toFunLike đ | CompOp | 11922 math, 2 bridgemath: Equiv.Perm.decomposeFin_symm_of_refl, Prod.Lex.toLex_lt_toLex', FirstOrder.Language.PartialEquiv.toEmbedding_apply, Equiv.sumEmpty_symm_apply, SSet.OneTruncationâ.nerveEquiv_apply, MeasurableEquiv.injective, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right, val_toAddUnits_apply, OrthonormalBasis.singleton_repr, DirectSum.decompose_sub, Pi.comul_eq_adjoint, LinearMap.det_toContinuousLinearMap, OrderDual.isBounded_preimage_toDual, DirectSum.IsInternal.ofBijective_coeLinearMap_same, SymAlg.unsym_comp_sym, LinearEquiv.multilinearMapCongrLeft_symm_apply, ContinuousLinearEquiv.preimage_symm_preimage, MultilinearMap.domDomCongrLinearEquiv'_symm_apply, continuous_decomposeProdAdjoint, TensorProduct.finsuppRight_apply, LieModule.shiftedGenWeightSpace.shift_apply, Homeomorph.isClosed_preimage, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv, ContinuousLinearEquiv.antilipschitz, UniformConvergenceCLM.isEmbedding_coeFn, MonoidAlgebra.mapDomainRingEquiv_single, SSet.op_δ, LinearMap.IsSymmetric.clm_adjoint_eq, AddMonoidAlgebra.singleHom_apply, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply', FreeAddMonoid.lift_symm_apply, Polynomial.Gal.galActionHom_restrict, CategoryTheory.Limits.Fork.IsLimit.homIso_natural, AffineEquiv.coe_symm_toEquiv, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, AddSubgroup.centerToAddOpposite_apply_coe, pow_ofDual, Sequential.homeoOfIso_apply, isCompl_toDual_iff, nndist_ofMul, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, Finsupp.snd_sumFinsuppLEquivProdFinsupp, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, Rep.resCoindHomEquiv_symm_apply_hom, NumberField.basisMatrix_eq_embeddingsMatrixReindex, OrderMonoidIso.apply_symm_apply, LinearEquiv.coe_toEquiv, CategoryTheory.Functor.functorHomEquiv_apply_app, CoalgEquiv.coe_toCoalgHom, LinearIsometryEquiv.strictConvex_preimage, Rep.resCoindHomEquiv_apply_hom, DomMulAct.smul_monoidHom_apply, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', WithBot.coe_toDualTopEquiv_eq, RootPairing.InvariantForm.apply_reflection_reflection, CategoryTheory.Quiv.equivOfIso_symm_apply, CategoryTheory.PreZeroHypercover.isoMk_hom_hâ, AffineIsometryEquiv.coe_constVSub, GrpCat.SurjectiveOfEpiAuxs.Ď_apply_fromCoset, PiLp.continuousLinearEquiv_symm_apply, IsLocalizedModule.iso_symm_apply', Homeomorph.isInducing, WithBot.ofDual_map, WithZero.logOrderIso_apply, ContinuousMap.isUniformInducing_equivBoundedOfCompact, 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, LinearMap.restrictScalars_toMatrix, IsometryEquiv.image_sphere, Matrix.comp_diagonal_diagonal, RingEquiv.piCongrRight_apply, SupBotHom.dual_comp, StarModule.decomposeProdAdjointL_symm_apply, fderiv_iteratedFDeriv, RCLike.sqrt_eq_ite, WithTop.map_ofDual, Equiv.sumAssoc_symm_apply_inl, ContinuousLinearEquiv.symm_preimage_preimage, AffineIsometryEquiv.pointReflection_apply, CategoryTheory.uliftCoyonedaEquiv_apply, Equiv.extendSubtype_mem, CategoryTheory.TwoSquare.equivNatTrans_symm_apply, MeasurableEquiv.piCurry_apply, DFinsupp.liftAddHom_apply, unitsEquivNeZero_symm_apply, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, Equiv.prodSumDistrib_apply_left, Matrix.natCast_kronecker, Submonoid.mem_map_equiv, AddCircle.coe_equivIco_mk_apply, LinearMap.apply_symm_toPerfPair_self, LinearMap.SeparatingRight.toMatrixâ', FreeMonoid.map_apply_map_symm_eq, LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff, MeasurableEquiv.surjective, Submodule.rTensorOne_symm_apply, Finset.Colex.toColex_le_singleton, Finsupp.mulHom_ext'_iff, iSupIndep.linearEquiv_symm_apply, Equiv.invFun_as_coe, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, LinearIsometryEquiv.hasStrictFDerivAt, CategoryTheory.mateEquiv_counit_symm, 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TensorProduct.LieModule.liftLie_apply, LinearEquiv.multilinearMapCongrRight_apply, List.Nodup.getEquiv_apply_coe, NonemptyInterval.dual_map, Nat.divModEquiv_apply, ConjAct.toConjAct_inv, FreeAddMonoid.toList_sum, Matrix.transposeInvertibleEquivInvertible_symm_apply, PiTensorProduct.lift.tprod, Monovary.sum_mul_comp_perm_eq_sum_mul_iff, Equiv.subtypeUnivEquiv_apply, CategoryTheory.Arrow.equivSigma_symm_apply_left, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg, Matrix.det_apply, DFA.reindex_apply_accept, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd, OrderDual.ofDual_le_ofDual, OrderIsoClass.toSupHomClass, CategoryTheory.conjugateEquiv_iso, Equiv.prodCongrLeft_apply_snd, LinearIsometryEquiv.coe_symm_toIsometryEquiv, RingEquiv.toRingCatIso_inv, ContinuousLinearEquiv.coe_toHomeomorph, Metric.Snowflaking.uniformContinuous_ofSnowflaking, Diffeomorph.contMDiffWithinAt, WithBot.lt_ofDual_iff, OrderMonoidIso.val_inv_unitsWithZero_symm_apply, Finset.geomSum_lt_geomSum_iff_toColex_lt_toColex, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, AddMonoidAlgebra.domCongr_comp_lsingle, Equiv.coe_vaddConst, ofAdd_multiset_prod, LinearMap.BilinForm.toMatrix_toBilin, WithZero.val_expOrderIso_apply, RingEquiv.coe_ringHom_trans, InfTopHom.symm_dual_id, Fin.cycleRange_succAbove, Module.Basis.end_repr_apply, Homeomorph.finTwoArrow_apply, DirectSum.Decomposition.decompose'_eq, TopCat.isoOfHomeo_inv, Algebra.Presentation.differentials.commââ_single, ValuationSubring.coe_mem_principalUnitGroup_iff, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_apply, IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, Homeomorph.coe_mulRightâ, isLeftRegular_ofColex, Equiv.Perm.SameCycle.exists_pow_eq, Pretrivialization.linearEquivAt_symm_apply, ContinuousLinearEquiv.differentiable, Subgroup.IsComplement.equiv_fst_eq_iff_leftCosetEquivalence, AddSubmonoid.LocalizationMap.symm_comp_ofAddEquivOfLocalizations_apply, WithConv.addEquiv_symm_apply_ofConv, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval, Equiv.ulift_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add, Language.reverseIso_apply, IndexedPartition.proj_fiber, LinearMap.adjoint_adjoint, Polynomial.roots_expand, AffineEquiv.coe_toEquiv, Matrix.SeparatingRight.toLinearMapâ, Equiv.plift_apply, CategoryTheory.Abelian.Ext.homLinearEquiv_apply, Fin.cycleIcc.trans_right_one, RingEquiv.toOpposite_symm_apply, FirstOrder.Language.Equiv.bijective, FractionalIdeal.mapEquiv_apply, Rep.MonoidalClosed.linearHomEquiv_symm_hom, List.equivSigmaTuple_symm_apply, AffineEquiv.sOppSide_map_iff, IntermediateField.algHomEquivAlgHomOfSplits_symm_apply, sigmaFinsuppEquivDFinsupp_support, Nat.Primes.prodNatEquiv_symm_apply, Equiv.image_swap_of_mem_of_notMem, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_comp, MultilinearMap.fromDFinsuppEquiv_apply, AffineIsometryEquiv.pointReflection_involutive, galRestrict_symm_algebraMap_apply, Equiv.Perm.exists_fixed_point_of_prime, LinearIsometryEquiv.surjective, Subgroup.quotientEquivOfEq_mk, Equiv.uniqueProd_symm_apply, MeasurableEquiv.smul_apply, UniformEquiv.funUnique_apply, CategoryTheory.Iso.eHomCongr_inv_comp_assoc, SSet.OneTruncationâ.ofNerveâ.natIso_hom_app_map, Subgroup.equivSMul_apply_coe, LinearEquiv.extendScalarsOfIsLocalizationEquiv_symm_apply, affineHomeomorph_image_Ico, Submonoid.equivOp_symm_apply_coe, LinearEquiv.ofBijective_symm_apply_apply, LinearIsometryEquiv.analyticOnNhd, LinearEquiv.flip_apply, CategoryTheory.Limits.Types.Small.productIso_hom_comp_eval_apply, ContinuousLinearEquiv.image_closure, nndist_ofAdd, EuclideanGeometry.reflection_orthogonal_vadd, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two, CategoryTheory.GrothendieckTopology.yonedaOpCompCoyoneda_hom_app_app_down, FreeMonoid.toList_prod, LinearEquiv.restrictScalars_apply, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, OrderIso.map_covBy, hasFDerivAt_iff_hasGradientAt, TensorProduct.AlgebraTensorModule.rid_symm_apply, LinearIsometryEquiv.coe_ofLinearIsometry_symm, PiTensorProduct.liftAlgHom_apply, MulEquiv.map_eq_one_iff, MulAut.one_apply, CircleDeg1Lift.translate_inv_apply, unitInterval.symmHomeomorph_apply, Equiv.inv_def, nhds_ofMul, DFinsupp.lex_lt_iff_of_unique, ConjAct.toConjAct_mul, FreeMonoid.ofList_smul, SimpleGraph.lapMatrix_toLinearMapâ', Quiver.SingleObj.pathEquivList_nil, FreeGroupBasis.repr_apply_coe, toLex_mul, CategoryTheory.Localization.Preadditive.homEquiv_symm_apply, FreeAddMonoid.lift_ofList, UniformEquiv.refl_apply, NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply, OrderIsoClass.toInfHomClass, FundamentalGroupoid.equiv_symm_apply_as, Orientation.inner_rotation_pi_div_two_right_smul, ContinuousAlgEquiv.map_nhds_eq, CategoryTheory.Classifier.SubobjectRepresentableBy.pullback_homEquiv_symm_obj_Ίâ, extDeriv_constOfIsEmpty, Equiv.toPEquiv_apply, Orientation.oangle_add_left_smul_rotation_pi_div_two, SimpleGraph.incidenceSetEquivNeighborSet_apply_coe, AddEquivClass.instAddMonoidHomClass, RootPairing.coroot_eq_polarizationEquiv_apply_root, Real.fourierIntegral_comp_linearIsometry, Ideal.exists_comap_galRestrict_eq, Trivialization.preimageHomeomorph_symm_apply, WithTop.toDualBotEquiv_coe, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_eq, Submodule.orthogonalDecomposition_symm_apply, AffineEquiv.pointReflection_fixed_iff_of_injective_two_nsmul, MeasurableEquiv.coe_smulâ, MulEquivClass.map_finprod, IsometryEquiv.preimage_sphere, val_inv_unitsEquivProdSubtype_symm_apply, CategoryTheory.Limits.IsLimit.equivIsoLimit_apply, Int.quotientSpanEquivZMod_comp_Quotient_mk, MeasureTheory.ComplexMeasure.equivSignedMeasure_symm_apply, MvPolynomial.rTensor_apply_tmul_apply, IsLowerSet.ofDual, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, Set.dual_ordConnectedComponent, ContinuousMulEquiv.surjective, Equiv.Set.union_symm_apply_left, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, AlternatingMap.constLinearEquivOfIsEmpty_symm_apply, SetTheory.PGame.exists_leftMoves_neg, MulEquiv.coe_trans, reindex_mem_doublyStochastic_iff, MeasurableEquiv.measurableEmbedding, AddEquiv.addMonoidHomCongrLeftEquiv_apply, Additive.toMul_mono, Topology.IsGeneratedBy.homeomorph_symm_coe, AffineIsometryEquiv.coe_symm_toAffineEquiv, LinearMap.Nondegenerate.congr, LightCondensed.ihomPoints_apply, SetTheory.PGame.Domineering.shiftUp_apply, Subgroup.centerCongr_symm_apply_coe, zpowersMulHom_symm_apply, Equiv.sumCompl_symm_apply_pos, CategoryTheory.shrinkYonedaEquiv_comp, UniformOnFun.gen_eq_preimage_restrict, Equiv.optionIsSomeEquiv_symm_apply_coe, PiTensorProduct.tmulEquiv_symm_apply, Equiv.coe_constVSub_symm, FreeAddMonoid.count_apply, NumberField.Units.logEmbedding_fundSystem, toColex_ofColex, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection', Lex.forall, dotProductEquiv_symm_apply, Matrix.abs_det_reindex, ofBoolRing_sub, nsmul_finEquivZMultiples_symm_apply, LinearEquiv.piCongrRight_apply, Equiv.piComm_apply, MulEquiv.monoidHomCongrLeft_apply, addMonoidHomLequivNat_symm_apply, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, MonomialOrder.degree_add_of_ne, rootsOfUnityEquivOfPrimitiveRoots_apply_coe_inv_val, Matrix.separatingRight_toLinearMapâ'_iff, frobeniusEquiv_apply, ZSpan.volume_real_fundamentalDomain, CategoryTheory.Iso.conjAut_apply, BitVec.equivFin_symm_apply_toFin, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_Κ_presheafHom, UniformFun.ofFun_one, PiTensorProduct.isEmptyEquiv_apply_tprod, AddEquiv.toMultiplicative_apply_symm_apply, PartENat.withTopEquiv_symm_apply, AddMonoidHom.toMultiplicative_add, SimpleGraph.Walk.IsHamiltonian.getVertEquiv_apply, Rack.toEnvelGroup.univ_uniq, Multiset.toFinsupp_add, AddAut.apply_inv_self, CategoryTheory.Functor.curryingEquiv_symm_apply_obj_obj, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, Order.height_ofDual, QuadraticMap.sum_polar_sub_repr_sq, ContinuousAlgEquiv.symm_apply_eq, Finsupp.curryEquiv_apply, CategoryTheory.Bicategory.conjugateEquiv_whiskerRight, Diffeomorph.contMDiffOn_comp_diffeomorph_iff, IntermediateField.algHomEquivAlgHomOfSplits_apply_apply, finSumFinEquiv_apply_left, AlgebraicGeometry.coprodSpec_apply, Finsupp.equivCongrLeft_apply, SetTheory.PGame.relabel_moveLeft', CategoryTheory.iterated_mateEquiv_conjugateEquiv, strictAntiOn_toDual_comp_iff, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, AlgebraicGeometry.Scheme.Hom.fiberHomeo_apply, Polynomial.Gal.smul_def, Homeomorph.isPathConnected_preimage, UniformOnFun.toFun_one, FreeAddMonoid.toPiTensorProduct, MulEquiv.coe_monoidHom_symm_comp_coe_monoidHom, RootPairing.chainTopCoeff_reflectionPerm_right, MulEquivClass.map_mul, MvPolynomial.scalarRTensor_apply_monomial_tmul, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, MvPolynomial.comapEquiv_symm_coe, ofDual_max, List.form_perm_zpow_apply_mem_imp_mem, Polynomial.toMatrix_sylvesterMap', Module.basisUnique_repr_eq_zero_iff, Homeomorph.piCongr_apply, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, MulChar.toUnitHom_eq, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_unitIso, isMin_toDual_iff, AbstractCompletion.mapEquiv_coe, LeftOrdContinuous.rightOrdContinuous_dual, Matrix.toLinearMapRight'_mul, toColex_sub, Hamming.toHamming_sub, WithBot.orderIsoPUnitSumLex_symm_inl, MonotoneOn.dual_left, Quiver.starEquivCostar_symm_apply_fst, Finset.product_self_eq_disjiUnion_perm_aux, OrderedFinpartition.extendEquiv_apply, WithAbs.algebraMap_left_apply, finsuppTensorFinsupp_apply, CategoryTheory.Subfunctor.Subpresheaf.range_eq_ofSection, Homeomorph.finTwoArrow_symm_apply, OrderIso.sumCongr_apply, map_finset_sum, iterateFrobeniusEquiv_symm_add_apply, Equiv.Perm.smul_def, DirectSum.decompose_of_mem_same, SSet.Κâ_snd_assoc, MonoidHom.toAdditive_apply_apply, TensorPower.cast_cast, Fintype.coe_finsetEquivSet, OrderIso.coe_dualDual_symm, Additive.ofMul_eq_top, Representation.ofMulActionSelfAsModuleEquiv_symm_apply, Module.Basis.equivFun_symm_apply, Equiv.symm_preimage_preimage, IsometryEquiv.range_eq_univ, LinearMap.isPositive_adjoint_comp_self, autAdjoinRootXPowSubCEquiv_root, Manifold.IsImmersionAt.map_target_subset_target, FreeAddMonoid.lift_apply, CoxeterMatrix.reindex_relationsSet, Combinatorics.Subspace.IsMono.reindex, CategoryTheory.ReflQuiv.adj.homEquiv_symm_apply, Rep.diagonalSuccIsoFree_inv_hom_single, Set.Ioi_ofDual, coe_frobeniusEquiv_symm_comp_coe_frobenius, CategoryTheory.Iso.isoCongr_symm_apply, Equiv.Perm.SameCycle.exists_nat_pow_eq, RingEquiv.coe_prodComm_symm, Equiv.Perm.Basis.toCentralizer_equivariant, Subgroup.equivMapOfInjective_coe_mulEquiv, CategoryTheory.ExponentiableMorphism.homEquiv_symm_apply_eq, StrictAntiOn.dual_left, skewAdjointMatricesLieSubalgebraEquivTranspose_apply, Ideal.ramificationIdx_comap_eq, RingEquiv.surjective, hasFTaylorSeriesUpToOn_top_iff_right, TensorProduct.congr_congr, MonoidHom.restrictHomKerEquiv_apply_coe, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, CategoryTheory.Limits.IsLimit.liftConeMorphism_eq_isTerminal_from, IsCoveringMap.comp_homeomorph_iff, RingEquiv.ofHomInv'_apply, RingHom.IsStandardSmoothOfRelativeDimension.equiv, WithTop.toDual_top, Additive.ofMul_bot, IsCoveringMapOn.homeomorph_comp_iff, RootPairing.reflectionPerm_eq_iff_smul_root, CategoryTheory.FunctorToTypes.functorHomEquiv_symm_apply_app_app, Matrix.separatingRight_toLinearMapâ_iff, CategoryTheory.iterated_mateEquiv_conjugateEquiv_symm, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_apply_val, AddGroupExtension.Equiv.refl_apply, RingEquiv.op_apply_apply, AddEquiv.addSubgroupMap_symm_apply, NumberField.Units.fun_eq_repr, SSet.Subcomplex.Pairing.IsProper.isUniquelyCodimOneFace, ModuleCat.freeHomEquiv_apply, isLeftRegular_toLex, Bifunctor.mapEquiv_apply, Matrix.compAlgEquiv_apply, Matrix.spectrum_toEuclideanLin, supClosed_preimage_ofDual, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, AddEquiv.piAdditive_apply, NumberField.IsCMField.unitsComplexConj_torsion, ConjAct.stabilizer_eq_centralizer, LinearMap.rTensor_comm, RingEquiv.idealComapOrderIso_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, AddMonoidAlgebra.liftNCRingHom_single, MulEquiv.inv'_apply, Multiset.equivDFinsupp_symm_apply, CategoryTheory.CountableCategory.instObjAsType, CompactlyGenerated.homeoOfIso_apply, MeasureTheory.VectorMeasure.equivMeasure_apply, Finset.uIcc_toDual, KaehlerDifferential.polynomialEquiv_symm, TensorProduct.equivFinsuppOfBasisLeft_symm_apply, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv_symm, RootPairing.Hom.root_weightMap, ContinuousLinearEquiv.contDiff_comp_iff, Subgroup.comap_equiv_eq_map_symm, addMonoidHomLequivInt_apply, MeasurableEquiv.bijective, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, contDiff_prodAssoc_symm, MeasureTheory.integral_domSMul, Equiv.Perm.card_support_swap_mul, IsAddQuotientCoveringMap.homeomorph_comp, SupBotHom.symm_dual_comp, DFinsupp.liftAddHom_apply_single, Submodule.tensorEquivSpan_apply_tmul, DilationEquiv.coe_toHomeomorph, IsBaseChange.basis_repr_comp_apply, finEquivZPowers_symm_apply, MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure, WithLp.addEquiv_apply, PiTensorProduct.ofDirectSumEquiv_tprod_lof, MeasureTheory.measurePreserving_funUnique, RootPairing.two_nsmul_reflection_eq_of_perm_eq, Padic.withValUniformEquiv_norm_le_one_iff, CategoryTheory.shrinkYonedaEquiv_symm_map_assoc, Module.DualBases.basis_repr_symm_apply, AddEquiv.toAddMonoidHom_eq_coe, WithZero.withZeroUnitsEquiv_symm_apply_coe, TopHom.symm_dual_id, Multiplicative.ofAdd_eq_top, ArchimedeanOrder.le_def, Module.Basis.constr_comp, AddMonoidHom.toMultiplicativeRight_apply_apply, AddCircle.homeomorphCircle'_apply_mk, Equiv.neg_def, Module.Basis.constr_symm_apply, mulEquivOfOrderOfEq_symm_apply_gen, Cardinal.extend_function_finite, Multiset.coe_consEquiv_of_eq_of_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_apply, ProbabilityTheory.Kernel.partialTraj_succ_of_le, Homeomorph.vadd_symm_apply, LinearMap.BilinForm.toMatrixAux_eq, IsPerfectClosure.equiv_comp_equiv_apply_eq_self, Matrix.mul_mul_left, RingHom.eq_liftOfRightInverse, AffineEquiv.constVAdd_apply, Algebra.Extension.H1Cotangent.equiv_apply, Finsupp.sumFinsuppLEquivProdFinsupp_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_app_apply, OrderAddMonoidIso.symm_comp_self, CategoryTheory.Bicategory.mateEquiv_comp_id_right, Subgroup.transferTransversal_apply, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', MulEquiv.prodProdProdComm_apply, Matrix.det_det, ContinuousLinearEquiv.coe_prodAssoc, Monoid.Foldl.ofFreeMonoid_apply, OrderIsoClass.toHeytingHomClass, lt_map_inv_iff, IsAdjoinRootMonic.coeff_apply, Equiv.Perm.IsCycle.exists_pow_eq, AddAutAdditive_apply_symm_apply, StarAlgEquiv.norm_map, Equiv.isHomeomorph_of_discrete, MulAut.inv_apply, Matrix.toLinearMapâ'_comp, SkewMonoidAlgebra.lift_apply', Matrix.adjugate_fin_two, Topology.WithUpper.continuous_toUpper, Finsupp.supportedEquivFinsupp_symm_single, PiTensorProduct.lift_reindex_symm, Complex.equivRealProdAddHom_symm_apply, Matrix.l2_opNorm_mulVec, RingEquiv.asBoolRingAsBoolAlg_apply, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_inv, IsometryEquiv.apply_symm_apply, ComplexShape.Embedding.AreComplementary.desc'_inl, Matrix.diagonal_vec3, orderOf_ofAdd_eq_addOrderOf, finSumEquivOfFinset_inr, Equiv.apply_swap_eq_self, kroneckerTMulAlgEquiv_symm_single_tmul, Multiset.cast_symm_apply_fst, AddMonoidHom.liftOfRightInverse_comp_apply, sSupHom.symm_dual_id, LinearIsometry.coe_toLinearIsometryEquiv, ExteriorAlgebra.lift_symm_apply, ContinuousLinearEquiv.map_sub, PiTensorProduct.map_reindex_symm, RelIso.sumLexComplRight_apply, DFinsupp.equivFunOnFintype_symm_coe, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp, WithLp.coe_linearEquiv, AffineIsometryEquiv.coe_refl, ContinuousMultilinearMap.alternatization_apply_apply, CategoryTheory.FunctorToTypes.shrinkMap_app, Representation.finsupp_apply, Hamming.ofHamming_zero, isAddRightRegular_ofMul, CategoryTheory.eHomEquiv_id, normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity, List.sortedGT_map_ofDual, MvPolynomial.isEmptyRingEquiv_apply, LinearMap.toMatrix_apply', Polynomial.opRingEquiv_op_monomial, DoubleQuot.coe_quotQuotEquivQuotOfLEâ_symm, MeasureTheory.Measure.InnerRegular.map, Submonoid.mul_leftInvEquiv, CategoryTheory.Quiv.homEquivOfIso_symm_apply, Finset.Colex.toColex_univ, HahnModule.coeff_single_smul_vadd, FreeAddMonoid.toList_comp_ofList, InfHom.symm_dual_comp, CategoryTheory.InducedCategory.endEquiv_symm_apply_hom, InverseSystem.piEquivSucc_self, Finsupp.toColex_monotone, GenLoop.fromLoop_apply, Matrix.one_kronecker, LinearMap.toMatrixâ_mul, Equiv.boolArrowEquivProd_symm_apply, NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply', StarMulEquiv.coe_mk, LieEquiv.map_lie, Flag.coe_map, toDegLex_inj, DirectSum.decomposeAlgEquiv_symm_apply, Matrix.lieConj_apply, Homeomorph.image_interior, DFinsupp.equivProdDFinsupp_smul, Rep.leftRegularHom_hom, CompleteLatticeHom.dual_symm_apply_toFun, CategoryTheory.InducedCategory.endEquiv_apply, Topology.WithLawson.ofLawson_toLawson, ZMod.LFunction_one_sub, Equiv.piCongrLeft_apply, MulAut.conjNormal_symm_apply, Finset.map_filter, PrimeSpectrum.primeSpectrumProd_symm_inl, TopologicalSpace.Closeds.complOrderIso_symm_apply, EquicontinuousOn.tendsto_uniformOnFun_iff_pi', Orientation.rotation_eq_self_iff, AddConstEquiv.trans_apply, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, AddMagma.FreeAddSemigroup.lift_symm_apply, Equiv.Perm.apply_inv_self, IsometryEquiv.withLpUniqueProd_symm_apply, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, map_equiv_removeNone, Module.Basis.dualBasis_coord_toDualEquiv_apply, Matrix.repr_toLin, LieAlgebra.Orthogonal.soIndefiniteEquiv_apply, UniformFun.edist_eval_le, FDRep.endRingEquiv_symm_comp_Ď, AlternatingMap.map_perm, CategoryTheory.WithInitial.isColimitEquiv_apply_desc_right, OrderHom.dual_id, NumberField.IsCMField.equivInfinitePlace_symm_apply, WType.equivSigma_apply, Subgroup.equivOp_symm_apply_coe, Submodule.reflection_orthogonal_apply, FreeMagma.lift_of, isBot_ofDual_iff, toDual_pow, CategoryTheory.Bicategory.Adjunction.homEquivâ_symm_apply, AddSubmonoid.addUnitsTypeEquivIsAddUnitAddSubmonoid_apply_coe, Quaternion.imK_equivProd_symm_apply, CategoryTheory.PreGaloisCategory.endEquivSectionsFibers_Ď, CartanMatrix.C_two, KaehlerDifferential.mvPolynomialBasis_repr_D_X, AddMonoidHom.ker_comp_addEquiv, Finset.exists_equiv_extend_of_card_eq, MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar, Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero, AddEquiv.invFun_eq_symm, RingEquiv.toOpposite_apply, AddSubgroup.index_map_equiv, AlternatingMap.constLinearEquivOfIsEmpty_apply, AddMonoidHom.toAddEquiv_symm_apply, SubMulAction.ofStabilizer.conjMap_comp_inv_apply, Subring.addEquivOp_apply_coe, Lex.exists, Matrix.det_permute, WithZero.coe_unitsWithZeroEquiv_eq_units_val, OrderIso.sumLexIicIoi_symm_apply_of_lt, MeasureTheory.Measure.InnerRegular.map_iff, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearIsometryEquiv.comp_fderivWithin, TensorProduct.sum_tmul_basis_right_injective, Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_mem, CategoryTheory.Functor.CorepresentableBy.equivOfIsoObj_symm_apply, FintypeCat.uSwitch_map_uSwitch_map, val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe, stdSimplexHomeomorphUnitInterval_symm_apply_coe, ZMod.dft_even_iff, PiTensorProduct.reindex_reindex, Submonoid.leftInvEquiv_symm_mul, CategoryTheory.Sieve.overEquiv_pullback, RootPairing.reflectionPerm_involutive, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_Ď, RingEquiv.map_sub, pow_toColex, Matrix.abs_det_submatrix_equiv_equiv, AddEquiv.prodUnique_apply, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, CategoryTheory.Adjunction.homEquiv_naturality_left_square, StarMulEquiv.symm_apply_apply, Equiv.piOptionEquivProd_symm_apply, Cardinal.mk_preimage_equiv_lift, LightCondensed.ihomPoints_symm_comp, ContinuousLinearEquiv.snd_equivOfRightInverse, FirstOrder.Language.Embedding.equivRange_toEquiv_apply, WithZero.lift'_symm_apply_apply, ZMod.invDFT_apply, LinearEquiv.mapMatrix_apply, Subsemigroup.centerToMulOpposite_apply_coe, PiTensorProduct.subsingletonEquiv_symm_apply, AddSubsemigroup.coe_toSubsemigroup_symm_apply, AffineIsometryEquiv.ofTop_apply, OrderAddMonoidIso.symm_comp_eq, Function.fromTypes_cons_equiv_symm_apply, Matrix.liftLinear_single, MulOpposite.coe_opLinearEquiv_symm, sInfHom.dual_id, Polynomial.sylvester_comm, skewAdjointLieSubalgebraEquiv_apply, LinearIsometryEquiv.antilipschitz, Finset.Ioi_toDual, LinearEquiv.coe_mk, AntivaryOn.dual, Pi.toColex_monotone, Equiv.apply_symm_apply, toLex_inj, RootPairing.Equiv.coweightEquiv_symm_coweightMap, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, CategoryTheory.MonoidalClosed.ofEquiv_uncurry_def, DilationEquiv.smulTorsor_symm_apply, TensorProduct.piScalarRight_symm_algebraMap, BoolRing.Iso.mk_hom_hom', iteratedFDerivWithin_succ_eq_comp_right, mem_derangements_iff_fixedPoints_eq_empty, ofColex_one, Equiv.piSplitAt_symm_apply, AddSubgroup.mem_toSubgroup', Topology.WithUpperSet.toUpperSet_inj, SSet.stdSimplex.objâEquiv_symm_apply, CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition', Prod.Lex.lt_iff', FirstOrder.Language.Equiv.symm_apply_apply, Pi.colex_asc, IsometryEquiv.subLeft_symm_apply, Matrix.reindex_mem_colStochastic_iff, LaurentSeries.LaurentSeriesRingEquiv_def, Sequential.homeoOfIso_symm_apply, tangentMap_chart, FreeMonoid.lift_restrict, LinearMap.BilinForm.congr_apply, Matrix.entryAddHom_eq_comp, AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_apply, SSet.OneTruncationâ.nerveHomEquiv_id, DomMulAct.symm_mk_pow, CategoryTheory.Iso.commGroupIsoToMulEquiv_symm_apply, LocallyConstant.congrLeftRingEquiv_apply_apply, SupHom.dual_id, UniformEquiv.self_comp_symm, Finsupp.sumFinsuppAddEquivProdFinsupp_symm_inl, Order.succ_toAdd, Set.up_union, DomMulAct.smul_linearMap_apply, Multiset.coe_subsingletonEquiv, Multiplicative.toAdd_image_setMul, Metric.Snowflaking.preimage_ofSnowflaking_closedBall, Equiv.restrictPreimageFinset_symm_apply_coe, RootPairing.coreflection_image_eq, LinearMap.BilinForm.toMatrix_compRight, isTop_toDual_iff, TensorProduct.enorm_comm, CategoryTheory.Bicategory.mateEquiv_vcomp, CategoryTheory.InducedCategory.homLinearEquiv_apply, OrderMonoidIso.withZero_symm_apply_symm_apply, AddMonoidAlgebra.mapRangeAddEquiv_apply, SimpleGraph.walkLengthTwoEquivCommonNeighbors_symm_apply_coe, IsCyclic.val_mulAutMulEquiv_apply, CategoryTheory.ShrinkHoms.id_def, equivShrink_symm_div, LinearEquiv.restrictScalars_symm_apply, toMul_uzpow, CategoryTheory.conjugateEquiv_symm_id, Homeomorph.coe_uniqueProd, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, LinearIsometryEquiv.fderivWithin, even_ofMul_iff, LinearMap.adjoint_innerââ_apply, dist_toDual, AddEquiv.coprodPUnit_symm_apply, OrderAddMonoidIso.strictMono_symm, HasFTaylorSeriesUpTo.hasFDerivAt, TensorProduct.AlgebraTensorModule.rid_tmul, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_right_symm, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, CongruenceSubgroup.exists_Gamma_le_conj', OrderDual.instNeBotNhdsWithinIio, RingHomSurjective.instToRingHomRingEquiv, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id_symm, MeasureTheory.Measure.toSphere_apply_aux, Orientation.neg_rotation, Equiv.piCongrSigmaFiber_symm_apply, OrderMonoidIso.withZero_symm_apply_apply, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Submodule.dualQuotEquivDualAnnihilator_apply, AddSubgroup.IsComplement.quotientAddGroupMk_leftQuotientEquiv, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, HahnSeries.addOppositeEquiv_symm_support, DomAddAct.map_mk_symm_nhds, RingHom.quotientKerEquivOfSurjective_symm_apply, unitsNonZeroDivisorsEquiv_apply, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_pullbackObjUnitToUnit, AddAut.mulRight_symm_apply, TensorAlgebra.Κ_comp_lift, LinearEquiv.domMulActCongrRight_symm_apply, WittVector.IsocrystalHom.frob_equivariant, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, CategoryTheory.nerve.functorOfNerveMap_map, isSquare_toMul_iff, LieSubalgebra.equivOfLe_apply, StandardEtalePair.homEquiv_symm_apply, LinearEquiv.conj_apply_apply, SSet.opFunctorCompOpFunctorIso_inv_app_app, equivEquivIso_hom, Algebra.IsPushout.cancelBaseChange_tmul, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, Matrix.diagonal_fin_two, LinearMap.adjoint_eq_toCLM_adjoint, LinearEquiv.skewSwap_symm_apply, AlgEquiv.toRingEquiv_toRingHom, Disjoint.dual, strictAntiOn_comp_ofDual_iff, UniformOnFun.uniformContinuous_ofUniformFun, TensorProduct.tensorTensorTensorComm_tmul, Equiv.refl_apply, MulEquiv.toAdditive_apply_apply, AddMonoidAlgebra.mapDomainAddEquiv_single, finEquivPowers_apply, Complex.lipschitz_equivRealProd, Prod.Lex.compare_def, OnePoint.equivOfIsEmbeddingOfRangeEq_apply_infty, Topology.WithLawson.isOpen_preimage_ofLawson, Equiv.piCongr_apply_apply, Diffeomorph.uniqueMDiffOn_preimage, exteriorPower.basis_repr_ne, TensorProduct.gradedComm_tmul_one, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Set.ordConnected_range, Action.diagonalSuccIsoTensorDiagonal_inv_hom, PolynomialModule.aeval_equivPolynomial, FreeAddSemigroup.lift_comp_of, Equiv.sumAssoc_apply_inr, finCongr_apply, CategoryTheory.Abelian.Ext.mkâ_addEquivâ_apply, ContinuousLinearEquiv.map_tsum, LinearEquiv.coe_withLpCongr, TensorProduct.AlgebraTensorModule.congr_symm_tmul, Equiv.arrowCongr'_apply, MulEquiv.symm_comp_self, AddEquiv.toMultiplicativeRight_apply_apply, SubAddAction.ofStabilizer.conjMap_comp, WittVector.frobeniusEquiv_symm_apply, Orientation.eq_rotation_self_iff_angle_eq_zero, RingEquiv.prodProdProdComm_apply, Ideal.comap_symm, Submonoid.fromLeftInv_leftInvEquiv_symm, strictMono_dual_iff, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, LinearEquiv.conjAlgEquiv_symm_apply_apply, Matrix.toLinearMapâ_toMatrixâ, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, Equiv.Perm.Basis.toCentralizer_apply, LinearMap.toMatrix_one, Equiv.sigmaSigmaSubtypeEq_apply, ContinuousAddEquiv.eq_comp_symm, Equiv.swap_apply_apply, Equiv.Perm.notMem_support, PreQuasiregular.equiv_symm_apply, CliffordAlgebra.lift_Κ_apply, Equiv.subtypeEquivRight_apply_coe, MulAction.stabilizerEquivStabilizer_symm_apply, OrderDual.ofDual_bot, DualNumber.range_lift, AffineIsometryEquiv.range_eq_univ, CategoryTheory.Limits.biproduct.whiskerEquiv_inv, MvPowerSeries.exists_finsupp_eq_lexOrder_of_ne_zero, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, ContinuousLinearEquiv.hasSum', IsometryEquiv.toRealLinearIsometryEquiv_apply, Module.Basis.mk_repr, SSet.Subcomplex.range_eq_ofSimplex, MulHom.op_symm_apply_apply, pow_toLex, AddAut.mul_apply, AddEquiv.additiveMultiplicative_apply, LieModuleEquiv.injective, Unitary.mapEquiv_symm_apply, starLinearEquiv_symm_apply, FreeAlgebra.lift_comp_Κ, OrderRingIso.apply_symm_apply, AlgEquiv.coe_ringEquiv', Matrix.toSquareBlock_def, LinearIsometryEquiv.range_eq_univ, RingEquiv.map_list_sum, IsMinFilter.dual, Monovary.sum_smul_comp_perm_le_sum_smul, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_Ď, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_f, Equiv.Perm.ofFn_comp_perm, CofiniteTopology.continuous_of, sigmaFinsuppAddEquivDFinsupp_apply, toBoolRing_inf, Equiv.mulLeftâ_apply, Set.dual_ordConnectedSection, TopCat.uliftFunctorObjHomeo_symm_naturality_apply, CongruenceSubgroup.conjGL_coe, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, AddSubmonoid.fromLeftNeg_leftNegEquiv_symm, WithLp.coe_congr, Equiv.comp_swap_eq_update, Rep.diagonalHomEquiv_symm_apply, SupIrred.ofDual, Homeomorph.induced_eq, Matrix.submatrix_vecMul_equiv, MulEquiv.map_one, Matrix.separatingRight_toBilin_iff, ContinuousAddEquiv.symm_comp_eq, AddConstEquiv.refl_apply, Subgroup.isCoatom_map, associatesEquivOfUniqueUnits_symm_apply, MeasurableEquiv.map_apply, OpenPartialHomeomorph.transHomeomorph_symm_apply, SemidirectProduct.inl_aut, TwoSidedIdeal.equivMatrix_symm_apply_ringCon, Homeomorph.vaddConst_apply, IsBaseChange.of_fintype_basis_eq, DFA.comap_reindex, Ideal.inertiaDeg_comap_eq, Matrix.spectrum_toLpLin, Homeomorph.homeomorph_mk_coe, RelIso.relHomCongr_symm_apply, MulEquiv.piMultiplicative_apply, MeasureTheory.Measure.OuterRegular.comap, Finsupp.linearEquivFunOnFinite_symm_coe, Set.Ioc_ofDual, AddEquiv.neg_apply, Int.quotientSpanNatEquivZMod_comp_Quotient_mk, RingEquiv.map_neg, Subsemigroup.centerCongr_symm_apply_coe, Module.Basis.repr_isUnitSMul, Equiv.sigmaCongrLeft_apply, CategoryTheory.Functor.RepresentableBy.homEquiv_eq, Equiv.divRight_symm_apply, CoxeterSystem.lift_apply_simple, OrderIso.invENNReal_symm_apply, MulOpposite.opAddEquiv_apply, IsSymmetricAlgebra.equiv_apply, Equiv.swap_apply_self, OrderMonoidIso.val_unitsCongr_symm_apply, AddSubgroup.comap_equiv_eq_map_symm, PresheafOfModules.homEquivOfIsLocallyBijective_symm_apply, DomMulAct.coe_mkHomeomorph_symm, supIrred_ofDual, RingAut.smul_def, InnerProductSpace.toDual_symm_apply, CategoryTheory.SingleObj.mapHom_id, Prod.Lex.monotone_fst, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, Matrix.charmatrix_reindex, Equiv.Perm.cycleOf_self_apply_zpow, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, NumberField.Units.regOfFamily_eq_det, Submonoid.LocalizationMap.mulEquivOfLocalizations_apply, ofDual_inf, MulEquiv.eq_symm_apply, IsHilbertSum.linearIsometryEquiv_symm_apply, ContinuousLinearMap.coprodEquiv_apply, ContinuousMulEquiv.coe_trans, Homeomorph.coe_addLeft, Equiv.prod_assoc_image, CartanMatrix.D_four, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left, LinearEquiv.map_mem_invtSubmodule_conj_iff, Coalgebra.coassoc_symm_apply, Equiv.Perm.iterate_eq_pow, equivShrink_symm_sub, Complex.equivRealProd_apply, Subgroup.comap_toSubmonoid, InfiniteGalois.normalAutEquivQuotient_apply, WithTop.lt_toDual_iff, CategoryTheory.ShiftedHom.opEquiv_symm_add, Equiv.sigmaPreimageEquiv_symm_apply_snd_coe, Equiv.Perm.next_toList_eq_apply, Matrix.toLin_mul_apply, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C, ofBoolAlg_inj, RingHom.liftOfSurjective_comp, MeasureTheory.volume_measurePreserving_piCongrLeft, AddMonoidAlgebra.domCongr_toAlgHom, DilationEquiv.map_cobounded, isCompl_ofDual_iff, LinearMap.tensorEqLocusEquiv_apply, toMatrix_distrib_mul_action_toLinearMap, MeasurableEquiv.image_preimage, Equiv.Perm.SameCycle.apply_left, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, finSuccEquiv_zero, NonUnitalSubsemiring.coe_equivMapOfInjective_apply, IsLocalHomeomorph.Homeomorph.isLocalHomeomorph, FirstOrder.Language.Equiv.coe_toElementaryEmbedding, Subgroup.IsComplement.equiv_snd_eq_self_iff_mem, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, LinearIsometryEquiv.ext_iff, Equiv.Perm.disjoint_ofSubtype_noncommPiCoprod, ModuleCat.Iso.homCongr_eq_arrowCongr, Complex.conjLIE_apply, OrderIso.neg_apply, UniformOnFun.ofFun_sum, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm_assoc, WithOne.lift_coe, LinearIsometryEquiv.coe_symm_toHomeomorph, toMul_ofMul, toLex_ofNat, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left, AlgEquiv.linearEquivConj_mulLeft, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_Îź, AddSubmonoid.val_neg_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, CategoryTheory.Functor.FullyFaithful.homMulEquiv_apply, CategoryTheory.Limits.Types.isColimit_iff_coconeTypesIsColimit, VertexOperator.of_coeff_apply_coeff, DomMulAct.smul_mulDistribActionHom_apply, IndexedPartition.equivQuotient_symm_proj_apply, MeasureTheory.Measure.domSMul_apply, CategoryTheory.Limits.opCompYonedaSectionsEquiv_symm_apply_coe, norm_ofAdd, Multiplicative.ofAdd_le, AddMonoidAlgebra.toRingHom_mapRangeRingEquiv, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_symm_apply_snd_coe, Specialization.ofEquiv_toEquiv, IsCoveringMap.comp_homeomorph, AddConstMap.coe_addLeftHom_apply, UniformOnFun.uniformContinuous_eval, NonUnitalSubsemiring.mem_map_equiv, CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app, MeasureTheory.charFun_toDual_symm_eq_charFunDual, MvPolynomial.mvPolynomialEquivMvPolynomial_symm_apply, Equiv.coe_fn_symm_mk, CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_true, CategoryTheory.nerve.homEquiv_edgeMk_map_nerveMap, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, Equiv.sumIsRight_apply, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff', unitInterval.coe_symmMeasurableEquiv, OpenPartialHomeomorph.transHomeomorph_target, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, MonoidAlgebra.domCongr_toAlgHom, genericPoints.equiv_symm_apply, BoundedLatticeHom.dual_id, DomAddAct.isOpenEmbedding_mk, LinearMap.BilinForm.toMatrix'_apply, Set.unitEquivUnitsInteger_symm_apply_coe, Quiver.SingleObj.toPrefunctor_symm_id, BoundedOrderHom.symm_dual_id, SSet.S.equivElements_symm_apply_dim, PEquiv.toMatrix_toPEquiv_mulVec, Sym.coe_equivNatSumOfFintype_apply_apply, PowerBasis.quotientEquivQuotientMinpolyMap_apply, Equiv.Perm.val_equivUnitsEnd_apply, CategoryTheory.PreGaloisCategory.toAutMulEquiv_isHomeomorph, toDegLex_injective, ContinuousAlternatingMap.piLIE_apply_apply, DFinsupp.equivFunOnFintype_single, PartENat.withTopEquiv_one, toColex_vadd, Finsupp.equivFunOnFinite_apply, AffineIsometryEquiv.coe_symm_trans, Localization.mulEquivOfQuotient_symm_monoidOf, MvPolynomial.comapEquiv_coe, StrictAntiOn.dual, LinearMap.BilinForm.SeparatingRight.toMatrix, Homeomorph.shearAddRight_symm_coe, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_symm_apply_val, Equiv.sigmaAssocProd_apply_snd_snd, Equiv.Perm.subtypeCongr.apply, IntermediateField.algHomEquivAlgHomOfSplits_apply, CategoryTheory.Iso.refl_conj, UniformOnFun.ofFun_toFun, Homeomorph.piCongrLeft_symm_apply, Bundle.TotalSpace.toProd_apply, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm_assoc, val_unitarySubgroupUnitsEquiv_symm_apply_coe, Matrix.kroneckerMap_reindex_right, RootPairing.Hom.root_weightMap_apply, AddMonoidAlgebra.mapDomainAddEquiv_apply, LinearMap.nondegenerate_toLinearMapâ'_of_det_ne_zero', CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_inverse_obj_str, AlgEquiv.op_apply_apply, MvPolynomial.scalarRTensor_apply_X_tmul_apply, Equiv.permCongr_symm_apply, ContinuousLinearEquiv.coe_toDiffeomorph_symm, Equiv.vanishesTrivially_comp, toDual_vadd', MulEquiv.comapSubgroup_symm_apply, CategoryTheory.Functor.FullyFaithful.homEquiv_apply, LinearEquiv.congrRightâ_apply, ofLex_add, ZMod.dft_mul_const, Pi.single_comp_equiv, MeasureTheory.Measure.pi_map_piCongrLeft, Shrink.linearEquiv_symm_apply, ContinuousSemilinearEquivClass.map_continuous, MultilinearMap.domDomCongrEquiv_symm_apply, ULift.moduleEquiv_symm_apply, finsum_comp_equiv, isRightRegular_ofLex, WithTop.le_toDual_iff, LieAlgebra.lieCharacterEquivLinearDual_apply, DFinsupp.toLex_monotone, LieAlgebra.of_smul, WithCStarModule.equiv_symm_snd, NonUnitalSubring.map_equiv_eq_comap_symm, Rep.to_Module_monoidAlgebra_map_aux, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_id, toLex_eq_one, Equiv.exists_congr_right, Submodule.LinearDisjoint.op, AddSubmonoid.LocalizationMap.addEquivOfLocalizations_symm_apply, CategoryTheory.tensorRightHomEquiv_symm_naturality, toColex_inv, RestrictScalars.ringEquiv_algebraMap, Matrix.Nondegenerate.toLinearMapâ, isUpperSet_preimage_toDual_iff, SetTheory.PGame.add_moveLeft_inl, MonoidAlgebra.opRingEquiv_single, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, AffineIsometryEquiv.edist_map, ContinuousAlgEquiv.continuousOn, CliffordAlgebra.range_lift, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply, Module.Basis.prod_repr_inl, WithLp.prodContinuousLinearEquiv_symm_apply, PrimeSpectrum.primeSpectrumProd_symm_inr_asIdeal, Matrix.kroneckerTMul_assoc', LinearEquiv.cast_symm_apply, MonomialOrder.degree_sub_le, SSet.horn.yonedaEquiv_Κ, Multiset.coeEquiv_apply_coe, Valuation.IsEquiv.orderRingIso_apply, Codisjoint.dual, ContinuousMultilinearMap.piLinearEquiv_symm_apply, Antitone.dual_right, Homeomorph.toOpenPartialHomeomorph_apply, MulDistribMulAction.toMulEquiv_apply, Module.AEval.of_symm_smul, Equiv.Perm.eq_on_support_mem_disjoint, EuclideanGeometry.reflection_map, Matrix.intrinsicStar_toLin', HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, DomMulAct.mem_stabilizer_iff, Module.Basis.ofZLatticeComap_apply, RelIso.map_rel_iff', Monoid.CoprodI.lift_of, AffineEquiv.coe_mul, AffineEquiv.continuous_of_finiteDimensional, CategoryTheory.conjugateEquiv_symm_comp_assoc, CategoryTheory.Limits.coyonedaCompLimIsoCones_inv_app, Delone.DeloneSet.mapIsometry_trans, Sym.coe_equivNatSum_apply_apply, ContinuousLinearMap.adjoint_id, isMinOn_dual_iff, Specialization.isOpen_toEquiv_preimage, LinearMap.coe_toContinuousLinearMap', Equiv.withBotCongr_apply, MeasurableEquiv.preimage_image, CategoryTheory.Subfunctor.ofSection_eq_range, KaehlerDifferential.polynomialEquiv_D, Equiv.symm_comp_self, Equiv.ofLeftInverse_apply_coe, SemimoduleCat.Iso.homCongr_eq_arrowCongr, iteratedFDerivWithin_succ_eq_comp_left, Sequential.isoEquivHomeo_apply, SimpleGraph.Iso.connectedComponentEquiv_symm_apply, Equiv.exists_congr_left, List.SortedLT.of_map_ofDual, MeasurableEquiv.finTwoArrow_apply, toMul_neg, CategoryTheory.Localization.SmallHom.equiv_equiv_symm, WithBot.ofDual_le_iff, ofLex_ratCast, Equiv.Perm.IsCycleOn.exists_pow_eq', BialgEquiv.coe_toEquiv, CommRing.Pic.mul_eq_tensor, ArchimedeanClass.FiniteResidueField.mk_eq_zero, affineIndependent_equiv, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv, Finsupp.sigmaFinsuppAddEquivPiFinsupp_apply, Equiv.finsuppUnique_symm_apply_support_val, ContinuousMap.val_unitsLift_apply_apply, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, AddEquivClass.apply_coe_symm_apply, Equiv.semiconj_conj, OnePoint.equivOfIsEmbeddingOfRangeEq_apply_coe, Equiv.divLeft_involutive, zpowersHom_symm_apply, Finset.map_ofDual_max, toColex_add, Cardinal.mk_preimage_equiv, RelIso.sumLexComplLeft_symm_apply, AddSubmonoid.add_leftNegEquiv_symm, IsLocalizedModule.iso_symm_apply, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_apply, Finset.Colex.toColex_lt_toColex_iff_max'_mem, UniformOnFun.isometry_restrict, continuous_equivFun_basis, GrpCat.SurjectiveOfEpiAuxs.Ď_symm_apply_infinity, TensorProduct.AlgebraTensorModule.rightComm_symm_tmul, Sequential.isoEquivHomeo_symm_apply, optionProdEquiv_symm_inr, Equiv.Perm.set_support_zpow_subset, AddEquiv.map_zero, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one, Equiv.Perm.IsCycle.pow_eq_one_iff', Pi.ofLex_apply, Equiv.Set.rangeInl_symm_apply_coe, multiplesAddHom_apply, rootsOfUnity.integer_power_of_ringEquiv, Algebra.IsPushout.cancelBaseChange_symm_tmul, Equiv.embeddingEquivOfFinite_apply, LinearMap.toMatrixOrthonormal_reindex, autEquivZmod_symm_apply_natCast, ContinuousLinearEquiv.apply_symm_apply, Fintype.linearIndependent_iff', CategoryTheory.ForgetEnrichment.equivFunctor_map, Finset.image_univ_equiv, Lat.dual_map, ofDual_iInf, Equiv.boolNot_apply, HVertexOperator.coeff_isPWOsupport, StarAlgHom.prodEquiv_apply, Equiv.Perm.set_support_mul_subset, Matrix.permanent_permute_rows, Sum.Lex.inr_le_inr_iff, contMDiff_equivTangentBundleProd_symm, finSuccEquiv_symm_none, AddChar.directSum_apply, AddCircle.homeomorphAddCircle_apply_mk, FreeGroup.lift_of_eq_id, Valuation.IsEquiv.valuedCompletion_le_one_iff, QuadraticMap.toMatrix'_comp, InfTopHom.symm_dual_comp, FreeMonoid.countP_of, SheafOfModules.unitHomEquiv_symm_comp, LinearEquiv.piFinTwo_symm_apply, Matrix.mul_val_succ, Polynomial.leadingCoeff_opRingEquiv, Fin.insertNthEquiv_apply, CategoryTheory.yonedaEquiv_apply, finSuccEquiv_succ, Matrix.GeneralLinearGroup.coe_toLin, RingEquiv.toCommSemiRingCatIso_inv, equivShrink_top, ContinuousAddEquiv.coe_refl, Subgroup.IsComplement.equiv_one, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, WithBot.orderIsoPUnitSumLex_symm_inr, ofAdd_toAdd, Matrix.kroneckerMap_assocâ, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp, Topology.IsQuotientMap.lift_apply, AddEquiv.val_neg_piAddUnits_apply, OrderDual.toDual_le_toDual, uliftMultiplesHom_symm_apply, Module.Basis.repr_self_apply, Algebra.PreSubmersivePresentation.jacobiMatrix_reindex, AddCircle.homeomorphCircle'_symm_apply, CategoryTheory.Localization.LeftBousfield.galoisConnection, AddEquiv.funUnique_symm_apply, OrderRingIso.coe_toOrderRingHom, MonoidHom.coe_toMultiplicative_range, CategoryTheory.FreeGroupoid.functorEquiv_apply, CategoryTheory.ForgetEnrichment.equivInverse_map, exteriorPower.alternatingMapLinearEquiv_ΚMulti, MeasurableEquiv.trans_apply, IsometryEquiv.withLpProdUnique_apply, TensorProduct.directSum_lof_tmul_lof, LinearEquiv.coe_inv, IsLocalizedModule.iso_apply_mk, OrderIso.subLeft_apply, FirstOrder.Language.Term.constantsVarsEquiv_symm_apply, DirectSum.lequivCongrLeft_apply, LinearEquiv.bijective, AffineEquiv.prodComm_apply, star_dotProduct_toMatrixâ_mulVec, RingHom.ker_equiv, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, LieEquiv.one_apply, LinearIsometryEquiv.norm_map, LocallyConstant.congrRightâ_symm_apply_apply, AddHom.toAddEquiv_apply, Equiv.comp_surjective, Homeomorph.funSplitAt_symm_apply, Topology.WithLowerSet.ofLowerSet_inj, IsLocalFrameOn.coeff_apply_of_mem, ContinuousLinearEquiv.hasTemperateGrowth, IsometryEquiv.neg_apply, toDual_sInf, AddEquiv.coe_prodComm_symm, Homeomorph.shearMulRight_coe, Equiv.prodPiEquivSumPi_apply, CategoryTheory.Functor.Final.colimitCoconeOfComp_isColimit, Sym2.lift_comp_map, LinearIsometryEquiv.map_zero, CategoryTheory.Functor.equivCatHom_symm_apply, AffineIsometryEquiv.coe_constVAdd, MulEquiv.toMonoidHom_eq_coe, Subring.centerCongr_apply_coe, NonUnitalStarAlgHom.prodEquiv_symm_apply, contDiff_prodAssoc, MultilinearMap.currySumEquiv_apply, setBasisOfLinearIndependentOfCardEqFinrank_repr_apply, map_dvd_iff_dvd_symm, DomMulAct.smul_addMonoidHom_apply, FreeMonoid.ofList_append, Orientation.map_of_isEmpty, Finsupp.equivMapDomain_single, SymAlg.sym_bijective, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_apply, CategoryTheory.InducedCategory.homEquiv_apply, LinOrd.dual_map, CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str, RingEquiv.mopMatrix_symm_apply, CategoryTheory.Bicategory.Adjunction.homEquivâ_apply, AddAction.stabilizer_vadd_eq_stabilizer_map_conj, AddEquiv.symm_comp_eq, SetSemiring.up_lt_up, LinearIsometryEquiv.apply_symm_apply, groupCohomology.isMulCoboundaryâ_of_mem_coboundariesâ, Homeomorph.toEquiv_piCongr, OrderIso.sumLexIioIci_symm_apply_Ici, SymAlg.sym_neg, CoalgEquiv.toCoalgHom_inj, Matrix.diagonal_vec1, CategoryTheory.Limits.WidePullbackCone.reindex_pt, OrderMonoidIso.trans_apply, Int.divModEquiv_apply, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, Finset.ofDual_inf, TensorProduct.quotientTensorQuotientEquiv_symm_apply_mk_tmul, AddHom.toAddEquiv_symm_apply, MulEquiv.toSingleObjEquiv_inverse_map, OrderIso.dualAntisymmetrization_symm_apply, skewAdjointLieSubalgebraEquiv_symm_apply, Finsupp.Lex.single_strictAnti, RootPairing.Hom.comp_indexEquiv_symm_apply, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, NonUnitalSubsemiring.centerCongr_symm_apply_coe, RingEquiv.ofLeftInverse_symm_apply, MeasureTheory.mulEquivHaarChar_eq, ContinuousLinearEquiv.isOpenMap, LinearMap.sum_repr_mul_repr_mulââ, SymAlg.sym_zero, AddSubmonoid.coe_equivMapOfInjective_apply, CategoryTheory.tensorRightHomEquiv_whiskerLeft_comp_evaluation, OrderAddMonoidIso.eq_symm_comp, FreeAddSemigroup.lift_symm_apply, Multiplicative.toAdd_mono, groupCohomology.mem_cocyclesâ_of_addMonoidHom, RingHom.liftOfSurjective_comp_apply, Equiv.Perm.OnCycleFactors.kerParam_range_card, Equiv.coe_toEmbedding, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, LinearMap.ringLmapEquivSelf_symm_apply, SSet.Subcomplex.Pairing.dim_p, norm_ofMul, Module.Basis.equiv_apply, Matrix.adjp_apply, Equiv.piCongrSet_apply, LinearIsometryEquiv.coe_toAffineIsometryEquiv, Abelianization.lift_unique, Affine.Simplex.excenterWeightsUnnorm_reindex, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_hom, AffineEquiv.span_eq_top_iff, Equiv.Perm.cycleOf_eq_one_iff, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, Equiv.toPartialEquiv_apply, Fin.consEquiv_apply, GrpCat.SurjectiveOfEpiAuxs.