id 📖 | CompOp | 11324 mathmath: AdicCompletion.of_surjective_iff, PrimeSpectrum.mapPiLocalization_id, ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, CliffordAlgebra.unop_reverseOp, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, DFinsupp.coprodMap_apply, MvPolynomial.pUnitAlgEquiv_symm_monomial, MvPowerSeries.coeff_zero_eq_constantCoeff_apply, LinearMap.det_toContinuousLinearMap, DirectSum.IsInternal.ofBijective_coeLinearMap_same, CliffordAlgebra.ι_range_map_map, LinearEquiv.multilinearMapCongrLeft_symm_apply, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, Polynomial.support_monomial, MultilinearMap.domDomCongrLinearEquiv'_symm_apply, continuous_decomposeProdAdjoint, TensorProduct.finsuppRight_apply, LieModule.shiftedGenWeightSpace.shift_apply, TangentBundle.continuousLinearMapAt_model_space, hasFDerivAt_iff_hasDerivAt, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, CuspFormClass.qExpansion_isBigO, DFinsupp.comul_single, VectorBundleCore.toFiberBundleCore_coordChange, ContMDiffAt.coordChangeL, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, geometric_hahn_banach_open, DistribMulAction.toModuleAut_apply, TensorProduct.mapInclIsometry_apply, IsSymmetricAlgebra.lift_eq, MvPowerSeries.hasSubst_def, Ideal.toCotangent_to_quotient_square, LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm, mfderiv_prod_eq_add, LinearMap.comp_toSpanSingleton, LinearMap.isSymm_zero, ContinuousMap.toLp_inj, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, Finsupp.snd_sumFinsuppLEquivProdFinsupp, KaehlerDifferential.kerCotangentToTensor_toCotangent, Rep.resCoindHomEquiv_symm_apply_hom, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, HasStrictFDerivAt.log, Representation.repOfTprodIso_inv_apply, LinearIsometryEquiv.strictConvex_preimage, Finset.weightedVSub_sdiff, Rep.resCoindHomEquiv_apply_hom, TemperedDistribution.lineDerivOpCLM_eq, ContinuousLinearMap.sum_comp_single, RootPairing.InvariantForm.apply_reflection_reflection, MvPolynomial.dvd_monomial_one_iff_exists, PiLp.continuousLinearEquiv_symm_apply, CliffordAlgebra.contractRight_algebraMap_mul, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr, Finsupp.fst_sumFinsuppLEquivProdFinsupp, LinearMap.restrictScalars_toMatrix, Submodule.starProjection_apply_eq_isComplProjection, Lagrange.interpolate_one, MeasureTheory.Lp.toTemperedDistributionCLM_apply, StarModule.decomposeProdAdjointL_symm_apply, fderiv_iteratedFDeriv, MeasureTheory.convolution_flip, ModuleCat.hom_zero, Algebra.normalizedTrace_map, RootPairing.rootForm_self_smul_coroot, CliffordAlgebra.toBaseChange_reverse, MeasureTheory.LpToLpRestrictCLM_coeFn, StarModule.selfAdjointPart_add_skewAdjointPart, ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, ContinuousLinearMap.hasFPowerSeriesOnBall, Polynomial.taylor_eval, MDifferentiable.coordChangeL, AlgHom.coe_toLinearMap, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, LinearMap.BilinForm.linMulLin_compRight, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, Bialgebra.comulAlgHom_apply, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, isConformalMap_conj, TensorProduct.forall_vanishesTrivially_iff_forall_fg_rTensor_injective, LieDerivation.IsKilling.ad_mem_ker_killingForm_ad_range_of_mem_orthogonal, LinearMap.apply_symm_toPerfPair_self, LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff, PowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, ContinuousLinearMap.toSpanSingleton_zero, Submodule.rTensorOne_symm_apply, ModuleCat.forget_preservesLimits, iSupIndep.linearEquiv_symm_apply, Matrix.toLinAlgEquiv_one, LinearIsometryEquiv.hasStrictFDerivAt, Bialgebra.comul_natCast, Finsupp.linearCombination_apply_of_mem_supported, ContinuousLinearMap.derivWithin_of_bilinear, Perfection.pthRoot_frobenius, LinearMap.inl_map_mul, PowerSeries.hasSum_aeval, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, TopModuleCat.hom_zero, LinearMap.prod_eq_inf_comap, mapMatrix_id, HasStrictFDerivAt.isLittleOTVS, RootPairing.RootPositiveForm.algebraMap_rootLength, Finset.weightedVSubOfPoint_map, LinearMap.range_prodMap, Algebra.SubmersivePresentation.cotangentComplexAux_injective, SemimoduleCat.Hom.hom₂_apply, Bundle.ContMDiffRiemannianMetric.isVonNBounded, NormedSpace.isBounded_polar_of_mem_nhds_zero, MeasureTheory.OuterMeasure.map_iInf, SchwartzMap.lineDerivOpCLM_eq, LinearMap.baseChange_eq_ltensor, Module.Flat.iff_lTensor_exact', Algebra.normalizedTrace_algebraMap_eq_id, Module.Basis.det_comp_basis, Module.Basis.equivFun_self, TensorProduct.enorm_lid, PositiveLinearMap.monotone', Module.Basis.coe_map, Submodule.topEquiv_symm_apply_coe, LinearMap.charpoly_def, Lagrange.eval_iterate_derivative_eq_sum, LinearEquiv.congrRight₂_refl, ClosedSubmodule.comap_comap, TrivSqZeroExt.fstCLM_apply, MonomialOrder.sPolynomial_leadingTerm_mul', iSupIndep.dfinsupp_lsum_injective, LinearMap.BilinForm.dualSubmoduleParing_spec, Polynomial.eraseLead_monomial, SymmetricAlgebra.lift_ι_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, CommRingCat.KaehlerDifferential.map_d, MeasureTheory.condExpInd_of_measurable, Submodule.FG.rTensor.directedSystem, cfcₙL_integral, HasStrictFDerivAt.fun_mul', Derivation.apply_eval_eq, CategoryTheory.preadditiveCoyonedaObj_map, ModuleCat.MonoidalCategory.braiding_hom_apply, PiTensorProduct.lift_reindex, fderivWithin_ofNat, Rep.coe_linearization_obj_ρ, Algebra.idealMap_eq_ofEq_comp_toLocalized₀, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, MvPowerSeries.coeff_zero_eq_constantCoeff, LinearMap.BilinForm.zero_right, dot_self_cross, Finset.affineCombination_vsub, HasMFDerivAt.mul, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, CliffordAlgebra.contractRight_algebraMap, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, LinearIsometryEquiv.comp_fderiv, DFinsupp.lsum_lsingle, Matrix.toLin_kronecker, Lagrange.interpolate_eq_of_values_eq_on, Matrix.toLin'_symm, QuaternionAlgebra.coe_linearEquivTuple_symm, ContinuousLinearEquiv.unitsEquiv_apply, Orthonormal.inner_left_finsupp, ModuleCat.restrictScalars.map_apply, MvPolynomial.totalDegree_monomial, AlgEquiv.moduleEndSelfOp_apply_apply, Polynomial.derivative_X_sq, Matrix.SeparatingLeft.toBilin', ProbabilityTheory.isGaussian_iff_gaussian_charFun, LinearMap.detAux_def'', ContinuousLinearMap.mulLeftRight_isBoundedBilinear, WittVector.map_id, RootPairing.posRootForm_posForm_apply_apply, QuadraticMap.smul_toBilin, ModuleCat.forget₂_reflectsLimitsOfSize, TensorProduct.LieModule.liftLie_apply, LinearEquiv.multilinearMapCongrRight_apply, PowerSeries.coeff_mul_one_sub_of_lt_order, Finsupp.mapRange.linearEquiv_refl, LinearMap.BilinForm.dualSubmoduleToDual_apply_apply, HasFDerivWithinAt.continuousMultilinearMap_apply, IsLocalizedModule.liftOfLE_apply, ContinuousLinearEquiv.symm_neg, Polynomial.smeval_monomial_mul, PiTensorProduct.lift.tprod, RCLike.map_apply, LinearMap.iterateRange_succ, Coalgebra.lTensor_counit_comul, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, CliffordAlgebra.contractRight_eq, OrthonormalBasis.orthogonalProjection_eq_sum, IsStandardOpenImmersion.id, IsIsotypic.linearEquiv_fun, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', LinearMap.toMatrixAlgEquiv'_mul, MeasureTheory.aestronglyMeasurable_condExpInd, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, AddMonoidAlgebra.domCongr_comp_lsingle, HasCompactSupport.convolution_integrand_bound_left, LinearMap.BilinForm.toMatrix_toBilin, Pretrivialization.linearMapAt_def_of_notMem, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, Module.Basis.end_repr_apply, ContinuousLinearMap.HasRightInverse.comp_continuousLinearEquivalence, LinearMap.IsSymmetric.inner_map_polarization, RCLike.geometric_hahn_banach_point_open, Complex.coe_realPart, Polynomial.ofFn_zero, Algebra.Presentation.differentials.comm₁₂_single, CategoryTheory.Functor.mapExtLinearMap_toAddMonoidHom, fderivWithin_comp_derivWithin_of_eq, Pretrivialization.linearEquivAt_symm_apply, ContinuousLinearEquiv.differentiable, Submodule.linearProjOfIsCompl_apply_left, ContinuousLinearMap.opNorm_prod, IsSelfAdjoint.quasispectrumRestricts, MvPowerSeries.coeff_zero, ContinuousLinearMap.snd_comp_inr, LinearMap.coe_toSeminorm, Submodule.subtype_comp_inclusion, MvPowerSeries.weightedOrder_monomial, Algebra.Extension.Cotangent.span_eq_top_of_span_eq_ker, Module.Basis.map_equivFun, AdicCompletion.mk_zero_of, MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum, LinearMap.adjoint_adjoint, IsSemisimpleModule.exists_submodule_linearEquiv_quotient, DoubleCentralizer.star_snd, Matrix.SeparatingRight.toLinearMap₂, ContinuousLinearMap.norm_inr_le_one, PowerSeries.coeff_mul_of_lt_order, LinearMap.IsReflective.regular, RootPairing.linearIndepOn_root_baseOf', taylorWithin_succ, LinearMap.BilinForm.symmCompOfNondegenerate_left_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, LinearEquiv.lTensor_pow, CategoryTheory.Abelian.Ext.homLinearEquiv_apply, AlgEquiv.refl_toRingHom, PolyEquivTensor.toFunBilinear_apply_eq_sum, LinearMap.BilinForm.dualSubmoduleToDual_injective, Rep.MonoidalClosed.linearHomEquiv_symm_hom, MeasureTheory.Measure.addHaar_image_continuousLinearMap, binomialSeries_eq_ordinaryHypergeometricSeries, HasFDerivWithinAt.ccos, Polynomial.lcoeff_comp_mapAlgHom_eq, Polynomial.coe_taylorAlgHom, InnerProductSpace.toLinearIsometry_toDual, groupCohomology.isoCocycles₁_hom_comp_i_apply, RCLike.ofRealCLM_apply, DFinsupp.lsingle_apply, SchwartzMap.integral_sesq_fourier_fourier, MultilinearMap.fromDFinsuppEquiv_apply, HasMFDerivAt.add, Module.Presentation.cokernelSolution_var, LinearMap.exists_monic_and_aeval_eq_zero, Subspace.dualAnnihilator_dualAnnihilator_eq_map, Polynomial.monomial_eq_monomial_iff, Real.hasFDerivAt_fourierChar_neg_bilinear_left, AddValuation.comap_id, LinearMap.inr_apply, RootPairing.Polarization_apply, LinearEquiv.extendScalarsOfIsLocalizationEquiv_symm_apply, LinearIsometryEquiv.analyticOnNhd, PolynomialModule.comp_single, geometric_hahn_banach_point_point, LinearEquiv.flip_apply, PolynomialModule.map_lsingle, Submodule.range_snd, GradedTensorProduct.hom_ext_iff, Complex.linearEquiv_det_conjLIE, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_same, Module.Relations.Solution.postcomp_comp, LinearEquiv.restrictScalars_apply, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, MeasureTheory.convolution_eq_right', hasStrictFDerivAt_exp_of_mem_ball, Polynomial.coeff_derivative, LinearMap.funLeft_id, hasFDerivAt_iff_hasGradientAt, TensorProduct.AlgebraTensorModule.rid_symm_apply, PowerSeries.coeff_of_lt_order_toNat, PiTensorProduct.liftAlgHom_apply, groupCohomology.mem_cocycles₂_def, RootPairing.root'In_corootSpanMem_eq_pairingIn, RCLike.reCLM_apply, LinearMap.toAddMonoidHom_proj, BilinForm.toMatrix_symm, PowerSeries.constantCoeff_subst, ExteriorAlgebra.ι_eq_algebraMap_iff, RootPairing.rootForm_restrict_nondegenerate_of_ordered, PowerSeries.WithPiTopology.continuous_coeff, LinearIsometry.norm_compContinuousAlternatingMap, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, LinearIsometryEquiv.trans_one, IsHilbertSum.surjective_isometry, SimpleGraph.lapMatrix_toLinearMap₂', curveIntegral_smul, LinearMap.coe_compAlternatingMap, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, Matrix.reindexLinearEquiv_trans, Submodule.reflection_trans_reflection, LinearMap.pow_mulRight, groupHomology.coinfNatTrans_app, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, Orientation.inner_rotation_pi_div_two_right_smul, PowerSeries.coeff_mul_C, extDeriv_constOfIsEmpty, Module.FaithfullyFlat.iff_exact_iff_lTensor_exact, RCLike.separate_convex_open_set, Orientation.oangle_add_left_smul_rotation_pi_div_two, RootPairing.coroot_eq_polarizationEquiv_apply_root, Real.fourierIntegral_comp_linearIsometry, ContinuousAffineMap.neg_contLinear, IsGroupLikeElem.comul_eq_tmul_self, ContinuousLinearMap.HasRightInverse.continuousLinearEquivalence_comp, LinearMap.compAlternatingMap_apply, Real.fderiv_fourierIntegral, Submodule.orthogonalDecomposition_symm_apply, ModuleCat.forget_preservesLimitsOfSize, hasStrictFDerivAt_list_prod_finRange', Module.End.exists_ker_pow_eq_ker_pow_succ, groupCohomology.d₂₃_hom_apply, OrthogonalFamily.linearIsometry_apply_single, Algebra.PreSubmersivePresentation.cotangentComplexAux_apply, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, MvPolynomial.rTensor_apply_tmul_apply, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, MvPolynomial.degrees_monomial, Submodule.IsOrtho.starProjection_comp_starProjection, LinearEquiv.symm_mem_transvections_iff, fderiv_intCast, ContinuousLinearEquiv.hasRightInverse, AlternatingMap.constLinearEquivOfIsEmpty_symm_apply, LinearMap.subtype_comp_codRestrict, LinearMap.prodMap_one, CliffordAlgebraQuaternion.j_quaternionBasis, LinearMap.id_fgModuleCat_comp, PiTensorProduct.tmulEquiv_symm_apply, ExteriorAlgebra.ι_inj, Filter.EventuallyEq.fderivWithin, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, dotProductEquiv_symm_apply, IsBaseChange.comp_iff, fderivWithin_one, groupHomology.d₁₀_single_one, ContinuousLinearMap.continuous_det, LinearEquiv.piCongrRight_apply, addMonoidHomLequivNat_symm_apply, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, HasStrictFDerivAt.csin, DirectSum.component.of, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_symm, Polynomial.hasseDeriv_zero', LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, Matrix.separatingRight_toLinearMap₂'_iff, LinearMap.baseChange_smul, LinearIsometryEquiv.piLpCongrRight_symm, realPart_idem, MvPolynomial.one_def, ContinuousLinearMap.smulRight_one_eq_toSpanSingleton, PiTensorProduct.mapLMonoidHom_apply, Complex.ofRealCLM_coe, Algebra.Generators.H1Cotangent.