_toFun, UniformOnFun.precomp_uniformContinuous, MvPolynomial.IsHomogeneous.rename_isHomogeneous_iff, NumberField.mixedEmbedding_injective, Polynomial.aeval_neg, MvPolynomial.vars_bind₁, OrderEmbedding.gtEmbedding_apply, DFinsupp.coe_inf, MeasureTheory.AddContent.ext_iff, PowerSeries.rescale_injective, Monotone.partialSups_eq, Polynomial.coeToPowerSeries.ringHom_apply, Orientation.oangle_map, Polynomial.support_C_mul_X_pow, RCLike.measurable_im, WittVector.bind₁_verschiebungPoly_wittPolynomial, Valued.mem_nhds_zero, MeasureTheory.Measure.addHaar_preimage_linearMap, isGroupLikeElem_map_equiv, CategoryTheory.InjectiveResolution.extMk_hom, WithTop.coeOrderHom_apply, sSupHom.id_apply, MvPolynomial.prod_C_add_X_eq_sum_esymm, spectrum.algebraMap_eq_of_mem, Equiv.Perm.decomposeFin_symm_of_one, SubMulAction.fixingSubgroup_map_conj_eq, DomMulAct.smul_apply, TopCat.GlueData.image_inter, NormedAddGroupHom.IsQuotient.norm, Polynomial.modByMonic_X_sub_C_eq_C_eval, Algebra.Generators.toKaehler_cotangentSpaceBasis, curveIntegral_eq_intervalIntegral_deriv, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, SubAddAction.ofStabilizer.snoc_castSucc, fderivWithin_clm_comp, Metric.measure_closedBall_pos, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Polynomial.coeff_opRingEquiv, Matrix.SpecialLinearGroup.map_intCast_inj, Polynomial.binomial_eq_binomial, RCLike.inv_def, sign_eq_zero_iff, Quiver.SingleObj.toPrefunctor_apply_obj, ContinuousAlgHom.prodEquiv_apply, DividedPowers.IsDPMorphism.dpow_comp, PowerSeries.map_expand, MeasureTheory.addContent_biUnion, UniformEquiv.prodPUnit_apply, IsLocalization.map_id, HahnSeries.SummableFamily.neg_apply, AdicCompletion.evalₐ_liftAlgHom, NumberField.RingOfIntegers.coe_eq_algebraMap, LocallyBoundedMapClass.comap_cobounded_le, Valuation.HasExtension.val_map_eq_one_iff, List.sublist_iff_exists_fin_orderEmbedding_get_eq, Polynomial.iterate_derivative_X_pow_eq_C_mul, AddAut.inv_apply, AffineMap.coe_homothetyHom, Real.volume_Ici, LinearEquiv.symmEquiv_apply_symm_apply, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, AdicCompletion.surjective_evalₐ, IsAdjoinRootMonic.coeff_algebraMap, ContinuousMap.equivFnOfDiscrete_symm_apply_apply, MvPolynomial.eval₂_map_comp_C, ContinuousMap.Homotopy.continuous, Subspace.dualLift_rightInverse, AffineBasis.surjective_coord, Path.trans_apply, PNat.equivNonZeroDivisorsNat_apply_coe, SupBotHom.toFun_eq_coe, Matrix.GeneralLinearGroup.coe_map_mul_map_inv, MvPowerSeries.rescaleAlgHom_apply, Representation.Coinvariants.mk_eq_iff, ContinuousMap.Homotopy.affine_apply, PseudoMetric.IsUltra.isTrans_ball, Finset.Colex.lt_iff_max'_mem, StarMulEquiv.symm_trans_apply, DualNumber.algHom_ext_iff, Valued.isOpen_ball, MvPowerSeries.coeff_zero_C, TensorProduct.rightComm_tmul, IntermediateField.topEquiv_symm_apply_coe, LinearMap.coprodEquiv_apply, QuadraticMap.associated_linMulLin, MeasureTheory.SimpleFunc.memLp_of_isFiniteMeasure, Primrec.of_equiv_symm, CategoryTheory.Limits.Sigma.ι_reindex_hom, RatFunc.liftOn'_div, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, Polynomial.derivative_X_pow, AddCircle.liftIoc_eq_lift_Icc, ContDiffAt.continuousLinearMap_comp, MeasurableEquiv.coe_curry_symm, ContinuousMonoidHom.pow_apply, Representation.isTrivial_apply, MeasurableEquiv.coe_sumPiEquivProdPi_symm, MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq, AffineMap.linear_bijective_iff, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map, MvPolynomial.optionEquivRight_apply, Rep.ihom_map_hom, Module.Basis.equivFun_apply, LinearMap.rTensor_map, Int.toAdd_zpow, Ideal.natAbs_det_equiv, coe_injective, FreeMagma.toFreeSemigroup_map, Polynomial.coeff_expand, RelEmbedding.coe_natGT, ArchimedeanClass.mk_map_of_archimedean, ZSpan.quotientEquiv.symm_apply, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity, MeasureTheory.AEEqFun.toGermAddMonoidHom_apply, MvPolynomial.finSuccEquiv_apply, Subfield.closure_preimage_le, IsPerfectClosure.equiv_comp_apply, LinearMap.map_coe_ker, Finsupp.add_sum_erase', OrderIso.symm_apply_le, SSet.skeletonOfMono_obj_eq_top, Magma.AssocQuotient.lift_of, AlgCat.free_map, Finsupp.sum_option_index_smul, QuadraticForm.associated_isSymm, Submodule.torsion_gc, Polynomial.sumIDeriv_derivative, Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, Module.apply_evalEquiv_symm_apply, OrderHom.comp_coe, Matrix.SpecialLinearGroup.coe_to_GLPos_to_GL_det, TensorProduct.finsuppScalarLeft_apply_tmul, MvPowerSeries.coeff_monomial, MeasureTheory.Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Real.tendsto_integral_exp_smul_cocompact, MonCat.Colimits.cocone_naturality_components, CategoryTheory.uliftCoyonedaEquiv_naturality, Polynomial.rootsExpandToRoots_apply, ZeroAtInftyContinuousMap.ext_iff, InitialSeg.strictMono, ArithmeticFunction.vonMangoldt_nonneg, isAddRegular_ofMul, MvPowerSeries.X_dvd_iff, MeasureTheory.measure_preimage_vadd_le, finProdFinEquiv_apply_val, MonoidHom.map_inv, Homeomorph.coe_prodUnique, NumberField.FinitePlace.pos_iff, AddMonoid.Coprod.lift_apply_mk, RootPairing.Base.root_mem_or_neg_mem, MonoidHom.coe_ofClosureMEqTopRight, Polynomial.degree_C_mul, CategoryTheory.Subobject.mapIsoToOrderIso_symm_apply, UpperHalfPlane.exp_half_dist, ValuationSubring.mem_principalUnitGroup_iff, HeytAlg.coe_id, TensorAlgebra.tprod_apply, Polynomial.Splits.map_roots, ArithmeticFunction.LSeriesSummable_moebius_iff, MeasureTheory.mul_meas_ge_le_lintegral, QuotientGroup.exists_norm_mul_lt, MeasureTheory.volume_pi_closedBall, NormedField.v_eq_valuation, HasCompactSupport.fderiv_apply, Complex.normSq_add_mul_I, HomogeneousLocalization.awayMapAux_mk, Polynomial.X_mul_monomial, TensorProduct.directSumRight_tmul, Measurable.lintegral_kernel_prod_right, fderiv_continuousMultilinear_apply_const, nhdsAddHom_apply, FreeMonoid.hom_map_lift, FixedPoints.linearIndependent_smul_of_linearIndependent, Orientation.kahler_mul, MvPowerSeries.coeff_C, Polynomial.gaussNorm_C, Subgroup.inclusion_inj, NumberField.mem_span_integralBasis, TensorProduct.gradedComm_tmul_algebraMap, ContinuousMapZero.coe_sum, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, Equiv.arrowProdEquivProdArrow_symm_apply, MvPolynomial.C_eq_coe_nat, Lagrange.interpolate_eq_add_interpolate_erase, Submodule.reflection_map_apply, SubalgebraClass.coe_algebraMap, CategoryTheory.Limits.IsLimit.homEquiv_symm_π_app_assoc, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real, WittVector.liftEquiv_symm_apply_coe, Ideal.coe_smul_primesOver_eq_map_galRestrict, LieSubmodule.incl_eq_val, LinearMap.trace_conj', CategoryTheory.Limits.WalkingPair.swap_symm_apply_ff, ProbabilityTheory.covarianceBilinDual_comm, Equiv.sumSigmaDistrib_apply, AffineMap.lineMap_eq_left_iff, Matrix.of_mem_specialOrthogonalGroup_fin_two_iff, RingQuot.mkAlgHom_rel, LinearIsometryEquiv.continuousAt, nsmulCoprime_zero, AddSubgroup.inclusion_inj, Quaternion.imJ_equivProd_symm_apply, UniformFun.toFun_neg, Affine.Simplex.closedInterior_restrict, Module.Invertible.rTensor_surjective_iff, MeasureTheory.Measure.measure_pos_of_nonempty_interior, ModuleCat.piIsoPi_hom_ker_subtype_apply, OrderEmbedding.preimage_Ico, StandardEtalePair.HasMap.isUnit_derivative_f, ContinuousMonoidHom.diag_toFun, SemiNormedGrp₁.zero_apply, Matrix.SpecialLinearGroup.toLin'_to_linearMap, TwoSidedIdeal.coe_subtype, ModularFormClass.qExpansion_coeff_eq_circleIntegral, ProbabilityTheory.isGaussian_iff_charFunDual_eq, Polynomial.Splits.eq_prod_roots_of_monic, CommBialgCat.bialgEquivOfIso_symm_apply, SubAddAction.fixingAddSubgroupEquivFixingAddSubgroup_coe_apply, Valued.mem_nhds, Subalgebra.lTensorBot_tmul, Homeomorph.isCompact_image, IsCompl.ofDual, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, IntermediateField.adjoin_eq_range_algebraMap_adjoin, TopCat.isEmbedding_pullback_to_prod, MeasureTheory.measure_union_toMeasurable, ArithmeticFunction.sum_moebius_mul_log_eq, AffineIsometry.map_vadd, OrderIso.map_top, MvPolynomial.tensorEquivSum_X_tmul_X, RootPairing.Base.toWeightBasis_apply, CategoryTheory.isArtinianObject_iff_antitone_chain_condition, AddMonoidHom.fst_mono, Ordinal.lsub_typein, ofBoolRing_neg, Quaternion.normSq_zpow, RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChange, ContinuousMap.isUniformEmbedding_uniformFunOfFun, OrderMonoidWithZeroHom.coe_mul, ZeroHom.zero_apply, RCLike.re_eq_ofReal_of_isSelfAdjoint, Cardinal.aleph0_lt_aleph_one, ProbabilityTheory.condDistrib_comp_self, Equiv.piOptionEquivProd_apply, WittVector.quotientPEquiv_mk, abs_sub_map_le_sub, MeasureTheory.measure_biUnion_finset₀, Module.Basis.coe_repr_symm, Representation.IsIntertwiningMap.isIntertwining, Finsupp.coe_equivFunOnFinite_symm, TopHom.symm_dual_comp, groupHomology.H1AddEquivOfIsTrivial_apply, InverseSystem.piLTLim_symm_apply, NumberField.RingOfIntegers.mapRingEquiv_apply, ContinuousLinearMap.opNNNorm_mul_flip_apply, AdjoinRoot.mk_X, ContinuousLinearMap.compLeftContinuousBounded_apply, CuspForm.coe_zero, AddMonoidHom.coe_mul, Equiv.prodPUnit_symm_apply, Module.Basis.smulTower'_repr, AddMonoidAlgebra.curryAlgEquiv_symm_single, fixingSubmonoid_fixedPoints_gc, FiniteArchimedeanClass.withTopOrderIso_symm_apply, Function.Injective.swap_apply, IsLocalization.injective_iff_map_algebraMap_eq, ModuleCat.MonoidalCategory.whiskerRight_apply, LieSubalgebra.topEquiv_apply, TensorProduct.norm_lid, FinPartOrd.comp_apply, FreeAddGroup.lift_symm_apply, Composition.ones_embedding, LinearMap.mul_toMatrix₂'_mul, IsFractionRing.fieldEquivOfAlgEquivHom_injective, Archimedean.exists_orderAddMonoidHom_real_injective, CommRingCat.inv_hom_apply, AlgEquiv.prodUnique_apply, InverseSystem.piSplitLE_lt, MeasureTheory.OuterMeasure.ofFunction_union_of_top_of_nonempty_inter, IsometryEquiv.withLpProdUnique_symm_apply, Module.Relations.toQuotient_map_apply, LocallyConstant.congrRightRingEquiv_symm_apply_apply, Algebra.discr_isUnit_of_basis, LinearMap.toMatrix₂'_mul, BoundedContinuousFunction.compContinuous_apply, Polynomial.toFinsuppIso_apply, Polynomial.leadingCoeff_expand, SmoothPartitionOfUnity.exists_pos_of_mem, ContinuousMonoidHom.comp_toFun, OrderedFinpartition.applyOrderedFinpartition_apply, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, LinearMap.snd_prodOfFinsuppNat, ContinuousMap.nnnorm_eq_iSup_nnnorm, Antitone.measure_iInter, Real.volume_uIoo, ContinuousAffineEquiv.coe_symm_toEquiv, Ideal.absNorm_eq_one_iff, MvPolynomial.comp_aeval_apply, MeasureTheory.eventually_nhds_one_measure_smul_diff_lt, Path.trans_range, AffineMap.coe_neg, SSet.stdSimplex.objEquiv_toOrderHom_apply, MeasureTheory.SimpleFunc.coe_comp, WithZeroMulInt.toNNReal_eq_one_iff, CategoryTheory.Localization.SmallHom.equiv_comp, AffineMap.coe_add, CliffordAlgebra.reverseEquiv_symm_apply, cfc_const_add, MeasurableEquiv.measurable_comp_iff, HasFPowerSeriesOnBall.hasFDerivAt, Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent, coe_setBasisOfLinearIndependentOfCardEqFinrank, WittVector.toPadicInt_comp_fromPadicInt_ext, MeasureTheory.charFun_eq_charFunDual_toDualMap, addAddHom_apply, AlgebraicGeometry.Flat.stalkMap, Equiv.piCongrFiberwise_symm_apply, ProbabilityTheory.measurableSet_kernel_integrable, Algebra.Presentation.relation_comp_localizationAway_inl, Polynomial.aeval_sumIDeriv_eq_eval, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, ProfiniteGrp.toLimit_injective, Equiv.toFun_inducedStructureEquiv, WithTop.toDualBotEquiv_symm_coe, CategoryTheory.Presieve.compatibleEquivGenerateSieveCompatible_apply_coe, ModularForm.coe_prod, Submodule.apply_mem_span_image_of_mem_span, fourier_neg, CompleteLatticeHom.coe_tosInfHom, WittVector.coeff_select, IsAntichain.image_embedding_iff, WithLp.linearEquiv_apply, Polynomial.leadingCoeff_X_sub_C, AdicCompletion.transitionMap_map_pow, Subalgebra.topEquiv_symm_apply_coe, MeasureTheory.Measure.Regular.comap, LinearEquiv.ofSubmodule'_apply, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, AddMonoidAlgebra.uniqueRingEquiv_symm_apply, PowerSeries.coeff_expand_of_not_dvd, cfcHom_isStrictlyPositive_iff, Equiv.prodUnique_apply, ModuleCat.free_δ_freeMk, Homeomorph.preimage_closure, RatFunc.denom_C, Finsupp.toFinset_toMultiset, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, AddSubgroup.centerToAddOpposite_symm_apply_coe, IsLocalization.mk'_one, map_finsuppSum, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, AlternatingMap.prod_apply, AlgebraicGeometry.Scheme.Pullback.range_snd, Equiv.Perm.apply_mem_support, spectralAlgNorm_of_finiteDimensional_normal_def, AddSubmonoid.centerCongr_apply_coe, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, Submonoid.LocalizationMap.ofMulEquivOfLocalizations_apply, ContinuousMultilinearMap.analyticOn, measurable_measure_prodMk_right, Subalgebra.coe_comap, Submodule.FG.directedSystem, DomAddAct.vadd_Lp_const, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv, AddEquiv.injective, MonoidWithZeroHom.coe_comp, Finsupp.apply_single, Subsemiring.ringEquivOpMop_symm_apply_coe, Finsupp.degree_single, upperBounds_range_partialSups, ContinuousLinearEquiv.symm_image_image, ContMDiffWithinAt.clm_apply_of_inCoordinates, AlgebraicGeometry.Scheme.Hom.stalkMap_comp, Polynomial.expand_eq_C, partialSups_eq_ciSup_Iic, RingEquiv.ofNonUnitalRingHom_symm_apply, MeasureTheory.exists_measurable_superset_iff_measure_eq_zero, Finsupp.single_of_embDomain_single, toLex_smul', AddSubgroup.orderIsoAddCon_apply, MeasureTheory.SimpleFunc.sub_apply, Prod.Lex.toLex_mono, RatFunc.num_div_dvd', Module.Projective.exists_dual_eq_one, IsCoprime.wronskian_eq_zero_iff, zero_mem_absConvexHull, Fin.addRothNumber_le_rothNumberNat, IsTensorProduct.lift_eq, Ordinal.toNatOrdinal_eq_zero, LinearIndependent.of_isLocalizedModule, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero, CategoryTheory.nerve.σ_zero_nerveEquiv_symm, MvPolynomial.aeval_unique, WeierstrassCurve.Jacobian.baseChange_polynomialX, Path.symm_subpath, Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv_apply, WeierstrassCurve.Φ_two, OrderIso.apply_eq_iff_eq, AlgEquiv.toAlgHom_unop, MonoidAlgebra.mul_apply, CyclotomicRing.algebraBase_injective, Equiv.setValue_eq, InitialSeg.antisymm_toFun, CategoryTheory.Functor.homEquivOfIsRightKanExtension_symm_apply, OrderIso.emptySumLex_apply_inr, ArithmeticFunction.carmichael_finset_prod, ContinuousAffineEquiv.image_eq_preimage_symm, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, LinearMap.IsSymmetric.eigenvalues_def, DomAddAct.isEmbedding_mk, Finsupp.LinearEquiv.finsuppUnique_apply, OnePoint.smul_infty_def, Set.image_nsmul, idealFactorsEquivOfQuotEquiv_is_dvd_iso, Polynomial.aeval_C, RelHomClass.map_rel, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, ZLattice.volume_image_eq_volume_div_covolume', PowerBasis.exists_eq_aeval', Polynomial.Monic.roots_map_of_card_eq_natDegree, MeasureTheory.Measure.InnerRegularWRT.measure_eq_iSup, LinearIsometryEquiv.withLpProdUnique_symm_apply, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Algebra.trace_complex_apply, MvPowerSeries.homogeneousComponent_mul_of_le_order, ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, Set.piCongrLeft_comp_restrict, Finsupp.applyAddHom_apply, HahnSeries.SummableFamily.coeff_hsum, Algebra.toMatrix_lsmul, HasFDerivWithinAt.comp_hasDerivAt, AlgEquiv.moduleEndSelf_apply_apply, AddOpposite.opAddEquiv_symm_apply, FiniteGaloisIntermediateField.adjoin_simple_map_algEquiv, SchwartzMap.compCLM_apply, EuclideanGeometry.orthogonalProjection_orthogonalProjection, exteriorPower.map_injective, DirectSum.SetLike.IsHomogeneous.mem_iff, Quaternion.coe_starAe, Sum.Lex.inl_lt_inr, Topology.WithLower.toLower_le_toLower, LinearEquiv.rTensor_trans_apply, SimplexCategory.const_apply, LinearMap.mulRight_apply, ContinuousAlgHom.coe_pow, AugmentedSimplexCategory.inl'_eval, TopCat.pullbackIsoProdSubtype_hom_apply, addMonoidHomOfForallMemZMultiples_apply_gen, toMatrix_innerSL_apply, Finset.weightedVSub_eq_linear_combination, OrthonormalBasis.equiv_apply_basis, WeakDual.CharacterSpace.mem_spectrum_iff_exists, DirectSum.of_zero_pow, OrderDual.lt_toDual, Finsupp.mapDomain_equiv_apply, Module.Basis.map_orientation_eq_det_inv_smul, RestrictedProduct.zero_apply, isAssociatedPrime_iff_exists_injective_linearMap, MeasureTheory.ProbabilityMeasure.tendsto_measure_of_isClopen_of_tendsto, MeasureTheory.StronglyMeasurable.integral_kernel_prod_left'', NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, Polynomial.aeval_eq_prod_aroots_sub_of_splits, AlternatingMap.coeFn_smul, Function.Embedding.optionEmbeddingEquiv_symm_apply, Algebra.SubmersivePresentation.basisKaehler_apply, Complex.conj_re, MeasureTheory.measure_biUnion_finset, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, Affine.Simplex.eulerPoint_reindex, OrderEmbedding.orderIso_apply, ContinuousMap.toLp_comp_toContinuousMap, Finset.map_noncommProd, AddMonoidHom.ext_int_iff, KaehlerDifferential.polynomial_D_apply, CommAlgCat.isoEquivAlgEquiv_symm_apply, VitaliFamily.ae_tendsto_rnDeriv_of_absolutelyContinuous, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion, BoundedOrderHom.dual_symm_apply_toOrderHom, MeasureTheory.IsAddFundamentalDomain.covolume_eq_volume, isAddRegular_ofDual, AlgebraicGeometry.Scheme.Cover.exists_eq, RestrictedProduct.range_inclusion, MvPolynomial.bind₁_bind₁, TensorProduct.toIntegralClosure_injective_of_flat, EReal.le_iff_sign, imageToKernel_arrow_apply, spectrum.add_mem_iff, AffineEquiv.image_symm, BoundedLatticeHom.coe_toBoundedOrderHom, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2, ofDual_wcovBy_ofDual_iff, LaurentSeries.powerSeriesEquivSubring_coe_apply, PathConnectedSpace.exists_path_through_family', StarAlgHom.coe_toNonUnitalStarAlgHom, OrderHom.antisymmetrization_apply_mk, WeierstrassCurve.Jacobian.Equation.map, ArithmeticFunction.coe_mul_zeta_apply, FirstOrder.Language.ElementaryEmbedding.ofModelsElementaryDiagram_toFun, MvPolynomial.support_sum_monomial_coeff, AddMonoidHomClass.isometry_iff_norm, ofDual_toAdd_eq_top_iff, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, MvPolynomial.degreeOf_mul_C_le, ArchimedeanClass.ofArchimedean_stdPart, ContinuousLinearEquiv.arrowCongrEquiv_symm_apply, ThreeGPFree.mulRothNumber_eq, SimpleGraph.Iso.degree_eq, MonoidHom.ker_eq_bot_iff, Bundle.Trivial.homeomorphProd_symm_apply_proj, AddCon.orderIsoOp_apply, Equiv.subtypeQuotientEquivQuotientSubtype_symm_mk, ProbabilityTheory.bayesRisk_const_of_neZero, Polynomial.toLaurent_inj, Matrix.separatingLeft_toLinearMap₂'_iff, Module.Relations.Solution.π_relation, StrictAnti.dual_right, AddCircle.equivIoc_coe_eq, Multiset.mapEmbedding_apply, Matrix.PosSemidef.re_dotProduct_nonneg, PerfectClosure.r_iff, AlgebraicGeometry.Scheme.ofArrows_mem_precoverage_iff, Path.coe_mk_mk, QuotientAddGroup.map_mk', NonUnitalAlgHom.coe_inl, AddMonoidAlgebra.mapDomain_mul, MeasureTheory.Measure.addHaar_ball_mul_of_pos, MeasureTheory.pdf.lintegral_eq_measure_univ, Algebra.exists_etale_bijective_residueFieldMap_and_map_eq_mul_and_isCoprime, LieModule.Weight.apply_lie, DirectSum.coeFnAddMonoidHom_apply, UniqueFactorizationMonoid.normalizedFactors_prod_eq, Orientation.volumeForm_robust', AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, ArithmeticFunction.vonMangoldt_apply, Submodule.eq_top_iff_forall_basis_mem, EuclideanGeometry.orthogonalProjection_vsub_mem_direction, QuadraticMap.exists_companion', infIrred_toDual, NormedAddGroupHom.coe_ker, Ordinal.enum_zero_eq_bot, AddActionHom.fst_apply, PolynomialModule.eval_apply, exteriorPower.basis_repr_apply, PresheafOfModules.Derivation'.app_apply, Finsupp.linearEquivFunOnFinite_symm_single, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, SemiNormedGrp₁.id_apply, Set.up_one, triple_product_permutation, exists_smooth_zero_one_of_isClosed, MeasureTheory.addContent_iUnion_eq_tsum_of_disjoint_of_IsSigmaSubadditive, BoundedContinuousFunction.toContinuousMapStarₐ_apply_apply, ProbabilityTheory.HasGaussianLaw.map_equiv_fun, DFinsupp.rangeIcc_apply, LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero', Polynomial.leval_apply, CommRingCat.comp_apply, DomMulAct.stabilizerMulEquiv_apply, MvPolynomial.algebraTensorAlgEquiv_symm_map, Set.Ioi_toDual, prodEquivPiFinTwo_symm_apply, TensorProduct.rid_symm_apply, MonoidWithZeroHom.map_ite_one_zero, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_symm_apply, Function.Embedding.subtype_apply, AlternatingMap.ext_iff, OrderMonoidIso.strictMono, isOpenMap_ofDual, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, legendreSym.at_neg_one, Homeomorph.self_comp_symm, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset, tendsto_measure_cthickening_of_isClosed, Matrix.comp_map_map, LinOrd.coe_id, Multiset.mapEquiv_apply, AlternatingMap.ofSubsingleton_symm_apply_apply, OmegaCompletePartialOrder.ContinuousHom.ext_iff, Similar.index_equiv, IntermediateField.intermediateFieldMap_apply_coe, AlgEquiv.rightInverse_symm, Filter.coe_pureAddMonoidHom, IntermediateField.topEquiv_apply, Diffeomorph.contMDiffAt, MeasureTheory.measure_eq_iInf, Module.Basis.toMatrix_update, RelEmbedding.ext_iff, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure, Algebra.TensorProduct.productMap_right_apply, Finsupp.range_single_subset, ContinuousLinearEquiv.comp_contDiffOn_iff, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, TensorPower.cast_tprod, ProbabilityTheory.Kernel.id_apply, Complex.im_eq_sub_conj, PiLp.basis_toMatrix_basisFun_mul, MeasureTheory.MemLp.meas_ge_lt_top', Fin.insertNthOrderIso_apply, finEquivZPowers_apply, Submodule.mk_quotientEquivOfIsCompl_apply, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, AddMonoid.Coprod.mclosure_range_inl_union_inr, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, Module.End.baseChangeHom_apply_apply, MvPolynomial.rename_polynomial_aeval_X, HahnSeries.embDomainOrderAddMonoidHom_apply, LatticeHom.coe_comp_inf_hom, Quaternion.inner_self, fderivWithin_continuousAlternatingMap_apply_const, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg, groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂, AddMagma.FreeAddSemigroup.lift_of, partialSups_iff_forall, Path.range_coe, dist_left_lineMap, Equiv.Perm.apply_mem_fixedPoints_iff_mem_of_mem_centralizer, PiTensorProduct.mul_tprod_tprod, Manifold.IsImmersionAt.target_subset_preimage_target, Polynomial.ofFn_degree_lt, Topology.WithLawson.isClosed_preimage_ofLawson, Polynomial.taylor_monomial, FinEnum.up_equiv_symm, MvPolynomial.weightedDecomposition.decompose'_eq, Equiv.coe_embeddingFinSucc_symm, SchwartzMap.coe_coeHom, Submodule.prodEquivOfIsCompl_symm_apply_right, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, NonUnitalAlgHom.map_adjoin_singleton, MeasureTheory.ProbabilityMeasure.map_apply, MeasureTheory.projectiveFamilyContent_iUnion_le, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, NonUnitalAlgHom.map_mul', infClosure_prod, iccHomeoI_symm_apply_coe, Real.volume_pi_Ico_toReal, Submodule.coe_mapIic_apply, Matrix.det_mul_aux, AddValuation.map_add_supp, Matrix.tail_transpose, Group.preimage_smul_set, Matrix.isRepresentation.toEnd_surjective, PartOrdEmb.Hom.injective, GroupSeminorm.coe_smul, CategoryTheory.equivYoneda_inv_app, Finsupp.subtypeDomain_eq_iff_forall, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, Polynomial.toFinsupp_apply, WittVector.map_eq_zero_iff, AddCommGrpCat.biprodIsoProd_inv_comp_desc_apply, MeasureTheory.SimpleFunc.integrable_approxOn, Rep.unit_iso_comm, Finsupp.linearCombination_equivMapDomain, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply, BilinForm.toMatrix_mul, Algebra.Extension.Hom.algebraMap_toRingHom, SkewMonoidAlgebra.of_injective, Diffeomorph.symm_image_eq_preimage, LinearMap.map_smul, PartENat.withTopEquiv_symm_zero, ProbabilityTheory.uniformOn_univ, Pi.basisFun_apply, Polynomial.comp_eq_aeval, Finset.sum_smul_sum_eq_sum_perm, Rep.leftRegularHomEquiv_symm_single, AddSubmonoid.LocalizationMap.lift_id, List.sortedGT_map_toDual, CategoryTheory.PreGaloisCategory.comp_autMap_apply, AddEquiv.toMultiplicative_symm_apply_symm_apply, QuaternionAlgebra.imJ_swapEquiv_symm_apply, Lagrange.interpolate_apply, CommMonCat.coyoneda_map_app, affineCombination_mem_convexHull, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, MonoidHom.rangeRestrict_injective_iff, Valuation.map_neg, SetTheory.PGame.toLeftMovesNim_symm_lt, Algebra.Generators.Hom.equivAlgHom_symm_apply_val, MultilinearMap.ofSubsingleton_symm_apply_apply, CategoryTheory.enrichedFunctorTypeEquivFunctor_apply_obj, FreeSemigroup.lift_comp_of', exists_lt_rieszContentAux_add_pos, Polynomial.C_mul, MvPolynomial.isHomogeneous_C_mul_X_pow, AlgebraicGeometry.Spec.homEquiv_apply, Trivialization.preimageHomeomorph_apply, StrictMono.dual, ProjectiveSpectrum.basicOpen_eq_union_of_projection, ContinuousLinearEquiv.eq_symm_apply, MeasureTheory.Measure.iSup_restrict_spanningSets, MeasureTheory.OuterMeasure.isCaratheodory_sum, LinearMap.toMatrix_comp, coe_normSeminorm, MeasureTheory.tendsto_measure_iInter_atBot, Algebra.normalizedTrace_algebraMap_apply, Finsupp.neg_apply, Equiv.piCongrRight_apply, MvPolynomial.tensorEquivSum_C_tmul_one, ContinuousMap.nndist_eq_iSup, Submodule.piQuotientLift_single, AlternatingMap.coe_multilinearMap, AlgebraicGeometry.Scheme.IsLocallyDirected.ι_jointly_surjective, Matrix.row_eq_self, LocallyConstant.eq_const, CategoryTheory.Adjunction.homAddEquiv_symm_apply, ContinuousLinearEquiv.arrowCongrSL_apply, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, Polynomial.natDegree_X_sub_C_le, Polynomial.splits_X_sub_C_mul_iff, MeasureTheory.tendstoInMeasure_iff_tendsto_toNNReal, signedDist_vadd_left, AlgebraicGeometry.basicOpen_eq_of_affine', Finsupp.le_weight_of_ne_zero, Ideal.spanNorm_singleton, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, AlgHom.toRingHom_unop, MulArchimedeanOrder.of_val, MvPolynomial.map_iterateFrobenius_expand, image_gaugeRescaleHomeomorph_closure, Finsupp.mapRange.linearEquiv_apply, CategoryTheory.NatTrans.appLinearMap_apply, MonoidHom.coe_toAdditive, ModularGroup.tendsto_lcRow0, Function.OfArity.uncurry_two_eq_uncurry, Subsemigroup.coe_toAddSubsemigroup_symm_apply, CompactlyGenerated.isoEquivHomeo_symm_apply, tangentBundleModelSpaceHomeomorph_coe_symm, ProbabilityTheory.integrable_kernel_prodMk_left, PseudoEpimorphism.ext_iff, AddEquiv.apply_eq_iff_eq, ProfiniteAddGrp.coe_comp, CochainComplex.HomComplex.CohomologyClass.descAddMonoidHom_cohomologyClass, CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, Ideal.FinrankQuotientMap.span_eq_top, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpace, DomMulAct.mk_inv, WithZero.toMulBot_coe, Matrix.submatrixEquivInvertibleEquivInvertible_apply, PowerSeries.coeff_zero_eq_constantCoeff, Finset.sum_map_equiv, DomMulAct.isInducing_mk, AlgebraicGeometry.IsPreimmersion.base_embedding, LocallyConstant.congrLeftₗ_apply_apply, cosetToCuspOrbit_apply_mk, Polynomial.factorial_smul_hasseDeriv, WithCStarModule.equiv_pi_apply, SubMulAction.SMulMemClass.coe_subtype, Matrix.toLinAlgEquiv_self, SameRay.sameRay_map_iff, finEquivMultiples_apply, RootPairing.coreflection_apply, DirectSum.of_natCast, ModularForm.smul_apply, Equiv.sumCompl_apply_symm_of_pos, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, ProbabilityTheory.Kernel.compProd_apply_univ, LieAlgebra.of_symm_nsmul, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, Finsupp.Lex.single_antitone, ContinuousLinearEquiv.submoduleMap_symm_apply, NumberField.Units.coe_zpow, CategoryTheory.codiscreteEquiv_symm_apply_as, Polynomial.toMvPolynomial_X, MvPowerSeries.constantCoeff_map, Equiv.prodCongrRight_apply_fst, AlgebraicGeometry.Scheme.Hom.coe_image, IsometryEquiv.piCongrLeft'_symm_apply, UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors, finSuccEquiv'_symm_none, NumberField.mem_span_basisOfFractionalIdeal, AlgebraicGeometry.Scheme.Hom.coe_preimage, AddEquiv.congr_fun, CircleDeg1Lift.lt_map_map_zero, GaussianInt.toComplex_neg, AffineIsometry.ediam_range, Equiv.Set.sumDiffSubset_symm_apply_of_mem, Ordinal.toGame_inj, Homeomorph.isClosedMap, MonoidWithZeroHom.valueMonoid_eq_closure, DirectSum.sigmaLuncurry_apply, IsNonarchimedeanLocalField.isCompact_closedBall, IsEvenlyCovered.comp_homeomorph_iff, Quiver.starEquivCostar_apply, Module.Basis.coe_toDual_self, ContinuousMultilinearMap.map_update_smul, ProbabilityTheory.avgRisk_const_left', MvPowerSeries.rescale_eq_subst, AddSubgroupClass.coe_inclusion, MeasurableEquiv.image_eq_preimage_symm, ContinuousMap.equivFnOfDiscrete_symm_apply, RootPairing.RootPositiveForm.exists_pos_eq, ContinuousLinearMap.toContinuousAddMonoidHom_id, MeasureTheory.lintegral_fintype, AddMonoidHom.coe_toIntLinearMap_range, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, ArithmeticFunction.pdiv_apply, MulEquiv.coprodComm_apply, MeasureTheory.Measure.id_comp, LieDerivation.lie_ad, PowerSeries.coe_X, Rat.int_algebraMap_injective, Cardinal.preAleph_lt_preAleph, Matrix.det_mul_column, PositiveLinearMap.ofPreGNS_toPreGNS, AddMonoidHom.mem_mgraph, Matrix.separatingLeft_toBilin'_iff, Polynomial.dickson_of_two_le, Module.Basis.baseChange_repr_tmul, ModelWithCorners.transContinuousLinearEquiv_range, SkewMonoidAlgebra.coeff_ofFinsupp, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, Subsemigroup.topEquiv_apply, Ring.DirectLimit.ringEquiv_symm_mk, TensorProduct.nnnorm_assoc, MulChar.IsQuadratic.gaussSum_frob, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, LieAlgebra.Extension.proj_incl, Matrix.kroneckerAlgEquiv_symm_apply, ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity, TopCat.ofHom_apply, SubgroupClass.coe_inclusion, SetSemiring.down_subset_down, Equiv.natSumNatEquivNat_apply, MeasureTheory.Measure.apply_eq_zero_of_isEmpty, Matrix.coeff_det_one_add_X_smul_one, Matrix.trace_toLin_eq, Homeomorph.compStarAlgEquiv'_apply, LieHom.mem_ker, MvPowerSeries.coe_aeval, CategoryTheory.Groupoid.invEquiv_symm_apply, NonemptyInterval.map_fst, Subalgebra.coe_pi, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, mem_convexHull_iff_exists_fintype, DirectSum.decompose_symm_mul, DoubleCentralizer.coe_eq_algebraMap, Localization.mulEquivOfQuotient_monoidOf, MvPolynomial.sumAlgEquiv_apply, ContinuousLinearMap.opNorm_mul_apply_le, MonoidHom.coe_dfinsuppProd, Additive.ofMul_lt, TensorPower.cast_eq_cast, AddCommGrpCat.ofHom_apply, OrderEmbedding.image_Icc, Coalgebra.TensorProduct.assoc_tmul, DFinsupp.coe_strictMono, coe_notMemRangeEquiv, PiTensorProduct.tprodL_apply, Seminorm.mem_ball, lineMap_lt_right_iff_lt, DirectSum.coe_mul_of_apply_add, FreeGroupBasis.lift_symm_apply, RCLike.re_le_norm, LatticeHom.coe_comp_sup_hom, circleAverage_log_norm_factorizedRational, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, LightDiagram.id_hom_hom_hom_apply, count_span_normalizedFactors_eq, Finsupp.lex_le_iff_of_unique, Differential.logDeriv_algebraMap, LinearIsometryEquiv.self_comp_symm, Equiv.sumSumSumComm_apply, Multiset.prod_hom, Polynomial.aeval_ofReal, eVariationOn.comp_ofDual, Diffeomorph.uniqueDiffOn_preimage, WithBot.subtypeOrderIso_apply_coe, DirectLimit.eq_of_le, Homeomorph.isConnected_image, FreeMonoid.lift_symm_apply, ContinuousLinearMap.smul_def, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, LinearMap.toMatrix₂_mul_basis_toMatrix, ZSpan.repr_fract_apply, ContinuousMap.add_apply, finsuppLEquivDirectSum_apply, AffineSubspace.topEquiv_apply, SimpleGraph.ConnectedComponent.map_mk, map_le_lineMap_iff_slope_le_slope, cfc_apply_pi, SmoothBumpCovering.embeddingPiTangent_injective, ContinuousLinearMap.orthogonal_range, IsometryEquiv.withLpProdAssoc_apply, Monoid.Coprod.inv_def, Basis.mem_ideal_iff, Unitary.conjStarAlgAut_mul_apply, AddMonoidAlgebra.algHom_ext_iff, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T, Real.toNNReal_abs, MeasureTheory.Measure.measure_Ioo_eq_zero, StarSubalgebra.coe_comap, Cardinal.aleph_mul_aleph, Matrix.GeneralLinearGroup.val_inv_scalar_apply, Multiset.toFinsupp_eq_iff, MeasureTheory.Measure.exists_positive_of_not_mutuallySingular, CategoryTheory.Functor.CorepresentableBy.homEquiv_comp, Submodule.lipschitzWith_starProjection, MDifferentiableWithinAt.clm_bundle_apply, LinearEquiv.ofTop_symm_apply, HasFPowerSeriesAt.hasDerivAt, TensorProduct.AlgebraTensorModule.lift_apply, ContinuousLinearMap.isPositive_iff_complex, Polynomial.degree_add_degree_leadingCoeff_inv, ContinuousLinearMap.toContinuousAddMonoidHom_sub, smulMonoidHom_apply, PseudoMetric.coe_sup, PMF.toOuterMeasure_map_apply, RootPairing.algebraMap_pairingIn', ofAdd_sub, MeasureTheory.tsum_measure_preimage_singleton, AffineMap.coe_homothetyAffine, BoundedContinuousFunction.norm_coe_le_norm, Finset.map_val, exists_contMDiffOn_section_forall_mem_convex_of_local, Topology.WithLowerSet.isOpen_ofLowerSet_preimage, ArithmeticFunction.LSeriesSummable_zeta_iff, LieAlgebra.IsKilling.rootSystem_pairing_apply, groupCohomology.cocyclesMk₂_eq, MonoidHom.map_one, MeromorphicOn.min_divisor_le_divisor_add, Module.Basis.toMatrix_eq_toMatrix_constr, ContinuousAlgHom.id_apply, LatticeHom.dual_comp, Matrix.det_reindexLinearEquiv_self, BoundedContinuousFunction.isBounded_range_integral, Module.Finite.toModuleEnd_moduleEnd_surjective, Finset.weightedVSub_vadd_affineCombination, CategoryTheory.Adjunction.homAddEquiv_symm_add, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, antitoneOn_dual_iff, MvPolynomial.degreeOf_C_mul_le, MeasureTheory.SimpleFunc.pair_apply, LieAlgebra.IsKilling.chainTopCoeff_zero_right, TensorProduct.comul_tmul, MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le, Functor.mapEquiv_symm_apply, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_hom_f, map_mem_algebraicClosure_iff, Submonoid.isLocalizationMap_iff_bijective, LinearMap.lcompₛₗ_apply, Finset.preimage_subset, Nucleus.toFun_eq_coe, HasFPowerSeriesAt.eventually_hasSum_sub, RelHom.smul_def, Polynomial.eval₂AddMonoidHom_apply, ProbabilityTheory.covarianceBilin_apply, Real.volume_pi_le_diam_pow, Affine.Simplex.mongePoint_restrict, MulEquiv.symmEquiv_symm_apply_symm_apply, Polynomial.trinomial_def, IsAntichain.image_embedding, AddCommGrpCat.biprodIsoProd_inv_comp_fst_apply, Algebra.TensorProduct.basis_repr_symm_apply, SemiconjBy.map, quadraticChar_odd_prime, absConvexHull_univ, LinearEquiv.isWeaklyRegular_congr', DirectLimit.Module.hom_ext_iff, AddEquiv.val_piAddUnits_symm_apply, AlternatingMap.map_update_self, FirstOrder.Language.DirectLimit.of_apply, smoothSheafCommRing.ι_forgetStalk_hom_apply, fourierIntegral_half_period_translate, BoxIntegral.integralSum_sub_partitions, OrderIso.equivalence_inverse, NonUnitalRingHom.coe_rangeRestrict, MeasureTheory.Measure.setLIntegral_condKernel_univ_left, finSuccAboveEquiv_symm_apply_last, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, Polynomial.hasDerivAt_aeval, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, Valued.extensionValuation_apply_coe, Polynomial.coe_algebraMap_eq_CC, ContinuousLinearMap.comp_cpolynomialOn, SubmonoidClass.subtype_injective, ValuativeRel.valuation_surjective, WeierstrassCurve.Projective.baseChange_dblX, InfTopHom.coe_top, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, SetTheory.PGame.moveRight_neg_toRightMovesNeg, DirectSum.lof_apply, LinearMap.polyCharpoly_map_eq_charpoly, AffineMap.snd_lineMap, selfZPow_natCast, DFinsupp.card_Ico, HasFDerivAt.linear_multilinear_comp, ProfiniteGrp.ofHom_apply, Ideal.pi_mkQ_rTensor, AddSubmonoid.LocalizationMap.mk'_add_cancel_left, MvPolynomial.coeffsIn_eq_span_monomial, qExpansion_neg, OrderEmbedding.minimal_apply_mem_inter_range_iff, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, FormalMultilinearSeries.compAlongComposition_apply, AlgebraicGeometry.stalkToFiberRingHom_germ, ContMDiffSection.contMDiff, HahnSeries.SummableFamily.coe_zero, DirectSum.map_apply, LTSeries.exists_relSeries_covBy, IsBaseChange.basis_apply, CocompactMap.isCompact_preimage, MeasureTheory.Measure.restrict_apply₀, MvPolynomial.sumToIter_Xr, Finset.sum_mul_sum_eq_sum_perm, toMul_smul, CategoryTheory.conjugateEquiv_symm_comm, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff, Submonoid.LocalizationMap.mul_mk'_one_eq_mk', Polynomial.aeval_root_derivative_of_splits, AbsoluteValue.map_units_int, MeasureTheory.withDensitySMulLI_apply, frobeniusEquiv_symm_pow_p, ContinuousMapZero.toContinuousMapHom_apply, IsBoundedBilinearMap.deriv_apply, Orthonormal.inner_finsupp_eq_zero, Path.add_apply, Polynomial.X_sub_C_scaleRoots, ContinuousMap.coe_natCast, Equiv.Perm.IsCycle.pow_eq_one_iff'', Algebra.Generators.ofComp_toAlgHom_monomial_sumElim, Quaternion.normSq_def, Submodule.mulLeftMap_apply_single, Polynomial.Chebyshev.aeval_C, OnePoint.exists_mem_SL2, convexHull_toCone_isLeast, MeasureTheory.Measure.addHaar_nnreal_smul, ModularForm.const_apply, OrderIso.equivClosureOperator_symm_apply, KaehlerDifferential.quotKerTotalEquiv_symm_apply, IsometryEquiv.withLpUniqueProd_apply, Pi.evalAddMonoidHom_apply, Finsupp.mapDomain.addMonoidHom_apply, AddEquiv.cast_symm_apply, MeasureTheory.measure_diff, Monoid.PushoutI.NormalWord.cons_eq_smul, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, NumberField.mixedEmbedding.logMap_apply, AddMonoidHom.coe_toMultiplicative_map, Complex.conj_ofNat, Polynomial.iterate_derivative_neg, AbsoluteValue.IsEquiv.one_lt_iff, IsDedekindDomain.selmerGroup.fromUnitLift_injective, LieModuleHom.coe_nsmul, OrderIso.sumLexDualAntidistrib_symm_inl, infIrred_ofDual, Submonoid.powLogEquiv_apply, Polynomial.aeval_eq_sum_range, AffineEquiv.coe_coe, MeasurableEquiv.inv_apply, finsuppTensorFinsuppLid_apply_apply, LieSubalgebra.coe_incl, Orientation.kahler_map, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, OrderIso.map_sup, mem_coeSubmodule_conductor, ContinuousLinearEquiv.skewProd_symm_apply, MeasureTheory.convolutionExistsAt_iff_integrable_swap, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, ProbabilityTheory.uniformOn_inter', ProbabilityTheory.Kernel.deterministic_apply', Module.toModuleEnd_apply, polyEquivTensor_apply, AddMonoid.IsTorsion.torsionAddEquiv_apply, AlgebraicGeometry.Scheme.Hom.isClosedEmbedding, Equiv.Perm.toCycle_next, MvPolynomial.exists_finset_rename₂, measure_Ioo_lt_top, FreeLieAlgebra.universalEnvelopingEquivFreeAlgebra_symm_apply, Polynomial.resultant_C_zero_left, lineMap_one_half, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, Matrix.mulVec_cramer, MonoidAlgebra.mapDomainNonUnitalAlgHom_apply, LaurentPolynomial.invert_apply, conjnegRingHom_apply, RCLike.ofNat_im, NormedAddGroupHom.mem_range_self, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_symm_tmul, AdicCompletion.of_injective, Matrix.reindex_refl_refl, MulEquivClass.coe_symm_apply_apply, DirectSum.apply_eq_component, MeasureTheory.StronglyMeasurable.tendsto_approx, MeasureTheory.innerRegularWRT_isCompact_isClosed_measure_ne_top_of_group, volume_regionBetween_eq_integral', AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiber, CliffordAlgebra.contractRight_one, Polynomial.C_eq_or_isOpenQuotientMap_eval, RingTheory.Sequence.IsWeaklyRegular.of_flat_of_isBaseChange, DistribMulActionHom.coe_fn_coe, NonUnitalAlgHom.prod_toFun, ArithmeticFunction.cardDistinctFactors_mul, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, affineCombination_mem_affineSpan_of_nonempty, Valuation.rel_one_iff, Polynomial.Gal.restrict_surjective, CoxeterMatrix.reindex_apply, PolyEquivTensor.toFunBilinear_apply_eq_smul, WeierstrassCurve.Projective.baseChange_dblU, Finset.prod_eraseNone, Set.partialSups_eq_accumulate, LinearMap.det_comp, LinearEquiv.smulOfNeZero_symm_apply, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, AffineEquiv.coe_homothetyUnitsMulHom_apply, RatFunc.C_injective, ofLex_smul', DFinsupp.piecewise_apply, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, CategoryTheory.Discrete.addMonoidalFunctor_μ, OrderIso.map_ciSup_set, MvPolynomial.eval_toMvPolynomial, Equiv.subRight_apply, Quiver.SingleObj.toHom_symm_apply, NumberField.Units.logEmbeddingQuot_injective, Homeomorph.Set.univ_apply, Subgroup.subgroupOfContinuousMulEquivOfLe_symm_apply, LinearMap.isOrthoᵢ_def, LinearIsometryEquiv.comp_differentiable_iff, AddEquiv.additiveMultiplicative_symm_apply, ContinuousAddEquiv.ext_iff, Monovary.sum_comp_perm_smul_eq_sum_smul_iff, Monovary.sum_comp_perm_smul_le_sum_smul, LocallyBoundedMap.ofMapBounded_apply, MonoidAlgebra.singleOneRingHom_apply, FractionalIdeal.one_le_extendedHomₐ_iff, LinearEquiv.refl_apply, CliffordAlgebraDualNumber.equiv_ι, groupHomology.chainsMap_f_hom, ArithmeticFunction.vonMangoldt_apply_one, Affine.Simplex.eulerPoint_restrict, Algebra.Presentation.algebraTensorAlgEquiv_symm_relation, MvPowerSeries.WithPiTopology.summable_iff_summable_coeff, MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict, CategoryTheory.PreGaloisCategory.autEmbedding_apply, Derivation.leibniz_pow, Equiv.piCongrLeft_sumInr, SimpleGraph.TripartiteFromTriangles.exists_mem_toTriangle, HahnSeries.single_div_single, groupHomology.d₃₂_apply_mem_cycles₂, Polynomial.sum_taylor_eq, Subalgebra.range_subset, LinearMap.BilinForm.isSymm_def, OrderHom.diag_coe, DirectSum.coe_of_mul_apply_of_le, PiTensorProduct.lift_tprod, Affine.Simplex.signedInfDist_reindex, Algebra.Generators.aeval_val_eq_zero, Equiv.piCongr'_apply, Cardinal.toNat_lt_toNat, Nat.coe_castRingHom, ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite, MeasureTheory.measure_eq_sub_vadd, AddSemigrp.coe_comp, Matrix.toLinOfInv_apply, DirectSum.support_of_subset, OrderIso.lowerBounds_image, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex, UnitAddTorus.hasSum_prod_mFourierCoeff, Polynomial.taylor_eval_sub, Finset.eraseNone_image_some, MvPolynomial.sum_C, LocalizedModule.algebraMap_mk, Equiv.Set.image_symm_apply, MulEquiv.piUnique_symm_apply, AddCon.ext_iff, Filter.prod_assoc_symm, TensorProduct.lcurry_apply, OrthonormalBasis.span_apply, Ideal.mem_quotient_iff_mem_sup, isRightRegular_ofDual, LocallyConstant.mul_apply, Padic.withValUniformEquiv_cast_apply, DirectSum.coe_mul_of_apply_of_le, Polynomial.Chebyshev.aeval_U, TrivSqZeroExt.snd_map, AddMonoidHom.map_div₂, Polynomial.algebraMap_hahnSeries_injective, AlternatingMap.map_zero, AddLocalization.addEquivOfQuotient_symm_mk, WithTop.ofDual_le_iff, RingAut.coe_one, TensorProduct.curry_apply, ContinuousMultilinearMap.analyticOnNhd, Module.End.generalized_eigenvec_disjoint_range_ker, Subalgebra.LinearDisjoint.val_mulMap_tmul, FirstOrder.Language.ElementarySubstructure.subtype_injective, MeasureTheory.OuterMeasure.boundedBy_eq_ofFunction, MeasureTheory.inducedOuterMeasure_eq, Nucleus.coe_le_coe, SetTheory.Game.neg_birthday_le, LinearIsometryEquiv.coe_refl, Scott.isωSup_iff_isLUB, NonemptyFinLinOrd.comp_apply, GroupExtension.Equiv.coe_toMulEquiv, OneHom.coe_coe, NumberField.mixedEmbedding.latticeBasis_apply, QuotientGroup.map_id_apply, Valuation.IsEquiv.eq_one_iff_eq_one, Path.map_coe, RingCon.quotientKerEquivRangeₐ_mkₐ, AddSubmonoid.coe_toSubmonoid_symm_apply, StronglyMeasurable.apply_continuousLinearMap, Polynomial.derivative_prod_finset, Cardinal.isRegular_aleph_one, Subgroup.conjAct_pointwise_smul_eq_self, HasFDerivAt.hasDerivAt, LeftInvariantDerivation.map_sub, Matrix.det_permute', OmegaCompletePartialOrder.Chain.exists_of_mem_map, PartOrdEmb.Hom.le_iff_le, EuclideanGeometry.vsub_orthogonalProjection_mem_direction, ProbabilityTheory.Kernel.boolKernel_true, IsAddFreimanIso.addRothNumber_congr, Matrix.diagonalInvertibleEquivInvertible_symm_apply, MeasureTheory.OuterMeasure.ofFunction_le, CategoryTheory.CountableCategory.instCountableHomObjAsType, Finset.map_singleton, MvPowerSeries.constantCoeff_X, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, ContinuousMap.Homotopy.coe_toContinuousMap, LinearEquiv.apply_symm_apply, Con.congr_mk, smoothSheafCommRing.ι_forgetStalk_hom_assoc, DistribMulAction.toAddEquiv_symm_apply, Finsupp.single_apply_mem, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, Trivialization.preimageSingletonHomeomorph_symm_apply, contMDiff_equivTangentBundleProd, toBoolAlg_inj, SeparationQuotient.normedMk_apply, nnnorm_ofMul, NonUnitalStarAlgHom.mem_equalizer, DistribMulAction.toAddAut_apply, dualTensorHomEquivOfBasis_symm_cancel_left, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span, Sublattice.coe_inclusion, cyclotomicCharacter.toZModPow_toFun, DirectSum.coe_of_mul_apply_of_mem_zero, TwoP.swapEquiv_inverse_map_hom_toFun, MulDistribMulAction.toMulAut_apply, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, MvPolynomial.esymmAlgHom_apply, ContinuousLinearMap.isPositive_iff, LaurentSeries.valuation_coe_ratFunc, MeasureTheory.Measure.addHaar_submodule, MvPolynomial.monomial_eq, DivisibleHull.archimedeanClassOrderIso_apply, TensorProduct.map_tmul, Equiv.boolProdEquivSum_symm_apply, UniformEquiv.isUniformInducing, AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton, Unitization.isUniformEmbedding_addEquiv, MeasureTheory.Content.outerMeasure_opens, UpperSet.map_Ioi, TensorProduct.mapIsometry_apply, GradedTensorProduct.comm_coe_tmul_coe, Trivialization.transFiberHomeomorph_apply, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, Polynomial.isNilpotent_C_iff, MeasurableSet.measure_eq_iSup_isClosed_of_ne_top, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, ValuativeRel.ValueGroupWithZero.embed_mk, Module.Basis.sumQuot_inr, ContinuousMultilinearMap.compContinuousLinearMapL_apply, QuadraticMap.IsometryEquiv.prodComm_toFun, ContinuousMap.Homotopy.apply_zero, CliffordAlgebra.star_algebraMap, Localization.mulEquivOfQuotient_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, ZMod.lift_injective, DilationEquiv.apply_symm_apply, SemilatInfCat.dual_map, addRothNumber_le, signedDist_apply_linear_apply, MeasurableEquiv.coe_addLeft, ContinuousLinearMap.IsInvertible.inverse_apply_self, LinearMap.transvection.det, IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure, Module.Basis.flag_le_iff, Module.Invertible.rTensorEquiv_symm_apply_apply, HasFDerivWithinAt.unique_on, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, VitaliFamily.ae_tendsto_rnDeriv, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, Algebra.left_comm, Complex.selfAdjointEquiv_symm_apply, AddValuation.toValuation_apply, Polynomial.disc_C, DomMulAct.smul_Lp_ae_eq, OrderIso.image_Ioc, CliffordAlgebra.changeForm_algebraMap, QuaternionAlgebra.coe_basisOneIJK_repr, LaurentPolynomial.counit_C_mul_T, AlgHom.addHomMk_coe, TemperedDistribution.fourierInv_apply, MvPolynomial.homogeneousSubmodule_eq_finsupp_supported, CategoryTheory.Limits.Sigma.ι_reindex_inv, MeasureTheory.measure_inter_neg_vadd, MeromorphicOn.extract_zeros_poles, MonoidWithZeroHom.inr_apply_unit, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, MvPolynomial.aeval_eq_eval₂Hom, VectorField.pullbackWithin_eq, Matrix.IsHermitian.cfcAux_id, Submonoid.LocalizationMap.ofMulEquivOfDom_apply, SimpleGraph.Subgraph.spanningCoeEquivCoeOfSpanning_symm_apply, IsometryEquiv.symm_apply_eq, cfcₙAux_mem_range_inr, zmultiplesHom_apply, LinearMap.eqLocus_toAddSubmonoid, QuadraticMap.IsometryEquiv.coe_toLinearEquiv, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, Algebra.TensorProduct.algebraMap_apply', GaussianInt.re_toComplex, TopCat.Presheaf.presieveOfCovering.mem_grothendieckTopology, IsCompact.exists_open_superset_measure_lt_top, DoubleQuot.coe_quotQuotToQuotSupₐ, MeasureTheory.SimpleFunc.integrable_of_isFiniteMeasure, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, Ideal.Quotient.norm_mk_lt, RingEquiv.map_sum, RootPairing.Equiv.weightHom_injective, ContinuousLinearMap.nhds_zero_eq, LinearEquiv.congr_arg, Module.Flat.iff_lift_lsmul_comp_subtype_injective, TopCat.induced_of_isLimit, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, MvPolynomial.vars_C, Algebra.TensorProduct.Algebra.TensorProduct.commRight_symm_tmul, isSemilinearSet_setOf_eq, Monoid.Coprod.swap_eq_one, Algebra.Extension.algebraMap_σ, Subsemiring.mem_map, ContinuousAlternatingMap.constOfIsEmpty_apply, FirstOrder.Language.Equiv.coe_injective, AffineSubspace.coe_inclusion_apply, Equiv.coe_prodUnique, MvPolynomial.rename_prod_mk_eval₂, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Path.extend_symm, LeftInvariantDerivation.map_neg, RootPairing.EmbeddedG2.indexEquivAllRoots_apply_coe, Matrix.mem_glpos, finprod_comp_equiv, FreeMagma.toFreeSemigroup_comp_of, DirectSum.equivCongrLeft_apply, Complex.ofRealHom_eq_coe, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, image_parallelepiped, LocallyConstant.evalₐ_apply, IsValuativeTopology.isClosed_ball, CategoryTheory.Functor.curryingFlipEquiv_apply_map, Differential.deriv_aeval_eq, Shrink.continuousLinearEquiv_symm_apply, RatFunc.liftRingHom_X, Unitary.map_mem, Polynomial.Gal.galActionHom_bijective_of_prime_degree, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, AlgebraicIndependent.aevalEquivField_apply_coe, ContinuousLinearMap.coeLMₛₗ_apply, ZMod.castHom_bijective, AlgebraicGeometry.Scheme.inv_hom_apply, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, CliffordAlgebra.foldr'Aux_apply_apply, ContinuousAlgHom.ext_iff, MvPolynomial.aeval_C, ProbabilityTheory.covarianceBilin_map, AddCircle.continuous_equivIco_symm, MeasurableEquiv.finTwoArrow_symm_apply, Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, Fin.insertNth_comp_cycleRange_symm, linearIndepOn_equiv, NonUnitalNonAssocSemiring.mem_center_iff, MvPolynomial.support_map_subset, IsSimpleRing.injective_ringHom_or_subsingleton_codomain, Affine.Simplex.mongePoint_map, ArithmeticFunction.IsMultiplicative.map_prod, SetTheory.PGame.exists_rightMoves_neg, BoundedContinuousFunction.integral_add_const, Affine.Simplex.centroid_eq_affineCombination, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, FreeAbelianGroup.liftMonoid_coe, LocallyConstant.congr_fun, UniformEquiv.range_coe, FreeMagma.lift_comp_of, Subgroup.toAddSubgroup_comap, ContinuousLinearEquiv.comp_differentiable_iff, MonoidHom.map_finprod_Prop, Affine.Simplex.eulerPoint_map, Nat.factorization_choose_eq_zero_of_lt, HahnSeries.inv_def, CategoryTheory.conjugateEquiv_id, CategoryTheory.Functor.mapAddHom_apply, Subalgebra.LinearDisjoint.basisOfBasisLeft_apply, groupHomology.map_id_comp_H0Iso_hom_apply, AddMonoidHom.coe_mulRight, Padic.coe_withValRingEquiv, IsometryEquiv.toDilationEquiv_apply, MeasurableEmbedding.equivRange_symm_apply_mk, NonUnitalAlgHom.toAlgHom_apply, Polynomial.hasseDeriv_C, Topology.WithGeneratedByTopology.isOpen_iff, Nucleus.iInf_apply, AlgEquiv.quotientBot_symm_mk, frobenius_apply_frobeniusEquiv_symm, Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top, Affine.Simplex.ExcenterExists.touchpoint_restrict, AlgEquiv.val_inv_algHomUnitsEquiv_symm_apply, Unitization.nnnorm_eq_sup, PMF.apply_pos_iff, Path.subpath_continuous_family, Valuation.Integer.not_isUnit_iff_valuation_lt_one, Finsupp.sum_smul_index_semilinearMap', Filter.pureMulHom_apply, MeasureTheory.measure_mono, MvPowerSeries.map_frobenius_expand, SchwartzMap.fourierTransformCLM_apply, QuadraticMap.polar_add_right, HNNExtension.of_injective, OrderAddMonoidHom.coe_comp, AffineSubspace.signedInfDist_singleton, RCLike.norm_sq_eq_def, Equiv.prodAssoc_symm_apply, PMF.toMeasure_apply_eq_of_inter_support_eq, OrderIso.isBoundedUnder_le_comp, zero_mem_lowerBounds_smoothingSeminormSeq_range, Set.OrdConnected.dual, IsDiscreteValuationRing.addVal_eq_top_iff, TruncatedWittVector.zmodEquivTrunc_apply, centralBinom_factorization_small, StarAlgHom.prod_apply, SL_reduction_mod_hom_val, Real.tsum_eq_tsum_fourier_of_rpow_decay, selfAdjointPart_apply_coe, DFinsupp.coe_sub, Metric.Snowflaking.uniformEquiv_symm_apply, AddCon.kerLift_injective, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, MeasureTheory.AddContent.extend_eq_top, DomAddAct.coe_mkHomeomorph_symm, CliffordAlgebra.reverse.map_one, Perfection.coeff_pthRoot, Trivialization.symm_continuousLinearEquivAt_eq, Polynomial.natDegree_linear_le, Circle.surjOn_exp_neg_pi_pi, algebraMap_mem, RingEquiv.ofRingHom_apply, MvPolynomial.toMvPowerSeries_pUnitAlgEquiv, AddMonoidAlgebra.basis_apply, Equiv.subtypeUnivEquiv_symm_apply, AddMonoidHom.vaddZeroHom_apply, CircleDeg1Lift.sup_apply, LieSubmodule.inclusion_apply, Equiv.arrowCongr_comp, ContinuousMap.apply_le_norm, BoxIntegral.Box.Icc_eq_pi, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_inv, LinearEquiv.conj_id, RingHom.coe_mk, IsLocalRing.basisQuotient_apply, AlgEquiv.moduleEndSelfOp_symm_apply, RingHomCompTriple.comp_apply, DFinsupp.linearEquivFunOnFintype_apply, MvPolynomial.transcendental_polynomial_aeval_X, MvPolynomial.pderiv_map, AddMonCat.hom_neg_apply, BoundedContinuousFunction.dist_extend_extend, ProbabilityTheory.iIndepSet_iff, PadicInt.fwdDiff_mahlerSeries, Polynomial.coeff_list_sum, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum', Action.FintypeCat.quotientToQuotientOfLE_hom_mk, skewAdjointPartL_apply_coe, isRightRegular_ofColex, Equiv.Perm.ofSubtype_swap_eq, MeasureTheory.SimpleFunc.coe_div, OrderIso.tendsto_atBot_iff, MeasureTheory.measure_add_lintegral_eq, AlternatingMap.toFun_eq_coe, Monoid.Coprod.snd_apply_inl, AddEquiv.coe_symm_toNatLinearEquiv, MeasureTheory.measure_diff', AlgebraicGeometry.isIso_SpecMap_stakMap_localization, groupHomology.cyclesMk₁_eq, finsuppLequivDFinsupp_apply_apply, StarAlgEquiv.ext_iff, Matrix.IsHermitian.coe_re_diag, uniformity_multiplicative, Module.End.mem_invtSubmodule_iff_forall_mem_of_mem, PowerSeries.exp_pow_eq_rescale_exp, Polynomial.derivation_C, Abelianization.lift_of, DomAddAct.mk_neg, Nat.prod_pow_factorization_choose, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_ae_of_monotone, minpoly_algEquiv_toLinearMap, PrincipalSeg.surjOn, NumberField.mixedEmbedding.fundamentalCone.intNorm_coe, CompactlySupportedContinuousMap.coe_comp_to_continuous_fun, AlgebraicGeometry.Scheme.residue_residueFieldMap_assoc, Orientation.coe_basisRightAngleRotation, NumberField.mixedEmbedding.norm_eq_zero_iff, Homeomorph.toMeasurableEquiv_symm_coe, PointwiseConvergenceCLM.tendsto_nhds_atTop, TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, AddMonoidHom.coe_comp, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, CommRingCat.coyonedaUnique_inv_app_hom_apply, Finset.weightedVSub_apply, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, Polynomial.smeval_monomial, OrderIso.map_ciInf, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, AddConstMapClass.map_int_add', OrderIso.asBoolAlgAsBoolRing_apply, WeierstrassCurve.Jacobian.eval_polynomial, MeasureTheory.ae_const_le_iff_forall_lt_measure_zero, MeasureTheory.AEDisjoint.exists_disjoint_diff, Submodule.FG.lTensor.directLimit_apply, OrderMonoidHom.coe_id, ContinuousMultilinearMap.alternatization_apply_toAlternatingMap, Surreal.dyadicMap_apply, PowerSeries.X_pow_eq, RootPairing.pairing_neg_one_neg_four_iff', PowerBasis.trace_gen_eq_sum_roots, ContinuousAlternatingMap.ext_ring_iff, ModularForm.coe_intCast, Polynomial.natDegree_det_X_add_C_le, continuousAt_sign_of_neg, ofMul_mul, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff, gcd_mul_right, equivShrink_symm_add, Ideal.injective_algebraMap_quotient_residueField, Polynomial.eval_C_X_comp_eval₂_map_C_X, Finsupp.liftAddHom_singleAddHom, MultilinearMap.support_dfinsuppFamily_subset, MeasureTheory.Lp.constL_apply, AdjoinRoot.algHom_subsingleton, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, EquivLike.bijective, Matrix.toBilin'Aux_eq, disjointed_succ, EsakiaHom.ext_iff, ProbabilityTheory.Kernel.borelMarkovFromReal_apply, SchwartzMap.fderivCLM_fourier_eq, AlgEquiv.map_det, TensorProduct.lift.equiv_symm_apply, MeasureTheory.measure_toMeasurable_union, MvPowerSeries.coeff_invOfUnit, BoundedContinuousFunction.star_apply, spectralNorm.eq_of_tower, GroupNormClass.toNormedGroup_norm_eq, MeasureTheory.MeasuredSets.continuous_measure, AddCircle.continuousAt_equivIoc, spectrum.scalar_eq, JoinedIn.somePath_mem, Complex.hasSum_conj', OrderDual.instNeBotNhdsWithinIoi, AlgebraicGeometry.Scheme.IdealSheafData.support_map, MeasureTheory.Measure.FiniteAtFilter.eventually, Pi.coe_evalMonoidHom, List.sortedLT_map_toDual, ProbabilityTheory.Kernel.lintegral_parallelComp_symm, Set.exists_isOpen_le_add, SemimoduleCat.inv_hom_apply, DirectSum.of_apply, LinearEquiv.det_mul_det_symm, CategoryTheory.Bicategory.Adj.Hom₂.conjugateEquiv_τl, Homeomorph.refl_apply, OrderIso.preimage_Ioi, Equiv.psigmaEquivSigmaPLift_apply, Pi.toColex_update_le_self_iff, supClosed_range, SubringClass.subtype_injective, addMonoidHomLequivNat_apply, Bundle.ContinuousRiemannianMetric.pos, Monoid.Coprod.lift_swap, Matrix.one_fin_three, WithCStarModule.equiv_sub, ContinuousLinearEquiv.contDiffOn_comp_iff, Polynomial.toLaurent_one, OrderEmbedding.addLeft_apply, CompactlySupportedContinuousMap.continuousMapEquiv_symm_apply, AffineIsometry.coe_one, Equiv.finsetSubtypeComm_apply_coe, Subgroup.quotientCenterEmbedding_apply, Function.MulExact.iff_of_ladder_mulEquiv, MeasureTheory.SimpleFunc.measurableSet_fiber, Equiv.setOf_apply_symm_eq_image_setOf, Homeomorph.piUnique_symm_apply, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, HasStrictFDerivAt.implicitToPartialHomeomorphOfComplemented_apply, Homeomorph.piEquivPiSubtypeProd_symm_apply, NumberField.norm_embedding_le_house, ContinuousMap.coe_star, AlgebraicIndependent.aevalEquiv_apply_coe, LinearOrderedCommGroupWithZero.fst_apply, TopCat.Presheaf.SheafConditionEqualizerProducts.w_apply, MvPolynomial.esymm_eq_sum_monomial, MonoidAlgebra.mapDomain_one, DirichletCharacter.changeLevel_eq_one_iff, Cardinal.lift_le_aleph_one, Polynomial.homogenize_monomial_of_lt, MeasureTheory.OuterMeasure.comap_boundedBy, Finset.weightedVSubOfPoint_eq_of_sum_eq_zero, AddEquiv.finsuppUnique_symm_apply_support_val, NonUnitalAlgHom.coe_id, MeasureTheory.measurePreserving_piFinsetUnion, Cardinal.toENat_le_natCast_iff, SchwartzMap.derivCLM_apply, aemeasurable_map_equiv_iff, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', AlgebraicGeometry.FormallyUnramified.stalkMap, Matrix.toLin_finTwoProd_toContinuousLinearMap, AlgebraicGeometry.specTargetImageFactorization_app_injective, HasFPowerSeriesOnBall.eventually_hasSum_sub, minpoly.root, NonUnitalRingHom.rangeRestrict_surjective, LightCondensed.ihom_map_val_app, Polynomial.mod_X_sub_C_eq_C_eval, Seminorm.gauge_ball, MvPowerSeries.coeff_map, Finsupp.logHeight_eq_log_mulHeight, HomogeneousLocalization.Away.eventually_smul_mem, WithCStarModule.equiv_snd, SetTheory.PGame.moveLeft_toLeftMovesNim, MeasureTheory.Measure.toBoxAdditive_apply, Set.toENat_cardinalMk, ContinuousMultilinearMap.opNNNorm_le_iff, HahnSeries.addOppositeEquiv_symm_leadingCoeff, ContMDiffSection.ext_iff, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, CoalgHom.coe_fn_injective, ProbabilityTheory.Kernel.measure_le_bound, LieDerivation.leibniz', NumberField.FinitePlace.norm_eq_one_iff_notMem, AlgebraicGeometry.Scheme.IsGermInjectiveAt.cond, AddHom.subsemigroupComap_apply_coe, Equiv.Perm.IsCycle.zpowersEquivSupport_symm_apply, LinearMap.coe_withLpMap, NumberField.canonicalEmbedding_injective, Derivation.map_add, CategoryTheory.Iso.toEquiv_symm_fun, RelIso.emptySumLex_symm_apply, LinearMap.map_add₂, MeasureTheory.SimpleFunc.pow_apply, RCLike.ratCast_im, PowerSeries.monomial_eq_C_mul_X_pow, R_apply, trace_quotient_eq_trace_localization_quotient, Topology.IsEmbedding.homeomorphOfSubsetRange_apply_coe, RootPairing.posRootForm_posForm_nondegenerate, Subrepresentation.subrepresentationSubmoduleOrderIso_symm_apply, UniformOnFun.uniformContinuous_eval_of_mem_sUnion, StandardEtalePair.cond, LieDerivation.map_neg, DirectSum.of_intCast, Function.locallyFinsuppWithin.restrictMonoidHom_apply, Hamming.ofHamming_toHamming, Subalgebra.rTensorBot_symm_apply, CategoryTheory.Abelian.Ext.addEquiv₀_symm_apply, SchwartzMap.isBigO_cocompact_zpow_neg_nat, Equiv.divLeft₀_apply, Equiv.sigmaProdDistrib_symm_apply, IsCoercive.continuousLinearEquivOfBilin_apply, AffineEquiv.apply_eq_iff_eq, AffineMap.ext_linear_iff, MvPolynomial.rename_C, Circle.exp_intCast_mul, LinearMap.toContinuousLinearMap₁_apply, OrderAddMonoidHom.inr_apply, MonoidHom.id_apply, Affine.Simplex.excenterWeightsUnnorm_restrict, Finsupp.toMultiset_sum, OrderIso.leftOrdContinuous, Ideal.Quotient.mk_eq_mk_iff_sub_mem, AlternatingMap.curryLeft_compAlternatingMap, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk, Ideal.quotientEquiv_mk, AddSubmonoidClass.subtype_injective, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom, LinearIsometryEquiv.continuousOn, Shrink.rec_equivShrink, dNext_eq_dFrom_fromNext, HahnSeries.addOppositeEquiv_leadingCoeff, Affine.Simplex.affineCombination_touchpointWeights, DomAddAct.map_mk_nhds, LinearMap.congr_arg, Finsupp.uncurry_apply_pair, Orientation.volumeForm_zero_neg, MeasureTheory.Measure.le_map_apply_image, SmoothPartitionOfUnity.contMDiff_finsum_smul, Submodule.mem_traceDual, TemperedDistribution.fourierTransformCLM_apply, IsometryEquiv.funUnique_symm_apply, BoundedContinuousFunction.nnnorm_coeFn_eq, WeierstrassCurve.Projective.map_dblXYZ, ContinuousLinearEquiv.fderivWithin, AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant, CategoryTheory.Linear.homCongr_symm_apply, ArithmeticFunction.mul_zeta_apply, Seminorm.coe_comp, LinearMap.map_smulₛₗ, mfderiv_comp_apply, HahnSeries.SummableFamily.sum_vAddAntidiagonal_eq, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, DirectSum.GAlgebra.smul_def, Continuous.matrix_reindex, AddMonoidHom.map_addCyclic, TopModuleCat.cokerπ_surjective, Valuation.vlt_one_iff, Equiv.Perm.IsCycle.isCycleOn, LinearMap.domRestrict₂_apply, RelIso.surjective, Unitary.inner_map_map, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist, NumberField.mixedEmbedding.normAtPlace_nonneg, ContinuousMonoidHom.coe_comp, TensorPower.gOne_def, ZMod.dft_const_mul, MvPowerSeries.expand_X, Matrix.toSquareBlockProp_def, CategoryTheory.Adjunction.homAddEquiv_neg, codisjoint_map_orderIso_iff, ProbabilityTheory.Kernel.lintegral_id, Matrix.of_symm_single, AlgHom.commutes, LinearMap.map_lTensor, MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc', FreeMagma.length_toFreeSemigroup, AddConstMapClass.map_nsmul_const, DFinsupp.mem_rangeIcc_apply_iff, TensorPower.one_mul, MulEquivClass.apply_coe_symm_apply, DFinsupp.single_add_erase, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, MvPowerSeries.map_expand, RootPairing.flip_toFun_apply, LinearMap.IsIdempotentElem.mem_range_iff, RCLike.I_mul_re, Multiset.toDFinsupp_injective, VectorField.lieBracketWithin_smul_right, Nat.factorization_prime_le_iff_dvd, AlgHom.subalgebraMap_surjective, Algebra.Extension.Hom.sub_aux, AddSubgroup.subtype_injective, SSet.mem_skeletonOfMono_obj_iff_of_nonDegenerate, MvPolynomial.eval₂_mul_C, Algebra.normalizedTrace_trans_apply, Finsupp.domLCongr_apply, OrderHomClass.coe_coe, SmoothPartitionOfUnity.sum_finsupport, StandardEtalePresentation.aeval_val_equivMvPolynomial, TensorProduct.enorm_map, CategoryTheory.Bicategory.conjugateEquiv_id, LaurentPolynomial.degree_C_ite, PreErgodic.prob_eq_zero_or_one, AddGrpCat.comp_apply, PrincipalSeg.acc, MeasureTheory.FiniteMeasure.prod_apply_symm, Set.Finite.latticeClosure, extremePoints_convexHull_subset, CategoryTheory.GrothendieckTopology.pullback_mem_iff_of_isIso, LinearMap.coe_toAddHom, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, Orientation.areaForm_map, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, AddSubsemigroup.coe_comap, MagmaCat.inv_hom_apply, LieModuleHom.id_apply, Finsupp.embDomain_eq_mapDomain, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_tmul, Perfection.coeff_frobeniusEquiv_symm, IsGroupLikeElem.counit_eq_one, MeasureTheory.volume_measurePreserving_arrowProdEquivProdArrow, AddSubmonoid.inclusion_injective, MulEquiv.opOp_apply, Polynomial.smul_C, Polynomial.derivative_sub, ModuleCat.FreeMonoidal.μIso_inv_freeMk, MulAut.congr_apply, StarMonoidHom.coe_comp, CategoryTheory.Adjunction.homEquiv_symm_id, LinearMap.derivWithin, MeasureTheory.Measure.smul_apply, Module.Basis.localizationLocalization_span, Polynomial.mem_rootSet', AlgHom.congr_fun, ULift.down_algebraMap, SimpleGraph.Embedding.map_apply, IsometryEquiv.constVSub_apply, PowerBasis.exists_gen_dvd_sub, Bialgebra.counit_algebraMap, Units.isClosedEmbedding_embedProduct, Equiv.Perm.VectorsProdEqOne.vectorEquiv_symm_apply, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, TensorProduct.mapOfCompatibleSMul_tmul, inner_gradientWithin_left, LinearIsometryEquiv.congr_fun, RCLike.conj_eq_iff_im, BoundedContinuousFunction.dist_set_exists, Complex.exp_conj, MeasureTheory.measure_inv_smul_inter, AddChar.coe_prod, Algebra.discr_localizationLocalization, DirectSum.mul_eq_sum_support_ghas_mul, Finsupp.coe_lt_coe, Nat.sum_divisors, ContinuousLinearMap.adjoint_comp, MeasureTheory.average_eq', Monoid.Coprod.fst_swap, Equiv.Perm.one_apply, LinearMap.coe_prodMap, affineHomeomorph_image_Ioo, BoundedContinuousFunction.natCast_apply, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, Finset.intervalGapsWithin_fst_of_lt_lt, AddCon.map_apply, Module.End.mem_genEigenspace_one, LieModule.toEnd_eq_zero_iff, FreeAddMonoid.map_symm_apply_map_eq, WithBot.toDualTopEquiv_bot, MeasureTheory.sum_measure_singleton, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd', OrthonormalBasis.adjustToOrientation_apply_eq_or_eq_neg, MultilinearMap.snoc_add, AbsoluteValue.IsEquiv.eq_one_iff, tsupport_fderiv_apply_subset, TopCat.prodIsoProd_hom_apply, isConformalMap_iff, LaurentSeries.valuation_compare, MeasureTheory.OuterMeasure.map_id, FreeGroupBasis.ofFreeGroup_apply, BoundedContinuousFunction.coe_star, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Cardinal.enat_gc, ProbabilityTheory.uniformOn_union, Padic.isUniformInducing_cast_withVal, KaehlerDifferential.derivationTensorProduct_algebraMap, PowerSeries.HasSubst.comp, SubMulAction.SMulMemClass.subtype_apply, Finsupp.prod_ite_eq, MeasureTheory.Content.empty, LinearEquiv.toFun_eq_coe, BoundedContinuousFunction.toReal_lintegral_coe_eq_integral, Equiv.piCongr_symm_apply, Pi.conj_apply, Polynomial.hasStrictDerivAt, Finsupp.range_single_one, PrimeSpectrum.isIdempotentElemEquivClopens_symm_top, DistribSMul.toLinearMap_apply, RingEquiv.coe_prodCongr, AddMonoidAlgebra.mapRangeRingEquiv_apply, pow_ofLex, MvPolynomial.C_neg, Ideal.powQuotSuccInclusion_injective, ContDiff.clm_apply, Equiv.symmEquiv_apply_symm_apply, LinearMap.IsProj.trace, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, MeasureTheory.Measure.ae_measure_lt_top, cfcHomSuperset_id, MvPolynomial.weightedHomogeneousComponent_eq_zero, LinearMap.map_neg₂, supClosed_preimage_toDual, LinearMap.update_apply, map_iSup, Matrix.GeneralLinearGroup.val_map_apply, ContinuousLinearEquiv.isBigO_comp_rev, Matrix.reindex_mem_rowStochastic, ContinuousAddMonoidHom.isClosedEmbedding_coe, RegularWreathProduct.rightHom_eq_right, FrameHom.coe_mk, LinearMap.charpoly_sub_smul, LaurentPolynomial.eval₂_T_neg_n, HahnSeries.support_single_subset, Function.locallyFinsuppWithin.logCounting_mono, Finsupp.extendDomain_toFun, Matrix.single_eq_of_single_single, OrderDual.toDual_eq_top, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_inv_app_hom_coe', deriv_clm_apply, IsAntichain.image_iso_iff, CliffordAlgebra.reverseOp_ι, nucleusIsoSublocale.eq_toSublocale, IsAdjoinRoot.lift_algEquiv, PEquiv.single_apply, ArithmeticFunction.cardFactors_zero, List.formPerm_apply_lt_getElem, AlgHom.bijective, NumberField.IsCMField.complexConj_eq_self_iff, Matrix.matrixOfPolynomials_blockTriangular, AddChar.toAddMonoidHom_apply, LinearMap.surjective, SSet.S.equivElements_apply_snd, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, LinearEquiv.conjRingEquiv_symm_apply_apply, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, AffineSubspace.sSameSide_lineMap_left, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, MvPolynomial.coeToMvPowerSeries.ringHom_apply, Equiv.Perm.mem_cycleFactorsFinset_iff, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X, Equiv.inducedStructure_RelMap, CategoryTheory.Subfunctor.orderIsoSubobject_symm_apply, MultilinearMap.neg_apply, CircleDeg1Lift.ceil_map_map_zero_le, ContinuousMap.coe_coe, AddSubgroup.topEquiv_apply, ContinuousMultilinearMap.ofSubsingleton_apply_apply, AddGroupExtension.Equiv.trans_symm_apply, nnnorm_ofDual, WeierstrassCurve.Jacobian.map_negAddY, IsometryEquiv.coe_mul, Function.ExtendByZero.hom_apply, OrderHom.uliftMap_coe_down, LatticeHomClass.map_inf, AddMonoidHom.map_sub, MeasureTheory.tilted_zero', SubMulAction.inclusion.coe_eq, ofBoolAlg_toBoolAlg, lineMap_le_left_iff_le, Submodule.factor_comp_apply, MeasureTheory.IsTightMeasureSet_iff_exists_isCompact_measure_compl_le, AlgebraicGeometry.Scheme.Pullback.range_fst, Polynomial.Gal.ext_iff, Polynomial.Bivariate.swap_C, FintypeCat.inv_hom_id_apply, SkewMonoidAlgebra.liftNC_single, ContinuousMapZero.coe_sub, TopologicalSpace.gc_generateFrom, NumberField.mixedEmbedding.commMap_apply_of_isReal, IsFractionRing.num_mul_den_eq_num_iff_eq, Finsupp.curryLinearEquiv_apply, Matrix.uniqueAlgEquiv_symm_apply, preordToCat_map, OrderIso.le_symm_apply, AffineEquiv.midpoint_pointReflection_left, Matrix.of_col, Matrix.submatrix_diagonal_embedding, TopHom.dual_apply_apply, Submodule.span_singleton_eq_one_iff, OrderIso.ofHomInv_symm_apply, Algebra.RingHom.adjoin_algebraMap_surjective, ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_right, RelIso.trans_apply, Topology.WithUpperSet.ofUpperSet_inj, Algebra.norm_one_add_smul, MulChar.inv_apply', Specialization.isUpperSet_ofEquiv_preimage, EuclideanGeometry.Sphere.IsTangent.isTangentAt, Rat.infinitePlace_apply, AlgHom.map_coe_real_complex, IsAlgebraic.exists_nonzero_eq_adjoin_mul, AffineMap.lineMap_lineMap_left, isDedekindRing_iff, SemiNormedGrp.coe_id, TensorProduct.AlgebraTensorModule.rTensor_id, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, RootPairing.coxeterWeight_eq_four_iff_not_linearIndependent, Matrix.transposeAlgEquiv_apply, AffineMap.hasStrictDerivAt, Matrix.kroneckerTMulBilinear_apply, Submodule.AddMonoidHom.coe_toIntLinearMap_comap, groupCohomology.mapCocycles₁_comp_i_apply, Function.Embedding.toEquivRange_symm_apply_self, WithCStarModule.norm_equiv_le_norm_pi, TensorProduct.map_map_assoc, QuadraticMap.apply_linearCombination', InnerProductSpace.toLinearMap_rankOne, Ideal.associatesEquivIsPrincipal_mul, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, Matrix.uniqueLinearEquiv_symm_apply, MvPolynomial.coeffs_map, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, KaehlerDifferential.tensorProductTo_surjective, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, SchwartzMap.memLp_top, BumpCovering.eventuallyEq_one', Polynomial.natSepDegree_X_sub_C, Polynomial.coe_normUnit, MeasureTheory.measure_union_neg_vadd, OrderDual.le_toDual, ContinuousLinearMap.adjointAux_inner_right, AddSubgroup.coe_map, MeasurableEmbedding.comap_preimage, Geometry.SimplicialComplex.face_subset_face_iff, MeasureTheory.Measure.le_count_apply, TopCat.comp_app, Finsupp.card_Iic, MonoidHom.inl_strictMono, WittVector.verschiebung_shift, FreeGroup.map.id, ContinuousLinearMap.isCompact_closure_image_coe_of_bounded, RatFunc.algebraMap_apply, smoothingSeminormSeq_bddBelow, AlgebraicGeometry.IsOpenImmersion.iff_stalk_iso, SupBotHom.ext_iff, Equiv.Perm.sameCycle_zpow_left, AlgebraicGeometry.Scheme.Cover.fromGlued_isOpenEmbedding, DomMulAct.mk_mul, UniformEquiv.uniformEquiv_mk_coe, LinearEquiv.sumArrowLequivProdArrow_apply_snd, MvPolynomial.totalDegree_monomial_le, LinearIsometryEquiv.map_eq_zero_iff, MulOpposite.opHomeomorph_symm_apply, Submonoid.leftInvEquiv_symm_eq_inv, ProbabilityTheory.Kernel.setLIntegral_compProd_univ_right, Submodule.quotEquivOfEq_mk, Finset.prod_insertNone, NormedAddCommGroup.toCompl_apply, Quaternion.normSq_neg, ENNReal.orderIsoIicCoe_apply_coe, ofLex_vadd', AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, Nat.factorization_pow_self, SubAddAction.of_fixingAddSubgroupEmpty_mapScalars_surjective, ofAdd_zsmul, Bundle.RiemannianMetric.pos, Set.image_sups, SemimoduleCat.forget_map, QuadraticMap.Anisotropic.eq_zero_iff, WittVector.ghostComponent_frobenius, RingEquiv.piCongrLeft'_symm_apply, DFinsupp.sumAddHom_apply, RingEquiv.toSemilinearEquiv_apply, Tuple.eq_sort_iff', MulChar.ofRootOfUnity_spec, ContinuousLinearEquiv.tsum_eq_iff, UniformOnFun.toFun_sub, MeasureTheory.Measure.IsCondKernel.isProbabilityMeasure, OrderIso.symm_apply_lt, PowerSeries.coeff_divXPowOrder, MvPolynomial.IsHomogeneous.rename_isHomogeneous, MeasureTheory.SimpleFunc.restrict_apply, WithBot.toDual_lt_iff, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, Nat.card_image_equiv, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, MeasureTheory.FiniteMeasure.coeFn_mk, HilbertBasis.repr_self, ContinuousMap.Homotopy.evalAt_affine, Equiv.eq_image_iff_symm_image_eq, SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv, Module.End.mapsTo_maxGenEigenspace_of_comm, groupHomology.mapCycles₂_id_comp_apply, Perfection.lift_apply_apply_coe, ExteriorAlgebra.algebraMap_leftInverse, CircleDeg1Lift.map_int_add, HasStrictFDerivAt.clm_apply, RCLike.conj_re_ax, Algebra.norm_apply, ContinuousAlternatingMap.map_eq_zero_of_not_injective, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, Submodule.image2_subset_map₂, AlgebraicGeometry.Scheme.residue_residueFieldMap, Polynomial.aroots_monomial, Coalgebra.rTensor_counit_comul, Equiv.coe_fn_mk, MeasureTheory.OuterMeasure.isometry_map_mkMetric, TensorProduct.commIsometry_apply, MeasureTheory.Measure.instNeZeroENNRealCoeSetUniv, RingHom.smulOneHom_apply, Algebra.norm_eq_zero_iff', InfTopHom.dual_symm_apply_toFun, Module.Basis.linearMap_apply_apply, Cardinal.extend_function, OrderIso.sumLexIioIci_symm_apply_of_ge, WittVector.polyOfInterest_vars_eq, AlgHom.coe_fn_injective, ContinuousLinearEquiv.coe_toDiffeomorph, Rep.trivial_def, Equiv.permCongr_eq_mul, AlgCat.comp_apply, Equiv.ofPreimageEquiv_apply, Finsupp.optionElim_apply_eq_elim, ContMDiffAt.clm_bundle_apply₂, Convex.convexHull_eq, ArchimedeanClass.lt_of_neg_of_archimedean, finsuppTensorFinsupp_symm_single, Encodable.instTotalPreimageNatCoeEmbeddingEncode'Le, Multiplicative.toAdd_bot, ofLex_smul, BoundedContinuousFunction.coe_ofNormedAddCommGroup, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Polynomial.det_taylorLinearEquiv, Module.Basis.toMatrix_isUnitSMul, addMonoidHomLequivInt_symm_apply, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, exists_smooth_forall_mem_convex_of_local_const, MeasureTheory.SimpleFunc.stronglyMeasurable, MeasureTheory.ProbabilityMeasure.mk_apply, PowerSeries.trunc_one, Matroid.mapEquiv_indep_iff, CliffordAlgebra.