Ď_apply_infinity, FintypeCat.equivEquivIso_apply_hom, Equiv.piSplitAt_apply, Set.opEquiv_apply, AddMonoidAlgebra.toRingHom_mapDomainRingEquiv, IsometryEquiv.preimage_emetric_closedBall, Topology.IsQuotientMap.homeomorph_apply, LinearMap.spectrum_toMatrix', autAdjoinRootXPowSubCEquiv_symm_smul, AddEquiv.addSubgroupCongr_apply, CategoryTheory.InjectiveResolution.of_def, DistLat.dual_map, Set.conj_mem_fixingAddSubgroup, Real.smul_map_diagonal_volume_pi, Equiv.Set.image_apply, iterateFrobeniusEquiv_def, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, ContinuousLinearEquiv.comp_hasFDerivAt_iff, QuotientAddGroup.equivIocMod_zero, FreeAbelianGroup.lift_add, MonoidHom.ofLeftInverse_symm_apply, Additive.ofMul_top, ContinuousLinearMap.eq_adjoint_iff, AddEquiv.piUnique_apply, Matrix.uniqueAddEquiv_apply, Equiv.piCongrRight_symm_apply, Equiv.Perm.disjoint_ofSubtype_of_memFixedPoints_self, CategoryTheory.Coyoneda.objOpOp_inv_app, CategoryTheory.GradedObject.comapEquiv_counitIso, SheafOfModules.freeHomEquiv_freeMap, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add, Orientation.volumeForm_map, Fin.cycleRange_apply, rotation_apply, toMatrix_rotation, WCovBy.toDual, IsBot.toDual, Matrix.blockTriangular_transvection', LinearIsometryEquiv.piLpCongrRight_apply, Finset.Colex.le_iff_max'_mem, RingEquiv.piOptionEquivProd_apply, CategoryTheory.Iso.homCongr_trans, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RingEquiv.op_apply_symm_apply, CategoryTheory.Subobject.wideCospan_map_term, RingCon.comapQuotientEquivRange_symm_mk, CategoryTheory.FunctorToTypes.binaryProductEquiv_apply, FourierTransform.fourierEquiv_apply, BotHom.dual_apply_apply, AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap, Diffeomorph.apply_symm_apply, RingEquiv.piCongrLeft_symm_apply, ofMul_list_prod, Homeomorph.toEquiv_piCongrLeft, LinearMap.separatingRight_congr_iff, ofLex_sub, Equiv.traverse_def, UniformFun.uniformSpace_eq_iInf_precomp_of_cover, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub, Equiv.Perm.permCongr_eq_mul, LinearMap.IsSymmetric.directSum_decompose_apply, RingEquiv.ofLeftInverse_apply, CategoryTheory.Limits.IsColimit.equivIsoColimit_apply, FreeNonUnitalNonAssocAlgebra.of_comp_lift, SSet.opFunctorCompOpFunctorIso_hom_app_app, Monovary.sum_comp_perm_mul_le_sum_mul, AddAutAdditive_apply_apply, Equiv.Perm.OnCycleFactors.kerParam_injective, Homeomorph.piCurry_apply, finTwoArrowEquiv'_apply, RingEquiv.snd_comp_coe_prodComm, CategoryTheory.Functor.FullyFaithful.isoEquiv_apply, CategoryTheory.Limits.MulticospanIndex.sectionsEquiv_apply_coe, Matrix.lift_cRank_submatrix, Derivation.linearEquiv_coe_to_linearMap_comp, NonemptyInterval.toLex_strictMono, UniversalEnvelopingAlgebra.lift_unique, AddOpposite.opMulEquiv_symm_apply, RCLike.realRingEquiv_symm_apply, Equiv.Perm.mem_support_iff_of_commute, Homeomorph.contDiff_unitBall, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, Homeomorph.isEmbedding, Equiv.trans_apply, Finset.Colex.cons_lt_cons, AnalyticOn.iteratedFDerivWithin_comp_perm, SubMulAction.ofStabilizer.inv_conjMap_comp_apply, CategoryTheory.CommSq.instHasLift, AffineIsometryEquiv.comp_continuous_iff, LieModule.shiftedGenWeightSpace.toEnd_eq, SetSemiring.imageHom_def, Unitary.coe_linearIsometryEquiv_apply, Finset.Nat.antidiagonalEquivFin_symm_apply_coe, Order.succ_ofAdd, ContinuousLinearEquiv.ext_iff, SemilinearIsometryEquivClass.norm_map, AffineIsometryEquiv.coe_trans, AlgebraicGeometry.sigmaMk_mk, Finset.Colex.toColex_sdiff_le_toColex_sdiff', Equiv.subtypeEquivCodomain_symm_apply, Matrix.sum_sum_single, AddMonoid.Coprod.neg_def, Equiv.left_inv', Opposite.equivToOpposite_coe, ContinuousLinearEquiv.map_smul, Fin.snocEquiv_apply, Submodule.reflection_singleton_apply, BoolRing.Iso.mk_inv_hom', Metric.PiNatEmbed.toPiNatEquiv_apply_ofPiNat, Equiv.sumSigmaDistrib_symm_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp, StarModule.decomposeProdAdjointL_apply, MonoidHom.toHomPerm_apply_symm_apply, HasFTaylorSeriesUpToOn.zero_eq', Equiv.sigmaPUnit_symm_apply_snd, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_symm_apply_fst, DFinsupp.subtypeSupportEqEquiv_apply_coe, Subgroup.quotientEquivProdOfLE_apply, Equiv.optionEquivSumPUnit_symm_inr, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, QuotSMulTop.equivTensorQuot_naturality_mk, CategoryTheory.Pi.equivalenceOfEquiv_unitIso, MvPolynomial.supDegree_esymmAlgHomMonomial, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, AffineIsometryEquiv.pointReflection_midpoint_left, AddEquivClass.apply_mem_center, comap_inv_leftUniformSpace, ofDual_min, MulEquiv.coe_refl, LieEquiv.coe_injective, CategoryTheory.WithInitial.isColimitEquiv_symm_apply_desc, Equiv.eq_symm_comp, TopologicalSpace.Opens.complOrderIso_apply, RingCon.comapQuotientEquivOfSurj_symm_mk, Colex.forall, Ideal.comap_isMaximal_of_equiv, Equiv.piCongrLeft_preimage_univ_pi, monotoneOn_comp_ofDual_iff, NormedSpace.Dual.toWeakDual_continuous, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_symm_apply, IsometryEquiv.coe_toHomeomorph, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_mk', Matrix.toLpLin_mul_same, ConjAct.forall, CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply, OrderAddMonoidIso.equivLike_neg_eq_symm, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_apply, Homeomorph.opensCongr_apply, OrderIso.inv_symm_apply, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_symm_apply, RingEquiv.ext_iff, RingEquiv.piCongrLeft'_apply, Equiv.ofFiberEquiv_map, FreeMonoid.toList_mul, stdSimplexHomeomorphUnitInterval_zero, CompleteLatticeHom.dual_id, TensorProduct.coe_directSumRight', toDual_smul', Subsemigroup.equivOp_symm_apply_coe, MeasurableEquiv.piFinTwo_symm_apply, ContinuousLinearEquiv.contDiffAt_comp_iff, NonemptyInterval.coe_dual, Submodule.quotEquivOfEqBot_symm_apply, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Orientation.inner_rightAngleRotation_swap', AddMonoidHom.coe_toMultiplicativeRight, Metric.Snowflaking.toSnowflaking.sizeOf_spec, CategoryTheory.Pi.equivalenceOfEquiv_counitIso, PresheafOfModules.freeYonedaEquiv_symm_app, IsometryEquiv.inv_apply_self, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom, IsSelfAdjoint.adjoint_eq, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, HNNExtension.equiv_eq_conj, Submonoid.topOrderMonoidIso_symm_apply_coe, ContinuousLinearEquiv.isBigO_comp, CategoryTheory.Limits.biproduct.matrixEquiv_symm_apply, Equiv.bijective, Finsupp.toMultiset_toFinsupp, ofLex_intCast, QuadraticAlgebra.linearEquivTuple_apply, ofBoolAlg_inf, LinearMap.toMatrix_baseChange, OrthonormalBasis.measurePreserving_repr, Equiv.piCongrLeft_symm_apply, Submodule.reflection_apply, Prod.Lex.monotone_fst_ofLex, Sym2.sortEquiv_apply_coe, Multiplicative.ofAdd_lt, AddSubmonoid.coe_toSubmonoid_apply, Tuple.sort_perm, Representation.asAlgebraHom_def, AddEquivClass.coe_symm_apply_apply, DomMulAct.continuous_mk, FreeLieAlgebra.of_comp_lift, Ordinal.one_toPGame_leftMoves_default_eq, IsCoercive.unique_continuousLinearEquivOfBilin, Multiplicative.ofAdd_image_setAdd, AddGroupExtension.Equiv.map_inl, GenLoop.homotopyTo_apply, CategoryTheory.tensorLeftHomEquiv_naturality, Homeomorph.coe_symm_toEquiv, RootPairing.toPerfPair_comp_root, isRegular_toLex, IsometryEquiv.piCongrLeft'_apply, Matrix.eRank_submatrix, CStarMatrix.ofMatrix_apply, ofAdd_zero, TensorProduct.adjoint_map, MeasureTheory.volume_preserving_piFinsetUnion, CategoryTheory.FinCategory.categoryAsType_comp, Sum.Lex.inr_strictMono, SSet.Subcomplex.Pairing.isUniquelyCodimOneFace, DFinsupp.equivFunOnFintype_apply, NonUnitalSubring.centerCongr_apply_coe, SetTheory.PGame.relabel_moveRight, AddMonoidAlgebra.divOfHom_apply_apply, FirstOrder.Language.Term.constantsVarsEquivLeft_apply, UniformOnFun.toFun_ofFun, LinearMap.GeneralLinearGroup.generalLinearEquiv_to_linearMap, CategoryTheory.leftAdjointOfStructuredArrowInitialsAux_symm_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_left, LinearEquiv.conj_comp, RootPairing.Equiv.id_indexEquiv_apply, toBoolRing_ofBoolRing, SymAlg.unsym_mul, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, TwoSidedIdeal.equivMatrix_apply, CategoryTheory.Bicategory.conjugateEquiv_symm_id, uliftZPowersHom_symm_apply, LinearEquiv.domMulActCongrRight_apply, Rep.coinvariantsTensorFreeLEquiv_symm_apply, Equiv.divLeft_symm_apply, LinearEquiv.piCurry_apply, RingEquiv.ofHomInv_symm_apply, AffineIsometryEquiv.continuousAt, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, Orientation.map_eq_neg_iff_det_neg, ofColex_div, UniformFun.toFun_sub, Unitization.starLift_symm_apply_apply, Maximal.dual, nnnorm_toMul, Fin.appendHomeomorph_apply, Homeomorph.coe_prodCongr, UniformOnFun.toFun_neg, AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv_symm_apply_coe, Finsupp.mapRange.addEquiv_apply, UniformEquiv.coe_toEquiv, Equiv.ofBijective_apply_symm_apply, RingEquiv.mopMatrix_apply, MulEquiv.map_div, Matrix.kroneckerMap_reindex, Nat.pairEquiv_apply, CategoryTheory.Limits.Bicone.whisker_pt, WithZero.coe_expEquiv_apply, ContinuousLinearMap.isPositive_self_comp_adjoint, toAdd_mul, CategoryTheory.Bicategory.conjugateEquiv_apply, LinearMap.trace_eq_matrix_trace_of_finset, Unitization.starLift_apply_apply, CategoryTheory.Adjunction.eq_homEquiv_apply, LinearMap.adjoint_toContinuousLinearMap, Finsupp.curryLinearEquiv_symm_apply_apply, Topology.WithLower.toLower_inj, Matrix.SeparatingLeft.toLinearMapâ', DirectSum.decompose_eq_mul_idempotent, AddAutAdditive_symm_apply_symm_apply, Homeomorph.isPreconnected_preimage, FreeMonoid.toList_nil, MonomialOrder.degree_reduce_lt, LinearIsometryEquiv.coe_neg, TensorProduct.dualDistrib_apply_comm, CategoryTheory.Iso.conj_pow, AddOpposite.opAddEquiv_apply, Homeomorph.sumArrowHomeomorphProdArrow_apply, Finsupp.llift_apply, StarMulEquiv.ofStarMonoidHom_symm_apply, SSet.prodStdSimplex.objEquiv_apply_fst, isRight_finSumNatEquiv_symm_apply, Subsemiring.centerCongr_symm_apply_coe, Unitary.linearIsometryEquiv_coe_apply, MonoidHom.fiberEquivKer_symm_apply, ofDual_ofNat, MvPolynomial.rename_msymm, LinearIsometryEquiv.image_eq_preimage_symm, QuotientAddGroup.liftEquiv_coe, Homeomorph.residual_map_eq, Equiv.arrowCongr_apply, ClosureOperator.conjBy_apply, LinearEquiv.coe_symm_toEquiv, LieHom.quotKerEquivRange_toFun, LinearEquiv.conj_refl, CategoryTheory.MonObj.ofRepresentableBy_one, IsometryEquiv.constVSub_symm_apply, Quiver.starEquivCostar_apply_fst, AddSubmonoid.LocalizationMap.ofAddEquivOfLocalizations_eq_iff_eq, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_snd, CategoryTheory.Iso.conjAut_mul, AddSubsemigroup.mem_map_equiv, Prod.Lex.toLexOrderHom_coe, UniformOnFun.lipschitzWith_one_ofFun_toFun, FreeGroup.lift_apply_of, MulAut.smul_def, Homeomorph.continuous, UniformFun.toFun_ofFun, RootPairing.mapsTo_reflection_root, CategoryTheory.Limits.Concrete.productEquiv_symm_apply_Ď, Prod.Lex.toLex_le_toLex', Function.FromTypes.curry_two_eq_curry, Module.Basis.toDualEquiv_apply, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_pointReflection_center_right, HahnSeries.support_abs, CategoryTheory.Functor.CorepresentableBy.equivOfIsoObj_apply, ofColex_add, LinearMap.BilinForm.nondegenerate_toMatrix_iff, LieModuleEquiv.refl_apply, CategoryTheory.FinCategory.asTypeToObjAsType_map, AddSubsemigroup.coe_toSubsemigroup_apply, PiLp.coe_continuousLinearEquiv, IsometryEquiv.image_emetric_ball, MonoidAlgebra.opRingEquiv_symm_apply, Monovary.dual_left, AddEquiv.comp_symm_eq, LinearEquiv.map_zero, Equiv.Perm.IsThreeCycle.support_eq_iff_mem_support, Finset.Colex.lt_iff_exists_forall_lt, DegLex.forall_iff, Matrix.updateCol_reindex, dotProductEquiv_apply_apply, DirectSum.decompose_of_mem, LinearMap.rank_diagonal, Multiset.toFinsupp_sum_eq, NumberField.RingOfIntegers.withValEquiv_symm_apply, Equiv.pprodEquivProd_apply, NumberField.mixedEmbedding.polarSpaceCoord_target, DomMulAct.map_mk_symm_nhds, LinearIsometryEquiv.adjoint_eq_symm, Equiv.transPartialEquiv_symm_apply, FundamentalGroupoid.equiv_apply, Matrix.comp_single_single, NumberField.mixedEmbedding.negAt_apply_snd, CliffordAlgebra.Κ_range_map_lift, DomMulAct.comap_mk_nhds, Equiv.mapMatrix_apply, TensorProduct.directLimitRight_tmul_of, AffineEquiv.apply_lineMap, MulEquiv.coe_submonoidMap_apply, zmultiples_equiv_zmultiples_apply, AddCircle.equivIco_coe_eq, MulEquiv.prodMultiplicative_symm_apply, CategoryTheory.Iso.homFromEquiv_symm_apply, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivLeft_apply, MulEquiv.val_piUnits_symm_apply, AlgHom.op_apply_apply, nndist_toMul, Orientation.neg_rotation_neg_pi_div_two, LinearMap.separatingRight_toMatrixâ'_iff, CategoryTheory.uliftCoyonedaEquiv_uliftCoyoneda_map, SheafOfModules.unitHomEquiv_symm_freeHomEquiv_apply, FreeAddMonoid.vadd_def, Matrix.toEuclideanLin_apply, BoundedContinuousFunction.isEmbedding_coeFn, Equiv.prodUnique_symm_apply, IsLeast.dual, Equiv.Perm.sameCycle_inv_apply_left, CategoryTheory.TwoSquare.equivNatTrans_apply, EquicontinuousOn.tendsto_uniformOnFun_iff_pi, AlgEquiv.toAlgHom_op, Submodule.biSup_eq_range_dfinsupp_lsum, Equiv.Perm.ofSubtype_apply_mem_iff_mem, Equiv.instIdempotentOpCoeForallForallArrowCongr, CategoryTheory.coyonedaEquiv_comp, CategoryTheory.uliftYonedaEquiv_symm_apply_app, WithAbs.equiv_algebraMap_apply, AddMonoidHom.fiberEquiv_symm_apply, Equiv.ofLeftInverse_symm_apply, Equiv.symm_apply_apply, ContinuousAlternatingMap.piEquiv_apply, Algebra.toMatrix_lmul_eq, val_unitsCentralizerEquiv_apply_coe, SymAlg.unsym_zero, Filter.tendsto_prodAssoc_symm, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_left, Complex.measurableEquivPi_apply, monotone_dual_iff, ContinuousLinearEquiv.symm_trans_apply, isAdjointPair_toLinearMapâ, IsHilbertSum.hasSum_linearIsometryEquiv_symm, OrderDual.isBounded_preimage_ofDual, LinearEquiv.congrLeft_symm_apply, Equiv.emptySum_apply_inr, SpecialLinearGroup.centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq, ContinuousMap.piEquiv_symm_apply, Equiv.altCongrHom_apply_coe, CategoryTheory.conjugateEquiv_symm_apply_app, Matrix.uniqueRingEquiv_apply, MulAction.toPerm_apply, unitInterval.symmMeasurableEquiv_apply, RingEquiv.coe_toMulEquiv, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, ModuleCat.endRingEquiv_symm_apply_hom, Fin.cycleIcc_of_last, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality, Monoid.CoprodI.inv_def, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply, AddMonoidHom.apply_ofInjective_symm, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, Equiv.prodPUnit_apply, ContinuousMap.continuous_iff_continuous_uniformOnFun, Submonoid.equivMapOfInjective_coe_mulEquiv, RingEquiv.map_mul, Diffeomorph.coe_coe, Equiv.Perm.congr_arg, TensorProduct.leftComm_tmul, exteriorPower.alternatingMapLinearEquiv_symm_map, frobeniusEquiv_symm_comp_frobenius, Fin.cycleIcc_of_gt, GroupExtension.Equiv.symm_symm_apply, SetSemiring.down_one, LinearEquiv.symm_apply_eq, toDual_zero, coe_equiv_lpPiLp_symm, Matrix.vandermonde_succ, TensorProduct.comm_comm, MeasurableEquiv.self_comp_symm, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, Finsupp.sumFinsuppAddEquivProdFinsupp_symm_apply, AddUnits.coe_unop_opEquiv, Module.Basis.repr_algebraMap, NonemptyInterval.dual_top, IsCusp.of_isFiniteRelIndex_conj, CategoryTheory.nerve.homEquiv_apply, ConjAct.toConjAct_zero, BoundedLatticeHom.symm_dual_comp, RCLike.conjCLE_apply, UniformOnFun.isEmbedding_toFun_finite, Rep.homEquiv_apply_hom, Magma.AssocQuotient.lift_comp_of', CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_toBiprod_apply, HahnEmbedding.Partial.truncLT_mem_range_extendFun, MulAutMultiplicative_symm_apply_apply, dite_comp_equiv_update, MulAut.mul_apply, toDegLex_ofDegLex, finCongr_symm_apply_coe, CategoryTheory.conjugateEquiv_apply_app, UniformEquiv.continuous_symm, TopologicalSpace.Opens.complOrderIso_symm_apply, Equiv.Perm.SameCycle.symm_apply_right, isExtrFilter_dual_iff, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_left, IsometryEquiv.toDilationEquiv_ratio, map_dvd_iff, MulEquiv.opOp_symm_apply, antivaryOn_toDual_left, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp, MonoidAlgebra.lift_symm_apply, Topology.IsQuotientMap.homeomorph_symm_apply, MeasureTheory.measurePreserving_finTwoArrow_vec, Equiv.equivCongr_refl_left, CoalgEquiv.toCoalgHom_eq_coe, AddMonoidAlgebra.uniqueRingEquiv_apply, AddSubgroup.mem_iff_toAddUnits_mem_addUnits, CategoryTheory.Limits.compYonedaSectionsEquiv_apply_app, Matrix.liftLinear_singleLinearMap, Finset.Ioc_ofDual, IsLocalization.isLocalization_iff_of_base_ringEquiv, Polynomial.evalâ_ofFinsupp, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, Multiset.consEquiv_symm_some, MvPolynomial.mvPolynomialEquivMvPolynomial_apply, Module.AEval'.X_smul_of, Fin.consEquivL_apply, ContinuousMulEquiv.eq_comp_symm, Module.Relations.Solution.directSumEquiv_apply_var, Euclidean.closedBall_eq_image, List.getEquivOfForallCountEqOne_apply, GroupExtension.Equiv.map_inl, Submodule.equivSubtypeMap_symm_apply, DirectSum.decompose_symm_sub, DomAddAct.isOpenEmbedding_mk_symm, Order.pred_ofAdd, AlgebraicGeometry.AffineSpace.homOverEquiv_symm_apply_coe, Matrix.submatrix_single_equiv, NumberField.mixedEmbedding.negAt_preimage, Submodule.botEquivPUnit_apply, CochainComplex.fromSingleâEquiv_apply_coe, sigmaFinsuppAddEquivDFinsupp_symm_apply, MulEquiv.monoidHomCongrLeftEquiv_apply, MonoidHom.map_frobeniusEquiv_symm, Finset.Colex.toColex_strictMono, Topology.WithLawson.toLawson_inj, IsometryEquiv.divLeft_apply, Matrix.liftLinear_comp_singleLinearMap, InfTopHom.dual_id, MonoidAlgebra.uniqueRingEquiv_apply, LieHom.equivRangeOfInjective_apply, ofDual_hnot, TotallyDisconnectedSpace.continuousMapEquivOfConnectedSpace_symm_apply_apply, Finsupp.basis_repr, ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_apply, Matrix.toBilin_apply, IsLocalRing.basisQuotient_repr, CategoryTheory.frobeniusMorphism_mate, LinearMap.toMatrixâ'_complââ, Equiv.optionSubtype_symm_apply_apply_coe, DilationEquiv.coe_one, FirstOrder.Language.Formula.equivSentence_not, AddMagmaCat.addEquiv_coe_eq, Function.update_updateFinset, AddMonoidAlgebra.opRingEquiv_symm_single, Homeomorph.measurableEmbedding, Metric.Snowflaking.ofSnowflaking_comp_toSnowflaking, zmultiplesAddHom_symm_apply, CategoryTheory.tensorRightHomEquiv_whiskerRight_comp_evaluation, DFinsupp.equivProdDFinsupp_apply, DualNumber.lift_apply_eps, modularCyclotomicCharacter.spec, Additive.toMul_le, AddEquiv.finsuppUnique_symm, LinearMap.prodEquiv_apply, AddEquiv.coe_addMonoidHom_refl, Equiv.congr_fun, Representation.smul_ofModule_asModule, isSquare_ofAdd_iff, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, MonomialOrder.toSyn_strictMono, SetTheory.PGame.add_moveRight_inr, Module.Relations.Solution.IsPresentation.linearMapEquiv_apply, Equiv.sigmaAssocProd_apply_snd_fst, RingEquiv.ofLeftInverseS_symm_apply, Quaternion.re_equivProd_symm_apply, MulEquiv.comp_symm_eq, Equiv.setSubtypeComm_apply, IsometryEquiv.subRight_apply, NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le, SimpleGraph.hasseDualIso_apply, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, Module.Basis.toLin_toMatrix, CategoryTheory.Limits.Pi.reindex_hom_Ď_assoc, LinearIsometryEquiv.inner_map_eq_flip, Finsupp.sum_equivMapDomain, WithConv.symm_linearEquiv_apply, WeierstrassCurve.Projective.Point.toAffineAddEquiv_apply, toDual_sSup, AddMonoidAlgebra.opRingEquiv_symm_apply, MeasurableEquiv.comap_apply, ContinuousLinearEquiv.continuousAlternatingMapCongrLeftEquiv_apply, Equiv.Perm.sign_eq_prod_prod_Ioi, Quaternion.linearIsometryEquivTuple_symm_apply, OrderMonoidIso.invFun_eq_symm, SetSemiring.down_mul, AlgEquiv.prodCongr_apply, CommBialgCat.isoEquivBialgEquiv_apply, Equiv.Perm.coe_mul, LieAlgebra.Extension.toKer_bracket, Matrix.toLinearEquivRight'OfInv_symm_apply, WithCStarModule.equiv_symm_neg, QuasilinearOn.dual, LatticeHom.dual_symm_apply_toFun, Equiv.Set.insert_symm_apply_inr, StrictMono.dual_right, Equiv.pnatEquivNat_apply, StarMulEquiv.coe_ofBijective, MulEquiv.mapSubgroup_apply, CategoryTheory.Bicategory.mateEquiv_id_comp_right, CategoryTheory.Localization.SmallShiftedHom.equiv_comp, Pi.counit_eq_adjoint, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointCompIso_inv, PartialEquiv.transEquiv_symm_apply, Metric.Snowflaking.image_toSnowflaking_emetricClosedBall, MulEquiv.op_apply_symm_apply, HahnSeries.SummableFamily.hsum_smul_module, MulEquiv.map_finprod, Equiv.Perm.decomposeFin_symm_apply_one, RootPairing.Equiv.toEndUnit_inv, 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_Ď, MonomialOrder.div_single, LinearEquiv.eq_symm_apply, isAddRightRegular_toColex, Matrix.toLin'_mul_apply, MultilinearMap.fromDirectSumEquiv_symm_apply, UniformEquiv.trans_apply, affineHomeomorph_symm_apply, Subsemiring.addEquivOp_apply_coe, MulSemiringAction.toRingEquiv_apply, Diffeomorph.mdifferentiableOn, SetTheory.PGame.mul_moveRight_inl, Equiv.toFun_as_coe, Topology.WithUpper.toUpper_ofUpper, Matrix.det_eval_matrixOfPolynomials_eq_det_vandermonde, RingEquivClass.toNonUnitalRingHomClass, Homeomorph.coe_neg, MeasurableEquiv.toLp_symm_apply, extDerivWithin_constOfIsEmpty, Matrix.toLinearMapâââ'_single, LieAlgebra.bracket_ofTwoCocycle, SheafOfModules.GeneratingSections.epi, SeparationQuotient.liftNormedAddGroupHomEquiv_apply, Antivary.sum_mul_le_sum_comp_perm_mul, Specialization.toEquiv_inj, toLex_vadd', SymAlg.unsym_add, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, UniformEquiv.uniformContinuous_symm, Matrix.nondegenerate_toBilin'_iff, Finsupp.liftAddHom_comp_single, Polynomial.rootsExpandPowEquivRoots_apply, Matrix.vec_of, Equiv.mulLeftâ_symm_apply, Representation.coinvariantsFinsuppLEquiv_apply, Algebra.Norm.Transitivity.comp_det_mul_pow, NonUnitalSubsemiring.centerToMulOpposite_symm_apply_coe, finSuccEquiv'_eq_some, Homeomorph.piCongrLeft_apply_apply, Finset.Colex.mem_initSeg, ContinuousLinearEquiv.coeFn_ofBijective, modularCyclotomicCharacter.toFun_spec', Homeomorph.comap_cocompact, RingEquiv.quotientBot_symm_mk, DilationEquiv.coe_symm_toHomeomorph, MonoidHom.toAdditive_symm_apply_apply, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp_symm_assoc, Diffeomorph.coe_prodCongr, OrderIso.map_wcovBy, nndist_toDual, LinearMap.BilinForm.congr_comp, LinearMap.toMatrixAlgEquiv_apply, MulEquiv.comp_right_injective, Matrix.updateRow_submatrix_equiv, FreeMonoid.toList_ofList, LocallyConstant.congrRightâ_apply_apply, PartialFun.Iso.mk_inv, CategoryTheory.Sieve.overEquiv_le_overEquiv_iff, Fin.cycleIcc.trans_left_one, AddAction.orbitZMultiplesEquiv_symm_apply', Ideal.quotEquivOfEq_mk, FreeNonUnitalNonAssocAlgebra.lift_unique, PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, Complex.equivRealProd_symm_apply, GradedTensorProduct.auxEquiv_one, Manifold.IsImmersionAtOfComplement.map_target_subset_target, Equiv.toOrderIsoSet_symm_apply, Algebra.TensorProduct.basis_repr_tmul, ContinuousMulEquiv.symm_apply_eq, Sym.coe_equivNatSum_symm_apply, sigmaAntidiagonalEquivProd_symm_apply_snd, tangentBundle_model_space_coe_chartAt, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range', IsometryEquiv.image_closedEBall, AffineEquiv.prodAssoc_symm_apply, IsometryEquiv.symm_apply_apply, NonUnitalAlgEquivClass.toMulActionSemiHomClass, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, RootPairing.reflection_apply_root', StandardEtalePair.homEquiv_apply_coe, toDual_eq_zero, LinearMap.toMatrix'_toLin', CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd, ContinuousAlgEquiv.continuous, RootPairing.flipEquiv_apply, Equiv.sumPiEquivProdPi_symm_apply, MonoidAlgebra.mapDomainAddEquiv_single, Sum.Lex.inl_bot, Equiv.leftInverse_symm, SSet.nonDegenerateEquivOfIso_symm_apply_coe, SymAlg.sym_add, Equiv.Perm.support_swap_mul_eq, CategoryTheory.Subobject.symm_apply_mem_iff_mem_image, Ideal.comap_of_equiv, OrderAddMonoidIso.coe_toEquiv_symm, Polynomial.mapEquiv_symm_apply, MeasurableEquiv.funUnique_symm_apply, NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, TensorProduct.toMatrix_assoc, MonoidAlgebra.mapRangeRingEquiv_single, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_symm_apply_right, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, CategoryTheory.nerve.edgeMk_id, FirstOrder.Ring.lift_genericPolyMap, multiplesAddHom_symm_apply, CategoryTheory.nerve.right_edge, Subring.mopRingEquivOp_apply_coe, Trivialization.continuousLinearEquivAt_apply, WithBot.map_ofDual, AddSubmonoid.centerCongr_symm_apply_coe, Matrix.toLinearMapâ'_apply', Homeomorph.map_punctured_nhds_eq, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_Ď, Sym.cast_rfl, BialgEquiv.toRingEquiv_toRingHom, Fin.coe_cycleRange_of_lt, OrthonormalBasis.coe_reindex, SubAddAction.ofStabilizer.conjMap_comp_neg_apply, Orientation.reindex_neg, Finset.geomSum_le_geomSum_iff_toColex_le_toColex, ofDual_preimage_latticeClosure, SimpleGraph.Iso.map_symm_apply, MulEquiv.apply_eq_iff_eq, SkewPolynomial.Ď_iterate_apply, AddAction.orbitZMultiplesEquiv_symm_apply, Equiv.equivCongr_apply_apply, AddSubgroup.coe_equivMapOfInjective_apply, Equiv.injective_pointReflection_left_of_injective_two_nsmul, SetTheory.PGame.mulOption_neg_neg, Diffeomorph.contMDiff_comp_diffeomorph_iff, RCLike.complexRingEquiv_apply, ZMod.AddAutEquivUnits_symm_apply, norm_toAdd, AlgEquiv.arrowCongr_apply, Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, Equiv.Perm.zpow_apply_mem_support_of_mem_cycleFactorsFinset_iff, Finsupp.LinearEquiv.finsuppUnique_symm_apply, StrictMonoOn.dual_left, MultilinearMap.domDomCongrLinearEquiv_symm_apply, starMulAut_apply, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, ofDual_smul, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub, AntivaryOn.dual_right, FreeAddGroup.lift_mk, SimpleGraph.lapMatrix_toLinearMapâ'_apply'_eq_zero_iff_forall_reachable, SkewPolynomial.monomial_def, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, Equiv.sigmaSumDistrib_symm_apply, HahnSeries.SummableFamily.Equiv_toFun, OrderIso.smulRightDual_apply, LinearMap.toMatrix_id, Homeomorph.isLocalHomeomorph, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, HNNExtension.inv_t_mul_of, unitsEquivProdSubtype_apply_coe, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_apply, Fintype.finsetEquivSet_apply, OpenPartialHomeomorph.toHomeomorphOfSourceEqUnivTargetEqUniv_symm_apply, Fin.revOrderIso_apply, RootPairing.IsOrthogonal.reflection_apply_left, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply_self, DoubleQuot.quotQuotEquivComm_comp_quotQuotMk, MeasurableEquiv.coe_toEquiv, ExteriorAlgebra.lift_Κ_apply, QuotientGroup.liftEquiv_coe, LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_apply_fst, AffineBasis.coord_reindex, LinearEquiv.coe_curry, zpowersHom_apply, 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, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_symm_apply, PositiveLinearMap.leftMulMapPreGNS_apply, MeasureTheory.addEquivAddHaarChar_smul_preimage, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub, ContinuousLinearEquiv.comp_differentiableOn_iff, Matrix.mul_reindexLinearEquiv_one, isAddLeftRegular_ofDual, Equiv.Set.univ_symm_apply, dist_left_pointReflection, RingEquiv.asBoolRingAsBoolAlg_symm_apply, LinearEquiv.image_symm_eq_preimage, Monoid.CoprodI.mrange_eq_iSup, OrderAddMonoidIso.symm_apply_eq, Finset.Colex.erase_le_erase, DoubleQuot.quotQuotEquivComm_quotQuotMk, SetTheory.PGame.mul_moveRight_inr, Fin.appendIsometry_symm_apply, strictMonoOn_dual_iff, MulEquiv.eq_symm_comp, Prod.Lex.prodLexAssoc_symm_apply, MeasureTheory.continuous_diracProbaEquiv, Homeomorph.isClosed_image, MeasureTheory.LevyProkhorov.toMeasureEquiv_symm_apply_toMeasure, TensorPower.algebraMapâ_mul, injective_comp, AddEquiv.symmEquiv_symm_apply_symm_apply, AddChar.toMonoidHomEquiv_symm_apply, ZSpan.quotientEquiv_apply_mk, AddSubsemigroup.toSubsemigroup'_closure, Equiv.Set.insert_apply_left, SupHom.symm_dual_comp, WithConv.equiv_apply, GenLoop.loopHomeo_apply, isAddLeftRegular_ofColex, WithZero.expOrderIso_symm_apply, TensorProduct.gradedComm_algebraMap_tmul, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_map_app, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality', OrderIso.dualDual_apply, HahnSeries.toMvPowerSeries_symm_apply_coeff, Diffeomorph.contMDiff_toFun, Equiv.coe_ofInjective_symm, RingEquiv.toNonUnitalRingHom_commutes, CategoryTheory.HomOrthogonal.matrixDecomposition_id, SeparatingDual.exists_continuousLinearEquiv_apply_eq, ContinuousMap.coe_homeoFnOfDiscrete, CategoryTheory.PreZeroHypercover.interLift_hâ, FirstOrder.Ring.realize_termOfFreeCommRing, IsAdjoinRootMonic.basis_repr, OpenPartialHomeomorph.homeomorphOfImageSubsetSource_symm_apply, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, MulAutMultiplicative_apply_apply, CategoryTheory.uliftCoyonedaEquiv_symm_apply_app, LinearMap.toMatrix_transpose, WeakDual.toStrongDual_inj, LieAlgebra.Orthogonal.indefiniteDiagonal_assoc, Equiv.toPartialEquiv_symm_apply, isAddRegular_toAdd, ofBoolAlg_bot, IsometryEquiv.diam_image, FirstOrder.Field.lift_genericMonicPoly, LinearMap.toMatrixâ_toLinearMapâââ, Multiplicative.ofAdd_eq_bot, isLowerSet_preimage_toDual_iff, CategoryTheory.Functor.representableByUliftFunctorEquiv_symm_apply_homEquiv, TensorProduct.finsuppLeft_smul', InverseSystem.globalEquiv_compatibility, Equiv.asEmbedding_apply, equivTangentBundleProd_apply, Finset.piCongrLeft_comp_restrict, Function.piCongrLeft'_symm_update, AddMagma.FreeAddSemigroup.lift_comp_of, PreQuasiregular.equiv_apply_val, Matrix.hadamard_of_one, Equiv.symm_symm_apply, starL_apply, MeasurableEquiv.piEquivPiSubtypeProd_apply, PreTilt.coeff_frobeniusEquiv_symm, Equiv.Perm.sign_of_cycleType_eq_replicate, FreeAbelianGroup.liftMonoid_coe_addMonoidHom, LinearIsometryEquiv.fderiv, Equiv.boolArrowEquivProd_apply, AddEquiv.withZeroCongr_apply, CliffordAlgebra.Κ_comp_lift, CategoryTheory.Discrete.equivalence_unitIso, Fin.castLEquiv_symm_apply, Submonoid.LocalizationMap.ofMulEquivOfDom_comp_symm, Algebra.TensorProduct.basisAux_map_smul, Matrix.coe_ofAddEquiv_symm, CategoryTheory.Adjunction.leftAdjointCompNatTransâââ_eq_conjugateEquiv_symm, Pi.basis_repr_single, EquicontinuousOn.inducing_uniformOnFun_iff_pi', Finset.Colex.toColex_le_toColex_iff_max'_mem, Equiv.add_def, Equiv.piCongrLeft_preimage_pi, PiTensorProduct.reindex_comp_tprod, Hamming.nndist_eq_hammingDist, ContinuousLinearEquiv.piUnique_symm_apply, LinearIsometryEquiv.measurePreserving, equivShrink_symm_bot, Function.OfArity.curryEquiv_symm_apply, MeasureTheory.Measure.infinitePi_map_piCongrLeft, Algebra.traceMatrix_reindex, LinearIsometryEquiv.coe_toLinearEquiv, Equiv.sum_comp, SSet.opFunctor_map, pow_finEquivZPowers_symm_apply, MeasureTheory.hausdorffMeasure_measurePreserving_piFinTwo, supPrime_toDual, dist_ofDual, TensorProduct.equivFinsuppOfBasisRight_apply_tmul, RingCon.comapQuotientEquivRangeS_symm_mk, Matrix.diagonal_vec2, AffineIsometryEquiv.dist_pointReflection_fixed, MvPowerSeries.lexOrder_def_of_ne_zero, MonomialOrder.degree_add_le, Submodule.coe_prodEquivOfIsCompl', MulAut.inv_apply_self, Module.Basis.ofEquivFun_repr_apply, Finset.toDual_min', toAdd_multiset_sum, toDual_compares_toDual, Normal.algHomEquivAut_symm_apply, AddSubsemigroup.topEquiv_apply, SlashInvariantForm.coe_translate, ArchimedeanClass.FiniteElement.val_add, Finset.Ioo_orderDual_def, Pi.toLex_update_le_self_iff, apply_wcovBy_apply_iff, groupCohomology.cocyclesâIsoOfIsTrivial_hom_hom_apply_apply, uniformContinuous_toMul, CliffordAlgebra.lift_unique, Complex.measurableEquivRealProd_apply, SetTheory.PGame.mul_moveLeft_inl, ofColex_vadd', Equiv.Perm.VectorsProdEqOne.vectorEquiv_apply_coe, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, UniformOnFun.ofFun_div, CategoryTheory.Limits.Cotrident.IsColimit.homIso_natural, AddEquiv.prodProdProdComm_apply, Module.Basis.sumQuot_repr_left, LinearEquiv.ofSubmodules_apply, DomMulAct.map_mk_nhds, edist_ofDual, Submonoid.topEquiv_symm_apply_coe, ContinuousAlternatingMap.ofSubsingleton_apply_toContinuousMultilinearMap, MeasureTheory.Measure.infinitePi_map_piCurry, OrderIso.dual_apply, Submodule.topEquiv_apply, Homeomorph.continuousMapCongr_symm_apply, Orientation.rotation_pi_apply, Coalgebra.comm_comul, Module.Relations.Solution.IsPresentation.linearEquiv_apply, CategoryTheory.FunctorToTypes.binaryCoproductEquiv_symm_apply, gc_upperPolar_lowerPolar, ContinuousLinearEquiv.uniqueProd_symm_apply, SSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff, Subgroup.coe_equivMapOfInjective_apply, Module.Basis.reindexRange_repr', Unitization.lift_symm_apply_apply, AddEquiv.toMultiplicativeLeft_apply_symm_apply, Sum.Lex.toLex_lt_toLex, CategoryTheory.Coyoneda.objOpOp_hom_app, RingEquiv.moduleEndSelf_symm_apply, Module.reflection_apply_self, CategoryTheory.Bicategory.Adj.Homâ.conjugateEquiv_symm_Ďr, Polynomial.degreeLT.addLinearEquiv_castAdd, AddEquiv.coe_addMonoidHom_comp_coe_addMonoidHom_symm, Orientation.rotation_rotation, KaehlerDifferential.polynomialEquiv_comp_D, Multiset.equivDFinsupp_apply, Invertible.mulRight_apply, PerfectRing.liftEquiv_comp_apply, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_map, LinearIsometryEquiv.coe_toHomeomorph, AddEquiv.self_comp_symm, disjoint_toDual_iff, powCoprime_symm_apply, SSet.Subcomplex.ofSimplexProd_eq_range, CategoryTheory.nerve.homEquiv_edgeMk, LinearEquiv.toSpanNonzeroSingleton_homothety, FreeMonoid.lift_of_comp_eq_map, Module.Basis.reindexRange_repr, Matrix.GeneralLinearGroup.upperRightHom_apply, Equiv.uniqueSigma_apply, AffineIsometryEquiv.continuousWithinAt, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, IsBaseChange.endHom_toMatrix, Finsupp.mapRange.equiv_refl, CategoryTheory.Over.postAdjunctionLeft_unit_app_left, Matrix.transposeRingEquiv_symm_apply, Pi.toLex_update_lt_self_iff, Submonoid.map_coe_toMulEquiv, OrderIso.sumLexIicIoi_symm_apply_of_le, BoundedOrderHom.dual_apply_toOrderHom, DistribMulAction.toLinearEquiv_symm_apply, LocalizedModule.equivTensorProduct_apply_mk, Field.Emb.Cardinal.succEquiv_coherence, ModuleCat.homLinearEquiv_symm_apply, Equiv.Perm.coe_support_eq_set_support, Real.map_matrix_volume_pi_eq_smul_volume_pi, Set.Countable.exists_cycleOn, QuotientGroup.quotientKerEquivOfRightInverse_apply, Equiv.bijective_comp, Topology.WithUpper.ofUpper_lt_ofUpper, Hamming.ofHamming_smul, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub, Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply, MeasurableEquiv.map_symm_map, FreeMonoid.lift_ofList, AddMonCat.equivalence_inverse_map, Equiv.prodAssoc_apply, Homeomorph.isProperMap, Subsemiring.coe_equivMapOfInjective_apply, VectorField.pullbackWithin_eq_of_fderivWithin_eq, Metric.Snowflaking.mk_eq_toSnowflaking, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul, ContinuousLinearEquiv.finTwoArrow_symm_apply, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_fst, ContinuousLinearEquiv.isAddHaarMeasure_map, WithZero.lt_ofAdd_iff, Module.Basis.toMatrix_map, CategoryTheory.Functor.homObjEquiv_symm_apply_app, PiTensorProduct.ofFinsuppEquiv'_tprod_single, TensorProduct.lidIsometry_apply, Metric.Snowflaking.val_eq_ofSnowflaking, finSigmaFinEquiv_apply, NumberField.InfinitePlace.mkReal_coe, HahnSeries.SummableFamily.smul_apply, CategoryTheory.Adjunction.mkOfHomEquiv_counit_app, MultilinearMap.curryFinFinset_apply, gc_upperBounds_lowerBounds, starRingAut_apply, ContinuousLinearEquiv.compContinuousAlternatingMap_coe, IsNoetherian.equivPUnitOfProdInjective_apply, StrongDual.toWeakDual_inj, FirstOrder.Language.LEquiv.onFormula_apply, SSet.stdSimplex.objâEquiv_apply, Subgroup.IsComplement.equiv_mul_left_of_mem, Orientation.map_eq_iff_det_pos, AffineEquiv.sSameSide_map_iff, LinearMap.BilinForm.Nondegenerate.congr, Subgroup.smul_leftQuotientEquiv, groupCohomology.isMulCoboundaryâ_of_mem_coboundariesâ, Rep.MonoidalClosed.linearHomEquivComm_hom, Homeomorph.image_closure, Quiver.SingleObj.toPrefunctor_apply_map, OpenPartialHomeomorph.toHomeomorphSourceTarget_apply_coe, PiLp.sumPiLpEquivProdLpPiLp_symm_apply_ofLp, LinearMap.tensorKerEquivOfSurjective_symm_tmul, CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom_mk, SemimoduleCat.homLinearEquiv_apply, PEquiv.toMatrix_toPEquiv_eq, MeasureTheory.volume_preserving_prodAssoc, continuous_toAdd, TensorProduct.equivFinsuppOfBasisLeft_symm, Homeomorph.divRight_apply, Equiv.Set.congr_symm_apply, LinearMap.IsProj.eq_conj_prodMap, OrderMonoidIso.val_unitsCongr_apply, Equiv.permCongrHom_coe, coe_galRestrict_apply, CategoryTheory.Functor.RepresentableBy.comp_homEquiv_symm, CategoryTheory.Functor.equivCatHom_apply, ofBoolRing_add, addEquivOfAddOrderOfEq_apply_gen, infClosed_preimage_toDual, Matrix.uniqueEquiv_symm_apply, HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_symm_mk, Module.Basis.coe_toOrthonormalBasis_repr, Matrix.piRingEquiv_apply, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, SSet.prodStdSimplex.objEquiv_δ_apply, SetTheory.PGame.toRightMovesNim_one_symm, RootPairing.IsOrthogonal.coreflection_apply_right, Equicontinuous.tendsto_uniformFun_iff_pi, Matrix.toLinearMapâ'_apply, NonUnitalSubring.topEquiv_symm_apply_coe, BialgEquivClass.toBialgHomClass, AddMonCat.equivalence_counitIso, toDual_sdiff, Matrix.uniqueAddEquiv_symm_apply, WeakDual.coe_toStrongDual, LinearIsometryEquiv.map_add, Equiv.divRightâ_symm_apply, Polynomial.degreeLT.addLinearEquiv_apply_fst, Submonoid.toAddSubmonoid_closure, lTensorHomEquivHomLTensor_apply, LinearMap.BilinForm.separatingLeft_toMatrix'_iff, Topology.WithUpper.ofUpper_le_ofUpper, midpoint_pointReflection_left, Equiv.Perm.SameCycle.zpow_right, TensorProduct.finsuppScalarRight_apply, ModularGroup.lcRow0Extend_symm_apply, AffineIsometryEquiv.map_vsub, RootPairing.reflection_same, LinearMap.extendScalarsOfIsLocalizationEquiv_apply, ofLex_vadd, LocallyConstant.congrRightâ_symm_apply_apply, ContinuousLinearEquiv.coe_toContinuousAffineEquiv, ContinuousCohomology.I_obj_Ď_apply, Subgroup.conjAct_pointwise_smul_iff, MulEquiv.coprodPUnit_symm_apply, Equiv.Perm.decomposeFin.symm_sign, MulAction.stabilizerEquivStabilizer_compTriple, MeasurableEquiv.quasiMeasurePreserving_symm, LinearEquiv.skewSwap_apply, MonovaryOn.dual_left, CategoryTheory.Iso.eHomCongr_comp_assoc, MvPolynomial.rename_psum, RootPairing.Hom.comp_indexEquiv_apply, CategoryTheory.Adjunction.homEquiv_unit, Sym.coe_equivNatSumOfFintype_symm_apply, CategoryTheory.Under.postAdjunctionRight_unit_app_right, CategoryTheory.Limits.WidePullbackCone.reindex_base, MeasurableEquiv.ofInvolutive_apply, CategoryTheory.Iso.toIsometryEquiv_toFun, MulEquiv.invFun_eq_symm, MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar, Orientation.kahler_comp_rightAngleRotation, ContinuousLinearEquiv.arrowCongr_apply, Equiv.Perm.mem_support_cycle_of_cycle, NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst, IsometryEquiv.edist_eq, CoxeterSystem.getElem_succ_leftInvSeq_alternatingWord, HahnSeries.addOppositeEquiv_support, pow_ofColex, AddSubmonoid.centerToAddOpposite_symm_apply_coe, CategoryTheory.conjugateEquiv_leftUnitor_hom, Homeomorph.continuousMapCongr_apply, SetSemiring.zero_def, OrderMonoidIso.coe_mulEquiv, Equiv.Perm.sameCycle_apply_right, Polynomial.opRingEquiv_op_C, SkewMonoidAlgebra.lift_of, LocalizedModule.equivTensorProduct_symm_apply_tmul, OrderMonoidIso.symm_apply_apply, Real.sinhHomeomorph_symm_apply, AddMonoidHom.ofLeftInverse_symm_apply, Complex.lift_apply, Subgroup.range_zpowersHom, AlgebraicGeometry.coprodMk_inl, LinearEquiv.arrowCongr_symm_apply, TensorProduct.finsuppScalarRight_apply_tmul, ContinuousLinearMap.coe_equivRange, PartOrd.dual_map, image_gaugeRescaleHomeomorph_interior, MeasureTheory.IsProbabilityMeasure_comap_equiv, Subalgebra.mopAlgEquivOp_symm_apply, Representation.single_smul, SkewMonoidAlgebra.lift_single, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm, SSet.op_Ď, ContinuousLinearMap.toUniformConvergenceCLM_apply, Module.Relations.Solution.IsPresentation.linearMapEquiv_symm_apply, DFinsupp.lex_lt_iff, CategoryTheory.Aut.toEnd_apply, AffineEquiv.linear_equivUnitsAffineMap_symm_apply, CategoryTheory.uliftYonedaEquiv_apply, HahnEmbedding.Partial.orderTop_eq_iff, multiplesEquivMultiples_apply, RingEquiv.coe_ofBijective, ofDual_himp, Module.FinitePresentation.linearEquivMap_symm_apply, norm_ofDual, CategoryTheory.Iso.homCongr_comp, LinearIsometryEquiv.coe_ofEq_apply, CategoryTheory.Limits.SingleObj.Types.colimitEquivQuotient_apply, ContinuousLinearEquiv.isBigO_sub, Polynomial.roots_X_pow_char_pow_sub_C_pow, Equiv.pointReflection_vsub_right, uniformContinuous_ofMul, AffineMap.homothety_neg_one_apply, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, Matrix.conjTransposeLinearEquiv_apply, AddSubsemigroup.centerToAddOpposite_symm_apply_coe, uliftPowersHom_symm_apply, UniformOnFun.postcomp_uniformContinuous, MulEquiv.coprodAssoc_symm_apply_inr_inr, CategoryTheory.Arrow.equivSigma_apply_snd_snd, Matrix.isNilpotent_toLin'_iff, CategoryTheory.bijection_natural, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, CategoryTheory.Functor.Initial.limitConeComp_isLimit, FreeCommRing.lift_of, Orientation.volumeForm_zero_pos, RingHom.eq_liftOfSurjective, ChainComplex.toSingleâEquiv_apply_coe, iterateFrobeniusEquiv_add_apply, ofLex_pow, CategoryTheory.Limits.Pi.reindex_inv_Ď_assoc, SetTheory.PGame.Domineering.shiftRight_apply, Module.Basis.constrL_apply, OrderDual.toDual_inj, SkewMonoidAlgebra.lift_apply, Module.AEval'.of_symm_X_smul, Equiv.algEquiv_apply, ofMul_multiset_prod, homTensorHomEquiv_apply, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero, CategoryTheory.Functor.FullyFaithful.homEquiv_symm_apply, CompHausLike.homeoOfIso_symm_apply, Equiv.equivPUnit_symm_apply, Subgroup.centerCongr_apply_coe, Equiv.pointReflection_midpoint_right, IsometryEquiv.hausdorffMeasure_image, WithVal.apply_symm_equiv, ContinuousLinearEquiv.hasMFDerivAt, Monoid.Coprod.con_inv_mul_cancel, Equiv.equivCongr_refl_right, Equiv.Perm.subtypeCongr.right_apply_subtype, AddChar.coe_toMonoidHomEquiv, Equiv.subtypeSubtypeEquivSubtype_apply_coe, 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, MvPolynomial.coe_mapEquivMonic_comp', ofColex_smul', Equiv.Perm.mem_list_cycles_iff, Monoid.IsTorsion.torsionMulEquiv_apply, DFinsupp.mapRange.addEquiv_apply, MulEquiv.prodMultiplicative_apply, pow_toDual, Subgroup.mem_map_equiv, QuadraticMap.IsometryEquiv.toIsometry_apply, IsLocalization.ringEquivOfRingEquiv_symm_apply, RootPairing.weylGroup_apply_root, Rack.envelAction_prop, AffineEquiv.pointReflection_fixed_iff_of_module, monovary_toDual_right, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, CategoryTheory.Bicategory.mateEquiv_symm_apply', CircleDeg1Lift.translate_iterate, MeasurableEquiv.coe_IicProdIoc_symm, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_symm_apply, RingEquiv.symm_apply_apply, unitarySubgroupUnitsEquiv_apply_coe, Equiv.sumAssoc_apply_inl_inl, Homeomorph.continuousMapOfUnique_apply, ExteriorAlgebra.lift_comp_Κ, Diffeomorph.image_eq_preimage_symm, Order.pred_toMul, Subgroup.map_equiv_top, WithBot.ofDual_apply_coe, AddSemigrp.addEquiv_coe_eq, AddAut.conj_symm_apply, Matrix.adjugate_fin_three, Matrix.natCast_fin_three, Finsupp.DegLex.single_lt_iff, Submonoid.centerToMulOpposite_apply_coe, CategoryTheory.Localization.homEquiv_eq, Matrix.toLinearEquiv'_symm_apply, LinearIsometryEquiv.smul_apply, PiTensorProduct.subsingletonEquiv_apply_tprod, LinearEquiv.uniqueProd_apply, DFinsupp.sigmaCurryLEquiv_apply, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_apply, Equiv.Perm.cycleOf_apply_apply_pow_self, Equiv.hasSum_iff, Equiv.punitProd_symm_apply, RingEquiv.sofLeftInverse'_apply, AddEquiv.toMultiplicativeRight_apply_symm_apply, LinearIsometryEquiv.coe_injective, LinearIsometryEquiv.contDiff, LinearMap.BilinForm.mul_toMatrix'_mul, CategoryTheory.Bicategory.conjugateEquiv_id_comp_right_apply, Matrix.entryAddMonoidHom_eq_comp, EisensteinSeries.gammaSetDivGcdSigmaEquiv_symm_eq, Trivialization.linearEquivAt_apply, AddEquiv.uniqueProd_symm_apply, IsSublattice.of_dual, Finset.Colex.singleton_le_toColex, AddHom.op_apply_apply, 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, Tropical.tropEquiv_coe_fn, ContinuousMulEquiv.eq_symm_apply, AddMonoidAlgebra.of_apply, FirstOrder.Language.Equiv.refl_apply, CartanMatrix.D_three, CategoryTheory.Bicategory.Adjunction.homEquivâ_apply, Equiv.Perm.extendDomain_apply_subtype, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, AlgEquiv.equivCongr_apply, Equiv.sigmaSigmaSubtype_symm_apply, finsuppTensorFinsupp'_single_tmul_single, Finsupp.mapDomain.coe_linearEquiv, ZFSet.coeEquiv_apply_coe, IsometryEquiv.ediam_preimage, UniversalEnvelopingAlgebra.Κ_comp_lift, AlgHom.opComm_symm_apply_apply, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, Homeomorph.sumProdDistrib_symm_apply, MonomialOrder.le_degree, Topology.IsQuotientMap.liftEquiv_symm_apply_coe, SubAddAction.conjMap_ofFixingAddSubgroup_bijective, LocallyConstant.congrRightâ_apply_apply, Diffeomorph.sumAssoc_coe, AddValuation.toValuation_ofValuation, DomMulAct.isInducing_mk_symm, QuaternionAlgebra.equivTuple_symm_apply, RingAut.one_apply, NumberField.Units.logEmbeddingQuot_apply, zpowersMulHom_apply, equicontinuousWithinAt_iff_continuousWithinAt, HahnEmbedding.Partial.coeff_eq_of_mem, ContAction.resEquiv_inverse, NumberField.canonicalEmbedding.integralBasis_repr_apply, ContinuousAffineEquiv.prodComm_symm_apply, mem_closure_isSwap, Delone.DeloneSet.mapIsometry_symm_apply_carrier, AddCommMonCat.equivalence_functor_map, CategoryTheory.Functor.map_isoCongr, sigmaFinsuppEquivDFinsupp_add, Matrix.neg_of, Subsemigroup.topEquiv_symm_apply_coe, Finset.Colex.toColex_image_lt_toColex_image, BilinForm.mul_toMatrix_mul, InfHom.dual_apply_toFun, CategoryTheory.Functor.coconeTypesEquiv_apply_pt, AffineBasis.coe_reindex, CategoryTheory.Adjunction.compPreadditiveYonedaIso_inv_app_app_apply, Topology.WithScott.toScott_ofScott, IsGalois.intermediateFieldEquivSubgroup_apply, SymAlg.unsym_inv, FreeLieAlgebra.lift_comp_of, AddSubsemigroup.comap_equiv_eq_map_symm, Equiv.sub_def, isQuasiregular_iff', QuadraticForm.tensorRId_symm_apply, Equiv.forall_congr_left, Equiv.funSplitAt_symm_apply, HasFPowerSeriesOnBall.fderiv_eq, val_toUnits_apply, SSet.prodStdSimplex.objEquiv_naturality, RootPairing.pairing_reflectionPerm_self_right, Equiv.prodSumDistrib_apply_right, NumberField.Units.basisOfIsMaxRank_apply, Module.Invertible.rTensorEquiv_apply_apply, AddMonoidHom.toMultiplicativeRight_symm_apply_apply, Rep.coindVEquiv_symm_apply_coe, AlternatingMap.map_congr_perm, LinearEquiv.lTensor_tmul, RingEquiv.map_neg_one, Equiv.Perm.prodExtendRight_apply_ne, DirectSum.coe_decompose_mul_add_of_left_mem, LinearIsometryEquiv.coe_trans, CategoryTheory.Limits.Concrete.prodEquiv_apply_fst, CategoryTheory.nerve.nonempty_compStruct_iff, SubAddAction.ofFixingAddSubgroup.append_left, Equiv.Finset.union_inl, Module.Basis.linearMap_apply, FreeMonoid.lift_comp_of, RootPairing.Equiv.root_indexEquiv_eq_smul, ContinuousAlgEquiv.symm_trans_apply, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_snd_coe, AddEquiv.map_dfinsuppSumAddHom, ProbabilityTheory.variance_map_equiv, CoalgEquiv.coe_toLinearEquiv, Matrix.eta_fin_three, lipschitzOnWith_cfc_fun_of_subset, Polynomial.rootsExpandEquivRoots_apply, Metric.Snowflaking.image_ofSnowflaking_eball, Matrix.toLinearMapâ_complââ, Matrix.eRank_reindex, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', CategoryTheory.Limits.Types.Small.productIso_inv_comp_Ď, LinearEquiv.coe_neg, LocallyConstant.congrLeftâ_apply_apply, CategoryTheory.Limits.FintypeCat.productEquiv_apply, GroupExtension.Equiv.refl_apply, MulAut.coe_inv, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left, CategoryTheory.uliftYonedaEquiv_symm_map, UniformFun.postcomp_isUniformInducing, TensorProduct.quotientTensorEquiv_symm_apply_mk_tmul, groupCohomology.H1IsoOfIsTrivial_H1Ď_apply_apply, DomAddAct.isInducing_mk, LinearIsometryEquiv.piLpCongrLeft_apply, PowerBasis.leftMulMatrix, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_Ď, TopHom.dual_symm_apply_apply, MeasurableEquiv.symm_preimage_preimage, MonoidAlgebra.domCongr_single, FreeAbelianGroup.liftAddEquiv_symm_apply, PiTensorProduct.ofDirectSumEquiv_symm_lof_tprod, toBoolAlg_zero, basisOfLinearIndependentOfCardEqFinrank_repr_apply, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, AddSubmonoid.LocalizationMap.of_addEquivOfAddEquiv_apply, Homeomorph.map_nhds_eq, NumberField.Units.regulator_eq_det, Module.Invertible.linearEquivOfRightInverse_symm_apply, finPiFinEquiv_apply, NonemptyInterval.dual_pure, unitary.linearIsometryEquiv_coe_symm_apply, OrthogonalIdempotents.equiv, MulEquiv.withZero_apply_symm_apply, Matrix.replicateRow_empty, MeasureTheory.Measure.map_piSingleton, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, Metric.Snowflaking.preimage_toSnowflaking_emetricClosedBall, continuousOn_cfc_setProd, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, ContinuousLinearEquiv.hasMFDerivWithinAt, PiTensorProduct.ofFinsuppEquiv_tprod_single, Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalence, MeasureTheory.Measure.InnerRegular.comap, QuotientGroup.liftEquiv_mk, Matrix.of_add_of, RingEquiv.cast_apply, OrderMonoidIso.symm_comp_self, IsometryEquiv.preimage_emetric_ball, Diffeomorph.sumCongr_inl, LinearMap.lsum_apply, OrderIso.coe_symm_toEquiv, IsometryEquiv.comp_continuousOn_iff, AddEquiv.addMonoidHomCongrLeft_apply, LinearEquiv.funUnique_symm_apply, Hamming.nnnorm_eq_hammingNorm, ZeroAtInftyContinuousMap.ContinuousMap.liftZeroAtInfty_apply_toFun, AffineIsometryEquiv.continuousOn, Finset.Ioo_ofDual, Cardinal.mk_subtype_of_equiv, OrderIso.coe_dualDual, Equiv.extendSubtype_not_mem, toDual_wcovBy_toDual_iff, AddMonoidHom.mulOp_apply_apply, Equiv.Perm.image_inv, Module.Ray.linearEquiv_smul_eq_map, DFinsupp.sum_eq_sum_fintype, MulAut.coe_one, FintypeCat.uSwitchEquiv_naturality, Equiv.Perm.fixed_point_card_lt_of_ne_one, MulEquiv.subgroupCongr_apply, finRotate_succ_eq_decomposeFin, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, MeasureTheory.addEquivAddHaarChar_eq, StarMulEquiv.apply_symm_apply, AddSubmonoid.LocalizationMap.symm_comp_ofAddEquivOfLocalizations_apply', Equiv.iSup_comp, UniformOnFun.tendsto_iff_tendstoUniformlyOn, OrthonormalBasis.coe_ofRepr, SemidirectProduct.congr'_apply_right, AddSubgroup.mem_ofAddUnits_iff_toAddUnits_mem, CategoryTheory.Limits.Sigma.whiskerEquiv_hom, LinearEquiv.coe_ofInjectiveEndo, subtypeOrEquiv_symm_inl, Equiv.withBotSubtypeNe_symm_apply_coe, infPrime_ofDual, isAddRegular_ofColex, Homeomorph.coe_unitBall_apply_zero, Homeomorph.isBigOWith_congr, Antivary.sum_mul_le_sum_mul_comp_perm, Metric.Snowflaking.isBounded_preimage_ofSnowflaking_iff, Submodule.adjoint_subtypeL, CompHausLike.isoEquivHomeo_symm_apply, Equiv.Perm.SameCycle.exists_pow_eq', AddOpposite.opHomeomorph_apply, GaloisConnection.dual, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, LinearMap.toLinearMap_toContPerfPair, AlgEquiv.sumArrowEquivProdArrow_symm_apply_inr, Homeomorph.smul_symm_apply, fixingAddSubmonoid_fixedPoints_gc, Matrix.comp_transpose, Equiv.optionSubtypeNe_symm_of_ne, AddEquiv.symm_apply_apply, MeasureTheory.Measure.sum_comp_equiv, Bundle.TotalSpace.toProd_symm_apply_proj, QuotientAddGroup.liftEquiv_mk, Equiv.pprodProd_apply, LatticeHom.dual_apply_toFun, continuous_decomposeProdAdjoint_symm, LinearMap.isSymmetric_adjoint_mul_self, AddSubgroup.addSubgroupOfEquivOfLe_apply_coe, OrderMonoidIso.val_inv_unitsCongr_symm_apply, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, Order.isPredPrelimit_toDual_iff, gelfandStarTransform_symm_apply, Matrix.reindex_mem_rowStochastic_iff, Matrix.piRingEquiv_symm_apply, TensorPower.mul_assoc, toDual_vadd, FintypeCat.equivEquivIso_symm_apply_symm_apply, ContinuousLinearEquiv.uniqueDiffOn_image, isLeftRegular_toMul, CategoryTheory.FinCategory.categoryAsType_id, LinearIsometry.equivRange_apply_coe, Metric.Snowflaking.image_toSnowflaking_eball, CategoryTheory.Limits.IsColimit.homEquiv_apply, FreeAddGroup.lift_apply_of, groupCohomology.isMulCocycleâ_of_mem_cocyclesâ, Submonoid.closure_singleton_eq, ofDual_pow, RCLike.conjLIE_apply, DilationEquiv.trans_apply, MonoidHom.apply_mnat, Submodule.reflection_orthogonalComplement_singleton_eq_neg, finSumNatEquiv_symm_apply_fin, WithAbs.tendsto_one_div_one_add_pow_nhds_one, ofMul_vadd, RootPairing.Equiv.weightMap_weightEquiv_symm, lipschitzGroup.conjAct_smul_Κ_mem_range_Κ, FreeGroupBasis.lift_apply_apply, InverseSystem.PEquivOn.compat, Pi.le_toLex_update_self_iff, ContinuousLinearEquiv.comp_fderiv, InfHom.dual_id, WithTop.ofDual_apply_top, CategoryTheory.Functor.Final.colimitCoconeComp_isColimit, Equiv.coe_subtypeEquivCodomain_symm, Subgroup.centerToMulOpposite_apply_coe, Complex.orthonormalBasisOneI_repr_apply, OrderMonoidIso.withZeroUnits_symm_apply, Equiv.Perm.sameCycle_symm_apply_right, Representation.coinvariantsTprodLeftRegularLEquiv_apply, Matrix.piLinearEquiv_apply, AddAut.coe_inv, ZMod.dft_comp_unitMul, LinearMap.toMatrixâ_complâ, Affine.Triangle.dist_circumcenter_reflection_orthocenter, dist_ofAdd, Bundle.Trivial.isInducing_toProd, RingCon.comapQuotientEquivRange_mk, finsuppTensorFinsuppLid_symm_single_smul, Module.reflection_mul_reflection_pow_apply, DFinsupp.sum_mapRange_index.linearMap, DomAddAct.continuous_mk_symm, PiTensorProduct.congr_symm_tprod, MulEquiv.ofLeftInverse_symm_apply, rTensorHomEquivHomRTensor_apply, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, TensorPower.algebraMapâ_one, ExteriorAlgebra.liftAlternatingEquiv_apply, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_symm_apply_desc, FreeAlgebra.liftAux_eq, LinearIsometryEquiv.coe_toContinuousLinearEquiv, CategoryTheory.opEquiv_apply, dualTensorHomEquivOfBasis_symm_cancel_right, RingEquiv.symm_apply_eq, SubAddAction.conjMap_ofFixingAddSubgroup_coe_apply, Equiv.Perm.cycleOf_pow_apply_self, Multiset.toFinsupp_union, AlgebraicGeometry.coe_opensRestrict_symm_apply, LinearEquiv.coe_pow, finCongr_apply_mk, Sym2.liftâ_mk, Matrix.toLpLin_symm_pow, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_apply_inv, ContinuousLinearEquiv.integral_comp_comm, Real.fourierIntegralInv_comp_linearIsometry, Diffeomorph.range_comp, spinGroup.units_involute_act_eq_conjAct, MvPolynomial.scalarRTensor_apply_tmul, TensorProduct.prodLeft_tmul, Matrix.smul_of, FreeAddMonoid.ofList_append, Matrix.replicateRow_cons, Semigrp.mulEquiv_coe_eq, Interval.coe_dual, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', AddEquiv.toAdditive_toMultiplicative_symm_apply, NonemptyInterval.fst_dual, TensorAlgebra.lift_symm_apply, CategoryTheory.Quiv.homEquivOfIso_apply, UniformFun.toFun_zero, Primrec.of_equiv_symm_iff, AffineEquiv.ofBijective_apply, ContinuousLinearEquiv.comp_right_fderiv, AlgEquiv.op_apply_symm_apply, LatticeHom.symm_dual_id, ContinuousAlgEquiv.symm_map_nhds_eq, Orientation.rotation_map, AddMonoidHom.fiberEquivKer_apply, FreeAddGroup.lift_unique, SymAlg.sym_sub, FirstOrder.Language.Equiv.ext_iff, Orientation.oangle_rotation_left, AbstractCompletion.uniformContinuous_compareEquiv, CategoryTheory.Equivalence.inverseFunctor_map, finsuppTensorFinsupp'_symm_single_mul, Setoid.quotientKerEquivOfRightInverse_apply, ContinuousMulEquiv.eq_symm_comp, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_apply_hom, IsGaloisGroup.mulEquivCongr_apply_smul, LinearEquiv.ofLeftInverse_symm_apply, WithVal.apply_equiv, List.formPerm_apply_mem_of_mem, OrderMonoidIso.withZeroUnits_apply, DirectSum.decompose_symm_neg, isOpenMap_toWeakSpace_symm, LinearMap.polyCharpolyAux_map_eval, Topology.WithUpperSet.toUpperSet_specializes_toUpperSet, FreeAbelianGroup.liftAddGroupHom_apply, Matrix.toLinearMapâââ'_aux_eq, powCoprime_inv, Con.comapQuotientEquivOfSurj_symm_mk', CommRing.Pic.inv_eq_dual, Fin.coe_cycleRange_of_le, ZSpan.repr_ceil_apply, IsometryEquiv.image_eball, RootPairing.EmbeddedG2.indexEquivAllRoots_symm_apply, finSumNatEquiv_apply_left, toColex_eq_zero, FinEnum.equiv_up, BddOrd.dual_map, WithTop.orderIsoSumLexPUnit_toLex, Affine.Simplex.excenterWeights_reindex, CategoryTheory.LiftLeftAdjoint.constructLeftAdjointEquiv_apply, MeasureTheory.mulEquivHaarChar_smul_map, AddSubmonoid.leftNegEquiv_add, Homeomorph.Set.univ_symm_apply_coe, KaehlerDifferential.linearMapEquivDerivation_apply_apply, ZLattice.comap_equiv_apply, Equiv.Perm.subtypeEquivSubtypePerm_apply_coe, UniformSpace.Completion.mapEquiv_coe, Unitization.cobounded_eq_aux, finSumNatEquiv_symm_apply_add_left, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, CategoryTheory.Limits.IsInitial.to_eq_descCoconeMorphism, Set.Iio_toDual, ofAdd_bot, Metric.Snowflaking.ediam_image_ofSnowflaking, Set.PartiallyWellOrderedOn.imageProdLex, Equiv.piCongrLeft_symm_preimage_univ_pi, SSet.Subcomplex.PairingCore.pairing_p_equivII, UniformFun.isometry_ofFun_continuousMap, DirectSum.addEquivProdDirectSum_symm_apply_toFun, 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, AddEquiv.map_eq_zero_iff, Matrix.linfty_opNNNorm_toMatrix, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerRight, QuadraticAlgebra.equivProd_symm_apply, CategoryTheory.Sheaf.