δAux_mul, Complex.kahler, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, CliffordAlgebra.changeForm_comp_changeForm, CliffordAlgebra.mul_ι_mul_ι_of_isOrtho, MvPowerSeries.coeff_mul_monomial, ContinuousLinearMap.map_add_add, LinearMap.prod_comp, LinearMap.convMul_def, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, PiTensorProduct.isEmptyEquiv_apply_tprod, HasFDerivWithinAt.pow, Finsupp.restrictDom_apply, Lagrange.eval_interpolate_not_at_node', Complex.areaForm, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, QuadraticMap.sum_polar_sub_repr_sq, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, hasFDerivWithinAt_const, ModuleCat.forget₂PreservesColimitsOfSize, Module.nonempty_linearEquiv_of_finrank_eq_one, Matrix.det_smul_inv_mulVec_eq_cramer, UniformSpace.Completion.mapRingHom_id, Ideal.toCotangent_eq, hasFDerivAt_one, LinearMap.range_id, CStarModule.innerₛₗ_apply, Module.Flat.toAlgebra_injective, Submodule.mulMap_tmul, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, fderivWithin_fun_smul, Polynomial.derivWithin_aeval, Matrix.UnitaryGroup.toGL_mul, Module.End.smul_def, Module.Baer.ExtensionOfMaxAdjoin.extensionToFun_wd, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.analyticWithinAt, Finset.weightedVSubOfPoint_apply, PowerSeries.coeff_rescale, Submodule.comm_trans_lTensorOne, Profinite.NobelingProof.injective_πs', ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, AlgebraicGeometry.StructureSheaf.comap_id, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, MvPolynomial.scalarRTensor_apply_monomial_tmul, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, HasFDerivWithinAt.add, MvPolynomial.homogeneousComponent_eq_zero', QuadraticMap.canLift, Polynomial.derivative_intCast_mul, LinearMap.lTensor_sub, LinearMap.injective_iff_surjective_of_finrank_eq_finrank, LieModule.toEnd_pow_apply_map, Polynomial.toMatrix_sylvesterMap', LaurentPolynomial.comul_T, Module.basisUnique_repr_eq_zero_iff, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, DirectSum.coe_toModule_eq_coe_toAddMonoid, Matrix.toLinearMapRight'_mul, RCLike.ofRealLI_apply, eval_minpolyDiv_self, Algebra.normalizedTrace_surjective, LinearMap.IsPositive.ne_zero_iff, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, Submodule.exists_fg_le_eq_rTensor_inclusion, finsuppTensorFinsupp_apply, Subspace.instModuleDualFiniteDimensional, curveIntegrable_segment, Algebra.normalizedTrace_eq_of_finiteDimensional, hasFDerivAt_multiset_prod, Polynomial.disjoint_ker_aeval_of_isCoprime, TensorPower.cast_cast, SeparationQuotient.mkCLM_comp_outCLM, Representation.ofMulActionSelfAsModuleEquiv_symm_apply, Module.Basis.equivFun_symm_apply, TensorProduct.range_mapIncl, SkewPolynomial.monomial_add, LinearMap.isPositive_adjoint_comp_self, ProbabilityTheory.covarianceBilinDual_apply', AddEquiv.toIntLinearEquiv_toAddEquiv, Manifold.IsImmersionAt.map_target_subset_target, LinearMap.BilinForm.IsAlt.neg_eq, Rep.diagonalSuccIsoFree_inv_hom_single, Submodule.toLinearEquiv_orthogonalDecomposition_symm, LinearMap.BilinMap.polar_toQuadraticMap, OrthonormalBasis.repr_injective, PolynomialModule.smul_def, CoalgHom.coe_addMonoidHom_injective, LinearMap.ker_pi, LinearMap.isAdjointPair_iff_comp_eq_compl₂, LinearMap.IsPerfPair.bijective_left, hasFTaylorSeriesUpToOn_top_iff_right, MeasureTheory.charFunDual_apply, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, MonomialOrder.degree_monomial, CategoryTheory.Functor.coe_mapLinearMap, LinearIsometry.map_smul, Submodule.map_dualCoannihilator_le, IsBaseChange.finsuppPow, Module.End.mem_invtSubmodule, LinearMap.exact_zero_iff_surjective, Matrix.separatingRight_toLinearMap₂_iff, Matrix.cramer_transpose_row_self, LinearEquiv.coe_toLinearMap_flip, LinearIsometryEquiv.withLpProdComm_symm, Complex.ofRealLI_apply, CommRing.Pic.mk_dual, AdicCompletion.map_val_apply, PowerSeries.coeff_expand_mul, conformalAt_iff, Module.End.HasUnifEigenvector.pow_apply, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, Representation.repOfTprodIso_apply, LinearMap.GeneralLinearGroup.congrLinearEquiv_refl, NumberField.Units.fun_eq_repr, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, covBy_iff_quot_is_simple, LinearIsometry.one_def, Polynomial.derivative_C_mul, lift_rank_map_le, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, ModuleCat.freeHomEquiv_apply, norm_jacobiTheta₂_term_fderiv_ge, AffineSubspace.map_pointwise_vadd, Matrix.spectrum_toEuclideanLin, eval₂_minpolyDiv_self, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, LinearMap.rTensor_comm, ContinuousLinearMap.norm_inl_le_one, MeasureTheory.norm_condExpL2_le, IsLocalMaxOn.hasFDerivWithinAt_nonpos, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, TensorProduct.equivFinsuppOfBasisLeft_symm_apply, ProbabilityTheory.IsGaussian.integrable_dual, RootPairing.Hom.root_weightMap, ContinuousLinearEquiv.contDiff_comp_iff, addMonoidHomLequivInt_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, SchwartzMap.pairing_apply_apply, ModuleCat.forget₂AddCommGroup_preservesLimitsOfSize, InnerProductSpace.isIdempotentElem_rankOne_self, Submodule.tensorEquivSpan_apply_tmul, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, Polynomial.iterate_derivative_zero, IsBaseChange.basis_repr_comp_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, MeasureTheory.weightedSMul_apply, LinearMap.baseChange_comp, MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure, PiTensorProduct.ofDirectSumEquiv_tprod_lof, RootPairing.two_nsmul_reflection_eq_of_perm_eq, ContinuousLinearMap.comp_condExp_comm, Submodule.linearMap_eq_zero_iff_of_eq_span, LinearEquiv.coe_baseChange, Module.DualBases.basis_repr_symm_apply, Trivialization.continuousLinearMapAt_apply, Module.Basis.toDual_linearCombination_left, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, PowerSeries.catalanSeries_coeff, ApproximatesLinearOn.lipschitz, AlgHom.coe_addMonoidHom_injective, AddMonoidHom.toZModLinearMap_injective, Module.Basis.constr_comp, Polynomial.card_rootSet_le_derivative, LinearEquiv.congrRight_symm, PowerSeries.coeff_X_mul_largeSchroderSeries, realPart_ofReal, Module.Basis.constr_symm_apply, LinearMap.mapMatrixLinear_apply, Module.End.iterate_succ', LightCondensed.forget_obj_val_map, Submodule.comap_neg, geometric_hahn_banach_open_point, LinearMap.BilinForm.toMatrixAux_eq, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, Orientation.linearEquiv_det_rotation, PowerSeries.coeff_trunc, StrongDual.polarSubmodule_eq_setOf, Algebra.Extension.H1Cotangent.equiv_apply, Finsupp.sumFinsuppLEquivProdFinsupp_apply, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, ClosedSubmodule.mem_comap, PolynomialModule.eval_map, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', ContinuousLinearMap.isUniformEmbedding_restrictScalars, LieModule.trace_toEnd_eq_zero_of_mem_lcs, ContinuousLinearEquiv.coe_prodAssoc, Rep.resCoindAdjunction_counit_app_hom_hom, CliffordAlgebra.involute_prod_map_ι, Polynomial.derivative_mul, IsAdjoinRootMonic.coeff_apply, PowerSeries.trunc_mul_trunc, Module.Relations.Solution.surjective_π_iff_span_eq_top, RingHomSurjective.ids, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, Matrix.toLinearMap₂'_comp, Finsupp.supportedEquivFinsupp_symm_single, groupHomology.d₃₂_single, PiTensorProduct.lift_reindex_symm, Matrix.l2_opNorm_mulVec, DirectLimit.Module.of_f, Finset.weightedVSubOfPoint_insert, MeasureTheory.OuterMeasure.comap_map, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U, norm_iteratedFDerivWithin_one, Module.FaithfullyFlat.lTensor_injective_iff_injective, TopModuleCat.hom_zero_apply, RootPairing.Base.forall_mem_support_invtSubmodule_iff, kroneckerTMulAlgEquiv_symm_single_tmul, ImplicitFunctionData.isCompl_ker, LinearIsometry.coe_toLinearIsometryEquiv, ExteriorAlgebra.lift_symm_apply, Rep.coindToInd_of_support_subset_orbit, PiTensorProduct.map_reindex_symm, ContinuousLinearMap.hasDerivAtFilter, WithLp.coe_linearEquiv, fderivWithin_csinh, DoubleCentralizer.intCast_snd, RootPairing.root_coroot_two, Representation.finsupp_apply, ModuleCat.extendScalarsId_hom_app_one_tmul, MvPolynomial.X_pow_eq_monomial, LinearMap.toMatrix_apply', HasDerivAtFilter.comp_hasFDerivAtFilter, Polynomial.opRingEquiv_op_monomial, Polynomial.natDegree_monomial_le, DoubleCentralizer.range_toProdMulOpposite, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, Module.Flat.iff_rTensor_preserves_injective_linearMap, Module.Presentation.directSum_var, Submodule.re_inner_starProjection_eq_normSq, RCLike.conjCLE_norm, WeakSpace.map_apply, LinearMap.llcomp_apply, LinearMap.toMatrix₂_mul, LinearEquiv.det_trans, LinearMap.BilinForm.smul_left_of_tower, HasDerivWithinAt.complexToReal_fderiv', groupHomology.mapCycles₁_comp_apply, Orientation.kahler_comp_rightAngleRotation', groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, AlgHom.comp_toLinearMap, VectorField.fderiv_apply_lieBracket, ZMod.LFunction_one_sub, LinearMap.le_ker_iff_comp_subtype_eq_zero, MeasureTheory.inner_condExpL2_left_eq_right, Orientation.rotation_eq_self_iff, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, ContinuousMap.toLp_denseRange, AnalyticOnNhd.compContinuousLinearMap, LinearMap.entryLinearMap_comp_mapMatrix, AffineIsometryEquiv.linear_eq_linear_isometry, AddMonoidAlgebra.comul_single, Module.Basis.dualBasis_coord_toDualEquiv_apply, PowerSeries.trunc_X_pow_self_mul, Matrix.repr_toLin, FDRep.endRingEquiv_symm_comp_ρ, AdicCompletion.of_ofAlgEquiv_symm, LieModule.traceForm_eq_sum_genWeightSpaceOf, ZLattice.covolume_eq_det_inv, ContinuousAlgEquiv.toContinuousLinearMap_toContinuousLinearEquiv_eq, Lagrange.derivative_nodal, Module.Basis.constrL_basis, CliffordAlgebra.even.lift.aux_mul, ModuleCat.ofHom_comp, LocalizedModule.restrictScalars_map_eq, ContinuousLinearMap.precompUniformConvergenceCLM_apply, Representation.Coinvariants.mk_inv_tmul, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, Submodule.reflection_orthogonal_apply, Submodule.linearEquiv_of_le_sSup, PolynomialModule.map_smul, Submodule.linearProjOfIsCompl_apply_right, MvPowerSeries.coeff_pow, Module.forall_dual_apply_eq_zero_iff, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, Polynomial.monomial_mem_lifts, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, KaehlerDifferential.mvPolynomialBasis_repr_D_X, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, Submodule.prodEquivOfIsCompl_symm_apply_snd_eq_zero, LinearMap.exists_linearEquiv_eq_graph, AlternatingMap.constLinearEquivOfIsEmpty_apply, Polynomial.taylor_mul, RootPairing.Equiv.id_coweightMap_apply, ModuleCat.ι_coprodIsoDirectSum_hom_apply, LinearMap.fst_prod, Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity_of_ne_zero, Finsupp.linearCombination_id_surjective, Real.fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.tensorKer_tmul, LinearMap.toMatrixAlgEquiv_comp, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearIsometryEquiv.comp_fderivWithin, LinearMap.lTensor_rTensor_comp_assoc, LinearMap.det_mulLeft, TensorProduct.sum_tmul_basis_right_injective, ModuleCat.restrictScalarsComp'App_hom_apply, Subspace.dualLift_of_subtype, Submodule.mem_colon', LinearMap.IsPositive.re_inner_nonneg_right, Ideal.map_pi, Module.Invertible.free_iff_linearEquiv, ZMod.dft_even_iff, PiTensorProduct.reindex_reindex, RootPairing.Hom.comp_coweightMap_apply, PresheafOfModules.epi_iff_surjective, Pi.comul_comp_dFinsuppCoeFnLinearMap, Submodule.mulMap_one_right_eq, RootPairing.EmbeddedG2.shortAddLongRoot_shortRoot, Polynomial.sum_bernoulli, fderivWithin_fun_pow', Finset.affineCombination_sdiff_sub, LinearMap.BilinForm.isPosSemidef_iff, intervalIntegral.fderiv_integral_of_tendsto_ae, ContDiffAt.fderiv_right_succ, flip_innerSL_real, LinearMap.compRight_apply, LightCondensed.ihomPoints_symm_comp, toWeakSpaceCLM_bijective, ZMod.invDFT_apply, Submodule.starProjection_orthogonal', PiTensorProduct.subsingletonEquiv_symm_apply, Representation.asAlgebraHom_single, Trivialization.linearMapAt_symmₗ, Polynomial.C_mul_X_eq_monomial, Matrix.liftLinear_single, MulOpposite.coe_opLinearEquiv_symm, DoubleCentralizer.natCast_fst, skewAdjointLieSubalgebraEquiv_apply, LinearMap.IsSymmetric.im_inner_self_apply, Submodule.comap_op_mul, imaginaryPart_I_smul, ContinuousLinearMap.IsPositive.toLinearMap, Submodule.toLinearEquiv_orthogonalDecomposition, RootPairing.Equiv.coweightEquiv_comp_toLin, Continuous.convolution_integrand_fst, Pi.counit_coe_dFinsupp, RootPairing.Equiv.coweightEquiv_symm_coweightMap, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, traceForm_nondegenerate_tfae, ContinuousLinearEquiv.symm_toDiffeomorph, TensorProduct.piScalarRight_symm_algebraMap, ContDiffMapSupportedIn.structureMapCLM_apply, iteratedFDerivWithin_succ_eq_comp_right, ContinuousAffineMap.const_contLinear, LinearPMap.mk_apply, eventually_enorm_mfderivWithin_symm_extChartAt_lt, CategoryTheory.whiskering_linearCoyoneda, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, Algebra.trace_eq_of_ringEquiv, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, tangentMap_snd, iteratedDerivWithin_vcomp_two, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, Subspace.dualRestrict_comp_dualLift, PowerSeries.coeff_of_lt_order, MvPowerSeries.constantCoeff_subst, Orientation.areaForm_le, Projectivization.map_id, LinearMap.BilinForm.congr_apply, Rep.indToCoindAux_self, LinearEquiv.conj_trans, TensorAlgebra.toTrivSqZeroExt_ι, Representation.asGroupHom_apply, LieModule.traceForm_eq_sum_finrank_nsmul', LinearMap.mul_apply_apply, eval₂_minpolyDiv_of_eval₂_eq_zero, MvPolynomial.divMonomial_add_modMonomial, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, TensorProduct.AlgebraTensorModule.congr_symm, RootPairing.coreflection_image_eq, LinearMap.BilinForm.toMatrix_compRight, TensorProduct.enorm_comm, LinearMap.det_pi, TensorPower.cast_trans, innerSL_apply_apply, LieSubalgebra.mem_map_submodule, LinearMap.fst_comp_inr, CategoryTheory.InducedCategory.homLinearEquiv_apply, SpecialLinearGroup.coe_zpow, ModuleCat.AlternatingMap.postcomp_apply, ContinuousLinearMap.IsInvertible.surjective, fderiv_multiset_prod, RootPairing.rootSpan_dualAnnihilator_le_ker_rootForm, LinearEquiv.restrictScalars_symm_apply, LinearIsometryEquiv.fderivWithin, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerₛₗ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, HasFTaylorSeriesUpTo.hasFDerivAt, TensorProduct.AlgebraTensorModule.rid_tmul, HasFDerivAtFilter.fun_sum, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, LinearMap.continuousLinearMapClassOfFiniteDimensional, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, LinearMap.BilinMap.toQuadraticMap_add, Polynomial.hasseDeriv_one', SpecialLinearGroup.toLinearEquiv_symm_to_linearMap, Polynomial.derivative_comp_one_sub_X, ContMDiffWithinAt.mfderivWithin_const, Orientation.neg_rotation, SemimoduleCat.instReflectsIsomorphismsAddCommMonCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Matrix.transposeLinearEquiv_symm, Submodule.dualQuotEquivDualAnnihilator_apply, HasFDerivAtFilter.sub, PolynomialModule.comp_smul, Unitization.splitMul_apply, LinearPMap.neg_graph, TensorAlgebra.ι_comp_lift, LinearEquiv.domMulActCongrRight_symm_apply, ContinuousLinearMap.toBilinForm_apply, WittVector.IsocrystalHom.frob_equivariant, MvPolynomial.eval₂Hom_monomial, ProbabilityTheory.covarianceBilin_apply_eq_cov, LinearEquiv.congrQuadraticMap_symm, ProbabilityTheory.covarianceBilin_self, LinearEquiv.conj_apply_apply, Coalgebra.sum_map_tmul_counit_eq, DoubleCentralizer.nnnorm_def', Algebra.IsPushout.cancelBaseChange_tmul, Polynomial.derivative_pow_eq_zero, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, LinearMap.BilinForm.IsNonneg.nonneg, HasFDerivAt.fun_mul, LinearEquiv.skewSwap_symm_apply, TensorProduct.tensorTensorTensorComm_tmul, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, fderivWithin_zero_of_not_accPt, MvPolynomial.homogeneousComponent_of_mem, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, dist_iteratedFDerivWithin_one, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, PowerSeries.coeff_succ_mul_X, LinearMap.IsPosSemidef.add, Module.exists_dual_forall_apply_eq_one, LinearIndependent.linearCombination_repr, ContinuousMap.range_toLp, ModuleCat.linearIndependent_shortExact, exteriorPower.basis_repr_ne, TensorProduct.gradedComm_tmul_one, Submodule.orthogonalProjection_mem_subspace_eq_self, PolynomialModule.aeval_equivPolynomial, Profinite.NobelingProof.coe_πs, ContinuousLinearMap.IsPositive.inner_nonneg_right, Rep.coe_res_obj_ρ, TensorAlgebra.adjoin_range_ι, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', TensorProduct.AlgebraTensorModule.congr_symm_tmul, Algebra.Presentation.differentials.comm₂₃, Coalgebra.sum_tmul_counit_eq, Orientation.eq_rotation_self_iff_angle_eq_zero, MvPolynomial.homogeneousComponent_mem, DFinsupp.subtypeDomainLinearMap_apply, Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, Submodule.factor_mk, MvPowerSeries.coeff_monomial_mul, LinearMap.det_zero, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, LinearEquiv.conjAlgEquiv_symm_apply_apply, Matrix.toLinearMap₂_toMatrix₂, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, LinearMap.toMatrix_one, ModuleCat.monoidalClosed_uncurry, QuaternionAlgebra.imIₗ_apply, LinearMap.IsReflective.smul_coroot, QuotSMulTop.equivTensorQuot_naturality, IsometryEquiv.toRealLinearIsometryEquiv_apply, LieAlgebra.IsKilling.rootSystem_coroot_apply, Module.Basis.mk_repr, Polynomial.roots_monomial, mfderiv_comp, Prod.counit_comp_inr, MvPowerSeries.coeff_X_pow, LinearMap.submoduleComap_apply_coe, LinearMap.intrinsicStar_mulRight, ContinuousLinearMap.id_apply, MvPolynomial.support_monomial, HasFDerivWithinAt.hasLineDerivWithinAt, CliffordAlgebraDualNumber.equiv_symm_eps, LinearMap.IsReflective.apply_self_mul_coroot_apply, MeasureTheory.OuterMeasure.restrict_trim, ProbabilityTheory.uncenteredCovarianceBilin_apply, Finset.weightedVSubOfPoint_congr, MonoidAlgebra.antipode_single, TemperedDistribution.lineDerivOp_fourier_eq, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, Polynomial.aeval_iterate_derivative_of_ge, Module.Flat.ker_lTensor_eq, MvPolynomial.monomial_finsupp_sum_index, KaehlerDifferential.cotangentComplexBaseChange_tmul, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, SpecialLinearGroup.mem_center_iff_spec, TensorProduct.tensorTensorTensorComm_comp_map, Rep.diagonalHomEquiv_symm_apply, Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span, cross_cross, Matrix.separatingRight_toBilin_iff, Ideal.span_pow_eq_map_homogeneousSubmodule, Polynomial.derivative_expand, TensorProduct.range_map, FormalMultilinearSeries.derivSeries_coeff_one, Polynomial.derivative_sum, VonNeumannAlgebra.ext_iff, Polynomial.isCoveringMapOn_eval, Complex.ofRealCLM_norm, IsBaseChange.of_fintype_basis_eq, Submodule.starProjection_add_starProjection_orthogonal, MvPolynomial.mul_def, FunOnFinite.linearMap_comp, Matrix.spectrum_toLpLin, ExteriorAlgebra.