ι_mul_ι_comm_of_isOrtho, LinearEquiv.congr_fun, continuousSMul_inducedₛₗ, ContinuousMulEquiv.injective, Ordinal.toPGame_moveLeft, OrderMonoidIso.coe_toEquiv_symm, ContinuousMap.coe_sum, ProbabilityTheory.indepFun_iff_measure_inter_preimage_eq_mul, NonUnitalStarRingHom.coe_toNonUnitalRingHom, CFC.sqrt_eq_cfc, CategoryTheory.FinCategory.objAsTypeToAsType_obj, Pi.evalNonUnitalStarAlgHom_apply, Algebra.IsAlgebraic.algEquivEquivAlgHom_apply, exists_continuousMap_one_of_isCompact_subset_isOpen, continuousMultilinearCurryRightEquiv_symm_apply', map_mul_eq_one, CategoryTheory.Bicategory.conjugateEquiv_symm_iso, Polynomial.derivative_monomial_succ, comp_dualTensorHom, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, Polynomial.resultant_deriv, MeasureTheory.condExpInd_smul', ContinuousLinearMap.isBigO_sub, groupCohomology.cocycles₂_ext_iff, Finsupp.single_le_iff, Compactum.str_hom_commute, Algebra.trace_quotient_eq_of_isDedekindDomain, OrderDual.toDual_lt, QuadraticForm.dualProdProdIsometry_toFun, Equiv.coe_mulRight, MeasureTheory.ProbabilityMeasure.map_apply', HahnSeries.lt_iff, IsometryClass.edist_eq, Polynomial.degree_le_zero_iff, PreTilt.coeff_iterate_frobenius, coe_finsetBasisOfLinearIndependentOfCardEqFinrank, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, UpperHalfPlane.det_J, finSuccEquivLast_symm_none, WeierstrassCurve.Jacobian.map_polynomial, Algebra.Extension.h1Cotangentι_apply, MeasureTheory.Measure.prod_comp_left, map_multiset_ne_zero_prod, Equiv.Perm.IsCycle.swap_mul, ContinuousMulEquiv.trans_apply, Homotopy.prevD_zero_cochainComplex, HahnSeries.C_mul_eq_smul, RingEquiv.zeroRingProd_apply, Finsupp.linearCombination_linearCombination, MeasureTheory.Content.innerContent_of_isCompact, Matrix.toLinearEquivRight'OfInv_apply, Module.End.IsFinitelySemisimple.genEigenspace_eq_eigenspace, ContinuousMonoidHom.range_toContinuousMap, GradedRing.projZeroRingHom'_surjective, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, IsAddFreimanHom.addRothNumber_mono, ArchimedeanClass.mk_le_mk_add_of_archimedean, MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop, ProbabilityTheory.iIndepFun.meas_iInter, Ordinal.preOmega_strictMono, Complex.conj_conj, CircleDeg1Lift.monotone, ContinuousLinearEquiv.continuousAt, Fin2.equivFin_apply, Monoid.Coprod.mk_of_inl, Submodule.coe_subtype, MeasureTheory.L1.setToL1_add_left, Multiplicative.toAdd_le, convexHull_convexHull_union_right, ContinuousMap.Homotopy.prod_apply, Function.Embedding.coeFn_mk, AddAction.stabilizerEquivStabilizer_apply, NonUnitalStarAlgHom.one_apply, Finsupp.mapRange.zeroHom_apply, AlgebraicGeometry.StructureSheaf.stalkAlgebra_map, Pi.ringHom_apply, IntermediateField.set_range_subset, IsAdjoinRoot.algebraMap_apply, OrderHom.symm_dual_comp, AddMonoidHom.surjective_of_card_ker_le_div, hasEigenvalue_toLin'_diagonal_iff, AddMonoidHom.coprod_apply, SchwartzMap.smul_apply, Function.Embedding.injective, ContinuousLinearMap.prodL_apply, Matrix.circulant_single, LinearEquiv.map_smul, ContinuousLinearEquiv.arrowCongrEquiv_apply, RCLike.mul_self_norm, equivTangentBundleProd_eq_tangentMap_prod_tangentMap, hausdorffMeasure_of_dimH_lt, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, AlgebraicGeometry.PresheafedSpace.stalkMap.comp, AdjoinRoot.lift_of, MeasureTheory.inducedOuterMeasure_union_of_false_of_nonempty_inter, AddChar.coe_add, ZMod.toAddCircle_injective, BoundedContinuousFunction.coe_toContinuousMapₐ, SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective, Submonoid.closure_image_isMulIndecomposable_baseOf, ContDiffMapSupportedIn.structureMapLM_zero_injective, LinearMap.surjective_or_eq_zero, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, DirichletCharacter.FactorsThrough.existsUnique, Equiv.Perm.IsCycleOn.zpow_apply_eq, ContinuousLinearMapWOT.continuous_inducingFn, OnePoint.not_continuous_cofiniteTopology_of_symm, Homeomorph.coe_mulRight, ArchimedeanOrder.lt_def, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, AffineIsometryEquiv.ediam_image, Coalgebra.TensorProduct.assoc_symm_tmul, PowerSeries.ext_iff, spectralValue_X_sub_C, StandardEtalePair.aeval_X_g_mul_mk_X, Sylow.coe_subgroup_smul, IsQuotientCoveringMap.homeomorph_comp_iff, Ordinal.principal_opow_omega, LinearEquiv.smul_id_of_finrank_eq_one_apply, FreeMagma.map_of, MvPolynomial.pderiv_inr_universalFactorizationMap_X, PrimeMultiset.coe_coeNatMonoidHom, ContinuousAlternatingMap.norm_ofSubsingleton_id, LinearMap.BilinForm.coe_injective, LinearIsometry.contDiff, RootPairing.algebraMap_coroot'In_apply, DFinsupp.liftAddHom_singleAddHom, Algebra.Extension.cotangentComplex_injective_iff, CochainComplex.HomComplex.Cochain.shiftAddHom_apply, PMF.bernoulli_apply, LinearMap.toMatrix'_toLinearMapₛₗ₂', ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atBot, MeasureTheory.addEquivAddHaarChar_smul_eq_comap, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, Complex.equivRealProdCLM_symm_apply_re, PseudoMetric.symm, RingSeminorm.ext_iff, IsExtrFilter.dual, Finset.Colex.toColex_lt_toColex_of_ssubset, CategoryTheory.ShortComplex.ab_zero_apply, CategoryTheory.FreeGroupoid.functorEquiv_symm_apply, TrivSqZeroExt.fst_map, MeasureTheory.FiniteMeasure.continuous_lintegral_continuousMap, Path.refl_range, Nucleus.idempotent, AdicCompletion.transitionMap_ideal_mk, ClosureOperator.mk₂_apply, LinearMap.BilinForm.smul_right, SetRel.gc_leftDual_rightDual, SSet.stdSimplex.objMk_apply, dvd_normalize_iff, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_integral, Trivialization.continuousLinearMapAt_symmL, AffineMap.continuous_linear_iff, LinearMap.isStarProjection_toContinuousLinearMap_iff, LieEquiv.ofSubalgebras_symm_apply, IsLocalRing.ResidueField.mapAut_apply, DirectSum.coeFnLinearMap_apply, AbsoluteValue.map_pow, Transcendental.aeval, Cardinal.toENat_le_nat, FirstOrder.Language.Hom.map_rel, AffineEquiv.surjective, MvPolynomial.sumAlgEquiv_symm_apply, UpperHalfPlane.sinh_half_dist_add_dist, Manifold.pathELength_eq_lintegral_mfderiv_Icc, Algebra.TensorProduct.tensorTensorTensorComm_tmul, OrderHom.fst_coe, Function.Exact.iff_addMonoidHom_rangeRestrict, Con.lift_mk', RingHom.coe_id, ContinuousMonoidHom.inl_toFun, Monoid.Coprod.snd_toProd, DistLat.coe_id, MeasureTheory.UnifTight.exists_measurableSet_indicator, WithLp.idemFst_apply, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, FinBddDistLat.coe_comp, IsLocalization.map_units, Equiv.restrictPreimageFinset_apply_coe, MvPowerSeries.constantCoeff_expand, ContinuousMap.HomotopyWith.prop, PowerSeries.coeff_X_pow_self, HasFDerivAtFilter.isLittleOTVS, QuadraticAlgebra.norm_def, Rep.MonoidalClosed.linearHomEquiv_hom, Multiplicative.toAdd_strictMono, RatFunc.liftAlgHom_apply, Representation.ofModule_asAlgebraHom_apply_apply, TopCat.pullbackIsoProdSubtype_inv_snd_assoc, Matrix.inv_submatrix_equiv, PowerSeries.trunc_succ, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, ContinuousMap.restrict_apply_mk, WithZeroMulInt.toNNReal_strictMono, Matrix.toLpLin_mul, Lat.hom_inv_apply, CategoryTheory.mateEquiv_vcomp, TopCat.epi_iff_surjective, exists_linearIndependent_algEquiv_apply, MeasurableEquiv.coe_setOf, iteratedDerivWithin_eq_equiv_comp, Unitary.coe_map, Rep.invariantsAdjunction_homEquiv_apply_hom, Traversable.Free.map_eq_map, CategoryTheory.Discrete.addMonoidalFunctor_ε, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, Finset.card_pow_quotient_mul_pow_inter_subgroup_le, CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, MvPolynomial.eval₂_comp, Polynomial.roots_C_mul_X_sub_C, MeasureTheory.measure_limsup_atTop_eq_zero, CompleteSublattice.coe_subtype, LinearMap.rTensor_exact_iff_lTensor_exact, Algebra.GrothendieckAddGroup.lift_apply, QuasispectrumRestricts.nnreal_of_nonneg, SupHom.comp_apply, Ordinal.card_preOmega, TensorAlgebra.equivDirectSum_symm_apply, RatFunc.single_one_eq_pow, MvPowerSeries.coeff_smul, ContinuousAffineMap.contLinear_map_vsub, conjneg_apply, LinearPMap.adjointDomainMkCLMExtend_apply, AddConstMap.coe_mk, InfiniteGalois.restrictNormalHom_continuous, Chebyshev.psi_eq_sum_Icc, MultilinearMap.alternatization_coe, MvPolynomial.weightedHomogeneousComponent_C_mul, List.prod_hom, realPart_imaginaryPart, Equiv.eq_conj, SimpleGraph.boxProdAssoc_symm_apply, AddGroupSeminorm.coe_comp, WeierstrassCurve.map_c₄, AlgEquiv.algebraMap_eq_apply, MvPolynomial.eval₂_pUnitAlgEquiv_symm, MeasureTheory.exists_null_frontiers_thickening, Equiv.sumCompl_symm_apply_neg, List.SortedLE.of_map_toDual, ModularForm.coe_norm, Function.Embedding.setValue_eq_of_ne, QuotientAddGroup.quotientBot_symm_apply, dimH_orthogonalProjection_le, CategoryTheory.Abelian.Ext.postcomp_mk₀_injective_of_mono, Matrix.toLin'_submatrix, ProbabilityTheory.Kernel.traj_map_frestrictLe_apply, TensorProduct.gradedMul_algebraMap, QuaternionAlgebra.imJₗ_apply, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, IsAdjoinRootMonic.coeff_one, Fin.castSuccOrderEmb_apply, Equiv.functionSwap_apply, MulEquiv.toAdditive_symm_apply_symm_apply, MeasureTheory.Measure.MutuallySingular.measure_compl_nullSet, Polynomial.monomial_one_right_eq_X_pow, SeparationQuotient.mkRingHom_apply, iteratedFDerivWithin_two_apply, Multiset.cast_symm_apply_snd, MonCat.coe_id, ClassGroup.exists_mk0_eq_mk0, QuaternionAlgebra.re_swapEquiv_apply, OrderDual.toDual_comp_ofDual, CategoryTheory.Meq.mk_apply, stdSimplex.add_eq_one, NonarchAddGroupNorm.lt_def, orderIsoShrink_apply, AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply, LinearMap.det_conj, AlgebraicGeometry.Scheme.SpecMap_residue_apply, finSumNatEquiv_symm_apply_add_right, Derivation.compAEval_eq, LaurentSeries.tendsto_valuation, finPiFinEquiv_single, galRestrictHom_symm_apply, CategoryTheory.yonedaEquiv_naturality, ContDiffMapSupportedIn.seminorm_postcompLM_le, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, SimpleGraph.Subgraph.spanningHom_apply, Polynomial.revAtFun_eq, MeasureTheory.Measure.restrict_iUnion_apply_ae, MulEquiv.monoidHomCongrRight_apply, SupHom.coe_mk, MeasureTheory.tendsto_measure_of_ae_tendsto_indicator, PowerSeries.continuous_aeval, RingHom.coe_comp, inner_mul_symm_re_eq_norm, CategoryTheory.Adjunction.homEquiv_apply, AlgEquiv.toLinearMap_apply, Finsupp.split_apply, Matrix.separatingLeft_toLinearMap₂_iff, Metric.Snowflaking.image_toSnowflaking_closedBall, BotHom.symm_dual_id, MeasureTheory.Measure.tendsto_IicSnd_atTop, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, ContinuousMultilinearMap.bound, Prod.Lex.toLex_covBy_toLex_iff, Path.id_apply, RingCat.comp_apply, finRotate_last', HahnSeries.SummableFamily.powers_toFun, stdSimplex.image_linearMap, ModuleCat.localizedModuleMap_hom_apply, Derivation.tensorProductTo_tmul, Module.End.mem_maxGenEigenspace, DoubleCentralizer.coe_fst, Rep.hom_comm_apply, RingHom.isIntegralElem_localization_at_leadingCoeff, derivationOfSectionOfKerSqZero_apply_coe, ofDual_sup, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, Equiv.continuous_symm_iff, CongruenceSubgroup.mem_conjGL', MvPolynomial.dvd_C_iff_exists, TopologicalSpace.Opens.coe_comap, GroupSeminorm.coe_le_coe, ContinuousLinearMap.coprod_apply, MeasureTheory.integrableOn_iUnion_of_summable_norm_restrict, HahnModule.of_smul, PowerSeries.map_C, Polynomial.hasseDeriv_apply_one, Finsupp.lift_symm_apply, SemiNormedGrp₁.hom_inv_apply, AdicCompletion.transitionMap_map_mul, Con.lift_coe, MeasureTheory.isZeroOrProbabilityMeasure_iff, RootPairing.ext_iff, MulChar.map_nonunit, ContinuousLinearMap.coe_fst', Matrix.reindex_mem_colStochastic, associated_normalize_iff, SheafOfModules.pushforwardNatTrans_app_val_app, AdjoinRoot.coe_mapAlgEquiv, PseudoMetric.bot_apply, Polynomial.aeval_endomorphism, ContinuousMap.equivBoundedOfCompact_symm_apply, eq_ratCast, ContinuousAlgHom.coe_prodMap', MeasureTheory.SimpleFunc.coe_inf, AddCommGrpCat.HasLimit.lift_hom_apply, Module.End.genEigenspace_div, DirichletCharacter.apply_eq_toArithmeticFunction_apply, OrderEmbedding.subtype_apply, DirectLimit.r_of_le, CompactlyGenerated.isoEquivHomeo_apply, Differential.logDeriv_eq_zero, MvPowerSeries.coeff_zero_X, IncidenceAlgebra.zeta_apply, Orientation.inner_rightAngleRotationAux₁_right, PreTilt.untilt_iterate_frobeniusEquiv_symm_pow, WithTop.top_mem_insertTop, Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eq, RingHom.range_eq_top, Matrix.diagonalInvertibleEquivInvertible_apply, IntermediateField.coe_equivMap_apply, Derivation.map_smul, LinearMap.ringLmapEquivSelf_apply, Submodule.re_inner_starProjection_nonneg, WeierstrassCurve.Affine.CoordinateRing.mk_ψ₂_sq, Module.Flat.iff_rTensor_preserves_injective_linearMapₛ, groupHomology.H2π_comp_map_apply, Equiv.Perm.IsCycleOn.zpow_apply_eq_zpow_apply, Equiv.Perm.ofSubtype_apply_of_not_mem, OrderMonoidHom.fst_apply, CategoryTheory.PreGaloisCategory.evaluation_aut_surjective_of_isGalois, Ordinal.typein_lt_self, Matrix.toLin_toMatrix, LieModule.traceForm_genWeightSpace_eq, BoundedContinuousFunction.mul_apply, PiTensorProduct.lift_comp_map, MeasureTheory.integrableOn_singleton_iff, BoundedContinuousFunction.intCast_apply, AddSubgroup.coe_toSubgroup_apply, edist_ofMul, NumberField.mixedEmbedding.latticeBasis_repr_apply, Homeomorph.shearAddRight_coe, Submodule.adjoint_orthogonalProjection, AntivaryOn.dual_left, Antivary.sum_mul_lt_sum_comp_perm_mul_iff, MulEquiv.punitCoprod_apply, ContinuousMap.HomotopyWith.refl_apply, RingEquiv.op_symm_apply_apply, PontryaginDual.map_apply, OrderIso.inv_apply, CategoryTheory.Iso.self_symm_conj, PartENat.withTopEquiv_zero, TensorProduct.homTensorHomMap_apply, AddSubmonoid.LocalizationMap.ofAddEquivOfDom_comp_symm, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, Valuation.IsEquiv.le_one_iff_le_one, Equiv.subLeft_apply, IntermediateField.mem_adjoin_simple_iff, MeasureTheory.MemLp.im, Submodule.lTensorOne_symm_apply, BoundedContinuousFunction.continuous_eval_const, LinearMap.tensorEqLocus_tmul, exteriorPower.map_comp_ιMulti_family, MultilinearMap.ext_iff, Matrix.isRepresentation.eq_toEnd_of_represents, ModularFormClass.qExpansion_isBigO, Surreal.zero_toGame, ZeroAtInftyContinuousMap.coe_toContinuousMap, BddLat.comp_apply, LaurentPolynomial.antipode_C, Real.fourierChar_apply', UniformEquiv.coe_punitProd, Polynomial.rootMultiplicity_le_iff, sInfHom.symm_dual_comp, Units.toAut_inv, LieModule.traceForm_apply_apply, MeasureTheory.mulEquivHaarChar_smul_eq_comap, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, WithBot.toDual_le_toDual_iff, NumberField.canonicalEmbedding.apply_at, Finsupp.card_Iio, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_symm_apply, Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zero, MulHom.op_apply_apply, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_add_of_squarefree, cross_dot_cross, NonarchAddGroupNorm.ext_iff, RingCon.kerLift_mk, AddMonoidAlgebra.liftNC_one, FreeCommRing.restriction_of, MvPolynomial.mul_monomial_mem_coeffsIn, LinearMap.toMatrix₂_apply, ModuleCat.Hom.hom₂_apply, AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange, AdicCompletion.sumEquivOfFintype_apply, BoundedContinuousFunction.continuous_eval, EuclideanGeometry.reflection_apply', coe_addEquiv_lpPiLp, ChainComplex.fromSingle₀Equiv_apply, SubgroupClass.inclusion_right, Homeomorph.divLeft_symm_apply, RatFunc.mk_one, OrthogonalFamily.sum_projection_of_mem_iSup, surjOn_extremePoints_image, AddEquiv.toAdditive_toMultiplicative_apply, LieAlgebra.IsKilling.finrank_rootSpace_eq_one, CategoryTheory.Limits.IsColimit.equivIsoColimit_symm_apply, SchwartzMap.integral_fourierInv_mul_eq, CategoryTheory.Iso.toIsometryEquiv_invFun, AddMonoidAlgebra.scalarTensorEquiv_symm_single, hasFDerivWithinAt_iff_hasGradientWithinAt, DFinsupp.mk_of_mem, MeasureTheory.OuterMeasure.top_apply', FirstOrder.Language.Term.relabelEquiv_symm_apply, PowerSeries.heval_unit, Multiset.normalize_lcm, Real.fourierIntegral_continuousLinearMap_apply', ContinuousAddEquiv.injective, ContinuousAddMonoidHom.diag_toFun, Multiset.toDFinsupp_le_toDFinsupp, Poly.coe_neg, AddMonoid.End.intCast_def, AlgebraicGeometry.AffineSpace.reindex_appTop_coord, IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe, CategoryTheory.ComposableArrows.opEquivalence_inverse_map, UniformEquiv.symm_apply_apply, InfTopHom.ext_iff, LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra, LinearMap.iterateRange_coe, RootPairing.rootFormIn_self_smul_coroot, Colex.exists, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, Finsupp.smul_eq, DirectSum.liftRingHom_symm_apply_coe, LinearEquiv.smul_def, ContinuousMap.mkD_eq_self, MeasureTheory.Measure.measure_Ioo_pos, MvPolynomial.C_mem_pow_idealOfVars_iff, Filter.pureAddHom_apply, iterate_map_sub, Multiset.toDFinsupp_toMultiset, Module.Basis.ext_elem_iff, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, AddEquiv.coe_toIntLinearEquiv, ofDual_sub, Equiv.setCongr_apply, ContinuousAffineMap.differentiableOn, ContinuousLinearMap.hasFDerivAt_of_bilinear, DomAddAct.coe_mkHomeomorph, ContinuousAffineMap.coe_continuousMap_mk, Set.preimage_equiv_eq_image_symm, CondensedMod.epi_iff_locallySurjective_on_compHaus, cfcₙHom_continuous, ContinuousLinearMap.comp_lsmul_flip_apply, LocallyConvexSpace.induced, AddEquiv.addSubgroupCongr_symm_apply, ContinuousAlternatingMap.neg_apply, FundamentalGroupoid.map_obj_as, Continuous.lineMap, Homeomorph.homeomorphOfUnique_apply, Submodule.tensorToSpan_apply_tmul, NonUnitalStarAlgHom.mem_range, MeasureTheory.MemLp.exists_boundedContinuous_eLpNorm_sub_le, SSet.OneTruncation₂.ofNerve₂.natIso_inv_app_map, AbsoluteValue.map_sub, ContinuousLinearEquiv.prodUnique_apply, TopologicalSpace.IrreducibleCloseds.equivSubtype'_apply, CompactlySupportedContinuousMap.lt_def, Complex.mul_conj, OrderIso.isMax_apply, LinearMap.adjoint_comp, LieDerivation.add_apply, AlgHom.toRingHom_op, AlgebraicGeometry.Scheme.Hom.mem_smoothLocus, ContinuousLinearEquiv.trans_apply, MonCat.FilteredColimits.colimit_mul_mk_eq, ofColex_eq_one, Finset.Colex.toColex_image_ofColex_strictMono, ContinuousAlternatingMap.opNorm_le_iff, SubMulAction.ofFixingSubgroup_of_singleton_bijective, RatFunc.algebraMap_injective, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, contDiffOn_succ_iff_fderiv_apply, Ideal.quotientInfToPiQuotient_mk', SubsemiringClass.subtype_apply, Cardinal.cast_toNat_of_lt_aleph0, Cardinal.toNat_eq_zero, OmegaCompletePartialOrder.Chain.map_coe, LieIdeal.mem_comap, LinearMap.intrinsicStar_apply, RootPairing.Equiv.weightEquiv_symm_weightMap, PolynomialModule.comp_eval, Module.Basis.ofVectorSpace_apply_self, MeasureTheory.measure_ball_lt_top, LinearMap.ofIsCompl_left_apply, Equiv.Perm.OnCycleFactors.toPermHom_apply, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two, Module.Basis.toMatrix_reindex, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, RootPairing.corootForm_self_smul_root, LieAlgebra.of_symm_zero, EuclideanGeometry.oangle_self_orthogonalProjection, FiniteField.unitsMap_norm_surjective, PiToModule.fromMatrix_apply, gaussSum_pow_eq_prod_jacobiSum, ArithmeticFunction.cardDistinctFactors_one, isIntegrallyClosed_iff, RootPairing.exists_form_eq_form_and_form_ne_zero, MeasureTheory.Measure.support_eq_sInter, ContinuousAffineMap.norm_comp_le, MulActionHom.snd_apply, MeasurableEquiv.measurableSet_preimage, SymmetricAlgebra.algHom_surjective, AlgebraicGeometry.ΓSpec.adjunction_homEquiv_symm_apply, Matrix.charmatrix_map, Trivialization.pullback_symm_apply_proj, quadraticChar_sq_one', MeasureTheory.measure_sUnion₀, Polynomial.surjective_toFn, PartitionOfUnity.le_one, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, Equiv.sumArrowEquivProdArrow_apply_fst, signedDist_right_lineMap, AddLocalization.addEquivOfQuotient_addMonoidOf, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalizedModule_of_mem, RelIso.image_eq_preimage_symm, SemilatInfCat.Iso.mk_hom_toFun, RingHom.surjective_respectsIso, ProbabilityTheory.IsRatCondKernelCDFAux.isRatStieltjesPoint_ae, Algebra.baseChange_lmul, KaehlerDifferential.mvPolynomialBasis_repr_D, Polynomial.modByMonic_X, IsDedekindDomain.primesOverEquivPrimesOver_symm_apply, QuadraticForm.tensorAssoc_apply, Complex.nndist_conj_comm, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, finSuccEquiv'_symm_coe_below, Matrix.empty_mul, MeasureTheory.measure_symmDiff_eq, StieltjesFunction.measure_Ioc, TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap, FiniteGrp.ofHom_apply, PEquiv.mem_single, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, LocallyConstant.div_apply, WeakDual.gelfandTransform_apply_apply, MeasureTheory.eLpNorm_indicator_const', SymAlg.unsym_eq_one_iff, PEquiv.mem_ofSet_iff, AddChar.toMonoidHomEquiv_symm_mul, RootPairing.coroot'_reflection, Monoid.PushoutI.NormalWord.of_smul_eq_smul, Submonoid.LocalizationMap.ofMulEquivOfLocalizations_eq_iff_eq, LieModuleHom.coe_zero, algebraicIndependent_equiv, UniformFun.toFun_add, NonUnitalRingHom.coe_mul, CategoryTheory.GrothendieckTopology.covering_iff_covers_id, OpenPartialHomeomorph.MDifferentiable.mfderiv_injective, LinearMap.toContPerfPair_apply, LieDerivation.congr_fun, ArithmeticFunction.carmichael_eq_exponent', MonomialOrder.sPolynomial_monomial_mul', AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, Submonoid.LocalizationMap.lift_left_inverse, MonoidAlgebra.liftNC_smul, NonUnitalSubsemiring.centerToMulOpposite_apply_coe, RootPairing.neg_coroot_mem, LinearMap.IsPositive.inner_nonneg_right, ProbabilityTheory.Kernel.finset_sum_apply, Metric.Snowflaking.image_ofSnowflaking_emetricClosedBall, Matrix.toEuclideanLin_apply_piLp_toLp, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, MeasureTheory.tendsto_diracProbaEquivSymm_iff_tendsto, DomAddAct.mk_vadd_mk_aeeqFun, ArchimedeanClass.mk_sub_pos_iff, CuspForm.IsGLPos.smul_apply, HahnSeries.coeff_toMvPowerSeries, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_apply, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, WeierstrassCurve.Affine.CoordinateRing.basis_zero, IsUpperSet.null_frontier, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, fixingAddSubgroup_fixedPoints_gc, MeasureTheory.IsFundamentalDomain.measure_eq_card_smul_of_smul_ae_eq_self, Module.AEval.of_aeval_smul, MeasureTheory.OuterMeasure.ofFunction_eq, Ideal.Quotient.mk_eq_mk, Equiv.Set.insert_apply_right, LocallyConstant.coe_injective, AddMonoidHom.closure_preimage_le, Finset.Ico_orderDual_def, Prefunctor.symmetrifyCostar, OrderEmbedding.coe_ofIsEmpty, Finset.insertNone_nonempty, Equiv.sigmaSigmaSubtypeEq_symm_apply, CategoryTheory.Bicategory.conjugateEquiv_mateEquiv_vcomp, MultilinearMap.map_sum_finset, ContinuousAlternatingMap.map_piecewise_add, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, Finsupp.restrictSupportEquiv_symm_single, RCLike.realRingEquiv_apply, Matrix.trace_fin_three_of, DividedPowers.DPMorphism.coe_toRingHom, LinearMap.dualMap_apply, LinearMap.ker_le_iff, MeasureTheory.SimpleFunc.simpleFunc_bot, monovary_toDual_left, MeasurableEquiv.symm_comp_self, LieModule.Cohomology.twoCochain_val_apply, Algebra.mem_ideal_map_adjoin, AddMonoid.Coprod.fst_surjective, Real.differentiable_fourierChar, Path.extend_zero, MeasureTheory.SimpleFunc.norm_approxOn_zero_le, Lagrange.interpolate_empty, LaurentSeries.coe_range_dense, Path.source, X_pow_sub_C_irreducible_of_prime_pow, InnerProductSpace.inner_gramSchmidtOrthonormalBasis_eq_zero, MonoidAlgebra.mapDomainRingEquiv_apply, Equiv.bijOn_symm, finSuccAboveEquiv_apply, LinearIsometry.norm_map', ModuleCat.AlternatingMap.ext_iff, Homotopy.comm, MeasureTheory.FiniteMeasure.prod_prod, Algebra.algebraMap_intNorm_of_isGalois, Field.Emb.Cardinal.iSup_adjoin_eq_top, LocallyConstant.coe_inv, iteratedWreathToPermHomInj, NumberField.AdeleRing.algebraMap_fst_apply, AddMonoidAlgebra.of_injective, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, Algebra.isEpi_iff_surjective_algebraMap_of_finite, MeasureTheory.Measure.infinitePi_cylinder, RelIso.sumLexComplLeft_apply, Metric.Snowflaking.edist_ofSnowflaking_ofSnowflaking, LinearMap.isSelfAdjoint_iff_map_star, Polynomial.mem_aroots, Polynomial.integralNormalization_mul_C_leadingCoeff, SubAddAction.inclusion.coe_eq, WeierstrassCurve.Affine.Point.map_some, toWellOrderExtension_strictMono, map_eq_zero_iff_eq_zero, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, InitialSeg.isSuccLimit_apply_iff, ContinuousMap.Homotopy.extend_zero, MvPolynomial.pderiv_eq_zero_of_notMem_vars, FiniteArchimedeanClass.coe_congrOrderIso_apply, Multiset.toDFinsupp_singleton, ContinuousAffineEquiv.preimage_image, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_snd, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, nonZeroDivisorsEquivUnits_apply, MulEquiv.toAdditive_apply_symm_apply, OrderRingHom.coe_orderMonoidWithZeroHom_apply, MeasureTheory.projectiveFamilyFun_congr, WittVector.map_frobeniusPoly, BoundedContinuousFunction.coe_nsmul, TensorAlgebra.ι_inj, bernsteinPolynomial.derivative_succ, ContinuousMap.nsmul_apply, sSupHom.symm_dual_comp, LinearMap.dualMap_surjective_iff, multilinearCurryLeftEquiv_symm_apply, Finset.attach_affineCombination_of_injective, MeasureTheory.Measure.comp_smul, Nat.nth_eq_orderEmbOfFin, ClassGroup.mk0_surjective, CompleteLatticeHomClass.map_sSup, BoundedContinuousFunction.bounded, Nat.factorization_eq_card_pow_dvd, ZMod.expand_card, Finsupp.prod_fintype, Homeomorph.coe_toHomotopyEquiv, SimpleGraph.UnitDistEmbedding.copy_p_apply, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd, MeasureTheory.lintegral_le_meas, Equiv.Perm.closure_cycle_adjacent_swap, map_intCast_smul, AddAut.mulLeft_apply_apply, Algebra.SubmersivePresentation.aevalDifferentialEquiv_apply, RCLike.mul_im, Matrix.trace_permutation, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, MeasureTheory.Measure.Regular.map, MvPolynomial.sum_eval_eq_zero, Equiv.boolProdNatEquivNat_symm_apply, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', ProbabilityTheory.Kernel.compProd_assoc, AddGroupSeminorm.le_def, PrincipalSeg.map_isSuccLimit, Submodule.starProjection_orthogonal_apply_eq_zero, Localization.mkHom_apply, groupCohomology.cochainsMap_f_hom, DFinsupp.toColex_monotone, VectorFourier.fourierPowSMulRight_apply, cfcₙHomSuperset_continuous, Equiv.Perm.ofSubtype_injective, skewAdjointPart_eq_I_smul_imaginaryPart, FirstOrder.Language.Hom.range_coe, Units.coeHom_apply, AlgEquiv.smul_units_def, MultilinearMap.piLinearMap_apply_apply_apply, extDeriv_apply_vectorField_of_pairwise_commute, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, CategoryTheory.Iso.conjAut_hom, finsuppTensorFinsuppRid_apply_apply, SimpleGraph.Iso.mapNeighborSet_symm_apply_coe, CategoryTheory.Iso.homCongr_symm_apply, ProbabilityTheory.setLIntegral_condKernel_eq_measure_prod, OrderIso.compl_apply, Module.Basis.repr_sum_self, WittVector.constantCoeff_wittZSMul, NormedSpace.expSeries_eq_expSeries_rat, HahnSeries.coeff.linearMap_apply, BumpCovering.nonneg, LinearEquiv.piFinTwo_apply, WeierstrassCurve.Jacobian.polynomialX_eq, TensorProduct.toLinearMap_symm_lid, LinearIsometry.coe_mul, WithTop.ofDual_lt_iff, GrpCat.ext_iff, CategoryTheory.ComposableArrows.arrowEquiv_apply, SkewMonoidAlgebra.erase_single, Complex.inv_im, CoheytingHom.toFun_eq_coe, Ordinal.toNatOrdinal_natCast, TensorAlgebra.ι_eq_zero_iff, IsLocalization.injective_iff_isRegular, MvPolynomial.aeval_C_comp_left, Subalgebra.LinearDisjoint.linearIndependent_left_of_flat_of_commute, MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction, LinearMap.rTensor_comp_apply, RootPairing.Base.toWeightBasis_repr_root, Equiv.prod_assoc_preimage, finsuppEquivDFinsupp_symm_apply, NormedAddGroupHom.lipschitz, Metric.Snowflaking.preimage_ofSnowflaking_eball, ProbabilityTheory.Kernel.compProd_def, ContinuousAlternatingMap.prodLIE_apply, Matrix.invertibleEquivDetInvertible_apply, ContMDiffWithinAt.clm_apply, RootPairing.GeckConstruction.ωConj_mem_of_mem, MvPolynomial.C_mul_X_pow_eq_monomial, groupCohomology.coboundaries₁_ext_iff, BoxIntegral.Box.coe_subset_Icc, IsometryEquiv.coe_symm_toEquiv, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, AbsoluteValue.map_prod, Rat.int_algebraMap_surjective, Equiv.coe_piCongr_symm, Finsupp.linearCombination_option, SMulMemClass.subtype_injective, OrderHom.curry_symm_apply, Padic.rat_dense', LinearMap.mulLeftRight_apply, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, HahnSeries.coeff_mul_single, PerfectionMap.surjective, ENat.map_add, Matrix.reindexAlgEquiv_apply, AddMonoid.Coprod.map_apply_inl, ContinuousAddEquiv.eq_symm_apply, Hamming.toHamming_zero, AddEquiv.coe_toEquiv, MultilinearMap.toFun_eq_coe, ContinuousLinearMap.coe_restrictScalars', Polynomial.iterate_derivative_X_sub_pow_self, Manifold.IsImmersionAtOfComplement.writtenInCharts, PowerSeries.intValuation_X, MeasureTheory.measure_le_integral_pos, Equiv.Perm.equivUnitsEnd_symm_apply_symm_apply, Path.coe_toContinuousMap, Algebra.traceMatrix_of_matrix_mulVec, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, Complex.conj_natCast, FreeCommRing.map_of, Equiv.coe_optionSubtype_apply_apply, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, QuadraticMap.associated_sq, Polynomial.derivativeFinsupp_one, LinearIsometry.inl_apply, LinearMap.dualMap_def, Finset.image_inv, Polynomial.X_dvd_sub_C, ProbabilityTheory.posterior_id, polarCoord_apply, SimpleGraph.mk'_apply_adj, MultilinearMap.coe_currySumEquiv, AffineEquiv.pointReflection_self, IsAdjoinRoot.map_self, Algebra.leftMulMatrix_mulVec_repr, MultilinearMap.uncurrySum_apply, DirectSum.coe_mul_of_apply, iSupIndep_iff_dfinsupp_lsum_injective, SchwartzMap.decay, ContinuousLinearEquiv.comp_continuous_iff, Equiv.prod_assoc_symm_image, image_extremePoints, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, MeasureTheory.addContent_sUnion_le_sum, ContinuousMulEquiv.refl_apply, MeasureTheory.FiniteMeasure.map_apply', WithCStarModule.inner_single_left, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, MvPowerSeries.order_monomial, LinearIsometryEquiv.comp_hasFDerivAt_iff', ExteriorAlgebra.map_apply_ιMulti, MeasureTheory.measure_union, NonUnitalStarRingHom.coe_one, MeasureTheory.lintegral_insert, IsLocalization.mapₐ_coe, SSet.nonDegenerateEquivOfIso_apply_coe, SSet.S.le_iff_nonempty_hom, MonoidHom.eval_apply_apply, MeasurableEquiv.coe_toEquiv_symm, Polynomial.eval_mul_X_sub_C, MeasureTheory.Measure.hausdorffMeasure_apply, ContinuousMultilinearMap.domDomCongrEquiv_apply, ContinuousMap.Homotopy.map_one_left, AddCircle.continuousAt_equivIco, RootPairing.toPerfPair_conj_reflection, NormedAddGroupHom.coe_id, QuadraticMap.associated_comp, PartENat.withTopEquiv_symm_le, RCLike.normSq_div, AlgebraicGeometry.Proj.stalkIso'_germ, AddMonoidHom.addCommute_inl_inr, RCLike.im_sq_le_normSq, ContinuousLinearMap.isBoundedLinearMap, LinearEquiv.ofSubsingleton_symm_apply, MeasureTheory.Conservative.measure_mem_forall_ge_image_notMem_eq_zero, DirectSum.mul_eq_dfinsuppSum, Finpartition.IsEquipartition.exists_partsEquiv, SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective, factorization_eq_count, ModularForm.coe_add, Nat.factorization_factorial_mul_succ, MvPolynomial.weightedHomogeneousComponent_mem, minpolyDiv_spec, Real.continuous_fourierChar, segment_eq_image_lineMap, AddConstEquiv.coe_toEquiv, Dilation.diam_range, TensorProduct.tmul_of_gradedMul_of_tmul, ContinuousLinearMap.opNorm_le_iff_lipschitz, Submonoid.LocalizationMap.mulEquivOfMulEquiv_mk', Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero, IsDiscreteValuationRing.addVal_eq_zero_of_unit, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, Matrix.det_matrixOfPolynomials, Ergodic.mem_extremePoints_measure_univ_eq, SubringClass.subtype_apply, MonoidWithZeroHom.fst_inr_apply_of_ne_zero, MvPolynomial.degrees_rename_of_injective, cyclotomicCharacter.spec, AbsoluteValue.not_isNontrivial_apply, Finsupp.supportedEquivFinsupp_symm_apply_coe, Metric.Snowflaking.uniformContinuous_toSnowflaking, FourierTransform.fourierCLE_symm_apply, MeasureTheory.left_measure_le_of_levyProkhorovEDist_lt, AffineMap.lineMap_continuous_uncurry, Dual.apply_one_mul_eq, RingCon.lift_mk', finSuccEquiv'_succAbove, continuousAt_sign_of_pos, ContMDiffMap.mdifferentiableAt, AlgebraicGeometry.Scheme.Pullback.Triplet.Spec_ofPointTensor_SpecTensorTo, AlgHom.restrictScalars_apply, DirichletCharacter.not_LSeriesSummable_at_one, NumberField.mixedEmbedding.normAtPlace_negAt, AddMonoidHom.coe_single, PadicInt.mahlerEquiv_apply, CategoryTheory.Arrow.cechNerve_map, sSupHom.setImage_toFun, Complex.nndist_conj_conj, Polynomial.reverse_C, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, Submodule.reflection_involutive, MeasureTheory.Measure.map_const, CommMonCat.id_apply, SchwartzMap.convolution_flip, OrderHom.prodₘ_coe_coe_coe, CuspForm.sub_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, MonoidAlgebra.curryAlgEquiv_symm_single, QuadraticMap.associated_isOrtho, ProbabilityTheory.Kernel.measure_eq_zero_or_one_or_top_of_indepSet_self, NonUnitalRingHom.coe_comp_addMonoidHom, QuadraticMap.polar_sub_left, Lagrange.eq_interpolate_of_eval_eq, Cardinal.aleph1_eq_lift, MeasureTheory.L1.norm_setToL1_le_mul_norm, ContinuousAlternatingMap.coe_toContinuousMultilinearMap, Dilation.diam_image, LinearEquiv.toSpanNonzeroSingleton_one, Submodule.lTensorOne'_one_tmul, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', IsUpperSet.image, RingHom.restrict_apply, ofColex_sub, RingHom.comp_apply, iSupIndep_map_orderIso_iff, Fin.orderIsoSubtype_symm_apply, Module.Basis.self_mem_flag, Subgroup.quotientiInfSubgroupOfEmbedding_apply, ModularFormClass.bdd_at_cusps, AddEquiv.ext_int_iff, CircleDeg1Lift.coe_toOrderHom, Polynomial.Splits.C_mul, Subsemiring.topEquiv_symm_apply_coe, LieRinehartAlgebra.Hom.map_smul_apply, PMF.bindOnSupport_eq_zero_iff, Module.Basis.parallelepiped_map, IsLocalMaxOn.fderivWithin_eq_zero, Subgroup.mem_strictPeriods_iff, LinearMap.mem_graph_iff, LinearMap.BilinForm.dualSubmodule_flip_dualSubmodule_of_basis, Field.finSepDegree_eq, Set.uIoo_ofDual, Polynomial.cardPowDegree_nonzero, cfcₙ_apply_pi, AlternatingMap.measure_def, RingEquiv.sumArrowEquivProdArrow_apply, Polynomial.toFinsuppIsoAlg_apply, ContinuousMap.Homotopy.apply_one, Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, MeasureTheory.maximal_ineq, LinearIsometryEquiv.comp_continuousOn_iff, Polynomial.reflect_C, nnnormHom_apply, Matrix.of_row, Polynomial.eval₂_C, PowerBasis.liftEquiv'_apply_coe, ProbabilityTheory.IsRatCondKernelCDFAux.nonneg', ProbabilityTheory.Kernel.IsProper.setLIntegral_inter_eq_indicator_mul_setLIntegral, TruncatedWittVector.coeff_truncate, abelianizationCongr_of, MeasureTheory.charFunDual_dirac, CliffordAlgebra.contractLeft_mul_algebraMap, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, LinearMap.coe_quotientInfToSupQuotient, ContinuousLinearMap.precompCompactConvergenceCLM_apply, AbsoluteValue.sub_le, MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight, DFA.accepts_reindex, Monoid.CoprodI.Word.prod_rcons, MvPolynomial.eval_C, map_dualTensorHom, VectorField.mpullbackWithin_apply, DirectSum.coe_mul_apply_eq_dfinsuppSum, LinearMap.isSymmetric_iff_sesqForm, MvPolynomial.IsWeightedHomogeneous.C_mul, CategoryTheory.Sheaf.ΓHomEquiv_naturality_right, CircleDeg1Lift.units_semiconj_of_translationNumber_eq, MeasureTheory.addContent_accumulate, MulSemiringAction.toAlgAut_apply, MeasureTheory.distribHaarChar_eq_div, Module.Basis.smulTower_repr_mk, LatticeHom.birkhoffFinset_injective, Cubic.equiv_apply_coe, MvPolynomial.mapAlgHom_apply, HNNExtension.NormalWord.unitsSMulEquiv_symm_apply, Polynomial.taylor_zero, Subspace.dualLift_injective, Algebra.Generators.cotangentRestrict_mk, minpoly.coe_equivAdjoin, Nat.factorization_ordCompl, QuotientAddGroup.map_mk, ContinuousLinearMap.IsPositive.adjoint_conj, Finsupp.liftAddHom_apply_single, AffineMap.prodMap_apply, LinearEquiv.prodAssoc_apply, ContinuousLinearMap.coe_snd', DomMulAct.stabilizerEquiv_invFun_eq, Polynomial.comp_zero, MultilinearMap.curryMidLinearEquiv_symm_apply, Polynomial.toMatrix_sylvesterMap, CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply, EisensteinSeries.G2_eq_tsum_cexp, Commute.map, MonoidHom.inr_strictMono, isAddLeftRegular_ofMul, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc, Finsupp.supportedEquivFinsupp_apply_support_val, AffineSubspace.WOppSide.map, GradedAlgebra.proj_apply, LinearMap.smulRightₗ_apply_apply, SubMulAction.fixingSubgroupEquivFixingSubgroup_coe_apply, NatOrdinal.toOrdinal_one, CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.comp, Representation.toCoinvariants_mk, Ideal.coe_piOrderIso_symm_apply, TopologicalSpace.Fiber.sigmaIsoHom_surj, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, ArchimedeanClass.mk_le_add_mk_of_archimedean, ContinuousMapZero.mkD_apply_of_continuous, toDual_bihimp, Module.DualBases.finite, GroupSeminorm.le_def, Subgroup.mem_map, CategoryTheory.map_yonedaEquiv, MvPolynomial.optionEquivLeft_monomial, RootPairing.Base.coroot_mem_or_neg_mem, Complex.isometryOfOrthonormal_apply, IsAdjoinRootMonic.modByMonicHom_root, GroupLike.val_inv_toUnits_apply, RingHom.map_geom_sum₂, Ordinal.relIso_enum', CircleDeg1Lift.le_iterate_pos_iff, finsuppLequivDFinsupp_symm_apply, Bialgebra.comul_pow, Algebra.TensorProduct.equivPiOfFiniteBasis_symm_apply, NonUnitalStarAlgHom.coe_prod, IncidenceAlgebra.toFun_eq_coe, DilationEquiv.refl_apply, coe_toLexMulEquiv, nndist_lineMap_lineMap, Heyting.Regular.toRegular_coe, dNext_eq, Finsupp.lsum_comp_lsingle, Shrink.continuousLinearEquiv_apply, Metric.Snowflaking.image_toSnowflaking_closedEBall, BddOrd.hom_inv_apply, IsCompactOperator.comp_clm, OrderIso.sumAssoc_symm_apply_inr_inr, Submodule.IsCompl.projection_eq_self_sub_projection, RatFunc.ofFractionRing_eq, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, AddLocalization.addEquivOfQuotient_symm_addMonoidOf, AffineEquiv.coe_ofEq_apply, OrderIso.rightOrdContinuous, Matrix.of_symm_apply, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, ProbabilityTheory.Kernel.iIndep.ae_isProbabilityMeasure, Finsupp.lex_lt_iff, LinearMap.IsRefl.eq_iff, MeasureTheory.Measure.count_apply_finite', CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_s, TensorProduct.AlgebraTensorModule.lTensor_one, SchwartzMap.laplacian_eq_sum, WeierstrassCurve.Projective.map_addU, List.sortedGE_map_toDual, CategoryTheory.eHomEquiv_comp, MonoidWithZeroHom.mem_valueGroup_iff_of_comm, AlgebraicGeometry.Scheme.mem_basicOpen_top, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, Polynomial.reflect_C_mul, TensorProduct.finsuppRight_symm_apply_single, tendsto_measure_Icc_nhdsWithin_right', Algebra.IsAlgebraic.algEquivEquivAlgHom_symm_apply, Matrix.dualNumberEquiv_apply, MonoidHom.ext_mnat_iff, SchwartzMap.lineDerivOp_apply_eq_fderiv, ContinuousMultilinearMap.map_sum_finset, supClosure_infClosure, Circle.normSq_coe, SimpleGraph.Iso.sumAssoc_apply, OrderIso.subLeft_symm_apply, toAdd_div, OrderAddMonoidHom.fstₗ_apply, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpen, MeasureTheory.Measure.sub_apply_eq_zero_of_isHahnDecomposition, CliffordAlgebra.toProd_one_tmul_ι, AlgEquiv.opComm_symm_apply_apply, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular, TensorProduct.gradedComm_one_tmul, RestrictedProduct.neg_apply, conformalFactorAt_inner_eq_mul_inner, Matrix.separatingRight_toBilin'_iff, MeasureTheory.SimpleFunc.aemeasurable, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, MonCat.val_inv_units_map_hom_apply, Ideal.finite_setOf_absNorm_le, measure_Ico_lt_top, MeasureTheory.Measure.dirac_apply, LieModule.maxGenEigenSpace_toEnd_eq_top, CommRingCat.coyonedaUnique_hom_app_hom_apply, MeasureTheory.OuterMeasure.IsMetric.finset_iUnion_of_pairwise_separated, toUnits_symm_apply, MeasureTheory.exists_measurable_superset_forall_eq, AlgEquiv.moduleEndSelf_symm_apply, IsometryEquiv.eq_symm_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp_assoc, AddSubgroup.quotientEquivProdOfLE'_apply, ContinuousMap.coe_div, Rat.AbsoluteValue.eq_on_nat_iff_eq, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply, LinearMap.vecEmpty₂_apply, WittVector.mapFun.intCast, MvPowerSeries.substAlgHom_monomial, Trivialization.coe_coordChangeL, Polynomial.derivative_neg, ArchimedeanClass.FiniteResidueField.mk_lt_mk, Representation.IsTrivial.out, groupCohomology.π_comp_H2Iso_hom_apply, LinearIsometryEquiv.withLpProdUnique_apply, CoalgEquiv.trans_symm_apply, UniformOnFun.isClosed_setOf_continuous, Composition.disjoint_range, RCLike.conj_to_real, AlgebraicGeometry.Scheme.Opens.range_ι, RootPairing.InvariantForm.apply_root_root_zero_iff, DFinsupp.mk_apply, UniformEquiv.bijective, NonemptyInterval.subset_coe_map, Finset.symInsertEquiv_apply_snd_coe, PointwiseConvergenceCLM.tendsto_iff_forall_tendsto, DFinsupp.coe_finset_sum, BoxIntegral.integral_const, SimpleGraph.Walk.map_cons, TensorProduct.prodRight_tmul, AlgebraicGeometry.IsAffineOpen.range_fromSpec, FiniteField.frobeniusAlgEquiv_apply, NumberField.mixedEmbedding.normAtPlace_smul, IsometryEquiv.injective, Subgroup.orderIsoCon_symm_apply_coe, Polynomial.coeff_homogenize, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, ClosureOperator.closure_inf_le, Algebra.Presentation.HasCoeffs.coeffs_subset_range, bddAbove_preimage_ofDual, FirstOrder.Language.Substructure.coe_topEquiv, CommGroupWithZero.normalize_eq_one, Polynomial.aeval_algEquiv, Matrix.charpoly_inv, galLiftEquiv_algebraMap_apply, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, ModularForm.coe_const, BumpCovering.exists_finset_toPOUFun_eventuallyEq, Matrix.toLin_finTwoProd, ModuleCat.HasLimit.lift_hom_apply, toMul_eq_one, MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closure, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit, norm_toDual, Polynomial.deriv, AddMonoidHom.mk'_apply, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Unitization.inrRangeEquiv_apply_coe, Complex.cpow_conj, Equiv.Set.sumCompl_apply_inr, QuadraticAlgebra.norm_one, Coalgebra.counitCoalgHom_apply, ContinuousLinearMap.differentiableOn, ContinuousMultilinearMap.uncurry0_apply, LinearMap.BilinForm.apply_toDual_symm_apply, Units.coe_opEquiv_symm, MulOpposite.opLinearIsometryEquiv_apply, LocallyConstant.mulIndicator_of_mem, DFinsupp.coe_le_coe, Ordinal.toNimber_zero, orderIsoShrink_symm_apply, ContinuousOrderHomClass.map_monotone, HilbertBasis.summable_inner_mul_inner, MeasureTheory.volume_preserving_piUnique, AddGrpCat.epi_iff_surjective, NormedAddGroupHom.nsmul_apply, BialgEquiv.coe_symm_toEquiv, DifferentiableWithinAt.continuousAlternatingMap_apply, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_invariant, ProbabilityTheory.cond_eq_zero, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, DirichletCharacter.changeLevel_self_toUnitHom, CategoryTheory.Functor.FullyFaithful.isoEquiv_symm_apply, ContinuousLinearMap.isPositive_iff', isAddRegular_ofLex, Function.Embedding.coe_prodMap, TopCat.Presheaf.stalkSpecializes_comp_apply, Finset.inf'_comp_eq_map, nucleusIsoSublocale.symm_eq_toNucleus, AlgebraicGeometry.isClosedImmersion_iff, WeierstrassCurve.map_b₄, qExpansion_mul_coeff_zero, CliffordAlgebra.even.lift.aux_apply, BooleanSubalgebra.coe_subtype, summable_iff_cauchySeq_finset_and_tsum_mem, Finsupp.mul_prod_erase, CategoryTheory.PreGaloisCategory.autEmbedding_range, LinearIsometryEquiv.comp_hasFDerivAt_iff, Ideal.radicalInfTopHom_apply, CliffordAlgebra.toBaseChange_involute, BoundedContinuousFunction.abs_diff_coe_le_dist, SubAddAction.ofStabilizer.neg_conjMap_comp_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul, PowerSeries.rescale_neg_one_X, Equiv.mulRight₀_symm_apply, IsGalois.map_fixingSubgroup, Module.Basis.linearMap_repr_symm_apply, Units.continuous_embedProduct, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, ContinuousAddEquiv.coe_mk, ContinuousAddMonoidHom.add_toFun, support_subset_support_matPolyEquiv, Matrix.toLinAlgEquiv'_toMatrixAlgEquiv', CategoryTheory.GrothendieckTopology.Plus.inj_of_sep, MeasureTheory.lintegral_indicator_one, ContinuousLinearEquiv.map_zero, CategoryTheory.conjugateIsoEquiv_apply_hom, ProbabilityTheory.Kernel.lintegral_prod_deterministic, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, MeasureTheory.Measure.mapₗ_eq_zero_iff, NatOrdinal.toOrdinal_toNatOrdinal, ContinuousMultilinearMap.le_of_opNorm_le, ProbabilityTheory.Kernel.measure_sum_seq, Polynomial.algEquivAevalNegX_apply, RingEquiv.image_eq_preimage_symm, LinearMap.funLeft_apply, ofDual_symmDiff, OrderEmbedding.sortedLE_listMap, infClosure_mono, Topology.WithLower.ofLower_inj, ContinuousLinearMap.star_eq_adjoint, CliffordAlgebra.even.lift.aux_ι, Polynomial.natDegree_sub_C, Hausdorffification.lift_of, SchwartzMap.integral_fourier_smul_eq, ContinuousMap.tendsto_nhds_compactOpen, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, HahnSeries.C_one, eventuallyConst_of_isNoetherian, ProbabilityTheory.meas_ge_le_evariance_div_sq, RingHom.prod_apply, Prod.Lex.toLex_strictMono, DomMulAct.mk_pow, Trivialization.sourceHomeomorphBaseSetProd_symm_apply, StarMulEquiv.rightInverse_symm, AffineMap.differentiableOn, LinearMap.BilinForm.neg_apply, PowerSeries.constantCoeff_exp, QuadraticMap.IsometryEquiv.prodProdProdComm_toFun, MaximalSpectrum.toPiLocalization_injective, RelEmbedding.orderEmbeddingOfLTEmbedding_apply, WittVector.bind₁_onePoly_wittPolynomial, MeasureTheory.exists_setLIntegral_compl_lt, RootPairing.rootForm_pos_of_ne_zero, Subring.opEquiv_apply, GaussianInt.toComplex_zero, ProperCone.mem_comap, Module.Basis.constr_basis, AddLocalization.r_iff_oreEqv_r, MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier, GroupSeminormClass.toSeminormedGroup_norm_eq, Path.truncate_const_continuous_family, IsBaseChange.equiv_tmul, ContinuousMultilinearMap.curryLeft_apply, ContinuousAlternatingMap.hasFDerivWithinAt, univ_option, Algebra.adjoin_eq_range_freeAlgebra_lift, Module.End.ker_aeval_ring_hom'_unit_polynomial, UniformEquiv.coe_prodCongr, MeasureTheory.diracProba_toMeasure_apply, AlgebraicGeometry.Spec_closedPoint, TwoSidedIdeal.gc, SimpleGraph.Embedding.comap_apply, ContinuousMultilinearMap.piEquiv_symm_apply, Algebra.lmul_isUnit_iff, MeasurableEquiv.coe_addRight, map_wittPolynomial, StarAlgHom.prodEquiv_symm_apply, PowerSeries.trunc_coe_eq_self, LinearEquiv.charpoly_conj, PartialEquiv.transEquiv_apply, QuadraticMap.IsOrtho.polar_eq_zero, AddConstMapClass.map_add_nat', ContDiffAt.laplacian_CLM_comp_left_nhds, ArithmeticFunction.IsMultiplicative.iff_ne_zero, Bialgebra.comul_one, AddSubmonoid.coe_toNatSubmodule, LinearMap.tensorProduct_apply, isAddRegular_toColex, OrderIso.withZeroUnits_apply, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, ModularForm.cuspFunction_mul, AlgebraicGeometry.Scheme.Hom.range_subset_ker_support, Derivation.mapCoeffs_apply, Homeomorph.transOpenPartialHomeomorph_symm_apply, LinearOrderedField.coe_inducedOrderRingIso, TestFunction.toFun_eq_coe, MvPolynomial.optionEquivLeft_symm_apply, RatFunc.denom_algebraMap, DFinsupp.filter_apply_pos, Derivation.ext_iff, WithVal.equivWithVal_apply, unitary.map_mem, LinearMap.map_sub, CompactlySupportedContinuousMap.coe_finsetInf', ModuleCat.homLinearEquiv_apply, exists_continuous_one_zero_of_isCompact_of_isGδ, Submodule.lipschitzWith_orthogonalProjection, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, FreeAddMagma.lift_symm_apply, Polynomial.hasseDeriv_natDegree_eq_C, Rep.coinvariantsTensorMk_apply, Polynomial.hasFDerivWithinAt_aeval, NumberField.isUnit_iff_norm, ContinuousAddMonoidHom.add_apply, OrderIso.preimage_symm_preimage, MeasureTheory.Measure.completion_apply, ofDual_inv, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, OrderIso.map_iInf₂, RootPairing.pairing_smul_coroot_eq, NonUnitalSubring.coe_map, RestrictedProduct.isEmbedding_coe_of_top, Finsupp.tsub_apply, MeasureTheory.Measure.le_join_apply, AddGroupExtension.Equiv.coe_toAddEquiv, MeasureTheory.measure_preimage_smul, Orientation.inner_rightAngleRotation_right, CochainComplex.HomComplex.Cocycle.equivHom_apply, OrderIso.map_csSup, ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSlice, MeasurableEquiv.coe_mulRight, AddCircle.openPartialHomeomorphCoe_symm_apply, continuousOn_cfcₙ_setProd, isMaxFilter_dual_iff, ContinuousAlgEquiv.image_symm_eq_preimage, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, SpecialLinearGroup.toGeneralLinearGroup_toLinearEquiv_apply, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, QuaternionAlgebra.coe_linearEquivTuple, HahnModule.of_sub, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, WeakBilin.eval_continuous, Polynomial.Splits.image_rootSet_of_map_ne_zero, Frm.ofHom_apply, TopModuleCat.kerι_apply, WeierstrassCurve.Jacobian.map_dblY, convexHull_convexHull_union_left, MeasureTheory.OuterMeasure.trim_eq, mulRothNumber_le, ModularForm.prod_fintype_slash, jacobiSum_eq_sum_sdiff, QuotSMulTop.map_comp, Nat.factorizationEquiv_inv_apply, Homeomorph.comp_continuousAt_iff, finsuppTensorFinsuppLid_single_tmul_single, MeasureTheory.measure_pos_iff_nonempty_of_isMulLeftInvariant, MonoidHom.coe_mgraph, OrderIso.map_sSup, Part.Fix.approx_mono', QuadraticAlgebra.algebraMap_dvd_iff_dvd, Topology.WithLower.isOpen_preimage_ofLower, MeasureTheory.Integrable.apply_continuousLinearMap, ContinuousLinearMap.coe_prodMap', Matrix.mul_fin_two, UniformSpace.Completion.coe_toComplL, RingHom.map_field_closure, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Polynomial.as_sum_range_C_mul_X_pow, Finsupp.embSigma_apply_self, FreeLieAlgebra.lift_symm_apply, TopCat.hom_inv_id_apply, MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae, LieModule.traceForm_apply_lie_apply, Valuation.IsEquiv.val_eq, LinearMap.snd_surjective, Submodule.IsPrincipal.contentIdeal_generator_dvd, MeasureTheory.hausdorffMeasure_smul, Polynomial.contDiff_aeval, AddConstMapClass.map_ofNat_add, PowerSeries.coe_orderHom, RCLike.wInner_one_const_left, AlgEquiv.opComm_symm_apply_symm_apply, WeierstrassCurve.Projective.map_addX, Projectivization.cross_mk_of_ne, AddEquiv.symmEquiv_apply_apply, Continuous.partialSups_apply, CategoryTheory.Limits.Sigma.whiskerEquiv_inv, ball_subset_range_iff_surjective, MonoidHom.one_apply, MeasureTheory.Measure.restrict_apply_eq_zero', WithZero.lift_unique, IsAdjoinRoot.ofAlgEquiv_map_apply, QuotientAddGroup.norm_eq_addGroupSeminorm, LinearEquiv.sumArrowLequivProdArrow_symm_apply_inl, Matrix.kroneckerTMulAlgEquiv_apply, ModularFormClass.bounded_at_infty_comp_ofComplex, HasOuterApproxClosed.indicator_le_apprSeq, AbsoluteValue.IsAdmissible.exists_approx_aux, TopCat.nonempty_isColimit_iff_eq_coinduced, Matrix.SpecialLinearGroup.coe_GLPos_coe_GL_coe_matrix, AlgEquiv.injective, NNReal.sqrt_one, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, PrimeSpectrum.BasicConstructibleSetData.map_f, ProperCone.hyperplane_separation_of_notMem, Ideal.quotientInfToPiQuotient_mk, MeasureTheory.pow_mul_meas_ge_le_eLpNorm, AddSubmonoid.apply_coe_mem_map, AlgebraicGeometry.Scheme.Hom.finite_preimage, MvPowerSeries.algebraMap_apply, ProbabilityTheory.Kernel.measurable, AlgebraicGeometry.Scheme.Opens.ι_apply, LightProfinite.surjective_transitionMap, FrameHom.ext_iff, ArithmeticFunction.LSeriesHasSum_zeta, NonarchAddGroupNorm.coe_sup, OrthonormalBasis.inner_eq_one, LinearMap.single_apply, Module.Basis.adjustToOrientation_apply_eq_or_eq_neg, MeasureTheory.Measure.exists_measure_inter_spanningSets_pos, CompHaus.epi_iff_surjective, NonUnitalRingHom.coe_toAddMonoidHom, OrderedFinpartition.applyOrderedFinpartition_update_left, IsometryEquiv.constVAdd_apply, VitaliFamily.FineSubfamilyOn.measure_le_tsum_of_absolutelyContinuous, CuspFormClass.exp_decay_atImInfty', TopCat.mono_iff_injective, MvPolynomial.isLocalization_C_mk', FractionalIdeal.exists_eq_spanSingleton_mul, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range, derivationToSquareZeroEquivLift_apply_coe_apply, Module.End.genEigenspace_nat, FirstOrder.Language.Equiv.coe_toHom, LinearMap.continuous_of_isClosed_ker, Behrend.map_zero, CommBialgCat.ofHom_apply, LinearIsometry.ediam_range, Finset.eraseNone_inter, FirstOrder.Language.LEquiv.onTerm_apply, Module.ker_algebraMap_end, ZSpan.map_fundamentalDomain, DifferentiableWithinAt.continuousMultilinear_apply_const, MonoidHom.coe_fst, RCLike.re_ofReal_pow, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, UpperSet.compl_map, FiniteGaloisIntermediateField.adjoin_simple_map_algHom, Module.Basis.finTwoProd_zero, MeasureTheory.Measure.setLIntegral_compProd, LocallyConstant.sub_apply, fderiv_clm_apply, MvPolynomial.algebraTensorAlgEquiv_tmul, CategoryTheory.CommSq.instHasLift_1, DirectSum.decomposeAddEquiv_symm_apply, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Equiv.Perm.SameCycle.cycleOf_apply, Set.measure_eq_iInf_isOpen, PowerSeries.coeff_derivative, ZeroAtInftyContinuousMap.bounded, Algebra.TensorProduct.comm_tmul, DomAddAct.symm_mk_nsmul, matPolyEquiv_symm_map_eval, Monoid.CoprodI.lift_symm_apply, MonoidAlgebra.single_eq_algebraMap_mul_of, ModularForm.holo', AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, Orientation.volumeForm_apply_le, MeasureTheory.eLpNorm_const, ContinuousAlternatingMap.curryLeftLI_apply, AffineSubspace.coe_subtype, ContinuousLinearMap.prodEquiv_apply, endVecAlgEquivMatrixEnd_symm_apply_apply, WeierstrassCurve.Projective.map_addZ, MeasureTheory.Measure.mkMetric_le_liminf_sum, ContinuousMap.natCast_apply, Homeomorph.mulRight₀_symm_apply, Equiv.sumAssoc_symm_apply_inr_inr, NonUnitalRingHom.coe_comp, re_inner_self_nonpos, LinearMap.det_zero'', MulEquiv.coe_subgroupMap_apply, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, MvPolynomial.vars_map, Representation.coind_apply, ofMul_prod, DFinsupp.coe_zsmul, NumberField.mixedEmbedding.polarSpaceCoord_apply, toMul_multiset_sum, CharacterModule.uncurry_apply, Polynomial.eval₂_at_apply, Topology.WithGeneratedByTopology.continuous_equiv, BoundedContinuousFunction.measurable_coe_ennreal_comp, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, ProbabilityTheory.Kernel.measurable_coe, ContinuousLinearEquiv.smul_apply, ProbabilityTheory.Kernel.withDensity_rnDeriv_mutuallySingularSetSlice, Padic.coe_withValRingEquiv_symm, AlgebraicGeometry.Scheme.basicOpen_res, AddGroupSeminorm.smul_apply, HahnModule.of_add, algebraMap_nonneg, Polynomial.derivative_C_mul_X_pow, RCLike.norm_sq_re_add_conj, AdicCompletion.of_bijective, Polynomial.signVariations_X_sub_C_mul_eraseLead_le, iteratedFDerivWithin_zero_eq_comp, CompactlySupportedContinuousMap.neg_apply, MonoidWithZeroHom.ext_iff, AlgebraicGeometry.Scheme.iso_inv_base_hom_base_apply, LinearMap.IsSymmetric.im_inner_apply_self, ContinuousLinearEquiv.submoduleMap_apply, MonoidAlgebra.mapRangeAddEquiv_single, Polynomial.support_binomial, Homeomorph.toOpenPartialHomeomorph_symm_apply, convexHull_min, MvPolynomial.mem_support_coeff_finSuccEquiv, Polynomial.derivative_C, CategoryTheory.Sieve.overEquiv_symm_top, QuadraticAlgebra.mk_eq_add_smul_omega, Topology.WithUpperSet.toUpperSet_ofUpperSet, Rep.homEquiv_symm_apply_hom, MeasureTheory.Measure.MeasureDense.nonempty', ContinuousLinearEquiv.ofBijective_symm_apply_apply, CuspForm.IsGLPos.coe_smul, ProbabilityTheory.Kernel.comapRight_apply', WeierstrassCurve.Affine.baseChange_slope, BoundedContinuousFunction.norm_integral_le_mul_norm, Filter.coe_pureOneHom, MeasureTheory.null_iff_of_isAddLeftInvariant, FractionalIdeal.abs_det_basis_change, AlgebraicGeometry.Scheme.Hom.continuous, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField, BoxIntegral.Box.volume_apply, Pi.constAddHom_apply, QuadraticMap.Ring.associated_pi, Polynomial.roots_X_pow_char_sub_C, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, BoundedContinuousFunction.toContinuousMapₐ_apply, Algebra.Generators.aeval_val_σ', EsakiaHom.toContinuousOrderHom_coe, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, MeasurableEquiv.piFinTwo_apply, Finsupp.embDomain.addMonoidHom_apply, SmoothPartitionOfUnity.finite_tsupport, Polynomial.degree_mul_C_of_isUnit, Submodule.ClosedComplemented.exists_submodule_equiv_prod, Polynomial.mem_rootSet, Unitization.inrNonUnitalAlgHom_apply, AdjoinRoot.minpoly_powerBasis_gen, FreeAddMonoid.comp_lift, Fin.cycleRange_of_gt, AdjoinRoot.aeval_algHom_eq_zero, GradedRing.projZeroRingHom_apply, LinearMap.nondegenerate_toMatrix₂_iff, Isometry.inr, Algebra.Generators.Hom.comp_val, MvPolynomial.degreeOf_C_mul, Rat.AbsoluteValue.real_eq_abs, Matrix.trace_kroneckerMapBilinear, le_map_mul_map_div, AddMonoidAlgebra.ext_iff, CategoryTheory.conjugateIsoEquiv_apply_inv, DFinsupp.subtypeDomain_apply, Polynomial.derivative_bernoulli_add_one, SimpleGraph.Iso.sumBoxProdDistrib_symm_apply, LinearMap.frobenius_def, NormedAddGroupHom.coeAddHom_apply, TopCat.homeoOfIso_symm_apply, DFA.eval_reindex, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, MulAutMultiplicative_apply_symm_apply, span_range_eq_top_iff_surjective_finsuppLinearCombination, InitialSeg.le_apply_iff, LieDerivation.IsKilling.ad_apply_eq_zero_iff, FunOnFinite.linearMap_piSingle, AlgEquiv.linearEquivConj_mulRight, LinearMap.inl_apply, LinearMap.map_span_le, CStarMatrix.neg_of, Nucleus.restrict_toSublocale, SimpleGraph.edgeSet_map, ProbabilityTheory.Kernel.eLpNorm_density_le, Polynomial.Chebyshev.algebraMap_eval_S, Finset.map_noncommSum, map_comp_inv, DirectSum.of_eq_of_gradedMonoid_eq, SubmonoidClass.subtype_apply, AffineMap.comp_lineMap, ProfiniteGrp.coe_comp, ContinuousLinearEquiv.isClosed_image, AlgebraicGeometry.Scheme.Pullback.Triplet.exists_preimage, CategoryTheory.Limits.Types.limitEquivSections_apply, ModuleCat.extendScalarsComp_hom_app_one_tmul, ProbabilityTheory.cond_apply', isLeftRegular_toDual, Polynomial.hasseDeriv_apply, ContinuousMultilinearMap.analyticWithinAt, Matrix.GeneralLinearGroup.map_apply, NumberField.mixedEmbedding.negAt_apply_norm_isReal, AddSubgroup.fg_iff_mul_fg, Submonoid.coe_toAddSubmonoid_symm_apply, Sym.oneEquiv_apply, CategoryTheory.Subobject.leInfCone_π_app_none, fixingSubgroup_fixedPoints_gc, MvPolynomial.C_injective, ContinuousAlgEquiv.self_comp_symm, Algebra.norm_eq_prod_roots, ModuleCat.Iso.conj_eq_conj, UniformFun.uniformContinuous_eval, Affine.Simplex.affineCombination_mem_closedInterior_face_iff_mem_Icc, ArithmeticFunction.cardDistinctFactors_pos, map_bihimp, AlgebraicGeometry.Scheme.Hom.isConstructible_image, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, PMF.hasSum_coe_one, MeasureTheory.distribHaarChar_mul, Polynomial.addSubmonoid_closure_setOf_eq_monomial, HasFPowerSeriesWithinAt.unshift, Topology.WithLowerSet.ofLowerSet_le_ofLowerSet, IsModuleTopology.continuous_of_distribMulActionHom, NonUnitalStarRingHom.coe_coe, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Module.Invertible.lTensor_surjective_iff, RestrictedProduct.coe_comp_inclusion, Convex.subset_interior_image_homothety_of_one_lt, innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, CoxeterSystem.reindex_simple, Cardinal.preAleph_le_of_strictMono, ContinuousLinearMap.det_smulRight, Equiv.subtypeSubtypeEquivSubtypeInter_apply_coe, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, MonoidHom.map_mul_inv, Valuation.HasExtension.mk_smul_mk, Polynomial.dickson_two_one_eq_chebyshev_U, RCLike.im_to_complex, Submonoid.coe_toAddSubmonoid_apply, Quiver.SingleObj.pathEquivList_symm_nil, OreLocalization.numerator_isUnit, OmegaCompletePartialOrder.ContinuousHom.congr_arg, IsometryEquiv.constSMul_apply, IsLocalization.algEquiv_symm_apply, Affine.Simplex.orthogonalProjectionSpan_reindex, ContDiffMapSupportedIn.support_subset, Matrix.toLinAlgEquiv'_one, CFC.sqrt_algebraMap, Real.expMonoidHom_apply, Finset.Colex.singleton_le_singleton, MeasureTheory.OuterMeasure.sInf_apply', MvPolynomial.C_mul, AlgebraicGeometry.Surjective.surj, Balanced.mulActionHom_preimage, AffineIsometryEquiv.bijective, ContinuousMap.coe_mabs, Subalgebra.coe_toSubmodule, innerSL_apply, Polynomial.eval₂_derivative_of_splits, Ring.DirectLimit.exists_of, ContinuousAlternatingMap.map_eq_zero_of_eq, BoundedLatticeHom.dual_comp, LinearPMap.vadd_apply, CFC.posPart_algebraMap, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst, ProbabilityTheory.Kernel.lintegral_comp, MeasureTheory.Measure.hausdorffMeasure_le_one_of_subsingleton, trace_eq_sum_embeddings, Multiset.coe_countAddMonoidHom, LinearMap.le_eqLocus, ContinuousLinearEquiv.hasFDerivAt, InnerProductSpace.Core.cauchy_schwarz_aux', ProbabilityTheory.absolutelyContinuous_boolKernel_comp_right, Matrix.toLin_one, DFA.reindex_apply_step, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, CliffordAlgebra.contractLeft_algebraMap_mul, divMonoidWithZeroHom_apply, MeasureTheory.measure_eq_inducedOuterMeasure, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1, PowerSeries.coeff_subst_finite, SlashInvariantForm.vAdd_width_periodic, Homeomorph.symm_apply_eq, CategoryTheory.Arrow.cechConerve_map, InitialSeg.eq_or_principal, RingHom.coe_mul, sigmaFinsuppEquivDFinsupp_apply, antivaryOn_toDual_right, IntermediateField.botEquiv_def, CategoryTheory.Iso.homToEquiv_symm_apply, IsAddFoelner.tendsto_nhds_mean, Dilation.lipschitz, Seminorm.smul_apply, ValuationSubring.mem_nonunits_iff, SubMulAction.map_ofFixingSubgroupUnion_bijective, MeasureTheory.pdf.IsUniform.integral_eq, TensorAlgebra.mk_reindex_fin_cast, Algebra.norm_zero, CategoryTheory.PreGaloisCategory.surjective_of_nonempty_fiber_of_isConnected, PrincipalSeg.eq, SemilinearEquivClass.map_smulₛₗ, LipschitzOnWith.hausdorffMeasure_image_le, ArithmeticFunction.pow_apply, liftOfDerivationToSquareZero_mk_apply', ContinuousLinearMap.tendsto_birkhoffAverage_orthogonalProjection, AlgHom.prodEquiv_apply, MvPolynomial.comap_apply, LinearMap.BilinForm.compLeft_apply, MeasurableEquiv.map_measurableEquiv_injective, CategoryTheory.unitCompPartialBijective_symm_natural, Cardinal.toENat_comp_ofENat, LaurentPolynomial.support_C_mul_T_of_ne_zero, ContinuousLinearEquiv.summable, Topology.WithLower.toLower_ofLower, Subgroup.IsComplement.equiv_mul_right_of_mem, ContinuousAlgEquiv.map_eq_zero_iff, InnerProductSpace.isIdempotentElem_rankOne_self_iff, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, Real.Angle.sign_toReal, Finset.gcd_mul_right, AddCommGrpCat.coyoneda_map_app, CategoryTheory.Functor.sectionsEquivHom_apply_app, QuadraticMap.toFun_eq_coe, Submodule.norm_starProjection_apply, Equiv.Perm.sign_extendDomain, Valued.toNormedField.norm_lt_iff, Ideal.quotientInfEquivQuotientProd_fst, ContinuousMultilinearMap.toUniformOnFun_toFun, Quaternion.re_snd_dualNumberEquiv, SubMulAction.of_fixingSubgroupEmpty_mapScalars_surjective, ProbabilityTheory.Kernel.condKernel_def, PseudoMetric.coe_finsetSup, contractRight_apply, cfc_eq_cfcL, MeasureTheory.hausdorffMeasure_affineSegment, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology, AddChar.doubleDualEquiv_symm_doubleDualEmb_apply, Order.pred_toAdd, CliffordAlgebra.reverseEquiv_apply, ContinuousMultilinearMap.coe_restrictScalars, HomogeneousLocalization.den_smul_val, FreeAlgebra.algebraMap_eq_one_iff, Finset.Colex.toColex_lt_toColex, PowerSeries.coeff_X_pow, Polynomial.C_mul_comp, Finsupp.single_apply, Matrix.toLin_transpose, IsAdjoinRoot.map_eq_zero_iff, Matrix.det_mul_row, NonemptyInterval.toLex_mono, Equiv.range_eq_univ, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Complex.conj_eq_iff_real, AddMonoidHom.coeFn_apply, Equiv.dvd_apply, OrderIso.coe_trans, Nucleus.map_inf, GradedTensorProduct.of_symm_of, Valuation.map_pow, Finsupp.sumFinsuppEquivProdFinsupp_symm_inl, Homeomorph.transOpenPartialHomeomorph_source, MonotoneOn.dual_right, CategoryTheory.Iso.homFromEquiv_apply, IsCompact.measure_eq_biInf_integral_hasCompactSupport, OrderDual.toDual_bot, Valuation.rel_iff_le, WittVector.verschiebung_frobenius_comm, isRegular_toDual, SymAlg.sym_inj, SemilinearEquivClass.semilinearEquiv_apply, AffineIsometry.ext_iff, MulSemiringAction.toAlgHom_apply, ZMod.toCircle_intCast, DirectSum.decompose_symm_zero, IsometryEquiv.image_symm, MvPolynomial.vars_rename, CompactlySupportedContinuousMap.nnrealPart_apply, Monovary.sum_mul_comp_perm_lt_sum_mul_iff, NonUnitalStarAlgHom.map_adjoin, stereographic_apply, AlgebraicGeometry.Scheme.stalkMap_inv_hom, SSet.OneTruncation₂.nerveEquiv_symm_apply_obj, MeasureTheory.inner_condExpL2_eq_inner_fun, Equiv.sumArrowEquivProdArrow_apply_snd, MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars, Set.powersetCard.mulActionHom_singleton_bijective, Complex.toMatrix_conjAe, Finsupp.lex_def, StrongDual.toLp_apply, LT.lt.dual, CategoryTheory.Discrete.addMonoidalFunctor_η, Additive.toMul_eq_bot, DilationEquiv.coe_mul, Cardinal.preAleph_le_preBeth, ArithmeticFunction.vonMangoldt_eq_zero_iff, EquivLike.comp_surjective, WithLp.coe_addEquiv, ContinuousMonoidHom.coe_coe, Equiv.preimage_image, FreeAddMonoid.ofList_flatten, OrthogonalFamily.norm_sum, MeasurableSpace.generateMeasurableRec_omega_one, BoundedContinuousFunction.coe_inf, OrderMonoidHom.coe_one, MvPowerSeries.isHomogeneous_homogeneousComponent, Orientation.rotation_apply, AlgebraicGeometry.germ_eq_zero_of_pow_mul_eq_zero, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, LaurentPolynomial.counit_T, OrderHom.coeFnHom_coe, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, CategoryTheory.PreGaloisCategory.mulAction_naturality, ContinuousAt.lineMap, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.Localization.Construction.objEquiv_apply, WittVector.bind₁_zero_wittPolynomial, measurable_piEquivPiSubtypeProd_symm, Representation.leftRegular_norm_apply, BilinForm.mul_toMatrix, TensorProduct.liftAux.smul, Function.locallyFinsuppWithin.logCounting_le, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, ZMod.toCircle_natCast, inner_map_polarization, Traversable.foldl.ofFreeMonoid_comp_of, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, MonoidWithZeroHom.map_ite_zero_one, Con.inf_iff_and, AddConstMapClass.strictMono_iff_Icc, MeasureTheory.AddContent.supClosure_apply_of_mem, ModularFormClass.hasSum_qExpansion_of_norm_lt, Submodule.inner_starProjection_left_eq_right, PiLp.proj_apply, nonZeroDivisorsEquivUnits_symm_apply_coe, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, MeasureTheory.Egorov.measure_notConvergentSeq_tendsto_zero, LieSubalgebra.mem_map, SemidirectProduct.inl_inj, Finsupp.weight_sub_single_add, preordToPartOrdCompToDualIsoToDualCompPreordToPartOrd_hom_app_hom_coe, ProbabilityTheory.Kernel.setIntegral_piecewise, Equiv.Perm.cycleFactorsFinset_conj, Polynomial.exists_separable_of_irreducible, LightProfinite.epi_iff_surjective, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, Complex.volume_ball, ContinuousLinearMap.IsPositive.spectrumRestricts, MeasureTheory.toMeasure_apply, AlgebraicGeometry.Scheme.comp_base_apply, AddAction.toPermHom_apply_apply, InfClosed.supClosure, Polynomial.roots_expand_image_iterateFrobenius, Field.finInsepDegree_def', Real.deriv_fourierChar, groupCohomology.π_comp_H1Iso_hom_apply, Ideal.quotientMap_algebraMap, Set.image_op_smul_distrib, IntermediateField.val_mk, AlgebraicGeometry.isGermInjectiveAt_iff_of_isOpenImmersion, MeasureTheory.FiniteMeasure.apply_le_mass, MeasureTheory.mem_ae_iff, Matrix.invOf_submatrix_equiv_eq, ProbabilityTheory.iIndepSet_iff_meas_biInter, WeakSpace.coe_map, map_add_eq_zero, OrthonormalBasis.sum_repr, Representation.coinvariantsToFinsupp_mk_single, RCLike.re_eq_complex_re, LinearMap.continuous_iff_isClosed_ker, homeomorphSphereProd_apply_snd_coe, AffineBasis.reindex_apply, Multiset.coeEquiv_symm_apply_fst, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Submodule.reflection_mem_subspace_eq_self, Matrix.submatrix_mul_transpose_submatrix, Coalgebra.TensorProduct.rid_symm_apply, Matrix.cons_vecMul, StieltjesFunction.measure_Iio, sign_eq_sign_or_eq_neg, Subalgebra.opEquiv_symm_apply, Finset.Colex.toColex_image_le_toColex_image, AdjoinRoot.lift_root, Homeomorph.isOpen_image, MatrixEquivTensor.right_inv, MeasureTheory.measureReal_def, IsLocalization.mk'_spec'_mk, OrderEmbedding.birkhoffSet_apply, Polynomial.sum_modByMonic_coeff, Function.Embedding.sectL_apply, Finsupp.single_add_apply, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, WithZero.withZeroUnitsEquiv_symm_apply, Con.coe_sInf, Commute.tprod, LocallyFiniteOrder.orderMonoidHom_strictMono, WittVector.quotEquivOfEq_ghostComponentModPPow, WithTop.subtypeOrderIso_apply_coe, CategoryTheory.Iso.conj_id, ContinuousMap.fst_apply, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, ZMod.χ₈'_apply, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, RatFunc.eq_C_iff, EquivLike.self_comp_coe_symm, MulEquiv.coprodCongr_symm_apply, Algebra.Generators.CotangentSpace.map_toComp_injective, Monoid.CoprodI.Word.mem_smul_iff, ArithmeticFunction.carmichael_eq_exponent, AffineIsometryEquiv.lipschitz, ModularFormClass.bdd_at_infty_slash, UniqueFactorizationMonoid.mem_normalizedFactors_iff', Filter.map_div, AdicCompletion.evalₐ_of, Module.Basis.det_mul_det, DirectSum.ofList_dProd, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Module.End.lTensorAlgHom_apply_apply, ContinuousLinearEquiv.analyticOnNhd, InitialSeg.ext_iff, RatFunc.num_mul_eq_mul_denom_iff, AddEquiv.subsemigroupMap_symm_apply_coe, Finset.Colex.toColex_sdiff_lt_toColex_sdiff', IsConformalMap.injective, InnerProductSpaceable.innerProp, PowerSeries.expand_monomial, MonomialOrder.lex_lt_iff, Continuous.clm_bundle_apply₂, TopCat.GlueData.MkCore.t_inter, AlgebraicGeometry.PresheafedSpace.GlueData.ι_jointly_surjective, WittVector.teichmuller_coeff_zero, Matrix.toLpLin_symm_comp, Monoid.Coprod.swap_bijective, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_comp_asIdeal, Module.Basis.SmithNormalForm.repr_comp_embedding_eq_smul, MulRingSeminorm.toFun_eq_coe, Nat.sub_one_mul_factorization_factorial, Polynomial.aeval_monomial, LeftInvariantDerivation.coe_zero, subtypeOrEquiv_symm_inr, MvPowerSeries.aeval_eq_sum, CategoryTheory.MonoidalClosed.homEquiv_apply_eq, Equiv.algebraMap_def, Lat.id_apply, ModularFormClass.cuspFunction_apply_zero, Polynomial.eval_map_algebraMap, NonarchAddGroupSeminorm.le_def, ContinuousOn.partialSups_apply, CategoryTheory.Limits.coneOfSectionCompCoyoneda_π, Representation.ind_mk, PartitionOfUnity.sum_nonneg, Module.Basis.toDual_linearCombination_right, AddEquiv.refl_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, Algebra.Norm.Transitivity.eval_zero_det_det, PresentedGroup.equivPresentedGroup_symm_apply_of, DirectSum.decomposeAddEquiv_apply, Matrix.toLinearMapₛₗ₂_apply_basis, Topology.WithLower.toLower_lt_toLower, CategoryTheory.conjugateEquiv_whiskerLeft, PositiveLinearMap.norm_apply_le_of_nonneg, Module.Ray.map_apply, CategoryTheory.ActionCategory.stabilizerIsoEnd_apply, Equiv.sigmaSumDistrib_apply, CochainComplex.fromSingle₀Equiv_symm_apply_f_zero, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, ContinuousMonoidHom.inr_toFun, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, Finset.ofDual_inf', Module.Ray.map_neg, MeasureTheory.SimpleFunc.iSup_eapprox_apply, IsLocalRing.CotangentSpace.span_image_eq_top_iff, RelIso.subrelUnivIso_apply, ZeroAtInftyContinuousMap.star_apply, Action.tensor_ρ, Antivary.sum_smul_comp_perm_eq_sum_smul_iff, LaurentPolynomial.counit_C, stdSimplexEquivIcc_apply_coe, MeasureTheory.condExpInd_disjoint_union_apply, LieAlgebra.ad_lie, SubMulAction.ofFixingSubgroup_of_eq_bijective, RingHom.SurjectiveOnStalks.localRingHom_surjective, IsTranscendenceBasis.sumElim_comp, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, ProbabilityTheory.measure_condCDF_Iic, RingEquiv.toNonUnitalRingHom_apply_symm_toNonUnitalRingHom_apply, OrderHom.const_coe_coe, BddLat.id_apply, AdjoinRoot.quotEquivQuotMap_symm_apply, DirectSum.GAlgebra.commutes, map_multiset_ne_zero_sum, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coe, Mathlib.Meta.Positivity.nnabs_pos_of_pos, TensorProduct.tensorTensorTensorAssoc_symm_tmul, norm_sub_le_mul_volume_of_norm_fderiv_le, Polynomial.bernoulli_one, AlgEquiv.piCongrLeft_symm_apply, RCLike.norm_to_complex, RelSeries.last_map, TensorProduct.finsuppLeft_apply_tmul, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_base_apply, AddCommGrpCat.forget_map, Polynomial.Chebyshev.iterate_derivative_T_eval_one, LinearEquiv.coord_apply_smul, Monoid.CoprodI.Word.smul_eq_of_smul, Unitization.lift_range_le, NNReal.sqrt_le_one, HahnSeries.order_C, MonoidHom.coe_mrangeRestrict, PiTensorProduct.ofFinsuppEquiv'_apply_apply, CompleteOrthogonalIdempotents.bijective_pi', FreeAbelianGroup.lift_comp, Algebra.TensorProduct.opAlgEquiv_tmul, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, AddMonoidAlgebra.single_zero_mul_apply, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, LinearMap.toSeminorm_ball_zero, ContinuousAddMonoidHom.comp_toFun, CliffordAlgebraRing.reverse_apply, AddSubgroup.toIntSubmodule_toAddSubgroup, Lagrange.eval_interpolate_at_node, WeierstrassCurve.map_Δ', PowerSeries.isWeierstrassDivisionAt_iff, Valuation.Integers.valuation_irreducible_pos, LinearIsometryEquiv.hasFDerivWithinAt, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply, MvPolynomial.divMonomial_monomial_mul, Matrix.det_fin_one_of, sbtw_lineMap_iff, Diffeomorph.contMDiffWithinAt_diffeomorph_comp_iff, Module.End.genEigenspace_le_maximal, EReal.expOrderIso_apply, AlgHom.normal_bijective, ProbabilityTheory.indepSet_iff_measure_inter_eq_mul, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, Finsupp.restrictSupportEquiv_apply, DFinsupp.counit_single, StandardEtalePresentation.toPresentation_val, Finset.mem_map', AddMonoidHom.coe_ofMapMidpoint, LocallyConstant.constₗ_apply_apply, FreeAddMonoid.lift_of_comp_eq_map, ExteriorAlgebra.liftAlternating_algebraMap, Finsupp.smul_apply_addAction, Nonneg.coeAddMonoidHom_apply, Finset.mapEmbedding_apply, Polynomial.algEquivOfCompEqX_apply, UpperHalfPlane.val_J, Equiv.piCongrLeft_apply_apply, quadraticChar_apply, MeasureTheory.measure_iUnion_fintype_le, NumberField.toNNReal_valued_eq_adicAbv, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, LinearMap.ofIsCompl_right_apply, MeasureTheory.SimpleFunc.zpow_apply, SupHomClass.map_sup, MeasureTheory.measure_symmDiff_neg_vadd, MeasureTheory.eLpNorm_le_eLpNorm_mul_rpow_measure_univ, TopHom.coe_comp, measurable_piCurry_symm, Equiv.bijOn_image, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, Orientation.kahler_apply_apply, Equiv.piCurry_apply, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, LinearMap.det_zero', AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, RCLike.re_sq_le_normSq, RingEquiv.toRingHom_apply_symm_toRingHom_apply, SubMulAction.SMulMemClass.subtype_injective, IsometryEquiv.vaddConst_symm_apply, AddSubmonoid.mem_iSup_iff_exists_dfinsupp, AffineIsometry.edist_map, Valuation.vlt_iff_lt, FiniteDimensional.exists_is_basis_integral, matPolyEquiv_eval, Topology.IsGeneratedBy.isClosed_iff, Subgroup.IsComplement.mk''_rightQuotientEquiv, groupHomology.d₂₁_single_one_snd, MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior, AffineEquiv.list_sbtw_map_iff, GroupExtension.Equiv.rightHom_map, FreeAddMagma.hom_ext_iff, ContinuousMap.concatCM_right, WithCStarModule.equiv_symm_add, ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv_apply, imaginaryPart_imaginaryPart, Cardinal.toENat_le_iff_of_lt_aleph0, PowerSeries.coeff_subst', finSigmaFinEquiv_one, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly, Orientation.inner_rightAngleRotationAux₁_left, Polynomial.mem_rootSet_of_ne, CentroidHom.centerToCentroidCenter_apply, Polynomial.mapAlg_comp, map_comp_zero, LinearMap.sub_apply, MonoidWithZeroHom.inr_strictMono, MeasureTheory.Lp.simpleFunc.aestronglyMeasurable, TensorProduct.AlgebraTensorModule.map_tmul, Diffeomorph.ext_iff, IsCompact.measure_lt_top_of_nhdsWithin, Polynomial.sylvesterMap_apply_coe, Nat.ordProj_dvd, PMF.toMeasure_bindOnSupport_apply, Valuation.IsUniformizer.iff, Cardinal.preAleph_pos, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, RCLike.conj_inv, LowerSet.coe_iicInfHom, LinearIsometry.map_zero, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, LinearMap.toMatrix_toSpanSingleton, map_dfinsuppProd, LinearEquiv.coe_inv_det, RootPairing.toPerfPair_flip_conj_coreflection, IsGaloisGroup.mulEquivAlgEquiv_symm_apply, CategoryTheory.Functor.WellOrderInductionData.map_lift, IsHilbertSum.linearIsometryEquiv_symm_apply_single, PolynomialLaw.isCompat_apply', IsSelfAdjoint.adjoint_conj, WittVector.exists_frobenius_solution_fractionRing_aux, ModelWithCorners.toHomeomorph_apply, OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge', AddConstMapClass.map_nsmul_add, Bornology.IsVonNBounded.image, Pi.evalAddActionHom_apply, CategoryTheory.Discrete.monoidalFunctor_obj, Equiv.Perm.mul_apply, ContinuousMap.Homotopy.congr_fun, List.formPerm_eq_head_iff_eq_getLast, AffineIsometryEquiv.map_vadd, Matrix.vecMulVec_cons, CompleteSublattice.comap_carrier, monotone_stabilizes_iff_artinian, ProbabilityTheory.Kernel.densityProcess_fst_univ, Ring.DirectLimit.Polynomial.exists_of, closedAbsConvexHull_eq_closure_absConvexHull, FirstOrder.Language.DirectLimit.instDirectedSystemSubtypeMemSubstructureDomCoeOrderHomPartialEquivEmbeddingInclusion, QuotientAddGroup.map_map, IsAdjoinRoot.aeval_root_self, Path.extend_extends', smoothSheafCommRing.ι_forgetStalk_hom, OrderMonoidIso.coe_trans, Algebra.norm_eq_one_of_not_module_finite, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, MonoidAlgebra.ext_iff, Differential.implicitDeriv_X, RingHom.toIntAlgHom_coe, ModularGroup.coe_T, IsLowerSet.toDual, Polynomial.natDegree_mul_C_le, MvPolynomial.sum_monomial_eq, Equiv.instCanLiftForallCoeBijective, LinearIsometry.nnnorm_map, exists_embedding_euclidean_of_compact, MeasureTheory.tendsto_measure_iUnion_accumulate, AffineEquiv.wOppSide_map_iff, DivisibleHull.archimedeanClassOrderIso_symm_apply, CoalgEquiv.symm_apply_apply, RootPairing.pairing_smul_root_eq, MeasureTheory.Integrable.measure_le_lt_top, Module.Invertible.bijective, Polynomial.aeval_eq_sum_range', UnitAddTorus.mFourierBasis_repr, Polynomial.degreeLT.addLinearEquiv_natAdd, AffineMap.coe_zero, MvPolynomial.rename_comp_bind₁, Ordinal.ToType.mk_apply, HahnSeries.coeff_truncLT_of_lt, DomAddAct.mk_zero, Seminorm.coe_zero, ContinuousLinearMap.coe_id', Equiv.equivPUnit_apply, SpectralMap.id_apply, AlgEquiv.mopMatrix_symm_apply, Finsupp.curryEquiv_symm_apply, ContinuousOpenMap.coe_comp, Finsupp.unique_ext_iff, AlgebraicGeometry.IsDominant.denseRange, TensorProduct.lidOfCompatibleSMul_tmul, Module.Invertible.lTensor_bijective_iff, LinearMap.toSeminorm_apply, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, AlgEquiv.restrictNormalHom_apply, LieModule.isNilpotent_iff_forall', InfiniteGalois.mk_toAlgEquivAux, Matrix.comp_symm_transpose, SSet.stdSimplex.spineId_vertex, CuspFormClass.cuspFunction_apply_zero, linearDepOn_iffₛ, Polynomial.expand_char, MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image₀, MeasureTheory.lintegral_pos_iff_support, IsLocalizedModule.fromLocalizedModule'_mk, LieAlgebra.Extension.ringModuleOf_bracket_proj, Complex.normSq_eq_conj_mul_self, riesz_extension, linearIndepOn_union_iff_quotient, Valued.hasBasis_uniformity, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, Subgroup.transferFunction_apply, Pi.comul_single, List.equivSigmaTuple_apply_snd, ModularForm.slash_def, AlgebraicGeometry.Flat.iff_flat_stalkMap, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app_surjective, ContinuousMap.coe_inv, TrivSqZeroExt.sndHom_apply, ApproximatesLinearOn.exists_homeomorph_extension, MvPolynomial.degrees_monomial_eq, LinearMap.mulRight_toAddMonoidHom, AddHom.mulRight_apply, AlgebraicGeometry.Scheme.preimage_zeroLocus, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Submodule.starProjection_minimal, CategoryTheory.SimplicialObject.cechNerveEquiv_apply, QuadraticMap.IsometryEquiv.map_app', Coalgebra.coassoc_apply, TwoSidedIdeal.subtypeMop_apply, rootsOfUnityEquivNthRoots_apply, QuotientAddGroup.lift_quot_mk, Finsupp.Icc_eq, List.sortedLE_map_ofDual, Polynomial.aeval_zero, OrderHom.dual_apply_coe, Equiv.divLeft₀_symm_apply, AffineEquiv.vaddConst_symm_apply, Function.Embedding.apply_eq_iff_eq, ContinuousLinearMap.contMDiffWithinAt, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, ZMod.invDFT_def, Algebra.norm_norm, NonUnitalRingHom.coe_srange, MeasureTheory.AddContent.measureCaratheodory_eq_inducedOuterMeasure, WittVector.iterate_verschiebung_mul_left, ContinuousMap.smul_apply', MulChar.trivial_apply, UniformConvergenceCLM.sum_apply, groupHomology.π_map_apply, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, LinearMap.map_smul', Fin.equivSubtype_symm_apply, OrderMonoidIso.coe_refl, Valuation.mem_ltSubmodule_iff, Finsupp.addCommute_iff_inter, MeasureTheory.OuterMeasure.sum_apply, FirstOrder.Language.HomClass.map_rel, ContinuousMap.const_apply, LinearMap.continuous_of_isClosed_graph, AffineEquiv.vaddConst_apply, StarSubalgebra.inclusion_injective, ProbabilityTheory.hasFiniteIntegral_compProd_iff, MvPolynomial.rename_X, CategoryTheory.pullbackShiftFunctorZero'_inv_app, AffineSubspace.wSameSide_lineMap_right, StieltjesFunction.outer_Ioc, ContinuousLinearEquiv.ofSubmodule'_symm_apply, pinGroup.involute_act_ι_mem_range_ι, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, Finset.Colex.toColex_empty, Module.End.mem_genEigenspace_nat, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, ProbabilityTheory.strong_law_ae_simpleFunc_comp, AlgebraicGeometry.isIso_iff_stalk_iso, Subalgebra.algebraMap_mem, AlgebraicGeometry.Scheme.instIsOverMapStalkMapOverInferInstanceOverClass, Submodule.inclusion_injective, AlgEquiv.coe_fun_injective, ContinuousLinearMap.dslope_comp, BoundingSieve.nu_pos_of_dvd_prodPrimes, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, SchwartzMap.seminorm_apply, OrderAddMonoidHom.inl_add_inr_eq_mk, ContinuousLinearMap.inl_apply, LinearEquiv.coe_toLinearMap, ProbabilityTheory.Kernel.comap_apply, MeasureTheory.IsProjectiveLimit.measure_univ_unique, PMF.uniformOfFinset_apply, UniformFun.lipschitzOnWith_ofFun_iff, ProbabilityTheory.variance_linearMap_gaussianReal, HopfAlgebra.mul_antipode_lTensor_comul_apply, Module.Basis.singleton_apply, LinearAlgebra.FreeProduct.lift_algebraMap, MulOpposite.coe_opLinearEquiv, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Fin.cycleIcc_of_lt, SymmetricAlgebra.algebraMap_leftInverse, Representation.coinvariantsFinsuppLEquiv_symm_apply, TwoSidedIdeal.coeOrderEmbedding_apply, Complex.conj_eq_iff_im, DividedPowers.Quotient.dpow_apply, ContinuousAlgHom.coe_coe, ContinuousAlgEquiv.coe_coe, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, LinearMap.Nondegenerate.toMatrix₂', RingHom.isUnit_map, ZeroHom.coe_neg, cfcHom_predicate, Algebra.adjoin_algebraMap, ZMod.injective_toCircle, IsUnit.map, AlgEquiv.liftNormal_commutes, RootPairing.Equiv.reflection_smul, ContinuousAlgEquiv.preimage_symm_preimage, MvPolynomial.IsSymmetric.C, MvPolynomial.pUnitAlgEquiv_monomial, FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm, SubringClass.coe_subtype, ModP.v_p_lt_val, Subalgebra.linearEquivOp_symm_apply_coe, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, ProbabilityTheory.condIndepFun_iff_condDistrib_prod_ae_eq_prodMkRight, Submodule.orthogonalProjection_orthogonal_apply_eq_zero, Derivation.zero_apply, CommGrpCat.one_apply, Subgroup.quotientEquivProdOfLE'_apply, AddSubmonoid.LocalizationMap.ofAddEquivOfDom_comp, WithZero.map'_surjective_iff, ProbabilityTheory.IndepFun_iff, RelIso.preimage_apply, HahnModule.support_smul_subset_vadd_support, CategoryTheory.PreGaloisCategory.AutGalois.π_apply, LocallyConstant.coe_div, AffineSubspace.signedInfDist_def, PartOrdEmb.ext_iff, WeakDual.CharacterSpace.continuousMapEval_apply_apply, OrderHom.uliftLeftMap_coe, AddActionHom.comp_apply, QuadraticAlgebra.coe_mem_nonZeroDivisors_iff, RatFunc.single_zpow, NNReal.coeNNRealReal_zero, Polynomial.support_derivativeFinsupp_subset_range, Matrix.cons_vecMul_cons, MonoidHom.map_dvd, CategoryTheory.Functor.homMonoidHom_apply, NonUnitalAlgHom.coe_injective, TwoSidedIdeal.coeAddMonoidHom_apply, MvPolynomial.coeff_monomial, TensorProduct.equivFinsuppOfBasisRight_symm, MeasureTheory.Measure.addHaar_closedBall, MeasureTheory.OuterMeasure.coe_mkMetric, ContinuousLinearMap.unit_le_opNorm, Function.Embedding.invOfMemRange_surjective, Localization.localRingHom_bijective_of_saturated_inf_eq_top, Equiv.boolProdEquivSum_apply, FirstOrder.Language.BoundedFormula.realize_constantsVarsEquiv, TopHom.coe_id, MvPolynomial.coeff_mul_monomial, CliffordAlgebraDualNumber.ι_mul_ι, ZeroAtInftyContinuousMap.isBounded_range, UniformConvergenceCLM.tendsto_iff_tendstoUniformlyOn, CategoryTheory.Abelian.Ext.mk₀_linearEquiv₀_apply, Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_lt, HahnSeries.orderTop_abs, Polynomial.monomial_zero_left, LinearIsometryEquiv.lipschitz, groupHomology.d₃₂_single_one_snd, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le', HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, DistLat.coe_comp, Path.truncate_continuous_family, LinearIsometryEquiv.piLpCongrLeft_single, DFA.evalFrom_reindex, Setoid.piQuotientEquiv_apply, Nat.exists_subseq_of_forall_mem_union, Bialgebra.TensorProduct.rid_symm_apply, FirstOrder.Language.Embedding.injective, IntermediateField.inclusion_inclusion, TopCat.GlueData.ι_jointly_surjective, Dilation.mulRight_toFun, RingEquiv.map_multiset_sum, AddGroupSeminorm.zero_apply, MvPolynomial.eval₂_eq, TopologicalSpace.Fiber.instCompactSpaceElemValSetMemRangeCoeLocallyConstantPreimageSingleton, AddMonoidHom.map_multiset_sum, Submodule.starProjection_mem_subspace_eq_self, Equiv.isTrivialRelation_comp, CategoryTheory.Iso.trans_conj, Ideal.Quotient.mk_eq_one_iff_sub_mem, ContinuousEval.continuous_eval, Algebra.smul_def, HomologicalComplex.alternatingConst_iCycles_odd_comp_apply, Polynomial.natDegree_mul_C, Field.Emb.Cardinal.adjoin_image_leastExt, WithZeroMulInt.toNNReal_pos_apply, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, NumberField.IsCMField.indexRealUnits_eq_two_iff, MeasureTheory.L1.setToL1_zero_left', MeasureTheory.BoundedContinuousFunction.inner_toLp, exteriorPower.basis_repr, MeasureTheory.Measure.haar.is_left_invariant_addHaarContent, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_π_assoc, CategoryTheory.HasLiftingProperty.transfiniteComposition.wellOrderInductionData.map_lift, RelEmbedding.not_acc, ContinuousLinearMap.adjoint_inner_right, AddGroupSeminorm.coe_zero, AddMonoidAlgebra.mapRangeAddEquiv_single, Circle.coeHom_apply, exists_extension_norm_eq, map_nonneg, LinearEquiv.lTensor_trans_apply, FirstOrder.Language.Hom.range_eq_top, ProbabilityTheory.Kernel.sectL_apply, MvPolynomial.ringHom_ext'_iff, Derivation.sub_apply, BddDistLat.ext_iff, MvPolynomial.mem_ideal_span_monomial_image_iff_dvd, map_nnratCast_smul, OrderIso.sumLexIioIci_apply_inl, AlternatingMap.map_swap, HVertexOperator.compHahnSeries_coeff, NormedAddGroupHom.extension_def, DifferentiableWithinAt.clm_apply, Complex.dist_conj_comm, HahnSeries.map_smul, finSuccEquiv'_eq_none, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, MulEquiv.funUnique_apply, ContinuousAlternatingMap.map_update_zero, SymAlg.unsym_mul_self, RingCon.ringConGen_idem, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, AffineIsometryEquiv.injective, CliffordAlgebra.EquivEven.involute_e0, GroupNorm.coe_lt_coe, Equiv.sumComm_apply, BotHom.coe_sup, Equiv.Perm.map_finRange_perm, CompHausLike.isoOfHomeo_inv_hom_hom_apply, AddSubmonoid.LocalizationMap.map_id, PMF.toOuterMeasure_apply, Equiv.Perm.equivUnitsEnd_symm_apply_apply, legendreSym.at_neg_two, Bialgebra.counit_one, IsRegular.monomial, map_sdiff', LieDerivation.smul_apply, Sum.Lex.inr_mono, Equiv.pointReflection_self, Finset.imageOneHom_apply, ZMod.χ₄_int_eq_if_mod_four, Valuation.integer.v_irreducible_lt_one, RatFunc.liftAlgHom_apply_div', Cardinal.ofENat_toENat_le, groupHomology.