ÎHomEquiv_naturality_left, Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, AddConstEquiv.ext_iff, KaehlerDifferential.tensorKaehlerEquivBase_tmul, Equiv.toHomeomorph_refl, CategoryTheory.Limits.biproduct.matrixEquiv_apply, coe_addEquiv_lpPiLp_symm, Function.update_comp_equiv, Module.Basis.coe_constrL, Subgroup.Commensurable.commensurator_mem_iff, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, ofMul_zpow, ContinuousAffineEquiv.coe_toEquiv, Equiv.Perm.SameCycle.exists_fin_pow_eq, Algebra.GrothendieckGroup.lift_symm_apply, StarMulEquiv.leftInverse_symm, Homeomorph.piSplitAt_symm_apply, DilationEquiv.bijective, MulOpposite.isometry_opLinearEquiv, ContinuousAlgEquiv.toContinuousLinearEquiv_apply, FirstOrder.Language.LEquiv.onSentence_apply, MeasureTheory.distribHaarChar_apply, AddSubgroup.IsComplement.mk''_rightQuotientEquiv, Topology.isGeneratedBy_iff, LinearEquiv.comp_symm_eq, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_apply_f, MulEquiv.prime_iff, ArchimedeanOrder.val_of, ContinuousMultilinearMap.range_toUniformOnFun, Submodule.botEquivPUnit_symm_apply, Equiv.Perm.subtypeCongr.left_apply_subtype, ContinuousLinearMap.IsPositive.conj_adjoint, TensorProduct.map_map_assoc_symm, Subgroup.map_symm_eq_iff_map_eq, algebraMap_galRestrict_apply, Module.Basis.addSubgroupOfClosure_repr_apply, Algebra.traceForm_toMatrix, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, WeakDual.CharacterSpace.homeoEval_naturality, CategoryTheory.Oplax.StrongTrans.Modification.equivOplax_symm_apply, antitone_toDual_comp_iff, DualNumber.lift_inlAlgHom_eps, GrpCat.SurjectiveOfEpiAuxs.g_apply_infinity, ContinuousAlternatingMap.piEquiv_symm_apply, GrpCat.toAddGrp_map, FreeAddMonoid.ofList_vadd, Finset.Colex.toColex_sdiff_lt_toColex_sdiff, Finsupp.sumFinsuppLEquivProdFinsupp_symm_apply, DFinsupp.prod_eq_prod_fintype, ZSpan.volume_fundamentalDomain, Affine.Simplex.median_reindex, Sum.Lex.inl_mono, DyckWord.equivTreesOfNumNodesEq_symm_apply_coe, PartialEquiv.transEquiv_target, OrderMonoidIso.equivLike_inv_eq_symm, val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe, basis_toMatrix_basisFun_mul, Fin.coe_of_injective_castSucc_symm, MvPolynomial.leadingCoeff_esymmAlgHomMonomial, spinGroup.conjAct_smul_Κ_mem_range_Κ, comap_upperCentralSeries, Matrix.toLin_scalar, InfPrime.dual, Pi.ofColex_apply, Matrix.submatrix_id_mul_right, Prod.Lex.sumLexProdLexDistrib_symm_apply, MulChar.equivToUnitHom_symm_coe, exteriorPower.presentation.relationsSolutionEquiv_symm_apply_var, IsometryEquiv.ext_iff, Equiv.Perm.SameCycle.pow_right, WithZero.lift'_coe, Unitary.coe_symm_linearIsometryEquiv_apply, LinearIsometryEquiv.diam_image, GradedTensorProduct.auxEquiv_symm_one, Function.Embedding.optionEmbeddingEquiv_apply_snd_coe, Function.fromTypes_nil_equiv_apply, Sum.Lex.toLexRelIsoLE_coe, WithBot.toDual_map, LinearMap.adjoint_rTensor, GradedTensorProduct.auxEquiv_comm, QuadraticAlgebra.lift_apply_apply, Hamming.ofHamming_sub, Equiv.image_eq_iff_eq, Matrix.reindex_apply, RingEquiv.piEquivPiSubtypeProd_symm_apply, FreeAddMonoid.ofList_map, CategoryTheory.uliftYonedaEquiv_naturality, Equiv.symmEquiv_apply_apply, Function.fromTypes_zero_equiv_symm_apply, ofLex_eq_one, TensorProduct.finsuppLeft_symm_apply_single, Finsupp.linearEquivFunOnFinite_symm_apply, dotProduct_comp_equiv_symm, CategoryTheory.Sieve.overEquiv_symm_iff, toDual_max, Height.mulHeight_comp_equiv, LieModuleEquiv.apply_eq_iff_eq_symm_apply, OrderMonoidIso.val_unitsWithZero_symm_apply, ofMul_pow, NumberField.InfinitePlace.orbitRelEquiv_apply_mk'', LinearEquiv.mul_apply, LinearMap.adjoint_inner_right, Homeomorph.subLeft_symm_apply, OrderIsoClass.toSupBotHomClass, BilinForm.dotProduct_toMatrix_mulVec, LinearEquiv.multilinearMapCongrRight_symm_apply, DirectSum.coe_decompose_mul_of_left_mem_of_le, InnerProductSpace.adjoint_rankOne, DihedralGroup.oddCommuteEquiv_symm_apply, Module.invOn_reflection_of_mapsTo, Homeomorph.smulOfNeZero_apply, CategoryTheory.Iso.trans_conjAut, LinearEquiv.piUnique_symm_apply, ContinuousAddEquiv.surjective, CategoryTheory.Subfunctor.Subpresheaf.IsGeneratedBy.of_equiv, MonoidHom.fiberEquiv_symm_apply, MultilinearMap.coe_currySumEquiv_symm, equivShrink_symm_zero, CategoryTheory.GrothendieckTopology.overEquiv_symm_mem_over, CategoryTheory.conjugateEquiv_counit_symm, RingEquiv.quotientBot_mk, List.formPerm_apply_getElem_zero, IsBot.ofDual, Submonoid.leftInvEquiv_apply, CategoryTheory.Sieve.functorPushforward_over_map, ContinuousMap.homeoFnOfDiscrete_symm_apply, Manifold.IsImmersionAt.writtenInCharts, ProbabilityTheory.isGaussian_map_equiv_iff, Equiv.Perm.sumCongr_apply, surjective_comp, Homeomorph.sumArrowHomeomorphProdArrow_symm_apply, DirectSum.decompose_symm_one, IsCoveringMapOn.comp_homeomorph_iff, LinearEquiv.eq_symm_comp, isMax_ofDual_iff, instDilationClassOfDilationEquivClass, ExteriorAlgebra.Κ_comp_lift, CommRing.Pic.mk_eq_iff, IsTensorProduct.equiv_symm_apply, MeasureTheory.integrable_map_equiv, MonomialOrder.lex_lt_iff_of_unique, TopCat.Sheaf.extend_hom_app, CategoryTheory.Functor.mapBicone_whisker, Finset.Colex.toColex_sdiff_le_toColex_sdiff, toDual_inv, Matrix.toLpLin_one, ofMul_inv, RingEquiv.prodZeroRing_symm_apply, Convex.toWeakSpace_closure, CategoryTheory.OverPresheafAux.YonedaCollection.yonedaEquivFst_eq, MulEquiv.toMonoidWithZeroHom_apply, finsuppTensorFinsupp'_apply_apply, Equiv.sumIsLeft_symm_apply_coe, Pi.mulSingle_comp_equiv, Homeomorph.isSimplyConnected_image, Equiv.sumProdDistrib_symm_apply_right, instNonUnitalAlgHomClassOfNonUnitalAlgEquivClass, Equiv.sumArrowEquivProdArrow_symm_apply_inr, IsEvenlyCovered.homeomorph_comp, SkewMonoidAlgebra.toFinsuppAddEquiv_apply, DFinsupp.colex_lt_iff_of_unique, Fin.appendIsometryOfEq_apply, MultilinearMap.curryFinFinset_symm_apply_piecewise_const, Matrix.natCast_fin_two, RingEquiv.ofBijective_apply, LinearIsometryEquiv.ofTop_symm_apply_coe, MulAutMultiplicative_symm_apply_symm_apply, CategoryTheory.PreGaloisCategory.autIsoFibers_inv_app, FreeAbelianGroup.equivFinsupp_symm_apply, HilbertBasis.hasSum_repr, ModuleCat.homAddEquiv_symm_apply_hom, PiTensorProduct.ofFinsuppEquiv_symm_single_tprod, bddBelow_preimage_toDual, map_inv_le_iff, AddSubmonoid.map_equiv_top, HasFDerivWithinAt.hasGradientWithinAt, MulEquiv.toSingleObjEquiv_unitIso_hom, MulEquiv.strictMono_subsemigroupCongr, Module.Basis.reindexRange_repr_self, UniformFun.tendsto_iff_tendstoUniformly, Real.fourier_comp_linearIsometry, DirectSum.coe_decompose_mul_of_left_mem, Set.Ici_ofDual, LinearMap.isPosSemidef_iff_posSemidef_toMatrix, UniformOnFun.one_apply, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, MonomialOrder.degLex_le_iff, Subring.comap_equiv_eq_map_symm, finCycle_eq_finRotate_iterate, powCoprime_one, LinearEquiv.ofSubmodule'_symm_apply, Equiv.mulEquiv_apply, CategoryTheory.Limits.Fork.IsLimit.homIso_symm_apply, AffineIsometryEquiv.coe_ofEq_apply, PositiveLinearMap.preGNS_inner_def, comap_neg_leftUniformSpace, continuous_ofDual, ofAdd_list_prod, CategoryTheory.Functor.natTransEquiv_symm_apply_app, Matrix.inv_reindex, RingEquiv.zeroRingProd_symm_apply, ContinuousAddEquiv.symm_apply_eq, AddEquiv.coe_prodAssoc, Valuation.IsEquiv.uniformContinuous_equivWithVal, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_symm_apply, Tuple.graphEquivâ_apply, AddEquiv.coprodAssoc_apply_inr, LinearEquiv.surjective, Equiv.eq_preimage_iff_image_eq, Matrix.det_map, Equiv.subtypeEquivRight_apply, Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, WithTop.orderIsoSumLexPUnit_symm_inl, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_fst, CategoryTheory.PreZeroHypercover.reindex_f, MeasureTheory.volume_preserving_piFinSuccAbove, Equiv.Perm.Basis.ofPermHom_apply, TensorProduct.prodLeft_symm_tmul, RootPairing.chainBotCoeff_reflectionPerm_right, Equiv.Perm.IsCycleOn.exists_pow_eq, UniformOnFun.edist_eval_le, RootPairing.Equiv.weightEquiv_apply, optionProdEquiv_mk_some, CommRingCat.HomTopology.precompHomeomorph_apply, DilationEquiv.coe_toEquiv, CategoryTheory.PreZeroHypercover.isoMk_hom_sâ, CategoryTheory.Presheaf.functorEnrichedHomCoyonedaObjEquiv_naturality, MeasurableEquiv.restrict_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_unit, CategoryTheory.Bicategory.conjugateEquiv_comp_id_right_apply, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, AffineEquiv.pointReflection_involutive, MvPolynomial.rename_esymm, SymAlg.sym_injective, LinearEquiv.rTensor_refl_apply, Equiv.tsum_eq, UniformOnFun.postcomp_isUniformInducing, Diffeomorph.coeFn_injective, ofBoolRing_toBoolRing, Topology.WithLowerSet.isLowerSet_toLowerSet_preimage, OrderMonoidIso.coe_mk, Iio_orderDual_def, IsometryEquiv.divRight_apply, toAdd_zpow, TensorAlgebra.lift_Κ_apply, FreeAddMagma.lift_comp_of, Polynomial.degreeLT.addLinearEquiv_apply_snd, KaehlerDifferential.linearMapEquivDerivation_symm_apply, AddSubmonoid.LocalizationMap.addEquivOfAddEquiv_eq_map_apply, AffineEquiv.prodAssoc_apply, Function.Injective.map_swap, SSet.prodStdSimplex.objEquiv_apply_snd, map_eq_top_iff, RingEquiv.map_one, Invertible.mulLeft_apply, starL'_apply, Homeomorph.funUnique_apply, TensorProduct.inner_lid_lid, PiTensorProduct.reindex_trans, WithCStarModule.equiv_neg, Submonoid.val_inv_unitsTypeEquivIsUnitSubmonoid_symm_apply, LinearMap.BilinForm.tensorDistribEquiv_apply, OrderMonoidIso.eq_symm_apply, AddMonoidAlgebra.lift_apply, AddSubgroup.map_equiv_top, RingEquiv.injective, Matrix.eta_fin_two, addMonoidAlgebraEquivDirectSum_symm_apply, ContinuousMap.equivFnOfDiscrete_apply, Finsupp.comp_liftAddHom, Matrix.piLp_ofLp_toEuclideanLin, MulEquiv.coprodPUnit_apply, Nonneg.val_unitsEquivPos_symm_apply_coe, MeasureTheory.Content.is_mul_left_invariant_innerContent, LinearMap.BilinForm.toMatrix_apply, Equiv.biSup_comp, Module.Basis.sumQuot_repr_inl, LinearMap.IsSymmetric.diagonalization_symm_apply, SSet.hoFunctor.unitHomEquiv_eq, Equiv.toEmbedding_apply, AddEquiv.piUnique_symm_apply, Finsupp.sigmaFinsuppEquivPiFinsupp_apply, PiTensorProduct.liftIsometry_tprodL, TopologicalSpace.Closeds.complOrderIso_apply, midpoint_pointReflection_right, LinearEquiv.piUnique_apply, LinearEquiv.sumPiEquivProdPi_apply, Homeomorph.comp_continuousWithinAt_iff, RingEquiv.map_eq_zero_iff, TensorProduct.norm_comm, RootPairing.reflectionPerm_coroot, ContinuousMultilinearMap.ofSubsingleton_symm_apply_apply, LinearEquiv.invFun_eq_symm, CliffordAlgebra.changeFormEquiv_apply, PowerBasis.constr_pow_algebraMap, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, SetTheory.PGame.mul_moveLeft_inr, Order.succ_ofMul, LinearIsometryEquiv.coe_toMeasurableEquiv, lieEquivMatrix'_apply, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, TensorProduct.dualDistribEquivOfBasis_symm_apply, BilinForm.toMatrix_toBilin, CommRing.Pic.mk_eq_self, Equiv.transPartialEquiv_source, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, FreeAddSemigroup.lift_of, HahnSeries.SummableFamily.smul_hsum, Antivary.dual_left, WeakDual.isCompact_closedBall, ContinuousLinearEquiv.bijective, IsLocalizedModule.linearEquiv_apply, LinearIsometryEquiv.image_sphere, SkewPolynomial.Ď_def, Finset.geomSum_ofColex_strictMono, spinGroup.conjAct_smul_range_Κ, AddEquiv.funUnique_apply, Matrix.toPerfectPairing_apply_apply, Matrix.updateRow_reindex, strictMono_comp_ofDual_iff, Topology.IsGeneratedBy.continuous_equiv_symm, Equiv.right_inv', Homeomorph.smul_apply, LinearMap.quotientInfEquivSupQuotient_apply_mk, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, Homeomorph.isPathConnected_image, SpecialLinearGroup.congr_linearEquiv_coe_apply, Metric.Snowflaking.image_ofSnowflaking_ball, IsMax.toDual, CategoryTheory.nerve.homEquiv_comp, LinearIsometryEquiv.nnnorm_map, ConjAct.ofConjAct_zero, InnerProductSpace.toDual_apply, CategoryTheory.nerve.left_edge, MeasurableEquiv.measurableSet_image, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, Homeomorph.comp_isOpenMap_iff, OrthonormalBasis.tensorProduct_repr_tmul_apply', MonoidHom.restrictHomKerEquiv_symm_coe_apply, CategoryTheory.nerve.mkâ_homEquiv_apply, Equiv.swap_comp_apply, Module.DirectLimit.congr_symm_apply_of, monoidEndToAdditive_apply_apply, finRotate_of_lt, Pi.mulSingle_multiplicativeOfAdd_eq, LieDerivation.exp_map_apply, MulEquiv.eq_comp_symm, Finset.map_toDual_max, SubAddAction.ofFixingAddSubgroup_of_eq_bijective, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_left, LinearEquiv.sumArrowLequivProdArrow_symm_apply_inr, finSuccEquiv'_symm_coe_above, Algebra.Generators.cotangentSpaceBasis_repr_tmul, Metric.Snowflaking.isBounded_image_ofSnowflaking_iff, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_left, LinearEquiv.funCongrLeft_apply, CategoryTheory.Limits.FintypeCat.productEquiv_symm_comp_Ď_apply, FreeAddMonoid.toList_of, Equiv.optionSubtype_apply_symm_apply, Equiv.Set.union_apply_left, isRegular_ofAdd, addOrderOf_ofMul_eq_orderOf, ArchimedeanClass.FiniteElement.val_mul, RootPairing.corootSpanMem_reflectionPerm_self, RelIso.relHomCongr_apply, Topology.WithLowerSet.toLowerSet_ofLowerSet, Finset.equivBitIndices_apply, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, WithBot.le_toDual_iff, Complex.equivRealProd_apply_le', Int.toAdd_pow, LinearMap.minpoly_toMatrix', Equiv.cast_eq_iff_heq, AddSubmonoid.closure_singleton_eq, RingEquiv.map_zero, FirstOrder.Language.Equiv.map_constants, AddEquiv.coe_addSubmonoidMap_apply, finsuppEquivDFinsupp_apply, Set.prod_self_eq_iUnion_perm, OrderAddMonoidIso.eq_comp_symm, Homeomorph.prodPUnit_apply, MeasureTheory.Measure.compProd_assoc', Real.fourierInv_comp_linearIsometry, IncidenceAlgebra.mu_ofDual, MulAction.toPerm_symm_apply, DFinsupp.Lex.le_iff_of_unique, ContinuousLinearEquiv.differentiableAt, FreeAlgebra.lift_Κ_apply, IsFreeGroup.lift_of, Interval.dual_top, DomMulAct.mk_smul_toLp, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, LinearMap.liftBaseChangeEquiv_symm_apply, AffineEquiv.coe_homothetyUnitsMulHom_apply_symm, AddEquiv.comp_left_injective, InfHom.dual_symm_apply_toFun, HahnSeries.embDomainOrderEmbedding_apply, Equiv.Perm.perm_mapsTo_inl_iff_mapsTo_inr, CategoryTheory.Localization.Preadditive.homEquiv_apply, MvPolynomial.mapEquiv_apply, iteratedFDerivWithin_eq_equiv_comp, cmp_toDual, RootPairing.RootPositiveForm.isOrthogonal_reflection, List.getEquivOfForallCountEqOne_symm_apply_val, UniformEquiv.image_preimage, WithTop.ofDual_lt_ofDual_iff, FreeAddMonoid.toList_zero, AddCommGrpCat.homAddEquiv_symm_apply_hom, Algebra.TensorProduct.equivFinsuppOfBasis_apply, LinearMap.toMatrixâ_comp, AddEquiv.ofLeftInverse_apply, CategoryTheory.Arrow.equivSigma_apply_fst, CategoryTheory.Functor.map_conj, dist_toAdd, Matrix.l2_opNNNorm_mulVec, MeasureTheory.integrable_comp, IsGreatest.dual, LinearIsometryEquiv.map_eq_iff, MulEquiv.withZero_apply_apply, AlgebraicGeometry.Scheme.coe_homeoOfIso_symm, Con.comapQuotientEquivOfSurj_mk, CategoryTheory.InducedCategory.homEquiv_symm_apply_hom, Matrix.charpoly.univ_coeff_evalâHom, Equiv.image_subset, AddMonoidHom.toMultiplicative_symm_apply_apply, DyckWord.equivTreesOfNumNodesEq_apply_coe, FreeAddMonoid.ofList_cons, Multiset.toFinsupp_inter, Equiv.mulRightâ_apply, Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl, AffineEquiv.coe_constVSub, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_inv_f, Equiv.Perm.sameCycle_zpow_right, PerfectRing.liftEquiv_id_apply, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, isClosedMap_ofAdd, CategoryTheory.Limits.Types.isLimitEquivSections_apply, CategoryTheory.GrothendieckTopology.mem_over_iff, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_pt, MonomialOrder.degree_le_iff, WithAbs.algebraMap_right_apply, TensorProduct.gradedComm_algebraMap, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_one_assoc, CategoryTheory.Limits.WalkingPair.swap_apply_right, AffineEquiv.map_vadd, ContinuousMultilinearMap.prodEquiv_symm_apply_fst, EuclideanGeometry.reflection_reflection, MeasurableEmbedding.equivRange_apply, antitoneOn_toDual_comp_iff, Complex.antilipschitz_equivRealProd, PartENat.withTopEquiv_ofNat, IsometryEquiv.divLeft_symm_apply, AddMonoidHom.coe_toMultiplicativeLeft, Matrix.SeparatingRight.toLinearMapâ', WithBot.toDual_bot, MeasureTheory.measurePreserving_piCongrLeft, Representation.asModuleEquiv_symm_map_smul, GradedAlgebra.proj_recompose, Monoid.CoprodI.lift_mrange_le, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, TensorProduct.norm_assoc, AddMonoidAlgebra.domCongr_single, OrderIso.sumLexIioIci_symm_apply_Iio, CategoryTheory.ProjectiveResolution.extMk_hom, FirstOrder.Language.PartialEquiv.le_iff, LinearEquiv.transvection.apply, DualNumber.lift_smul, Module.Basis.repr_linearCombination, DihedralGroup.oddCommuteEquiv_apply, LieAlgebra.lieCharacterEquivLinearDual_symm_apply, CategoryTheory.Functor.map_conjAut, exteriorPower.presentation.relationsSolutionEquiv_apply_apply, SkewMonoidAlgebra.coeff_equivMapDomain, TensorProduct.assoc_tmul, Equiv.symm_comp_eq, DilationEquiv.ext_iff, Equiv.sigmaEquivProd_symm_apply, Equiv.arrowProdEquivProdArrow_apply, Prod.Lex.le_iff, Equiv.embeddingFinSucc_snd, WittVector.IsocrystalEquiv.frob_equivariant, PiTensorProduct.reindex_tprod, GrpWithZero.Iso.mk_hom, Submodule.mem_iSup_iff_exists_dfinsupp, Subsemiring.centerCongr_apply_coe, MulEquiv.coe_prodAssoc, DomAddAct.symm_mk_neg, CategoryTheory.conjugateEquiv_symm_iso, AddSubgroup.toSubgroup_closure, Algebra.TensorProduct.equivFinsuppOfBasis_symm_apply, QuadraticForm.tensorRId_apply, Equiv.Perm.OnCycleFactors.mem_range_toPermHom'_iff, RingEquiv.map_eq_one_iff, Equiv.Perm.extendDomain_apply_image, BoundedOrderHom.dual_id, MvPolynomial.rTensor_apply_X_tmul, DomMulAct.continuous_mk_symm, HahnSeries.of_symm_smul_of_eq_mul, List.sortedGE_map_ofDual, UniformEquiv.piCongrLeft_symm_apply, IsometryEquiv.instIsometryClass, CategoryTheory.Equivalence.symmEquivFunctor_map, CategoryTheory.Limits.Cofork.IsColimit.homIso_apply_coe, ContinuousAlgEquiv.ext_iff, LinearEquiv.isAdjointPair_symm_iff, Topology.WithScott.ofScott_inj, AddHom.mulOp_apply_apply, MonoidHom.toAdditiveLeft_apply_apply, toBoolAlg_add, LinearMap.prodEquiv_symm_apply, AffineIsometryEquiv.ofTop_symm_apply_coe, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg, InfiniteGalois.mulEquivToLimit_symm_continuous, PiLp.basisFun_repr, AddGroupExtension.Equiv.trans_apply, CategoryTheory.Functor.partialRightAdjointHomEquiv_comp, HahnSeries.SummableFamily.smul_toFun, modularCyclotomicCharacter.toFun_spec, ContinuousLinearMap.adjoint_inner_left, Matrix.toLpLin_pow, AddGroupExtension.Equiv.refl_symm_apply, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, PowerBasis.liftEquiv_symm_apply, KaehlerDifferential.tensorKaehlerEquiv_tmul, Matrix.transpose_empty_cols, CartanMatrix.D_three', AddSubsemigroup.topEquiv_symm_apply_coe, Orientation.oangle_rotation_oangle_right, CongruenceSubgroup.IsArithmetic.conj, isTranscendenceBasis_equiv, Nonneg.val_unitsHomeomorphPos_symm_apply_coe, Module.AEval'.X_pow_smul_of, Set.uIoo_toDual, Homeomorph.isCompact_preimage, AddEquiv.op_symm_apply_symm_apply, Finsupp.domCongr_apply, Rep.toAdditive_symm_apply, Algebra.Generators.H1Cotangent.δAux_toAlgHom, RootPairing.InvariantForm.isOrthogonal_reflection, Matrix.kroneckerAlgEquiv_apply, IsCyclic.val_inv_mulAutMulEquiv_apply, ofColex_mul, LinearEquiv.extendScalarsOfSurjective_apply, Equiv.sigmaFiberEquiv_apply, LinearIsometryEquiv.coe_prodAssoc_symm, TopCat.uliftFunctorObjHomeo_naturality_apply, finSumFinEquiv_apply_right, AlgHom.opComm_apply_apply, CategoryTheory.Adjunction.conjugateEquiv_leftAdjointIdIso_hom, TopCat.homeoOfIso_apply, FiberwiseLinear.trans_openPartialHomeomorph_apply, DomMulAct.isClosedEmbedding_mk, CategoryTheory.Subfunctor.ofSection_eq_range', Homeomorph.isClosed_setOf_iff, Equiv.pointReflection_involutive, AddChar.coe_toAddMonoidHom, Equiv.Perm.IsCycle.pow_eq_one_iff, InnerProductSpace.AlgebraOfCoalgebra.mul_def, LinearMap.BilinForm.separatingRight_toMatrix'_iff, Matrix.isUnit_toLin'_iff, AddAut.coe_mul, AffineIsometryEquiv.coe_inv, NumberField.Units.fundSystem_mk, coe_ringEquiv_lpBCF, Equiv.bijOn_symm_image, HahnEmbedding.IsPartial.truncLT_mem_range, Subsemigroup.topEquiv_toMulHom, AddSubgroup.centerCongr_apply_coe, MeasureTheory.setIntegral_map_equiv, PrimitiveSpectrum.gc_closureOperator, Module.piEquiv_apply_apply, CategoryTheory.Limits.Pi.whiskerEquiv_inv, Equiv.Perm.sign_eq_prod_prod_Iio, Abelianization.coe_lift_symm, OrderAddMonoidIso.coe_addEquiv, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, finSuccEquivLast_castSucc, Finsupp.lift_apply, AddSubmonoid.comap_equiv_eq_map_symm, CategoryTheory.Functor.partialRightAdjointHomEquiv_map, ContinuousMultilinearMap.ofSubsingletonâᾢ_symm_apply, LinearIndependent.linearCombinationEquiv_apply_coe, LinearIsometryEquiv.preimage_ball, Function.Embedding.swap_apply, DomMulAct.smul_mulActionHom_apply, MulEquiv.arrowCongr_apply, FreeGroup.lift_unique, Subgroup.IsComplement.leftCosetEquivalence_equiv_fst, Equiv.Perm.sameCycle_inv_apply_right, NonUnitalAlgHom.prodEquiv_apply, AddEquiv.subsemigroupMap_apply_coe, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, TensorProduct.AlgebraTensorModule.leftComm_tmul, continuousMultilinearCurryFin0_symm_apply, ContinuousLinearEquiv.integrable_comp_iff, CategoryTheory.Limits.biproduct.reindex_inv, WithZero.withZeroUnitsEquiv_symm_strictMono, NonUnitalSubring.topEquiv_apply, Matrix.toLin'_mul, Matrix.of_one_hadamard, InverseSystem.invLimEquiv_apply_coe, OrderHom.symm_dual_id, SupClosed.dual, toLex_ofLex, CategoryTheory.Functor.CorepresentableBy.homEquiv_eq, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_naturality_right, LieEquiv.ext_iff, Cardinal.extend_function_of_lt, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_fst_apply, Submodule.iSup_eq_range_dfinsupp_lsum, ModularGroup.lcRow0Extend_apply, isOfFinOrder_ofAdd_iff, MeasurableEquiv.neg_apply, Equiv.pprodEquivProdPLift_apply, TensorProduct.gradedComm_tmul_of_zero, LinearMap.isNilpotent_toMatrix_iff, MulEquiv.coprodAssoc_apply_inl_inl, Monoid.CoprodI.range_eq_iSup, Metric.Snowflaking.image_ofSnowflaking_eq_preimage, ContinuousLinearEquiv.symm_smul_apply, SupHom.dual_comp, Equiv.sumCompl_apply_inl, TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply, LinearMap.BilinForm.dotProduct_toMatrix_mulVec, RingEquiv.toCommRingCatIso_inv, supIrred_toDual, Monoid.PushoutI.NormalWord.cons_head, Submonoid.leftInvEquiv_mul, ContinuousAlternatingMap.ofSubsingletonLIE_apply, Set.up_mul, LinearMap.det_eq_det_toMatrix_of_finset, Homeomorph.piEquivPiSubtypeProd_apply, RingEquiv.toAddMonoidMom_commutes, ContinuousAlgEquiv.continuousWithinAt, MulEquiv.restrictRootsOfUnity_coe_apply, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, LinearMap.toMatrix_reindexRange, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, MeasurableEquiv.measurable_toFun, Equiv.symm_apply_eq, FractionalIdeal.canonicalEquiv_mk0, AddMagma.FreeAddSemigroup.lift_comp_of', List.formPerm_apply_getElem, SemilinearEquivClass.instSemilinearMapClass, CategoryTheory.Limits.IsLimit.homEquiv_symm_Ď_app, even_toAdd_iff, Abelianization.lift_apply_of, IsometryEquiv.preimage_closedEBall, CategoryTheory.Limits.idZeroEquivIsoZero_apply_inv, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, Multiset.toFinsupp_apply, toMul_zero, CoalgEquiv.trans_apply, Matrix.isUnit_submatrix_equiv, IsCoveringMapOn.comp_homeomorph, CategoryTheory.PreGaloisCategory.toAutHomeo_apply, MulEquiv.prodUnique_symm_apply, Diffeomorph.sumComm_coe, CategoryTheory.Localization.SmallHom.equiv_mkInv, CategoryTheory.ComposableArrows.opEquivalence_functor_obj_map, AddEquiv.neg'_apply, Equiv.subtypePreimage_apply, Matrix.submatrix_updateCol_equiv, OrderIso.sumDualDistrib_symm_inl, CStarMatrix.of_sub_of, finSuccAboveEquiv_symm_apply_ne_last, CommAlgCat.isoEquivAlgEquiv_apply, Normal.algHomEquivAut_apply, ContinuousAlgEquiv.isOpenMap, Diffeomorph.coe_trans, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, CommRing.Pic.mapAlgebra_apply, Quiver.SingleObj.toPrefunctor_comp, LinearMap.IsReflective.reflective_reflection, NonUnitalAlgHom.prodEquiv_symm_apply, CategoryTheory.PreZeroHypercover.reindex_X, finRotate_apply_zero, Matrix.ofLp_toLpLin, Localization.mulEquivOfQuotient_mk, Pi.single_additiveOfMul_eq, AffineIsometryEquiv.continuous, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, TensorPower.galgebra_toFun_def, CategoryTheory.Adjunction.homAddEquiv_sub, FreeGroup.injective_lift_of_ping_pong, ContinuousLinearMap.equivRange_symm_apply, CategoryTheory.tensorLeftHomEquiv_tensor, OrderMonoidIso.withZero_apply_symm_apply, LinearIsometryEquiv.congr_arg, Module.range_piEquiv, LinearEquiv.cast_apply, Equiv.finsuppUnique_apply, SSet.Subcomplex.yonedaEquiv_coe, finAddFlip_apply_mk_right, AlgebraicGeometry.Scheme.homeoOfIso_apply, MeasureTheory.measurePreserving_arrowProdEquivProdArrow, affineHomeomorph_image_I, Ideal.mem_map_of_equiv, Equiv.pnatEquivNat_symm_apply, CommRing.Pic.ext_iff, FreeAddMonoid.toList_add, List.formPerm_apply_getElem_length, StarModule.decomposeProdAdjoint_symm_apply, Module.Basis.dualBasis_equivFun, AffineEquiv.map_midpoint, MulAction.stabilizerEquivStabilizer_apply, Equiv.zero_def, AddCircle.equivAddCircle_apply_mk, MulEquiv.coe_prodComm_symm, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, ofDual_compares_ofDual, isAddRightRegular_ofDual, Subgroup.IsComplement.equiv_fst_eq_self_of_mem_of_one_mem, WithTop.toDual_lt_iff, CategoryTheory.Abelian.Ext.homEquiv_chgUniv, ModularGroup.coe_T_inv, Unitization.starLift_range, ofBoolAlg_sup, associatesNonZeroDivisorsEquiv_mk_mk, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, OrderDual.ext_iff, RingEquiv.moduleEndSelfOp_apply, IsPrimitiveRoot.primitiveRootsPowEquiv_symm_apply_coe, Rep.ofMulDistribMulAction_Ď_apply_apply, SSet.OneTruncationâ.ofNerveâ.natIso_hom_app_obj, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, WithZeroMulInt.toNNReal_neg_apply, Set.Finite.equiv_image_eq_iff_subset, LinearMap.toMatrix_smulBasis_left, AdjoinRoot.quotEquivQuotMap_apply, CategoryTheory.enrichedFunctorTypeEquivFunctor_symm_apply_obj, Module.Basis.coe_toOrthonormalBasis_repr_symm, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_assoc, DomAddAct.symm_mk_add, toMul_add, CategoryTheory.CatEnrichedOrdinary.Hom.mk_comp, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_fst, ContinuousAddEquiv.eq_symm_comp, isClosedMap_toDual, CategoryTheory.FinCategory.asTypeToObjAsType_obj, sigmaFinsuppEquivDFinsupp_symm_apply, OrderMonoidIso.symm_comp_eq, toMul_sum, CategoryTheory.Sieve.overEquiv_top, AffineEquiv.coeFn_inj, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map, TensorProduct.congr_tmul, CategoryTheory.Limits.CofanTypes.equivOfIsColimit_symm_apply, ContinuousMap.addUnitsLift_apply_neg_apply, apply_eq_iff_eq, IsAzumaya.mulLeftRight_comp_congr, NumberField.IsCMField.equivInfinitePlace_apply, LinearMap.BilinForm.isSymm_iff_flip, HahnSeries.order_abs, OrderAddMonoidIso.coe_mk, FreeMonoid.ofList_toList, LieAlgebra.Extension.ringModuleOf_bracket, optionProdEquiv_symm_inl, Set.opEquiv_self_symm_apply_coe, Equiv.Perm.viaFintypeEmbedding_apply_image, Subgroup.mem_toAddSubgroup', Diffeomorph.isLocalDiffeomorph, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, isClosedMap_ofMul, Delone.DeloneSet.mapIsometry_symm_apply_coveringRadius, RelIso.compl_apply, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_three, DilationEquiv.mulRight_symm_apply, InnerProductSpace.toDual_apply_apply, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, ofColex_eq_zero, OrderMonoidIso.coe_orderIso, AddEquiv.finsuppUnique_apply, ContinuousLinearMap.adjointAux_apply, MultilinearMap.fromDFinsuppEquiv_single, isHomeomorph_iff_exists_homeomorph, MulEquiv.map_inv, SheafOfModules.freeHomEquiv_symm_comp, Orientation.inner_rotation_pi_div_two_right, coe_lpBCFâᾢ, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, LinearMap.det_toLin', AddSubsemigroup.centerCongr_apply_coe, MulEquiv.isUnit_map, CategoryTheory.CosimplicialObject.cechConerveEquiv_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality', SetTheory.PGame.relabel_moveLeft, WithZero.unitsWithZeroEquiv_symm_apply, Equiv.symm_trans_apply, CategoryTheory.Iso.homCongr_refl, OrderIso.equivClosureOperator_apply, ValuationSubring.coe_unitGroupMulEquiv_apply, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_uliftYoneda_map, DirectSum.coe_congr_linearEquiv, minimal_toDual, EuclideanGeometry.reflection_eq_self_iff, AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply, TensorAlgebra.lift_comp_Κ, RingEquiv.congr_arg, Matrix.submatrix_mulVec_equiv, LinearIsometryEquiv.comp_differentiableOn_iff, LinearIsometryEquiv.comp_differentiableAt_iff, disjoint_ofDual_iff, ContinuousMap.val_unitsLift_symm_apply_apply, CategoryTheory.Functor.RepresentableBy.equivOfIsoObj_symm_apply, coe_toLexLinearEquiv, Nat.ofAdd_mul, Nat.Primes.prodNatEquiv_apply, ofAdd_image_zmultiples_eq_zpowers_ofAdd, Representation.norm_ofMulDistribMulAction_eq, ContinuousAddEquiv.symm_comp_self, toLex_add, CategoryTheory.HomOrthogonal.equiv_of_iso, AffineIsometryEquiv.pointReflection_fixed_iff, Subgroup.smul_apply_eq_smul_apply_inv_smul, AddSubmonoid.toSubmonoid_closure, MeasurableEquiv.map_apply_eq_iff_map_symm_apply_eq, CategoryTheory.FunctorToTypes.binaryProductEquiv_symm_apply, LinearMap.SeparatingRight.congr, LinearEquiv.symm_apply_apply, Equiv.psigmaCongrRight_apply, Matrix.rank_eq_finrank_range_toLin, MvPolynomial.rTensor_apply_tmul, Equiv.Perm.closure_cycle_coprime_swap, ContinuousAlternatingMap.norm_ofSubsingleton, toDual_intCast, Matrix.toLinearMapRight'_mul_apply, RootPairing.Equiv.comp_indexEquiv_apply, Subgroup.subgroupOfEquivOfLe_symm_apply_coe_coe, MeasurableEquiv.coe_toLp, CategoryTheory.GradedObject.comapEquiv_unitIso, PerfectRing.liftEquiv_apply, Equiv.Perm.Disjoint.mul_apply_eq_iff, Diffeomorph.mfderivToContinuousLinearEquiv_coe, BilinForm.toMatrix_comp, ProbabilityTheory.Kernel.partialTraj_le_def, CommRing.Pic.instFreeAsModuleOfNat, AddSubgroup.map_equiv_eq_comap_symm, Homeomorph.comp_continuous_iff', Orientation.oangle_rotation, CharacterModule.intSpanEquivQuotAddOrderOf_apply, ContinuousLinearEquiv.injective, isRightRegular_toColex, Matrix.reindexLinearEquiv_one, Equiv.Perm.prodExtendRight_apply_eq, Subring.centerToMulOpposite_symm_apply_coe, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, Valuation.ofAddValuation_apply, ContinuousLinearMap.coe_flipâᾢ', RingEquiv.toRingCatIso_hom, Complex.preimage_equivRealProd_prod, SimpleGraph.Walk.IsHamiltonian.getVertEquiv_symm_apply, Module.Relations.Solution.directSumEquiv_symm_apply_var, FreeGroup.lift_symm_apply, AddSubgroup.range_zmultiplesHom, Equiv.permCongr_trans, DilationEquiv.symm_apply_apply, PiTensorProduct.norm_eval_le_injectiveSeminorm, FiniteDimensional.basisSingleton_repr_apply, Diffeomorph.sumComm_inr, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mkâ_f_comp_biprodAddEquiv_symm_biprodIsoProd_hom, autEquivZmod_symm_apply_intCast, PointwiseConvergenceCLM.equivWeakDual_apply, Subalgebra.linearEquivOp_apply_coe, Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero, ConjAct.units_smul_def, AddConstEquiv.coe_symm_toEquiv, Subsemiring.mem_map_equiv, AffineEquiv.val_equivUnitsAffineMap_apply, BoundedOrderHom.symm_dual_comp, Equiv.piCongrLeft_symm_preimage_pi, toMul_sub, FreeAddGroup.closure_eq_range, Matrix.toLin_mul, Finset.mapRange_finsuppAntidiag_eq, TensorProduct.AlgebraTensorModule.assoc_tmul, Set.graphOn_prod_graphOn, MonoidHom.toMulEquiv_symm_apply, Set.dual_ordConnected, Matrix.of_zero, CategoryTheory.PreGaloisCategory.toAutMulEquiv_apply, Rep.indResAdjunction_counit_app_hom_hom, QuaternionAlgebra.coe_addEquivProd, toDual_mul, RingEquiv.coe_toAddEquiv, zmultiplesHom_ker_eq, AddAction.stabilizerEquivStabilizer_symm_apply, Real.sinhEquiv_symm_apply, MulOpposite.coe_symm_opMulEquiv, Matrix.toLin_pow, MeasureTheory.volume_preserving_pi_empty, Submodule.coe_tensorSpanEquivSpan_apply_tmul, Module.Basis.equivFunL_symm_apply_repr, SetTheory.PGame.moveRight_nim, associatesNonZeroDivisorsEquiv_symm_mk_mk, DilationEquiv.mulLeft_symm_apply, Rack.act'_apply, IsometryEquiv.mulLeft_apply, Finsupp.prod_equivMapDomain, Submodule.FG.lTensor.directLimit_apply', TensorProduct.directSumLeft_tmul_lof, CartanMatrix.B_two, IsometryEquiv.map_midpoint, OrthonormalBasis.repr_apply_apply, IsGalois.normalAutEquivQuotient_apply, Subgroup.IsComplement.equiv_fst_eq_one_of_mem_of_one_mem, PowerBasis.repr_gen_pow_isIntegral, AddCon.comap_conGen_equiv, IsometryEquiv.addLeft_apply, FreeMonoid.toList_of, Module.Basis.det_reindex_symm, LinearEquiv.trans_apply, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow', Sequential.isoOfHomeo_inv, sSupHom.dual_symm_apply_toFun, Matrix.toLin_self, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, isAddLeftRegular_toLex, AddCircle.continuous_equivIoc_symm, Orientation.inner_rotation_pi_div_two_left, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, ContinuousMap.toLp_def, Finsupp.equivFunOnFinite_symm_apply_support, kroneckerTMulLinearEquiv_one, CategoryTheory.uliftYonedaEquiv_comp, AffineIsometryEquiv.apply_symm_apply, cmpLE_ofDual, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, Quiver.SingleObj.pathEquivList_symm_cons, Fin.cycleIcc_to_cycleRange, CochainComplex.HomComplex.CohomologyClass.equivOfIsKInjective_symm_apply, AlternatingMap.ofSubsingleton_apply_apply, SSet.stdSimplex.face_obj, LieEquiv.ofEq_apply, TensorProduct.AlgebraTensorModule.leftComm_symm_tmul, DomAddAct.mk_zsmul, Subsemigroup.toAddSubsemigroup_closure, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, ZMod.ringEquivCongr_refl_apply, Module.DirectLimit.linearEquiv_of, Equiv.Set.univPi_symm_apply_coe, finCongr_apply_coe, monotone_toDual_comp_iff, OrderMonoidHom.inrâ_apply, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, ofLex_neg, Orientation.oangle_rotation_self_left, CategoryTheory.Functor.sectionsEquivHom_naturality, Finsupp.lsum_single, TopCat.isoOfHomeo_hom, ContinuousLinearEquiv.contDiffPointwiseHolderAt, Set.Finite.subtypeEquivToFinset_apply_coe, CategoryTheory.evalEquiv_apply, MeasureTheory.Measure.IsFiniteMeasureOnCompacts.comap, AffineEquiv.apply_symm_apply, PositiveLinearMap.toPreGNS_ofPreGNS, MeasureTheory.diracProba_comp_diracProbaEquiv_symm_eq_val, MulEquiv.val_inv_piUnits_apply, ContinuousMultilinearMap.prodL_apply, LinearMap.BilinForm.sum_repr_mul_repr_mul, Finsupp.linearEquivFunOnFinite_single, Module.Basis.mulOpposite_repr_op, TensorProduct.AlgebraTensorModule.rightComm_tmul, QuadraticForm.dualProdIsometry_invFun, Homeomorph.comp_continuousAt_iff', CategoryTheory.Limits.IsLimit.equivIsoLimit_symm_apply, strictAnti_toDual_comp_iff, AffineBasis.basisOf_reindex, Real.sinhEquiv_apply, FintypeCat.equivEquivIso_apply_inv, finSumFinEquiv_symm_apply_castAdd, LinearMap.separatingLeft_toMatrixâ'_iff, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, Module.Basis.smulTower'_repr_mk, sInfHom.dual_apply_toFun, hasFTaylorSeriesUpToOn_succ_iff_right, AlgebraicGeometry.Scheme.Pullback.carrierEquiv_symm_snd, Equiv.sigmaUnique_apply, ContinuousMulEquiv.symm_trans_apply, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, derangements.Equiv.RemoveNone.mem_fiber, MonoidHom.coe_toAdditive_map, ContinuousAlgEquiv.comp_continuous_iff, AddEquiv.entryAddHom_comp_mapMatrix, AffineIsometryEquiv.dist_pointReflection_self, AlgEquiv.opComm_apply_apply, IsPGroup.powEquiv_apply, CategoryTheory.Adjunction.restrictFullyFaithful_homEquiv_apply, Equiv.plift_symm_apply, LinearEquiv.map_smulââ, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, Fin.snoc_eq_cons_rotate, SSet.stdSimplex.map_apply, Equiv.Perm.cycleOf_apply_apply_self, ofLex_natCast, QuaternionAlgebra.lift_apply, MulEquiv.apply_eq_iff_symm_apply, DFA.reindex_refl, MonomialOrder.degree_sum_le, AddCon.comapQuotientEquivOfSurj_symm_mk, MulOpposite.opContinuousLinearEquiv_symm_apply, TensorProduct.AlgebraTensorModule.assoc_symm_tmul, Subring.topEquiv_apply, AffineIsometryEquiv.dist_pointReflection_self_real, AddLocalization.addEquivOfQuotient_mk', RingEquiv.subsemiringMap_apply_coe, toAdd_pow, Matrix.comp_toSquareBlock, Interval.dual_bot, AddEquiv.symmEquiv_apply_symm_apply, Equiv.Perm.cycleOf_self_apply_pow, hasEigenvector_toLin'_diagonal, Pi.lex_desc, CategoryTheory.SingleObj.toEnd_def, AlgEquivClass.toAlgHomClass, Matrix.GeneralLinearGroup.toLin'_apply, CovBy.toDual, MeasurableEquiv.ext_iff, toColex_one, CategoryTheory.CartesianClosed.homEquiv_symm_apply_eq, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, LinearIsometryEquiv.coe_toIsometryEquiv, CategoryTheory.conjugateEquiv_whiskerRight, DomMulAct.smul_aeeqFun_aeeq, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, NonemptyInterval.dual_mapâ, IsFreeGroup.toFreeGroup_symm_apply, CongruenceSubgroup.isArithmetic_conj_SL2Z, Submodule.FG.rTensor.directLimit_apply, UniformEquiv.coe_prodComm, ofColex_inv, Equiv.sumIsLeft_apply, MeasureTheory.integral_map_equiv, TensorProduct.directLimitLeft_rTensor_of, Equiv.swap_apply_def, Equiv.Perm.cycleOf_apply_apply_zpow_self, OrderAddMonoidIso.self_comp_symm, NonUnitalRingHom.op_symm_apply_apply, TensorProduct.finsuppScalarRight_smul, InfHom.dual_comp, DFinsupp.Colex.le_iff_of_unique, RingEquiv.coe_mk, CategoryTheory.bijection_symm_apply_id, nhds_toAdd, Antivary.sum_smul_lt_sum_comp_perm_smul_iff, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, HNNExtension.NormalWord.unitsSMulGroup_snd, ofDual_sInf, Equiv.Set.rangeInr_apply_inr, QuotientGroup.quotientKerEquivOfRightInverse_symm_apply, AlgebraicGeometry.ÎSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, ContinuousMulEquiv.invFun_eq_symm, Sum.Lex.toLex_le_toLex, Matrix.reindexLinearEquiv_comp, isLocalHom_equiv, Submonoid.unitsTypeEquivIsUnitSubmonoid_apply_coe, Orientation.map_eq_det_inv_smul, ProbabilityTheory.Kernel.prodAssoc_symm_prod, Equiv.instAssociativeCoeForallForallArrowCongr, TensorProduct.lid_symm_apply, Specialization.toEquiv_le_toEquiv, Metric.Snowflaking.image_ofSnowflaking_closedEBall, SSet.Κâ_snd, IsFractionRing.ringEquivOfRingEquiv_algebraMap, ComplexShape.symmetryEquiv_apply_coe, IsTensorProduct.equiv_apply, Unitary.mapEquiv_apply, Matrix.toLinearMapâââ'_toMatrix', Homeomorph.coe_inv, BialgEquiv.trans_apply, LieEquiv.trans_apply, LinearMap.toMatrix'_algebraMap, WithZero.toMulBot_lt, ComplexShape.symmetryEquiv_symm_apply_coe, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, Matrix.cramer_reindex, Algebra.IsAlgebraic.algHomEquivAlgHomOfSplits_apply_apply, Subgroup.IsComplement.equiv_snd_eq_self_of_mem_of_one_mem, Sym.equivCongr_apply, Rep.resIndAdjunction_homEquiv_symm_apply, Equiv.Perm.ext_iff, Finset.toDual_inf', finsuppTensorFinsupp_single, DirectSum.decompose_mul_add_left, PiTensorProduct.liftEquiv_symm_apply, AddUnits.addRight_apply, dist_right_pointReflection, LocalizedModule.coe_map_eq, CategoryTheory.Localization.homEquiv_comp, LinearIsometryEquiv.piLpCurry_apply, Equiv.piFinsetUnion_right, Metric.Snowflaking.preimage_toSnowflaking_closedBall, Subgroup.quotientEquivProdOfLE_symm_apply, OrderIso.conj_apply, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, DomMulAct.isQuotientMap_mk_symm, RootPairing.pairingIn_reflectionPerm_self_left, HNNExtension.NormalWord.unitsSMul_one_group_smul, Homeomorph.preimage_symm, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, DilationEquiv.mulLeft_apply, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp, QuadraticMap.IsometryEquiv.map_app, CategoryTheory.ShortComplex.Homotopy.equivSubZero_symm_apply, RootPairing.bijOn_reflection_root, ContinuousLinearEquiv.prodComm_apply, CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp, Module.Basis.equiv'_symm_apply, MvPolynomial.isEmptyRingEquiv_symm_apply, TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage, Equiv.punitProd_apply, MonoidAlgebra.lift_apply', LinearIsometryEquiv.coe_ofLinearIsometry, toLex_pow, RingQuot.eq_lift_comp_mkRingHom, SymAlg.sym_inv, Matrix.adjugate_fin_three_of, Antivary.sum_smul_le_sum_smul_comp_perm, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_inv, LinearMap.IsReflective.isOrthogonal_reflection, Subring.mopRingEquivOp_symm_apply, CategoryTheory.ParametrizedAdjunction.inr_arrowHomEquiv_symm_apply_left_assoc, Diffeomorph.uniqueMDiffOn_image, MeasurableEquiv.comap_symm, equicontinuousOn_iff_continuousOn, SSet.StrictSegal.spineInjective, AddEquiv.map_finsum_mem, ContinuousMap.sigmaEquiv_symm_apply, Module.Basis.repr_reindex, BilinearForm.toMatrixAux_eq, AddMonoid.IsTorsion.torsionAddEquiv_symm_apply_coe, coe_ofLexMulEquiv, SymAlg.sym_unsym, AddEquiv.add_submonoid_map_symm_apply, TensorProduct.lid_tmul, Abelianization.lift_of_comp, RootPairing.rootForm_reflection_reflection_apply, NonUnitalSubsemiring.map_equiv_eq_comap_symm, MvPolynomial.renameEquiv_apply, toDual_compl, CategoryTheory.ProjectiveResolution.of_def, Polynomial.opRingEquiv_op_X, ArchimedeanClass.FiniteElement.val_sub, MonoidHom.fiberEquivKer_apply, Finsupp.DegLex.single_antitone, Subsemiring.centerToMulOpposite_symm_apply_coe, OrderRingIso.trans_apply, Finsupp.Lex.single_lt_iff, PerfectRing.liftEquiv_symm_apply, Primrec.of_equiv, Matrix.SeparatingLeft.toBilin, NumberField.mixedEmbedding.volume_preserving_negAt, WithCStarModule.equiv_symm_smul, FreeNonUnitalNonAssocAlgebra.lift_symm_apply, FreeSemigroup.lift_symm_apply, UniformEquiv.apply_symm_apply, Matrix.charpoly_toLin, Module.subsingletonEquiv_symm_apply, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_apply_homEquiv, Equiv.pow_def, IsometryEquiv.coe_withLpProdUnique, UniformOnFun.lipschitzWith_iff, LinearEquiv.extendScalarsOfIsLocalization_symm_apply, Equiv.prodCongr_apply, LinearEquiv.congrLeft_apply, OrderDual.toDual_lt_toDual, Equiv.Perm.preimage_inv, toBoolAlg_add_add_mul, AddHom.op_symm_apply_apply, Equiv.Perm.sameCycle_apply_left, Homeomorph.divRight_symm_apply, Module.Basis.algebraMapCoeffs_repr_apply_toFun, ofMul_image_powers_eq_multiples_ofMul, TruncatedWittVector.commutes_symm', QuadraticForm.tmul_tensorAssoc_apply, CategoryTheory.mateEquiv_hcomp, SemilinearIsometryEquivClass.toSemilinearIsometryClass, Equiv.image_compl, ContinuousAlgEquiv.image_closure, Topology.WithUpperSet.isUpperSet_toUpperSet_preimage, Valuation.toAddValuation_apply, RingEquiv.invFun_eq_symm, Shrink.ext_iff, Equiv.subtypeEquivRight_symm_apply, CategoryTheory.Functor.curryingEquiv_apply_obj, CategoryTheory.Sieve.overEquiv_symm_pullback, LinearEquiv.piRing_symm_apply, Module.DirectLimit.congr_apply_of, DomAddAct.comap_mk.symm_nhds, PEquiv.toMatrix_toPEquiv_mul, FreeAddGroup.lift_of_eq_id, CategoryTheory.yonedaEquiv_yoneda_map, CliffordAlgebra.even.lift_Κ, Matrix.reindex_isTotallyUnimodular, OrthonormalBasis.reindex_apply, Fin.insertNthEquiv_symm_apply, LinearMap.toMatrix_mulVec_repr, LinearMap.toMatrix_innerââ_apply, TensorProduct.piRight_symm_apply, Algebra.embeddingsMatrixReindex_eq_vandermonde, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem_ne, Tuple.self_comp_sort, Equiv.Perm.cycleOf_apply_of_not_sameCycle, CompleteOrthogonalIdempotents.equiv, Quaternion.equivProd_apply, OrderMonoidHom.inlâ_mul_inrâ_eq_toLex, isClosedMap_toAdd, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeasureTheory.Measure.infinitePiNat_map_piCongrLeft, AddSubmonoid.map_coe_toAddEquiv, toLex_ratCast, RingEquiv.piEquivPiSubtypeProd_apply, Equiv.mul_swap_eq_swap_mul, Zsqrtd.lift_symm_apply_coe, PointwiseConvergenceCLM.equivWeakDual_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, Algebra.adjoin_range_eq_range_freeAlgebra_lift, Orientation.rightAngleRotation_map', TensorProduct.gradedComm_one, AddSubmonoid.val_addUnitsTypeEquivIsAddUnitAddSubmonoid_symm_apply, CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc, SemilatSupCat.dual_map, MulEquiv.self_comp_symm, RingEquiv.map_add, NumberField.mixedEmbedding.negAt_apply_isComplex, Finsupp.snd_sumFinsuppAddEquivProdFinsupp, Equiv.Finset.union_symm_left, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, Matrix.toLin_apply_eq_zero_iff, WithZero.lift_coe, Matrix.kroneckerMap_reindex_left, Orientation.inner_rotation_pi_div_two_left_smul, RingEquiv.toCommRingCatIso_hom, Finset.Colex.ofColex_top, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, MulEquiv.coprodAssoc_apply_inl_inr, RootPairing.flipEquiv_symm_apply, CategoryTheory.Iso.ringCatIsoToRingEquiv_toRingHom, IsLocalizedModule.mapEquiv_apply, genericPoints.equiv_apply, Equiv.prodComm_apply, SemidirectProduct.congr'_apply_left, Submodule.span_image_linearEquiv, lipschitzOnWith_cfc_fun, MeasureTheory.measurePreserving_piFinTwo, AddEquiv.mapAddSubgroup_symm_apply, CategoryTheory.unit_conjugateEquiv_symm, MeasurableEquiv.curry_symm_apply, CategoryTheory.CatEnrichedOrdinary.Hom.id_eq, Additive.toMul_lt, Matrix.nondegenerate_toBilin_iff, ManyOneEquiv.of_equiv, CategoryTheory.Limits.opCompYonedaSectionsEquiv_apply_app, Equiv.addRight_symm_apply, Subgroup.coe_toAddSubgroup_symm_apply, Equiv.Set.sumCompl_symm_apply_of_mem, LinearMap.range_toContinuousLinearMap, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_symm_apply, Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe, WithCStarModule.linearEquiv_apply, ZMod.lift_castAddHom, Polynomial.mkDerivationEquiv_symm_apply, Finset.ofDual_sup', MonoidAlgebra.opRingEquiv_symm_single, Equiv.subtypeQuotientEquivQuotientSubtype_mk, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, Fin.cons_apply_cycleRange, LinearIsometryEquiv.image_ball, ContinuousLinearEquiv.dimH_image, CoalgEquiv.coe_coe, CoxeterSystem.rightInvSeq_concat, Nat.divModEquiv_symm_apply, Matrix.toLin'_reindex, HahnModule.coeff_smul_order_add_order, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, HahnModule.of_symm_smul, OrderIsoClass.toTopHomClass, Complex.equivRealProdAddHom_symm_apply_re, CategoryTheory.Discrete.equivalence_functor, ProbabilityTheory.Kernel.prodAssoc_prod, LinearMap.BilinForm.toDual_def, MulEquiv.symm_apply_eq, Module.Relations.Solution.IsPresentation.uniq_var, toEmbeddingLike, IsMaxOn.dual, MulEquiv.toSingleObjEquiv_counitIso_hom, IsLocalization.ringEquivOfRingEquiv_eq_map, CommRingCat.HomTopology.precompHomeomorph_symm_apply, Subgroup.IsComplement.equiv_snd_eq_one_of_mem_of_one_mem, WithLp.prodContinuousLinearEquiv_symm_apply_ofLp, MulAut.coe_mul, ContinuousLinearEquiv.finTwoArrow_apply, Module.Basis.algebraMapCoeffs_repr_apply_apply, CategoryTheory.unit_conjugateEquiv, LinearEquiv.ofInjective_apply, Matrix.PosSemidef.toLinearMapâ'_zero_iff, MultilinearMap.domDomCongrLinearEquiv_apply, sSupHom.dual_apply_toFun, LinearMap.BilinForm.toMatrix'_compLeft, PreTilt.coeff_iterate_frobeniusEquiv_symm, Matrix.toLinearMapâââ_apply, Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg, coe_symm_apply_apply, Matrix.mul_mul_right, isClosedMap_ofDual, AddEquiv.arrowCongr_apply, MultilinearMap.freeDFinsuppEquiv_single, DomAddAct.symm_mk_zsmul, IsLocalRing.ResidueField.mapEquiv_apply, Monoid.PushoutI.homEquiv_symm_apply, PNat.equivNonZeroDivisorsNat_symm_apply_coe, Sum.Lex.toLexRelIsoLE_symm_coe, equivShrink_symm_top, Equiv.Set.sumCompl_symm_apply, LieEquiv.ofSubalgebras_apply, WeakDual.isSeqCompact_closedBall, LinearMap.BilinForm.dualBasis_repr_apply, PiTensorProduct.liftEquiv_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_counit_app_right, DomMulAct.mk_smul_indicatorConstLp, DoubleQuot.coe_quotQuotEquivQuotSupâ, CategoryTheory.Groupoid.isoEquivHom_apply, CategoryTheory.Enriched.FunctorCategory.homEquiv_id, Equiv.addEquiv_apply, DFinsupp.Colex.lt_iff, Ideal.quotientMulEquivQuotientProd_snd, AddEquiv.coprodPUnit_apply, toLex_intCast, AddMonoidHom.ofLeftInverse_apply, PartENat.withTopEquiv_symm_ofNat, CategoryTheory.Groupoid.isoEquivHom_symm_apply_hom, MulEquiv.withOneCongr_apply, fderivWithin_iteratedFDerivWithin, LinearEquiv.ofBijective_apply, UniformOnFun.continuous_rng_iff, Diffeomorph.contMDiffAt_diffeomorph_comp_iff, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, AlgebraicGeometry.affineOpensRestrict_apply_coe_coe, AddMonoidAlgebra.commRingEquiv_single_single, Topology.WithScott.isOpen_iff_isUpperSet_and_scottHausdorff_open', Complex.equivRealProdAddHom_symm_apply_im, Orientation.eq_rotation_self_iff, ofDegLex_inj, GenLoop.toLoop_apply, HasCompactMulSupport.comp_homeomorph, MulEquiv.coe_toMonoidHom, HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff, CategoryTheory.GrothendieckTopology.map_yonedaEquiv', ContinuousMultilinearMap.piLinearEquiv_apply, FreeAddMonoid.ofList_nil, Prod.Lex.sumLexProdLexDistrib_apply, Subsemiring.addEquivOp_symm_apply_coe, Complex.selfAdjointEquiv_apply, CategoryTheory.FunctorToTypes.shrink_map, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_Ď, CategoryTheory.LocallyDiscrete.locallyDiscreteEquiv_symm_apply_as, LinearMap.isSelfAdjoint_iff', Matrix.ofNat_fin_three, LinearIsometryEquiv.piLpCongrRight_single, FreeAddMonoid.toList_map, finSuccEquiv'_at, Equiv.sumPiEquivProdPi_symm_preimage_univ_pi, Orientation.areaForm'_apply, Submodule.comap_equiv_self_of_inj_of_le_apply, Function.Embedding.congr_apply, Matrix.comp_apply, WithOne.lift_one, CategoryTheory.EnrichedOrdinaryCategory.homEquiv_id, pinGroup.conjAct_smul_Κ_mem_range_Κ, Monotone.dual_left, Equiv.psigmaEquivSigma_apply, DirectSum.linearEquivFunOnFintype_lof, CategoryTheory.Localization.homEquiv_symm_apply, SimpleGraph.incidenceSetEquivNeighborSet_symm_apply_coe, CategoryTheory.ObjectProperty.galoisConnection_isColocal, ZMod.lift_comp_coe, Module.Basis.sumQuot_repr_inl_of_mem, Module.Basis.end_apply, Rep.freeLiftLEquiv_apply, Equiv.Perm.subtypeEquivSubtypePerm_apply_of_mem, TensorPower.algebraMapâ_eq_smul_one, ContinuousLinearEquiv.mdifferentiableOn, Module.End.ringEquivEndFinsupp_apply_apply_apply, CategoryTheory.Groupoid.invEquiv_apply, Submodule.set_smul_eq_map, MulArchimedeanOrder.lt_def, Affine.Triangle.dist_orthocenter_reflection_circumcenter, finSuccEquiv'_ne_last_apply, RingEquiv.map_list_prod, Matrix.permanent_permute_cols, MeasureTheory.Measure.OuterRegular.map, Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, Matrix.adjugate_reindex, UniformConvergenceCLM.topologicalSpace_eq, ofAdd_smul, Ideal.ramificationIdx_map_eq, CategoryTheory.CountableCategory.instLocallySmallObjAsType, Subring.mem_map_equiv, isAddRightRegular_toLex, FractionalIdeal.canonicalEquiv_spanSingleton, Ideal.symm_apply_mem_of_equiv_iff, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, SemidirectProduct.congr'_symm_apply_right, Matrix.compRingEquiv_symm_apply, Multiplicative.ofAdd_strictMono, FourierTransform.fourierCLE_apply, equivShrink_div, CategoryTheory.unitCompPartialBijective_natural, AddGroupExtension.Equiv.symm_symm_apply, MulEquiv.AddMonoid.End_apply, MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, Matrix.Nondegenerate.toBilin, Finsupp.sumFinsuppEquivProdFinsupp_symm_inr, BoundedLatticeHom.dual_symm_apply_toFun, TensorProduct.finsuppScalarRight_apply_tmul_apply, LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, CategoryTheory.typeEquiv_counitIso_inv_app_val_app, MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero, Homeomorph.toCocompactMap_toFun, ofLex_toLex, Finsupp.coe_curryAddEquiv, AlgEquiv.coe_symm_toLinearEquiv, AddSubmonoid.LocalizationMap.ofAddEquivOfDom_apply, Bundle.Trivial.homeomorphProd_symm_apply_snd, Equiv.Perm.coe_one, UniformFun.isometry_ofFun_boundedContinuousFunction, Field.Emb.Cardinal.equivSucc_coherence, LinearMap.toMatrix'_apply, finCycle_symm_apply, LinearEquiv.baseChange_tmul, PiTensorProduct.ofDFinsuppEquiv_tprod_apply, DomMulAct.symm_mk_one, CategoryTheory.FinCategory.objAsTypeToAsType_map, WithBot.toDual_apply_bot, QuadraticForm.tmul_tensorComm_apply, WithTop.orderIsoSumLexPUnit_top, Module.Basis.repr_symm_single, Matrix.toLpLin_toLp, NumberField.CMExtension.equivMaximalRealSubfield_apply, UniformFun.toFun_smul, Function.fromTypes_succ_equiv_symm_apply, RingEquiv.moduleEndSelf_apply, CategoryTheory.Localization.SmallHom.equiv_mk, Equiv.hasProd_iff, ofMul_image_zpowers_eq_zmultiples_ofMul, apply_eq_dotProduct_toMatrixâ_mulVec, AddMonoidHom.liftOfRightInverse_comp, Ideal.fst_comp_quotientMulEquivQuotientProd, Polynomial.degreeLT.addLinearEquiv_apply, Equiv.subtypeEquivCodomain_apply, SchwartzMap.fourierTransformCLE_apply, Module.reflection_reflection_iterate, 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, MulEquiv.ofLeftInverse'_apply, LinearMap.coe_toContinuousLinearMap, Set.uIcc_ofDual, MonomialOrder.degree_smul_le, Equiv.Perm.set_support_inv_eq, CategoryTheory.MorphismProperty.gc_llp_rlp, LinearEquiv.coe_toContinuousLinearEquiv', Finpartition.exists_enumeration, RightOrdContinuous.orderDual, LinearMap.BilinForm.separatingRight_toMatrix_iff, MultilinearMap.freeDFinsuppEquiv_def, TensorProduct.finsuppLeft_apply, ContinuousLinearMap.toSpanSingletonLE_apply, Finset.Colex.lt_iff_exists_filter_lt, AntitoneOn.dual_right, LinearMap.BilinForm.SeparatingLeft.toMatrix', toAdd_eq_zero, FreeMonoid.ofList_nil, UniformFun.ofFun_zero, CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft, UniformEquiv.coe_symm_toEquiv, CompactlyGenerated.isoOfHomeo_hom, finsuppTensorFinsuppRid_symm_single_smul, CoxeterSystem.lengthParity_comp_simple, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_symm_apply, Homeomorph.image_compl, LinearEquiv.prodComm_apply, TensorProduct.prodRight_symm_tmul, LinearIsometryEquiv.dist_map, SetTheory.PGame.default_nim_one_leftMoves_eq, Multiplicative.toAdd_eq_top, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_hom_Ď, Function.FromTypes.curryEquiv_symm_apply, finsetBasisOfTopLeSpanOfCardEqFinrank_repr_apply, LinearEquiv.conj_apply, SheafOfModules.freeHomEquiv_comp_apply, AffineIsometryEquiv.coe_vaddConst, DFinsupp.mapRange.linearEquiv_apply, LinearEquiv.ofSubmodules_symm_apply, TopologicalSpace.Compacts.equiv_symm_apply, isLowerSet_preimage_ofDual_iff, WithZero.val_inv_expOrderIso_apply, Complex.equivRealProdLm_apply, Orientation.inner_comp_rightAngleRotation, CategoryTheory.shrinkYonedaEquiv_naturality, IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le, RingQuot.liftAlgHom_mkAlgHom_apply, OrderIso.compl_symm_apply, AffineEquiv.list_wbtw_map_iff, LinearMap.kerComplementEquivRange_apply_coe, UniformFun.ofFun_div, LinearIsometryEquiv.continuousWithinAt, Ioi_orderDual_def, Rack.invAct_apply, RingEquiv.ofHomInv_apply, ZMod.ringEquivCongr_ringEquivCongr_apply, Equiv.Perm.inv_apply_self, ContinuousMap.equivBoundedOfCompact_apply, Quiver.Hom.opEquiv_apply, Equiv.sumCompl_apply_inr, Equiv.withTopSubtypeNe_symm_apply_coe, Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, Subgroup.IsComplement.equiv_fst_mul_equiv_snd, Submodule.restrictScalarsEquiv_symm_apply, Subgroup.quotientEquivProdOfLE'_symm_apply, val_unitsNonZeroDivisorsEquiv_symm_apply_coe, ZMod.invDFT_def', AlgEquiv.coe_apply_coe_coe_symm_apply, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc, MonovaryOn.dual_right, HahnSeries.leadingCoeff_pos_iff, CategoryTheory.ComposableArrows.arrowEquiv_symm_apply, UniformEquiv.finTwoArrow_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, Module.Basis.restrictScalars_repr_apply, AddEquiv.bijective, RingQuot.lift_unique, Matrix.ker_toLin_eq_bot, FreeAddMonoid.freeAddMonoidCongr_of, NonUnitalSubring.centerCongr_symm_apply_coe, CategoryTheory.yonedaEquiv_naturality', FreeMonoid.count_of, AddEquiv.mulOp_symm_apply, monovaryOn_toDual_right, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left, ofBoolRing_le_ofBoolRing_iff, OrderIsoClass.toLatticeHomClass, RootPairing.Hom.coroot_coweightMap, Subsemiring.centerToMulOpposite_apply_coe, Topology.WithUpper.isOpen_preimage_ofUpper, Equiv.prodPProd_apply, antivary_toDual_right, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, IsAlgClosure.equivOfEquiv_comp_algebraMap, AddSubmonoid.add_leftNegEquiv, SubAddAction.ofFixingAddSubgroup_insert_map_bijective, ofBoolAlg_mul_ofBoolAlg_eq_left_iff, Topology.WithLower.isOpen_def, AddAut.conj_inv_apply, AddIrreducible.map, MaximalSpectrum.equivSubtype_symm_apply_asIdeal, Polynomial.toFinsuppIsoLinear_symm_apply_toFinsupp, Module.Basis.equivFunL_apply, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, CategoryTheory.Localization.SmallShiftedHom.equiv_mk, SymAlg.invOf_sym, CompactlyGenerated.isoOfHomeo_inv, SemidirectProduct.mul_def, CategoryTheory.Limits.Types.Small.productIso_inv_comp_Ď_apply, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_obj, QuotientAddGroup.equivIcoMod_symm_apply, toDual_min, inner_map_complex, EquicontinuousOn.isClosed_range_uniformOnFun_iff_pi, LieModuleEquiv.symm_apply_apply, DilationEquiv.ratio_inv, CompleteLatticeHom.symm_dual_id, StarMulEquiv.ext_iff, SSet.