ι_eq_zero_iff, ContinuousLinearEquiv.coe_comp_coe_symm, instIsZLatticeComap, Finsupp.linearEquivFunOnFinite_symm_coe, mdifferentiableOn_symm_coordChangeL, Complex.reLm_coe, Polynomial.derivative_pow_succ, ContinuousLinearMap.opNorm_lsmul_apply_le, Module.Basis.repr_isUnitSMul, LinearMap.prodMap_add, LinearEquiv.piCongrRight_trans, Submodule.comap_op_pow, rotation_injective, LinearMap.ofIsCompl_smul, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, LinearEquiv.symm_comp, CondensedMod.isDiscrete_tfae, RootPairing.InvariantForm.pairing_mul_eq_pairing_mul_swap, IsSymmetricAlgebra.equiv_apply, sum_smul_minpolyDiv_eq_X_pow, Polynomial.derivative_ofNat, ContinuousLinearMap.coprod_comp_prodComm, SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, Submodule.quotDualCoannihilatorToDual_apply, IsSMulRegular.linearMap_subsingleton_of_mem_annihilator, SchwartzMap.bilinLeftCLM_apply, ContinuousLinearMap.intCast_apply, LinearIndependent.of_isLocalizedModule_of_isRegular, Ideal.span_eq_map_homogeneousSubmodule, HasDerivAt.comp_hasFDerivAt_of_eq, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, Module.Dual.eval_comp_comp_evalEquiv_eq, Submodule.injective_inclusionSpan, LinearEquiv.symm_mem_dilatransvections_iff, IsConformalMap.is_complex_or_conj_linear, fderiv_continuousAlternatingMap_apply_const, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_apply, Polynomial.monomial_one_one_eq_X, IsHilbertSum.linearIsometryEquiv_symm_apply, ContinuousLinearMap.coe_restrictScalars, SmoothBumpCovering.exists_immersion_euclidean, ContinuousLinearMap.coprodEquiv_apply, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, LinearMap.toAddMonoidHom_mulLeft, CategoryTheory.Linear.comp_apply, LinearMap.BilinForm.toMatrix'_symm, LinearEquiv.map_mem_invtSubmodule_conj_iff, Coalgebra.coassoc_symm_apply, Module.End.isFinitelySemisimple_sub_algebraMap_iff, ContinuousLinearMap.cpolynomialAt, ExteriorAlgebra.map_comp_map, QuadraticMap.polarBilin_prod, Matrix.cramer_row_self, Span.repr_def, LinearMap.mem_isPairSelfAdjointSubmodule, AffineMap.hasDerivWithinAt, Polynomial.Splits.eval_derivative, Submodule.dualPairing_apply, Submodule.starProjection_singleton, MeasureTheory.VectorMeasure.mapₗ_apply, IsLocalization.algEquiv_apply, NonUnitalAlgHom.coe_lmul_eq_mul, LeftInvariantDerivation.left_invariant, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, mfderiv_comp_apply_of_eq, ContinuousLinearMap.comp_condExp_add_const_comm, Matrix.toLin_mul_apply, IsLocalizedModule.liftOfLE_comp, LinearMap.prodMap_apply, Polynomial.derivative_smul, LinearMap.tensorEqLocusEquiv_apply, toMatrix_distrib_mul_action_toLinearMap, groupCohomology.coe_mapCocycles₁, LinearMap.domRestrict'_apply, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, PowerSeries.gaussNorm_monomial, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Module.dualMap_dualMap_eq_iff, groupHomology.mem_cycles₂_iff, AlgebraicGeometry.StructureSheaf.comap_id', ModuleCat.Iso.homCongr_eq_arrowCongr, MvPowerSeries.X_pow_eq, Complex.conjLIE_apply, LinearMap.baseChange_baseChange, ContinuousLinearMap.measurable, Polynomial.Splits.monomial, LieDerivation.coe_sub_linearMap, AlgEquiv.linearEquivConj_mulLeft, curveIntegralFun_smul, PiToModule.fromEnd_apply, Module.Basis.exists_opNorm_le, ModuleCat.CoextendScalars.smul_apply', RootPairing.range_polarization_domRestrict_le_span_coroot, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, Localization.algEquiv_apply, MeasureTheory.charFun_toDual_symm_eq_charFunDual, RootPairing.finrank_range_polarization_eq_finrank_span_coroot, WithLp.sndL_apply, TensorPower.gMul_eq_coe_linearMap, hasStrictFDerivAt_iff_isLittleOTVS, CStarMatrix.mapₗ_reindexₐ, LinearAlgebra.FreeProduct.mul_injections, RatFunc.laurent_algebraMap, Polynomial.iterate_derivative_eq_factorial_smul_sum, ContinuousAlternatingMap.compContinuousLinearMapₗ_apply, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, LinearMap.lTensor_id_apply, LinearMap.BilinForm.IsRefl.groupSMul, LinearMap.BilinForm.toMatrix'_apply, Module.Basis.dual_rank_eq, TensorProduct.map_comp_comm_eq, OrthogonalFamily.orthonormal_sigma_orthonormal, ContinuousLinearMap.coe_restrictScalarsₗ, Polynomial.iterate_derivative_X_add_pow, Finsupp.sum_smul_index_linearMap', Algebra.Extension.formallySmooth_iff_split_injection, exposed_point_def, LinearMap.BilinMap.toQuadraticMapAddMonoidHom_apply, linearIndependent_iff_injective_finsuppLinearCombination, ContinuousAlternatingMap.piLIE_apply_apply, groupCohomology.d₁₂_hom_apply, ContinuousLinearMap.applySMulCommClass', ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, Module.FaithfullyFlat.lTensor_exact_iff_exact, fderivWithin_fderivWithin, Representation.IntertwiningMap.toLinearMap_injective, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, Module.End.id_pow, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, AdicCompletion.incl_apply, curveIntegrable_fun_neg_iff, AdicCompletion.map_ext'_iff, Submodule.exists_le_ker_of_lt_top, AdicCompletion.ofTensorProduct_surjective_of_finite, MeasureTheory.Measure.comapₗ_eq_comap, RootPairing.Hom.root_weightMap_apply, LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero', MvPolynomial.scalarRTensor_apply_X_tmul_apply, ContinuousLinearEquiv.coe_toDiffeomorph_symm, ContinuousLinearEquiv.prodProdProdComm_symm, DFinsupp.mapRange.linearMap_comp, Submodule.reflection_symm, LinearEquiv.congrRight₂_apply, PresheafOfModules.pushforward_map_app_apply, ZMod.dft_mul_const, Shrink.linearEquiv_symm_apply, ContinuousLinearMap.comp_inl_add_comp_inr, Orientation.map_symm, ULift.moduleEquiv_symm_apply, cross_self, eval_minpolyDiv_of_aeval_eq_zero, Module.Basis.mk_coord_apply_eq, CurveIntegrable.zero, Polynomial.derivative_X, fderiv_comp_deriv, CliffordAlgebra.contractRight_mul_ι, groupCohomology.coboundariesToCocycles₁_apply, SpecialLinearGroup.mem_center_iff, Polynomial.sumIDeriv_map, Module.FaithfullyFlat.lTensor_bijective_iff_bijective, Matrix.Nondegenerate.toLinearMap₂, rTensor_injective_iff_lcomp_surjective, MvPolynomial.smul_monomial, Representation.directSum_apply, Algebra.Extension.h1Cotangentι_injective, TensorProduct.gradedMul_assoc, CliffordAlgebra.op_reverse, curveIntegrable_smul_iff, Submodule.quotientPi_aux.map_smul, RootPairing.range_weylGroup_coweightHom, TensorProduct.toLinearEquiv_lidIsometry, contractLeft_assoc_coevaluation, LinearMap.inl_injective, Module.Basis.prod_repr_inl, Lagrange.eval_interpolate_not_at_node, AffineBasis.linear_eq_sumCoords, MonoidAlgebra.mapDomainRingHom_id, WithLp.prodContinuousLinearEquiv_symm_apply, LinearMap.toContinuousLinearMap₁_coe, RootPairing.Hom.coweightMap_mul, ContinuousLinearMap.isometry_mul_flip, Matrix.kroneckerTMul_assoc', LinearEquiv.cast_symm_apply, Module.Basis.flag_le_ker_dual, LieModule.lowerCentralSeries_one_inf_center_le_ker_traceForm, Polynomial.mirror_monomial, BoundedContinuousFunction.evalCLM_apply, ContinuousMultilinearMap.piLinearEquiv_symm_apply, Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff, AnalyticOnNhd.eval_linearMap', FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, HasStrictFDerivAt.mul', CliffordAlgebra.reverse_involute_commute, LinearMap.compPMap_apply, Module.AEval.of_symm_smul, inner_gradientWithin_right, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same, Matrix.intrinsicStar_toLin', fderiv_fun_pow, LieModule.isNilpotent_toEnd_genWeightSpace_zero, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, LinearMap.le_rank_iff_exists_linearIndependent, Module.Basis.ofZLatticeComap_apply, Polynomial.dvd_iterate_derivative_pow, QuaternionAlgebra.imKₗ_apply, Submodule.le_linearEquiv_of_sSup_eq_top, IsLocalizedModule.liftOfLE_mk', ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, PresheafOfModules.sections_property, HasStrictFDerivAt.comp_hasStrictDerivAt, Ideal.range_cotangentToQuotientSquare, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, Submodule.FG.lTensor.directedSystem, Polynomial.coeffs_monomial, HasFDerivAtFilter.const_sub, LinearMap.coe_toContinuousLinearMap', HasFDerivWithinAt.linear_multilinear_comp, KaehlerDifferential.polynomialEquiv_D, LinearMap.BilinMap.toQuadraticMap_zero, SemimoduleCat.Iso.homCongr_eq_arrowCongr, iteratedFDerivWithin_succ_eq_comp_left, ContinuousLinearMap.isPositive_natCast, minpoly_algHom_toLinearMap, Polynomial.ofFn_eq_sum_monomial, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, MvPolynomial.bind₂_C_left, hasStrictFDerivAt_exp_smul_const_of_mem_ball', Module.Basis.coe_mkFinConsOfLE, Matrix.coe_mulVecLin, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, linearEquivIsoModuleIso_hom, ContinuousLinearMap.coe_snd, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, LinearEquiv.dualMap_trans, Submodule.starProjection_comp_starProjection_eq_zero_iff, Module.Basis.coe_dualBasis, FDerivMeasurableAux.differentiable_set_subset_D, Matrix.mulVecLin_apply, Submodule.comap_le_comap_smul, rank_map_le, PowerSeries.coeff_ne_zero_C, Submodule.subtypeₗᵢ_toContinuousLinearMap, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, CStarModule.innerSL_apply, IsLocalizedModule.iso_symm_apply, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, QuadraticMap.toBilinHom_apply, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, continuous_equivFun_basis, ExteriorAlgebra.liftAlternating_ι_mul, TensorProduct.AlgebraTensorModule.rightComm_symm_tmul, LinearMap.tensorKer_coe, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv_symm, LinearIsometryEquiv.conjStarAlgEquiv_apply, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, Module.Relations.Solution.surjective_fromQuotient_iff_surjective_π, PointedCone.comap_comap, Real.vector_fourierIntegral_eq_integral_exp_smul, RootPairing.Hom.id_coweightMap_apply, HasFDerivAt.le_of_lipschitzOn, IsAdjoinRoot.lift_self, Algebra.IsPushout.cancelBaseChange_symm_tmul, RootPairing.coPolarization_apply_eq_zero_iff, PerfectionMap.id, PresheafOfModules.toSheafify_app_apply', Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, LinearMap.toMatrixOrthonormal_reindex, contDiff_one_iff_fderiv, Polynomial.abc, LinearMap.toMatrixAlgEquiv_toLinAlgEquiv, IsLocalization.instIsLocalizedModuleTensorProductMap, LinearMap.lift_rank_comp_le_right, MeasureTheory.ConvolutionExistsAt.integrable, Fintype.linearIndependent_iff', QuadraticMap.add_linMulLin, HasStrictFDerivAt.pow, HahnSeries.embDomainLinearMap_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, CommSemiRingCat.hom_id, Algebra.TensorProduct.piRightHom_mul, Module.le_rank_iff_exists_linearMap, HVertexOperator.coeff_isPWOsupport, LinearMap.intrinsicStar_toSpanSingleton, LinearMap.charpoly_nilpotent_tfae, Finsupp.linearCombination_zero_apply, id_apply, QuadraticMap.associated_eq_self_apply, isIsotypicOfType_submodule_iff, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, QuadraticMap.toMatrix'_comp, Representation.IntertwiningMap.coe_mul, LinearMap.trace_mul_cycle, Module.End.mul_eq_comp, ProbabilityTheory.covarianceOperator_apply, LinearEquiv.piFinTwo_symm_apply, BoundedContinuousFunction.toContinuousMapLinearMap_apply, fderivWithin_sinh, Module.exists_smul_eq_zero_and_mk_eq, LinearMap.separatingRight_iff_det_ne_zero, algebraMapCLM_coe, Submodule.val_mulMap'_tmul, ContDiffAt.laplacian_CLM_comp_left, TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensor, LinearMap.isUnit_iff_range_eq_top, Matrix.GeneralLinearGroup.coe_toLin, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, HasFDerivWithinAt.comp_of_tendsto, Finset.weightedVSub_apply_const, CoalgEquiv.left_inv, LinearEquiv.conjAlgEquiv_ext_iff', CommRing.Pic.mk_eq_mk_iff, LinearMap.lTensor_smul, LinearMap.fst_surjective, ContinuousAlternatingMap.toAlternatingMapLinear_apply, Module.Basis.repr_self_apply, TestFunction.continuous_iff_continuous_comp, RootPairing.coroot'In_rootSpanMem_eq_pairingIn, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, HasStrictFDerivAt.const_mul, LinearMap.ker_localizedMap_eq_localized'_ker, Polynomial.Splits.eval_root_derivative, exteriorPower.alternatingMapLinearEquiv_ιMulti, Algebra.normalizedTrace_comp_algHom, ModuleCat.forget_preservesEpimorphisms, ContinuousLinearMap.smulRight_one_pow, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, PresheafOfModules.Derivation.d_map, TensorProduct.directSum_lof_tmul_lof, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, LinearEquiv.coe_inv, IsLocalizedModule.iso_apply_mk, KaehlerDifferential.kerToTensor_apply, RatFunc.laurent_div, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, Submodule.coe_subtypeL', InnerProductSpace.inner_left_rankOne_apply, Finsupp.mem_span_iff_linearCombination, DirectSum.lequivCongrLeft_apply, star_dotProduct_toMatrix₂_mulVec, HasFDerivWithinAt.fst, TestFunction.toBoundedContinuousFunctionCLM_apply, isStablyFiniteRing_iff_injective_of_surjective, RootPairing.root_coroot_eq_pairing, LocallyConstant.congrRightₗ_symm_apply_apply, IsLocalFrameOn.coeff_apply_of_mem, SpecialLinearGroup.coe_one, IsBaseChange.linearMapLeftRightHom_comp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange, ContinuousLinearEquiv.hasTemperateGrowth, QuadraticModuleCat.forget₂_map_associator_inv, ContinuousLinearMap.HasLeftInverse.leftInverse_leftInverse, ContinuousLinearMap.isInvertible_comp_equiv, HasFDerivAt.finset_prod, coe_monoidHom_id, LinearMap.comp_id_fgModuleCat, AffineMap.slope_comp, SchwartzMap.fderivCLM_apply, Subspace.dualAnnihilator_dualAnnihilator_eq, Finset.weightedVSubOfPoint_indicator_subset, MultilinearMap.currySumEquiv_apply, selfAdjointPart_comp_subtype_skewAdjoint, setBasisOfLinearIndependentOfCardEqFinrank_repr_apply, IsSemisimpleRing.exists_linearEquiv_ideal_of_isSimpleModule, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, MvPowerSeries.monomial_mem_nonzeroDivisors, LocallyConstant.toContinuousMapLinearMap_apply, Algebra.Presentation.differentials.hom₁_single, Module.End.intCast_apply, Profinite.NobelingProof.Products.max_eq_eval, Submodule.norm_starProjection_apply_le, LocalizedModule.divBy_apply, ContinuousLinearMap.norm_extendTo𝕜, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, IsLocalMax.fderiv_eq_zero, ContinuousLinearMap.contMDiff, TensorProduct.AlgebraTensorModule.lTensor_id, ContinuousLinearMap.mdifferentiable, HasStrictFDerivAt.fun_sum, LinearIsometry.id_toContinuousLinearMap, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, LinearMap.BilinForm.linMulLin_comp, Pretrivialization.continuousLinearMap_symm_apply', HasFDerivAt.norm_sq, TensorProduct.quotientTensorQuotientEquiv_symm_apply_mk_tmul, VectorBundleCore.coordChange_self, skewAdjointLieSubalgebraEquiv_symm_apply, ContinuousAlternatingMap.curryLeft_smul, Algebra.Generators.exists_presentation_of_basis_cotangent, LinearMap.nondegenerate_of_det_ne_zero, Submodule.iSup_map_single_le, fderiv_const_smul_field, range_vecMulLinear, LinearIsometry.map_starProjection', Pi.comul_comp_single, Bialgebra.counitBialgHom_apply, instNontrivialLinearMapId, zero_prodMap_dualTensorHom, LinearMap.sum_repr_mul_repr_mulₛₗ, SemimoduleCat.hom_zsmul, LinearMap.mul'_comp_comm, Polynomial.derivative_monomial, cfcL_apply, Ideal.mem_toCotangent_ker, TensorProduct.AlgebraTensorModule.rTensor_one, NumberField.mixedEmbedding.commMap_apply_of_isComplex, ContinuousLinearMap.IsInvertible.inverse_comp_of_right, innerₛₗ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, LinearMap.ringLmapEquivSelf_symm_apply, Matrix.Represents.smul, groupCohomology.cocycles₂.d₂₃_apply, TensorAlgebra.