π_comp_H2Iso_hom_apply, Equiv.comp_symm_eq, OrderIso.map_ciSup_of_directed, Matrix.charpoly.univ_map_eval₂Hom, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, Matrix.transposeAlgEquiv_symm_apply, Matrix.det_fin_two_of, AlgebraicGeometry.Scheme.Hom.support_ker, rootsOfUnityCircleEquiv_apply, InfHom.symm_dual_id, Profinite.NobelingProof.CC_comp_zero, LieSubmodule.coe_toEnd_pow, CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality, RootPairing.InvariantForm.apply_eq_or, DistribMulActionHom.map_smulₑ, ConvexOn.comp_affineMap, SupClosed.preimage, CategoryTheory.Groupoid.isoEquivHom_symm_apply_inv, Equiv.piCongrLeft'_symm_apply, ContinuousAffineMap.prod_apply, SeparationQuotient.isEmbedding_outCLM, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, Submodule.lTensorOne_tmul, SheafOfModules.relationsOfIsCokernelFree_s, MeasurableEquiv.setOf_symm_apply, toUnits_val_apply, MeasureTheory.SimpleFunc.mem_image_of_mem_range_restrict, MeasurableEquiv.coe_piCurry, Polynomial.Splits.toPermHom_apply_eq_one_or_isSwap_of_ncard_le_of_mem_inertia, CuspFormClass.zero_at_infty_slash, EReal.sign_mul_inv_abs, BoxIntegral.Box.measurableSet_Ioo, FreeAbelianGroup.lift_add_apply, WithTop.orderIsoSumLexPUnit_symm_inr, SemidirectProduct.inv_left, Submodule.quotientPiLift_mk, CategoryTheory.ShiftedHom.opEquiv_symm_apply, AddChar.toAddMonoidHomEquiv_zero, Matrix.Nondegenerate.toBilin', Subsemigroup.apply_coe_mem_map, tendsto_measure_cthickening_of_isCompact, ContinuousLinearEquiv.prodProdProdComm_apply, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, Specialization.ofEquiv_specializes_ofEquiv, RCLike.mul_re, AbsoluteValue.add_le, StrictConvexOn.dual, ContDiff.contDiff_fderiv_apply, BddOrd.comp_apply, WeierstrassCurve.φ_four, CategoryTheory.Limits.Concrete.prodEquiv_apply_snd, FirstOrder.Language.ElementarySubstructure.coe_subtype, Polynomial.roots_expand_pow_image_iterateFrobenius_subset, Monoid.CoprodI.Word.equivPair_head, FDRep.Iso.conj_ρ, LinearMap.isPositive_iff, MonoidHom.map_isConj, FirstOrder.Language.StrongHomClass.realize_boundedFormula, WithBot.coeOrderHom_apply, TensorProduct.directLimitLeft_tmul_of, RingCon.coe_mk', BoundingSieve.nu_pos_of_prime, MeasureTheory.SimpleFunc.exists_upperSemicontinuous_le_lintegral_le, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_str, UniformSpace.Completion.continuous_toCompl, IsLocalization.ringEquivOfRingEquiv_eq, finsuppAddEquivDFinsupp_apply, Ordinal.typein_one_toType, Con.sSup_def, CategoryTheory.Limits.FintypeCat.jointly_surjective, Lagrange.interpolate_poly_eq_self, PowerSeries.C_inv, ContinuousLinearMap.measurable_apply', RingHom.surjectiveOnStalks_iff_of_isLocalHom, FreeAddMonoid.map_of, MulEquiv.coprodAssoc_symm_apply_inl, Polynomial.rootMultiplicity_X_sub_C_self, FractionalIdeal.map_canonicalEquiv_mk0, HasStrictFDerivAt.continuousAlternatingMap_apply_const, LinearMap.IsAlt.eq_of_add_add_eq_zero, ContDiffMapSupportedIn.coe_coeHom, ContinuousLinearMap.toSpanSingletonLE_symm_apply, AlgebraicGeometry.Scheme.Hom.homeomorph_apply, VectorFourier.fourierIntegral_comp_add_right, ContinuousMulEquiv.equivLike_inv_eq_symm, Behrend.bound_aux, UniformConvergenceCLM.uniformSpace_eq, FirstOrder.Language.Theory.CompleteType.mem_typeOf, AddConstMap.coe_vadd, AlgebraicGeometry.Scheme.Hom.stalkMap_congr, AlgEquiv.ofAlgHom_apply, DistribMulActionHom.toFun_eq_coe, eq_nnratCast, PMF.toOuterMeasure_apply_eq_zero_iff, IsometryEquiv.piFinTwo_apply, SemilinearIsometryClass.diam_image, LieModuleHom.add_apply, ContinuousMap.addEquivBoundedOfCompact_symm_apply, MeasureTheory.IsFiniteMeasureOnCompacts.lt_top_of_isCompact, ContDiffMapSupportedIn.postcompLM_apply, ContinuousAddMonoidHom.inr_toFun, Polynomial.taylor_coeff, LinearMap.toMatrix_singleton, LinearMap.isNonneg_def, AddSubgroup.toSubgroup'_closure, Rat.ringOfIntegersEquiv_symm_apply_coe, MulActionHom.id_apply, LinearMap.BilinForm.toMatrix'_mul, Equiv.Finset.union_inr, LinearMap.injOn_of_disjoint_ker, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, MvPolynomial.aeval_one_tmul, Algebra.trace_prod_apply, DifferentiableAt.clm_apply, SupHom.toFun_eq_coe, RelEmbedding.sorted_listMap, Module.Flat.iff_rTensor_injectiveₛ, minpoly.eq_iff_aeval_minpoly_eq_zero, dotProductBilin_apply_apply, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, signedDist_lineMap_right, Subgroup.IsComplement'.QuotientMulEquiv_symm_apply, MeasureTheory.measure_preimage_eq_zero_iff_of_countable, AlgHom.coe_equalizer, Nat.factorization_def, MulEquiv.symm_comp_eq, SimpleGraph.Walk.edgeSet_map, MvPolynomial.monomial_pow, TemperedDistribution.laplacian_apply_apply, Polynomial.splits_X_sub_C, Submodule.LinearDisjoint.val_mulMap_tmul, Matrix.blockDiagAddMonoidHom_apply, RestrictedProduct.continuous_eval, IsChain.image_iso_iff, AddMonoidAlgebra.domCongr_apply, LaurentSeries.derivative_iterate, ContinuousMap.HomotopyWith.symm_apply, MeasureTheory.Lp.toLp_compMeasurePreserving, Algebra.trace_trace_of_basis, AddConstMap.coe_id, Topology.WithUpper.isOpen_def, RingHom.surjective, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, OrthonormalBasis.coe_toHilbertBasis, MvPolynomial.eval_sum, Complex.GammaIntegral_conj, spectralNorm_extends_of_finiteDimensional, Submodule.mkQ_surjective, Algebra.discr_powerBasis_eq_prod'', VitaliFamily.ae_eventually_measure_pos, WittVector.iterate_verschiebung_coeff, convexHull_prod, ProbabilityTheory.posterior_posterior, Polynomial.algEquivCMulXAddC_symm_apply, RingHom.mem_fieldRange, ModularForm.is_invariant_one', Set.powersetCard.coe_mulActionHom_compl, Dilation.ext_iff, Traversable.foldMap_hom, dist_pointReflection_left, MeasureTheory.eLpNorm_indicator_const₀, PowerSeries.derivative_subst, MultilinearMap.piFamily_single, UpperSet.coe_map, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_ε, TensorAlgebra.algebraMap_leftInverse, AddAction.coe_toPermHom, ContinuousMap.homeoFnOfDiscrete_symm_apply_apply, Polynomial.taylor_inj, Matrix.diagonal_unique, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, AlgebraicGeometry.Scheme.map_basicOpen_map, MeasureTheory.SimpleFunc.aestronglyMeasurable, LocallyConstant.coe_algebraMap, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, PMF.toMeasure_apply_inter_support, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, StarAlgEquiv.nnnorm_map, MeasureTheory.Measure.infinitePi_singleton, Ideal.absNorm_eq_pow_inertiaDeg, AddEquiv.coe_toNatLinearEquiv, LinearIsometryEquiv.symm_smul_apply, MeasureTheory.isZeroOrProbabilityMeasureSMul, Polynomial.derivative_zero, EisensteinSeries.eisensteinSeriesSIF_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, Polynomial.opRingEquiv_symm_C, Algebra.traceMatrix_of_basis_mulVec, ContinuousMap.IccExtendCM_of_mem, SchwartzMap.tsupport_derivCLM_subset, IsBaseChange.basis_repr_comp, MvPowerSeries.monomial_zero_one, MeasureTheory.SimpleFunc.measurableSet_cut, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, DirectSum.smul_apply, MvPowerSeries.monomial_one_eq, WeierstrassCurve.Affine.baseChange_addY, CocompactMap.coe_comp, Algebra.Extension.Hom.sub_tmul, ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on, RCLike.normSq_zero, FreeAddGroup.lift_eq_sum_map, isLocalHomeomorph_circleExp, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, PowerSeries.IsRestricted.monomial, VectorField.pullback_eq_of_fderiv_eq, AddMonoidHom.coe_dfinsuppSum, CategoryTheory.Adjunction.homEquiv_counit, mulMulHom_apply, Matrix.ofNat_kronecker, Homeomorph.coe_mulLeft₀, GroupExtension.Section.rightInverse_rightHom, IsCyclotomicExtension.norm_zeta_eq_one, StarMulEquiv.trans_apply, IsDiscreteValuationRing.addVal_def, ProbabilityTheory.lintegral_preCDF_fst, OrderAddMonoidHom.snd_apply, SimpleGraph.Coloring.surjOn_of_card_le_isClique, ArithmeticFunction.cardFactors_eq_zero_iff_eq_zero_or_one, tendsto_integral_exp_inner_smul_cocompact, Topology.WithLower.continuous_toLower, exteriorPower.alternatingMapLinearEquiv_symm_apply, OrthonormalBasis.coe_toBasis_repr_apply, Finsupp.mapDomain.toLinearMap_linearEquiv, FractionalIdeal.mem_canonicalEquiv_apply, AddHom.coprod_apply, MvPolynomial.smul_eq_C_mul, MeasureTheory.Measure.coe_completion, FunctionField.inftyValuation.C, SemiNormedGrp.comp_apply, coe_normAddGroupSeminorm, MvPolynomial.eval₂_monomial, Affine.Simplex.mongePlane_reindex, det_rotation, TensorProduct.lid'_symm_apply, SkewPolynomial.monomial_mul_monomial, InfHom.coe_id, PowerSeries.coeff_expand, VitaliFamily.measure_limRatioMeas_top, ContinuousAddEquiv.apply_eq_iff_symm_apply, BoundedLatticeHom.coe_toInfTopHom, QuadraticMap.polar_smul_right_of_tower, AddCommMonCat.equivalence_counitIso, Monotone.measure_iUnion, Nat.coprime_ordCompl, Orientation.reindex_apply, MulOpposite.coe_opMulEquiv, UniformOnFun.toFun_add, NonUnitalSubringClass.subtype_apply, LieSubmodule.mem_map_of_mem, rootsOfUnity.integer_power_of_ringEquiv', MvPolynomial.counitNat_C, Hamming.dist_eq_hammingDist, RCLike.enorm_conj, ProbabilityTheory.Kernel.zero_apply, sign_finRotate, affineCombination_eq_centerMass, MeasureTheory.integrable_continuousLinearMap_prod, MeasureTheory.SimpleFunc.coe_intCast, SymAlg.sym_eq_zero_iff, Ideal.quotientMap_injective, Equiv.addLeft_symm_apply, Monoid.Coprod.mclosure_range_inl_union_inr, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, IntermediateField.adjoin_subset_adjoin_iff, RingEquiv.piFinTwo_symm_apply, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, Finset.map_subset_iff_subset_preimage, IsAdicComplete.mk_lift, RestrictedProduct.topologicalSpace_eq_of_bot, LieModule.mem_genWeightSpaceOf, IsAlgClosed.roots_eq_zero_iff, MeasureTheory.OuterMeasure.isCaratheodory_partialSups, DistribMulActionHom.ext_ring_iff, AdicCompletion.evalOneₐ_surjective, MeasureTheory.measure_preimage_add_right, LieDerivation.apply_lie_eq_sub, Derivation.coe_sub, ContinuousMap.C_apply, PiLp.coe_symm_continuousLinearEquiv, ZLattice.normBound_spec, IsDedekindDomain.adjoin_union_eq_top_of_isCoprime_differentialIdeal, OrderIso.sumDualDistrib_inr, PowerSeries.algebraMap_apply, Algebra.map_intTraceAux, LinearMap.sum_apply, LatticeHom.coe_comp_inf_hom', CompleteSublattice.mem_comap, SimpleGraph.IsVertexCover.preimage, ModuleCat.biproductIsoPi_inv_comp_π_apply, QuadraticMap.apply_linearCombination, Valuation.IsNontrivial.exists_lt_one, CategoryTheory.ShiftedHom.opEquiv'_apply, SSet.S.equivElements_symm_apply_simplex, CategoryTheory.Presheaf.equalizerSieve_apply, CochainComplex.toSingle₀Equiv_apply, TopologicalSpace.IrreducibleCloseds.equivSubtype_symm_apply, RelIso.self_comp_symm, ContinuousLinearEquiv.dimH_preimage, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd, BoundedContinuousFunction.coe_negPart, grade_ofDual, NonUnitalSubsemiring.mem_comap, Function.Embedding.coe_sumMap, Polynomial.natDegree_cubic, LinearMap.toMatrix₂'_compl₂, CliffordAlgebra.evenEquivEvenNeg_symm_apply, ProbabilityTheory.condDistrib_const, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, OmegaCompletePartialOrder.ContinuousHom.continuous, ContDiffWithinAt.fderivWithin_right_apply, CompleteLatticeHom.dual_apply_toFun, RatFunc.liftRingHom_algebraMap, LatticeHom.coe_comp_sup_hom', Disjoint.map_orderIso, OrderAddMonoidIso.strictMono, Polynomial.degree_leadingCoeff_inv, IsLocalization.mk'_mul_cancel_right, CommSemiRingCat.inv_hom_apply, LaurentPolynomial.comul_C_mul_T, Polynomial.algHom_eval₂_algebraMap, CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_apply, PiTensorProduct.map_reindex, ContinuousAffineMap.vsub_apply, OrderIso.symm_apply_apply, IsExtrOn.dual, Finset.symInsertEquiv_apply_fst, Units.embed_product_star, PseudoMetric.mk_apply, IsLocalization.exists_integer_multiple', ProbabilityTheory.Kernel.lintegral_prodMkLeft, CategoryTheory.isoOpEquiv_apply, SchwartzMap.integral_smul_laplacian_right_eq_left, Polynomial.IsMonicOfDegree.aeval_sub, uliftZPowersHom_apply_apply, CategoryTheory.Adjunction.leftAdjointCompNatTrans₀₂₃_eq_conjugateEquiv_symm, TensorPower.mul_algebraMap₀, AdicCompletion.factor_evalₐ_eq_eval, Profinite.NobelingProof.eval_eq_πJ, ContinuousMultilinearMap.smulRight_apply, IsLocalization.Away.surj, SchwartzMap.le_seminorm', Basis.multilinearMap_apply, MulHom.srangeRestrict_surjective, MulHom.map_mul, MeasureTheory.setToFun_const, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atTop, MvPolynomial.finSuccEquiv_rename_finSuccEquiv, Ordinal.toNimber_toOrdinal, Equiv.optionSubtypeNe_some, Cardinal.toENat_le_one, EuclideanGeometry.reflection_involutive, Equiv.symmEquiv_symm_apply_symm_apply, Nat.Prime.pow_dvd_iff_le_factorization, TrivSqZeroExt.map_inl, AddValuation.mem_supp_iff, Algebra.Presentation.HasCoeffs.relation_mem_range_map, LinearIsometryEquiv.coe_symm_trans, WithCStarModule.equiv_fst, PowerSeries.coe_aeval, InverseSystem.globalEquiv_naturality, MeasureTheory.Measure.dirac_compProd_apply, Rep.leftRegularHomEquiv_apply, MeasureTheory.AEStronglyMeasurable.integral_condDistrib, imaginaryPart_smul, map_sub_le_add, Submodule.mem_iSup_of_chain, AffineIndependent.injOn_affineCombination_fintypeAffineCoords, MvPolynomial.rename_expand, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, ContinuousLinearMapWOT.add_apply, Quaternion.snd_imI_dualNumberEquiv_symm, isStronglyTranscendental_mk_of_mem_minimalPrimes, Seminorm.coeFnAddMonoidHom_apply, Fin.appendHomeomorph_symm_apply, Equiv.Perm.IsCycle.sign, RCLike.re_le_neg_norm_iff_eq_neg_norm, CliffordAlgebraComplex.toComplex_involute, IsPrimitiveRoot.autToPow_spec, LaurentPolynomial.smeval_C_mul_T_n, OrthonormalBasis.coe_equiv_euclideanSpace, NumberField.mixedEmbedding.norm_real, LinearMap.map_sum₂, VectorFourier.fourierIntegral_probChar, Equiv.Perm.sign_inv, RCLike.conjAe_coe, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_str, MaximalSpectrum.toPiLocalization_not_surjective_of_infinite, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, RelIso.toInitialSeg_toFun, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, BoundedLatticeHom.coe_comp, InitialSeg.isSuccPrelimit_apply_iff, Subalgebra.restrictScalars_toSubmodule, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, SlashInvariantFormClass.norm_petersson_smul, Valuation.Integers.isUnit_iff_valuation_eq_one, Metric.Snowflaking.edist_def, Submodule.mem_map_of_mem, MeasureTheory.Lp.simpleFunc.measurable, ModuleCat.restrictScalars.smul_def', LinearEquiv.ext_iff, Affine.Simplex.sign_signedInfDist_incenter, Homeomorph.isOpenEmbedding, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, MeasureTheory.Measure.prod_comp_right, NormedSpace.algebraMap_exp_comm_of_mem_ball, PresheafOfModules.pushforward_obj_map_apply', ContinuousMap.polynomial_comp_attachBound, Orientation.rightAngleRotation_map, CategoryTheory.Preadditive.mono_iff_injective', HeytingHom.toFun_eq_coe, MeasureTheory.Measure.measure_prod_null, OrderIso.apply_blimsup, Polynomial.toFinsupp_C_mul_X_pow, Finsupp.Colex.single_le_iff, IsUpperSet.toDual, antivary_toDual_left, OrderDual.toDual_eq_bot, finsuppAddEquivDFinsupp_symm_apply, Polynomial.expand_eval, AlternatingMap.measure_parallelepiped, WeierstrassCurve.Projective.baseChange_neg, LieDerivation.injective_ad_of_center_eq_bot, OrderIso.setCongr_apply, map_zsmul_unit, AddSubgroup.quotientEquivProdOfLE'_symm_apply, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, MeasureTheory.OuterMeasure.map_top_of_surjective, MeasureTheory.ProbabilityMeasure.coeFn_toFiniteMeasure, DirectSum.Decomposition.left_inv, RootPairing.Hom.coroot_coweightMap_apply, Function.locallyFinsuppWithin.coe_add, PartENat.withTopEquiv_symm_coe, ContinuousWithinAt.coeFun, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap, SimpleGraph.Embedding.coe_completeGraph, Matrix.entryLinearMap_apply, Seminorm.preimage_metric_ball, Polynomial.logMahlerMeasure_const, SemidirectProduct.mulEquivSubgroup_apply, Equiv.simpleGraph_apply, ProbabilityTheory.Kernel.iIndepFun.meas_iInter, ENNReal.logHomeomorph_apply, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, ContinuousAffineMap.hasFDerivWithinAt, Set.image_div, MeasureTheory.Measure.count_apply_eq_top', MeasureTheory.Measure.ext_iff_singleton, Polynomial.natDegree_C_mul_of_isUnit, SymAlg.unsym_sub, Polynomial.hermite_zero, Real.volume_univ, Algebra.algebra_ext_iff, LinearEquiv.coe_injective, MeasureTheory.Measure.measure_support_eq_zero_iff, MeasureTheory.ProbabilityMeasure.measureReal_eq_coe_coeFn, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, WithTop.ofDual_symm_apply, ZMod.castHom_injective, ContinuousMonoidHom.coprod_toFun, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, sInfHom.ext_iff, MeasureTheory.Measure.finite_const_le_meas_of_disjoint_iUnion, CategoryTheory.Presheaf.coconeOfRepresentable_ι_app, isAlgebraic_iff_not_injective, Finsupp.embSigma_apply, CompareReals.compare_uc_symm, ContinuousAlternatingMap.nnnorm_ofSubsingleton, MvPolynomial.IsHomogeneous.sum_X_mul_pderiv, norm_cfcHom, AddActionHom.prodMap_apply, MvPolynomial.derivation_C_mul, LinearAlgebra.FreeProduct.lift_symm_apply, CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso, MulChar.coe_toUnitHom, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, LieAlgebra.IsKilling.traceForm_coroot, DomMulAct.isOpenEmbedding_mk_symm, RCLike.to_complex_nonneg_iff, Multiset.cast_apply_snd, Polynomial.dickson_two, Pi.evalMulHom_apply, Ordinal.toNimber_max, MonoidHom.coe_range, DirectSum.GAlgebra.map_one, FirstOrder.Language.PartialEquiv.symm_apply, IsCyclic.mulAutMulEquiv_symm_apply_apply, Profinite.NobelingProof.Products.evalFacProp, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, Polynomial.succ_signVariations_X_sub_C_mul_monomial, MeasureTheory.charFunDual_map, IsAdjoinRootMonic.coeff_apply_coe, Module.toAddMonoidEnd_apply_apply, InfiniteGalois.proj_of_le, EquivLike.surjective, StarAlgebra.adjoin_eq_span, Order.isSuccPrelimit_toDual_iff, ClassGroup.mk_eq_one_of_coe_ideal, ContinuousLinearMap.le_of_opNorm₂_le_of_le, Equiv.injective, QuadraticMap.Isometry.inr_apply, AlgebraicGeometry.Scheme.Hom.surjective, Polynomial.derivative_X_add_C_sq, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit, Subring.opEquiv_symm_apply, Orientation.kahler_rotation_right, LieIdeal.map_le, Nat.equivProdNatFactoredNumbers_apply', Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative, PointedCone.mem_comap, Set.dual_ordConnected_iff, Submodule.orthogonalProjectionFn_eq, CircleDeg1Lift.map_lt_add_translationNumber_add_one, ContinuousMap.isOpen_setOf_range_subset, MeasureTheory.countable_meas_le_ne_meas_lt, Algebra.Generators.ofAlgEquiv_val, ProbabilityTheory.Kernel.setIntegral_density, Fourier.fourierIntegral_def, CliffordAlgebraComplex.toComplex_ofComplex, LieModuleEquiv.apply_symm_apply, StarMulEquiv.coe_trans, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, Submonoid.toAddSubmonoid'_closure, Action.diagonalSuccIsoTensorDiagonal_hom_hom, LinearMap.BilinForm.comp_apply, ContDiffMapSupportedIn.coe_neg, ZSpan.discreteTopology_pi_basisFun, AddMonoid.Coprod.closure_range_inl_union_inr, CircleDeg1Lift.coe_pow, IsAddFoelner.tendsto_meas_vadd_symmDiff, ContinuousMapZero.comp_apply, Cubic.eq_sum_three_roots, iteratedFDerivWithin_clm_apply_const_apply, ModularFormClass.analyticAt_cuspFunction_zero, Finset.map_erase, HahnSeries.SummableFamily.hsum_smulFamily, ContinuousMultilinearMap.currySum_apply, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.sigma_ι_isOpenEmbedding, isOpenMap_barycentric_coord, QuotientAddGroup.kerLift_mk', CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm_assoc, Monoid.Foldr.ofFreeMonoid_apply, TensorProduct.nnnorm_comm, Polynomial.as_sum_support, MonoidHom.map_finprod, BoundingSieve.multSum_eq_main_err, MvPolynomial.aeval_sumElim_pderiv_inl, WittVector.frobeniusEquiv_apply, AlternatingMap.coe_compLinearMap, MeasureTheory.Measure.measure_pos_of_mem_nhds, Affine.Simplex.signedInfDist_affineCombination, wellQuasiOrdered_iff_exists_monotone_subseq, MvPolynomial.monomial_one_dvd_monomial_one, Ideal.cotangentEquivIdeal_symm_apply, equivShrink_inv, Module.flat_iff, CategoryTheory.Functor.IsCoverDense.is_cover, MultilinearMap.compLinearMap_apply, RingHom.RespectsIso.isLocalization_away_iff, FiniteField.expand_card, MeasureTheory.OuterMeasure.restrict_apply, Module.Basis.traceDual_repr_apply, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, RatFunc.mk_one', TwoSidedIdeal.mem_ker, ContinuousAlternatingMap.toContinuousLinearMap_apply, TensorAlgebra.mk_reindex_cast, UniformSpaceCat.coe_id, TemperedDistribution.lineDerivOp_apply_apply, AnalyticAt.aeval_mvPolynomial, quadraticChar_neg_one_iff_not_isSquare, Antivary.dual_right, MvPolynomial.mul_monomial_modMonomial, QuotientAddGroup.equivIcoMod_zero, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, MulHom.subsemigroupMap_apply_coe, AlgebraicGeometry.Scheme.IsLocallyDirected.exists_of_pullback_V_V, IsometryEquiv.coe_one, QuadraticAlgebra.norm_star, HahnModule.of_symm_zero, OrderIso.sumLexAssoc_apply_inr, FirstOrder.Language.DirectLimit.Equiv_isup_of_apply, MvPolynomial.tensorEquivSum_one_tmul_X, AlgHom.map_algebraMap, UniformFun.ofFun_sub, PiTensorProduct.lift.unique', Polynomial.coeff_expand_mul', Topology.WithUpper.toUpper_le_toUpper, Polynomial.comp_eq_sum_left, LowerSet.map_Iic, QuaternionAlgebra.imJ_equivProd_symm_apply, Polynomial.differentiableWithinAt_aeval, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_obj, Polynomial.coeff_mirror, Matrix.nondegenerate_toLinearMap₂'_iff, Nat.factorization_factorial_le_div_pred, AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology, CategoryTheory.regularTopology.mem_sieves_of_hasEffectiveEpi, OrderDual.ofDual_toDual, FreeAbelianGroup.ofMulHom_coe, signedDist_apply, Polynomial.rootMultiplicity_X_sub_C, LieDerivation.coe_zero, NormedAddGroupHom.ker.lift_apply_coe, Unitization.norm_splitMul_snd_sq, LinearMap.separatingRight_toMatrix₂_iff, AddAut.one_apply, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, MeasureTheory.measure_add_measure_compl₀, OrderIso.funUnique_symm_apply, Sym.coe_cast, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, CoxeterSystem.map_simple, GrpCat.one_apply, infClosure_supClosure, finRotate_symm_lt_iff_ne_zero, ContinuousMap.mabs_apply, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage, DirectSum.IsInternal.ofBijective_coeLinearMap_of_ne, AdjoinRoot.coe_algEquivOfEq, MonoidHom.ext_iff₂, cfc_predicate_algebraMap, Equiv.Perm.subtypeCongr.left_apply, Function.Embedding.coe_injective, MvPolynomial.iterToSum_C_C, FGModuleCat.FGModuleCatEvaluation_apply', Polynomial.natTrailingDegree_monomial_le, MvPolynomial.totalDegree_sub_C_le, BooleanSubalgebra.coe_comap, LieModule.traceForm_eq_sum_finrank_nsmul_mul, Set.OrdConnected.apply_covBy_apply_iff, Ordinal.mem_range_preOmega_iff, ContinuousMap.evalAlgHom_apply, WeakDual.CharacterSpace.equivAlgHom_coe, ContinuousMap.HomotopyWith.continuous, DirectSum.coe_mul_apply_eq_sum_antidiagonal, MulEquiv.withZero_symm_apply_apply, Matrix.SpecialLinearGroup.toLin'_injective, QuadraticMap.coeFn_sum, Equiv.Perm.IsThreeCycle.sign, MeasurableEquiv.measurable, ProbabilityTheory.uniformOn_compl, AddGrpCat.coe_comp, CentroidHom.coe_smul, MvPolynomial.coeffAddMonoidHom_apply, EuclideanGeometry.angle_self_orthogonalProjection, convexHull_eq_union, MeasureTheory.tendstoInMeasure_iff_enorm, MeasureTheory.StronglyMeasurable.stronglyMeasurable_in_set, WeierstrassCurve.Jacobian.map_dblU, ProbabilityTheory.condDistrib_fst_prod, OrderHom.dual_symm_apply_coe, Equiv.optionSubtypeNe_none, EReal.sign_mul_abs, Submodule.exists_fg_le_eq_rTensor_subtype, WeierstrassCurve.Projective.Equation.map, HahnSeries.ofPowerSeries_apply, Equiv.pointReflection_midpoint_left, RelHom.comp_apply, SemilinearIsometryClass.norm_map, AddEquiv.trans_apply, RootPairing.Base.span_root_support, OrderIso.map_ciSup_set_of_directedOn, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add, HahnModule.of_zero, TensorProduct.piScalarRight_apply, continuousMultilinearCurryRightEquiv_apply', AdjoinRoot.aeval_eq, DistLat.Iso.mk_hom, MeasurableEquiv.coe_mulLeft₀, CliffordAlgebra.lift_comp_ι, DistribMulActionHom.map_zero, Module.Basis.range_reindex, NormedAddGroupHom.completion_coe', DirectSum.decompose_mul, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, Subgroup.IsComplement.equiv_mul_right, AddGroupExtension.Equiv.inl_comm, ValuativeExtension.mapPosSubmonoid_apply_coe, isOpenMap_ofAdd, DilationEquiv.surjective, Finsupp.liftAddHom_symm_apply_apply, groupHomology.coe_mapCycles₁, Metric.Snowflaking.preimage_ofSnowflaking_emetricBall, MonoidHom.map_zpowers, NumberField.Units.logEmbeddingEquiv_apply, RootPairing.coreflection_same, ContinuousMultilinearMap.compAlongComposition_apply, MulEquiv.op_symm_apply_symm_apply, LinearEquiv.lTensor_symm_tmul, MeasureTheory.Lp.meas_ge_le_mul_pow_enorm, Cardinal.toENat_injOn, Coalgebra.lTensor_counit_comp_comul, AddMonoid.End.one_apply, LieModule.coe_maxTrivEquiv_apply, SlashInvariantForm.coe_add, IsClosed.measure_eq_univ_iff_eq, LinearIndepOn.encard_le_toENat_rank, Equiv.Perm.isCycleOn_singleton, TopologicalSpace.Opens.apply_mk, Polynomial.coeff_zero_eq_aeval_zero', PowerSeries.eval₂_trunc_eq_sum_range, Orthonormal.comp_linearIsometryEquiv, equicontinuousAt_iff_continuousAt, Ordinal.sup_typein_limit, UniformOnFun.toFun_inv, Differential.algEquiv_deriv', Con.map_apply, SpecialLinearGroup.coe_toGeneralLinearGroup_apply, IsLocalizedModule.map_units, SymmetricPower.tprod_equiv, TopologicalSpace.Opens.infLELeft_apply, AddEquiv.toMultiplicativeLeft_symm_apply_apply, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, CategoryTheory.ShrinkHoms.comp_def, AddMonoidAlgebra.single_mul_apply_aux, TemperedDistribution.lineDerivOp_fourierInv_eq, AlternatingMap.curryLeft_compLinearMap, RCLike.im_ofReal_mul, CategoryTheory.Iso.conjAut_zpow, IsLocalization.adjoin_inv, LieAlgebra.nilpotent_ad_of_nilpotent_algebra, TopCat.isOpen_iff_of_isColimit_cofork, quadraticChar_eq_pow_of_char_ne_two, ContinuousAffineEquiv.bijective, IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one, finSumNatEquiv_symm_apply_of_ge, WeierstrassCurve.Affine.Equation.map, fourierCoeffOn_eq_integral, LinearMap.det_ring, Subgroup.mem_iff_toUnits_mem_units, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, FreeAbelianGroup.lift_ext_iff, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_injective, AddMonoidHom.add_apply, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, SMulMemClass.subtype_apply, CliffordAlgebra.changeForm.associated_neg_proof, MeasureTheory.measure_average_le_pos, WithBot.toDual_symm_apply, NonemptyInterval.toLex_lt_toLex, AlternatingMap.domDomCongr_perm, LinearMap.coe_det, ContDiffMapSupportedIn.bounded_iteratedFDeriv, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, Matrix.mulVecLin_reindex, factor_orderIso_map_one_eq_bot, LieModule.genWeightSpace_chainTopCoeff_add_one_nsmul_add, Submodule.iSup_eq_toSubmodule_range, inner_self_re_eq_norm, PowerSeries.trunc_one_X, Dilation.mapsTo_emetric_ball, CompactlySupportedContinuousMap.coe_neg, OrderAddMonoidIso.invFun_eq_symm, Subgroup.closure_preimage_eq_top, Module.Relations.toQuotient_relation, ProbabilityTheory.Kernel.integral_integral_indicator, prevD_comp_right, Polynomial.leval_coe_eq_smeval, Derivation.commutator_apply, Equiv.surjective, MvPolynomial.isSymmetric_rename, FirstOrder.Language.HomClass.toHom_toFun, Circle.expHom_apply, IsEvenlyCovered.comp_homeomorph, WeierstrassCurve.Projective.map_add, convexHull_eq, SimpleGraph.support_map, HasFiniteFPowerSeriesOnBall.hasFDerivAt, SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquiv, Subsemiring.ringEquivOpMop_apply, AddConstMapClass.map_ofNat, AddValuation.map_div, BoolAlg.inv_hom_apply, ContinuousMap.coe_prod, HomeomorphClass.coe_coe, CategoryTheory.Discrete.monoidalFunctor_μ, LinearMap.BilinForm.neg_right, GrpCat.forget_map, homeomorphUnitSphereProd_apply_snd_coe, ProbabilityTheory.variance_dual_prod, IsSublattice.image, CliffordAlgebra.ofEven_ι, CategoryTheory.Limits.WalkingPair.swap_apply_left, IsLocalHomeomorph.isTopologicalBasis, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atTop_one, Cardinal.toENat_eq_nat, Polynomial.dvd_comp_X_sub_C_iff, CategoryTheory.Localization.SmallShiftedHom.precompEquiv_apply, exteriorPower.map_apply_ιMulti, SSet.yonedaEquiv_comp, ProbabilityTheory.isGaussian_map_equiv, AddEquiv.addIrreducible_iff, LieAlgebra.Extension.proj_surjective, sSupHom.ext_iff, Filter.HasBasis.nhds_continuousMapConst, MvPolynomial.mkDerivationₗ_X, Module.Basis.prod_apply_inl_fst, LaurentPolynomial.leftInverse_trunc_toLaurent, LightDiagram.comp_hom_hom_hom_apply, MvPolynomial.eval₂_C_mk_eq_zero, HasFDerivAt.hasGradientAt, Algebra.H1Cotangent.exact_map_δ, EuclideanGeometry.dist_affineCombination, NumberField.basisOfFractionalIdeal_apply, AbsoluteValue.IsEquiv.one_le_iff, AlgEquiv.op_symm_apply_apply, DirectSum.Decomposition.right_inv, Ordinal.omega_max, Equiv.Perm.IsCycle.forall_commute_iff, WellFoundedGT.monotone_chain_condition', SSet.op_map, Module.End.isUnit_apply_inv_apply_of_isUnit, CliffordAlgebra.ofBaseChange_tmul_one, MulActionHom.oneEmbeddingMap_bijective, Function.fromTypes_zero_equiv_apply, MeasureTheory.Measure.join_apply, contMDiff_tangentBundleModelSpaceHomeomorph, Nat.orderEmbeddingOfSet_range, MulHom.map_dvd, ContinuousAlgEquiv.cast_apply, ContinuousLinearMap.isBigOTVS_fun_comp, Orientation.oangle_sign_smul_add_smul_right, LocallyConstant.coeFnₗ_apply, DomMulAct.symm_mk_inv, groupCohomology.d₀₁_comp_d₁₂_apply, OrderIso.image_eq_preimage_symm, CategoryTheory.ObjectProperty.isColocal.homEquiv_apply, Module.Basis.ofZLatticeComap_repr_apply, RCLike.normSq_eq_zero, ProbabilityTheory.posterior_comp_self, MvPowerSeries.monomial_eq, MeasureTheory.Measure.tsum_indicator_apply_singleton, NonUnitalSubring.coe_comap, UniformOnFun.ofFun_mul, Polynomial.roots_expand_pow, signedDist_eq_dist_iff_vsub_mem_span, AlternatingMap.map_swap_add, ContinuousMap.pi_eval, FirstOrder.Language.BoundedFormula.mapTermRelEquiv_symm_apply, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, Sum.Lex.not_inr_le_inl, AlgHom.map_adjoin_singleton, SubAddAction.ofFixingAddSubgroup.append_right, AlgEquiv.piCongrRight_apply, RelSeries.head_map, thickenedIndicator_one, ArithmeticFunction.cardFactors_eq_one_iff_prime, Coalgebra.TensorProduct.rid_tmul, ClosureOperator.monotone, Frm.comp_apply, Matrix.GeneralLinearGroup.map_one, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, Equiv.Perm.subtypeEquivSubtypePerm_symm_apply, DomMulAct.coe_mkHomeomorph, MulAut.conjNormal_inv_apply, LipschitzWith.hausdorffMeasure_image_le, AnalyticOnNhd.aeval_polynomial, Algebra.Generators.Hom.toAlgHom_monomial, WittVector.truncate_mk', Finset.sum_smul_vsub_const_eq_weightedVSub, TestFunction.hasCompactSupport, Algebra.normalizedTrace_algebraMap_of_lifts, MeasureTheory.right_measure_le_of_levyProkhorovEDist_lt, SSet.stdSimplex.spineId_arrow_apply_one, ArithmeticFunction.mul_apply, Equiv.Perm.IsSwap.sign_eq, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, RootPairing.pairingIn_neg_two_neg_two_iff, RootPairing.reflectionPerm_eq_of_pairing_eq_zero', Finset.sum_smul_vsub_const_eq_affineCombination_vsub, volume_regionBetween_eq_integral, realPart_apply_coe, Submodule.mulExact_unitsMap_spanSingleton_unitsToPic, CategoryTheory.Limits.CofanTypes.equivOfIsColimit_apply, AddConstMapClass.map_zsmul_const, MulEquiv.bijective, PEquiv.toMatrix_apply, Con.kerLift_injective, FreeMonoid.smul_def, Ideal.associatesEquivIsPrincipal_map_zero, QuotSMulTop.map_apply_mk, Lat.inv_hom_apply, LinearMap.IsSymmetric.conj_inner_sym, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, IsometryEquiv.coe_symm_toDilationEquiv, Subgroup.subgroupOfEquivOfLe_apply_coe, MeasureTheory.continuous_diracProbaEquivSymm, Monoid.CoprodI.of_leftInverse, OrderHom.isGreatest_gfp, ContinuousLinearMap.coeFn_compLp, CategoryTheory.Abelian.Ext.addEquivBiprod_symm_apply, MonoidHom.subgroupMap_surjective, AddEquiv.coprodAssoc_apply_inl_inl, ModuleCat.free_map_apply, ProbabilityTheory.setLIntegral_condCDF, starLinearEquiv_apply, TopCat.isQuotientMap_of_isColimit_cofork, MultilinearMap.mkPiAlgebraFin_apply_const, Matrix.represents_iff', Subsemiring.subtype_apply, LieAlgebra.IsKilling.chainBotCoeff_zero_right, BialgHom.congr_fun, RootPairing.posRootForm_posForm_anisotropic, Equiv.piCurry_symm_apply, AddSubsemigroup.toSubsemigroup_closure, MeasureTheory.Measure.restrictₗ_apply, MeasureTheory.measure_setAverage_le_pos, Equiv.Set.sumDiffSubset_apply_inl, MeasureTheory.withDensity_apply', conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, PowerSeries.map_exp, SemidirectProduct.mulEquivProd_apply, IsAntichain.preimage_relIso, MeasureTheory.Integrable.measure_le_integral, AlternatingMap.domDomCongrₗ_symm_apply, FreeAddMonoid.map_apply_map_symm_eq, QuaternionAlgebra.algebraMap_eq, Finset.coe_singletonAddHom, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, Module.projective_def, Finsupp.coe_univ_sum_single, TensorProduct.gradedCommAux_lof_tmul, DualNumber.lift_apply_inl, AddActionHom.congr_fun, Valuation.extendToLocalization_apply_map_apply, Ideal.absNorm_eq_zero_iff, BddOrd.ofHom_apply, PadicInt.continuousAddCharEquiv_symm_apply, Finset.Colex.le_iff_sdiff_subset_lowerClosure, CliffordAlgebraComplex.Q_apply, Set.FiniteExhaustion.iUnion_eq, ContDiffWithinAt.iteratedFDerivWithin_comp_perm, MonoidHom.op_apply_apply, OrderIso.preimage_image, ContinuousLinearMapWOT.ext_iff, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, Representation.linHom.mem_invariants_iff_comm, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, supClosure_idem, Matrix.GeneralLinearGroup.map_mul, algebraMap_mono, Algebra.TensorProduct.prodRight_tmul, QuotientAddGroup.equivIcoMod_coe, MonoidHom.restrict_surjective, InitialSeg.refl_apply, rotation_symm, Polynomial.pow_mul_divByMonic_rootMultiplicity_eq, Localization.awayMap_injective_iff, Nucleus.coe_top, Unitization.antilipschitzWith_addEquiv, MeasurableSet.exists_isCompact_isClosed_lt_add, HahnSeries.toMvPowerSeries_apply, modularCyclotomicCharacter'.spec', QuotientAddGroup.quotientQuotientEquivQuotientAux_mk, CategoryTheory.OverPresheafAux.MakesOverArrow.of_arrow, Equiv.optionSubtype_symm_apply_apply_some, MvPolynomial.coe_expand, PEquiv.toMatrix_mul_apply, Algebra.TensorProduct.prodRight_tmul_snd, Module.End.ringEquivEndFinsupp_apply_apply_support, CategoryTheory.Functor.flippingEquiv_apply_obj_map, IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one, Filter.HasBasis.comp_equiv, ContinuousLinearMap.extendTo𝕜'_apply, Subgroup.conj_smul_eq_self_of_mem, AddEquiv.map_finsum, Cardinal.aleph0_toNat, IsDiscreteValuationRing.addVal_one, Polynomial.contract_mul_expand, Matrix.cons_mulVec, CompletelyPositiveMap.map_cstarMatrix_nonneg', ContinuousMultilinearMap.domDomCongrEquiv_symm_apply, IsLocalFrameOn.coeff_eq_of_eq, LinearMap.BilinForm.linMulLin_apply, ProbabilityTheory.Kernel.pow_succ_apply_eq_lintegral, HeytAlg.Iso.mk_hom, ProbabilityTheory.Kernel.iIndepFun.meas_biInter, PowerSeries.coe_one, NonUnitalStarSubalgebra.inclusion_injective, Affine.Simplex.ninePointCircle_map, ProbabilityTheory.Kernel.IndepFun.measure_inter_preimage_eq_mul, RCLike.I_re, MeasureTheory.measure_lt_top_of_isCompact_of_isAddLeftInvariant', ContinuousMultilinearMap.norm_ofSubsingleton, DFinsupp.lapply_apply, CategoryTheory.GrothendieckTopology.Cover.Arrow.to_middle_condition, ContinuousLinearMap.isAdjointPair_inner, SSet.OneTruncation₂.nerveHomEquiv_apply, TensorProduct.directLimitLeft_symm_of_tmul, Homeomorph.isSimplyConnected_preimage, Representation.IntertwiningMap.isIntertwining, Multiplicative.exists, IsSemilinearSet.preimage, Set.OrdConnected.apply_wcovBy_apply_iff, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, Polynomial.algEquivAevalXAddC_apply, LinearMap.coe_smulRight, OrderIso.map_ciInf_set_of_directedOn, WeierstrassCurve.inv_map_Δ', HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, Polynomial.leadingCoeff_C, NonUnitalAlgHom.inr_apply, Polynomial.signVariations_eq_eraseLead_add_ite, ofAdd_nsmul, FintypeCat.uSwitchEquiv_symm_naturality, TopCat.Presheaf.Γgerm_res_apply, Matrix.mul_fin_three, ProbabilityTheory.posterior_eq_withDensity_of_countable, Finsupp.coe_tsub, groupHomology.mapCycles₂_comp_i_apply, CategoryTheory.regularTopology.exists_effectiveEpi_iff_mem_induced, MvPolynomial.aeval_sumElim, ContinuousMap.exists_disjoint_nonempty_clopen_cover_of_mem_nhds_diagonal, ProbabilityTheory.Kernel.lintegral_deterministic, Orientation.map_apply, MvPolynomial.universalFactorizationMapPresentation_σ', CStarMatrix.uniformEmbedding_ofMatrix, AddEquiv.neg'_symm_apply, Quaternion.imI_equivProd_symm_apply, TensorProduct.norm_map, RootPairing.Equiv.id_weightMap_apply, PolynomialModule.monomial_smul_apply, jacobiSum_ringHomComp, LinearIsometryEquiv.norm_map', ConjAct.ofConjAct_mul, LieSubmodule.inclusion_injective, Complex.equivRealProdCLM_symm_apply_im, UniformOnFun.uniformSpace_eq_inf_precomp_of_cover, Polynomial.map_frobenius_expand, Ordinal.toNimber_eq_one, DirectSum.decompose_coe, PiTensorProduct.mapMonoidHom_apply, CategoryTheory.Discrete.equivOfEquivalence_symm_apply, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, AdicCompletion.eval_of, isAlgebraic_algebraMap, Multiset.toDFinsupp_inter, CoxeterSystem.lengthParity_eq_ofAdd_length, Module.Basis.ofSpan_apply_self, mulEquivOfOrderOfEq_apply_gen, Valuation.mem_leIdeal_iff, Polynomial.leadingCoeff_map, coe_ringEquiv_lpBCF_symm, ContinuousLinearEquiv.analyticWithinAt, vadd_preimage_set_subsetₛₗ, PowerSeries.coeff_succ_X_mul, OrderMonoidHom.coe_monoidHom, SimpleGraph.induceUnivIso_symm_apply_coe, SmoothPartitionOfUnity.mem_fintsupport_iff, ContinuousLinearMap.coe_sub', CategoryTheory.ShrinkHoms.inverse_map, nndist_homothety_center, CompleteLatticeHom.coe_setPreimage, AddGroupSeminormClass.toSeminormedAddCommGroup_norm_eq, Submodule.setSemiring_smul_def, SupBotHom.coe_bot, LocallyConstant.toFun_eq_coe, AbsoluteValue.IsEuclidean.map_lt_map_iff, LinearMap.toMvPolynomial_eval_eq_apply, LinearMap.mk₂'_apply, Emetric.exists_smooth_forall_closedBall_subset, Equiv.Perm.Basis.cycleOf_eq, LinearEquiv.coe_one, OrderEmbedding.sorted_le_listMap, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, MeasureTheory.SimpleFunc.integrable_iff_finMeasSupp, UnitAddTorus.mFourier_single, ProbabilityTheory.IsFiniteKernel.exists_univ_le, IsLocalizedModule.map_comp, Cardinal.aleph_eq_preAleph, Real.hasFDerivAt_fourierChar_neg_bilinear_right, MulEquiv.coe_toEquiv, AddGroupExtension.Section.rightInverse_rightHom, ContinuousMap.coe_mulLeft, ContinuousMap.Homotopy.ext_iff, Finset.Iic_toDual, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_jointly_surjective₂, MeasureTheory.lintegral_nnnorm_condExpIndSMul_le, LinearMap.BilinForm.comp_symmCompOfNondegenerate_apply, EuclideanGeometry.orthogonalProjection_eq_self_iff, IsLocalRing.ResidueField.residue_smul, SymAlg.sym_comp_unsym, HVertexOperator.coeff_comp, AlgebraicGeometry.StructureSheaf.comap_basicOpen, BoundedContinuousFunction.lipschitz_eval_const, convexHull_smul, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, LinearIsometryEquiv.differentiableAt, ContinuousAffineEquiv.prodAssoc_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_assoc, QuotientGroup.quotientBot_apply, Algebra.TensorProduct.liftEquiv_symm_apply_coe, ProbabilityTheory.avgRisk_const_right', CoxeterMatrix.reindexGroupEquiv_symm_apply_simple, MvPowerSeries.coeff_monomial_ne, AddSubsemigroup.opEquiv_apply, Real.nnabs_pos, ContinuousAlgEquiv.surjective, GroupExtension.inl_injective, Real.fourier_continuousMultilinearMap_apply, AddMemClass.subtype_injective, Polynomial.Splits.surjective_toPermHom_of_iSup_inertia_eq_top, Matrix.SpecialLinearGroup.coe_matrix_coe, Algebra.IsPushout.equiv_symm_algebraMap_right, Polynomial.eval₂_eq_sum_range, BooleanSubalgebra.mem_map_equiv, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, Polynomial.toFinsuppIso_symm_apply, Ordinal.omega_pos, AddSubmonoid.LocalizationMap.lift_localizationMap_mk', ModularFormClass.differentiableOn_cuspFunction_ball, LinearIsometryEquiv.differentiable, MeasureTheory.measure_le_average_pos, ContinuousAffineEquiv.coe_symm_toAffineEquiv, CompleteLatticeHom.dual_comp, groupCohomology.cocyclesIso₀_hom_comp_f_apply, NonUnitalSubalgebra.coe_inclusion, volume_preimage_coe, Derivation.compAlgebraMap_apply, Equiv.Set.sumCompl_apply_inl, RCLike.im_eq_complex_im, MeasureTheory.Measure.prodAssoc_prod, ModuleCat.ofHom₂_hom_apply_hom, Equiv.funUnique_symm_apply, AddConstMap.toFun_eq_coe, Padic.norm_rat_le_one_iff_padicValuation_le_one, Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, Finset.singletonMulHom_apply, SheafOfModules.conjugateEquiv_pullbackId_hom, MonoidWithZeroHom.ext_nat_iff, ProbabilityTheory.iIndep.meas_iInter, Unitization.splitMul_injective, Sublattice.map_symm_eq_iff_eq_map, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, QuadraticAlgebra.algebraMap_norm_eq_mul_star, groupHomology.boundariesToCycles₂_apply, RingEquiv.map_eq_neg_one_iff, AddConstMapClass.map_ofNat_add', Magma.AssocQuotient.map_of, Setoid.prodQuotientEquiv_apply, AlgebraicGeometry.Scheme.mem_basicOpen'', LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot, CategoryTheory.ConcreteCategory.congr_hom, PseudoMetric.isSymmetricRel_closedBall, Ordinal.to_leftMoves_one_toPGame_symm, Matrix.SpecialLinearGroup.mapGL_coe_matrix, Polynomial.logMahlerMeasure_monomial, WeierstrassCurve.Jacobian.map_addU, Function.ExtendByZero.linearMap_apply, ProbabilityTheory.measure_condCDF_univ, AddSubgroup.surjOn_iff_le_map, LaurentPolynomial.smul_eq_C_mul, Polynomial.cauchyBound_X_add_C, Polynomial.degree_cubic_le, PowerSeries.trunc_trunc, MulHom.single_apply, ContinuousMulEquiv.symm_comp_eq, IsLocalization.AtPrime.isUnit_to_map_iff, CategoryTheory.PreGaloisCategory.endEquivAutGalois_π, finRotate_last, HNNExtension.NormalWord.of_smul_eq_smul, AddMonoidHom.toMultiplicativeLeft_apply_apply, Module.Basis.toMatrix_transpose_apply, CategoryTheory.Meq.equiv_symm_eq_apply, NonUnitalSubalgebraClass.subtype_apply, AffineEquiv.val_inv_equivUnitsAffineMap_apply, Cube.insertAt_boundary, ContinuousMapClass.map_continuous, MonoidAlgebra.domCongr_support, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, HasCompactSupport.exists_simpleFunc_approx_of_prod, RingHom.smul_toAlgebra, CategoryTheory.Presieve.extension_iff_amalgamation, quadraticChar_eq_pow_of_char_ne_two', WeierstrassCurve.Ψ_four, Function.Embedding.ext_iff, DirectSum.sigmaUncurry_apply, AddMonoidAlgebra.decomposeAux_single, MeasureTheory.OuterMeasure.sInfGen_def, CompactlySupportedContinuousMap.coe_add, EuclideanGeometry.reflection_subtype, Valued.isClosed_closedBall, HahnSeries.SummableFamily.coeff_apply, SubAddAction.ofFixingAddSubgroup_equivariantMap_injective, ContinuousLinearMap.smulRight_comp, MeasureTheory.Measure.IsFiniteMeasureOnCompacts.map, Tuple.comp_perm_comp_sort_eq_comp_sort, Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer, Finsupp.indicator_of_mem, HasFPowerSeriesAt.coeff_zero, SimpleGraph.Copy.coe_ofLE, Fin.appendIsometry_apply, LieHom.mem_range, RingEquiv.unop_map_list_prod, cfcₙ_eq_cfcₙL, LinearEquiv.arrowCongrAddEquiv_apply, AdicCompletion.component_sumInv, DifferentiableOn.continuousAlternatingMap_apply_const, MeasureTheory.measure_null_iff_singleton, DualNumber.lift_op_smul, Submonoid.leftInvEquiv_symm_fromLeftInv, RingHom.map_mul, RingOfIntegers.algebraMap_norm_algebraMap, LinearMap.trace_conj, ModelWithCorners.coe_transContinuousLinearEquiv, Bialgebra.TensorProduct.rid_tmul, Encodable.instAntisymmPreimageNatCoeEmbeddingEncode'Le, SchwartzMap.integral_inner_fourier_fourier, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, AddCon.comapQuotientEquivOfSurj_symm_mk', Finset.Colex.cons_le_cons, QuadraticMap.Isometry.tmul_apply, BotHom.symm_dual_comp, PseudoMetric.isSymmetricRel_ball, MeasureTheory.AEDisjoint.measure_diff_right, toMul_list_sum, Set.Nonempty.convexHull, LinearIsometry.withLpProdMap_apply, CompactExhaustion.subset_interior_succ, QuadraticMap.nonneg_prod_iff, ModularFormClass.holo, AbsoluteValue.IsNontrivial.exists_abv_lt_one, ContDiffOn.comp_continuousLinearMap, Seminorm.uniformContinuous', VectorFourier.norm_fourierSMulRight, RCLike.ofReal_im_ax, AffineIsometryEquiv.comp_continuousOn_iff, LinearMap.det_eq_det_mul_det, ZMod.toCircle_apply, MeasureTheory.measure_eq_trim, LocallyConstant.indicator_apply_eq_if, ContinuousAlgEquiv.comp_continuous_iff', Behrend.map_eq_iff, bijective_rangeRestrict_comp_of_valuationRing, SimpleGraph.Walk.map_append, IsLocalization.Away.associated_sec_fst, zmultiplesHom_symm_apply, isSMulRegular_on_quot_iff_lsmul_comap_eq, RestrictedProduct.evalMonoidHom_apply, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, IsLocalization.mul_toInvSubmonoid, Lat.Iso.mk_hom, IsLocalization.algebraMap_mk', ZeroHom.coe_single, InnerProductSpace.volume_closedBall, Rep.freeLift_hom, Polynomial.rootSet_monomial, RingEquiv.map_multiset_prod, FreeMonoid.lift_apply, RegularExpression.matches'_map, UniformEquiv.isUniformEmbedding, Rack.act'_symm_apply, LinearEquiv.coe_ofTop_symm_apply, matPolyEquiv_symm_X, Set.integer_valuation_le_one, HahnSeries.coeff_toOrderTopSubOnePos_pow, OrderIso.sumAssoc_apply_inl_inr, ProfiniteGrp.toLimitFun_continuous, BoundedContinuousFunction.zsmul_apply, Ideal.coe_torsionOf, DirectSum.decompose_one, Nat.dvd_ordProj_of_dvd, UniformOnFun.edist_eq_restrict_sUnion, ContinuousLinearMap.smulRight_one_one, NumberField.InfinitePlace.eq_iff_eq, HahnSeries.SummableFamily.hsum_unique, Matrix.comp_diagonal, Monovary.dual, AddValuation.IsEquiv.val_eq, HasFPowerSeriesOnBall.hasSum_sub, PEquiv.transpose_toMatrix_toPEquiv_apply, Module.Basis.extendLe_apply_self, DirectSum.support_subset, FirstOrder.Language.Equiv.comp_apply, fderivWithin_continuousAlternatingMap_apply, RingEquiv.symm_toNonUnitalRingHom_apply_toNonUnitalRingHom_apply, LieModuleHom.map_lie, CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀Inv, PreTilt.map_eq_zero, Equiv.Perm.sign_prodCongrRight, finTwoArrowEquiv'_sum_eq, isRegular_toMul, Finset.finsetCongr_piAntidiag_eq_antidiag, Valuation.coe_ltAddSubgroup, MeasureTheory.Measure.compProd_eq_zero_iff, ofLex_mul, LinearMap.map_smul_of_tower, HurwitzZeta.jacobiTheta₂''_conj, DilationEquiv.coe_inv, Submonoid.LocalizationMap.eq_mk'_iff_mul_eq, OrderIso.smulRightDual_symm_apply, AlgHom.toEnd_apply, Subalgebra.setRange_algebraMap, RelEmbedding.mul_apply, Polynomial.monomial_left_inj, AlgebraicGeometry.specTargetImageRingHom_surjective, Cardinal.ofENat_toENat_eq_self, toColex_zero, Action.isContinuous_def, Seminorm.sup_apply, RatFunc.taylor_mem_nonZeroDivisors, MvPolynomial.eval₂_rename_prod_mk, EquivLike.pairwise_comp_iff, RestrictedProduct.mk_apply, MeasureTheory.measure_preimage_vadd, Cardinal.toNat_natCast, LinearMap.injective_domRestrict_iff, ProbabilityTheory.Kernel.measurable_singularPart, PartOrd.hom_inv_apply, Finsupp.sumFinsuppAddEquivProdFinsupp_symm_inr, SemiRingCat.id_apply, absConvexHull_eq_convexHull_balancedHull, AddGroupExtension.Equiv.rightHom_map, CategoryTheory.MonoidalClosed.curryHomEquiv'_apply, AlgebraicGeometry.Scheme.stalkMap_inv_hom_assoc, map_normEDS, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, FreeLieAlgebra.lift_of_apply, FirstOrder.Language.Substructure.map_closure, LinearMap.BilinForm.congr_fun, jacobi_cross, BoundedContinuousFunction.sum_apply, Directed.measure_iInter, AlgebraicGeometry.Scheme.Cover.RelativeGluingData.preimage_toBase_eq_range_ι, ProbabilityTheory.Kernel.comapRight_apply, CategoryTheory.Limits.Cone.w_apply, AffineMap.lineMap_apply_ring', AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, affineHomeomorph_image_Icc, DirichletCharacter.delta_mul, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, Pi.ωScottContinuous_curry, CliffordAlgebra.toBaseChange_ι, AddChar.doubleDualEmb_inj, ContinuousMap.HomotopyRel.cast_apply, Cubic.equiv_symm_apply_d, norm_toMul, HahnSeries.addOppositeEquiv_symm_apply_coeff, MeasureTheory.eLpNorm_const_lt_top_iff, Polynomial.newtonMap_apply, LinearMap.separatingLeft_toMatrix₂_iff, TopCat.isOpen_iff_of_isColimit, SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply, DomMulAct.symm_mk_mul, Finsupp.DegLex.le_iff, ENNReal.orderIsoRpow_apply, AddHom.mem_eqLocus, Rat.surjective_padicValuation, Equiv.one_def, MeasureTheory.Measure.IicSnd_univ, OrderEmbedding.lt_iff_lt, Equiv.coe_sigmaUnique, RelSeries.map_apply, NonUnitalAlgebra.range_eq_top, IsIntegral.fg_adjoin_singleton, Subalgebra.LinearDisjoint.linearIndependent_left_of_flat, Polynomial.toLaurent_C_mul_eq, ContinuousLinearEquiv.map_nhds_eq, HVertexOperator.coeff_apply_apply, Equiv.Perm.decomposeOption_symm_apply, NormedAddGroupHom.coe_mk, ContinuousLinearMap.toUniformConvergenceCLM_continuous, AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singleton, SymmetricAlgebra.algebraMap_inj, AddEquiv.val_neg_piAddUnits_symm_apply, hasStrictFDerivAt_inv', AffineIsometryEquiv.coe_vaddConst', measure_Ioc_lt_top, MeasureTheory.Measure.le_dirac_apply, basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix, AdicCompletion.evalₐ_mk, AlgEquiv.uniqueProd_apply, Module.Basis.toDualFlip_apply, LinearMap.toSpanSingleton_one, CategoryTheory.Bicategory.mateEquiv_apply, ProbabilityTheory.Kernel.setLIntegral_piecewise, WeierstrassCurve.Affine.Equation.baseChange, RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot, Bialgebra.TensorProduct.lid_tmul, Equiv.swap_bijOn_exchange, UniformFun.uniformContinuous_toFun, cfcₙL_apply, TensorProduct.comm_tmul, Representation.asModuleEquiv_map_smul, Set.Finite.convexHull_eq_image, homeomorphSphereProd_apply_fst_coe, Metric.Snowflaking.isBounded_preimage_toSnowflaking_iff, ZeroHom.withBotMap_apply, PowerSeries.inv_eq_inv_aux, Submodule.mapHom_apply, Submodule.fstEquiv_symm_apply_coe, SimpleGraph.one_add_adjMatrix_add_compl_adjMatrix_eq_allOnes, MeasureTheory.Measure.volumeIoiPow_apply_Iio, NonUnitalStarRingHom.comp_apply, Nat.ordProj_pos, Algebra.discr_powerBasis_eq_prod', MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap, QuotientAddGroup.mk'_surjective, QuaternionAlgebra.coe_algebraMap, MonoidWithZeroHom.inl_mono, ProbabilityTheory.integrable_toReal_condDistrib, PadicAlgCl.coe_eq, Polynomial.X_sub_C_mul_removeFactor, Subalgebra.iSupLift_inclusion, WithCStarModule.equiv_symm_fst, AdicCompletion.piEquivOfFintype_apply, QuaternionAlgebra.imI_equivProd_symm_apply, MvPolynomial.monomial_sum_one, MeasureTheory.Measure.copy_comp_map, Circle.arg_exp, Algebra.algebraMap_intTrace, Finsupp.curryAddEquiv_symm_apply, MulOpposite.opContinuousLinearEquiv_apply, Polynomial.logMahlerMeasure_C_mul_X_add_C, AddConstEquiv.equivUnits_symm_apply_symm_apply, Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct, BotHom.dual_comp, bind₁_wittPolynomial_xInTermsOfW, ZMod.χ₄_nat_mod_four, Finsupp.liftAddHom_symm_apply, SemidirectProduct.mulEquivSubgroup_symm_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, Matroid.mapEmbedding_isBasis_iff, Finset.coe_map, MeasureTheory.Measure.countable_meas_level_set_pos₀, OrderIso.map_sInf, MonoidAlgebra.mul_apply_right, EquivLike.injective, CategoryTheory.Functor.mapExtAddHom_coe, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff, OmegaCompletePartialOrder.ContinuousHom.coe_apply, ProbabilityTheory.Kernel.comp_apply', CategoryTheory.eHomEquiv_comp_assoc, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, RingHom.fieldRange_eq_top_iff, LatticeHom.coe_withBot, antitone_comp_ofDual_iff, MeasureTheory.Lp.toTemperedDistribution_apply, TensorProduct.dualDistrib_apply, MeasureTheory.lintegral_add_mul_meas_add_le_le_lintegral, Submodule.snd_orthogonalDecomposition_apply, Nat.ordCompl_eq_self_iff_zero_or_not_dvd, cfcHomSuperset_continuous, MeasureTheory.Egorov.exists_notConvergentSeq_lt, CategoryTheory.Pi.equivalenceOfEquiv_inverse, AlternatingMap.uncurryFin_apply, TemperedDistribution.smulLeftCLM_const, LinearIsometryEquiv.withLpProdComm_apply, Matrix.det_submatrix_equiv_self, List.formPerm_apply_getLast, Metric.Snowflaking.image_ofSnowflaking_closedBall, UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow, AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_symm_apply, SchwartzMap.smulLeftCLM_apply_apply, MDifferentiable.clm_apply, ContinuousMap.isComplete_setOf_eqOn, AlternatingMap.map_add_swap, LinearEquiv.det_coe_symm, FinBddDistLat.id_apply, CategoryTheory.Functor.mapAction_map_hom, AddMagmaCat.comp_apply, BialgHom.map_smul_of_tower, IsometryEquiv.symm_comp_self, Subgroup.coe_subgroupOf, Homeomorph.homeomorph_mk_coe_symm, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, Module.Basis.ofZLatticeBasis_repr_apply, QuadraticMap.Isometry.id_apply, IsLocalization.mk'_eq_iff_eq', IsometryEquiv.mul_apply, MonoidHom.zpow_apply, IsSimpleRing.iff_injective_ringHom, groupHomology.d₁₀_single_inv, AlgebraicGeometry.basicOpen_eq_of_affine, CentroidHom.centerToCentroid_apply, groupHomology.mkH1OfIsTrivial_apply, Set.initialSegIicIicOfLE_toFun_coe, LinearEquiv.neg_apply, Module.Basis.smul_apply, groupCohomology.π_map_apply, Ideal.KerLift.map_smul, InnerProductSpace.Core.inner_self_im, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, Rep.indToCoindAux_snd_mul_inv, QuotientGroup.congr_mk, SimpleGraph.card_edgeFinset_induce_support, Equiv.vadd_def, RingHom.congr_arg, CliffordAlgebra.ι_mem_evenOdd_one, freeGroupEquivCoprodI_apply, OrderEmbedding.preimage_Ioi, IsLocalization.eq_mk'_of_mul_eq, addAddMonoidHom_apply, Dioph.abs_poly_dioph, Subgroup.transferTransversal_apply'', OrdinalApprox.lfp_mem_range_lfpApprox, MvPolynomial.schwartz_zippel_sum_degreeOf, AddMonoidHom.mulOp_symm_apply_apply, Representation.ofMulDistribMulAction_apply_apply, Sum.Lex.le_def, restrictRootsOfUnity_coe_apply, Algebra.IsStandardSmooth.iff_exists_basis_kaehlerDifferential, NonUnitalStarAlgHom.coe_inr, FreeAddMonoid.toList_ofList, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, Composition.boundary_last, MvPolynomial.isHomogeneous_C, Module.Basis.tensorProduct_apply', fwdDiff_addChar_eq, fromModuleCatToModuleCatLinearEquiv_apply, Equiv.listUniqueEquiv_apply, ContinuousMap.HomotopyWith.coe_toHomotopy, Subalgebra.algebraMap_apply, Ici_orderDual_def, Finset.image_add, AbsoluteValue.apply_natAbs_eq, FirstOrder.Language.PartialEquiv.toEmbeddingOfEqTop_apply, ZeroHom.map_zero, AddCommMonCat.id_apply, FixedPoints.toAlgAut_bijective, SchwartzMap.fourier_fderivCLM_eq, Cubic.eq_prod_three_roots, SSet.Subcomplex.PairingCore.ancestralRel_iff, SpectrumRestricts.nnreal_iff_spectralRadius_le, NonUnitalAlgHom.coe_zero, FrameHom.toFun_eq_coe, Multiplicative.forall, Algebra.adjoin_res_eq_adjoin_res, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, DirectSum.linearEquivFunOnFintype_symm_single, Fin.appendEquiv_symm_apply, Submodule.map_span, TopologicalSpace.OpenNhds.map_id_obj, WithTop.Ioc_coe_top, ContinuousLinearMap.integral_comp_id_comm, PartitionOfUnity.finite_tsupport, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, Submonoid.LocalizationMap.map_units, LinearMap.BilinForm.toMatrix'_toBilin', CircleDeg1Lift.map_lt_of_translationNumber_lt_nat, MeasureTheory.prob_compl_eq_one_sub, Dilation.ediam_image, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, zpowersHom_ker_eq, IncidenceAlgebra.lambda_apply, Fintype.linearCombination_apply_single, LinearEquiv.symm_smul_apply, NumberField.InfinitePlace.map_intCast, Function.Embedding.some_apply, Polynomial.coe_aeval_eq_eval, DoubleQuot.quotQuotEquivComm_mk_mk, Algebra.FinitePresentation.out, Matrix.aeval_self_charpoly, Function.OfArity.curryEquiv_apply, Nat.ordProj_mul, AlgebraicGeometry.Scheme.Opens.ι_appLE, UniformOnFun.toFun_mul, Trivialization.apply_symm_apply_eq_coordChangeL, MeasureTheory.SimpleFunc.integral_eq, map_le_lineMap_iff_slope_le_slope_left, DistribMulActionHom.map_add, CategoryTheory.conjugateEquiv_adjunction_id, map_comp_neg, CircleDeg1Lift.tendsto_translationNumber, SimplexCategory.coe_toTopMap, IsometryEquiv.image_ball, AlgHom.toRingHom_toAddMonoidHom, CategoryTheory.Limits.Concrete.colimit_exists_rep, NNReal.sqrt_div, IsometryClass.continuous, AddEquiv.eq_iff_eq_on_generator, dist_algebraMap, MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv, infClosure_idem, isSimpleModule_iff_toSpanSingleton_surjective, ProbabilityTheory.Kernel.integral_piecewise, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, Nat.factorization_eq_zero_of_remainder, AbsoluteValue.isEquiv_iff_exists_rpow_eq, SchwartzMap.fourier_convolution_apply, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat, AlternatingMap.compLinearMap_apply, AddMonoidHom.coe_mulLeft, ArchimedeanClass.orderHom_top, MeasureTheory.null_iff_of_isMulLeftInvariant, MonoidHom.map_multiset_prod, CategoryTheory.SmallObject.restrictionLT_map, ContinuousMap.compRightAlgHom_continuous, map_zpow₀, Multiset.prod_X_add_C_eq_sum_esymm, PseudoEpimorphism.id_apply, MvPolynomial.rename_leftInverse, Fintype.linearCombination_apply, MulChar.ext_iff, IsometryEquiv.withLpProdAssoc_symm_apply, AddMagmaCat.id_apply, CircleDeg1Lift.translationNumber_translate, Matrix.conjTransposeRingEquiv_apply, WittVector.IsPoly₂.map, MulCharClass.map_nonunit, FirstOrder.Language.instDirectedSystemSubtypeMemSubstructureCoeOrderHomEmbeddingInclusion, Filter.Tendsto.pathExtend, MeasureTheory.SimpleFunc.setToSimpleFunc_const', GaloisConnection.closureOperator_apply, AddSubgroup.quotientEquivProdOfLE_apply, Finset.symInsertEquiv_symm_apply_coe, CategoryTheory.coyonedaEquiv_symm_map, neg_cross, ArithmeticFunction.sum_Ioc_sigma0_eq_sum_div, Matrix.compRingEquiv_apply, ProbabilityTheory.IdentDistrib.measure_mem_eq, MeasureTheory.OuterMeasure.boundedBy_union_of_top_of_nonempty_inter, iteratedFDeriv_two_apply, partialSups_bot, Diffeomorph.contMDiff_diffeomorph_comp_iff, CategoryTheory.PreZeroHypercover.interFst_h₀, MvPowerSeries.invOfUnit_eq, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, toColex_div, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux2, Polynomial.coeff_C_zero, Equiv.embeddingCongr_apply_trans, CategoryTheory.Adjunction.homEquiv_naturality_right_square, LinearAlgebra.FreeProduct.lift_apply, LinearMap.surjective_rangeRestrict, Language.reverseIso_symm_apply, LocalizedModule.map_mk, PowerBasis.liftEquiv'_symm_apply_apply, MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint, PiTensorProduct.lift_comp_reindex_symm, AffineSubspace.isometryEquivMap.apply_symm_apply, CategoryTheory.Functor.FullyFaithful.mulEquivEnd_apply, MeasureTheory.Lp.compMeasurePreserving_continuous, TwoSidedIdeal.orderIsoIsTwoSided_apply_coe, Quaternion.normSq_intCast, CategoryTheory.PreOneHypercover.inter_p₁, TwoSidedIdeal.asIdeal_matrix, EuclideanSpace.coe_measurableEquiv, Polynomial.natDegree_iterate_derivative, ConjAct.ofConjAct_inv, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition, RootPairing.span_root_image_eq_top_of_forall_orthogonal, MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier, QuadraticMap.Isometry.ofEq_apply, image_commutatorSet_closureCommutatorRepresentatives, TestFunction.coe_toBoundedContinuousFunction, MeasureTheory.tendsto_measure_smul_diff_isCompact_isClosed, Module.exists_surjective_quotient_of_finite, QuadraticMap.separatingLeft_of_anisotropic, AlgHom.IsArithFrobAt.restrict_mk, IsCyclotomicExtension.fromZetaAut_spec, IsAdicComplete.StrictMono.of_lift, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, DirectSum.decompose_mul_add_right, InnerProductSpace.volume_closedBall_of_dim_odd, PiTensorProduct.ofDFinsuppEquiv_symm_single_tprod, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, Antisymmetrization.prodEquiv_apply_mk, QuasiconcaveOn.dual, Metric.Snowflaking.uniformEquiv_apply, Finsupp.optionEquiv_symm_apply, Pi.le_toColex_update_self_iff, Pi.comul_coe_dFinsupp, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, LocallyConstant.coe_add, MultilinearMap.linearDeriv_apply, MeasureTheory.IsAddFundamentalDomain.addProjection_respects_measure_apply, Quiver.starEquivCostar_symm_apply_snd, Homeomorph.apply_symm_apply, RCLike.wInner_cWeight_const_right, AdicCompletion.evalₐ_mkₐ, LieAlgebra.mem_zeroRootSubalgebra, Finsupp.equivFunOnFinite_symm_single, mahler_apply, Algebra.FiniteType.iff_quotient_mvPolynomial'', Equiv.withTopSubtypeNe_apply, Subgroup.toAddSubgroup'_closure, Cardinal.ofENat_toENat, Ordinal.typein_le_typein', StieltjesFunction.measure_Ico, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, AlgebraicGeometry.Scheme.affineBasisCover_map_range, ArithmeticFunction.vonMangoldt_le_log, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, Frm.forget_map, MeasureTheory.FiniteMeasure.ennreal_mass, Finset.prod_map, RCLike.inv_eq_conj, ProbabilityTheory.Kernel.parallelComp_apply, Ordinal.toGame_injective, SymAlg.sym_smul, finSuccEquiv'_symm_some, ContinuousLinearMap.analyticOnNhd, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_integral, DirectSum.list_prod_ofFn_of_eq_dProd, CoheytingHom.coe_comp, Multiplicative.ofAdd_mono, ContinuousMap.isClosed_setOf_mapsTo, PolynomialLaw.isCompat_apply, BddDistLat.comp_apply, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, Equiv.subset_symm_image, Equiv.piFinsetUnion_left, ProbabilityTheory.Kernel.compProd_apply_eq_compProd_sectR, Equiv.Perm.IsCycle.commute_iff, LaurentPolynomial.eval₂_T_n, LieHom.mem_idealRange_iff, MonoidHom.dfinsuppProd_apply, ContinuousMonoidHom.prod_toFun, MeasureTheory.tendsto_setToFun_approxOn_of_measurable, Polynomial.exists_prod_multiset_X_sub_C_mul, Polynomial.degree_linear_le, Matrix.blockDiagonalRingHom_apply, AffineMap.differentiable, HahnEmbedding.Partial.eval_eq_truncLT, SubMulAction.mem_one', Finsupp.degree_eq_zero_iff, PrimeSpectrum.piLocalizationToMaximal_bijective, Algebra.Presentation.quotientEquiv_mk, ofMul_toMul, Equiv.div_def, AddMonoidHom.coe_toIntLinearMap, ProbabilityTheory.uniformOn_singleton, IsLocalMaxOn.hasFDerivWithinAt_eq_zero, PiTensorProduct.span_tprod_eq_top, FreeMonoid.ofList_flatten, ContinuousMap.HomotopyRel.eq_fst, Finsupp.toMultiset_single, CountableInterFilter.toCardinalInterFilter, PrimeSpectrum.primeSpectrumProd_symm_inl_asIdeal, MvPolynomial.esymmAlgHom_fin_bijective, IsAdjoinRoot.algEquiv_root, Dilation.dist_eq, SimpleGraph.Walk.map_eq_of_eq, InfiniteGalois.algEquivToLimit_continuous, QuadraticMap.nonneg_pi_iff, List.support_formPerm_of_nodup', IsSMulRegular.of_flat, AddMonoidHom.transfer_def, StrongDual.coe_toWeakDual, ContMDiffAt.clm_apply, ContinuousAddEquiv.symm_apply_apply, AddAut.mulLeft_apply_symm_apply, WithTop.toDual_map, LieModuleEquiv.coe_toLieModuleHom, mem_convexHull_of_exists_fintype, ContinuousAffineEquiv.coe_coe, Equiv.coe_fn_injective, Orientation.oangle_rotation_self_right, Submodule.span_preimage_le, affineHomeomorph_apply, LieAlgebra.IsKilling.rootSpace_two_smul, LinearMap.det_toMatrix', Equiv.prodShear_apply, Matrix.separatingLeft_toBilin_iff, RingHom.toNatAlgHom_apply, DirichletCharacter.isMultiplicative_toArithmeticFunction, PresheafOfModules.freeYonedaEquiv_comp, Nat.toAdd_pow, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, ContinuousAlternatingMap.differentiable, WeakDual.toStrongDual_apply, Equiv.comp_injective, Cardinal.aleph_one_eq_lift, NormedAddGroupHom.mem_range, Equiv.preimage_piEquivPiSubtypeProd_symm_pi, Module.Basis.toMatrix_reindex', MeasureTheory.SimpleFunc.extend_apply', OmegaCompletePartialOrder.ContinuousHom.toMono_coe, AddCommMonCat.coyoneda_obj_map, AffineEquiv.coe_toHomeomorphOfFiniteDimensional, ProbabilityTheory.condIndepFun_iff_condDistrib_prod_ae_eq_prodMkLeft, ContinuousLinearEquiv.uniqueDiffOn_image_iff, Matrix.charmatrix_apply, Submodule.equivOpposite_symm_apply, AddMonCat.equivalence_functor_map, LinearIsometryEquiv.withLpProdAssoc_apply, IsLocalization.Away.mapₐ_apply, Behrend.threeAPFree_image_sphere, mulTSupport_comp_eq_preimage, AlgebraicGeometry.Flat.isQuotientMap_of_surjective, SMulMemClass.coe_subtype, ZeroAtInftyContinuousMap.tendsto_iff_tendstoUniformly, MeasureTheory.SimpleFunc.tsum_eapproxDiff, LinearMap.eq_adjoint_iff_basis_right, AlgebraicGeometry.Scheme.Opens.ι_app, Ordinal.enum_inj, Algebra.PowerBasis.norm_gen_eq_prod_roots, Module.Basis.ofIsLocalizedModule_span, Function.Embedding.coe_sumSet, Path.target, Finset.image_sups, DomAddAct.vadd_apply, OrderEmbedding.isEmbedding_of_ordConnected, ContinuousLinearMap.hasMFDerivWithinAt, AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber, Finsupp.mem_graph_iff, MvPolynomial.esymmAlgEquiv_apply, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, convexHull_rangle_single_eq_stdSimplex, subtypeOrLeftEmbedding_apply_right, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, RestrictedProduct.isEmbedding_coe_of_bot, Real.differentiable_fourierChar_neg_bilinear_left, Polynomial.eval_add_of_sq_eq_zero, HahnSeries.single_eq_zero, Unitization.starLift_range_le, HahnModule.coeff_smul_left, AddSubsemigroup.equivOp_apply_coe, CharacterModule.intSpanEquivQuotAddOrderOf_apply_self, DirichletCharacter.convolution_mul_moebius, FirstOrder.Language.Embedding.comp_apply, Polynomial.derivative_X_add_C_pow, DilationEquiv.smulTorsor_preimage_ball, Polynomial.homogenize_C, AddEquiv.eq_symm_apply, UniformFun.toFun_inv, RingHom.map_add, ProbabilityTheory.IsRatCondKernelCDF.isRatStieltjesPoint_ae, Module.Finite.exists_fin', Sym2.lift_mk, Polynomial.natDegree_opRingEquiv, PowerSeries.aeval_coe, MeasureTheory.addContent_iUnion, WittVector.verschiebung_coeff_add_one, Finsupp.tail_apply, MeasureTheory.Measure.count_apply_lt_top', WeierstrassCurve.Affine.Point.toClass_eq_zero, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, AffineBasis.centroid_mem_interior_convexHull, LinearMap.Nondegenerate.toMatrix₂, HahnSeries.finiteArchimedeanClassOrderIso_apply, LaurentSeries.ratfuncAdicComplRingEquiv_apply, Matrix.map_pow, le_algebraMap_of_spectrum_le, LocallyConstant.inv_apply, UniformConvergenceCLM.eventually_nhds_zero_mapsTo, MeasureTheory.OuterMeasure.map_top, BoundedLatticeHomClass.map_bot, FreeAddSemigroup.hom_ext_iff, MultilinearMap.mkPiRing_apply, AffineMap.image_convexHull, FirstOrder.Language.LEquiv.onBoundedFormula_apply, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, LinearMap.toMatrixAlgEquiv_apply', IsLocalizedModule.eq_iff_exists, LinearMap.lTensor_map, DFinsupp.sumZeroHom_single, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, Equiv.Perm.sign_one, Polynomial.content_C, trace_eq_sum_automorphisms, LinearMap.evalAddMonoidHom_apply, MulChar.ofUnitHom_coe, MvPolynomial.mem_vanishingIdeal_iff, AlgebraicGeometry.instIsPreimmersionAsFiberHom, DFinsupp.mk_of_notMem, OrderRingHom.id_apply, isMaxOn_dual_iff, MvPolynomial.mem_vanishingIdeal_singleton_iff, Matrix.toLin'OfInv_apply, gelfandTransform_isometry, AddMonoidAlgebra.curryRingEquiv_single, finFunctionFinEquiv_apply_val, Hamming.toHamming_inj, AEMeasurable.re, Quaternion.coe_ofComplex, AlgebraicGeometry.Scheme.grothendieckTopology_cover, Homeomorph.subLeft_apply, MonoidAlgebra.singleOneAlgHom_apply, Order.pred_ofMul, EMetric.exists_continuous_eNNReal_forall_closedBall_subset, ContinuousAlgEquiv.apply_symm_apply, LieDerivation.coe_sub, MvPowerSeries.coeff_subst_finite, BoxIntegral.unitPartition.volume_box, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, MonomialOrder.div, UpperHalfPlane.σ_conj, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Basis.equivFun_symm_single, continuousMultilinearCurryLeftEquiv_symm_apply, GroupNorm.sup_apply, WeierstrassCurve.Jacobian.Point.toAffineAddEquiv_symm_apply, RingHom.surjective_localizationPreserves, Matrix.SpecialLinearGroup.det_mapGL, Path.Homotopy.source, NonarchAddGroupNorm.apply_one, MeasureTheory.Measure.measure_univ_eq_zero, Profinite.NobelingProof.injective_πs, UniformOnFun.isUniformEmbedding_toFun_finite, convexHull_union, MultilinearMap.map_smul_univ, OrderIso.map_iSup₂, Finsupp.equivFunOnFinite_symm_sum, IntermediateField.LinearDisjoint.linearIndependent_mul', MeasureTheory.measure_mul_lintegral_eq, MeasureTheory.Measure.addHaar_closedBall_mul, IsTranscendenceBasis.algebraMap_comp, QuotientAddGroup.kerLift_injective, SSet.Truncated.HomotopyCategory.homToNerveMk_app_zero, Equiv.sigmaPreimageEquiv_symm_apply_fst, MultilinearMap.toLinearMap_apply, MeasureTheory.measurePreserving_sumPiEquivProdPi_symm, FreeAddMonoid.countP_apply, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_comp_asIdeal, AddChar.doubleDualEmb_eq_zero, toLex_eq_zero, dist_right_lineMap, Semigrp.coe_id, IsModuleTopology.continuous_bilinear_of_finite_right, MeasureTheory.measure_eq_zero_iff_ae_notMem, BotHom.dual_id, Submonoid.map_powers, MonoidHom.coe_toAdditiveRight, Complex.volume_sum_rpow_lt_one, AddMonoidHom.exact_of_comp_eq_zero_of_ker_le_range, FormalMultilinearSeries.changeOriginIndexEquiv_apply_snd, AffineBasis.affineCombination_coord_eq_self, MeasureTheory.Measure.tendsto_IicSnd_atBot, PrimeSpectrum.toPiLocalization_injective, LineDeriv.lineDerivOpCLM_apply, Submodule.coe_mapAlgHom_apply, quasispectrum.preimage_algebraMap, UniformOnFun.postcomp_isUniformEmbedding, FreeAbelianGroup.lift_neg_apply, convexHull_sub, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom_assoc, BddLat.ext_iff, LinearMap.exact_of_comp_of_mem_range, Hamming.ofHamming_neg, Finsupp.linearCombination_surjective, FirstOrder.Language.DirectLimit.instDirectedSystemSubtypeMemSubstructureCodCoeOrderHomPartialEquivEmbeddingInclusion, IsScalarTower.AlgEquiv.restrictNormalHom_comp_apply, MeasureTheory.IsFundamentalDomain.measure_eq, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, PseudoMetric.coe_bot, Cardinal.aleph_toENat, AddSubgroup.mem_map, MonoidAlgebra.lift_def, Finset.preimage_map, geometric_hahn_banach_closed_point, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, Continuous.partialSups, CommGrpCat.coyoneda_obj_map, ZMod.toAddCircle_eq_zero, LinearMap.BilinForm.isOrtho_def, Matroid.mapEquiv_isBasis_iff, ContinuousMultilinearMap.smulRightL_apply, MulEquiv.coe_toEquiv_symm, FirstOrder.Language.Hom.map_constants, ContinuousLinearMap.contDiff, Multiset.toDFinsupp_lt_toDFinsupp, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, FintypeCat.hom_inv_id_apply, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, MvPolynomial.scalarRTensor_symm_apply_single, FractionalIdeal.equivNum_apply, SimpleGraph.degree_induce_of_support_subset, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, DFinsupp.liftAddHom_comp_single, DFinsupp.mapRange.linearMap_apply, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, CompHausLike.LocallyConstant.incl_comap, BoundedContinuousFunction.coe_le_coe_add_dist, Equiv.ofLeftInverseOfCardLE_symm_apply, MvPolynomial.expand_zmod, Polynomial.splits_iff_exists_multiset', PowerSeries.coeff_heval_zero, ArithmeticFunction.natCoe_apply, Subgroup.HasDetPlusMinusOne.abs_det, CategoryTheory.Limits.kernelSubobject_arrow_apply, Polynomial.toFinsupp_C_mul_X, AddMonoidHom.eq_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero', Equiv.Perm.sameCycle_pow_left, Equiv.transPartialEquiv_apply, Associated.map, Polynomial.natDegree_monomial_eq, PowerSeries.order_ne_zero_iff_constCoeff_eq_zero, MeasureTheory.Measure.measure_Ioi_pos, AddMonoidHom.eq_iff_eq_on_generator, ModuleCat.FreeMonoidal.εIso_hom_one, EuclideanSpace.nnnorm_eq, SimpleGraph.Embedding.mapEdgeSet_apply, affineSegment_image, NonarchAddGroupSeminorm.sup_apply, OrderHom.prodIso_symm_apply, ContinuousLinearEquiv.symm_apply_apply, SimpleGraph.Embedding.coe_toHom, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_apply, UniformFun.ofFun_sum, le_partialSups, CliffordAlgebra.involute_involutive, ProbabilityTheory.Kernel.iIndepSets_singleton_iff, Convex.second_derivative_within_at_symmetric_of_mem_interior, LinearIndepOn.image, innerₛₗ_apply_coe, MonomialOrder.lex_le_iff, Equiv.ringEquiv_apply, AlgebraicGeometry.quasiCompact_iff_spectral, AffineMap.coe_mul, Equiv.piCongrLeft'_symm_apply_apply, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, AlternatingMap.neg_one_pow_smul_map_insertNth, InfClosed.dual, ContinuousAlternatingMap.coe_neg, AffineIsometryEquiv.coe_toHomeomorph, Homeomorph.image_preimage, Matrix.submatrix_mul_equiv, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, Subalgebra.val_mulMap'_tmul, AlgebraicGeometry.Scheme.iso_hom_base_inv_base_apply, MeasurableEquiv.coe_piCurry_symm, ContinuousLinearMap.exists_mul_lt_of_lt_opNorm, NonUnitalRingHom.coe_zero, MeasureTheory.measure_iUnion_eq_iSup_accumulate, TopCat.prodIsoProd_inv_fst_apply, Finset.sumEquiv_apply_fst, AddEquivClass.map_finsum, CircleDeg1Lift.map_fract_sub_fract_eq, MultilinearMap.constLinearEquivOfIsEmpty_symm_apply, Cardinal.countable_iff_lt_aleph_one, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply, Polynomial.Monic.expand, CategoryTheory.Sieve.overEquiv_generate, IsLocalization.invertible_mk'_one_invOf, Homotopy.dNext_cochainComplex, OrderHom.iSup_apply, BooleanSubalgebra.inclusion_apply, Algebra.algebraMapSubmonoid_powers, Module.End.natCast_apply, Pi.uncurry_curry_ωScottContinuous, ClassGroup.equiv_mk0, Fin.castSuccEmb_apply, Polynomial.dvd_iff_isRoot, Perfection.coeff_iterate_frobeniusEquiv_symm, isTop_ofDual_iff, SchwartzMap.integrable, HahnSeries.ofPowerSeries_injective, MvPolynomial.aeval_zero', CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, toWeakSpaceCLM_eq_toWeakSpace, DistLat.comp_apply, NumberField.RingOfIntegers.map_mk, closure_subset_closedConvexHull, ClassGroup.mem_finsetApprox, GroupExtension.Splitting.rightHom_splitting, bernstein.probability, RootPairing.Base.sub_notMem_range_root, TensorProduct.equivFinsuppOfBasisLeft_apply, AddSubmonoid.LocalizationMap.eq_iff_eq, CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply, FreeAddMonoid.ofList_comp_toList, IsLocalMinOn.fderivWithin_nonneg, isMin_ofDual_iff, MeasureTheory.measure_neg_vadd_union, CharacterModule.dual_surjective_iff_injective, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, ContinuousMap.mem_idealOfSet_compl_singleton, AlgebraicGeometry.quasiCompact_iff_isSpectralMap, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, ContinuousMap.compStarAlgHom'_apply, OrderAddMonoidIso.symm_apply_apply, MeasureTheory.SimpleFunc.iSup_approx_apply, Module.Basis.prod_repr_inr, IsAlgebraic.algebraMap, AddSubgroup.relIndex_eq_natAbs_det, LocallyBoundedMap.comp_apply, Multiset.toDFinsupp_union, MvPolynomial.weightedTotalDegree_rename_of_injective, Finsupp.support_subset_iff, OrderIso.map_top', ContMDiffSection.mdifferentiable', ConcaveOn.bddBelow_convexHull, Polynomial.iterate_derivative_mul, ModularForm.SL_slash_apply, LinearMap.BilinMap.toQuadraticMap_apply, contMDiff_tangentBundleModelSpaceHomeomorph_symm, Equiv.biInf_comp, toBoolRing_inj, OrderIso.bddBelow_image, Functor.mapEquiv_apply, stdSimplexEquivIcc_symm_apply_coe, LinearEquiv.pow_apply, Rep.freeLift_hom_single_single, MeasureTheory.Measure.pi_empty_univ, Submodule.orthogonalDecomposition_apply, Subgroup.inclusion_injective, addMonoidAlgebraAddEquivDirectSum_symm_apply, iteratedFDeriv_succ_eq_comp_left, MulSemiringActionHom.map_mul, Additive.exists, AddSemigrp.id_apply, Finsupp.extendDomain_apply, Metric.Snowflaking.ediam_preimage_toSnowflaking, Zsqrtd.toReal_apply, Ideal.absNorm_bot, Seminorm.closedBall_zero_eq, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, wellFoundedGT_iff_monotone_chain_condition', Equiv.image_preimage, MeasureTheory.Measure.setLIntegral_condKernel_univ_right, AddConstMapClass.map_add_ofNat, MvPolynomial.range_mapAlgHom, ProbabilityTheory.condDistrib_map, Equiv.pprodEquivProdPLift_symm_apply, Ideal.Quotient.quotient_ring_saturate, CategoryTheory.IsIso.hom_inv_id_apply, AddEquiv.coprodCongr_symm_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, MonoidHom.map_mclosure, LinearEquiv.symmEquiv_symm_apply_symm_apply, AddEquiv.finsuppUnique_symm_apply_apply, nnnorm_map', Finsupp.add_sum_erase, LinearMap.BilinForm.Nondegenerate.toMatrix', MvPolynomial.counit_C, CategoryTheory.evalEquiv_symm_apply, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, IsSublattice.dual, AffineBasis.coe_coord_of_subsingleton_eq_one, ProbabilityTheory.setLIntegral_condDistrib_of_measurableSet, map_lt_lineMap_iff_slope_lt_slope, Finsupp.sum_smul_index_addMonoidHom, HilbertBasis.coe_toOrthonormalBasis, Finset.mem_map, Matrix.of_sub_of, AddChar.wInner_cWeight_eq_boole, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, AddMonoidHom.exact_iff, AlternatingMap.domLCongr_apply, Subalgebra.LinearDisjoint.norm_algebraMap, Ideal.relNorm_apply, LinearMap.isSymm_iff_basis, Metric.Snowflaking.preimage_ofSnowflaking_emetricClosedBall, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, Action.leftDual_ρ, SSet.Subcomplex.PairingCore.equivII_apply_coe, continuousOn_cfc_nnreal_setProd, starContinuousMap_apply, Equiv.Perm.congr_fun, MvPolynomial.weightedHomogeneousComponent_of_mem, TopHom.dual_comp, CoalgEquiv.apply_symm_apply, Quiver.SingleObj.pathEquivList_cons, QuadraticMap.map_sum, Prod.Lex.prodUnique_apply, UniformFun.toFun_sum, Module.Basis.constr_self, Matrix.charpoly_reindex, RootPairing.neg_mem_range_root_iff, Complex.conj_ofReal, ContinuousMultilinearMap.zero_apply, Equiv.Perm.subtypeCongr.right_apply, AddEquiv.prodUnique_symm_apply, ContinuousLinearMap.contMDiffOn, Polynomial.qsmul_eq_C_mul, MeasureTheory.OuterMeasure.trim_eq_trim_iff, OrderAddMonoidHom.coe_id, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, Polynomial.derivative_map, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, IsPurelyInseparable.bijective_algebraMap_of_isSeparable, RelHom.map_rel, TopCat.effectiveEpi_iff_isQuotientMap, ContinuousMap.compRightContinuousMap_apply, Polynomial.Gal.restrictProd_injective, PerfectClosure.iterate_frobenius_mk, CategoryTheory.hom_isIso, ArithmeticFunction.carmichael_mul, AddHom.restrict_apply, IsFractionRing.algEquiv_commutes, CategoryTheory.Functor.Elements.initialOfRepresentableBy_snd, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_measurableSet, TopCat.colimit_isOpen_iff, Homeomorph.symm_trans_apply, DomMulAct.isOpenEmbedding_mk, LinearMap.toMatrix_basis_equiv, MeasurableEquiv.coe_trans, AlgebraicGeometry.isomorphisms_eq_stalkwise, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, Convex.norm_image_sub_le_of_norm_fderiv_le', IsStronglyTranscendental.iff_of_isLocalization, AffineIsometryEquiv.antilipschitz, AddSubmonoid.subtype_apply, AddSubmonoidClass.subtype_apply, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, le_map_inv_iff, WithCStarModule.equivL_symm_apply, LinearMap.restrictScalars₁₂_apply_apply, WeierstrassCurve.Projective.baseChange_polynomialZ, UniformFun.ofFun_add, Metric.Snowflaking.homeomorph_symm_apply, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, AlternatingMap.map_insertNth, IntermediateField.equivOfEq_apply, SpectrumRestricts.rightInvOn, MonoidWithZeroHom.mem_valueMonoid_iff, MeasureTheory.Measure.ext_iff', isAddLeftRegular_ofLex, Multiset.prod_X_add_C_coeff', AddSubgroup.equivOp_apply_coe, UniqueFactorizationMonoid.prod_normalizedFactors_eq, Finsupp.mem_span_image_iff_linearCombination, Homeomorph.compStarAlgEquiv'_symm_apply, ContinuousLinearEquiv.arrowCongrSL_symm_apply, Matrix.reindexLinearEquiv_comp_apply, CommBialgCat.forget_map, Equiv.sigmaFiberEquiv_symm_apply_fst, Derivation.congr_fun, norm_algebraMap', IncidenceAlgebra.sub_apply, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ, CategoryTheory.Functor.CorepresentableBy.ext_iff, AddMonoidHom.dfinsuppSumAddHom_apply, Finsupp.comapDomain.addMonoidHom_apply, ProfiniteGrp.id_apply, HahnSeries.coeff_mul_single_add, Part.Fix.mem_iff, FreeAbelianGroup.lift_apply_of, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousLinearMap.nnbound, CategoryTheory.Equivalence.toOrderIso_symm_apply, MvPowerSeries.order_eq_nat, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, AddMonoid.End.coe_smul, AffineEquiv.range_eq, AddHom.coe_snd, Complex.normSq_apply, Nat.factorization_choose_prime_pow, LinearMap.CompatibleSMul.map_smul, PowerSeries.substAlgHom_coe, Polynomial.degree_linear_lt_degree_C_mul_X_sq, InfHom.subtypeVal_coe, map_tsub_of_le, DirectSum.coe_of_apply, zpowersEquivZPowers_apply, convexHull_list_sum, Derivation.coe_zero, CategoryTheory.Functor.CorepresentableBy.homEquiv_symm_comp, DomMulAct.isQuotientMap_mk, LieHom.map_smul, Monoid.PushoutI.NormalWord.Transversal.injective, quadraticChar_neg_one, isClosedMap_toMul, Module.End.mul_apply, RingEquiv.coe_trans, Polynomial.cauchyBound_X_sub_C, WithZero.toMulBot_le, MultilinearMap.compLinearMapMultilinear_apply, MvPolynomial.irreducible_sumSMulXSMulY, ContinuousAlgHom.coe_snd', AffineBasis.toMatrix_self, CategoryTheory.Abelian.Ext.linearEquiv₀_symm_apply, SimpleGraph.Copy.coe_comp, starRingEquiv_apply, Circle.coe_exp, Polynomial.splits_of_exists_multiset, MeasureTheory.addContent_biUnion_le, RCLike.re_ofReal_mul, BotHom.inf_apply, WeierstrassCurve.Jacobian.comp_smul, FreeAddMagma.lift_of, meas_lt_essInf, norm_add_pow_two, IsLocalization.mul_mk'_eq_mk'_of_mul, ContinuousMap.unitsLift_symm_apply_apply_inv', PointwiseConvergenceCLM.evalCLM_apply, LieModule.traceForm_apply_eq_zero_of_mem_lcs_of_mem_center, Finset.sum_smul_vsub_eq_affineCombination_vsub, MulEquiv.op_symm_apply_apply, Algebra.norm_algebraMap, Polynomial.map_C, Submodule.map_toAddSubgroup, Filter.EventuallyLE.measure_le, AddHom.mclosure_preimage_le, groupHomology.