Κâ_snd_assoc, PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm, Homeomorph.map_cocompact, finTwoArrowEquiv_symm_apply, GradedTensorProduct.auxEquiv_mul, Prod.Lex.uniqueProd_apply, Fintype.linearIndependent_iff'â, Equiv.withTopCongr_apply, QuadraticForm.tmul_tensorRId_apply, RingEquiv.coe_addMonoidHom_refl, MulEquiv.prodUnique_apply, LinearMap.IsSymmetric.adjoint_eq, Trivialization.continuousLinearEquivAt_apply', Matrix.ofNat_fin_two, IsCoveringMap.homeomorph_comp_iff, FreeMonoid.toList_cons, NormedAddGroupHom.Equalizer.liftEquiv_apply, ZMod.AddAutEquivUnits_apply, Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe, AddChar.coe_toAddMonoidHomEquiv, HasGradientAt.hasFDerivAt, TensorProduct.piRight_symm_single, toLex_zero, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_apply_asIdeal, CategoryTheory.Limits.compCoyonedaSectionsEquiv_symm_apply_coe, CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app, CategoryTheory.Functor.flippingEquiv_symm_apply_obj_obj, AlgebraicGeometry.ÎSpec.locallyRingedSpaceAdjunction_homEquiv_apply', Module.FinitePresentation.linearEquivMap_apply, Submodule.equivOpposite_apply, finEquivMultiples_symm_apply, CStarMatrix.toCLM_apply_single, AddEquiv.comp_right_injective, Sequential.isoOfHomeo_hom, RingCon.quotientQuotientEquivQuotient_coe_coe, FourierTransform.fourierEquiv_symm_apply, MonoidAlgebra.curryRingEquiv_symm_single, Finset.Colex.toColex_le_toColex, Equiv.graph_inv, Finset.equivBitIndices_symm_apply, t1Space_TFAE, Submodule.reflection_reflection, Equiv.piCongr'_symm_apply_symm_apply, DirectSum.decompose_symm_algebraMap, OrderIso.sumLexCongr_apply, MulEquiv.coprodCongr_apply, RingEquiv.ofRingHom_symm_apply, WithVal.lt_def, Equiv.eq_comp_symm, Topology.WithLawson.isOpen_def, Monoid.IsTorsion.torsionMulEquiv_symm_apply_coe, CategoryTheory.Functor.curryingFlipEquiv_apply_obj, FreeAddMonoid.ofList_toList, MulHom.toMulEquiv_symm_apply, FirstOrder.Language.Embedding.substructureEquivMap_apply, AddEquiv.toMultiplicativeLeft_symm_apply_symm_apply, CategoryTheory.Iso.toEquiv_fun, FirstOrder.Language.Equiv.apply_symm_apply, Equiv.injective_comp, Homeomorph.comap_nhds_eq, StrictAnti.dual_left, WithCStarModule.equiv_zero, hasFTaylorSeriesUpTo_succ_nat_iff_right, Submonoid.centerToMulOpposite_symm_apply_coe, edist_toAdd, Finset.Icc_orderDual_def, Equiv.Finset.union_symm_right, MonoidAlgebra.mapRangeAddEquiv_apply, AlgEquiv.funUnique_apply, AddSubmonoid.IsLocalizationMap.addEquiv_comp, ContinuousAlgEquiv.cast_symm_apply, StarMulEquiv.ofBijective_apply, LinearIsometryEquiv.coe_symm_toLinearEquiv, Finset.Ioo_toDual, Fin.cycleRange_symm_zero, AddEquiv.coprodAssoc_symm_apply_inr_inr, Concept.swapEquiv_apply, AddEquiv.mapMatrix_apply, mulAutArrow_apply_apply, Set.Ico_toDual, Finset.map_toDual_min, Equiv.Perm.SameCycle.apply_right, Matroid.mapEquiv_dep_iff, AlgEquiv.toRingEquiv_unop, Set.powersetCard.ofFinEmbEquiv_symm_apply, WithBot.toDualTopEquiv_coe, CategoryTheory.Functor.FullyFaithful.mulEquivEnd_symm_apply, LinearEquiv.coe_toAffineEquiv, Matrix.det_reindex, SSet.OneTruncationâ.nerveEquiv_symm_apply_map, IsLocalizedModule.mapEquiv_symm_apply, AlgebraicGeometry.IsOpenImmersion.opensEquiv_apply_coe, ofBoolRing_zero, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, RingQuot.liftAlgHom_unique, Diffeomorph.sumCongr_coe, ofDual_eq_one, ofDual_compl, range_eq_univ, multiplesHom_symm_apply, MvPolynomial.universalFactorizationMapPresentation_map, EuclideanGeometry.reflection_apply_of_mem, isLeft_finSumNatEquiv_symm_apply, IsTop.ofDual, isOpenMap_toAdd, Equiv.ulift_symm_apply, Module.Invertible.linearEquivOfLeftInverse_symm_apply, SetSemiring.add_def, ContinuousMap.unitsLift_apply_inv_apply, DirectSum.decompose_symm_add, ProperCone.dual_singleton, codisjoint_ofDual_iff, Set.Icc_ofDual, Additive.ofMul_strictMono, CategoryTheory.uliftYonedaEquiv_uliftYoneda_map, Module.involutive_reflection, CategoryTheory.Localization.SmallShiftedHom.equiv_shift', Algebra.TensorProduct.basisAux_tmul, MulEquiv.ofLeftInverse_apply, groupCohomology.norm_ofAlgebraAutOnUnits_eq, ofDual_neg, Matrix.reindexLieEquiv_apply, FreeGroup.range_lift_eq_closure, iccHomeoI_apply_coe, MonomialOrder.degree_mul_le, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_apply_asIdeal, DilationEquiv.ratio_zpow, Additive.ofMul_mono, MeasureTheory.VectorMeasure.equivMeasure_symm_apply, Module.Basis.singleton_repr, AddChar.toMonoidHom_apply, Orthonormal.linearIsometryEquiv_symm_apply_single_one, TensorProduct.map_comm, UniformFun.edist_le, WithLp.equiv_symm_apply, Equiv.Perm.sign_of_pow_two_eq_one, MulEquivClass.apply_mem_center, LinearEquiv.coe_toContinuousLinearEquiv_symm', finCycle_apply, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_map_term, ArchimedeanOrder.of_val, Affine.Simplex.touchpointWeights_reindex, Multiplicative.toAdd_image_nsmul, AffineEquiv.wSameSide_map_iff, Fin.coe_of_injective_castLE_symm, DomMulAct.isClosedEmbedding_mk_symm, isMax_toDual_iff, InnerProductSpace.harmonicAt_comp_CLE_iff, Set.powersetCard.mem_compl, CategoryTheory.Adjunction.mkOfHomEquiv_unit_app, Module.AEval.X_pow_smul_of, Antivary.sum_mul_eq_sum_mul_comp_perm_iff, AddMonoidHom.toMultiplicative_id, IsometryEquiv.map_hausdorffMeasure, Additive.toMul_strictMono, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero, Module.infinite_range_reflection_reflection_iterate_iff, iteratedFDeriv_eq_equiv_comp, Equiv.coe_addRight, Localization.mulEquivOfQuotient_mk', LinearMap.polyCharpolyAux_map_eq_charpoly, ofAdd_sum, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Monovary.sum_comp_perm_smul_lt_sum_smul_iff, MulEquiv.toMultiplicative_toAdditive_symm_apply, UniformOnFun.topologicalSpace_eq, linearMap_toMatrix_mul_basis_toMatrix, FreeMonoid.comp_lift, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, TrivSqZeroExt.liftEquiv_apply, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, AddChar.toAddMonoidHomEquiv_symm_zero, Equiv.coe_vaddConst_symm, Homeomorph.continuous_symm, isAtom_dual_iff_isCoatom, Module.Basis.coe_reindex, Subsemigroup.strictMono_topEquiv, CategoryTheory.Limits.Fork.IsLimit.homIso_apply_coe, LinearEquiv.toSpanNonzeroSingleton_apply, CategoryTheory.Adjunction.instMonoCoeEquivHomObjHomEquivOfReflectsMonomorphisms, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_apply_snd, AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero, AddSubmonoid.leftNegEquiv_symm_add, Sym.cast_cast, Homeomorph.ext_iff, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_symm_app, CategoryTheory.InducedCategory.homAddEquiv_symm_apply_hom, MonoidAlgebra.toRingHom_mapDomainRingEquiv, Matrix.kroneckerTMulAlgEquiv_symm_apply, ContinuousAlgEquiv.isClosed_image, Irreducible.map, ContinuousLinearEquiv.coe_toLinearEquiv, MeasurableEquiv.measurable_invFun, Polynomial.mkDerivationEquiv_apply, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Equiv.sumAssoc_apply_inl_inr, Equiv.Perm.SameCycle.zpow_left, DomMulAct.mk_smul_mulActionHom_apply, Diffeomorph.symm_apply_apply, Set.Ioo_ofDual, 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, RingQuot.lift_mkRingHom_apply, CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom, groupCohomology.isMulCocycleâ_of_mem_cocyclesâ, MvPolynomial.supDegree_esymm, CStarMatrix.toCLM_apply_eq_sum, CategoryTheory.coyonedaEquiv_naturality, Matrix.cons_transpose, RootPairing.toPerfPair_flip_comp_coroot, Rep.toAdditive_apply, Int.quotientSpanEquivZMod_comp_castRingHom, DFinsupp.linearEquivFunOnFintype_symm_apply, Equiv.Perm.decomposeOption_symm_of_none_apply, LinearMap.toMatrix_transpose_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_comp, LieAlgebra.LieEquiv.ofCoboundary_toFun, DirectSum.coe_decompose_mul_of_right_mem_of_not_le, PadicInt.coe_adicCompletionIntegersEquiv_apply, MeasureTheory.measurePreserving_prodAssoc, DomAddAct.mk_add, Equiv.invOn, Order.IsSuccLimit.dual, AffineIsometryEquiv.diam_image, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, DirectSum.coe_decompose_mul_of_left_mem_of_not_le, RingCon.quotientKerEquivOfRightInverse_apply, Pi.basis_repr, FreeCommRing.lift_comp_of, DFinsupp.equivCongrLeft_apply, CategoryTheory.coyonedaEquiv_apply, Matrix.kroneckerTMulStarAlgEquiv_apply, UniformFun.toFun_one, Matrix.transposeRingEquiv_apply, MulEquiv.congr_fun, Topology.WithUpper.ofUpper_toUpper, Metric.Snowflaking.toSnowflaking_ofSnowflaking, AddEquiv.eq_comp_symm, ComplexShape.Embedding.AreComplementary.equiv_inl, Subgroup.topEquiv_symm_apply_coe, AlgEquiv.piCongrLeft'_apply, Topology.WithUpper.toUpper_lt_toUpper, Equiv.Perm.IsCycleOn.pow_card_apply, Unitary.linearIsometryEquiv_coe_symm_apply, HasCompactSupport.comp_homeomorph, Subgroup.normalizerMonoidHom_apply_apply_coe, toMatrix_dualTensorHom, Subgroup.IsComplement.equiv_symm_apply, CochainComplex.HomComplex.CohomologyClass.equiv_toSmallShiftedHom_mk, Equiv.pprodCongr_symm_apply, MulEquiv.congr_arg, CategoryTheory.Limits.compCoyonedaSectionsEquiv_apply_app, SemimoduleCat.homAddEquiv_apply, UniversalEnvelopingAlgebra.lift_Κ_apply, SSet.Κâ_snd, MeasurableEquiv.memLp_map_measure_iff, OrderMonoidIso.strictMono_symm, LinearEquiv.arrowCongr_apply, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, FreeLieAlgebra.lift_unique, AlgEquiv.piCongrLeft_apply, Rack.toEnvelGroup.univ, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Homeomorph.comp_continuous_iff, ofDegLex_toDegLex, Equiv.semiconjâ_conj, SSet.Truncated.StrictSegal.spineInjective, Orientation.oangle_rotation_oangle_left, DyckWord.equivTree_symm_apply, UniformEquiv.symm_comp_self, Equiv.conj_comp, exteriorPower.alternatingMapLinearEquiv_apply_ΚMulti, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Algebra.Generators.H1Cotangent.δAux_ofComp, SimpleGraph.incMatrix_mul_transpose, RingEquiv.prodCongr_apply, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, FreeAddGroup.map_eq_lift, Homeomorph.piCongrLeft_apply, RootPairing.reflectionPerm_root, Equiv.Perm.IsCycle.pow_eq_pow_iff, QuaternionAlgebra.lift_symm_apply, Homeomorph.comap_coclosedCompact, LinearMap.isPositive_toContinuousLinearMap_iff, Prod.Lex.toLex_lt_toLex, Equiv.piCongrSigmaFiber_apply, Matrix.range_toLin', LinearIsometryEquiv.analyticWithinAt, LinearIsometryEquiv.toSpanUnitSingleton_apply, ContinuousMultilinearMap.prodEquiv_symm_apply, Continuous.homeoOfEquivCompactToT2.t1_counterexample, AddSubgroup.IsComplement.rightQuotientEquiv_apply, Multiset.map_univ_val_equiv, AddMonoidHom.op_symm_apply_apply, IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, AlgEquivClass.commutes, LinearEquiv.finTwoArrow_apply, DirectSum.addEquivProdDirectSum_apply, OrderRingIso.coe_mk, DilationEquiv.smulTorsor_apply, LocallyConstant.congrLeftRingEquiv_symm_apply_apply, ContinuousLinearEquiv.lipschitz, frobeniusEquiv_symm_pow, Specialization.ofEquiv_inj, Tropical.tropEquiv_symm_coe_fn, Submodule.prodEquivOfIsCompl_symm_apply, AddEquiv.comapAddSubgroup_apply, ZMod.dft_apply, sigmaFinsuppEquivDFinsupp_smul, CuspForm.coe_translate, Diffeomorph.coe_prodComm, OrderMonoidIso.val_inv_unitsCongr_apply, MonomialOrder.le_add_right, LinearEquiv.skewProd_symm_apply, Homeomorph.image_symm, FreeAddMonoid.toList_of_add, Equiv.ofLeftInverseOfCardLE_apply, Submodule.Quotient.restrictScalarsEquiv_symm_mk, HNNExtension.of_mul_inv_t, LinearMap.mul_toMatrix', AddEquiv.mulOp_apply, Matrix.liftLinear_apply, toAdd_ofAdd, Monoid.CoprodI.Word.equivPair_symm, ContinuousAlgEquiv.image_eq_preimage_symm, Set.up_empty, AddEquiv.toMultiplicativeRight_symm_apply_apply, Quaternion.equivTuple_apply, AddSubmonoid.LocalizationMap.ofAddEquivOfLocalizations_apply, evalRingHom_mapMatrix_comp_compRingEquiv, ContinuousMap.val_addUnitsLift_apply_apply, unitInterval.symmMeasurableEquiv_symm_apply, strictMonoOn_toDual_comp_iff, AddEquiv.coe_trans, AffineIsometry.coe_toAffineIsometryEquiv, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_map, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_functor_map, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, OrderMonoidIso.withZero_apply_apply, Equiv.optionSubtypeNe_symm_apply, CategoryTheory.PreOneHypercover.inter_pâ, Matrix.of_apply, exteriorPower.ΚMultiDual_apply_ΚMulti, Homeomorph.continuous_sumAssoc, InnerProductSpace.gramSchmidt_triangular, Matrix.diagonal_kroneckerTMul, edist_toMul, Set.ordConnected_image, finSuccEquiv'_below, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none, UniformFun.lipschitzWith_ofFun_iff, PiTensorProduct.lift_comp_reindex, ContinuousSemilinearEquivClass.continuousSemilinearMapClass, CategoryTheory.WithTerminal.isLimitEquiv_symm_apply_lift, isRightRegular_toDual, FreeGroupBasis.reindex_apply, Fin.succAbove_cycleRange, OrderRingIso.symm_apply_apply, QuadraticAlgebra.basis_repr_apply, DomMulAct.isEmbedding_mk, Submodule.starProjection_map_apply, AddSubgroup.addSubgroupOfEquivOfLe_symm_apply_coe_coe, FirstOrder.Language.Formula.equivSentence_inf, Submodule.natAbs_det_equiv, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, HomotopicalAlgebra.AttachCells.reindex_Ď, CategoryTheory.Sheaf.ÎObjEquivSections_naturality_symm, Equiv.coe_mulLeft, UniformEquiv.image_symm, LinearMap.star_eq_adjoint, nnnorm_ofAdd, MulEquiv.surjective, Equiv.prodCongrLeft_apply_fst, Matrix.vecMul_permMatrix, Finset.Colex.toColex_lt_singleton, MonomialOrder.degree_pow_le, AddEquiv.piAdditive_symm_apply, PrimeSpectrum.primeSpectrumProd_symm_inr, AddOpposite.opEquiv_apply, RingEquiv.map_det, ContinuousMap.homeoFnOfDiscrete_apply, LinearEquiv.conjRingEquiv_apply_apply, List.formPerm_pow_apply_head, LinearMap.toMatrix_smulBasis_right, MeasurableEquiv.curry_apply, Matrix.toLpLin_symm_id, MulEquiv.toSingleObjEquiv_unitIso_inv, List.SortedGT.of_map_ofDual, LieEquiv.lieSubalgebraMap_apply, Fin.cycleRange_of_le, Module.Basis.toDual_eq_repr, IsGLB.dual, AlgEquiv.toLieEquiv_symm_apply, AddSubsemigroup.strictMono_topEquiv, Matrix.range_toLin_eq_top, Set.val_unitEquivUnitsInteger_apply_coe, toMul_zsmul, Equiv.funUnique_apply, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, Finsupp.prod_hom_add_index, WithZero.toMulBot_coe_ofAdd, Submonoid.LocalizationMap.ofMulEquivOfDom_comp, LinearIsometryEquiv.coe_coe, TensorProduct.lid'_apply_tmul, SubMulAction.ofFixingSubgroup_of_eq_apply, Algebra.TensorProduct.liftEquiv_apply, Matrix.toLin_finTwoProd_apply, Metric.Snowflaking.ediam_preimage_ofSnowflaking, MulOpposite.opMulEquiv_apply, Homeomorph.continuousMapOfUnique_symm_apply, FreeLieAlgebra.universalEnvelopingEquivFreeAlgebra_apply, LatticeHom.dual_id, Rep.leftRegularHomEquiv_symm_apply, CategoryTheory.Limits.Types.limitEquivSections_symm_apply, RingEquiv.subsemiringMap_symm_apply_coe, RingCon.comapQuotientEquivRangeS_mk, coe_finRotate, CategoryTheory.Adjunction.homAddEquiv_add, Antitone.dual, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, HasFPowerSeriesAt.fderiv_eq, Module.Basis.sum_repr_mul_repr, Equiv.Perm.perm_symm_mapsTo_iff_mapsTo, Matrix.isPositive_toEuclideanLin_iff, isExtrOn_dual_iff, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, FreeMonoid.lift_eval_of, RootPairing.coreflection_apply_self, InfIrred.dual, toDual_hnot, MulEquiv.cast_symm_apply, Matrix.diagonal_fin_one, RingEquiv.trans_apply, coe_frobeniusEquiv, RingEquiv.coe_ringHom_inj_iff, addMonoidEndRingEquivInt_apply, StarMulEquiv.toStarMonoidHom_coe, BddDistLat.dual_map, ProbabilityTheory.Kernel.partialTraj_succ_self, LinearEquiv.symm_trans_apply, DFA.reindex_apply_start, quotAdjoinEquivQuotMap_apply_mk, IsCyclotomicExtension.Rat.galEquivZMod_apply_of_pow_eq, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, RingEquiv.mapTwoSidedIdeal_apply, RootPairing.polarizationEquiv_apply, ContinuousMulEquiv.symm_apply_apply, Finset.Colex.singleton_lt_singleton, CliffordAlgebra.reverseOpEquiv_opComm, CStarMatrix.reindexâ_apply, ContinuousAlgEquiv.coe_toAlgEquiv, ContinuousLinearEquiv.refl_apply, ofDual_ratCast, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor, NumberField.integralBasis_repr_apply, Equiv.sigmaUnique_symm_apply, AddGrpCat.toGrp_map, continuousMultilinearCurryFin0_apply, CStarMatrix.ofMatrix_eq_ofMatrixL, Matrix.rank_submatrix, comp_injective, Prod.Lex.covBy_iff, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, toAdd_one, MulOpposite.opEquiv_apply, AddSubmonoid.leftNegEquiv_symm_fromLeftNeg, Multiplicative.toAdd_eq_bot, exteriorPower.pairingDual_ΚMulti_ΚMulti, UniformFun.toFun_prod, unitInterval.symmHomeomorph_symm_apply, Con.quotientKerEquivOfRightInverse_symm_apply, MeasurableEquiv.apply_symm_apply, FreeMonoid.toList_of_mul, Equiv.Set.sumDiffSubset_symm_apply_of_notMem, Homeomorph.image_apply_coe, Pi.lt_toColex_update_self_iff, LinearMap.mul_toMatrixâ, homeomorphUnitSphereProd_symm_apply_coe, Equiv.ofBijective_symm_apply_apply, Shrink.algEquiv_apply, Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_apply, Orientation.rightAngleRotation_rightAngleRotation, WittVector.dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeff, CategoryTheory.Bicategory.conjugateEquiv_symm_comm, BialgEquiv.toCoalgEquiv_toCoalgHom, DirectSum.addEquivProdDirectSum_symm_apply_support', LaurentSeries.coe_X_compare, Set.uIcc_toDual, IsSelfAdjoint.conj_adjoint, TensorProduct.inner_assoc_assoc, ContinuousMultilinearMap.curryMidEquiv_apply, AddSubmonoid.leftNegEquiv_apply, Matrix.lieConj_symm_apply, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, AffineEquiv.injective_pointReflection_left_of_injective_two_nsmul, Setoid.prodQuotientEquiv_symm_apply, AddSubgroup.vadd_leftQuotientEquiv, comp_bijective, Matrix.val_planeConformalMatrix, AddSubgroup.comap_toAddSubmonoid, kroneckerTMulLinearEquiv_mul, Homeomorph.vaddConst_symm_apply, CategoryTheory.Bicategory.mateEquiv_symm_apply, CategoryTheory.Functor.Elements.initialOfCorepresentableBy_snd, FractionalIdeal.canonicalEquiv_coeIdeal, QuadraticMap.discr_comp, finTwoArrowEquiv_apply, Equiv.iInf_comp, Finsupp.fst_sumFinsuppEquivProdFinsupp, Module.Basis.linearMap_repr_apply, Equiv.ofBijective_apply, MulEquiv.trans_apply, exteriorPower.alternatingMapLinearEquiv_comp_ΚMulti, mulAutArrow_apply_symm_apply, StrictMono.dual_left, RingEquiv.toNonUnitalRingHom_eq_coe, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, toColex_neg, groupHomology.H1AddEquivOfIsTrivial_single, SymAlg.sym_eq_one_iff, PresheafOfModules.homEquivOfIsLocallyBijective_apply, WithTop.ofDual_apply_coe, kroneckerTMulLinearEquiv_symm_kroneckerTMul, Units.coe_unop_opEquiv, Module.Basis.det_reindex, LinearEquiv.zero_apply, MultilinearMap.curryFinFinset_apply_const, RootPairing.bijOn_coreflection_coroot, CategoryTheory.Limits.Concrete.prodEquiv_symm_apply_snd, Relation.cutExpand_le_invImage_lex, Set.opEquiv_self_apply_coe, ContinuousLinearEquiv.hasSum, MultilinearMap.freeFinsuppEquiv_def, Set.Ioc_toDual, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', MulEquiv.mapSubgroup_symm_apply, WithZero.lift'_unique, Finsupp.liftAddHom_apply, LinearMap.lsum_single, UniformOnFun.uniformSpace_eq_iInf_precomp_of_cover, equicontinuous_iff_continuous, MeasurableEquiv.sigmaFinite_map, Equiv.optionSubtype_symm_apply_apply_none, PresheafOfModules.unitHomEquiv_apply_coe, Equiv.optionEquivSumPUnit_none, MonomialOrder.toSyn_monotone, frobenius_comp_frobeniusEquiv_symm, AddSubsemigroup.map_equiv_eq_comap_symm, LinearMap.nondegenerate_congr_iff, Rep.coindResAdjunction_homEquiv_apply, ContinuousMap.continuous_iff_continuous_uniformFun, SimpleGraph.Walk.IsHamiltonian.supportGetEquiv_apply, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_apply, CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv_functor_obj_some, Matroid.mapEquiv_ground_eq, AddMonoidAlgebra.lift_single, UniformEquiv.finTwoArrow_symm_apply, MulEquiv.ext_iff, Finsupp.Colex.le_iff_of_unique, Equiv.Perm.IsCycleOn.range_pow, tangentBundle_model_space_coe_chartAt_symm, CategoryTheory.PreZeroHypercover.interSnd_hâ, Equiv.coe_piCongr', Finsupp.Lex.le_iff_of_unique, Topology.WithUpperSet.ofUpperSet_le_iff, SemidirectProduct.inl_aut_inv, CategoryTheory.conjugateEquiv_symm_comp, ZMod.invDFT_apply', Orientation.areaForm_comp_linearIsometryEquiv, PerfectionMap.comp_equiv', Affine.Simplex.range_faceOpposite_reindex, WithTop.toDual_apply_top, coe_equiv_lpPiLp, inv_apply_eq, HahnEmbedding.Seed.coeff_baseEmbedding, Affine.Simplex.altitudeFoot_reindex, Matrix.dualNumberEquiv_symm_apply, LinearMap.toMatrix'_mul, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_app_apply, finSumFinEquiv_symm_last, LinearIsometryEquiv.ofTop_apply, LinearIsometryEquiv.comp_differentiableWithinAt_iff, tangentBundleModelSpaceHomeomorph_coe, CategoryTheory.MonoidalClosed.enrichedOrdinaryCategorySelf_homEquiv, FreeMonoid.ofList_cons, Subgroup.mem_ofUnits_iff_toUnits_mem, IsometryEquiv.bijective, Matrix.cons_mul, LinearMap.adjoint_toSpanSingleton, MulOpposite.opEquiv_symm_apply, ContinuousLinearEquiv.equivOfInverse_apply, mul_basis_toMatrix, UniformFun.toFun_div, DirectSum.decompose_algebraMap, Monoid.CoprodI.Word.mem_equivPair_tail_iff, Iic_orderDual_def, SupHom.symm_dual_id, ofBoolAlg_symmDiff, CategoryTheory.Limits.Trident.IsLimit.homIso_apply_coe, LinearMap.GeneralLinearGroup.congrLinearEquiv_apply, ContinuousAlgEquiv.trans_apply, UniformOnFun.ofFun_sub, SubAddAction.ofFixingAddSubgroup_of_eq_apply, starL_symm_apply, MulEquiv.inv'_symm_apply, AddMonoidHom.coe_toMultiplicative', LieEquiv.apply_symm_apply, Equiv.image_eq_preimage, LinearEquiv.image_eq_preimage_symm, CategoryTheory.Sheaf.ÎObjEquivHom_naturality_symm, Equiv.subLeft_symm_apply, RingEquiv.ofNonUnitalRingHom_apply, AddEquiv.coprodAssoc_apply_inl_inr, Subring.topEquiv_symm_apply_coe, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply, starMulEquiv_apply, MonoidHom.op_symm_apply_apply, SetSemiring.one_def, Units.toAut_hom, Module.dualProdDualEquivDual_apply_apply, RootPairing.Equiv.comp_indexEquiv_symm_apply, AddEquiv.coprodCongr_apply, DilationEquiv.mulRight_apply, IndexedPartition.equivQuotient_index_apply, Equiv.ofInjective_symm_apply, Equiv.subtypeEquivRight_symm_apply_coe, WeierstrassCurve.Jacobian.Point.toAffineAddEquiv_apply, Submodule.quotientPi_apply, Equiv.Perm.zpow_apply_mem_support, Additive.ofMul_le, Submodule.rTensorOne_tmul, nnnorm_toDual, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, Function.piCongrLeft'_update, Finsupp.DegLex.lt_iff, CategoryTheory.tensorRightHomEquiv_naturality, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, LinearIsometryEquiv.withLpProdCongr_symm_apply, Equiv.piCongrLeft_sumInl, equivTangentBundleProd_symm_apply_snd, ContinuousLinearEquiv.analyticOn, CircleDeg1Lift.translate_apply, Valuation.ofAddValuation_toAddValuation, CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorCorepresentingIso_hom_app_app, Traversable.foldl.unop_ofFreeMonoid, LinearEquiv.conj_symm_conj, MonomialOrder.degLex_single_le_iff, Function.updateFinset_updateFinset, OrderIsoClass.tosSupHomClass, RingCon.coe_comapQuotientEquivRange_mk, MulEquiv.equivLike_inv_eq_symm, Equiv.option_symm_apply_none_iff, Submodule.reflection_sub, AddSubgroup.topEquiv_symm_apply_coe, CategoryTheory.Groupoid.vertexGroupIsomOfMap_apply, LinearMap.toMatrix_algebraMap, IsAlgClosure.equivOfEquiv_symm_algebraMap, AlgEquiv.coe_ringEquiv, LinearEquiv.coe_curry_symm, LinearMap.spectrum_toMatrix, CategoryTheory.Abelian.Ext.homAddEquiv_apply, MvPolynomial.leadingCoeff_toLex_C, PowerBasis.constr_pow_gen, Equiv.smul_def, AddMonoidAlgebra.lift_symm_apply, MulAut.conj_apply, Nonneg.unitsHomeomorphPos_apply_coe, IsBaseChange.equiv_symm_apply, RootPairing.coroot_eq_neg_iff, TensorProduct.congr_symm_tmul, toColex_smul, Orientation.rotation_eq_self_iff_angle_eq_zero, SkewMonoidAlgebra.toFinsuppAddEquiv_symm_apply, LinearMap.SeparatingRight.toMatrixâ, Matrix.one_submatrix_mul, FinPartOrd.dual_map, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ContinuousMap.coe_equivFnOfDiscrete, CompleteLat.dual_map, Matrix.isUnit_toLin_iff, Polynomial.degreeLT.addLinearEquiv_apply', Equiv.Perm.coe_inv, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_symm_apply, RingCon.coe_quotientKerEquivRangeS_mk, SimpleGraph.Walk.IsHamiltonian.supportGetEquiv_symm_apply_val, Matrix.uniqueLinearEquiv_apply, Representation.ofMulActionSelfAsModuleEquiv_apply, Submodule.singleton_smul, MulEquiv.ofBijective_apply_symm_apply, toColex_vadd', AddEquiv.apply_symm_apply, Subspace.quotAnnihilatorEquiv_apply, MulEquiv.op_apply_apply, circleEquivGen_symm_apply, Equiv.Perm.apply_pow_apply_eq_iff, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, Quiver.Hom.opEquiv_symm_apply, Matrix.reindex_updateRow, InfTopHom.dual_comp, ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply, WeakDual.CharacterSpace.compContinuousMap_apply, CategoryTheory.tensorRightHomEquiv_tensor, CategoryTheory.Hom.mulEquivCongrRight_symm_apply, lipschitzOnWith_cfcâ_fun, maximal_toDual, iterateFrobeniusEquiv_one_apply, Matrix.diagonal_toLin', LinearMap.re_inner_adjoint_mul_self_nonneg, RootPairing.root_eq_neg_iff, TensorPower.mul_one, DomAddAct.vadd_aeeqFun_aeeq, Diffeomorph.contDiff, Hamming.toHamming_smul, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_symm_apply_f_coe, CategoryTheory.Localization.SmallShiftedHom.equiv_chgUniv, CStarMatrix.toCLM_apply, CategoryTheory.Subfunctor.range_eq_ofSection', AddEquiv.symm_map_add, ContinuousLinearEquiv.hasFDerivWithinAt, Orientation.oangle_rotation_right, inv_apply_apply, AddLocalization.addEquivOfQuotient_apply, Equiv.Perm.IsCycle.cycleOf, QuotientAddGroup.quotientAddEquivOfEq_mk, exteriorPower.oneEquiv_symm_apply, CategoryTheory.Limits.WalkingPair.swap_symm_apply_tt, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, LinearMap.isPositive_self_comp_adjoint, Hamming.toHamming_add, NonUnitalStarAlgHom.prodEquiv_apply, QuadraticForm.tensorLId_symm_apply, RingEquiv.coe_nonUnitalRingHom_inj_iff, RingEquiv.idealComapOrderIso_symm_apply, Matrix.charpoly_toLin', FreeAddMagma.lift_comp_of', IsometryEquiv.piFinTwo_symm_apply, BoundedLatticeHom.symm_dual_id, CategoryTheory.Subfunctor.IsGeneratedBy.of_equiv, uliftMultiplesHom_apply_apply, CategoryTheory.CatEnrichedOrdinary.Hom.base_comp, Multiset.cast_apply_fst, starâᾢ_apply, CategoryTheory.Functor.RepresentableBy.equivOfIsoObj_apply, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, MulEquiv.toFun_eq_coe, MulEquiv.uniqueProd_symm_apply, Matrix.toLinearMapâ'_toMatrix', SheafOfModules.conjugateEquiv_pullbackComp_inv, MulEquiv.multiplicativeAdditive_apply, PiTensorProduct.ofFinsuppEquiv_apply, OpenPartialHomeomorph.toHomeomorphOfSourceEqUnivTargetEqUniv_apply, Submonoid.centerCongr_symm_apply_coe, ContinuousMulEquiv.apply_symm_apply, DoubleQuot.coe_quotQuotEquivQuotSupâ_symm, Additive.toMul_bot, Finsupp.equivFunOnFinite_symm_coe, AddEquiv.addMonoidHomCongrRightEquiv_symm_apply, finSumFinEquiv_symm_apply_natAdd, Metric.Snowflaking.ofSnowflaking_toSnowflaking, Delone.DeloneSet.mapIsometry_refl, Submodule.isIdempotentElemEquiv_apply_coe, powCoprime_apply, Equiv.Perm.IsCycleOn.apply_mem_iff, LinearEquiv.piCongrLeft'_symm_apply, Matrix.toLinearMapâââ'_apply, IsPerfectClosure.equiv_comp, MagmaCat.mulEquiv_coe_eq, ContinuousLinearEquiv.comp_continuousOn_iff, TensorProduct.finsuppScalarRight_symm_apply_single, List.sortedLE_map_toDual, AddChar.toAddMonoidHomEquiv_symm_apply, MulEquiv.monoidHomCongrRightEquiv_apply, multiplicity_map_eq, CategoryTheory.Functor.corepresentableByUliftFunctorEquiv_symm_apply_homEquiv, SymAlg.unsym_smul, Rat.HeightOneSpectrum.natGenerator_dvd_iff, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply, Equiv.Perm.ofSubtype_apply_of_mem, Homeomorph.onePointCongr_symm_apply, CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_symm_apply_homEquiv, LinearEquiv.submoduleMap_apply, Equiv.preimage_subset, ContinuousLinearEquiv.ofSubmodule'_apply, AffineEquiv.equivUnitsAffineMap_symm_apply_apply, FirstOrder.Language.BoundedFormula.realize_relabelEquiv, Matrix.BlockTriangular.comp, RingEquiv.comp_ofBijective_symm, Equiv.finsuppUnique_symm_apply_apply, Matrix.toLin'_pow, RootPairing.IsOrthogonal.reflection_apply_right, Homeomorph.unitBall_apply_coe, Polynomial.roots_X_pow_char_sub_C_pow, Function.FromTypes.uncurry_two_eq_uncurry, CategoryTheory.discreteEquiv_symm_apply_as, Module.Basis.mem_span_image, AddEquiv.toMultiplicative_apply_apply, Order.IsPredLimit.dual, Sym.mem_cast, Encodable.decode_ofEquiv, Metric.Snowflaking.image_toSnowflaking_eq_preimage, Topology.IsGeneratedBy.equiv_symm_comp_continuous_iff, IsometryEquiv.hausdorffMeasure_preimage, WittVector.inv_pairâ, Unitary.toAlgEquiv_conjStarAlgAut, Finsupp.sumFinsuppAddEquivProdFinsupp_apply, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_of_eq, Unitization.lift_range, LieModuleEquiv.trans_apply, StarMulEquiv.ofStarMonoidHom_apply, DomAddAct.vadd_Lp_ae_eq, FintypeCat.equivEquivIso_symm_apply_apply, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Sym2.coe_lift_symm_apply, LinearMap.BilinForm.SeparatingLeft.toMatrix, LinearEquiv.rTensor_symm_tmul, AddAction.IsBlock.of_addSubgroup_of_conjugate, Finset.mapRange_finsuppAntidiag_subset, AddEquiv.equivLike_neg_eq_symm, AlgebraicGeometry.IsOpenImmersion.opensEquiv_symm_apply, MeasureTheory.measurePreserving_piFinSuccAbove, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two, RootPairing.Hom.indexEquiv_mul, AffineEquiv.coe_one, Finsupp.lex_lt_iff_of_unique, groupCohomology.exists_mul_galRestrict_of_norm_eq_one, LinearIsometryEquiv.analyticOn, Module.Basis.localizationLocalization_repr_algebraMap, CategoryTheory.Limits.IsColimit.homEquiv_symm_naturality, CStarMatrix.smul_of, RelIso.IsWellOrder.preimage, LinearIsometryEquiv.analyticAt, IsometryEquiv.sumArrowIsometryEquivProdArrow_symm_apply, Complex.equivRealProdLm_symm_apply, Matrix.l2_opNNNorm_def, ContinuousLinearEquiv.strictConvex_image, GroupExtension.Equiv.rightHom_comm, map_lt_map_iff, UniformFun.dist_le, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, LinearMap.lTensor_comm, CategoryTheory.Equivalence.induced_inverse_map, CategoryTheory.Presieve.FamilyOfElements.singletonEquiv_symm_apply, Equiv.existsUnique_congr_left, Module.Basis.dualBasis_apply, LinearMap.apply_toPerfPair_flip, TensorProduct.quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, FreeGroup.closure_eq_range, SupBotHom.dual_id, AddEquiv.strictMono_subsemigroupCongr, CategoryTheory.nerve.homEquiv_id, AddChar.toMonoidHomEquiv_symm_one, WithCStarModule.linearEquiv_symm_apply, Complex.equivRealProdLm_symm_apply_im, CategoryTheory.Functor.coconeTypesEquiv_symm_apply_Κ, MeasurableEquiv.piUnique_symm_apply, gc_Ici_sInf, FormalMultilinearSeries.changeOriginIndexEquiv_apply_fst, apply_eq_star_dotProduct_toMatrixâ_mulVec, tensorKaehlerQuotKerSqEquiv_tmul_D, SetTheory.PGame.moveRight_neg, LinearMap.toMatrix_mul, IsMin.ofDual, Complex.coe_basisOneI_repr, Matrix.submatrix_updateRow_equiv, LinearMap.polar_gc, LinearMap.det_map, Monovary.sum_mul_comp_perm_le_sum_mul, Zsqrtd.lift_apply_apply, Equiv.induced_symm, val_unitsEquivProdSubtype_symm_apply, Equiv.Set.image_symm_preimage, Subgroup.quotientEquivSigmaZMod_apply, CategoryTheory.Functor.isIso_ranAdjunction_homEquiv_iff, LinearMap.toMatrixâ_complââ, TensorProduct.tensorQuotientEquiv_apply_mk_tmul, toAdd_vadd, LE.le.dual, TwoSidedIdeal.coe_equivMatrix_symm_apply, Fin.consEquiv_symm_apply, Subring.centerToMulOpposite_apply_coe, Matrix.minpoly_toLin', FreeMonoid.toList_map, Equiv.sumCompl_apply_symm_of_neg, Module.Basis.reindexFinsetRange_repr_self, Equiv.cast_apply, ContinuousLinearEquiv.coe_prodProdProdComm, Equiv.sumCongr_apply, LinearEquiv.symm_comp_eq, IsLocalizedModule.linearEquiv_symm_apply, LinearMap.equivProdOfSurjectiveOfIsCompl_apply, BoundedOrderHom.dual_comp, CategoryTheory.HomOrthogonal.matrixDecomposition_comp, Nonneg.unitsEquivPos_apply_coe, Representation.coind'_apply_apply, LinearMap.eq_adjoint_iff, Equiv.subtypeEquivCodomain_symm_apply_eq, Equiv.swap_mul_eq_mul_swap, WittVector.exists_frobenius_solution_fractionRing, derivationToSquareZeroEquivLift_symm_apply_apply_coe, Delone.DeloneSet.mapIsometry_symm_apply_packingRadius, GradedTensorProduct.mulHom_apply, BilinForm.toMatrix_compRight, CategoryTheory.Enriched.Functor.natTransEquiv_symm_app_app_apply, MulSemiringAction.toRingEquiv_symm_apply, LinearMap.BilinForm.nondegenerate_toMatrix'_iff, LaurentSeries.exists_powerSeries_of_memIntegers, sbtw_pointReflection_of_ne, Homeomorph.preimage_interior, Module.DirectLimit.linearEquiv_symm_mk, MonoidHom.coe_toAdditiveLeft, LinearMap.toMatrixâ_toLinearMapâ, FirstOrder.Language.Equiv.surjective, LinearMap.detAux_def', CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_map, MultilinearMap.fromDirectSumEquiv_lof, TensorProduct.directSumRight_tmul_lof, LinearMap.toMatrix_transpose_apply', Denumerable.ofEquiv_ofNat, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, MeasurableEquiv.piUnique_apply, FirstOrder.Language.Term.constantsVarsEquivLeft_symm_apply, surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, CliffordAlgebra.lift_symm_apply, SSet.Truncated.HomotopyCategory.descOfTruncation_map_homMk, Int.tendsto_zmultiplesHom_cofinite, Subgroup.IsComplement.rightCosetEquivalence_equiv_snd, Equiv.inducedStructure_funMap, MeasurableEquiv.piCongrLeft_apply_apply, ContinuousAddEquiv.self_comp_symm, LieIdeal.topEquiv_apply, EuclideanSpace.basisFun_repr, Module.Basis.repr_symm_single_one, CategoryTheory.CoreSmallCategoryOfSet.functor_map, Matrix.submatrix_id_mul_left, Ideal.quotEquivOfEq_eq_factor, Equiv.sigmaAssocProd_symm_apply_snd, MulEquiv.toSingleObjEquiv_counitIso_inv, WithBot.toDual_le_iff, ContinuousLinearMap.coprodEquivL_apply_apply, HasFTaylorSeriesUpToOn.hasFDerivAt, Nat.image_piFinTwoEquiv_finMulAntidiag, Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero, Equiv.swap_apply_of_ne_of_ne, LinearMap.toMatrix'_intrinsicStar, RCLike.realLinearIsometryEquiv_symm_apply, finEquivZMultiples_apply, AlgEquiv.spectrum_eq, galRestrictHom_symm_algebraMap_apply, LinearMap.BilinForm.congr_congr, FreeAddGroup.freeAddGroupCongr_apply, AddMonoidAlgebra.GradesBy.decompose_single, Equiv.Set.rangeSplittingImageEquiv_symm_apply_coe, MeasurableEquiv.coe_IicProdIoc, ZeroAtInftyContinuousMap.ContinuousMap.liftZeroAtInfty_symm_apply, Nat.pairEquiv_symm_apply, Equiv.comp_bijective, Matrix.compLinearEquiv_symm_apply, AddEquiv.prodAdditive_apply, ContinuousLinearEquiv.skewProd_apply, freeGroupEquivCoprodI_symm_apply, coe_frobenius_comp_coe_frobeniusEquiv_symm, Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_support, WithBot.ofDual_lt_iff, QuadraticForm.tensorComm_apply, AffineSubspace.topEquiv_symm_apply_coe, Filter.Realizer.ofEquiv_F, UniformOnFun.lipschitzWith_eval, Submodule.coe_isComplEquivProj_apply, MvPolynomial.monic_esymm, AddMonoidHom.toAddEquiv_apply, AffineSubspace.isometryEquivMap.coe_apply, CategoryTheory.mateEquiv_symm_apply, QuadraticAlgebra.lift_symm_apply_coe, Equiv.ofFiberEquiv_apply, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_apply, Orientation.oangle_sub_right_smul_rotation_pi_div_two, AlgEquiv.op_symm_apply_symm_apply, FractionalIdeal.coeFun_mapEquiv, ArchimedeanClass.FiniteResidueField.mk_eq_mk, Con.comapQuotientEquivOfSurj_symm_mk, Submodule.prodEquivOfIsCompl_symm_apply_left, Equiv.Perm.getElem_toList, CategoryTheory.Limits.IsColimit.descCoconeMorphism_eq_isInitial_to, Antivary.sum_smul_lt_sum_smul_comp_perm_iff, ofLex_one, LinearEquiv.lieConj_apply, Interval.dual_pure, IsBaseChange.linearMapLeftRightHom_toMatrix, UniversalEnvelopingAlgebra.lift_symm_apply, ContinuousLinearEquiv.isBigO_sub_rev, Finset.Ico_ofDual, ContinuousLinearMap.isSelfAdjoint_iff', Topology.WithLowerSet.toLowerSet_inj, OrthonormalBasis.equiv_apply_euclideanSpace, MaximalSpectrum.equivSubtype_apply_coe, OnePoint.equivProjectivization_symm_apply_mk, translate_eq_domAddActMk_vadd, AddSubsemigroup.map_equiv_top, ContinuousLinearEquiv.isUniformEmbedding, GroupExtension.Equiv.inl_comm, RootPairing.pairingIn_reflectionPerm_self_right, List.formPerm_pow_apply_getElem, Metric.Snowflaking.preimage_toSnowflaking_eball, HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRight_symm_apply, Submodule.quotientEquivOfIsCompl_apply_mk_coe, Fin.cycleIcc_of_ge_of_lt, Finsupp.equivMapDomain_eq_mapDomain, RingEquiv.coe_toEquiv, Additive.ext_iff, Monoid.CoprodI.Word.equivPair_tail, VectorBundleCore.localTriv_coordChange_eq, WithBot.toDual_apply_coe, Finset.toDual_inf, AddEquiv.coe_addSubgroupMap_apply, CategoryTheory.Functor.curryingEquiv_symm_apply_map_app, ContinuousMap.toUniformOnFun_toFun, AddValuation.ofValuation_toValuation, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem, isAddRegular_toLex, coe_finRotate_symm_of_ne_zero, SetTheory.PGame.forall_rightMoves_neg, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow, Multiset.toFinsupp_singleton, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, ConjAct.toConjAct_smul, Topology.WithUpperSet.toUpperSet_le_iff, Finset.Ioc_orderDual_def, GroupExtension.Equiv.refl_symm_apply, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_fst, SSet.Subcomplex.PairingCore.equivI_apply_coe, CategoryTheory.Presheaf.uliftYonedaAdjunction_homEquiv_app, SetTheory.PGame.forall_leftMoves_neg, Quiver.SingleObj.toHom_apply, Finset.toDual_max', DFinsupp.lsum_single, Complex.orthonormalBasisOneI_repr_symm_apply, Finset.Colex.insert_le_insert, Order.PFilter.sInf_gc, LinearEquiv.uniqueProd_symm_apply, CategoryTheory.Bicategory.conjugateEquiv_symm_comp, Matrix.conjTransposeAddEquiv_apply, IsAddQuotientCoveringMap.homeomorph_comp_iff, AlternatingMap.domDomCongrEquiv_apply, Matrix.toLinOfInv_symm_apply, ContinuousLinearEquiv.coe_neg, CommBialgCat.isoEquivBialgEquiv_symm_apply, LinearMap.toMatrix_smulRight, HahnModule.ext_iff, Multiplicative.ofAdd_bot, IsometryEquiv.withLpProdCongr_apply, Homeomorph.isHomeomorph, midpoint_eq_iff', Set.coe_snd_unionEqSigmaOfDisjoint, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_assoc, CategoryTheory.Limits.Types.Small.limitCone_pt_ext_iff, AddGroupExtension.Equiv.rightHom_comm, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst_assoc, kroneckerTMulLinearEquiv_tmul, LinearEquiv.alternatingMapCongrRight_apply_apply, CategoryTheory.CommSq.right_adjoint_hasLift_iff, AddSubsemigroup.coe_equivMapOfInjective_apply, LinearMap.toMatrixâAux_eq, RingEquiv.sumArrowEquivProdArrow_symm_apply, MulHom.toMulEquiv_apply, WithBot.toDual_lt_toDual_iff, FreeAddMonoid.lift_comp_of, Ring.DirectLimit.ringEquiv_of, Quiver.starEquivCostar_apply_snd, Multiset.toFinsupp_symm_apply, CategoryTheory.Limits.Types.Small.limitCone_Ď_app, ofBoolAlg_sdiff, CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv_symm_snd_apply, ofColex_inj, List.sortedLT_map_ofDual, Homeomorph.comp_continuousOn_iff, LinearEquiv.extendScalarsOfIsLocalizationEquiv_apply, LinearIsometryEquiv.symm_comp_self, UniformOnFun.uniformContinuous_toFun, Subsemigroup.centerToMulOpposite_symm_apply_coe, RingHom.liftOfRightInverse_comp_apply, iteratedDeriv_eq_equiv_comp, CartanMatrix.A_three, CategoryTheory.Bicategory.mateEquiv_hcomp, FreeAbelianGroup.equivFinsupp_apply, CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_fst, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl, pinGroup.conjAct_smul_range_Κ, Equiv.Perm.card_fixedPoints, Topology.image_snd_preimageImageRestrict, FreeCommRing.of_cons, Finsupp.sumFinsuppEquivProdFinsupp_symm_apply, CategoryTheory.Iso.homCongr_apply, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis, Equiv.natSumNatEquivNat_symm_apply, Equiv.Perm.toList_pow_apply_eq_rotate, Homeomorph.mulLeftâ_symm_apply, PrincipalSeg.subrelIso_symm_apply, AddEquiv.ofBijective_apply, FirstOrder.Language.Equiv.injective, OrderIso.dualAntisymmetrization_apply, Diffeomorph.symm_image_image, HasFTaylorSeriesUpToOn.shift_of_succ, Equiv.permCongr_apply, Fintype.coe_finsetOrderIsoSet_symm, OrderAddMonoidIso.apply_symm_apply, LocallyConstant.congrLeftâ_symm_apply_apply, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, isAdjointPair_toLinearMapâ', Orientation.areaForm_comp_rightAngleRotation, Matrix.cRank_reindex, RootPairing.Equiv.coweightMap_coweightEquiv_symm, antitoneOn_comp_ofDual_iff, Matrix.col_eq_transpose, Matrix.toLin'_apply', AddEquiv.cast_apply, IsometryEquiv.piCongrLeft_symm_apply, Set.up_image, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, Representation.asModuleEquiv_symm_map_rho, apply_covBy_apply_iff, RootPairing.Base.toCoweightBasis_repr_coroot, ContinuousMultilinearMap.prodEquiv_apply, LinearMap.isPairSelfAdjoint_equiv, NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff, Set.exists_equiv_range_eq_graphOn_univ, CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet_comp, FirstOrder.Language.Term.realize_constantsVarsEquivLeft, AdjoinRoot.powerBasisAux'_repr_symm_apply, OrderDual.toDual_le, IsometryEquiv.ediam_image, AddSubmonoid.topEquiv_symm_apply_coe, CategoryTheory.ReflQuiv.adj.homEquiv_naturality_left_symm, CategoryTheory.Adjunction.homEquiv_naturality_right_square_iff, CategoryTheory.conjugateEquiv_counit, RootPairing.reflectionPerm_eq_reflectionPerm_iff_of_span, Homeomorph.continuous_sumAssoc_symm, GradedRing.mem_support_iff, ZMod.dft_comp_neg, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, TensorProduct.directSumLeft_symm_lof_tmul, Homeomorph.coe_refl, Matrix.ker_toLin'_eq_bot_iff, WCovBy.ofDual, RingHom.quotientKerEquivOfRightInverse.Symm.apply, AddLocalization.addEquivOfQuotient_mk, Representation.ofModule_asModule_act, LinearMap.quotKerEquivRange_symm_apply_image, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, Equiv.Perm.IsCycle.exists_zpow_eq, Equiv.Perm.Basis.ofPermHomFun_commute_zpow_apply, codisjoint_toDual_iff, DualNumber.lift_apply_apply, Topology.WithUpper.ofUpper_inj, Finsupp.lsum_apply, CategoryTheory.Functor.flippingEquiv_symm_apply_obj_map, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, WithBot.ofDual_lt_ofDual_iff, WithCStarModule.norm_single, LinearMap.SeparatingLeft.toMatrixâ, Equiv.Perm.subtypeEquivSubtypePerm_apply_of_not_mem, LinearMap.toMatrix'_toLinearMapâ', AffineEquiv.pointReflection_apply_eq_equivPointReflection_apply, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, WithTop.ofDual_le_ofDual_iff, EquivFunctor.mapEquiv_apply, MultilinearMap.iteratedFDeriv_aux, Matrix.rank_reindex, Topology.IsEmbedding.toHomeomorph_apply_coe, HahnModule.of_symm_add, Topology.WithLowerSet.ofLowerSet_le_iff, Isometry.isometryEquivOnRange_apply, MeasureTheory.integral_comp, map_finset_prod, Equiv.Perm.SameCycle.apply_eq_self_iff, Basis.multilinearMap_apply_apply, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, Equiv.finsetCongr_apply, CategoryTheory.Limits.isLimitConeOfAdj_lift, CategoryTheory.InducedCategory.homAddEquiv_apply, CategoryTheory.Adjunction.compPreadditiveYonedaIso_hom_app_app_apply, RCLike.complexLinearIsometryEquiv_symm_apply, PolynomialModule.equivPolynomial_single, AddMonoidHom.op_apply_apply, Equiv.optionCongr_apply, Topology.WithUpper.toUpper_inj, BilinForm.toMatrix_mul_basis_toMatrix, OrderIso.sumLexIicIoi_apply_inr, DFinsupp.subtypeSupportEqEquiv_symm_apply_coe, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, AlgEquiv.arrowCongr_comp, Nat.Primes.coe_prodNatEquiv_apply, FreeRing.lift_comp_of, AddEquiv.congr_arg, WeakDual.isClosed_closedBall, MulRingNorm.mulRingNormEquivAbsoluteValue_symm_apply, antitone_dual_iff, UniformEquiv.comap_eq, RingEquiv.height_comap, Matrix.piAddEquiv_symm_apply, UniformOnFun.continuousOn_evalâ, Monoid.foldlM.ofFreeMonoid_apply, Unitization.lift_symm_apply, coe_lpPiLpâᾢ, AntitoneOn.dual_left, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Topology.WithUpperSet.ofUpperSet_toUpperSet, Matrix.lift_cRank_reindex, Submodule.Quotient.equiv_symm_apply, ofDual_one, ContinuousLinearEquiv.smulLeft_apply_apply, iSupIndep.linearEquiv_apply, MulDistribMulAction.toMulEquiv_symm_apply, stdSimplexHomeomorphUnitInterval_apply_coe, Equiv.permCongr_mul, NumberField.RingOfIntegers.withValEquiv_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_map_comp, Multiplicative.mem_toSubgroup, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Module.Basis.coe_finTwoProd_repr, Equiv.Set.univ_apply, QuadraticForm.dualProdIsometry_toFun, IsometryEquiv.measurePreserving_hausdorffMeasure, LinearMap.BilinForm.mul_toMatrix', WithCStarModule.equiv_symm_sub, CategoryTheory.Adjunction.homAddEquiv_symm_zero, Complex.volume_preserving_equiv_real_prod, AddEquiv.addMonoidHomCongrLeftEquiv_symm_apply, Localization.mulEquivOfQuotient_symm_mk, QuotientAddGroup.quotientKerEquivOfRightInverse_symm_apply, Homeomorph.Set.prod_apply, Monoid.PushoutI.homEquiv_apply_coe, QuadraticForm.tensorAssoc_symm_apply, Homeomorph.isBigO_congr, Equiv.Perm.sameCycle_pow_right, MulEquivClass.apply_mem_center_iff, LinearIsometryEquiv.coe_coe'', emultiplicity_map_eq, Set.PartiallyWellOrderedOn.fiberProdLex, HomotopicalAlgebra.AttachCells.reindex_cofanâ, PiTensorProduct.isEmptyEquiv_symm_apply, CategoryTheory.Functor.RepresentableBy.homEquiv_comp, Finset.Ioc_toDual, DistribMulAction.toLinearEquiv_apply, Equiv.Perm.decomposeFin_symm_apply_succ, LinearEquiv.map_add, CategoryTheory.Limits.idZeroEquivIsoZero_apply_hom, PiTensorProduct.subsingletonEquiv_symm_apply', HahnSeries.addOppositeEquiv_orderTop, val_unitsCentralizerEquiv_symm_apply_coe, toLex_natCast, CategoryTheory.conjugateEquiv_rightUnitor_hom, Topology.IsGeneratedBy.homeomorph_coe, CategoryTheory.LocalizerMorphism.equiv_smallShiftedHomMap, Finsupp.coe_lsum, Set.Iic_toDual, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, WittVector.liftEquiv_apply, AlgebraicGeometry.coprodSpec_coprodMk, CStarMatrix.mul_entry_mul_eq_inner_toCLM, RingCon.congr_mk, Matrix.kronecker_assoc, ZMod.lift_comp_castAddHom, MulEquivClass.map_nonZeroDivisors, homeomorphSphereProd_symm_apply_coe, Matrix.trace_fin_one_of, AddMonoidAlgebra.lift_of, nsmulCoprime_neg, RelIso.sumLexComplRight_symm_apply, ContinuousLinearEquiv.prodUnique_symm_apply, Diffeomorph.uniqueDiffOn_image, ContinuousAlgEquiv.symm_symm_apply, ContinuousLinearEquiv.coe_mk, powersHom_apply, CoxeterMatrix.reindexGroupEquiv_apply_simple, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, List.zipWith_swap_prod_support', ofAdd_add, Submodule.unitsQuotEquivRelPic_symm_apply, WithTop.toDual_lt_toDual_iff, Finset.mem_map_equiv, ofDual_iSup, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, MulEquiv.symm_map_mul, Set.dual_ordSeparatingSet, FractionalIdeal.canonicalEquiv_canonicalEquiv, LinearMap.toMatrixRight'_id, CategoryTheory.Limits.Multifork.IsLimit.sectionsEquiv_symm_apply_val, MulEquiv.coprodAssoc_apply_inr, Diffeomorph.sumCongr_inr, AddMonoidHom.coe_toMultiplicative, Orientation.inner_rightAngleRotation_left, SkewMonoidAlgebra.lift_unique', ConvexOn.dual, MulAction.orbitZPowersEquiv_symm_apply, CategoryTheory.Functor.RepresentableBy.isRepresentedBy, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, Tuple.comp_sort_eq_comp_iff_monotone, OrderHom.dual_comp, Topology.WithScott.toScott_inj, TensorProduct.rid_tmul, CategoryTheory.Linear.homCongr_apply, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, IsPrimitiveRoot.primitiveRootsPowEquivOfCoprime_apply_coe, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul, SetSemiring.down_imageHom, Sum.Lex.inl_strictMono, DilationEquiv.ratio_toDilation, LinearMap.minpoly_toMatrix, Equiv.toIso_hom, MeasurableEquiv.coe_piCongrLeft, RingEquiv.map_prod, Homeomorph.sumProdDistrib_apply, MulChar.ofUnitHom_eq, PartENat.withTopEquiv_symm_one, Sym2.sortEquiv_symm_apply, FreeAbelianGroup.lift_unique, AddEquiv.coprodAssoc_symm_apply_inl, CharacterModule.homEquiv_symm_apply_apply_apply, CStarMatrix.ofMatrix_symm_apply, AddOpposite.coe_opAddEquiv, Finset.Colex.toColex_mono, WittVector.inv_pairâ, LinearIsometryEquiv.coe_toLinearIsometry, ModuleCat.homEquiv_extendScalarsComp, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, AddEquiv.punitCoprod_symm_apply, DirectSum.coe_decompose_mul_of_right_mem, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_apply_snd, CategoryTheory.CommSq.left_adjoint_hasLift_iff, WithBot.ofDual_symm_apply, HNNExtension.t_mul_of, CategoryTheory.Limits.Pi.reindex_inv_Ď, WithAbs.norm_eq_abv, AddEquiv.symmEquiv_symm_apply_apply, LinearMap.adjoint_lTensor, Matrix.conjTransposeRingEquiv_symm_apply, Matrix.nondegenerate_toLinearMapâ'_iff_nondegenerate_toLinearMapâ, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, Equiv.sigmaSigmaSubtype_apply, LinearEquiv.smulOfNeZero_apply, MeasurableEquiv.funUnique_apply, IsometryEquiv.funUnique_apply, Homeomorph.isDenseEmbedding, multilinearCurryLeftEquiv_apply, LinearIsometryEquiv.coe_withLpProdUnique, IsFreeGroup.lift_symm_apply, Equiv.prodProdProdComm_apply, FirstOrder.Language.Theory.models_formula_iff_onTheory_models_equivSentence, SchwartzMap.fourierTransformCLE_symm_apply, PartENat.withTopEquiv_natCast, Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe, QuaternionAlgebra.re_equivProd_symm_apply, starL'_symm_apply, Module.reflection_mul_reflection_pow_apply_self, OrthonormalBasis.map_apply, ofColex_smul, MonoidAlgebra.mapRangeRingEquiv_apply, MvPolynomial.supDegree_toLex_C, ContinuousLinearEquiv.unitsEquivAut_symm_apply, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_counitIso, PiTensorProduct.tmulEquivDep_symm_apply, Homeomorph.piCongrRight_apply, Submodule.rTensorOne_tmul_one, OrderAddMonoidIso.comp_symm_eq, Sym.cons_equiv_eq_equiv_cons, Matrix.replicateRow_mul_replicateCol, AddSubgroup.centerCongr_symm_apply_coe, Fin.revPerm_apply, MeasurableEquiv.refl_apply, LinearIsometryEquiv.trans_apply, OrderMonoidIso.self_comp_symm, AddEquiv.prodAdditive_symm_apply, Equiv.sumProdDistrib_apply_left, LieAlgebra.of_zero, Invertible.mulLeft_symm_apply, Algebra.leftMulMatrix_complex, Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff, RingHom.equivRatAlgHom_apply, Equiv.mul_def, ContinuousMultilinearMap.prodEquiv_symm_apply_snd, CategoryTheory.conjugateEquiv_mateEquiv_vcomp, isRightRegular_toLex, Algebra.Norm.Transitivity.eval_zero_comp_det, Monotone.dual_right, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, IsAdjoinRootMonic.coeff_apply_lt, DomMulAct.mk_smul_mulDistribActionHom_apply, MultilinearMap.constLinearEquivOfIsEmpty_apply, MulEquiv.symmEquiv_apply_apply, LinearEquiv.finTwoArrow_symm_apply, WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv, IsPrimitiveRoot.primitiveRootsPowEquiv_apply_coe, CategoryTheory.Limits.WidePullbackCone.reindex_Ď, AffineEquiv.pointReflection_midpoint_right, Equiv.existsUnique_congr_right, MulAut.conj_inv_apply, CategoryTheory.ShiftedHom.opEquiv'_symm_apply, AlgEquiv.algHomUnitsEquiv_apply_symm_apply, Homeomorph.trans_apply, Finset.Icc_toDual, AddCircle.measurePreserving_equivIoc, powersMulHom_apply, BoolAlg.dual_map, Circle.argEquiv_symm_apply, MeasureTheory.measurePreserving_piUnique, ContinuousLinearEquiv.coe_symm_toHomeomorph, RingEquiv.cast_symm_apply, UniformFun.ofFun_smul, AddConstEquiv.coe_val_inv_equivUnits_apply, LinearEquiv.map_dfinsuppSumAddHom, Equiv.neg_apply, RingEquiv.map_pow, RingEquiv.prodZeroRing_apply, OrthonormalBasis.sum_repr_symm, groupCohomology.cocyclesOfIsMulCocycleâ_coe, homeomorphUnitSphereProd_apply_fst_coe, Subgroup.toAddSubgroup_closure, DirectSum.IsInternal.collectedBasis_repr_of_mem_ne, Module.dualProdDualEquivDual_apply, RingHom.quotientKerEquivOfSurjective_apply_mk, Module.Basis.toMatrix_apply, RootPairing.RootPositiveForm.rootLength_reflectionPerm_self, FirstOrder.Language.Term.constantsVarsEquiv_apply, Diffeomorph.contMDiffOn_diffeomorph_comp_iff, AffineEquiv.injective_pointReflection_left_of_module, Equiv.sigmaAssocProd_symm_apply_fst, Equiv.sumProdDistrib_apply_right, Equiv.divRight_apply, Homeomorph.prodUnique_symm_apply_snd, RootPairing.Hom.weight_coweight_transpose_apply, Hamming.ofHamming_add, MultilinearMap.curryFinFinset_symm_apply_const, KaehlerDifferential.mvPolynomialBasis_repr_apply, MulEquiv.funUnique_symm_apply, RingInvo.involution, MulEquiv.uniqueProd_apply, ofDegLex_injective, MulEquiv.comapSubgroup_apply, sSupHom.dual_comp, LinearEquiv.coe_symm_mk, MeasureTheory.Measure.infinitePi_map_curry_symm, Matrix.isHermitian_submatrix_equiv, Orientation.inner_smul_rotation_pi_div_two_right, Set.powersetCard.coe_compl, ContinuousLinearEquiv.map_neg, ContAction.resEquiv_functor, Finsupp.sigmaFinsuppLEquivPiFinsupp_apply, DFinsupp.equivProdDFinsupp_add, Equiv.coe_prodComm, Monovary.dual_right, ArchimedeanClass.FiniteElement.val_zero, Equiv.set_forall_iff, CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv_symm_apply, AlgEquiv.coe_coe_symm_apply_coe_apply, CategoryTheory.mateEquiv_conjugateEquiv_vcomp, CategoryTheory.CommSq.LiftStruct.opEquiv_symm_apply, CategoryTheory.Iso.toLinearEquiv_apply, Diffeomorph.contMDiffAt_comp_diffeomorph_iff, SymmetricAlgebra.lift_comp_Κ, WithZero.toMulBot_zero, InfPrime.ofDual, Fin.castLEquiv_apply, RootPairing.chainTopCoeff_reflectionPerm_left, CategoryTheory.Bicategory.mateEquiv_eq_iff, DomMulAct.stabilizer_card', ContinuousLinearEquiv.uniqueProd_apply, finsuppTensorFinsuppRid_single_tmul_single, toLex_inv, CategoryTheory.Arrow.equivSigma_symm_apply_hom, LinearIndependent.linearCombinationEquiv_symm_apply, WithZero.lift_zero, Submodule.equivSubtypeMap_apply, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, AlgEquiv.val_algHomUnitsEquiv_symm_apply, SymmetricAlgebra.lift_Κ, OrderMonoidHom.inlâ_apply, ContinuousMultilinearMap.piEquiv_apply, Module.DualBases.basis_repr_apply, LinearEquiv.toLinearMap_eq_coe, SymAlg.unsym_injective, CircleDeg1Lift.translate_zpow, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, Equiv.preimage_symm_preimage, SpecialLinearGroup.congr_linearEquiv_apply_apply, Algebra.toMatrix_lmul', Submodule.isIdempotentElemEquiv_symm_apply_coe, AffineEquiv.prodCongr_apply, List.formPerm_mem_iff_mem, DFinsupp.sigmaCurryLEquiv_symm_apply, Homeomorph.shearMulRight_symm_coe, FirstOrder.Language.Formula.realize_equivSentence_symm_con, Multiplicative.toAdd_lt, MonoidHom.toAdditiveRight_symm_apply_apply, Subsemiring.mopRingEquivOp_apply_coe, FirstOrder.Language.PartialEquiv.toEquiv_inclusion_apply, Equiv.symm_trans_swap_trans, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, Equiv.optionIsSomeEquiv_apply, TopologicalSpace.IrreducibleCloseds.equivSubtype_apply, isRightRegular_toMul, AddMonoidHom.toMultiplicativeLeft_symm_apply_apply, Fin.succFunEquiv_symm_apply, Homeomorph.nhds_eq_comap, LinearIsometryEquiv.strictConvex_image, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, linearIndependent_equiv, groupCohomology.coboundariesOfIsMulCoboundaryâ_coe, toWeakSpace_closedConvexHull_eq, WithCStarModule.inner_single_right, CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply, FreeAddMonoid.freeAddMonoidCongr_symm_of, Matrix.cRank_submatrix, List.formPerm_apply_mem_eq_self_iff, Quiver.SingleObj.toPrefunctor_id, Algebra.Extension.contangentEquiv_tmul, CategoryTheory.Limits.Cotrident.IsColimit.homIso_symm_apply, DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSum, Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, CategoryTheory.Discrete.equivOfEquivalence_apply, IsPerfectClosure.equiv_self_apply, toColex_inj, AffineEquiv.ext_iff, isAddRightRegular_toDual, LieModuleEquiv.coe_toLinearEquiv, OrderIsoClass.toBotHomClass, WithLp.equiv_apply, GenLoop.toLoop_apply_coe, AddEquiv.coe_prodComm, AddEquiv.coe_toEquiv_symm, HahnModule.coeff_smul, UniformFun.precomp_uniformContinuous, Submonoid.map_equiv_eq_comap_symm, Equiv.Perm.extendDomain_apply_not_subtype, Equiv.Perm.ofSubtype_apply_coe, PerfectionMap.comp_equiv, MulEquiv.eq_iff_eq_on_generator, parallelepiped_comp_equiv, OrderMonoidIso.apply_eq_iff_symm_apply, RingEquiv.piUnique_symm_apply, SSet.S.equivElements_apply_fst, Finsupp.llift_symm_apply, Int.ofAdd_mul, Finsupp.Colex.lt_iff, finAddFlip_apply_mk_left, Orientation.kahler_rotation_left', Representation.linHom.invariantsEquivRepHom_symm_apply_coe, CategoryTheory.codiscreteEquiv_apply, Nat.equivProdNatSmoothNumbers_apply', AffineMap.toConstProdLinearMap_apply, LinearMap.quotKerEquivRange_apply_mk, CategoryTheory.Limits.Concrete.prodEquiv_symm_apply_fst, CategoryTheory.ObjectProperty.isLocal.homEquiv_apply, TensorProduct.finsuppScalarLeft_apply_tmul_apply, AddEquiv.surjective, Equiv.mulLeft_symm_apply, Matrix.ker_diagonal_toLin', ContinuousMultilinearMap.norm_ofSubsingleton_id_le, Equiv.ofRightInverseOfCardLE_apply, LatticeHom.symm_dual_comp, CompactlyGenerated.homeoOfIso_symm_apply, FreeAlgebra.