ι_def, Module.Basis.equiv_apply, LinearIsometryEquiv.coe_toAffineIsometryEquiv, DoubleCentralizer.pow_snd, LinearMap.lTensor_surj_iff_rTensor_surj, LinearMap.liftBaseChange_one_tmul, ProperCone.mem_map, groupCohomology.d₀₁_hom_apply, OrthonormalBasis.repr_self, RootPairing.self_comp_coPolarization_eq_corootForm, QuadraticMap.associated_rightInverse, Polynomial.aeval_sumIDeriv, Representation.ofMulAction_apply, geometric_hahn_banach_compact_closed, ContDiffAt.continuousAt_fderiv, fderiv_fun_pow', DirectSum.lmap_apply, Matrix.toBilin_symm, AddMonoidHom.toRatLinearMap_injective, Rep.linearization_single, LinearEquiv.dilatransvections_pow_mono, LinearMap.spectrum_toMatrix', LinearMap.iSup_range_single, Profinite.NobelingProof.Products.eval_πs, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd, LieModule.trace_toEnd_genWeightSpace, Real.integrable_prod_sub, Bialgebra.counitAlgHom_apply, HasFDerivWithinAt.csin, OrthogonalFamily.norm_sq_diff_sum, Polynomial.sumIDeriv_C, Polynomial.Chebyshev.T_derivative_eq_U, Real.smul_map_diagonal_volume_pi, Algebra.traceMatrix_apply, DFinsupp.mapRange.linearEquiv_trans, SemimoduleCat.hom_nsmul, MvPowerSeries.coeff_mul_right_one_sub_of_lt_weightedOrder, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, ContinuousLinearEquiv.comp_hasFDerivAt_iff, ContinuousLinearMap.eq_adjoint_iff, ContinuousLinearMap.hasFDerivAt, fderivWithin_intCast, Polynomial.coeff_taylor_natDegree, RootPairing.span_coroot'_eq_top, groupHomology.d₃₂_single_one_thd, LinearMap.mulLeft_zero_eq_zero, Submodule.starProjection_tendsto_self, ContDiffAt.fderiv_succ, Orientation.volumeForm_map, rotation_apply, toMatrix_rotation, LinearIsometryEquiv.piLpCongrRight_apply, ContinuousLinearMap.IsInvertible.inverse_comp_of_left, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, LinearMap.BilinForm.sum_right, ModuleCat.hom_surjective, FourierTransform.fourierEquiv_apply, LinearMap.eventually_iSup_ker_pow_eq, SchwartzMap.toLpCLM_apply, ContinuousLinearMap.single_apply, LinearMap.separatingRight_congr_iff, DirectSum.lmap_comp, ContinuousLinearMap.toSpanSingleton_apply, LinearMap.IsSymmetric.directSum_decompose_apply, LinearMap.rTensor_id_apply, Submodule.comap_fst, Module.eval_apply_injective, AlgHom.mulLeftRightMatrix.inv_comp, Submodule.dualAnnihilator_map_dualMap_le, LinearEquiv.rTensor_mul, Derivation.linearEquiv_coe_to_linearMap_comp, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, LieAlgebra.IsKilling.ker_traceForm_eq_bot_of_isCartanSubalgebra, IsSelfAdjoint.selfAdjointPart_apply, le_comap_range_lTensor, HasFDerivAt.continuousMultilinear_apply_const, Submodule.dualCopairing_eq, HasFDerivWithinAt.continuousAlternatingMap_apply, ContinuousLinearMap.IsPositive.smul_of_nonneg, InnerProductSpace.rankOne_apply, Matrix.diagLinearMap_apply, LinearMap.polar_singleton, Matrix.diagonalLinearMap_apply, LieModule.shiftedGenWeightSpace.toEnd_eq, Unitary.coe_linearIsometryEquiv_apply, ModuleCat.hom_tensorHom, Ideal.finsuppTotal_apply_eq_of_fintype, ConcaveOn.comp_linearMap, ContinuousLinearEquiv.map_smul, ContinuousLinearMap.coe_toContinuousLinearEquivOfDetNeZero, groupHomology.isoCycles₁_inv_comp_iCycles_apply, Submodule.reflection_singleton_apply, Polynomial.aeval_iterate_derivative_self, StarModule.decomposeProdAdjointL_apply, HasFDerivAt.of_notMem_tsupport, HasFTaylorSeriesUpToOn.zero_eq', KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, fderiv_sum, strongRankCondition_iff_forall_not_injective, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, RootPairing.RootPositiveForm.zero_lt_posForm_iff, QuotSMulTop.equivTensorQuot_naturality_mk, RootPairing.toLinearMap_apply_CoPolarization, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, LinearMap.BilinForm.ext_iff_of_isSymm, LieDerivation.inner_apply_apply, HarmonicAt.analyticAt_complex_partial, Submodule.IsCompl.projection_apply_left, IsLocalRing.map_mkQ_eq, dot_cross_self, ModuleCat.forget₂_addCommGrp_essSurj, surjective_of_nonzero_of_finrank_eq_one, ContinuousLinearMap.toSpanSingleton_apply_one, groupCohomology.map_H0Iso_hom_f_apply, NormedSpace.Dual.toWeakDual_continuous, MeasureTheory.Lp.compMeasurePreservingₗ_apply, LieModule.Cohomology.twoCochain_alt, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, groupCohomology.d₁₂_comp_d₂₃_apply, Module.endTensorEndAlgHom_apply, PointedCone.coe_map, Matrix.toLpLin_mul_same, HasFDerivWithinAt.const_mul, groupCohomology.H0IsoOfIsTrivial_inv_apply, Polynomial.toFinsupp_monomial, LinearMap.mem_skewAdjointSubmodule, Submodule.quotDualCoannihilatorToDual_nondegenerate, MeasureTheory.weightedSMul_nonneg, CliffordAlgebra.toProd_ι_tmul_one, cfcₙ_eq_cfcₙL_mkD, fderiv_ofNat, PresheafOfModules.congr_map_apply, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, RootPairing.Hom.weight_coweight_transpose, Polynomial.coe_monomial, ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, TensorProduct.coe_directSumRight', Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity, ContinuousLinearEquiv.contDiffAt_comp_iff, Submodule.quotEquivOfEqBot_symm_apply, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective, LinearMap.ker_restrictScalars, Module.DualBases.coe_dualBasis, ContinuousLinearMap.precompL_apply, CliffordAlgebra.changeForm_self_apply, DoubleCentralizer.nnnorm_snd, Orientation.inner_rightAngleRotation_swap', PowerSeries.aeval_eq_sum, PresheafOfModules.freeYonedaEquiv_symm_app, Algebra.normalizedTrace_algebraMap, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom, Representation.apply_sub_id_partialSum_eq, Rep.finsuppToCoinvariantsTensorFree_single, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, Submodule.mem_dualAnnihilator, MulOpposite.coe_opLinearEquiv_symm_addEquiv, PolyEquivTensor.toFunAlgHom_apply_tmul, groupCohomology.eq_d₂₃_comp_inv_apply, PiTensorProduct.mul_assoc, QuadraticAlgebra.linearEquivTuple_apply, HasStrictFDerivAt.star, PolynomialLaw.exists_lift', HahnSeries.SummableFamily.lsum_apply, LinearMap.toMatrix_baseChange, OrthonormalBasis.measurePreserving_repr, groupCohomology.eq_d₁₂_comp_inv_apply, Submodule.reflection_apply, LinearMap.isPosSemidef_def, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, curveIntegralFun_segment, Polynomial.eval₂_id, Coalgebra.sum_counit_tmul_eq, Finset.weightedVSub_map, Representation.asAlgebraHom_def, fderivWithin_zero, Module.Presentation.cokernel_relation, PresheafOfModules.restrictScalarsObj_map, RCLike.reCLM_norm, SemimoduleCat.hom_inv_rightUnitor, PolynomialLaw.toFun_eq_rTensor_φ_toFun', QuadraticMap.linMulLin_apply, RCLike.geometric_hahn_banach_closed_point, RootPairing.toPerfPair_comp_root, Submodule.dualAnnihilator_eq_top_iff, groupHomology.chains₁ToCoinvariantsKer_surjective, TensorProduct.adjoint_map, MeasureTheory.OuterMeasure.comap_iInf, curveIntegral_neg, LinearMap.GeneralLinearGroup.generalLinearEquiv_to_linearMap, LinearMap.IsContPerfPair.bijective_left, ContinuousAlgEquiv.toContinuousLinearEquiv_symm, LinearEquiv.conj_comp, ContinuousLinearMap.HasLeftInverse.comp_continuousLinearEquivalence, HasFDerivAt.sub, Algebra.trace_eq_of_algEquiv, VectorBundleCore.contMDiffOn_coordChange, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, mfderiv_comp_of_eq, LinearEquiv.domMulActCongrRight_apply, Rep.coinvariantsTensorFreeLEquiv_symm_apply, linearIndependent_iff_ker, LinearEquiv.piCurry_apply, TensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse, CliffordAlgebra.contractRight_comm, adjoin_monomial_eq_reesAlgebra, InnerProductSpace.gramSchmidt_def, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, LinearMap.submoduleMap_coe_apply, Orientation.map_eq_neg_iff_det_neg, TrivSqZeroExt.map_inr, LinearMap.rTensor_comp_lTensor, HasFDerivAt.star, Matrix.coe_vecMulLinear, Module.End.mem_invtSubmodule_iff_mapsTo, LinearEquiv.toModuleIso_inv, LinearMap.coprod_zero_right, CliffordAlgebra.EquivEven.reverse_e0, CStarMatrix.toCLM_injective, Pi.counit_comp_finsuppLcoeFun, enorm_fderiv_norm_rpow_le, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, ContinuousLinearMap.isPositive_self_comp_adjoint, MvPolynomial.monomial_zero, LinearMap.rTensor_comp_map, AffineSubspace.linear_topEquiv, Polynomial.monomial_mul_C, CommRingCat.ofHom_id, ContinuousLinearMap.hasFPowerSeriesAt, LinearMap.trace_eq_matrix_trace_of_finset, LinearMap.adjoint_toContinuousLinearMap, Polynomial.X_pow_eq_monomial, Finsupp.curryLinearEquiv_symm_apply_apply, fderivWithin_const_sub, Matrix.SeparatingLeft.toLinearMap₂', Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, LinearIsometryEquiv.coe_neg, LinearMap.rTensor_comp_flip_mk, Submodule.toLinearPMap_range, TensorProduct.dualDistrib_apply_comm, LinearMap.BilinForm.IsAlt.eq_of_add_add_eq_zero, Submodule.coe_dualCoannihilator_span, Finsupp.llift_apply, ExteriorAlgebra.liftAlternating_comp, Unitary.linearIsometryEquiv_coe_apply, Representation.Coinvariants.mk_tmul_inv, LinearMap.IsSymm.ortho_comm, Algebra.isIntegral_trace, LieHom.quotKerEquivRange_toFun, MvPolynomial.eval₂_id, SeparatingDual.exists_eq_one, LinearMap.iInf_ker_proj, LinearEquiv.conj_refl, CharacterModule.curry_apply_apply, hasStrictFDerivAt_pi', HasFDerivAtFilter.neg, fderiv_eq_deriv_mul, Submodule.starProjection_inner_eq_zero, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, LinearEquiv.coe_lTensor, Matrix.sum_cramer, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, ContinuousLinearMap.toSesqForm_apply_coe, coe_algebraMapCLM, Finsupp.linearCombination_smul, ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape, finrank_algHom, signedDist_linear_apply_apply, mem_vectorSpan_iff_eq_weightedVSub, Algebra.algebraMap_self, RootPairing.mapsTo_reflection_root, HasFDerivWithinAt.fun_const_smul, SpecialLinearGroup.mem_range_toGeneralLinearGroup_iff, Module.Basis.toDualEquiv_apply, TensorProduct.map₂_eq_range_lift_comp_mapIncl, Module.End.mapsTo_genEigenspace_of_comm, CliffordAlgebra.changeFormAux_changeFormAux, ModuleCat.forget_reflectsLimitsOfSize, HasStrictFDerivAt.const_smul, hasStrictFDerivAt_natCast, Fintype.bilinearCombination_apply_single, HasFPowerSeriesWithinOnBall.fderivWithin, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, LinearMap.BilinForm.nondegenerate_toMatrix_iff, Matrix.derivative_det_one_add_X_smul, LinearMap.coe_inr, IsPRadical.of_id, inTangentCoordinates_eq_mfderiv_comp, FormalMultilinearSeries.radius_compNeg, LinearMap.toMatrixₛₗ₂'_symm, hasFDerivAtFilter_ofNat, IsGroupLikeElem.antipode_antipode, PiLp.coe_continuousLinearEquiv, hasFDerivAtFilter_zero, Ideal.range_mul', PositiveLinearMap.coe_toLinearMap, Submodule.biSup_comap_subtype_eq_top, Module.FaithfullyFlat.iff_zero_iff_rTensor_zero, HasFDerivAt.multilinear_comp, BoxIntegral.hasIntegral_GP_pderiv, CliffordAlgebra.ι_mul_ι_comm, ContinuousMultilinearMap.linearDeriv_apply, SchwartzMap.integral_bilin_fourierIntegral_eq, Module.equiv_directSum_of_isTorsion, PowerSeries.binomialSeries_coeff, PointedCone.subset_dual_dual, LinearMap.isSymm_iff_eq_flip, RootPairing.root'_coroot_eq_pairing, dotProductEquiv_apply_apply, LinearMap.rank_diagonal, LinearPMap.adjointAux_unique, LinearMap.ker_localizedMap_eq_localized₀_ker, QuotSMulTop.map_comp_mkQ, ContinuousAffineMap.decomp, Polynomial.derivative_rootMultiplicity_of_root, RootPairing.injOn_dualMap_subtype_span_root_coroot, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, AlgEquiv.pow_toLinearMap, DFinsupp.mapRange.linearEquiv_symm, LinearIsometryEquiv.adjoint_eq_symm, SemimoduleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, NumberField.mixedEmbedding.negAt_apply_snd, TensorProduct.directLimitRight_tmul_of, fderivWithin_ccosh, Ideal.finsuppTotal_apply, ContinuousAlternatingMap.toAlternatingMap_curryLeft, RootPairing.disjoint_corootSpan_ker_corootForm, TensorProduct.flip_mk_surjective, LinearMap.rTensor_tmul, Orientation.neg_rotation_neg_pi_div_two, LinearMap.separatingRight_toMatrix₂'_iff, Matrix.toEuclideanLin_apply, TensorProduct.exists_finite_submodule_of_finite', LieSubmodule.Quotient.toEnd_comp_mk', PiTensorProduct.map_comp, Submodule.biSup_eq_range_dfinsupp_lsum, Rep.resCoindAdjunction_unit_app_hom_hom, CliffordAlgebra.changeForm.add_proof, Polynomial.taylor_injective, HasFDerivWithinAt.mul, groupCohomology.mem_cocycles₁_def, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, Polynomial.iterate_derivative_mul_X, Algebra.toMatrix_lmul_eq, RootPairing.Equiv.weightHom_toLinearMap, NormedSpace.isClosed_polar, IsIsotypic.submodule_linearEquiv_fun, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousLinearMap.finiteDimensional, LieModule.traceForm_eq_zero_of_isNilpotent, LinearIsometryEquiv.trans_smul, MeasureTheory.charFunDual_eq_charFun_map_one, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, hasFDerivWithinAt_pi', TensorProduct.tensorQuotEquivQuotSMul_comp_mkQ_lTensor, LinearMap.toMatrixAlgEquiv'_id, fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, isAdjointPair_toLinearMap₂, IsHilbertSum.hasSum_linearIsometryEquiv_symm, HahnSeries.single.linearMap_apply, MvPowerSeries.monomial_mem_nonzeroDivisorsLeft, LinearEquiv.congrLeft_symm_apply, ContinuousLinearMap.opNorm_mul, LinearEquiv.conjAlgEquiv_apply, Submodule.IsOrtho.map_iff, CliffordAlgebra.ι_sq_scalar, LieModule.Cohomology.d₂₃_apply, Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway, Representation.Coinvariants.le_comap_ker, DoubleCentralizer.smul_toProd, LinearMap.withLpMap_id, AddEquiv.toIntLinearEquiv_trans, LinearMap.id_apply, mfderivWithin_projIcc_one, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, AddMonoidHom.toNatLinearMap_injective, ModuleCat.endRingEquiv_symm_apply_hom, LinearMap.BilinForm.sub_left, Algebra.intTrace_eq_of_isLocalization, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, BialgHom.coe_linearMap_injective, TensorProduct.leftComm_tmul, exteriorPower.alternatingMapLinearEquiv_symm_map, frobeniusEquiv_symm_comp_frobenius, LieIdeal.coe_killingCompl_top, PowerSeries.coeff_subst, Polynomial.sumIDeriv_eq_self_add, Submodule.span_range_inclusion_restrictScalars_eq_top, SemimoduleCat.forget_obj, TemperedDistribution.smulLeftCLM_neg, selfAdjointPart_comp_subtype_selfAdjoint, TensorProduct.comm_comm, LinearMap.restrictScalars_apply, HasFDerivAt.arctan, Algebra.trace_algebraMap, Polynomial.self_sub_monomial_natDegree_leadingCoeff, AffineMap.map_vadd', fderivWithin_star, PiTensorProduct.mapL_one, Module.Basis.repr_algebraMap, BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt, LinearMap.det_baseChange, DoubleCentralizer.toProdMulOpposite_injective, RCLike.conjCLE_apply, ContinuousLinearMap.norm_fst_le, Rep.homEquiv_apply_hom, Submodule.comap_id, QuadraticForm.tmul_tensorMap_apply, HahnEmbedding.Partial.truncLT_mem_range_extendFun, ContMDiffAt.mfderiv_apply, WeierstrassCurve.map_id, Polynomial.iterate_derivative_X, Submodule.mulMap_comm, LinearEquiv.one_mem_transvections, ModN.basis_apply_eq_mkQ, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Complex.reCLM_nnnorm, DoubleCentralizer.norm_fst_eq_snd, Module.Flat.out, Unitization.nnnorm_def, LinearMap.coprod_zero_left, RootPairing.finrank_rootSpan_map_polarization_eq_finrank_corootSpan, HasStrictFDerivAt.abs, ExteriorAlgebra.