π_comp_H1Iso_inv_apply, topDualPairing_apply, IsPurelyInseparable.algebraMap_elemReduct_eq, RingInvo.map_eq_zero_iff, RootPairing.reflectionPerm_eq_of_pairing_eq_zero, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, RestrictedProduct.zpow_apply, DualNumber.lift_comp_inlHom, zmultiplesAddHom_apply, ContinuousMap.coe_one, FormalMultilinearSeries.applyComposition_update, NonnegHomClass.apply_nonneg, LinearMap.trace_prodMap', CartanMatrix.A_one, BotHom.comp_apply, StarMulEquiv.ofClass_symm_apply, EisensteinSeries.eisSummand_SL2_apply, Cycle.formPerm_eq_self_of_notMem, AddMonoidHom.coe_toZModLinearMap, MvPowerSeries.IsWeightedHomogeneous.coeff_eq_zero, LinearMap.quotientInfEquivSupQuotient_symm_apply_left, comp_equiv_dotProduct_comp_equiv, DomMulAct.isEmbedding_mk_symm, ZSpan.vadd_mem_fundamentalDomain, IsCoatom.dual, DomMulAct.smul_Lp_const, MvPolynomial.counitNat_X, AffineEquiv.sbtw_map_iff, MulEquiv.Monoid.End_apply, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, LinearMap.toSeminormFamily_apply, MonomialOrder.degree_sPolynomial_le, OrderEmbedding.range_inj, WeierstrassCurve.Affine.map_addPolynomial, AddEquiv.coprodComm_symm_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, coe_notMemRangeEquiv_symm, PowerSeries.coeff_C_mul, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, OrthogonalIdempotents.lift_of_isNilpotent_ker_aux, TensorProduct.AlgebraTensorModule.lift_tmul, YoungDiagram.equivListRowLens_symm_apply, MonomialOrder.degree_X_add_C, ProbabilityTheory.Kernel.compProd_eq_iff, Polynomial.eval₂_at_ofNat, PowerSeries.X_pow_dvd_iff, NNReal.agmSequences_succ', exteriorPower.ιMultiDual_apply_nondiag, AddChar.map_neg_eq_conj, AdjoinRoot.map_of, EReal.sign_neg, MvPolynomial.eval₂Hom_bind₂, NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, MvPolynomial.mem_ideal_span_monomial_image, Polynomial.iterate_derivative_intCast_mul, SimpleGraph.Coloring.odd_length_iff_not_congr, Polynomial.taylor_mem_degreeLT, List.equivSigmaTuple_apply_fst, Polynomial.C_neg, MulHom.coe_id, Polynomial.leadingCoeff_monomial, IsLocalization.integerNormalization_spec, AddMonoidAlgebra.antipode_single, Equiv.Perm.sumCongrHom_apply, SubMulAction.ofStabilizer.conjMap_bijective, Sublocale.range_toNucleus, FreeAbelianGroup.liftAddEquiv_apply_apply, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left, AddMonoidAlgebra.decomposeAux_eq_decompose, QuotientAddGroup.exists_norm_add_lt, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, IsLocalizedModule.fromLocalizedModule.surj, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ArithmeticFunction.carmichael_factorization, Finsupp.sum_apply, Lagrange.eval_nodal_derivative_eval_node_eq, WeierstrassCurve.map_a₃, UniformEquiv.piCongr_apply, ContinuousMap.isometryEquivBoundedOfCompact_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, OrderIso.image_Ioo, MvPolynomial.rename_toMvPolynomial, WithVal.le_def, EuclideanSpace.inner_single_right, LightProfinite.proj_surjective, Matrix.scalar_apply, Finset.weightedVSub_subtype_eq_filter, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, norm_eq_sqrt_re_inner, CentroidHom.starCenterToCentroid_apply, dite_apply, LinearIsometryEquiv.prodComm_apply, TemperedDistribution.fourier_apply, Matrix.SeparatingRight.toBilin', Polynomial.natDegree_expand, FreeAddMagma.length_toFreeAddSemigroup, RCLike.iInter_halfSpaces_eq, IsChain.image_embedding, Matrix.kroneckerTMul_assoc, HahnEmbedding.Partial.evalCoeff_eq, ProbabilityTheory.Kernel.compProd_apply, AddHom.add_apply, exteriorPower.presentation_var, LinearMap.bijective_of_ne_zero, MvPolynomial.aeval_rename, NumberField.IsCMField.infinitePlace_complexConj, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_map_surjective, partialSups_eq_biUnion_range, addRothNumber_Ico, inner_self_nonneg, Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq, IsAdjoinRootMonic.coeff_apply_le, CStarAlgebra.nonneg_TFAE, Polynomial.ringHom_eval₂_intCastRingHom, LieRinehartAlgebra.Hom.apply_lie', CategoryTheory.Functor.flippingEquiv_apply_map_app, ContinuousMultilinearMap.piₗᵢ_apply, GroupExtension.Section.rightHom_comp_section, nnnorm_cfcHom, Module.Basis.traceDual_powerBasis_eq, LinearMap.ltoFun_apply, RCLike.normSq_to_complex, Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range, AddSubgroup.index_toSubgroup, BoundedContinuousFunction.coe_zero, Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent, ArithmeticFunction.LSeriesSummable_vonMangoldt, Polynomial.prod_X_sub_C_coeff_card_pred, IsDiscreteValuationRing.addVal_le_iff_dvd, ContinuousMultilinearMap.ext_iff, CliffordAlgebra.EquivEven.reverse_v, IsCompl.dual, AddActionHom.prod_apply, Polynomial.card_support_le_one_iff_monomial, OrderEmbedding.sortedGT_listMap, addMonoidAlgebraRingEquivDirectSum_apply, GradedTensorProduct.tmul_algebraMap_mul_coe_tmul, Localization.localRingHom_bijective_of_not_conductor_le, Submonoid.fromCommLeftInv_apply, Orientation.areaForm_rightAngleRotation_right, SemilinearIsometryClass.nnnorm_map, LinearMap.convMul_apply, SemidirectProduct.mulEquivProd_symm_apply_right, WittVector.bind₁_frobeniusPolyRat_wittPolynomial, LinearEquiv.injective, CategoryTheory.ConcreteCategory.coe_comp, IsSublattice_range, MeasureTheory.setIntegral_condExpL1CLM, OrderRingHom.comp_apply, Algebra.injective_lift_lsmul, MvPolynomial.optionEquivLeft_symm_C_X, ArchimedeanClass.liftOrderHom_mk, SchwartzMap.lineDerivOp_apply, DFinsupp.zipWith_apply, NonarchAddGroupNorm.sup_apply, IsIntegral.algebraMap, ofDual_bihimp, Subsemiring.subtype_injective, ZeroHomClass.map_zero, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, Polynomial.not_irreducible_C, ZSpan.fract_apply, ProbabilityTheory.IndepSets_iff, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, Profinite.NobelingProof.coe_πs', groupCohomology.isoCocycles₂_hom_comp_i_apply, Equiv.Perm.eq_inv_iff_eq, Abelianization.lift_symm_apply, AdicCompletion.ofLinearEquiv_apply, Submonoid.LocalizationMap.symm_comp_ofMulEquivOfLocalizations_apply, Polynomial.coeff_mul_monomial, Polynomial.degree_quadratic_lt_degree_C_mul_X_cb, MeasureTheory.FinStronglyMeasurable.fin_support_approx, IsLocalization.eq_mk'_iff_mul_eq, Setoid.quotientKerEquivOfRightInverse_symm_apply, Algebra.algebraMap_intTrace_fractionRing, PiTensorProduct.map_comp_reindex_eq, Valuation.HasExtension.val_map_lt_one_iff, BoxIntegral.BoxAdditiveMap.coe_inj, WeakDual.CharacterSpace.equivAlgHom_symm_coe, DomMulAct.stabilizer_ncard, Nat.moebius_eq, SupHom.ext_iff, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, List.sum_hom, toLex_div, RingAut.mul_apply, Nat.factorization_choose, fourier_add', RCLike.continuous_im, Polynomial.coeff_C_mul_X_pow, CategoryTheory.Localization.Construction.objEquiv_symm_apply, LaurentPolynomial.trunc_C_mul_T, ProperCone.hyperplane_separation, AffineIsometryEquiv.coe_symm_toIsometryEquiv, MonoidWithZeroHom.map_mul, Module.Basis.map_addHaar, MulAut.apply_inv_self, MeasureTheory.SimpleFunc.map_apply, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, Finset.map_ofDual_min, Circle.exp_zsmul, Monoid.Coprod.mk_surjective, InfHom.coe_bot, Multiset.consEquiv_symm_none, AffineIsometryEquiv.norm_map, ArchimedeanClass.orderHom_mk, Homeomorph.funSplitAt_apply, LinearMap.compBilinForm_apply_apply, ProbabilityTheory.cond_mul_eq_inter, ContinuousAlgEquiv.preimage_closure, IntermediateField.liftAlgEquiv_apply, Polynomial.aeval_pi_apply₂, ContinuousLinearMap.cpolynomialOn, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, AddSubmonoid.LocalizationMap.sec_spec, ProbabilityTheory.IsCondKernelCDF.lintegral, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_str, CategoryTheory.Functor.CoconeTypes.IsColimit.equiv_apply, MeasureTheory.Measure.sigmaFinite_iff_measure_singleton_lt_top, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, Rep.diagonalHomEquiv_apply, MeasureTheory.Integrable.fourier_smul, QuadraticMap.posDef_iff_nonneg, LinearMap.coe_toContinuousLinearMap_symm, Matrix.range_diagonal, Submodule.mulMap_op, Unitization.lift_apply_apply, List.formPerm_eq_self_of_notMem, ZMod.completedLFunction_one_sub_even, SimpleGraph.Subgraph.inclusion_apply_coe, RingEquiv.eq_symm_apply, MvPolynomial.bind₂_bind₂, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, Metric.PiNatEmbed.toPiNatHomeo_symm_apply, LinearMap.prod_apply, AlgebraicGeometry.IsAffineOpen.isCompactOpenCovered, OrderIso.divLeft_symm_apply, ContinuousMap.nhds_compactOpen, OrderHom.piIso_apply, LinearIsometry.toLinearIsometryEquiv_apply, ContinuousMap.HomotopyWith.apply_zero, AdicCompletion.mk_apply_coe, Prod.counit_apply, HahnSeries.coeff_mul_single_zero, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.base_open, WittVector.teichmuller_mul_pow_coeff, AddGroupNorm.lt_def, RatFunc.num_div_denom, Submodule.span_image, CategoryTheory.Limits.cokernel.π_desc_apply, Equiv.self_comp_ofInjective_symm, OrderEmbedding.coe_subtype, Submodule.torsionBySet.mk_smul, ContinuousLinearMap.le_opENorm, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, continuousMultilinearCurryFin1_symm_apply, Subgroup.quotientEquivSigmaZMod_symm_apply, ValuationSubring.subtype_apply, PowerSeries.derivative_C, Quaternion.hasSum_expSeries_of_imaginary, MonoidHom.toAdditiveLeft_symm_apply_apply, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, Polynomial.derivative_natCast, Equiv.addEquiv_symm_apply, NormedAddGroupHom.coe_add, Trivialization.symmL_apply, ContinuousAlgHom.coe_restrictScalars', MeasureTheory.ae_eq_univ, coe_normGroupSeminorm, Module.End.ofNat_apply, MonoidHom.toHomPerm_apply_apply, ProbabilityTheory.Kernel.withDensity_apply', MvPolynomial.IsSymmetric.antitone_supDegree, OrderEmbedding.ltEmbedding_apply, ContinuousMultilinearMap.opNorm_le_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_aestronglyMeasurable, AddHom.coe_mk, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, Pi.evalOrderHom_coe, WittVector.aeval_verschiebungPoly, ContinuousLinearMap.coe_mul, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, Valuation.toValuation_ofValuation, dNext_comp_right, BoundedContinuousFunction.lipschitz_evalx, RingHom.mem_eqLocusField, Valuation.one_le_val_iff, toColex_pow, StrongDual.mem_polar_iff, Cardinal.toENat_eq_iff_of_le_aleph0, exists_smooth_forall_mem_convex_of_local, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, LaurentPolynomial.support_C_mul_T, Finmap.keysLookupEquiv_symm_apply_lookup, MeasureTheory.toFinite_apply_eq_zero_iff, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, QuotientGroup.mk'_surjective, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, TwoSidedIdeal.subtypeMop_injective, Submonoid.closure_image_one_lt_and_isMulIndecomposable, Submodule.orthogonal_eq_inter, groupHomology.d₂₁_single, Real.coe_sqrt, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply, MeasureTheory.measure_sUnion, Zsqrtd.lift_injective, WeierstrassCurve.φ_two, MvPolynomial.eval₂Hom_bind₁, Cubic.equiv_symm_apply_a, ContinuousLinearMap.mdifferentiableOn, Homeomorph.image_frontier, TopologicalSpace.Opens.apply_def, RCLike.normSq_add, Matrix.piLinearEquiv_symm_apply, UniqueFactorizationMonoid.radical_pow_of_prime, isMinFilter_dual_iff, MeasureTheory.eLpNorm_condExpL2_le, isSublattice_preimage_toDual, LieModule.iterate_toEnd_mem_lowerCentralSeries, MeasureTheory.Measure.count_apply_finite, RelEmbedding.coe_mul, PadicInt.mahlerEquiv_symm_apply, OrderDual.isCobounded_preimage_ofDual, GroupSeminorm.coe_add, LinearMap.extendScalarsOfIsLocalizationEquiv_symm_apply, RCLike.div_re, SupIrred.dual, toDual_eq_one, ContinuousLinearMap.lsmul_flip_apply, CategoryTheory.ActionCategory.curry_apply_right, CategoryTheory.Adjunction.homAddEquiv_apply, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, PMF.filter_apply, Cardinal.toNat_apply_of_lt_aleph0, Orientation.inner_smul_rotation_pi_div_two_smul_left, Subtype.orderEmbedding_apply_coe, LinearMap.coe_coe, Polynomial.degree_C_mul_X, CategoryTheory.Iso.conj_comp, MvPolynomial.eval₂_comp_left, IsSelfAdjoint.coe_realPart, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, Interval.dual_map, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, Module.Flat.tensorProduct_mapIncl_injective_of_right, ProbabilityTheory.Kernel.const_apply, LieModuleHom.coe_sub, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, MeasureTheory.SimpleFunc.eapprox_lt_top, BialgHom.ext_of_ring_iff, convexHull_nonempty_iff, ofDual_add, BoundedLatticeHom.coe_comp_inf_hom', isLeftRegular_ofLex, SchwartzMap.coe_apply, OrderAddMonoidIso.trans_apply, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, MeasureTheory.Measure.addHaar_ball, IncidenceAlgebra.mu_eq_neg_sum_Ico_of_ne, MulEquiv.map_mul, EquicontinuousOn.isInducing_uniformOnFun_iff_pi, MulActionHom.map_mem_fixedBy, LinearMap.proj_surjective, mulLeftLinearMap_apply, Module.Basis.constr_def, Equiv.Perm.set_support_apply_mem, ArithmeticFunction.abs_moebius_le_one, ArchimedeanClass.stdPart_of_mk_nonneg, FractionalIdeal.den_mul_self_eq_num', ContinuousLinearEquiv.coord_self, Complex.im_sq_le_normSq, CompactlySupportedContinuousMap.coe_finsetSup', MvPolynomial.finSuccEquiv_X_zero, AlgebraicGeometry.Scheme.Γevaluation_naturality, Monoid.CoprodI.Word.rcons_eq_smul, WittVector.verschiebung_isPoly, ValuationSubring.valuation_eq_one_iff, Polynomial.comp_X_add_C_eq_zero_iff, SkewMonoidAlgebra.domCongr_apply, MonomialOrder.monic_one, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, MvPolynomial.degreeOf_eq_natDegree, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, Equiv.Perm.extendDomainHom_apply, Polynomial.resultant_X_sub_C_left, IsIdempotentElem.map, RootPairing.chainBotCoeff_eq_zero_iff, isLocalization_iff_isLocalizationMap, MeasureTheory.eLpNorm_sub_le_of_dist_bdd, CategoryTheory.hom_comp, MeasureTheory.integrable_average, Equiv.prodPProd_symm_apply, CompHausLike.isoEquivHomeo_apply, uniformContinuous_ofAdd, Valuation.Compatible.vle_iff_le, ContinuousAddMonoidHom.id_toFun, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, SimpleGraph.hasseDualIso_symm_apply, MvPowerSeries.support_expand_subset, KaehlerDifferential.map_D, UniformEquiv.uniformEquiv_mk_coe_symm, Algebra.adjoin_toSubsemiring, RingHom.sub_mem_ker_iff, Polynomial.hasseDeriv_X, ContinuousAlternatingMap.unit_le_opNorm, isAddLeftRegular_toColex, setIntegral_re_add_im, ContinuousAlgEquiv.coe_apply, ContinuousAddEquiv.bijective, SetTheory.PGame.nim_grundyValue, MeasureTheory.laverage_add_measure, NonUnitalStarAlgHom.coe_inl, RCLike.geometric_hahn_banach_compact_closed, addMonoidEndRingEquivInt_symm_apply, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac, SchwartzMap.smulLeftCLM_ofReal, MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_degree, extDerivWithin_apply, Derivation.liftKaehlerDifferential_apply, WithLp.addEquiv_symm_apply, Rep.freeLiftLEquiv_symm_apply, Circle.exp_eq_one, Trivialization.sourceHomeomorphBaseSetProd_apply, MvPolynomial.coeff_weightedHomogeneousComponent, TopCat.GlueData.ι_eq_iff_rel, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, realPart_smul, MeasureTheory.Measure.Regular.map_iff, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_apply, LieModule.chainTop_isNonZero, CliffordAlgebra.involuteEquiv_symm_apply, QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff, Multiset.sum_hom, RingCon.coe_top, MeasureTheory.measure_eq_extend, BilinForm.toMatrix_compLeft, WeierstrassCurve.Projective.dblX_eq, MeasurableSpace.generateMeasurableRec_omega1, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, Finsupp.coe_sum, Equiv.Perm.ofSubtype_support_disjoint, StieltjesFunction.measure_Iic, supPrime_ofDual, Polynomial.aeval_mem_adjoin_singleton, LinearMap.IsPositive.adjoint_eq, AffineIsometry.antilipschitz, RingCon.rel_eq_coe, LinearIsometryEquiv.comp_continuous_iff, groupHomology.eq_d₂₁_comp_inv_apply, Trivialization.prod_apply', NonUnitalAlgHom.coe_to_mulHom, AffineBasis.exists_affine_subbasis, ContinuousAt.clm_bundle_apply, PowerSeries.order_eq, continuous_coeFun, Group.preimage_smul_setₛₗ, PowerSeries.expand_X, Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace, Polynomial.toLaurent_X, PMF.toOuterMeasure_apply_finset, Finset.restrict_comp_piCongrLeft, Algebra.coe_lmul_eq_mul, Algebra.Presentation.baseChange_relation, FreeAddGroup.lift_of_apply, Homeomorph.measurable, Equiv.subtypeEquivCodomain_symm_apply_ne, minpoly_add_algebraMap_splits, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, ContinuousLinearMap.prodₗ_apply, ContinuousLinearEquiv.comp_fderivWithin, Polynomial.derivative_bernoulli, UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, ContinuousLinearMap.coprodEquiv_symm_apply, SimpleGraph.Walk.support_map, MonomialOrder.degree_sub_leadingTerm_lt_degree, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_lintegral, Polynomial.scaleRoots_C, iteratedDeriv_vcomp_two, AdicCompletion.congr_apply, Encodable.encode_ofEquiv, Module.Basis.toDual_apply_left, AlgEquiv.trans_apply, ArithmeticFunction.cardFactors_mul, NonUnitalRingHom.coe_srangeRestrict, MeasureTheory.measurePreserving_piEquivPiSubtypeProd, LinearMap.nilRank_le_natTrailingDegree_charpoly, toDual_symmDiff, ContinuousAlternatingMap.opNNNorm_le_iff, LinearMap.toPerfPair_apply, FiniteDimensional.subalgebra_toSubmodule, fderiv_norm_rpow, dist_ofMul, map_prime_of_factor_orderIso, SlashInvariantForm.slash_action_eqn', AddChar.doubleDualEmb_doubleDualEquiv_symm_apply, ContMDiffSection.mdifferentiableAt, SimpleGraph.boxProdRight_apply, Field.Emb.Cardinal.iSup_filtration, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, Cubic.d_eq_three_roots, smul_preimage_set_subsetₛₗ, PartOrd.forget_map, ContinuousAlgHom.one_apply, Equiv.functionSwap_symm_apply, Group.fg_iff_exists_freeGroup_hom_surjective, mulRothNumber_lt_of_forall_not_threeGPFree, Equiv.Perm.decomposeOption_apply, ExteriorAlgebra.comp_ι_sq_zero, MeasureTheory.Measure.map_apply₀, AffineEquiv.preimage_symm, Int.ideal_span_absNorm_eq_self, Cardinal.aleph_limit, Finsupp.optionEquiv_apply, StrictConcaveOn.dual, KaehlerDifferential.DLinearMap_apply, Subgroup.equivSMul_symm_apply_coe, MeasurableEquiv.map_eq, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, toDual_smul, AddChar.coe_complexBasis, PartitionOfUnity.mem_fintsupport_iff, DFinsupp.singleAddHom_apply, map_addUnits_neg, LieAlgebra.lieCharacter_apply_lie, HahnSeries.SummableFamily.embDomain_image, MeasureTheory.L1.integral_eq', Localization.r_iff_oreEqv_r, DirichletCharacter.Odd.toUnitHom_eval_neg_one, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, ContinuousMultilinearMap.map_zero, DoubleQuot.coe_quotQuotEquivCommₐ, DirectSum.coe_congrAddEquiv, ContMDiffMap.coe_one, CategoryTheory.Adjunction.homEquiv_naturality_right_square_assoc, MeasureTheory.volume_preserving_finTwoArrow, Polynomial.toAddCircle_X_eq_fourier_one, LinearIsometryEquiv.map_smul, AddSubgroup.toIntSubmodule_closure, RootPairing.pairing_one_four_iff, CategoryTheory.Under.postAdjunctionRight_counit_app_right, LinearMap.toMatrix₂'_comp, AdjoinRoot.mk_self, map_comp_add_neg, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, optionProdEquiv_mk_none, toAddUnits_symm_apply, PerfectRing.lift_comp_apply, MeasureTheory.FiniteMeasure.continuous_integral_continuousMap, MvPolynomial.rTensor_apply, BoundedLatticeHom.comp_apply, LinearEquiv.congrQuadraticMap_apply, minpoly.iterateFrobenius_of_isSeparable, ProbabilityTheory.Kernel.rnDeriv_add, TopologicalSpace.Compacts.equiv_apply, WeierstrassCurve.map_a₁, Complex.inv_eq_conj, isRightRegular_ofAdd, groupCohomology.coboundaries₂_ext_iff, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, QuadraticMap.coeFn_zero, AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso, RootPairing.IsOrthogonal.coreflection_apply_left, Matrix.toLinearMap₂_apply_basis, AddCon.lift_coe, Polynomial.ofFn_coeff_eq_val_of_lt, SlashInvariantForm.coe_smul, Finset.weightedVSubOfPoint_erase, LocallyConstant.mulIndicator_apply_eq_if, monotone_comp_ofDual_iff, ContinuousMap.Homotopy.refl_apply, IsAdjoinRootMonic.coeff_root, MvPolynomial.C_mem_coeffsIn, ContMDiffMap.coeFnRingHom_apply, Finsupp.degree_mono, Set.partiallyWellOrderedOn_iff_exists_monotone_subseq, Subgroup.comap_normalClosure, ContinuousLinearMap.norm_adjoint_comp_self, ContinuousMap.HomotopyWith.cast_apply, ModularForm.qExpansion_mul, map_expect, LinearPMap.mem_adjoint_domain_iff, CategoryTheory.SmallObject.coconeOfLE_ι_app, Polynomial.map_monic_eq_zero_iff, MvPolynomial.bind₁_X_right, Matrix.coe_ofLinearEquiv_symm, MvPolynomial.coeff_rename_eq_zero, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, MvPolynomial.disjoint_support_monomial, Pi.evalStarAlgHom_apply, MeasureTheory.Measure.pi_map_piOptionEquivProd, QuotientGroup.norm_eq_groupSeminorm, DirichletCharacter.Even.to_fun, OrderEmbedding.map_inf_le, CliffordAlgebra.ofProd_ι_mk, MeasureTheory.Measure.instSFiniteBindCoeKernelOfIsSFiniteKernel, Orientation.inner_smul_rotation_pi_div_two_smul_right, Module.Basis.coe_mkFinCons, IsLocalization.mem_coeSubmodule, WeierstrassCurve.Affine.map_negY, RCLike.geometric_hahn_banach_point_closed, ContinuousLinearEquiv.coe_coe, MvPowerSeries.monomial_mul_monomial, BialgHom.coe_mk, Module.DualBases.lc_def, RootPairing.nsmul_notMem_range_root, GroupExtension.Section.equivComp_apply, ModuleCat.MonoidalCategory.whiskerLeft_apply, ContinuousLinearMap.map_add₂, DirectSum.liftRingHom_apply, ContinuousAlgHom.coe_comp', addMonoidAlgebraRingEquivDirectSum_symm_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, ProbabilityTheory.setLIntegral_preimage_condDistrib, RootPairing.Base.exists_eq_sum_and_forall_sum_mem_of_isPos, Finsupp.card_support_le_one, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, MulEquiv.coprodAssoc_symm_apply_inr_inl, MeasureTheory.OuterMeasureClass.measure_iUnion_nat_le, CoalgEquiv.congr_fun, summable_iff_summable_compl_and_tsum_mem, AffineBasis.coord_apply_combination_of_mem, CliffordAlgebra.GradedAlgebra.lift_ι_eq, MeasureTheory.Measure.tprod_tprod, WithConv.symm_equiv_apply, UniformOnFun.ofFun_add, PolynomialModule.monomial_smul_lsingle, RingHom.map_dfinsuppSumAddHom, OrderIso.symm_image_image, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, Finsupp.single_eq_pi_single, OrderIso.setIsotypicComponents_symm_apply, Sublocale.restrict_of_mem, ValuativeRel.ValueGroupWithZero.lift_valuation, MonoidHom.subgroupComap_apply_coe, Fin.coe_castLEEmb, Function.locallyFinsuppWithin.restrictLatticeHom_apply, Polynomial.tendsto_abv_aeval_atTop, AddSubgroup.mem_toZModSubmodule, MonoidAlgebra.mapDomainAddEquiv_apply, TensorPower.toTensorAlgebra_galgebra_toFun, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, MeasureTheory.measure_union', MvPolynomial.join₂_map, VectorField.fderivWithin_apply_lieBracket, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, Monoid.Coprod.lift_apply_mk, ContinuousMap.HomotopyEquiv.continuous, WithZero.map_map, MeasureTheory.ProbabilityMeasure.coeFn_univ, SchwartzMap.integrable_pow_mul, AddMonoidAlgebra.lift_unique, FirstOrder.Language.StrongHomClass.toEmbedding_toFun, TensorProduct.Algebra.moduleAux_apply, FreeAddSemigroup.lift_of_add, Matrix.det_apply', RingEquiv.image_symm_eq_preimage, ofDual_sSup, LieModule.coe_maxTrivHom_apply, ProbabilityTheory.eq_condKernel_of_kernel_eq_compProd, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, Rep.indToCoindAux_of_not_rel, VectorPrebundle.coordChange_apply, Convex.closure_subset_image_homothety_interior_of_one_lt, Polynomial.degree_mul_C, Subgroup.IsComplement.rightQuotientEquiv_apply, Ordinal.preOmega_le_preOmega, Subfield.extendScalars.orderIso_symm_apply_coe, PowerSeries.coeff_zero_X_mul, MeasureTheory.SimpleFunc.inf_apply, SimpleGraph.chromaticNumber_eq_iff_forall_surjective, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, ContinuousMultilinearMap.norm_map_cons_le, DilationEquiv.coe_pow, LinearMap.not_hasEigenvalue_zero_tfae, NonUnitalAlgHom.fst_apply, ContinuousMonoidHom.one_toFun, Equiv.subtypeSubtypeEquivSubtypeInter_symm_apply_coe_coe, AlgebraicGeometry.ExistsHomHomCompEqCompAux.range_g_subset, EuclideanGeometry.orthogonalProjection_apply, NNReal.sum_sqrt_mul_sqrt_le, MvPolynomial.transcendental_supported_polynomial_aeval_X_iff, Module.Basis.extendOfIsLattice_apply, OrderMonoidHom.inr_apply, LinearMap.toMatrix_pow, AddCommMonCat.equivalence_inverse_map, TensorProduct.map_range_eq_span_tmul, TensorAlgebra.algebraMap_eq_zero_iff, MvPolynomial.aeval_monomial, LinearMap.exact_iff, BumpCovering.toPOUFun_eq_mul_prod, OrderHom.sInf_apply, TopologicalSpace.Opens.toTopCat_map, Fin.orderIsoTriple_two, Polynomial.div_C_mul, PowerSeries.X_dvd_iff, Subalgebra.range_le, groupHomology.cyclesMk₀_eq, CategoryTheory.Localization.SmallShiftedHom.equiv_mk₀, SummationFilter.support_comap, Multiset.coeEquiv_symm_apply_snd_val, Homeomorph.symm_apply_apply, SimpleGraph.Iso.mapEdgeSet_apply, Polynomial.resultant_C_mul_left, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, AlgHom.mem_equalizer, Finsupp.coe_mul, MeasureTheory.exists_measurable_superset, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, Sum.Lex.inr_top, isAddRegular_toDual, LeftInvariantDerivation.commutator_apply, OrderIso.coe_toHomeomorph, Ideal.relNorm_bot, subset_supClosure, Algebra.intNorm_map_algEquiv, CommSemiring.counit_apply, ContinuousMap.eval_apply, HahnSeries.map_coeff, AddMonoidAlgebra.lift_def, Subgroup.IsComplement'.QuotientMulEquiv_apply, Perfection.lift_symm_apply, Antivary.sum_smul_le_sum_comp_perm_smul, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Complex.conj_neg_I, Ideal.norm_mem_relNorm, Rep.applyAsHom_hom, WittVector.constantCoeff_apply, CategoryTheory.Bicategory.Adjunction.homEquiv₁_symm_apply, fourier_add_half_inv_index, OrderMonoidHom.coe_mk, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, NNRealRMK.integral_rieszMeasure, Algebra.intNorm_intNorm, LieDerivation.coe_ad_apply_eq_ad_apply, CategoryTheory.Bicategory.toNatTrans_conjugateEquiv, HahnSeries.addOppositeEquiv_apply, ProbabilityTheory.Kernel.sum_apply', Module.Relations.Solution.IsPresentation.exact, Module.End.hasGenEigenvector_iff, StandardEtalePresentation.toPresentation_relation, PowerSeries.invUnitsSub_mul_X, fwdDiff_aux.coe_fwdDiffₗ_pow, ContinuousLinearEquiv.strictConvex_preimage, Filter.comap_add_comap_le, CauSeq.Completion.ofRatRingHom_apply, CategoryTheory.Discrete.equivalence_inverse, Complex.rightAngleRotation, EuclideanGeometry.eq_reflection_of_eq_subspace, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, OrthonormalBasis.coe_singleton, MulArchimedeanClass.orderHom_mk, AlgEquiv.prodUnique_symm_apply, CategoryTheory.Limits.IsColimit.ι_app_homEquiv_symm, MonoidHom.map_neg_one, PEquiv.le_def, MonoidHom.mem_graph, fourierCoeffOn_of_hasDerivAt, NonarchAddGroupSeminorm.coe_le_coe, ContinuousAlternatingMap.bound, ExteriorAlgebra.ι_mul_prod_list, Polynomial.cyclotomic_expand_eq_cyclotomic, CategoryTheory.Preadditive.epi_iff_surjective', equivShrink_smul, MeasureTheory.Measure.ae_compProd_iff, Sublattice.mem_comap, DFinsupp.eq_mk_support, Polynomial.eval₂_eq_sum, Equiv.extend_apply, ProbabilityTheory.Kernel.trajContent_eq_lmarginalPartialTraj, Sublattice.coe_subtype, MvPolynomial.leadingCoeff_toLex, IsBaseChange.linearMapLeftRightHom_apply, ZMod.χ₈_nat_eq_if_mod_eight, ProbabilityTheory.Kernel.IndepSet.measure_inter_eq_mul, Algebra.trace_apply, ContinuousLinearMap.hasDerivWithinAt, Finsupp.sum_ite_self_eq', isDedekindDomain_iff, HeytingHom.comp_apply, preimage_smul_setₛₗ', CategoryTheory.Equivalence.induced_functor, Polynomial.toMvPolynomial_injective, LeftInvariantDerivation.commutator_coe_derivation, Equiv.Perm.sign_prod_list_swap, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, isAddRightRegular_toAdd, AddSubmonoid.coe_negOrderIso_apply, Filter.map_one, IsCyclotomicExtension.Rat.discr_odd_prime', Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix, LinearIsometry.rTensor_apply, SetSemiring.down_up, Equiv.isOpenMap_symm_iff, RestrictedProduct.add_apply, TensorAlgebra.toDirectSum_ι, ContinuousMap.snd_apply, FormalMultilinearSeries.derivSeries_apply_diag, ModuleCat.forget_map, DirichletCharacter.changeLevel_primitiveCharacter, PEquiv.self_trans_symm, Path.extend_of_le_zero, NonUnitalSubsemiring.centerCongr_apply_coe, Nat.factorization_eq_zero_iff, LinearMap.coprodEquiv_symm_apply, NumberField.InfiniteAdeleRing.denseRange_algebraMap, spectrum.algebraMap_mem, UniformFun.ofFun_toFun, TopCat.Presheaf.stalkSpecializes_stalkFunctor_map_apply, AlgEquiv.invFun_eq_symm, LinearEquiv.arrowCongrAddEquiv_symm_apply, ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_on', CompactlySupportedContinuousMap.monotone_of_nnreal, FreeAddMonoid.hom_map_lift, MvPolynomial.coeff_eval_eq_eval_coeff, Seminorm.coe_iSup_eq, stdSimplex.le_one, OneOneEquiv.of_equiv, LinearMap.BilinForm.toMatrix_comp, LinearEquiv.map_mem_invtSubmodule_iff, AbsoluteValue.isAbsoluteValue, ExteriorAlgebra.ιMulti_succ_curryLeft, HahnSeries.leadingCoeff_neg_iff, LinearMap.mul'_comm, HasDerivAt.conj_conj, Real.volume_uIoc, Matrix.SpecialLinearGroup.toLin'_symm_apply, AddMonoidAlgebra.singleZeroAlgHom_apply, ContinuousLinearEquiv.differentiableWithinAt, ClassGroup.mk0_eq_mk0_inv_iff, PMF.pure_apply_self, Module.Basis.span_eq, DirectSum.lmap_of, StarMulEquiv.ofClass_apply, RingSeminorm.apply_one, MeasureTheory.le_addContent_diff, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, MvPolynomial.C_pow, CompactExhaustion.exists_superset_of_isCompact, Equiv.sigmaFiberEquiv_symm_apply_snd_coe, InverseSystem.invLimEquiv_symm_apply_coe, Finsupp.coe_mk, FirstOrder.Language.LHom.mem_substructureReduct, Valuation.coe_mk, QuadraticAlgebra.coe_algebraMap, ComplexShape.Embedding.AreComplementary.equiv_inr, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, DirectSum.coe_decompose_mul_of_left_mem_zero, integrable_mulExpNegMulSq_comp, AddConstMap.coe_conjNeg_apply, Prod.Lex.toLex_le_toLex, Monoid.CoprodI.Word.equivPair_eq_of_fstIdx_ne, iteratedFDeriv_clm_apply_const_apply, LinearMap.map_smul_inv, Finset.weightedVSub_sdiff_sub, ContinuousAlgEquiv.image_symm_image, CoalgHom.ext_iff, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, Partition.partscopyEquiv_apply_coe, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, IsExposed.eq_inter_halfSpace', Ordinal.lift_omega, InfHom.coe_inf, MonoidAlgebra.mul_single_apply, BoundedContinuousFunction.const_apply, Primrec.of_equiv_iff, MeasureTheory.measure_setLAverage_le_pos, addMonoidAlgebraAddEquivDirectSum_apply, MultilinearMap.sum_apply, CFC.log_algebraMap, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, QuadraticAlgebra.det_toLinearMap_eq_norm, RelEmbedding.sorted_swap_listMap, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one, QuaternionAlgebra.imJ_swapEquiv_apply, CoalgHomClass.map_comp_comul_apply, ExteriorAlgebra.leftInverse_map_iff, ModularGroup.coe_T_zpow, Real.ringEquivCauchy_apply, Matrix.trace_map, MvPolynomial.coeffs_C_subset, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, Polynomial.eval₂_eq_sum_range', IsLocalizedModule.map_integerMultiple, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, AList.lookupFinsupp_apply, Cardinal.toNat_lift_add_lift, Finsupp.eraseAddHom_apply, Algebra.GrothendieckGroup.lift_apply, CuspFormClass.exp_decay_atImInfty, Set.graphOn_prod_prodMap, EuclideanGeometry.orthogonalProjection_mem_orthogonal, IsMin.toDual, Polynomial.opRingEquiv_op_C_mul_X_pow, HasFPowerSeriesWithinOnBall.hasSum, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', Polynomial.degreeLT.basisProd_natAdd, BialgEquiv.symm_apply_apply, Finsupp.mem_frange, equivShrink_le_equivShrink, MeasureTheory.OuterMeasureClass.measure_empty, coe_innerₛₗ_apply, DirichletCharacter.map_zero', LieAlgebra.lieCharacter_apply_lie', Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk, LocallyConstant.smul_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp, FirstOrder.Language.Term.relabelEquiv_apply, Coalgebra.Repr.eq, CondensedSet.toTopCatMap_hom_apply, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, Ordinal.preOmega_omega0, AlgEquiv.toAlgHomHom_apply, TruncatedWittVector.commutes', HahnSeries.truncLT_smul, SemidirectProduct.right_inl, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, CategoryTheory.Localization.SmallHom.equiv_shift, WithZero.withZeroUnitsEquiv_apply, MeasureTheory.OuterMeasure.biInf_apply', CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_symm_apply_coe, BoundedLatticeHom.coe_mk, Module.Basis.continuous_coe_repr, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, OrderEmbedding.preimage_Ioo, Polynomial.eval₂_smul, TopCat.Presheaf.germToPullbackStalk_stalkPullbackHom_assoc, AddCommGrpCat.hom_neg_apply, Finsupp.sym2Mul_apply_mk, Finsupp.mapDomain_apply', TensorProduct.finsuppScalarLeft_apply, MonomialOrder.degree_monomial_le, NonUnitalStarAlgHom.ext_iff, LinearMap.trace_comp_cycle, MvPolynomial.C_sub, MonoidHom.coe_toAdditive'', HNNExtension.equiv_symm_eq_conj, OrderEmbedding.coe_ofMapLEIff, Module.Basis.det_unitsSMul_self, Unitization.uniformity_eq_aux, OrderHom.equivFunctor_symm_apply, NonUnitalSubringClass.subtype_injective, Homeomorph.isClosedEmbedding, map_symmDiff, GradedTensorProduct.tmul_coe_mul_algebraMap_tmul, FreeGroup.freeGroupCongr_apply, RingCon.quotientQuotientEquivQuotient_symm_mk, CompleteSublattice.map_carrier, Matrix.uniqueEquiv_apply, AddSubgroup.inclusion_injective, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, HasGradientAt.hasDerivAt, Equiv.Perm.sameCycle_extendDomain, LieModuleHom.sub_apply, UpperHalfPlane.denom_cocycle', CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_integral, DirectSum.coe_decompose_mul_of_right_mem_of_le, Submodule.lTensorOne_one_tmul, ModularGroup.lcRow0_apply, IsChain.preimage_relEmbedding, PowerSeries.WithPiTopology.tendsto_trunc_atTop, Polynomial.roots_X_add_C, CategoryTheory.Functor.WellOrderInductionData.Extension.map_limit, Subfield.mem_map, ContinuousLinearEquiv.preimage_closure, MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero, MulOpposite.coe_opLinearEquiv_symm_toLinearMap, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe, MeasureTheory.Measure.absolutelyContinuous_compProd_right_iff, Complex.ofRealAm_coe, Module.Basis.smulTower_repr, Diffeomorph.contMDiff, HasFTaylorSeriesUpTo.zero_eq', ContinuousLinearMap.prod_apply, MeasureTheory.measure_eq_zero_iff_eq_empty_of_vaddInvariant, Module.Basis.toDual_apply_right, Cardinal.aleph0_mul_aleph, Subgroup.IsComplement.equiv_fst_eq_mul_inv, CircleDeg1Lift.floor_map_map_zero_le, InfiniteGalois.limitToAlgEquiv_symm_apply, Complex.imCLM_apply, Action.Iso.conj_ρ, NumberField.coe_discr, MeasureTheory.charFun_map_eq_charFunDual_smul, AddValuation.map_add, RelEmbedding.prodLexMkLeft_apply, SchwartzMap.isBigO_cocompact_zpow, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, Function.OfArity.curry_two_eq_curry, iterateFrobenius_add_apply, Finsupp.toMultiset_sup, Module.End.mem_genEigenspace_zero, IsometryEquiv.nndist_eq, OneHom.withBotMap_apply, ContinuousLinearEquiv.analyticAt, Differentiable.continuousAlternatingMap_apply, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, LinearMap.trace_comp_cycle', ArithmeticFunction.zeta_eq_zero, IsLinearMap.mk'_apply, IsDedekindDomain.exists_representative_mod_finset, Equiv.Perm.pow_mod_orderOf_cycleOf_apply, ContinuousAlternatingMap.coe_restrictScalars, FreeGroup.lift_mk, MvPolynomial.coeff_mul_monomial', Polynomial.map_surjective_iff, AddSubmonoid.coe_subtype, Ordinal.preOmega_lt_preOmega, Matrix.mem_range_scalar_of_commute_transvectionStruct, Equiv.sumArrowEquivProdArrow_symm_apply_inl, LinearMap.toMatrix'_one, Representation.dual_apply, LieAlgebra.of_symm_add, LieAlgebra.SpecialLinear.val_singleSubSingle, MeasureTheory.SignedMeasure.toJordanDecompositionEquiv_apply, MulChar.apply_mem_rootsOfUnity_orderOf, normalize_eq_one, LinearMap.IsProj.codRestrict_apply, MvPowerSeries.eval₂_C, Cardinal.lift_lt_aleph1, Valuation.IsEquiv.lt_one_iff_lt_one, AddSubmonoid.coe_comap, AddMonoid.Coprod.swap_inr, MeasureTheory.SimpleFunc.mem_range_self, Path.subpath_zero_one, AffineEquiv.map_vadd', Submodule.restrictScalarsEmbedding_apply, AffineEquiv.pointReflection_midpoint_left, AddValuation.map_one, MvPowerSeries.lexOrder_le_of_coeff_ne_zero, HahnSeries.support_embDomain_subset, exists_tsupport_one_of_isOpen_isClosed, InnerProductSpace.continuousLinearMapOfBilin_apply, Algebra.smulTower_leftMulMatrix_algebraMap_eq, lipschitzGroup.involute_act_ι_mem_range_ι, NormedAddGroupHom.sum_apply, ContinuousAlternatingMap.map_smul_univ, OrderIso.map_ciInf_set, Circle.toUnits_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, Polynomial.monomial_natDegree_leadingCoeff_eq_self, Combinatorics.Subspace.reindex_isMono, OrderEmbedding.le_iff_le, AdicCompletion.transitionMap_comp_eval_apply, OrderHom.withTopMap_coe, Equiv.apply_eq_iff_eq, map_rat_smul, ofDual_vadd', Finset.singletonOneHom_apply, Finsupp.linearCombination_comapDomain, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, NormedSpace.double_dual_bound, Module.DualBases.coeffs_apply, AddSubmonoid.LocalizationMap.map_isAddRegular, WeierstrassCurve.Affine.baseChange_addX, CategoryTheory.Pseudofunctor.StrongTrans.Modification.equivOplax_apply, FreeMonoid.ofList_comp_toList, CategoryTheory.opEquiv_symm_apply, HasDerivAt.comp_ringHom, AlgebraicGeometry.Scheme.preimage_basicOpen, AdicCompletion.of_injective_iff, DFinsupp.toMultiset_inj, Submodule.map_coe, AddMonoidHom.noncommPiCoprod_single, Metric.Snowflaking.image_toSnowflaking_image_ofSnowflaking, Matrix.cstar_norm_def, IntermediateField.adjoin_toSubfield, spectralAlgNorm_isPowMul, Equiv.Perm.cycle_zpow_mem_support_iff, Submodule.baseChange_span, finsetInf'_mem_infClosure, iSupIndep.map_orderIso, MeasureTheory.Measure.snd_apply, CategoryTheory.ObjectProperty.galoisConnection_isLocal, Monoid.CoprodI.lift_word_ping_pong, ArithmeticFunction.sum_Ioc_mul_eq_sum_sum, norm_sub_pow_two, MvPolynomial.pderiv_X_self, Polynomial.aeval_algHom_apply, UpperHalfPlane.tanh_half_dist, AlternatingMap.domDomCongrₗ_apply, OrderEmbedding.ofAntisymmetrization_apply, isRegular_ofDual, MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse, SubAddAction.ofStabilizer.conjMap_comp_apply, Polynomial.coe_toLaurentAlg, MonoidWithZeroHom.id_apply, MeasureTheory.convolution_eq_swap, CategoryTheory.ShrinkHoms.functor_map, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, mem_convexHull_iff, MulRingNorm.apply_one, Int.sign_eq_sign, ContinuousLinearMap.map_zero₂, Real.fourierInv_eq, CentroidHom.intCast_apply, QuaternionAlgebra.imI_swapEquiv_apply, MeasureTheory.Measure.dirac_unit_compProd, Set.coe_singletonAddMonoidHom, Module.Basis.det_smul_mk_coord_eq_det_update, PerfectClosure.eq_iff, Ideal.height_le_spanRank_toENat, Archimedean.embedReal_one, Module.surjective_piEquiv_apply_iff, WittVector.mul_polyOfInterest_aux3, Fin.revPerm_symm_apply, ModelWithCorners.coe_transContinuousLinearEquiv_symm, Fin.castLEOrderIso_apply, CategoryTheory.orderDualEquivalence_inverse_obj, LinearMap.transvection.congr, BoundedLatticeHom.coe_comp_inf_hom, Nat.Prime.exists_addOrderOf_eq_pow_padic_val_nat_add_exponent, NNReal.sqrt_mul_le_half_add, Matrix.blockDiagonalAddMonoidHom_apply, MeasureTheory.SimpleFunc.support_eq, RestrictedProduct.topologicalSpace_eq_of_top, unitInterval.volume_uIoc, Quaternion.equivTuple_symm_apply, jacobiSym.at_neg_one, Nat.card_pair_lcm_eq, ModularForm.coe_translate, LieEquiv.coe_coe, addRothNumber_map_add_right, Unitization.starLift_symm_apply, Function.Embedding.sigmaSet_preimage, MvPolynomial.pderiv_C, PowerSeries.coeff_C_mul_X_pow, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, Equiv.forall_congr_right, Nat.factorization_eq_zero_of_non_prime, MonomialOrder.degLex_single_lt_iff, Matrix.diagonal_fin_three, LinearPMap.coe_vadd, MvPowerSeries.trunc'_one, ContinuousMultilinearMap.curryFinFinset_symm_apply, equivTangentBundleProd_symm_apply_proj, BoundedLatticeHom.coe_id, VectorField.mlieBracketWithin_apply, LieAlgebra.isNilpotent_iff_forall, AlternatingMap.pi_apply, measurable_piCurry, LocallyConstant.lift_comp_proj, homothety_inv_two, RCLike.conj_eq_re_sub_im, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, SchwartzMap.smulLeftCLM_apply, MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix, MulEquiv.piCongrRight_apply, TensorAlgebra.lift_unique, AlgEquiv.uniqueProd_symm_apply, Equiv.Perm.IsSwap.of_subtype_isSwap, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, Continuous.eval, sInfHom.comp_apply, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, RingHom.map_geom_sum, TensorProduct.quotTensorEquivQuotSMul_comp_mk, MeasureTheory.ofReal_average, SchwartzMap.tsum_eq_tsum_fourierIntegral, CategoryTheory.Abelian.Ext.homEquiv₀_symm_apply, List.toFinsupp_apply, AddSubmonoid.LocalizationMap.mk'_eq_iff_eq, edist_toDual, AffineIndependent.affineCombination_eq_lineMap_iff_weight_lineMap, Submodule.map_toAddSubmonoid', FormalMultilinearSeries.id_apply_one, Homeomorph.image_connectedComponentIn, ofColex_neg, SimpleGraph.Walk.edges_map, Bialgebra.TensorProduct.lid_symm_apply, MeasureTheory.AddContent.onIoc_apply, DirectSum.sum_support_decompose, AffineMap.coeFn_injective, ContinuousLinearEquiv.comp_contDiff_iff, constantCoeff_xInTermsOfW, toDual_iInf, Algebra.norm_eq_zero_iff, ContMDiffSection.mdifferentiable, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, AddMonoidAlgebra.scalarTensorEquiv_tmul, Finsupp.toLex_monotone, RingHom.coe_toSemilinearMap, MvPolynomial.C_dvd_iff_zmod, AlgebraicGeometry.Scheme.exists_le_and_germ_injective, CStarMatrix.of_zero, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, Polynomial.shiftedLegendre_eval_symm, PartOrd.ofHom_apply, ProbabilityTheory.Kernel.iIndepFun.ae_isProbabilityMeasure, ProbabilityTheory.Kernel.lintegral_deterministic', TestFunctionClass.tsupport_map_subset, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', isPRadical_iff, bernsteinPolynomial.derivative_zero, Profinite.NobelingProof.list_prod_apply, OnePoint.equivProjectivization_apply_coe, CFC.spectrum_algebraMap_subset, RingCat.hom_inv_apply, ContinuousAlgHom.map_zero, ZSpan.repr_floor_apply, MeromorphicOn.divisor_def, PointedCone.mem_maxTensorProduct, Equiv.subRight_symm_apply, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, AddUnits.coe_opEquiv_symm, Polynomial.iterate_derivative_map, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly_of_splits, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, MeasureTheory.measurePreserving_pi_empty, Polynomial.sumIDeriv_apply_of_le, AddActionHom.map_mem_fixedPoints, ContinuousMapZero.mkD_apply_of_continuousOn, SubAddAction.fixingAddSubgroup_map_conj_eq, HahnSeries.SummableFamily.powers_of_orderTop_pos, MvPolynomial.aeval_prod, Topology.IsEmbedding.toHomeomorph_symm_apply, Matrix.comp_symm_apply, Finsupp.equivFunOnFinite_single, Subgroup.IsComplement.leftQuotientEquiv_apply, SemidirectProduct.mul_left, RootPairing.Equiv.id_indexEquiv_symm_apply, selfZPow_of_nonneg, NumberField.Units.finrank_mul_regulator_eq_det, Path.range_subpath_of_le, ofAdd_eq_one, FreeGroupBasis.map_apply, Matrix.rank_submatrix_le, ModularForm.coe_smul, MeasureTheory.condExpIndSMul_ae_eq_smul, Rep.indResHomEquiv_apply_hom, Finset.card_eraseNone_eq_card_erase, LinearEquiv.automorphismGroup.toLinearMapMonoidHom_apply, ContinuousLinearMap.iteratedFDeriv_comp_right, RingHom.coe_pow, Cardinal.toNat_pos, QuadraticMap.exists_companion, OrderIso.toCompleteLatticeHom_toFun, DirectSum.lmap_injective, FrameHom.id_apply, lineMap_lt_lineMap_iff_of_lt', IsLocalization.ringEquivOfRingEquiv_apply, cross_cross_eq_smul_sub_smul', Quaternion.linearIsometryEquivTuple_apply, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, MulEquiv.subsemigroupMap_apply_coe, RingEquiv.opOp_symm_apply, RatFunc.aeval_X_left_eq_algebraMap, Function.fromTypes_cons_equiv_apply, ModuleCat.homAddEquiv_apply, map_sub_le_max, Module.Basis.repr_symm_apply, SupHom.dual_symm_apply_toFun, Int.padicValuation_le_one, Module.fgSystem.instDirectedSystemSubtypeSubmoduleFGMemValCoeLinearMapId, Finsupp.coe_sub, DomMulAct.mk_one, Finsupp.apply_linearCombination_id, MulEquiv.subsemigroupMap_symm_apply_coe, Matrix.toMvPolynomial_mul, ClassGroup.mk_canonicalEquiv, Submodule.linearProjOfIsCompl_apply_eq_zero_iff, NumberField.InfinitePlace.prod_eq_abs_norm, Polynomial.Bivariate.pderiv_one_equivMvPolynomial, TensorProduct.rTensorHomToHomRTensor_apply, LinearAlgebra.FreeProduct.lift_comp_ι, MeasureTheory.Measure.addHaar_closedBall_center, AddHom.coe_ofDense, Equiv.Perm.cycleOf_zpow_apply_self, Module.Dual.congr_apply_apply, Polynomial.base_mul_mem_lifts, RestrictedProduct.div_apply, Delone.DeloneSet.mapIsometry_apply_coveringRadius, Preord.comp_apply, MonoidAlgebra.single_apply, Equiv.swap_apply_right, Real.volume_Ioi, OrderIso.sumAssoc_symm_apply_inl, ModularForm.coe_sub, Algebra.coe_linearMap, ContinuousMultilinearMap.apply_zero_uncurry0, MonoidAlgebra.mapDomainRingHom_apply, TensorProduct.fromDirectLimit_of_tmul, AlgebraicGeometry.Scheme.Hom.SpecMap_residueFieldMap_fromSpecResidueField, Polynomial.residueFieldMapCAlgEquiv_symm_X, PiTensorProduct.ofDirectSumEquiv_tprod_apply, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, MeasureTheory.OuterMeasure.iSup_apply, Polynomial.support_monomial', CategoryTheory.nerve.functorOfNerveMap_obj, TopCat.coe_comp, Matrix.map_mul, ProbabilityTheory.Kernel.swapLeft_apply', ArchimedeanClass.addValuation_apply, CategoryTheory.Adjunction.homAddEquiv_symm_sub, StarAlgEquiv.coe_mk, PiTensorProduct.injectiveSeminorm_tprod_le, LinearMap.tensorKerEquiv_apply, Matrix.transpose_empty_rows, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, AbsoluteValue.listSum_le, Nucleus.top_apply, Valuation.isEquiv_iff_val_lt_one, HeytAlg.forget_map, MeasureTheory.Measure.toENNRealVectorMeasure_apply_measurable, UniformOnFun.isUniformInducing_pi_restrict, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, Cardinal.natCast_eq_toENat_iff, ContinuousMap.measurable, basis_toMatrix_mul_linearMap_toMatrix, RingHom.op_apply_apply, LinearMap.IsAlt.self_eq_zero, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, PMF.bind_apply, parallelepiped_eq_convexHull, ValuationRing.coe_equivInteger_apply, Path.segment_apply, lipschitzWith_lineMap, Polynomial.revAt_add, MonoidHom.mclosure_range, Ideal.exists_notMem_dvd_algebraMap_of_primesOver_eq_singleton, CategoryTheory.PreGaloisCategory.toAut_bijective, Equiv.smulRight_apply, MonoidHom.transfer_eq_pow, Submodule.map_mem_span_algebraMap_image, AddChar.toAddMonoidHomEquiv_apply, ContinuousLinearEquiv.symm_apply_eq, ContDiff.continuousLinearMap_comp, LinearMap.toMatrixₛₗ₂'_apply, Seminorm.mem_closedBall, Representation.dualTensorHom_comm, ContinuousLinearMap.precomp_apply, rothNumberNat_le_ruzsaSzemerediNumberNat', equiv_lpPiLp_norm, Dilation.mulLeft_toFun, Algebra.algebraMap_ofSubring_apply, AdicCompletion.eval_lift_apply, MulEquiv.monoidHomCongrRightEquiv_symm_apply, MulEquiv.subgroupMap_symm_apply, fourier_add, ModuleCat.span_rightExact, HahnSeries.inv_single, SmoothPartitionOfUnity.contMDiff_smul, CompHausLike.isoOfHomeo_hom_hom_hom_apply, Quiver.SingleObj.toPrefunctor_symm_comp, LinearMap.baseChange_tmul, MvPowerSeries.trunc_C_mul, MvPolynomial.exists_restrict_to_vars, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_y, Sum.Lex.toLexRelIsoLT_symm_coe, ContMDiffMap.coeFn_mk, WithZero.lift'_zero, gaugeSeminorm_lt_one_of_isOpen, IsLocalization.mem_map_algebraMap_iff, CategoryTheory.Abelian.Ext.addEquivBiprod_apply_snd, Path.Homotopy.symm₂_apply, MvPolynomial.lcoeff_apply, CommRingCat.KaehlerDifferential.ext_iff, PolynormableSpace.withSeminorms, wittStructureInt_rename, Nonneg.val_inv_unitsEquivPos_symm_apply_coe, WithVal.valuation_equiv_symm, map_comp_mul, map_iSup₂, Matrix.piEquiv_apply, LinearMap.transvection.baseChange, List.formPerm_cons_concat_apply_last, WithTop.toDual_le_iff, Algebra.algebraMap_pUnit, MeasureTheory.charFun_eq_integral_innerProbChar, WittVector.constantCoeff_wittNeg, UniformOnFun.uniformContinuous_ofFun_toFun, coe_algEquiv_lpBCF_symm, NormedField.valuation_apply, MeasureTheory.SimpleFunc.tendsto_approxOn_L1_enorm, Valuation.IsUniformizer.val_lt_one, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, UniformEquiv.toHomeomorph_symm_apply, SkewMonoidAlgebra.single_add_erase, LinearMap.polar_mem_iff, map_wittStructureInt, mulLeftEmbedding_apply, HahnSeries.C_apply, Submodule.mem_biSup_iff_exists_dfinsupp, LinearMap.IsContPerfPair.continuous_uncurry, Module.Basis.tensorProduct_repr_tmul_apply, Antivary.sum_comp_perm_mul_eq_sum_mul_iff, ofLex_div, AddCommGroup.DirectLimit.map_apply_of, Matrix.GeneralLinearGroup.val_scalar_apply, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, MultilinearMap.map_sub_map_piecewise, exteriorPower.ιMulti_family_linearIndependent_ofBasis, Equiv.mulRight_symm_apply, exists_reduced_fraction', Equiv.subtypeSubtypeEquivSubtype_symm_apply_coe_coe, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assoc, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, cfc_algebraMap, skewAdjointMatricesLieSubalgebraEquiv_apply, Finsupp.Colex.single_lt_iff, MvPowerSeries.map_X, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C, Unitization.lipschitzWith_addEquiv, Module.Basis.coe_ofEquivFun, Isometry.toDilation_toFun, Equiv.sigmaProdDistrib_apply, DirichletCharacter.modZero_eq_delta, FirstOrder.Language.ElementaryEmbedding.coe_toHom, PolynomialLaw.ground_apply, UniformSpace.Completion.isDenseInducing_toCompl, spectralNorm_eq_of_equiv, UniformEquiv.piCongrLeft_apply_apply, Equiv.Perm.sign_prodCongrLeft, Matrix.toLinearMapRight'_one, Module.injective_iff, MvPolynomial.restrictSupport_eq_span, CategoryTheory.SimplicialObject.augmentedCechNerve_obj_left_map, PiLp.continuousLinearEquiv_apply, Monoid.CoprodI.lift_comp_of', IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, Subsemiring.mopRingEquivOp_symm_apply, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, ringHom_monotone, Finset.mem_map_of_mem, Nat.prod_pow_factorization_centralBinom, AlgHom.restrictNormal_commutes, RingHom.ker_eq, Real.volume_Ioo, RingHom.rangeRestrictFieldEquiv_apply_coe, Equiv.sumIsRight_symm_apply_coe, LinearEquiv.ofLinear_symm_apply, Equiv.sigmaSubtype_apply, MonomialOrder.degree_sub_LTerm_lt, GroupSeminorm.coe_sSup_apply, cfcₙL_integrable, ContinuousAlgEquiv.continuousAt, Submodule.span.ringHom_apply, RCLike.sqrt_normSq_eq_norm, UniformOnFun.edist_le, wbtw_pointReflection, IsLocalization.orderIsoOfPrime_apply_coe, OrderRingIso.refl_apply, Subgroup.commute_subtype_of_commute, isSMulRegular_iff_ker_lsmul_eq_bot, UniformEquiv.toHomeomorph_apply, Matrix.IsHermitian.charpoly_eq, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, CategoryTheory.Limits.Sigma.ι_reindex_hom_assoc, bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt, AffineMap.lineMap_apply_one_sub, PresheafOfModules.germ_ringCat_smul, FreeAddGroup.map.of, MeasureTheory.ProbabilityMeasure.null_iff_toMeasure_null, Set.FiniteExhaustion.toFun_eq_coe, Polynomial.taylor_X, nnnorm_toAdd, RCLike.conj_ofNat, Polynomial.multiset_prod_X_sub_C_coeff_card_pred, QuadraticForm.associated_tmul, QuadraticMap.polarSym2_map_smul, SimpleGraph.Reachable.coe_subgraphMap, Ergodic.symm_iff, groupCohomology.cocyclesMk₀_eq, MeasureTheory.prob_add_prob_compl, HasGradientAt.fderiv_apply, Polynomial.Splits.roots_map_of_ne_zero, OrderHom.onDiag_coe, CompositionAsSet.boundary_length, Equiv.sumPiEquivProdPi_apply, NumberField.mulHeight₁_eq, Seminorm.comp_smul_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, Homeomorph.surjective, MonoidWithZeroHom.snd_apply_coe, AddMonoidHom.comp_apply, ContinuousLinearMap.comp_analyticOnNhd, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, AugmentedSimplexCategory.inr'_eval, LinearEquiv.alternatingMapCongrRight_symm_apply_apply, ModN.instModuleFinite, MultilinearMap.prod_apply, AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpec, TemperedDistribution.derivCLM_apply_apply, WithLp.linearEquiv_symm_apply, OrthonormalBasis.tensorProduct_apply, AddMonoidHom.finset_sum_apply, MonoidHom.mulExact_iff, FreeMonoid.countP_apply, equivShrink_neg, FirstOrder.Language.LEquiv.onSentence_symm_apply, RingEquiv.bijective, ModuleCat.endRingEquiv_apply, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, AffineBasis.linear_combination_coord_eq_self, sSupHom.apply_blimsup_le, Metric.measure_ball_pos, MultilinearMap.curryFinFinset_symm_apply, DirectSum.coe_decompose_mul_of_right_mem_zero, OrderAddMonoidHom.fst_apply, NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral, Multiplicative.ext_iff, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, TrivSqZeroExt.fstHom_apply, Nimber.toOrdinal_zero, SemiRingCat.forget₂_monCat_map, Polynomial.separable_X_sub_C, Equiv.image_symm_apply_coe, Affine.Simplex.interior_eq_image_Ioo, groupHomology.lsingle_comp_chainsMap_f_assoc, ProbabilityTheory.absolutelyContinuous_boolKernel_comp_left, LinearIsometryEquiv.integrable_comp_iff, MultilinearMap.pi_apply, MonoidHom.compr₂_apply, CategoryTheory.Iso.eHomCongr_inv_comp, OrderDual.ofDual_lt_ofDual, Pretrivialization.symmₗ_linearMapAt, MeasureTheory.ProbabilityMeasure.prod_apply_symm, FreeMonoid.freeMonoidCongr_symm_of, MonoidHom.compAddChar_apply, integral_re, MonoidWithZero.inverse_apply, Matrix.invertibleEquivDetInvertible_symm_apply, Cardinal.toNat_add, NatOrdinal.toOrdinal_zero, Sum.Lex.toLex_strictMono, Module.DualBases.coe_basis, Submonoid.LocalizationMap.surj, bernsteinPolynomial.iterate_derivative_at_0, LinearMap.toMatrixAlgEquiv_reindexRange, AlgebraicGeometry.Scheme.range_fromSpecResidueField, Polynomial.finiteMultiplicity_X_sub_C, MulAction.IwasawaStructure.is_conj, LieModuleHom.ext_iff, Valued.loc_const, Matroid.mapSetEmbedding_ground, MeasureTheory.SimpleFunc.approx_comp, Prod.Lex.prodLexCongr_apply, AddSubmonoid.LocalizationMap.mk'_add_cancel_right, ModularForm.toFun_eq_coe, LieModuleHom.map_add, OrderDual.ofDual_comp_toDual, LinearEquiv.lTensor_refl_apply, WithTop.some_mem_insertTop, AddMonoidHom.mapDMatrix_apply, ProbabilityTheory.lintegral_condKernel_mem, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, PowerSeries.coeff_X_pow_mul', MulEquiv.coe_toMulHom, Basis.piTensorProduct_repr_tprod_apply, RootPairing.toLinearMap_apply_apply_mem_range_algebraMap, finRotate_succ_apply, TensorProduct.star_map_apply_eq_map_intrinsicStar, ContinuousMap.exists_mem_subalgebra_near_continuous_of_separatesPoints, TopCat.Sheaf.eq_of_locally_eq_iff, Matrix.cramer_transpose_apply, AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, LeftInvariantDerivation.ext_iff, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp, CategoryTheory.Localization.homEquiv_map, Ideal.absNorm_relNorm, QuotientGroup.map_map, Module.End.genEigenspace_le_genEigenspace_finrank, OmegaCompletePartialOrder.Chain.isChain_range, abs_signedDist_le_dist, OrderIso.isLUB_preimage', ClassGroup.equivPic_apply, ProbabilityTheory.IndepSet.measure_inter_eq_mul, MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq, MvPowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto, StarSubalgebra.mem_map, map_nsmul, Submodule.subtype_injective, DirectSum.toModule.unique, Orientation.norm_kahler, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, ContMDiffSection.coe_neg, NumberField.mixedEmbedding.disjoint_span_commMap_ker, Equiv.Perm.SameCycle.symm_apply_left, mfderiv_subtype_coe_Icc_one, BumpCovering.locallyFinite', Matrix.comp_map_transpose, Finsupp.mul_prod_erase', IsAntichain.preimage_relEmbedding, NumberField.FinitePlace.norm_le_one, MeasureTheory.measure_preimage_mul_right, infIccOrderIsoIccSup_symm_apply_coe, SlashInvariantFormClass.petersson_smul, Complex.conj_tsum, StarAlgHom.map_adjoin, Finset.weightedVSub_indicator_subset, MvPolynomial.aevalTower_algebraMap, ContinuousLinearMap.exists_nnnorm_eq_one_lt_apply_of_lt_opNNNorm, Module.Relations.Solution.π_comp_map_apply, ProbabilityTheory.compProd_posterior_eq_swap_comp, WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq, NumberField.InfinitePlace.map_natCast, PresheafOfModules.naturality_apply, ArithmeticFunction.cardFactors_one, RootPairing.indexNeg_neg, AddMonoid.Coprod.lift_swap, ProbabilityTheory.Kernel.setLIntegral_const, NumberField.Units.sum_mult_mul_log, Submodule.dualRestrict_apply, RingHom.Bijective.stableUnderComposition, Polynomial.hasFDerivWithinAt, LinearMap.hasDerivAt, Submonoid.val_unitsTypeEquivIsUnitSubmonoid_symm_apply, TopCat.exists_mem_zeroHypercover_range, OrderAddMonoidIso.coe_orderIso, TrivSqZeroExt.liftEquiv_symm_apply_coe, Con.quot_mk_eq_coe, TensorProduct.one_gradedMul, subtypeOrEquiv_apply, EsakiaHom.id_apply, MvPolynomial.optionEquivLeft_elim_eval, CategoryTheory.coherentTopology.exists_effectiveEpiFamily_iff_mem_induced, ContinuousLinearMap.coe_pi', Subfield.coe_map, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, Equiv.boolNot_symm_apply, ZeroAtInftyContinuousMap.coe_sub, HahnSeries.support_truncLT_subset, WeierstrassCurve.Projective.Point.toAffineAddEquiv_symm_apply, PseudoMetric.finsetSup_apply, MeasureTheory.StronglyMeasurable.integral_kernel_prod_left', Complex.isometryOfOrthonormal_symm_apply, Trunc.finChoiceEquiv_symm_apply, MvPolynomial.optionEquivLeft_symm_X, ContinuousAlternatingMap.coe_toAlternatingMap, WithLp.unitizationAlgEquiv_apply, TopologicalGroup.isOpenMap_iff_nhds_zero, Ideal.mem_comap, IsLocalizedModule.map_iso_commute, AddCon.orderIsoOp_symm_apply, AlgebraicGeometry.PresheafedSpace.stalkMap.stalkSpecializes_stalkMap_assoc, Equiv.Perm.monotone_iff, MvPowerSeries.map_C, Subalgebra.LinearDisjoint.leftMulMatrix_basisOfBasisRight_algebraMap, Nat.nth_eq_orderIsoOfNat, Subsemigroup.equivOp_apply_coe, VitaliFamily.ae_tendsto_limRatioMeas, ContinuousMap.Homotopy.extend_one, Module.Basis.sum_equivFun, Module.End.mem_genEigenspace, Field.Emb.Cardinal.adjoin_basis_eq_top, Polynomial.leadingCoeff_X_add_C, List.formPerm_apply_mem_eq_next, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, WithLp.coe_symm_linearEquiv, LieModule.iSupIndep_genWeightSpace', MonoidHom.toHomUnitsMulEquiv_symm_apply, ContinuousLinearMap.postcompUniformConvergenceCLM_apply, Multiset.sum_hom', Algebra.coe_trace_int, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, groupHomology.single_mem_cycles₂_iff, AddMonoidHom.map_add, RootPairing.chainBotCoeff_reflectionPerm_left, LieModule.traceForm_apply_lie_apply', DirectSum.AddSubmonoidClass.IsHomogeneous.mem_iff, Matrix.submatrixEquivInvertibleEquivInvertible_symm_apply, AddOpposite.opMulEquiv_apply, Valuation.mem_integer_iff, TensorProduct.finsuppScalarLeft_symm_apply_single, MvPowerSeries.isWeightedHomogeneous_iff_eq_weightedHomogeneousComponent, Polynomial.degree_sum_fin_lt, VectorField.lieBracket_smul_right, PMF.ofFintype_apply, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_apply, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, ClosureOperator.eq_ofPred_closed, MeasureTheory.OuterMeasure.restrict_mono, Language.map_id, finSumNatEquiv_symm_apply_of_lt, UpperHalfPlane.σ_mul_comm, CStarMatrix.of_add_of, SlashInvariantForm.neg_apply, TensorProduct.piScalarRightHom_tmul, Fin.cycleIcc_def_le, AlgebraicGeometry.Scheme.Modules.Hom.app_smul, PowerSeries.algebraMap_apply', RCLike.normSq_apply, LinearMap.hasDerivAtFilter, LatticeHom.coe_id, RingInvoClass.involution, ProbabilityTheory.Kernel.rnDeriv_self, FreeMagma.lift_comp_of', IsAntichain.volume_eq_zero, HahnSeries.ofPowerSeries_C, GradedAlgebra.mem_support_iff, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, MonoidHom.fiberEquiv_apply, NumberField.ComplexEmbedding.conjugate_coe_eq, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, exists_C_coeff_notMem, Int.absNorm_under_eq_sInf, AddHom.mem_srange, FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion_apply, OrderAddMonoidHom.comp_apply, CoalgHom.congr_arg, Submodule.comapSubtypeEquivOfLe_apply_coe, RatFunc.toFractionRingRingEquiv_apply, Topology.lawsonOpen_iff_scottOpen_of_isUpperSet, AffineBasis.isUnit_toMatrix, Ideal.algebraMap_residueField_eq_zero, LinearMap.flip_surjective_iff₂, MvPolynomial.eval₂Hom_C, EsakiaHom.toFun_eq_coe, Valuation.one_apply_def, MulEquiv.val_piUnits_apply, Algebra.norm_eq_of_ringEquiv, ProbabilityTheory.Kernel.measurable_kernel_prodMk_right, PartitionOfUnity.exists_finset_nhds', LieDerivation.mem_ad_idealRange_iff, Seminorm.coe_lt_coe, monotoneOn_dual_iff, MeasurableEquiv.eq_image_iff_symm_image_eq, Ideal.absNorm_span_singleton, FinBddDistLat.dual_map, DFinsupp.toMultiset_lt_toMultiset, Module.Basis.repr_smul', OmegaCompletePartialOrder.Chain.mem_map_iff, FreeAddMonoid.map_map, FirstOrder.Language.DirectedSystem.map_map, Polynomial.expand_aeval, CategoryTheory.Discrete.monoidalFunctor_η, PowerSeries.coe_pow, LatticeHom.coe_fst, Polynomial.ringHom_ext'_iff, Equiv.mulEquiv_symm_apply, PowerSeries.substAlgHom_comp_substAlgHom_apply, MeasureTheory.OuterMeasure.f_iUnion, AffineIsometry.injective, LieModuleEquiv.coe_coe, LieModuleHom.congr_fun, MeasurableSet.exists_isOpen_symmDiff_lt, InnerProductSpace.HarmonicAt.comp_CLM, RootPairing.RootPositiveForm.algebraMap_posForm, Monoid.Coprod.map_mk_ofList, Monoid.Coprod.swap_swap, Finsupp.Lex.lt_iff, MvPolynomial.counitNat_surjective, lmap_finsuppLEquivDirectSum_eq, Orientation.inner_rightAngleRotation_self, Subalgebra.pointwise_smul_toSubmodule, LinearMap.lsum_piSingle, HasFiniteFPowerSeriesOnBall.fderiv_eq, Bialgebra.counit_pow, Finset.imageAddMonoidHom_apply, Polynomial.irreducible_X_sub_C, CategoryTheory.conjugateEquiv_comp, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, CategoryTheory.Abelian.Ext.homLinearEquiv_symm_apply, Equiv.Perm.mem_conj_support, OrderHom.uliftRightMap_coe_down, LinearIsometryEquiv.continuous, Finsupp.DegLex.monotone_degree, BddOrd.coe_comp, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, cfcHom_mono, ModularForm.coe_trace, Cardinal.isSuccLimit_omega, Metric.Snowflaking.image_toSnowflaking_ball, TopCat.sigmaIsoSigma_hom_ι_apply, NumberField.ComplexEmbedding.lift_algebraMap_apply, RootPairing.EmbeddedG2.allRoots_subset_range_root, MeasureTheory.OuterMeasure.le_boundedBy, RingEquiv.coe_toNonUnitalRingHom, CategoryTheory.map_shrinkYonedaEquiv, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, PreTilt.mk_untilt_eq_coeff_zero, AlgEquiv.sumArrowEquivProdArrow_apply, IsLocalFrameOn.coeff_sum_eq, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, AddChar.map_sub_eq_div, Algebra.SubmersivePresentation.cotangentComplex_injective, LinearEquiv.isRegular_congr', AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, PEquiv.mul_toMatrix_toPEquiv, partialSups_add_one_eq_sup_disjointed, Subalgebra.mulMap_tmul, Module.Projective.out, AddMonoidHom.coe_ofClosureMEqTopLeft, MulEquiv.toSingleObjEquiv_functor_map, IsometricContinuousFunctionalCalculus.isometric, Polynomial.Monic.as_sum, SimpleGraph.Iso.connectedComponentEquiv_apply, ContinuousMap.intCast_apply, Equiv.Perm.SameCycle.extendDomain, MeasureTheory.SimpleFunc.edist_nearestPt_le, MeasureTheory.hausdorffMeasure_homothety_preimage, Equiv.image_apply_coe, IsEvenlyCovered.homeomorph_comp_iff, ContinuousLinearEquiv.comp_contDiffAt_iff, MeasureTheory.Measure.restrict_apply', FractionalIdeal.coeIdeal_absNorm, AddCommGrpCat.hom_add_apply, WithSeminorms.isVonNBounded_iff_seminorm_bounded, ContinuousAlternatingMap.hasFDerivAt, CentroidHom.one_apply, Ordinal.cof_omega, EquivFunctor.mapEquiv_symm_apply, Algebra.GrothendieckGroup.of_injective, Module.Basis.constr_range, FreeMonoid.count_apply, ContinuousMap.coe_smul, CategoryTheory.PreGaloisCategory.AutGalois.π_surjective, LinearMap.ker_lsmul, Quiver.SingleObj.toPrefunctor_symm_apply, Diffeomorph.sumComm_inl, ContinuousLinearMap.smulRight_apply, DFinsupp.single_eq_pi_single, FormalMultilinearSeries.summable, Module.Basis.repr_unitsSMul, Module.compHom.toLinearEquiv_symm_apply, Valuation.RankOne.hom_eq_zero_iff, Finpartition.IsEquipartition.exists_partPreservingEquiv, toDual_sup, AlgEquiv.subalgebraMap_symm_apply_coe, InnerProductSpace.laplacian_CLE_comp_left, RingCon.liftₐ_mk, WeierstrassCurve.Jacobian.baseChange_negY, ProbabilityTheory.Kernel.lmarginalPartialTraj_succ, AddEquiv.coe_toAddHom, BoundedContinuousFunction.coe_sub, Cardinal.aleph_one_lt_lift, Equiv.Perm.perm_inv_mapsTo_iff_mapsTo, MeasureTheory.VAddInvariantMeasure.measure_preimage_vadd, OrderMonoidIso.eq_symm_comp, ContinuousAlgHom.map_sub, ZeroHom.id_apply, GroupSeminorm.add_apply, PiTensorProduct.mul_comm, ArithmeticFunction.zeta_mul_apply, RootPairing.Base.IsPos.reflectionPerm, Subsemiring.topEquiv_apply, matPolyEquiv_coeff_apply_aux_2, AlgEquiv.commutes', RootPairing.reflection_apply, ContinuousLinearMap.analyticAt_bilinear, inner_gradient_left, FormalMultilinearSeries.compContinuousLinearMap_apply, TensorProduct.piRight_apply, ProbabilityTheory.gaussianReal_apply_eq_integral, addMonoidEndToMultiplicative_apply_apply, WithTop.ofDual_top, AddSubgroup.quotientAddSubgroupOfEmbeddingOfLE_apply_mk, Matrix.toLpLin_apply, AddMonoidHom.compLeft_apply, Representation.ind_apply, Affine.Simplex.face_points', AlgebraicGeometry.quasiCompactCover_iff, MeasureTheory.OuterMeasure.smul_dirac_apply, Equiv.toOrderIsoSet_apply, TensorProduct.congrIsometry_apply, Equiv.Perm.sameCycle_symm_apply_left, MvPolynomial.isEmptyRingEquiv_eq_coeff_zero, Finsupp.equivFunOnFinite_symm_eq_sum, lcm_units_coe_right, AlgEquiv.funUnique_symm_apply, BoundedContinuousFunction.extend_comp, List.sym2_eq_sym_two, ZMod.dft_eq_fourier, Submonoid.topOrderMonoidIso_apply, Polynomial.aeval_natCast, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', nhds_ofAdd, Equiv.conj_apply, RelIso.range_eq, CategoryTheory.GrothendieckTopology.covers_iff, MonoidHom.map_finprod_plift, CategoryTheory.Adjunction.homEquiv_apply_eq, PolynomialModule.eval_map', ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', norm_lt_iff_of_nonempty_compactlySupported, Ordinal.typein_inj, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, MeasureTheory.SimpleFunc.restrict_preimage, HasFDerivWithinAt.comp_hasDerivAt_of_eq, absConvexHull_eq_empty, MeasureTheory.Measure.prodMkLeft_comp_compProd, lineMap_mono_left, OrderIso.image_preimage, HahnSeries.addVal_apply, AlgHom.kerSquareLift_mk, HasFPowerSeriesAt.hasStrictFDerivAt, CategoryTheory.yonedaEquiv_symm_map, MeasureTheory.measure_union_add_inter₀, WithTop.Icc_coe_top, MvPolynomial.sumToIter_C, Polynomial.iterate_derivative_one, contDiffOn_fderivWithin_apply, toDual_iSup, AlgebraicGeometry.Scheme.image_zeroLocus, Polynomial.preimage_eval_singleton, Topology.IsEmbedding.toHomeomorphOfSurjective_apply, AddSubgroupClass.subtype_injective, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, Algebra.TensorProduct.piScalarRight_tmul_apply, LieHom.le_ker_iff, Cardinal.toENat_nat, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, ProbabilityTheory.IsRatCondKernelCDF.mono, FreeMonoid.map_symm_apply_map_eq, CategoryTheory.Cat.Hom.equivFunctor_apply, MeasurableEquiv.coe_mulLeft, AddGroupExtension.Section.add_neg_mem_range_inl, PowerSeries.coeff_pow, Equiv.psigmaEquivSigmaPLift_symm_apply, Quaternion.im_sq, PartitionOfUnity.exists_pos, NormedAddGroupHom.IsQuotient.surjective, WeierstrassCurve.Projective.dblX_eq', RingHom.FaithfullyFlat.injective, IsometryEquiv.mulRight_apply, trace_eq_sum_embeddings_gen, MvPolynomial.eval_expand, ZMod.dft_odd_iff, SimpleGraph.Subgraph.hom_apply, WithTop.lt_ofDual_iff, IsTop.toDual, VitaliFamily.eventually_measure_lt_top, SimpleGraph.Coloring.mem_colorClasses, OrderHom.compₘ_coe_coe_coe, AddConstMapClass.map_add_ofNat', Matrix.toLin'_apply, QuadraticMap.coeFn_smul, Magma.AssocQuotient.lift_symm_apply, Representation.isIntertwiningMap_iff, ZMod.ringEquivCongr_val, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, WeierstrassCurve.map_j, InfTopHom.toFun_eq_coe, CliffordAlgebra.contractRight_ι, AddConstMapClass.map_sub_int, Monoid.Coprod.fst_surjective, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, Equiv.optionSubtypeNe_apply, QuotSMulTop.map_id, AddMonoidHom.inr_strictMono, ContinuousMap.Homotopy.curry_one, Finset.singletonZeroHom_apply, UniformSpaceCat.extensionHom_val, LaurentSeries.mem_integers_of_powerSeries, CompleteOrthogonalIdempotents.map, ZeroHom.add_apply, toDual_ofNat, AddUnits.continuous_embedProduct, Ideal.bijective_algebraMap_quotient_residueField, MulChar.coe_equivToUnitHom, Homeomorph.range_coe, OrderIso.withTopCongr_symm_apply, IsometryEquiv.subLeft_apply, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, MeasureTheory.SimpleFunc.approx_apply, AddMonoidHom.smulLeft_apply, ModuleCat.extendScalarsId_inv_app_apply, ProbabilityTheory.Kernel.measure_mutuallySingularSetSlice, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_apply, Polynomial.natDegree_derivative_lt, Subgroup.normalizerMonoidHom_apply_symm_apply_coe, AddChar.complexBasis_apply, AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen, LinearEquiv.det_refl, PEquiv.toMatrix_toPEquiv_apply, Equiv.rightInverse_symm, WeierstrassCurve.IsGoodReduction.goodReduction, UniformConvergenceCLM.nhds_zero_eq, IsConjRoot.sub_algebraMap, algebraMap_galRestrict'_apply, NonarchAddGroupSeminorm.coe_sSup_apply', ModuleCat.semilinearMapAddEquiv_symm_apply_apply, SymAlg.sym_one, Homeomorph.coe_mulLeft, LinearEquiv.arrowCongr_comp, isSMulRegular_on_quot_iff_lsmul_comap_le, FreeAddMonoid.countP_of, Ideal.absNorm_algebraMap, OrderAddMonoidHom.toFun_eq_coe, SemidirectProduct.mk_eq_inl_mul_inr, MonoidHom.flip_apply, RingOfIntegers.coe_algebraMap_norm, ofColex_toColex, Path.coe_reparam, MeasureTheory.Measure.haar.haarContent_outerMeasure_closure_pos, Polynomial.mapEquiv_apply, Homeomorph.symm_map_nhds_eq, WittVector.teichmuller_coeff_pos, WittVector.mk_fontaineTheta, MulRingSeminorm.ext_iff, LieAlgebra.isNilpotent_ad_of_isNilpotent, CompareReals.compare_uc, IsLocalization.surjective_piRingHom_algebraMap_comp_piEvalRingHom, Cubic.C_mul_prod_X_sub_C_eq, AddGroupSeminormClass.map_zero, lineMap_le_map_iff_slope_le_slope_left, innerSL_apply_coe, Algebra.TensorProduct.lidOfCompatibleSMul_tmul, Polynomial.aeval_algHom, Polynomial.coe_aevalAeval_eq_evalEval, Nat.ordCompl_dvd, AffineSubspace.signedInfDist_apply_of_mem, Polynomial.map_mapRingHom_eval_map_eval, Module.Basis.constr_apply, AddSubgroupClass.inclusion_right, AddChar.coe_nsmul, AlgebraicGeometry.Proj.res_apply, Polynomial.toLaurent_C, AbsoluteValue.map_zero, AddEquiv.coprodAssoc_symm_apply_inr_inl, Dilation.isEmbedding, Equiv.coe_trans, ContinuousLinearMap.bound, FreeAddMonoid.toList_cons, Derivation.leibniz_invOf, Function.locallyFinsuppWithin.coe_zero, Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le, ProbabilityTheory.Kernel.iIndepFun.cond_iInter, Polynomial.ofMultiset_injective, PowerSeries.binomialSeries_constantCoeff, Multiplicative.monoidHom_ext_iff, NumberField.mixedEmbedding.convexBodySum_volume, CoalgHom.coe_comp, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, IncidenceAlgebra.coe_mk, Rep.coinvariantsAdjunction_homEquiv_apply_hom, OrderIso.tendsto_atBot, tendsto_algebraMap_cobounded, AddGroupNorm.coe_lt_coe, LinearEquiv.piCongrLeft'_apply, MvPolynomial.supportedEquivMvPolynomial_symm_C, Multiset.normalize_gcd, Polynomial.IsSplittingField.IsScalarTower.splits, isRegular_toColex, TopCat.Presheaf.app_injective_iff_stalkFunctor_map_injective, AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom, tendsto_algebraMap_inv_atTop_nhds_zero_nat, PEquiv.mem_single_iff, Polynomial.revAt_invol, strictMono_iff_map_neg, ContinuousAddEquiv.comp_symm_eq, PowerBasis.aeval_minpolyGen, Measurable.setLIntegral_kernel_prod_right, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eq_poly_in_U, PowerSeries.coeff_one_pow, AbsoluteValue.map_mul, Trivialization.linearMapAt_apply, Equiv.Perm.sign_of_cycleType', AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, Equiv.ofUnique_symm_apply, WithCStarModule.equiv_symm_pi_apply, Homeomorph.funUnique_symm_apply, IsAdjoinRoot.ofAlgEquiv_root, coe_iterateFrobeniusEquiv, Valued.isClopen_closedBall, Real.probChar_apply, ContinuousLinearEquiv.prodCongr_apply, Equiv.prodSumDistrib_symm_apply_left, Ideal.map_pointwise_smul, WeierstrassCurve.Affine.Point.map_zero, StrongDual.polar_singleton, Fin.coe_castAddEmb, MonoidAlgebra.mul_apply_antidiagonal, Module.Flat.iff_rTensor_preserves_injective_linearMap', MeasureTheory.SimpleFunc.coe_one, MeasureTheory.SimpleFunc.finMeasSupp_iff, Equiv.optionSubtype_symm_apply_symm_apply, DFinsupp.lsum_apply_apply, RatFunc.algebraMap_monomial, toDual_div, NonemptyInterval.snd_dual, MultilinearMap.congr_arg, powMonoidHom_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_assoc, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, MeasureTheory.le_measure_diff, HahnSeries.toPowerSeries_apply, CategoryTheory.Bicategory.conjugateEquiv_iso, CentroidHomClass.map_mul_right, MvPowerSeries.monomial_smul_const, Path.coe_mk', finSuccAboveOrderIso_symm_apply_ne_last, FreeAbelianGroup.lift_neg, MeasureTheory.SimpleFunc.finset_sup_apply, powersEquivPowers_apply, SimplexCategory.toCat_map, CategoryTheory.Bicategory.conjugateEquiv_comm, Path.truncate_one_one, AdjoinRoot.coe_algHomOfDvd, PowerSeries.coeff_mul_X_pow, MeasureTheory.FiniteMeasure.map_snd_prod, SlashInvariantForm.coe_const, Subsemiring.coe_map, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, IsNilpotent.isUnit_quotient_mk_iff, Matrix.toMvPolynomial_constantCoeff, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, Nimber.toOrdinal_toNimber, FirstOrder.Language.DirectLimit.exists_of, NumberField.Units.regulator_eq_det', Representation.self_comp_norm, ProbabilityTheory.Kernel.comp_apply_univ_le, MeasureTheory.OuterMeasure.top_apply, ZeroAtInftyContinuousMap.coe_add, FreeNonUnitalNonAssocAlgebra.lift_of_apply, Height.AdmissibleAbsValues.product_formula, Equiv.Perm.sign_subtypeCongr, galRestrictHom_apply, LinearMap.BilinForm.SeparatingRight.toMatrix', ModuleCat.MonoidalCategory.braiding_inv_apply, RootPairing.IsRootSystem.span_coroot_eq_top, Function.locallyFinsuppWithin.negPart_apply, Concept.swapEquiv_symm_apply, RatFunc.denom_dvd, PresheafOfModules.Sheafify.map_smul, CategoryTheory.ComposableArrows.opEquivalence_counitIso_hom_app_app, ZSpan.fract_eq_fract, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, CategoryTheory.uliftCoyonedaEquiv_symm_map, RingHom.surjective_isStableUnderBaseChange, AddChar.injective_iff, NormedAddGroupHom.coe_smul, TensorProduct.toLinearMap_symm_rid, Matrix.GeneralLinearGroup.coe_map_inv_mul_map, Subalgebra.prod_toSubmodule, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, MeasureTheory.OuterMeasure.exists_measurable_superset_eq_trim, MvPowerSeries.trunc'_map, ContinuousMap.HomotopyRel.pi_apply, ContinuousMap.coe_pow, Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero, AddMonoidHom.coe_ofClosureMEqTopRight, AlgEquiv.bijective, HasStrictDerivAt.hasStrictFDerivAt_equiv, WittVector.ghostComponent_zero_verschiebungFun, MeasureTheory.lintegral_deriv_eq_volume_image_of_monotoneOn, RingCon.matrix_apply, MeasureTheory.ContinuousMap.inner_toLp, Specialization.toEquiv_ofEquiv, gradient_eq_deriv, RingCon.coe_liftₐ, SimpleGraph.Iso.coe_comp, Submodule.toLocalized'_apply_coe, GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset, Rep.diagonalSuccIsoFree_hom_hom_single, Polynomial.coeff_reverse, Finsupp.ext_iff, re_inner_le_norm, Polynomial.toLaurentAlg_apply, Equiv.extendSubtype_apply_of_mem, CategoryTheory.TwoSquare.lanBaseChange_app, Sublocale.toNucleus_apply, exteriorPower.ιMulti_span_fixedDegree, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, IsLowerSet.null_frontier, SlashInvariantForm.coeHom_injective, RootPairing.root_chainTopIdx, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, ContMDiffMap.coe_inv, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, ConvexOn.real_sSup_of_nat_affine_eq, IsSymmetricAlgebra.equiv_toAlgHom, dist_algebraMap', Sum.Lex.inr_lt_inr_iff, MeasureTheory.SimpleFunc.map_preimage, CategoryTheory.Linear.toCatCenter_apply_app, volume_image_subtype_coe, Polynomial.taylor_pow, OrderAddMonoidHom.coe_mk, skewAdjoint.I_smul_neg_I, ModularGroup.coe_S, Complex.tan_conj, Derivation.linearEquiv_coe_comp, SchwartzMap.toZeroAtInfty_apply, ofDual_mul, FiniteField.coe_frobeniusAlgHom, Finsupp.linearCombination_eq_fintype_linearCombination_apply, hasFDerivAt_inv', NormedAddGroupHom.coe_inj_iff, Set.image_inv, ProbabilityTheory.uniformOn_disjoint_union, LinearMap.toMatrix_adjoint, PowerSeries.smul_eq_C_mul, IsometryEquiv.coe_mk, IsometryEquiv.withLpProdCongr_symm_apply, TopHom.comp_apply, AddMagma.FreeAddSemigroup.map_of, RingHom.field_closure_preimage_le, SemiNormedGrp.iso_isometry_of_normNoninc, GradedTensorProduct.of_one, Matrix.vecMul_cons, NonemptyFinLinOrd.mono_iff_injective, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, AffineIndependent.units_lineMap, Algebra.IsAlgebraic.bijective_of_isScalarTower, Polynomial.irreducible_C_mul_X_add_C, DomAddAct.isClosedEmbedding_mk, Module.Basis.ofIsCoprimeDifferentIdeal_apply, ProbabilityTheory.IsRatCondKernelCDF.integrable, Metric.Snowflaking.continuous_ofSnowflaking, MvPolynomial.tensorEquivSum_X_tmul_one, exists_continuous_add_one_of_isCompact_nnreal, AlgebraicGeometry.Scheme.Pullback.Triplet.ofPoint_SpecTensorTo, MonoidAlgebra.mapDomain_mul, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, Polynomial.smul_X_eq_monomial, ContinuousMonoidHom.fst_toFun, WeierstrassCurve.Projective.baseChange_dblY, Matrix.compLinearEquiv_apply, CategoryTheory.Sheaf.ΓObjEquivSections_naturality, Ideal.Quotient.norm_mk_le, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, Nat.factorization_eq_zero_of_lt, ContinuousLinearMap.coe_mk', AbsoluteValue.coe_toMonoidWithZeroHom, EisensteinSeries.eisensteinSeries_slash_apply, MeasureTheory.OuterMeasure.trim_eq_iInf, CategoryTheory.yonedaEquiv_symm_naturality_left, NonUnitalAlgHom.comp_apply, Complex.coe_basisOneI, DirectSum.of_zero_one, PMF.toOuterMeasure_apply_eq_one_iff, MeasureTheory.Measure.ofMeasurable_apply, Invertible.mulRight_symm_apply, Affine.Simplex.height_reindex, FirstOrder.Language.Embedding.refl_apply, TensorProduct.AlgebraTensorModule.coe_rTensor, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, SemimoduleCat.ofHom_apply, MultilinearMap.mk'_apply, Polynomial.Sequence.basis_degree_strictMono, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, PresheafOfModules.germ_smul, MonoidAlgebra.mapDomainAlgHom_apply, isLUB_supClosure, Module.Basis.sumQuot_inl, MonoidAlgebra.liftNC_one, LinearOrderedCommGroupWithZero.inl_apply, WeakDual.CharacterSpace.exists_apply_eq_zero, Equiv.Perm.cycleOf_apply_self, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, SpecialLinearGroup.baseChange_apply_coe, exists_smooth_zero_one_nhds_of_isClosed, Set.Ici_toDual, Polynomial.succ_signVariations_le_X_sub_C_mul, ZLattice.sum_piFinset_Icc_rpow_le, exists_continuousLinearEquiv_fderiv_symm_eq, ContinuousMap.enorm_eq_iSup_enorm, BoundedContinuousFunction.norm_eq_iSup_norm, Pi.evalAlgHom_apply, MvPolynomial.C_inj, CongruenceSubgroup.IsCongruenceSubgroup.conjGL, UniformOnFun.uniformContinuous_eval_of_mem, Set.Icc_toDual, RelIso.coe_fn_toEquiv, SSet.Subcomplex.Pairing.exists_or, RCLike.conj_smul, CategoryTheory.PreGaloisCategory.exists_galois_representative, Circle.isCoveringMap_exp, SlashInvariantForm.coe_mul, AddSubmonoid.opEquiv_symm_apply, QuadraticMap.tensorDistrib_tmul, Unitization.val_unitsFstOne_mulEquiv_quasiregular_apply, UniformFun.uniformSpace_eq_inf_precomp_of_cover, AlternatingMap.domCoprod_apply, OpenPartialHomeomorph.transHomeomorph_apply, Con.comap_conGen_equiv, Subgroup.IsComplement.equiv_mul_left, Metric.PiNatEmbed.toPiNatEquiv_symm_apply, Function.Embedding.toEquivRange_apply, CategoryTheory.PreZeroHypercover.isoMk_inv_h₀, AdjoinRoot.liftAlgHom_root, IsPrimitiveRoot.norm_of_cyclotomic_irreducible, NonarchAddGroupNorm.coe_lt_coe, DirichletCharacter.LSeriesSummable_zetaMul, sSupHom.dual_id, MeasureTheory.measure_biUnion_null_iff, WeierstrassCurve.Jacobian.map_polynomialY, Submonoid.surjOn_iff_le_map, Polynomial.one_lt_rootMultiplicity_iff_isRoot, MeasureTheory.tilted_apply_eq_ofReal_integral', ValueDistribution.logCounting_coe, AlgebraicGeometry.Scheme.JointlySurjective.exists_eq, DirectSum.decompose_symm_of, HilbertBasis.tsum_inner_mul_inner, Finset.orderIsoColex_symm_apply, OrderDual.isCobounded_preimage_toDual, lineMap_slope_lineMap_slope_lineMap, Int.cast_mem_ideal_iff, IsometryEquiv.withLpProdComm_apply, Orthonormal.exists_orthonormalBasis_extension, AddEquiv.map_sub, MvPowerSeries.rescale_zero_apply, OrderIso.sumLexDualAntidistrib_symm_inr, AddChar.zmod_intCast, ContinuousMap.isometryEquivBoundedOfCompact_apply, DistLat.inv_hom_apply, LinearOrderedCommGroupWithZero.inr_apply, Polynomial.monomial_sub, SubadditiveHomClass.map_add_le_add, LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero, TemperedDistribution.fourierTransformInv_apply, NonUnitalStarRingHom.ext_iff, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Finsupp.Lex.single_le_iff, Polynomial.coeff_monomial_succ, BoxIntegral.unitPartition.diam_boxIcc, QuaternionAlgebra.equivProd_apply, Submonoid.centerCongr_apply_coe, map_invOf, FormalMultilinearSeries.summable_norm_apply, Module.Basis.dvd_coord_smul, Preorder.piCongrLeft_comp_restrictLe, Orientation.oangle_sign_smul_add_smul_left, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, Matroid.mapEquiv_eq_map, LightCondSet.toTopCatMap_hom_apply, Pi.addMonoidHom_apply, Equiv.Perm.SameCycle.pow_left, MeasureTheory.measure_le_measure_union_right, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_univ_le_one, RingHom.surjectiveOnStalks_iff_forall_ideal, CharacterModule.homEquiv_apply_apply, cfcₙHom_of_cfcHom_map_quasispectrum, ContMDiffMap.ext_iff, LinearMap.map_smulₛₗ₂, IncidenceAlgebra.mu_toDual, Polynomial.Splits.C, Submodule.mem_map_equiv, lt_finRotate_iff_ne_neg_one, LinearMap.isSymmetric_iff_inner_map_self_real, GrpCat.epi_iff_surjective, CategoryTheory.Functor.CoconeTypes.isColimit_iff, MvPolynomial.eval₂_pUnitAlgEquiv, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, Ideal.relNorm_map_algEquiv, MeasureTheory.measure_add_right_null, ExteriorAlgebra.GradedAlgebra.