Κ_comp_lift, TensorProduct.inner_comm_comm, Equiv.divLeft_apply, CategoryTheory.Functor.RepresentableBy.homEquiv_unop_comp, FreeAbelianGroup.lift_comp_apply, Ideal.pointwise_smul_eq_comap, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Equiv.coe_addLeft, gc_upperClosure_coe, Finsupp.equivMapDomain_symm_apply, finSuccEquiv_symm_some, CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_hom, Sym2.coe_liftâ_symm_apply, ContinuousAlgEquiv.symm_apply_apply, Multiset.coe_consEquiv_of_eq_of_lt, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, MulEquiv.submonoidMap_symm_apply, IsometryEquiv.coe_withLpUniqueProd, Unitary.toRingEquiv_conjStarAlgAut, RingEquiv.mapMatrix_apply, SimpleGraph.Iso.mapNeighborSet_apply_coe, Ideal.snd_comp_quotientMulEquivQuotientProd, Matrix.kronecker_assoc', UniformOnFun.edist_def', Equiv.Perm.zpow_eq_zpow_on_iff, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Module.Basis.map_apply, HahnSeries.coeff_toPowerSeries, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_apply, Module.Basis.symmetricAlgebra_repr_apply, Monoid.CoprodI.lift_of', CategoryTheory.yonedaGrpObjIsoOfRepresentableBy_inv, LinearEquiv.prodProdProdComm_apply, RingHom.map_iterate_frobeniusEquiv_symm, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, Subgroup.coe_toAddSubgroup_apply, Cubic.equiv_symm_apply_b, DomAddAct.continuous_mk, Module.AEval.of_symm_X_smul, LinearEquiv.sumPiEquivProdPi_symm_apply, AddEquiv.coe_prodAssoc_symm, OrderAddMonoidIso.coe_trans, isAddLeftRegular_toAdd, WithTop.toDual_symm_apply, SheafOfModules.Presentation.map_relations_I, Equiv.Set.rangeSplittingImageEquiv_apply_coe_coe, FGModuleCat.Iso.conj_eq_conj, Finsupp.supportedEquivFinsupp_symm_apply_coe_support_val, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', WithTop.ofDual_map, AddLocalization.addEquivOfQuotient_symm_mk', AffineIsometryEquiv.symm_apply_apply, Metric.Snowflaking.preimage_toSnowflaking_closedEBall, DomMulAct.comap_mk.symm_nhds, Set.conj_mem_fixingSubgroup, ZLattice.exists_forall_abs_repr_le_norm, LinearEquiv.symmEquiv_apply_apply, Equicontinuous.isUniformInducing_uniformFun_iff_pi, Matrix.toBilin'_apply, ContinuousLinearEquiv.neg_apply, sInfHom.dual_comp, MultilinearMap.domDomCongrLinearEquiv'_apply, WithTop.map_toDual, LinearIsometryEquiv.edist_map, ContinuousAddEquiv.isAddHaarMeasure_map, finEquivZMultiples_symm_apply, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, AnalyticOn.iteratedFDeriv_comp_perm, Diffeomorph.mdifferentiable, LieAlgebra.conj_ad_apply, AffineIsometryEquiv.map_eq_iff, AddEquiv.addDissociated_preimage, Submonoid.LocalizationMap.mulEquivOfLocalizations_symm_apply, Equiv.Perm.IsCycle.zpowersEquivSupport_apply, CategoryTheory.Localization.homEquiv_apply, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, Quotient.finChoiceEquiv_apply, RestrictScalars.ringEquiv_map_smul, ComplexShape.Embedding.homEquiv_symm_apply, Equiv.prodSumDistrib_symm_apply_right, Matrix.adjugate_def, Equiv.permCongr_refl, AddChar.toMonoidHomEquiv_apply, Metric.Snowflaking.preimage_ofSnowflaking_ball, monoidEndToAdditive_symm_apply_apply, SSet.prodStdSimplex.objEquiv_map_apply, Equiv.tprod_eq, AddAut.coe_one, Equiv.left_vsub_pointReflection, frobeniusEquiv_def, RestrictScalars.lsmul_apply_apply, Equiv.trans_swap_trans_symm, MonoidHom.apply_mint, SemidirectProduct.mulEquivProd_symm_apply_left, ContinuousMultilinearMap.domDomCongr_apply, LinearMap.toMatrix_prodMap, AddEquiv.coe_addMonoidHom_trans, HahnModule.coeff_single_zero_smul, Matrix.toLin_apply, SimpleGraph.Iso.comap_apply, Equiv.optionSubtype_apply_apply, Matrix.toLin'_one, groupHomology.H1AddEquivOfIsTrivial_symm_apply, SSet.stdSimplex.objEquiv_symm_mem_nonDegenerate_iff_mono, Matrix.submatrix_diagonal_equiv, PiTensorProduct.tmulEquivDep_apply, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset', ContinuousLinearEquiv.unitsEquivAut_apply_symm, Polynomial.toFinsuppIsoLinear_apply, Affine.Simplex.altitude_reindex, CategoryTheory.conjugateEquiv_comm, Homeomorph.divLeft_apply, QuaternionAlgebra.equivTuple_apply, AddEquiv.toMultiplicativeRight_symm_apply_symm_apply, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three, isLeftRegular_ofDual, RingHom.op_symm_apply_apply, LinearAlgebra.FreeProduct.lift_unique, finSuccEquiv'_symm_some_below, DualNumber.coe_lift_symm_apply, Algebra.TensorProduct.linearEquivIncludeRange_symm_tmul, Homeomorph.isSigmaCompact_image, MultilinearMap.freeFinsuppEquiv_apply, MonoidAlgebra.domCongr_comp_lsingle, Finset.sigmaAntidiagonalEquivProd_symm_apply_snd_coe, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, Ideal.quotientInfEquivQuotientProd_snd, AlgEquiv.linearEquivConj_mulLeftRight, Module.Basis.constr_apply_fintype, ContinuousLinearEquiv.comp_right_differentiableOn_iff, hasGradientAt_iff_hasFDerivAt, CategoryTheory.Functor.isIso_lanAdjunction_homEquiv_symm_iff, LinearEquiv.symm_conj_apply, AddMonoidAlgebra.liftMagma_apply_apply, Polynomial.opRingEquiv_symm_C_mul_X_pow, TensorProduct.LieModule.lift_apply, Matrix.cramer_submatrix_equiv, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_symm_apply_fst, ContinuousLinearEquiv.symm_comp_self, RingEquiv.coe_prodComm, Homeomorph.image_symm_apply_coe, MultilinearMap.ofSubsingletonâ_apply, MeasureTheory.hausdorffMeasure_measurePreserving_funUnique, List.SortedLE.of_map_ofDual, Equiv.prod_comp, Matrix.mulVecLin_submatrix, BoundedLatticeHom.asBoolRing_apply, DFinsupp.lsum_symm_apply, Diffeomorph.sumEmpty_apply_inl, QuaternionAlgebra.imK_equivProd_symm_apply, ZMod.dft_dft, List.SortedGT.of_map_toDual, coe_finRotate_of_ne_last, MulEquiv.symm_trans_apply, ContinuousLinearEquiv.iteratedFDeriv_comp_left, WithConv.linearEquiv_apply, piFinTwoEquiv_apply, Equiv.piEquivPiSubtypeProd_symm_apply, AlgEquiv.coe_toLinearEquiv, AddAut.mulRight_apply, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, AddMonoid.Coprod.map_mk_ofList, LinearEquiv.conjAlgEquiv_apply_apply, DFinsupp.Lex.lt_iff_of_unique, List.SortedLT.of_map_toDual, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_fst, InverseSystem.piSplitLE_eq, finRotate_succ_symm_apply, RingEquiv.toMonoidHom_commutes, MultilinearMap.fromDirectSumEquiv_apply, TrivSqZeroExt.liftEquivOfComm_apply, ComplexShape.Embedding.homEquiv_apply_coe, Matrix.BlockTriangular.transpose, Equiv.sigmaSubtype_symm_apply_coe_snd, Pi.toColex_apply, LinearEquiv.algEquivOfRing_symm_apply, IsHomeomorphicTrivialFiberBundle.proj_eq, CategoryTheory.Localization.SmallShiftedHom.equiv_shift, IsGalois.intermediateFieldEquivSubgroup_symm_apply, Matrix.reindexLinearEquiv_mul, Homeomorph.piUnique_apply, OrderMonoidIso.comp_symm_eq, AddChar.coe_doubleDualEquiv, CategoryTheory.CommSq.right_adjoint, DomMulAct.mk_zpow, FormalMultilinearSeries.leftInv_coeff_one, Finsupp.coe_orderIsoMultiset_symm, Nat.Partition.ofSym_map, Matrix.comp_symm_diagonal, finsuppLEquivDirectSum_single, HilbertBasis.repr_symm_single, CategoryTheory.OverPresheafAux.unitAuxAux_inv_app_snd_coe, CategoryTheory.Functor.sectionsEquivHom_naturality_symm, UniformConvergenceCLM.isUniformInducing_coeFn, HilbertBasis.repr_apply_apply, Polynomial.opRingEquiv_symm_monomial, ContinuousMulEquiv.coe_mk, RingEquiv.toCommSemiRingCatIso_hom, SetTheory.PGame.relabel_moveRight', RingCon.quotientQuotientEquivQuotient_mk_mk, PartENat.withTopEquiv_top, IsLocalization.algEquivOfAlgEquiv_symm_apply, MulEquiv.punitCoprod_symm_apply, CategoryTheory.ParametrizedAdjunction.homEquiv_symm_naturality_two_assoc, TensorProduct.assocIsometry_apply, Matrix.toLin_conjTranspose, LieEquiv.symm_apply_apply, MulEquiv.coprodComm_symm_apply, Submodule.linearDisjoint_op, PiTensorProduct.mem_lifts_iff, CliffordAlgebra.toBaseChange_comp_reverseOp, Equiv.preimage_eq_iff_eq_image, ContinuousOn.continuous_restrict_iff_continuous_uniformOnFun, Subgroup.transferTransversal_apply', Submodule.quotientEquivOfIsCompl_symm_apply, GenLoop.loopHomeo_symm_apply, NonUnitalSubring.comap_equiv_eq_map_symm, Module.Relations.Solution.IsPresentation.uniq_symm_var, CategoryTheory.Equivalence.congrLeftFunctor_map, Metric.Snowflaking.continuous_toSnowflaking, AffineIsometryEquiv.dist_map, LinearIsometryEquiv.injective, CategoryTheory.Equalizer.Presieve.Arrows.compatible_iff_of_small, LieAlgebra.Extension.bracket, ContinuousLinearEquiv.coe_apply, MeasureTheory.addEquivAddHaarChar_smul_map, LinearEquiv.conj_conj_symm, SubAddAction.ofStabilizer.conjMap_bijective, Bifunctor.mapEquiv_symm_apply, CategoryTheory.Adjunction.homAddEquiv_symm_neg, invertibleEquivOfLeftInverse_apply, GradedTensorProduct.auxEquiv_tmul, MulOpposite.opLinearIsometryEquiv_symm_apply, ContinuousLinearEquiv.image_eq_preimage_symm, Ideal.cotangentEquivIdeal_apply, Complex.expMonoidHom_apply, OrderIso.conj_symm_apply, Sum.Lex.inl_lt_inl_iff, IsometryEquiv.dimH_image, LinearIsometryEquiv.hasFDerivAt, IsPerfectClosure.equiv_comp_equiv_apply, ContinuousLinearEquiv.surjective, OrderIso.sumLexAssoc_apply_inl_inl, Equiv.coe_constVSub, CoalgEquiv.coe_symm_toEquiv, Subgroup.subgroupOfContinuousMulEquivOfLe_apply, UniformFun.ofFun_prod, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, AdicCompletion.congr_symm_apply, FirstOrder.Language.LEquiv.onBoundedFormula_symm_apply, Rat.HeightOneSpectrum.span_natGenerator, Equiv.swap_apply_eq_iff, CategoryTheory.ReflQuiv.adj.homEquiv_apply, NumberField.mixedEmbedding.polarCoord_symm_eq, Finset.Ioi_ofDual, EuclideanGeometry.dist_reflection_eq_of_mem, LinearEquiv.ofSubsingleton_apply, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, ArchimedeanClass.FiniteResidueField.mk_ne_zero, exists_homeomorph_image_eq, UniformEquiv.injective, Diffeomorph.contMDiff_invFun, LinearIsometryEquiv.rTensor_apply, LinearIsometryEquiv.inner_map_map, groupHomology.H1ToTensorOfIsTrivial_H1Ď_single, WithCStarModule.equiv_smul, MulAction.orbitEquivQuotientStabilizer_symm_apply, ContinuousLinearEquiv.self_comp_symm, Orientation.neg_rotation_pi_div_two, AddEquiv.addOrderOf_eq, PolynomialModule.equivPolynomialSelf_apply_eq, GrpCat.SurjectiveOfEpiAuxs.h_apply_infinity, Finsupp.fst_sumFinsuppAddEquivProdFinsupp, CategoryTheory.Bicategory.toNatTrans_mateEquiv, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_hom, SymAlg.sym_surjective, LinearEquiv.coe_ofEq_apply, Polynomial.degreeLT.addLinearEquiv_symm_apply, LinearEquiv.eq_comp_symm, DoubleQuot.coe_quotQuotEquivQuotOfLEâ, PerfectRing.lift_apply, Trivialization.apply_eq_prod_continuousLinearEquivAt, ContinuousAlternatingMap.piLIE_symm_apply_apply, IsometryEquiv.diam_preimage, toLex_vadd, NonemptyFinLinOrd.dual_map, DomMulAct.mk_smul_linearMap_apply, MeasureTheory.integrableOn_map_equiv, Ideal.apply_mem_of_equiv_iff, ContinuousAddEquiv.apply_eq_iff_eq, Partition.partscopyEquiv_symm_apply_coe, HasFPowerSeriesAt.hasFDerivAt, Submodule.dualAnnihilator_gc, OrthonormalBasis.measurePreserving_repr_symm, SpecialLinearGroup.centerEquivRootsOfUnity_apply, AddMonoidAlgebra.liftNC_single, Homeomorph.Set.prod_symm_apply_coe, Topology.WithLowerSet.toLowerSet_le_iff, Orientation.linearIsometryEquiv_comp_rightAngleRotation, ContinuousAlgEquiv.symm_image_image, Equiv.Perm.decomposeOption_symm_sign, Topology.WithGeneratedByTopology.continuous_from_iff, Finsupp.DegLex.single_le_iff, Units.mulLeft_apply, Equiv.ofInjective_apply, AffineMap.toConstProdLinearMap_symm_apply, PiTensorProduct.ofDFinsuppEquiv_tprod_single, Equiv.locallyFinite_comp_iff, IsometryEquiv.toDilationEquiv_toDilation, CategoryTheory.Localization.SmallHom.equiv_chgUniv, LinearEquiv.smul_apply, HahnSeries.archimedeanClassOrderIsoWithTop_apply, Order.succ_toMul, SetTheory.PGame.Domineering.shiftRight_symm_apply, DirectSum.decomposeLinearEquiv_apply, Polynomial.support_opRingEquiv, prodEquivPiFinTwo_apply, EuclideanSpace.piLpCongrLeft_single, AffineEquiv.equivUnitsAffineMap_symm_apply_symm_apply, Order.isPredLimit_toDual_iff, Equiv.Perm.mem_cycleFactorsFinset_support, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, range_comp, bddBelow_preimage_ofDual, CategoryTheory.Limits.Bicone.whisker_Ď, isSemilinearSet_image_iff, PerfectionMap.comp_symm_equiv, BddBelow.dual, Submonoid.equivOp_apply_coe, Ideal.associatesEquivIsPrincipal_symm_apply, LinearMap.BilinForm.nondegenerate_congr_iff, Matrix.transposeAddEquiv_apply, CategoryTheory.equivYoneda_hom_app, EuclideanGeometry.dist_reflection, NumberField.conj_basisMatrix, Topology.WithUpperSet.ofUpperSet_le_ofUpperSet, exteriorPower.alternatingMapLinearEquiv_comp, Matrix.trace_toLin'_eq, TensorProduct.gradedComm_of_zero_tmul, Homeomorph.injective, NumberField.IsCMField.unitsMulComplexConjInv_apply, CategoryTheory.Limits.Pi.whiskerEquiv_hom, coe_addEquiv_lpBCF_symm, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, LocallyConstant.congrLeftâ_symm_apply_apply, OrderIso.neg_symm_apply, Matrix.submatrix_one_equiv, Matrix.toLin'OfInv_symm_apply, Orientation.rotation_eq_matrix_toLin, CategoryTheory.unit_mateEquiv_symm, MonotoneOn.dual, OrderAddMonoidHom.inlâ_apply, MeasurableEquiv.piEquivPiSubtypeProd_symm_apply, LinearMap.BilinForm.flip_apply, toDual_sub, ProbabilityTheory.Kernel.prodComm_prod, HasDerivAt.hasFDerivAt_equiv, AddEquiv.toMultiplicative_symm_apply_apply, OrderMonoidHom.fstâ_apply, Filter.tendsto_prodAssoc, Matrix.mul_submatrix_one, WithSeminorms.congr_equiv, Function.RightInverse.homeomorph_symm_apply, Orientation.inner_rightAngleRotation_swap, CategoryTheory.Iso.homToEquiv_apply, Module.Basis.sumQuot_repr_inr_of_mem, NumberField.Units.abs_det_eq_abs_det, RingHom.rangeRestrictFieldEquiv_apply_symm_apply, UniformEquiv.piCongrLeft_toEquiv, unitsEquivNeZero_apply_coe, Topology.WithLower.ofLower_le_ofLower, infClosed_preimage_ofDual, AffineIsometryEquiv.ext_iff, continuous_toDual, RCLike.complexRingEquiv_symm_apply, CategoryTheory.Functor.curryingEquiv_apply_map, IsSimpleOrder.equivBool_symm_apply, LinearIsometryEquiv.piLpCurry_symm_apply, AffineEquiv.symm_apply_apply, AffineEquiv.coe_trans, DistribMulAction.toAddEquiv_apply, EuclideanGeometry.Sphere.IsTangent.eq_orthRadius_or_eq_orthRadius_pointReflection_of_parallel_orthRadius, AffineEquiv.ofLinearEquiv_apply, MulRingNorm.mulRingNormEquivAbsoluteValue_apply, WithBot.lt_toDual_iff, Monotone.dual, AffineEquiv.coe_refl, Equiv.finsetSubtypeComm_symm_apply, CategoryTheory.Limits.Types.Small.limitConeIsLimit_lift, ContinuousLinearEquiv.image_symm_eq_preimage, FreeMonoid.mrange_lift, BoundedLatticeHom.dual_apply_toFun, QuadraticAlgebra.linearEquivTuple_symm_apply, RingEquiv.ofLeftInverse'_symm_apply, WithAbs.equivWithAbs_equiv_symm_apply, OrderIsoClass.toBiheytingHomClass, Equiv.image_eq_preimage_symm, rotationOf_coe, LinearIsometryEquiv.coe_inv, AddMonoidAlgebra.lift_unique', MulEquiv.toAdditive_symm_apply_apply, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_symm_apply_homEquiv, Equiv.sumProdDistrib_symm_apply_left, Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsLocalizedModule.iso_symm_apply_aux, IsBaseChange.endHom_apply, Antitone.dual_left, NumberField.mixedEmbedding.volume_negAt_plusPart, ZMod.lift_coe, CategoryTheory.FunctorToTypes.functorHomEquiv_apply_app, Orientation.oangle_sub_left_smul_rotation_pi_div_two, ContinuousLinearEquiv.prodAssoc_apply, AffineEquiv.affineIndependent_set_of_eq_iff, uliftPowersHom_apply_apply, AffineIsometryEquiv.coe_vaddConst_symm, Homeomorph.isConnected_preimage, FractionalIdeal.canonicalEquiv_flip, Topology.WithLawson.ofLawson_inj, CartanMatrix.A_two, Module.Basis.parallelepiped_eq_map, IsLocalization.isLocalization_of_base_ringEquiv, Equiv.swap_eq_update, AddChar.toMonoidHomEquiv_add, Algebra.discr_powerBasis_eq_prod, FreeAddMonoid.lift_eval_of, TensorProduct.piScalarRight_symm_single, finSuccEquiv'_above, LinearEquiv.map_eq_zero_iff, DirectSum.coe_decompose_mul_add_of_right_mem, Module.Basis.repr_apply_eq, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_right, ContinuousAlternatingMap.piLinearEquiv_symm_apply, Equiv.Perm.pow_apply_mem_support, measurable_equivCurry_symm, UniformFun.postcomp_uniformContinuous, MulEquiv.multiplicativeAdditive_symm_apply, Equiv.uniqueSigma_symm_apply, ContinuousAlgEquiv.eq_symm_apply, TensorPower.algebraMapâ_mul_algebraMapâ, TensorPower.gMul_def, Diffeomorph.contMDiffWithinAt_comp_diffeomorph_iff, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, IsFreeGroup.toFreeGroup_apply, SymAlg.sym_mul_self, LieAlgebra.of_add, MulEquiv.piUnique_apply, SetTheory.PGame.moveLeft_neg_toLeftMovesNeg, CategoryTheory.WithTerminal.widePullbackShapeEquiv_inverse_obj, Function.Involutive.toPerm_involutive, LinearEquiv.isUnit_det, UniformFun.edist_def, AddMonoidAlgebra.opRingEquiv_single, addEquivOfAddOrderOfEq_symm_apply_gen, CategoryTheory.Sheaf.ÎHomEquiv_naturality_right_symm, CategoryTheory.Sieve.overEquiv_symm_generate, FirstOrder.Language.StrongHomClass.realize_formula, SubAddAction.ofFixingAddSubgroup_insert_map_apply, Tuple.eq_sort_iff, FreeAddMonoid.mrange_lift, OrderMonoidIso.symm_apply_eq, SSet.stdSimplex.objâEquiv_symm_mem_face_iff, CategoryTheory.Limits.FormalCoproduct.inclHomEquiv_symm_apply_f, ContinuousLinearEquiv.map_smulââ, Sym.append_comm, CategoryTheory.Equivalence.induced_unitIso, AddMonoidAlgebra.ofMagma_apply, LinearMap.polyCharpolyAux_map_aeval, CartanMatrix.D_two, CategoryTheory.CatEnrichedOrdinary.Hom.comp_eq, AffineEquiv.pointReflection_apply, WithZero.le_ofAdd_iff, OrderIso.sumLexEmpty_apply_inl, sInfHom.dual_symm_apply_toFun, Homeomorph.vadd_apply, UniformFun.ofFun_neg, TensorProduct.directSumLeft_tmul, WithBot.toDualTopEquiv_symm_coe, ContinuousMap.piEquiv_apply, OrderIso.sumLexIicIoi_apply_inl, Nat.equivProdNatFactoredNumbers_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, Homeomorph.homeomorphOfUnique_symm_apply, LE.le.ofDual, OrderIso.sumDualDistrib_inl, Matrix.blockTriangular_transpose_iff, Subring.map_equiv_eq_comap_symm, Finset.Ici_toDual, Equiv.embeddingEquivOfFinite_symm_apply, NonUnitalSubsemiring.comap_equiv_eq_map_symm, CategoryTheory.GradedObject.comapEquiv_inverse, Algebra.traceMatrix_of_basis, LinearEquiv.prodUnique_symm_apply, OrderAddMonoidIso.apply_eq_iff_symm_apply, TensorProduct.quotTensorEquivQuotSMul_symm_mk, OrderAddMonoidIso.coe_refl, Subalgebra.algEquivOpMop_apply, DomAddAct.isQuotientMap_mk_symm, OrderDual.toDual_top, Sum.Lex.lt_def, Equiv.pprodProd_symm_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, isAddRightRegular_ofLex, SSet.stdSimplex.objEquiv_symm_comp, nsmulCoprime_symm_apply, finProdFinEquiv_symm_apply, AdicCompletion.of_ofLinearEquiv_symm, Trivialization.coordChangeL_symm_apply, AddEquiv.toAddHom_eq_coe, SpecialLinearGroup.toLinearEquiv_symm_apply, MeasurableEquiv.map_map_symm, Topology.lawsonClosed_of_scottClosed, Equiv.symmEquiv_symm_apply_apply, AddEquiv.addSubmonoidMap_symm_apply, NumberField.inverse_basisMatrix_mulVec_eq_repr, IsometryEquiv.apply_inv_self, MonoidAlgebra.liftMagma_symm_apply, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, AddMonoidAlgebra.liftMagma_symm_apply, LinearIsometryEquiv.map_sub, HahnSeries.coeff_toPowerSeries_symm, WithBot.ofDual_bot, CategoryTheory.ShortComplex.Homotopy.equivSubZero_apply, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, AddSubmonoid.topEquiv_apply, Sym2.lift_smul_lift, Affine.Simplex.faceOppositeCentroid_reindex, AddConstEquiv.equivUnits_symm_apply_apply, SemidirectProduct.equivProd_apply, Orientation.oangle_add_right_smul_rotation_pi_div_two, Equiv.Perm.viaEmbedding_apply, FirstOrder.Language.Equiv.map_rel, Equiv.piCongrFiberwise_apply, LinearIsometryEquiv.symm_apply_apply, UniformEquiv.continuous, Matrix.spectrum_toLin, Equiv.permCongr_def, AlgEquiv.opComm_apply_symm_apply, IsTranscendenceBasis.comp_equiv, Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_mem, Complex.equivRealProdAddHom_apply, CategoryTheory.Equivalence.induced_inverse_obj, MulEquiv.coe_prodAssoc_symm, AlexDisc.Iso.mk_inv, StarRingEquivClass.instNonUnitalStarRingHomClass, Unitization.starLift_apply, Fin.succFunEquiv_apply, finSuccEquiv_eq_some, Monovary.sum_comp_perm_mul_eq_sum_mul_iff, LinearMap.toMatrix'_comp, Matrix.toLinearEquiv'_apply, LinearMap.isUnit_toMatrix'_iff, Orientation.inner_smul_rotation_pi_div_two_left, MvPolynomial.IsSymmetric.rename, Submodule.quotientPi_symm_apply, CategoryTheory.Sheaf.ÎObjEquivHom_naturality, SimpleGraph.coe_recolorOfEquiv, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, IsHomeomorph.homeomorph_symm_apply, CategoryTheory.HomOrthogonal.matrixDecomposition_apply, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, Matrix.toBilin_toMatrix, IsBaseChange.toDual_apply, Equiv.Perm.fst_prodExtendRight, ZLattice.volume_image_eq_volume_div_covolume, Delone.DeloneSet.mapIsometry_apply_packingRadius, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_symm, MeasurableEquiv.symm_apply_apply, ofMul_one, RootPairing.reflection_apply_self, CategoryTheory.Functor.IsRepresentedBy.uliftYonedaIso_hom, AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff, LinearIsometryEquiv.isometry, CategoryTheory.Bicategory.conjugateIsoEquiv_apply_hom, Module.AEval.mem_mapSubmodule_symm_apply, OrderIso.invENNReal_apply, SetTheory.PGame.Domineering.shiftUp_symm_apply, Subsemigroup.mem_map_equiv, DirectSum.decompose_zero, groupCohomology.cocyclesOfIsMulCocycleâ_coe, Con.quotientKerEquivOfRightInverse_apply, isBot_toDual_iff, CoxeterSystem.lengthParity_simple, WithAbs.equiv_equivWithAbs_symm_apply, AddSubmonoid.equivMapOfInjective_coe_addEquiv, ContinuousMulEquiv.self_comp_symm, CategoryTheory.Limits.biproduct.whiskerEquiv_hom, RootPairing.equiv_of_mapsTo_apply, UniformEquiv.funUnique_symm_apply, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_hom, Matrix.nondegenerate_toLinearMapâ_iff, AddEquivClass.instAddHomClass, SimpleGraph.Iso.boxProdSumDistrib_symm_apply, AddAction.toPermHom_apply_symm_apply, CategoryTheory.MonObj.ofRepresentableBy_mul, edist_ofAdd, LinearIsometryEquiv.submoduleMap_symm_apply_coe, CategoryTheory.Limits.Cofork.IsColimit.homIso_natural, Matrix.reindexLinearEquiv_apply, LinearMap.BilinForm.comp_congr, ofLex_inj, OpenPartialHomeomorph.homeomorphOfImageSubsetSource_apply, Euclidean.closedBall_eq_preimage, Matrix.toBilin'_comp, Matrix.isHermitian_iff_isSymmetric, CategoryTheory.Limits.Concrete.productEquiv_apply_apply, CategoryTheory.Localization.homEquiv_refl, ContinuousMap.sigmaEquiv_apply, MonomialOrder.toSyn_eq_zero_iff, MeasureTheory.volume_preserving_piFinTwo, Order.PFilter.mem_mk, AddAut.conj_apply, OrderAddMonoidIso.toFun_eq_coe, Equiv.Perm.OnCycleFactors.coe_toPermHom, RingEquivClass.map_add, Tuple.antitone_pair_of_not_sorted', NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, Equiv.coe_constVAdd, LinearMap.toMatrix_directSum_collectedBasis_eq_blockDiagonal', ofLex_inv, Equiv.Set.Equiv.strictMono_setCongr, HomotopicalAlgebra.AttachCells.reindex_cofanâ, CategoryTheory.Localization.homEquiv_trans, NumberField.mixedEmbedding.logMap_unit_smul, UniformOnFun.lipschitzOnWith_iff, WithZero.logEquiv_apply, MultilinearMap.freeFinsuppEquiv_single, CategoryTheory.Functor.FullyFaithful.autMulEquivOfFullyFaithful_symm_apply_inv, AddOpposite.coe_symm_opAddEquiv, Equiv.Perm.IsThreeCycle.nodup_iff_mem_support, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv', Matrix.compAlgEquiv_symm_apply, LinearMap.kerComplementEquivRange_symm_apply, CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_fst_apply, Additive.toMul_top, CategoryTheory.SingleObj.mapHom_comp, FirstOrder.Language.order.instStrongHomClassOfOrderIsoClass, Module.AEval.X_smul_of, Equiv.prodCongrRight_apply_snd, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal, CategoryTheory.Limits.limitCompYonedaIsoCocone_inv, InnerProductSpace.rankOne_comp, LaurentSeries.powerSeriesRingEquiv_coe_apply, Trivialization.mk_coordChangeL, QuotientAddGroup.quotientBot_apply, Equiv.Perm.sign_permCongr, Complex.measurableEquivPi_symm_apply, Equiv.Set.sumDiffSubset_apply_inr, CategoryTheory.SimplicialObject.cechNerveEquiv_symm_apply, SupPrime.dual, OrderRingIso.lt_symm_apply, Equiv.embeddingCongr_apply, AffineEquiv.coe_constVSub_symm, ClassGroup.equivPic_symm_apply, QuotientAddGroup.equivIocMod_symm_apply, Orientation.kahler_rightAngleRotation_left, dist_toMul, Matrix.isUnit_comp_iff, Equiv.Perm.IsCycleOn.pow_apply_eq_pow_apply, MulEquiv.irreducible_iff, CategoryTheory.Bicategory.iterated_mateEquiv_conjugateEquiv_symm, IsometryEquiv.coe_eq_toEquiv, CategoryTheory.conjugateEquiv_comp_assoc, UniformOnFun.uniformContinuous_restrict, IsPerfectClosure.equiv_apply, AddSubsemigroup.centerCongr_symm_apply_coe, tangentMap_chart_symm, CoalgEquiv.toLinearEquiv_toLinearMap, LinearMap.separatingLeft_congr_iff, Module.Basis.end_repr_symm_apply, AddEquiv.symm_trans_apply, LinearMap.GeneralLinearGroup.coe_ofLinearEquiv, AffineSubspace.comap_span, FirstOrder.Ring.MvPolynomialSupportLEEquiv_symm_apply_coeff, Equiv.polishSpace_induced, Module.evalEquiv_apply, Orientation.kahler_comp_linearIsometryEquiv, HahnEmbedding.Partial.coeff_eq_zero_of_mem, CategoryTheory.coyonedaEquiv_coyoneda_map, Diffeomorph.coe_toEquiv, InnerProductSpace.toMatrix_rankOne, isOfFinAddOrder_ofMul_iff, Matrix.uniqueRingEquiv_symm_apply, SubMulAction.ofFixingSubgroup.append_left, Set.Iic_ofDual, List.support_formPerm_le', QuadraticForm.tmul_tensorLId_apply, AddEquiv.mapAddSubgroup_apply, FirstOrder.Language.Theory.CompleteType.formula_mem_typeOf, Equiv.bijOn_swap, ofColex_vadd, Finmap.keysLookupEquiv_apply_coe_snd, AffineEquiv.apply_eq_iff_eq_symm_apply, PeriodPair.latticeEquiv_symm_apply, MvPolynomial.rTensor_symm_apply_single, finTwoArrowEquiv'_symm_apply, nhds_ofDual, AlgebraicGeometry.ÎSpec.adjunction_homEquiv_apply, Complex.equivRealProdLm_symm_apply_re, Module.Basis.equiv'_apply, PartENat.withTopEquiv_le, Diffeomorph.uniqueMDiffOn_image_aux, AffineIsometryEquiv.coe_toIsometryEquiv, MvPolynomial.renameSymmetricSubalgebra_symm_apply_coe, ProbabilityTheory.covariance_map_equiv, Order.IsPredPrelimit.dual, CategoryTheory.Groupoid.vertexGroupIsomOfMap_symm_apply, PiTensorProduct.liftIsometry_comp_mapL, CStarMatrix.reindexâ_apply, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, CategoryTheory.Limits.coneOfSectionCompYoneda_Ď, QuadraticForm.tensorLId_apply, OrderAddMonoidIso.ext_iff, AddAction.toPerm_symm_apply, Equiv.Perm.cycleOf_self_apply, dist_pointReflection_right, IsAlgClosure.equivOfEquiv_symm_comp_algebraMap, OrderRingIso.apply_eq_self, LinearMap.mul_toMatrixâ_mul, toMul_nsmul, LinearEquiv.coord_self, Sum.Lex.toLexRelIsoLT_coe, AlgEquiv.subalgebraMap_apply_coe, MeasurableEquiv.image_symm, coe_ofLexAddEquiv, MeasureTheory.OuterMeasure.isometryEquiv_map_mkMetric, Finsupp.lcongr_symm_single, CategoryTheory.Iso.isoCongr_apply, Equiv.Perm.cycleOf_apply, Module.Basis.apply_eq_iff, UniformEquiv.uniformContinuous, WithTop.toDual_le_toDual_iff, AffineIsometryEquiv.pointReflection_self, RingEquiv.height_map, Orientation.map_neg, CStarMatrix.ofMatrix_eq_ofMatrixStarAlgEquiv, continuousMultilinearCurryLeftEquiv_apply, ProbabilityTheory.HasGaussianLaw.map_equiv, Set.coe_unionEqSigmaOfDisjoint_symm_apply, UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv_symm, Prefunctor.costar_conj_star, QuotientAddGroup.quotientKerEquivOfRightInverse_apply, exteriorPower.alternatingMapToDual_apply_ΚMulti, NumberField.InfinitePlace.isReal_comap_iff, sigmaFinsuppLequivDFinsupp_symm_apply, YoungDiagram.equivListRowLens_apply_coe, SubMulAction.ofStabilizer.conjMap_comp, Subgroup.index_map_equiv, DilationEquiv.injective, Equiv.surjective_comp, sigmaFinsuppEquivDFinsupp_single, LinearMap.BilinForm.tensorDistribEquiv_tmul, Order.isSuccLimit_toDual_iff, CategoryTheory.Limits.IsColimit.ofCoconeEquiv_apply_desc, InfTopHom.dual_apply_toFun, ContinuousAlternatingMap.ofSubsingleton_apply_apply, RingHom.liftOfRightInverse_comp, Equiv.ofPreimageEquiv_map, SetSemiring.up_le_up, QuasiconvexOn.dual, isAddRightRegular_ofColex, Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk, Monoid.PushoutI.NormalWord.summand_smul_def', LaurentSeries.powerSeriesEquivSubring_apply, CategoryTheory.forgetAdjToOver.homEquiv_symm, FinEnum.down_equiv_symm, Homeomorph.uniqueProd_symm_apply_snd, DFinsupp.lex_le_iff_of_unique, Equiv.self_comp_symm, FirstOrder.Language.Equiv.instStrongHomClass, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, Set.Ioo_toDual, MeasurableEquiv.piMeasurableEquivTProd_apply, ConjAct.ofConjAct_toConjAct, AddEquiv.symm_comp_self, OrderMonoidIso.toFun_eq_coe, Homeomorph.isPreconnected_image, TensorProduct.leftComm_symm_tmul, Finsupp.equivMapDomain_apply, uliftZMultiplesHom_apply_apply, Multiset.toFinsupp_zero, ofDual_natCast, AlgebraicGeometry.Scheme.Cover.overEquiv_generate_toPresieveOver_eq_ofArrows, ContinuousLinearEquiv.fderiv, FreeAddMonoid.lift_restrict, EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi, ArchimedeanClass.FiniteElement.val_one, PartENat.withTopEquiv_lt, RingEquiv.piCongrLeft_apply, ChainComplex.fromSingleâEquiv_symm_apply_f_zero, IsAtom.dual, iterate_frobeniusEquiv_symm_pow_p_pow, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, ofDual_intCast, Ideal.map_isPrime_of_equiv, Homeomorph.coe_prodComm, ContinuousLinearEquiv.mdifferentiableWithinAt, IsometryEquiv.addRight_apply, CategoryTheory.OverPresheafAux.MakesOverArrow.app, ContinuousMap.piComparison_fac, AddSubsemigroup.equivOp_symm_apply_coe, OrderDual.exists, TensorAlgebra.range_lift, PartENat.withTopEquiv_apply, Homeomorph.piFinTwo_apply, ContinuousLinearEquiv.mdifferentiable, IsometryEquiv.comp_continuous_iff', CoalgEquiv.coe_toEquiv, QuotSMulTop.equivQuotTensor_naturality_mk, SymAlg.unsym_bijective, MonoidHom.coe_toAdditive_range, AddEquiv.opOp_symm_apply, DirectSum.decomposeLinearEquiv_symm_apply, CategoryTheory.Bicategory.mateEquiv_square, Finset.Colex.le_def, Equiv.sumAssoc_symm_apply_inr_inl, FreeMonoid.ofList_singleton, Affine.Simplex.touchpoint_reindex, PresheafOfModules.comp_toPresheaf_map_sheafifyHomEquiv'_symm_hom, AddHom.mulOp_symm_apply_apply, WType.NatÎąEquivPUnitSumPUnit_apply, LinearEquiv.ofLeftInverse_apply, LinearMap.toMatrix'_id, CategoryTheory.Discrete.equivalence_counitIso, Multiset.toFinsupp_toMultiset, setBasisOfTopLeSpanOfCardEqFinrank_repr_apply, LinearMap.polyCharpolyAux_coeff_eval, AddAction.orbitEquivQuotientStabilizer_symm_apply, AlgebraicGeometry.Scheme.IsLocallyDirected.glueDataΚ_naturality, isAddLeftRegular_toDual, Equiv.Perm.coe_subsingleton, RingEquiv.toSemilinearEquiv_symm_apply, Preord.dual_map, AddMonoidAlgebra.lift_of', Equiv.Perm.SameCycle.conj, AffineEquiv.equivUnitsAffineMap_symm_apply_toFun, Equiv.withBotSubtypeNe_apply, MonomialOrder.degree_prod_le, CategoryTheory.OverPresheafAux.OverArrows.app_val, Orientation.kahler_rotation_left, strictAnti_dual_iff, Homeomorph.onePointCongr_apply, CategoryTheory.Functor.coconeTypesEquiv_apply_Κ_app, Set.Iio_ofDual, Ideal.associatesEquivIsPrincipal_apply, PiTensorProduct.liftIsometry_symm_apply, LinearEquiv.coe_ofInvolutive, Homeomorph.piCurry_symm_apply, Homeomorph.image_eq_preimage_symm, LinearEquiv.symmEquiv_symm_apply_apply, equivShrink_lt_equivShrink, IsPGroup.powEquiv_symm_apply, IsometryEquiv.piCongrLeft_apply, HomeomorphClass.map_continuous, WithCStarModule.norm_equiv_le_norm_prod, ContinuousMultilinearMap.iteratedFDerivComponent_apply, NonUnitalSubring.centerToMulOpposite_symm_apply_coe, Matrix.diagonal_kronecker, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add, SemimoduleCat.Iso.conj_eq_conj, CategoryTheory.Subfunctor.range_eq_ofSection, IsometryEquiv.coe_toEquiv, ContinuousLinearEquiv.comp_differentiableAt_iff, HahnSeries.leadingCoeff_nonneg_iff, CategoryTheory.orderDualEquivalence_counitIso, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, Ideal.map_of_equiv, Metric.Snowflaking.toSnowflaking_comp_ofSnowflaking, RestrictScalars.addEquiv_symm_map_smul_smul, OrderIso.sumDualDistrib_symm_inr, LinearMap.BilinForm.mul_toMatrix_mul, associatesEquivOfUniqueUnits_apply, List.formPerm_apply_of_notMem, StarRingEquivClass.map_star, apply_coe_symm_apply, Equiv.inv_apply, equivShrink_add, FreeAbelianGroup.mul_def, OrderRingIso.coe_toOrderRingHom_refl, Matrix.updateCol_submatrix_equiv, Hamming.norm_eq_hammingNorm, Equiv.ulift_symm_down, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_unit_f_aux, iteratedFDeriv_succ_eq_comp_right, MulAction.zpowersQuotientStabilizerEquiv_symm_apply, ContinuousLinearEquiv.comp_hasFDerivAt_iff', RingAut.inv_apply, Finset.Icc_ofDual, Set.ordConnected_dual, Pi.toLex_apply, CFilter.ofEquiv_val, Setoid.piQuotientEquiv_symm_apply, LinearMap.BilinForm.toMatrix_mul_basis_toMatrix, AffineEquiv.injective, RingEquiv.op_symm_apply_symm_apply, Abelianization.equivOfComm_apply, Equiv.subtypeSubtypeEquivSubtypeExists_apply_coe, List.formPerm_apply_head, WithConv.addEquiv_apply, infPrime_toDual, FreeAlgebra.lift_unique, Matrix.toLinAlgEquiv_apply, DomAddAct.mk_nsmul, ContinuousLinearEquiv.map_eq_zero_iff, Submonoid.LocalizationMap.of_mulEquivOfMulEquiv_apply, NumberField.IsCMField.unitsComplexConj_eq_self_iff, Module.Basis.coe_ofRepr, AlgEquiv.toRingEquiv_op, CategoryTheory.ShiftedHom.opEquiv_symm_apply_comp, RingEquiv.nonUnitalSubsemiringMap_symm_apply_coe, LinearMap.nondegenerate_toMatrixâ'_iff, Monovary.sum_smul_comp_perm_lt_sum_smul_iff, CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_counit, BotHom.dual_symm_apply_apply, AddMonoidAlgebra.curryRingEquiv_symm_single, RingEquiv.image_eq_preimage, LinearMap.BilinForm.toMatrix'_comp, DirectSum.decomposeAlgEquiv_apply, AddSubgroup.mem_map_equiv, Equiv.funSplitAt_apply, AddMonoidAlgebra.opRingEquiv_apply, OrderAddMonoidHom.inlâ_add_inrâ_eq_toLex, HNNExtension.toSubgroupEquiv_neg_apply, finSuccEquiv'_last_apply, OrderHom.equivFunctor_apply, MonomialOrder.div_set, Fin.cycleRange_of_lt, SemidirectProduct.congr'_symm_apply_left, AddMonoidAlgebra.grade.decompose_single, NonUnitalSubring.coe_equivMapOfInjective_apply, SetSemiring.down_add, NumberField.mixedEmbedding.indexEquiv_apply_isReal, MonoidHom.toAdditive_id, CategoryTheory.PreGaloisCategory.autMulEquivAutGalois_Ď, ContinuousLinearMap.adjoint_toSpanSingleton, isLeftRegular_ofAdd, Equiv.curry_apply, Quiver.starEquivCostar_symm_apply, Equiv.prodPiEquivSumPi_symm_apply, MulEquiv.symmEquiv_symm_apply_apply, TensorProduct.equivFinsuppOfBasisRight_apply, Equiv.ofUnique_apply, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_apply, RingEquiv.ofLeftInverse'_apply, LinearIsometryEquiv.coe_one, CategoryTheory.Limits.Bicone.whisker_Κ, Ordinal.type_lift_preimage, CategoryTheory.PreGaloisCategory.fiberPullbackEquiv_symm_snd_apply, ContinuousMultilinearMap.nnnorm_ofSubsingleton, UniformOnFun.edist_eq_pi_restrict, Metric.Snowflaking.preimage_toSnowflaking_ball, AddMonoidAlgebra.mapDomainRingEquiv_single, AddMonoidHom.toMultiplicative_apply_apply, Equiv.emptySum_symm_apply, AddOpposite.opEquiv_symm_apply, MonoidAlgebra.curryRingEquiv_single, Subsemigroup.map_equiv_eq_comap_symm, WittVector.StandardOneDimIsocrystal.frobenius_apply, CategoryTheory.orderDualEquivalence_functor_obj, MulEquiv.toMultiplicative_toAdditive_apply, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, LinearEquiv.dualMap_apply, GroupExtension.inl_conjAct_comm, Subring.centerCongr_symm_apply_coe, CategoryTheory.isoOpEquiv_symm_apply, Fin.revOrderIso_symm_apply, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, CategoryTheory.unit_mateEquiv, Homeomorph.sigmaProdDistrib_symm_apply, CategoryTheory.conjugateEquiv_associator_hom, Equiv.subtypePreimage_symm_apply_coe_pos, CategoryTheory.Bicategory.conjugateEquiv_apply', Fin.appendIsometryOfEq_symm_apply, Set.coe_snd_biUnionEqSigmaOfDisjoint, WithTop.le_ofDual_iff, Finset.Iio_toDual, Function.fromTypes_succ_equiv_apply, Equiv.prodCongrLeft_apply, Metric.PiNatEmbed.toPiNatHomeo_apply_ofPiNat, uniformEquicontinuousOn_iff_uniformContinuousOn, isUpperSet_preimage_ofDual_iff, LieAlgebra.LieEquiv.ofCoboundary_invFun, Metric.Snowflaking.edist_toSnowflaking_toSnowflaking, LinearEquiv.funUnique_apply, CategoryTheory.Functor.RepresentableBy.ext_iff, TensorProduct.directSum_symm_lof_tmul, CategoryTheory.Bicategory.mateEquiv_conjugateEquiv_vcomp, LinearEquiv.sumArrowLequivProdArrow_apply_fst, Equiv.Perm.OnCycleFactors.Subgroup.Centralizer.toConjAct_smul_mem_cycleFactorsFinset, RootPairing.GeckConstruction.ĎConj_toFun, AddMonoidHom.fiberEquiv_apply, Matrix.piEquiv_symm_apply, MeasurableEquiv.vadd_apply, toDual_neg, Homeomorph.comp_isOpenMap_iff', HahnSeries.addOppositeEquiv_symm_orderTop, CochainComplex.toSingleâEquiv_symm_apply_f_succ, DFinsupp.comp_liftAddHom, UniformOnFun.edist_def, IsometryEquiv.image_closedBall, Equiv.coinduced_symm, HahnSeries.iterateEquiv_apply, polynomial_expand_eq, Rep.coindResAdjunction_homEquiv_symm_apply, ValuationSubring.principalUnitGroupEquiv_apply, AlgEquiv.autCongr_apply, Finset.UV.toColex_compress_lt_toColex, continuous_ofMul, coe_lpBCFâᾢ_symm, SetSemiring.down_ssubset_down, toColex_mul, Monoid.CoprodI.Word.equivPair_head_smul_equivPair_tail, Complex.volume_preserving_equiv_pi, LocallyConstant.congrLeft_symm_apply, LinearEquiv.coe_zero, AddEquiv.symm_apply_eq, iterateFrobeniusEquiv_apply, CategoryTheory.Adjunction.homAddEquiv_zero, coe_lpPiLpâᾢ_symm, Equiv.smulRight_symm_apply, monotoneOn_toDual_comp_iff, Matrix.toLinearMapRight'_apply, AlgebraicGeometry.ÎSpec.locallyRingedSpaceAdjunction_homEquiv_apply, DirectSum.decompose_of_mem_ne, map_inv_lt_iff, Equiv.coe_refl, WithBot.le_ofDual_iff, LinearMap.BilinForm.toMatrix_mul, toAdd_prod, Pi.lt_toLex_update_self_iff, SupBotHom.symm_dual_id, Subgroup.equivOp_apply_coe, FirstOrder.Language.BoundedFormula.mapTermRelEquiv_apply, Finset.ofDual_min', ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, ofBoolRing_inj, LinearIsometryEquiv.coe_ofSurjective, Submodule.reflection_eq_self_iff, Equiv.ext_iff, HasFPowerSeriesWithinOnBall.fderivWithin_eq, AffineIsometryEquiv.surjective, CategoryTheory.Localization.SmallShiftedHom.postcompEquiv_symm_apply, galRestrict_apply, finSumFinEquiv_symm_apply_castSucc, ContinuousMultilinearMap.piâᾢ_symm_apply, NonUnitalRingHom.op_apply_apply, CategoryTheory.Limits.WalkingPair.equivBool_symm_apply_false, MulAut.conj_symm_apply, CategoryTheory.ReflQuiv.adj.homEquiv_naturality_right, ContinuousMap.val_addUnitsLift_symm_apply_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_naturality, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, MulAction.orbitZPowersEquiv_symm_apply', hahnEmbedding_isOrderedModule_rat, Finsupp.lcongr_single, AddEquiv.map_add, Affine.Simplex.reindex_points, AddEquiv.ext_iff, LieModuleEquiv.ofTop_apply, CategoryTheory.typeEquiv_counitIso_hom_app_val_app, FreeRing.lift_of, Sym.equivCongr_symm_apply, LinearEquiv.submoduleMap_symm_apply, Submodule.IsHomogeneous.mem_iff, FreeMagma.lift_symm_apply, SheafOfModules.unitHomEquiv_comp_apply, NonUnitalSubring.mem_map_equiv, CategoryTheory.CategoryOfElements.toCostructuredArrow_obj, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_symm_apply_f, LinearMap.GeneralLinearGroup.coe_toLinearEquiv, SimpleGraph.Iso.boxProdSumDistrib_apply, ContinuousLinearEquiv.map_add, Matrix.ofLp_toEuclideanLin_apply, Homeomorph.toContinuousMap_comp_symm, WithBot.orderIsoPUnitSumLex_toLex, lipschitzOnWith_cfcâ_fun_of_subset, OrderDual.forall, CategoryTheory.Presheaf.uliftYonedaAdjunction_unit_app_app, StrictAnti.dual, Matrix.det_reindex_self, Matrix.toLinearMapâ_apply, CategoryTheory.ShiftedHom.opEquiv'_symm_add, AlgebraicGeometry.ÎSpecIso_inv_ÎSpec_adjunction_homEquiv, LieModuleEquiv.coe_mk, Finsupp.linearEquivFunOnFinite_apply, Equiv.coe_inj, MeasureTheory.LevyProkhorov.toMeasureEquiv_apply, CategoryTheory.Bicategory.conjugateEquiv_adjunction_id, ofBoolRing_mul, AffineSubspace.sOppSide_pointReflection, AddMonoidHom.fiberEquivKer_symm_apply, ZLattice.abs_repr_lt_of_norm_lt, Matrix.swap_mulVec, Matrix.IsTotallyUnimodular.reindex, Complex.coe_selfAdjointEquiv, ContinuousLinearEquiv.symm_symm_apply, Ideal.quotientMulEquivQuotientProd_fst, midpoint_eq_iff, map_eq_bot_iff, MultilinearMap.freeDFinsuppEquiv_apply, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_apply, CliffordAlgebra.even.lift_symm_apply_bilin, LieModuleEquiv.ext_iff, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, Magma.AssocQuotient.lift_comp_of, t1Space_iff_continuous_cofinite_of, AlgEquiv.coe_toEquiv, IsAlgClosure.equivOfEquiv_algebraMap, ContinuousAddEquiv.invFun_eq_symm, Rep.coindVEquiv_apply_hom, IsLUB.dual, Monoid.CoprodI.Word.equivPair_smul_same, Equiv.ofRightInverseOfCardLE_symm_apply, ContinuousLinearEquiv.comp_right_differentiableAt_iff, isOpenMap_ofMul, MulEquiv.orderOf_eq, tsupport_comp_eq_preimage, Polynomial.degreeLT.addLinearEquiv_symm_apply', LieAlgebra.LoopAlgebra.residuePairing_apply_apply, Complex.conjCLE_apply, UniformFun.lipschitzWith_iff, LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul, SSet.stdSimplex.yonedaEquiv_map, CategoryTheory.LocallyDiscrete.locallyDiscreteEquiv_apply, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, DomAddAct.mk_vadd_toLp, Equiv.summable_iff, AffineEquiv.refl_apply, UniformOnFun.ofFun_prod, Finmap.keysLookupEquiv_symm_apply_keys, LinearMap.nondegenerate_toLinearMapâ'_iff_det_ne_zero, LinearIsometryEquiv.prodComm_symm_apply, ContinuousLinearEquiv.differentiableOn, Additive.ofMul_eq_bot, MvPolynomial.rTensor_apply_monomial_tmul, Homeomorph.preimage_frontier, sigmaAntidiagonalEquivProd_symm_apply_fst, ContinuousLinearEquiv.hasStrictFDerivAt, CoalgEquiv.coe_symm_toLinearEquiv, Equiv.optionEquivSumPUnit_symm_inl, UniformEquiv.preimage_symm, CategoryTheory.CatEnrichedOrdinary.homEquiv_comp, coe_addEquiv_lpBCF, Matrix.mul_empty, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow', SetTheory.PGame.add_moveRight_inl, coe_apply, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, MulEquiv.coe_monoidHom_trans, Algebra.Generators.repr_CotangentSpaceMap, MonoidAlgebra.lift_apply, ContinuousLinearEquiv.mfderiv_eq, LinearEquiv.congrQuadraticMap_symm_apply, Module.Basis.dualBasis_repr, Trivialization.coe_continuousLinearEquivAt_eq, CategoryTheory.Enriched.Functor.natTransEquiv_symm_whiskerRight_functorHom_app, Algebra.Generators.reindex_val, MeasureTheory.locallyIntegrable_map_homeomorph, CategoryTheory.Localization.SmallShiftedHom.precompEquiv_symm_apply, ContinuousMulEquiv.apply_eq_iff_eq, MulEquiv.cast_apply, PiTensorProduct.tmulEquiv_apply, BialgEquiv.trans_symm_apply, lieEquivMatrix'_symm_apply, Finset.Iic_ofDual, Hamming.ofHamming_inj, MulEquivClass.toMonoidWithZeroHomClass, Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr, MonomialOrder.degLex_lt_iff, DilationEquivClass.edist_eq', Matrix.proj_diagonal, AddGroupExtension.Section.equivComp_apply, Module.Dual.baseChange_baseChange, Bundle.TotalSpace.toProd_symm_apply_snd, CategoryTheory.CommSq.left_adjoint, ContinuousMulEquiv.ext_iff, Cycle.formPerm_apply_mem_eq_next, Matrix.adjugate_submatrix_equiv_self, MeasureTheory.Measure.compProd_assoc, Matrix.permMatrix_mulVec, CategoryTheory.Iso.symm_self_conj, Equiv.Set.insert_symm_apply_inl, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, ChainComplex.toSingleâEquiv_symm_apply_f_zero, MonoidAlgebra.lift_mapRangeRingHom_algebraMap, Homeomorph.preimage_image, DFinsupp.equivProdDFinsupp_symm_apply, SymAlg.unsym_surjective, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv', Rat.ringOfIntegersEquiv_apply_coe, finSuccEquivLast_last, Euclidean.ball_eq_preimage, HahnModule.orderTop_vAdd_le_orderTop_smul, CategoryTheory.Limits.limitCompCoyonedaIsoCone_inv, DilationEquiv.ratio_trans, CategoryTheory.ShiftedHom.opEquiv'_zero_add_symm, Equiv.Perm.pow_mod_card_support_cycleOf_self_apply, finCongr_symm_apply, LinearEquiv.prodCongr_apply, SetTheory.PGame.add_moveLeft_inr, Subring.ringEquivOpMop_symm_apply_coe, Trivialization.continuousLinearEquivAt_symm_apply, ofLex_ofNat, LocallyConstant.congrRightRingEquiv_apply_apply, FreeAddGroup.range_lift_le, AddEquiv.addMonoidHomCongrRightEquiv_apply, Trivialization.coordChangeHomeomorph_coe, NumberField.mixedEmbedding.stdBasis_apply_isReal, Finset.toDual_sup, Finsupp.mapRange.addEquiv_toAddMonoidHom, OrderIsoClass.tosInfHomClass, LinearIsometryEquiv.coe_symm_toContinuousLinearEquiv, CategoryTheory.ShiftedHom.opEquiv'_symm_op_opShiftFunctorEquivalence_counitIso_inv_app_op_shift, Monovary.sum_comp_perm_mul_lt_sum_mul_iff, Diffeomorph.continuous, Cubic.equiv_symm_apply_c, Equiv.embeddingFinSucc_fst, HahnSeries.coeff_toMvPowerSeries_symm, ZMod.completedLFunction_one_sub_odd, MonoidAlgebra.uniqueRingEquiv_symm_apply, CategoryTheory.MonoidalClosed.homEquiv_symm_apply_eq, RootPairing.rootSpanMem_reflectionPerm_self, Trivialization.coordChangeL_apply, LinearMap.isUnit_toMatrix_iff, QuaternionAlgebra.coe_symm_addEquivProd, ContDiffAt.iteratedFDeriv_comp_perm, OrderIsoClass.toBoundedLatticeHomClass, CompHausLike.homeoOfIso_apply, AlgEquiv.coe_mk, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, PiTensorProduct.map_comp_reindex_symm, MeasurableEquiv.piCurry_symm_apply, Module.Basis.linearCombination_repr, TensorProduct.enorm_assoc, Submonoid.IsLocalizationMap.mulEquiv_comp, UniformEquiv.piCongr_toEquiv, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_apply, ContinuousMultilinearMap.ofSubsingleton_apply_toMultilinearMap, union_support_maximal_linearIndependent_eq_range_basis, Equiv.Perm.pow_apply_mem_toList_iff_mem_support, OrthonormalBasis.repr_symm_single, RingInvo.coe_ringEquiv, ContinuousMulEquiv.isHaarMeasure_map, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.curryMidLinearEquiv_apply, LinearMap.BilinForm.toMatrix_compLeft, CategoryTheory.Iso.eHomCongr_comp, LinearMap.trace_eq_matrix_trace, TensorProduct.quotientTensorEquiv_apply_tmul_mk, RootPairing.polarizationEquiv_symm_apply_coroot, ofBoolAlg_top, Filter.prod_assoc, Nat.factorization_eq_primeFactorsList_multiset, BilinForm.toMatrix_apply, MonoidHom.ext_mint_iff, WeakDual.CharacterSpace.norm_le_norm_one, UniformFun.mem_gen, AddEquiv.opOp_apply, ContinuousLinearEquiv.continuous, RootPairing.pairingIn_reflectionPerm, MulEquiv.mulDissociated_preimage, Pretrivialization.linearEquivAt_apply, MonoidHom.ofLeftInverse_apply, CategoryTheory.PreGaloisCategory.endEquivAutGalois_mul, Fin.cycleRange_symm_succ, ContinuousMap.sigmaCodHomeomorph_symm_apply, Matrix.linfty_opNorm_toMatrix, exteriorPower.zeroEquiv_ΚMulti, ContinuousAlgEquiv.refl_apply, Ideal.map_comap_of_equiv, Equiv.image_symm_image, LinearEquiv.transvection.coe_apply, Additive.forall, Equiv.Set.rangeInl_apply_inl, Equiv.piCongrLeft_apply_eq_cast, LinearIsometryEquiv.withLpProdCongr_apply, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_hom_app_app_down, IsometryEquiv.dist_eq, Prefunctor.symmetrifyStar, Matrix.toBilin'_apply', Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity, coe_starâᾢ, Equiv.Set.rangeInr_symm_apply_coe, IsometryEquiv.vaddConst_apply, CategoryTheory.Oplax.StrongTrans.Modification.equivOplax_apply, AffineIsometryEquiv.coe_one, Equiv.Perm.IsCycleOn.range_zpow, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Equiv.Set.congr_apply, AffineIsometry.toAffineIsometryEquiv_apply, CategoryTheory.Presheaf.compULiftYonedaIsoULiftYonedaCompLan.uliftYonedaEquiv_presheafHom_uliftYoneda_obj, Matrix.toLinearMapâ'_single, AffineEquiv.coe_toAffineMap, Pi.toColex_strictMono, MeasureTheory.ComplexMeasure.equivSignedMeasureâ_symm_apply, CategoryTheory.Functor.representableByUliftFunctorEquiv_apply_homEquiv, WType.equivSigma_symm_apply, BddAbove.dual, CategoryTheory.ShiftedHom.homEquiv_apply, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, LinearMap.separatingRight_toLinearMapâ'_of_det_ne_zero', AddSubmonoid.LocalizationMap.addEquivOfLocalizations_left_neg_apply, LinearMap.adjoint_inner_left, Topology.WithScott.ofScott_toScott, RingEquiv.symm_trans_apply, DilationEquiv.ratio_refl, UniformOnFun.toFun_sum, LinearEquiv.piCurry_symm_apply, LightCondensed.ihomPoints_symm_apply, UniformEquiv.ext_iff, List.SortedGE.of_map_ofDual, Polynomial.eval_eq_sum_degreeLTEquiv, ofColex_pow, finSuccEquiv_eq_none, RingEquiv.congr_fun, CategoryTheory.Limits.SingleObj.Types.limitEquivFixedPoints_apply_coe, stdSimplexHomeomorphUnitInterval_one, Complex.lift_symm_apply_coe, LinearMap.BilinForm.mul_toMatrix, CategoryTheory.Functor.CorepresentableBy.equivUliftCoyonedaIso_apply, Matrix.piAlgEquiv_symm_apply, MeasureTheory.mulEquivHaarChar_smul_preimage, Homeomorph.subRight_symm_apply, Module.Basis.tensorAlgebra_repr_apply, FreeAlgebra.lift_symm_apply, UniformOnFun.uniformContinuous_restrict_toFun, UniformOnFun.precomp_uniformContinuous, Orientation.oangle_map, isGroupLikeElem_map_equiv, CategoryTheory.InjectiveResolution.extMk_hom, Equiv.Perm.decomposeFin_symm_of_one, DomMulAct.smul_apply, CategoryTheory.MonoidalCategory.DayConvolution.corepresentableBy_homEquiv_apply_app, Polynomial.coeff_opRingEquiv, Ideal.map_symm, Quiver.SingleObj.toPrefunctor_apply_obj, ContinuousAlgHom.prodEquiv_apply, UniformEquiv.prodPUnit_apply, AddAut.inv_apply, LinearEquiv.symmEquiv_apply_symm_apply, ContinuousMap.equivFnOfDiscrete_symm_apply_apply, PNat.equivNonZeroDivisorsNat_apply_coe, Finset.Colex.lt_iff_max'_mem, StarMulEquiv.symm_trans_apply, TensorProduct.rightComm_tmul, LinearMap.coprodEquiv_apply, Primrec.of_equiv_symm, CategoryTheory.Limits.Sigma.