ιMulti_succ_apply, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Orientation.rightAngleRotation_def, Matrix.liftLinear_singleLinearMap, LieModule.Cohomology.d₁₂_apply_apply, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, Polynomial.eval₂_monomial, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, ImplicitFunctionData.range_leftDeriv, LinearMap.smulRight_apply, HasFDerivAt.fun_smul, Module.AEval'.X_smul_of, Fin.consEquivL_apply, fderivWithin_fun_neg, LinearMap.isUnit_iff_isUnit_det, Function.HasTemperateGrowth.toTemperedDistribution_apply, Euclidean.closedBall_eq_image, ContinuousLinearMap.flipMultilinear_apply_apply, Submodule.equivSubtypeMap_symm_apply, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotent, NumberField.mixedEmbedding.negAt_preimage, PowerSeries.coeff_coe, Submodule.botEquivPUnit_apply, ContinuousLinearMap.fst_comp_prod, LieModule.mem_posFittingCompOf, TensorProduct.AlgebraTensorModule.map_smul_left, ZLattice.comap_toAddSubgroup, Finsupp.iInf_ker_lapply_le_bot, Matrix.liftLinear_comp_singleLinearMap, LinearMap.ofIsComplProd_apply, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, LinearMap.mul_apply', SemimoduleCat.MonoidalCategory.tensorHom_tmul, LocalizedModule.divBy_mul_by, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, Finsupp.basis_repr, LinearMap.toMatrix_symm, Matrix.toBilin_apply, IsLocalRing.basisQuotient_repr, ModuleCat.forget_preservesMonomorphisms, Submodule.coe_orthogonalDecomposition_symm, LinearMap.range_mkQ_comp, LinearMap.toMatrix₂'_compl₁₂, groupCohomology.mapCocycles₂_comp_i_apply, AffineMap.const_linear, Submodule.ker_subtype, PiTensorProduct.mapL_smul, Module.End.maxGenEigenspace_eq_maxGenEigenspace_zero, SchwartzMap.integral_sesq_fourier_eq, Module.Relations.surjective_toQuotient, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MvPolynomial.monomial_eq_monomial_iff, LinearEquiv.det_baseChange, MeasureTheory.aestronglyMeasurable_condExpL2, RootPairing.flip_comp_polarization_eq_rootForm, TensorProduct.gradedMul_def, cfcL_integrable, MeasureTheory.L1.SimpleFunc.setToL1S_add_left, Polynomial.derivative'_apply, Submodule.orthogonalProjection_bot, Real.fderiv_fourier, DoubleCentralizer.norm_def', ApproximatesLinearOn.norm_fderiv_sub_le, MeasureTheory.charFunDual_pi', LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, ContinuousLinearMap.adjointAux_norm, Module.End.ringHomEndFinsupp_apply_apply, LinearMap.prodEquiv_apply, Representation.smul_ofModule_asModule, CStarMatrix.norm_def', NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Profinite.NobelingProof.Products.eval_πs', Polynomial.mem_support_derivative, Submodule.range_starProjection, MvPowerSeries.coeff_X, Module.Relations.Solution.IsPresentation.linearMapEquiv_apply, ContinuousLinearMap.fderiv, PowerSeries.eq_shift_mul_X_pow_add_trunc, Polynomial.monomial_pow, Representation.ofMulAction_single, fderiv_neg, Module.Basis.toLin_toMatrix, LinearIsometryEquiv.inner_map_eq_flip, Submodule.linearProjOfIsCompl_apply_right', ModuleCat.MonoidalCategory.associator_hom_apply, WithConv.symm_linearEquiv_apply, groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂, ContinuousLinearEquiv.continuousAlternatingMapCongrLeftEquiv_apply, TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, Quaternion.linearIsometryEquivTuple_symm_apply, LinearMap.iInf_ker_proj_le_iSup_range_single, MvPolynomial.eval₂_mul_monomial, Submodule.map_smul'', MvPolynomial.weightedHomogeneousComponent_zero, LinearMap.flip_injective_iff₁, Finsupp.linearCombination_one_tmul, ExteriorAlgebra.map_comp_ι, Matrix.toLinearEquivRight'OfInv_symm_apply, RootPairing.Hom.id_weightMap_apply, ContinuousAffineMap.coe_mk_contLinear_eq_linear, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, EuclideanGeometry.orthogonalProjection_apply_mem, SModEq.map, ContinuousAffineMap.smul_contLinear, Pi.counit_eq_adjoint, ConvexCone.coe_map, Module.FaithfullyFlat.lTensor_surjective_iff_surjective, Rep.norm_comm_apply, LinearMap.BilinForm.coeFnAddMonoidHom_apply, CategoryTheory.Linear.leftComp_apply, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.BilinForm.isNonneg_iff, HasDerivAt.comp_hasFDerivWithinAt, LinearMap.ker_smul', LinearMap.toMatrixOrthonormal_apply_apply, IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite, MeasureTheory.condExpInd_nonneg, IsLocalizedModule.map_linearMap_of_isLocalization, Submodule.coe_isComplEquivProj_symm_apply, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, MvPolynomial.homogeneousComponent_C_mul, Module.Basis.map_repr, ContinuousLinearMap.fpowerSeries_apply_zero, CliffordAlgebra.EquivEven.ι_eq_v_add_smul_e0, AdicCompletion.pi_apply_coe, Matrix.toLin'_mul_apply, MultilinearMap.fromDirectSumEquiv_symm_apply, Orientation.areaForm_to_volumeForm, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, VectorPrebundle.mk_contMDiffCoordChange, ContinuousLinearMap.mul_apply, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, Polynomial.toLaurent_C_mul_T, LinearMap.ker_id, MeasureTheory.OuterMeasure.map_apply, Polynomial.card_roots_le_derivative, extDerivWithin_constOfIsEmpty, Matrix.toLinearMapₛₗ₂'_single, LieAlgebra.bracket_ofTwoCocycle, LinearMap.exact_subtype_mkQ, Representation.ofDistribMulAction_apply_apply, ContinuousAffineMap.norm_def, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, Algebra.Extension.Cotangent.val_mk, Matrix.nondegenerate_toBilin'_iff, Representation.coinvariantsFinsuppLEquiv_apply, TensorProduct.AlgebraTensorModule.restrictScalars_curry, ContinuousLinearMap.IsInvertible.bijective, ModuleCat.HasColimit.colimitCocone_ι_app, ContinuousLinearMap.norm_iteratedFDerivWithin_comp_left, HasStrictFDerivAt.arsinh, LinearMap.trace_eq_contract_of_basis', PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, LinearMap.id_coe, Module.Presentation.cokernel_R, Submodule.linearDisjoint_iff, QuadraticForm.tmul_comp_tensorComm, LinearMap.BilinForm.congr_comp, LinearMap.toMatrixAlgEquiv_apply, LinearMap.IsSymmetric.coe_re_inner_self_apply, Lagrange.eq_interpolate_iff, LocalizedModule.lift'_mk, HasFDerivWithinAt.exp, LinearIsometry.coe_one, Polynomial.derivative_eval, Pi.compRightL_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, HasStrictFDerivAt.list_prod', Module.Basis.equiv_trans, Algebra.traceForm_apply, ContinuousLinearMap.map_smul_of_tower, SchwartzMap.fourier_lineDerivOp_eq, LinearEquiv.comm_trans_lTensor_trans_comm_eq, ContinuousLinearEquiv.hasLeftInverse, GradedTensorProduct.auxEquiv_one, Manifold.IsImmersionAtOfComplement.map_target_subset_target, Algebra.TensorProduct.basis_repr_tmul, CliffordAlgebra.changeFormEquiv_symm, LinearMap.BilinForm.apply_dualBasis_left, ContinuousLinearMapWOT.inducingFn_apply, QuadraticMap.add_toBilin, DFinsupp.injective_pi_lapply, Submodule.prod_comap_inr, TemperedDistribution.instLineDerivLeftSMulReal, Basis.linearEquiv_dual_iff_finiteDimensional, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, CStarMatrix.inner_toCLM_conjTranspose_left, CoalgHom.map_comp_comul, RootPairing.reflection_apply_root', Orientation.areaForm_neg_orientation, Module.exists_finite_presentation, LinearMap.toMatrix'_toLin', ModuleCat.MonoidalCategory.tensorHom_tmul, DFinsupp.range_mapRangeLinearMap, PolynomialModule.monomial_smul_single, Finsupp.lmapDomain_comp, MultilinearMap.curryRight_apply, IntermediateField.LinearDisjoint.trace_algebraMap, Pi.counit_comp_dFinsuppCoeFnLinearMap, groupHomology.d₂₁_single_inv_mul_ρ_add_single, Submodule.toLocalized₀_apply_coe, MvPolynomial.weightedDecomposition.decompose'_apply, isBoundedBilinearMap_comp, fderivWithin_sin, Module.mapEvalEquiv_apply, LinearMap.IsSymm.domRestrict, CliffordAlgebra.changeForm.zero_proof, RootPairing.ker_copolarization_eq_ker_corootForm, Orientation.rightAngleRotation_trans_rightAngleRotation, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, ContinuousAlgHom.coe_toContinuousLinearMap, QuadraticModuleCat.forget₂_map, AlgHom.toLinearMap_toOpposite, TensorProduct.toMatrix_assoc, ContinuousLinearMap.inverse_equiv, Subspace.finrank_dualCoannihilator_eq, LinearMap.applyₗ'_apply_apply, Submodule.sup_eq_range, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, LinearMap.commute_mulLeft_right, Trivialization.continuousLinearEquivAt_apply, Module.End.IsSemisimple.add_of_commute, Matrix.toLinearMap₂'_apply', PresheafOfModules.Derivation.postcomp_d_apply, Pretrivialization.linearMapAt_eq_zero, ContinuousLinearMap.pi_apply, TemperedDistribution.fourierInv_lineDerivOp_eq, LieSubmodule.lie_top_eq_of_span_sup_eq_top, Module.FaithfullyFlat.zero_iff_rTensor_zero, RootPairing.exists_ge_zero_eq_rootForm, MeasureTheory.condExpL2_indicator_ae_eq_smul, exteriorPower.ιMultiDual_apply_diag, fderiv_fun_sub, LinearMap.lTensor_comp_comm, Representation.instIsTrivialSubtypeMemSubgroupSubmoduleInvariantsCompLinearMapIdSubtypeToInvariants, mfderivWithin_comp_projIcc_one, Module.DualBases.eval_of_ne, MvPolynomial.expand_monomial, ModuleCat.forget₂_addCommGroup_full, IsMIntegralCurveOn.hasDerivWithinAt, LinearMap.sumOfConjugatesEquivariant_apply, Polynomial.X_pow_smul_rTensor_monomial, Algebra.TensorProduct.linearEquivIncludeRange_toLinearMap, Finset.weightedVSubOfPoint_vadd, Finsupp.LinearEquiv.finsuppUnique_symm_apply, PiToModule.fromEnd_injective, MultilinearMap.domDomCongrLinearEquiv_symm_apply, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, retractionOfSectionOfKerSqZero_comp_kerToTensor, LinearMap.coe_lTensorHom, Module.Basis.mk_coord_apply_ne, KaehlerDifferential.mapBaseChange_tmul, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, Module.DirectLimit.quotMk_of, SkewPolynomial.monomial_def, Complex.hasStrictFDerivAt_cpow', MvPolynomial.monomial_mul_mem_coeffsIn, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, PresheafOfModules.sectionsMap_coe, MvPowerSeries.coeff_monomial_same, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq, HasCompactSupport.fderiv, LinearMap.toMatrix_id, LinearIsometry.toAffineIsometry_toAffineMap, Real.fourier_iteratedFDeriv, Polynomial.smul_monomial, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, RingEquiv.symm_toRingHom_comp_toRingHom, SchwartzMap.smulLeftCLM_real_smul, ContinuousAffineMap.comp_contLinear, InnerProductSpace.toDualMap_apply_apply, RootPairing.IsOrthogonal.reflection_apply_left, NNRealRMK.lintegral_rieszMeasure, AddEquiv.toNatLinearEquiv_toAddEquiv, CharacterModule.dual_comp, groupHomology.d₁₀_comp_coinvariantsMk_apply, LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec, Orientation.kahler_eq_zero_iff, hasFDerivWithinAt_intCast, LinearEquiv.coe_curry, KaehlerDifferential.kerTotal_eq, ContinuousLinearEquiv.unitsEquivAut_apply, PositiveLinearMap.preGNS_norm_def, LinearMap.eq_adjoint_iff_basis_left, contDiff_succ_iff_fderiv, Ideal.toCotangent_range, LinearMap.BilinForm.isNonneg_def, PositiveLinearMap.leftMulMapPreGNS_apply, ContinuousAlgEquiv.trans_toContinuousLinearEquiv, Finsupp.span_image_eq_map_linearCombination, ContinuousLinearMap.opNNNorm_prod, ContinuousLinearEquiv.comp_differentiableOn_iff, MvPowerSeries.hasSum_aeval, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.ρ_hom, Matrix.mul_reindexLinearEquiv_one, LinearMap.baseChange_one, MeasureTheory.condExpL1CLM_of_aestronglyMeasurable', Rep.diagonalSuccIsoFree_inv_hom_single_single, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, Module.Invertible.exists_linearEquiv_ideal, Matrix.ker_mulVecLin_conjTranspose_mul_self, ProperCone.mem_dual, InnerProductSpace.HarmonicOnNhd.comp_CLM, Subspace.finiteDimensional_quot_dualCoannihilator_iff, HasMFDerivAt.neg, MvPowerSeries.weightedOrder_monomial_of_ne_zero, TensorPower.algebraMap₀_mul, groupCohomology.H1IsoOfIsTrivial_inv_apply, Algebra.Generators.H1Cotangent.δAux_C, Polynomial.iterate_derivative_X_sub_pow, ContinuousLinearMap.one_smulRight_eq_toSpanSingleton, LinearEquiv.coe_toLinearMap_mul, HasStrictFDerivAt.hasStrictDerivAt_norm_smul_neg, QuadraticMap.associated_prod, Pretrivialization.coe_linearMapAt, LinearMap.isIdempotentElem_iff_eq_isCompl_projection_range_ker, LinearMap.IsSymmetricProjection.isIdempotentElem, HasFDerivAt.fun_const_smul, ConvexCone.coe_comap, LinearIndependent.repr_eq_single, Submodule.map_id, SemimoduleCat.ofHom₂_hom_apply_hom, CliffordAlgebra.star_def', LieModuleHom.coe_toLinearMap, TensorProduct.gradedComm_algebraMap_tmul, PowerSeries.coeff_inv_aux, MvPowerSeries.X_pow_dvd_iff, PresheafOfModules.map_comp_apply, Module.Presentation.cokernelSolution.isPresentation, MeasureTheory.OuterMeasure.restrict_iInf, MeasureTheory.OuterMeasure.comap_apply, SeparatingDual.exists_continuousLinearEquiv_apply_eq, UnitAddTorus.mFourierCoeff_toLp, MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero, ProbabilityTheory.gaussianReal_map_continuousLinearMap, PowerSeries.degree_trunc_lt, IsAdjoinRootMonic.basis_repr, Manifold.pathELength_def, Module.Baer.ExtensionOf.is_extension, LinearMap.isCompl_range_inl_inr, LinearMap.toMatrix_transpose, WeakDual.toStrongDual_inj, Representation.leftRegular_norm_eq_zero_iff, FirstOrder.Field.lift_genericMonicPoly, LinearMap.toMatrix₂_toLinearMapₛₗ₂, MeasureTheory.VectorMeasure.restrictₗ_apply, ModuleCat.biprodIsoProd_inv_comp_snd_apply, ContinuousLinearMap.uniformContinuous_restrictScalars, LinearMap.prodMap_comap_prod, TensorProduct.finsuppLeft_smul', ModuleCat.RestrictionCoextensionAdj.counit'_app, LinearMap.identityMapOfZeroModuleIsZero, MvPowerSeries.coeff_mul_prod_one_sub_of_lt_order, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange_residueField, ContinuousLinearMap.mulLeftRight_apply, PresheafOfModules.pushforward_map_app_apply', PowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, LinearMap.extendTo𝕜'_apply, LieIdeal.mem_killingCompl, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, LinearIsometryEquiv.fderiv, Orientation.areaForm_swap, curveIntegral_fun_smul, ContinuousLinearMap.holderₗ_apply_apply, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, LinearMap.smul_compMultilinearMap, HopfAlgebra.sum_mul_antipode_eq_smul, LinearMap.isSymm_dualProd, Algebra.Extension.subsingleton_h1Cotangent, Matrix.mulVecLin_add, ext_inner_map, ProbabilityTheory.covarianceOperator_zero, LinearMap.trace_smulRight, Algebra.TensorProduct.basisAux_map_smul, Pi.basis_repr_single, LinearMap.prodMap_comp, Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, LinearMap.convOne_apply, AdicCompletion.factor_eval_eq_evalₐ, Module.Relations.Solution.fromQuotient_toQuotient, PiTensorProduct.reindex_comp_tprod, ContinuousLinearMap.analyticOn_bilinear, AddMonoidAlgebra.counit_single, ContinuousLinearEquiv.piUnique_symm_apply, LinearIsometryEquiv.measurePreserving, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, fderiv.log, LinearMap.funLeft_comp, Pi.intrinsicStar_comul_commSemiring, LocalizedModule.mem_ker_mkLinearMap_iff, LinearMap.isIdempotentElem_map_one_iff, Algebra.Generators.exists_presentation_of_free_cotangent, Subalgebra.range_isScalarTower_toAlgHom, Submodule.goursat, FDerivMeasurableAux.norm_sub_le_of_mem_A, TensorProduct.equivFinsuppOfBasisRight_apply_tmul, MvPolynomial.X_mul_pderiv_monomial, HasFDerivAt.add, ContinuousLinearMap.deriv, PerfectRing.lift_comp_lift_eq_id, Submodule.coe_prodEquivOfIsCompl', hasStrictFDerivAt_multiset_prod, Module.Basis.ofEquivFun_repr_apply, TensorProduct.congr_zpow, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, Matrix.toLinAlgEquiv_mul, TemperedDistribution.instFourierAdd, QuadraticAlgebra.imₗ_apply, fderiv_continuousAlternatingMap_apply, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, HahnEmbedding.Seed.strictMono_coeff, Submodule.subtypeₗᵢ_toLinearMap, LinearMap.det_mulRight, symm_toLexLinearEquiv, LieModule.traceForm_isSymm, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, MvPowerSeries.coeff_index_single_X, PowerSeries.WithPiTopology.uniformContinuous_coeff, Ideal.map_id, MeasureTheory.OuterMeasure.restrict_ofFunction, Module.one_le_rank_iff, IsLocalizedModule.fromLocalizedModule.bij, curveIntegral_fun_zero, LieDerivation.coe_neg_linearMap, LinearMap.nonneg_iff_isPositive, Lagrange.interpolate_eq_sum, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, Module.Basis.sumQuot_repr_left, LieDerivation.coe_smul_linearMap, LieModuleEquiv.left_inv, Algebra.Extension.CotangentSpace.map_tmul, Submodule.quotientQuotientEquivQuotientAux_mk, Orientation.kahler_swap, coe_innerSL_apply, RootPairing.mem_invtRootSubmodule_iff, LinearMap.lTensor_range, groupCohomology.H2π_comp_map_apply, Matrix.vecMulBilin_apply, ContinuousAlternatingMap.ofSubsingleton_apply_toContinuousMultilinearMap, fderivWithin_finset_prod, Orientation.det_rotation, Submodule.topEquiv_apply, HasFDerivWithinAt.const_sub, Orientation.rotation_pi_apply, MvPowerSeries.LinearTopology.mem_basis_iff, Coalgebra.comm_comul, Module.Relations.Solution.IsPresentation.linearEquiv_apply, MvPowerSeries.subst_monomial, ContinuousLinearEquiv.uniqueProd_symm_apply, LinearMap.IsSymmetric.inner_map_self_eq_zero, LinearMap.disjoint_inl_inr, Module.Basis.reindexRange_repr', cross_anticomm, OrthonormalBasis.prod_apply, RingEquiv.moduleEndSelf_symm_apply, RegularNormedAlgebra.isometry_mul', Polynomial.degreeLT.addLinearEquiv_castAdd, Orientation.rotation_rotation, AffineSubspace.map_mk', KaehlerDifferential.polynomialEquiv_comp_D, RingHomInvPair.triples, ContDiffWithinAt.hasFDerivWithinAt_nhds, Submodule.subtype_apply, FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq, KaehlerDifferential.span_range_map_derivation_of_isLocalization, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, Ideal.powQuotSuccInclusion_apply_coe, LaurentPolynomial.antipode_T, HasFDerivAt.sum, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, LieModuleHom.toSubmodule_range, DoubleCentralizer.central, Rep.ihom_ev_app_hom, LinearEquiv.toSpanNonzeroSingleton_homothety, Module.Basis.reindexRange_repr, SemimoduleCat.MonoidalCategory.whiskerRight_apply, MeasureTheory.integral_condExpL2_eq, IsBaseChange.endHom_toMatrix, Representation.Coinvariants.sub_mem_ker, MeasureTheory.OuterMeasure.map_iInf_comap, ContinuousLinearMap.instStarOrderedRing, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, Ideal.range_mul, hasFDerivAtFilter_const, VectorBundleCore.localTriv_symm_fst, Submodule.prod_le_iff, DistribMulAction.toLinearEquiv_symm_apply, LocalizedModule.equivTensorProduct_apply_mk, ModuleCat.homLinearEquiv_symm_apply, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, TrivSqZeroExt.algHom_ext'_iff, QuadraticMap.IsometryEquiv.prodProdProdComm_invFun, Submodule.dualAnnihilator_anti, Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply, IsAdicComplete.of_liftRingHom, Algebra.discr_powerBasis_eq_norm, LinearMap.BilinForm.sum_left, ModuleCat.hom_smul, LinearMap.surjective_iff_ne_zero, GradedTensorProduct.mul_def, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, Module.Flat.iff_lTensor_preserves_injective_linearMap, TensorProduct.equivFinsuppOfBasisLeft_apply_tmul, ContinuousLinearEquiv.finTwoArrow_symm_apply, MvPolynomial.weightedHomogeneousComponent_eq_zero', CommSemiRingCat.ofHom_id, hasFDerivAtFilter_iff_isLittleO, PowerSeries.coeff_zero_one, Module.Basis.toMatrix_map, QuadraticForm.polarBilin_tmul, PiTensorProduct.ofFinsuppEquiv'_tprod_single, TensorProduct.lidIsometry_apply, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, eventually_norm_mfderivWithin_symm_extChartAt_lt, LieModule.isNilpotent_toEnd_of_isNilpotent, LinearEquiv.mul_eq_trans, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, LinearMap.graph_eq_range_prod, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, Finset.weightedVSubOfPoint_filter_of_ne, orzechProperty_iff, MultilinearMap.curryFinFinset_apply, ModuleCat.uliftFunctorForgetIso_hom_app, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, MvPowerSeries.coeff_of_lt_order, ContinuousLinearMap.hasDerivAt, QuadraticMap.Ring.polarBilin_pi, LinearEquiv.refl_mem_transvections, RootPairing.toLinearMap_apply_apply_Polarization, ContinuousLinearEquiv.compContinuousAlternatingMap_coe, LinearEquiv.lTensor_zpow, Algebra.Extension.H1Cotangent.val_zero, StrongDual.toWeakDual_inj, ContinuousLinearMap.det_pi, Trivialization.comp_continuousLinearEquivAt_eq_coord_change, Orientation.map_eq_iff_det_pos, LinearMap.BilinForm.Nondegenerate.congr, Rep.MonoidalClosed.linearHomEquivComm_hom, Polynomial.map_monomial, rieszContentAux_image_nonempty, Complex.reCLM_coe, VectorFourier.hasFDerivAt_fourierIntegral, PiLp.sumPiLpEquivProdLpPiLp_symm_apply_ofLp, isGroupLikeElem_iff, PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sq, SemimoduleCat.homLinearEquiv_apply, ProperCone.subset_dual_dual, ModuleCat.smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, TensorProduct.equivFinsuppOfBasisLeft_symm, Submodule.range_mkQ, TensorProduct.comm_trans_lid, Submodule.comap_smul, LinearMap.flip_surjective_iff₁, LinearMap.tensorEqLocus_coe, TensorAlgebra.toExterior_ι, AlternatingMap.alternatizeUncurryFin_apply, Module.Basis.coe_toOrthonormalBasis_repr, ContinuousLinearMap.iInf_ker_proj, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, AlgEquiv.trans_toLinearMap, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, DirectSum.ker_lmap, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, Derivation.toFun_eq_coe, RootPairing.IsOrthogonal.coreflection_apply_right, contDiffAt_one_iff, Matrix.toLinearMap₂'_apply, HasFDerivAt.continuousAlternatingMap_apply, Profinite.NobelingProof.GoodProducts.smaller_factorization, HasFDerivWithinAt.of_notMem_tsupport, Submodule.map_unop_mul, ContinuousLinearMap.instCStarRingId, matPolyEquiv_coeff_apply_aux_1, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, LinearMap.funLeft_surjective_of_injective, LinearMap.mem_submoduleImage_of_le, Polynomial.degreeLT.addLinearEquiv_apply_fst, hasFDerivAt_finCons, Submodule.mulLeftMap_apply, lTensorHomEquivHomLTensor_apply, LinearMap.BilinForm.separatingLeft_toMatrix'_iff, FGModuleCat.hom_comp, Matrix.linfty_opNNNorm_eq_opNNNorm, TensorProduct.finsuppScalarRight_apply, VectorFourier.fourierIntegral_iteratedFDeriv, HasMFDerivWithinAt.neg, Algebra.FormallySmooth.iff_injective_lTensor_residueField, ModularGroup.lcRow0Extend_symm_apply, AffineIsometryEquiv.map_vsub, RootPairing.reflection_same, LinearMap.extendScalarsOfIsLocalizationEquiv_apply, hasFDerivWithinAt_finCons, rank_lt_rank_dual', AdicCompletion.sumInv_apply, ContinuousLinearEquiv.coe_toContinuousAffineEquiv, ContinuousCohomology.I_obj_ρ_apply, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, LinearMap.det_def, LinearEquiv.skewSwap_apply, Polynomial.derivative_X_sub_C_sq, ModuleCat.imageIsoRange_hom_subtype, Module.dual_finite, MvPolynomial.homogeneousComponent_isHomogeneous, TensorPower.cast_symm, Module.Relations.Solution.ofQuotient_var, fderiv_smul, LinearMap.trace_mul_comm, LinearMap.trace_eq_contract, OrthonormalBasis.orthogonalProjection_apply_eq_sum, Submodule.ker_inl, Orientation.kahler_comp_rightAngleRotation, LinearMap.toKerLocalized_isLocalizedModule, ContinuousLinearEquiv.arrowCongr_apply, FiniteField.algebraMap_trace_eq_sum_pow, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, ModuleCat.CoextendScalars.smul_apply, CliffordAlgebra.changeFormAux_apply_apply, Submodule.isOpenQuotientMap_mkQ, HasFDerivWithinAt.star, HasStrictFDerivAt.fst, rank_range_le, LinearEquiv.rTensor_trans_congr, LocalizedModule.equivTensorProduct_symm_apply_tmul, LinearMap.rTensor_sub, ContinuousLinearMap.norm_toSpanSingleton, Submodule.factor_eq_factor, DirectSum.coeLinearMap_of, fderivWithin_eventually_congr_set', AdicCompletion.sum_lof, TensorProduct.finsuppScalarRight_apply_tmul, Representation.single_smul, Polynomial.smeval.linearMap_apply, Submodule.coe_prodEquivOfIsCompl, LinearMap.trace_eq_sum_inner, VectorField.fderivWithin_pullbackWithin, TensorProduct.rightComm_symm, Polynomial.eval_derivative_of_splits, MvPolynomial.sum_homogeneousComponent, ContinuousLinearMap.toUniformConvergenceCLM_apply, TemperedDistribution.delta_apply, LinearMap.BilinForm.not_nondegenerate_zero, Derivation.coe_neg_linearMap, Module.Relations.Solution.IsPresentation.linearMapEquiv_symm_apply, DirectSum.coeLinearMap_eq_dfinsuppSum, AffineEquiv.linear_equivUnitsAffineMap_symm_apply, ContinuousAlternatingMap.curryLeft_apply_apply, Polynomial.isAlt_wronskianBilin, ContinuousLinearMap.contDiffPointwiseHolderAt, LieSubmodule.coe_map_toEnd_le, Module.FinitePresentation.linearEquivMap_symm_apply, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, exists_basis_of_pairing_ne_zero, RootPairing.polarizationIn_Injective, LinearIsometryEquiv.coe_ofEq_apply, LinearMap.isUnit_iff_ker_eq_bot, Algebra.IsEpi.injective_lift_mul, LinearMap.restrictScalarsₗ_apply, MulOpposite.coe_opLinearEquiv_addEquiv, SeparationQuotient.outCLM_uniformContinuous, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, LinearMap.BilinMap.toQuadraticMap_eq_zero, Subspace.dualPairing_nondegenerate, Matrix.isNilpotent_toLin'_iff, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, divRadical_dvd_derivative, Orientation.volumeForm_zero_pos, ModuleCat.exteriorPower.desc_mk, MvPolynomial.coe_monomial, LinearMap.trace_one, Module.Basis.constrL_apply, PresheafOfModules.unit_map_one, LinearMap.span_inl_union_inr, Module.AEval'.of_symm_X_smul, CliffordAlgebra.reverse_involute, TensorAlgebra.equivFreeAlgebra_symm_ι, selfAdjoint.imaginaryPart_coe, homTensorHomEquiv_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, QuadraticMap.associated_apply, hasMFDerivAt_neg, HasFDerivWithinAt.const_smul, LieModule.mem_genWeightSpace, Polynomial.aeval_add_of_sq_eq_zero, monomial_mem_adjoin_monomial, MvPowerSeries.X_def, Polynomial.derivativeFinsupp_apply_toFun, ExteriorAlgebra.GradedAlgebra.ι_sq_zero, ContinuousLinearEquiv.hasMFDerivAt, MeasureTheory.ConvolutionExistsAt.integrable_swap, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, MvPolynomial.C_apply, ModuleCat.HasColimit.colimitCocone_pt_isModule, LinearMap.detAux_def, SchwartzMap.laplacianCLM_eq', Polynomial.deriv_aeval, VectorBundleCore.trivializationAt_coordChange_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, IsModuleTopology.continuous_bilinear_of_pi_fintype, DoubleCentralizer.nnnorm_def, TensorProduct.mk_apply, MeasureTheory.Measure.comapₗ_apply, PointedCone.map_map, IsLocalizedModule.finsetIntegerMultiple_image, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, CliffordAlgebra.star_def, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, LinearMap.isCompl_iSup_ker_pow_iInf_range_pow, Finset.weightedVSub_eq_weightedVSubOfPoint_of_sum_eq_zero, MeasureTheory.charFunDual_prod, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, ExteriorAlgebra.lift_comp_ι, Profinite.NobelingProof.πs'_apply_apply, DifferentiableAt.fderiv_norm_self, continuousOn_tangentCoordChange, WittVector.fromPadicInt_comp_toPadicInt, AlternatingMap.alternatizeUncurryFin_add, MeasureTheory.OuterMeasure.map_comap_le, Polynomial.ofFinsupp_single, Matrix.toLinearEquiv'_symm_apply, MvPowerSeries.ext_iff, LinearMap.BilinForm.IsSymm.eq, AffineMap.linear_injective_iff, RootPairing.InvariantForm.symm, CommRing.Pic.mapRingHom_id_apply, LinearIsometryEquiv.smul_apply, PiTensorProduct.subsingletonEquiv_apply_tprod, LinearEquiv.uniqueProd_apply, DFinsupp.sigmaCurryLEquiv_apply, LinearMap.hasStrictDerivAt, AddMonoidAlgebra.lsingle_apply, LinearIsometryEquiv.contDiff, LinearMap.BilinForm.mul_toMatrix'_mul, Module.Basis.repr_smul, HasFDerivAt.comp_hasFDerivWithinAt, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, CategoryTheory.preadditiveYoneda_obj, Matrix.toLin_symm, SemimoduleCat.forget₂_obj_moduleCat_of, ContDiff.continuous_fderiv_apply, TensorProduct.mapOfCompatibleSMul_surjective, LinearMap.toMatrixAlgEquiv_id, Trivialization.linearEquivAt_apply, Polynomial.le_trailingDegree_monomial, fderivWithin_continuousAlternatingMap_apply_const_apply, Module.Ray.map_symm, ContinuousLinearEquiv.piUnique_apply, Complex.equivRealProdCLM_symm_apply, Polynomial.iterate_derivative_derivative_mul_X_sq, MvPolynomial.single_eq_monomial, finsuppTensorFinsupp'_single_tmul_single, TemperedDistribution.instContinuousFourier, LinearMap.det_eq_one_of_not_module_finite, Finsupp.mapDomain.coe_linearEquiv, Submodule.linearMap_qext_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, AddMonoidAlgebra.grade_eq_lsingle_range, Finset.weightedVSub_empty, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, LocallyConstant.congrRightₗ_apply_apply, Derivation.comp_aeval_eq, ContinuousLinearMap.const_apply_apply, CliffordAlgebraQuaternion.k_quaternionBasis, Submodule.traceDual_top', MeasureTheory.Measure.mapₗ_congr, Module.Flat.iff_rTensor_injective, LieModule.Weight.coe_coe, ModuleCat.MonoidalCategory.tensorHom_def, Representation.prod_apply_apply, LinearMap.baseChange_pow, CompactlySupportedContinuousMap.coe_toRealLinearMap, SeparatingDual.dualMap_surjective_iff, LinearIsometry.id_apply, NumberField.canonicalEmbedding.integralBasis_repr_apply, Representation.tprod_apply, InnerProductGeometry.norm_toLp_symm_crossProduct, dualTensorHom_apply, IsLocalExtr.fderiv_eq_zero, BilinForm.mul_toMatrix_mul, isNoetherian_linearMap_pi, EuclideanGeometry.orthogonalProjection_apply', CoalgHom.comp_toLinearMap, Finsupp.lcoeFun_comp_lsingle, Polynomial.comap_taylorEquiv_degreeLT, TensorProduct.Algebra.exists_of_fg, FunOnFinite.continuous_linearMap, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, QuadraticForm.tensorRId_symm_apply, LinearEquiv.lTensor_trans_congr, HasFPowerSeriesOnBall.fderiv_eq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, Module.Invertible.rTensorEquiv_apply_apply, Rep.coindVEquiv_symm_apply_coe, LinearMap.localized'_range_eq_range_localizedMap, exists_extension_of_le_sublinear, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, lTensorHomEquivHomLTensor_toLinearMap, LinearEquiv.lTensor_tmul, Submodule.range_fg_iff_ker_cofg, LinearEquiv.extendScalarsOfSurjective_symm, mfderivWithin_comp_of_preimage_mem_nhdsWithin_of_eq, Ideal.map_includeRight_eq, MeasureTheory.OuterMeasure.map_le_restrict_range, ContinuousLinearMap.restrictScalars_neg, PowerSeries.trunc_trunc_mul_trunc, RootPairing.coreflection_inv, Module.Basis.linearMap_apply, ContinuousLinearMap.flip_mul, AlgHom.comp_mul', Submodule.dualCoannihilator_iSup_eq, Module.comap_eval_surjective, CoalgEquiv.coe_toLinearEquiv, NormedSpace.inclusionInDoubleDual_norm_eq, Module.FinitePresentation.exists_lift_of_isLocalizedModule, LinearMap.map_coprod_prod, LinearMap.intrinsicStar_mul', PowerSeries.coeff_invOfUnit, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapId, SchwartzMap.smulLeftCLM_sum, Matrix.toLinearMap₂_compl₁₂, LinearMap.dualMap_id, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, LinearAlgebra.FreeProduct.