ι_apply, MeasureTheory.OuterMeasure.iUnion_eq_of_caratheodory, StarAlgHom.coe_id, Equiv.sigmaPUnit_symm_apply_fst, CategoryTheory.Bicategory.conjugateEquiv_whiskerLeft, SimpleGraph.Hom.injective_of_top_hom, LocalizedModule.algebraMap_mk', ModularFormClass.qExpansionFormalMultilinearSeries_coeff, ContinuousLinearMap.map_neg, WeierstrassCurve.Affine.CoordinateRing.map_smul, PowerSeries.trunc_sub, MvPolynomial.eval_X, VectorBundle.pullback, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, HahnSeries.leadingCoeff_of_single, ModularForm.coe_zero, Ordinal.familyOfBFamily'_enum, MeasureTheory.tendsto_measure_Ico_atTop, Algebra.SubmersivePresentation.basisCotangent_apply, Equiv.Perm.isInvariant_of_support_le, AddSubgroup.normedMk.apply, Submodule.linearProjOfIsCompl_surjective, LinearMap.exists_extend_of_notMem, toBoolRing_top, LinearMap.BilinForm.Nondegenerate.toMatrix, ContinuousLinearMap.IsInvertible.self_apply_inverse, FreeMonoid.map_of, CategoryTheory.Hom.mulEquivCongrRight_apply, Derivation.coe_injective, EuclideanGeometry.Sphere.secondInter_eq_lineMap, CategoryTheory.mateEquiv_counit, RCLike.mul_re_ax, Subgroup.centerToMulOpposite_symm_apply_coe, dNext_nat, Ideal.mem_span_pow_iff_exists_isHomogeneous, Convex.affine_preimage, AlgebraicGeometry.AffineSpace.map_appTop_coord, MeasureTheory.lintegral_map_equiv, Module.End.genEigenspace_zero, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, ProbabilityTheory.Kernel.apply_congr_of_mem_measurableAtom, Subfield.subtype_injective, ContinuousLinearMap.isOpenMap_of_ne_zero, OrderMonoidHom.coe_orderHom, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, Finset.weightedVSubOfPoint_subtype_eq_filter, ContinuousLinearMap.integral_comp_comm, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset, hasFDerivWithinAt_iff_tendsto, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, Polynomial.reverse_C_add, FreeGroup.lift_eq_prod_map, Equiv.Perm.OnCycleFactors.kerParam_range_eq, Matroid.toENat_cRank_eq, Complex.measurableEquivRealProd_symm_apply, MeasureTheory.Measure.countable_meas_pos_of_disjoint_of_meas_iUnion_ne_top₀, lineMap_strict_mono_left, Module.Basis.coe_extend, UniformOnFun.toFun_smul, DFinsupp.single_apply, MonoidHom.map_frobenius, map_commutatorElement, RootPairing.pairing_reflectionPerm, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor', ContinuousMap.coe_const, nhds_toDual, FirstOrder.Language.DirectedSystem.coe_natLERec, ArithmeticFunction.vonMangoldt_apply_prime, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, PowerSeries.IsWeierstrassDivisorAt.seq_one, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, Polynomial.natDegree_linear, FirstOrder.Language.ElementaryEmbedding.coe_toEmbedding, weightedVSub_mem_vectorSpan_pair, QuadraticMap.associated_flip, QuadraticMap.Ring.polar_pi, Matrix.IsHermitian.mulVec_eigenvectorBasis, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, CategoryTheory.Functor.flippingEquiv_apply_obj_obj, ValueDistribution.log_counting_zero_sub_logCounting_top, ContinuousAffineEquiv.image_symm, ContinuousLinearEquiv.image_symm_image, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, ValuationSubring.algebraMap_injective, Representation.IntertwiningMap.coe_nsmul, FiberwiseLinear.trans_PartialHomeomorph_apply, IsLocalization.bijective, Subgroup.coe_comap, MeasureTheory.Measure.FiniteAtFilter.exists_mem_basis, UniformSpace.Completion.toCompl_apply, IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomain, AddChar.coe_eq_one, Algebra.trace_eq_of_equiv_equiv, SimpleGraph.comap_map_eq, AddSubmonoid.closure_eq_mrange, TestFunction.coeFnAddMonoidHom_apply, ContinuousLinearMapWOT.sub_apply, Nat.Partition.coeff_genFun, Diffeomorph.toEquiv_coe_symm, CategoryTheory.yonedaEquiv_symm_naturality_right, IsometryClass.isometry, AddMonoidHom.map_one₂, Equiv.optionEquivSumPUnit_coe, matPolyEquiv_smul_one, AffineMap.coe_sub, SheafOfModules.pushforwardSections_unitHomEquiv, Finset.orderEmbOfFin_mem, FirstOrder.Language.ElementaryEmbedding.map_formula, autAdjoinRootXPowSubC_root, Equiv.sigmaPreimageEquiv_apply, TensorProduct.tensorQuotientEquiv_symm_apply_tmul_mk, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone_app, LinearEquiv.coe_symm_mk', Polynomial.degree_monomial, RelIso.preimage_symm_apply, ContinuousLinearMap.map_neg₂, Semigrp.ofHom_apply, LinearMap.compr₂ₛₗ_apply, TopCat.ext_iff, Monoid.CoprodI.lift_comp_of, strongRankCondition_iff_succ, IsGroupLikeElem.map, Matrix.l2_opNorm_def, spectrum.map_polynomial_aeval, Submonoid.inclusion_injective, ContinuousMap.uniform_continuity, Polynomial.toLaurent_C_mul_X_pow, PowerSeries.map_id, mem_finsuppAffineCoords_iff_linearCombination, ProbabilityTheory.condKernel_const, continuous_toMul, Ordinal.toNatOrdinal_toOrdinal, LieSubmodule.Quotient.mk'_apply, AddSubgroup.pointwise_smul_def, CategoryTheory.mateEquiv_square, UniformOnFun.ofFun_smul, RootPairing.EmbeddedG2.ofPairingInThree_long, exteriorPower.oneEquiv_ιMulti, Submonoid.LocalizationMap.mulEquivOfLocalizations_right_inv_apply, Rep.free_ext_iff, LieSubmodule.injective_incl, GradedTensorProduct.symm_of_of, CircleDeg1Lift.map_map_zero_le, spinGroup.involute_eq, Matroid.mapSetEquiv_indep_iff, RingHom.codomain_trivial_iff_range_trivial, UniformFun.dist_def, ContinuousLinearMap.coe_toContinuousAffineMap, FreeAbelianGroup.liftMonoid_symm_coe, Representation.inv_self_apply, RestrictScalars.addEquiv_symm_map_algebraMap_smul, MonoidHom.map_iterate_frobeniusEquiv_symm, ContinuousNeg.induced, Equiv.Perm.ofSubtype_mem_stabilizer, LinearMap.toMatrixAlgEquiv_mul, BoundedOrderHom.ext_iff, LieModuleEquiv.surjective, StrictMonoOn.dual_right, PresheafOfModules.toSheafify_app_apply, signedDist_apply_linear, LinearMap.detAux_id, EuclideanGeometry.Sphere.secondInter_map, ZMod.ringEquivCongr_intCast, RingEquiv.ofHomInv'_symm_apply, ProbabilityTheory.Kernel.lintegral_compProd, MeasureTheory.measurePreserving_finTwoArrow, MeasurableSet.exists_isClosed_diff_lt, AddCircle.equivAddCircle_symm_apply_mk, DirectSum.gsmulHom_apply_apply, CircleDeg1Lift.mul_floor_map_zero_le_floor_iterate_zero, mulRothNumber_map_mul_right, WeierstrassCurve.map_Δ, OrthogonalFamily.linearIsometry_apply, MeasureTheory.Measure.measure_preimage_inv, ContinuousMultilinearMap.le_opNNNorm, MeasureTheory.Measure.pi_pi, Ideal.ResidueField.liftₐ_algebraMap, MeasureTheory.OuterMeasure.comap_iSup, HeytAlg.ext_iff, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, WeierstrassCurve.Projective.comp_smul, matrixEquivTensor_apply, frobenius_add, Homeomorph.piSplitAt_apply, TopCat.limit_topology, MeasureTheory.Measure.setLIntegral_rnDeriv_le, RootPairing.Base.span_int_coroot_support, NonUnitalStarAlgHom.coe_id, OrderHom.map_inf_fixedPoints_le, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, AbsoluteValue.sub_le_add, Ctop.ofEquiv_val, AddAut.smul_def, continuousAt_sign_of_ne_zero, Ideal.toIdeal_homogeneousHull_eq_iSup, AffineSubspace.wOppSide_pointReflection, isClosed_closedAbsConvexHull, Localization.mulEquivOfQuotient_symm_mk', IntermediateField.mem_bot, Function.locallyFinsuppWithin.coe_injective, Algebra.isIntegral_norm, Affine.Simplex.restrict_map_subtype, Polynomial.toContinuousMapOn_apply, MeasureTheory.Content.outerMeasure_lt_top_of_isCompact, OmegaCompletePartialOrder.Chain.pair_succ, ContinuousLinearMapWOT.continuous_dual_apply, MonoidHom.map_mul, integral_re_add_im, Equiv.subtypePreimage_symm_apply_coe_neg, Algebra.Extension.Cotangent.map_mk, InfTopHom.coe_inf, RootPairing.CoPolarizationIn_apply, PrimeSpectrum.BasicConstructibleSetData.map_g, Finsupp.optionElim_apply_none, parallelepiped_orthonormalBasis_one_dim, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, PowerSeries.trunc_derivativeFun, toColex_eq_one, MatrixEquivTensor.toFunAlgHom_apply, DomMulAct.symm_mk_zpow, LinearAlgebra.FreeProduct.lof_map_one, Set.image_list_sum, IsValuativeTopology.mem_nhds_iff, ArithmeticFunction.carmichael_lcm, ContinuousLinearMap.iteratedFDeriv_comp_left, Monoid.CoprodI.lift_range_le, Seminorm.closedBall_comp, LinearMap.BilinForm.baseChange_tmul, MeasureTheory.innerRegularWRT_isCompact_isClosed_measure_ne_top_of_addGroup, ContinuousLinearMap.isCompact_image_coe_of_bounded_of_weak_closed, PMF.map_apply, OrderIso.map_bot, PartialFun.Iso.mk_hom, Submodule.orthogonalProjection_eq_zero_iff, AddEquivClass.map_add, MeasureTheory.Integrable.condDistrib_ae_map, ContinuousLinearMap.holderL_apply_apply, ContinuousMap.Homotopy.extend_apply_of_le_zero, Module.Basis.repr_eq_iff', linearDepOn_iff', ContinuousMap.HomotopyEquiv.trans_symm_apply, ArithmeticFunction.IsMultiplicative.map_lcm, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, CategoryTheory.PreZeroHypercover.isoMk_inv_s₀, OrderIso.sumLexDualAntidistrib_inr, Matrix.mulVec_cons, RatFunc.single_inv, QuadraticAlgebra.norm_mem_nonZeroDivisors_iff, ValuationSubring.valuation_surjective, MeasureTheory.tendsto_integral_norm_approxOn_sub, AddChar.expect_apply_eq_ite, RingHom.mem_eqLocusS, stdSimplexEquivIcc_one, NumberField.Units.dirichletUnitTheorem.logEmbedding_ker, AddSubsemigroup.centerToAddOpposite_apply_coe, Matrix.charpoly_diagonal, LinearMap.toLinearMap_toPerfPair, LeftInvariantDerivation.toFun_eq_coe, PowerSeries.heval_mul, Function.Embedding.inr_apply, groupCohomology.cocycles₁_ext_iff, NonUnitalAlgHom.mem_equalizer, normalize_associated, Equiv.Set.union_apply_right, OmegaCompletePartialOrder.OrderHom.omegaCompletePartialOrder_ωSup_coe, Cubic.b_eq_three_roots, DirectSum.sum_support_of, Matrix.comp_symm_single, TopCat.Presheaf.stalkSpecializes_stalkPushforward_assoc, AdicCompletion.eval_surjective, LaurentPolynomial.eval₂_C_mul_T_n, LocallyConstant.coe_charFn, Perfection.coeff_pow_p, Matrix.head_transpose, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Matrix.GeneralLinearGroup.injective_upperRightHom, Semigrp.forget_map, StarRingEquiv.coe_trans, ContMDiffOn.clm_bundle_apply, Ordinal.preOmega_natCast, RootPairing.coroot_reflectionPerm, Digraph.mk'_apply_Adj, SemilinearIsometryClass.diam_range, MeasureTheory.SimpleFunc.edist_approxOn_le, MeasureTheory.Measure.restrict_apply₀', Profinite.NobelingProof.GoodProducts.max_eq_eval, MulChar.map_zero, Polynomial.degree_add_C, ContinuousAlgEquiv.coe_mk, QuotientGroup.lift_quot_mk, Valuation.pos_iff, SetSemiring.mul_def, quadraticChar_eq_neg_one_iff_not_one, Equiv.Perm.coe_pow, Finset.image_div, Ctop.Realizer.ofEquiv_F, AlgebraicGeometry.Scheme.coe_homeoOfIso, CategoryTheory.Abelian.Ext.biprodAddEquiv_symm_apply, Finsupp.snd_sumFinsuppEquivProdFinsupp, ContDiffMapSupportedIn.compact_supp, Polynomial.toAddCircle_C_eq_smul_fourier_zero, ProbabilityTheory.condExp_prod_ae_eq_integral_condDistrib', MeasureTheory.condExpL1CLM_smul, Matrix.entryLinearMap_toAddMonoidHom, WithCStarModule.equivL_apply, ArithmeticFunction.intCoe_apply, Valued.norm_pos_iff_valuation_pos, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero, Module.Basis.mk_eq_spanRank, TopCat.Presheaf.stalkPushforward.comp, OrderMonoidWithZeroHom.coe_monoidWithZeroHom, MeasureTheory.ProbabilityMeasure.coeFn_mk, Set.image_equiv_eq_preimage_symm, BoundedContinuousFunction.enorm_eq_iSup_enorm, MeasureTheory.AEStronglyMeasurable.convolution_integrand, SkewMonoidAlgebra.mem_span_support, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_assoc, LinearMap.BilinForm.isSymm_iff_basis, RootPairing.isFixedPt_reflectionPerm_iff, Equiv.prodShear_symm_apply, ConvexOn.comp_linearMap, AddEquiv.op_symm_apply_apply, MonCat.id_apply, Equiv.apply_ofInjective_symm, Submonoid.coe_inclusion, IsometryEquiv.continuous, TensorProduct.gradedComm_of_tmul_of, UniformEquiv.surjective, CategoryTheory.IsIso.inv_hom_id_apply, Function.locallyFinsuppWithin.coe_neg, Representation.apply_eq_of_coe_eq, LinearMap.range_coe, RingEquiv.refl_apply, Polynomial.evalEval_C, MeasureTheory.measure_eq_top_of_lintegral_ne_top, AlgEquiv.toLieEquiv_apply, RelEmbedding.map_rel_iff', Perfection.coeff_iterate_frobenius', FinEnum.equiv_down, Function.locallyFinsuppWithin.min_apply, VectorFourier.hasFDerivAt_fourierChar_smul, partialSups_le_iff, IsFractionRing.num_mul_den_eq_num_iff_eq', exteriorPower.ιMulti_span, SemidirectProduct.right_splitting, DirichletCharacter.LSeries_eulerProduct, BoundedOrderHom.id_apply, Module.Basis.toMatrix_self, MeasureTheory.OuterMeasure.le_ofFunction, CategoryTheory.Functor.IsCoverDense.functorPullback_pushforward_covering, Submonoid.LocalizationMap.mk'_eq_iff_eq_mul, OrthonormalBasis.measurePreserving_measurableEquiv, NonUnitalStarAlgHom.map_star', RingEquiv.nonUnitalSubsemiringMap_apply_coe, ModuleCat.ofHom_apply, SSet.stdSimplex.objEquiv_symm_apply, MeasureTheory.distribHaarChar_pos, DFinsupp.finite_support, AddSubgroup.subtype_apply, AddAut.neg_conj_apply, InfTopHom.top_apply, Real.fourierIntegral_real_eq, Module.End.ringEquivEndFinsupp_symm_apply_apply, HeytingHom.coe_id, Coalgebra.Repr.induced_right, CompleteLatticeHom.symm_dual_comp, Matrix.scalar_commute_iff, RingEquiv.piOptionEquivProd_symm_apply, MeasureTheory.measure_preimage_snd_singleton_eq_tsum, ContinuousLinearMap.IsInvertible.injective, MonoidHom.coe_finset_prod, CoalgEquiv.congr_arg, MeasureTheory.measure_union_inv_smul, MeasureTheory.MeasuredSets.edist_def, Quaternion.hom_ext_iff, PowerSeries.rescale_neg_one_invOneSubPow, FractionalIdeal.absNorm_eq_zero_iff, Finsupp.supportedEquivFinsupp_symm_apply_coe_apply, Polynomial.algHom_ext'_iff, CategoryTheory.GrothendieckTopology.Cover.Arrow.from_middle_condition, measurable_equivCurry, HahnSeries.algebraMap_apply', AddSubsemigroup.apply_coe_mem_map, UniformFun.toFun_mul, PeriodPair.lattice_eq_span_range_basis, Algebra.TensorProduct.opAlgEquiv_symm_tmul, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, AddMagmaCat.neg_hom_apply, OrderAddMonoidHom.inrₗ_apply, cfcₙHomSuperset_apply, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, MonoidHom.coe_toMultiplicative, PseudoMetric.sup_apply, MeasureTheory.measure_unitBall_eq_integral_div_gamma, PowerSeries.coeff_subst_finite', WeierstrassCurve.VariableChange.map_r, NonemptyInterval.toDualProd_apply, isRegular_ofLex, Algebra.norm_eq_prod_embeddings_gen, DFinsupp.sub_apply, Ordinal.enum_zero_le', AlgEquiv.toAlgHom_apply, Submonoid.powLogEquiv_symm_apply, Submodule.orthogonalProjection_starProjection_of_le, Sylow.smul_def, InverseSystem.piLTLim_apply, CategoryTheory.PreZeroHypercover.presieve₀_restrictIndex_equiv, QuadraticMap.Isometry.coe_toLinearMap, Real.exists_extension_norm_eq, OrthonormalBasis.sum_repr', CategoryTheory.Functor.mem_inducedTopology_sieves_iff, Ordinal.toLeftMovesToPGame_symm_lt, PowerSeries.HasSubst.monomial, RootPairing.root_coroot'_eq_pairing, CliffordAlgebra.EvenHom.contract_mid, FreeAddGroup.sum.of, continuousMultilinearCurryRightEquiv_apply, antilipschitzWith_lineMap, RCLike.norm_le_im_iff_eq_I_mul_norm, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, Polynomial.coe_eval₂RingHom, LieRinehartAlgebra.Hom.toLinearMap'_apply, RelHom.injective_of_increasing, Equiv.symm_image_image, Submodule.IsCompl.projection_apply_mem, starAddEquiv_apply, cfcₙ_apply, GrpCat.id_apply, LinearMap.det_toMatrix, MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun, exteriorPower.toTensorPower_apply_ιMulti, iterate_map_zpow, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm, WeierstrassCurve.Projective.dblY_of_Y_eq', Finsupp.sumElim_inl, NormedAddGroupHom.coe_zero, Submodule.coe_orthogonalProjection_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, NumberField.Units.dirichletUnitTheorem.exists_unit, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, NonarchAddGroupSeminormClass.map_zero, Polynomial.natDegree_pow_X_add_C, LaurentPolynomial.toLaurent_reverse, supClosure_prod, MeasureTheory.SimpleFunc.coe_algebraMap, IsScalarTower.algebraMap_apply, Algebra.traceForm_toMatrix_powerBasis, MvPolynomial.IsHomogeneous.C_mul, Matrix.minpoly_toLin, ContinuousMap.coe_mul, toDual_ratCast, ProbabilityTheory.Kernel.parallelComp_apply_univ, Submonoid.LocalizationMap.toMonoidHom_apply, HolderOnWith.hausdorffMeasure_image_le, MvPolynomial.rename_hsymm, ZeroAtInftyContinuousMap.coe_neg, LieDerivation.coeFn_coe, SubAddAction.inclusion_injective, basis_toMatrix_mul, Ordinal.toZFSetIso_symm_apply, LocallyFiniteOrder.orderAddMonoidEquiv_apply, PowerSeries.trunc_map, MeasureTheory.OuterMeasure.map_biInf_comap, DFinsupp.card_Iio, SimpleGraph.walkLengthTwoEquivCommonNeighbors_apply_coe, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, Module.End.HasEigenvector.pow_apply, AffineMap.image_vsub_image, Complex.UnitDisc.coe_star, FractionalIdeal.mem_extended_iff, ContinuousLinearEquiv.smulLeft_apply_toLinearEquiv, ContDiffMapSupportedIn.structureMapLM_zero_apply, SchwartzMap.differentiableAt, CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift, AddEquiv.map_neg, RCLike.ofRealAm_coe, Polynomial.natDegree_eq_zero, UniformFun.postcomp_isUniformEmbedding, MeasureTheory.mul_meas_ge_le_pow_eLpNorm, Right.sign_neg, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, Metric.Snowflaking.image_ofSnowflaking_image_toSnowflaking, UniformOnFun.toFun_prod, CommAlgCat.id_apply, Subalgebra.mopAlgEquivOp_apply_coe, LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero, addMonoidAlgebraAlgEquivDirectSum_apply, RCLike.normSq_one, Equiv.Perm.IsCycleOn.extendDomain, Monoid.Coprod.toProd_apply_inl, Ideal.span_singleton_absNorm_le, IndexedPartition.index_out, ProbabilityTheory.Kernel.lintegral_parallelComp, BitVec.equivFin_apply, LinearMap.BilinForm.isAdjointPairLeftAdjointOfNondegenerate, bddAbove_range_partialSups, AffineEquiv.coeFn_injective, RCLike.re_to_complex, dimH_def, MonoidHom.subgroupMap_apply_coe, SkewMonoidAlgebra.lift_def, LinearMap.injective_iff_antilipschitz, Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod, AlgCat.ofHom_apply, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, SymAlg.unsym_sym, FreeSemigroup.length_map, CoalgHom.coe_toAddMonoidHom, SemimoduleCat.homLinearEquiv_symm_apply, CategoryTheory.Functor.CoconeTypes.IsColimit.equiv_symm_ι_apply, Ideal.Factors.piQuotientEquiv_mk, ContinuousLinearEquiv.iteratedFDerivWithin_comp_left, SeparationQuotient.mkCLM_apply, MvPolynomial.constantCoeff_map, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_symm_apply_snd, AffineIndependent.convexHull_inter, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, AffineMap.deriv, MeasureTheory.Measure.haar.haarContent_outerMeasure_self_pos, MulChar.coeToFun_mul, Matrix.toLin'_toMatrix', SmoothBumpCovering.embeddingPiTangent_coe, MeasureTheory.Integrable.condExpKernel_ae, MeasureTheory.setLIntegral_le_meas, ContinuousAlternatingMap.prodLIE_symm_apply, MeasureTheory.measure_symmDiff_eq_zero_iff, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, fderiv_comp_deriv_of_eq, Metric.Snowflaking.image_ofSnowflaking_emetricBall, Matroid.IsBase.mapEmbedding, Ideal.quotient_map_mkₐ, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, Polynomial.monic_normalize, MeasureTheory.Measure.measure_inv, AddCircle.homeomorphCircle'_apply, LinOrd.comp_apply, AlternatingMap.alternatizeUncurryFinLM_apply, LinearMap.compMultilinearMap_apply, NatOrdinal.toOrdinal_eq_one, LinearMap.det_toLin, RootPairing.coroot'_reflectionPerm, Real.volume_pi_closedBall, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible, CoheytingHom.ext_iff, ContinuousAlternatingMap.coe_continuous, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_apply, Real.nndist_eq', RingHom.kerLift_mk, LinearMap.injective_or_eq_zero, OneHom.zpow_apply, Seminorm.continuous_of_forall, IsSelfAdjoint.le_algebraMap_norm_self, Equiv.ringEquiv_symm_apply, HahnSeries.SummableFamily.coeff_hsum_eq_sum, Homeomorph.sigmaProdDistrib_apply, finsetSup'_mem_supClosure, CategoryTheory.Subobject.underlyingIso_arrow_apply, finFunctionFinEquiv_apply, DirectSum.decompose_neg, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, equivShrink_symm_mul, Composition.coe_embedding, QuadraticMap.polar_smul_right, RingEquiv.piFinTwo_apply, MeasureTheory.lintegral_indicator_const₀, ContinuousLinearMap.apply_apply', SemidirectProduct.left_inr, SmoothPartitionOfUnity.nonneg', AlgebraicGeometry.isClosedMap_iff_specializingMap, HasFPowerSeriesWithinAt.hasFDerivWithinAt, Equiv.subtypeSubtypeEquivSubtypeExists_symm_apply_coe_coe, MeasurableEquiv.setOf_apply, LinOrd.coe_comp, Subgroup.surjOn_iff_le_map, ZMod.injective_stdAddChar, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, LinearMap.det_eq_one_of_subsingleton, MeasureTheory.eLpNorm'_const, UniformConvergenceCLM.isUniformEmbedding_coeFn, lineMap_slope_slope_sub_div_sub, MeasureTheory.Measure.exists_isOpen_measure_lt_top, AddMonoidHom.map_mul_iff, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, Finset.prod_map_equiv, NormedAddGroupHom.ext_iff, groupCohomology.cocycles₁.coe_mk, Topology.WithLowerSet.ofLowerSet_toLowerSet, IsCompact.exists_isOpen_lt_add, Module.Basis.det_map, qExpansion_of_pow, SetTheory.PGame.moveLeft_nim, ProbabilityTheory.covarianceBilinDual_of_not_memLp', BotHom.coe_inf, TopCat.pullback_snd_range, AddMonoidHom.coe_toMultiplicative'', AddMonoidHom.coe_range, ModuleCat.restrictScalarsCongr_inv_app, LieModule.shiftedGenWeightSpace.shift_symm_apply, LinearMap.posSemidef_toMatrix_iff, tendsto_measure_thickening_of_isClosed, finFunctionFinEquiv_single, PrincipalSeg.subrelIso_apply, CategoryTheory.Pretopology.mem_ofGrothendieck, Representation.linHom.invariantsEquivRepHom_apply_hom, NonUnitalRingHom.coe_comp_mulHom, DomMulAct.mk_smul_monoidHom_apply, RingHom.map_frobenius, PowerSeries.coeff_coe_trunc_of_lt, IsLocalization.Away.integralClosure, Matrix.coe_ofLinearEquiv, ContinuousMulEquiv.bijective, Affine.Simplex.affineCombination_mem_setInterior_iff, ContinuousAlgEquiv.symm_preimage_preimage, MonoidHom.map_zpow, MonoidHom.flipHom_apply, Polynomial.IsUnitTrinomial.irreducible_aux1, ofDegLex_add, AffineAddMonoid.embedding_injective, Polynomial.roots_C_mul_X_add_C_of_IsUnit, DirichletCharacter.changeLevel_self, Dense.orderDual, LaurentSeries.X_order_mul_powerSeriesPart, ofLex_eq_zero, Submodule.starProjection_apply_eq_zero_iff, Finsupp.mapRange_finset_sum, DFinsupp.liftAddHom_symm_apply, Function.Exact.inl_snd, MeasureTheory.Measure.restrict_eq_self, Algebra.Extension.exact_cotangentComplex_toKaehler, CategoryTheory.Functor.curryingEquiv_symm_apply_obj_map, RelIso.coe_toRelEmbedding, AddEquiv.addMonoidHomCongrRight_apply, Ideal.natAbs_det_basis_change, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_pointReflection_center_left, MvPolynomial.aeval_natDegree_le, SchwartzMap.fourier_convolution, LinearMap.trace_mul_cycle', PMF.toOuterMeasure_uniformOfFintype_apply, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit_f_aux, HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_mk, Set.Finite.subtypeEquivToFinset_symm_apply_coe, Equiv.uniqueProd_apply, OrderDual.ofDual_inj, Polynomial.isMonicOfDegree_monomial_one, Module.Basis.unitsSMul_apply, AnalyticOnNhd.eval_continuousLinearMap', AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback, ContinuousAffineMap.continuous, SimpleGraph.card_edgeFinset_induce_of_support_subset, MonoidAlgebra.single_mul_apply_of_not_exists_mul, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, MeasureTheory.FiniteMeasure.map_apply_of_aemeasurable, ModularForm.add_apply, MonoidAlgebra.counit_single, RCLike.hasSum_im, AlgEquiv.prodCongr_symm_apply, Valuation.map_zero, Orientation.rotation_symm_apply, AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, ZMod.LFunction_dft, Algebra.GrothendieckAddGroup.lift_symm_apply, LocallyConstant.coe_vadd, Finset.listMap_orderEmbOfFin_finRange, FinBoolAlg.dual_map, DomAddAct.isEmbedding_mk_symm, PowerSeries.trunc_zero', UniformFun.lipschitzOnWith_iff, ContinuousLinearMap.apply_val_ker, RingHom.coe_prodMap, Module.Basis.norm_repr_le_norm, LieModule.coe_chainTop', infClosure_empty, Pretrivialization.coe_linearMapAt_of_mem, Polynomial.mirror_C, Ordinal.familyOfBFamily_enum, LinearIsometryEquiv.withLpUniqueProd_apply, MeasureTheory.FiniteMeasure.coe_toWeakDualBCNN, AddMonoidHom.mrangeRestrict_surjective, MeasureTheory.Integrable.integral_norm_condKernel, BialgHom.mul_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, MeasureTheory.volume_measurePreserving_sumPiEquivProdPi, Module.Flat.iff_rTensor_injective', AlgebraicGeometry.LocallyRingedSpace.stalkMap_comp, LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero', ZeroAtInftyContinuousMap.mul_apply, Valued.toNormedField.norm_lt_one_iff, equivEquivIso_inv, ContinuousAlgHom.prod_apply, MultilinearMap.snoc_smul, Equiv.Set.union_symm_apply_right, Setoid.quotientEquivClasses_mk_eq, MulSemiringActionHom.ext_iff, AlgEquiv.surjective, BoundedContinuousFunction.smul_apply, Equiv.swap_apply_left, DistribMulActionHom.map_sub, PMF.toOuterMeasure_bind_apply, Equiv.Perm.SameCycle.exists_pow_eq'', FirstOrder.Language.StrongHomClass.map_fun, Matrix.mulVec.addMonoidHomLeft_apply, Equiv.optionCongr_sign, IsometryEquiv.preimage_symm, AlgebraicGeometry.Scheme.GlueData.ι_jointly_surjective, FractionalIdeal.trace_mem_dual_one, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, AddCircle.homeomorphCircle_apply, MeasureTheory.tendsto_measure_biUnion_Ici_zero_of_pairwise_disjoint, CommMonCat.ofHom_apply, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, Polynomial.nextCoeff_map_eq_of_isUnit_leadingCoeff, LinearMap.BilinForm.sum_apply, MeasureTheory.projectiveFamilyContent_mono, OrderMonoidWithZeroHom.coe_id, ProbabilityTheory.Kernel.densityProcess_def, MvPolynomial.scalarRTensor_apply_tmul_apply, AlgebraicGeometry.SheafedSpace.isColimit_exists_rep, LinearMap.coe_injective, ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply, ModuleCat.imageIsoRange_hom_subtype_apply, MulAction.coe_toPermHom, ArithmeticFunction.IsMultiplicative.map_div_of_coprime, Matrix.posSemidef_submatrix_equiv, Homeomorph.coe_sumComm, qExpansion_smul, Homeomorph.coe_toEquiv, MvPolynomial.optionEquivLeft_symm_C_C, PerfectionMap.lift_apply, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalization_of_mem, Matrix.Represents.algebraMap, grade_toDual, MulEquiv.injective, Module.Basis.mem_span_repr_support, TopCat.Presheaf.stalkFunctor_map_germ_apply', Derivation.compAEval_apply, OrderIso.asBoolAlgAsBoolRing_symm_apply, MeasurableEquiv.map_ae, Pi.basisFun_repr, Cubic.of_c_eq_zero, NonUnitalSubring.centerToMulOpposite_apply_coe, PowerSeries.coeff_mul_prod_one_sub_of_lt_order, InfTopHom.subtypeVal_apply, LinearIsometryEquiv.coe_mul, PointwiseConvergenceCLM.isUniformEmbedding_coeFn, PrimeSpectrum.maximalSpectrumToPiLocalization_surjective_of_discreteTopology, Multiset.gcd_map_mul, PrimeSpectrum.isIdempotentElemEquivClopens_mul, convex_closedConvexHull, Subgroup.IsComplement.equiv_snd_eq_inv_mul, ConjAct.toConjAct_ofConjAct, toAddUnits_val_apply, BoundedContinuousFunction.mkOfDiscrete_apply, RingCat.id_apply, Set.matrix_eq_pi, toBoolAlg_one, AmpleSet.image, NonUnitalRingHom.coe_toMulHom, Prod.Lex.lt_iff, SkewMonoidAlgebra.DistribMulActionHom.single_toFun, closure_subset_closedAbsConvexHull, QuotientRing.isOpenQuotientMap_mk, AddUnits.addLeft_apply, continuousOn_cfcₙ_nnreal_setProd, strictMonoOn_comp_ofDual_iff, DFinsupp.coe_nsmul, Module.Basis.toMatrix_mul_toMatrix, SheafOfModules.generatorsOfIsCokernelFree_s, mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactors, AffineEquiv.bijective, sSupHom.coe_mk, RootPairing.InvariantForm.apply_eq_or_of_apply_ne, matPolyEquiv_eq_X_pow_sub_C, ContinuousLinearEquiv.continuousOn, fderivWithin_clm_apply, Algebra.leftMulMatrix_eq_repr_mul, Algebra.Generators.Hom.algebraMap_toAlgHom, IsLocalizedModule.mk'_cancel, AddChar.zmodAddEquiv_apply, QuadraticMap.associated_isSymm, rootsOfUnityEquivNthRoots_symm_apply, Polynomial.hasseDeriv_eq_zero_of_lt_natDegree, StrictMonoOn.dual, ContinuousLinearMap.postcomp_uniformConvergenceCLM_apply, MeasureTheory.SimpleFunc.coe_const, exists_continuousLinearEquiv_fderivWithin_symm_eq, AddUnits.isClosedEmbedding_embedProduct, IncidenceAlgebra.ext_iff, continuous_skewAdjointPart, DirectSum.toAddMonoid_of, CircleDeg1Lift.iterate_pos_eq_iff, Finsupp.apply_eq_of_mem_graph, ENNReal.mulLeftOrderIso_apply, DFinsupp.support_sum, SimpleGraph.map_subgraphOfAdj, Finset.product_self_eq_disjiUnion_perm, nnnorm_map, MulActionHom.coe_add, Equiv.Set.univPi_apply_coe, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, BoundedContinuousFunction.dist_le_two_norm, RestrictedProduct.map_apply, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, SimpleGraph.Hom.coe_ofLE, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, Polynomial.coeff_divByMonic_X_sub_C, Fin.appendEquiv_apply, SSet.Truncated.HomotopyCategory.descOfTruncation_obj_mk, Quaternion.normSq_div, Polynomial.ofFn_coeff_eq_zero_of_ge, TensorProduct.directLimitRight_symm_of_tmul, PartOrdEmb.coe_id, BoundedContinuousFunction.coe_npowRec, DFinsupp.coe_lt_coe, FGModuleCat.Iso.conj_hom_eq_conj, Action.FunctorCategoryEquivalence.functor_obj_map, Finsupp.finsuppProdLEquiv_symm_apply_apply, Measurable.lintegral_kernel_prod_right', OrthonormalBasis.abs_det_adjustToOrientation, AdicCompletion.transitionMap_map_one, RootPairing.InvariantForm.two_mul_apply_root_root, MeasureTheory.ProbabilityMeasure.toFiniteMeasure_apply_eq_apply, HasGradientWithinAt.hasFDerivWithinAt, Module.Basis.toDual_eq_equivFun, ModularGroup.coeHom_apply, DirectSum.of_zero_ofNat, Subalgebra.algEquivOpMop_symm_apply_coe, MeasureTheory.OuterMeasure.restrict_iInf_restrict, ContinuousLinearMap.dist_le_opNorm, FormalMultilinearSeries.rightInv_coeff_one, FourierTransform.fourierCLM_apply, ContinuousMap.continuousAt, HahnSeries.single_zero_ratCast, Real.tsum_eq_tsum_fourierIntegral_of_rpow_decay, LinearMap.SeparatingLeft.toMatrix₂', Monoid.CoprodI.lift_injective_of_ping_pong, Circle.exp_sub_two_pi, AlgHom.op_symm_apply_apply, DFinsupp.card_Icc, Polynomial.degreeLT.basisProd_castAdd, Matrix.derivative_det_one_add_X_smul_aux, Hamming.toHamming_neg, dNext_eq_zero, MvPolynomial.coeffsIn_le, Equiv.Perm.IsCycleOn.conj, RingHom.surjectiveOnStalks_iff_forall_maximal, MeasureTheory.Measure.instIsZeroOrProbabilityMeasureBindCoeKernelOfIsZeroOrMarkovKernel, TensorProduct.toMatrix_comm, Polynomial.degree_C_mul_X_pow, Fin.cycleIcc_of_le_of_le, SimpleGraph.TripartiteFromTriangles.toTriangle_apply, RelIso.pairwise_listMap, Module.Basis.sum_repr, RCLike.isCauSeq_re, EReal.expHomeomorph_apply, TopCat.GlueData.MkCore.cocycle, powersMulHom_symm_apply, MeasureTheory.measure_iUnion_toMeasurable, Polynomial.trailingDegree_monomial, ContinuousAddEquiv.refl_apply, SymAlg.unsym_neg, ContinuousMapZero.coe_toContinuousMapHom, Polynomial.C_pow, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Pi.orthonormalBasis_repr, MulOpposite.opMulEquiv_symm_apply, fderiv_continuousAlternatingMap_apply_const_apply, HahnSeries.SummableFamily.coeff_def, Subtype.relEmbedding_apply, Sublattice.inclusion_injective, Polynomial.C_add, RCLike.hasSum_conj', MonomialOrder.C_mul_leadingCoeff_monomial_degree, CommGrpCat.coyoneda_map_app, ProbabilityTheory.Kernel.HasSubgaussianMGF.aestronglyMeasurable, MeasureTheory.SimpleFunc.coe_inv, EuclideanGeometry.inversion_eq_lineMap, ContinuousAlgEquiv.isUniformEmbedding, RootPairing.coreflection_apply_coroot, DomMulAct.stabilizer_card, ZMod.dft_const_smul, Algebra.TensorProduct.lid_symm_apply, RootPairing.Equiv.coweightHom_toLinearMap, Monoid.PushoutI.NormalWord.summand_smul_def, AlgHom.toLieHom_apply, Polynomial.hasDerivWithinAt, Equiv.sigmaCongrRight_apply, toBoolAlg_ofBoolAlg, Finsupp.supportedEquivFinsupp_apply_apply, Polynomial.zero_notMem_multiset_map_X_add_C, Path.Homotopy.refl_apply, Seminorm.ball_zero_eq, FrameHom.comp_apply, MeasureTheory.ProbabilityMeasure.prod_apply, NNReal.sqrt_mul_self, WittVector.coeff_frobenius, fwdDiff_aux.coe_fwdDiffₗ, MeasureTheory.volume_preserving_piEquivPiSubtypeProd, SpecialLinearGroup.coe_div, TensorAlgebra.ι_eq_algebraMap_iff, SkewMonoidAlgebra.equivMapDomain_eq_mapDomain, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, InnerProductGeometry.IsConformalMap.preserves_angle, NumberField.Units.complexEmbedding_inj, MonoidHom.surjective_of_card_ker_le_div, AddMonoidAlgebra.of'_eq_of, SemidirectProduct.equivProd_symm_apply_left, WeierstrassCurve.Affine.map_addX, LieModuleHom.map_zero, Cardinal.mem_range_aleph_iff, AddCon.congr_mk, LinearMap.map_algebraMap_mul, dualTensorHomEquivOfBasis_apply, NumberField.RingOfIntegers.algebraMap.injective, CategoryTheory.Abelian.subobjectIsoSubobjectOp_symm_apply, NormedSpace.Dual.coe_toWeakDual, ofAdd_toDual_eq_zero_iff, ContinuousAlternatingMap.coe_add, HahnSeries.coeff.addMonoidHom_apply, LinearMap.polar_mem, InnerProductSpace.conj_inner_symm, MonoidHom.snd_mono, LinearMap.toMatrix₂'_apply, ArithmeticFunction.cardFactors_apply_prime, RCLike.I_im', Finsupp.nsmul_single_one_image, ApproximatesLinearOn.lipschitzOnWith, FreeMonoid.ofList_map, Matrix.aeval_eq_aeval_mod_charpoly, EquivLike.coe_coe, OrderDual.ofDual_eq_top, Polynomial.mod_def, MeasureTheory.Lp.pow_mul_meas_ge_le_enorm, AddMonoidHom.inr_apply, Units.range_embedProduct, AffineMap.lineMap_mem_affineSpan_pair, PiTensorProduct.tprod_mul_tprod, Subring.ringEquivOpMop_apply, Real.log_of_ne_zero, ContinuousAddEquiv.equivLike_neg_eq_symm, Submodule.FG.rTensor.directLimit_apply', MeasureTheory.Measure.compProd_eq_parallelComp_comp_copy_comp, isCoatom_dual_iff_isAtom, Finsupp.DegLex.lt_def, MeasureTheory.AddContent.supClosure_apply, Set.MapsTo.exists_equiv_extend_of_card_eq, TopologicalSpace.OpenNhds.inclusionMapIso_inv_app, QuotientGroup.quotientBot_symm_apply, Equiv.Perm.val_inv_equivUnitsEnd_apply, ContinuousLinearMap.isBigOTVS_id, AlgebraicGeometry.Scheme.stalkClosedPointTo_comp, AddEquiv.piCongrRight_apply, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, ArchimedeanClass.mk_map_of_archimedean', PadicInt.cast_toZModPow, UniformEquiv.piFinTwo_symm_apply, Submonoid.LocalizationMap.symm_comp_ofMulEquivOfLocalizations_apply', LieDerivation.toFun_eq_coe, Unitary.conjStarAlgAut_star_apply, Module.End.genEigenspace_le_smul, Homeomorph.symm_comp_self, Additive.addMonoidHom_ext_iff, IsLocalization.algebraMap_pi_surjective_of_isLocalization, IsAdjoinRootMonic.liftPolyₗ_apply, MonoidWithZeroHom.inr_injective, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum, LinearMap.isAdjointPair_inner, BoolAlg.id_apply, RingCon.quotientQuotientEquivQuotientₐ_coe_coe, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, IsLocalizedModule.mk'_eq_zero, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, LinearMap.IsPositive.adjoint_conj, Polynomial.aeval_algebraMap_apply, Module.Flat.injective_characterModule_iff_rTensor_preserves_injective_linearMap, Polynomial.polynomial_map_coe, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, HahnSeries.toPowerSeries_symm_apply_coeff, Function.update_apply_equiv_apply, Module.Basis.toMatrix_mulVec_repr, IsLocalRing.local_hom_TFAE, ClosedSubmodule.coe_comap, PowerSeries.trunc_derivative, TensorProduct.assoc_symm_tmul, Valuation.Integers.one_of_isUnit, MeasureTheory.StronglyMeasurable.integral_kernel, ContinuousLinearEquiv.prodAssoc_symm_apply, Cardinal.aleph_lt_aleph, LieIdeal.incl_apply, Matrix.transpose_reindex, AddCircle.liftIco_eq_lift_Icc, Algebra.Generators.basisCotangentAway_apply, AlgEquiv.opOp_symm_apply, Subspace.quotDualCoannihilatorToDual_bijective, Algebra.Generators.comp_σ, IsSelfAdjoint.imaginaryPart, Homeomorph.isSigmaCompact_preimage, Prod.Lex.prodLexAssoc_apply, AddConstMap.coe_pow, AddEquiv.coe_toAddMonoidHom, Fin.coe_succAboveEmb, groupHomology.single_mem_cycles₁_iff, Monoid.foldrM.ofFreeMonoid_apply, ProbabilityTheory.Kernel.lmarginalPartialTraj_eq_lintegral_map, Circle.argPartialEquiv_symm_apply, one_le_thickenedIndicator_apply, AlternatingMap.map_coord_zero, LinearMap.ker_tensorProductMk, CliffordAlgebraQuaternion.toQuaternion_ι, Complex.isUniformEmbedding_equivRealProd, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, AdicCompletion.sumEquivOfFintype_symm_apply, AlgebraicGeometry.map_injective_of_isIntegral, Ideal.ringChar_quot, VitaliFamily.ae_tendsto_lintegral_enorm_sub_div_of_integrable, ContinuousMulEquiv.apply_eq_iff_symm_apply, ProbabilityTheory.Kernel.lintegral_swapLeft, MeasureTheory.StronglyMeasurable.integral_kernel_prod_left, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Polynomial.leadingCoeff_divByMonic_X_sub_C, AnalyticOnNhd.eval_mvPolynomial, Homeomorph.isOpenQuotientMap, Unitization.lift_apply, AddMonoidHom.mem_ker, IsQuotientCoveringMap.homeomorph_comp, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, Action.ρAut_apply_inv, UniformConvergenceCLM.isVonNBounded_iff, ProbabilityTheory.setBernoulli_apply, groupHomology.d₂₁_single_ρ_add_single_inv_mul, Complex.normSq_neg, Algebra.Generators.CotangentSpace.map_ofComp_surjective, bernsteinPolynomial.derivative_succ_aux, Polynomial.pairwise_coprime_X_sub_C, MvPowerSeries.monomial_smul_eq, MeasureTheory.SimpleFunc.smul_apply, ConjAct.toConjAct_one, LaurentSeries.coeff_coe_powerSeries, EquivLike.bijective_comp, CategoryTheory.Limits.biproduct.reindex_hom, AbsoluteValue.IsNontrivial.exists_abv_gt_one, OrderIso.map_csSup_of_directedOn', RingEquiv.coe_toRingHom, Matrix.sub_scalar_sq_eq_discr, AffineIsometry.angle_map, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, Ideal.toCotangent_surjective, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, AlgebraicGeometry.Scheme.Spec_map_residue_apply, Orientation.rotation_oangle_eq_iff_norm_eq, AlgHom.mem_resolventSet_apply, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, Matrix.kroneckerStarAlgEquiv_apply, Subrepresentation.subrepresentationSubmoduleOrderIso_apply, SlashInvariantFormClass.slash_action_eq, SeminormedRing.toRingSeminorm_apply, AlgHom.equalizer_toSubmodule, LieModule.commute_toEnd_of_mem_center_left, toDual_natCast, Affine.Simplex.signedInfDist_apply_of_ne, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, Equiv.piEquivPiSubtypeProd_apply, CircleDeg1Lift.translate_pow, OrderIso.finsetSetFinite_apply_coe, LinearMap.lTensor_inj_iff_rTensor_inj, CategoryTheory.Iso.conjAut_pow, Algebra.TensorProduct.leftComm_symm_tmul, ContinuousMap.zsmul_apply, Homeomorph.piFinTwo_symm_apply, ContinuousLinearMap.hasStrictDerivAt, MeasureTheory.forall_measure_preimage_add_right_iff, Ideal.coe_piOrderIso_apply, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, AffineIsometry.coe_toContinuousAffineMap, BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space, IsUltrametricDist.isPowMul_invariantExtension, exists_contMDiffMap_one_nhds_of_subset_interior, WeierstrassCurve.Projective.map_polynomialY, TensorProduct.comm_symm_tmul, MeasureTheory.OuterMeasure.ofFunction_apply, MonoidWithZeroHom.commute_inl_inr, dist_sq_lineMap_of_inner_eq_zero, LinearMap.BilinForm.separatingLeft_toMatrix_iff, CategoryTheory.Arrow.equivSigma_apply_snd_fst, BiheytingHom.coe_comp, MvPolynomial.tensorEquivSum_C_tmul_C, LinearMap.trace_comp_comm', ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap, measurable_fderiv_apply_const_with_param, WeierstrassCurve.Projective.baseChange_addY, MeasurableEquiv.toLp_apply, Seminorm.coeFnAddMonoidHom_injective, Polynomial.derivative_X_sub_C, CharacterModule.dual_apply, strictMono_toDual_comp_iff, AddChar.coe_one, MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous, MvPolynomial.finsum_weightedHomogeneousComponent, BoundedContinuousFunction.coe_prod, TensorProduct.sum_tmul_basis_left_injective, IntermediateField.mem_fixingSubgroup_iff, CovBy.ofDual, Subalgebra.rTensorBot_tmul, AlgebraicGeometry.Proj.stalkIso'_symm_mk, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, StrictMono.orderIsoOfRightInverse_apply, IsometryEquiv.sumArrowIsometryEquivProdArrow_apply, TopCat.GlueData.ι_injective, MvPowerSeries.order_monomial_of_ne_zero, ofDual_vadd, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, RingCon.toCon_coe_eq_coe, Path.uniformContinuous_extend, LinearMap.quotientInfEquivSupQuotient_symm_apply_right, Opposite.equivToOpposite_symm_coe, ClosureOperator.IsClosed.closure_eq, toDual_add, IntermediateField.intermediateFieldMap_symm_apply_coe, map_complEDS, Ideal.eval₂_C_mk_eq_zero, HasStrictFDerivAt.clm_comp, Matrix.SpecialLinearGroup.isInducing_toGL, exteriorPower.zeroEquiv_symm_apply, mulRothNumber_union_le, Equiv.optionEquivSumPUnit_some, WithLp.fstL_apply, Matrix.coe_ofAddEquiv, ZMod.dft_smul_const, PMF.toMeasure_apply_eq_toOuterMeasure, AddGroupSeminorm.lt_def, ProbabilityTheory.Kernel.integral_withDensity, RingEquiv.piUnique_apply, finsetBasisOfLinearIndependentOfCardEqFinrank_repr_apply, Module.AEval.mem_mapSubmodule_apply, Rat.AbsoluteValue.apply_le_sum_digits, cfcHom_map_spectrum, NumberField.mixedEmbedding.norm_negAt, VitaliFamily.ae_tendsto_lintegral_enorm_sub_div, Module.End.ringHomEndFinsupp_surjective, AlgebraicGeometry.Scheme.residueFieldMap_comp, RingHom.map_dotProduct, DoubleCentralizer.toProdHom_apply, FreeGroup.range_lift_le, LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, OrderHom.isFixedPt_gfp, EisensteinSeries.gammaSetDivGcdEquiv_eq, FreeSemigroup.lift_of_mul, PMF.bindOnSupport_apply, LieEquiv.refl_apply, SmoothPartitionOfUnity.sum_le_one, WeierstrassCurve.Projective.map_polynomial, EMetric.measure_closedBall_pos, Path.symm_range, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_φ, normalize_zero, Affine.Simplex.restrict_map_inclusion, CategoryTheory.Iso.inv_hom_id_apply, TopologicalSpace.OpenNhds.apply_mk, CoalgHom.comp_apply, PiTensorProduct.algebraMap_apply, SpecialLinearGroup.toLinearEquiv_injective, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two', ArithmeticFunction.sigma_eq_sum_div, WithVal.equivWithVal_symm_apply, derangements.Equiv.RemoveNone.fiber_some, SlashInvariantForm.slash_action_eqn, LT.lt.ofDual, LieAlgebra.of_symm_smul, Equiv.multipliable_iff, MeasureTheory.Egorov.measure_iUnionNotConvergentSeq, Submodule.basis_of_pid_aux, CochainComplex.HomComplex.CohomologyClass.toHom_mk, ContMDiffSection.coe_zsmul, NumberField.mixedEmbedding.norm_unit, Module.Basis.orientation_map, TensorProduct.equivFinsuppOfBasisRight_symm_apply, FreeMonoid.toList_one, MeasureTheory.measure_union_add_inter', algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, QuadraticForm.associated_baseChange, LocallyConstant.coeFnRingHom_apply, Action.Hom.comm, QuotientAddGroup.rangeKerLift_injective, ProbabilityTheory.Kernel.const_comp, Finset.Colex.toColex_le_toColex_of_subset, HasOuterApproxClosed.apprSeq_apply_le_one, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, Module.Basis.toMatrix_unitsSMul, Subsemigroup.toAddSubsemigroup'_closure, Derivation.coe_neg, Representation.IntertwiningMap.coe_smul, Real.volume_preserving_transvectionStruct, seminormFromConst_seq_def, RingTheory.Sequence.IsWeaklyRegular.of_isLocalization, Pi.evalAddHom_apply, ProbabilityTheory.bayesRisk_const', Finset.ofDual_max', disjointed_partialSups, ClosureOperator.closure_sup_closure_le, CliffordAlgebra.reverseOpEquiv_apply, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree, HahnSeries.orderTop_embDomain, Pi.algebraMap_def, ContinuousLinearMap.fpowerSeries_apply_one, OrderEmbedding.withBotMap_apply, CategoryTheory.Adjunction.homEquiv_naturality_right, StarRingEquiv.coe_mk, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atBot, AddSubmonoid.LocalizationMap.map_addUnits, RingCon.map_apply, Action.ρ_inv_self_apply, Polynomial.aroots_C, FirstOrder.Language.Substructure.mem_map_of_mem, MeasureTheory.L1.integral_eq, ContinuousLinearMap.smulRightL_apply_apply, Multiset.prod_hom_ne_zero, continuousOn_clm_apply, Polynomial.Gal.restrictDvd_surjective, ProbabilityTheory.Kernel.compProd_apply_prod, MvPowerSeries.subst_coe, HahnEmbedding.Partial.apply_of_mem_stratum, AddAction.stabilizerEquivStabilizer_compTriple, AlgebraicGeometry.Scheme.Hom.fiberι_fiberHomeo_symm, Ordinal.nmul_eq_mul, KaehlerDifferential.map_liftBaseChange_smul, CategoryTheory.Limits.cokernelOrderHom_coe, ContinuousAlternatingMap.piLinearEquiv_apply, Set.Finite.convexHull_eq, OrderIso.dual_symm_apply, CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy, GenLoop.boundary, VitaliFamily.ae_tendsto_lintegral_enorm_sub_div'_of_integrable, Subalgebra.pi_toSubmodule, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, SubMulAction.ofStabilizer.conjMap_apply, FreeSemigroup.hom_ext_iff, GenLoop.homotopyFrom_apply, GenLoop.const_apply, ModularFormClass.hasSum_qExpansion, SchwartzMap.one_add_le_sup_seminorm_apply, MeasureTheory.OuterMeasure.map_ofFunction_le, supClosed_supClosure, OrderHom.isLeast_lfp_le, WithZero.coeAddHom_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, NNReal.sqrt_inv, Matrix.toLpLinAlgEquiv_symm_apply, RootPairing.Equiv.coweightHom_apply, ValuativeRel.ValueGroupWithZero.embed_valuation, addOrderOf_map_dvd, MvPowerSeries.IsHomogeneous.coeff_eq_zero, CentroidHom.coe_natCast, AddEquiv.uniqueProd_apply, AddValuation.ofValuation_apply, Matrix.toBilin'_toMatrix', ContinuousMultilinearMap.toMultilinearMapLinear_apply, Seminorm.continuous_iff_continuous_comp, LieDerivation.iterate_apply_lie', MvPolynomial.mapEquivMonic_symm_map_algebraMap, Sbtw.mem_image_Ioo, le_map_add_map_sub, MeasureTheory.Measure.measure_Iio_pos, Ring.DirectLimit.map_apply_of, Rep.linearization_map_hom_single, WCovBy.image, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int, BddOrd.inv_hom_apply, CategoryTheory.CosimplicialObject.cechConerveEquiv_apply, Matrix.reindex_updateCol, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, minpoly.eq_X_sub_C, PartitionOfUnity.continuous_smul, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, Ideal.Quotient.mk_smul_mk_quotient_map_quotient, NonUnitalStarSubalgebraClass.subtype_apply, MonoidAlgebra.opRingEquiv_apply, ContinuousAffineMap.coe_neg, IsometryEquiv.preimage_closedBall, AdicCompletion.eval_apply, ProbabilityTheory.Kernel.partialTraj_compProd_eq_map_traj, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, Units.embedProduct_injective, Sublattice.prodEquiv_symm_apply, Set.injOn_iff_map_eq_one, HNNExtension.NormalWord.unitsSMulEquiv_apply, Multiset.coe_consEquiv_of_ne, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk, AddSubmonoid.opEquiv_apply, WittVector.frobenius_verschiebung, ContinuousMap.id_apply, TopCat.Presheaf.pushforwardPullbackAdjunction_unit_pullback_map_germToPullbackStalk_assoc, OrderEmbedding.subtype_injective, eq_natCast, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, LinearMap.trace_baseChange, CategoryTheory.Meq.equiv_apply, Finset.mem_eraseNone, Submodule.sndEquiv_apply, Real.fourierIntegralInv_eq, FreeAlgebra.hom_ext_iff, IncidenceAlgebra.mu_self, HasStrictFDerivAt.continuousMultilinearMap_apply, RingCon.sup_eq_ringConGen, LinearEquiv.multilinearMapCongrLeft_apply, DirectSum.decompose_symm_sum, CliffordAlgebra.contractLeftAux_apply_apply, Finsupp.lex_lt_of_lt_of_preorder, Polynomial.roots_C, Finsupp.toMultiset_sum_single, ProbabilityTheory.Kernel.iIndepSets.meas_iInter, Matrix.charmatrix_diagonal, PresentedMonoid.surjective_mk, RootPairing.Hom.id_indexEquiv_apply, AddChar.zpow_apply, LightProfinite.proj_comp_transitionMap', List.Nodup.getEquiv_symm_apply_val, LinearPMap.adjointAux_inner, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, IsGroupLikeElem.mul_antipode_cancel, AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, HilbertBasis.hasSum_inner_mul_inner, OrderHom.coe_iSup, Equiv.sumCompl_symm_apply_of_neg, PowerSeries.coeff_one_mul, NonUnitalStarAlgHom.norm_apply_le, Submodule.sndEquiv_symm_apply_coe, Algebra.idealMap_apply_coe, RingEquiv.opOp_apply, NumberField.Units.regOfFamily_eq_det', Int.liesOver_span_absNorm, Matrix.toLinearMapₛₗ₂_toMatrix₂, AddSubgroup.toSubgroup_comap, MulChar.inv_apply, Submodule.comapSubtypeEquivOfLe_symm_apply, GroupSeminorm.mul_bddBelow_range_add, OrderHom.iterate_sup_le_sup_iff, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, WeierstrassCurve.Projective.eval_polynomialY, SupHom.coe_id, Monoid.PushoutI.lift_of, OrderEmbedding.sorted_gt_listMap, Composition.mem_range_embedding_iff, LaurentPolynomial.comul_C_mul_T_self, CochainComplex.toSingle₀Equiv_symm_apply_f_zero, FractionalIdeal.den_mem_inv, Module.Basis.prod_apply_inr_snd, ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_left, ofDual_covBy_ofDual_iff, Lagrange.nodal_erase_eq_nodal_div, ProbabilityTheory.Kernel.rnDeriv_withDensity, ContinuousLinearMap.opNNNorm_mul_apply, Finset.mem_dfinsupp_iff, OrderIso.coe_toEquiv, RingNorm.ext_iff, Polynomial.monic_prod_X_sub_C, fderivInnerCLM_apply, MeasureTheory.Measure.lt_iff, Complex.log_conj, TopHom.id_apply, Equiv.coe_subtypeEquivCodomain, finSumEquivOfFinset_inl, MeasureTheory.Measure.sub_apply_eq_zero_of_restrict_le_restrict, AffineIsometry.image_intrinsicFrontier, Module.Basis.coord_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, CliffordAlgebra.contractLeft_one, MeasureTheory.volume_measurePreserving_sumPiEquivProdPi_symm, le_comap_range_rTensor, Matrix.eval_matrixOfPolynomials_eq_vandermonde_mul_matrixOfPolynomials, Fin.castLEEmb_apply, BoundedContinuousFunction.coe_pow, Finset.prod_comp_equiv, Multiset.toFinsupp_support, IsValuativeTopology.isOpen_sphere, ContinuousMultilinearMap.curryFinFinset_apply, groupHomology.eq_d₁₀_comp_inv_apply, Set.image_pow, RingTheory.Sequence.IsWeaklyRegular.of_isLocalizedModule, Fin.equivSubtype_apply, Finset.apply_coe_mem_map, Set.powersetCard.mem_map_iff_mem_range, MultilinearMap.domCoprodDep'_apply, Polynomial.natDegree_cubic_le, MulOpposite.opAddEquiv_symm_apply, Quaternion.normSq_star, MulActionHom.ext_iff, bddAbove_preimage_toDual, ArithmeticFunction.one_apply, FreeAlgebra.algebraMap_leftInverse, MeasureTheory.Lp.const_val, AddSubgroup.coe_toSubgroup_symm_apply, EuclideanGeometry.orthogonalProjection_eq_iff_mem, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, ofDual_div, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, Matrix.blockTriangular_single', BddLat.dual_map, LinearMap.toMatrix'_mulVec, RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot, OrderIso.sumLexDualAntidistrib_inl, DomAddAct.isClosedEmbedding_mk_symm, CategoryTheory.SimplicialThickening.functor_obj_as, Unitization.inrRangeEquiv_symm_apply, Filter.map_equiv_symm, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_point, Units.mulRight_apply, PMF.pure_apply, RelIso.apply_inv_self, DFinsupp.filterAddMonoidHom_apply, NumberField.RingOfIntegers.mapRingEquiv_symm_apply, PartitionOfUnity.sum_finsupport', SkewMonoidAlgebra.equivMapDomain_single, IsFoelner.tendsto_nhds_mean, PEquiv.bot_apply, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, Equiv.Set.sumCompl_symm_apply_compl, LaurentPolynomial.invert_C, exists_integral_inj_algHom_of_fg, ModuleCat.semilinearMapAddEquiv_apply, MonovaryOn.dual, WittVector.mapFun.natCast, VertexOperator.coeff_eq_ncoeff, nndist_self_homothety, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, Order.coheight_ofDual, FunctionField.inftyValuation_apply, PartOrd.ext_iff, OrderedFinpartition.applyOrderedFinpartition_update_right, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom, Absorbent.subset_range_iff_surjective, Algebra.FormallyUnramified.iff_exists_tensorProduct, LinearMap.lsum_symm_apply, Module.Basis.mem_span_iff_repr_mem, PowerSeries.monomial_zero_eq_C_apply, ModuleCat.CoextendScalars.map'_hom_apply_apply, QuaternionAlgebra.coe_addEquivTuple, Equiv.subtypePreimage_symm_apply_coe, Ideal.Quotient.mkₐ_surjective, FiniteField.algebraMap_norm_eq_pow_sum, NonUnitalRingHom.closure_preimage_le, Equiv.image_eq_iff_bijOn, IsBaseChange.toDualBaseChange_tmul, Equiv.Perm.zpow_apply_comm, SchwartzMap.smooth, IsLocalizedModule.map_LocalizedModules, AffineSubspace.coe_comap, Matrix.SeparatingLeft.toLinearMap₂, AlgebraicGeometry.coe_opensRestrict_apply_coe, YoungDiagram.transposeOrderIso_apply, Derivation.map_sub, Equiv.prodCongrRight_apply, KaehlerDifferential.quotKerTotalEquiv_apply, AddMonoid.Coprod.mk_of_inl, MeasureTheory.FiniteMeasure.toMeasureAddMonoidHom_apply, BoxIntegral.BoxAdditiveMap.sum_boxes_congr, AffineMap.lineMap_vadd, PrimeSpectrum.coe_isIdempotentElemEquivClopens_apply, SetSemiring.down_zero, FreeSemigroup.lift_comp_of, RelHom.id_apply, List.Nodup.getEquivOfForallMemList_apply, BoundedContinuousFunction.tendsto_iff_tendstoUniformly, AddMonoidAlgebra.mul_apply_right, Perfection.coeff_pow_p', IsLocalRing.ResidueField.lift_residue_apply, DirectSum.map_eq_iff, Polynomial.card_roots_toFinset_le_derivative, MeasureTheory.exists_measure_iInter_lt, Polynomial.map_aeval_eq_aeval_map, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd, Poly.mul_apply, Finsupp.notMem_neLocus, CategoryTheory.Meq.condition, AddConstMap.mk_coe, SimpleGraph.coe_recolorOfCardLE, AddEquiv.apply_eq_iff_symm_apply, MagmaCat.comp_apply, Subgroup.topEquiv_apply, ULift.moduleEquiv_apply, WeierstrassCurve.Jacobian.baseChange_addY, Homeomorph.subRight_apply, AlgHom.toFun_eq_coe, IsAntichain.image_relEmbedding_iff, Representation.mem_invtSubmodule, SimplexCategory.epi_iff_surjective, MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp, AffineEquiv.affineIndependent_iff, FirstOrder.Language.ElementaryEmbedding.comp_apply, MulArchimedeanOrder.le_def, LinearMap.IsSymmetric.hasEigenvector_eigenvectorBasis, SimpleGraph.map_le_iff_le_comap, Diffeomorph.image_symm_image, Equiv.pprodCongr_apply, VectorBundleCore.coordChange_comp, DirectSum.decompose_add, StarMulEquiv.coe_refl, TannakaDuality.FiniteGroup.equivHom_surjective, Equiv.image_symm_eq_preimage, Equiv.Perm.IsCycleOn.pow_apply_eq, UniformEquiv.piCongrLeft_apply, IsometryClass.ediam_image, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, MvPowerSeries.substAlgHom_apply, Set.smul_graphOn, StarSubalgebra.isEmbedding_inclusion, Bundle.Trivial.homeomorphProd_apply, Submodule.mulExact_unitsToPic_mapAlgebra, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, LieHom.map_zero, RestrictedProduct.single_eq_of_ne', Antivary.sum_mul_lt_sum_mul_comp_perm_iff, SchwartzMap.denseRange_toLpCLM, IsDedekindDomain.quotientEquivPiFactors_mk, Submonoid.LocalizationMap.sec_spec, Finset.map_disjiUnion, ModuleCat.freeHomEquiv_symm_apply, isClosed_closedConvexHull, SubgroupClass.inclusion_self, Finset.centroid_def, TensorProduct.instDirectedSystemCoeLinearMapIdLTensor, ValuationSubring.primeSpectrumEquiv_apply, WithZero.val_logOrderIso_symm_apply, equivShrink_symm_inv, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, SchwartzMap.toZeroAtInftyCLM_apply, CategoryTheory.CommSq.LiftStruct.opEquiv_apply, MeasureTheory.Content.innerContent_le, FirstOrder.Language.Substructure.mem_map, MeasureTheory.Measure.condKernel_apply, NonUnitalStarSubalgebra.iSupLift_mk, ContinuousMap.mul_apply, ContDiffMapSupportedIn.coeHom_injective, IsMinOn.dual, Preorder.piCongrLeft_comp_frestrictLe, SeparationQuotient.liftNormedAddGroupHomEquiv_symm_apply_coe, IntermediateField.coe_algebraMap_apply, FirstOrder.Language.Substructure.mem_comap, hasEigenvector_toLin_diagonal, LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, cfcₙHom_nonneg_iff, ContinuousMap.dist_le_iff_of_nonempty, AddMonoidHom.map_finsum_mem, RelHom.ext_iff, AddCommMonCat.forget_map, QuasispectrumRestricts.left_inv, IsPrimitiveRoot.norm_sub_one_two, Bialgebra.TensorProduct.assoc_symm_tmul, OrderHom.map_lfp_comp, FreeMonoid.toList_comp_ofList, PrincipalSeg.le_apply_iff, Finsupp.sumFinsuppEquivProdFinsupp_apply, CategoryTheory.PreGaloisCategory.toAut_injective_of_non_trivial, MeasureTheory.tendsto_integral_meas_thickening_le, MvPolynomial.eval₂_eq_eval_map, MulEquiv.symm_apply_apply, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, SymAlg.sym_mul_sym, AddMonoidHom.ext_iff₂, AlgHom.prod_apply, Finsupp.Colex.lt_iff_of_unique, WeierstrassCurve.Affine.baseChange_negAddY, ZMod.castHom_surjective, AffineIsometryEquiv.isometry, AffineEquiv.trans_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, Module.Basis.coord_equivFun_symm, ContinuousLinearEquiv.symm_map_nhds_eq, ContinuousMap.compRightAlgHom_apply, UniformOnFun.ofFun_neg, QuadraticMap.polar_zero_right, Polynomial.iterate_derivative_sum, RootPairing.reflection_reflectionPerm, Submonoid.mem_map_of_mem, AlgEquiv.piCongrLeft'_symm_apply, AdjoinRoot.coe_mapRingEquiv, MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot, SchwartzMap.integrable_pow_mul_iteratedFDeriv, AlgebraicGeometry.RingedSpace.mem_basicOpen, multiplesHom_apply, Equiv.swap_bijOn_self, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, StarAlgEquiv.trans_apply, Finsupp.weight_eq_zero_iff_eq_zero, LocallyConstant.ofIsClopen_fiber_one, Finsupp.embDomain_some_none, MeasureTheory.Content.sup_disjoint, ChainComplex.fromSingle₀Equiv_symm_apply_f_succ, PartENat.withTopEquiv_symm_lt, Equiv.extendSubtype_apply_of_not_mem, AdjoinRoot.algHomOfDvd_apply_root, Real.fderiv_fourierChar_neg_bilinear_left_apply, AddMonoidAlgebra.curryAlgEquiv_single, WeierstrassCurve.ψ_four, NumberField.IsCMField.complexConj_torsion, Function.locallyFinsuppWithin.logCounting_even, AlgebraicGeometry.Scheme.Hom.app_injective, Module.Basis.addHaar_self, Polynomial.residueFieldMapCAlgEquiv_algebraMap, Surreal.dyadicMap_apply_pow, ContinuousMap.addUnitsLift_symm_apply_apply_neg', Finsupp.toMultiset_map, ArithmeticFunction.vonMangoldt_apply_pow, Cardinal.zero_toNat, LinearMap.domRestrict₁₂_apply, ProbabilityTheory.Kernel.measurable_kernel_prodMk_left, CategoryTheory.GrothendieckTopology.mem_toCoverage_iff, DirectSum.toLieAlgebra_apply, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, TannakaDuality.FiniteGroup.equivHom_injective, ZMod.dft_def, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, MeasureTheory.FiniteMeasure.apply_union_le, ContinuousAlgEquiv.coe_refl', DirectSum.add_apply, OrderIso.mulRight_apply, AlternatingMap.domDomCongr_apply, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, AddMonoidHom.mem_range, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, ValuationSubring.mapOfLE_comp_valuation, StieltjesFunction.measure_Iio_of_tendsto_atBot_atBot, Equiv.sumEmpty_apply_inl, spectrum.vadd_eq, CategoryTheory.Iso.conj_apply, Equiv.sigmaEquivProd_apply, Polynomial.Bivariate.equivMvPolynomial_C_C, CStarMatrix.mapₙₐ_apply, AddHom.withBotMap_apply, groupHomology.H0π_comp_H0Iso_hom_apply, SimpleGraph.Walk.map_eq_nil_iff, MultilinearMap.coe_injective, ContinuousLinearMap.apply_apply, MeasureTheory.L1.setToL1_const, finAddFlip_apply_natAdd, Equiv.curry_symm_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, Rep.barComplex.d_single, ContinuousMap.sub_apply, ContinuousMul.induced, MeasureTheory.Measure.infinitePi_map_piCurry_symm, AddEquiv.isAddUnit_map, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, MulChar.apply_mem_rootsOfUnity, map_div, FreeAlgebra.algebraMap_eq_zero_iff, dotProduct_toMatrix₂_mulVec, MeasureTheory.eq_add_disjointOfDiff_of_subset, WithTop.coe_addHom, lineMap_lt_map_iff_slope_lt_slope_right, IsometryEquiv.preimage_ball, OrderIso.coe_toHomeomorph_symm, WeierstrassCurve.Ψ_odd, toLex_smul, CategoryTheory.Presieve.compatibleEquivGenerateSieveCompatible_symm_apply_coe, Metric.Snowflaking.preimage_ofSnowflaking_closedEBall, CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq, ModuleCat.freeDesc_apply, MonoidHom.toAdditiveRight_apply_apply, Algebra.Extension.CotangentSpace.map_comp_apply, MvPolynomial.isWeightedHomogeneous_C, LinearMap.compAlternatingMapₗ_apply, BialgHom.one_apply, SemidirectProduct.inl_injective, RatFunc.toFractionRingAlgEquiv_apply, OrthogonalFamily.summable_iff_norm_sq_summable, piFinTwoEquiv_symm_apply, CategoryTheory.Abelian.Ext.addEquivBiprod_apply_fst, ContinuousLinearMap.norm_map_removeNth_le, Monoid.Coprod.mk_of_inv_mul, Submonoid.opEquiv_symm_apply, Polynomial.natDegree_quadratic, Left.sign_neg, Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff, Fin.addNatEmb_apply, DirectSum.decompose_sum, FirstOrder.Language.DirectLimit.cod_partialEquivLimit, LinearMap.associated_det_comp_equiv, LinearIndependent.map, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, LieAlgebra.Extension.lie_toKer_apply, MonoidWithZeroHom.ext_int_iff, algebraMap_cobounded_le_cobounded, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, MvPolynomial.map_X, FinPartOrd.id_apply, RatFunc.laurentAux_ofFractionRing_mk, Filter.Tendsto.partialSups, AddConstEquiv.coe_val_equivUnits_apply, MeasureTheory.Measure.le_restrict_apply, WithZero.toMulBot_symm_bot, FDRep.hom_action_ρ, Rep.mono_iff_injective, MeasureTheory.OuterMeasure.map_sup, Polynomial.natDegree_C_mul_X_pow_le, normalize_idem, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, Units.isInducing_embedProduct, DirichletCharacter.changeLevel_eq_cast_of_dvd, Profinite.NobelingProof.Products.eval_πs_image, MonoidAlgebra.commRingEquiv_single_single, Finset.ofDual_sup, HasGradientAtFilter.hasDerivAtFilter, LinearMap.le_rank_iff_exists_linearIndependent_finset, ShelfHom.toFun_eq_coe, SimpleGraph.isClique_map_iff, InfHom.toFun_eq_coe, HVertexOperator.comp_apply, TensorProduct.gradedComm_gradedMul, PiTensorProduct.smul_tprod_mul_smul_tprod, Finset.filter_map, Polynomial.aeval_add, iSupIndep_iff_dfinsuppSumAddHom_injective, volume_regionBetween_eq_lintegral, IsSymmSndFDerivWithinAt.eq, cmpLE_toDual, ContinuousLinearMap.map_smulₛₗ₂, Equiv.sigmaSubtype_symm_apply_coe_fst, MeasureTheory.AEDisjoint.measure_diff_left, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, TestFunctionClass.map_contDiff, Condensed.locallyConstantIsoFinYoneda_hom_app, Polynomial.continuousOn_aeval, MeasureTheory.measure_mul_setLAverage, Valuation.val_le_one_iff, fderivWithin_restrictScalars_comp, CategoryTheory.Localization.homEquiv_isoOfHom_inv, Complex.range_normSq, CliffordAlgebra.equivOfIsometry_apply, AlgebraicGeometry.Scheme.Hom.Spec_map_residueFieldMap_fromSpecResidueField, MvPowerSeries.WithPiTopology.continuous_constantCoeff, MvPowerSeries.substAlgHom_comp_substAlgHom, CategoryTheory.Localization.homEquiv_id, BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, Ring.DirectLimit.of_f, Seminorm.uniformContinuous_of_forall', MeasureTheory.prob_compl_eq_zero_iff₀, Polynomial.aeval_sub, toLex_one, ContinuousMultilinearMap.norm_image_sub_le', AlgebraicGeometry.Scheme.Opens.toSpecΓ_preimage_zeroLocus, MeasureTheory.OuterMeasure.coe_smul, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, PartENat.withTopEquiv_symm_top, Quaternion.normSq_ratCast, Real.volume_preimage_mul_right, finAddFlip_apply_castAdd, NumberField.InfinitePlace.apply, OrderIso.sumLexAssoc_symm_apply_inl, Matrix.diagonal_comp_single, partialSups_add_const, SemimoduleCat.comp_apply, FreeAddMonoid.ofList_singleton, Units.coeHom_injective, LinearMap.inr_map_mul, MeasureTheory.SimpleFunc.extend_comp_eq', NNReal.dist_gm_am_le, HahnSeries.leadingCoeff_nonpos_iff, ProbabilityTheory.Kernel.setLIntegral_rnDerivAux, LinearIsometryEquiv.differentiableOn, IncidenceAlgebra.zeta_prod_mk, MeasureTheory.SimpleFunc.add_apply, CircleDeg1Lift.map_add_one, ProbabilityTheory.Kernel.comp_boolKernel, RCLike.geometric_hahn_banach_closed_compact, PowerSeries.IsRestricted.C, AlgebraicGeometry.Scheme.Cover.fromGlued_open_map, Finsupp.prod_ite_eq', MulChar.sum_eq_zero_of_ne_one, BoundedContinuousFunction.dist_lt_iff_of_compact, RootPairing.isReduced_iff, AddSubmonoid.mem_map_equiv, ModuleCat.homEquiv_extendScalarsId, SSet.horn.const_val_apply, Finsupp.some_apply, OrderIso.preimage_Ico, UniformOnFun.lipschitzWith_restrict, ofAdd_neg, RestrictedProduct.continuous_rng_of_bot, OrderEmbedding.image_Ico, Units.mapContinuousMulEquiv_apply, MeasureTheory.eLpNorm_conj, Module.Basis.toMatrix_map_vecMul, MonCat.ofHom_apply, Equiv.symm_image_subset, Orientation.map_positiveOrientation_of_isEmpty, ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, ContinuousOn.clm_bundle_apply, inner_gradient_right, isAddFoelner_iff, FreeNonUnitalNonAssocAlgebra.hom_ext_iff, ContinuousAffineEquiv.symm_image_image, Algebra.Generators.H1Cotangent.equiv_apply, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, NormedAddGroupHom.zsmul_apply, ModuleCat.ExtendScalars.hom_ext_iff, Ordinal.IsInitial.mem_range_preOmega, Module.IsTorsionBy.mk_smul, AffineIsometryEquiv.dist_pointReflection_self', MvPolynomial.eval_assoc, HeytingHom.ext_iff, MeasureTheory.Measure.neg_apply, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, toBoolRing_symmDiff, AddAction.IsBlock.preimage, Algebra.commutes, TensorPower.toTensorAlgebra_tprod, PrimitiveSpectrum.gc, MeasureTheory.measure_closedBall_lt_top, MvPolynomial.monomial_single_add, FirstOrder.Language.HomClass.map_fun, HahnSeries.single_zero_ofNat, ContinuousAffineEquiv.prodAssoc_symm_apply, LaurentSeries.exists_ratFunc_eq_v, Algebra.TensorProduct.rid_symm_apply, InnerProductSpace.laplacianWithin_CLE_comp_left, Finset.eraseNone_empty, RingTheory.Sequence.isRegular_cons_iff', SemiNormedGrp.hom_inv_apply, Equiv.optionSubtypeNe_symm_self, Finset.eraseNone_insertNone, Real.ringEquivCauchy_symm_apply_cauchy, HahnSeries.SummableFamily.powerSeriesFamily_smul, ax_grothendieck_zeroLocus, Homeomorph.isLittleO_congr, ModularFormClass.exp_decay_sub_atImInfty', LinearMap.toMatrixAlgEquiv_transpose_apply, VertexOperator.ncoeff_add, coe_toLexAddEquiv, Monoid.Coprod.mk_eq_mk, Quotient.finChoiceEquiv_symm_apply, LinearEquiv.rTensor_tmul, groupCohomology.coe_mapCocycles₂, Transcendental.linearIndependent_sub_inv, FirstOrder.Language.DirectLimit.comp_unify, TopCat.inv_hom_id_apply, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, Finmap.keysLookupEquiv_apply_coe_fst, Cardinal.natCast_le_toENat_iff, Submonoid.LocalizationMap.map_isRegular, MeasureTheory.lintegral_comp_eq_lintegral_meas_lt_mul, Submodule.Quotient.restrictScalarsEquiv_mk, Coalgebra.TensorProduct.lid_symm_apply, UpperHalfPlane.smulAux'_im, Submonoid.LocalizationMap.mk'_spec, wittPolynomial_eq_sum_C_mul_X_pow, Ring.map_choose, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, MeasureTheory.Measure.lintegral_compProd, NormedRing.toRingNorm_apply, IsAdjoinRoot.map_surjective, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, DMatrix.map_sub, ContinuousAffineMap.differentiableAt, InitialSeg.le_iff_le, OrderIso.equivalence_unitIso, Finsupp.mapRange_multiset_sum, PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl, CategoryTheory.GrothendieckTopology.Plus.toPlus_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, Finset.normalize_gcd, List.sublist_iff_exists_orderEmbedding_getElem?_eq, toDual_covBy_toDual_iff, MeasureTheory.StronglyMeasurable.norm_approxBounded_le, Module.Basis.repr_self, DFinsupp.support_subset_iff, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_inv, InnerProductSpace.volume_ball_of_dim_even, PMF.toMeasure_mono, Monoid.Coprod.inr_injective, LinearMap.injective_rangeRestrict_iff, Valued.toNormedField.one_le_norm_iff, Seminorm.zero_apply, Finset.sumEquiv_symm_apply, IsMax.ofDual, MultilinearMap.compLinearMapₗ_apply, MeasureTheory.Measure.addHaar_singleton, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, LinearMap.quotientInfEquivSupQuotient_surjective, exists_contMDiffMap_forall_mem_convex_of_local_const, AdicCompletion.piEquivFin_apply, Polynomial.coeff_coe, iteratedFDerivWithin_zero_apply, EuclideanSpace.volume_closedBall, Matrix.piAlgEquiv_apply, Orientation.rightAngleRotation_neg_orientation, Combinatorics.Subspace.reindex_apply, LieModule.genWeightSpace_neg_add_chainBot, Sublattice.mem_map_equiv, AddChar.eq_one_iff, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, CategoryTheory.Presheaf.isLocallyInjective_iff_injective_of_separated, SubMulAction.image_inclusion, Finsupp.restrictSupportEquiv_symm_apply_coe, Orientation.rotationAux_apply, Fourier.fourierIntegral_comp_add_right, derivWithin_clm_apply, Metric.Snowflaking.preimage_toSnowflaking_emetricBall, NonarchAddGroupNorm.toNonarchAddGroupSeminorm_eq_coe, lcm_eq_normalize, MvPolynomial.monomial_one_mul_cancel_right_iff, Fin.consEquivL_symm_apply, Polynomial.sumIDeriv_apply_of_lt, EReal.sign_mul_inv_abs', FractionalIdeal.coe_mk0, ClassGroup.mk_def, ofMul_eq_zero, ENNReal.logOrderIso_apply, Equiv.Perm.sign_swap', Algebra.intNorm_eq_zero, BumpCovering.sum_toPOUFun_eq, MonoidAlgebra.domCongr_apply, EquivLike.apply_inv_apply, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, equivShrink_symm_one, CategoryTheory.Pi.equivalenceOfEquiv_functor, RelHom.coe_mul, Polynomial.erase_monomial, Quaternion.fst_re_dualNumberEquiv_symm, Polynomial.continuousAt_aeval, RCLike.intCast_im, Equiv.sigmaPUnit_apply, Equiv.Perm.apply_zpow_apply_eq_iff, IsBaseChange.lift_eq, StarMulEquiv.coe_toMulEquiv, IsSepClosed.exists_aeval_eq_zero, PowerSeries.derivative_inv, Module.Basis.is_basis_iff_det, AlgebraicGeometry.coprodMk_inr, NormedSpace.Dual.toWeakDual_inj, gaussSum_sq, LinearMap.const_apply, PowerSeries.isUnit_constantCoeff, ZMod.χ₈_apply, Polynomial.card_roots_sub_C, SpecialLinearGroup.coe_dualMap, WittVector.ghostComponent_teichmuller, GrpCat.comp_apply, MulEquiv.monoidHomCongrLeftEquiv_symm_apply, Algebra.mem_algebraMapSubmonoid_of_mem, constantCoeff_wittStructureInt_zero, TensorProduct.finsuppRight_apply_tmul_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, CommGrpCat.forget₂_map, Shrink.linearEquiv_apply, QuadraticMap.basisRepr_apply, TensorProduct.directSumRight_symm_lof_tmul, ModuleCat.toKernelSubobject_arrow, Equiv.piUnique_symm_apply, Complex.conj_I, Order.coheight_orderIso, Polynomial.homogenizeLM_apply, CategoryTheory.CatEnrichedOrdinary.homEquiv_id, LinearIsometryEquiv.withLpUniqueProd_symm_apply, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, HasOuterApproxClosed.exAppr, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, Submodule.orthogonalProjection_orthogonal, InitialSeg.coe_toOrderEmbedding, AddGroupSeminorm.inf_apply, Finsupp.sum_ite_self_eq, IsSeparable.of_equiv_equiv, AddAutAdditive_symm_apply_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, Metric.Snowflaking.dist_toSnowflaking_toSnowflaking, AffineEquiv.wbtw_map_iff, continuousFunctionalCalculus_map_id, coe_algEquiv_lpBCF, Quaternion.continuous_normSq, Subgroup.IsComplement.equiv_fst_eq_self_iff_mem, PMF.filter_apply_eq_zero_of_notMem, GroupExtension.Equiv.trans_apply, Polynomial.degree_derivative_le, fourierCoeffOn_of_hasDeriv_right, inner_conj_symm, AlgEquiv.coe_restrictScalars_symm', Ideal.associatesEquivIsPrincipal_map_one, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, Module.Basis.SmithNormalForm.coord_apply_embedding_eq_smul_coord, ofDual_zero, LinearMap.domRestrict_apply, NonarchAddGroupSeminorm.coe_sSup_apply, SimpleGraph.map_edgeFinset_induce, MvPolynomial.degreeOf_monomial_eq, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, AlgebraicGeometry.Scheme.Hom.isProperMap, IsBaseChange.endHom_comp, Module.End.eigenspace_aeval_polynomial_degree_1, inv_eq_of_aeval_divX_ne_zero, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, finEquivPowers_symm_apply, Polynomial.lifts_iff_coeffs_subset_range, CategoryTheory.Limits.Types.colimitEquivColimitType_symm_apply, Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, IsSMulRegular.of_isLocalizedModule, Module.Basis.det_apply, Polynomial.exists_monic_aeval_eq_zero_forall_mem_of_mem_map, minpoly.map_eq_of_equiv_equiv, Quaternion.imI_snd_dualNumberEquiv, Polynomial.resultant_C_mul_right, IsSimpleOrder.equivBool_apply, QuotientGroup.sound, SupPrime.ofDual, MeasureTheory.L1.setToL1_lipschitz, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, AffineIsometry.ediam_image, List.SortedGE.of_map_toDual, Filter.HasBasis.mem_measureSupport, Polynomial.derivative_one, Polynomial.taylorLinearEquiv_apply_coe, AddEquiv.val_piAddUnits_apply, QuadraticMap.restrictScalars_apply, LieEquiv.coe_toLieHom, Equiv.piUnique_apply, Multiset.toFinsupp_strictMono, AddEquiv.toFun_eq_coe, Set.powersetCard.mulActionHom_of_embedding_surjective, MeasureTheory.OuterMeasure.univ_eq_zero_iff, TemperedDistribution.fourierTransformInvCLM_apply, DirectSum.coe_of_mul_apply, ContinuousLinearEquiv.mdifferentiableAt, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, LieAlgebra.ExtendScalars.map_apply_tmul, PowerSeries.natDegree_trunc_lt, List.Nodup.getEquivOfForallMemList_symm_apply_val, MDifferentiableWithinAt.clm_apply, HasCompactSupport.convolution_integrand_bound_right, Polynomial.map_scaleRoots, LieHom.range_eq_ker_iff, MvPowerSeries.HasSubst.expand, AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompact, IsometryEquiv.coe_toDilationEquiv, ValuationSubring.coe_subtype, MeasureTheory.OuterMeasure.comap_ofFunction, LinearMap.traceAux_def, Algebra.TensorProduct.mapOfCompatibleSMul_tmul, SubMulAction.ofFixingSubgroup_insert_map_bijective, ContinuousMap.toFun_eq_coe, Function.Injective.swap_comp, SemiNormedGrp₁.inv_hom_apply, OrderIso.sumLexIioIci_apply_inr, LinearMap.mem_span_iff_continuous, CircleDeg1Lift.commute_sub_nat, Filter.map_zero, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, LinearMap.surjective_of_ne_zero, CategoryTheory.GradedObject.comapEquiv_functor, nndist_toAdd, Traversable.toList_spec, Hamming.toHamming_ofHamming, Polynomial.coe_evalEvalRingHom, MeasureTheory.ProbabilityMeasure.limsup_measure_closed_le_of_tendsto, LowerSet.map_map, MultilinearMap.fromDFinsuppEquiv_symm_apply, SetSemiring.up_down, CategoryTheory.Linear.rightComp_apply, AddMonoidHom.flipHom_apply, ArithmeticFunction.IsMultiplicative.map_mul_of_coprime, PresentedGroup.equivPresentedGroup_apply_of, LieAlgebra.rootSpaceProduct_tmul, FirstOrder.Language.Equiv.coe_toEmbedding, Module.Flat.iff_lTensor_injective', MonomialOrder.degree_sPolynomial_lt_sup_degree, modularCyclotomicCharacter.aux_spec, Padic.isDenseInducing_cast_withVal, QuadraticAlgebra.norm_eq_zero_iff_eq_zero, SkewPolynomial.smul_monomial, groupCohomology.H1π_eq_iff, Basis.piTensorProduct_apply, toDual_inf, DirectSum.decompose_smul, ContinuousLinearEquiv.piCongrRight_symm_apply, IsLocalization.map_id_mk', Semigrp.coe_comp, AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assoc, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, Algebra.leftMulMatrix_apply, AddMonoidHom.apply_int, AddChar.inv_apply_eq_conj, Homeomorph.isOpen_preimage, ContinuousMap.sup'_apply, CompleteSublattice.subtype_apply, BumpCovering.coe_single, left_lt_lineMap_iff_pos, WeierstrassCurve.Projective.map_negY, PowerSeries.coe_substAlgHom, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, SlashInvariantForm.vAdd_apply_of_mem_strictPeriods, FractionRing.mk_eq_div, Complex.imLm_coe, PiTensorProduct.congr_tprod, MeasureTheory.Lp.simpleFunc.aemeasurable, MeasureTheory.setToFun_eq, Polynomial.degree_linear, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, isPrimePow_iff_minFac_pow_factorization_eq, Polynomial.Chebyshev.derivative_T_eval_one, DifferentiableAt.lineDeriv_eq_fderiv, Equiv.algEquiv_symm_apply, Ideal.mapHom_apply, OrthonormalBasis.repr_reindex, Topology.WithLower.ofLower_lt_ofLower, ContinuousMap.isUniformEmbedding_equivBoundedOfCompact, ArithmeticFunction.cardFactors_apply_prime_pow, Ideal.ResidueField.mapₐ_apply, HasDerivAt.comp_semilinear, Subsemigroup.coe_map, AlgebraicGeometry.Scheme.AffineZariskiSite.mem_grothendieckTopology_iff_sectionsOfPresieve, CompleteLat.Iso.mk_inv, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, AddAut.congr_apply, WeierstrassCurve.Affine.CoordinateRing.basis_apply, IsLocalization.surj₂, IsUnit.preimage_smul_setₛₗ, MeasureTheory.condExpL2_comp_continuousLinearMap, balanced_absConvexHull, Polynomial.taylor_C, Cardinal.aleph_toNat, Equiv.Perm.OnCycleFactors.kerParam_apply, inner_im_symm, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, SchwartzMap.laplacian_apply, NormedAddGroupHom.Equalizer.liftEquiv_symm_apply_coe, SimpleGraph.Subgraph.inclusion.injective, TopologicalSpace.IrreducibleCloseds.equivSubtype'_symm_apply, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, AdicCompletion.ofLinearEquiv_symm_of, Transcendental.aeval_of_transcendental, MvPolynomial.hom_bind₁, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.volume_preserving_funUnique, WeierstrassCurve.map_b₂, LinearMap.BilinForm.toMatrix'_compRight, WeierstrassCurve.Jacobian.map_polynomialX, WeierstrassCurve.Jacobian.map_neg, convexHull_subset_affineSpan, ClosureOperator.idempotent, MvPolynomial.coeff_expand_zero, AddGroupNorm.toAddGroupSeminorm_eq_coe, TensorProduct.finsuppRight_apply_tmul, ContDiffMapSupportedIn.toFun_eq_coe, ContinuousAffineEquiv.image_symm_image, CFC.log_smul, AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpen, Ideal.relNorm_eq_pow_of_isMaximal, DoubleQuot.coe_liftSupQuotQuotMkₐ, QuaternionAlgebra.imK_swapEquiv_apply, MulDistribMulAction.toMonoidHom_apply, NormedSpace.expSeries_hasSum_exp_of_mem_ball, LocalizedModule.mkLinearMap_apply, Finsupp.toMultiset_inf, ZSpan.setFinite_inter, CategoryTheory.Functor.IsDenseSubsite.imageSieve_mem, LinearEquiv.ofTop_apply, LinearIsometryEquiv.differentiableWithinAt, Cardinal.natCast_toNat_le, ModularForm.mul_coe, Polynomial.derivative_apply, convexHull_eq_self, UniformEquiv.piFinTwo_apply, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, CategoryTheory.Limits.IsTerminal.from_eq_liftConeMorphism, EquivLike.coe_symm_comp_self, PowerSeries.trunc_X, Module.subsingletonEquiv_apply, FintypeCat.homMk_apply, RingCon.lift_injective_iff, Real.sinhOrderIso_symm_apply, RootPairing.root_chainBotIdx, Trivialization.preimageSingletonHomeomorph_apply, Polynomial.C_injective, ProbabilityTheory.Kernel.comap_apply', RestrictedProduct.mulSingle_eq_of_ne, HomogeneousLocalization.algebraMap_apply, Homeomorph.bijective, DFinsupp.equivFunOnFintype_symm_single, ofAdd_image_multiples_eq_powers_ofAdd, ContinuousAffineMap.coe_prod, ContinuousLinearEquiv.continuousWithinAt, StarAlgHom.fst_apply, CommRing.Pic.mapAlgebra_mapAlgebra, EuclideanSpace.coe_measurableEquiv_symm, AddAction.toPerm_apply, Equiv.prod_assoc_symm_preimage, HopfAlgebra.antipode_one, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, ContinuousMap.Homotopy.congr_arg, LinearMap.toAddMonoidHom_mulRight, SimpleGraph.Iso.sumAssoc_symm_apply, OrderIso.sumLexIioIci_symm_apply_of_lt, Ordinal.range_preOmega, Algebra.normalizedTrace_self_apply, SimpleGraph.Coloring.even_length_iff_congr, CategoryTheory.Presheaf.imageSieve_mem, AnalyticOnNhd.eval_continuousLinearMap, AddConstMapClass.map_zsmul_add, Polynomial.aeval_X, Surreal.one_toGame, AddMonoidHom.prod_apply, CategoryTheory.Abelian.Ext.mk₀_homEquiv₀_apply, FirstOrder.Language.PartialEquiv.ext_iff, ofDual_eq_zero, Submodule.map_toAddSubmonoid, HahnSeries.cardSupp_hsum_le, Additive.toMul_eq_top, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Fin.castLEOrderEmb_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, AddChar.nsmul_apply, GaussianInt.toComplex_one, WeierstrassCurve.Affine.Point.toClass_apply, IsStronglyTranscendental.of_isLocalization, CategoryTheory.Adjunction.homEquiv_id, WeierstrassCurve.Jacobian.eval_polynomialZ, TopCat.pullback_fst_range, Circle.argEquiv_apply_coe, MeasureTheory.memLp_re_im_iff, Equiv.Perm.sign_swap, Finset.disjiUnion_Iic_disjointed, MeasureTheory.exists_isCompact_closure_measure_compl_lt, HasFDerivAt.clm_comp, BialgEquiv.coe_coe, PMF.binomial_apply_last, ContinuousMapZero.toNNReal_apply, AffineIsometryEquiv.coe_symm_toHomeomorph, OrderMonoidIso.eq_comp_symm, strictAntiOn_dual_iff, sign_eq_neg_one_iff, MulEquivClass.map_eq_one_iff, ContinuousLinearMap.adjoint_innerSL_apply, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso_apply, CommGrpCat.toAddCommGrp_map, FiniteArchimedeanClass.withTopOrderIso_apply_coe, Module.Basis.reindex_apply, Congruent.index_equiv, CompactlySupportedContinuousMap.finsetSup'_apply, ValuativeRel.ValueGroupWithZero.mk_eq_valuation, WType.NatαEquivPUnitSumPUnit_symm_apply, Polynomial.degreeLT.basis_repr, MeasureTheory.Integrable.integral_condKernel, AddChar.div_apply', ZLattice.coe_comap, AddMonoidHom.mulRight₃_apply, ConjAct.ofConjAct_one, EuclideanGeometry.reflection_mem_of_le_of_mem, RingOfIntegers.dvd_norm, FreeAddSemigroup.lift_comp_of', GroupExtension.Equiv.trans_symm_apply, Finset.Nat.antidiagonalEquivFin_apply_val, ClosureOperator.isClosed_closure, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, gaugeSeminorm_toFun, MeasureTheory.SimpleFunc.mul_apply, hasFDerivAt_iff_isLittleO_nhds_zero, AlgebraicGeometry.LocallyRingedSpace.stalkMap_congr_hom, Subalgebra.coe_valA', LaurentPolynomial.exists_T_pow, Finset.orderEmbOfFin_compl_singleton_apply, AddSubmonoid.fg_iff_mul_fg, SimpleGraph.Walk.getVert_map, CategoryTheory.Adjunction.homEquiv_naturality_left, BddDistLat.hom_inv_apply, NormedAddGroupHom.continuous, AdicCompletion.evalOneₐ_liftAlgHom, Affine.Simplex.faceOppositeCentroid_eq_affineCombination, SchwartzMap.hasTemperateGrowth, polyEquivTensor_symm_apply_tmul_eq_smul, LinearIsometry.submoduleMap_apply_coe, MeasureTheory.SimpleFunc.tendsto_approxOn_Lp_eLpNorm, OrthogonalFamily.inner_right_fintype, AffineMap.coe_snd, AffineMap.vectorSpan_image_eq_submodule_map, Polynomial.nextCoeff_C_mul, WCovBy.fst_ofLex, CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply, spectrum.sub_singleton_eq, iterateFrobenius_zero_apply, ContinuousAffineMap.coe_prodMap, CategoryTheory.Limits.limit.w_apply, AddUnits.isEmbedding_embedProduct, TopologicalSpace.OpenNhds.inclusionMapIso_hom_app, OrderRingIso.symm_apply_lt, AddMonoidHom.coe_mrange, SemilinearIsometryClass.isometry, Pi.evalLatticeHom_apply, Pi.counit_single, FirstOrder.Language.DirectedSystem.natLERec.directedSystem, AddChar.sub_apply', MeasureTheory.MemLp.meas_ge_lt_top_enorm, Valuation.coeff_zero_minpoly, CategoryTheory.ConcreteCategory.forget_map_eq_coe, ContDiffMapSupportedIn.structureMapLM_apply, NNReal.agmSequences_succ, Complex.normSq_eq_zero, SemiRingCat.forget_map, Ordinal.preOmega_max, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, Path.extend_trans_of_half_le, AddGroupExtension.Section.neg_add_mem_range_inl, MeasureTheory.Measure.count_injective_image, ExteriorAlgebra.liftAlternating_ι, SimpleGraph.map_comap_le, ContinuousLinearMap.circleAverage_comp_comm, monovaryOn_toDual_left, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, CategoryTheory.Discrete.monoidalFunctor_δ, RatFunc.map_apply_div_ne_zero, FirstOrder.Language.HomClass.strictMono, MeasureTheory.Measure.infinitePi_pi_univ, TensorProduct.AlgebraTensorModule.lcurry_apply, partialSups_disjoint_of_disjoint, Finsupp.coe_zero, ContMDiffSection.coeFn_mk, Fin.cons_comp_cycleRange, Nat.ordCompl_self_pow, toBoolRing_bot, RCLike.normSq_sub, EmbeddingLike.map_eq_zero_iff, trace_adjoinSimpleGen, PowerSeries.derivative_X, CategoryTheory.orderDualEquivalence_inverse_map, UniformEquiv.preimage_image, AddMonoidAlgebra.mul_single_apply_of_not_exists_add, OrderIso.toRelIsoGT_apply, MultilinearMap.map_update_sum, ProbabilityTheory.aestronglyMeasurable_integral_condExpKernel, Polynomial.self_sub_C_mul_X_pow, Differential.algEquiv_deriv, Matrix.mvPolynomialX_mapMatrix_aeval, StarAlgEquiv.invFun_eq_symm, ContinuousLinearMap.coprodEquivL_symm_apply, Polynomial.monomial_comp, VectorPrebundle.contMDiffCoordChange_apply, Function.FromTypes.curryEquiv_apply, algebraicIndependent_empty_type_iff, Equiv.coe_uniqueProd, Set.FiniteExhaustion.prod_apply, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, MeasureTheory.Content.outerMeasure_of_isOpen, MeasureTheory.Measure.setLIntegral_condKernel_eq_measure_prod, nndist_homothety_self, Module.length_eq_rank, Matrix.SeparatingRight.toBilin, TwoSidedIdeal.subtype_apply, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, supClosure_univ, Polynomial.natDegree_add_C, Subgroup.IsArithmetic.conj, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, IsAdjoinRoot.algEquiv_apply_map, Module.Basis.repr_reindex_apply, Equiv.Perm.disjoint_iff_eq_or_eq, Finset.affineCombination_subtype_eq_filter, StarMonoidHom.coe_one, MeasureTheory.SimpleFunc.approxOn_zero, ContinuousMultilinearMap.prod_apply, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, map_comp_zpow, Homeomorph.transOpenPartialHomeomorph_apply, EuclideanGeometry.reflection_apply, WeierstrassCurve.VariableChange.map_u, HasCompactSupport.convolution_integrand_bound_right_of_subset, ENNReal.orderIsoIicOneBirational_symm_apply, Tropical.tropOrderIso_coe_fn, PreTilt.coeff_def, Finset.sum_comp_equiv, LinearIsometryEquiv.comp_fderiv', Polynomial.coe_evalRingHom, LinearPMap.adjoint_apply_of_dense, AlgebraicGeometry.Scheme.Hom.isOpen_smoothLocus, MulEquiv.subgroupCongr_symm_apply, Polynomial.eval_C_mul, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, ProbabilityTheory.Kernel.setLIntegral_rnDeriv_le, VitaliFamily.exists_measurable_supersets_limRatio, PadicInt.val_toZMod_eq_zmodRepr, Finsupp.weight_apply, AffineMap.coe_one, Tactic.NormNum.isNat_nnrealSqrt, ContinuousAdd.induced, RootPairing.Hom.weightHom_injective, CategoryTheory.PreGaloisCategory.evaluation_aut_injective_of_isConnected, BoundedLatticeHom.subtypeVal_apply, starRingEnd_self_apply, SlashInvariantForm.coe_norm, Tuple.proj_equiv₁', LieModule.genWeightSpace_add_chainTop, Additive.foMul_strictMono, TestFunction.coe_mk, Equiv.setCongr_symm_apply, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, Matrix.adjugate_fin_two_of, Matrix.kroneckerMap_diagonal_left, ClosureOperator.id_apply, Subrel.coe_inclusionEmbedding, SetTheory.PGame.nim_add_nim_equiv, lineMap_strict_mono_right, ofColex_zero, Set.image_add, RingHomSurjective.is_surjective, OneHom.comp_apply, cmp_ofDual, InitialSeg.isLowerSet_range, UpperHalfPlane.