Κ_reindex_hom, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, AddCircle.liftIoc_eq_lift_Icc, MeasurableEquiv.coe_curry_symm, MeasurableEquiv.coe_sumPiEquivProdPi_symm, Module.Basis.equivFun_apply, Int.toAdd_zpow, Ideal.natAbs_det_equiv, ZSpan.quotientEquiv.symm_apply, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity, IsPerfectClosure.equiv_comp_apply, Magma.AssocQuotient.lift_of, AlgCat.free_map, Submodule.torsion_gc, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, Module.apply_evalEquiv_symm_apply, TensorProduct.finsuppScalarLeft_apply_tmul, CategoryTheory.uliftCoyonedaEquiv_naturality, isAddRegular_ofMul, finProdFinEquiv_apply_val, Homeomorph.coe_prodUnique, AddMonoid.Coprod.lift_apply_mk, TensorProduct.directSumRight_tmul, FreeMonoid.hom_map_lift, AddEquiv.ofLeftInverse'_symm_apply, TensorProduct.gradedComm_tmul_algebraMap, Equiv.arrowProdEquivProdArrow_symm_apply, Submodule.reflection_map_apply, CategoryTheory.Limits.IsLimit.homEquiv_symm_Ď_app_assoc, WittVector.liftEquiv_symm_apply_coe, Ideal.coe_smul_primesOver_eq_map_galRestrict, LinearMap.trace_conj', CategoryTheory.Limits.WalkingPair.swap_symm_apply_ff, Equiv.sumSigmaDistrib_apply, Matrix.of_mem_specialOrthogonalGroup_fin_two_iff, LinearIsometryEquiv.continuousAt, nsmulCoprime_zero, Quaternion.imJ_equivProd_symm_apply, UniformFun.toFun_neg, Matrix.SpecialLinearGroup.toLin'_to_linearMap, SubAddAction.fixingAddSubgroupEquivFixingAddSubgroup_coe_apply, Homeomorph.isCompact_image, IsCompl.ofDual, ofBoolRing_neg, ContinuousMap.isUniformEmbedding_uniformFunOfFun, HomeomorphClass.instContinuousMapClass, Equiv.piOptionEquivProd_apply, WittVector.quotientPEquiv_mk, Finsupp.coe_equivFunOnFinite_symm, TopHom.symm_dual_comp, groupHomology.H1AddEquivOfIsTrivial_apply, InverseSystem.piLTLim_symm_apply, NumberField.RingOfIntegers.mapRingEquiv_apply, Equiv.prodPUnit_symm_apply, Module.Basis.smulTower'_repr, fixingSubmonoid_fixedPoints_gc, Function.Injective.swap_apply, LieSubalgebra.topEquiv_apply, TensorProduct.norm_lid, FreeAddGroup.lift_symm_apply, LinearMap.mul_toMatrixâ'_mul, InverseSystem.piSplitLE_lt, IsometryEquiv.withLpProdUnique_symm_apply, LocallyConstant.congrRightRingEquiv_symm_apply_apply, LinearMap.toMatrixâ'_mul, Polynomial.toFinsuppIso_apply, ContinuousAffineEquiv.coe_symm_toEquiv, SSet.stdSimplex.objEquiv_toOrderHom_apply, CategoryTheory.Localization.SmallHom.equiv_comp, CliffordAlgebra.reverseEquiv_symm_apply, MeasurableEquiv.measurable_comp_iff, HasFPowerSeriesOnBall.hasFDerivAt, Equiv.piCongrFiberwise_symm_apply, Equiv.toFun_inducedStructureEquiv, WithTop.toDualBotEquiv_symm_coe, CategoryTheory.Presieve.compatibleEquivGenerateSieveCompatible_apply_coe, WithLp.linearEquiv_apply, MeasureTheory.Measure.Regular.comap, LinearEquiv.ofSubmodule'_apply, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_left, AddMonoidAlgebra.uniqueRingEquiv_symm_apply, Equiv.prodUnique_apply, Homeomorph.preimage_closure, AddSubgroup.centerToAddOpposite_symm_apply_coe, CategoryTheory.Grpd.freeForgetAdjunction_homEquiv_apply, Equiv.Perm.apply_mem_support, AddSubmonoid.centerCongr_apply_coe, Submonoid.LocalizationMap.ofMulEquivOfLocalizations_apply, MonoidHom.eq_liftOfRightInverse, AddEquiv.injective, Subsemiring.ringEquivOpMop_symm_apply_coe, ContinuousLinearEquiv.symm_image_image, RingEquiv.ofNonUnitalRingHom_symm_apply, toLex_smul', Prod.Lex.toLex_mono, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero, CategoryTheory.nerve.Ď_zero_nerveEquiv_symm, Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv_apply, AlgEquiv.toAlgHom_unop, Equiv.setValue_eq, CategoryTheory.Functor.homEquivOfIsRightKanExtension_symm_apply, OrderIso.emptySumLex_apply_inr, LinearMap.IsSymmetric.eigenvalues_def, DomAddAct.isEmbedding_mk, Finsupp.LinearEquiv.finsuppUnique_apply, OnePoint.smul_infty_def, ZLattice.volume_image_eq_volume_div_covolume', LinearIsometryEquiv.withLpProdUnique_symm_apply, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Set.piCongrLeft_comp_restrict, Algebra.toMatrix_lsmul, AddOpposite.opAddEquiv_symm_apply, DirectSum.SetLike.IsHomogeneous.mem_iff, Sum.Lex.inl_lt_inr, Topology.WithLower.toLower_le_toLower, LinearEquiv.rTensor_trans_apply, toMatrix_innerSL_apply, OrthonormalBasis.equiv_apply_basis, OrderDual.lt_toDual, Finsupp.mapDomain_equiv_apply, Module.Basis.map_orientation_eq_det_inv_smul, Function.Embedding.optionEmbeddingEquiv_symm_apply, Affine.Simplex.eulerPoint_reindex, CommAlgCat.isoEquivAlgEquiv_symm_apply, BoundedOrderHom.dual_symm_apply_toOrderHom, isAddRegular_ofDual, AffineEquiv.image_symm, ofDual_wcovBy_ofDual_iff, LaurentSeries.powerSeriesEquivSubring_coe_apply, ofDual_toAdd_eq_top_iff, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_apply, ContinuousLinearEquiv.arrowCongrEquiv_symm_apply, Bundle.Trivial.homeomorphProd_symm_apply_proj, Equiv.subtypeQuotientEquivQuotientSubtype_symm_mk, Matrix.separatingLeft_toLinearMapâ'_iff, StrictAnti.dual_right, AddCircle.equivIoc_coe_eq, infIrred_toDual, exteriorPower.basis_repr_apply, Finsupp.linearEquivFunOnFinite_symm_single, Set.up_one, ProbabilityTheory.HasGaussianLaw.map_equiv_fun, LinearMap.separatingLeft_toLinearMapâ'_of_det_ne_zero', DomMulAct.stabilizerMulEquiv_apply, Set.Ioi_toDual, prodEquivPiFinTwo_symm_apply, TensorProduct.rid_symm_apply, CategoryTheory.Limits.SingleObj.colimitTypeRelEquivOrbitRelQuotient_symm_apply, OrderMonoidIso.strictMono, isOpenMap_ofDual, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, Homeomorph.self_comp_symm, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset, Matrix.comp_map_map, Multiset.mapEquiv_apply, AlternatingMap.ofSubsingleton_symm_apply_apply, Similar.index_equiv, Diffeomorph.contMDiffAt, Module.Basis.toMatrix_update, ContinuousLinearEquiv.comp_contDiffOn_iff, TensorPower.cast_tprod, PiLp.basis_toMatrix_basisFun_mul, MonoidHom.ker_comp_mulEquiv, finEquivZPowers_apply, Submodule.mk_quotientEquivOfIsCompl_apply, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg, AddMagma.FreeAddSemigroup.lift_of, Equiv.Perm.apply_mem_fixedPoints_iff_mem_of_mem_centralizer, Manifold.IsImmersionAt.target_subset_preimage_target, Topology.WithLawson.isClosed_preimage_ofLawson, FinEnum.up_equiv_symm, Equiv.coe_embeddingFinSucc_symm, Submodule.prodEquivOfIsCompl_symm_apply_right, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, iccHomeoI_symm_apply_coe, Matrix.det_mul_aux, Matrix.tail_transpose, CategoryTheory.equivYoneda_inv_app, CategoryTheory.uliftCoyonedaEquiv_symm_map_assoc, Rep.unit_iso_comm, Finsupp.linearCombination_equivMapDomain, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply, BilinForm.toMatrix_mul, Diffeomorph.symm_image_eq_preimage, PartENat.withTopEquiv_symm_zero, Finset.sum_smul_sum_eq_sum_perm, Rep.leftRegularHomEquiv_symm_single, List.sortedGT_map_toDual, AddEquiv.toMultiplicative_symm_apply_symm_apply, 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', AlgebraicGeometry.Spec.homEquiv_apply, Trivialization.preimageHomeomorph_apply, StrictMono.dual, ContinuousLinearEquiv.eq_symm_apply, LinearMap.toMatrix_comp, Equiv.piCongrRight_apply, Matrix.row_eq_self, CategoryTheory.Adjunction.homAddEquiv_symm_apply, ContinuousLinearEquiv.arrowCongrSL_apply, Module.reflection_mul_reflection_zpow_apply_self, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_symm_apply_f, AlgHom.toRingHom_unop, MulArchimedeanOrder.of_val, image_gaugeRescaleHomeomorph_closure, Finsupp.mapRange.linearEquiv_apply, MonoidHom.coe_toAdditive, Function.OfArity.uncurry_two_eq_uncurry, Subsemigroup.coe_toAddSubsemigroup_symm_apply, CompactlyGenerated.isoEquivHomeo_symm_apply, tangentBundleModelSpaceHomeomorph_coe_symm, AddEquiv.apply_eq_iff_eq, CategoryTheory.Limits.biproduct.whiskerEquiv_inv_eq_lift, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum_of_completeSpace, DomMulAct.mk_inv, WithZero.toMulBot_coe, Matrix.submatrixEquivInvertibleEquivInvertible_apply, Finset.sum_map_equiv, DomMulAct.isInducing_mk, LocallyConstant.congrLeftâ_apply_apply, WithCStarModule.equiv_pi_apply, SameRay.sameRay_map_iff, finEquivMultiples_apply, RootPairing.coreflection_apply, Equiv.sumCompl_apply_symm_of_pos, CategoryTheory.Limits.Trident.IsLimit.homIso_symm_apply, WithZero.lift'_surjective, LieAlgebra.of_symm_nsmul, Finsupp.Lex.single_antitone, ContinuousLinearEquiv.submoduleMap_symm_apply, CategoryTheory.codiscreteEquiv_symm_apply_as, Equiv.prodCongrRight_apply_fst, IsometryEquiv.piCongrLeft'_symm_apply, finSuccEquiv'_symm_none, AddEquiv.congr_fun, Equiv.Set.sumDiffSubset_symm_apply_of_mem, Homeomorph.isClosedMap, IsEvenlyCovered.comp_homeomorph_iff, Quiver.starEquivCostar_apply, MeasurableEquiv.image_eq_preimage_symm, ContinuousMap.equivFnOfDiscrete_symm_apply, MulEquiv.coprodComm_apply, RingEquiv.toSemiRingCatIso_hom, Matrix.det_mul_column, PositiveLinearMap.ofPreGNS_toPreGNS, Matrix.separatingLeft_toBilin'_iff, Module.Basis.baseChange_repr_tmul, ModelWithCorners.transContinuousLinearEquiv_range, Subsemigroup.topEquiv_apply, Ring.DirectLimit.ringEquiv_symm_mk, RingEquiv.coe_ringHom_refl, TensorProduct.nnnorm_assoc, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, Matrix.kroneckerAlgEquiv_symm_apply, SetSemiring.down_subset_down, Equiv.natSumNatEquivNat_apply, Matrix.trace_toLin_eq, Homeomorph.compStarAlgEquiv'_apply, CategoryTheory.Groupoid.invEquiv_symm_apply, DirectSum.decompose_symm_mul, Localization.mulEquivOfQuotient_monoidOf, Additive.ofMul_lt, TensorPower.cast_eq_cast, coe_notMemRangeEquiv, FreeGroupBasis.lift_symm_apply, Finsupp.lex_le_iff_of_unique, LinearIsometryEquiv.self_comp_symm, Equiv.sumSumSumComm_apply, eVariationOn.comp_ofDual, Diffeomorph.uniqueDiffOn_preimage, Homeomorph.isConnected_image, FreeMonoid.lift_symm_apply, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_apply, LinearMap.toMatrixâ_mul_basis_toMatrix, ZSpan.repr_fract_apply, finsuppLEquivDirectSum_apply, AffineSubspace.topEquiv_apply, ContinuousLinearMap.orthogonal_range, IsometryEquiv.withLpProdAssoc_apply, Monoid.Coprod.inv_def, Multiset.toFinsupp_eq_iff, CategoryTheory.Functor.CorepresentableBy.homEquiv_comp, LinearEquiv.ofTop_symm_apply, ofAdd_sub, Topology.WithLowerSet.isOpen_ofLowerSet_preimage, Module.Basis.toMatrix_eq_toMatrix_constr, LatticeHom.dual_comp, Matrix.det_reindexLinearEquiv_self, CategoryTheory.Adjunction.homAddEquiv_symm_add, antitoneOn_dual_iff, TensorProduct.comul_tmul, Functor.mapEquiv_symm_apply, CategoryTheory.Limits.FormalCoproduct.isoOfComponents_hom_f, MulEquiv.symmEquiv_symm_apply_symm_apply, Algebra.TensorProduct.basis_repr_symm_apply, AddEquiv.val_piAddUnits_symm_apply, finSuccAboveEquiv_symm_apply_last, CategoryTheory.LocalizerMorphism.equiv_smallHomMap, Diffeomorph.instContinuousMapClassSomeENatTop, SetTheory.PGame.moveRight_neg_toRightMovesNeg, LinearMap.polyCharpoly_map_eq_charpoly, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, Finset.sum_mul_sum_eq_sum_perm, toMul_smul, CategoryTheory.conjugateEquiv_symm_comm, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff, frobeniusEquiv_symm_pow_p, Equiv.Perm.IsCycle.pow_eq_one_iff'', OrderIso.equivClosureOperator_symm_apply, KaehlerDifferential.quotKerTotalEquiv_symm_apply, IsometryEquiv.withLpUniqueProd_apply, AddEquiv.cast_symm_apply, AddMonoidHom.coe_toMultiplicative_map, LinearMap.quotKerEquivOfSurjective_symm_apply, OrderIso.sumLexDualAntidistrib_symm_inl, infIrred_ofDual, Submonoid.powLogEquiv_apply, AffineEquiv.coe_coe, MeasurableEquiv.inv_apply, finsuppTensorFinsuppLid_apply_apply, Orientation.kahler_map, CategoryTheory.Functor.CorepresentableBy.uniqueUpToIso_hom, ContinuousLinearEquiv.skewProd_symm_apply, AddMonoid.IsTorsion.torsionAddEquiv_apply, Equiv.Perm.toCycle_next, FreeLieAlgebra.universalEnvelopingEquivFreeAlgebra_symm_apply, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_symm_tmul, Matrix.reindex_refl_refl, MulEquivClass.coe_symm_apply_apply, CategoryTheory.ParametrizedAdjunction.inl_arrowHomEquiv_symm_apply_left_assoc, CoxeterMatrix.reindex_apply, LinearEquiv.smulOfNeZero_symm_apply, AffineEquiv.coe_homothetyUnitsMulHom_apply, ofLex_smul', Equiv.subRight_apply, Quiver.SingleObj.toHom_symm_apply, Homeomorph.Set.univ_apply, Subgroup.subgroupOfContinuousMulEquivOfLe_symm_apply, 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, LinearEquiv.refl_apply, Equiv.piCongrLeft_sumInr, PiTensorProduct.lift_tprod, Affine.Simplex.signedInfDist_reindex, Equiv.piCongr'_apply, Matrix.toLinOfInv_apply, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex, Equiv.Set.image_symm_apply, MulEquiv.piUnique_symm_apply, Filter.prod_assoc_symm, isRightRegular_ofDual, Padic.withValUniformEquiv_cast_apply, AddLocalization.addEquivOfQuotient_symm_mk, WithTop.ofDual_le_iff, RingAut.coe_one, LinearIsometryEquiv.coe_refl, GroupExtension.Equiv.coe_toMulEquiv, AddSubmonoid.coe_toSubmonoid_symm_apply, Subgroup.conjAct_pointwise_smul_eq_self, Matrix.det_permute', Matrix.diagonalInvertibleEquivInvertible_symm_apply, CategoryTheory.CountableCategory.instCountableHomObjAsType, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, LinearEquiv.apply_symm_apply, Con.congr_mk, DistribMulAction.toAddEquiv_symm_apply, Trivialization.preimageSingletonHomeomorph_symm_apply, contMDiff_equivTangentBundleProd, toBoolAlg_inj, nnnorm_ofMul, dualTensorHomEquivOfBasis_symm_cancel_left, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, Equiv.boolProdEquivSum_symm_apply, UniformEquiv.isUniformInducing, Unitization.isUniformEmbedding_addEquiv, Trivialization.transFiberHomeomorph_apply, CategoryTheory.Bicategory.conjugateEquiv_associator_hom, QuadraticMap.IsometryEquiv.prodComm_toFun, Localization.mulEquivOfQuotient_apply, ZMod.lift_injective, DilationEquiv.apply_symm_apply, SemilatInfCat.dual_map, MeasurableEquiv.coe_addLeft, Module.Invertible.rTensorEquiv_symm_apply_apply, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, Complex.selfAdjointEquiv_symm_apply, AddValuation.toValuation_apply, DomMulAct.smul_Lp_ae_eq, QuaternionAlgebra.coe_basisOneIJK_repr, CategoryTheory.Limits.Sigma.Κ_reindex_inv, Submonoid.LocalizationMap.ofMulEquivOfDom_apply, Ideal.map_comap_eq_self_of_equiv, IsometryEquiv.symm_apply_eq, zmultiplesHom_apply, QuadraticMap.IsometryEquiv.coe_toLinearEquiv, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down_assoc, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_obj, RingEquiv.map_sum, LinearEquiv.congr_arg, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, FirstOrder.Language.Equiv.coe_injective, Equiv.coe_prodUnique, RootPairing.EmbeddedG2.indexEquivAllRoots_apply_coe, finprod_comp_equiv, DirectSum.equivCongrLeft_apply, CategoryTheory.Functor.curryingFlipEquiv_apply_map, Shrink.continuousLinearEquiv_symm_apply, Ideal.map_isMaximal_of_equiv, 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, SetTheory.PGame.exists_rightMoves_neg, FreeAbelianGroup.liftMonoid_coe, UniformEquiv.range_coe, FreeMagma.lift_comp_of, Subgroup.toAddSubgroup_comap, ContinuousLinearEquiv.comp_differentiable_iff, CategoryTheory.conjugateEquiv_id, Padic.coe_withValRingEquiv, IsometryEquiv.toDilationEquiv_apply, MeasurableEmbedding.equivRange_symm_apply_mk, Topology.WithGeneratedByTopology.isOpen_iff, frobenius_apply_frobeniusEquiv_symm, AlgEquiv.val_inv_algHomUnitsEquiv_symm_apply, Equiv.prodAssoc_symm_apply, Set.OrdConnected.dual, TruncatedWittVector.zmodEquivTrunc_apply, Metric.Snowflaking.uniformEquiv_symm_apply, DomAddAct.coe_mkHomeomorph_symm, Trivialization.symm_continuousLinearEquivAt_eq, RingEquiv.ofRingHom_apply, Equiv.subtypeUnivEquiv_symm_apply, Equiv.arrowCongr_comp, CategoryTheory.Functor.RepresentableBy.uniqueUpToIso_inv, LinearEquiv.conj_id, DFinsupp.linearEquivFunOnFintype_apply, isRightRegular_ofColex, AddEquiv.coe_symm_toNatLinearEquiv, finsuppLequivDFinsupp_apply_apply, uniformity_multiplicative, Abelianization.lift_of, DomAddAct.mk_neg, Orientation.coe_basisRightAngleRotation, Homeomorph.toMeasurableEquiv_symm_coe, TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, OrderIso.asBoolAlgAsBoolRing_apply, Submodule.FG.lTensor.directLimit_apply, ofMul_mul, equivShrink_symm_add, Finsupp.liftAddHom_singleAddHom, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, bijective, Matrix.toBilin'Aux_eq, TensorProduct.lift.equiv_symm_apply, AddCircle.continuousAt_equivIoc, OrderDual.instNeBotNhdsWithinIoi, List.sortedLT_map_toDual, CategoryTheory.Bicategory.Adj.Homâ.conjugateEquiv_Ďl, Homeomorph.refl_apply, Equiv.psigmaEquivSigmaPLift_apply, Pi.toColex_update_le_self_iff, addMonoidHomLequivNat_apply, Matrix.one_fin_three, WithCStarModule.equiv_sub, ContinuousLinearEquiv.contDiffOn_comp_iff, CompactlySupportedContinuousMap.continuousMapEquiv_symm_apply, Equiv.finsetSubtypeComm_apply_coe, Equiv.setOf_apply_symm_eq_image_setOf, Homeomorph.piUnique_symm_apply, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, Homeomorph.piEquivPiSubtypeProd_symm_apply, LinearOrderedCommGroupWithZero.fst_apply, AddEquiv.finsuppUnique_symm_apply_support_val, MeasureTheory.measurePreserving_piFinsetUnion, aemeasurable_map_equiv_iff, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', Matrix.toLin_finTwoProd_toContinuousLinearMap, LightCondensed.ihom_map_val_app, WithCStarModule.equiv_snd, SetTheory.PGame.moveLeft_toLeftMovesNim, HahnSeries.addOppositeEquiv_symm_leadingCoeff, Equiv.Perm.IsCycle.zpowersEquivSupport_symm_apply, CategoryTheory.Iso.toEquiv_symm_fun, trace_quotient_eq_trace_localization_quotient, Topology.IsEmbedding.homeomorphOfSubsetRange_apply_coe, UniformOnFun.uniformContinuous_eval_of_mem_sUnion, Hamming.ofHamming_toHamming, CategoryTheory.Abelian.Ext.addEquivâ_symm_apply, Equiv.divLeftâ_apply, Equiv.sigmaProdDistrib_symm_apply, IsCoercive.continuousLinearEquivOfBilin_apply, AffineEquiv.apply_eq_iff_eq, LinearIsometryEquiv.continuousOn, Shrink.rec_equivShrink, HahnSeries.addOppositeEquiv_leadingCoeff, DomAddAct.map_mk_nhds, Orientation.volumeForm_zero_neg, IsometryEquiv.funUnique_symm_apply, ContinuousLinearEquiv.fderivWithin, CategoryTheory.Linear.homCongr_symm_apply, Continuous.matrix_reindex, Equiv.Perm.IsCycle.isCycleOn, ZMod.dft_const_mul, Matrix.toSquareBlockProp_def, CategoryTheory.Adjunction.homAddEquiv_neg, Matrix.of_symm_single, TensorPower.one_mul, MulEquivClass.apply_coe_symm_apply, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, Finsupp.domLCongr_apply, RootPairing.isFixedPt_reflection_of_isOrthogonal, CategoryTheory.Bicategory.conjugateEquiv_id, LinearMap.linearEquivOfInjective_apply, Orientation.areaForm_map, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, Perfection.coeff_frobeniusEquiv_symm, MeasureTheory.volume_measurePreserving_arrowProdEquivProdArrow, MulEquiv.opOp_apply, MulAut.congr_apply, CategoryTheory.Adjunction.homEquiv_symm_id, IsometryEquiv.constVSub_apply, Equiv.Perm.VectorsProdEqOne.vectorEquiv_symm_apply, LinearIsometryEquiv.congr_fun, ContinuousLinearMap.adjoint_comp, Equiv.Perm.one_apply, affineHomeomorph_image_Ioo, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, FreeAddMonoid.map_symm_apply_map_eq, LinearEquiv.toFun_eq_coe, Equiv.piCongr_symm_apply, RingEquiv.coe_prodCongr, AddMonoidAlgebra.mapRangeRingEquiv_apply, pow_ofLex, Equiv.symmEquiv_apply_symm_apply, DilationEquiv.smulTorsor_ratio, supClosed_preimage_toDual, ContinuousLinearEquiv.isBigO_comp_rev, Matrix.reindex_mem_rowStochastic, Matrix.single_eq_of_single_single, OrderDual.toDual_eq_top, List.formPerm_apply_lt_getElem, Matrix.matrixOfPolynomials_blockTriangular, AddChar.toAddMonoidHom_apply, SSet.S.equivElements_apply_snd, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, LinearEquiv.conjRingEquiv_symm_apply_apply, CategoryTheory.ShiftedHom.opEquiv'_symm_comp, Equiv.Perm.mem_cycleFactorsFinset_iff, Equiv.inducedStructure_RelMap, AddSubgroup.topEquiv_apply, ContinuousMultilinearMap.ofSubsingleton_apply_apply, AddGroupExtension.Equiv.trans_symm_apply, nnnorm_ofDual, IsometryEquiv.coe_mul, ofBoolAlg_toBoolAlg, Polynomial.Gal.ext_iff, TopologicalSpace.gc_generateFrom, Finsupp.curryLinearEquiv_apply, Matrix.uniqueAlgEquiv_symm_apply, AffineEquiv.midpoint_pointReflection_left, Matrix.of_col, TopHom.dual_apply_apply, Topology.WithUpperSet.ofUpperSet_inj, Specialization.isUpperSet_ofEquiv_preimage, CategoryTheory.Adjunction.homEquiv_naturality_left_square_iff, Function.Embedding.toEquivRange_symm_apply_self, WithCStarModule.norm_equiv_le_norm_pi, TensorProduct.map_map_assoc, Ideal.associatesEquivIsPrincipal_mul, Matrix.uniqueLinearEquiv_symm_apply, Module.reflection_mul_reflection_zpow_apply, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm, OrderDual.le_toDual, AlexDisc.Iso.mk_hom, Equiv.Perm.sameCycle_zpow_left, DomMulAct.mk_mul, UniformEquiv.uniformEquiv_mk_coe, LinearEquiv.sumArrowLequivProdArrow_apply_snd, LinearIsometryEquiv.map_eq_zero_iff, MulOpposite.opHomeomorph_symm_apply, Submonoid.leftInvEquiv_symm_eq_inv, Submodule.quotEquivOfEq_mk, ofLex_vadd', ofAdd_zsmul, RingEquiv.piCongrLeft'_symm_apply, RingEquiv.toSemilinearEquiv_apply, Tuple.eq_sort_iff', ContinuousLinearEquiv.tsum_eq_iff, UniformOnFun.toFun_sub, WithBot.toDual_lt_iff, CategoryTheory.Adjunction.homEquiv_naturality_right_symm, Nat.card_image_equiv, HilbertBasis.repr_self, Equiv.eq_image_iff_symm_image_eq, SSet.prodStdSimplex.nonDegenerate_iff_injective_objEquiv, Perfection.lift_apply_apply_coe, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, Equiv.coe_fn_mk, TensorProduct.commIsometry_apply, InfTopHom.dual_symm_apply_toFun, Cardinal.extend_function, OrderIso.sumLexIioIci_symm_apply_of_ge, ContinuousLinearEquiv.coe_toDiffeomorph, Equiv.permCongr_eq_mul, Equiv.ofPreimageEquiv_apply, finsuppTensorFinsupp_symm_single, MulEquiv.ofLeftInverse'_symm_apply, Multiplicative.toAdd_bot, ofLex_smul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', addMonoidHomLequivInt_symm_apply, Matroid.mapEquiv_indep_iff, LinearEquiv.congr_fun, ContinuousMulEquiv.injective, Ordinal.toPGame_moveLeft, OrderMonoidIso.coe_toEquiv_symm, CategoryTheory.FinCategory.objAsTypeToAsType_obj, Algebra.IsAlgebraic.algEquivEquivAlgHom_apply, continuousMultilinearCurryRightEquiv_symm_apply', CategoryTheory.Bicategory.conjugateEquiv_symm_iso, OrderDual.toDual_lt, QuadraticForm.dualProdProdIsometry_toFun, Equiv.coe_mulRight, HahnSeries.lt_iff, CategoryTheory.WithTerminal.isLimitEquiv_apply_lift_left, finSuccEquivLast_symm_none, Equiv.Perm.IsCycle.swap_mul, ContinuousMulEquiv.trans_apply, RingEquiv.zeroRingProd_apply, Matrix.toLinearEquivRight'OfInv_apply, ContinuousLinearEquiv.continuousAt, Fin2.equivFin_apply, Multiplicative.toAdd_le, AddAction.stabilizerEquivStabilizer_apply, OrderHom.symm_dual_comp, hasEigenvalue_toLin'_diagonal_iff, ContinuousLinearMap.prodL_apply, LinearEquiv.map_smul, ContinuousLinearEquiv.arrowCongrEquiv_apply, equivTangentBundleProd_eq_tangentMap_prod_tangentMap, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, Equiv.Perm.IsCycleOn.zpow_apply_eq, OnePoint.not_continuous_cofiniteTopology_of_symm, Homeomorph.coe_mulRight, ArchimedeanOrder.lt_def, AffineIsometryEquiv.ediam_image, IsQuotientCoveringMap.homeomorph_comp_iff, LinearEquiv.smul_id_of_finrank_eq_one_apply, ContinuousAlternatingMap.norm_ofSubsingleton_id, DFinsupp.liftAddHom_singleAddHom, LinearMap.toMatrix'_toLinearMapâââ', MeasureTheory.addEquivAddHaarChar_smul_eq_comap, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm, Complex.equivRealProdCLM_symm_apply_re, IsExtrFilter.dual, Finset.Colex.toColex_lt_toColex_of_ssubset, CategoryTheory.FreeGroupoid.functorEquiv_symm_apply, SetRel.gc_leftDual_rightDual, LinearMap.isStarProjection_toContinuousLinearMap_iff, LieEquiv.ofSubalgebras_symm_apply, AffineEquiv.surjective, Equiv.restrictPreimageFinset_apply_coe, Rep.MonoidalClosed.linearHomEquiv_hom, Multiplicative.toAdd_strictMono, Representation.ofModule_asAlgebraHom_apply_apply, Matrix.inv_submatrix_equiv, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, Matrix.toLpLin_mul, CategoryTheory.mateEquiv_vcomp, MeasurableEquiv.coe_setOf, iteratedDerivWithin_eq_equiv_comp, Rep.invariantsAdjunction_homEquiv_apply_hom, Traversable.Free.map_eq_map, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, CategoryTheory.Functor.IsRepresentedBy.iff_isIso_uliftYonedaEquiv, Algebra.GrothendieckAddGroup.lift_apply, MeasureTheory.Content.is_add_left_invariant_innerContent, Equiv.eq_conj, Equiv.sumCompl_symm_apply_neg, List.SortedLE.of_map_toDual, QuotientAddGroup.quotientBot_symm_apply, Matrix.toLin'_submatrix, Equiv.functionSwap_apply, MulEquiv.toAdditive_symm_apply_symm_apply, Multiset.cast_symm_apply_snd, OrderDual.toDual_comp_ofDual, orderIsoShrink_apply, finSumNatEquiv_symm_apply_add_right, Derivation.compAEval_eq, finPiFinEquiv_single, galRestrictHom_symm_apply, CategoryTheory.yonedaEquiv_naturality, MulEquiv.monoidHomCongrRight_apply, CategoryTheory.Adjunction.homEquiv_apply, Matrix.separatingLeft_toLinearMapâ_iff, Metric.Snowflaking.image_toSnowflaking_closedBall, RingHom.ker_coe_equiv, BotHom.symm_dual_id, HomologicalComplex.evalCompCoyonedaCorepresentableByDoubleId_homEquiv_symm_apply, Prod.Lex.toLex_covBy_toLex_iff, finRotate_last', ofDual_sup, Equiv.continuous_symm_iff, HahnModule.of_smul, Finsupp.lift_symm_apply, Matrix.reindex_mem_colStochastic, RingHomInvPair.of_ringEquiv, ContinuousMap.equivBoundedOfCompact_symm_apply, CompactlyGenerated.isoEquivHomeo_apply, PreTilt.untilt_iterate_frobeniusEquiv_symm_pow, Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eq, Matrix.diagonalInvertibleEquivInvertible_apply, LinearMap.ringLmapEquivSelf_apply, Equiv.Perm.IsCycleOn.zpow_apply_eq_zpow_apply, Equiv.Perm.ofSubtype_apply_of_not_mem, Matrix.toLin_toMatrix, PiTensorProduct.lift_comp_map, 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, RingEquiv.op_symm_apply_apply, OrderIso.inv_apply, CategoryTheory.Iso.self_symm_conj, PartENat.withTopEquiv_zero, AddSubmonoid.LocalizationMap.ofAddEquivOfDom_comp_symm, Equiv.subLeft_apply, Submodule.lTensorOne_symm_apply, UniformEquiv.coe_punitProd, sInfHom.symm_dual_comp, Units.toAut_inv, MeasureTheory.mulEquivHaarChar_smul_eq_comap, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom, WithBot.toDual_le_toDual_iff, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_symm_apply, MulHom.op_apply_apply, LinearMap.toMatrixâ_apply, AdicCompletion.sumEquivOfFintype_apply, EuclideanGeometry.reflection_apply', coe_addEquiv_lpPiLp, ChainComplex.fromSingleâEquiv_apply, Homeomorph.divLeft_symm_apply, AddEquiv.toAdditive_toMultiplicative_apply, CategoryTheory.Limits.IsColimit.equivIsoColimit_symm_apply, hasFDerivWithinAt_iff_hasGradientWithinAt, FirstOrder.Language.Term.relabelEquiv_symm_apply, ContinuousAddEquiv.injective, IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe, UniformEquiv.symm_apply_apply, Colex.exists, DirectSum.liftRingHom_symm_apply_coe, LinearEquiv.smul_def, Module.Basis.ext_elem_iff, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, MonoidAlgebra.toRingHom_mapRangeRingEquiv, AddEquiv.coe_toIntLinearEquiv, ofDual_sub, Equiv.setCongr_apply, DomAddAct.coe_mkHomeomorph, Set.preimage_equiv_eq_image_symm, AddEquiv.addSubgroupCongr_symm_apply, Homeomorph.homeomorphOfUnique_apply, SSet.OneTruncationâ.ofNerveâ.natIso_inv_app_map, ContinuousLinearEquiv.prodUnique_apply, TopologicalSpace.IrreducibleCloseds.equivSubtype'_apply, LinearMap.adjoint_comp, AlgHom.toRingHom_op, ContinuousLinearEquiv.trans_apply, ofColex_eq_one, Finset.Colex.toColex_image_ofColex_strictMono, RootPairing.Equiv.weightEquiv_symm_weightMap, Equiv.Perm.OnCycleFactors.toPermHom_apply, Module.Basis.toMatrix_reindex, LieAlgebra.of_symm_zero, MeasurableEquiv.measurableSet_preimage, AlgebraicGeometry.ÎSpec.adjunction_homEquiv_symm_apply, Equiv.sumArrowEquivProdArrow_apply_fst, AddLocalization.addEquivOfQuotient_addMonoidOf, KaehlerDifferential.mvPolynomialBasis_repr_D, QuadraticForm.tensorAssoc_apply, finSuccEquiv'_symm_coe_below, Matrix.empty_mul, SymAlg.unsym_eq_one_iff, AddChar.toMonoidHomEquiv_symm_mul, RootPairing.coroot'_reflection, Submonoid.LocalizationMap.ofMulEquivOfLocalizations_eq_iff_eq, algebraicIndependent_equiv, UniformFun.toFun_add, LinearMap.toContPerfPair_apply, NonUnitalSubsemiring.centerToMulOpposite_apply_coe, Metric.Snowflaking.image_ofSnowflaking_emetricClosedBall, Matrix.toEuclideanLin_apply_piLp_toLp, MeasureTheory.tendsto_diracProbaEquivSymm_iff_tendsto, DomAddAct.mk_vadd_mk_aeeqFun, HahnSeries.coeff_toMvPowerSeries, CategoryTheory.Bicategory.mateEquiv_leftUnitor_hom_rightUnitor_inv, fixingAddSubgroup_fixedPoints_gc, Module.AEval.of_aeval_smul, Equiv.Set.insert_apply_right, Finset.Ico_orderDual_def, Prefunctor.symmetrifyCostar, Equiv.sigmaSigmaSubtypeEq_symm_apply, CategoryTheory.Bicategory.conjugateEquiv_mateEquiv_vcomp, Finsupp.restrictSupportEquiv_symm_single, RCLike.realRingEquiv_apply, Matrix.trace_fin_three_of, monovary_toDual_left, MeasurableEquiv.symm_comp_self, MonoidAlgebra.mapDomainRingEquiv_apply, Equiv.bijOn_symm, finSuccAboveEquiv_apply, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_symm_apply, RelIso.sumLexComplLeft_apply, Metric.Snowflaking.edist_ofSnowflaking_ofSnowflaking, toWellOrderExtension_strictMono, AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackComp_inv, nonZeroDivisorsEquivUnits_apply, MulEquiv.toAdditive_apply_symm_apply, sSupHom.symm_dual_comp, multilinearCurryLeftEquiv_symm_apply, Homeomorph.coe_toHomotopyEquiv, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_naturality, Equiv.Perm.closure_cycle_adjacent_swap, AddAut.mulLeft_apply_apply, Algebra.SubmersivePresentation.aevalDifferentialEquiv_apply, Matrix.trace_permutation, MeasureTheory.Measure.Regular.map, Equiv.boolProdNatEquivNat_symm_apply, ProbabilityTheory.Kernel.compProd_assoc, DFinsupp.toColex_monotone, CategoryTheory.Iso.conjAut_hom, finsuppTensorFinsuppRid_apply_apply, SimpleGraph.Iso.mapNeighborSet_symm_apply_coe, CategoryTheory.Iso.homCongr_symm_apply, OrderIso.compl_apply, Module.Basis.repr_sum_self, LinearEquiv.piFinTwo_apply, WithTop.ofDual_lt_iff, CategoryTheory.ComposableArrows.arrowEquiv_apply, Function.Exact.linearEquivOfSurjective_apply, RootPairing.Base.toWeightBasis_repr_root, Equiv.prod_assoc_preimage, finsuppEquivDFinsupp_symm_apply, Metric.Snowflaking.preimage_ofSnowflaking_eball, ProbabilityTheory.Kernel.compProd_def, ContinuousAlternatingMap.prodLIE_apply, Matrix.invertibleEquivDetInvertible_apply, RootPairing.GeckConstruction.ĎConj_mem_of_mem, IsometryEquiv.coe_symm_toEquiv, Equiv.coe_piCongr_symm, Submonoid.coe_equivMapOfInjective_apply, PerfectionMap.surjective, Matrix.reindexAlgEquiv_apply, ContinuousAddEquiv.eq_symm_apply, Hamming.toHamming_zero, AddEquiv.coe_toEquiv, Manifold.IsImmersionAtOfComplement.writtenInCharts, Equiv.Perm.equivUnitsEnd_symm_apply_symm_apply, CategoryTheory.Functor.partialRightAdjointHomEquiv_symm_comp_assoc, Equiv.coe_optionSubtype_apply_apply, polarCoord_apply, MultilinearMap.coe_currySumEquiv, AffineEquiv.pointReflection_self, Algebra.leftMulMatrix_mulVec_repr, iSupIndep_iff_dfinsupp_lsum_injective, ContinuousLinearEquiv.comp_continuous_iff, Equiv.prod_assoc_symm_image, image_extremePoints, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, ContinuousMulEquiv.refl_apply, WithCStarModule.inner_single_left, LinearIsometryEquiv.comp_hasFDerivAt_iff', SSet.nonDegenerateEquivOfIso_apply_coe, SSet.S.le_iff_nonempty_hom, MeasurableEquiv.coe_toEquiv_symm, ContinuousMultilinearMap.domDomCongrEquiv_apply, AddCircle.continuousAt_equivIco, RootPairing.toPerfPair_conj_reflection, PartENat.withTopEquiv_symm_le, AlgebraicGeometry.Proj.stalkIso'_germ, LinearEquiv.ofSubsingleton_symm_apply, Finpartition.IsEquipartition.exists_partsEquiv, AddConstEquiv.coe_toEquiv, Submonoid.LocalizationMap.mulEquivOfMulEquiv_mk', Matrix.det_matrixOfPolynomials, AddSubgroup.equivMapOfInjective_coe_addEquiv, cyclotomicCharacter.spec, Finsupp.supportedEquivFinsupp_symm_apply_coe, Metric.Snowflaking.uniformContinuous_toSnowflaking, FourierTransform.fourierCLE_symm_apply, finSuccEquiv'_succAbove, NumberField.mixedEmbedding.normAtPlace_negAt, PadicInt.mahlerEquiv_apply, Submodule.reflection_involutive, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, LinearEquiv.toSpanNonzeroSingleton_one, ofColex_sub, AddEquiv.ext_int_iff, Subsemiring.topEquiv_symm_apply_coe, Module.Basis.parallelepiped_map, Set.uIoo_ofDual, RingEquiv.sumArrowEquivProdArrow_apply, LinearIsometryEquiv.comp_continuousOn_iff, LieEquiv.ofInjective_apply, Matrix.of_row, PowerBasis.liftEquiv'_apply_coe, abelianizationCongr_of, LinearMap.coe_quotientInfToSupQuotient, DFA.accepts_reindex, CategoryTheory.Sheaf.ÎHomEquiv_naturality_right, Module.Basis.smulTower_repr_mk, Module.Basis.repr_support_subset_of_mem_span, Cubic.equiv_apply_coe, HNNExtension.NormalWord.unitsSMulEquiv_symm_apply, AddEquiv.coe_addMonoidHom_symm_comp_coe_addMonoidHom, ContinuousLinearMap.IsPositive.adjoint_conj, Finsupp.liftAddHom_apply_single, LinearEquiv.prodAssoc_apply, DomMulAct.stabilizerEquiv_invFun_eq, MultilinearMap.curryMidLinearEquiv_symm_apply, Polynomial.toMatrix_sylvesterMap, CategoryTheory.MonoidalClosed.curryHomEquiv'_symm_apply, isAddLeftRegular_ofMul, Finsupp.supportedEquivFinsupp_apply_support_val, GradedAlgebra.proj_apply, SubMulAction.fixingSubgroupEquivFixingSubgroup_coe_apply, CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorCorepresentingIso_hom_app_app, toDual_bihimp, CategoryTheory.map_yonedaEquiv, Complex.isometryOfOrthonormal_apply, finsuppLequivDFinsupp_symm_apply, Algebra.TensorProduct.equivPiOfFiniteBasis_symm_apply, DilationEquiv.refl_apply, coe_toLexMulEquiv, Finsupp.lsum_comp_lsingle, Shrink.continuousLinearEquiv_apply, Metric.Snowflaking.image_toSnowflaking_closedEBall, CategoryTheory.rightAdjointOfCostructuredArrowTerminalsAux_symm_apply, AddLocalization.addEquivOfQuotient_symm_addMonoidOf, AffineEquiv.coe_ofEq_apply, Matrix.of_symm_apply, CategoryTheory.tensorLeftHomEquiv_symm_coevaluation_comp_whiskerRight, Finsupp.lex_lt_iff, CategoryTheory.GrothendieckTopology.map_uliftYonedaEquiv, List.sortedGE_map_toDual, CategoryTheory.eHomEquiv_comp, TensorProduct.finsuppRight_symm_apply_single, Algebra.IsAlgebraic.algEquivEquivAlgHom_symm_apply, Matrix.dualNumberEquiv_apply, MonoidHom.ext_mnat_iff, OrderIso.subLeft_symm_apply, toAdd_div, OrderAddMonoidHom.fstâ_apply, AlgEquiv.opComm_symm_apply_apply, TensorProduct.gradedComm_one_tmul, Matrix.separatingRight_toBilin'_iff, CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber, toUnits_symm_apply, IsometryEquiv.eq_symm_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_symm_comp_assoc, AddSubgroup.quotientEquivProdOfLE'_apply, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply, Trivialization.coe_coordChangeL, LinearIsometryEquiv.withLpProdUnique_apply, CoalgEquiv.trans_symm_apply, UniformOnFun.isClosed_setOf_continuous, UniformEquiv.bijective, Finset.symInsertEquiv_apply_snd_coe, TensorProduct.prodRight_tmul, IsometryEquiv.injective, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, bddAbove_preimage_ofDual, FirstOrder.Language.Substructure.coe_topEquiv, Matrix.toLin_finTwoProd, toMul_eq_one, SheafOfModules.pullbackPushforwardAdjunction_homEquiv_symm_unitToPushforwardObjUnit, MulEquivClass.instMonoidHomClass, norm_toDual, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Equiv.Set.sumCompl_apply_inr, LinearMap.BilinForm.apply_toDual_symm_apply, Units.coe_opEquiv_symm, MulOpposite.opLinearIsometryEquiv_apply, orderIsoShrink_symm_apply, MeasureTheory.volume_preserving_piUnique, BialgEquiv.coe_symm_toEquiv, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, CategoryTheory.Functor.FullyFaithful.isoEquiv_symm_apply, isAddRegular_ofLex, LinearIsometryEquiv.comp_hasFDerivAt_iff, SubAddAction.ofStabilizer.neg_conjMap_comp_apply, Equiv.mulRightâ_symm_apply, Module.Basis.linearMap_repr_symm_apply, CategoryTheory.MonoidalCategory.DayConvolution.associatorCorepresentingIso_hom_app_app, ContinuousAddEquiv.coe_mk, ContinuousLinearEquiv.map_zero, CategoryTheory.conjugateIsoEquiv_apply_hom, RingEquiv.image_eq_preimage_symm, ofDual_symmDiff, Topology.WithLower.ofLower_inj, ContinuousLinearMap.star_eq_adjoint, Prod.Lex.toLex_strictMono, DomMulAct.mk_pow, Trivialization.sourceHomeomorphBaseSetProd_symm_apply, StarMulEquiv.rightInverse_symm, QuadraticMap.IsometryEquiv.prodProdProdComm_toFun, Module.Basis.constr_basis, IsBaseChange.equiv_tmul, Algebra.adjoin_eq_range_freeAlgebra_lift, UniformEquiv.coe_prodCongr, ContinuousMultilinearMap.piEquiv_symm_apply, MeasurableEquiv.coe_addRight, StarAlgHom.prodEquiv_symm_apply, LinearEquiv.charpoly_conj, PartialEquiv.transEquiv_apply, isAddRegular_toColex, Homeomorph.transOpenPartialHomeomorph_symm_apply, LinearOrderedField.coe_inducedOrderRingIso, WithVal.equivWithVal_apply, ModuleCat.homLinearEquiv_apply, FreeAddMagma.lift_symm_apply, ofDual_inv, AddGroupExtension.Equiv.coe_toAddEquiv, Algebra.Generators.snd_cotangentCompLocalizationAwayEquiv, Orientation.inner_rightAngleRotation_right, CochainComplex.HomComplex.Cocycle.equivHom_apply, MeasurableEquiv.coe_mulRight, AddCircle.openPartialHomeomorphCoe_symm_apply, continuousOn_cfcâ_setProd, isMaxFilter_dual_iff, ContinuousAlgEquiv.image_symm_eq_preimage, CategoryTheory.Localization.structuredArrowEquiv_symm_apply, QuaternionAlgebra.coe_linearEquivTuple, HahnModule.of_sub, Nat.factorizationEquiv_inv_apply, Homeomorph.comp_continuousAt_iff, finsuppTensorFinsuppLid_single_tmul_single, Topology.WithLower.isOpen_preimage_ofLower, Matrix.mul_fin_two, FreeLieAlgebra.lift_symm_apply, AlgEquiv.opComm_symm_apply_symm_apply, AddEquiv.symmEquiv_apply_apply, CategoryTheory.Limits.Sigma.whiskerEquiv_inv, WithZero.lift_unique, LinearEquiv.sumArrowLequivProdArrow_symm_apply_inl, Matrix.kroneckerTMulAlgEquiv_apply, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, ProperCone.hyperplane_separation_of_notMem, IsometryEquiv.constVAdd_apply, GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range, derivationToSquareZeroEquivLift_apply_coe_apply, FirstOrder.Language.Equiv.coe_toHom, FirstOrder.Language.LEquiv.onTerm_apply, ZSpan.map_fundamentalDomain, MonoidHom.ofInjective_apply, CategoryTheory.CommSq.instHasLift_1, DirectSum.decomposeAddEquiv_symm_apply, Equiv.Perm.SameCycle.cycleOf_apply, DomAddAct.symm_mk_nsmul, ExteriorAlgebra.lift_unique, Monoid.CoprodI.lift_symm_apply, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, ContinuousLinearMap.prodEquiv_apply, Homeomorph.mulRightâ_symm_apply, Equiv.sumAssoc_symm_apply_inr_inr, MulEquiv.coe_subgroupMap_apply, ofMul_prod, NumberField.mixedEmbedding.polarSpaceCoord_apply, toMul_multiset_sum, Topology.WithGeneratedByTopology.continuous_equiv, ContinuousLinearEquiv.smul_apply, Padic.coe_withValRingEquiv_symm, HahnModule.of_add, RingEquiv.sofLeftInverse'_symm_apply, iteratedFDerivWithin_zero_eq_comp, ContinuousLinearEquiv.submoduleMap_apply, MonoidAlgebra.mapRangeAddEquiv_single, Homeomorph.toOpenPartialHomeomorph_symm_apply, CategoryTheory.Sieve.overEquiv_symm_top, MulEquivClass.instMulHomClass, Topology.WithUpperSet.toUpperSet_ofUpperSet, Rep.homEquiv_symm_apply_hom, ContinuousLinearEquiv.ofBijective_symm_apply_apply, Polynomial.roots_X_pow_char_sub_C, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, MeasurableEquiv.piFinTwo_apply, Submodule.ClosedComplemented.exists_submodule_equiv_prod, FreeAddMonoid.comp_lift, Fin.cycleRange_of_gt, GradedRing.projZeroRingHom_apply, LinearMap.nondegenerate_toMatrixâ_iff, CategoryTheory.conjugateIsoEquiv_apply_inv, TopCat.homeoOfIso_symm_apply, DFA.eval_reindex, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, MulAutMultiplicative_apply_symm_apply, AlgEquiv.linearEquivConj_mulRight, CStarMatrix.neg_of, ContinuousLinearEquiv.isClosed_image, CategoryTheory.Limits.Types.limitEquivSections_apply, isLeftRegular_toDual, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Submonoid.coe_toAddSubmonoid_symm_apply, Sym.oneEquiv_apply, CategoryTheory.Subobject.leInfCone_Ď_app_none, fixingSubgroup_fixedPoints_gc, ContinuousAlgEquiv.self_comp_symm, ModuleCat.Iso.conj_eq_conj, UniformFun.uniformContinuous_eval, Topology.WithLowerSet.ofLowerSet_le_ofLowerSet, MeasureTheory.Measure.addHaar_preimage_linearEquiv, CoxeterSystem.reindex_simple, Equiv.subtypeSubtypeEquivSubtypeInter_apply_coe, Submonoid.coe_toAddSubmonoid_apply, Quiver.SingleObj.pathEquivList_symm_nil, IsometryEquiv.constSMul_apply, Real.expMonoidHom_apply, Finset.Colex.singleton_le_singleton, AffineIsometryEquiv.bijective, BoundedLatticeHom.dual_comp, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst, ContinuousLinearEquiv.hasFDerivAt, Matrix.toLin_one, DFA.reindex_apply_step, Homeomorph.symm_apply_eq, sigmaFinsuppEquivDFinsupp_apply, antivaryOn_toDual_right, CategoryTheory.Iso.homToEquiv_symm_apply, TensorAlgebra.mk_reindex_fin_cast, SemilinearEquivClass.map_smulââ, AlgHom.prodEquiv_apply, MeasurableEquiv.map_measurableEquiv_injective, CategoryTheory.unitCompPartialBijective_symm_natural, ContinuousLinearEquiv.summable, Topology.WithLower.toLower_ofLower, Subgroup.IsComplement.equiv_mul_right_of_mem, ContinuousAlgEquiv.map_eq_zero_iff, ContinuousAlgEquiv.comp_coe, CategoryTheory.Functor.sectionsEquivHom_apply_app, Ideal.quotientInfEquivQuotientProd_fst, ContinuousMultilinearMap.toUniformOnFun_toFun, AddChar.doubleDualEquiv_symm_doubleDualEmb_apply, Order.pred_toAdd, CliffordAlgebra.reverseEquiv_apply, AddConstEquiv.instAddConstMapClass, Finset.Colex.toColex_lt_toColex, Matrix.toLin_transpose, Matrix.det_mul_row, NonemptyInterval.toLex_mono, Equiv.range_eq_univ, Equiv.dvd_apply, GradedTensorProduct.of_symm_of, Finsupp.sumFinsuppEquivProdFinsupp_symm_inl, Homeomorph.transOpenPartialHomeomorph_source, MonotoneOn.dual_right, CategoryTheory.Iso.homFromEquiv_apply, OrderDual.toDual_bot, isRegular_toDual, SymAlg.sym_inj, SemilinearEquivClass.semilinearEquiv_apply, DirectSum.decompose_symm_zero, IsometryEquiv.image_symm, Monovary.sum_mul_comp_perm_lt_sum_mul_iff, SSet.OneTruncationâ.nerveEquiv_symm_apply_obj, Equiv.sumArrowEquivProdArrow_apply_snd, Complex.toMatrix_conjAe, LT.lt.dual, OrderIsoClass.toOrderHomClass, Additive.toMul_eq_bot, DilationEquiv.coe_mul, comp_surjective, WithLp.coe_addEquiv, Equiv.preimage_image, FreeAddMonoid.ofList_flatten, Orientation.rotation_apply, ContinuousLinearMap.coe_flipâᾢ, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_fst, CategoryTheory.Localization.Construction.objEquiv_apply, measurable_piEquivPiSubtypeProd_symm, BilinForm.mul_toMatrix, CategoryTheory.GrothendieckTopology.uliftYonedaOpCompCoyoneda_inv_app_app, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, nonZeroDivisorsEquivUnits_symm_apply_coe, Equiv.Perm.cycleFactorsFinset_conj, AddAction.toPermHom_apply_apply, Matrix.invOf_submatrix_equiv_eq, OrthonormalBasis.sum_repr, MulEquiv.toMulHom_eq_coe, homeomorphSphereProd_apply_snd_coe, AffineBasis.reindex_apply, Multiset.coeEquiv_symm_apply_fst, Submodule.reflection_mem_subspace_eq_self, Matrix.submatrix_mul_transpose_submatrix, Matrix.cons_vecMul, Finset.Colex.toColex_image_le_toColex_image, Homeomorph.isOpen_image, WithZero.withZeroUnitsEquiv_symm_apply, WittVector.quotEquivOfEq_ghostComponentModPPow, CategoryTheory.Iso.conj_id, self_comp_coe_symm, MulEquiv.coprodCongr_symm_apply, AffineIsometryEquiv.lipschitz, ContinuousLinearEquiv.analyticOnNhd, AddEquiv.subsemigroupMap_symm_apply_coe, Finset.Colex.toColex_sdiff_lt_toColex_sdiff', MonomialOrder.lex_lt_iff, Matrix.toLpLin_symm_comp, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_comp_asIdeal, Module.Basis.SmithNormalForm.repr_comp_embedding_eq_smul, AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv_apply_coe, subtypeOrEquiv_symm_inr, CategoryTheory.MonoidalClosed.homEquiv_apply_eq, Equiv.algebraMap_def, CategoryTheory.Limits.coneOfSectionCompCoyoneda_Ď, AddEquiv.refl_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, PresentedGroup.equivPresentedGroup_symm_apply_of, DirectSum.decomposeAddEquiv_apply, Matrix.toLinearMapâââ_apply_basis, Topology.WithLower.toLower_lt_toLower, CategoryTheory.conjugateEquiv_whiskerLeft, Module.Ray.map_apply, CategoryTheory.ActionCategory.stabilizerIsoEnd_apply, Equiv.sigmaSumDistrib_apply, CochainComplex.fromSingleâEquiv_symm_apply_f_zero, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_symm_apply, Finset.ofDual_inf', Module.Ray.map_neg, Antivary.sum_smul_comp_perm_eq_sum_smul_iff, MulEquiv.comp_left_injective, stdSimplexEquivIcc_apply_coe, SubMulAction.ofFixingSubgroup_of_eq_bijective, AdjoinRoot.quotEquivQuotMap_symm_apply, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coe, TensorProduct.tensorTensorTensorAssoc_symm_tmul, AlgEquiv.piCongrLeft_symm_apply, TensorProduct.finsuppLeft_apply_tmul, LinearEquiv.coord_apply_smul, Unitization.lift_range_le, PiTensorProduct.ofFinsuppEquiv'_apply_apply, FreeAbelianGroup.lift_comp, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_comp, LinearIsometryEquiv.hasFDerivWithinAt, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply, Matrix.det_fin_one_of, Diffeomorph.contMDiffWithinAt_diffeomorph_comp_iff, Finsupp.restrictSupportEquiv_apply, FreeAddMonoid.lift_of_comp_eq_map, UpperHalfPlane.val_J, Equiv.piCongrLeft_apply_apply, CategoryTheory.Presheaf.map_comp_uliftYonedaEquiv_down, measurable_piCurry_symm, Equiv.bijOn_image, Equiv.piCurry_apply, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, IsometryEquiv.vaddConst_symm_apply, Subgroup.IsComplement.mk''_rightQuotientEquiv, AffineEquiv.list_sbtw_map_iff, GroupExtension.Equiv.rightHom_map, WithCStarModule.equiv_symm_add, ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv_apply, finSigmaFinEquiv_one, AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly, Diffeomorph.ext_iff, CategoryTheory.Adjunction.equivHomsetLeftOfNatIso_apply, LinearMap.toMatrix_toSpanSingleton, RootPairing.toPerfPair_flip_conj_coreflection, IsGaloisGroup.mulEquivAlgEquiv_symm_apply, IsHilbertSum.linearIsometryEquiv_symm_apply_single, IsSelfAdjoint.adjoint_conj, WittVector.exists_frobenius_solution_fractionRing_aux, ModelWithCorners.toHomeomorph_apply, Equiv.Perm.mul_apply, List.formPerm_eq_head_iff_eq_getLast, AffineIsometryEquiv.map_vadd, Matrix.vecMulVec_cons, IsPerfectClosure.equiv_symm_apply, OrderMonoidIso.coe_trans, ModularGroup.coe_T, IsLowerSet.toDual, Equiv.instCanLiftForallCoeBijective, AffineEquiv.wOppSide_map_iff, UnitAddTorus.mFourierBasis_repr, Polynomial.degreeLT.addLinearEquiv_natAdd, DomAddAct.mk_zero, Equiv.equivPUnit_apply, Finsupp.curryEquiv_symm_apply, TensorProduct.lidOfCompatibleSMul_tmul, CategoryTheory.conjugateIsoEquiv_symm_apply_inv, Matrix.comp_symm_transpose, SSet.stdSimplex.spineId_vertex, LieAlgebra.Extension.ringModuleOf_bracket_proj, RingEquiv.toRingHom_eq_coe, Subgroup.transferFunction_apply, List.equivSigmaTuple_apply_snd, ApproximatesLinearOn.exists_homeomorph_extension, CategoryTheory.SimplicialObject.cechNerveEquiv_apply, Coalgebra.coassoc_apply, rootsOfUnityEquivNthRoots_apply, List.sortedLE_map_ofDual, OrderHom.dual_apply_coe, Equiv.divLeftâ_symm_apply, AffineEquiv.vaddConst_symm_apply, CategoryTheory.Functor.LeibnizAdjunction.adj_unit_app_right, ZMod.invDFT_def, Fin.equivSubtype_symm_apply, OrderMonoidIso.coe_refl, AffineEquiv.vaddConst_apply, ContinuousLinearEquiv.ofSubmodule'_symm_apply, Finset.Colex.toColex_empty, LinearEquiv.coe_toLinearMap, UniformFun.lipschitzOnWith_ofFun_iff, LinearAlgebra.FreeProduct.lift_algebraMap, MulOpposite.coe_opLinearEquiv, Fin.cycleIcc_of_lt, Representation.coinvariantsFinsuppLEquiv_symm_apply, ContinuousAlgEquiv.coe_coe, fourierBasis_repr, LinearMap.Nondegenerate.toMatrixâ', Homeomorph.coe_trans, RootPairing.Equiv.reflection_smul, ContinuousAlgEquiv.preimage_symm_preimage, Subalgebra.linearEquivOp_symm_apply_coe, Subgroup.quotientEquivProdOfLE'_apply, AddSubmonoid.LocalizationMap.ofAddEquivOfDom_comp, RelIso.preimage_apply, HahnModule.support_smul_subset_vadd_support, Matrix.cons_vecMul_cons, TensorProduct.equivFinsuppOfBasisRight_symm, Equiv.boolProdEquivSum_apply, FirstOrder.Language.BoundedFormula.realize_constantsVarsEquiv, CategoryTheory.Abelian.Ext.mkâ_linearEquivâ_apply, HahnSeries.orderTop_abs, LinearIsometryEquiv.lipschitz, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, HomologicalComplex.evalCompCoyonedaCorepresentableBySingle_homEquiv_apply, LinearIsometryEquiv.piLpCongrLeft_single, DFA.evalFrom_reindex, Setoid.piQuotientEquiv_apply, RingEquiv.map_multiset_sum, Equiv.isTrivialRelation_comp, CategoryTheory.Iso.trans_conj, CategoryTheory.Adjunction.homEquiv_naturality_left_symm, exteriorPower.basis_repr, CategoryTheory.Enriched.FunctorCategory.homEquiv_apply_Ď_assoc, ContinuousLinearMap.adjoint_inner_right, AddMonoidAlgebra.mapRangeAddEquiv_single, LinearEquiv.lTensor_trans_apply, OrderIso.sumLexIioIci_apply_inl, AlternatingMap.map_swap, finSuccEquiv'_eq_none, MulEquiv.funUnique_apply, SymAlg.unsym_mul_self, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, AffineIsometryEquiv.injective, Equiv.sumComm_apply, Equiv.Perm.map_finRange_perm, CompHausLike.isoOfHomeo_inv_hom_hom_apply, Equiv.Perm.equivUnitsEnd_symm_apply_apply, Sum.Lex.inr_mono, Equiv.pointReflection_self, Equiv.comp_symm_eq, Matrix.charpoly.univ_map_evalâHom, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, Matrix.det_fin_two_of, rootsOfUnityCircleEquiv_apply, InfHom.symm_dual_id, CategoryTheory.Groupoid.isoEquivHom_symm_apply_inv, Equiv.piCongrLeft'_symm_apply, AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, Action.resEquiv_inverse, Submodule.lTensorOne_tmul, SheafOfModules.relationsOfIsCokernelFree_s, MeasurableEquiv.setOf_symm_apply, toUnits_val_apply, MeasurableEquiv.coe_piCurry, FreeAbelianGroup.lift_add_apply, WithTop.orderIsoSumLexPUnit_symm_inr, SemidirectProduct.inv_left, CategoryTheory.ShiftedHom.opEquiv_symm_apply, AddChar.toAddMonoidHomEquiv_zero, Matrix.Nondegenerate.toBilin', ContinuousLinearEquiv.prodProdProdComm_apply, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, Specialization.ofEquiv_specializes_ofEquiv, StrictConvexOn.dual, CategoryTheory.Limits.Concrete.prodEquiv_apply_snd, Monoid.CoprodI.Word.equivPair_head, FDRep.Iso.conj_Ď, FirstOrder.Language.StrongHomClass.realize_boundedFormula, TensorProduct.directLimitLeft_tmul_of, CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv_functor_obj_str, IsLocalization.ringEquivOfRingEquiv_eq, finsuppAddEquivDFinsupp_apply, MulEquivClass.toZeroHomClass, MulEquiv.coprodAssoc_symm_apply_inl, FractionalIdeal.map_canonicalEquiv_mk0, ContinuousLinearMap.toSpanSingletonLE_symm_apply, AlgebraicGeometry.Scheme.Hom.homeomorph_apply, ContinuousMulEquiv.equivLike_inv_eq_symm, UniformConvergenceCLM.uniformSpace_eq, FirstOrder.Language.Theory.CompleteType.mem_typeOf, IsometryEquiv.piFinTwo_apply, ContinuousMap.addEquivBoundedOfCompact_symm_apply, LinearMap.toMatrix_singleton, AddSubgroup.toSubgroup'_closure, Rat.ringOfIntegersEquiv_symm_apply_coe, LinearMap.BilinForm.toMatrix'_mul, Equiv.Finset.union_inr, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, RingEquiv.coe_ringHom_ofRingHom, Subgroup.IsComplement'.QuotientMulEquiv_symm_apply, MulEquiv.symm_comp_eq, Submodule.LinearDisjoint.val_mulMap_tmul, AddMonoidAlgebra.domCongr_apply, Topology.WithUpper.isOpen_def, Equiv.Perm.viaFintypeEmbedding_apply_notMem_range, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left, Algebra.discr_powerBasis_eq_prod'', dist_pointReflection_left, CategoryTheory.Adjunction.rightAdjointLaxMonoidal_Îľ, ContinuousMap.homeoFnOfDiscrete_symm_apply_apply, Matrix.diagonal_unique, StarAlgEquiv.nnnorm_map, AddEquiv.coe_toNatLinearEquiv, LinearIsometryEquiv.symm_smul_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_comp_assoc, Polynomial.opRingEquiv_symm_C, Algebra.traceMatrix_of_basis_mulVec, IsBaseChange.basis_repr_comp, FreeAddGroup.lift_eq_sum_map, AlgebraicGeometry.affineOpensRestrict_symm_apply_coe, VectorField.pullback_eq_of_fderiv_eq, CategoryTheory.Adjunction.homEquiv_counit, Matrix.ofNat_kronecker, Homeomorph.coe_mulLeftâ, StarMulEquiv.trans_apply, Topology.WithLower.continuous_toLower, exteriorPower.alternatingMapLinearEquiv_symm_apply, OrthonormalBasis.coe_toBasis_repr_apply, Finsupp.mapDomain.toLinearMap_linearEquiv, FractionalIdeal.mem_canonicalEquiv_apply, Affine.Simplex.mongePlane_reindex, TensorProduct.lid'_symm_apply, ContinuousAddEquiv.apply_eq_iff_symm_apply, AddCommMonCat.equivalence_counitIso, Orientation.reindex_apply, MulOpposite.coe_opMulEquiv, UniformOnFun.toFun_add, rootsOfUnity.integer_power_of_ringEquiv', Hamming.dist_eq_hammingDist, SymAlg.sym_eq_zero_iff, Equiv.addLeft_symm_apply, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, RingEquiv.piFinTwo_symm_apply, PiLp.coe_symm_continuousLinearEquiv, ZLattice.normBound_spec, OrderIso.sumDualDistrib_inr, ContinuousAffineEquiv.toContinuousAffineMap_toContinuousMap, CategoryTheory.ShiftedHom.opEquiv'_apply, SSet.S.equivElements_symm_apply_simplex, CochainComplex.toSingleâEquiv_apply, TopologicalSpace.IrreducibleCloseds.equivSubtype_symm_apply, ContinuousLinearEquiv.dimH_preimage, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd, grade_ofDual, LinearMap.toMatrixâ'_complâ, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, CompleteLatticeHom.dual_apply_toFun, OrderAddMonoidIso.strictMono, CategoryTheory.Functor.RepresentableBy.equivUliftYonedaIso_apply, PiTensorProduct.map_reindex, IsExtrOn.dual, Finset.symInsertEquiv_apply_fst, CategoryTheory.isoOpEquiv_apply, uliftZPowersHom_apply_apply, CategoryTheory.Adjunction.leftAdjointCompNatTransâââ_eq_conjugateEquiv_symm, TensorPower.mul_algebraMapâ, MvPolynomial.finSuccEquiv_rename_finSuccEquiv, Equiv.optionSubtypeNe_some, EuclideanGeometry.reflection_involutive, Equiv.symmEquiv_symm_apply_symm_apply, LinearIsometryEquiv.coe_symm_trans, WithCStarModule.equiv_fst, InverseSystem.globalEquiv_naturality, Rep.leftRegularHomEquiv_apply, Fin.appendHomeomorph_symm_apply, OrthonormalBasis.coe_equiv_euclideanSpace, SSet.stdSimplex.mem_nonDegenerate_iff_mono, CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf_obj_str, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, Metric.Snowflaking.edist_def, AddSubgroup.map_symm_eq_iff_map_eq, Submonoid.comap_equiv_eq_map_symm, LinearEquiv.ext_iff, Homeomorph.isOpenEmbedding, Orientation.rightAngleRotation_map, Finsupp.Colex.single_le_iff, IsUpperSet.toDual, antivary_toDual_left, OrderDual.toDual_eq_bot, finsuppAddEquivDFinsupp_symm_apply, AddSubgroup.quotientEquivProdOfLE'_symm_apply, RootPairing.Hom.coroot_coweightMap_apply, PartENat.withTopEquiv_symm_coe, Function.Exact.linearEquivOfSurjective_symm_apply, SemidirectProduct.mulEquivSubgroup_apply, Equiv.simpleGraph_apply, ENNReal.logHomeomorph_apply, SymAlg.unsym_sub, LinearEquiv.coe_injective, WithTop.ofDual_symm_apply, CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation, Subsemigroup.map_equiv_top, CategoryTheory.Presheaf.coconeOfRepresentable_Κ_app, CompareReals.compare_uc_symm, ContinuousAlternatingMap.nnnorm_ofSubsingleton, LinearAlgebra.FreeProduct.lift_symm_apply, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, LieAlgebra.IsKilling.traceForm_coroot, DomMulAct.isOpenEmbedding_mk_symm, Multiset.cast_apply_snd, FirstOrder.Language.PartialEquiv.symm_apply, IsCyclic.mulAutMulEquiv_symm_apply_apply, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, IsAdjoinRootMonic.coeff_apply_coe, surjective, Order.isSuccPrelimit_toDual_iff, Equiv.injective, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit, Orientation.kahler_rotation_right, Nat.equivProdNatFactoredNumbers_apply', Set.dual_ordConnected_iff, LieEquiv.ofBijective_toFun, LieModuleEquiv.apply_symm_apply, StarMulEquiv.coe_trans, Submonoid.toAddSubmonoid'_closure, Action.diagonalSuccIsoTensorDiagonal_hom_hom, CategoryTheory.Limits.IsColimit.