ι_apply, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', LinearEquiv.coe_neg, ContinuousLinearMap.proj_apply, TensorProduct.exists_finite_submodule_left_of_setFinite, AffineMap.smul_linear, Finsupp.lcoeFun_apply, Module.Finite.exists_nat_not_surjective, TensorProduct.quotientTensorEquiv_symm_apply_mk_tmul, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, LinearEquiv.mem_dilatransvections_iff_rank, LinearIsometryEquiv.piLpCongrLeft_apply, ModuleCat.imageIsoRange_inv_image_ι_apply, Rat.castHom_rat, Polynomial.C_mul_X_pow_eq_monomial, mfderiv_prod_eq_add_comp, ContinuousLinearMap.fderiv_of_bilinear, Submodule.exists_le_ker_of_notMem, has_fderiv_at_filter_real_equiv, PiTensorProduct.ofDirectSumEquiv_symm_lof_tprod, basisOfLinearIndependentOfCardEqFinrank_repr_apply, ExteriorAlgebra.liftAlternating_ιMulti, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, MonomialOrder.leadingTerm_monomial, MvPowerSeries.WithPiTopology.continuous_coeff, hasFDerivAt_of_subsingleton, linearIndependent_algHom_toLinearMap', unitary.linearIsometryEquiv_coe_symm_apply, LinearMap.coprod_inr, MeasureTheory.setIntegral_condExpInd, ContinuousLinearMap.isPositive_def, AdicCompletion.map_comp_apply, CondensedMod.isDiscrete_iff_isDiscrete_forget, PowerSeries.trunc_mul_C, ContinuousLinearMap.nnnorm_toSpanSingleton, Representation.IntertwiningMap.isIntertwiningMap_of_mem_center, Complex.ringHom_eq_id_or_conj_of_continuous, LinearIsometryEquiv.symm_prodComm, ContinuousLinearEquiv.hasMFDerivWithinAt, iteratedFDerivWithin_succ_apply_right, PiTensorProduct.ofFinsuppEquiv_tprod_single, ContinuousAlternatingMap.alternatizeUncurryFin_smul, CliffordAlgebra.changeForm_ι_mul, IsLocalizedModule.iso_symm_comp, PresheafOfModules.map_smul, LinearEquiv.rTensor_zpow, contDiffAt_map_inverse, fderiv_mul_const', LieModule.traceForm_lieSubalgebra_mk_right, Matrix.cramer_apply, tendsto_integral_exp_smul_cocompact, LinearMap.lsum_apply, FGModuleCat.FGModuleCatEvaluation_apply, TensorProduct.AlgebraTensorModule.rTensor_tensor, ModuleCat.epi_iff_surjective, LinearEquiv.funUnique_symm_apply, SchwartzMap.toBoundedContinuousFunctionCLM_apply, Matrix.toLinearMapₛₗ₂'_symm, Module.Relations.range_map, Module.Basis.forall_coord_eq_zero_iff, LinearMap.localized'_ker_eq_ker_localizedMap, extDeriv_apply_vectorField, curveIntegral_segment, Submodule.strictMono_comap_prod_map, Module.Ray.linearEquiv_smul_eq_map, TestFunction.postcompCLM_apply, Module.End.map_genEigenrange_le, Submodule.mem_annihilator', IsIdempotentElem.ker_toSpanSingleton_eq_span, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, OrthonormalBasis.coe_ofRepr, LinearIsometry.mul_def, Submodule.starProjection_top', Module.Relations.Solution.postcomp_var, ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, LinearMap.mk₂_apply, HasFDerivWithinAt.abs_of_neg, Orientation.rotation_symm, LinearMap.polyCharpoly_baseChange, CliffordAlgebra.changeForm_self, RootPairing.PolarizationIn_eq, Submodule.adjoint_subtypeL, RootPairing.RootPositiveForm.exists_eq, MeasureTheory.convolutionExistsAt_flip, RootPairing.corootSpan_map_flip_toPerfPair, AdicCompletion.AdicCauchySequence.map_zero, hasStrictFDerivAt_exp, LinearMap.toLinearMap_toContPerfPair, TensorProduct.AlgebraTensorModule.rTensor_comp, PresheafOfModules.Monoidal.tensorObj_map_tmul, LinearMap.snd_comp_inl, LinearMap.coe_restrictScalars, Module.Basis.trace_traceDual_mul, LinearIsometryEquiv.self_trans_symm, PowerSeries.hasSum_of_monomials_self, Polynomial.monomial_eq_zero_iff, IsCoercive.range_eq_top, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, coevaluation_apply_one, CliffordAlgebraQuaternion.i_quaternionBasis, MatrixEquivTensor.toFunBilinear_apply, AnalyticOn.fderivWithin, continuous_decomposeProdAdjoint_symm, LinearMap.isSymmetric_adjoint_mul_self, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, Representation.isProj_averageMap, ContinuousLinearMap.opNorm_mul_apply, ModuleCat.exteriorPower.map_mk, ContinuousLinearMap.norm_smulRightL, TensorPower.mul_assoc, ContinuousLinearEquiv.uniqueDiffOn_image, mfderiv_comp_mfderivWithin, Submodule.dualRestrict_ker_eq_dualAnnihilator, AffineMap.decomp', IsBaseChange.transvection, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, RCLike.conjLIE_apply, MvPowerSeries.le_lexOrder_iff, Submodule.reflection_orthogonalComplement_singleton_eq_neg, LinearMap.toBilin'Aux_toMatrixAux, RootPairing.Equiv.weightMap_weightEquiv_symm, lipschitzGroup.conjAct_smul_ι_mem_range_ι, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, IsTensorProduct.map_map, ContinuousLinearEquiv.comp_fderiv, Finset.weightedVSub_weightedVSubVSubWeights, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, IsLocalRing.map_tensorProduct_mk_eq_top, HasFDerivWithinAt.fun_smul, Complex.orthonormalBasisOneI_repr_apply, Module.Dual.eval_apply, SemiRingCat.hom_id, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, Representation.coinvariantsTprodLeftRegularLEquiv_apply, Matrix.piLinearEquiv_apply, ModuleCat.id_apply, ContDiffAt.fderiv_right, ZMod.dft_comp_unitMul, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, LinearMap.toMatrix₂_compl₂, MeasureTheory.norm_condExpL2_coe_le, Module.End.isUnit_inv_apply_apply_of_isUnit, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousLinearEquiv.toContinuousAffineEquiv_toContinuousAffineMap, ContinuousMultilinearMap.curryLeft_norm, HasStrictFDerivAt.of_notMem_tsupport, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, finsuppTensorFinsuppLid_symm_single_smul, SameRay.map, Finset.weightedVSubOfPoint_sdiff, DFinsupp.sum_mapRange_index.linearMap, groupCohomology.infNatTrans_app, Finsupp.ker_mapRange, InnerProductSpace.trace_rankOne, PiTensorProduct.congr_symm_tprod, MonomialOrder.span_leadingTerm_eq_span_monomial, TensorProduct.congr_refl_refl, Ideal.pi_mkQ_surjective, rTensorHomEquivHomRTensor_apply, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, LinearMap.trace_eq_contract_apply, TensorPower.algebraMap₀_one, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, ExteriorAlgebra.liftAlternatingEquiv_apply, RCLike.imLm_coe, RootPairing.Equiv.coweightHom_injective, dualTensorHomEquivOfBasis_symm_cancel_right, LinearMap.iSup_range_single_eq_iInf_ker_proj, LinearMap.toPMap_apply, MonomialOrder.span_leadingTerm_eq_span_monomial₀, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, ContMDiffVectorBundle.continuousLinearMap, LinearMap.GeneralLinearGroup.ofLinearEquiv_inv, LinearEquiv.coe_pow, NormedSpace.eq_iff_forall_dual_eq, Matrix.toLpLin_symm_pow, Module.Invertible.embAlgebra_injective, ModuleCat.hom_inv_apply, Polynomial.mkDerivation_one_eq_derivative', ContinuousLinearEquiv.integral_comp_comm, Real.fourierIntegralInv_comp_linearIsometry, spinGroup.units_involute_act_eq_conjAct, MvPolynomial.scalarRTensor_apply_tmul, TensorProduct.prodLeft_tmul, Finsupp.supported_comap_lmapDomain, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, Polynomial.derivative_X_add_C, TensorProduct.tensorTensorTensorComm_symm, IsLocalization.tensorProduct_isLocalizedModule, ContDiffOn.fderiv_of_isOpen, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', Submodule.coe_linearProjOfIsCompl_apply, Submodule.inclusion_apply, ContinuousLinearMap.continuous_restrictScalars, HasFDerivWithinAt.neg, TensorAlgebra.lift_symm_apply, SchwartzMap.delta_apply, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, RootPairing.rootForm_root_self, IsLocalizedModule.is_universal, isBoundedBilinearMap_compMultilinear, ContinuousLinearEquiv.comp_right_fderiv, MvPowerSeries.monomial_mem_nonzeroDivisorsRight, ModuleCat.monoidalClosed_curry, Submodule.isIdempotentElem_starProjection, IsTensorProduct.map_pow, Polynomial.hermite_succ, Orientation.rotation_map, groupCohomology.d₀₁_apply_mem_cocycles₁, ContinuousLinearEquiv.prodCongr_symm, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, Orientation.oangle_rotation_left, hasFDerivAt_norm_rpow, LinearMap.proj_apply, finsuppTensorFinsupp'_symm_single_mul, IsBaseChange.det_endHom, ContinuousLinearMap.toLinearMapRingHom_apply, ContinuousLinearMap.compL_apply, isOpenMap_toWeakSpace_symm, ContinuousLinearMap.lsmul_flip_inj, LinearMap.polyCharpolyAux_map_eval, SpecialLinearGroup.coe_inv, AlternatingMap.curryLeft_apply_apply, Matrix.toLinearMapₛₗ₂'_aux_eq, IsLocalizedModule.mapExtendScalars_apply_apply, CommRing.Pic.inv_eq_dual, ZSpan.repr_ceil_apply, stdSimplex.map_coe, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, Finsupp.domLCongr_trans, LinearMap.BilinForm.isRefl_zero, MvPolynomial.C_mul_X_eq_monomial, LinearIsometry.inner_map_map, DoubleCentralizer.neg_snd, Module.End.algebraMap_isUnit_inv_apply_eq_iff', summable_jacobiTheta₂_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, LinearEquiv.det_symm_mul_det, PowerSeries.coeff_derivativeFun, LinearMap.IsPerfectCompl.isCompl_right, ContinuousLinearMap.ringInverse_equiv, KaehlerDifferential.linearMapEquivDerivation_apply_apply, ZLattice.comap_equiv_apply, Submodule.surjective_tensorToSpan, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, LinearMap.mulLeft_eq_zero_iff, LieSubmodule.toSubmodule_map, PolyEquivTensor.toFunLinear_mul_tmul_mul, ContinuousLinearMap.analyticAt, Representation.Coinvariants.mk_self_apply, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, Polynomial.hermite_eq_iterate, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, AffineMap.continuous_iff, Polynomial.hasseDeriv_comp, ContinuousLinearMap.isInvertible_zero_iff, Rep.indToCoindAux_fst_mul_inv, Submodule.orthogonalProjection_mem_subspace_orthogonalComplement_eq_zero, TensorProduct.directSumRight_comp_rTensor, Matrix.ker_mulVecLin_eq_bot_iff, MvPowerSeries.coeff_index_single_self_X, HasFPowerSeriesWithinAt.fderivWithin_eq, SemimoduleCat.hom_hom_rightUnitor, QuadraticMap.comp_apply, Matrix.linfty_opNNNorm_toMatrix, LinearIsometryEquiv.ofTop_toLinearEquiv, MvPowerSeries.WithPiTopology.as_tsum, MeasureTheory.OuterMeasure.isometry_comap_mkMetric, inCoordinates_apply_eq₂, Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, Module.Basis.end_apply_apply, KaehlerDifferential.tensorKaehlerEquivBase_tmul, AnalyticOnNhd.fderiv_of_isOpen, Module.Basis.coe_constrL, ModuleCat.exteriorPower.iso₀_hom_apply, MeasureTheory.OuterMeasure.map_comap, Module.End.IsSemisimple.sub_of_commute, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.applyAsHom_comm_apply, FourierTransform.fourierInvCLM_apply, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, MulOpposite.isometry_opLinearEquiv, HahnSeries.coe_truncLTLinearMap, ContinuousAlgEquiv.toContinuousLinearEquiv_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, Submodule.range_subtypeL, MeasureTheory.L1.integral_def, Submodule.biInf_comap_proj, contDiffOn_infty_iff_fderivWithin, Submodule.botEquivPUnit_symm_apply, groupHomology.chainsMap_f_single, QuadraticMap.toQuadraticMap_associated, ContinuousLinearMap.IsPositive.conj_adjoint, TensorProduct.map_map_assoc_symm, MvPolynomial.bind₂_monomial, IsLocalizedModule.fromLocalizedModule.inj, tangentMapWithin_snd, Matrix.toEuclideanCLM_toLp, Module.Basis.addSubgroupOfClosure_repr_apply, ContinuousLinearMap.pi_eq_zero, Module.Invertible.bijective_curry, Algebra.traceForm_toMatrix, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, LinearMap.ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank, groupCohomology.subtype_comp_d₀₁_apply, MvPolynomial.monomialOneHom_apply, Module.Basis.coe_sumCoords_of_fintype, ContinuousCohomology.Iobj_ρ_apply, Finsupp.sumFinsuppLEquivProdFinsupp_symm_apply, LinearMap.coprod_apply, realPart.norm_le, Module.Basis.repr_range, SheafOfModules.pushforwardComp_inv_app_val_app, Submodule.span_range_inclusion_eq_top, LinearEquiv.fst_comp_prodComm, ProbabilityTheory.covarianceBilin_zero, RCLike.conjCLE_coe, TensorProduct.comm_symm, HasFDerivAt.comp_hasDerivAt, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, VectorFourier.differentiable_fourierIntegral, basis_toMatrix_basisFun_mul, cross_anticomm', LinearMap.ker_prodMap, spinGroup.conjAct_smul_ι_mem_range_ι, LinearMap.mul_eq_one_comm, Matrix.toLin_scalar, TensorProduct.instDirectedSystemCoeLinearMapIdRTensor, LeftInvariantDerivation.evalAt_coe, AdicCompletion.map_comp, ModuleCat.FilteredColimits.forget_preservesFilteredColimits, Unitary.coe_symm_linearIsometryEquiv_apply, Polynomial.iterate_derivative_natCast_mul, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', Module.rank_linearMap, GradedTensorProduct.auxEquiv_symm_one, SchwartzMap.smulLeftCLM_fun_neg, groupCohomology.H2π_eq_iff, DirectSum.sigmaLcurry_apply, HasFPowerSeriesOnBall.fderiv, LinearMap.adjoint_rTensor, toBilin'Aux_toMatrixAux, IsSimpleModule.toSpanSingleton_surjective, GradedTensorProduct.auxEquiv_comm, BoundedContinuousFunction.toLp_inj, LinearMap.comap_leq_ker_subToSupQuotient, MvPolynomial.coeff_homogeneousComponent, ContinuousMultilinearMap.restrictScalarsLinear_apply, LinearMap.IsPositive.add, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, Submodule.LinearDisjoint.linearIndependent_right_of_flat, TensorProduct.finsuppLeft_symm_apply_single, Finsupp.linearEquivFunOnFinite_symm_apply, ContinuousLinearMap.toSpanSingleton_apply_map_one, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, LieModule.coe_genWeightSpaceOf_zero, LinearEquiv.mul_apply, LinearMap.adjoint_inner_right, Complex.hasStrictFDerivAt_cpow, RootPairing.reflection_sq, TensorAlgebra.equivFreeAlgebra_ι_apply, BilinForm.dotProduct_toMatrix_mulVec, LinearEquiv.multilinearMapCongrRight_symm_apply, InnerProductSpace.adjoint_rankOne, ContinuousLinearMap.compFormalMultilinearSeries_apply', ContinuousLinearMap.coe_coprod, LinearMap.BilinForm.tensorDistrib_tmul, LinearEquiv.piUnique_symm_apply, AdjoinRoot.mk_leftInverse, PiLp.hasFDerivAt_toLp, CliffordAlgebra.coe_toEven_reverse_involute, Submodule.map_mkQ_eq_top, PiTensorProduct.mapL_coe, MultilinearMap.coe_currySumEquiv_symm, Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, TensorProduct.AlgebraTensorModule.mk_apply, LinearMap.toMvPolynomial_add, LinearMap.trace_transpose', Manifold.IsImmersionAt.writtenInCharts, fderiv_pow, InnerProductSpace.rankOne_eq_zero, ProbabilityTheory.isGaussian_map_equiv_iff, Polynomial.natTrailingDegree_monomial, DoubleCentralizer.range_toProd, MvPowerSeries.WithPiTopology.uniformContinuous_coeff, Real.fourierIntegral_convergent_iff', fderiv_one, fderivWithin_continuousMultilinear_apply_const_apply, ContinuousAffineMap.coe_linear_eq_coe_contLinear, CommRing.Pic.mk_eq_iff, LinearMap.IntrinsicStar.starLinearEquiv_eq_arrowCongr, BoundedContinuousFunction.toLp_injective, IsTensorProduct.equiv_symm_apply, LinearEquiv.symm_conjAlgEquiv, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, Projectivization.cross_mk_of_cross_ne_zero, one_def, Matrix.toLpLin_one, Convex.toWeakSpace_closure, Module.Basis.trace_mul_traceDual, LinearIsometry.lTensor_apply, CliffordAlgebra.ι_mul_ι_mul_ι, LinearIsometry.norm_compContinuousMultilinearMap, ContinuousAlternatingMap.norm_curryLeft, finsuppTensorFinsupp'_apply_apply, Polynomial.eval_monomial_one_add_sub, groupCohomology.cocycles₂_map_one_snd, Module.End.HasEigenvector.apply_eq_smul, Submodule.norm_sq_eq_add_norm_sq_starProjection, AffineIsometry.linear_eq_linearIsometry, inner_map_polarization', MultilinearMap.curryFinFinset_symm_apply_piecewise_const, Bundle.ContMDiffRiemannianMetric.symm, RootPairing.Equiv.coweightEquiv_one, ContMDiffOn.coordChangeL, LinearMap.mul'_apply, LinearIsometryEquiv.ofTop_symm_apply_coe, RootPairing.InvariantForm.exists_apply_eq_or, MeasureTheory.charFunDual_eq_prod_iff, LinearMap.submoduleImage_apply_of_le, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ModuleCat.homAddEquiv_symm_apply_hom, Rep.coinvariantsTensorFreeLEquiv_apply, VectorField.fderiv_pullback, Submodule.snd_map_fst, PiTensorProduct.ofFinsuppEquiv_symm_single_tprod, HasFDerivWithinAt.hasGradientWithinAt, SchwartzMap.pairing_apply, LinearIsometry.id_toLinearMap, MvPolynomial.monomial_left_inj, Finsupp.leftInverse_lcomapDomain_mapDomain, Module.Dual.transpose_apply, Module.Basis.reindexRange_repr_self, HasFDerivAt.pow, Real.fourier_comp_linearIsometry, Module.Invertible.instDual, LinearMap.det_prodMap, LinearMap.BilinForm.compLeft_injective, Polynomial.map_taylor, fderivWithin_comp_derivWithin, LinearMap.isPosSemidef_iff_posSemidef_toMatrix, MvPolynomial.X_dvd_monomial, ContDiff.continuous_fderiv, ContinuousAlternatingMap.apply_apply, RootPairing.zero_le_rootForm, mdifferentiableAt_hom_bundle, groupHomology.toCycles_comp_isoCycles₁_hom_apply, innerSL_inj, subset_tangentConeAt_prod_right, PositiveLinearMap.preGNS_inner_def, fderivWithin_inv', TannakaDuality.FiniteGroup.sumSMulInv_apply, TensorProduct.AlgebraTensorModule.rTensor_tmul, SpecialLinearGroup.congr_linearEquiv_symm, RootPairing.Equiv.comp_coweightMap_apply, Representation.mem_invariants_iff_of_forall_mem_zpowers, Orthonormal.equiv_symm, Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, spinGroup.involute_act_ι_mem_range_ι, CategoryTheory.Functor.mapExtLinearMap_coe, Derivation.mapCoeffs_monomial, MeasureTheory.ae_ae_add_linearMap_mem_iff, TensorProduct.prodLeft_symm_tmul, HasFDerivWithinAt.cpow, RootPairing.Equiv.weightEquiv_apply, MeasureTheory.lintegral_nnnorm_condExpL2_le, Module.FaithfullyFlat.rTensor_exact_iff_exact, IsLocalizedModule.map_comp', MvPowerSeries.monomial_zero_eq_C, MvPowerSeries.coeff_inv, CliffordAlgebra.reverse_comp_reverse, DirectSum.congr_linearEquiv_toAddEquiv, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, Module.Basis.equiv_symm, StrongDual.toLp_of_not_memLp, LinearEquiv.rTensor_refl_apply, ContinuousLinearMap.fderivWithin_of_bilinear, LaurentSeries.derivative_iterate_coeff, MeasureTheory.Lp.compMeasurePreservingₗᵢ_apply_coe, QuadraticMap.toBilin_apply, Finsupp.linearCombination_linear_comp, Submodule.comap_dualAnnihilator, DoubleCentralizer.add_fst, linearIndependent_algHom_toLinearMap, Module.End.isNilpotent_iff_of_finite, TensorAlgebra.lift_ι_apply, HasStrictFDerivAt.const_cpow, Matrix.singleLinearMap_apply, MeasureTheory.OuterMeasure.restrict_univ, Module.Basis.repr_eq_iff, LinearMap.IsSymmetric.coe_toSelfAdjoint, Polynomial.degreeLT.addLinearEquiv_apply_snd, MvPowerSeries.constantCoeff_comp_C, KaehlerDifferential.linearMapEquivDerivation_symm_apply, PowerSeries.eval₂_eq_tsum, HasFDerivWithinAt.csinh, MvPolynomial.C_mul_monomial, starL'_apply, Algebra.normalizedTrace_intermediateField, LinearMap.BilinForm.smul_right_of_tower, TensorProduct.inner_lid_lid, PiTensorProduct.reindex_trans, LinearMap.BilinForm.tensorDistribEquiv_apply, ContinuousLinearMap.applyFaithfulSMul, OrthonormalBasis.toBasis_map, ContDiffMapSupportedIn.uniformSpace_eq_iInf, Representation.ofQuotient_coe_apply, ModuleCat.range_eq_top_of_epi, LinearEquiv.mem_transvections_iff, linearIndependent_toLinearMap, SeparationQuotient.outCLM_isUniformEmbedding, Algebra.Generators.H1Cotangent.exact_map_δ, Matrix.piLp_ofLp_toEuclideanLin, Algebra.Generators.H1Cotangent.