σ_denom, CliffordAlgebra.contractLeftAux_contractLeftAux, Polynomial.roots_map, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, ZMod.rootsOfUnityAddChar_val, CategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom, AddCommGrpCat.homAddEquiv_apply, RCLike.re_tsum, Matrix.algebraMap_matrix_apply, Submonoid.topEquiv_apply, CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, InitialSeg.coe_coe_fn, lipschitzGroup.conjAct_smul_range_ι, LinearMap.coe_finsupp_sum, DirectSum.lmap_eq_iff, MulHom.coprod_apply, MvPolynomial.support_C, AddEquivClass.apply_mem_center_iff, UniformSpaceCat.hom_comp, PseudoMetric.nonneg, FormalMultilinearSeries.applyComposition_ones, Finsupp.degree_def, HahnSeries.iterateEquiv_symm_apply, postcomp_compactConvergenceCLM_apply, Valuation.map_add_supp, Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range, Finsupp.sum_mapDomain_index_addMonoidHom, groupHomology.H0π_comp_map_apply, MeasureTheory.addContent_empty, BoundedContinuousFunction.ext_iff, BiheytingHom.comp_apply, Matrix.transposeInvertibleEquivInvertible_apply, BoundedContinuousFunction.isBounded_image, MvPowerSeries.monomial_eq', Matrix.transposeLinearEquiv_apply, AddSubmonoid.LocalizationMap.lift_left_inverse, Polynomial.roots_expand_map_frobenius_le, CommMonCat.ext_iff, Matroid.mapEquiv_isBase_iff, LeftInvariantDerivation.coeFnAddMonoidHom_apply, Matrix.one_fin_two, PerfectionMap.equiv_apply, Complex.det_conjLIE, ContinuousLinearEquiv.coe_funUnique_symm, Monoid.Coprod.snd_apply_inr, MeasureTheory.trim_comap_apply, WithBot.ofDual_le_ofDual_iff, Submodule.exists_smith_normal_form_of_le, measurable_piCongrLeft, IntermediateField.AdjoinPair.algebraMap_gen₂, LinearMap.toMatrix_apply, AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective, ContinuousLinearMap.integral_id_map, SupHom.top_apply, PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, PMF.ofMultiset_apply_of_notMem, AlgEquiv.coe_coe, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_assoc, linearDepOn_iff'ₛ, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, BoundedContinuousFunction.apply_le_nndist_zero, WithZero.toMulBot_strictMono, MeasureTheory.addContent_le_sum_of_subset_sUnion, PiTensorProduct.map_range_eq_span_tprod, IsometryEquiv.coe_toHomeomorph_symm, Polynomial.isCoprime_X_sub_C_of_isUnit_sub, ArithmeticFunction.coe_zeta_mul_apply, second_derivative_symmetric_of_eventually_of_real, MonomialOrder.degree_sub_leadingTerm_lt_iff, BoundedContinuousFunction.toLp_denseRange, IsLocalization.eq_iff_exists, CategoryTheory.discreteEquiv_apply, WithZero.logEquiv_unitsMk0, Ordinal.toGame_nadd, MeasureTheory.Measure.coe_zero, AdicCompletion.evalₐ_liftRingHom, Valuation.IsRankOneDiscrete.generator_mem_range, SetTheory.PGame.moveRight_toRightMovesNim, MeasureTheory.volume_sum_rpow_lt_one, AlgHom.coe_toAddMonoidHom, antilipschitzWith_iff_exists_mul_le_norm, FreeAbelianGroup.map_comp_apply, BoxIntegral.BoxAdditiveMap.restrict_apply, MvPolynomial.eval₂_comp_right, PresheafOfModules.map_comp_assoc, OrderHom.coe_sup, MeasureTheory.condExpL2_const_inner, AlgEquiv.congr_fun, RootPairing.mapsTo_coreflection_coroot, Nat.factorization_zero_right, ContinuousLinearMap.HasRightInverse.surjective, AddConstMapClass.map_fract, NumberField.house.basis_repr_norm_le_const_mul_house, WithZero.val_inv_logOrderIso_symm_apply, Complex.dist_conj_self, LinearPMap.toFun_eq_coe, AlgebraicGeometry.Scheme.Opens.ι_base_apply, OrderIso.sumLexAssoc_apply_inl_inr, balancedHull_convexHull_subseteq_absConvexHull, PMF.toMeasure_uniformOfFinset_apply, Unitary.path_apply, MonoidAlgebra.neg_apply, Function.locallyFinsuppWithin.max_apply, Polynomial.ofFn_natDegree_lt, SpectrumRestricts.nnreal_iff_nnnorm, SkewMonoidAlgebra.mapDomain_apply, Fin.cycleIcc.trans, MvPolynomial.weightedHomogeneousComponent_apply, ModuleCat.restrictScalarsId'App_inv_apply, CliffordAlgebra.EquivEven.involute_v, MeasureTheory.IsFundamentalDomain.measure_eq_tsum, MeasureTheory.FiniteMeasure.continuous_lintegral_boundedContinuousFunction, cyclotomicCharacter.continuous, Dilation.congr_arg, SubMulAction.conjMap_ofFixingSubgroup_bijective, OrderIso.map_csInf_of_directedOn', CircleDeg1Lift.tendsto_translation_number₀', DomAddAct.isQuotientMap_mk, Unitization.inlRingHom_apply, TensorProduct.toMatrix_map, CompositionAsSet.boundary_zero, ContinuousAffineEquiv.eq_symm_apply, comp_equiv_symm_dotProduct, Unitary.conjStarAlgAut_ext_iff, Matrix.toLinAlgEquiv_toMatrixAlgEquiv, Matrix.rank_vecMulVec, IsometryEquiv.symm_trans_apply, RCLike.realLinearIsometryEquiv_apply, LinearMap.continuous_uncurry_of_isContPerfPair, sign_eq_one_iff, Monoid.CoprodI.Word.equivPair_tail_eq_inv_smul, Finsupp.Set.indicator_singleton_eq, TemperedDistribution.laplacianCLM_apply, Polynomial.aeval_homogenize_of_eq_one, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, Nat.pow_factorization_choose_le, Nat.absNorm_under_prime, Finsupp.coe_orderIsoMultiset, MeasureTheory.measure_union_le, FirstOrder.Language.Embedding.domRestrict_apply, toAdd_list_sum, MonoidAlgebra.lift_single, GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset', MonoidHom.coe_ker, UniformOnFun.zero_apply, AdicCompletion.map_of, NumberField.IsCMField.Units.complexConj_eq_self_iff, CategoryTheory.Limits.Multifork.toSections_fac, ZMod.toCircle_eq_circleExp, ContinuousLinearMap.toWOT_apply, AddMonoidAlgebra.mapRangeAlgHom_apply, AlgEquiv.coe_trans, Equiv.Perm.sign_ofSubtype, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, Polynomial.toContinuousMapOnAlgHom_apply, TopCat.Presheaf.stalkSpecializes_stalkPushforward_apply, MeasureTheory.Lp.isometry_compMeasurePreserving, Nat.factorization_le_of_le_pow, SimpleGraph.chromaticNumber_eq_card_iff_forall_surjective, PartOrd.id_apply, equivShrink_symm_neg, ContinuousMonoidHom.prodMap_toFun, Units.coe_mapEquiv, BoundedContinuousFunction.nndist_le_two_nnnorm, HasDerivAt.star_conj, ContinuousMapZero.coeFnAddMonoidHom_apply, AffineEquiv.equivUnitsAffineMap_symm_apply_invFun, BoundedContinuousFunction.NNReal.upper_bound, WithCStarModule.equiv_symm_zero, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, PowerSeries.coeff_X_pow_mul, WithBot.some_mem_insertBot, ContinuousLinearEquiv.piCongrRight_apply, ContinuousAt.partialSups_apply, IsometryEquiv.isometry, MvPolynomial.map_eval, ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_on, GradedRing.coe_projZeroRingHom'_apply, SupBotHom.id_apply, CStarMatrix.mapₗ_apply, RootPairing.polarization_apply_eq_zero_iff, Finset.orderIsoColex_apply, MeasureTheory.ae_measure_preimage_add_right_lt_top, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, MonoidHom.mulExact_of_comp_eq_one_of_ker_le_range, QuotientAddGroup.rangeKerLift_surjective, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, Cardinal.toENat_lt_top, Order.height_toDual, Submodule.coe_prodEquivOfClosedCompl, AlgebraicGeometry.Scheme.Hom.isDiscrete_preimage, Circle.exp_nsmul, WithTop.toDual_apply_coe, Module.Basis.restrictScalars_toMatrix, SimpleGraph.locallyLinear_comap, InnerProductSpaceable.inner_.conj_symm, QuotientAddGroup.quotientQuotientEquivQuotientAux_mk_mk, IsLocalizedModule.mk'_eq_iff, finFunctionFinEquiv_symm_apply_val, MonomialOrder.degree_sub_leadingTerm_le, IsValuativeTopology.isClopen_closedBall, UniformOnFun.toFun_zero, WittVector.truncate_liftFun, MonCat.inv_hom_apply, ContinuousLinearMap.ext_ring_iff, ProbabilityTheory.tilted_mul_apply_cgf', LatticeHom.withBot_apply, Polynomial.monomial_mul_monomial, Homeomorph.map_coclosedCompact, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Matrix.vecMul_swap, AddUnits.isInducing_embedProduct, Seminorm.continuousAt_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, Submodule.torsionBy.mk_smul, ContinuousLinearMap.intervalIntegral_comp_comm, AddMonoidAlgebra.mapRangeRingEquiv_single, CategoryTheory.ConcreteCategory.bijective_of_isIso, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, MulDistribMulAction.toMonoidEnd_apply, Subalgebra.rank_toSubmodule, PowerSeries.coeff_zero_mul_X, Filter.coe_pureAddHom, Polynomial.coe_mapAlgHom, Equiv.ofFiberEquiv_symm_apply, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_longRoot, finSuccEquiv'_symm_some_above, groupHomology.π_comp_H2Iso_inv_apply, Module.Basis.orientation_reindex, TannakaDuality.FiniteGroup.rightRegular_apply, MeasureTheory.Measure.map_snd_prod, Algebra.Extension.Hom.toAlgHom_apply, Finset.Colex.insert_lt_insert, Cardinal.succ_aleph0, Orientation.areaForm_rightAngleRotation_left, spinGroup.toUnits_injective, LocallyConstant.mapAddMonoidHom_apply, MvPowerSeries.coeff_mul_C, Metric.Snowflaking.image_toSnowflaking_emetricBall, Matrix.piAddEquiv_apply, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, homothety_one_half, WithZero.coeMonoidHom_apply, LaurentPolynomial.invert_comp_C, AbsoluteValue.IsEquiv.log_div_log_eq_log_div_log, Matrix.center_eq_scalar_image, coeFn_fourierLp, CliffordAlgebraQuaternion.Q_apply, IndexedPartition.equivQuotient_index, LinearMap.BilinForm.restrict_apply, MvPolynomial.rename_eq, ContinuousLinearMap.contMDiffAt, SimpleGraph.Iso.mapEdgeSet_symm_apply, MeasureTheory.ae_iff_measure_eq, ContinuousMap.hasProd_apply, toAdd_inv, Submonoid.mem_closure_image_one_lt_iff, LinearEquiv.coe_coe, Finset.Ico_toDual, AffineMap.homothety_eq_lineMap, Path.truncate_range, IsLocalRing.residue_surjective, BoundedLatticeHom.coe_comp_lattice_hom, ContinuousLinearMap.zero_apply, algebraMap_le_algebraMap, ComplexShape.Embedding.AreComplementary.desc.aux_trans, Algebra.H1Cotangent.exact_δ_mapBaseChange, LaurentPolynomial.antipode_C_mul_T, Antivary.dual, LinearMap.map_finsupp_linearCombination, PadicInt.toZMod_spec, Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det, Polynomial.signVariations_C_mul, MvPolynomial.totalDegree_coeff_optionEquivLeft_le, AlternatingMap.toMultilinearMapLM_apply, isClosed_setOf_isCompactOperator, AlternatingMap.domDomCongrEquiv_symm_apply, OmegaCompletePartialOrder.ContinuousHom.map_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, BoundedContinuousFunction.coe_toContinuousMap, Metric.Snowflaking.ediam_image_toSnowflaking, TopCat.GlueData.preimage_image_eq_image', Module.FinitePresentation.exists_basis_localizedModule_powers, DoubleCentralizer.coe_snd, Set.map_finite_biInf, CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_snd, ProbabilityTheory.Kernel.lintegral_restrict, ContinuousMultilinearMap.fin0_apply_norm, ConcaveOn.dual, LinearIsometry.angle_map, LinearMap.snd_apply, coe_injective', CompactExhaustion.mem_diff_shiftr_find, WeierstrassCurve.Jacobian.map_addXYZ, ZeroHom.coe_coe, CuspForm.coe_add, ofBoolAlg_compl, PolynomialModule.map_single, Subalgebra.fg_bot_toSubmodule, CuspForm.toSlashInvariantForm_coe, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, Equiv.congr_arg, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, AddSubmonoid.toSubmonoid'_closure, RelEmbedding.toOrderHom_injective, MvPolynomial.derivation_ext_iff, Algebra.botEquiv_symm_apply, NumberField.mixedEmbedding.disjoint_negAt_plusPart, SSet.Subcomplex.PairingCore.pairing_p_symm_equivI, ContinuousMap.Homotopy.map_zero_left, Algebra.SubmersivePresentation.cotangentEquiv_apply, MonoidHom.coe_toAdditive', DFinsupp.card_Ioc, Function.Embedding.sigmaMap_apply, PMF.toMeasure_apply_eq_zero_iff, NNReal.sqrt_lt_sqrt, MeasureTheory.integral_convolution, strictAnti_comp_ofDual_iff, Algebra.PreSubmersivePresentation.reindex_map, LinearMap.toMatrix_id_eq_basis_toMatrix, MultilinearMap.zero_apply, ContinuousLinearMap.le_opNorm_enorm, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, Finsupp.Lex.lt_iff_of_unique, DirectSum.lequivProdDirectSum_symm_apply, RingHom.coe_rangeS, MeasureTheory.StronglyMeasurable.tendsto_approxBounded_of_norm_le, GaussianInt.normSq_div_sub_div_lt_one, Sum.Lex.toLex_mono, BialgEquiv.refl_apply, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, MonoidHom.coe_toAdditive_ker, CuspForm.smul_apply, Int.nonneg_iff_normalize_eq_self, AddMonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, MeasureTheory.SimpleFunc.extend_apply, RCLike.imCLM_apply, ZMod.stdAddChar_apply, PiLp.nndist_eq_of_L2, LinearMap.toMatrixAlgEquiv_transpose_apply', TensorProduct.dualDistribEquivOfBasis_apply_apply, CategoryTheory.Cat.Hom.equivFunctor_symm_apply, RootPairing.root_reflectionPerm, Polynomial.opRingEquiv_symm_X, RingQuot.mkRingHom_rel, AddMonoidHom.map_finsum_of_preimage_zero, Polynomial.mkDerivation_apply, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, MeasureTheory.measureReal_restrict_apply₀', AlgebraicGeometry.Scheme.homOfLE_apply, MonoidAlgebra.curryAlgEquiv_single, MeasureTheory.Measure.infinitePi_pi_of_countable, MeasureTheory.IsFiniteMeasure.measure_univ_lt_top, RelIso.eq_symm_apply, cfcHom_apply_mem_elemental, LinearMap.baseChangeHom_apply, MeasureTheory.eLpNorm_le_of_ae_bound, Module.Relations.Solution.π_single, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, MeasureTheory.AddContent.extend_eq_extend, AddSubmonoid.LocalizationMap.top_injective_iff, Projectivization.Subspace.mem_submodule_iff, Module.Basis.finTwoProd_one, ContinuousLinearEquiv.piFinTwo_symm_apply, ProbabilityTheory.Kernel.swap_apply', GroupSeminorm.sup_apply, Finsupp.lmapDomain_apply, Homeomorph.sumEmpty_apply, MeasureTheory.SimpleFunc.restrict_preimage_singleton, Polynomial.coeff_monomial_mul, LocallyConstant.coe_continuousMap, linearIndepOn_iff_linearCombinationOnₛ, GroupSeminorm.coe_lt_coe, LinearMap.toMatrixRight'_comp, DomAddAct.comap_mk_nhds, WeakDual.eval_continuous, RingHom.equivRatAlgHom_symm_apply, Function.Embedding.left_inv_of_invOfMemRange, NucleusClass.le_apply, WeierstrassCurve.Jacobian.baseChange_negAddY, OrthonormalBasis.tensorProduct_repr_tmul_apply, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, SMulZeroClass.toZeroHom_apply, LinearEquiv.ofLinear_apply, Trivialization.coordChangeL_apply', ContinuousLinearEquiv.coe_refl', Derivation.evalAt_apply, ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone, IsometryEquiv.surjective, MeasureTheory.measure_preimage_add, WithTop.coe_toDualBotEquiv, LinearMap.isOrtho_def, MeasurableEquiv.map_symm, IntermediateField.coe_map, LieDerivation.sub_apply, AddChar.coe_mk, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap, TwoSidedIdeal.coe_asIdeal, DirectSum.Gmodule.smul_def, GradedRing.proj_apply, latticeClosure_min, LocallyConstant.indicator_of_mem, SemimoduleCat.forget₂_map, RingHom.map_frobeniusEquiv_symm, Equiv.Set.sumCompl_symm_apply_of_notMem, MeasureTheory.Measure.IsCondKernel.apply_of_ne_zero, WithLp.coe_symm_addEquiv, Function.instCanLiftForallEmbeddingCoeInjective, AddMonoidHom.coe_mrangeRestrict, TrivSqZeroExt.snd_expSeries_of_smul_comm, Finsupp.DegLex.single_strictAnti, finSuccEquivLast_symm_some, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, PositiveLinearMap.preGNS_norm_sq, Equiv.Perm.set_support_symm_eq, RCLike.conj_neg_I, WithBot.bot_mem_insertBot, Matrix.kroneckerStarAlgEquiv_symm_apply, MeasureTheory.lintegral_one, ConvexOn.univ_sSup_of_nat_affine_eq, CommSemiring.comul_apply, Finsupp.instCanLift, CompactlySupportedContinuousMap.coe_sum, AddChar.expect_eq_ite, Algebra.Generators.H1Cotangent.δ_map, RootPairing.Equiv.indexEquiv_inv, IsLocalization.Away.algebraMap_isUnit, HahnSeries.SummableFamily.finite_co_support, MvPolynomial.mapEquivMonic_symm_map, Module.dualProdDualEquivDual_symm_apply, AddGroupExtension.rightHom_surjective, Equiv.toFun_inducedStructureEquiv_Symm, IsCoveringMapOn.homeomorph_comp, toColex_smul', Ordinal.toNatOrdinal_max, modularCyclotomicCharacter.toFun_spec'', ModuleCat.restrictScalarsComp'App_inv_apply, ContinuousLinearEquiv.comp_right_differentiable_iff, MeasureTheory.measure_preimage_fst_singleton_eq_sum, RestrictedProduct.pow_apply, WithBot.Icc_bot_coe, OrderHom.partBind_coe, AffineMap.lineMap_vadd_lineMap, AlgebraicGeometry.IsAffineOpen.fromSpec_primeIdealOf, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, AddGrpCat.ofHom_apply, Finset.map_some_eraseNone, CategoryTheory.ShortComplex.ShortExact.ab_exact_iff_function_exact, Quaternion.norm_toLp_equivTuple, QuotientAddGroup.mk'_apply, Equiv.boolProdNatEquivNat_apply, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_symm_apply, LinearMap.uncurryLeft_apply, convexHull_range_eq_exists_affineCombination, MvPolynomial.IsHomogeneous.pderiv, DomAddAct.symm_mk_zero, LieIdeal.inclusion_apply, Polynomial.IsRoot.map, ProbabilityTheory.Kernel.indepSets_singleton_iff, InnerProductGeometry.ConformalAt.preserves_angle, MeasureTheory.SimpleFunc.finMeasSupp_iff_support, Set.Definable.image_comp_equiv, DomMulAct.mk_smul_mk_aeeqFun, LinearMap.trace_map, Localization.AtPrime.mapPiEvalRingHom_algebraMap_apply, ContinuousAlternatingMap.ratio_le_opNorm, WithLp.equiv_symm_apply_ofLp, convexIndependent_iff_notMem_convexHull_diff, mem_map_indicator_ae_iff_of_zero_notMem, MeasureTheory.SimpleFunc.lintegral_eq_lintegral, MeasureTheory.measurePreserving_sumPiEquivProdPi, Homeomorph.isOpenMap, DegLex.exists_iff, TopCat.pullback_snd_image_fst_preimage, AdicCompletion.of_apply, AffineIsometry.dist_map, MeasureTheory.Subgroup.index_mul_measure, Ordinal.relIso_enum, TensorProduct.assocIsometry_symm_apply, Submonoid.LocalizationMap.sec_zero_fst, SupBotHom.coe_mk, Submodule.starProjection_tendsto_closure_iSup, IsLocalization.smul_toInvSubmonoid, WittVector.ghostComponentModPPow_map_mk, Matrix.trace_fin_two_of, toBoolAlg_mul, LieSubmodule.mem_map, SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_one, LaurentSeries.valuation_X_pow, MeasureTheory.ae_le_set, OrderAddMonoidIso.eq_symm_apply, Stonean.effectiveEpi_tfae, equivShrink_symm_smul, LaurentPolynomial.degree_C_le, MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc, ClosureOperator.closure_isGLB, OrderHom.map_gfp_comp, InnerProductSpace.Core.inner_conj_symm, AffineMap.coe_prod, InfTopHom.coe_toTopHom, SSet.stdSimplex.face_singleton_compl, Equiv.subLeft_involutive, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, ProbabilityTheory.ofReal_cdf, char_dvd_card_solutions_of_fintype_sum_lt, Matrix.compAddEquiv_symm_apply, Nimber.toOrdinal_eq_zero, OrderIso.mulLeft_apply, domain_mvt, CliffordAlgebra.reverse_ι, Profinite.NobelingProof.factors_prod_eq_basis_of_eq, isConjRoot_iff_eq_algebraMap', AddSubmonoid.leftNegEquiv_symm_eq_neg, groupCohomology.coboundaries₁.coe_mk, HasCompactSupport.toSchwartzMap_toFun, IsCyclotomicExtension.autEquivPow_symm_apply, Fintype.finsetEquivSet_symm_apply, MeasureTheory.Lp.toTemperedDistribution_smul_eq, RingHom.closure_preimage_le, Fin.consLinearEquiv_symm_apply, Equiv.Perm.extendDomainHom_injective, AddHom.coe_srange, Fin.snocEquiv_symm_apply, MeasureTheory.iInf_mul_le_setLIntegral, DFinsupp.extendWith_none, CliffordAlgebra.reverse_involutive, quadraticChar_one_iff_isSquare, Submodule.reflection_mem_subspace_orthogonalComplement_eq_neg, NormedSpace.dual_def, MulAlgebraNorm.extends_norm, ContinuousMap.coe_IccExtend, Finset.sigmaAntidiagonalEquivProd_apply, Finset.coe_singletonZeroHom, Nat.equivProdNatSmoothNumbers_apply, HasFDerivAtFilter.hasDerivAtFilter, normalize_eq_normalize_iff_associated, Finsupp.domLCongr_single, AffineIsometryEquiv.coeFn_injective, NumberField.house_eq_sup', CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_symm_apply, TensorProduct.inner_map_map, FirstOrder.Language.Formula.realize_equivSentence_symm, Orientation.measure_orthonormalBasis, SlashInvariantForm.coe_intCast, RCLike.geometric_hahn_banach_open_open, PresentedMonoid.ext_iff, MeasureTheory.measure_sigmaFiniteSetGE_ge, Equiv.ofPreimageEquiv_symm_apply, WithBot.map_toDual, SpecialLinearGroup.toLinearEquiv_to_linearMap, ContinuousAlternatingMap.ofSubsingleton_symm_apply_apply, ProbabilityTheory.Kernel.coe_comap, TopologicalSpace.Opens.val_apply, Pi.toLex_strictMono, equivShrink_bot, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, HomologicalComplex.Hom.fAddMonoidHom_apply, FirstOrder.Language.Formula.realize_equivSentence, ContinuousMap.edist_eq_iSup, Fin.castAddOrderEmb_apply, LinearMap.lTensor_tmul, Topology.WithGeneratedByTopology.isClosed_iff, groupHomology.mem_cycles₁_iff, AlgebraicGeometry.LocallyRingedSpace.iso_hom_base_inv_base_apply, Equiv.pointReflection_vsub_left, quadraticChar_exists_neg_one, GaussianInt.intCast_complex_norm, OrderEmbedding.ofIsEmpty_apply, RCLike.lipschitzWith_im, Polynomial.residueFieldMapCAlgEquiv_symm_C, Ordinal.toGame_natCast, Minimal.dual, fderiv_norm_sq, Int.padicValuation_eq_zero_iff, Nat.factorization_eq_of_coprime_left, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, LaurentSeries.hasseDeriv_single, LinearMap.applyₗ_apply_apply, RingHom.injective_int, PolynomialLaw.exists_lift_of_mem_range_rTensor, WithZero.unitsWithZeroEquiv_apply, SimpleGraph.boxProdLeft_apply, Topology.IsGeneratedBy.continuous_iff, finSuccEquiv'_last_apply_castSucc, LinearMap.IsAlt.neg, CategoryTheory.GrothendieckTopology.Cover.coe_pullback, FreeGroup.map_eq_lift, CompHausLike.coe_comp, MeasureTheory.addEquivAddHaarChar_smul_integral_map, MeasureTheory.Measure.toSphere_apply_univ', AlgEquiv.algHomUnitsEquiv_apply_apply, RingHom.coe_range, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, LightProfinite.isClosedEmbedding_natUnionInftyEmbedding, GaussianInt.intCast_re, Homeomorph.isQuotientMap, CompHausLike.finiteCoproduct.ι_jointly_surjective, Algebra.SubmersivePresentation.basisDeriv_apply, NonUnitalStarSubalgebra.coe_comap, MvPolynomial.bind₁_monomial, IsOpen.measure_eq_zero_iff, Lagrange.interpolate_singleton, MonoidHom.mul_apply, StrictAntiOn.dual_right, AlgebraicGeometry.Scheme.fromSpecResidueField_apply, HeytingHom.id_apply, MeasureTheory.OuterMeasure.map_mono, WithAbs.equivWithAbs_symm_equiv_symm_apply, Complex.coe_reAddGroupHom, Fin.coe_succOrderEmb, LieModule.Weight.coe_neg, OneHom.toFun_eq_coe, Matrix.toBilin_comp, Polynomial.C_content_dvd, ProbabilityTheory.Kernel.map_apply_eq_iff_map_symm_apply_eq, AlternatingMap.curryLeft_same, Cardinal.toENat_congr, NonemptyInterval.toLex_le_toLex, SkewMonoidAlgebra.singleAddHom_apply, FreeGroup.lift_of_apply, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, IsCusp.smul, OrderMonoidWithZeroHom.mul_apply, IsLocalization.mk'_spec, exists_orderEmbedding_covby_of_forall_covby_finite_of_bot, TensorProduct.coe_finsuppScalarRight', Complex.equivRealProdCLM_apply, CliffordAlgebra.changeForm_changeForm, map_inv_intCast_smul, Finset.sigmaAntidiagonalEquivProd_symm_apply_fst, CategoryTheory.discreteSieve_mem, Con.comap_rel, Multiplicative.ofAdd_image_nsmul, CategoryTheory.Pseudofunctor.StrongTrans.Modification.equivOplax_symm_apply, WithZero.mapAddHom_mapAddHom, cyclotomicCharacter.toFun_spec, Ordinal.toPGameEmbedding_apply, NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart, AddMonoidHom.coe_fst, LinearMap.polyCharpoly_coeff_eval, NumberField.FinitePlace.norm_def, finSumNatEquiv_apply_right, Subgroup.IsComplement.quotientGroupMk_leftQuotientEquiv, mulLeft_bound, Function.Involutive.coe_toPerm, ContinuousLinearEquiv.coe_symm_toLinearEquiv, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, ContinuousLinearMap.coe_mulₗᵢ, Rat.ringOfIntegersWithValEquiv_apply, Finset.Colex.ofColex_bot, MeasureTheory.tsum_meas_le_meas_iUnion_of_disjoint₀, CategoryTheory.PreGaloisCategory.autGaloisSystem_map_surjective, commute_rmul_rmul_sq, MonoidHom.coe_prod, Nucleus.bot_apply, OrderIso.addLeft_apply, ProbabilityTheory.Kernel.integral_deterministic, LieModuleHom.map_lie₂, MeasureTheory.charFun_eq_integral_probChar, lineMap_lt_lineMap_iff_of_lt, OrthogonalFamily.inner_right_dfinsupp, PiLp.sumPiLpEquivProdLpPiLp_apply_ofLp, AddSubmonoid.equivOp_symm_apply_coe, DirectSum.linearEquivFunOnFintype_symm_coe, RingCon.coe_quotientKerEquivRangeₐ_mkₐ, FreeAddMonoid.hom_eq_iff, CategoryTheory.Equivalence.inducedFunctorOfEquiv, Units.map_neg_one, RestrictedProduct.mul_apply, MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto, PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijective, InitialSeg.eq, isOpenMap_toDual, LinearMap.BilinForm.apply_smul_sub_smul_sub_eq, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, Sym2.lift_map_apply, Ordinal.le_omega_self, AdjoinRoot.ringHom_ext_iff, lsum_comp_mapRange_toSpanSingleton, SpecialLinearGroup.centerEquivRootsOfUnity_apply_of_finrank_le_one, AddGroupSeminorm.coe_sup, ContinuousLinearMap.isUnit_iff_bijective, MulEquiv.map_finprod_mem, NumberField.mixedEmbedding.convexBodySum_mem, AddMonoidHom.coe_finsuppSum, iterateFrobeniusEquiv_zero_apply, Matrix.SpecialLinearGroup.toGL_inj, MvPolynomial.degreeOf_lt_iff, map_smul, MeasureTheory.OuterMeasure.restrict_le_self, HahnSeries.SummableFamily.coe_ofFinsupp, Polynomial.coeff_X_add_C_pow, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', MeasureTheory.OuterMeasure.smul_apply, FirstOrder.Language.DirectLimit.le_partialEquivLimit, MeasureTheory.MeasurePreserving.measure_preimage, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, MDifferentiableOn.clm_bundle_apply₂, ClassGroup.equiv_mk, ofLex_zero, PowerSeries.X_eq_normalizeX, Finsupp.sum_of_support_subset, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two, SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left, FirstOrder.Language.Embedding.equivRange_apply, Module.Basis.repr_unop_eq_mulOpposite_repr, IsAdicComplete.StrictMono.mk_lift, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, Multiset.toDFinsupp_inj, Function.locallyFinsuppWithin.lt_def, Seminorm.sSup_apply, AddSubgroup.IsComplement.leftQuotientEquiv_apply, LocallyConstant.toContinuousMapAlgHom_apply, ArchimedeanClass.FiniteElement.ext_iff, Diffeomorph.coe_toHomeomorph_symm, StandardEtalePresentation.equivRing_symm_X, MeasureTheory.condExpL1_eq, DirectSum.linearEquivFunOnFintype_apply, RootPairing.algebraMap_root'In_apply, Quaternion.normSq_coe, MeasureTheory.Content.measure_apply, Representation.trivial_apply, MeasurableEquiv.coe_curry, MonoidAlgebra.of_apply, Cardinal.aleph_zero, val_addUnitsCenterToCenterAddUnits_apply_coe, Trunc.finChoiceEquiv_apply, Ideal.kerLiftAlg_mk, groupHomology.boundariesToCycles₁_apply, Polynomial.degree_linear_lt, MonoidWithZeroHom.inl_apply_unit, Ideal.relNorm_comap_algEquiv, groupHomology.single_mem_cycles₂_iff_inv, ProbabilityTheory.Kernel.iIndepSets.ae_isProbabilityMeasure, MulEquiv.symmEquiv_apply_symm_apply, EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi', ModularGroup.smul_eq_lcRow0_add, SimplexCategory.toTopObj_zero_apply_zero, Matrix.compAddEquiv_apply, MultilinearMap.ofSubsingletonₗ_symm_apply, MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ball, groupHomology.d₁₀_single, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, PreTilt.coeff_iterate_frobenius', OrderRingIso.coe_toOrderIso, Cardinal.toNat_eq_ofNat, OrthogonalFamily.projection_directSum_coeAddHom, AddOpposite.opHomeomorph_symm_apply, LinearMap.det_toMatrix_eq_det_toMatrix, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply, ContinuousAlternatingMap.toMultilinearAddHom_apply, Additive.mem_toAddSubgroup, HasFDerivWithinAt.continuousAlternatingMap_apply_const, Algebra.TensorProduct.mul_apply, sSupHom.coe_comp, MeasureTheory.Measure.infinitePi_map_curry, UniversalEnvelopingAlgebra.lift_ι_apply', CategoryTheory.shrinkYonedaEquiv_symm_map, ContinuousLinearMap.innerSL_apply_comp, MeasureTheory.Lp.compMeasurePreserving_val, Real.cast_natAbs_eq_nnabs_cast, conformalAt_iff', uniformContinuous_toAdd, TensorProduct.lidIsometry_symm_apply, NonUnitalStarAlgHom.zero_apply, Cardinal.one_toNat, LinearEquiv.coe_addEquiv_apply, Algebra.TensorProduct.linearEquivIncludeRange_tmul, normalize_associated_iff, Matrix.SpecialLinearGroup.toLin'_apply, CategoryTheory.Sieve.overEquiv_iff, PerfectRing.lift_aux, SemistandardYoungTableau.row_weak, AbstractCompletion.uniformContinuous_compareEquiv_symm, AddValuation.ext_iff, ConjAct.smul_eq_mulAut_conj, Lat.coe_comp, PowerSeries.order_monomial_of_ne_zero, ContinuousLinearMap.mdifferentiableAt, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, addMonoidEndToMultiplicative_symm_apply_apply, MatrixModCat.fromMatrixLinear_apply_coe, Submonoid.subtype_apply, Valuation.one_rel_iff, MulArchimedeanClass.orderHom_top, ContinuousLinearEquiv.coe_funUnique, MvPolynomial.continuous_eval, Matrix.GeneralLinearGroup.toLin_apply, PowerSeries.trunc_C_mul, ProbabilityTheory.Kernel.comp_null, Equiv.toIso_inv, MeasureTheory.tilted_apply', LieIdeal.mem_map, CompactExhaustion.toFun_eq_coe, Valuation.le_one_of_subsingleton, PadicInt.lift_self, Polynomial.X_eq_normalize, Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U, SymAlg.unsym_one, ContinuousLinearMap.toSesqForm_apply_norm_le, IsLinearSet.image, HahnSeries.order_single, WithOne.lift_unique, DirichletCharacter.FactorsThrough.eq_changeLevel, MonoidWithZeroHom.snd_surjective, RingAut.coe_pow, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, Filter.comap_equiv_symm, RingHom.FaithfullyFlat.codescendsAlong_bijective, TannakaDuality.FiniteGroup.equivHom_apply, MeasureTheory.OuterMeasureClass.measure_mono, TensorProduct.AlgebraTensorModule.congr_tmul, MvPolynomial.C_eq_smul_one, Submonoid.closure_eq_mrange, Monoid.PushoutI.NormalWord.cons_toList, MonoidHom.ext_int_iff, CategoryTheory.map_coyonedaEquiv, CategoryTheory.Adjunction.homEquiv_symm_apply, Polynomial.coeffList_monomial, AddEquiv.toMultiplicativeLeft_apply_apply, AlgebraicGeometry.Scheme.Hom.coe_opensRange, MeasureTheory.IsFundamentalDomain.projection_respects_measure_apply, ContinuousLinearMap.coeFn_holder, OrderEmbedding.birkhoffFinset_sup, Part.Fix.approx_mono, NNRat.castOrderEmbedding_apply, ContinuousAddMonoidHom.swap_toFun, Subsemigroup.centerCongr_apply_coe, QuadraticAlgebra.coe_dvd_iff, sInfHom.top_apply, addUnitsCenterToCenterAddUnits_injective, RingQuot.eq_liftAlgHom_comp_mkAlgHom, MvPowerSeries.coeff_mul, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow, Finsupp.lsingle_apply, lineMap_mono_right, NonUnitalRingHom.coe_fst, MeasureTheory.Measure.haarMeasure_eq_iff, MvPolynomial.vars_monomial_single, Submodule.piQuotientLift_mk, QuadraticMap.polarBilin_apply_apply, Path.Homotopic.concat_subpath, FractionalIdeal.extendedHomₐ_le_one_iff, CoalgHom.one_apply, Subalgebra.opEquiv_apply, LinearMap.extendScalarsOfIsLocalization_apply', Algebra.lsmul_coe, SchwartzMap.isBigO_cocompact_rpow, MvPolynomial.evalₗ_apply, CategoryTheory.Functor.Initial.limitConeOfComp_isLimit, GradedRing.proj_recompose, NonUnitalStarSubalgebra.inclusion_inclusion, LinearMap.toKerIsLocalized_apply_coe, Representation.self_norm_apply, AddEquiv.op_apply_symm_apply, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', Equiv.Perm.decomposeFin_symm_apply_zero, ContinuousLinearMap.map_smul, CStarMatrix.norm_def, ContinuousAlternatingMap.norm_image_sub_le, ContinuousAlternatingMap.smulRight_apply, OrderDual.toDual_ofDual, ContinuousOn.eval, LocallyConstant.congrLeft_apply, MultilinearMap.ofSubsingleton_apply_apply, AlgHom.IsArithFrobAt.restrict_apply, DirectSum.zero_apply, ContinuousOrderHom.ext_iff, Homeomorph.coinduced_eq, Homeomorph.coe_addRight, InfHom.coe_top, Ideal.pi_quotient_surjective, AlgebraicGeometry.Scheme.stalkMap_congr, IsGalois.mem_bot_iff_fixed, ContinuousLinearMap.coe_deriv₂, MeasurableEquiv.coe_mulRight₀, AffineIsometry.continuous, MeasureTheory.eLpNorm_indicator_const, IsMIntegralCurveAt.eventually_hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, toDegLex_add, LinearMap.submoduleMap_surjective, IsAlgClosed.exists_aeval_eq_zero, LieRinehartAlgebra.Hom.apply_lie, SimpleGraph.Iso.map_apply, RestrictScalars.smul_def, Fin.orderIsoPair_one, SimpleGraph.boxProdComm_apply, MeasureTheory.Lp.norm_compMeasurePreserving, OrderIso.ext_iff, Cardinal.continuum_toNat, AlgebraicGeometry.Spec.homEquiv_symm_apply, Homeomorph.coe_punitProd, SimpleGraph.Iso.comap_symm_apply, ModuleCat.ihom_ev_app, MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty, ContMDiffOn.clm_bundle_apply₂, Finsupp.Colex.single_strictMono, LinearMap.mapMatrixModule_comp_apply, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, UniformConvergenceCLM.ext_iff, Polynomial.expand_injective, LinearMap.adjoint_id, NonarchimedeanHomClass.map_add_le_max, PolynomialLaw.isCompat', MultilinearMap.alternatization_def, RingHom.coe_rangeRestrict, inner_smul_left, Pi.partialSups_apply, WithTop.toDualBotEquiv_top, dist_lineMap_lineMap, MeasureTheory.withDensity_apply, MonoidHom.mem_mrange, AffineIsometryEquiv.coe_mul, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, MeasureTheory.Measure.ext_prod_iff, Polynomial.coeff_det_X_add_C_zero, MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, Module.Relations.Solution.IsPresentation.π_desc_apply, iterateFrobenius_mul_apply, LinearIsometryEquiv.withLpProdAssoc_symm_apply, OrderRingIso.coe_toRingEquiv, MultilinearMap.currySumEquiv_symm_apply, DyckWord.equivTree_apply, Polynomial.derivative_C_mul_X_sq, ContinuousAt.eval_const, AffineMap.homothety_mul_apply, MvPolynomial.esymmAlgHom_surjective, LieModule.Weight.hasEigenvalueAt, integral_im, LinearMap.BilinForm.add_apply, ContinuousWithinAt.clm_bundle_apply, PowerSeries.WithPiTopology.summable_iff_summable_coeff, ContinuousAddEquiv.coe_trans, extDeriv_apply, AddConstMap.coe_one, ModularForm.constℝ_toFun, Polynomial.content_monomial, mfderiv_prod_eq_add_apply, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, Finsupp.mem_pi, AddCon.refl, SetTheory.PGame.toRightMovesNim_symm_lt, DomMulAct.mk_smul_addMonoidHom_apply, Monoid.Coprod.swap_inj, SymAlg.mul_def, AffineMap.lineMap_vsub_lineMap, isRegular_ofColex, Subring.addEquivOp_symm_apply_coe, MvPolynomial.aevalTower_ofNat, exteriorPower.basis_repr_self, TensorProduct.finsuppLeft'_apply, hausdorffMeasure_of_lt_dimH, QuaternionAlgebra.coe_symm_addEquivTuple, ValuationSubring.principalUnitGroup_symm_apply, MeasureTheory.condExpL2_indicator_nonneg, CategoryTheory.map_yonedaEquiv', Lagrange.nodal_eq, OrderIso.map_atTop, MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant', NormedAddGroupHom.norm_incl, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, OrderHom.const_comp, DFinsupp.sigmaFinsetFunEquiv_apply_fst, AbsoluteValue.exists_lt_one_one_le_of_not_isEquiv, ContinuousLinearMap.adjoint_adjoint, Module.DirectLimit.exists_of₂, Path.eqOn_extend_segment, Pi.toColex_update_lt_self_iff, StarRingEquiv.ext_iff, ProbabilityTheory.Kernel.swapLeft_apply, Coalgebra.Repr.induced_left, MeasureTheory.MeasurableEquiv.measurePreserving_symm, AddHom.map_multiset_ne_zero_sum, RootPairing.EmbeddedG2.mem_allRoots, nhds_toMul, Polynomial.derivativeFinsupp_C, AffineIsometryEquiv.coe_toAffineIsometry, AddChar.coe_toMonoidHomEquiv_symm, MeasurableEquiv.coe_toLp_symm, AddHom.map_add, Submodule.flip_quotDualCoannihilatorToDual_injective, Seminorm.cont_normedSpace_to_withSeminorms, GradedTensorProduct.of_symm_one, PointedCone.coe_comap, LinearMap.lflip_apply, Subgroup.hasDetPlusMinusOne_iff_abs_det, Submodule.coe_prodEquivOfClosedCompl_symm, WithZero.withZeroUnitsEquiv_strictMono, ProbabilityTheory.Kernel.fst_compProd_apply, HahnSeries.coeff_single_mul, SkewMonoidAlgebra.liftNC_smul, groupCohomology.cocycles₁.d₁₂_apply, frobeniusEquiv_symm_apply_frobenius, AddEquiv.comapAddSubgroup_symm_apply, LinearIsometryEquiv.coe_prodAssoc, Polynomial.card_support_trinomial, Submonoid.LocalizationMap.eq_iff_eq, SimpleGraph.Walk.toSubgraph_map, Bundle.ContinuousRiemannianMetric.isVonNBounded, TensorProduct.lift.equiv_apply, hahnEmbedding_isOrderedAddMonoid, IsSublattice.preimage, Valuation.HasExtension.algebraMap_injective, IsBaseChange.linearMapLeftRightHom_comp, TensorProduct.finsuppRight_tmul_single, MvPolynomial.monomial_modMonomial, Algebra.Extension.cotangentComplex_mk, ULift.algebraMap_eq, AddActionHom.coe_vadd, Submodule.mulRightMap_apply_single, PseudoEpimorphism.toOrderHom_eq_coe, AddMonoidAlgebra.mapDomainRingHom_apply, PartitionOfUnity.sum_finsupport, ContinuousLinearMap.comp_toSpanSingleton, LinearMap.prodMapRingHom_apply, HasStrictDerivAt.clm_apply, Matroid.toENat_cRk_eq, Rep.indResHomEquiv_symm_apply_hom, Polynomial.taylor_one, AddEquiv.punitCoprod_apply, CategoryTheory.GrothendieckTopology.covering_of_eq_top, TemperedDistribution.smulLeftCLM_apply_apply, X_pow_sub_C_irreducible_iff_of_prime, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, MonoidHom.toMulEquiv_apply, AlgebraicGeometry.Scheme.Hom.stalkMap_congr_hom, MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp_eLpNorm, Matrix.SpecialLinearGroup.mem_center_iff, Poly.sub_apply, CircleDeg1Lift.semiconjBy_iff_semiconj, RingHom.surjective_localRingHom_iff, AlgHom.coe_pow, CompleteOrthogonalIdempotents.bijective_pi, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, OpenPartialHomeomorph.toHomeomorphSourceTarget_symm_apply_coe, BoundedContinuousFunction.lintegral_le_edist_mul, toDual_one, FreeAddGroup.range_lift_eq_closure, Finset.Iio_ofDual, CategoryTheory.GrothendieckTopology.OneHypercover.mem₁, ModelWithCorners.toHomeomorph_symm_apply, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal, Multiplicative.toAdd_top, LieModuleEquiv.one_apply, Filter.pureZeroHom_apply, FirstOrder.Language.DirectLimit.rangeLiftInclusion, ContinuousMulEquiv.comp_symm_eq, DFinsupp.Lex.lt_iff, ClassGroup.exists_mem_finset_approx', IsScalarTower.toAlgHom_apply, MeasureTheory.Measure.InnerRegularWRT.measurableSet_of_isOpen, IsometryEquiv.preimage_eball, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, IsSymmSndFDerivWithinAt.iteratedFDerivWithin_cons, BoundedContinuousFunction.coe_compContinuous, QuadraticForm.dualProdProdIsometry_invFun, CategoryTheory.PreGaloisCategory.toAut_continuous, LinearMap.SeparatingLeft.congr, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, ContinuousAddEquiv.apply_symm_apply, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, MvPolynomial.esymmAlgEquiv_symm_apply, SimpleGraph.Iso.sumComm_symm_apply, Pi.basisFun_det_apply, CompleteLatticeHom.id_apply, RootPairing.Equiv.toEndUnit_val, nndist_lineMap_left, OrderRingIso.toFun_eq_coe, GroupSeminormClass.toSeminormedCommGroup_norm_eq, MulSemiringActionHom.map_add, Finsupp.card_support_eq_one, RCLike.im_le_norm, Submodule.fstEquiv_apply, AdjoinRoot.mk_C, Matrix.Nondegenerate.toLinearMap₂', Shrink.algEquiv_symm_apply, ModuleCat.FilteredColimits.colimit_add_mk_eq, Subrepresentation.submoduleSubrepresentationOrderIso_symm_apply, LinearIsometryEquiv.preimage_sphere, Polynomial.map_iterateFrobenius_expand, Polynomial.derivativeFinsupp_X, Int.divModEquiv_symm_apply, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto, ContinuousMap.isClopen_setOf_mapsTo, ContinuousMap.coeFnMonoidHom_apply, Tuple.monotone_sort, ModuleCat.free_hom_ext_iff, ProbabilityTheory.deterministic_comp_posterior, Function.Embedding.inl_apply, Finset.sum_smul_vsub_eq_weightedVSub_sub, NNReal.sq_sqrt, Polynomial.map_normalize, Orientation.inner_mul_areaForm_sub, Polynomial.roots_X_pow_char_pow_sub_C, Topology.WithLower.ofLower_toLower, toLex_neg, Order.coheight_toDual, IsInvariantSubring.coe_subtypeHom, AddSubgroup.coe_inclusion, fderiv_inner_apply, retractionOfSectionOfKerSqZero_tmul_D, finsuppLEquivDirectSum_symm_lof, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, AddCommGrpCat.toCommGrp_map, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, ZMod.χ₄_nat_eq_if_mod_four, FirstOrder.Language.BoundedFormula.IsExistential.realize_embedding, PMF.toMeasure_apply_fintype, ContinuousLinearMap.hasDerivAt_of_bilinear, IsHomeomorph.homeomorph_apply, ArithmeticFunction.carmichael_two_pow_of_ne_two, UniformFun.ofFun_mul, normalize_eq, IsometryEquiv.inv_apply, Ideal.IsHomogeneous.mem_iff, LinearEquiv.extendScalarsOfIsLocalization_apply, Finset.Ici_ofDual, ContinuousMap.HomotopyEquiv.refl_apply, Pi.lex_eq_finsupp_lex, MeasurableEquiv.piMeasurableEquivTProd_symm_apply, Trivialization.linearEquivAt_symm_apply, Sum.Lex.not_inr_lt_inl, OrderMonoidIso.ext_iff, isSelfAdjoint_map, MulEquiv.coe_prodComm, AffineIsometryEquiv.pointReflection_midpoint_right, DirectSum.IsInternal.subordinateOrthonormalBasisIndex_def, TwoSidedIdeal.comap_le_comap, Ordinal.toGame_le_iff, MeasureTheory.Measure.addHaar_closedBall', Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map_apply, RingHom.map_vecMul, Matrix.blockTriangular_reindex_iff, Units.embedProduct_apply, Abelianization.equivOfComm_symm_apply, CategoryTheory.Pretriangulated.preadditiveCoyoneda_homologySequenceδ_apply, Matrix.isUnit_comp_symm_iff, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, MonoidHom.mem_mgraph, Equiv.eq_symm_apply, ContinuousMonoidHom.isClosedEmbedding_coe, groupHomology.H2π_eq_zero_iff, MvPolynomial.rename_surjective, Finsupp.toMultiset_eq_iff, Finsupp.curryLinearEquiv_symm_apply, Finset.weightedVSubOfPoint_sdiff_sub, RingEquiv.prodCongr_symm_apply, CategoryTheory.PreGaloisCategory.autEmbedding_isClosedEmbedding, second_derivative_symmetric_of_eventually, KaehlerDifferential.linearCombination_surjective, CategoryTheory.Bicategory.mateEquiv_apply', nsmulCoprime_apply, Fin.accumulate_injective, IsometryEquiv.trans_apply, HasFDerivAt.comp_hasDerivAt_of_eq, UniformOnFun.lipschitzWith_one_ofFun_toFun', AddGroupExtension.Section.add_neg_add_add_mem_range_inl, NumberField.mixedEmbedding.norm_apply, IsLocalizedModule.map_lTensor, Equiv.setSubtypeComm_symm_apply, CategoryTheory.nerve.edgeMk_surjective, Finsupp.lsubtypeDomain_apply, RatFunc.ofFractionRing_algebraMap, IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow', LinearEquiv.coe_det, ArithmeticFunction.toFun_eq, AlgebraicGeometry.SheafedSpace.GlueData.ι_jointly_surjective, CommMonCat.hom_inv_apply, SmoothPartitionOfUnity.contMDiff_sum, MulMemClass.subtype_injective, NonUnitalAlgHom.snd_toFun, Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂, le_map_add_map_div, RatFunc.eval_algebraMap, LinearMap.mulLeft_toAddMonoidHom, HahnSeries.coeff_ofFinsuppLinearMap, SeparationQuotient.outCLM_injective, AddCircle.homeomorphAddCircle_symm_apply_mk, Module.Basis.sumQuot_repr_inr, MvPolynomial.map_id, SimpleGraph.Subgraph.coe_hom, LinearIsometryEquiv.coe_withLpUniqueProd, ContinuousLinearEquiv.ofSubmodules_apply, SemidirectProduct.monoidHomSubgroup_apply, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, Action.FintypeCat.toEndHom_trivial_of_mem, Module.Basis.coord_toDualEquiv_symm_apply, MeasureTheory.SimpleFunc.map_preimage_singleton, Cardinal.lift_preAleph, SkewMonoidAlgebra.coeff_erase_apply, Convex.combo_affine_apply, CFC.eq_algebraMap_of_spectrum_subset_singleton, DomAddAct.isInducing_mk_symm, IsCyclotomicExtension.autEquivPow_apply, ContinuousMultilinearMap.norm_ofSubsingleton_id, DeltaGeneratedSpace.continuous_iff, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, FreeAddMonoid.toList_nil, Ordinal.omega_eq_preOmega, unitInterval.volume_Iio, congr_arg, SimpleGraph.Subgraph.comap_adj, Set.opEquiv_symm_apply, Finsupp.linearCombination_onFinset, QuadraticAlgebra.algebraMap_im, RCLike.normSq_conj, Real.volume_interval, LinearIsometryEquiv.image_closedBall, CategoryTheory.Localization.SmallShiftedHom.postcompEquiv_apply, Finsupp.lsum_symm_apply, Module.Basis.baseChange_linearMap, IsCyclotomicExtension.discr_prime_pow, ZSpan.fundamentalDomain_ae_parallelepiped, Real.sinhHomeomorph_apply, QuaternionAlgebra.reₗ_apply, Polynomial.eval₂_algebraMap_X, GaussianInt.toComplex_div_im, ContinuousMap.dist_eq_iSup, Cardinal.lift_lt_aleph_one, SSet.skeletonOfMono_succ, MulEquiv.refl_apply, MvPowerSeries.coeff_add_monomial_mul, IsAdjoinRootMonic.coeff_root_pow, Cardinal.toENat_eq_one, Complex.equivRealProd_apply_le, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, OrthonormalBasis.inner_eq_ite, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', MeasureTheory.SignedMeasure.im_toComplexMeasure, CharacterModule.dual_injective_iff_surjective, ZeroHom.coe_add, algebraMap_comp_natCast, FreeSemigroup.map_of, ContinuousMap.coe_abs, Topology.WithLowerSet.toLowerSet_specializes_toLowerSet, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, QuotientAddGroup.equivIocMod_coe, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_apply, PMF.ofMultiset_apply, LinearMap.BilinForm.sub_right, AddMonoidAlgebra.mul_apply_antidiagonal, AlgebraicGeometry.PresheafedSpace.stalkMap.congr_point, CategoryTheory.Bicategory.conjugateEquiv_comp, ContinuousLinearMap.orthogonal_ker, LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul, Fin.insertNth_apply_cycleRange_symm, RelEmbedding.trans_apply, ProbabilityTheory.iIndepSets_singleton_iff, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ProbabilityTheory.setLIntegral_toKernel_Iic, OrderIso.isCompl_iff, MeasureTheory.MemLp.exists_eLpNorm_indicator_compl_lt, Module.Basis.coord_repr_symm, TensorProduct.toDirectLimit_tmul_of, LinearMap.id'_apply, ContinuousLinearMap.HasLeftInverse.injective, ContinuousMap.exists_extension', le_algebraMap_iff_spectrum_le, le_map_sub_add_map_sub, DirectSum.map_surjective, Module.Basis.groupSMul_apply, Complex.rotation, Composition.single_embedding, AddAut.inv_apply_self, MvPowerSeries.expand_C, Module.Relations.Solution.linearCombination_var_relation, Finset.max_abv_sum_one_le, Module.End.coe_one, MeasureTheory.compl_mem_ae_iff, ZMod.dft_apply_zero, isLeftRegular_toColex, Polynomial.toMvPolynomial_C, Finsupp.lcongr_apply_apply, MeasureTheory.ae_iff_prob_eq_one, Real.coe_sinOrderIso_apply, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, TopHom.dual_id, LinearMap.toMatrixAlgEquiv'_comp, CategoryTheory.Limits.Sigma.ι_reindex_inv_assoc, WittVector.mapFun.neg, Metric.exists_contMDiffMap_forall_closedEBall_subset, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, Diffeomorph.coe_toHomeomorph, RingHom.mem_eqLocus, Subalgebra.coe_inclusion, Ideal.Factors.piQuotientEquiv_map, ClassGroup.exists_mem_finsetApprox, CochainComplex.HomComplex_d_hom_apply, Algebra.TensorProduct.includeLeftRingHom_apply, WeierstrassCurve.Projective.map_dblX, GrpCat.coe_id, MonomialOrder.degree_sub_LTerm_le, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, RingEquiv.coe_refl, StarModule.decomposeProdAdjoint_apply, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm, StarAlgEquiv.isometry, AlgebraicGeometry.IsAffineOpen.appLE_eq_away_map, Rat.padicValuation_le_one_iff, BiheytingHomClass.map_himp, SupBotHom.coe_id, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, AffineMap.coe_homothety, MeasureTheory.OuterMeasure.mkMetric'.le_pre, SchwartzMap.norm_pow_mul_le_seminorm, HahnSeries.orderTop_single, OrderEmbedding.eq_iff_eq, contMDiff_circleExp, NonUnitalSubsemiring.topEquiv_symm_apply_coe, spectrum.notMem_iff, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_tmul, Nat.factorization_le_factorization_of_dvd_right, ContDiffMapSupportedInClass.map_zero_on_compl, algebraMap_star_comm, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, Polynomial.exists_mul_add_mul_eq_C_resultant, HahnSeries.leadingCoeff_abs, Valuation.one_apply_eq_one_iff, Matrix.charpoly_of_card_eq_two, CategoryTheory.Limits.Types.colimitEquivColimitType_apply, left_le_lineMap_iff_nonneg, Nat.ordCompl_of_not_prime, thickenedIndicator.coeFn_eq_comp, MonomialOrder.lex_le_iff_of_unique, Polynomial.eval_multiset_prod_X_sub_C_derivative, MulOpposite.opHomeomorph_apply, ContinuousAlternatingMap.le_of_opNNNorm_le, Polynomial.toFinsupp_C, SemidirectProduct.equivProd_symm_apply_right, MonomialOrder.sPolynomial_mul_monomial, lineMap_lt_left_iff_neg, Topology.WithUpperSet.isOpen_ofUpperSet_preimage, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_emultiplicity, Subgroup.relIndex_toAddSubgroup, LinearMap.toMatrix₂Aux_apply, CategoryTheory.Limits.kernelSubobjectMap_arrow_apply, HahnModule.single_zero_smul_eq_smul, GroupNormClass.toNormedCommGroup_norm_eq, ProbabilityTheory.Kernel.IsProper.lintegral_mul, DFinsupp.orderEmbeddingToFun_apply, Submodule.span_range_inclusionSpan, SubMulAction.conjMap_ofFixingSubgroup_coe_apply, BoundedContinuousFunction.probCharDual_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, Function.Embedding.swap_comp, AdjoinRoot.coe_ofAlgHom, SymAlg.unsym_inj, Equiv.sumCompl_symm_apply_of_pos, MeasureTheory.measure_union₀, AlgebraicGeometry.Scheme.Modules.map_smul, Nat.factorization_factorial_mul, Subsemigroup.coe_toAddSubsemigroup_apply, ArchimedeanClass.stdPart_eq_sSup, WithLp.fstₗ_apply, AlgebraicGeometry.RingedSpace.mem_basicOpen', Submodule.coe_iSup_of_chain, Unitization.algebraMap_eq_inl_comp, IsOpen.measure_pos_iff, OrderEmbedding.mulLeft_apply, IsMaxFilter.dual, LinearEquiv.skewProd_apply, Module.mapEvalEquiv_symm_apply, LieModule.rank_le_natTrailingDegree_charpoly_ad, InnerProductSpace.norm_rankOne, Delone.DeloneSet.mapIsometry_apply_carrier, SchwartzMap.tsum_eq_tsum_fourier, Submodule.surjOn_iff_le_map, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, RingEquiv.moduleEndSelfOp_symm_apply, RingHom.map_closure, Fin.accumulate_last, MulEquiv.val_inv_piUnits_symm_apply, ContinuousMapZero.range_toContinuousMap, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, Dilation.injective, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, Equiv.some_removeNone_iff, Submodule.unitsQuotEquivRelPic_apply_coe, RestrictScalars.addEquiv_map_smul, ModuleCat.MonoidalCategory.associator_inv_apply, CircleDeg1Lift.map_lt_of_translationNumber_lt_int, derivationQuotKerSq_mk, ArithmeticFunction.cardDistinctFactors_eq_cardFactors_iff_squarefree, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, AlgEquiv.congr_arg, Subspace.dualEquivDual_apply, LieSubalgebra.coe_ad, UniformConvergenceCLM.nhds_zero_eq_of_basis, LinearMap.BilinForm.iIsOrtho_def, Subfield.mem_comap, ContinuousMap.prod_eval, IsFractionRing.self_iff_bijective, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, MvPowerSeries.trunc'_C, ContMDiffMap.coeFnLinearMap_apply, MvPowerSeries.prod_monomial, OnePoint.equivProjectivization_apply_infinity, Multiset.coe_mapAddMonoidHom, MonoidHom.toHomUnitsMulEquiv_apply, AdjoinRoot.of.injective_of_degree_ne_zero, FirstOrder.Language.DirectLimit.dom_partialEquivLimit, Matrix.cramer_eq_adjugate_mulVec, Affine.Simplex.restrict_points_coe, RCLike.inv_re, TensorProduct.uncurry_apply, MonoidAlgebra.mul_single_apply_aux, Ideal.isoBaseOfIsPrincipal_apply, iterate_map_zsmul, GromovHausdorff.HD_below_aux1, MeasureTheory.Measure.piContent_eq_infinitePiNat, Function.Embedding.embFinTwo_apply_one, nhdsMulHom_apply, Multiplicative.ofAdd_top, ContinuousAffineMap.vadd_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, Antivary.sum_comp_perm_smul_eq_sum_smul_iff, LinearMap.BilinForm.apply_dualBasis_right, Polynomial.X_sub_C_pow_dvd_iff, Pi.mulHom_apply, AddSubgroupClass.coe_subtype, PiTensorProduct.mapLMultilinear_toFun_apply, FirstOrder.Language.StrongHomClass.toEquiv_toFun, IsLocalizedModule.eq_zero_iff, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, CategoryTheory.Functor.mapLinearMap_apply, LinearEquiv.prodUnique_apply, LaurentPolynomial.degree_C_mul_T_le, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors', ZLattice.abs_repr_le, CategoryTheory.Equivalence.essSurjInducedFunctor, IsAlgClosed.ringHom_bijective_of_isIntegral, isOpenMap_toMul, TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CStarMatrix.inner_toCLM_conjTranspose_right, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, SlashInvariantForm.T_zpow_width_invariant, NonUnitalRingHom.mem_eqLocus, PrincipalSeg.map_isMin, ContinuousMap.coe_sup, PrincipalSeg.image_Iio, MulEquiv.apply_symm_apply, MonCat.hom_inv_apply, DFinsupp.subtypeDomainAddMonoidHom_apply, GaussianInt.toComplex_eq_zero, measurable_piEquivPiSubtypeProd, QuadraticMap.add_apply, IsOrderRightAdjoint.orderIso_comp, AffineSubspace.mem_map_of_mem, LinearIsometryEquiv.map_smulₛₗ, ArithmeticFunction.moebius_apply_isPrimePow_not_prime, Derivation.map_intCast, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, BoundedLatticeHom.id_apply, AlgebraicGeometry.Scheme.mem_basicOpen, BialgEquiv.ofAlgEquiv_apply, Module.Dual.congr_symm_apply_apply, DirectSum.IsInternal.collectedBasis_repr_of_mem, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_apply, Module.Basis.coe_sumCoords, QuotientGroup.quotientMulEquivOfEq_mk, IsLocalizedModule.surj', Affine.Simplex.excenterExists_restrict, AddSubmonoid.centerToAddOpposite_apply_coe, Finsupp.equivFunOnFinite_symm_apply_apply, Matrix.det_smul_inv_vecMul_eq_cramer_transpose, iteratedDerivWithin_vcomp_three, CategoryTheory.yonedaGrp_naturality, Matrix.PosDef.re_dotProduct_pos, spinGroup.val_toUnits_apply, Algebra.Generators.Hom.equivAlgHom_apply_coe, QuadraticMap.congr_fun, AlgebraicGeometry.IsOpenImmersion.affineOpensEquiv_symm_apply_coe, CliffordAlgebra.even.lift.aux_one, Complex.normSq_one, RingHom.FaithfullyFlat.codescendsAlong_injective, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Equiv.Perm.sign_surjective, LieModule.Weight.toLinear_apply, CategoryTheory.Iso.commGroupIsoToMulEquiv_apply, Matroid.mapEmbedding_isLoop_iff, RingCat.forget_map, ZMod.χ₈_int_eq_if_mod_eight, MonoidHom.submonoidMap_surjective, Set.image_op_vadd_distrib, circleEquivGen_apply, MvPolynomial.decomposition.decompose'_eq, ContinuousLinearEquiv.piFinTwo_apply, Submodule.restrictScalarsEquiv_apply, ZLattice.covolume_eq_det, Equiv.Perm.commute_ofSubtype_noncommPiCoprod, coe_ofLexLinearEquiv, IsLocalizedModule.surj, Matrix.charmatrix_zero, InfTopHom.id_toFun, Algebra.Generators.C_mul_X_sub_one_mem_ker, NonUnitalRingHom.prod_apply, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, RootPairing.reflection_image_eq, StarMulEquiv.invFun_eq_symm, SetTheory.PGame.toLeftMovesNim_one_symm, MDifferentiableAt.clm_apply, UniformConvergenceCLM.neg_apply, equivShrink_sub, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, Subsemiring.coe_comap, AddAut.congr_symm_apply, DirectSum.coe_congrLinearEquiv, PointedCone.dual_singleton, RootPairing.Equiv.coweightEquiv_apply, map_zsmul, Equiv.listUniqueEquiv_symm_apply, InfIrred.ofDual, MulArchimedeanOrder.val_of, DirectSum.lequivProdDirectSum_apply, MultilinearMap.domDomCongr_apply, NumberField.mixedEmbedding.normAtPlace_real, isCyclic_tfae, ContinuousMap.HomotopyRel.eq_snd, ContinuousMultilinearMap.curryMidEquiv_symm_apply, Polynomial.roots_prod_X_sub_C, bernsteinApproximation.apply, ContDiffMapSupportedIn.coe_zero, ofDual_smul', HahnModule.of_symm_sub, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero_of_measurable, Polynomial.integralNormalization_eval₂_leadingCoeff_mul, PMF.ofFinset_apply_of_notMem, OneHom.div_apply, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Behrend.map_monotone, Finset.mem_insertNone, Fin.cycleRange_self, MvPowerSeries.prod_smul_X_eq_smul_monomial_one, Con.ext_iff, Finset.imageZeroHom_apply, PowerSeries.coeff_one_X, TensorPower.pairingDual_tprod_tprod, LinearMap.sum_repr_mul_repr_mul, CategoryTheory.ShiftedHom.opEquiv'_add_symm, uniformEquicontinuous_iff_uniformContinuous, FreeSemigroup.lift_of, fderiv_eq_smul_deriv, MonoidAlgebra.lift_of, FirstOrder.Language.Substructure.closure_image, MonomialOrder.sPolynomial_leadingTerm_mul, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap, unitary.inner_map_map, MulEquiv.toMonoidWithZeroHom_surjective, Valuation.IsEquiv.orderRingIso_symm_apply, CStarMatrix.toCLM_apply_single_apply, MultilinearMap.domDomCongrEquiv_apply, Set.Ico_ofDual, AbsConvex.absConvexHull_eq, bernsteinPolynomial.iterate_derivative_at_1, SimpleGraph.comap_monotone, Subgroup.opEquiv_apply, LinearMap.IsPositive.conj_adjoint, CategoryTheory.Functor.functorHomEquiv_symm_apply_app_app, injective_iff_map_eq_one, ContinuousLinearMap.flipAlternating_apply_apply, MonoidHom.coe_toMultiplicative_ker, lcm_one_right, nndist_ofDual, Nat.squarefree_iff_factorization_le_one, Monoid.Coprod.swap_inl, ZeroAtInftyContinuousMap.coe_star, LaurentPolynomial.invert_T, BoundingSieve.prod_primeFactors_nu, cfc_comp_polynomial, IsCoveringMap.homeomorph_comp, Fin.consLinearEquiv_apply, Finsupp.mem_supported', MonoidAlgebra.mapRangeRingHom_apply, LinearMap.ker_toContinuousLinearMap, TensorProduct.AlgebraTensorModule.lTensor_tmul, AddValuation.map_inv, WithBot.orderIsoPUnitSumLex_bot, mulRothNumber_singleton, isometry_cfcHom, Ordinal.sup_typein_succ, Equiv.piCongrLeft'_apply, Lagrange.nodalWeight_eq_eval_derivative_nodal, CliffordAlgebra.ι_mul_ι_mul_of_isOrtho, hasSum_iff_hasSum_compl, ProbabilityTheory.Kernel.prod_apply_prod, Finset.toDual_sup', Metric.Snowflaking.homeomorph_apply, Polynomial.derivative_intCast, FirstOrder.Language.Substructure.apply_coe_mem_map, ContinuousMap.Homotopy.curry_zero, MultilinearMap.coeAddMonoidHom_apply, ProbabilityTheory.Kernel.IsProper.inter_eq_indicator_mul, IsLocalizedModule.iso_mk_one, OmegaCompletePartialOrder.isLUB_range_ωSup, TopCat.prodIsoProd_inv_snd_apply, SSet.stdSimplex.isoNerve_inv_app_apply, AbsoluteValue.map_one, LinearIsometryEquiv.ediam_image, AddHom.map_mclosure, SemiRingCat.forget₂_addCommMonCat_map, CategoryTheory.colimitYonedaHomEquiv_π_apply, Equiv.pointReflection_apply, MulEquiv.withZero_symm_apply_symm_apply, MeasureTheory.measure_sUnion_null_iff, isLinearSet_iff_exists_fin_addMonoidHom, CategoryTheory.Equivalence.induced_counitIso, MvPolynomial.esymmAlgHom_injective, AddCon.coe_inf, Polynomial.C_smul_derivation_apply, AlgebraicGeometry.Scheme.Cover.mem_grothendieckTopology, Multiset.prod_hom', LinearMap.charpoly_toMatrix, MeasureTheory.Measure.iSup_restrict_spanningSets_of_measurableSet, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, Polynomial.leadingCoeff_taylor, MvPowerSeries.trunc'_C_mul, MeasureTheory.inducedOuterMeasure_eq_extend', Module.Basis.coe_ofSpan, MvPolynomial.commAlgEquiv_C_X, MvPolynomial.expand_zero_apply, LinearMap.toLinearMap₂'Aux_toMatrix₂Aux, LieModule.toEnd_pow_comp_lieHom, AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk_assoc, ContinuousAddEquiv.trans_apply, map_isSelfAdjoint, IsAddIndecomposable.baseOf_subset_pos, Polynomial.homogenize_monomial, UniformFun.isClosed_setOf_continuous, Set.powersetCard.ofFinEmbEquiv_apply, Polynomial.X_pow_mul_C, ContinuousSMul.induced, Fin.addNatOrderEmb_apply, AddChar.coe_toAddMonoidHomEquiv_symm, OrderIso.apply_bliminf, AdjoinRoot.evalEval_mk, MulAut.congr_symm_apply, Polynomial.derivative_add, Ordinal.enum_type, MeasureTheory.SimpleFunc.sum_range_measure_preimage_singleton, MeasureTheory.diracProba_toMeasure_apply_of_mem, AddSubgroup.equivOp_symm_apply_coe, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, Function.locallyFinsuppWithin.memAddSubgroup, Polynomial.expand_pow, Polynomial.degree_sub_C, BoundedContinuousFunction.isInducing_coeFn, DoubleCentralizer.toProdMulOppositeHom_apply, LinearMap.isSymm_iff_isHermitian_toMatrix, OrderDual.ofDual_top, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, Submodule.quotientQuotientEquivQuotientAux_mk_mk, SSet.Truncated.liftOfStrictSegal.spineEquiv_f₂_arrow_zero, OrderIso.map_minimal_mem, Fin.succAboveOrderEmb_apply, Function.locallyFinsuppWithin.toClosedBall_eval_within, coe_negAddMonoidHom, SkewMonoidAlgebra.support_erase, ContinuousLinearMap.coeFn_compLp', CompactExhaustion.mem_iff_find_le, BumpCovering.support_toPartitionOfUnity_subset, ContinuousOpenMapClass.map_open, OrderIso.dualDual_symm_apply, LinearIndepOn.quotient_iff_union, FractionalIdeal.coe_extended_eq_span, NonUnitalSubsemiring.topEquiv_apply, LinearMap.trace_lie, PowerBasis.liftEquiv_apply_coe, ModularForm.slash_apply, Module.Basis.ofIsLocalizedModule_repr_apply, LinearMap.withSeminorms_induced, AddMagmaCat.hom_neg_apply, AddGroupExtension.Splitting.rightInverse_rightHom, Multiset.prod_X_sub_C_coeff, supClosure_min, MeasureTheory.addContent_union_le, MeasureTheory.AEStronglyMeasurable.apply_continuousLinearMap, InitialSeg.isMin_apply_iff, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, IsLowerSet.image, sInfHom.coe_mk, ContinuousLinearMap.algebraMap_apply, IsAdjoinRootMonic.basis_one, Fin.range_natAdd_castLEEmb, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, ContinuousLinearMap.comp_apply, IsCyclotomicExtension.discr_prime_pow_ne_two', Seminorm.uniformity_eq_of_hasBasis, WeierstrassCurve.Projective.negDblY_of_Y_eq', DiscreteQuotient.map_proj, DoubleQuot.quotQuotEquivComm_algebraMap, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_lintegral_tendsto, Set.PartiallyWellOrderedOn.ProdLex_iff, LinearMap.lsmul_eq_distribSMultoLinearMap, DFinsupp.domLCongr_apply, QuadraticAlgebra.algebraMap_injective, Filter.coe_pureMonoidHom, MultilinearMap.map_add_univ, Submodule.factor_surjective, MonomialOrder.degree_sPolynomial, Submonoid.LocalizationMap.surj₂, ContMDiffMap.comp_apply, ZeroHom.toFun_eq_coe, RelIso.sumLexEmpty_apply, MeasureTheory.forall_measure_preimage_mul_right_iff, IsAzumaya.AlgHom.mulLeftRight_bij, CategoryTheory.GrothendieckTopology.top_covering, Polynomial.degree_X_add_C, CentroidHom.coe_mul, ContinuousLinearEquiv.mfderivWithin_eq, IsometryEquiv.self_comp_symm, EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, IsPRadical.pow_mem', Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap', IsometryEquiv.comp_continuous_iff, Module.Relations.Solution.IsPresentationCore.desc_var, Matrix.toBilin'_single, MeasureTheory.measure_biUnion₀, PMF.toMeasure_map_apply, LinearIsometryEquiv.bijective, Polynomial.monomial_add_erase, PadicInt.addChar_of_value_at_one_def, MvPowerSeries.WithPiTopology.continuous_C, CategoryTheory.uliftCoyonedaEquiv_comp, IntermediateField.LinearDisjoint.linearIndependent_left, ProbabilityTheory.condExpKernel_apply_eq_condDistrib, Profinite.NobelingProof.GoodProducts.max_eq_eval_unapply, CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles, PMF.toOuterMeasure_apply_fintype, map_comp_mul_inv, ContinuousMap.Homotopy.eq_diag_path, Ordinal.nadd_eq_add, AddMonoidAlgebra.apply_supDegree_add_supDegree, MeasureTheory.Integrable.im, CategoryTheory.Quiv.equivOfIso_apply, Polynomial.isMonicOfDegree_sub_add_two, HasStrictFDerivAt.implicitToOpenPartialHomeomorphOfComplemented_apply, Submodule.Quotient.equiv_apply, TensorProduct.liftAux.smulₛₗ, RootPairing.Hom.id_indexEquiv_symm_apply, PrincipalSeg.lt_iff_lt, CategoryTheory.enrichedFunctorTypeEquivFunctor_symm_apply_map, CategoryTheory.Iso.conjAut_trans, Submodule.natAbs_det_basis_change, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, Action.FintypeCat.ofMulAction_apply, PMF.toMeasure_apply_eq_tsum, AffineMap.continuous_of_finiteDimensional, ArithmeticFunction.abscissaOfAbsConv_moebius, Equiv.pprodEquivProd_symm_apply, Monoid.Coprod.snd_surjective, FaithfulSMul.algebraMap_eq_zero_iff, Finsupp.single_of_single_apply, ContinuousMapZero.coe_zero, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, closedAbsConvexHull_closure_eq_closedAbsConvexHull, MeasurableEquiv.piFinSuccAbove_symm_apply, BoundedContinuousFunction.extend_apply, Prod.Lex.le_iff', Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, ContinuousLinearMap.coe_completion, MeasureTheory.Measure.bind_const, iteratedFDeriv_succ_apply_left, Fin2.equivFin_symm_apply, CategoryTheory.CatEnrichedOrdinary.Hom.base_id, WittVector.frobenius_zmodp, LinearMap.separatingLeft_dualProd, CategoryTheory.yonedaEquiv_symm_app_apply, Polynomial.valuation_X_eq_neg_one, hahnEmbedding_isOrderedModule, Ordinal.one_toType_eq, ContinuousMap.neg_apply, ContDiffWithinAt.fderivWithin_apply, Polynomial.coe_mapAlgEquiv, IsSymmSndFDerivAt.eq, NonUnitalStarAlgHom.coe_range, Ordinal.isNormal_omega, LinearEquiv.conjAlgEquiv_ext_iff, AffineEquiv.midpoint_pointReflection_right, groupHomology.H1π_eq_iff, LinearMap.fst_prodOfFinsuppNat, Ideal.Quotient.mk_algebraMap, MulEquiv.piMultiplicative_symm_apply, AntitoneOn.dual, LinearMap.toMatrix_toLin, LinearMap.IsPositive.re_inner_nonneg_left, OrderIso.preimage_Iic, MvPolynomial.renameSymmetricSubalgebra_apply_coe, Real.volume_emetric_ball, MeasureTheory.MemLp.toLp_const, RingHom.surjective_ofLocalizationSpan, Convex.linear_preimage, Cardinal.isRegular_preAleph_succ, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply, ball_zero_subset_range_iff_surjective, ModuleCat.biprodIsoProd_inv_comp_fst_apply, Perfection.coeff_frobenius, TensorProduct.includeRight_lid, Polynomial.degree_C_le, MonoidHom.compl₂_apply, SemimoduleCat.homAddEquiv_symm_apply_hom, Polynomial.eval_monomial, Finset.coe_map_subset_range, OrderIso.map_maximal_mem, MeasureTheory.OuterMeasure.isometryEquiv_comap_mkMetric, AlgEquiv.mapMatrix_apply, NormedAddGroupHom.coe_zsmul, BoolAlg.ofHom_apply, FreeNonUnitalNonAssocAlgebra.lift_comp_of, ContinuousLinearMapWOT.zero_apply, groupHomology.d₃₂_comp_d₂₁_apply, Equiv.divRight₀_apply, Subgroup.MapSubtype.orderIso_symm_apply, LieEquiv.coe_toLinearEquiv, CategoryTheory.Arrow.equivSigma_symm_apply_right, Algebra.FinitePresentation.iff_quotient_mvPolynomial', AddGroupExtension.Section.exists_eq_add_inl, AddSubmonoid.LocalizationMap.addEquivOfLocalizations_apply, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, CliffordAlgebra.even.lift.aux_algebraMap, Homeomorph.unitBall_symm_apply, Homeomorph.toMeasurableEquiv_coe, TensorProduct.tensorTensorTensorAssoc_tmul, ProbabilityTheory.Kernel.lintegral_prod_id, Submonoid.mul_leftInvEquiv_symm, BoolAlg.forget_map, CliffordAlgebraComplex.reverse_apply, DirichletCharacter.Even.eval_neg, PowerSeries.eq_span_insert_X_of_X_mem_of_span_eq, sInfHom.symm_dual_id, HasFDerivAt.continuousMultilinearMap_apply, ContinuousAddEquiv.symm_trans_apply, LinearMap.injective_of_ne_zero, AddMonoid.End.zero_apply, OneHom.coe_id, QuadraticMap.hasLineDerivAt, MeasureTheory.Measure.OuterRegular.measure_closure_eq_of_isCompact, ContinuousAlgHom.map_neg, IsAdjoinRootMonic.modByMonic_repr_map, ofMul_uzpow, MvPowerSeries.commute_monomial, thickenedIndicator_mono, UniformFun.ofFun_inv, CategoryTheory.tensorLeftHomEquiv_symm_naturality, RCLike.zero_im, DFinsupp.sigmaFinsetFunEquiv_apply_snd_coe, LinearIsometryEquiv.submoduleMap_apply_coe, Quaternion.imK_snd_dualNumberEquiv, ModuleCat.CoextendScalars.map_apply, LinearMap.range_localizedMap_eq_localized₀_range, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, AddEquiv.coe_symm_toIntLinearEquiv, prod_galRestrict_eq_norm, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', fderiv_inv', CategoryTheory.nerve.homEquiv_symm_apply, DFinsupp.sigmaCurry_apply, ProbabilityTheory.Kernel.singularPart_of_subset_mutuallySingularSetSlice, Module.Basis.traceDual_eq_iff, CategoryTheory.Functor.mapExtLinearMap_apply, ProbabilityTheory.Kernel.traj_eq_prod, SemimoduleCat.MonoidalCategory.associator_hom_apply, MvPolynomial.monomial_dvd_monomial, Sum.Lex.inl_le_inr, MeasurableSpace.generateMeasurable_eq_rec, TensorProduct.finsuppLeft_apply_tmul_apply, WithBot.ofDual_apply_bot, Set.mem_image_equiv, sum_conjneg, ContinuousLinearEquiv.contDiff, WithZero.map'_injective_iff, IsLocalization.ringEquivOfRingEquiv_mk', SeparationQuotient.outCLM_isUniformInducing, ContinuousLinearMapWOT.ext_inner_iff, Module.compHom.toLinearEquiv_apply, Algebra.discr_reindex, LocallyConstant.mulIndicator_of_notMem, groupHomology.chainsMap_f, MeasurableEquiv.piFinSuccAbove_apply, AddMonoid.Coprod.con_neg_add_cancel, BoundedContinuousFunction.integrable_of_nnreal, MonomialOrder.degree_X_le_single, ContinuousLinearMap.coeFn_ofIsClosedGraph, PowerSeries.derivative_pow, MvPolynomial.coe_mapEquivMonic_comp, Matrix.comp_one, Localization.mk_eq_mk_iff, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd', MultilinearMap.currySum_apply, Topology.WithLawson.toLawson_ofLawson, MeasureTheory.AddContent.measureCaratheodory_eq, MvPolynomial.transcendental_supported_polynomial_aeval_X, UniformEquiv.piCongrRight_apply, SimpleGraph.Hom.apply_mem_neighborSet, algebraMap_le_cfc_iff, AddSubgroup.relIndex_toSubgroup, Ordinal.toPGame_moveLeft', SheafOfModules.unitHomEquiv_apply_coe, Ideal.absNorm_dvd_norm_of_mem, AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHom, WithTop.map_add, Trivialization.localFrame_apply_of_mem_baseSet, BialgHom.coe_id, Monovary.sum_smul_comp_perm_eq_sum_smul_iff, Nat.card_finMulAntidiag_of_squarefree, stdSimplexEquivIcc_zero, Complex.rectangle_eq_convexHull, PowerSeries.order_eq_nat, IsTopologicalGroup.isInducing_iff_nhds_one, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, AlgebraicGeometry.Scheme.Cover.fromGlued_injective, Monoid.CoprodI.of_injective, uniformity_additive, IsTensorProduct.map_eq, SymAlg.unsym_eq_zero_iff, PolynomialModule.eval_single, RCLike.im_eq_zero, Algebra.PreSubmersivePresentation.localizationAway_jacobian, AddGrpCat.coe_id, IsLocalMinOn.fderivWithin_eq_zero, CategoryTheory.Iso.addCommGroupIsoToAddEquiv_apply, CategoryTheory.PreGaloisCategory.autEmbedding_range_isClosed, RCLike.geometric_hahn_banach_open_point, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, LieDerivation.ad_apply_apply, WeierstrassCurve.Affine.Point.map_id, IsometryClass.coe_coe, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, RingCon.lift_coe, DFinsupp.coe_zero, Matrix.conjTranspose_reindex, AffineIsometryEquiv.coe_toAffineEquiv, LaurentPolynomial.involutive_invert, AlgebraicGeometry.Spec.map_base_apply, CategoryTheory.mateEquiv_apply, ComplexShape.Embedding.AreComplementary.desc'_inr, Representation.IntertwiningMap.coe_one, ContinuousMap.instCanLiftForallCoeContinuous, RootPairing.baseOf_pairwise_pairing_le_zero, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, MvPolynomial.monomial_mul_modMonomial, MvPolynomial.eval_polynomial_eval_finSuccEquiv, continuous_ofAdd, DirectSum.gMulLHom_apply_apply, MeasureTheory.Measure.addHaar_smul, MvPolynomial.sumToIter_Xl, LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly, Submodule.mem_iff_norm_starProjection, Finsupp.image_pow_eq_finsuppProd_image, Polynomial.continuousWithinAt_aeval, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg, Nucleus.le_apply, SpecialLinearGroup.toLinearEquiv_apply, IsAdjoinRootMonic.basis_apply, PMF.toMeasure_apply_finset, Representation.ofMulAction_def, CliffordAlgebraQuaternion.ofQuaternion_toQuaternion, IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure, CategoryTheory.Limits.IsLimit.homEquiv_apply, Complex.reCLM_apply, Function.Embedding.optionEmbeddingEquiv_apply_fst, Module.Relations.Solution.IsPresentation.desc_var, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, AlgHom.norm_apply_le_self_mul_norm_one, gaussSum_mulShift, MvPolynomial.pderiv_inl_universalFactorizationMap_X, Algebra.Extension.H1Cotangent.map_toInfinitesimal_bijective, LocallyConstant.congrRight_symm_apply, CategoryTheory.ShiftedHom.opEquiv_symm_comp, ProbabilityTheory.posterior_comp, Matrix.toLinearEquiv_apply, SupHom.dual_apply_toFun, LinearIsometryEquiv.preimage_closedBall, LinearEquiv.piRing_apply, PartitionOfUnity.mem_finsupport, InfHom.subtypeVal_apply, frobenius_inj, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, UniformFun.lipschitzWith_eval, NonUnitalSubsemiring.coe_comap, map_add_neg, Finsupp.sym2_support_eq_preimage_support_mul, AddSemigrp.ext_iff, ArithmeticFunction.abs_moebius, CuspForm.add_apply, AffineIsometryEquiv.coe_toContinuousAffineEquiv, NonUnitalAlgHom.coe_to_distribMulActionHom, FreeCommRing.map_subtype_val_restriction, SimpleGraph.card_edgeFinset_induce_compl_singleton, WittVector.constantCoeff_wittSub, Ideal.Quotient.algebraMap_mk_of_liesOver, CompactlySupportedContinuousMap.continuousMapEquiv_apply_toFun, OrderDual.ofDual_eq_bot, Finsupp.mapDomain_notin_range, map_finset_sup, SkewMonoidAlgebra.lift_symm_apply, AlgHom.id_apply, ModuleCat.forget₂_map, ContinuousMap.exists_mul_le_one_eqOn_ge, hasEigenvalue_toLin_diagonal_iff, CategoryTheory.Adjunction.homEquiv_naturality_left_square_assoc, AffineBasis.basisOf_apply, ContinuousMap.mkD_apply_of_continuous, RingHom.asBoolAlg_toFun, ContinuousLinearEquiv.ofBijective_apply_symm_apply, Orientation.abs_volumeForm_apply_le, AddChar.coe_sum, CategoryTheory.Limits.cokernel.condition_apply, Set.image_neg, AddEquiv.op_apply_apply, MvPolynomial.counit_X, Representation.Coinvariants.mk_surjective, continuousMultilinearCurryFin1_apply, Finset.coe_singletonMonoidHom, PiTensorProduct.lift_symm, AffineEquiv.constVAddHom_apply, AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero, MulEquiv.inv_apply, CompHausLike.finiteCoproduct.ι_desc_apply, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero, Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff, WithLp.prodContinuousLinearEquiv_apply, ContinuousLinearEquiv.ofSubmodules_symm_apply, AddSubgroup.map_centralizer_le_centralizer_image, Sum.Lex.inl_le_inl_iff, IsCoercive.antilipschitz, Equiv.piCongrSet_symm_apply, subtypeOrLeftEmbedding_apply, MonoidHom.map_pow, Matrix.GeneralLinearGroup.val_det_apply, Finsupp.sum_option_index, LeftInvariantDerivation.evalAt_apply, AddEquiv.eq_symm_comp, AddMonoidHom.map_exists_right_neg, MeasureTheory.Content.contentRegular_exists_compact, convexHull_subset_closedConvexHull, MonoidAlgebra.lift_unique', sigmaFinsuppLequivDFinsupp_apply, RootPairing.reflection_apply_root, CategoryTheory.yonedaEquiv_comp, Equiv.apply_eq_iff_eq_symm_apply, MvPowerSeries.le_order_map, PowerSeries.coeff_zero_X, UpperHalfPlane.petersson_slash, Localization.algEquiv_symm_apply, MeasureTheory.FiniteMeasure.null_iff_toMeasure_null, IsLocalizedModule.injective_iff_isRegular, CliffordAlgebra.contractLeft_algebraMap, ProbabilityTheory.Kernel.lintegral_id', RelEmbedding.swap_apply, Matrix.spectrum_toLin', LinearMap.IsSymmetric.apply_clm, subAddMonoidHom_apply, KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span, associated_normalize, MeasureTheory.Measure.InnerRegularWRT.exists_subset_lt_add, SubAddAction.map_ofFixingAddSubgroupUnion_def, Orthonormal.comp_linearIsometry, TensorProduct.eq_repr_basis_right, IsLocalization.coeSubmodule_span_singleton, VAddCommClass.toAddActionHom_apply, CategoryTheory.unitCompPartialBijective_symm_apply, Finsupp.curry_apply, AddSubmonoid.coe_inclusion, AddCommGrpCat.coyoneda_obj_map, RootPairing.reflectionPerm_eq_iff_smul_coroot, Ordinal.type_preimage, ofMul_div, Function.fromTypes_nil_equiv_symm_apply, Algebra.TensorProduct.closure_range_union_range_eq_top, WithZero.map'_map', MeasureTheory.SignedMeasure.toJordanDecompositionEquiv_symm_apply, Hyperreal.coeRingHom_toFun, MeasureTheory.measure_mul_closure_one, ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_condDistrib_prod_condDistrib, Equiv.Perm.viaEmbeddingHom_injective, SSet.skeleton_zero, RingQuot.ringQuotToIdealQuotient_apply, fourierCoeff_fourier, AddActionHom.zeroEmbeddingMap_bijective, MulAut.conjNormal_apply, AdjoinRoot.coe_algEquivOfAssociated, PerfectRing.lift_self_apply, unitary.linearIsometryEquiv_coe_apply, SubAddAction.ofStabilizer.conjMap_apply, RootPairing.pairing_neg_two_neg_two_iff, Affine.Simplex.signedInfDist_incenter, Nat.factorization_factorial_eq_zero_of_lt, Equiv.pointReflection_fixed_iff_of_injective_two_nsmul, AdicCompletion.ofAlgEquiv_symm_of, HilbertBasis.finite_spans_dense, SubmultiplicativeHomClass.map_mul_le_mul, Derivation.apply_aeval_eq, FractionalIdeal.absNorm_one, LieSubalgebra.ad_comp_incl_eq, SimpleGraph.Copy.coe_toHom, SimpleGraph.Hom.ofLE_apply, uliftZMultiplesHom_symm_apply, Metric.Snowflaking.isBounded_image_toSnowflaking_iff, SkewMonoidAlgebra.mapDomain_comp, MeasureTheory.Measure.addHaar_image_homothety, AddConstMapClass.map_const_add, CategoryTheory.Localization.structuredArrowEquiv_apply, Algebra.ZariskisMainProperty.exists_fg_and_exists_notMem_and_awayMap_bijective, IsCoveringMap.liftPath_trans, SimpleGraph.IsClique.map, LieAlgebra.of_nsmul, Pi.toLex_monotone, SetTheory.PGame.moveLeft_neg, ContinuousMap.restrict_apply, Equiv.psigmaEquivSigma_symm_apply, Submonoid.LocalizationMap.lift_id, RingHom.map_pow, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, PowerSeries.trunc_derivative', LocallyConstant.comapₐ_apply_apply, ProbabilityTheory.Kernel.iIndepFun_iff_measure_inter_preimage_eq_mul, ContinuousLinearMap.IsInvertible.inverse_apply_eq, KummerDedekind.quotMapEquivQuotQuotMap_symm_apply, PNat.coe_coeMonoidHom, NNRat.coe_coeHom, norm_iteratedFDeriv_clm_apply_const, MeasureTheory.Measure.toPMF_apply, MonoidHom.comp_apply, Ideal.mulQuot_injective, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isOpen, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, kroneckerLinearEquiv_tmul, isSimplyConnected_iff_exists_homotopy_refl_forall_mem, AlgebraicGeometry.IsAffineOpen.mem_ideal_iff, RatFunc.toFractionRing_eq, ConvexCone.mem_comap, unitInterval.volume_Ioi, LieAlgebra.killingForm_of_equiv_apply, MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint, AlgEquiv.toLinearEquiv_apply, ProbabilityTheory.Kernel.integral_indicator₂, Finset.centerMass_mem_convexHull_of_nonpos, AlgebraicGeometry.Scheme.toSpecΓ_base, MonoidAlgebra.mul_apply_left, PMF.normalize_apply, QuotientAddGroup.map_id_apply, MvPolynomial.rTensorAlgHom_apply_eq, AffineSubspace.coe_map, Zsqrtd.toReal_injective, HahnEmbedding.Partial.toOrderAddMonoidHom_injective, DirectSum.of_eq_of_ne bridge: CategoryTheory.Limits.WalkingPair.equivBool_apply_right, MeasureTheory.SimpleFunc.hasBoxIntegral, CategoryTheory.Limits.WalkingPair.equivBool_apply_left, MeasureTheory.SimpleFunc.box_integral_eq_integral