Κ_app_homEquiv_symm_assoc, Monoid.Foldr.ofFreeMonoid_apply, TensorProduct.nnnorm_comm, WittVector.frobeniusEquiv_apply, Ideal.cotangentEquivIdeal_symm_apply, equivShrink_inv, Module.Basis.traceDual_repr_apply, TensorAlgebra.mk_reindex_cast, Antivary.dual_right, QuotientAddGroup.equivIcoMod_zero, IsometryEquiv.coe_one, HahnModule.of_symm_zero, OrderIso.sumLexAssoc_apply_inr, FirstOrder.Language.DirectLimit.Equiv_isup_of_apply, UniformFun.ofFun_sub, PiTensorProduct.lift.unique', Topology.WithUpper.toUpper_le_toUpper, QuaternionAlgebra.imJ_equivProd_symm_apply, CategoryTheory.Functor.curryingFlipEquiv_symm_apply_obj_obj, Matrix.nondegenerate_toLinearMapâ'_iff, OrderDual.ofDual_toDual, LinearMap.separatingRight_toMatrixâ_iff, AddAut.one_apply, CategoryTheory.conjugateEquiv_adjunction_id_symm, CategoryTheory.LiftRightAdjoint.constructRightAdjointEquiv_symm_apply, Sym.coe_cast, CoxeterSystem.map_simple, RingEquiv.symm_comp, finRotate_symm_lt_iff_ne_zero, DirectSum.IsInternal.ofBijective_coeLinearMap_of_ne, Equiv.Perm.subtypeCongr.left_apply, WeakDual.CharacterSpace.equivAlgHom_coe, MulEquiv.withZero_symm_apply_apply, MeasurableEquiv.measurable, OrderHom.dual_symm_apply_coe, Equiv.optionSubtypeNe_none, HahnSeries.ofPowerSeries_apply, Equiv.pointReflection_midpoint_left, AddEquiv.trans_apply, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add, HahnModule.of_zero, TensorProduct.piScalarRight_apply, continuousMultilinearCurryRightEquiv_apply', RingHom.quotientKerEquivOfRightInverse.apply, MeasurableEquiv.coe_mulLeftâ, CliffordAlgebra.lift_comp_Κ, DirectSum.decompose_mul, AddSubsemigroup.topEquiv_toAddHom, Subgroup.IsComplement.equiv_mul_right, AddGroupExtension.Equiv.inl_comm, isOpenMap_ofAdd, DilationEquiv.surjective, Finsupp.liftAddHom_symm_apply_apply, Metric.Snowflaking.preimage_ofSnowflaking_emetricBall, NumberField.Units.logEmbeddingEquiv_apply, RootPairing.coreflection_same, MulEquiv.op_symm_apply_symm_apply, LinearEquiv.lTensor_symm_tmul, LieModule.coe_maxTrivEquiv_apply, Equiv.Perm.isCycleOn_singleton, Orthonormal.comp_linearIsometryEquiv, equicontinuousAt_iff_continuousAt, UniformOnFun.toFun_inv, Module.Invertible.linearEquivOfRightInverse_apply, SymmetricPower.tprod_equiv, AddEquiv.toMultiplicativeLeft_symm_apply_apply, CategoryTheory.ShrinkHoms.comp_def, CategoryTheory.Iso.conjAut_zpow, finSumNatEquiv_symm_apply_of_ge, Subgroup.mem_iff_toUnits_mem_units, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis, WithBot.toDual_symm_apply, NonemptyInterval.toLex_lt_toLex, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, Matrix.mulVecLin_reindex, OrderAddMonoidIso.invFun_eq_symm, Equiv.surjective, MvPolynomial.isSymmetric_rename, Circle.expHom_apply, IsEvenlyCovered.comp_homeomorph, HasFiniteFPowerSeriesOnBall.hasFDerivAt, SSet.prodStdSimplex.nonDegenerate_iff_strictMono_objEquiv, Subsemiring.ringEquivOpMop_apply, HomeomorphClass.coe_coe, homeomorphUnitSphereProd_apply_snd_coe, CategoryTheory.Limits.WalkingPair.swap_apply_left, CategoryTheory.Localization.SmallShiftedHom.precompEquiv_apply, SSet.yonedaEquiv_comp, ProbabilityTheory.isGaussian_map_equiv, AddEquiv.addIrreducible_iff, HasFDerivAt.hasGradientAt, AlgEquiv.op_symm_apply_apply, SSet.op_map, Function.fromTypes_zero_equiv_apply, contMDiff_tangentBundleModelSpaceHomeomorph, CategoryTheory.Iso.commRingCatIsoToRingEquiv_toRingHom, ContinuousAlgEquiv.cast_apply, DomMulAct.symm_mk_inv, CategoryTheory.ObjectProperty.isColocal.homEquiv_apply, Module.Basis.ofZLatticeComap_repr_apply, UniformOnFun.ofFun_mul, Polynomial.roots_expand_pow, AlternatingMap.map_swap_add, FirstOrder.Language.BoundedFormula.mapTermRelEquiv_symm_apply, Sum.Lex.not_inr_le_inl, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_app_apply, Equiv.Perm.subtypeEquivSubtypePerm_symm_apply, DomMulAct.coe_mkHomeomorph, MulAut.conjNormal_inv_apply, Submonoid.map_equiv_top, RootPairing.reflectionPerm_eq_of_pairing_eq_zero', CategoryTheory.Limits.CofanTypes.equivOfIsColimit_apply, MulEquiv.bijective, FreeMonoid.smul_def, Ideal.associatesEquivIsPrincipal_map_zero, IsometryEquiv.coe_symm_toDilationEquiv, Subgroup.subgroupOfEquivOfLe_apply_coe, MeasureTheory.continuous_diracProbaEquivSymm, Monoid.CoprodI.of_leftInverse, CategoryTheory.Abelian.Ext.addEquivBiprod_symm_apply, AddEquiv.coprodAssoc_apply_inl_inl, starLinearEquiv_apply, Equiv.piCurry_symm_apply, AddSubsemigroup.toSubsemigroup_closure, Equiv.Set.sumDiffSubset_apply_inl, SemidirectProduct.mulEquivProd_apply, AlternatingMap.domDomCongrâ_symm_apply, FreeAddMonoid.map_apply_map_symm_eq, DualNumber.lift_apply_inl, PadicInt.continuousAddCharEquiv_symm_apply, Finset.Colex.le_iff_sdiff_subset_lowerClosure, ContDiffWithinAt.iteratedFDerivWithin_comp_perm, MonoidHom.op_apply_apply, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, QuotientAddGroup.equivIcoMod_coe, Unitization.antilipschitzWith_addEquiv, HahnSeries.toMvPowerSeries_apply, modularCyclotomicCharacter'.spec', CategoryTheory.OverPresheafAux.MakesOverArrow.of_arrow, Equiv.optionSubtype_symm_apply_apply_some, Module.End.ringEquivEndFinsupp_apply_apply_support, CategoryTheory.Functor.flippingEquiv_apply_obj_map, Filter.HasBasis.comp_equiv, AddEquiv.map_finsum, Matrix.cons_mulVec, ContinuousMultilinearMap.domDomCongrEquiv_symm_apply, ContinuousMultilinearMap.norm_ofSubsingleton, ContinuousLinearMap.isAdjointPair_inner, SSet.OneTruncationâ.nerveHomEquiv_apply, TensorProduct.directLimitLeft_symm_of_tmul, Homeomorph.isSimplyConnected_preimage, Multiplicative.exists, ofAdd_nsmul, FintypeCat.uSwitchEquiv_symm_naturality, Matrix.mul_fin_three, Orientation.map_apply, CStarMatrix.uniformEmbedding_ofMatrix, AddEquiv.neg'_symm_apply, Quaternion.imI_equivProd_symm_apply, LinearIsometryEquiv.norm_map', ConjAct.ofConjAct_mul, Complex.equivRealProdCLM_symm_apply_im, UniformOnFun.uniformSpace_eq_inf_precomp_of_cover, DirectSum.decompose_coe, CategoryTheory.Discrete.equivOfEquivalence_symm_apply, Subsemiring.map_equiv_eq_comap_symm, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, CoxeterSystem.lengthParity_eq_ofAdd_length, mulEquivOfOrderOfEq_apply_gen, CategoryTheory.Iso.semiRingCatIsoToRingEquiv_toRingHom, coe_ringEquiv_lpBCF_symm, ContinuousLinearEquiv.analyticWithinAt, AddCon.quotientKerEquivOfRightInverse_apply, CategoryTheory.ShrinkHoms.inverse_map, Submodule.setSemiring_smul_def, LinearMap.toMvPolynomial_eval_eq_apply, LinearEquiv.coe_one, MulEquiv.coe_toEquiv, Finset.Iic_toDual, SymAlg.sym_comp_unsym, HVertexOperator.coeff_comp, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, LinearIsometryEquiv.differentiableAt, QuotientGroup.quotientBot_apply, Algebra.TensorProduct.liftEquiv_symm_apply_coe, CoxeterMatrix.reindexGroupEquiv_symm_apply_simple, ContinuousAlgEquiv.surjective, Polynomial.toFinsuppIso_symm_apply, LinearIsometryEquiv.differentiable, ContinuousAffineEquiv.coe_symm_toAffineEquiv, CompleteLatticeHom.dual_comp, Equiv.Set.sumCompl_apply_inl, MeasureTheory.Measure.prodAssoc_prod, Equiv.funUnique_symm_apply, Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking, SheafOfModules.conjugateEquiv_pullbackId_hom, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, RingEquiv.map_eq_neg_one_iff, Setoid.prodQuotientEquiv_apply, Ordinal.to_leftMoves_one_toPGame_symm, ContinuousMulEquiv.symm_comp_eq, CategoryTheory.PreGaloisCategory.endEquivAutGalois_Ď, finRotate_last, AddMonoidHom.toMultiplicativeLeft_apply_apply, Module.Basis.toMatrix_transpose_apply, CategoryTheory.Meq.equiv_symm_eq_apply, AffineEquiv.val_inv_equivUnitsAffineMap_apply, Cube.insertAt_boundary, CategoryTheory.Presieve.extension_iff_amalgamation, EuclideanGeometry.reflection_subtype, MeasureTheory.Measure.IsFiniteMeasureOnCompacts.map, Tuple.comp_perm_comp_sort_eq_comp_sort, Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer, Fin.appendIsometry_apply, RingEquiv.unop_map_list_prod, LinearEquiv.arrowCongrAddEquiv_apply, DualNumber.lift_op_smul, Submonoid.leftInvEquiv_symm_fromLeftInv, ModelWithCorners.coe_transContinuousLinearEquiv, AddCon.comapQuotientEquivOfSurj_symm_mk', Finset.Colex.cons_le_cons, BotHom.symm_dual_comp, toMul_list_sum, AffineIsometryEquiv.comp_continuousOn_iff, autEquivRootsOfUnity_apply_rootOfSplit, ContinuousAlgEquiv.comp_continuous_iff', zmultiplesHom_symm_apply, RingEquiv.map_multiset_prod, FreeMonoid.lift_apply, UniformEquiv.isUniformEmbedding, Rack.act'_symm_apply, LinearEquiv.coe_ofTop_symm_apply, DirectSum.decompose_one, UniformOnFun.edist_eq_restrict_sUnion, Matrix.comp_diagonal, Monovary.dual, PEquiv.transpose_toMatrix_toPEquiv_apply, FirstOrder.Language.Equiv.comp_apply, CategoryTheory.Localization.SmallShiftedHom.equiv_mkâInv, finTwoArrowEquiv'_sum_eq, isRegular_toMul, Finset.finsetCongr_piAntidiag_eq_antidiag, ofLex_mul, DilationEquiv.coe_inv, OrderIso.smulRightDual_symm_apply, toColex_zero, pairwise_comp_iff, Finsupp.sumFinsuppAddEquivProdFinsupp_symm_inr, AddGroupExtension.Equiv.rightHom_map, CategoryTheory.MonoidalClosed.curryHomEquiv'_apply, FreeLieAlgebra.lift_of_apply, affineHomeomorph_image_Icc, Cubic.equiv_symm_apply_d, norm_toMul, HahnSeries.addOppositeEquiv_symm_apply_coeff, LinearMap.separatingLeft_toMatrixâ_iff, SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply, DomMulAct.symm_mk_mul, Finsupp.DegLex.le_iff, Equiv.one_def, Equiv.coe_sigmaUnique, ContinuousLinearEquiv.map_nhds_eq, HVertexOperator.coeff_apply_apply, Equiv.Perm.decomposeOption_symm_apply, ContinuousLinearMap.toUniformConvergenceCLM_continuous, AddEquiv.val_neg_piAddUnits_symm_apply, AffineIsometryEquiv.coe_vaddConst', basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix, CategoryTheory.Bicategory.mateEquiv_apply, Equiv.swap_bijOn_exchange, UniformFun.uniformContinuous_toFun, TensorProduct.comm_tmul, Representation.asModuleEquiv_map_smul, homeomorphSphereProd_apply_fst_coe, Metric.Snowflaking.isBounded_preimage_toSnowflaking_iff, Submodule.fstEquiv_symm_apply_coe, SimpleGraph.one_add_adjMatrix_add_compl_adjMatrix_eq_allOnes, Algebra.discr_powerBasis_eq_prod', WithCStarModule.equiv_symm_fst, AdicCompletion.piEquivOfFintype_apply, QuaternionAlgebra.imI_equivProd_symm_apply, Finsupp.curryAddEquiv_symm_apply, MulOpposite.opContinuousLinearEquiv_apply, AddConstEquiv.equivUnits_symm_apply_symm_apply, BotHom.dual_comp, Finsupp.liftAddHom_symm_apply, SemidirectProduct.mulEquivSubgroup_symm_apply, injective, CategoryTheory.eHomEquiv_comp_assoc, antitone_comp_ofDual_iff, Submodule.snd_orthogonalDecomposition_apply, PerfectionMap.comp_symm_equiv', CategoryTheory.Pi.equivalenceOfEquiv_inverse, LinearIsometryEquiv.withLpProdComm_apply, Matrix.det_submatrix_equiv_self, List.formPerm_apply_getLast, Metric.Snowflaking.image_ofSnowflaking_closedBall, AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_symm_apply, AlternatingMap.map_add_swap, IsometryEquiv.symm_comp_self, Homeomorph.homeomorph_mk_coe_symm, Module.Basis.ofZLatticeBasis_repr_apply, IsometryEquiv.mul_apply, groupHomology.mkH1OfIsTrivial_apply, LinearEquiv.neg_apply, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, Equiv.vadd_def, freeGroupEquivCoprodI_apply, Subgroup.transferTransversal_apply'', AddMonoidHom.mulOp_symm_apply_apply, Representation.ofMulDistribMulAction_apply_apply, Sum.Lex.le_def, FreeAddMonoid.toList_ofList, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, fromModuleCatToModuleCatLinearEquiv_apply, Equiv.listUniqueEquiv_apply, Ici_orderDual_def, FirstOrder.Language.PartialEquiv.toEmbeddingOfEqTop_apply, SSet.Subcomplex.PairingCore.ancestralRel_iff, Multiplicative.forall, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, DirectSum.linearEquivFunOnFintype_symm_single, Fin.appendEquiv_symm_apply, LinearMap.BilinForm.toMatrix'_toBilin', CategoryTheory.Enriched.FunctorCategory.enrichedHom_condition'_assoc, zpowersHom_ker_eq, LinearEquiv.symm_smul_apply, HVertexOperator.of_coeff_apply, DoubleQuot.quotQuotEquivComm_mk_mk, Function.OfArity.curryEquiv_apply, UniformOnFun.toFun_mul, Trivialization.apply_symm_apply_eq_coordChangeL, CategoryTheory.conjugateEquiv_adjunction_id, IsometryEquiv.image_ball, AddEquiv.eq_iff_eq_on_generator, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat, IsometryEquiv.withLpProdAssoc_symm_apply, CircleDeg1Lift.translationNumber_translate, Matrix.conjTransposeRingEquiv_apply, AddSubgroup.quotientEquivProdOfLE_apply, Finset.symInsertEquiv_symm_apply_coe, CategoryTheory.coyonedaEquiv_symm_map, Matrix.compRingEquiv_apply, Diffeomorph.contMDiff_diffeomorph_comp_iff, CategoryTheory.PreZeroHypercover.interFst_hâ, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, toColex_div, RingEquiv.coe_addMonoidHom_trans, Equiv.embeddingCongr_apply_trans, CategoryTheory.Adjunction.homEquiv_naturality_right_square, LinearAlgebra.FreeProduct.lift_apply, Language.reverseIso_symm_apply, PowerBasis.liftEquiv'_symm_apply_apply, PiTensorProduct.lift_comp_reindex_symm, AffineSubspace.isometryEquivMap.apply_symm_apply, CategoryTheory.Functor.FullyFaithful.mulEquivEnd_apply, CategoryTheory.PreOneHypercover.inter_pâ, EuclideanSpace.coe_measurableEquiv, ConjAct.ofConjAct_inv, DirectSum.decompose_mul_add_right, PiTensorProduct.ofDFinsuppEquiv_symm_single_tprod, RingEquiv.ofLeftInverseS_apply, QuasiconcaveOn.dual, Metric.Snowflaking.uniformEquiv_apply, Finsupp.optionEquiv_symm_apply, Pi.le_toColex_update_self_iff, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_symm_map, Quiver.starEquivCostar_symm_apply_snd, Homeomorph.apply_symm_apply, Finsupp.equivFunOnFinite_symm_single, Topology.IsQuotientMap.liftEquiv_apply, Equiv.withTopSubtypeNe_apply, Subgroup.toAddSubgroup'_closure, PowerBasis.constr_pow_mul, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, SymAlg.sym_smul, finSuccEquiv'_symm_some, Multiplicative.ofAdd_mono, Equiv.subset_symm_image, Equiv.piFinsetUnion_left, HahnEmbedding.Partial.eval_eq_truncLT, ofMul_toMul, Equiv.div_def, AddSubmonoid.map_equiv_eq_comap_symm, FreeMonoid.ofList_flatten, PrimeSpectrum.primeSpectrumProd_symm_inl_asIdeal, List.support_formPerm_of_nodup', StrongDual.coe_toWeakDual, ContinuousAddEquiv.symm_apply_apply, AddAut.mulLeft_apply_symm_apply, WithTop.toDual_map, LieModuleEquiv.coe_toLieModuleHom, ContinuousAffineEquiv.coe_coe, Equiv.coe_fn_injective, Orientation.oangle_rotation_self_right, affineHomeomorph_apply, LinearMap.det_toMatrix', Equiv.prodShear_apply, Matrix.separatingLeft_toBilin_iff, PresheafOfModules.freeYonedaEquiv_comp, Nat.toAdd_pow, AlgebraicGeometry.ÎSpec_adjunction_homEquiv_eq, WeakDual.toStrongDual_apply, Equiv.comp_injective, Equiv.preimage_piEquivPiSubtypeProd_symm_pi, Module.Basis.toMatrix_reindex', AffineEquiv.coe_toHomeomorphOfFiniteDimensional, ContinuousLinearEquiv.uniqueDiffOn_image_iff, Submodule.equivOpposite_symm_apply, AddMonCat.equivalence_functor_map, LinearIsometryEquiv.withLpProdAssoc_apply, mulTSupport_comp_eq_preimage, LinearMap.eq_adjoint_iff_basis_right, DomAddAct.vadd_apply, Unitization.starLift_range_le, HahnModule.coeff_smul_left, AddSubsemigroup.equivOp_apply_coe, CharacterModule.intSpanEquivQuotAddOrderOf_apply_self, DilationEquiv.smulTorsor_preimage_ball, AddEquiv.eq_symm_apply, UniformFun.toFun_inv, Sym2.lift_mk, Polynomial.natDegree_opRingEquiv, Action.resEquiv_functor, LinearMap.Nondegenerate.toMatrixâ, HahnSeries.finiteArchimedeanClassOrderIso_apply, LaurentSeries.ratfuncAdicComplRingEquiv_apply, FirstOrder.Language.LEquiv.onBoundedFormula_apply, LinearMap.toMatrixAlgEquiv_apply', isMaxOn_dual_iff, Matrix.toLin'OfInv_apply, AddMonoidAlgebra.curryRingEquiv_single, finFunctionFinEquiv_apply_val, Hamming.toHamming_inj, Homeomorph.subLeft_apply, Order.pred_ofMul, ContinuousAlgEquiv.apply_symm_apply, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right_assoc, MonomialOrder.div, Basis.equivFun_symm_single, continuousMultilinearCurryLeftEquiv_symm_apply, WeierstrassCurve.Jacobian.Point.toAffineAddEquiv_symm_apply, UniformOnFun.isUniformEmbedding_toFun_finite, Finsupp.equivFunOnFinite_symm_sum, SSet.Truncated.HomotopyCategory.homToNerveMk_app_zero, Equiv.sigmaPreimageEquiv_symm_apply_fst, MeasureTheory.measurePreserving_sumPiEquivProdPi_symm, FreeAddMonoid.countP_apply, IsArtinianRing.primeSpectrumEquivMaximalSpectrum_symm_comp_asIdeal, toLex_eq_zero, BotHom.dual_id, MonoidHom.coe_toAdditiveRight, FormalMultilinearSeries.changeOriginIndexEquiv_apply_snd, UniformOnFun.postcomp_isUniformEmbedding, FreeAbelianGroup.lift_neg_apply, Hamming.ofHamming_neg, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk, MonoidAlgebra.lift_def, Matroid.mapEquiv_isBasis_iff, MulEquiv.coe_toEquiv_symm, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, MvPolynomial.scalarRTensor_symm_apply_single, FractionalIdeal.equivNum_apply, DFinsupp.liftAddHom_comp_single, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, Equiv.ofLeftInverseOfCardLE_symm_apply, Equiv.Perm.sameCycle_pow_left, Equiv.transPartialEquiv_apply, ContinuousLinearEquiv.symm_apply_apply, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_apply, UniformFun.ofFun_sum, MonomialOrder.lex_le_iff, Equiv.ringEquiv_apply, Equiv.piCongrLeft'_symm_apply_apply, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, InfClosed.dual, AffineIsometryEquiv.coe_toHomeomorph, Homeomorph.image_preimage, Matrix.submatrix_mul_equiv, MeasurableEquiv.coe_piCurry_symm, AddEquivClass.map_finsum, MultilinearMap.constLinearEquivOfIsEmpty_symm_apply, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply, CategoryTheory.Sieve.overEquiv_generate, ClassGroup.equiv_mk0, Perfection.coeff_iterate_frobeniusEquiv_symm, isTop_ofDual_iff, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, toWeakSpaceCLM_eq_toWeakSpace, Subsemiring.comap_equiv_eq_map_symm, TensorProduct.equivFinsuppOfBasisLeft_apply, CategoryTheory.Pretriangulated.preadditiveYoneda_shiftMap_apply, FreeAddMonoid.ofList_comp_toList, isMin_ofDual_iff, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_symm_naturality_right, CategoryTheory.Enriched.FunctorCategory.homEquiv_comp_assoc, OrderAddMonoidIso.symm_apply_apply, Module.Basis.prod_repr_inr, AddMonoidHom.eq_liftOfRightInverse, contMDiff_tangentBundleModelSpaceHomeomorph_symm, Equiv.biInf_comp, toBoolRing_inj, Functor.mapEquiv_apply, stdSimplexEquivIcc_symm_apply_coe, LinearEquiv.pow_apply, Submodule.orthogonalDecomposition_apply, addMonoidAlgebraAddEquivDirectSum_symm_apply, iteratedFDeriv_succ_eq_comp_left, Additive.exists, Metric.Snowflaking.ediam_preimage_toSnowflaking, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, Equiv.image_preimage, Equiv.pprodEquivProdPLift_symm_apply, AddEquiv.coprodCongr_symm_apply, LinearEquiv.symmEquiv_symm_apply_symm_apply, AddEquiv.finsuppUnique_symm_apply_apply, LinearMap.BilinForm.Nondegenerate.toMatrix', CategoryTheory.evalEquiv_symm_apply, IsSublattice.dual, Matrix.of_sub_of, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, AlternatingMap.domLCongr_apply, Equiv.Perm.viaFintypeEmbedding_apply_mem_range, Metric.Snowflaking.preimage_ofSnowflaking_emetricClosedBall, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app, SSet.Subcomplex.PairingCore.equivII_apply_coe, Ideal.map_equiv_liesOver, continuousOn_cfc_nnreal_setProd, Equiv.Perm.congr_fun, TopHom.dual_comp, MonoidHom.liftOfRightInverse_comp, Quiver.SingleObj.pathEquivList_cons, Prod.Lex.prodUnique_apply, UniformFun.toFun_sum, Module.Basis.constr_self, Matrix.charpoly_reindex, Equiv.Perm.subtypeCongr.right_apply, AddEquiv.prodUnique_symm_apply, PresheafOfModules.sheafificationAdjunction_homEquiv_apply, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl, CategoryTheory.Functor.Elements.initialOfRepresentableBy_snd, Homeomorph.symm_trans_apply, DomMulAct.isOpenEmbedding_mk, LinearMap.toMatrix_basis_equiv, MeasurableEquiv.coe_trans, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, AffineIsometryEquiv.antilipschitz, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one, le_map_inv_iff, WithCStarModule.equivL_symm_apply, UniformFun.ofFun_add, Metric.Snowflaking.homeomorph_symm_apply, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, isAddLeftRegular_ofLex, AddSubgroup.equivOp_apply_coe, Homeomorph.compStarAlgEquiv'_symm_apply, ContinuousLinearEquiv.arrowCongrSL_symm_apply, Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inr, Matrix.reindexLinearEquiv_comp_apply, Equiv.sigmaFiberEquiv_symm_apply_fst, CategoryTheory.Functor.CorepresentableBy.ext_iff, FreeAbelianGroup.lift_apply_of, AffineEquiv.range_eq, zpowersEquivZPowers_apply, CategoryTheory.Functor.CorepresentableBy.homEquiv_symm_comp, DomMulAct.isQuotientMap_mk, isClosedMap_toMul, RingEquiv.coe_trans, WithZero.toMulBot_le, CategoryTheory.Abelian.Ext.linearEquivâ_symm_apply, starRingEquiv_apply, FreeAddMagma.lift_of, ContinuousMap.unitsLift_symm_apply_apply_inv', MulEquiv.op_symm_apply_apply, RingInvo.map_eq_zero_iff, RootPairing.reflectionPerm_eq_of_pairing_eq_zero, DualNumber.lift_comp_inlHom, zmultiplesAddHom_apply, CartanMatrix.A_one, StarMulEquiv.ofClass_symm_apply, Cycle.formPerm_eq_self_of_notMem, LinearMap.quotientInfEquivSupQuotient_symm_apply_left, comp_equiv_dotProduct_comp_equiv, DomMulAct.isEmbedding_mk_symm, IsCoatom.dual, AffineEquiv.sbtw_map_iff, MulEquiv.Monoid.End_apply, MonomialOrder.degree_sPolynomial_le, AddEquiv.coprodComm_symm_apply, coe_notMemRangeEquiv_symm, YoungDiagram.equivListRowLens_symm_apply, List.equivSigmaTuple_apply_fst, SubMulAction.ofStabilizer.conjMap_bijective, FreeAbelianGroup.liftAddEquiv_apply_apply, CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left, AddMonoidAlgebra.decomposeAux_eq_decompose, UniformEquiv.piCongr_apply, ContinuousMap.isometryEquivBoundedOfCompact_symm_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left, WithVal.le_def, LinearIsometryEquiv.prodComm_apply, Matrix.SeparatingRight.toBilin', Matrix.kroneckerTMul_assoc, HahnEmbedding.Partial.evalCoeff_eq, Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq, CategoryTheory.Functor.flippingEquiv_apply_map_app, ContinuousMultilinearMap.piâᾢ_apply, NumberField.ComplexEmbedding.isReal_comp_iff, IsCompl.dual, addMonoidAlgebraRingEquivDirectSum_apply, Orientation.areaForm_rightAngleRotation_right, SemidirectProduct.mulEquivProd_symm_apply_right, LinearEquiv.injective, ofDual_bihimp, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, Equiv.Perm.eq_inv_iff_eq, Abelianization.lift_symm_apply, AdicCompletion.ofLinearEquiv_apply, Submonoid.LocalizationMap.symm_comp_ofMulEquivOfLocalizations_apply, Homeomorph.instContinuousMapClass, Setoid.quotientKerEquivOfRightInverse_symm_apply, PiTensorProduct.map_comp_reindex_eq, WeakDual.CharacterSpace.equivAlgHom_symm_coe, DomMulAct.stabilizer_ncard, ContinuousMultilinearMap.ofSubsingletonâᾢ_apply, toLex_div, RingAut.mul_apply, CategoryTheory.Localization.Construction.objEquiv_symm_apply, AffineIsometryEquiv.coe_symm_toIsometryEquiv, Module.Basis.map_addHaar, MulAut.apply_inv_self, Finset.map_ofDual_min, Multiset.consEquiv_symm_none, AffineIsometryEquiv.norm_map, Homeomorph.funSplitAt_apply, ContinuousAlgEquiv.preimage_closure, CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app, CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_str, CategoryTheory.Functor.CoconeTypes.IsColimit.equiv_apply, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, Rep.diagonalHomEquiv_apply, 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, RingEquiv.eq_symm_apply, CategoryTheory.Limits.IsLimit.homEquiv_symm_naturality, Metric.PiNatEmbed.toPiNatHomeo_symm_apply, OrderIso.divLeft_symm_apply, LinearIsometry.toLinearIsometryEquiv_apply, Equiv.self_comp_ofInjective_symm, CategoryTheory.conjugateIsoEquiv_symm_apply_hom, continuousMultilinearCurryFin1_symm_apply, Subgroup.quotientEquivSigmaZMod_symm_apply, MonoidHom.toAdditiveLeft_symm_apply_apply, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_apply, Equiv.addEquiv_symm_apply, MonoidHom.toHomPerm_apply_apply, MvPolynomial.IsSymmetric.antitone_supDegree, Valuation.toValuation_ofValuation, toColex_pow, Finmap.keysLookupEquiv_symm_apply_lookup, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply, Zsqrtd.lift_injective, Cubic.equiv_symm_apply_a, OrderRingIso.toOrderRingHom_eq_coe, Homeomorph.image_frontier, Matrix.piLinearEquiv_symm_apply, isMinFilter_dual_iff, isSublattice_preimage_toDual, PadicInt.mahlerEquiv_symm_apply, OrderDual.isCobounded_preimage_ofDual, LinearMap.extendScalarsOfIsLocalizationEquiv_symm_apply, SupIrred.dual, toDual_eq_one, CategoryTheory.Adjunction.homAddEquiv_apply, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Orientation.inner_smul_rotation_pi_div_two_smul_left, CategoryTheory.Iso.conj_comp, Module.reflection_apply, Interval.dual_map, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, CoalgEquivClass.toCoalgHomClass, ofDual_add, isLeftRegular_ofLex, OrderAddMonoidIso.trans_apply, MulEquiv.map_mul, EquicontinuousOn.isInducing_uniformOnFun_iff_pi, Module.Basis.constr_def, Equiv.Perm.set_support_apply_mem, SkewMonoidAlgebra.domCongr_apply, MvPolynomial.degreeOf_eq_natDegree, Equiv.prodPProd_symm_apply, AddCon.comapQuotientEquivOfSurj_mk, CompHausLike.isoEquivHomeo_apply, Equiv.Perm.viaEmbedding_apply_of_notMem, uniformContinuous_ofAdd, SimpleGraph.hasseDualIso_symm_apply, UniformEquiv.uniformEquiv_mk_coe_symm, isAddLeftRegular_toColex, ContinuousAlgEquiv.coe_apply, ContinuousAddEquiv.bijective, addMonoidEndRingEquivInt_symm_apply, WithLp.addEquiv_symm_apply, Rep.freeLiftLEquiv_symm_apply, Trivialization.sourceHomeomorphBaseSetProd_apply, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, MeasureTheory.Measure.Regular.map_iff, MeasureTheory.ComplexMeasure.equivSignedMeasureâ_apply, BilinForm.toMatrix_compLeft, Equiv.Perm.ofSubtype_support_disjoint, supPrime_ofDual, LinearMap.IsPositive.adjoint_eq, LinearIsometryEquiv.comp_continuous_iff, Trivialization.prod_apply', Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace, Finset.restrict_comp_piCongrLeft, FreeAddGroup.lift_of_apply, Homeomorph.measurable, Equiv.subtypeEquivCodomain_symm_apply_ne, ContinuousLinearMap.prodâ_apply, ContinuousLinearEquiv.comp_fderivWithin, UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv, CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_id, ContinuousLinearMap.coprodEquiv_symm_apply, MonomialOrder.degree_sub_leadingTerm_lt_degree, AdicCompletion.congr_apply, Encodable.encode_ofEquiv, Module.Basis.toDual_apply_left, MeasureTheory.measurePreserving_piEquivPiSubtypeProd, toDual_symmDiff, LinearMap.toPerfPair_apply, dist_ofMul, AddChar.doubleDualEmb_doubleDualEquiv_symm_apply, Equiv.functionSwap_symm_apply, Equiv.Perm.decomposeOption_apply, AffineEquiv.preimage_symm, LinearMap.equivOfIsUnitDet_apply, Finsupp.optionEquiv_apply, StrictConcaveOn.dual, Subgroup.equivSMul_symm_apply_coe, MeasurableEquiv.map_eq, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, toDual_smul, QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, DoubleQuot.coe_quotQuotEquivCommâ, CategoryTheory.Adjunction.homEquiv_naturality_right_square_assoc, MeasureTheory.volume_preserving_finTwoArrow, LinearIsometryEquiv.map_smul, CategoryTheory.Under.postAdjunctionRight_counit_app_right, LinearMap.toMatrixâ'_comp, optionProdEquiv_mk_none, toAddUnits_symm_apply, MvPolynomial.rTensor_apply, LinearEquiv.congrQuadraticMap_apply, TopologicalSpace.Compacts.equiv_apply, isRightRegular_ofAdd, PadicInt.continuousAddCharEquiv_apply, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, RootPairing.IsOrthogonal.coreflection_apply_left, Matrix.toLinearMapâ_apply_basis, monotone_comp_ofDual_iff, Subgroup.comap_normalClosure, ContinuousLinearMap.norm_adjoint_comp_self, Matrix.coe_ofLinearEquiv_symm, CategoryTheory.unitCompPartialBijectiveAux_symm_apply, MeasureTheory.Measure.pi_map_piOptionEquivProd, Orientation.inner_smul_rotation_pi_div_two_smul_right, ContinuousLinearEquiv.coe_coe, RingEquivClass.toRingHomClass, GroupExtension.Section.equivComp_apply, DirectSum.liftRingHom_apply, addMonoidAlgebraRingEquivDirectSum_symm_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, MulEquiv.coprodAssoc_symm_apply_inr_inl, CliffordAlgebra.GradedAlgebra.lift_Κ_eq, WithConv.symm_equiv_apply, UniformOnFun.ofFun_add, MonoidAlgebra.mapDomainAddEquiv_apply, Monoid.Coprod.lift_apply_mk, FreeAddSemigroup.lift_of_add, Matrix.det_apply', RingEquiv.image_symm_eq_preimage, ofDual_sSup, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_app_naturality_left_assoc, Subgroup.IsComplement.rightQuotientEquiv_apply, CategoryTheory.PreGaloisCategory.fiberEqualizerEquiv_symm_Κ_apply, DilationEquiv.coe_pow, Equiv.subtypeSubtypeEquivSubtypeInter_symm_apply_coe_coe, LinearMap.toMatrix_pow, AddCommMonCat.equivalence_inverse_map, CategoryTheory.Localization.SmallShiftedHom.equiv_mkâ, Multiset.coeEquiv_symm_apply_snd_val, Homeomorph.symm_apply_apply, SimpleGraph.Iso.mapEdgeSet_apply, Sum.Lex.inr_top, isAddRegular_toDual, OrderIso.coe_toHomeomorph, AddMonoidAlgebra.lift_def, Subgroup.IsComplement'.QuotientMulEquiv_apply, Perfection.lift_symm_apply, Antivary.sum_smul_le_sum_comp_perm_smul, CategoryTheory.Bicategory.Adjunction.homEquivâ_symm_apply, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, CategoryTheory.Bicategory.toNatTrans_conjugateEquiv, HahnSeries.addOppositeEquiv_apply, ContinuousLinearEquiv.strictConvex_preimage, CategoryTheory.Discrete.equivalence_inverse, Complex.rightAngleRotation, EuclideanGeometry.eq_reflection_of_eq_subspace, CategoryTheory.Limits.IsColimit.Κ_app_homEquiv_symm, equivShrink_smul, Ideal.fst_comp_quotientInfEquivQuotientProd, Equiv.extend_apply, MvPolynomial.leadingCoeff_toLex, IsBaseChange.linearMapLeftRightHom_apply, RingEquiv.coe_monoidHom_trans, Ideal.map_prodComm_prod, CategoryTheory.Equivalence.induced_functor, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, isAddRightRegular_toAdd, SetSemiring.down_up, Equiv.isOpenMap_symm_iff, NonUnitalSubsemiring.centerCongr_apply_coe, LinearMap.coprodEquiv_symm_apply, UniformFun.ofFun_toFun, LinearEquiv.arrowCongrAddEquiv_symm_apply, FreeAddMonoid.hom_map_lift, OneOneEquiv.of_equiv, LinearMap.BilinForm.toMatrix_comp, LinearEquiv.map_mem_invtSubmodule_iff, HahnSeries.leadingCoeff_neg_iff, LinearMap.mul'_comm, Matrix.SpecialLinearGroup.toLin'_symm_apply, ContinuousLinearEquiv.differentiableWithinAt, StarMulEquiv.ofClass_apply, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, Equiv.sigmaFiberEquiv_symm_apply_snd_coe, InverseSystem.invLimEquiv_symm_apply_coe, ComplexShape.Embedding.AreComplementary.equiv_inr, DirectSum.coe_decompose_mul_of_left_mem_zero, AddConstMap.coe_conjNeg_apply, Prod.Lex.toLex_le_toLex, Monoid.CoprodI.Word.equivPair_eq_of_fstIdx_ne, ContinuousAlgEquiv.image_symm_image, Partition.partscopyEquiv_apply_coe, Primrec.of_equiv_iff, addMonoidAlgebraAddEquivDirectSum_apply, CategoryTheory.Limits.Cofork.IsColimit.homIso_symm_apply, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one, ModularGroup.coe_T_zpow, Real.ringEquivCauchy_apply, Matrix.trace_map, Algebra.GrothendieckGroup.lift_apply, Set.graphOn_prod_prodMap, Module.Basis.reindexFinsetRange_repr, IsMin.toDual, Polynomial.opRingEquiv_op_C_mul_X_pow, equivShrink_le_equivShrink, Subring.coe_equivMapOfInjective_apply, Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk, FirstOrder.Language.Term.relabelEquiv_apply, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, TruncatedWittVector.commutes', CategoryTheory.Localization.SmallHom.equiv_shift, WithZero.withZeroUnitsEquiv_apply, CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints_symm_apply_coe, Module.Basis.continuous_coe_repr, TensorProduct.finsuppScalarLeft_apply, MonomialOrder.degree_monomial_le, MonoidHom.coe_toAdditive'', HNNExtension.equiv_symm_eq_conj, Unitization.uniformity_eq_aux, OrderHom.equivFunctor_symm_apply, Homeomorph.isClosedEmbedding, FreeGroup.freeGroupCongr_apply, RingCon.quotientQuotientEquivQuotient_symm_mk, Matrix.uniqueEquiv_apply, Equiv.Perm.sameCycle_extendDomain, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_left_inv_assoc, DirectSum.coe_decompose_mul_of_right_mem_of_le, Submodule.lTensorOne_one_tmul, ContinuousLinearEquiv.preimage_closure, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe, Module.Basis.smulTower_repr, Diffeomorph.contMDiff, HasFTaylorSeriesUpTo.zero_eq', Submonoid.topEquiv_toMonoidHom, Module.Basis.toDual_apply_right, Subgroup.IsComplement.equiv_fst_eq_mul_inv, Action.Iso.conj_Ď, Function.OfArity.curry_two_eq_curry, IsometryEquiv.nndist_eq, ContinuousLinearEquiv.analyticAt, Equiv.Perm.pow_mod_orderOf_cycleOf_apply, FreeGroup.lift_mk, Equiv.sumArrowEquivProdArrow_symm_apply_inl, LinearMap.toMatrix'_one, LieAlgebra.of_symm_add, MeasureTheory.SignedMeasure.toJordanDecompositionEquiv_apply, AffineEquiv.map_vadd', AffineEquiv.pointReflection_midpoint_left, MvPowerSeries.lexOrder_le_of_coeff_ne_zero, Combinatorics.Subspace.reindex_isMono, Equiv.apply_eq_iff_eq, ofDual_vadd', CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right_symm_assoc, CategoryTheory.Pseudofunctor.StrongTrans.Modification.equivOplax_apply, FreeMonoid.ofList_comp_toList, CategoryTheory.opEquiv_symm_apply, Metric.Snowflaking.image_toSnowflaking_image_ofSnowflaking, Equiv.Perm.cycle_zpow_mem_support_iff, CategoryTheory.ObjectProperty.galoisConnection_isLocal, Monoid.CoprodI.lift_word_ping_pong, AlternatingMap.domDomCongrâ_apply, isRegular_ofDual, SubAddAction.ofStabilizer.conjMap_comp_apply, CategoryTheory.ShrinkHoms.functor_map, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Module.surjective_piEquiv_apply_iff, Fin.revPerm_symm_apply, ModelWithCorners.coe_transContinuousLinearEquiv_symm, CategoryTheory.orderDualEquivalence_inverse_obj, LinearMap.transvection.congr, Quaternion.equivTuple_symm_apply, ModularForm.coe_translate, LieEquiv.coe_coe, Unitization.starLift_symm_apply, CategoryTheory.MonoidalClosed.ofEquiv_curry_def, Equiv.forall_congr_right, MonomialOrder.degLex_single_lt_iff, Matrix.diagonal_fin_three, ContinuousMultilinearMap.curryFinFinset_symm_apply, equivTangentBundleProd_symm_apply_proj, measurable_piCurry, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix, MulEquiv.piCongrRight_apply, TensorAlgebra.lift_unique, CategoryTheory.Adjunction.homEquiv_symm_rightAdjointUniq_hom_app, CategoryTheory.Abelian.Ext.homEquivâ_symm_apply, edist_toDual, Homeomorph.image_connectedComponentIn, ofColex_neg, DirectSum.sum_support_decompose, ContinuousLinearEquiv.comp_contDiff_iff, toDual_iInf, Orientation.kahler_rightAngleRotation_right, Finsupp.toLex_monotone, CStarMatrix.of_zero, CategoryTheory.Bicategory.conjugateEquiv_symm_apply', OnePoint.equivProjectivization_apply_coe, ZSpan.repr_floor_apply, Equiv.subRight_symm_apply, AddUnits.coe_opEquiv_symm, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, MeasureTheory.measurePreserving_pi_empty, 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, NumberField.Units.finrank_mul_regulator_eq_det, ofAdd_eq_one, FreeGroupBasis.map_apply, Matrix.rank_submatrix_le, Rep.indResHomEquiv_apply_hom, IsLocalization.ringEquivOfRingEquiv_apply, Quaternion.linearIsometryEquivTuple_apply, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, MulEquiv.subsemigroupMap_apply_coe, RingEquiv.opOp_symm_apply, Function.fromTypes_cons_equiv_apply, ModuleCat.homAddEquiv_apply, Module.Basis.repr_symm_apply, SupHom.dual_symm_apply_toFun, DomMulAct.mk_one, MulEquiv.subsemigroupMap_symm_apply_coe, ClassGroup.mk_canonicalEquiv, LinearAlgebra.FreeProduct.lift_comp_Κ, Equiv.Perm.cycleOf_zpow_apply_self, Module.Dual.congr_apply_apply, Delone.DeloneSet.mapIsometry_apply_coveringRadius, Equiv.swap_apply_right, PiTensorProduct.ofDirectSumEquiv_tprod_apply, CategoryTheory.nerve.functorOfNerveMap_obj, CategoryTheory.Adjunction.homAddEquiv_symm_sub, LinearMap.tensorKerEquiv_apply, Matrix.transpose_empty_rows, CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm, UniformOnFun.isUniformInducing_pi_restrict, basis_toMatrix_mul_linearMap_toMatrix, RingHom.op_apply_apply, ValuationRing.coe_equivInteger_apply, Equiv.smulRight_apply, AddChar.toAddMonoidHomEquiv_apply, ContinuousLinearEquiv.symm_apply_eq, LinearMap.toMatrixâââ'_apply, equiv_lpPiLp_norm, MulEquiv.monoidHomCongrRightEquiv_symm_apply, MulEquiv.subgroupMap_symm_apply, CompHausLike.isoOfHomeo_hom_hom_hom_apply, Quiver.SingleObj.toPrefunctor_symm_comp, Sum.Lex.toLexRelIsoLT_symm_coe, WithZero.lift'_zero, CategoryTheory.Abelian.Ext.addEquivBiprod_apply_snd, Nonneg.val_inv_unitsEquivPos_symm_apply_coe, WithVal.valuation_equiv_symm, Matrix.piEquiv_apply, List.formPerm_cons_concat_apply_last, WithTop.toDual_le_iff, UniformOnFun.uniformContinuous_ofFun_toFun, UniformEquiv.toHomeomorph_symm_apply, Submodule.mem_biSup_iff_exists_dfinsupp, Module.Basis.tensorProduct_repr_tmul_apply, Antivary.sum_comp_perm_mul_eq_sum_mul_iff, ofLex_div, Equiv.mulRight_symm_apply, Equiv.subtypeSubtypeEquivSubtype_symm_apply_coe_coe, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, skewAdjointMatricesLieSubalgebraEquiv_apply, Finsupp.Colex.single_lt_iff, val_rootsOfUnityEquivOfPrimitiveRoots_apply_coe, Unitization.lipschitzWith_addEquiv, Module.Basis.coe_ofEquivFun, Equiv.sigmaProdDistrib_apply, PolynomialLaw.ground_apply, UniformEquiv.piCongrLeft_apply_apply, Matrix.toLinearMapRight'_one, PiLp.continuousLinearEquiv_apply, Monoid.CoprodI.lift_comp_of', Subsemiring.mopRingEquivOp_symm_apply, RingHom.rangeRestrictFieldEquiv_apply_coe, Equiv.sumIsRight_symm_apply_coe, LinearEquiv.ofLinear_symm_apply, Equiv.sigmaSubtype_apply, MonomialOrder.degree_sub_LTerm_lt, ContinuousAlgEquiv.continuousAt, Submodule.span.ringHom_apply, UniformOnFun.edist_le, wbtw_pointReflection, OrderRingIso.refl_apply, UniformEquiv.toHomeomorph_apply, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, CategoryTheory.Limits.Sigma.Κ_reindex_hom_assoc, nnnorm_toAdd, Ergodic.symm_iff, Equiv.sumPiEquivProdPi_apply, Homeomorph.surjective, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, LinearEquiv.alternatingMapCongrRight_symm_apply_apply, WithLp.linearEquiv_symm_apply, FreeMonoid.countP_apply, equivShrink_neg, FirstOrder.Language.LEquiv.onSentence_symm_apply, RingEquiv.bijective, ModuleCat.endRingEquiv_apply, MultilinearMap.curryFinFinset_symm_apply, DirectSum.coe_decompose_mul_of_right_mem_zero, Multiplicative.ext_iff, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, Equiv.image_symm_apply_coe, LinearIsometryEquiv.integrable_comp_iff, CategoryTheory.Iso.eHomCongr_inv_comp, OrderDual.ofDual_lt_ofDual, FreeMonoid.freeMonoidCongr_symm_of, Matrix.invertibleEquivDetInvertible_symm_apply, Sum.Lex.toLex_strictMono, Prod.Lex.prodLexCongr_apply, OrderDual.ofDual_comp_toDual, LinearEquiv.lTensor_refl_apply, CategoryTheory.sheafHomSectionsEquiv_symm_apply_coe_apply, MulEquiv.coe_toMulHom, Basis.piTensorProduct_repr_tprod_apply, finRotate_succ_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp, CategoryTheory.Localization.homEquiv_map, ClassGroup.equivPic_apply, MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq, Equiv.Perm.SameCycle.symm_apply_left, Matrix.comp_map_transpose, WittVector.ghostEquiv_coe, StarMulEquiv.instStarHomClass, RootPairing.indexNeg_neg, Submonoid.val_unitsTypeEquivIsUnitSubmonoid_symm_apply, OrderAddMonoidIso.coe_orderIso, TrivSqZeroExt.liftEquiv_symm_apply_coe, subtypeOrEquiv_apply, Equiv.boolNot_symm_apply, WeierstrassCurve.Projective.Point.toAffineAddEquiv_symm_apply, Complex.isometryOfOrthonormal_symm_apply, Trunc.finChoiceEquiv_symm_apply, Equiv.Perm.monotone_iff, Subsemigroup.equivOp_apply_coe, Module.Basis.sum_equivFun, List.formPerm_apply_mem_eq_next, WithLp.coe_symm_linearEquiv, MonoidHom.toHomUnitsMulEquiv_symm_apply, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, RootPairing.chainBotCoeff_reflectionPerm_left, DirectSum.AddSubmonoidClass.IsHomogeneous.mem_iff, Matrix.submatrixEquivInvertibleEquivInvertible_symm_apply, AddOpposite.opMulEquiv_apply, TensorProduct.finsuppScalarLeft_symm_apply_single, CochainComplex.HomComplex.CohomologyClass.equivOfIsKProjective_apply, Module.Basis.SmithNormalForm.toMatrix_restrict_eq_toMatrix, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def, finSumNatEquiv_symm_apply_of_lt, CStarMatrix.of_add_of, RingInvoClass.involution, FreeMagma.lift_comp_of', GradedAlgebra.mem_support_iff, MonoidHom.fiberEquiv_apply, FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion_apply, Submodule.comapSubtypeEquivOfLe_apply_coe, RatFunc.toFractionRingRingEquiv_apply, Topology.lawsonOpen_iff_scottOpen_of_isUpperSet, MulEquiv.val_piUnits_apply, MulEquiv.coe_monoidHom_comp_coe_monoidHom_symm, monotoneOn_dual_iff, MeasurableEquiv.eq_image_iff_symm_image_eq, FinBddDistLat.dual_map, Module.Basis.repr_smul', Equiv.mulEquiv_symm_apply, LieModuleEquiv.coe_coe, Monoid.Coprod.map_mk_ofList, Finsupp.Lex.lt_iff, lmap_finsuppLEquivDirectSum_eq, Orientation.inner_rightAngleRotation_self, LinearMap.lsum_piSingle, HasFiniteFPowerSeriesOnBall.fderiv_eq, CategoryTheory.conjugateEquiv_comp, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, CategoryTheory.Abelian.Ext.homLinearEquiv_symm_apply, Equiv.Perm.mem_conj_support, LinearIsometryEquiv.continuous, Finsupp.DegLex.monotone_degree, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, Metric.Snowflaking.image_toSnowflaking_ball, RingEquiv.coe_toNonUnitalRingHom, CategoryTheory.map_shrinkYonedaEquiv, AlgEquiv.sumArrowEquivProdArrow_apply, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, PEquiv.mul_toMatrix_toPEquiv, MulEquiv.toSingleObjEquiv_functor_map, SimpleGraph.Iso.connectedComponentEquiv_apply, Equiv.Perm.SameCycle.extendDomain, DilationEquiv.ratio_symm, Equiv.image_apply_coe, IsEvenlyCovered.homeomorph_comp_iff, ContinuousLinearEquiv.comp_contDiffAt_iff, EquivFunctor.mapEquiv_symm_apply, Module.Basis.constr_range, FreeMonoid.count_apply, Quiver.SingleObj.toPrefunctor_symm_apply, Diffeomorph.sumComm_inl, Module.Basis.repr_unitsSMul, Module.compHom.toLinearEquiv_symm_apply, Finpartition.IsEquipartition.exists_partPreservingEquiv, toDual_sup, AlgEquiv.subalgebraMap_symm_apply_coe, InnerProductSpace.laplacian_CLE_comp_left, AddEquiv.coe_toAddHom, Equiv.Perm.perm_inv_mapsTo_iff_mapsTo, OrderMonoidIso.eq_symm_comp, RootPairing.Base.IsPos.reflectionPerm, Subsemiring.topEquiv_apply, RootPairing.reflection_apply, Ideal.inertiaDeg_map_eq, TensorProduct.piRight_apply, addMonoidEndToMultiplicative_apply_apply, WithTop.ofDual_top, Matrix.toLpLin_apply, MulEquiv.ofBijective_apply, Equiv.toOrderIsoSet_apply, TensorProduct.congrIsometry_apply, Equiv.Perm.sameCycle_symm_apply_left, MvPolynomial.isEmptyRingEquiv_eq_coeff_zero, Finsupp.equivFunOnFinite_symm_eq_sum, AlgEquiv.funUnique_symm_apply, List.sym2_eq_sym_two, ZMod.dft_eq_fourier, Submonoid.topOrderMonoidIso_apply, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', nhds_ofAdd, Equiv.conj_apply, CategoryTheory.Adjunction.homEquiv_apply_eq, HasFPowerSeriesAt.hasStrictFDerivAt, CategoryTheory.yonedaEquiv_symm_map, toDual_iSup, Topology.IsEmbedding.toHomeomorphOfSurjective_apply, CategoryTheory.tensorLeftHomEquiv_whiskerRight_comp_evaluation, FreeMonoid.map_symm_apply_map_eq, CategoryTheory.Cat.Hom.equivFunctor_apply, MeasurableEquiv.coe_mulLeft, Equiv.psigmaEquivSigmaPLift_symm_apply, IsometryEquiv.mulRight_apply, ZMod.dft_odd_iff, WithTop.lt_ofDual_iff, IsTop.toDual, Matrix.toLin'_apply, Magma.AssocQuotient.lift_symm_apply, ZMod.ringEquivCongr_val, Equiv.optionSubtypeNe_apply, LaurentSeries.mem_integers_of_powerSeries, toDual_ofNat, MulChar.coe_equivToUnitHom, Homeomorph.range_coe, IsometryEquiv.subLeft_apply, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_apply, Subgroup.normalizerMonoidHom_apply_symm_apply_coe, PEquiv.toMatrix_toPEquiv_apply, Equiv.rightInverse_symm, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, SymAlg.sym_one, Homeomorph.coe_mulLeft, LinearEquiv.arrowCongr_comp, ofColex_toColex, Polynomial.mapEquiv_apply, Homeomorph.symm_map_nhds_eq, PerfectRing.liftAux_apply, CompareReals.compare_uc, Module.Basis.constr_apply, AddEquiv.coprodAssoc_symm_apply_inr_inl, Equiv.coe_trans, FreeAddMonoid.toList_cons, Multiplicative.monoidHom_ext_iff, Rep.coinvariantsAdjunction_homEquiv_apply_hom, LinearEquiv.piCongrLeft'_apply, isRegular_toColex, ContinuousAddEquiv.comp_symm_eq, Equiv.ofUnique_symm_apply, WithCStarModule.equiv_symm_pi_apply, Homeomorph.funUnique_symm_apply, coe_iterateFrobeniusEquiv, ContinuousLinearEquiv.prodCongr_apply, Equiv.prodSumDistrib_symm_apply_left, Equiv.optionSubtype_symm_apply_symm_apply, DFinsupp.lsum_apply_apply, toDual_div, NonemptyInterval.snd_dual, AffineSubspace.equivMapOfInjective_toFun, CategoryTheory.GrothendieckTopology.map_yonedaEquiv, HahnSeries.toPowerSeries_apply, OrderIsoClass.toCompleteLatticeHomClass, CategoryTheory.Bicategory.conjugateEquiv_iso, finSuccAboveOrderIso_symm_apply_ne_last, FreeAbelianGroup.lift_neg, powersEquivPowers_apply, CategoryTheory.Bicategory.conjugateEquiv_comm, NumberField.Units.regulator_eq_det', FreeNonUnitalNonAssocAlgebra.lift_of_apply, galRestrictHom_apply, LinearMap.BilinForm.SeparatingRight.toMatrix', Concept.swapEquiv_symm_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, CategoryTheory.uliftCoyonedaEquiv_symm_map, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero, HasStrictDerivAt.hasStrictFDerivAt_equiv, Specialization.toEquiv_ofEquiv, GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset, Equiv.extendSubtype_apply_of_mem, CategoryTheory.TwoSquare.lanBaseChange_app, IsSymmetricAlgebra.equiv_toAlgHom, Sum.Lex.inr_lt_inr_iff, ModularGroup.coe_S, Derivation.linearEquiv_coe_comp, ofDual_mul, Finsupp.linearCombination_eq_fintype_linearCombination_apply, LinearMap.toMatrix_adjoint, IsometryEquiv.coe_mk, IsometryEquiv.withLpProdCongr_symm_apply, GradedTensorProduct.of_one, Matrix.vecMul_cons, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, DomAddAct.isClosedEmbedding_mk, Metric.Snowflaking.continuous_ofSnowflaking, CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv_apply_coe, Matrix.compLinearEquiv_apply, CategoryTheory.Sheaf.ÎObjEquivSections_naturality, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, CategoryTheory.yonedaEquiv_symm_naturality_left, Ideal.snd_comp_quotientInfEquivQuotientProd, Invertible.mulRight_symm_apply, Affine.Simplex.height_reindex, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, LinearOrderedCommGroupWithZero.inl_apply, Equiv.Perm.cycleOf_apply_self, CategoryTheory.Pseudofunctor.presheafHomObjHomEquiv_symm_apply, Set.Ici_toDual, LinearMap.diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne, LinearEquiv.ofInjective_symm_apply, UniformOnFun.uniformContinuous_eval_of_mem, Set.Icc_toDual, RelIso.coe_fn_toEquiv, SSet.Subcomplex.Pairing.exists_or, Unitization.val_unitsFstOne_mulEquiv_quasiregular_apply, UniformFun.uniformSpace_eq_inf_precomp_of_cover, 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_hâ, sSupHom.dual_id, DirectSum.decompose_symm_of, Finset.orderIsoColex_symm_apply, OrderDual.isCobounded_preimage_toDual, IsometryEquiv.withLpProdComm_apply, AddEquiv.map_sub, OrderIso.sumLexDualAntidistrib_symm_inr, ContinuousMap.isometryEquivBoundedOfCompact_apply, LinearOrderedCommGroupWithZero.inr_apply, LinearMap.separatingLeft_toLinearMapâ'_iff_det_ne_zero, MulEquiv.coe_monoidHom_refl, Finsupp.Lex.single_le_iff, QuaternionAlgebra.equivProd_apply, Submonoid.centerCongr_apply_coe, Preorder.piCongrLeft_comp_restrictLe, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, Matroid.mapEquiv_eq_map, Equiv.Perm.SameCycle.pow_left, CharacterModule.homEquiv_apply_apply, IncidenceAlgebra.mu_toDual, Submodule.mem_map_equiv, lt_finRotate_iff_ne_neg_one, CategoryTheory.Functor.CoconeTypes.isColimit_iff, Equiv.sigmaPUnit_symm_apply_fst, CategoryTheory.Bicategory.conjugateEquiv_whiskerLeft, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, RingEquiv.coe_monoidHom_refl, Equiv.Perm.isInvariant_of_support_le, toBoolRing_top, LinearMap.BilinForm.Nondegenerate.toMatrix, CategoryTheory.Hom.mulEquivCongrRight_apply, CategoryTheory.mateEquiv_counit, Subgroup.centerToMulOpposite_symm_apply_coe, MeasureTheory.lintegral_map_equiv, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, ContinuousLinearMap.isPositive_adjoint_comp_self, GrpCat.SurjectiveOfEpiAuxs.