DivisibleHull

Definitions

Name	Category	Theorems
coe 📖	CompOp	5 math math: coe_inj, coeAddMonoidHom_apply, coeOrderAddMonoidHom_apply, coe_injective, coe_add

DoubleCentralizer

Definitions

Name	Category	Theorems
coe 📖	CompOp	4 math math: coeHom_apply, coe_eq_algebraMap, coe_fst, coe_snd

EquivLike

Definitions

Name	Category	Theorems
coe 📖	CompOp	3 math math: right_inv, coe_apply, left_inv

Finset.Nontrivial

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe 📖	mathematical	Finset.Nontrivial	Set.Nontrivial SetLike.coe Finset Finset.instSetLike	—	Finset.nontrivial_coe

FirstOrder.Language.Substructure.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

GenContFract.IntFractPair

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

LowerSet.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Mathlib.Meta.FunProp.Mor.App

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Mathlib.Meta.FunProp.Mor.Arg

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

ModularGroup

Definitions

Name	Category	Theorems
coe 📖	CompOp	6 math math: SLOnGLPos_smul_apply, coe_apply_complex, coe_one, coe_inj, det_coe, coeHom_apply

NNReal.HolderConjugate

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe 📖	mathematical	NNReal.HolderConjugate	Real.HolderConjugate NNReal.toReal	—	NNReal.holderConjugate_coe_iff

NNReal.HolderTriple

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe 📖	mathematical	NNReal.HolderTriple	Real.HolderTriple NNReal.toReal	—	NNReal.holderTriple_coe_iff

OrderHom.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

PFun

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Partition.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

QuadraticAlgebra

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Quaternion

Definitions

Name	Category	Theorems
coe 📖	CompOp	70 math math: star_mul_self, coe_normSq_add, coe_natCast, coe_inv, coe_ratCast, coe_pow, coe_commutes, algebraMap_def, imJ_coe, coe_re, coe_zpow, re_add_im, coe_zero, star_eq_two_re_sub, star_add_self, sub_re_self, imK_coe, smul_coe, coe_smul, norm_coe, sub_self_im, exp_of_re_eq_zero, im_coe, re_exp, coe_inj, coe_imI, expSeries_even_of_imaginary, sub_self_re, coe_div, mul_star_eq_coe, star_add_self', coeComplex_coe, self_add_star', coe_mul_eq_smul, summable_coe, sq_eq_neg_normSq, coe_one, tsum_coe, sq_eq_normSq, re_coe, coe_sub, self_mul_star, coe_mul, coe_nnratCast, sub_im_self, self_add_star, continuous_coe, coe_commute, coe_injective, star_mul_eq_coe, coe_imK, coe_imJ, mul_coe_eq_smul, coe_intCast, eq_re_iff_mem_range_coe, coe_add, hasSum_expSeries_of_imaginary, coe_im, im_sq, coe_neg, hasSum_coe, imI_coe, coe_real_complex_mul, normSq_ratCast, exp_coe, star_coe, exp_eq, normSq_coe, nnnorm_coe, star_eq_self

QuaternionAlgebra

Definitions

Name	Category	Theorems
coe 📖	CompOp	46 math math: coe_sub, coe_mul_eq_smul, self_add_star, coe_pow, re_coe, star_eq_two_re_sub, mul_star_eq_coe, sub_re_self, smul_coe, star_mul_eq_coe, star_im, star_coe, sub_self_re, coe_add, star_eq_self, star_add_self, coe_intCast, coe_neg, coe_imI, comm, star_add_self', coe_inj, coe_im, coe_commute, self_add_star', sub_self_im, coe_zero, coe_re, coe_imK, im_coe, coe_commutes, imK_coe, coe_ofNat, coe_imJ, coe_one, coe_mul, coe_smul, eq_re_iff_mem_range_coe, coe_natCast, coe_algebraMap, mul_coe_eq_smul, imI_coe, re_add_im, sub_im_self, imJ_coe, coe_injective

RayVector

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Real.Angle

Definitions

Name	Category	Theorems
coe 📖	CompOp	175 math math: abs_toReal_neg_coe_eq_self_iff, Sbtw.oangle₁₂₃_eq_pi, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, sign_two_zsmul_eq_sign_iff, neg_coe_abs_toReal_of_sign_nonpos, Orientation.inner_rotation_pi_div_two_right_smul, Orientation.oangle_add_left_smul_rotation_pi_div_two, two_zsmul_eq_pi_iff, sin_add_pi_div_two, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, sign_neg_coe_nonpos_of_nonneg_of_le_pi, EuclideanGeometry.oangle_eq_pi_sub_two_zsmul_oangle_of_dist_eq, Complex.arg_cos_add_sin_mul_I_coe_angle, sin_eq_zero_iff, Orientation.neg_rotation, Sbtw.oangle_eq_add_pi_left, Complex.arg_coe_angle_eq_iff, EuclideanGeometry.oangle_eq_angle_or_eq_neg_angle, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, cos_eq_real_cos_iff_eq_or_eq_neg, Complex.oangle, toReal_coe_eq_self_iff_mem_Ioc, Orientation.oangle_eq_pi_iff_oangle_rev_eq_pi, Orientation.oangle_neg_right, cos_sin_inj, abs_toReal_eq_pi_div_two_iff, toReal_eq_pi_iff, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, toReal_coe, two_zsmul_coe_div_two, Orientation.neg_rotation_neg_pi_div_two, toReal_pi, Orientation.oangle_eq_pi_iff_angle_eq_pi, toReal_neg_pi_div_two, sign_pi_sub, Complex.arg_coe_angle_eq_iff_eq_toReal, sign_eq_zero_iff, Orientation.rotation_pi_apply, EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_left, Orientation.oangle_eq_angle_or_eq_neg_angle, sin_add_pi, toReal_coe_eq_self_iff, EuclideanGeometry.oangle_eq_pi_iff_sbtw, cos_add_pi, two_zsmul_coe_pi, cos_add_pi_div_two, two_nsmul_eq_zero_iff, coe_add, Orientation.oangle_neg_self_left, Sbtw.oangle_eq_add_pi_right, coe_abs_toReal_of_sign_nonneg, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, coe_eq_zero_iff, coe_coeHom, cos_sub_pi, Sbtw.oangle₃₂₁_eq_pi, tan_sub_pi, sub_coe_pi_eq_add_coe_pi, sign_coe_pi, Orientation.inner_rotation_pi_div_two_right, sin_eq_iff_coe_eq_or_add_eq_pi, EuclideanGeometry.oangle_eq_pi_iff_angle_eq_pi, toReal_pi_div_two, sign_sub_pi, Orientation.inner_rotation_pi_div_two_left, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Complex.arg_mul_cos_add_sin_mul_I_coe_angle, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, arg_toCircle, toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, two_zsmul_neg_pi_div_two, Orientation.inner_rotation_pi_div_two_left_smul, EuclideanGeometry.oangle_orthogonalProjection_self, cos_eq_zero_iff, angle_eq_iff_two_pi_dvd_sub, toCircle_coe, Orientation.oangle_neg_left, sin_coe_pi, coe_sub, intCast_mul_eq_zsmul, EuclideanGeometry.oangle_add_oangle_add_oangle_eq_pi, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, cos_eq_iff_coe_eq_or_eq_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, sign_two_nsmul_eq_sign_iff, coe_toReal, Orientation.oangle_sub_right_smul_rotation_pi_div_two, sin_pi_div_two_sub, Orientation.oangle_eq_angle_of_sign_eq_one, two_zsmul_eq_iff, sign_pi_add, Orientation.oangle_neg_self_right, two_nsmul_eq_pi_iff, Orientation.inner_smul_rotation_pi_div_two_right, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, Complex.continuousAt_arg_coe_angle, Complex.arg_div_coe_angle, Orientation.neg_rotation_pi_div_two, Orientation.oangle_sub_left_smul_rotation_pi_div_two, sin_coe, Orientation.oangle_add_right_smul_rotation_pi_div_two, Orientation.inner_smul_rotation_pi_div_two_left, continuous_coe, EuclideanGeometry.Sphere.oangle_eq_pi_sub_two_zsmul_oangle_center_right, sin_eq_iff_eq_or_add_eq_pi, cos_coe, Orientation.oangle_eq_pi_sub_two_zsmul_oangle_sub_of_norm_eq, coe_nsmul, coe_toIocMod, sign_add_pi, abs_toReal_coe_eq_self_iff, Complex.arg_conj_coe_angle, natCast_mul_eq_nsmul, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, sign_coe_pi_div_two, zsmul_eq_iff, Orientation.oangle_add_cyc3_neg_left, eq_neg_self_iff, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, neg_coe_pi, two_nsmul_coe_div_two, neg_eq_self_iff, EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi, coe_toIcoMod, Complex.arg_coe_angle_toReal_eq_arg, tan_coe_pi, cos_pi_div_two_sub, EuclideanGeometry.oangle_self_orthogonalProjection, EuclideanGeometry.oangle_eq_angle_of_sign_eq_one, sign_coe_nonneg_of_nonneg_of_le_pi, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, coe_two_pi, coe_zsmul, eq_add_pi_of_two_zsmul_eq_of_sign_eq_neg, Complex.arg_pow_coe_angle, Orientation.rotation_pi_div_two, coe_zero, Orientation.oangle_eq_pi_iff_sameRay_neg, Complex.arg_inv_coe_angle, cos_sub_pi_div_two, Orientation.inner_smul_rotation_pi_div_two_smul_left, Orientation.oangle_map_complex, EuclideanGeometry.oangle_eq_pi_iff_oangle_rev_eq_pi, Orientation.inner_smul_rotation_pi_div_two_smul_right, two_zsmul_eq_zero_iff, two_nsmul_neg_pi_div_two, tan_add_pi, toReal_coe_eq_self_add_two_pi_iff, sin_antiperiodic, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, two_nsmul_coe_pi, toReal_eq_pi_div_two_iff, toReal_coe_eq_self_sub_two_pi_iff, Complex.arg_mul_coe_angle, sin_eq_real_sin_iff_eq_or_add_eq_pi, cos_antiperiodic, Orientation.rotation_pi, EuclideanGeometry.oangle_eq_neg_angle_of_sign_eq_neg_one, sin_sub_pi_div_two, tan_periodic, coe_pi_add_coe_pi, toReal_eq_neg_pi_div_two_iff, Orientation.oangle_eq_neg_angle_of_sign_eq_neg_one, Orientation.oangle_add_cyc3_neg_right, Complex.arg_zpow_coe_angle, two_nsmul_eq_iff, sign_coe_neg_pi_div_two, sign_antiperiodic, nsmul_eq_iff, sin_sub_pi, Complex.arg_neg_coe_angle, coe_neg, cos_coe_pi, tan_coe