Ď_symm_apply_fromCoset, FreeGroup.lift_eq_prod_map, Equiv.Perm.OnCycleFactors.kerParam_range_eq, Complex.measurableEquivRealProd_symm_apply, UniformOnFun.toFun_smul, RootPairing.pairing_reflectionPerm, CategoryTheory.Pseudofunctor.isPrestackFor_iff_isSheafFor', nhds_toDual, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, CategoryTheory.Functor.flippingEquiv_apply_obj_obj, ContinuousLinearEquiv.image_symm_image, FiberwiseLinear.trans_PartialHomeomorph_apply, AddSubmonoid.closure_eq_mrange, Nat.Partition.coeff_genFun, Diffeomorph.toEquiv_coe_symm, CategoryTheory.yonedaEquiv_symm_naturality_right, Equiv.optionEquivSumPUnit_coe, SheafOfModules.pushforwardSections_unitHomEquiv, Equiv.sigmaPreimageEquiv_apply, TensorProduct.tensorQuotientEquiv_symm_apply_tmul_mk, LinearEquiv.coe_symm_mk', RelIso.preimage_symm_apply, Monoid.CoprodI.lift_comp_of, Matrix.l2_opNorm_def, continuous_toMul, Algebra.kerTensorProductMapIdToAlgHomEquiv_symm_apply, CategoryTheory.mateEquiv_square, UniformOnFun.ofFun_smul, RootPairing.EmbeddedG2.ofPairingInThree_long, exteriorPower.oneEquiv_ΚMulti, GradedTensorProduct.symm_of_of, Matroid.mapSetEquiv_indep_iff, UniformFun.dist_def, FreeAbelianGroup.liftMonoid_symm_coe, RestrictScalars.addEquiv_symm_map_algebraMap_smul, MonoidHom.map_iterate_frobeniusEquiv_symm, LieModuleEquiv.surjective, StrictMonoOn.dual_right, ZMod.ringEquivCongr_intCast, RingEquiv.ofHomInv'_symm_apply, MeasureTheory.measurePreserving_finTwoArrow, AddCircle.equivAddCircle_symm_apply_mk, Homeomorph.piSplitAt_apply, Matrix.toEuclideanLin_toLp, Ctop.ofEquiv_val, AddAut.smul_def, AffineSubspace.wOppSide_pointReflection, Localization.mulEquivOfQuotient_symm_mk', Equiv.subtypePreimage_symm_apply_coe_neg, CategoryTheory.Localization.SmallShiftedHom.equiv_apply, toColex_eq_one, DomMulAct.symm_mk_zpow, Monoid.CoprodI.lift_range_le, PartialFun.Iso.mk_hom, AddEquivClass.map_add, Module.Basis.repr_eq_iff', CategoryTheory.PreZeroHypercover.isoMk_inv_sâ, OrderIso.sumLexDualAntidistrib_inr, Matrix.mulVec_cons, stdSimplexEquivIcc_one, AddSubsemigroup.centerToAddOpposite_apply_coe, LinearMap.toLinearMap_toPerfPair, Equiv.Set.union_apply_right, Matrix.comp_symm_single, Matrix.head_transpose, RootPairing.coroot_reflectionPerm, ContinuousAlgEquiv.coe_mk, SetSemiring.mul_def, RingCon.quotientKerEquivOfSurjective_mk, Equiv.Perm.coe_pow, Ctop.Realizer.ofEquiv_F, AlgebraicGeometry.Scheme.coe_homeoOfIso, CategoryTheory.Abelian.Ext.biprodAddEquiv_symm_apply, Finsupp.snd_sumFinsuppEquivProdFinsupp, WithCStarModule.equivL_apply, CategoryTheory.Functor.partialLeftAdjointHomEquiv_comp_symm, Set.image_equiv_eq_preimage_symm, RootPairing.isFixedPt_reflectionPerm_iff, Equiv.prodShear_symm_apply, AddEquiv.op_symm_apply_apply, Equiv.apply_ofInjective_symm, IsometryEquiv.continuous, TensorProduct.gradedComm_of_tmul_of, UniformEquiv.surjective, PowerBasis.constr_pow_aeval, RingEquiv.refl_apply, AlgEquiv.toLieEquiv_apply, FinEnum.equiv_down, Submodule.map_equivMapOfInjective_symm_apply, OrthonormalBasis.measurePreserving_measurableEquiv, RingEquiv.nonUnitalSubsemiringMap_apply_coe, SSet.stdSimplex.objEquiv_symm_apply, AddAut.neg_conj_apply, Module.End.ringEquivEndFinsupp_symm_apply_apply, CompleteLatticeHom.symm_dual_comp, RingEquiv.piOptionEquivProd_symm_apply, Finsupp.supportedEquivFinsupp_symm_apply_coe_apply, measurable_equivCurry, UniformFun.toFun_mul, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, OrderAddMonoidHom.inrâ_apply, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, MonoidHom.coe_toMultiplicative, NonemptyInterval.toDualProd_apply, isRegular_ofLex, Submonoid.powLogEquiv_symm_apply, InverseSystem.piLTLim_apply, CategoryTheory.PreZeroHypercover.presieveâ_restrictIndex_equiv, Ordinal.toLeftMovesToPGame_symm_lt, continuousMultilinearCurryRightEquiv_apply, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, Equiv.symm_image_image, starAddEquiv_apply, LinearMap.det_toMatrix, exteriorPower.toTensorPower_apply_ΚMulti, CategoryTheory.Functor.sheafAdjunctionCocontinuous_homEquiv_apply_val, Algebra.traceForm_toMatrix_powerBasis, Matrix.minpoly_toLin, toDual_ratCast, MvPolynomial.rename_hsymm, basis_toMatrix_mul, LocallyFiniteOrder.orderAddMonoidEquiv_apply, SimpleGraph.walkLengthTwoEquivCommonNeighbors_apply_coe, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_one_assoc, CategoryTheory.Limits.biproduct.whiskerEquiv_hom_eq_lift, AddEquiv.map_neg, UniformFun.postcomp_isUniformEmbedding, Metric.Snowflaking.image_ofSnowflaking_image_toSnowflaking, UniformOnFun.toFun_prod, Equiv.Perm.IsCycleOn.extendDomain, BitVec.equivFin_apply, AffineEquiv.coeFn_injective, SkewMonoidAlgebra.lift_def, Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod, CategoryTheory.GrothendieckTopology.yonedaULiftEquiv_yonedaULift_map, SymAlg.unsym_sym, SemimoduleCat.homLinearEquiv_symm_apply, CategoryTheory.Functor.CoconeTypes.IsColimit.equiv_symm_Κ_apply, Ideal.Factors.piQuotientEquiv_mk, ContinuousLinearEquiv.iteratedFDerivWithin_comp_left, CategoryTheory.Limits.PullbackCone.IsLimit.equivPullbackObj_symm_apply_snd, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, Matrix.toLin'_toMatrix', ContinuousAlternatingMap.prodLIE_symm_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, Metric.Snowflaking.image_ofSnowflaking_emetricBall, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, AddCircle.homeomorphCircle'_apply, LinearMap.det_toLin, RootPairing.coroot'_reflectionPerm, Equiv.ringEquiv_symm_apply, Homeomorph.sigmaProdDistrib_apply, finFunctionFinEquiv_apply, DirectSum.decompose_neg, equivShrink_symm_mul, RingEquiv.piFinTwo_apply, HasFPowerSeriesWithinAt.hasFDerivWithinAt, Equiv.subtypeSubtypeEquivSubtypeExists_symm_apply_coe_coe, MeasurableEquiv.setOf_apply, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, UniformConvergenceCLM.isUniformEmbedding_coeFn, CategoryTheory.uliftYonedaEquiv_symm_map_assoc, Finset.prod_map_equiv, Topology.WithLowerSet.ofLowerSet_toLowerSet, Module.Basis.det_map, SetTheory.PGame.moveLeft_nim, AddMonoidHom.coe_toMultiplicative'', LieModule.shiftedGenWeightSpace.shift_symm_apply, LinearMap.posSemidef_toMatrix_iff, finFunctionFinEquiv_single, Representation.linHom.invariantsEquivRepHom_apply_hom, DomMulAct.mk_smul_monoidHom_apply, Matrix.coe_ofLinearEquiv, ContinuousMulEquiv.bijective, ContinuousAlgEquiv.symm_preimage_preimage, ofDegLex_add, Dense.orderDual, ofLex_eq_zero, DFinsupp.liftAddHom_symm_apply, CategoryTheory.Functor.curryingEquiv_symm_apply_obj_map, AddEquiv.addMonoidHomCongrRight_apply, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_pointReflection_center_left, CategoryTheory.Comonad.ComonadicityInternal.comparisonAdjunction_counit_f_aux, HomotopicalAlgebra.leftHomotopyClassEquivRightHomotopyClass_mk, Set.Finite.subtypeEquivToFinset_symm_apply_coe, Equiv.uniqueProd_apply, OrderDual.ofDual_inj, AlgEquiv.prodCongr_symm_apply, Orientation.rotation_symm_apply, ZMod.LFunction_dft, Algebra.GrothendieckAddGroup.lift_symm_apply, FinBoolAlg.dual_map, DomAddAct.isEmbedding_mk_symm, UniformFun.lipschitzOnWith_iff, Module.Basis.norm_repr_le_norm, LinearIsometryEquiv.withLpUniqueProd_apply, MeasureTheory.volume_measurePreserving_sumPiEquivProdPi, LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero', equivEquivIso_inv, Equiv.Set.union_symm_apply_right, Setoid.quotientEquivClasses_mk_eq, Equiv.swap_apply_left, Equiv.Perm.SameCycle.exists_pow_eq'', IsometryEquiv.preimage_symm, AddCircle.homeomorphCircle_apply, MvPolynomial.scalarRTensor_apply_tmul_apply, Matrix.posSemidef_submatrix_equiv, Homeomorph.coe_sumComm, Homeomorph.coe_toEquiv, PerfectionMap.lift_apply, grade_toDual, MulEquiv.injective, Module.Basis.mem_span_repr_support, Derivation.compAEval_apply, OrderIso.asBoolAlgAsBoolRing_symm_apply, MeasurableEquiv.map_ae, Pi.basisFun_repr, NonUnitalSubring.centerToMulOpposite_apply_coe, LinearIsometryEquiv.coe_mul, Subgroup.IsComplement.equiv_snd_eq_inv_mul, ConjAct.toConjAct_ofConjAct, toAddUnits_val_apply, Set.matrix_eq_pi, toBoolAlg_one, Prod.Lex.lt_iff, AddUnits.addLeft_apply, continuousOn_cfcâ_nnreal_setProd, strictMonoOn_comp_ofDual_iff, SheafOfModules.generatorsOfIsCokernelFree_s, AffineEquiv.bijective, ContinuousLinearEquiv.continuousOn, Algebra.leftMulMatrix_eq_repr_mul, AddChar.zmodAddEquiv_apply, rootsOfUnityEquivNthRoots_symm_apply, StrictMonoOn.dual, Finset.product_self_eq_disjiUnion_perm, Equiv.Set.univPi_apply_coe, Fin.appendEquiv_apply, SSet.Truncated.HomotopyCategory.descOfTruncation_obj_mk, TensorProduct.directLimitRight_symm_of_tmul, FGModuleCat.Iso.conj_hom_eq_conj, Finsupp.finsuppProdLEquiv_symm_apply_apply, HasGradientWithinAt.hasFDerivWithinAt, Module.Basis.toDual_eq_equivFun, FormalMultilinearSeries.rightInv_coeff_one, LinearMap.SeparatingLeft.toMatrixâ', Monoid.CoprodI.lift_injective_of_ping_pong, AlgHom.op_symm_apply_apply, MonoidHom.apply_ofInjective_symm, Hamming.toHamming_neg, Equiv.Perm.IsCycleOn.conj, TensorProduct.toMatrix_comm, Fin.cycleIcc_of_le_of_le, Module.Basis.sum_repr, Orientation.volumeForm_comp_linearIsometryEquiv, EReal.expHomeomorph_apply, powersMulHom_symm_apply, ContinuousAddEquiv.refl_apply, SymAlg.unsym_neg, Pi.orthonormalBasis_repr, MulOpposite.opMulEquiv_symm_apply, Subsemigroup.coe_equivMapOfInjective_apply, ContinuousAlgEquiv.isUniformEmbedding, RootPairing.coreflection_apply_coroot, DomMulAct.stabilizer_card, ZMod.dft_const_smul, Monoid.PushoutI.NormalWord.summand_smul_def, Equiv.sigmaCongrRight_apply, toBoolAlg_ofBoolAlg, Finsupp.supportedEquivFinsupp_apply_apply, MeasureTheory.volume_preserving_piEquivPiSubtypeProd, SkewMonoidAlgebra.equivMapDomain_eq_mapDomain, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, AddMonoidAlgebra.of'_eq_of, SemidirectProduct.equivProd_symm_apply_left, AddCon.congr_mk, dualTensorHomEquivOfBasis_apply, NormedSpace.Dual.coe_toWeakDual, ofAdd_toDual_eq_zero_iff, LinearMap.toMatrixâ'_apply, FreeMonoid.ofList_map, coe_coe, OrderDual.ofDual_eq_top, Subring.ringEquivOpMop_apply, ContinuousAddEquiv.equivLike_neg_eq_symm, Submodule.FG.rTensor.directLimit_apply', isCoatom_dual_iff_isAtom, Finsupp.DegLex.lt_def, Set.MapsTo.exists_equiv_extend_of_card_eq, QuotientGroup.quotientBot_symm_apply, Equiv.Perm.val_inv_equivUnitsEnd_apply, AddEquiv.piCongrRight_apply, UniformEquiv.piFinTwo_symm_apply, Submonoid.LocalizationMap.symm_comp_ofMulEquivOfLocalizations_apply', Homeomorph.symm_comp_self, Additive.addMonoidHom_ext_iff, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin_eq_sum, LinearMap.isAdjointPair_inner, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app, LinearMap.IsPositive.adjoint_conj, HahnSeries.toPowerSeries_symm_apply_coeff, Function.update_apply_equiv_apply, Module.Basis.toMatrix_mulVec_repr, TensorProduct.assoc_symm_tmul, ContinuousLinearEquiv.prodAssoc_symm_apply, Matrix.transpose_reindex, AddCircle.liftIco_eq_lift_Icc, Homeomorph.isSigmaCompact_preimage, Prod.Lex.prodLexAssoc_apply, AddEquiv.coe_toAddMonoidHom, Monoid.foldrM.ofFreeMonoid_apply, Complex.isUniformEmbedding_equivRealProd, AdicCompletion.sumEquivOfFintype_symm_apply, ContinuousMulEquiv.apply_eq_iff_symm_apply, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Homeomorph.isOpenQuotientMap, Unitization.lift_apply, IsQuotientCoveringMap.homeomorph_comp, ConjAct.toConjAct_one, bijective_comp, CategoryTheory.Limits.biproduct.reindex_hom, RingEquiv.coe_toRingHom, Orientation.rotation_oangle_eq_iff_norm_eq, SSet.stdSimplex.nonDegenerateEquiv_symm_apply_coe, Matrix.kroneckerStarAlgEquiv_apply, toDual_natCast, Matrix.separatingLeft_toLinearMapâ'_iff_separatingLeft_toLinearMapâ, AddCon.quotientKerEquivOfRightInverse_symm_apply, CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, Equiv.piEquivPiSubtypeProd_apply, CircleDeg1Lift.translate_pow, CategoryTheory.Iso.conjAut_pow, Homeomorph.piFinTwo_symm_apply, StarRingEquivClass.instStarHomClass, TensorProduct.comm_symm_tmul, LinearMap.BilinForm.separatingLeft_toMatrix_iff, CategoryTheory.Arrow.equivSigma_apply_snd_fst, ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap, MeasurableEquiv.toLp_apply, strictMono_toDual_comp_iff, TensorProduct.sum_tmul_basis_left_injective, ContinuousLinearEquiv.fst_equivOfRightInverse, CovBy.ofDual, AlgebraicGeometry.Proj.stalkIso'_symm_mk, IsometryEquiv.sumArrowIsometryEquivProdArrow_apply, ofDual_vadd, LinearMap.quotientInfEquivSupQuotient_symm_apply_right, Opposite.equivToOpposite_symm_coe, toDual_add, exteriorPower.zeroEquiv_symm_apply, Equiv.optionEquivSumPUnit_some, Matrix.coe_ofAddEquiv, ZMod.dft_smul_const, RingEquiv.piUnique_apply, finsetBasisOfLinearIndependentOfCardEqFinrank_repr_apply, Module.AEval.mem_mapSubmodule_apply, NumberField.mixedEmbedding.norm_negAt, FreeGroup.range_lift_le, LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, EisensteinSeries.gammaSetDivGcdEquiv_eq, FreeSemigroup.lift_of_mul, LieEquiv.refl_apply, RingEquiv.fst_comp_coe_prodComm, CategoryTheory.Limits.FormalCoproduct.cofanHomEquiv_apply_Ď, PiTensorProduct.lift.unique, WithVal.equivWithVal_symm_apply, derangements.Equiv.RemoveNone.fiber_some, LT.lt.ofDual, LieAlgebra.of_symm_smul, Equiv.multipliable_iff, CochainComplex.HomComplex.CohomologyClass.toHom_mk, Module.Basis.orientation_map, TensorProduct.equivFinsuppOfBasisRight_symm_apply, FreeMonoid.toList_one, algebraMap_galRestrictHom_apply, Finset.Colex.toColex_le_toColex_of_subset, Subsemigroup.toAddSubsemigroup'_closure, Real.volume_preserving_transvectionStruct, Finset.ofDual_max', Homeomorph.symm_comp_toContinuousMap, ContinuousLinearMap.fpowerSeries_apply_one, CategoryTheory.Adjunction.homEquiv_naturality_right, StarRingEquiv.coe_mk, HahnEmbedding.Partial.apply_of_mem_stratum, AddAction.stabilizerEquivStabilizer_compTriple, AlgebraicGeometry.Scheme.Hom.fiberΚ_fiberHomeo_symm, ContinuousAlternatingMap.piLinearEquiv_apply, OrderIso.dual_symm_apply, CategoryTheory.Functor.IsRepresentedBy.iff_exists_representableBy, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, SubMulAction.ofStabilizer.conjMap_apply, GenLoop.homotopyFrom_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Matrix.toLpLinAlgEquiv_symm_apply, AddEquiv.uniqueProd_apply, AddValuation.ofValuation_apply, Matrix.toBilin'_toMatrix', MvPolynomial.mapEquivMonic_symm_map_algebraMap, Module.Basis.algebraMapCoeffs_repr, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int, CategoryTheory.CosimplicialObject.cechConerveEquiv_apply, Matrix.reindex_updateCol, CategoryTheory.CategoryOfElements.costructuredArrowULiftYonedaEquivalence_inverse_map, MonoidAlgebra.opRingEquiv_apply, IsometryEquiv.preimage_closedBall, CategoryTheory.Bicategory.conjugateEquiv_symm_apply, HNNExtension.NormalWord.unitsSMulEquiv_apply, Multiset.coe_consEquiv_of_ne, Module.Invertible.linearEquivOfLeftInverse_apply, CoalgEquiv.trans_toCoalgHom, CategoryTheory.Meq.equiv_apply, Submodule.sndEquiv_apply, LinearEquiv.multilinearMapCongrLeft_apply, DirectSum.decompose_symm_sum, LieEquiv.ofBijective_invFun, RootPairing.Hom.id_indexEquiv_apply, List.Nodup.getEquiv_symm_apply_val, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, Equiv.sumCompl_symm_apply_of_neg, Submodule.sndEquiv_symm_apply_coe, RingEquiv.opOp_apply, NumberField.Units.regOfFamily_eq_det', Matrix.toLinearMapâââ_toMatrixâ, AddSubgroup.toSubgroup_comap, Submodule.comapSubtypeEquivOfLe_symm_apply, CochainComplex.toSingleâEquiv_symm_apply_f_zero, ofDual_covBy_ofDual_iff, OrderIso.coe_toEquiv, RingEquiv.ofBijective_symm_comp, Equiv.coe_subtypeEquivCodomain, finSumEquivOfFinset_inl, Module.Basis.coord_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, MeasureTheory.volume_measurePreserving_sumPiEquivProdPi_symm, Matrix.eval_matrixOfPolynomials_eq_vandermonde_mul_matrixOfPolynomials, Finset.prod_comp_equiv, Multiset.toFinsupp_support, ContinuousMultilinearMap.curryFinFinset_apply, Fin.equivSubtype_apply, MulOpposite.opAddEquiv_symm_apply, bddAbove_preimage_toDual, AddSubgroup.coe_toSubgroup_symm_apply, ofDual_div, Matrix.blockTriangular_single', BddLat.dual_map, LinearMap.toMatrix'_mulVec, OrderIso.sumLexDualAntidistrib_inl, DomAddAct.isClosedEmbedding_mk_symm, Filter.map_equiv_symm, Units.mulRight_apply, NumberField.RingOfIntegers.mapRingEquiv_symm_apply, SkewMonoidAlgebra.equivMapDomain_single, Equiv.Set.sumCompl_symm_apply_compl, ModuleCat.semilinearMapAddEquiv_apply, MonovaryOn.dual, Order.coheight_ofDual, LinearMap.lsum_symm_apply, Module.Basis.mem_span_iff_repr_mem, QuaternionAlgebra.coe_addEquivTuple, Module.Basis.SmithNormalForm.repr_eq_zero_of_notMem_range, Equiv.subtypePreimage_symm_apply_coe, Equiv.image_eq_iff_bijOn, IsBaseChange.toDualBaseChange_tmul, Equiv.Perm.zpow_apply_comm, Matrix.SeparatingLeft.toLinearMapâ, AlgebraicGeometry.coe_opensRestrict_apply_coe, Equiv.prodCongrRight_apply, KaehlerDifferential.quotKerTotalEquiv_apply, SetSemiring.down_zero, FreeSemigroup.lift_comp_of, List.Nodup.getEquivOfForallMemList_apply, AddEquiv.apply_eq_iff_symm_apply, Subgroup.topEquiv_apply, ULift.moduleEquiv_apply, Homeomorph.subRight_apply, AffineEquiv.affineIndependent_iff, MulArchimedeanOrder.le_def, Diffeomorph.image_symm_image, Equiv.pprodCongr_apply, DirectSum.decompose_add, StarMulEquiv.coe_refl, Equiv.image_symm_eq_preimage, Equiv.Perm.IsCycleOn.pow_apply_eq, UniformEquiv.piCongrLeft_apply, Bundle.Trivial.homeomorphProd_apply, Antivary.sum_mul_lt_sum_mul_comp_perm_iff, IsDedekindDomain.quotientEquivPiFactors_mk, ModuleCat.freeHomEquiv_symm_apply, ValuationSubring.primeSpectrumEquiv_apply, WithZero.val_logOrderIso_symm_apply, equivShrink_symm_inv, CategoryTheory.CommSq.LiftStruct.opEquiv_apply, IsMinOn.dual, Preorder.piCongrLeft_comp_frestrictLe, SeparationQuotient.liftNormedAddGroupHomEquiv_symm_apply_coe, hasEigenvector_toLin_diagonal, LinearMap.separatingRight_toLinearMapâ'_iff_det_ne_zero, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop, FreeMonoid.toList_comp_ofList, Finsupp.sumFinsuppEquivProdFinsupp_apply, MulEquiv.symm_apply_apply, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, SymAlg.sym_mul_sym, Finsupp.Colex.lt_iff_of_unique, AffineIsometryEquiv.isometry, AffineEquiv.trans_apply, Module.Basis.coord_equivFun_symm, ContinuousLinearEquiv.symm_map_nhds_eq, UniformOnFun.ofFun_neg, RootPairing.reflection_reflectionPerm, AlgEquiv.piCongrLeft'_symm_apply, multiplesHom_apply, Equiv.swap_bijOn_self, Function.RightInverse.homeomorph_apply, ChainComplex.fromSingleâEquiv_symm_apply_f_succ, PartENat.withTopEquiv_symm_lt, Equiv.extendSubtype_apply_of_not_mem, ContinuousMap.addUnitsLift_symm_apply_apply_neg', ZMod.dft_def, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, ContinuousAlgEquiv.coe_refl', AlternatingMap.domDomCongr_apply, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, Equiv.sumEmpty_apply_inl, CategoryTheory.Iso.conj_apply, Equiv.sigmaEquivProd_apply, finAddFlip_apply_natAdd, Equiv.curry_symm_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, MeasureTheory.Measure.infinitePi_map_piCurry_symm, AddEquiv.isAddUnit_map, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_right, MulChar.apply_mem_rootsOfUnity, dotProduct_toMatrixâ_mulVec, GenLoop.fromLoop_coe, IsometryEquiv.preimage_ball, OrderIso.coe_toHomeomorph_symm, toLex_smul, CategoryTheory.Presieve.compatibleEquivGenerateSieveCompatible_symm_apply_coe, Metric.Snowflaking.preimage_ofSnowflaking_closedEBall, CategoryTheory.ExponentiableMorphism.homEquiv_apply_eq, MonoidHom.toAdditiveRight_apply_apply, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, piFinTwoEquiv_symm_apply, CategoryTheory.Abelian.Ext.addEquivBiprod_apply_fst, DirectSum.decompose_sum, LieAlgebra.Extension.lie_toKer_apply, AddConstEquiv.coe_val_equivUnits_apply, WithZero.toMulBot_symm_bot, MonoidAlgebra.commRingEquiv_single_single, Finset.ofDual_sup, HVertexOperator.comp_apply, TensorProduct.gradedComm_gradedMul, cmpLE_toDual, Equiv.sigmaSubtype_symm_apply_coe_fst, CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi, CategoryTheory.Localization.homEquiv_isoOfHom_inv, CategoryTheory.Localization.homEquiv_id, toLex_one, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_two_assoc, PartENat.withTopEquiv_symm_top, finAddFlip_apply_castAdd, Matrix.diagonal_comp_single, FreeAddMonoid.ofList_singleton, HahnSeries.leadingCoeff_nonpos_iff, LinearIsometryEquiv.differentiableOn, AddSubmonoid.mem_map_equiv, ModuleCat.homEquiv_extendScalarsId, rootsOfUnityEquivOfPrimitiveRoots_symm_apply, UniformOnFun.lipschitzWith_restrict, ofAdd_neg, Units.mapContinuousMulEquiv_apply, Equiv.symm_image_subset, Orientation.map_positiveOrientation_of_isEmpty, Algebra.Generators.H1Cotangent.equiv_apply, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, AffineIsometryEquiv.dist_pointReflection_self', LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, toBoolRing_symmDiff, PrimitiveSpectrum.gc, ContinuousAffineEquiv.prodAssoc_symm_apply, InnerProductSpace.laplacianWithin_CLE_comp_left, Equiv.optionSubtypeNe_symm_self, Real.ringEquivCauchy_symm_apply_cauchy, Homeomorph.isLittleO_congr, LinearMap.toMatrixAlgEquiv_transpose_apply, coe_toLexAddEquiv, Quotient.finChoiceEquiv_symm_apply, LinearEquiv.rTensor_tmul, Orthonormal.equiv_apply, CategoryTheory.GrothendieckTopology.map_yonedaULiftEquiv, Finmap.keysLookupEquiv_apply_coe_fst, Submodule.Quotient.restrictScalarsEquiv_mk, ContinuousLinearEquiv.equivOfRightInverse_symm_apply, CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv_apply, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, toDual_covBy_toDual_iff, Module.Basis.repr_self, CategoryTheory.Bicategory.conjugateIsoEquiv_symm_apply_inv, AddEquiv.ofBijective_apply_symm_apply, IsMax.ofDual, CategoryTheory.Subfunctor.Subpresheaf.ofSection_eq_range, AdicCompletion.piEquivFin_apply, Orientation.rightAngleRotation_neg_orientation, Combinatorics.Subspace.reindex_apply, Finsupp.restrictSupportEquiv_symm_apply_coe, Orientation.rotationAux_apply, Metric.Snowflaking.preimage_toSnowflaking_emetricBall, Fin.consEquivL_symm_apply, ClassGroup.mk_def, ofMul_eq_zero, MonoidAlgebra.domCongr_apply, apply_inv_apply, CategoryTheory.Limits.Trident.IsLimit.homIso_natural, equivShrink_symm_one, CategoryTheory.Pi.equivalenceOfEquiv_functor, Equiv.sigmaPUnit_apply, Equiv.Perm.apply_zpow_apply_eq_iff, StarMulEquiv.coe_toMulEquiv, AlgebraicGeometry.coprodMk_inr, NormedSpace.Dual.toWeakDual_inj, IsLocalizedModule.lift_iso, MulEquiv.monoidHomCongrLeftEquiv_symm_apply, TensorProduct.finsuppRight_apply_tmul_apply, Shrink.linearEquiv_apply, TensorProduct.directSumRight_symm_lof_tmul, Equiv.piUnique_symm_apply, CategoryTheory.CatEnrichedOrdinary.homEquiv_id, LinearIsometryEquiv.withLpUniqueProd_symm_apply, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app, AddAutAdditive_symm_apply_apply, CategoryTheory.Presheaf.freeYonedaHomEquiv_symm_comp_assoc, Metric.Snowflaking.dist_toSnowflaking_toSnowflaking, AffineEquiv.wbtw_map_iff, Subgroup.IsComplement.equiv_fst_eq_self_iff_mem, GroupExtension.Equiv.trans_apply, Ideal.associatesEquivIsPrincipal_map_one, ofDual_zero, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, finEquivPowers_symm_apply, CategoryTheory.Limits.Types.colimitEquivColimitType_symm_apply, IsSimpleOrder.equivBool_apply, SupPrime.ofDual, List.SortedGE.of_map_toDual, Polynomial.taylorLinearEquiv_apply_coe, AddEquiv.val_piAddUnits_apply, LieEquiv.coe_toLieHom, Equiv.piUnique_apply, Multiset.toFinsupp_strictMono, AddEquiv.toFun_eq_coe, ContinuousLinearEquiv.mdifferentiableAt, List.Nodup.getEquivOfForallMemList_symm_apply_val, IsometryEquiv.coe_toDilationEquiv, LinearMap.traceAux_def, SubMulAction.ofFixingSubgroup_insert_map_bijective, Function.Injective.swap_comp, OrderIso.sumLexIioIci_apply_inr, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, CategoryTheory.GradedObject.comapEquiv_functor, nndist_toAdd, Traversable.toList_spec, Hamming.toHamming_ofHamming, OrderIsoClass.toInfTopHomClass, MultilinearMap.fromDFinsuppEquiv_symm_apply, SetSemiring.up_down, PresentedGroup.equivPresentedGroup_apply_of, FirstOrder.Language.Equiv.coe_toEmbedding, MonomialOrder.degree_sPolynomial_lt_sup_degree, modularCyclotomicCharacter.aux_spec, toDual_inf, DirectSum.decompose_smul, ContinuousLinearEquiv.piCongrRight_symm_apply, Algebra.leftMulMatrix_apply, Homeomorph.isOpen_preimage, PiTensorProduct.congr_tprod, Equiv.algEquiv_symm_apply, OrthonormalBasis.repr_reindex, Topology.WithLower.ofLower_lt_ofLower, ContinuousMap.isUniformEmbedding_equivBoundedOfCompact, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, AddAut.congr_apply, Equiv.Perm.OnCycleFactors.kerParam_apply, NormedAddGroupHom.Equalizer.liftEquiv_symm_apply_coe, TopologicalSpace.IrreducibleCloseds.equivSubtype'_symm_apply, AdicCompletion.ofLinearEquiv_symm_of, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.volume_preserving_funUnique, LinearMap.BilinForm.toMatrix'_compRight, TensorProduct.finsuppRight_apply_tmul, MonoidHom.liftOfRightInverse_comp_apply, LinearEquiv.ofTop_apply, LinearIsometryEquiv.differentiableWithinAt, UniformEquiv.piFinTwo_apply, AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf_app_toGlued, CategoryTheory.Limits.IsTerminal.from_eq_liftConeMorphism, AddEquiv.ofLeftInverse_symm_apply, coe_symm_comp_self, Module.subsingletonEquiv_apply, Trivialization.preimageSingletonHomeomorph_apply, Homeomorph.bijective, DFinsupp.equivFunOnFintype_symm_single, ofAdd_image_multiples_eq_powers_ofAdd, ContinuousLinearEquiv.continuousWithinAt, EuclideanSpace.coe_measurableEquiv_symm, AddAction.toPerm_apply, Equiv.prod_assoc_symm_preimage, OrderIso.sumLexIioIci_symm_apply_of_lt, CategoryTheory.Abelian.Ext.mkâ_homEquivâ_apply, FirstOrder.Language.PartialEquiv.ext_iff, ofDual_eq_zero, Additive.toMul_eq_top, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, WeierstrassCurve.Affine.Point.toClass_apply, CategoryTheory.Adjunction.homEquiv_id, Circle.argEquiv_apply_coe, AffineIsometryEquiv.coe_symm_toHomeomorph, OrderMonoidIso.eq_comp_symm, strictAntiOn_dual_iff, ContinuousLinearMap.adjoint_innerSL_apply, CommGrpCat.toAddCommGrp_map, Module.Basis.reindex_apply, Congruent.index_equiv, WType.NatÎąEquivPUnitSumPUnit_symm_apply, Polynomial.degreeLT.basis_repr, ConjAct.ofConjAct_one, EuclideanGeometry.reflection_mem_of_le_of_mem, FreeAddSemigroup.lift_comp_of', GroupExtension.Equiv.trans_symm_apply, Finset.Nat.antidiagonalEquivFin_apply_val, Subgroup.map_equiv_eq_comap_symm, CategoryTheory.Adjunction.homEquiv_naturality_left, WCovBy.fst_ofLex, CategoryTheory.Functor.IsRepresentedBy.representableBy_homEquiv_apply, OrderRingIso.symm_apply_lt, monovaryOn_toDual_left, Fin.cons_comp_cycleRange, toBoolRing_bot, CategoryTheory.orderDualEquivalence_inverse_map, UniformEquiv.preimage_image, ContinuousLinearMap.coprodEquivL_symm_apply, Function.FromTypes.curryEquiv_apply, Equiv.coe_uniqueProd, Matrix.SeparatingRight.toBilin, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Module.reflection_mul_reflection_mul_reflection_pow_apply_self, Subgroup.IsArithmetic.conj, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, Module.Basis.repr_reindex_apply, Equiv.Perm.disjoint_iff_eq_or_eq, Homeomorph.transOpenPartialHomeomorph_apply, EuclideanGeometry.reflection_apply, Finset.sum_comp_equiv, LinearIsometryEquiv.comp_fderiv', MulEquiv.subgroupCongr_symm_apply, Tuple.proj_equivâ', Additive.foMul_strictMono, Equiv.setCongr_symm_apply, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, Matrix.adjugate_fin_two_of, Matrix.kroneckerMap_diagonal_left, ofColex_zero, Module.reflection_mul_reflection_mul_reflection_zpow_apply_self, cmp_ofDual, CategoryTheory.Limits.Cotrident.IsColimit.homIso_apply_coe, CategoryTheory.CatEnrichedOrdinary.Hom.base_eqToHom, AddCommGrpCat.homAddEquiv_apply, Submonoid.topEquiv_apply, CategoryTheory.ActionCategory.stabilizerIsoEnd_symm_apply, lipschitzGroup.conjAct_smul_range_Κ, AddEquivClass.apply_mem_center_iff, HahnSeries.iterateEquiv_symm_apply, Matrix.transposeInvertibleEquivInvertible_apply, Matrix.transposeLinearEquiv_apply, Matroid.mapEquiv_isBase_iff, Matrix.one_fin_two, PerfectionMap.equiv_apply, ContinuousLinearEquiv.coe_funUnique_symm, WithBot.ofDual_le_ofDual_iff, AddSubmonoid.topEquiv_toAddMonoidHom, measurable_piCongrLeft, LinearMap.toMatrix_apply, AlgEquiv.coe_coe, CategoryTheory.Presheaf.restrictedULiftYonedaHomEquiv'_symm_naturality_right, WithZero.toMulBot_strictMono, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk, IsometryEquiv.coe_toHomeomorph_symm, MonomialOrder.degree_sub_leadingTerm_lt_iff, CategoryTheory.discreteEquiv_apply, WithZero.logEquiv_unitsMk0, SetTheory.PGame.moveRight_toRightMovesNim, RootPairing.mapsTo_coreflection_coroot, NumberField.house.basis_repr_norm_le_const_mul_house, WithZero.val_inv_logOrderIso_symm_apply, OrderIso.sumLexAssoc_apply_inl_inr, Fin.cycleIcc.trans, map_prime_of_equiv, SubMulAction.conjMap_ofFixingSubgroup_bijective, DomAddAct.isQuotientMap_mk, TensorProduct.toMatrix_map, comp_equiv_symm_dotProduct, Matrix.rank_vecMulVec, IsometryEquiv.symm_trans_apply, LinearMap.quotKerEquivOfSurjective_apply_mk, RCLike.realLinearIsometryEquiv_apply, Monoid.CoprodI.Word.equivPair_tail_eq_inv_smul, toAdd_list_sum, MonoidAlgebra.lift_single, GrpCat.SurjectiveOfEpiAuxs.Ď_apply_fromCoset', UniformOnFun.zero_apply, CategoryTheory.Limits.Multifork.toSections_fac, ContinuousLinearMap.toWOT_apply, DilationEquiv.ratio_pow, equivShrink_symm_neg, Units.coe_mapEquiv, AffineEquiv.equivUnitsAffineMap_symm_apply_invFun, WithCStarModule.equiv_symm_zero, ContinuousLinearEquiv.piCongrRight_apply, IsometryEquiv.isometry, Finset.orderIsoColex_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three, Order.height_toDual, Submodule.coe_prodEquivOfClosedCompl, WithTop.toDual_apply_coe, SimpleGraph.locallyLinear_comap, Int.quotientSpanNatEquivZMod_comp_castRingHom, finFunctionFinEquiv_symm_apply_val, MonomialOrder.degree_sub_leadingTerm_le, UniformOnFun.toFun_zero, Homeomorph.map_coclosedCompact, Matrix.vecMul_swap, AddMonoidAlgebra.mapRangeRingEquiv_single, CategoryTheory.GrothendieckTopology.yonedaEquiv_yoneda_map, Equiv.ofFiberEquiv_symm_apply, finSuccEquiv'_symm_some_above, Module.Basis.orientation_reindex, Finset.Colex.insert_lt_insert, Orientation.areaForm_rightAngleRotation_left, Metric.Snowflaking.image_toSnowflaking_emetricBall, Matrix.piAddEquiv_apply, IndexedPartition.equivQuotient_index, SimpleGraph.Iso.mapEdgeSet_symm_apply, toAdd_inv, LinearEquiv.coe_coe, Finset.Ico_toDual, ComplexShape.Embedding.AreComplementary.desc.aux_trans, Antivary.dual, AlternatingMap.domDomCongrEquiv_symm_apply, Metric.Snowflaking.ediam_image_toSnowflaking, CategoryTheory.Abelian.Ext.biprodAddEquiv_apply_snd, ConcaveOn.dual, ofBoolAlg_compl, Equiv.congr_arg, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, AddSubmonoid.toSubmonoid'_closure, NumberField.mixedEmbedding.disjoint_negAt_plusPart, SSet.Subcomplex.PairingCore.pairing_p_symm_equivI, Algebra.SubmersivePresentation.cotangentEquiv_apply, MonoidHom.coe_toAdditive', strictAnti_comp_ofDual_iff, Algebra.PreSubmersivePresentation.reindex_map, LinearMap.toMatrix_id_eq_basis_toMatrix, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, Finsupp.Lex.lt_iff_of_unique, DirectSum.lequivProdDirectSum_symm_apply, Sum.Lex.toLex_mono, MonoidHom.coe_toAdditive_ker, AddMonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, LinearMap.toMatrixAlgEquiv_transpose_apply', TensorProduct.dualDistribEquivOfBasis_apply_apply, CategoryTheory.Cat.Hom.equivFunctor_symm_apply, RootPairing.root_reflectionPerm, Polynomial.opRingEquiv_symm_X, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, ContinuousLinearEquiv.piFinTwo_symm_apply, Homeomorph.sumEmpty_apply, LinearMap.toMatrixRight'_comp, DomAddAct.comap_mk_nhds, RingHom.equivRatAlgHom_symm_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply, PresheafOfModules.toPresheaf_map_sheafificationHomEquiv, LinearEquiv.ofLinear_apply, Trivialization.coordChangeL_apply', ContinuousLinearEquiv.coe_refl', IsometryEquiv.surjective, WithTop.coe_toDualBotEquiv, MeasurableEquiv.map_symm, GradedRing.proj_apply, RingHom.map_frobeniusEquiv_symm, Equiv.Set.sumCompl_symm_apply_of_notMem, WithLp.coe_symm_addEquiv, Finsupp.DegLex.single_strictAnti, finSuccEquivLast_symm_some, PositiveLinearMap.preGNS_norm_sq, Equiv.Perm.set_support_symm_eq, Matrix.kroneckerStarAlgEquiv_symm_apply, Submodule.coe_equivMapOfInjective_apply, MvPolynomial.mapEquivMonic_symm_map, Module.dualProdDualEquivDual_symm_apply, Equiv.toFun_inducedStructureEquiv_Symm, IsCoveringMapOn.homeomorph_comp, toColex_smul', modularCyclotomicCharacter.toFun_spec'', ContinuousLinearEquiv.comp_right_differentiable_iff, CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_comp, Quaternion.norm_toLp_equivTuple, Equiv.boolProdNatEquivNat_apply, CategoryTheory.CartesianMonoidalCategory.homEquivToProd_symm_apply, DomAddAct.symm_mk_zero, Set.Definable.image_comp_equiv, DomMulAct.mk_smul_mk_aeeqFun, LinearMap.trace_map, WithLp.equiv_symm_apply_ofLp, MeasureTheory.measurePreserving_sumPiEquivProdPi, Homeomorph.isOpenMap, DegLex.exists_iff, TensorProduct.assocIsometry_symm_apply, Matrix.trace_fin_two_of, toBoolAlg_mul, SSet.Truncated.liftOfStrictSegal.spineEquiv_fâ_arrow_one, OrderAddMonoidIso.eq_symm_apply, equivShrink_symm_smul, SSet.stdSimplex.face_singleton_compl, Equiv.subLeft_involutive, CategoryTheory.Functor.partialRightAdjointHomEquiv_map_comp, Matrix.compAddEquiv_symm_apply, AddSubmonoid.leftNegEquiv_symm_eq_neg, Module.Basis.constr_eq, IsCyclotomicExtension.autEquivPow_symm_apply, Fintype.finsetEquivSet_symm_apply, Fin.consLinearEquiv_symm_apply, Fin.snocEquiv_symm_apply, Submodule.reflection_mem_subspace_orthogonalComplement_eq_neg, Finset.sigmaAntidiagonalEquivProd_apply, Nat.equivProdNatSmoothNumbers_apply, FDRep.endRingEquiv_comp_Ď, Finsupp.domLCongr_single, AffineIsometryEquiv.coeFn_injective, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_symm_apply, FirstOrder.Language.Formula.realize_equivSentence_symm, Equiv.ofPreimageEquiv_symm_apply, WithBot.map_toDual, ContinuousAlternatingMap.ofSubsingleton_symm_apply_apply, Pi.toLex_strictMono, equivShrink_bot, FirstOrder.Language.Formula.realize_equivSentence, Topology.WithGeneratedByTopology.isClosed_iff, Equiv.pointReflection_vsub_left, Minimal.dual, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, WithZero.unitsWithZeroEquiv_apply, finSuccEquiv'_last_apply_castSucc, FreeGroup.map_eq_lift, MeasureTheory.addEquivAddHaarChar_smul_integral_map, AlgEquiv.algHomUnitsEquiv_apply_apply, Homeomorph.isQuotientMap, StrictAntiOn.dual_right, WithAbs.equivWithAbs_symm_equiv_symm_apply, Matrix.toBilin_comp, ProbabilityTheory.Kernel.map_apply_eq_iff_map_symm_apply_eq, LieAlgebra.Extension.oneCochainOfTwoSplitting_apply, NonemptyInterval.toLex_le_toLex, FreeGroup.lift_of_apply, LinearEquiv.apply_ofBijective_symm_apply, IsCusp.smul, TensorProduct.coe_finsuppScalarRight', Complex.equivRealProdCLM_apply, Finset.sigmaAntidiagonalEquivProd_symm_apply_fst, Multiplicative.ofAdd_image_nsmul, CategoryTheory.Pseudofunctor.StrongTrans.Modification.equivOplax_symm_apply, cyclotomicCharacter.toFun_spec, LinearMap.polyCharpoly_coeff_eval, finSumNatEquiv_apply_right, Subgroup.IsComplement.quotientGroupMk_leftQuotientEquiv, Function.Involutive.coe_toPerm, ContinuousLinearEquiv.coe_symm_toLinearEquiv, SimpleGraph.lapMatrix_toLinearMapâ'_apply'_eq_zero_iff_forall_adj, Rat.ringOfIntegersWithValEquiv_apply, Finset.Colex.ofColex_bot, PiLp.sumPiLpEquivProdLpPiLp_apply_ofLp, AddSubmonoid.equivOp_symm_apply_coe, DirectSum.linearEquivFunOnFintype_symm_coe, CategoryTheory.Equivalence.inducedFunctorOfEquiv, RootPairing.equiv_of_mapsTo_symm_apply, isOpenMap_toDual, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, Sym2.lift_map_apply, lsum_comp_mapRange_toSpanSingleton, SpecialLinearGroup.centerEquivRootsOfUnity_apply_of_finrank_le_one, MulEquiv.map_finprod_mem, iterateFrobeniusEquiv_zero_apply, CategoryTheory.GrothendieckTopology.yonedaEquiv_apply, ClassGroup.equiv_mk, ofLex_zero, FirstOrder.Language.Embedding.equivRange_apply, Module.Basis.repr_unop_eq_mulOpposite_repr, AddSubgroup.IsComplement.leftQuotientEquiv_apply, ArchimedeanClass.FiniteElement.ext_iff, Diffeomorph.coe_toHomeomorph_symm, DirectSum.linearEquivFunOnFintype_apply, MeasurableEquiv.coe_curry, Trunc.finChoiceEquiv_apply, Ideal.relNorm_comap_algEquiv, MulEquiv.symmEquiv_apply_symm_apply, EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi', Matrix.compAddEquiv_apply, MultilinearMap.ofSubsingletonâ_symm_apply, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, OrderRingIso.coe_toOrderIso, AddOpposite.opHomeomorph_symm_apply, LinearMap.det_toMatrix_eq_det_toMatrix, AlgEquiv.extendScalarsOfSurjective_apply, Additive.mem_toAddSubgroup, RingEquiv.toSemiRingCatIso_inv, MeasureTheory.Measure.infinitePi_map_curry, UniversalEnvelopingAlgebra.lift_Κ_apply', CategoryTheory.shrinkYonedaEquiv_symm_map, ContinuousLinearMap.innerSL_apply_comp, uniformContinuous_toAdd, TensorProduct.lidIsometry_symm_apply, LinearEquiv.coe_addEquiv_apply, Algebra.TensorProduct.linearEquivIncludeRange_tmul, Matrix.SpecialLinearGroup.toLin'_apply, CategoryTheory.Sieve.overEquiv_iff, AbstractCompletion.uniformContinuous_compareEquiv_symm, ConjAct.smul_eq_mulAut_conj, addMonoidEndToMultiplicative_symm_apply_apply, ContinuousLinearEquiv.coe_funUnique, Matrix.GeneralLinearGroup.toLin_apply, Equiv.toIso_inv, SymAlg.unsym_one, WithOne.lift_unique, RingAut.coe_pow, Filter.comap_equiv_symm, TensorProduct.AlgebraTensorModule.congr_tmul, Submonoid.closure_eq_mrange, Monoid.PushoutI.NormalWord.cons_toList, CategoryTheory.map_coyonedaEquiv, CategoryTheory.Adjunction.homEquiv_symm_apply, AddEquiv.toMultiplicativeLeft_apply_apply, Subsemigroup.centerCongr_apply_coe, RingQuot.eq_liftAlgHom_comp_mkAlgHom, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow, Submodule.piQuotientLift_mk, CategoryTheory.Functor.Initial.limitConeOfComp_isLimit, GradedRing.proj_recompose, AddEquiv.op_apply_symm_apply, HilbertBasis.hasSum_repr_symm, Equiv.Perm.decomposeFin_symm_apply_zero, OrderDual.toDual_ofDual, LocallyConstant.congrLeft_apply, MultilinearMap.ofSubsingleton_apply_apply, Homeomorph.coinduced_eq, Homeomorph.coe_addRight, Subsemigroup.comap_equiv_eq_map_symm, MeasurableEquiv.coe_mulRightâ, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, toDegLex_add, SimpleGraph.Iso.map_apply, RestrictScalars.smul_def, AlgebraicGeometry.Spec.homEquiv_symm_apply, Homeomorph.coe_punitProd, SimpleGraph.Iso.comap_symm_apply, Finsupp.Colex.single_strictMono, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, LinearMap.adjoint_id, AffineIsometryEquiv.coe_mul, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, LinearIsometryEquiv.withLpProdAssoc_symm_apply, OrderRingIso.coe_toRingEquiv, MultilinearMap.currySumEquiv_symm_apply, DyckWord.equivTree_apply, AddMonoidHom.ofInjective_apply, ContinuousAddEquiv.coe_trans, SetTheory.PGame.toRightMovesNim_symm_lt, DomMulAct.mk_smul_addMonoidHom_apply, SymAlg.mul_def, isRegular_ofColex, Subring.addEquivOp_symm_apply_coe, exteriorPower.basis_repr_self, TensorProduct.finsuppLeft'_apply, QuaternionAlgebra.coe_symm_addEquivTuple, ValuationSubring.principalUnitGroup_symm_apply, CategoryTheory.map_yonedaEquiv', DFinsupp.sigmaFinsetFunEquiv_apply_fst, ContinuousLinearMap.adjoint_adjoint, Pi.toColex_update_lt_self_iff, MeasureTheory.MeasurableEquiv.measurePreserving_symm, nhds_toMul, AffineIsometryEquiv.coe_toAffineIsometry, AddChar.coe_toMonoidHomEquiv_symm, MeasurableEquiv.coe_toLp_symm, GradedTensorProduct.of_symm_one, LinearMap.lflip_apply, Submodule.coe_prodEquivOfClosedCompl_symm, WithZero.withZeroUnitsEquiv_strictMono, frobeniusEquiv_symm_apply_frobenius, AddEquiv.comapAddSubgroup_symm_apply, LinearIsometryEquiv.coe_prodAssoc, TensorProduct.lift.equiv_apply, hahnEmbedding_isOrderedAddMonoid, TensorProduct.finsuppRight_tmul_single, Rep.indResHomEquiv_symm_apply_hom, AddEquiv.punitCoprod_apply, MonoidHom.toMulEquiv_apply, CategoryTheory.CategoryOfElements.toCostructuredArrow_map, OpenPartialHomeomorph.toHomeomorphSourceTarget_symm_apply_coe, toDual_one, FreeAddGroup.range_lift_eq_closure, Finset.Iio_ofDual, ModelWithCorners.toHomeomorph_symm_apply, Multiplicative.toAdd_top, LieModuleEquiv.one_apply, ContinuousMulEquiv.comp_symm_eq, DFinsupp.Lex.lt_iff, IsometryEquiv.preimage_eball, QuadraticForm.dualProdProdIsometry_invFun, LinearMap.SeparatingLeft.congr, CategoryTheory.Pretriangulated.shift_opShiftFunctorEquivalenceSymmHomEquiv_unop_assoc, ContinuousAddEquiv.apply_symm_apply, CategoryTheory.Functor.homEquivOfIsLeftKanExtension_apply_app, Pi.basisFun_det_apply, RootPairing.Equiv.toEndUnit_val, OrderRingIso.toFun_eq_coe, Submodule.fstEquiv_apply, Matrix.Nondegenerate.toLinearMapâ', Shrink.algEquiv_symm_apply, LinearIsometryEquiv.preimage_sphere, Int.divModEquiv_symm_apply, Tuple.monotone_sort, OrderIsoClass.toBoundedOrderHomClass, Polynomial.roots_X_pow_char_pow_sub_C, Topology.WithLower.ofLower_toLower, toLex_neg, Order.coheight_toDual, finsuppLEquivDirectSum_symm_lof, AddCommGrpCat.toCommGrp_map, CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_right, IsHomeomorph.homeomorph_apply, UniformFun.ofFun_mul, IsometryEquiv.inv_apply, Ideal.IsHomogeneous.mem_iff, LinearEquiv.extendScalarsOfIsLocalization_apply, Finset.Ici_ofDual, MeasurableEquiv.piMeasurableEquivTProd_symm_apply, Trivialization.linearEquivAt_symm_apply, Sum.Lex.not_inr_lt_inl, OrderMonoidIso.ext_iff, MulEquiv.coe_prodComm, AffineIsometryEquiv.pointReflection_midpoint_right, DirectSum.IsInternal.subordinateOrthonormalBasisIndex_def, Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map_apply, Matrix.blockTriangular_reindex_iff, Abelianization.equivOfComm_symm_apply, Matrix.isUnit_comp_symm_iff, Equiv.eq_symm_apply, Finsupp.toMultiset_eq_iff, Finsupp.curryLinearEquiv_symm_apply, RingEquiv.prodCongr_symm_apply, CategoryTheory.Bicategory.mateEquiv_apply', nsmulCoprime_apply, IsometryEquiv.trans_apply, UniformOnFun.lipschitzWith_one_ofFun_toFun', Equiv.setSubtypeComm_symm_apply, CategoryTheory.nerve.edgeMk_surjective, Matrix.separatingRight_toLinearMapâ'_iff_separatingRight_toLinearMapâ, AddCircle.homeomorphAddCircle_symm_apply_mk, Module.Basis.sumQuot_repr_inr, LinearIsometryEquiv.coe_withLpUniqueProd, ContinuousLinearEquiv.ofSubmodules_apply, CategoryTheory.Functor.LeftExtension.IsPointwiseLeftKanExtensionAt.comp_homEquiv_symm_assoc, Module.Basis.coord_toDualEquiv_symm_apply, DomAddAct.isInducing_mk_symm, IsCyclotomicExtension.autEquivPow_apply, ContinuousMultilinearMap.norm_ofSubsingleton_id, CategoryTheory.Over.postAdjunctionLeft_counit_app_left, FreeAddMonoid.toList_nil, Set.opEquiv_symm_apply, LinearIsometryEquiv.image_closedBall, CategoryTheory.Localization.SmallShiftedHom.postcompEquiv_apply, Finsupp.lsum_symm_apply, Real.sinhHomeomorph_apply, MulEquiv.refl_apply, Complex.equivRealProd_apply_le, CategoryTheory.Adjunction.equivHomsetRightOfNatIso_symm_apply, Topology.WithLowerSet.toLowerSet_specializes_toLowerSet, QuotientAddGroup.equivIocMod_coe, CategoryTheory.Bicategory.conjugateEquiv_comp, ContinuousLinearMap.orthogonal_ker, Fin.insertNth_apply_cycleRange_symm, CategoryTheory.Iso.commSemiRingCatIsoToRingEquiv_toRingHom, Module.Basis.coord_repr_symm, Complex.rotation, AddAut.inv_apply_self, ZMod.dft_apply_zero, isLeftRegular_toColex, Finsupp.lcongr_apply_apply, TopHom.dual_id, CategoryTheory.Limits.Sigma.Κ_reindex_inv_assoc, Diffeomorph.coe_toHomeomorph, Ideal.Factors.piQuotientEquiv_map, RCLike.complexLinearIsometryEquiv_apply, MonomialOrder.degree_sub_LTerm_le, CategoryTheory.Functor.IsCoverDense.restrictHomEquivHom_naturality_left_symm, RingEquiv.coe_refl, StarModule.decomposeProdAdjoint_apply, StarAlgEquiv.isometry, NonUnitalSubsemiring.topEquiv_symm_apply_coe, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_tmul, CategoryTheory.ParametrizedAdjunction.homEquiv_naturality_three_assoc, HahnSeries.leadingCoeff_abs, CategoryTheory.Limits.Types.colimitEquivColimitType_apply, MonomialOrder.lex_le_iff_of_unique, MulOpposite.opHomeomorph_apply, SemidirectProduct.equivProd_symm_apply_right, Topology.WithUpperSet.isOpen_ofUpperSet_preimage, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_emultiplicity, SubMulAction.conjMap_ofFixingSubgroup_coe_apply, CategoryTheory.Pretriangulated.opShiftFunctorEquivalenceSymmHomEquiv_apply_assoc, Function.Embedding.swap_comp, SymAlg.unsym_inj, Equiv.sumCompl_symm_apply_of_pos, Subsemigroup.coe_toAddSubsemigroup_apply, IsMaxFilter.dual, LinearEquiv.skewProd_apply, Delone.DeloneSet.mapIsometry_apply_carrier, RingEquiv.moduleEndSelfOp_symm_apply, MulEquiv.val_inv_piUnits_symm_apply, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, Equiv.some_removeNone_iff, Submodule.unitsQuotEquivRelPic_apply_coe, RestrictScalars.addEquiv_map_smul, Subspace.dualEquivDual_apply, OnePoint.equivProjectivization_apply_infinity, MonoidHom.toHomUnitsMulEquiv_apply, Ideal.isoBaseOfIsPrincipal_apply, Multiplicative.ofAdd_top, Antivary.sum_comp_perm_smul_eq_sum_smul_iff, FirstOrder.Language.StrongHomClass.toEquiv_toFun, LinearEquiv.prodUnique_apply, ZLattice.abs_repr_le, CategoryTheory.Equivalence.essSurjInducedFunctor, isOpenMap_toMul, CategoryTheory.shrinkYonedaEquiv_shrinkYoneda_map, CategoryTheory.Adjunction.CoreHomEquivUnitCounit.homEquiv_counit, MulEquiv.apply_symm_apply, measurable_piEquivPiSubtypeProd, LinearIsometryEquiv.map_smulââ, Module.Dual.congr_symm_apply_apply, DirectSum.IsInternal.collectedBasis_repr_of_mem, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_apply, Module.Basis.coe_sumCoords, QuotientGroup.quotientMulEquivOfEq_mk, AddSubmonoid.centerToAddOpposite_apply_coe, Finsupp.equivFunOnFinite_symm_apply_apply, Algebra.Generators.Hom.equivAlgHom_apply_coe, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, CategoryTheory.Iso.commGroupIsoToMulEquiv_apply, circleEquivGen_apply, ContinuousLinearEquiv.piFinTwo_apply, Submodule.restrictScalarsEquiv_apply, ZLattice.covolume_eq_det, Equiv.Perm.commute_ofSubtype_noncommPiCoprod, coe_ofLexLinearEquiv, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, RootPairing.reflection_image_eq, StarMulEquiv.invFun_eq_symm, SetTheory.PGame.toLeftMovesNim_one_symm, equivShrink_sub, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, AddAut.congr_symm_apply, DirectSum.coe_congrLinearEquiv, RootPairing.Equiv.coweightEquiv_apply, Equiv.listUniqueEquiv_symm_apply, InfIrred.ofDual, MulArchimedeanOrder.val_of, DirectSum.lequivProdDirectSum_apply, MultilinearMap.domDomCongr_apply, ContinuousMultilinearMap.curryMidEquiv_symm_apply, ofDual_smul', HahnModule.of_symm_sub, Fin.cycleRange_self, LinearMap.sum_repr_mul_repr_mul, CategoryTheory.ShiftedHom.opEquiv'_add_symm, uniformEquicontinuous_iff_uniformContinuous, FreeSemigroup.lift_of, MonoidAlgebra.lift_of, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap, Valuation.IsEquiv.orderRingIso_symm_apply, CStarMatrix.toCLM_apply_single_apply, MultilinearMap.domDomCongrEquiv_apply, Set.Ico_ofDual, LinearMap.IsPositive.conj_adjoint, CategoryTheory.Functor.functorHomEquiv_symm_apply_app_app, MonoidHom.coe_toMultiplicative_ker, RingEquiv.comp_symm, nndist_ofDual, IsCoveringMap.homeomorph_comp, Fin.consLinearEquiv_apply, LinearMap.ker_toContinuousLinearMap, WithBot.orderIsoPUnitSumLex_bot, Equiv.piCongrLeft'_apply, Finset.toDual_sup', Metric.Snowflaking.homeomorph_apply, IsLocalizedModule.iso_mk_one, LinearIsometryEquiv.ediam_image, CategoryTheory.colimitYonedaHomEquiv_Ď_apply, Equiv.pointReflection_apply, MulEquiv.withZero_symm_apply_symm_apply, CategoryTheory.Equivalence.induced_counitIso, LinearMap.charpoly_toMatrix, ContinuousAddEquiv.trans_apply, UniformFun.isClosed_setOf_continuous, Set.powersetCard.ofFinEmbEquiv_apply, AddChar.coe_toAddMonoidHomEquiv_symm, MulAut.congr_symm_apply, AddSubgroup.equivOp_symm_apply_coe, BoundedContinuousFunction.isInducing_coeFn, LinearMap.isSymm_iff_isHermitian_toMatrix, OrderDual.ofDual_top, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, SSet.Truncated.liftOfStrictSegal.spineEquiv_fâ_arrow_zero, OrderIso.dualDual_symm_apply, NonUnitalSubsemiring.topEquiv_apply, PowerBasis.liftEquiv_apply_coe, invertibleEquivOfLeftInverse_symm_apply, Module.Basis.ofIsLocalizedModule_repr_apply, CategoryTheory.Limits.Types.isLimitEquivSections_symm_apply, DoubleQuot.quotQuotEquivComm_algebraMap, Set.PartiallyWellOrderedOn.ProdLex_iff, DFinsupp.domLCongr_apply, MonomialOrder.degree_sPolynomial, ContinuousLinearEquiv.mfderivWithin_eq, IsometryEquiv.self_comp_symm, GrpWithZero.Iso.mk_inv, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap', IsometryEquiv.comp_continuous_iff, Matrix.toBilin'_single, LinearIsometryEquiv.bijective, CategoryTheory.uliftCoyonedaEquiv_comp, CategoryTheory.Quiv.equivOfIso_apply, Submodule.Quotient.equiv_apply, RootPairing.Hom.id_indexEquiv_symm_apply, CategoryTheory.enrichedFunctorTypeEquivFunctor_symm_apply_map, CategoryTheory.Iso.conjAut_trans, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Equiv.pprodEquivProd_symm_apply, MeasurableEquiv.piFinSuccAbove_symm_apply, Prod.Lex.le_iff', Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, Fin2.equivFin_symm_apply, CategoryTheory.CatEnrichedOrdinary.Hom.base_id, CategoryTheory.yonedaEquiv_symm_app_apply, hahnEmbedding_isOrderedModule, LinearEquiv.conjAlgEquiv_ext_iff, AffineEquiv.midpoint_pointReflection_right, OrderIsoClass.toCoheytingHomClass, MulEquiv.piMultiplicative_symm_apply, AntitoneOn.dual, LinearMap.toMatrix_toLin, MvPolynomial.renameSymmetricSubalgebra_apply_coe, Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply, TensorProduct.includeRight_lid, SemimoduleCat.homAddEquiv_symm_apply_hom, MeasureTheory.OuterMeasure.isometryEquiv_comap_mkMetric, FreeNonUnitalNonAssocAlgebra.lift_comp_of, Equiv.divRightâ_apply, LieEquiv.coe_toLinearEquiv, CategoryTheory.Arrow.equivSigma_symm_apply_right, AddSubmonoid.LocalizationMap.addEquivOfLocalizations_apply, Homeomorph.unitBall_symm_apply, Homeomorph.toMeasurableEquiv_coe, TensorProduct.tensorTensorTensorAssoc_tmul, Submonoid.mul_leftInvEquiv_symm, sInfHom.symm_dual_id, ContinuousAddEquiv.symm_trans_apply, ofMul_uzpow, UniformFun.ofFun_inv, CategoryTheory.tensorLeftHomEquiv_symm_naturality, DFinsupp.sigmaFinsetFunEquiv_apply_snd_coe, LinearIsometryEquiv.submoduleMap_apply_coe, AddEquiv.coe_symm_toIntLinearEquiv, prod_galRestrict_eq_norm, CategoryTheory.nerve.homEquiv_symm_apply, ProbabilityTheory.Kernel.traj_eq_prod, Sum.Lex.inl_le_inr, TensorProduct.finsuppLeft_apply_tmul_apply, WithBot.ofDual_apply_bot, Set.mem_image_equiv, ContinuousLinearEquiv.contDiff, IsLocalization.ringEquivOfRingEquiv_mk', AlgEquiv.coe_ringHom_commutes, RingCon.comapQuotientEquivOfSurj_mk, Module.compHom.toLinearEquiv_apply, Algebra.discr_reindex, MeasurableEquiv.piFinSuccAbove_apply, AddMonoid.Coprod.con_neg_add_cancel, MonomialOrder.degree_X_le_single, MvPolynomial.coe_mapEquivMonic_comp, Matrix.comp_one, Topology.WithLawson.toLawson_ofLawson, UniformEquiv.piCongrRight_apply, Ordinal.toPGame_moveLeft', SheafOfModules.unitHomEquiv_apply_coe, Monovary.sum_smul_comp_perm_eq_sum_smul_iff, stdSimplexEquivIcc_zero, uniformity_additive, SymAlg.unsym_eq_zero_iff, CategoryTheory.Iso.addCommGroupIsoToAddEquiv_apply, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, IsNoetherian.equivPUnitOfProdInjective_symm_apply, IsometryClass.coe_coe, Matrix.conjTranspose_reindex, AffineIsometryEquiv.coe_toAffineEquiv, Subgroup.isCoatom_comap, CategoryTheory.mateEquiv_apply, ComplexShape.Embedding.AreComplementary.desc'_inr, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, continuous_ofAdd, LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg, SpecialLinearGroup.toLinearEquiv_apply, CategoryTheory.Limits.IsLimit.homEquiv_apply, Function.Embedding.optionEmbeddingEquiv_apply_fst, CategoryTheory.ParametrizedAdjunction.arrowHomEquiv_apply_right_snd_assoc, LocallyConstant.congrRight_symm_apply, CategoryTheory.ShiftedHom.opEquiv_symm_comp, autEquivRootsOfUnity_smul, Matrix.toLinearEquiv_apply, SupHom.dual_apply_toFun, LinearIsometryEquiv.preimage_closedBall, LinearEquiv.piRing_apply, UniformFun.lipschitzWith_eval, AffineIsometryEquiv.coe_toContinuousAffineEquiv, CompactlySupportedContinuousMap.continuousMapEquiv_apply_toFun, OrderDual.ofDual_eq_bot, SkewMonoidAlgebra.lift_symm_apply, hasEigenvalue_toLin_diagonal_iff, CategoryTheory.Adjunction.homEquiv_naturality_left_square_assoc, RingHom.asBoolAlg_toFun, ContinuousLinearEquiv.ofBijective_apply_symm_apply, AddEquiv.op_apply_apply, continuousMultilinearCurryFin1_apply, PiTensorProduct.lift_symm, AffineEquiv.constVAddHom_apply, MulEquiv.inv_apply, CategoryTheory.Limits.compYonedaSectionsEquiv_symm_apply_coe, WithLp.prodContinuousLinearEquiv_apply, ContinuousLinearEquiv.ofSubmodules_symm_apply, Sum.Lex.inl_le_inl_iff, Equiv.piCongrSet_symm_apply, AddEquiv.eq_symm_comp, MonoidAlgebra.lift_unique', sigmaFinsuppLequivDFinsupp_apply, RootPairing.reflection_apply_root, CategoryTheory.yonedaEquiv_comp, Equiv.apply_eq_iff_eq_symm_apply, Matrix.spectrum_toLin', KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span, CategoryTheory.unitCompPartialBijective_symm_apply, RootPairing.reflectionPerm_eq_iff_smul_coroot, Ordinal.type_preimage, ofMul_div, Function.fromTypes_nil_equiv_symm_apply, MeasureTheory.SignedMeasure.toJordanDecompositionEquiv_symm_apply, MulAut.conjNormal_apply, unitary.linearIsometryEquiv_coe_apply, SubAddAction.ofStabilizer.conjMap_apply, Equiv.pointReflection_fixed_iff_of_injective_two_nsmul, uliftZMultiplesHom_symm_apply, Metric.Snowflaking.isBounded_image_toSnowflaking_iff, CategoryTheory.Localization.structuredArrowEquiv_apply, LieAlgebra.of_nsmul, Pi.toLex_monotone, SetTheory.PGame.moveLeft_neg, Equiv.psigmaEquivSigma_symm_apply, KummerDedekind.quotMapEquivQuotQuotMap_symm_apply, kroneckerLinearEquiv_tmul, LieAlgebra.killingForm_of_equiv_apply, AlgEquiv.toLinearEquiv_apply, MvPolynomial.rTensorAlgHom_apply_eq
bridge: CategoryTheory.Limits.WalkingPair.equivBool_apply_right, CategoryTheory.Limits.WalkingPair.equivBool_apply_left
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