SetLike

Definitions

Name	Category	Theorems
coe 📖	CompOp	3681 math math: RingCone.coe_set_mk, NonUnitalSubalgebra.coe_starClosure, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.SimpleFunc.coe_range, Fintype.all_card_le_rel_image_card_iff_exists_injective, ProbabilityTheory.iIndepSets.piiUnionInter_of_notMem, AddSubgroup.coe_prod, Finset.coe_eq_singleton, Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe, Equiv.Perm.support_closure_subset_union, PrimeSpectrum.closure_range_comap, DoubleCoset.doubleCoset_union_rightCoset, Finsupp.range_subset_insert_frange, GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset, RestrictedProduct.single_injective, UV.compress_injOn, Subsemigroup.coe_inf, ConvexCone.convex, Flag.coe_ofIsMaxChain, CompleteLatticeHom.range_coe, MeasureTheory.Measure.haar.nonempty_iInter_clAddPrehaar, AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq, AddMonoidHom.coe_ker, LinearMap.eqOn_span', Affine.Simplex.altitudeFoot_restrict, UpperSet.coe_Ici, Ideal.mem_image_of_mem_map_of_surjective, TopologicalSpace.Compacts.isClosed_subsets_of_isClosed, Submodule.mem_colon_span_singleton, roth_3ap_theorem, Topology.RelCWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succ, Subring.coe_sSup_of_directedOn, Finset.coe_sort_coe, NonUnitalStarSubalgebra.ofClass_carrier, TopologicalSpace.NonemptyCompacts.coe_top, NonUnitalAlgebra.gc, Ideal.Filtration.submodule_closure_single, ConjAct.fixedPoints_eq_center, AddSubgroup.isClosed_topologicalClosure, TopologicalSpace.Opens.coe_interior, Ideal.span_le, StarSubalgebra.coe_sInf, LowerSet.coe_eq_univ, PrimeSpectrum.isClopen_iff_mul_add, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right, rothNumberNat_spec, Subgroup.characteristic_centralizer, ContinuousLinearMap.IsIdempotentElem.isClosed_range, Sublattice.coe_prod, Irreducible.maximalIdeal_eq_setOf_le_v_coe, Ideal.Filtration.submodule_eq_span_le_iff_stable_ge, NonUnitalSubring.coe_top, AlgebraicGeometry.Scheme.zeroLocus_iInf, LieSubmodule.coe_map, Finset.coe_one, MonoidHom.coe_mrange, Subring.coe_unop, Filter.mem_pi', Subgroup.sup_eq_closure_mul, Submonoid.coe_ofClass, SimpleGraph.ComponentCompl.subset_hom, NonUnitalSubalgebra.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallForallHSMul, LowerAdjoint.closure_iUnion₂_closure, Ideal.subset_union, Submonoid.subsemiringClosure_toAddSubmonoid, AddAction.stabilizer_addSubgroup_op, ArchimedeanClass.subsemigroup_eq_addSubgroup_of_ne_top, Subalgebra.adjoin_rank_le, MeasureTheory.SimpleFunc.sum_measure_preimage_singleton, TopologicalSpace.Opens.map_coe, AddSubmonoid.le_centralizer_centralizer, Ideal.pow_multiset_sum_mem_span_pow, Subgroup.closure_eq, Topology.RelCWComplex.skeleton_top, Nat.bijOn_digitsAppend', Subsemiring.closure_le, Finset.pairwise_subtype_iff_pairwise_finset, Module.support_quotient, UpperSet.coe_one, Fintype.coe_image_univ, Submodule.smul_def, TopologicalSpace.OpenNhdsOf.canLiftSet, IsOpenMap.exists_opens_image_eq_of_prespectralSpace, IsOfFinOrder.natCard_powers_le_orderOf, Subgroup.equivSMul_apply_coe, QuotientGroup.norm_mk, isApproximateAddSubgroup_zero, Finsupp.mem_supported_support, isConnected_compl_of_one_lt_codim, QuotientGroup.image_coe_inj, Submonoid.le_centralizer_centralizer, Submodule.bot_coe, Polynomial.mem_image_comap_C_basicOpen, Isometry.preimage_perpBisector, Order.Ideal.PrimePair.I_union_F, Subalgebra.coe_iSup_of_directed, AddSubmonoid.add_subset_closure, Subsemiring.closure_addSubmonoid_closure, isOpen_pi_iff, Submodule.span_subset_span, Subring.coe_comap, Subsemiring.isClosed_topologicalClosure, LocalizedModule.subsingleton_iff_disjoint, ClopenUpperSet.coe_toUpperSet, MonoidHom.eqOn_closureM, ValuationSubring.image_maximalIdeal, RestrictedProduct.mulSingle_inv, FirstOrder.Language.Substructure.closure_eq_of_isRelational, tendsto_tsum_div_pow_atTop_integral, MulHom.coe_srange, Finpartition.isPartition_parts, upperClosure_eq, Order.Ideal.ext_iff, IsOpen.lowerClosure, Finset.isUnit_coe, Subgroup.coe_pointwise_smul, Finset.preimage_add_left_singleton, TopologicalSpace.Closeds.iInf_def, MeasureTheory.MeasuredSets.real_sub_real_le_dist, rootsOfUnityEquivOfPrimitiveRoots_apply_coe_inv_val, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic, Geometry.SimplicialComplex.vertex_mem_convexHull_iff, OpenPartialHomeomorph.subtypeRestr_symm_trans_subtypeRestr, LowerSet.coe_mk, Submodule.span_span_of_tower, RootPairing.Base.span_coroot_support, Finset.coe_infs, BddBelow.upperClosure, PrimeSpectrum.eq_biUnion_of_isOpen, Summable.sum_add_tsum_compl, PrimeSpectrum.localization_specComap_range, MvPolynomial.mem_image_support_coeff_finSuccEquiv, Ideal.subset_span, AlgebraicGeometry.IsAffineOpen.isCompact, NonUnitalSubring.coe_sInf, Geometry.SimplicialComplex.convexHull_subset_space, TopologicalSpace.Opens.coe_iSup, IdealFilter.ringFilterBasis_sets, LinearMap.injOn_iff_surjOn, Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt, ProbabilityTheory.iCondIndepSets.piiUnionInter_of_notMem, Fintype.coe_finsetEquivSet, MeasureTheory.sum_measureReal_singleton, Finset.prod_mulIndicator_subset, BooleanSubalgebra.coe_mk, TopologicalSpace.PositiveCompacts.coe_top, AddSubmonoid.sup_eq_closure, mem_own_rightCoset, Submonoid.coe_invOrderIso_apply, NonUnitalStarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer, Submonoid.coe_pi, Subgroup.isOpen_of_isClosed_of_finiteIndex, IsLocalization.AtPrime.coe_orderIsoOfPrime_apply_coe, IsLinearSet.closure_finset, smoothSheafCommRing.nonunits_stalk, TopologicalSpace.Clopens.coe_mk, Finset.inf_id_set_eq_sInter, TopologicalSpace.Closeds.coe_compl, Ideal.isHomogeneous_iff_subset_iInter, AddEquiv.addSubgroupMap_symm_apply, AffineSubspace.setOf_sSameSide_eq_image2, LowerAdjoint.mem_iff, Finsupp.support_extendDomain_subset, Topology.RelCWComplex.Subcomplex.cellFrontier_subset_of_mem, PrimeSpectrum.zeroLocus_nilradical, ProperCone.convex, StarSubalgebra.coe_map, ZFSet.coe_inter, Finset.coe_Ico, Submodule.tensorEquivSpan_apply_tmul, TopologicalSpace.Opens.isCompactElement_iff, Finset.preimage_mul_left_one, IsConcreteLE.coe_subset_coe', Subfield.closure_le, Subgroup.dense_of_not_isolated_one, Finset.coe_eq_empty, Geometry.SimplicialComplex.mem_space_iff, TopCat.GlueData.open_image_open, AddSubsemigroup.closure_le_centralizer_centralizer, Submodule.coe_mapAlgEquiv_symm_apply, PrimeSpectrum.zeroLocus_eq_univ_iff, AddMonoidHom.noncommPiCoprod_apply, MeasureTheory.MeasuredSets.sub_le_edist, StrongDual.polarSubmodule_eq_setOf, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ, Subgroup.transferTransversal_apply, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zero, ConvexCone.canLift, Subring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg, bddBelow_upperClosure, ZFSet.coe_image, ZFSet.mem_toSet, OpenPartialHomeomorph.subtypeRestr_coe, LieSubmodule.coe_toSet_mk, SubMulAction.closure_le, TopologicalSpace.Clopens.coe_bot, Geometry.SimplicialComplex.subset_space, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, DFinsupp.mapRange_def, Flag.coe_map, IsOfFinOrder.finite_zpowers, Ring.coe_jacobson_quotient, Affine.Simplex.restrict_reindex, Subalgebra.coe_toAddSubmonoid, Sublattice.isSublattice, Finset.sigma_image_fst_preimage_mk, AddSubmonoid.mem_closure_finset, Affine.Simplex.faceOppositeCentroid_restrict, TopologicalSpace.NonemptyCompacts.coe_prod, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, AddSemigroupIdeal.subset_closure, HahnSeries.coe_cardSuppLTAddSubmonoid, QuotientGroup.leftRel_r_eq_leftCosetEquivalence, AddSubgroup.coe_addSubgroupOf, Subring.centralizer_eq_top_iff_subset, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_assoc, Submodule.dense_iff_topologicalClosure_eq_top, LowerSet.coe_subset_coe, ProjectiveSpectrum.zeroLocus_mul_ideal, ProjectiveSpectrum.subset_zeroLocus_vanishingIdeal, finrank_vectorSpan_image_finset_le, IntermediateField.coe_bot, Submodule.mem_colon', Subgroup.le_normalClosure, IsUniformGroup.uniformContinuous_iff_isOpen_ker, Submonoid.top_closure_mul_self_subset, Finset.neg_filter_univ, AddSubsemigroup.coe_toSubsemigroup_symm_apply, Finset.multipliable, FiniteGaloisIntermediateField.subset_adjoin, Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free, Finset.coe_biUnion, Topology.IsUpperSet.nhdsKer_eq_upperClosure, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, ProjectiveSpectrum.gc_homogeneousIdeal, Set.subset_toFinset, LowerAdjoint.closure_union_closure, Finset.ordConnected_range_coe, Ideal.mem_colon_span_singleton, StarSubalgebra.range_le, AffineMap.eqOn_affineSpan, ProjectiveSpectrum.zeroLocus_mul_homogeneousIdeal, range_comap_of_surjective, AlgebraicGeometry.isCompact_iff_exists, TopologicalSpace.Compacts.isEmbedding_coe, linearIndepOn_finset_iff, AddSubgroup.iSup_eq_closure, Ideal.exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition, Equiv.restrictPreimageFinset_symm_apply_coe, PrimeSpectrum.isRetrocompact_zeroLocus_compl_of_fg, Submonoid.isClosed_topologicalClosure, AddSubgroup.exists_isComplement_left, ConvexCone.coe_eq_empty, Finset.doubling_lt_three_halves, Orthonormal.codRestrict, LieAlgebra.InvariantForm.orthogonal_carrier, NonUnitalAlgebra.coe_bot, AddSubgroup.coe_top, Subgroup.isClosed_topologicalClosure, DoubleCoset.mem_doubleCoset_self, UpperSet.sdiff_eq_left, RestrictedProduct.instContinuousMulCoePrincipal, Polynomial.monic_restriction, Subring.coe_op, normalClosure_of_stabilizer_eq_top, AlgebraicGeometry.Scheme.RationalMap.dense_domain, FirstOrder.Language.Substructure.fg_closure_singleton, Submodule.coe_toAddSubmonoid, EuclideanGeometry.preimage_inversion_perpBisector_inversion, RestrictedProduct.one_apply, coe_sort_coe, NonUnitalAlgebra.span_eq_toSubmodule, NonUnitalStarAlgebra.coe_bot, MeasureTheory.Measure.haarMeasure_closure_self, RootPairing.Base.root_mem_span_int, RingPreordering.coe_support, TopologicalSpace.Compacts.coe_inf, TopologicalSpace.Closeds.isClosed, Submonoid.coe_map, Order.PFilter.ext_iff, Module.isTorsionBySet_quotient_ideal_smul, rightAddCoset_mem_rightAddCoset, AddSubgroup.dense_of_no_min, SimpleGraph.TripartiteFromTriangles.toTriangle_surjOn, NonUnitalAlgebra.coe_inf, Ideal.isHomogeneous_iff_forall_subset, NonUnitalSubalgebra.coe_toNonUnitalStarSubalgebra, ProperCone.coe_positive, AddSubgroup.le_centralizer_iff, MeasureTheory.Measure.haarMeasure_apply, AlgebraicGeometry.Scheme.Hom.iUnion_support_ker_openCover_map_comp, Finset.coe_singleton, AddSubgroup.coe_comap, QuotientAddGroup.univ_eq_iUnion_vadd, AddSubsemigroup.coe_inf, NonUnitalSubsemiring.isClosed_topologicalClosure, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, Finset.coe_empty, TopologicalSpace.Compacts.isClosed_inter_nonempty_of_isClosed, TopologicalSpace.IsOpenCover.iSup_set_eq_univ, NumberField.mixedEmbedding.mem_idealLattice, NonUnitalSubsemiring.coe_map, Subgroup.conjugatesOfSet_subset_normalClosure, TopologicalSpace.Opens.CompleteCopy.dist_eq, Submodule.injective_inclusionSpan, Submonoid.coe_inf, Subalgebra.topologicalClosure_coe, Sublattice.coe_map, NonUnitalStarSubalgebra.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallForallHSMulForallForallStar, ClopenUpperSet.coe_bot, IntermediateField.coe_iSup_of_directed, Finset.disjoint_coe, Finset.pairwiseDisjoint_coe, Subalgebra.coe_center, Submonoid.instCanLiftSetCoeAndMemOfNatForallForallForallForallHMul, IsGaloisGroup.fixingSubgroup_top, Interval.coe_sInf, AlgebraicGeometry.Scheme.zeroLocus_mul, Ideal.exists_finset_card_eq_height_of_isNoetherianRing, PrimeSpectrum.gc, MvPolynomial.image_comap_C_basicOpen, Sylow.coe_smul, Submonoid.coe_iSup_of_directed, DoubleCoset.doubleCoset_union_leftCoset, Geometry.SimplicialComplex.vertices_eq, Affine.Simplex.restrict_map_restrict, Valuation.Integers.isPrincipal_iff_exists_isGreatest, TopologicalSpace.Compacts.coe_toCloseds, ClosedSubmodule.coe_sSup, subset_lowerClosure, ConvexCone.coe_inf, TopologicalSpace.Opens.ne_bot_iff_nonempty, Algebra.sSup_def, QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure, Sublattice.coe_bot, UpperSet.coe_add, MulAction.stabilizer_mul_self, MvPolynomial.mem_range_map_iff_coeffs_subset, TwoSidedIdeal.coe_top, RestrictedProduct.mulSingle_zpow, AddSubgroup.isComplement_iff_bijective, Submodule.ClosedComplemented.exists_isClosed_isCompl, Algebra.basicOpen_subset_etaleLocus_iff_etale, IsClosed.upperClosure, Behrend.sphere_subset_preimage_metric_sphere, range_specComap_of_surjective, AffineSubspace.WSameSide.nonempty, Sublattice.coe_pi, coe_convexAddSubmonoid, YoungDiagram.coe_bot, Subring.coe_toSubsemiring, LowerAdjoint.le_iff_subset, TopologicalSpace.Clopens.ext_iff, Interval.coe_iInf₂, SimpleGraph.ComponentCompl.disjoint_right, Finset.coe_filter, Order.Ideal.lower, RootPairing.invtRootSubmodule.eq_top_iff, Finset.coe_prod, FirstOrder.Language.Theory.models_iff_finset_models, LowerSet.disjoint_coe, RestrictedProduct.single_eq_zero_iff, AddSubgroup.normal_add, Finset.preimage_inr, Finset.erase_injOn, Submodule.mem_span_image_iff_exists_fun, PrimeSpectrum.basicOpen_eq_zeroLocus_of_mul_add, Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct, TopologicalSpace.Closeds.isUniformEmbedding_coe, Submonoid.subsemiringClosure_eq_closure, MeasureTheory.Measure.haarMeasure_unique, Set.Finite.ssubset_toFinset, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, Topology.IsLowerSet.nhdsKer_eq_lowerClosure, UpperSet.carrier_eq_coe, StarAlgebra.adjoin_eq, Submonoid.coe_invOrderIso_symm_apply, ConvexCone.coe_closure, Finset.coeMonoidHom_apply, Finset.coe_attachFin, isLinearTopology_iff_hasBasis_open_twoSidedIdeal, IsSemilinearSet.closure_finset, SemigroupIdeal.fg_iff, IsUpperSet.upperClosure, OpenSubgroup.isOpen, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, Order.Ideal.isPrime_iff, ConvexCone.coe_zero, MeasureTheory.Measure.haar.addCHaar_mem_clAddPrehaar, LowerSet.coe_sdiff, Subalgebra.SeparatesPoints.strongly, Subalgebra.centralizer_coe_iSup, RestrictedProduct.sub_apply, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity, Polynomial.eval₂_restriction, Order.PFilter.IsPrime.compl_ideal, ValuationSubring.nonunits_subset, AddSubgroup.coe_unop, FirstOrder.Language.Substructure.small_closure, FractionalIdeal.coe_extendedHomₐ_eq_span, Filter.HasBasis.uniformity_nonemptyCompacts, FirstOrder.Language.Substructure.coe_inf, GradeZero.coe_submonoid, Finset.set_biUnion_coe, Set.IsPWO.addSubmonoid_closure, Function.Embedding.exists_of_card_le_finset, Finset.coe_Iic, Finset.coe_vadd_finset, MeasureTheory.Measure.haar.le_index_mul, Finset.coe_eq_pair, OpenNormalSubgroup.instIsClosedCoePathComponentOne, ZFSet.coe_pair, Submodule.closure_subset_topologicalClosure_span, Finset.coe_univ, Module.basicOpen_subset_freeLocus_iff, LieSubalgebra.bot_coe, Finsupp.mem_supported, RingPreordering.coe_mk', Ideal.map_spanIntNorm, TopologicalSpace.Compacts.edist_eq, SubMulAction.subset_coe_pow, Topology.RelCWComplex.Subcomplex.closedCell_subset_of_mem, FirstOrder.Language.Substructure.cg_def, Finset.not_injOn_of_card_image_lt, Subgroup.le_centralizer_iff, dimH_coe_finset, Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free, TopologicalSpace.IrreducibleCloseds.coe_mk, prod_eq_tprod_mulIndicator, Subfield.coe_top, SimpleGraph.isMaximumClique_iff, TopCat.Presheaf.germ_stalkSpecializes_apply, Submodule.coe_sup, RestrictedProduct.single_mul, Finset.weightedVSubOfPoint_indicator_subset, IsClopen.upperClosure_pi, hasSum_sum_support_of_ne_finset_zero, DFinsupp.mk_neg, Finset.isGδ_compl, Topology.RelCWComplex.Subcomplex.union, Finset.sized_compls, AddSubgroup.add_normal, RestrictedProduct.instLocallyCompactSpaceCoeCofiniteOfSubgroupClassOfIsTopologicalGroupOfCompactSpaceSubtypeMem, OpenAddSubgroup.coe_comap, Submodule.coe_toSubalgebra, GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity, Topology.RelCWComplex.coe_skeletonLT, Order.Ideal.coe_sup, Subgroup.mul_normal, StarSubalgebra.ofClass_carrier, NonUnitalAlgebra.adjoin_le_centralizer_centralizer, Finpartition.disjoint, MeasureTheory.Measure.haar.addHaarContent_outerMeasure_self_pos, FirstOrder.Language.Substructure.mem_closure, Polynomial.contentIdeal_def, Finsupp.comapDomain_smul_of_injective, Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_left, corners_theorem, Polynomial.lift_of_splits, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Topology.CWComplex.Subcomplex.coe_mk', TopologicalSpace.CompactOpens.isCompact, Monoid.PushoutI.NormalWord.Transversal.compl, Subfield.coe_iSup_of_directed, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic, hasProd_prod_support_of_ne_finset_one, Algebra.basicOpen_subset_unramifiedLocus_iff, Finset.dimH_zero, Topology.IsLocallyConstructible.iff_of_isOpenCover, Polynomial.restriction_one, Nat.exists_mem_span_nat_finset_of_ge, Finset.summable, Submonoid.centralizer_eq_top_iff_subset, Set.Infinite.exists_subset_card_eq, Subgroup.isComplement_range_right, MeasureTheory.Measure.haarMeasure_self, ZFSet.coe_insert, ringKrullDim_quotient, AlgHom.le_equalizer, Finset.coe_nonempty, Subgroup.coe_pi, Finset.noncommSum_union_of_disjoint, NonUnitalSubalgebra.coe_toNonUnitalSubring, Subsemigroup.top_closure_mul_self_subset, PrimeSpectrum.vanishingIdeal_zeroLocus_eq_radical, image_range_addOrderOf, AddSubgroup.coe_zmultiples, TopologicalSpace.PositiveCompacts.carrier_eq_coe, TopologicalSpace.Closeds.coe_iInf, TopologicalSpace.Closeds.ext_iff, Subgroup.exists_left_transversal_of_le, MonoidAlgebra.mem_adjoin_support, NonUnitalSubsemiring.subset_closure, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, Topology.RelCWComplex.cellFrontier_subset_skeletonLT, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_mk', PointedCone.coe_map, Subgroup.coe_mul_of_left_le_normalizer_right, BooleanSubalgebra.coe_bot, Topology.IsLowerSet.closure_eq_upperClosure, Finset.preimage_mul_left_singleton, SummationFilter.support_eq_limsInf, AddSubgroup.closure_le_centralizer_centralizer, NonemptyInterval.coe_dual, MeasureTheory.Content.le_outerMeasure_compacts, Subalgebra.coe_pointwise_smul, MeasureTheory.Measure.haar.prehaar_le_index, Finset.coe_range, IsClosed.lowerClosure_pi, RootPairing.Base.linearIndepOn_coroot, Topology.CWComplex.iUnion_openCell_eq_skeletonLT, DirectSum.mk_smul, UpperSet.coe_inf, AddSubmonoid.coe_toSubmonoid_apply, IntermediateField.coe_iInf, Submonoid.subsemiringClosure_coe, SemigroupIdeal.subset_closure, adjoin_monomial_eq_reesAlgebra, ContinuousLinearMap.isComplete_ker, Module.End.mem_invtSubmodule_iff_mapsTo, DirectSum.mk_injective, coe_mul_coe, Finset.inf_id_eq_sInf, Finset.prod_indicator_biUnion_finset_sub_indicator, biUnion_associatedPrimes_eq_compl_regular, Submodule.prod_coe, PrimeSpectrum.isCompact_isOpen_iff, finite_powers, Subfield.coe_toIntermediateField, Submodule.coe_dualCoannihilator_span, SimpleGraph.ComponentCompl.pairwise_disjoint, Finset.coe_powerset, IsClopen.lowerClosure_pi, rightCoset_eq_iff, AlgHom.coe_range, Finset.image_mul_left', subset_upperClosure, MeasureTheory.Measure.haar.addHaarContent_outerMeasure_closure_pos, Module.End.mapsTo_genEigenspace_of_comm, AddGroup.fg_iff', isLinearSet_iff, AddSubsemigroup.coe_toSubsemigroup_apply, UpperSet.coe_ssubset_coe, add_upperClosure, linearIndepOn_finset_iffₒₛ, PointedCone.subset_dual_dual, Geometry.SimplicialComplex.convexHull_inter_convexHull, AddSubsemigroup.coe_iSup_of_directed, UpperSet.ext_iff, IsLinearTopology.hasBasis_open_submodule, UpperSet.coe_eq_empty, RingSubgroupsBasis.rightMul, Dynamics.netMaxcard_infinite_iff, TensorProduct.exists_finite_submodule_of_finite', OpenAddSubgroup.isClopen, InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois, Finset.coe_bipartiteBelow, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, finite_zpowers, Algebra.adjoin_attach_biUnion, coe_primesOverFinset, TopologicalSpace.Closeds.closure_le, upperClosure_interior_subset', MeasureTheory.Measure.addHaarMeasure_closure_self, Set.IsPWO.submonoid_closure, Ideal.subset_union_prime', AddSubmonoid.closure_le_centralizer_centralizer, Algebra.adjoin_span, Submonoid.iSup_eq_closure, TotallyBounded.exists_prodMk_finset_mem_hausdorffEntourage, TopologicalSpace.PositiveCompacts.ext_iff, StarAlgebra.adjoin_nonUnitalStarSubalgebra, AddSemigroupIdeal.closure_le, DFinsupp.subtypeDomain_def, FirstOrder.Language.Substructure.fg_closure, Subsemiring.coe_prod, NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk, OrderIso.infIrredUpperSet_symm_apply, TopologicalSpace.NonemptyCompacts.isEmbedding_coe, Affine.Simplex.circumradius_restrict, Projectivization.Subspace.span_sup, BooleanSubalgebra.coe_eq_univ, PrimeSpectrum.union_zeroLocus, TopologicalSpace.Closeds.coe_eq_empty, Finset.op_vadd_stabilizer_of_no_doubling, AlgebraicGeometry.Scheme.zeroLocus_biInf, FirstOrder.Language.Substructure.coe_comap, AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subset, BooleanSubalgebra.coe_top, SimpleGraph.componentComplFunctor_obj, Finsupp.fun_support_eq, Affine.Simplex.medial_restrict, convexHull_toCone_eq_sInf, Submonoid.mk_eq_bot, QuotientGroup.norm_mk_eq_zero_iff_mem_closure, Submonoid.coe_sSup_of_directedOn, TopologicalSpace.NoetherianSpace.exists_finset_irreducible, Set.powersetCard.coe_coe, LocallyFinite.exists_finset_nhds_support_subset, DependsOn.updateFinset, LowerSet.coe_eq_empty, NonarchimedeanRing.left_mul_subset, AddSubmonoid.coe_top, MonoidAlgebra.support_gen_of_gen', TopologicalSpace.Closeds.coe_preimage, Finset.sum_indicator_eq_sum_inter, not_mulDissociated, TopologicalSpace.NonemptyCompacts.isCompact_biUnion_coe_of_isCompact, BoxIntegral.unitPartition.integralSum_eq_tsum_div, ProperCone.coe_bot, Topology.CWComplex.Subcomplex.cell_def, NonUnitalStarAlgebra.coe_top, ConvexCone.coe_map, NonUnitalStarSubalgebra.coe_toNonUnitalSubring, AffineSubspace.SOppSide.nonempty, TopologicalSpace.Closeds.gc, AddSubgroup.characteristic_centralizer, NonUnitalSubalgebra.coe_toNonUnitalSubsemiring, DFinsupp.zipWith_def, NonUnitalStarAlgebra.coe_sInf, LowerSet.coe_map, Subring.coe_iSup_of_directed, IntermediateField.adjoin_le_iff, Submodule.coe_torsion', Finset.coe_coeMonoidHom, Submodule.isClosed_topologicalClosure, RootPairing.Base.exists_root_eq_sum_nat_or_neg, Finset.mem_convexHull', TopologicalSpace.NonemptyCompacts.ext_iff, PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, TopologicalSpace.Compacts.carrier_eq_coe, UpperSet.coe_div, Subgroup.coe_map, Equiv.Perm.isCycleOn_support_cycleOf, tendsto_card_div_pow_atTop_volume, MulAction.op_smul_set_stabilizer_subset, FirstOrder.Language.Substructure.coe_inclusion, MeasureTheory.Measure.haar.prehaar_sup_le, Algebra.adjoin_adjoin_of_tower, OpenNormalSubgroup.pathComponentOne_carrier, MulAction.mul_stabilizer_self, ZFSet.toSet_empty, finsum_mem_coe_finset, TopologicalSpace.CompactOpens.coe_sdiff, Finset.image_surjOn_powerset, LieIdeal.coe_toLieSubalgebra, Submonoid.coe_bot, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic, Finset.pow_right_strictMonoOn, Sublattice.inclusion_apply, orbit_subgroup_eq_self_of_mem, AddSubsemigroup.coe_top, Set.Finset.coe_einfsep, AddSubsemigroup.coe_prod, Finset.coe_sub, Finsupp.span_le_supported_biUnion_support, SimpleGraph.coe_edgeFinset, SimpleGraph.infinite_iff_in_eventualRange, SimpleGraph.extend_finset_to_connected, Fintype.finsetEquivSet_apply, MulArchimedeanClass.subsemigroup_eq_subgroup_of_ne_top, Finset.infsep_pos_iff_nontrivial, Finset.nontrivial_coe, Finset.singleton_subset_set_iff, Ordinal.coe_toZFSet, Finset.insert_inj_on, AddSubsemigroup.coe_bot, Submonoid.coe_center, Topology.IsScott.lowerClosure_subset_closure, Finset.equitableOn_iff_le_le_add_one, PrimeSpectrum.zeroLocus_subset_zeroLocus_iff, Finset.coe_cons, RestrictedProduct.zsmul_apply, Algebra.coe_iInf, AffineSubspace.perpBisector_nonempty, AlgebraicGeometry.Scheme.zeroLocus_singleton, Equiv.Perm.cycleFactorsFinset_eq_finset, ConvexCone.coe_comap, QuotientGroup.preimage_image_mk_eq_mul, Finset.coe_wcovBy_coe, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_apply_coe_asIdeal, RestrictedProduct.instIsTopologicalRingCoePrincipal, Submodule.coe_toConvexCone, not_addDissociated, ProperCone.nonempty, Finset.piCongrLeft_comp_restrict, AlgebraicGeometry.IsOpenImmersion.range_pullbackSnd, DoubleCoset.left_bot_eq_left_quot, Filter.HasBasis.uniformity_closeds, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, Polynomial.nthRootsFinset_toSet, PeriodPair.compl_lattice_diff_singleton_mem_nhds, OpenSubgroup.coe_comap, UpperSet.codisjoint_coe, Geometry.SimplicialComplex.inter_subset_convexHull, StarAlgebra.elemental.isClosed, AddSubgroup.coe_iSup_of_directed, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι_eq_support_inter, Ideal.iSup_eq_span, AffineSubspace.direction_affineSpan_insert, TopologicalSpace.NonemptyCompacts.uniformContinuous_coe, RingHom.eqOn_field_closure, SimpleGraph.coe_cliqueFinset, IsCompactOperator.codRestrict, Finset.hasSum_support, Subring.coe_matrix, AffineSubspace.sSameSide_self_iff, Set.powersetCard.stabilizer_coe, List.coe_toFinset, Submodule.mem_span_finset, AlgebraicGeometry.IsOpenImmersion.range_pullback_fst_of_right, upperClosure_interior_subset, TopologicalSpace.CompactOpens.coe_toClopens, PrimeSpectrum.isConstructible_basicOpen, Finset.set_biInter_coe, TopologicalSpace.Compacts.instCanLiftSetCoeIsCompact, Module.isTorsionBySet_annihilator, Order.PFilter.nonempty, TopologicalSpace.PositiveCompacts.coe_map, PrimeSpectrum.zeroLocus_span, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, TopologicalSpace.Opens.frameHom_toFun, IntermediateField.coe_toSubalgebra, IsTopologicalGroup.exist_openNormalSubgroup_sub_clopen_nhds_of_one, SubMulAction.mem_carrier, Subsemiring.coe_iSup_of_directed, AffineSubspace.coe_eq_univ_iff, corners_theorem_nat, Topology.RelCWComplex.Subcomplex.union_closedCell, NonUnitalAlgebra.subset_adjoin, lowerClosure_interior_subset', Finset.preimage_add_left_zero, Equiv.Perm.coe_support_eq_set_support, TopologicalSpace.CompactOpens.coe_bot, Submonoid.coe_pointwise_smul, LowerSet.sdiff_eq_left, AddSubmonoid.coe_map, prod_mem_ideal_map_of_mem_conductor, PartitionOfUnity.exists_finset_nhds, Affine.Simplex.ninePointCircle_restrict, Finset.partiallyWellOrderedOn, NonUnitalStarSubalgebra.unitization_range, Nat.subset_span_setGcd, Subgroup.smul_leftQuotientEquiv, IsAdic.hasBasis_nhds, MeasureTheory.Content.measure_eq_content_of_regular, MeasureTheory.Measure.haar.prehaar_pos, Submodule.span_nat_eq, Finset.noncommProd_union_of_disjoint, RootPairing.Base.coroot_mem_span_int, Finset.finite_toSet_toFinset, ProperCone.subset_dual_dual, Finset.centerMass_id_mem_convexHull, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv, mem_adjoin_map_integralClosure_of_isStandardEtale, RestrictedProduct.instContinuousAddCoePrincipal, StarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar, Set.Finite.toFinset_subset, LieSubalgebra.mem_carrier, setOf_mem_eq, Finset.coe_coeAddMonoidHom, PrimeSpectrum.isClosed_iff_zeroLocus_radical_ideal, Polynomial.degree_restriction, LinearIsometry.isComplete_map_iff, LowerSet.coe_Iio, ZLattice.covolume.tendsto_card_div_pow, HomogeneousIdeal.coe_bot, Finset.centerMass_id_mem_convexHull_of_nonpos, Finset.iSup_coe, Topology.RelCWComplex.skeletonLT_mono, PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElem, MeasureTheory.Measure.infinitePi_pi, LieSubmodule.bot_coe, IsLinearTopology.hasBasis_submodule, NonUnitalRingHom.eqOn_set_closure, YoungDiagram.coe_inf, NonUnitalSubalgebra.unitization_range, Finset.coe_erase, Affine.Simplex.face_restrict, AffineSubspace.affineSpan_eq_sInf, NonUnitalSubsemiring.coe_iSup_of_directed, OrderEmbedding.coe_birkhoffFinset, LieSubalgebra.engel_carrier, Algebra.coe_bot, Topology.IsUpper.isClosed_lowerClosure, SimpleGraph.end_componentCompl_infinite, IsApproximateSubgroup.subgroup, RestrictedProduct.mul_single, IsTopologicalAddGroup.exist_openAddSubgroup_sub_clopen_nhds_of_zero, Topology.RelCWComplex.Subcomplex.cellFrontier_eq, AffineIndependent.indicator_eq_of_affineCombination_eq, Finset.iInf_coe, TopologicalSpace.Closeds.uniformity_def, finrank_vectorSpan_insert_le, Group.conjugates_subset_normal, IntermediateField.fg_adjoin_finset, Finset.image_add_right, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, Subgroup.normalCore_isClosed, AffineSubspace.coe_smul, Finset.coe_infsep_of_offDiag_nonempty, ProperlyDiscontinuousVAdd.finite_stabilizer, ZFSet.coe_singleton, LieSubmodule.iInf_coe, mulRothNumber_spec, Affine.Simplex.interior_restrict, Finset.card_sups_iff, AddSubgroup.rank_closure_finset_le_card, Ideal.map_relNorm, Finset.toFinset_coe, RestrictedProduct.mulSingle_injective, DoubleCoset.right_bot_eq_right_quot, SimpleGraph.isClique_map_finset_iff, SimpleGraph.isMaximalIndepSet_compl, AddCircle.dense_addSubgroup_iff_ne_zmultiples, AddHom.eqOn_closure, monomial_mem_adjoin_monomial, OrderIso.supIrredLowerSet_symm_apply, Submonoid.sup_eq_closure_mul, Finset.coe_mem, ProjectiveSpectrum.subset_zeroLocus_iff_le_vanishingIdeal, Finset.coe_sdiff, IsLocalizedModule.finsetIntegerMultiple_image, Finset.preimage_mul_right_one', LieSubalgebra.coe_injective, PrimeSpectrum.zeroLocus_eq_basicOpen_of_isIdempotentElem, AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff_of_mem, Subsemiring.coe_sInf, Subsemigroup.coe_prod, TopCat.Presheaf.germ_stalkSpecializes_assoc, Sublattice.coe_inf', Finset.isLUB_sup_id, TopologicalSpace.Opens.chartAt_inclusion_symm_eventuallyEq, Algebra.subset_adjoin, Subring.coe_toAddSubgroup, Submodule.smul_subset_smul, Ideal.isTorsionBySet_cotangent, AffineSubspace.inclusion_linear, OpenSubgroup.coe_inf, ProjectiveSpectrum.union_zeroLocus, ZFSet.coeEquiv_apply_coe, Subring.coe_pointwise_smul, NonUnitalSubsemiring.closure_addSubmonoid_closure, TopologicalSpace.Compacts.coe_map, AddSubgroup.isComplement_addSubgroup_left_iff_bijective, Subgroup.closure_le, IsLinearSet.closure_of_finite, Partition.pairwiseDisjoint, TopologicalSpace.CompactOpens.coe_mk, Set.Finite.submoduleSpan, IsNoetherianRing.isClosed_ideal, OpenSubgroup.coe_prod, AddSemigroupIdeal.coe_closure, Subalgebra.le_centralizer_iff, NonUnitalStarSubsemiring.coe_ofClass, PrimeSpectrum.isIrreducible_zeroLocus_iff_of_radical, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ι, Set.union_finset_finite_of_range_finite, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, TopologicalSpace.Opens.partialHomeomorphSubtypeCoe_target, MeasureTheory.Measure.haar.prehaar_empty, HomogeneousIdeal.coe_inf, Ideal.span_eq_top_iff_finite, Submodule.coe_span_smul, ProfiniteGrp.closedSubgroup_eq_sInf_open, Subgroup.isComplement_iff_bijective, TensorProduct.exists_finite_submodule_left_of_setFinite, TopologicalSpace.NonemptyCompacts.uniformity_def, Finset.bddAbove, iInf_valuationSubring_superset, ContinuousLinearMap.isClosed_ker, Subgroup.leftCoset_cover_const_iff_surjOn, Subgroup.coe_square, Subsemigroup.coe_topologicalClosure, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, MeasureTheory.dense_of_generateFrom_isSetRing, Order.Ideal.coe_sup_eq, MeasureTheory.Content.innerContent_exists_compact, AddAction.stabilizer_add_self, RingSubgroupsBasis.hasBasis_nhds_zero, LowerSet.coe_sSup, Submodule.span_attach_biUnion, Finsupp.mapDomain_injOn, NonarchimedeanGroup.exists_openSubgroup_separating, ContinuousMap.idealOfSet_closed, CommGroup.coe_primaryComponent, MeasureTheory.Measure.haar.le_addIndex_mul, UpperSet.coe_prod, IsPrimitiveRoot.injOn_pow, BooleanSubalgebra.coe_map, MeasureTheory.Measure.haar.prehaar_sup_eq, Submonoid.closure_eq_one_union, Submodule.instIsTwoSidedColonCoe, Finset.prod_mulIndicator_subset_of_eq_one, IsChain.exists_subset_flag, Ideal.disjoint_powers_iff_notMem, isIrreducible_iff_sInter, NonarchimedeanGroup.prod_subset, Submodule.span_int_eq, ProjectiveSpectrum.subset_zeroLocus_iff_subset_vanishingIdeal, Subgroup.normalClosure_subset_iff, FiniteDimensional.span_finset, AlgebraicGeometry.Scheme.Opens.nonempty_iff, Algebra.SubmersivePresentation.HasCoeffs.coeffs_subset_range, RestrictedProduct.instIsTopologicalAddGroupCoePrincipal, Subgroup.subset_normalizer_of_normal, IsLinearTopology.hasBasis_twoSidedIdeal, QuotientGroup.eq_class_eq_leftCoset, Finset.isGLB_inf, Finset.sized_slice, MeasureTheory.Measure.haar.mem_prehaar_empty, Algebra.coe_top, Finset.coe_offDiag, SimpleGraph.IsCycles.toSimpleGraph, MeasureTheory.Measure.addHaarMeasure_eq_iff, Valued.isClopen_valuationSubring, Finset.coe_pair, Set.powersetCard.addAction_stabilizer_coe, TopologicalSpace.Compacts.uniformity_def, LocallyFinite.exists_finset_support, AlgebraicGeometry.coe_opensRestrict_symm_apply, Algebra.Presentation.coeffs_relation_subset_coeffs, Set.coe_unit, TopologicalSpace.NonemptyCompacts.coe_toCloseds, ConvexBody.coe_smul, Finset.mem_insert_coe, PartitionOfUnity.coe_finsupport, Interval.coe_dual, AddAction.stabilizer_op_addSubgroup, UniqueDiffWithinAt.dense_tangentConeAt, NonUnitalSubsemiring.closure_le_centralizer_centralizer, SemigroupIdeal.coe_closure, MeasureTheory.IsSetSemiring.mem_supClosure_iff, IsOfFinOrder.finite_powers, FirstOrder.Language.Substructure.fg_def, Finset.support_of_fiberwise_sum_subset_image, AddSubmonoid.mem_closure_iff_exists_finset_subset, PowerSeries.coe_hasEvalIdeal, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_ideal, AffineSubspace.le_def, Submodule.surjective_tensorToSpan, AddMonoidHom.coe_mker, MeasureTheory.Content.outerMeasure_interior_compacts, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, PrimeSpectrum.zeroLocus_radical, Subsemigroup.coe_centralizer, PrimeSpectrum.zeroLocus_minimalPrimes, Subgroup.set_mul_normal_comm, LieSubalgebra.sInf_coe, PartitionOfUnity.exists_finset_nhds_support_subset, Finset.coe_Icc, RestrictedProduct.smul_apply, AddSubmonoid.coe_centralizer, Submodule.coe_ofClass, infinite_zpowers, TopologicalSpace.IrreducibleCloseds.instCanLiftSetCoeAndIsIrreducibleIsClosed, Finset.pairwiseDisjoint_smul_iff, PrimeSpectrum.isIrreducible_zeroLocus_iff, Polynomial.exists_image_comap_of_monic, SimpleGraph.neighborFinset_subset_between_union, EuclideanGeometry.preimage_inversion_perpBisector, Interval.subset_coe_map, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, Finset.card_preimage_eq_sum_card_image_eq, PeriodPair.isClosed_lattice, AddSubgroup.isOpen_of_isClosed_of_finiteIndex, Set.subgroupClosure_mul_pow, Valued.isClosed_valuationSubring, IsDedekindDomain.HeightOneSpectrum.valuation_def, TwoSidedIdeal.coe_mk', Part.coe_toFinset, Subgroup.le_centralizer, Finset.coe_bipartiteAbove, ClopenUpperSet.coe_sup, MeasureTheory.Measure.haar.add_prehaar_le_addIndex, AddSubmonoid.coe_add_self_eq, TopologicalSpace.PositiveCompacts.interior_nonempty, Topology.IsLower.isClosed_upperClosure, Submodule.image_span_subset_span, Subgroup.isComplement_subgroup_left_iff_existsUnique_quotientMk'', LinearRecurrence.sol_eq_of_eq_init, MonoidAlgebra.mem_span_support, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, range_cfcₙ, AffineSubspace.WOppSide.nonempty, Cardinal.mk_compl_finset_of_infinite, RestrictedProduct.nsmul_apply, SummationFilter.HasSupport.eventually_le_support, DFinsupp.filter_def, Subalgebra.fg_adjoin_finset, AffineSubspace.bot_coe, RingSubgroupsBasis.leftMul, LieSubalgebra.inf_coe, GroupCone.coe_oneLE, Isometry.mapsTo_perpBisector, Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, Finset.tprod_subtype', ConvexBody.coe_mk, Ideal.image_subset_nonunits_valuationSubring, Algebra.basicOpen_subset_smoothLocus_iff_smooth, Subring.closure_eq, ClosedSubmodule.coe_sInf, AddMonoidHom.coe_graph, Subring.coe_inf, Flag.chain_le, QuotientGroup.rightRel_r_eq_rightCosetEquivalence, Subalgebra.coe_op, StarMemClass.star_coe_eq, FirstOrder.Language.Substructure.coe_sInf, Finset.map_subtype_subset, LowerSet.coe_iSup, TopologicalSpace.Compacts.totallyBounded_subsets_of_totallyBounded, Ideal.disjoint_map_primeCompl_iff_comap_le, Subgroup.coe_ofClass, IsGaloisGroup.fixedPoints_fixingSubgroup, Finset.injOn_of_card_image_eq, ClopenUpperSet.isClopen, IsCompactOpenCovered.exists_mem_of_isBasis, Subring.closure_le_centralizer_centralizer, Subgroup.centralizer_eq_top_iff_subset, orbit_addSubgroup_eq_self_of_mem, NonarchimedeanGroup.is_nonarchimedean, LieSubalgebra.coe_toSubmodule, MonoidHom.noncommPiCoprod_apply, AddSubmonoid.subset_closure, Topology.RelCWComplex.Subcomplex.openCell_subset_of_mem, Units.val_set_image_rootsOfUnity_one, NonemptyInterval.coe_zero, Topology.RelCWComplex.cellFrontier_subset_skeleton, Polynomial.restriction_zero, Submodule.closed_of_finiteDimensional, AffineSubspace.inf_coe, Ideal.IsMaximal.isClosed, HahnSeries.cardSuppLTSubfield_carrier, Affine.Simplex.altitude_restrict_eq_comap_subtype, TopologicalSpace.Compacts.continuous_coe, Algebra.essFiniteType_cond_iff, QuotientAddGroup.norm_mk, ContinuousLinearMap.eqOn_closure_span, AffineSubspace.lt_def, smul_coe_set, Sublattice.supClosed, TopologicalSpace.NonemptyCompacts.isOpen_inter_nonempty_of_isOpen, Set.injOn_iff_map_eq_zero, QuotientGroup.univ_eq_iUnion_smul, Filter.HasBasis.uniformity_compacts, eq_affineCombination_of_mem_affineSpan_image, FirstOrder.Language.Substructure.lift_card_closure_le_card_term, ProperCone.isClosed, Finset.coe_mul, MeasureTheory.dense_of_generateFrom_isSetSemiring, Polynomial.bUnion_roots_finite, Algebra.elemental.le_centralizer_centralizer, leftCoset_eq_iff, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, AffineSubspace.setOf_wOppSide_eq_image2, TopologicalSpace.Clopens.coe_disjoint, AddSubgroup.neg_subset_closure, AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_index, AddSubmonoid.mk_add_mk_neg_eq_zero, Finsupp.coe_neLocus, Submodule.iInf_coe, NonUnitalSubsemiring.coe_center, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, AffineSubspace.coe_inf, Metric.uniformContinuous_infDist_Hausdorff_dist, Subsemigroup.closure_le_centralizer_centralizer, Subsemiring.coe_toSubmonoid, IsLocalization.finsetIntegerMultiple_image, TopologicalSpace.Closeds.coe_singleton, ConvexBody.convex, RestrictedProduct.mulSingle_eq_of_ne', HahnSeries.SummableFamily.smul_support_subset_prod, Polynomial.Chebyshev.strictAntiOn_node, AddSubmonoid.coe_even, IsGaloisGroup.fixingSubgroup_le_of_le, AddSubmonoid.coe_nonneg, LowerSet.sdiff_lt_left, Module.isTorsionBySet_span_singleton_iff, NonUnitalSubring.isClosed_topologicalClosure, MonoidWithZeroHom.valueGroup_eq_range, UpperSet.coe_mk, TopologicalSpace.Compacts.coe_bot, Projectivization.Subspace.span_coe, Subsemiring.subset_closure, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, Subgroup.normalizerMonoidHom_ker, IsFractionRing.algHom_fieldRange_eq_of_comp_eq, FirstOrder.Language.LHom.coe_substructureReduct, MeasureTheory.Measure.addHaarMeasure_unique, Set.coe_integer, AddSubgroup.centralizer_closure, ExteriorAlgebra.ιMulti_range, Finset.supIndep_iff_pairwiseDisjoint, PrimeSpectrum.mem_image_comap_basicOpen, FirstOrder.Language.Substructure.mem_closure_iff_exists_term, Module.le_rank_iff_exists_finset, AffineSubspace.coe_pointwise_vadd, PrimitiveSpectrum.hull_finsetInf, LowerSet.coe_ssubset_coe, Finset.coe_eq_zero, GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_range, Finset.isGreatest_max', Besicovitch.exist_finset_disjoint_balls_large_measure, IsLinearTopology.hasBasis_open_ideal, Submodule.mem_span_iff_exists_finset_subset, AddSubgroup.card_add_eq_card_addSubgroup_add_card_quotient, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff, Algebra.Presentation.coeffs_subset_core, Submodule.mem_span_mul_finite_of_mem_mul, ClopenUpperSet.coe_mk, AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeι, ZFSet.toSet_image, ZFSet.coe_range, QuotientAddGroup.strictMono_comap_prod_image, LowerSet.coe_sub, ContDiffMapSupportedIn.zero_on_compl', AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iff, Sublattice.coe_comap, TopologicalSpace.Clopens.isClopen, Order.Ideal.IsPrime.compl_filter, upperClosure_mul, Algebra.Presentation.coeffs_relation_subset_core, Order.Ideal.PrimePair.isCompl_I_F, LinearIndepOn.subset_span_extend, NonUnitalSubsemiring.coe_bot, TopologicalSpace.IsSeparable.span, Interval.coe_zero, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, NonUnitalAlgebra.adjoin_le_iff, PrimeSpectrum.isClopen_iff, QuotientAddGroup.discreteTopology_iff, Finset.coe_inj, Subgroup.centralizer_closure, TopologicalSpace.Opens.gc, IsDiscreteValuationRing.isOpen_iff, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous, AddSubgroup.coe_add_of_left_le_normalizer_right, Finset.coe_image_subset_range, IntermediateField.sSup_def, AlgebraicGeometry.morphismRestrict_appLE, MulHom.eqOn_closure, MeasureTheory.IsSetSemiring.sUnion_disjointOfDiff, IsOfFinAddOrder.natCard_multiples_le_addOrderOf, AlgebraicGeometry.Scheme.Opens.toScheme_carrier, TensorProduct.exists_finite_submodule_right_of_setFinite, IsExposed.sInter, LowerSet.coe_sup, TopologicalSpace.Compacts.isOpen_inter_nonempty_of_isOpen, SubAddAction.subset_closure, Caratheodory.mem_minCardFinsetOfMemConvexHull, Order.Ideal.IsMaximal.maximal_proper, TopologicalSpace.Opens.coe_eq_empty, EuclideanGeometry.image_inversion_perpBisector, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ, Subgroup.subgroup_mul_singleton, StarSubsemiring.coe_toSubsemiring, Topology.CWComplex.Subcomplex.union, SimpleGraph.neighborFinset_subset_between_union_compl, Submodule.mapsTo_smul_closure, Submonoid.coe_prod, Subsemiring.closure_le_centralizer_centralizer, Submodule.norm_eq_iInf_iff_real_inner_eq_zero, Finset.coe_image, vectorSpan_eq_span_vsub_finset_right_ne, Subalgebra.le_centralizer_centralizer, ContinuousLinearMap.closed_complemented_range_of_isCompl_of_ker_eq_bot, op_smul_coe_set, ConvexBody.ext_iff, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, AddSubgroup.isClosed_of_discrete, Ideal.IsMinimalPrimaryDecomposition.minimalPrimes_subset_image_radical, Topology.RelCWComplex.openCell_subset_skeletonLT, Order.Ideal.PrimePair.compl_I_eq_F, FreeCommRing.exists_finset_support, SimpleGraph.IsMaximumIndepSet.isMaximalIndepSet, Submodule.coe_restrictScalars, Topology.RelCWComplex.closedCell_subset_skeletonLT, UniqueAdd.addHom_preimage, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, LowerSet.coe_top, Representation.coe_coindV, DFinsupp.mk_zero, Finset.setOf_mem, Unitization.starLift_range, TopologicalSpace.IrreducibleCloseds.is_irreducible', ContDiffMapSupportedIn.zero_on_compl, Algebra.adjoin_nonUnitalSubalgebra_eq_span, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_inv_assoc, Topology.RelCWComplex.Subcomplex.finiteDimensional_subcomplex_of_finiteDimensional, Module.support_of_algebra, Nat.bijOn_ofDigits', AddSubsemigroup.subset_closure, NonemptyInterval.coe_ssubset_coe, TopologicalSpace.CompactOpens.coe_inf, Order.Ideal.directed, Submonoid.exists_minimal_closure_eq_top, LieSubmodule.subset_lieSpan, NonUnitalSubring.ofClass_carrier, ZFSet.toSet_inj, Subgroup.instCanLiftSetCoeAndMemOfNatForallForallForallForallHMulForallForallInv, exists_linearIndepOn_extension, Submodule.comap_coe, isNoetherian_adjoin_finset, HallMarriageTheorem.hall_cond_of_restrict, Finset.sup'_eq_csSup_image, Finset.image_add_right', isClosed_nullSubgroup, coe_nonZeroDivisorsRight_eq, PeriodPair.differentiableOn_derivWeierstrassP, VonNeumannAlgebra.coe_mk, Subgroup.coe_top, MeasureTheory.Measure.haar.prehaar_nonneg, Algebra.QuasiFiniteAt.exists_basicOpen_eq_singleton, ofAdd_image_zmultiples_eq_zpowers_ofAdd, Submodule.coe_pointwise_smul, MeasureTheory.Measure.haar.addPrehaar_sup_eq, Subgroup.smul_apply_eq_smul_apply_inv_smul, AddMonoid.closure_finset_fg, lowerClosure_eq_Iic_csSup, ConvexCone.coe_strictlyPositive, Partition.coe_copy, HahnSeries.SummableFamily.support_pow_subset_closure, AddGroup.rank_spec, Affine.Simplex.ExcenterExists.touchpointWeights_restrict, PrimeSpectrum.mem_zeroLocus, affineSpan_le, TopologicalSpace.Clopens.coe_sdiff, NonUnitalSubring.closure_eq, Set.powersetCard.coe_ofFinEmb, Finset.subset_powersetCard_univ_iff, uniqueDiffWithinAt_iff, AddSubmonoid.coe_iInf, AddSubgroup.dense_iff_ne_zmultiples, IsLocalization.isPrime_iff_isPrime_disjoint, Subring.mem_closure_iff, Units.val_set_image_rootsOfUnity, QuotientAddGroup.t1Space_iff, OpenSubgroup.mem_nhds_one, RestrictedProduct.coe_single_apply, NonemptyInterval.coe_subset_coe, AddSubmonoid.coe_negOrderIso_symm_apply, ProjectiveSpectrum.mem_zeroLocus, coe_set_eq_zero, Submodule.fg_span_iff_fg_span_finset_subset, Submodule.annihilator_map_mkQ_eq_colon, LieSubmodule.mem_baseChange_iff, NonUnitalSubring.coe_iInf, TopologicalSpace.Opens.nonempty_coe, PrimeSpectrum.subset_vanishingIdeal_zeroLocus, MulAction.isBlock_subgroup', Sublattice.infClosed, closure_upperClosure_comm_pi, AddSubsemigroup.instCanLiftSetCoeForallForallForallMemForallHAdd, NonUnitalStarAlgebra.adjoin_eq_span, Group.rank_spec, AddSubmonoid.exists_minimal_closure_eq_top, Polynomial.derivativeFinsupp_derivative, op_vadd_coe_set, AddSubgroup.isComplement_range_left, alternatingGroup.coe_kleinFour_of_card_eq_four, TopologicalSpace.CompactOpens.coe_compl, ProperCone.coe_comap, NonUnitalStarAlgebra.gc, EMetric.isClosed_subsets_of_isClosed, EuclideanGeometry.image_inversion_affineSubspace_of_mem, DirectSum.mk_apply_of_notMem, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, NonUnitalStarAlgebra.subset_adjoin, Subalgebra.centralizer_coe_map_includeRight_eq_center_tensorProduct, TopologicalSpace.Compacts.coe_top, RestrictedProduct.single_zero, Submonoid.mk_mul_mk_inv_eq_one, IntermediateField.rank_adjoin_eq_one_iff, TopologicalSpace.NonemptyCompacts.isUniformEmbedding_coe, Finset.intervalGapsWithin_surjOn, Finset.isClosed, TopologicalSpace.Compacts.coe_sup, Finset.measurableSet, PrimeSpectrum.subset_zeroLocus_iff_le_vanishingIdeal, AlgebraicGeometry.Scheme.zeroLocus_iInf_of_nonempty, MeasureTheory.Lp.boundedContinuousFunction_dense, EuclideanGeometry.image_inversion_sphere_dist_center, Submonoid.mk_inv_mul_mk_eq_one, TopologicalSpace.Opens.coe_overEquivalence_functor_obj, Subring.coe_set_mk, HNNExtension.NormalWord.unitsSMulGroup_snd, TopologicalSpace.CompactOpens.isOpen, affineIndependent_iff_indicator_eq_of_affineCombination_eq, inv_coe_set, Order.exists_orderEmbedding_insert, finiteDimensional_direction_affineSpan_insert, StrongDual.polarSubmodule_eq_polar, RestrictedProduct.locallyCompactSpace_of_group, RestrictedProduct.comp_single, Submodule.inclusionSpan_apply_coe, AddSubgroup.coe_topologicalClosure_bot, unitInterval.coe_unitIntervalSubmonoid, coe_smulCardAddSubgroup, coe_topologicalNilradical, TopologicalSpace.Closeds.coe_bot, AddSubmonoid.top_closure_add_self_subset, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, GrpCat.SurjectiveOfEpiAuxs.agree, SimpleGraph.isNIndepSet_iff, Nucleus.coe_toSublocale, TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage, lowerBounds_upperClosure, powers_eq_zpowers, RestrictedProduct.single_add, lowerClosure_interior_subset, ProjectiveSpectrum.gc_set, Finset.coe_sups, ClosedSubmodule.coe_bot, MvPolynomial.mem_supported, Finset.coe_Ioc, SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph, AddEquiv.add_submonoid_map_symm_apply, Subfield.coe_iInf, Affine.Simplex.ExcenterExists.excenter_restrict, LocallyFinite.exists_finset_mulSupport, Sublattice.prodEquiv_toEquiv, Finsupp.comapDomain_surjective, TopologicalSpace.Closeds.edist_eq, Finsupp.comapDomain_mapDomain, AffineSubspace.closed_of_finiteDimensional, TopologicalSpace.Opens.coe_finset_sup, Finset.coe_Ioo, coe_div_coe, Finset.Nonempty.csSup_mem, biUnion_associatedPrimes_eq_zero_divisors, LinearPMap.sub_apply, Finset.invMulSubgroup_eq_mul_inv, addRothNumber_spec, LowerSet.coe_sInf, ofMul_image_powers_eq_multiples_ofMul, AddCommMonoid.coe_primaryComponent, FirstOrder.Language.DefinableSet.le_iff, TensorProduct.exists_finite_submodule_left_of_finite, SimpleGraph.isClique_map_finset_iff_of_nontrivial, ConvexCone.disjoint_hull_left_of_convex, Subsemigroup.coe_sInf, MulAction.stabilizer_subgroup, ZFSet.coe_subset_coe, SemigroupIdeal.closure_le, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_apply, IsUniformAddGroup.uniformContinuous_iff_isOpen_ker, Affine.Simplex.range_face_points, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, SeparatedNhds.of_finset_finset, MvPolynomial.coe_coeffs_map, Subring.coe_map, NonUnitalStarAlgebra.elemental.isClosed, TopologicalSpace.CompactOpens.coe_map, Subgroup.coe_toAddSubgroup_symm_apply, dense_addSubmonoidClosure_iff_addSubgroupClosure, Submodule.traceDual_le_span_map_traceDual, ZFSet.coe_sUnion, LieSubalgebra.coe_sInf, Set.Finite.coe_toFinset, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, IsGaloisGroup.fixingSubgroup_fixedPoints, Submodule.mem_colon_iff_le, IsSemilinearSet.closure_of_finite, AddSubmonoid.isClosed_topologicalClosure, TwoSidedIdeal.mem_fromIdeal, AddSemigroupIdeal.coe_closure', RestrictedProduct.instIsTopologicalGroupCoePrincipal, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom, TopologicalSpace.OpenNhdsOf.isOpen, partialSups_eq_sUnion_image, NonemptyInterval.coe_one, FirstOrder.Language.DefinableSet.coe_compl, Subsemigroup.nonUnitalSubsemiringClosure_coe, Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontier, VonNeumannAlgebra.mem_carrier, Subgroup.coe_pathComponentOne, FirstOrder.Language.Substructure.coe_top, AlgebraicGeometry.Scheme.zeroLocus_radical, Subsemigroup.instCanLiftSetCoeForallForallForallMemForallHMul, Matrix.convex_colStochastic, EuclideanGeometry.preimage_inversion_sphere_dist_center, Submodule.coe_finsetInf, LieSubalgebra.coe_set_eq, HahnSeries.coe_cardSuppLTAddSubgroup, StarSubalgebra.topologicalClosure_coe, AddSubgroup.inf_add_assoc, ConvexCone.coe_mk, AddSubgroup.coe_toAddSubmonoid, Submodule.mem_span_set, VonNeumannAlgebra.centralizer_centralizer, ContinuousMap.exists_finite_sum_const_indicator_approximation_of_mem_nhds_diagonal, Finset.singleton_subset_coe, PrimeSpectrum.zeroLocus_ideal_mem_irreducibleComponents, AddSubmonoid.coe_sInf, Finset.range_orderEmbOfFin, Subfield.coe_comap, Submodule.exists_fg_le_subset_range_rTensor_subtype, YoungDiagram.isLowerSet, Set.powersetCard.coe_map, UpperSet.coe_iInf₂, Subsemigroup.closure_le, AddSubmonoid.coe_neg, Subalgebra.adjoin_eq_span_basis, TopologicalSpace.Clopens.coe_top, TopologicalSpace.Closeds.coe_finset_inf, Subsemiring.coe_carrier_toSubmonoid, TopologicalSpace.NonemptyCompacts.coe_map, LinearMap.coe_range, Sublattice.prodEquiv_apply, AddSubsemigroup.coe_map, AddSubgroup.isComplement_addSubgroup_right_iff_bijective, Affine.Simplex.map_altitude_restrict, UpperSet.coe_eq_univ, RestrictedProduct.evalRingHom_apply, IntermediateField.coe_inf, RingHom.eqOn_set_closure, TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_left, UpperSet.coe_compl, Affine.Simplex.faceOpposite_restrict, ofMul_image_zpowers_eq_zmultiples_ofMul, RestrictedProduct.single_sub, PrimeSpectrum.zeroLocus_iSup, RestrictedProduct.instContinuousNegCoe, MeasureTheory.Measure.addHaarMeasure_apply, Descriptive.coe_def, Finset.doubling_lt_two, AffineSubspace.convex, AddSubgroup.isComplement_addSubgroup_right_iff_existsUnique_quotientAddGroupMk, Submonoid.coe_op, NonUnitalSubring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg, PointedCone.convex, Ideal.homogeneousHull_eq_iSup, AlgebraicGeometry.Scheme.zeroLocus_map, Submodule.mem_span_finset', Topology.CWComplex.Subcomplex.coe_mk'', MulAction.smul_set_stabilizer_subset, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_apply, Submodule.map₂_eq_span_image2, IsAdic.hasBasis_nhds_zero, TopCat.GlueData.range_fromOpenSubsetsGlue, Sylow.normalizer_le_centralizer_or_le_commutator, NonUnitalStarSubalgebra.coe_centralizer, ConvexCone.subset_hull, ConvexCone.IsGenerating.top_le_span, ZFSet.coe_sep, TopologicalSpace.Opens.IsBasis.of_isInducing, TopologicalSpace.IrreducibleCloseds.isIrreducible, RestrictedProduct.mulSingle_mul, TopologicalSpace.NonemptyCompacts.isOpen_subsets_of_isOpen, AddSubsemigroup.closure_eq, Submodule.IsMinimalPrimaryDecomposition.distinct, IsSelfAdjoint.dense_domain, AlgebraicGeometry.Scheme.zeroLocus_inf, image_comap_zeroLocus_eq_zeroLocus_comap, affineSpan_subset_span, Topology.IsUpperSet.closure_eq_lowerClosure, Affine.Simplex.exradius_restrict, BooleanSubalgebra.coe_inj, range_cfcₙ_eq_range_cfcₙHom, QuotientAddGroup.image_coe_inj, ContinuousMap.adjoin_id_eq_span_one_union, Finset.coe_coeEmb, ContinuousMap.AlgHom.closure_ker_inter, Submonoid.mul_subset_closure, Subbimodule.coe_mk, Finset.coe_ssubset, NonUnitalAlgebra.elemental.isClosed, PrimeSpectrum.zeroLocus_eq_iff, Finset.preimage_compl, Finset.coe_attach, Subring.subset_closure, NonUnitalStarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar, Subsemiring.isHomogeneous_iff_subset_iInter, Submodule.toSubalgebra_mk, isProperLinearSet_iff, normal_iff_eq_cosets, Subsemigroup.centralizer_eq_top_iff_subset, Submodule.colon_span, FirstOrder.Language.DefinableSet.coe_bot, TensorProduct.exists_finite_submodule_right_of_setFinite', Ideal.isCompact_of_fg, Topology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succ, Valued.isOpen_valuationSubring, AlgebraicGeometry.exists_isAffineOpen_mem_and_subset, MulAction.stabilizer_subset_div_right, Finset.inv_filter_univ, RingPreordering.coe_toSubsemiring, Subgroup.isClosed_of_discrete, ContDiffMapSupportedIn.tsupport_subset, Finset.doubling_lt_golden_ratio, Valuation.IsRankOneDiscrete.generator_zpowers_eq_range, FirstOrder.Language.Substructure.mem_closed_of_isRelational, TopologicalSpace.Compacts.coe_prod, Submodule.baseChange_eq_span, Polynomial.rootSet_def, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, AddSubsemigroup.coe_sInf, Finset.Nonempty.csInf_eq_min', MeasureTheory.Measure.addHaarMeasure_self, LieSubalgebra.subset_lieSpan, Ideal.coe_restrictScalars, AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated, BooleanSubalgebra.closure_le, ClosedSubmodule.coe_toCloseds, SimpleGraph.IsNClique.isClique, closure_addSubmonoidClosure_eq_closure_addSubgroupClosure, RingSubgroupsBasis.mem_addGroupFilterBasis, Submodule.coe_mapAlgEquiv_apply, Subsemigroup.coe_unop, upperClosure_min, FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_family, TopologicalSpace.Compacts.coe_singleton, BooleanSubalgebra.coe_inclusion, ContinuousAlgHom.eqOn_closure_adjoin, Finset.preimage_mul_right_one, AddSubgroup.coe_set_mk, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', LowerSet.coe_erase, TopologicalSpace.Opens.coe_finset_inf, LieHom.coe_range, conductor_subset_adjoin, AffineIndependent.finrank_vectorSpan_image_finset, Subgroup.exists_leftTransversal_of_FiniteIndex, Derivation.eqOn_adjoin, Algebra.adjoin_toSubmodule_le, Finset.affineCombination_indicator_subset, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, AddSubgroup.coe_add_of_right_le_normalizer_left, NonUnitalSubring.coe_toAddSubgroup, Ideal.isOpen_pow_of_isMaximal, Subgroup.exists_isComplement_left, Subgroup.topologicalClosure_coe, Subgroup.rank_closure_finset_le_card, Subgroup.singleton_mul_subgroup, FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup, ProperlyDiscontinuousSMul.finite_stabilizer, PMF.support_ofMultiset, Topology.RelCWComplex.Subcomplex.map_def, Submodule.injective_tensorToSpan, ClopenUpperSet.upper, QuotientAddGroup.preimage_image_mk_eq_add, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_apply, Subalgebra.starClosure_eq_adjoin, IntermediateField.coe_toSubfield, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, AddMonoidHom.coe_mgraph, AddSubgroup.le_centralizer_iff_isAddCommutative, DoubleCoset.rel_bot_eq_right_group_rel, TopologicalSpace.Closeds.isClosed_subsets_of_isClosed, Sublattice.coe_inj, IsLinearSet.closure, Submonoid.coe_oneLE, AddSubgroup.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallNeg, Topology.RelCWComplex.iUnion_skeletonLT_eq_complex, coe_injective, NormedAddGroupHom.isClosed_ker, StarSubalgebra.coe_bot, MvPolynomial.pointToPoint_zeroLocus_le, Finset.coe_compl, MonoidAlgebra.exists_finset_adjoin_eq_top, AddSubmonoid.coe_prod, TopologicalSpace.NonemptyCompacts.coe_toCompacts, IntermediateField.finrank_adjoin_eq_one_iff, MulAction.stabilizer_subgroup_op, MeasureTheory.IsSetSemiring.diff_eq_sUnion', Topology.RelCWComplex.skeletonLT_zero_eq_base, Set.Finite.toFinset_ssubset, ConvexBody.isBounded, AddSubgroup.coe_op, LieModuleHom.coe_range, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_apply, UpperSet.coe_mul, Subgroup.commutator_eq_bot_iff_le_centralizer, Finset.coe_smul_finset, Subfield.coe_set_mk, LieDerivation.eqOn_lieSpan, Sym2.coe_mk, Finset.sum_indicator_subset_of_eq_zero, Submodule.span_eq, MeasureTheory.Measure.haar.mem_addPrehaar_empty, ZLattice.covolume.tendsto_card_le_div', TopologicalSpace.Opens.set_range_inclusion', SimpleGraph.TripartiteFromTriangles.cliqueSet_eq_image, AddSubgroup.vadd_leftQuotientEquiv, NonUnitalSubalgebra.coe_iSup_of_directed, not_addDissociated_iff_exists_disjoint, Finset.infs_self, rank_span_finset_le, PointedCone.coe_closure, DirectSum.mk_apply_of_mem, isLinearTopology_iff_hasBasis_ideal, exists_positiveCompacts_subset, Interval.coe_iInf, pi_eq_generateFrom, Submodule.coe_iInf, TopologicalSpace.Clopens.coe_inf, MonoidHom.coe_mker, Finset.coe_vadd, TopologicalSpace.NonemptyCompacts.isClosed_inter_nonempty_of_isClosed, Subgroup.coe_set_mk, LowerAdjoint.closure_union_closure_subset, Ideal.span_eq, coe_subset_nonunits, SimpleGraph.ComponentCompl.coe_inj, UniqueMul.mulHom_preimage, Ideal.Filtration.submodule_span_single, mem_own_leftAddCoset, SimpleGraph.ConnectedComponent.spanningCoe_toSubgraph, BooleanSubalgebra.latticeClosure_subset_closure, Subsemigroup.coe_comap, SmoothPartitionOfUnity.coe_finsupport, TopologicalSpace.IrreducibleCloseds.isClosed, DFinsupp.erase_def, Opens.coe_mayerVietorisSquare_X₁, TopologicalSpace.Closeds.coe_nonempty, IntermediateField.subset_adjoin_of_subset_right, StarAlgebra.star_subset_adjoin, AddSubgroup.coe_inf, PointedCone.tmul_subset_maxTensorProduct, Finset.coe_infsep, TopologicalSpace.Compacts.coe_mk, Submonoid.closure_eq, Interval.coe_coe, Set.powersetCard.coe_finset, NonUnitalSubring.coe_bot, TopologicalSpace.CompactOpens.coe_prod, Submodule.annihilator_top_inter_nonZeroDivisors, Algebra.basicOpen_subset_etaleLocus_iff, QuotientGroup.discreteTopology_iff, TopologicalSpace.OpenNhdsOf.basis_nhds, Subgroup.normalClosure_eq_iInf, MeasureTheory.sum_measure_preimage_singleton, Submonoid.coe_top, Ideal.hasBasis_nhds_zero_adic, TwoSidedIdeal.le_iff, OpenAddSubgroup.isOpen, SubMulAction.coe_mul, IntermediateField.subset_adjoin, NonUnitalSubalgebra.starClosure_eq_adjoin, NonUnitalRingHom.coe_range, coe_affineSpan, neg_coe_set, FirstOrder.Language.Substructure.closure_insert, Subsemiring.comap_toSubmonoid, Affine.Simplex.circumcenter_restrict, Set.powersetCard.coe_nonempty_iff, Module.isTorsionBySet_iff_subseteq_ker_lsmul, NonUnitalSubalgebra.coe_comap, TopologicalSpace.Opens.nonempty_coeSort, Affine.Simplex.height_restrict, BooleanSubalgebra.infClosed, RootPairing.Base.linearIndepOn_root, Subsemiring.coe_sumSq, AddSubmonoid.coe_iSup_of_directed, Set.nsmul_add_addSubgroupClosure, RestrictedProduct.vadd_apply, Finset.mem_convexHull, Subgroup.dense_or_cyclic, TopologicalSpace.NonemptyCompacts.coe_sup, LowerSet.coe_inf, DiscreteQuotient.comp_finsetClopens, TensorProduct.exists_finite_submodule_left_of_finite', StarAlgebra.subset_adjoin, LinearPMap.add_apply, IntermediateField.adjoin.range_algebraMap_subset, SimpleGraph.coe_finsetWalkLength_eq, Finset.pairwiseDisjoint_map_sigmaMk, MultilinearMap.map_nonempty, AddSubmonoid.coe_sSup_of_directedOn, TopologicalSpace.IrreducibleCloseds.is_closed', AddSubmonoid.pow_eq_closure_pow_set, DFinsupp.coe_neLocus, Module.Basis.mem_span_image, NonUnitalAlgebra.coe_iInf, Subalgebra.coe_matrix, Subgroup.coe_iInf, Unitization.lift_range, BoxIntegral.Prepartition.pairwiseDisjoint, Submodule.mem_span_mul_finite_of_mem_span_mul, AddSubgroupClass.subset_union, IntermediateField.sup_def, AddAction.coe_aestabilizer, ZFSet.coe_iUnion, TopologicalSpace.Closeds.continuous_infEDist, Submodule.closure_subset_span, PrimeSpectrum.isClosed_iff_zeroLocus_ideal, RestrictedProduct.inv_apply, Measurable.dependsOn_of_piFinset, Finset.hasSum, span_selfAdjoint, Subalgebra.coe_star, LowerSet.coe_prod, PrimeSpectrum.isOpen_basicOpen, Submodule.colon_eq_top_iff_subset, MvPolynomial.mem_supported_vars, Module.Basis.addHaar_eq_iff, Order.PFilter.directed, NonUnitalSubsemiring.closure_subsemigroup_closure, ZSpan.span_top, PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen, Submodule.IsLattice.span_eq_top, LowerAdjoint.subset_closure, TwoSidedIdeal.coe_equivMatrix_symm_apply, TensorProduct.exists_finite_submodule_of_finite, LowerSet.coe_Iic, RootPairing.Base.span_int_root_support, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left, PiNat.cylinder_eq_pi, AlgebraicGeometry.isCompactOpen_iff_eq_finset_affine_union, LowerSet.coe_iInf₂, UpperSet.lt_sdiff_left, Ideal.iSup_iInf_eq_top_iff_pairwise, OpenAddSubgroup.mem_nhds_zero, Submodule.closure_coe_iSup_map_single, FirstOrder.Language.DefinableSet.coe_top, Set.pow_mul_subgroupClosure, MvPolynomial.mem_restrictSupport_iff, LinearMap.eqOn_span_iff, Convex.exists_subset_interior_convexHull_finset_of_isCompact, Interval.coe_top, MeasureTheory.IntegrableOn.finset, PrimeSpectrum.isTopologicalBasis_basic_opens, IntermediateField.fixingSubgroup_isClosed, LowerSet.coe_iInf, SubMulAction.fg_iff, Subbimodule.coe_toSubbimoduleInt, Submonoid.coe_comap, Subalgebra.coe_restrictScalars, Topology.RelCWComplex.iUnion_cellFrontier_subset_skeleton, Subsemiring.closure_eq, MulAction.stabilizer_op_subgroup, AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdeal, MeasureTheory.IsSetSemiring.sUnion_insert_disjointOfDiff, lowerClosure_add, NonUnitalAlgHom.coe_range, TopologicalSpace.NonemptyCompacts.coe_singleton, Monoid.closure_finset_fg, Set.toFinset_subset, TopologicalSpace.Clopens.isOpen, LieHom.range_coe, Finset.sum_indicator_subset, Interval.coe_one, infinite_zmultiples, Finset.coe_neg, LinearMap.coe_domRestrict, Subalgebra.centralizer_eq_top_iff_subset, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, Submodule.localized'_eq_span, Submonoid.coe_inv, Order.PFilter.sInf_gc, StarSubalgebra.isClosed_topologicalClosure, AddSubgroup.coe_center, AddSubgroup.isComplement_addSubgroup_left_iff_existsUnique_quotientMk'', SimpleGraph.degree_le_between_add, Projectivization.Subspace.subset_span, Finset.Nonempty.csSup_eq_max', Submodule.mem_span_finite_of_mem_span, Subgroup.normal_mul, MeasureTheory.Measure.haar.addCHaar_mem_addHaarProduct, CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizers, AddSubsemigroup.iSup_eq_closure, TopologicalSpace.NonemptyCompacts.totallyBounded_subsets_of_totallyBounded, RestrictedProduct.isTopologicalRing, QuotientGroup.orbit_eq_out_smul, coe_subset_coe, Subgroup.coe_iSup_of_directed, Finset.convexHull_eq, infinite_multiples, Subgroup.closure_le_centralizer_centralizer, Submodule.smul_closure_subset, coe_lowerClosure, spectrum_subset_unitary_of_mem_unitary, finrank_span_finset_le_card, Valued.isClosed_integer, NonUnitalStarAlgebra.star_subset_adjoin, separableClosure.adjoin_eq_of_isAlgebraic, ConvexCone.disjoint_coe, IntermediateField.coe_restrictScalars, Topology.RelCWComplex.Subcomplex.subset_complex, Ideal.coe_toTwoSided, NonUnitalSubalgebra.coe_map, FirstOrder.Language.DefinableSet.coe_sdiff, PrimeSpectrum.exists_idempotent_basicOpen_eq_of_isClopen, TopologicalSpace.Clopens.coe_sup, TopologicalSpace.IrreducibleCloseds.coe_singleton, TopologicalSpace.Compacts.coe_finset_sup, coe_ssubset_coe, StarSubsemiring.coe_mk, Set.Finite.subset_toFinset, ContinuousMap.exists_finite_sum_const_mulIndicator_approximation_of_mem_nhds_diagonal, Submodule.span_eq_iUnion_nat, TopologicalSpace.NonemptyCompacts.carrier_eq_coe, Module.isTorsionBySet_iff_is_torsion_by_span, PointedCone.tmul_subset_minTensorProduct, TopologicalSpace.CompactOpens.coe_finsetSup, UpperSet.upperClosure, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, TopologicalSpace.Opens.overEquivalence_counitIso_inv_app, finprod_mem_coe_finset, Filter.tendsto_finset_preimage_atTop_atTop, Submonoid.coe_unitSphere, StarAlgebra.elemental.le_centralizer_centralizer, Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free, Submodule.complete_of_finiteDimensional, Finset.card_mul_iff, intrinsicClosure_eq_closure_inter_affineSpan, Equiv.Perm.cycleFactorsFinset_pairwise_disjoint, SimpleGraph.IsNIndepSet.isIndepSet, Order.PFilter.isPrime_iff, roth_3ap_theorem_nat, Algebra.adjoin_insert_adjoin, LieSubmodule.coe_inf, Finset.coe_eraseNone, AddSubmonoid.closure_eq, TopologicalSpace.noetherianSpace_iff_opens, Submodule.convex, AddSubgroup.coe_matrix, quotient_norm_mk_eq, Finset.coe_filterMap, SimpleGraph.coe_incidenceFinset, List.zipWith_swap_prod_support', TopologicalSpace.Opens.coe_mk, Topology.RelCWComplex.iUnion_cellFrontier_subset_skeletonLT, AffineSubspace.wSameSide_self_iff, Affine.Simplex.incenter_restrict, AlgebraicGeometry.isRetrocompact_basicOpen, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, IsOpen.upperClosure, PrimeSpectrum.zeroLocus_bot, Submodule.isClosed_orthogonal, Subalgebra.coe_ofClass, LowerAdjoint.closure_union_closure_right, MeasurableSpace.measurableSet_generateFrom_memPartition_iff, Submodule.coe_torsionBySet, PointedCone.subset_span, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, AffineSubspace.mk'_nonempty, Submodule.iSup_eq_span, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_left, AddSubgroup.leftCoset_cover_const_iff_surjOn, TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_left, SimpleGraph.IsMaximumClique.isClique, Subfield.coe_inf, TwoSidedIdeal.coe_bot, TopologicalSpace.PositiveCompacts.coe_mk, IntermediateField.adjoin_eq_bot_iff, rightAddCoset_eq_iff, Module.Basis.coe_parallelepiped, SimpleGraph.cliqueFreeOn_of_card_lt, Finset.coe_list_prod, range_cfc_eq_range_cfcHom, PMF.support_ofFinset, UpperSet.coe_zero, Subalgebra.coe_toSubsemiring, Subbimodule.coe_toSubbimoduleNat, Subsemigroup.isClosed_topologicalClosure, Topology.IsUpperSet.nhdsSet_eq_principal_upperClosure, NonUnitalSubalgebra.coe_star, PrimitiveSpectrum.preimage_upperClosure_compl_finset, Topology.RelCWComplex.skeleton_inter_closedCell_eq_skeleton_inter_cellFrontier, Order.Ideal.carrier_eq_coe, IntermediateField.coe_extendScalars, StarAlgebra.adjoin_le_centralizer_centralizer, FirstOrder.Language.Substructure.closure_empty, sum_eq_tsum_indicator, QuotientGroup.strictMono_comap_prod_image, Submodule.sInf_coe, Valued.integer.coe_span_singleton_eq_closedBall, Finset.hasProd_support, Submodule.span_range_natDegree_eq_adjoin, AddSubsemigroup.coe_unop, Submodule.ClosedComplemented.isClosed, Fintype.coe_piFinset, List.pairwise_iff_coe_toFinset_pairwise, Set.indicator_pi_one_apply, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, Matroid.setOf_indep_eq, AddSubgroup.coe_toZModSubmodule, SimpleGraph.isMaximalClique_compl, IsLowerSet.lowerClosure, PrimeSpectrum.range_comap_snd, Algebra.adjoin_nonUnitalSubalgebra, ZFSet.coe_sdiff, Finset.coe_eq_univ, AddSubgroup.coe_bot, QuotientAddGroup.dense_image_mk, TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe_target, IsLinearTopology.hasBasis_submodule', Submodule.coe_inf, MeasureTheory.Content.outerMeasure_exists_open, AffineSubspace.coe_eq_bot_iff, NonUnitalSubsemiring.coe_toSubsemigroup, MeasureTheory.Measure.addHaar_affineSubspace, Polynomial.map_restriction, LieSubmodule.lieSpan_eq, Finset.sups_subset_self, Finset.coe_injective, TopologicalSpace.Closeds.coe_inf, NonUnitalStarSubalgebra.coe_map, FractionalIdeal.coeToSet_coeToSubmodule, Finset.coe_covBy_coe, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens, gc_upperClosure_coe, FirstOrder.Language.Substructure.iSup_eq_closure, Submonoid.closure_le_centralizer_centralizer, ProjectiveSpectrum.homogeneousIdeal_le_vanishingIdeal_zeroLocus, ZFSet.toSet_pair, NonUnitalStarAlgebra.elemental.le_centralizer_centralizer, AddMonoidHom.eqOn_closure, TopologicalSpace.NonemptyCompacts.nonempty, AddAction.op_vadd_set_stabilizer_subset, MulEquiv.submonoidMap_symm_apply, Submodule.starConvex, Finset.restrict_preimage_univ, Subgroup.coe_toAddSubgroup_apply, IsPrimitiveRoot.injOn_pow_mul, MeasureTheory.MeasuredSets.lipschitzWith_measureReal, leftAddCoset_eq_iff, PMF.support_uniformOfFinset, Affine.Simplex.inradius_restrict, AffineSubspace.mem_affineSpan_insert_iff, AddSubsemigroup.closure_le, Finset.preimage_neg, IsApproximateSubgroup.of_small_tripling, Submodule.isPrimary_decomposition_pairwise_ne_radical, Subgroup.subset_closure, SimpleGraph.componentCompl_finite, PrimeSpectrum.zeroLocus_mul, exists_finset_linearIndependent_of_le_rank, eq_addCosets_of_normal, UpperSet.coe_top, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset', AddSubmonoid.coe_sup, ProjectiveSpectrum.zeroLocus_bot, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, Finset.isLUB_sup', ZFSet.toSet_sep, PeriodPair.isOpen_compl_lattice_diff, NonUnitalSubsemiring.coe_sumSq, TopologicalSpace.NonemptyCompacts.range_map, Ideal.coe_comap, NonUnitalSubalgebra.ofClass_carrier, AddMonoidAlgebra.exists_finset_adjoin_eq_top, MeasureTheory.lintegral_finset, AddSubgroup.coe_eq_singleton, NonUnitalSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer, multiples_eq_zmultiples, TopologicalSpace.Closeds.carrier_eq_coe, AddSubmonoid.coe_unop, MeasureTheory.StronglyMeasurable.dependsOn_of_piFinset, Valued.isClopen_integer, Subsemiring.coe_inf, MvPolynomial.mem_support_finSuccEquiv, LieDerivation.IsKilling.rangeAdOrthogonal_carrier, MeasurableSpace.measurableSet_generateFrom_countablePartition_iff, Subsemiring.coe_toNonUnitalSubsemiring, Set.toFinset_ssubset, Subalgebra.coe_map, AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpens, doublyStochastic_eq_convexHull_permMatrix, LieSubalgebra.top_coe, MonoidHom.coe_graph, FirstOrder.Language.DefinableSet.coe_sup, Finset.subset_set_image_iff, Subsemigroup.coe_set_mk, subset_affineSpan, HomogeneousIdeal.coe_sup, Interval.disjoint_coe, AddSubsemigroup.coe_topologicalClosure, Subsemiring.isHomogeneous_iff_forall_subset, Subring.coe_top, coe_strictMono, LieSubmodule.sSup_image_lieSpan_singleton, Subgroup.transferTransversal_apply', TopologicalSpace.Closeds.coe_sup, OpenNormalAddSubgroup.instIsClosedCoePathComponentZero, Finset.coe_infsep_of_offDiag_empty, NormedAddGroupHom.SurjectiveOnWith.surjOn, Submodule.spanRank_toENat_eq_iInf_finset_card, Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free, UpperSet.coe_iSup, AddCommGroup.coe_primaryComponent, TopologicalSpace.Closeds.coe_top, AddSubgroup.sup_eq_closure, TopologicalSpace.Compacts.uniformContinuous_coe, AlgHom.coe_fieldRange, TestFunction.tsupport_subset, FirstOrder.Language.Substructure.coe_map, TopologicalSpace.Opens.carrier_eq_coe, add_lowerClosure, ZFSet.toSet_injective, Subsemiring.coe_top, OpenAddSubgroup.coe_toAddSubgroup, Ideal.sum_pow_mem_span_pow, Partition.partscopyEquiv_symm_apply_coe, Submodule.coe_torsionBy, Finsupp.finite_vaddAntidiagonal, ConvexCone.coe_positive, Finset.centroid_mem_convexHull, NonUnitalSubsemiring.coe_iInf, PrimeSpectrum.closure_image_comap_zeroLocus, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, AddSubmonoid.top_closure_add_self_eq, alternatingGroup.coe_two_sylow_of_card_eq_four, Finset.coe_nsmul, RingHom.coe_fieldRange, rightCoset_mem_rightCoset, RestrictedProduct.instContinuousConstSMulCoe, NonarchimedeanRing.is_nonarchimedean, MeasureTheory.Filtration.piFinset_eq_comap_restrict, Fintype.coe_finsetOrderIsoSet, commutator_centralizer_commutator_le_center, Submodule.topologicalClosure_coe, RestrictedProduct.instContinuousMulCoeCofinite, MeasureTheory.Measure.haar.prehaar_mem_haarProduct, FractionalIdeal.mem_span_mul_finite_of_mem_mul, ordConnected_iff_upperClosure_inter_lowerClosure, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, StarSubalgebra.coe_mk, range_deriv_subset_closure_span_image, MulAction.isBlock_subgroup, ZLattice.covolume.tendsto_card_div_pow', upperBounds_lowerClosure, stabilizer_isOpen_of_isIntegral, AddSubmonoid.mk_neg_add_mk_eq_zero, not_mulDissociated_iff_exists_disjoint, Finset.isLUB_sup, MeasureTheory.Measure.haar.chaar_mem_haarProduct, Module.isTorsionBySet_annihilator_top, ProperCone.dual_flip_dual, PrimeSpectrum.closure_singleton, IsFractionRing.ringHom_fieldRange_eq_of_comp_eq, RelLowerSet.isRelLowerSet, AddSubmonoid.surjOn_iff_le_map, Projectivization.Subspace.sup_span, MeasureTheory.sum_measureReal_preimage_singleton, RestrictedProduct.instContinuousConstVAddCoe, AddEquiv.addSubmonoidMap_symm_apply, Submodule.coe_set_mk, PrimeSpectrum.isClopen_basicOpen_of_mul_add, AddSubsemigroup.centralizer_eq_top_iff_subset, NormedAddGroupHom.ker_completion, NonUnitalSubring.coe_sSup_of_directedOn, ClosedSubmodule.coe_inf, MulAction.coe_aestabilizer, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, Affine.Simplex.centroid_restrict, Subring.isClosed_topologicalClosure, StarSubalgebra.range_subset, FirstOrder.Language.Substructure.subset_closure, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, PrimitiveSpectrum.closedsGC_closureOperator, Equiv.Perm.isPretransitive_of_isCycle_mem, LinearPMap.coprod_apply, TensorProduct.exists_finite_submodule_of_setFinite', FirstOrder.Language.Substructure.closure_iUnion, Finset.equitableOn_iff, pi_generateFrom_eq, MonoidAlgebra.support_gen_of_gen, LinearMap.disjoint_ker_iff_injOn, Finset.centroidWeightsIndicator_def, ProjectiveSpectrum.isTopologicalBasis_basic_opens, dense_submonoidClosure_iff_subgroupClosure, leftCoset_mem_leftCoset, TwoSidedIdeal.coe_mk, IntermediateField.iSup_eq_adjoin, BooleanSubalgebra.subset_closure, Subgroup.isComplement_range_left, PointedCone.mem_span_set, AddSubgroup.coe_toIntSubmodule, closure_submonoidClosure_eq_closure_subgroupClosure, MeasureTheory.Content.outerMeasure_caratheodory, AlgHom.eqOn_adjoin_iff, TopologicalSpace.Clopens.coe_compl, ProjectiveSpectrum.gc_ideal, Subgroup.isOpen_of_openSubgroup, TopologicalSpace.Closeds.coe_finset_sup, Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT, Subsemiring.coe_centralizer, AlgebraicGeometry.IsOpenImmersion.range_pullback_snd_of_left, MeasureTheory.Content.outerMeasure_exists_compact, Cardinal.mk_eq_nat_iff_finset, TopologicalSpace.Opens.isOpen, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, List.support_formPerm_le', NonUnitalStarAlgebra.coe_iInf, Finset.dependsOn_restrict, Finset.coe_symmDiff, Algebra.adjoin_le_centralizer_centralizer, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, IsLinearSet.of_fg, Set.ssubset_toFinset, NonUnitalSubring.coe_center, AlgEquiv.subalgebraMap_apply_coe, Ideal.subset_union_prime_finite, inf_sSup_eq_iSup_inf_sup_finset, RestrictedProduct.instContinuousSMulCoePrincipal, Interval.coe_subset_coe, UpperSet.coe_iInf, IsNoetherian.coe_finsetBasisIndex, ProjectiveSpectrum.zeroLocus_vanishingIdeal_eq_closure, AddSubgroup.centralizer_eq_top_iff_subset, Affine.Simplex.orthogonalProjectionSpan_restrict, Submodule.nonempty, IsLowerSet.disjoint_upperClosure_left, isClosed_nullSubmodule, UpperSet.coe_sub, ConvexBody.nonempty, LieIdeal.coe_derivedSeries_eq_int, Finset.measure_zero, lowerClosure_le, Algebra.adjoin_eq_span, NonarchimedeanRing.mul_subset, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, FirstOrder.Language.Substructure.closure_union, TopologicalSpace.Clopens.isClosed, ClosedSubmodule.coe_iInf, AffineSubspace.direction_eq_vectorSpan, Tree.coe_treesOfNumNodesEq, QuotientAddGroup.preimage_image_coe, AddSubmonoid.mul_subset_mul, ConjClasses.mk_bijOn, Submonoid.coe_sup, Finset.pairwiseDisjoint_piAntidiag_map_addRightEmbedding, NonUnitalSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul, AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι, LieSubmodule.coe_lieSpan_submodule_eq_iff, NonUnitalSubalgebra.isClosed_topologicalClosure, Subsemigroup.subset_closure, HomogeneousIdeal.irrelevant_eq_span, Topology.RelCWComplex.Subcomplex.eq_iff, Affine.Simplex.setInterior_restrict, isLinearTopology_iff_hasBasis_open_ideal, SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges, ClosedSubmodule.isClosed, Polynomial.image_comap_C_basicOpen, PrimeSpectrum.gc_set, IsLocalization.orderIsoOfPrime_symm_apply_coe, StarAlgebra.gc, Finset.coeAddMonoidHom_apply, Subfield.coe_sInf, MeasureTheory.Measure.count_apply_finset, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, ZLattice.covolume.tendsto_card_le_div, RingEquiv.nonUnitalSubsemiringMap_symm_apply_coe, BooleanSubalgebra.coe_iInf, ProjectiveSpectrum.zeroLocus_anti_mono_ideal, OpenSubgroup.coe_top, Submodule.torsionBySet_span_singleton_eq, NonUnitalSubsemiring.coe_toAddSubmonoid, DFinsupp.lmk_apply, FirstOrder.Language.Structure.cg_iff, Order.PFilter.isPFilter, AffineSubspace.ext_iff, Finset.preimage_add_right_singleton, OpenSubgroup.coe_toOpens, LieHom.idealRange_eq_lieSpan_range, AddMonoidAlgebra.mem_adjoin_support, AddSubmonoid.centralizer_eq_top_iff_subset, IsGaloisGroup.intermediateField, IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime, OpenAddSubgroup.coe_top, Finset.isPWO, Subbimodule.coe_toSubmodule, Affine.Simplex.excenterWeights_restrict, AddSubmonoid.coe_multiples, ClopenUpperSet.ext_iff, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, DoubleCoset.rel_iff, Finset.bddBelow, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, Subgroup.coe_unop, LieSubalgebra.coe_inf, StarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer, QuotientAddGroup.image_coe, Finset.coe_zero, Subgroup.coe_inf, Submodule.image_span_subset, Finset.Nontrivial.coe, Projectivization.Subspace.span_le_subspace_iff, Topology.RelCWComplex.openCell_subset_skeleton, MeasureTheory.Measure.haar.nonempty_iInter_clPrehaar, Order.Ideal.inter_nonempty, Set.image_finset_sum_pi, Subsemiring.coe_pointwise_smul, Subgroup.coe_topologicalClosure_bot, AlgebraicGeometry.StructureSheaf.comapₗ_const, TopologicalSpace.Closeds.coe_eq_univ, Finset.coe_diffs, AddSubmonoid.pow_subset_pow, NonUnitalSubalgebra.coe_centralizer, IsLocalization.disjoint_comap_iff, NonUnitalStarSubalgebra.coe_center, Subsemigroup.coe_bot, finite_multiples, AffineIndependent.convexHull_inter', Algebra.adjoin_le_iff, polynomialFunctions_coe, ConvexBody.isClosed, Interval.coe_sSubset_coe, NonUnitalSubalgebra.coe_center, TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducible, coe_set_eq_one, Finset.sup_mem_of_nonempty, List.pairwiseDisjoint_consFixedLengthDigits, SimpleGraph.IsMaximumClique.isMaximalClique, SimpleGraph.ComponentCompl.hom_eq_iff_le, Dense.diff_finset, IsZLattice.span_top, TopologicalSpace.Compacts.isCompact, algebraicClosure.adjoin_le, TopologicalSpace.Compacts.coe_eq_empty, Subfield.coe_toSubring, RestrictedProduct.comp_mulSingle, LowerSet.ext_iff, NonemptyInterval.coe_coeHom, RestrictedProduct.coe_mulSingle_apply, Subbimodule.coe_toSubmodule', NonemptyInterval.coe_def, linearIndepOn_finset_iffₛ, AddSubmonoid.coe_pathComponentZero, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, ProjectiveSpectrum.basicOpen_eq_zeroLocus_compl, AffineSubspace.top_coe, SubAddAction.compl_def, Affine.Simplex.median_restrict, Sublattice.coe_mk, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, RestrictedProduct.single_eq_of_ne, ZFSet.toSet_subset_iff, Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint, OpenAddSubgroup.isClosed, BddAbove.lowerClosure, extremePoints_doublyStochastic, coe_nonZeroDivisorsLeft_eq, LinearMap.range_liftBaseChange, TopologicalSpace.PositiveCompacts.coe_toCompacts, IsLowerSet.disjoint_upperClosure_right, RealRMK.exists_open_approx, AddSubgroup.normal_centralizer, mem_own_leftCoset, AddSubsemigroup.coe_centralizer, HasUpperLowerClosure.isOpen_upperClosure, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, convexHull_eq_union_convexHull_finite_subsets, Submodule.coe_span_eq_span_of_surjective, Interval.coe_bot, union_support_maximal_linearIndependent_eq_range_basis, MeasureTheory.Measure.haar.addPrehaar_nonneg, dense_addSubgroupClosure_pair_iff, AddSubmonoid.coe_pi, Module.FinitePresentation.out, RootPairing.Base.exists_root_eq_sum_int, Submodule.exists_finset_span_eq_linearIndepOn, TopologicalSpace.Clopens.coe_himp, Topology.RelCWComplex.Subcomplex.base_subset, orbit_addSubgroup_zero_eq_self, Subsemiring.map_toSubmonoid, IntermediateField.exists_finset_of_mem_adjoin, TopologicalSpace.Closeds.coe_mk, ConvexBody.isCompact, Subring.coe_toSubmonoid, Convex.toCone_isLeast, ENNReal.sum_add_tsum_compl, TopologicalSpace.Opens.iSup_def, TopologicalSpace.Closeds.coe_sSup, ZFSet.toSet_insert, AddSubgroup.isOpen_of_openAddSubgroup, mem_coe, isLinearSet_iff_exists_fg_eq_vadd, AddSubgroup.coe_even, Subgroup.coe_center, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, MonoidWithZeroHom.valueGroup_def, FirstOrder.Language.ElementarySubstructure.coe_top, Finset.coe_Ioi, PeriodPair.analyticOnNhd_derivWeierstrassP, SubMulAction.subset_coe_one, MvPowerSeries.coe_hasEvalIdeal, AffineSubspace.coe_direction_eq_vsub_set_left, ValuationSubring.coe_comap, LieSubmodule.coe_injective, Algebra.restrictScalars_adjoin, FirstOrder.Language.distinctConstantsTheory_eq_iUnion, ProjectiveSpectrum.isOpen_basicOpen, Subrepresentation.coe_inf, NormedAddGroupHom.IsQuotient.norm, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_eq_eq_iInter_zeroLocus, Submodule.mem_smul_span, RestrictedProduct.mulSingle_one, Finset.sized_shadow_iff, FractionalIdeal.spanFinset_coe, IntermediateField.adjoin_finset_isCompactElement, AddSubmonoid.sup_eq_closure_add, Submodule.torsion_gc, Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype, Subgroup.isComplement_subgroup_left_iff_bijective, Submodule.coe_dualAnnihilator_span, Units.val_set_image_rootsOfUnity_two, Multipliable.prod_mul_tprod_compl, RootPairing.Base.root_mem_or_neg_mem, Finset.card_add_iff, NonUnitalSubsemiring.coe_centralizer, Affine.Simplex.closedInterior_restrict, ZFSet.nonempty_coe, IntermediateField.adjoin_eq_range_algebraMap_adjoin, Polynomial.coeff_restriction, AddSubmonoid.closure_eq_image_sum, AddSubgroup.closure_eq, OpenAddSubgroup.coe_toOpens, StarSubalgebra.coe_centralizer_centralizer, Submodule.mem_carrier, AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonempty, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, StarAlgebra.adjoin_le_iff, HomogeneousIdeal.coe_top, AlgebraicGeometry.Scheme.Opens.germ_stalkIso_hom_assoc, AddSubmonoid.coe_sumSq, Subalgebra.coe_comap, AddSubmonoid.smul_subset_smul, UpperSet.coe_iSup₂, Set.mem_sym2_iff_subset, Set.addSubgroupClosure_add, MeasureTheory.Measure.haar.addPrehaar_pos, MeasureTheory.MeasuredSets.dist_def, ProperCone.dual_dual_flip, SubMulAction.subset_closure, Set.piCongrLeft_comp_restrict, Topology.CWComplex.iUnion_openCell_eq_skeleton, TopologicalSpace.Compacts.isUniformEmbedding_coe, NonUnitalSubalgebra.coe_prod, RestrictedProduct.zero_apply, Finset.isLowerSet_shatterer, vectorSpan_add_self, TopologicalSpace.Clopens.coe_finset_sup, MvPolynomial.mem_coeffsIn_iff_coeffs_subset, UpperSet.coe_nonempty, NormedAddGroupHom.coe_ker, Submodule.iSup_eq_span', GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset, ZFSet.toSet_sInter, Finset.coe_eq_one, MvPolynomial.weightedDecomposition.decompose'_eq, TopologicalSpace.Opens.coe_compl, ZFSet.coe_empty, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply, Topology.RelCWComplex.Subcomplex.closed, Finset.isGLB_iff_isLeast, Finset.pairwiseDisjoint_vadd_iff, ProjectiveSpectrum.ideal_le_vanishingIdeal_zeroLocus, TopologicalSpace.exists_finite_open_cover_prod_subset_of_mem_nhds_diagonal_of_compact, Subgroup.inv_subset_closure, ConvexCone.coe_add, Flag.coe_mk, Subsemigroup.coe_toAddSubsemigroup_symm_apply, NonUnitalStarSubalgebra.coe_centralizer_centralizer, Subfield.isClosed_topologicalClosure, Submodule.pow_eq_span_pow_set, Subsemiring.coe_closure_eq, QuotientAddGroup.orbit_eq_out_vadd, AlgebraicGeometry.Scheme.Hom.coe_image, NumberField.mem_span_basisOfFractionalIdeal, AlgebraicGeometry.Scheme.Hom.coe_preimage, Submodule.exists_isInternal_prime_power_torsion, LinearIndepOn.image_subset_span_image_extend, NonUnitalStarSubalgebra.coe_iSup_of_directed, NonUnitalAlgebra.elemental.le_centralizer_centralizer, Subbimodule.coe_baseChange, TopologicalSpace.Opens.coe_bot, ValuationSubring.coe_pointwise_smul, ContinuousMap.norm_restrict_mono_set, Subalgebra.coe_pi, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, Dynamics.netMaxcard_finite_iff, affineSegment_subset_affineSpan, StarSubalgebra.coe_comap, ZFSet.toSet_singleton, AddSubmonoid.coe_ofClass, Subsemiring.topologicalClosure_coe, Finset.preimage_subset, Affine.Simplex.mongePoint_restrict, rank_span_of_finset, Dynamics.exists_isDynCoverOf_of_isCompact_uniformContinuous, NonarchimedeanAddGroup.prod_subset, IsOfFinAddOrder.multiples_eq_image_range_addOrderOf, Finset.pairwise_subtype_iff_pairwise_finset', IntermediateField.adjoin_rank_le_of_isAlgebraic, Topology.RelCWComplex.disjoint_skeleton_openCell, convexHull_toCone_isLeast, ConvexCone.IsGenerating.span_eq_top, NonUnitalSubring.unitization_range, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_subset_zeroLocus, TopologicalSpace.Opens.coe_sSup, support_of_supportDim_eq_zero, SimpleGraph.ComponentCompl.nonempty, Finset.infsep_zero_iff_subsingleton, TwoSidedIdeal.span_le, RootedTree.subtrees_disjoint, AddSubgroup.coe_iInf, Affine.Simplex.eulerPoint_restrict, NonUnitalAlgebra.coe_top, Subalgebra.range_subset, Flag.chain_lt, isApproximateSubgroup_one, TopologicalSpace.Opens.coe_overEquivalence_inverse_obj_left, DFinsupp.mk_add, OrthonormalBasis.span_apply, Partition.sSupIndep, AddSubmonoid.coe_toSubmonoid_symm_apply, Submodule.span_sSup', SubMulAction.compl_def, AddMonoidAlgebra.support_divOf, Sublattice.coe_inclusion, MeasureTheory.Measure.addHaar_submodule, MeasureTheory.Content.outerMeasure_opens, Finset.preimage_inv, IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, MonoidWithZeroHom.valueMonoid_eq_valueGroup', ContinuousMap.adjoin_id_eq_span_one_add, ClosedSubmodule.instCanLiftSubmoduleToSubmoduleIsClosedCoe, AffineSubspace.coe_inclusion_apply, Subgroup.exists_right_transversal_of_le, AddSubmonoid.closure_le, Submonoid.coe_pathComponentOne, TopologicalSpace.CompactOpens.ext_iff, LieModule.coe_lowerCentralSeries_eq_int, Affine.Simplex.ExcenterExists.touchpoint_restrict, coe_upperClosure, Sublattice.coe_sInf, ProjectiveSpectrum.zeroLocus_anti_mono_homogeneousIdeal, Subfield.coe_sSup_of_directedOn, Group.fg_iff', mem_own_rightAddCoset, Subgroup.coe_eq_univ, Finset.card_image_iff, AddSubgroup.add_inf_assoc, Order.Ideal.nonempty, biUnion_associatedPrimes_eq_compl_nonZeroDivisors, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_right, AddAction.isBlock_addSubgroup, affineSpan_nonempty, Algebra.elemental.isClosed, Finset.sigma_preimage_mk, LieSubmodule.coe_toSubmodule, Submodule.finrank_span_eq_finrank, MeasureTheory.MeasuredSets.continuous_measure, AlgebraicGeometry.Scheme.IdealSheafData.support_map, Set.encard_coe_eq_coe_finsetCard, Topology.RelCWComplex.Subcomplex.closedCell_eq, RestrictedProduct.instLocallyCompactSpaceCoeCofiniteOfAddSubgroupClassOfIsTopologicalAddGroupOfCompactSpaceSubtypeMem, Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct, HomogeneousLocalization.Away.eventually_smul_mem, NonarchimedeanAddGroup.is_nonarchimedean, TopologicalSpace.Clopens.coe_toCloseds, LieSubmodule.top_coe, coe_add_coe, isLinearTopology_iff_hasBasis_open_submodule, coe_sub_coe, Affine.Simplex.excenterWeightsUnnorm_restrict, Subsemiring.coe_ofClass, AlgebraicGeometry.Scheme.IdealSheafData.zeroLocus_inter_subset_supportSet, Submodule.coe_iSup_of_directed, orbit_subgroup_eq_rightCoset, Ideal.coe_closure, TopologicalSpace.NonemptyCompacts.coe_mk, Finset.coe_pimage, NonUnitalStarAlgebra.adjoin_le_iff, image_range_orderOf, SimpleGraph.isMaximumIndepSet_iff, AddSubsemigroup.coe_comap, Submodule.mul_subset_mul, UpperSet.coe_sup, Subsemiring.coe_sSup_of_directedOn, PointedCone.mem_closure, MeasureTheory.sum_measure_singleton, UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrime, SimpleGraph.end_hom_mk_of_mk, ZFSet.nonempty_toSet_iff, Submonoid.mem_closure_finset, LieSubalgebra.lieSpan_le, MeasureTheory.dependsOn_cylinder_indicator_const, Subfield.closure_eq, Valued.isOpen_integer, SubMulAction.coe_one, unitary_iff_isStarNormal_and_spectrum_subset_unitary, LieSubalgebra.mk_coe, IsLocalRing.isOpen_maximalIdeal_pow, StarSubalgebra.coe_inf, Subalgebra.adjoin_eq_span_of_eq_span, TopologicalSpace.Closeds.isAtom_coe, Finset.coe_div, ConvexBody.iInter_smul_eq_self, upperClosure_add, LinearMap.isClosed_or_dense_ker, AddSubgroup.coe_map, Geometry.SimplicialComplex.face_subset_face_iff, NonUnitalStarAlgebra.span_eq_toSubmodule, Submodule.isInternal_prime_power_torsion, LinearMap.polar_subMulAction, AddSubgroup.exists_isComplement_right, Module.End.mapsTo_maxGenEigenspace_of_comm, Subsemigroup.closure_eq, Topology.RelCWComplex.Subcomplex.coe_mk'', Submodule.image2_subset_map₂, IsGaloisGroup.fixingSubgroup_bot, Submodule.coe_closure, ProjectiveSpectrum.zeroLocus_sup_homogeneousIdeal, Finset.coe_Iio, Finset.shatterer_eq, AddSubgroup.vadd_toLeftFun, TopologicalSpace.CompactOpens.coe_top, IntermediateField.set_range_subset, Subgroup.mul_inf_assoc, IsClosed.convexHull_subset_affineSpan_isVisible, Set.instCanLiftFinsetCoeFinite, Finset.sup_eq_sSup_image, LieHom.range_subset_idealRange, Finset.preimage_mul_left_one', NonUnitalSubsemiring.coe_prod, TopologicalSpace.IrreducibleCloseds.ext_iff, NonUnitalSubring.coe_set_mk, AddAction.stabilizer_coe_finset, Equiv.restrictPreimageFinset_apply_coe, Finset.restrict_preimage, Matrix.convex_rowStochastic, ext'_iff, Finset.image_add_left', Subsemiring.coe_matrix, Set.OrdConnected.upperClosure_inter_lowerClosure, AddSubgroup.coe_pi, LowerSet.coe_compl, Subalgebra.centralizer_coe_sup, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, TopologicalSpace.Opens.coe_comap, Submodule.span_span, IntermediateField.adjoin_insert_adjoin, TopologicalSpace.IsOpenCover.iUnion_inter, AddSubgroup.coe_toSubgroup_apply, RestrictedProduct.single_nsmul, AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRange, DFinsupp.mk_of_mem, Submonoid.coe_topologicalClosure, Equiv.Perm.cycleFactorsFinset_mem_commute, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic, Flag.mk_coe, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, IsUpperSet.disjoint_lowerClosure_left, AlgebraicGeometry.quasiCompact_iff_forall_isAffineOpen, Submodule.tensorToSpan_apply_tmul, krullTopology_mem_nhds_one_iff, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, Finset.prod_finset_coe, Finset.card_mul_finset_lt_two, Subalgebra.coe_starClosure, NonUnitalSubsemiring.centralizer_eq_top_iff_subset, Order.Ideal.coe_subset_coe, AddAction.stabilizer_addSubgroup, NonUnitalSubsemiring.closure_le, OpenSubgroup.coe_toSubgroup, AddSubgroup.dense_or_cyclic, VonNeumannAlgebra.coe_toStarSubalgebra, RingPreordering.coe_supportAddSubgroup, Group.closure_finset_fg, Finsupp.restrictSupportEquiv_symm_single, LinearMap.ker_le_iff, Finset.coe_product, continuousSMul_iff_stabilizer_isOpen, image_specComap_zeroLocus_eq_zeroLocus_comap, ConvexCone.disjoint_hull_right_of_convex, Subgroup.normalClosure_closure_eq_normalClosure, vadd_coe_set, Subalgebra.coe_unop, Finset.card_infs_iff, AlgebraicGeometry.Scheme.zeroLocus_span, Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMul, AddSubmonoid.FG.exists_minimal_closure_eq, MvPolynomial.support_divMonomial, FirstOrder.Language.Hom.range_coe, Finset.sup'_id_eq_csSup, Finset.coe_sym2, Algebra.adjoin_eq, OpenPartialHomeomorph.subtypeRestr_symm_eqOn_of_le, FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize, Set.iUnion_finset_eq_set, Polynomial.degreeLT_eq_span_X_pow, Set.Finite.lowerClosure, Finset.coe_compls, PrimeSpectrum.basicOpen_eq_zeroLocus_compl, Submodule.span_biUnion, Submonoid.LocalizationMap.mulEquivOfMulEquiv_mk', LowerSet.coe_add, LowerSet.coe_div, StarSubalgebra.coe_top, PrimeSpectrum.isCompact_basicOpen, PolynomialLaw.range_φ, Submodule.span_singleton_eq_range, Ideal.disjoint_primeCompl_of_liesOver, List.pairwiseDisjoint_iff_coe_toFinset_pairwise_disjoint, MeasureTheory.Measure.haar.prehaar_self, Ideal.colon_span, NonUnitalStarAlgebra.coe_inf, FirstOrder.Language.Substructure.closed, AlgebraicIndependent.matroid_closure_eq, coe_injective', Module.Basis.repr_support_subset_of_mem_span, TopologicalSpace.Clopens.coe_toOpens, TensorProduct.exists_finite_submodule_right_of_finite, Finsupp.supportedEquivFinsupp_apply_support_val, Finset.coe_inv, Ideal.coe_piOrderIso_symm_apply, krullTopology_mem_nhds_one_iff_of_normal, RootPairing.Base.coroot_mem_or_neg_mem, AddSubgroup.coe_pointwise_smul, TopologicalSpace.Closeds.totallyBounded_subsets_of_totallyBounded, Irreducible.maximalIdeal_eq_closedBall, Subgroup.inf_mul_assoc, NonUnitalStarAlgebra.adjoin_eq, PrimeSpectrum.coe_vanishingIdeal, AlgebraicGeometry.QuasiCompactCover.isCompactOpenCovered_of_isAffineOpen, Subgroup.subset_normalClosure, RestrictedProduct.neg_apply, Submodule.span_inter, TopologicalSpace.IrreducibleCloseds.coe_map, AlgebraicGeometry.Scheme.Opens.range_ι, Finset.SupIndep.pairwiseDisjoint, DFinsupp.mk_apply, NonemptyInterval.subset_coe_map, Finset.countable_toSet, AlgebraicGeometry.IsAffineOpen.range_fromSpec, coe_set_eq, Finset.sigma_preimage_mk_of_subset, Submodule.coe_span_eq_self, IsIdempotentElem.coe_powers, isPathConnected_compl_of_isPathConnected_compl_zero, TopologicalSpace.Compacts.isCompact_subsets_of_isCompact, SubgroupClass.subset_union, NonUnitalSubsemiring.unitization_range, Subsemiring.coe_op, AddSubmonoid.coe_pointwise_smul, RestrictedProduct.instContinuousAddCoeCofinite, AddSubmonoid.coe_toNatSubmodule, AlgebraicGeometry.Scheme.Hom.range_subset_ker_support, Finset.invMulSubgroup_eq_inv_mul, IntermediateField.fixingSubgroup_isOpen, le_upperClosure, LieSubmodule.coe_sInf, ContinuousMap.coe_opensOfIdeal, UpperSet.upper, NonUnitalSubring.coe_map, MonoidHom.coe_mgraph, Submodule.exists_fg_le_subset_range_rTensor_inclusion, ProperCone.hyperplane_separation_of_notMem, AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectField, RestrictedProduct.mulSingle_pow, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range, coe_set_pow, Submodule.exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition, linearIndepOn_iff_linearIndepOn_finset, Module.support_eq_zeroLocus, NonUnitalSubsemiring.coe_inf, ProfiniteGrp.exist_openNormalSubgroup_sub_open_nhds_of_one, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_left, Metric.lipschitz_infDist, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, AddSubsemigroup.coe_sSup_of_directed_on, SimpleGraph.completeBipartiteGraph_isContained_iff, ConvexCone.hull_le_iff, AddGroup.closure_finset_fg, TwoSidedIdeal.subset_span, Submodule.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallHSMul, Submonoid.coe_toAddSubmonoid_symm_apply, AddMonoidHom.eqOn_closureM, Submonoid.coe_toAddSubmonoid_apply, ContDiffMapSupportedIn.support_subset, Finset.inf_eq_sInf_image, Subalgebra.coe_toSubmodule, LinearMap.le_eqLocus, Submodule.span_sup, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, Order.Ideal.PrimePair.F_union_I, PrimeSpectrum.existsUnique_idempotent_basicOpen_eq_of_isClopen, Ideal.univ_eq_iUnion_image_add, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ, ProjectiveSpectrum.zeroLocus_iSup_homogeneousIdeal, IsOfFinAddOrder.finite_multiples, Set.mul_subgroupClosure, SimpleGraph.isNClique_iff, FirstOrder.Language.DefinableSet.coe_inf, Subring.coe_prod, not_linearIndepOn_finset_iff, LinearMap.continuous_iff_isClosed_ker, Finset.card_image₂_iff, OrderEmbedding.birkhoffSet_apply, TopologicalSpace.Opens.coe_sup, OpenSubgroup.isClosed, StarSubalgebra.coe_iInf, Subsemiring.coe_set_mk, FirstOrder.Language.Theory.CompleteType.iInter_setOf_subset, TensorProduct.exists_finite_submodule_right_of_finite', Subsemiring.centralizer_eq_top_iff_subset, FirstOrder.Language.Theory.CompleteType.setOf_subset_eq_empty_iff, TopologicalSpace.NonemptyCompacts.isCompact, NonUnitalStarSubalgebra.coe_toNonUnitalSubalgebra, StarSubalgebra.instCanLiftSetCoeAndForallForallForallMemForallHAddForallForallForallForallHMulForallCoeRingHomAlgebraMapForallForallStar, NonUnitalSubring.mem_closure_iff, Cardinal.mk_set_eq_nat_iff_finset, Submonoid.coe_square, convex_doublyStochastic, Submodule.CoFG.sInf, Finsupp.restrictSupportEquiv_apply, QuotientGroup.orbit_mk_eq_smul, ConvexCone.coe_iInf, isPathConnected_compl_of_one_lt_codim, NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMap, Ideal.coe_prod, ZFSet.coe_sInter, Algebra.adjoin_eq_sInf, StarSubalgebra.coe_centralizer, RestrictedProduct.single_zsmul, CompleteSublattice.comap_carrier, AlgebraicIndependent.matroid_isFlat_iff, Finset.sups_eq_self, eq_cosets_of_normal, PeriodPair.differentiableOn_weierstrassPExcept, NonUnitalRingHom.coe_srange, PrimeSpectrum.subset_zeroLocus_vanishingIdeal, Opens.coe_mayerVietorisSquare_X₄, lowerClosure_min, Subgroup.normalClosure_idempotent, ZFSet.toSet_sdiff, ZFSet.toSet_inter, TopologicalSpace.Opens.coe_disjoint, TwoSidedIdeal.coeOrderEmbedding_apply, Set.exists_finite_iff_finset, Finset.inf'_id_eq_csInf, Submodule.span_closure, SubAddAction.mem_carrier, sSupIndep_iff_finite, TwoSidedIdeal.lt_iff, Finset.coe_filter_univ, YoungDiagram.coe_sup, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_inter, Subsemigroup.coe_iSup_of_directed, ProjectiveSpectrum.zeroLocus_sup_ideal, AddSubmonoid.coe_inf, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic, Subrepresentation.coe_sup, Polynomial.natDegree_restriction, AlgebraicGeometry.Scheme.Hom.support_ker, MeasureTheory.Measure.haar.index_pos, Finset.powerset_card_disjiUnion, MeasureTheory.Measure.haar.is_left_invariant_addPrehaar, Submodule.coe_pi, QuotientGroup.preimage_image_coe, Algebra.coe_inf, PeriodPair.differentiableOn_weierstrassP, Subgroup.IsComplement'.QuotientMulEquiv_symm_apply, AlgHom.coe_equalizer, NonUnitalStarSubalgebra.coe_prod, ConvexCone.gc_hull_coe, Finset.nodup_map_iff_injOn, IsOfFinOrder.powers_eq_image_range_orderOf, Submodule.FG.span, Caratheodory.minCardFinsetOfMemConvexHull_subseteq, Submodule.pow_subset_pow, UpperSet.coe_map, LieSubmodule.lieSpan_le, TopologicalSpace.IsOpenCover.exists_finite_clopen_cover, ClosedSubmodule.coe_top, Topology.RelCWComplex.Subcomplex.coe_mk', Topology.RelCWComplex.iUnion_skeleton_eq_complex, Subgroup.coe_mul_of_right_le_normalizer_left, AddSubsemigroup.top_closure_add_self_subset, UpperSet.coe_Ioi, isLinearTopology_iff_hasBasis_submodule, IntermediateField.adjoin_subset_adjoin_iff, Finset.isGLB_inf_id, Finset.map_subset_iff_subset_preimage, Finset.vadd_stabilizer_of_no_doubling, Module.isTorsionBySet_iff_subset_annihilator, TopologicalSpace.PositiveCompacts.coe_prod, DoubleCoset.disjoint_out, Finset.isAddUnit_coe, Finset.coe_zpow, AffineIndependent.injOn_affineCombination_fintypeAffineCoords, TopologicalSpace.Closeds.coe_closure, AffineIndependent.exists_affineCombination_eq_smul_eq, BooleanSubalgebra.coe_sInf, FirstOrder.Language.Substructure.closure_withConstants_eq, Finpartition.parts_top_subsingleton, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, SimpleGraph.degree_le_between_add_compl, MonoidHom.coe_range, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, MulAction.stabilizer_finite, StarAlgebra.adjoin_eq_span, LieIdeal.map_le, RestrictedProduct.single_neg, Finset.finite_toSet, Dynamics.coverMincard_finite_iff, Submodule.mul_eq_span_mul_set, BooleanSubalgebra.coe_inf, Finset.hasProd, ProjectiveSpectrum.subset_vanishingIdeal_zeroLocus, BooleanSubalgebra.coe_comap, Submodule.coe_toNonUnitalSubalgebra, convexHull_eq_union, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, RootPairing.Base.span_root_support, TopologicalSpace.Compacts.isOpen_subsets_of_isOpen, lowerClosure_mul, Subsemiring.closure_submonoid_closure, ZLattice.covolume.tendsto_card_le_div'', untrop_sum_eq_sInf_image, LowerSet.coe_iSup₂, AddMonoidAlgebra.support_gen_of_gen, Metric.lipschitz_infDist_set, Topology.CWComplex.Subcomplex.map_def, RelUpperSet.isRelUpperSet, RestrictedProduct.continuousSMul, Sublocale.infClosed, VonNeumannAlgebra.coe_commutant, Topology.RelCWComplex.disjoint_skeletonLT_openCell, AddAction.stabilizer_finite, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_assoc, ProjectiveSpectrum.mem_coe_basicOpen, TensorProduct.exists_finite_submodule_of_setFinite, Interval.coe_inf, TensorProduct.exists_finite_submodule_left_of_setFinite', MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, FirstOrder.Language.DefinableSet.coe_himp, NonUnitalAlgebra.coe_sInf, TopologicalSpace.Opens.isOpenEmbedding_of_le, NonUnitalSubring.subset_closure, TopologicalSpace.Closeds.uniformContinuous_coe, NonUnitalSubring.coe_comap, LieSubalgebra.coe_lieSpan_submodule_eq_iff, Finset.sized_falling, AddSubgroup.coe_sInf, AddSubsemigroup.coe_set_mk, Finset.op_smul_stabilizer_of_no_doubling, Submodule.mem_sSup_iff_exists_finset, Submonoid.mem_closure_finset', Finset.Colex.le_iff_sdiff_subset_lowerClosure, PrimeSpectrum.zeroLocus_inf, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, RestrictedProduct.locallyCompactSpace_of_addGroup, PrespectralSpace.isBasis_opens, LieSubmodule.mem_carrier, AddMonoidAlgebra.mem_span_support', Submodule.finset_inf_coe, AddSubgroup.coe_pathComponentZero, ContinuousMap.exists_disjoint_nonempty_clopen_cover_of_mem_nhds_diagonal, Subsemigroup.coe_top, Subfield.subset_closure, Topology.RelCWComplex.Subcomplex.finiteType_subcomplex_of_finiteType, ConvexBody.hausdorffDist_coe, not_linearIndepOn_finset_iffₛ, Finset.inf'_eq_csInf_image, EMetric.NonemptyCompacts.isClosed_subsets_of_isClosed, Submodule.torsionBySet_eq_torsionBySet_span, AddSubgroup.subset_normalizer_of_normal, ZFSet.toSet_iUnion, HNNExtension.NormalWord.TransversalPair.compl, Ideal.subset_union_prime, Module.Finite.span_finset, ConvexCone.coe_top, AddSubgroup.surjOn_iff_le_map, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Submodule.subset_span, Order.Ideal.isMaximal_iff, Submonoid.coe_iInf, UpperSet.coe_sInf, Subalgebra.instCanLiftSetCoeAndForallForallForallMemForallHAddForallForallForallForallHMulForallCoeRingHomAlgebraMap, RestrictedProduct.evalMonoidHom_apply, IsLinearTopology.hasBasis_ideal, Finset.nullMeasurableSet, Ideal.coe_torsionOf, DirectSum.support_subset, Finset.Nonempty.csInf_mem, Subfield.coe_toAddSubgroup, Valuation.coe_ltAddSubgroup, LowerSet.coe_nonempty, Subalgebra.setRange_algebraMap, AddAction.add_stabilizer_self, FirstOrder.Language.Substructure.map_closure, Subgroup.coe_toSubmonoid, Topology.CWComplex.skeletonLT_zero_eq_empty, Subring.coe_bot, FirstOrder.Language.Theory.CompleteType.setOf_subset_eq_univ_iff, NonUnitalSubsemiring.coe_sInf, Finset.coe_map, Submodule.coe_set_smul, asymptoticCone_submodule, Subgroup.coe_subgroupOf, TwoSidedIdeal.coe_unop, TopologicalSpace.NonemptyCompacts.continuous_coe, Set.Nonempty.affineSpan, Flag.ext_iff, tendsto_card_div_pow_atTop_volume', IsLocalization.span_invSubmonoid, Subgroup.transferTransversal_apply'', AddSubgroup.exists_right_transversal_of_le, QuotientGroup.preimage_mk_one, ConvexBody.hausdorffEDist_coe, Partition.sSup_eq, AlgebraicGeometry.Scheme.Opens.ι_appLE, Subgroup.le_centralizer_iff_isMulCommutative, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, Submodule.top_coe, Submodule.isCompact_of_fg, Submodule.coe_torsion_eq_annihilator_ne_bot, AlgebraicGeometry.IsOpenImmersion.range_pullbackFst, MeasureTheory.Measure.haar.addIndex_pos, AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus, HallMarriageTheorem.hall_cond_of_compl, NonUnitalSubring.coe_iSup_of_directed, Partition.coe_removeBot, AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff_of_mem, Finset.prod_mulIndicator_eq_prod_inter, Polynomial.coeff_restriction', Sublattice.coe_iInf, Irreducible.maximalIdeal_pow_eq_closedBall_pow, TopCat.Presheaf.germ_stalkSpecializes, List.support_formPerm_of_nodup', PrimeSpectrum.exists_image_comap_of_finite_of_free, AffineSubspace.coe_injective, Subgroup.coe_op, Behrend.threeAPFree_image_sphere, DFinsupp.mk_sub, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, FirstOrder.Language.Substructure.closure_le, ConvexBody.hausdorffEdist_coe, HomogeneousIdeal.irrelevant_eq_closure, AffineSubspace.coe_iInf, AddSubmonoid.coe_bot, Finset.coe_add, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_inter, HasUpperLowerClosure.isOpen_lowerClosure, IsFractionRing.liftAlgHom_fieldRange, Turing.TM1to0.tr_supports, QuotientAddGroup.eq_class_eq_leftCoset, ClosedSubmodule.coe_iSup, Submodule.coe_mapAlgHom_apply, Finset.preimage_map, TwoSidedIdeal.coe_op, Ideal.isPrimary_decomposition_pairwise_ne_radical, FirstOrder.Language.Substructure.mem_closed_iff, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, DoubleCoset.union_quotToDoubleCoset, AddSubgroup.sup_eq_closure_add, Ideal.iUnion_minimalPrimes, IsSemilinearSet.closure, WCovBy.finset_coe, BooleanSubalgebra.inclusion_apply, NonUnitalSubring.coe_inf, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, FirstOrder.Language.Theory.CompleteType.toList_foldr_inf_mem, AddSubgroup.exists_leftTransversal_of_FiniteIndex, Finsupp.support_subset_iff, Finset.coe_Ici, ZFSet.toSet_sUnion, Subring.coe_center, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, Ideal.relNorm_apply, isClosed_nullAddSubgroup, Finset.intervalGapsWithin_mapsTo, Subgroup.isComplement_subgroup_right_iff_existsUnique_quotientGroupMk, Subgroup.card_mul_eq_card_subgroup_mul_card_quotient, Set.Countable.substructure_closure, DoubleCoset.bot_rel_eq_leftRel, Finset.mulSupport_of_fiberwise_prod_subset_image, addDissociated_iff_sum_eq_subsingleton, Submonoid.subsemiringClosure_mem, LinearIsometry.isComplete_map_iff', ProbabilityTheory.Kernel.iIndepSets.piiUnionInter_of_notMem, LieSubalgebra.mem_coe, FirstOrder.Language.Substructure.subset_closure_withConstants, orbit_addSubgroup_eq_rightCoset, NonUnitalSubring.coe_toNonUnitalSubsemiring, IsDedekindDomain.isOpen_of_ne_bot, ProjectiveSpectrum.zeroLocus_span, Module.Basis.toFlag_carrier, PrimeSpectrum.zeroLocus_eq_basicOpen_of_mul_add, Subgroup.normalClosure_eq_self, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, RestrictedProduct.zpow_apply, Subgroup.dense_of_no_min, EMetric.Closeds.edist_eq, SimpleGraph.Walk.coe_edges_toFinset, IntermediateField.gc, Submonoid.top_closure_mul_self_eq, TopologicalSpace.PositiveCompacts.isCompact, Sublocale.range_toNucleus, OpenSubgroup.isClopen, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, Polynomial.support_restriction, Submodule.finset_span_isCompactElement, Set.add_addSubgroupClosure, IsLinearTopology.hasBasis_subbimodule, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ, Finset.wellFoundedOn, MeasureTheory.Measure.haar.addPrehaar_mem_addHaarProduct, AlgebraicGeometry.IsAffineOpen.isCompactOpenCovered, Submodule.torsionBySet.mk_smul, TopologicalSpace.Closeds.coe_sInf, Convex.toCone_eq_sInf, TopologicalSpace.CompactOpens.coe_toOpens, TopologicalSpace.CompactOpens.coe_sup, AddSubmonoid.coe_topologicalClosure, AddSubmonoid.coe_op, NonUnitalAlgebra.adjoin_toSubmodule, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply, Subsemiring.coe_toAddSubmonoid, Order.Ideal.coe_inf, StarSubalgebra.coe_toSubalgebra, Affine.Simplex.setInterior_subset_affineSpan, IsFractionRing.lift_fieldRange, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_vanishingIdeal, Submodule.isPathConnected, PointedCone.isClosed_dual, Finset.preimage_add_left_zero', ConvexCone.coe_hull_of_convex, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, CovBy.finset_coe, TopologicalSpace.PositiveCompacts.coe_sup, normal_iff_eq_addCosets, TopologicalSpace.Opens.coe_inj, AlgebraicGeometry.Scheme.PartialMap.dense_domain, RingSubgroupsBasis.mem_addGroupFilterBasis_iff, PMF.toOuterMeasure_apply_finset, Finset.restrict_comp_piCongrLeft, QuotientGroup.image_coe, AddSubsemigroup.isClosed_topologicalClosure, TopologicalSpace.Opens.coe_inf, Subgroup.equivSMul_symm_apply_coe, LocallyFinite.exists_finset_nhds_mulSupport_subset, Subring.coe_ofClass, Subgroup.smul_toLeftFun, Convex.subset_toCone, TopologicalSpace.Compacts.range_map, TopologicalSpace.Opens.mk_coe, isTopologicalBasis_pi, RootPairing.Base.exists_eq_sum_and_forall_sum_mem_of_isPos, AddSubgroup.isComplement'_def, SemigroupIdeal.coe_closure', Lagrange.nodal_subgroup_eq_X_pow_card_sub_one, Submonoid.coe_centralizer, mul_upperClosure, Algebra.adjoin.powerBasis'_gen, Subsemigroup.iSup_eq_closure, AlgebraicGeometry.ExistsHomHomCompEqCompAux.range_g_subset, coe_powCardSubgroup, Submonoid.coe_set_mk, Subalgebra.range_le, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_right, AffineIndependent.affineSpan_disjoint_of_disjoint, AlgebraicGeometry.quasiCompact_iff_forall_affine, Ideal.exists_disjoint_powers_of_span_eq_top, Subgroup.IsComplement'.QuotientMulEquiv_apply, Set.addSubgroupClosure_add_nsmul, ContinuousMapZero.adjoin_id_dense, Finset.coe_zsmul, DFinsupp.eq_mk_support, Submodule.Convex.semilinear_range, PeriodPair.analyticOnNhd_weierstrassPExcept, AddSubmonoid.coe_negOrderIso_apply, NonemptyInterval.coe_pure, RestrictedProduct.add_apply, AddAction.stabilizer_subset_sub_right, EMetric.Closeds.isClosed_subsets_of_isClosed, Set.Finite.exists_finset_coe, Partition.partscopyEquiv_apply_coe, AddSubmonoid.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAdd, Equiv.Perm.isCycleOn_support_of_mem_cycleFactorsFinset, PrimeSpectrum.zeroLocus_sup, ProjectiveSpectrum.zeroLocus_iSup_ideal, Finset.coe_inter, Submodule.mem_set_smul, ConvexCone.closure_eq, Subsemigroup.coe_op, le_rank_iff_exists_linearIndependent_finset, CompleteSublattice.map_carrier, Subsemiring.le_centralizer_centralizer, mul_lowerClosure, NonUnitalSubsemiring.coe_sSup_of_directedOn, AffineSubspace.setOf_sOppSide_eq_image2, TopologicalSpace.Compacts.isCompact_biUnion_coe_of_isCompact, Finset.preimage_add_right_zero, AddSubmonoid.coe_comap, ConvexBody.coe_add, Finset.infs_self_subset, Submodule.map_coe, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, Finset.set_biUnion_preimage_singleton, NonUnitalSubring.coe_toSubsemigroup, UpperSet.coe_sSup, Submodule.span_range_eq_top_of_injective_of_rank_le, TestFunctionClass.tsupport_map_subset, Finsupp.comapDomain_add_of_injective, MeasureTheory.squareCylinders_eq_iUnion_image, Finset.isGLB_inf', LieSubalgebra.lieSpan_eq, IsOfFinAddOrder.multiples_eq_zmultiples, RestrictedProduct.div_apply, Topology.IsLowerSet.nhdsSet_eq_principal_lowerClosure, Flag.mem_coe_iff, AlgebraicGeometry.IsAffineOpen.isQuasiSeparated, AddSubmonoid.coe_center, Finset.Nonempty.to_set, MulEquiv.subgroupMap_symm_apply, ConvexCone.coe_sInf, UpperSet.coe_sdiff, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, orbit_subgroup_one_eq_self, Topology.RelCWComplex.skeletonLT_top, stabilizer_isOpen, IsTopologicalGroup.exist_openSubgroup_sub_clopen_nhds_of_one, val_rootsOfUnityEquivOfPrimitiveRoots_apply_coe, PrimeSpectrum.localization_comap_range, AddSubgroup.dense_of_not_isolated_zero, RingHom.ker_eq, Subgroup.exists_isComplement_right, Finset.coe_insert, Subsemiring.coe_iInf, IsLocalization.orderIsoOfPrime_apply_coe, PointedCone.dual_flip_dual_dual_flip, Algebra.essFiniteType_iff, Finset.card_diffs_iff, AddSubgroup.exists_left_transversal_of_le, Subalgebra.coe_centralizer, Algebra.EssFiniteType.cond, Set.Finite.upperClosure, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, AffineSubspace.setOf_wSameSide_eq_image2, Submodule.coe_toSubMulAction, range_derivWithin_subset_closure_span_image, vsub_set_subset_vectorSpan, TopologicalSpace.NonemptyCompacts.isCompact_subsets_of_isCompact, Flag.rangeFin_carrier, AddGroupCone.coe_nonneg, Subsemiring.coe_center, Set.MapsTo.submoduleSpan, DoubleCoset.out_eq', Finset.weightedVSub_indicator_subset, Submodule.mem_div_iff_smul_subset, IsSemilinearSet.of_fg, Subfield.coe_map, Submodule.neg_coe, NonUnitalSubsemiring.ofClass_carrier, TopologicalSpace.Opens.ext_iff, PartitionOfUnity.exists_finset_nhds', AddSubmonoid.coe_matrix, LieSubalgebra.le_def, IsApproximateAddSubgroup.addSubgroup, RootPairing.EmbeddedG2.allRoots_subset_range_root, LowerSet.lower, PrimeSpectrum.range_comap_fst, SimpleGraph.componentComplFunctor_map, IsGaloisGroup.card_fixingSubgroup_eq_finrank, AmpleSet.of_one_lt_codim, Polynomial.degreeLE_eq_span_X_pow, Subring.closure_le, AddSubmonoid.mem_closure_finset', UpperSet.coe_subset_coe, AlgEquiv.subalgebraMap_symm_apply_coe, Subalgebra.coe_toSubring, piiUnionInter_singleton_left, ContinuousMap.instCompactSpaceElemCoeCompacts, IsOfFinAddOrder.finite_zmultiples, AlgebraicGeometry.quasiCompactCover_iff, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, NonUnitalAlgebra.adjoin_eq, SimpleGraph.coe_finsetWalkLengthLT_eq, Sublattice.coe_eq_empty, IsOpenMap.coe_functor_obj, IsClosed.upperClosure_pi, PrimeSpectrum.zeroLocus_empty_iff_eq_top, MeasureTheory.Measure.haar.haarContent_outerMeasure_closure_pos, ProjectiveSpectrum.zeroLocus_inf, AddSubsemigroup.coe_iInf, Projectivization.Subspace.span_eq_span_iff, Topology.RelCWComplex.Subcomplex.mem_carrier, NonUnitalSubsemiring.mem_closure_iff, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen, Submodule.span_biInter, Submodule.sup_span, FirstOrder.Language.Substructure.cg_iff_empty_or_exists_nat_generating_family, TopologicalSpace.Compacts.coe_nonempty, AffineSubspace.equivMapOfInjective_toFun, Subsemiring.coe_map, MeasureTheory.IsSetSemiring.exists_finpartition_diff, Order.Ideal.coe_top, TopologicalSpace.Opens.overEquivalence_counitIso_hom_app, NonUnitalSubsemiring.coe_top, isDiscrete_iff_discreteTopology, SimpleGraph.IsMaximumIndepSet.isIndepSet, Finsupp.support_indicator_subset, Submodule.mul_def, StructureGroupoid.LocalInvariantProp.liftPropAt_iff_comp_inclusion, GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ_assoc, MeasureTheory.SimpleFunc.map_preimage, QuotientGroup.dense_image_mk, SimpleGraph.coe_neighborFinset, PrimeSpectrum.zeroLocus_anti_mono_ideal, Algebra.coe_sInf, Algebra.sup_def, AlgebraicGeometry.Scheme.zeroLocus_univ, Submonoid.subset_closure, OpenNormalAddSubgroup.pathComponentZero_carrier, Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right, Submonoid.surjOn_iff_le_map, Orthonormal.exists_orthonormalBasis_extension, FirstOrder.Language.Substructure.coe_iInf, Finset.coe_smul, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, Set.powersetCard.ncard_eq, Finset.pairwiseDisjoint_pair_insert, gc_lowerClosure_coe, AffineSubspace.eq_bot_or_nonempty, RestrictedProduct.continuousVAdd, not_linearIndepOn_finset_iffₒₛ, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset, Submonoid.coe_sInf, Subgroup.coe_comap, ZFSet.toSet_range, Affine.Simplex.map_subtype_restrict, IntermediateField.adjoin_self, Finset.sum_finset_coe, Finset.coe_list_sum, Subsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul, ConvexBody.coe_nsmul, Topology.CWComplex.Subcomplex.union_closedCell, RootPairing.Base.span_int_coroot_support, ConvexCone.coe_bot, BooleanSubalgebra.supClosed, Order.Ideal.isIdeal, Ideal.toIdeal_homogeneousHull_eq_iSup, Affine.Simplex.restrict_map_subtype, Finset.preimage_mul_right_singleton, Sublattice.coe_top, Subsemigroup.coe_sSup_of_directed_on, Subgroup.coe_nonempty, ZLattice.covolume.tendsto_card_div_pow'', MeasureTheory.IsSetSemiring.subset_disjointOfDiff, Algebra.basicOpen_subset_smoothLocus_iff, isAdic_iff, Submonoid.coe_unop, SkewMonoidAlgebra.mem_span_support, LinearMap.range_coe, ClopenUpperSet.coe_inf, Subgroup.dense_xor'_cyclic, ConvexCone.IsReproducing.sub_eq_univ, RingEquiv.nonUnitalSubsemiringMap_apply_coe, LowerSet.lowerClosure, MeasureTheory.MeasuredSets.edist_def, ClosedSubmodule.coe_sup, Submonoid.coe_pos, NonUnitalSubalgebra.coe_toSubmodule, Submodule.toNonUnitalSubalgebra_mk, FractionalIdeal.mem_extended_iff, AffineIndependent.convexHull_inter, MeasureTheory.Measure.haar.haarContent_outerMeasure_self_pos, Submodule.coe_matrix, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, NonUnitalSubring.coe_prod, MeasureTheory.Measure.haar.addPrehaar_sup_le, SeparatedNhds.of_singleton_finset, Submodule.carrier_eq_coe, AffineSubspace.mem_coe, NonarchimedeanGroup.prod_self_subset, Subgroup.surjOn_iff_le_map, Subalgebra.coe_mk, AddMonoidHom.coe_range, FirstOrder.Language.Theory.CompleteType.isMaximal, Finset.image_mul_right', IsUpperSet.disjoint_lowerClosure_right, TopologicalSpace.Opens.not_nonempty_iff_eq_bot, AddSubsemigroup.coe_ofClass, Finset.sup_id_eq_sSup, TestFunction.tsupport_subset', PeriodPair.analyticOnNhd_weierstrassP, Partition.parts_nonempty, SimpleGraph.edgeFinset_deleteEdges, Order.Ideal.PrimePair.disjoint, RingHom.eqOn_sclosure, EuclideanGeometry.mapsTo_inversion_affineSubspace_of_mem, Topology.RelCWComplex.Subcomplex.finite_subcomplex_of_finite, Module.Basis.mem_span_repr_support, Submonoid.subsemiringClosure_toNonUnitalSubsemiring, AddMonoidAlgebra.support_gen_of_gen', RestrictedProduct.isTopologicalGroup, Subsemigroup.nonUnitalSubsemiringClosure_toAddSubmonoid, isLinearTopology_iff_hasBasis_twoSidedIdeal, AddSubsemigroup.coe_even, Topology.RelCWComplex.Subcomplex.openCell_eq, RestrictedProduct.instContinuousInvCoe, Finset.mem_coe, Subalgebra.isClosed_topologicalClosure, Finset.monotone_preimage, AddSubgroup.set_add_normal_comm, Submodule.connectedComponentIn_eq_self_of_one_lt_codim, SubmodulesRingBasis.mul, Projectivization.Subspace.span_eq_sInf, Subring.coe_centralizer, IsLocalization.map_algebraMap_ne_top_iff_disjoint, NonUnitalSubsemiring.coe_closure_eq, Submodule.FG.generators_mem, Finsupp.supportedEquivFinsupp_apply_apply, Equiv.Perm.signBijAux_injOn, Submonoid.FG.exists_minimal_closure_eq, AlgebraicGeometry.Scheme.codisjoint_zeroLocus, IsOpen.exists_positiveCompacts_closure_subset, Finsupp.nsmul_single_one_image, Topology.RelCWComplex.skeleton_mono, MeasureTheory.Measure.haar.chaar_mem_clPrehaar, FirstOrder.Language.Hom.eqOn_closure, RestrictedProduct.instContinuousVAddCoePrincipal, IsLocalRing.local_hom_TFAE, ClosedSubmodule.coe_comap, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Finset.coe_pow, IntermediateField.coe_top, Affine.Simplex.closedInterior_subset_affineSpan, Finset.image_add_left, TopologicalSpace.Closeds.coe_eq_singleton_of_isAtom, OrderIso.finsetSetFinite_apply_coe, PrimeSpectrum.localization_away_comap_range, range_cfc, Order.Ideal.coe_ssubset_coe, Ideal.coe_piOrderIso_apply, SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint, Submodule.coe_scott_continuous, Topology.RelCWComplex.Subcomplex.cell_def, MonoidHom.eqOn_closure, Submodule.coe_eq_univ, Affine.Simplex.restrict_map_inclusion, IntermediateField.coe_sInf, Nat.mod_injOn_Ico, Finset.coe_vsub, AddSubgroup.coe_eq_univ, Order.Ideal.coe_toLowerSet, AddSubmonoid.coe_set_mk, LieSubmodule.coe_iInf, AddAction.isBlock_addSubgroup', Finset.preimage_add_right_zero', Sublattice.prodEquiv_symm_apply, Set.injOn_iff_map_eq_one, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, FirstOrder.Language.exists_elementarySubstructure_card_eq, Subsemigroup.coe_ofClass, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, PrimeSpectrum.subset_zeroLocus_iff_subset_vanishingIdeal, StarSubsemiring.coe_ofClass, Set.powersetCard.mem_map_iff_mem_range, InfiniteGalois.fixingSubgroup_isClosed, AddSubgroup.coe_toSubgroup_symm_apply, IsLocalRing.isOpen_iff_finite_quotient, Subgroup.isComplement_subgroup_right_iff_bijective, leftAddCoset_mem_leftAddCoset, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic, NonemptyInterval.coe_top, Topology.RelCWComplex.closedCell_subset_skeleton, Absorbent.subset_range_iff_surjective, PrimeSpectrum.isRetrocompact_basicOpen, affineSpan_insert_affineSpan, AffineSubspace.coe_comap, AlgebraicGeometry.coe_opensRestrict_apply_coe, Partition.coe_parts, PrimeSpectrum.coe_isIdempotentElemEquivClopens_apply, Dynamics.exists_isDynCoverOf_of_isCompact_invariant, IsCyclic.normalizer_le_centralizer, PrimeSpectrum.isCompact_isOpen_iff_ideal, AffineMap.linear_eqOn_vectorSpan, LowerSet.carrier_eq_coe, RestrictedProduct.single_eq_of_ne', Submodule.bot_colon, AddSubgroup.coe_ofClass, Subgroup.iSup_eq_closure, lowerClosure_eq, AffineSubspace.nonempty_iff_ne_bot, RingSubgroupsBasis.mul, Finset.coe_sum, Finset.sup_id_set_eq_sUnion, Finset.coe_image₂, RestrictedProduct.mulSingle_div, Submonoid.coe_mul_self_eq, NonUnitalSubsemiring.topologicalClosure_coe, LinearMap.le_rank_iff_exists_linearIndependent_finset, Flag.coe_smul, ProjectiveSpectrum.coe_vanishingIdeal, AffineSubspace.SSameSide.nonempty, TopologicalSpace.Opens.coe_top, ClosedSubmodule.carrier_eq_coe, MeasureTheory.Measure.haar.is_left_invariant_prehaar, IntermediateField.restrictScalars_adjoin, closure_lowerClosure_comm_pi, Submodule.span_le, DFinsupp.support_subset_iff, TopologicalSpace.PositiveCompacts.nonempty, MeasureTheory.Measure.haar.addPrehaar_self, Submodule.span_sInf, Finsupp.restrictSupportEquiv_symm_apply_coe, Submodule.colon_bot, PrimeSpectrum.zeroLocus_pow, OpenAddSubgroup.coe_prod, LowerSet.coe_bot, MulAction.stabilizer_coe_finset, Polynomial.coeffs_ofSubring, Order.Ideal.PrimePair.compl_F_eq_I, Polynomial.lifts_iff_coeffs_subset_range, affineSpan_insert_zero, Subgroup.isComplement'_def, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, Polynomial.taylorLinearEquiv_apply_coe, UpperSet.coe_bot, isBigO_norm_restrict_cocompact, RestrictedProduct.isTopologicalAddGroup, Subsemiring.mem_closure_iff, GromovHausdorff.eq_toGHSpace_iff, Order.Ideal.coe_sInf, Submonoid.sup_eq_closure, TopologicalSpace.Opens.coe_eq_univ, Submonoid.closure_le, Subsemigroup.coe_map, convexHull_subset_affineSpan, Ideal.hasBasis_nhds_adic, Submodule.mapsTo_span, Subgroup.coe_zpowers, ZSpan.setFinite_inter, AddSubgroup.coe_nonempty, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, Submodule.coe_set_neg, RestrictedProduct.mulSingle_eq_of_ne, Topology.RelCWComplex.Subcomplex.coe_eq_carrier, ofAdd_image_multiples_eq_powers_ofAdd, AlgebraicGeometry.PresheafedSpace.restrictStalkIso_inv_eq_germ_assoc, Set.sized_powersetCard, SubAddAction.closure_le, AffineSubspace.affineSpan_coe, MvPowerSeries.LinearTopology.hasBasis_nhds_zero, PointedCone.closure_eq, Finset.disjiUnion_Iic_disjointed, Subalgebra.topologicalClosure_adjoin_le_centralizer_centralizer, ClosedSubmodule.coe_toSubmodule, TopologicalSpace.IsOpenCover.isOpen_iff_inter, ZLattice.coe_comap, mem_generatePiSystem_iUnion_elim', AddSubgroup.le_centralizer, TopologicalSpace.Closeds.instCanLiftSetCoeIsClosed, AddMonoidHom.coe_mrange, CStarAlgebra.span_unitary, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, Cardinal.finset_card_lt_aleph0, AddMonoidAlgebra.mem_gradeBy_iff, Subsemigroup.nonUnitalSubsemiringClosure_eq_closure, trop_sInf_image, Matroid.IsRkFinite.exists_finset_isBasis', Submonoid.mem_closure_iff_exists_finset_subset, Subring.coe_sInf, DFinsupp.mk_smul, Submodule.inf_coe, Finset.preimage_inl, coe_set_nsmul, MvPolynomial.supported_eq_vars_subset, Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range, separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparable, Behrend.threeAPFree_sphere, ContinuousMap.idealOfSet_isMaximal_iff, NonarchimedeanAddGroup.prod_self_subset, Finset.powersetCard_empty_subsingleton, Subsemigroup.coe_iInf, AddAction.vadd_set_stabilizer_subset, Subgroup.coe_eq_singleton, PrimeSpectrum.le_vanishingIdeal_zeroLocus, OpenAddSubgroup.coe_inf, IsCoercive.isClosed_range, IsOfFinOrder.powers_eq_zpowers, GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset', MonoidHom.coe_ker, ConvexBody.coe_smul', Subring.coe_iInf, Finset.exists_cycleOn, ProperCone.innerDual_innerDual, Set.ncard_coe_finset, AddSubgroup.closure_le, Nat.coe_maximalIdeal, Algebra.gc, TopologicalSpace.IsOpenCover.exists_finite_nonempty_disjoint_clopen_cover, AddMonoidAlgebra.mem_span_support, MeasureTheory.Measure.haar.addPrehaar_empty, LowerSet.coe_mul, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, MeasureTheory.Lp.simpleFunc.dense, IsLinearTopology.hasBasis_open_twoSidedIdeal, Subfield.coe_toSubmonoid, AddSubsemigroup.coe_op, ConvexBody.coe_zero, RingCone.coe_nonneg, SimpleGraph.componentCompl_nonempty_of_infinite, Subsemiring.coe_nonneg, Subfield.coe_extendScalars, PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closure, infinite_powers, RingHom.coe_rangeS, coe_mono, Set.subgroupClosure_mul, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, Subsemiring.coe_unop, Submonoid.coe_powers, IntermediateField.coe_map, TwoSidedIdeal.coe_asIdeal, Finset.coe_subset_singleton, RestrictedProduct.pow_apply, SubAddAction.fg_iff, Subgroup.normal_centralizer, Subgroup.coe_bot, Set.powersetCard.coe_nontrivial_iff, Subgroup.coe_prod, AddSubgroup.topologicalClosure_coe, AddHom.coe_srange, IsLinearTopology.hasBasis_right_ideal, Finset.smul_stabilizer_of_no_doubling, Finpartition.part_surjOn, ConvexCone.mem_closure, Finpartition.exists_subset_part_bijOn, FirstOrder.Language.Substructure.lift_card_closure_le, RingHom.coe_range, NonUnitalStarSubalgebra.coe_comap, IsDedekindDomain.isOpen_iff, UpperSet.coe_erase, TopologicalSpace.Compacts.ext_iff, FirstOrder.Language.Substructure.closure_eq, Interval.coe_pure, RestrictedProduct.mul_apply, ZFSet.toSet_union, TopologicalSpace.NonemptyCompacts.isClosed_subsets_of_isClosed, ZFSet.coe_union, MvPolynomial.coe_coeffsIn, Finset.instNonemptyElemCoeInsert, QuotientAddGroup.preimage_mk_zero, TopologicalSpace.CompactOpens.coe_himp, LieSubmodule.sInf_coe, MvPolynomial.mem_image_comap_C_basicOpen, EMetric.continuous_infEdist_hausdorffEdist, QuotientAddGroup.orbit_mk_eq_vadd, Submodule.coe_ofLinearComb, Submodule.coe_toAddSubgroup, IsLocalRing.isOpen_maximalIdeal, AlgebraicGeometry.Scheme.Hom.coe_opensRange, PointedCone.dual_eq_iInter_dual_singleton, MeasureTheory.Measure.haarMeasure_eq_iff, Finset.image_mul_left, separableClosure.adjoin_le, AlgebraicGeometry.quasiSeparatedSpace_iff_affine, Submodule.coe_sInf, FirstOrder.Language.Substructure.mem_closure_iff_of_isRelational, NonUnitalSubsemiring.closure_eq, AffineSubspace.isClosed_direction_iff, finiteDimensional_vectorSpan_insert, IntermediateField.induction_on_adjoin_finset, PointedCone.dual_dual_flip_dual, FirstOrder.Language.Substructure.closure_mono, Finset.coe_uIcc, PointedCone.coe_comap, Submodule.isClosed_or_dense_of_isCoatom, TopologicalSpace.Opens.IsBasis.le_iff, Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct, schnirelmannDensity_finset, AffineSubspace.coe_affineSpan_singleton, Finset.coe_sigma, Finset.isLeast_min', IdealFilter.isUniform_iff_exists_ringFilterBasis, AddSubgroup.subset_closure, Sublattice.coe_eq_univ, Finset.isWF, TopologicalSpace.Opens.instCanLiftSetCoeIsOpen, Finset.piecewise_coe, Flag.maxChain, MeasureTheory.SimpleFunc.map_preimage_singleton, AffineSubspace.coe_direction_eq_vsub_set_right, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, intrinsicClosure_subset_affineSpan, Finset.image_mul_right, AddSubgroup.dense_xor'_cyclic, AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus, FirstOrder.Language.Theory.CompleteType.subset, FirstOrder.Language.Substructure.closure_univ, AddSubmonoid.iSup_eq_closure, ContDiffMapSupportedInClass.map_zero_on_compl, isClosed_unitary, Set.image_finset_prod_pi, Submodule.span_range_inclusionSpan, Subsemigroup.coe_toAddSubsemigroup_apply, Submodule.coe_iSup_of_chain, Submodule.span_coe_eq_restrictScalars, Submonoid.closure_eq_image_prod, Submodule.surjOn_iff_le_map, ClopenUpperSet.coe_top, Affine.Simplex.restrict_points_coe, mulDissociated_iff_sum_eq_subsingleton, upperClosure_eq_Ici_csInf, Affine.Simplex.excenterExists_restrict, AddSemigroupIdeal.fg_iff, AffineSubspace.coe_sInf, NonUnitalRingHom.eqOn_sclosure, MvPolynomial.decomposition.decompose'_eq, LowerAdjoint.closure_union_closure_left, Subsemiring.coe_comap, RingFilterBasis.SubmodulesBasis.smul, Set.coe_toFinset, Finset.coe_disjUnion, TopologicalSpace.IsOpenCover.exists_mem_nhds, Metric.NonemptyCompacts.dist_eq, FirstOrder.Language.Substructure.closure_image, QuotientGroup.t1Space_iff, IsLinearTopology.hasBasis_open_subbimodule, PointedCone.salient_iff_inter_neg_eq_singleton, AddSubgroup.isComplement_range_right, Finset.insert_inj_on', SubMulAction.coe_pow, NonUnitalAlgebra.adjoin_eq_span, Ideal.isOpen_of_isMaximal, FractionalIdeal.coe_extended_eq_span, Finset.nsmul_right_strictMonoOn, Subsemiring.coe_bot, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, NonUnitalStarAlgHom.coe_range, Subalgebra.coe_prod, Finset.coe_union, Finset.coe_map_subset_range, NonUnitalStarAlgebra.adjoin_le_centralizer_centralizer, AddSubmonoid.mk_eq_bot, LieSubmodule.mem_coe, LieSubmodule.inf_coe, Finset.isLUB_iff_isGreatest, Submodule.spanFinrank_eq_iInf, bddAbove_lowerClosure, PointedCone.dual_span, LowerAdjoint.closure_iUnion_closure, NonUnitalSubring.closure_le, IsApproximateAddSubgroup.of_small_tripling, AddSubmonoid.mul_eq_closure_mul_set, FirstOrder.Language.Substructure.cg_closure_singleton, Subgroup.sup_eq_closure, Finset.tsum_subtype', CommMonoid.coe_primaryComponent, Subgroup.coe_sInf, eq_sUnion_finset_of_isTopologicalBasis_of_isCompact_open, Finset.coe_subset, Finsupp.image_pow_eq_finsuppProd_image, PMF.toMeasure_apply_finset, IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure, NonUnitalSubsemiring.coe_comap, Finsupp.sym2_support_eq_preimage_support_mul, RingPreordering.coe_set_mk, Subsemigroup.coe_square, PeriodPair.differentiableOn_derivWeierstrassPExcept, PrimeSpectrum.zeroLocus_eq_singleton, finite_zmultiples, IntermediateField.adjoin_contains_field_as_subfield, KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span, TopologicalSpace.Closeds.isOpen_inter_nonempty_of_isOpen, AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPoint, FirstOrder.Language.Structure.fg_iff, FirstOrder.Language.Substructure.cg_closure, HilbertBasis.finite_spans_dense, RestrictedProduct.mulSingle_eq_one_iff, exists_linearIndepOn_id_extension, Polynomial.toSubring_one, DoubleCoset.mk_out_eq_mul, Set.definable_iff_finitely_definable, NonUnitalStarSubalgebra.isClosed_topologicalClosure, Subgroup.dense_iff_ne_zpowers, AffineSubspace.coe_map

SimpleGraph.Subgraph

Definitions

Name	Category	Theorems
coe 📖	CompOp	49 math math: deleteVerts_mono', coeSubgraph_injective, verts_coeSubgraph, SimpleGraph.induce_eq_coe_induce_top, SimpleGraph.isContained_iff_exists_iso_subgraph, image_coe_edgeSet_coe, SimpleGraph.Copy.range_toSubgraph, SimpleGraph.IsTree.coe_subgraphOfAdj, coe_degree, SimpleGraph.ConnectedComponent.coe_toSubgraph, SimpleGraph.Walk.map_mapToSubgraph_eq_induce, coe_adj, SimpleGraph.ConnectedComponent.odd_matches_node_outside, SimpleGraph.IsContained.exists_iso_subgraph, isAcyclic_coe_bot, preconnected_iff, map_hom_top, SimpleGraph.Reachable.coe_coeSubgraph, deleteEdges_coe_eq, SimpleGraph.IsTree.coe_singletonSubgraph, coe_deleteEdges_le, spanningCoeEquivCoeOfSpanning_apply_coe, Preconnected.coe, SimpleGraph.Walk.map_mapToSubgraph_hom, SimpleGraph.Walk.map_mapToSubgraph_eq_induce_id, hom_injective, SimpleGraph.isIndepSet_induce, connected_iff', spanningCoeEquivCoeOfSpanning_symm_apply, SimpleGraph.IsAcyclic.subgraph, SimpleGraph.Copy.toSubgraph_surjOn, edgeSet_coe, spanningCoe_coe, SimpleGraph.isNIndepSet_induce, SimpleGraph.Reachable.coe_toSubgraph, inclusion_apply_coe, coeSubgraph_adj, SimpleGraph.Reachable.coe_subgraphMap, Adj.coe, hom_apply, SimpleGraph.killCopies_def, IsInduced.isIndContained, inclusion.injective, coe_hom, coe_deleteEdges_eq, restrict_adj, coe_isContained, Connected.coe, coe_bot

SimpleGraph.Subgraph.Adj

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe 📖	mathematical	SimpleGraph.Subgraph.Adj	SimpleGraph.Adj Set.Elem SimpleGraph.Subgraph.verts SimpleGraph.Subgraph.coe Set Set.instMembership SimpleGraph.Subgraph.edge_vert symm	—	—

SimpleGraph.Subgraph.Connected

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe 📖	mathematical	SimpleGraph.Subgraph.Connected	SimpleGraph.Connected Set.Elem SimpleGraph.Subgraph.verts SimpleGraph.Subgraph.coe	—	—

SimpleGraph.Subgraph.Preconnected

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe 📖	mathematical	SimpleGraph.Subgraph.Preconnected	SimpleGraph.Preconnected Set.Elem SimpleGraph.Subgraph.verts SimpleGraph.Subgraph.coe	—	—

SlashInvariantForm.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

StarMonoidHom.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

Sublattice.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TestFunction.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.Clopens.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.Closeds.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.CompactOpens.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.Compacts.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.IrreducibleCloseds.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.NonemptyCompacts.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.Opens.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

TopologicalSpace.PositiveCompacts.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

UpperHalfPlane

Definitions

Name	Category	Theorems
coe 📖	CompOp	137 math math: mdifferentiable_num, EisensteinSeries.hasSum_e2Summand_symmetricIcc, normSq_pos, image_coe_sphere, re_smul, int_div_mem_integerComplement, isOpenEmbedding_coe, EisensteinSeries.summand_bound_of_mem_verticalStrip, dist_le_iff_dist_coe_center_le, im_smul_eq_div_normSq, specialLinearGroup_apply, canLift, iteratedDerivWithin_tsum_cexp_eq, ModularGroup.one_lt_normSq_T_zpow_smul, SlashInvariantFormClass.eq_cuspFunction, jacobiTheta_T_sq_smul, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, glPos_smul_def, coe_pos_real_smul, ModularGroup.coe_T_zpow_smul_eq, comp_ofComplex, ext_iff, denom_cocycle_σ, re_add_im, mdifferentiable_inv_denom, dist_eq_iff_eq_sinh, contMDiff_coe, ModularGroup.denom_apply, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, dist_eq_iff_eq_sq_sinh, image_coe_ball, contMDiff_inv_denom, EisensteinSeries.D2_S, cosh_dist, image_coe_closedBall, EisensteinSeries.G2_S_transform, dist_coe_center, jacobiTheta_S_smul, lt_dist_iff_lt_dist_coe_center, coe_smul_of_det_pos, norm_exp_two_pi_I_lt_one, modular_S_smul, EisensteinSeries.hasSum_e2Summand_symmetricIco, dist_lt_iff_dist_coe_center_lt, EisensteinSeries.q_expansion_riemannZeta, ModularGroup.denom_S, contMDiff_num, mdifferentiable_denom, dist_self_center, coe_mem_integerComplement, im_smul, coe_smul, dist_eq, norm_qParam_lt_one, EisensteinSeries.auxbound1, denom_J, qParam_tendsto_atImInfty, dist_eq_iff_dist_coe_center_eq, ModularForm.logDeriv_eta_eq_E2, ModularGroup.tendsto_normSq_coprime_pair, ModularForm.slash_action_eq'_iff, J_smul, SlashInvariantForm.slash_action_eqn'', cmp_dist_eq_cmp_dist_coe_center, le_dist_coe, EisensteinSeries.isBigO_linear_add_const_vec, contMDiff_denom_zpow, ext_iff', EisensteinSeries.auxbound2, EisensteinSeries.qExpansion_identity_pnat, le_dist_iff_le_dist_coe_center, EisensteinSeries.r_mul_max_le, ModularForm.SL_slash_def, ofComplex_apply, coe_J_smul, dist_center_dist, dist_le_dist_coe_div_sqrt, eventuallyEq_coe_comp_ofComplex, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, SlashInvariantForm.slash_action_eqn_SL'', coe_I, EisensteinSeries.q_expansion_bernoulli, coe_specialLinearGroup_apply, ModularGroup.im_smul_eq_div_normSq, cosh_half_dist, exp_half_dist, EisensteinSeries.tendsto_double_sum_S_act, coe_mk, coe_injective, SlashInvariantForm.slash_S_apply, sinh_half_dist_add_dist, mdifferentiable_jacobiTheta, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, EisensteinSeries.G2_eq_tsum_cexp, EisensteinSeries.qExpansion_identity, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, coe_vadd, denom_one, im_inv_neg_coe_pos, contMDiffAt_iff, ModularForm.slash_def, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, mdifferentiable_coe, dist_coe_le, coe_re, coe_mk_subtype, sinh_half_dist, dist_le_iff_le_sinh, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, ModularForm.SL_slash_apply, dist_coe_center_sq, EisensteinSeries.eisSummand_SL2_apply, tendsto_coe_atImInfty, SlashInvariantForm.slash_action_eqn', mdifferentiableAt_iff, denom_cocycle', tanh_half_dist, coe_inj, range_coe, im_pnat_div_pos, coe_im, contMDiff_denom, mdifferentiable_denom_zpow, ModularForm.summable_eta_q, summable_pow_mul_cexp, ModularFormClass.hasSum_qExpansion, c_mul_im_sq_le_normSq_denom, continuous_coe, coe_im_pos, EisensteinSeries.summand_bound, isEmbedding_coe, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, ModularGroup.smul_eq_lcRow0_add, pi_mul_cot_pi_q_exp, ModularForm.slash_apply, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, ModularGroup.coe_truncatedFundamentalDomain

UpperSet.Simps

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

WithBot

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

WithBotTop

Definitions

Name	Category	Theorems
coe 📖	CompOp	6 math math: coe_strictMono, coe_le_coe, coe_monotone, rec_coe, coe_injective, coe_lt_coe

WithOne

Definitions

Name	Category	Theorems
coe 📖	CompOp	18 math math: coeMulHom_apply, map_coe, exists, lift_coe, coe_inj, mapMulHom_coe, coe_unone, coe_mul, instCanLift, recOneCoe_coe, map₂_coe_coe, map₂_coe_right, map₂_coe_left, ne_one_iff_exists, coe_injective, unone_coe, forall, coe_inv

WithTop

Definitions

Name	Category	Theorems
coe 📖	CompOp	—

WithZero

Definitions

Name	Category	Theorems
coe 📖	CompOp	84 math math: OrderMonoidIso.val_inv_unitsWithZero_symm_apply, val_expOrderIso_apply, unzero_coe, withZeroUnitsEquiv_symm_apply_coe, map'_coe, coe_unitsWithZeroEquiv_eq_units_val, lift'_symm_apply_apply, OrderMonoidIso.withZero_symm_apply_symm_apply, OrderMonoidIso.withZero_symm_apply_apply, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, coe_inj, coe_le_iff, lt_iff_exists, coe_zpow, lt_ofAdd_iff, coe_div, lt_iff_exists_coe, OrderMonoidIso.withZeroUnits_symm_apply, lift'_coe, OrderMonoidIso.val_unitsWithZero_symm_apply, OrderIso.withZeroUnits_symm_apply, coe_sup, coe_inv, coe_pow, unitsWithZeroEquiv_symm_apply, le_max_iff, coe_unzero, coe_le_one, coe_neg, le_def, lift_coe, LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ, val_inv_expOrderIso_apply, MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit, toMulBot_coe_ofAdd, coe_inf, mapAddHom_coe, ne_zero_iff_exists, map₂_coe_left, le_ofAdd_of_toAdd_unzero_le, exists, one_lt_coe, unbot_le_iff, coe_lt_one, lt_unzero_iff, le_unzero_iff, map₂_coe_right, le_ofAdd_iff, LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ, forall, one_le_coe, MonoidWithZeroHom.fst_apply_coe, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, toMulBot_coe, MonoidWithZeroHom.inr_apply_unit, map_coe, le_coe_iff, withZeroUnitsEquiv_symm_apply, MulEquiv.withZero_symm_apply_apply, coe_injective, zero_lt_coe, coe_le_coe, not_coe_le_zero, map₂_coe_coe, MonoidWithZeroHom.snd_apply_coe, unzero_lt_iff, coe_lt_coe, coe_one, lt_coe_iff, IsMax.withZero, coe_mul, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, min_le_iff, coeAddHom_apply, val_logOrderIso_symm_apply, lt_def, val_inv_logOrderIso_symm_apply, coeMonoidHom_apply, lt_ofAdd_of_toAdd_unzero_lt, MonoidWithZeroHom.inl_apply_unit, coe_add, instCanLift, MulEquiv.withZero_symm_apply_symm_apply, recZeroCoe_coe

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