δAux_monomial, LinearMap.coe_fst, LinearMap.BilinForm.toMatrix_apply, Module.Basis.sumQuot_repr_inl, RootPairing.Hom.coweightHom_injective, MvPolynomial.vars_monomial, LinearMap.IsSymmetric.diagonalization_symm_apply, Polynomial.modByMonicHom_apply, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, Algebra.trace_isNilpotent_of_isNilpotent, LinearEquiv.piUnique_apply, LinearEquiv.sumPiEquivProdPi_apply, MvPolynomial.pow_idealOfVars_eq_span, TensorProduct.norm_comm, LieAlgebra.killingForm_apply_eq_zero_of_mem_rootSpace_of_add_ne_zero, TrivSqZeroExt.map_comp_inrHom, RootPairing.reflectionPerm_coroot, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, NormedSpace.inclusionInDoubleDual_norm_le, Polynomial.addHom_ext'_iff, ContinuousMultilinearMap.ofSubsingleton_symm_apply_apply, CliffordAlgebra.adjoin_range_ι, LieSubmodule.traceForm_eq_zero_of_isTrivial, CliffordAlgebra.changeFormEquiv_apply, SeparatingDual.instNontrivialContinuousLinearMapIdOfContinuousSMul, PowerBasis.constr_pow_algebraMap, LinearMap.dualProd_apply_apply, AnalyticOnNhd.eval_linearMap, LinearEquiv.coe_toContinuousLinearEquiv_symm, LinearIsometryEquiv.coe_toMeasurableEquiv, lieEquivMatrix'_apply, PresheafOfModules.mono_iff_surjective, curveIntegral_segment_const, Finite.id, ContinuousLinearMap.coprod_comp_inl_inr, Algebra.Generators.CotangentSpace.compEquiv_symm_zero, PowerSeries.trunc_X_of, mfderiv_sub, TensorProduct.dualDistribEquivOfBasis_symm_apply, BilinForm.toMatrix_toBilin, TensorProduct.AlgebraTensorModule.congr_eq, RingHomInvPair.triples₂, AlgHom.toLinearMap_apply, SemimoduleCat.MonoidalCategory.tensorLift_tmul, VectorBundleCore.localTriv_symm_apply, Module.dual_free, HasFDerivAt.abs, WeakDual.isCompact_closedBall, LinearMap.IsPerfectCompl.flip_iff, WithLp.toAddEquiv_linearEquiv, MeasureTheory.L1.integral_eq_setToL1, IsLocalizedModule.linearEquiv_apply, Polynomial.derivative_X_pow_succ, LieModule.weight_vector_multiplication, ContinuousLinearMap.isPositive_toLinearMap_iff, BoxIntegral.BoxAdditiveMap.volume_apply, LinearMap.isSymm_def, spinGroup.conjAct_smul_range_ι, Matrix.toPerfectPairing_apply_apply, TangentBundle.trivializationAt_apply, CliffordAlgebra.EquivEven.neg_e0_mul_v, ConvexOn.sSup_of_countable_affine_eq, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, Representation.mem_invariants, Matrix.mulVecLin_zero, LinearMap.quotientInfEquivSupQuotient_apply_mk, KaehlerDifferential.kerTotal_mkQ_single_add, HasStrictFDerivAt.abs_of_neg, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, SpecialLinearGroup.congr_linearEquiv_coe_apply, RCLike.reCLM_coe, FunOnFinite.linearMap_apply_apply, LinearMap.BilinForm.IsRefl.smul, HasFDerivWithinAt.abs, LinearMap.intrinsicStar_zero, ProbabilityTheory.gaussianReal_map_linearMap, AdicCompletion.range_eval, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, realPart_add_I_smul_imaginaryPart, TensorProduct.leftComm_def, LinearMap.BilinForm.IsNonneg.add, Rep.indToCoindAux_comm, MeasureTheory.Measure.map_def, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, subset_tangentConeAt_prod_left, ContinuousLinearMap.derivWithin, LinearEquiv.sumArrowLequivProdArrow_symm_apply_inr, Module.End.ker_pow_eq_ker_pow_finrank_of_le, Algebra.Generators.cotangentSpaceBasis_repr_tmul, LinearEquiv.funCongrLeft_apply, LinearMap.ker_toSpanSingleton, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, Submodule.localized'_span, LinearMap.compr₂_apply, ContinuousLinearMap.precompR_apply, ContinuousAffineMap.norm_eq, HarmonicAt.differentiableAt_complex_partial, LinearMap.IsPerfPair.compl₁₂, LinearMap.rTensor_lTensor_comp_assoc_symm, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, LinearMap.minpoly_toMatrix', LieSubalgebra.coe_ad_pow, LinearMap.BilinForm.IsPosSemidef.smul, HasFDerivWithinAt.mul_const, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', MvPolynomial.bind₂_monomial_one, Derivation.leibniz', Real.fourierInv_comp_linearIsometry, MeasureTheory.hasFDerivAt_convolution_right_with_param, Module.Basis.flag_le_ker_coord, ContinuousLinearEquiv.differentiableAt, Polynomial.degree_monomial_le, LinearMap.trace_prodMap, ProbabilityTheory.IsGaussian.charFun_eq', Submodule.iSup_dualAnnihilator_le_iInf, fderiv_pow', Module.End.genEigenspace_inf_le_add, ProbabilityTheory.covarianceBilinDual_eq_covariance, LinearMap.rank_comp_le_left, ContMDiffAt.mfderiv_const, CliffordAlgebra.range_ι_le_evenOdd_one, Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd, fderiv_mul, LinearMap.liftBaseChangeEquiv_symm_apply, LieModuleHom.toLinearMap_comp, MeasureTheory.condExpL1CLM_indicatorConstLp, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, LinearIsometry.isConformalMap, LinearIsometryEquiv.reflections_generate, Finsupp.comul_comp_lapply, ContinuousLinearMap.toSpanSingleton_pow, Submodule.map_orthogonal_equiv, iteratedFDerivWithin_eq_equiv_comp, QuadraticForm.dualProd_apply, RootPairing.RootPositiveForm.isOrthogonal_reflection, Fintype.bilinearCombination_apply, Polynomial.coeff_monomial_of_ne, Algebra.TensorProduct.equivFinsuppOfBasis_apply, CompactlySupportedContinuousMap.toRealLinearMap_apply, LinearMap.compQuadraticMap_polar, Polynomial.derivative_X_sub_C_pow, LinearMap.toMatrix₂_comp, exteriorPower.map_apply_ιMulti_family, Matrix.l2_opNNNorm_mulVec, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, LinearMap.restrictScalars_smul, Lagrange.degree_interpolate_erase_lt, LinearEquiv.conj_exact_iff_exact, HasStrictFDerivAt.isLittleO, HasCompactSupport.hasFDerivAt_convolution_right, Finsupp.sumFinsuppLEquivProdFinsupp_symm_inl, Algebra.isNilpotent_trace_of_isNilpotent, PerfectRing.liftEquiv_id_apply, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, VonNeumannAlgebra.centralizer_centralizer', differentialIdeal_le_iff, TrivSqZeroExt.sndCLM_apply, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, TensorProduct.gradedComm_algebraMap, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, TensorProduct.map_map_comp_assoc_eq, AffineEquiv.map_vadd, LinearMap.lsmul_flip_apply, ProbabilityTheory.covarianceBilinDual_zero, groupHomology.cyclesIso₀_comp_H0π_apply, Algebra.TensorProduct.opAlgEquiv_apply, Submodule.norm_orthogonalProjection_apply_le, ContinuousAffineMap.coe_mk_const_linear_eq_linear, Bialgebra.counit_surjective, isLocalizedModule_iff, LinearMap.deriv, Matrix.SeparatingRight.toLinearMap₂', Algebra.Extension.Hom.sub_one_tmul, Module.Basis.toDual_ker, Continuous.fderiv, killingForm_eq_zero_of_mem_zeroRoot_mem_posFitting, Representation.asModuleEquiv_symm_map_smul, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, GradedAlgebra.proj_recompose, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, TensorProduct.norm_assoc, Module.Basis.repr_linearCombination, groupHomology.eq_d₃₂_comp_inv_apply, Module.Basis.dualBasis_apply_self, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, SpecialLinearGroup.det_eq_one, AffineEquiv.linear_symm, PowerSeries.order_monomial, DoubleCentralizer.smul_fst, Coalgebra.sum_counit_smul, fderivWithin.snd, Module.DirectLimit.of_f, LinearEquiv.symm_neg, TensorProduct.assoc_tmul, ContinuousLinearMap.coprod_add, PointedCone.mem_dual, WittVector.IsocrystalEquiv.frob_equivariant, PiTensorProduct.reindex_tprod, norm_fderiv_le_of_lipschitz, Submodule.mem_iSup_iff_exists_dfinsupp, Submodule.map₂_map_left, Algebra.TensorProduct.equivFinsuppOfBasis_symm_apply, QuadraticForm.tensorRId_apply, InnerProductSpace.toDualMap_apply, geometric_hahn_banach_point_closed, MvPolynomial.rTensor_apply_X_tmul, CondensedMod.epi_iff_surjective_on_stonean, QuadraticForm.comp_tensorLId_eq, IsSelfAdjoint.skewAdjointPart_apply, MvPowerSeries.coeff_homogeneousComponent, RingHomInvPair.comp_eq₂, KaehlerDifferential.exact_mapBaseChange_map, PowerSeries.monomial_mul_monomial, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, LinearEquiv.isAdjointPair_symm_iff, LinearMap.pow_eq_aeval_mod_charpoly, LinearMap.prodEquiv_symm_apply, LinearMap.BilinForm.add_left, isArtinian_range, TangentBundle.coordChange_model_space, PiLp.basisFun_repr, LinearMap.zero_compMultilinearMap, LinearMap.toSpanSingleton_apply_one, LinearMap.tensorProductEnd_apply, ContinuousLinearMap.adjoint_inner_left, ModuleCat.hom_inv_associator, MeasureTheory.condExpInd_disjoint_union, fderivWithin_cos, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, lift_rank_lt_rank_dual', LinearMap.snd_eq_coprod, PointwiseConvergenceCLM.isInducing_inducingFn, Matrix.toLpLin_pow, KaehlerDifferential.tensorKaehlerEquiv_tmul, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, TensorProduct.inner_mapIncl_mapIncl, Orientation.oangle_rotation_oangle_right, Module.AEval'.X_pow_smul_of, LinearMap.trace_eq_contract', RootPairing.toLinearMap_apply_PolarizationIn, AlgEquiv.toLinearEquiv_symm, Algebra.Generators.H1Cotangent.δAux_toAlgHom, RootPairing.InvariantForm.isOrthogonal_reflection, Module.finrank_linearMap, Matrix.kroneckerAlgEquiv_apply, LinearEquiv.extendScalarsOfSurjective_apply, AlgEquiv.toLinearMap_injective, LinearIsometryEquiv.coe_prodAssoc_symm, ContinuousLinearEquiv.arrowCongr_symm, Finsupp.linearCombination_single_index, exteriorPower.zeroEquiv_naturality, Polynomial.derivWithin, ContinuousLinearMap.isBoundedBilinearMap, LinearEquiv.symm_flip, LieIdeal.map_toSubmodule, fdifferential_apply, KaehlerDifferential.D_apply, MeasureTheory.OuterMeasure.map_iInf_le, CliffordAlgebra.EquivEven.e0_mul_v_mul_e0, IsSymmetricAlgebra.equiv_symm_comp, CliffordAlgebraComplex.ofComplex_I, InnerProductSpace.AlgebraOfCoalgebra.mul_def, LinearMap.BilinForm.separatingRight_toMatrix'_iff, LinearMap.extendTo𝕜_apply, Matrix.isUnit_toLin'_iff, TensorProduct.exists_finite_submodule_right_of_setFinite, HahnEmbedding.IsPartial.truncLT_mem_range, LinearEquiv.refl_toLinearMap, Module.piEquiv_apply_apply, Submodule.span_algebraMap_image, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T, RootPairing.EmbeddedG2.long_eq_three_mul_short, LinearMap.BilinForm.smul_left, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, Finsupp.lift_apply, Module.End.pow_apply, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, LinearIndependent.linearCombinationEquiv_apply_coe, LinearMap.range_dualMap_eq_dualAnnihilator_ker, Submodule.dualCoannihilator_map_linearEquiv_flip, RootPairing.rootSpan_map_toPerfPair, Polynomial.adjSylvester_comp_sylveserMap, Polynomial.exists_iterate_derivative_eq_factorial_smul, innerₗ_apply, fderivWithin_continuousMultilinear_apply_const, TopModuleCat.hom_add, FormalMultilinearSeries.le_radius_compContinuousLinearMap, TensorProduct.AlgebraTensorModule.leftComm_tmul, ContinuousLinearMap.prod_ext_iff, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, IsIsotypicOfType.linearEquiv_fun, Finset.weightedVSub_smul, Module.Relations.Solution.range_π, Orientation.rightAngleRotation_symm, MeasureTheory.weightedSMul_empty, TensorAlgebra.toClifford_ι, RootPairing.GeckConstruction.trace_toEnd_eq_zero, ContinuousLinearMap.toSpanSingleton_smul, CliffordAlgebra.hom_ext_iff, Polynomial.monomial_injective, Matrix.toLin'_mul, Polynomial.taylor_eq_zero, MonoidAlgebra.lsingle_apply, fderivWithin_ccos, IsArtinian.range_smul_pow_stabilizes, Algebra.Extension.Hom.id_toRingHom, Submodule.iSup_eq_range_dfinsupp_lsum, ModularGroup.lcRow0Extend_apply, CoalgCat.MonoidalCategoryAux.tensorObj_comul, TensorProduct.gradedComm_tmul_of_zero, LinearMap.isNilpotent_toMatrix_iff, LinearMap.BilinForm.lieInvariant_iff, ContinuousLinearEquiv.symm_smul_apply, LieModule.Cohomology.twoCochain_skew, MDifferentiableOn.coordChangeL, Module.Relations.Solution.directSum_var, TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply, AffineMap.vadd_linear, VectorField.lieBracketWithin_smul_left, LocallyConstant.evalₗ_apply, LinearMap.BilinForm.dotProduct_toMatrix_mulVec, Lagrange.degree_interpolate_lt, ContinuousLinearMap.IsPositive.isSymmetric, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ModuleCat.inv_hom_apply, HasStrictFDerivAt.clog, Module.End.rTensorAlgHom_apply_apply, LinearMap.det_eq_det_toMatrix_of_finset, LieModule.traceForm_comm, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, fderiv_fun_add, Algebra.linearMap_apply, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, ModuleCat.forget₂AddCommGroup_preservesLimits, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, LinearMap.toMatrix_reindexRange, ExteriorAlgebra.liftAlternating_apply_ιMulti, ContinuousLinearMap.coe_smulRightₗ, Module.Flat.iff_lTensor_exact, PolynomialLaw.exists_lift, LinearMap.toMvPolynomial_zero, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict, QuadraticAlgebra.reₗ_apply, LaurentSeries.derivative_apply, DFinsupp.iSup_range_lsingle, fderiv_pow_ring, groupHomology.mapCycles₁_id_comp_apply, ContinuousLinearMap.lsmul_apply, AdicCompletion.transitionMap_comp_eval, inTangentCoordinates_eq, extDerivWithin_apply_vectorField_of_pairwise_commute, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, LinearMap.vecCons_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, Bundle.ContMDiffRiemannianMetric.pos, HasStrictFDerivAt.sqrt, RatFunc.laurentAux_div, Matrix.ofLp_toLpLin, traceForm_dualSubmodule_adjoin, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, TensorPower.galgebra_toFun_def, HasDerivWithinAt.complexToReal_fderiv, CategoryTheory.Iso.toLinearEquiv_symm, Module.range_piEquiv, DirectSum.lof_eq_of, LinearEquiv.cast_apply, polyEquivTensor_symm_apply_tmul, RootPairing.coroot'_apply_apply_mem_of_mem_span, LinearIndependent.linearCombination_comp_repr, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, LinearMap.IsSymmetric.continuous, CoalgHom.id_toLinearMap, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, IsContMDiffRiemannianBundle.exists_contMDiff, Ideal.quotientToQuotientRangePowQuotSucc_mk, MvPowerSeries.weightedHomogeneousComponent_of_lt_weightedOrder_eq_zero, ContDiffWithinAt.fderivWithin'', CommRing.Pic.ext_iff, Matrix.toBilin'_symm, StarModule.decomposeProdAdjoint_symm_apply, Module.Basis.dualBasis_equivFun, PresheafOfModules.presheaf_map_apply_coe, LinearMap.charpoly_eq_X_pow_iff, MvPowerSeries.WithPiTopology.hasSum_iff_hasSum_coeff, ContinuousLinearEquiv.coe_symm_comp_coe, PiTensorProduct.piTensorHomMap_tprod_tprod, PowerSeries.eq_X_mul_shift_add_const, Submodule.coe_inclusion, RootPairing.corootSpan_dualAnnihilator_map_eq, LinearIsometry.extend_apply, MvPowerSeries.coeff_subst, RingEquiv.moduleEndSelfOp_apply, CoalgHomClass.counit_comp_apply, Rep.ofMulDistribMulAction_ρ_apply_apply, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, ContinuousLinearMap.iteratedFDerivWithin_comp_left, InnerProductSpace.rank_rankOne, AffineEquiv.linear_toAffineMap, LinearMap.isSymmetric_sum, MeasureTheory.OuterMeasure.comap_top, LinearMap.toMatrix_smulBasis_left, Module.Basis.coe_toOrthonormalBasis_repr_symm, IsAdjoinRootMonic.modByMonicHom_map, ContinuousLinearMap.HasRightInverse.rightInverse_rightInverse, LinearMap.toSeminorm_comp, RootPairing.EmbeddedG2.allRoots_eq_map_allCoeffs, VertexOperator.ncoeff_apply, Module.Dual.transpose_comp, CoalgHom.counit_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, Polynomial.derivativeFinsupp_apply_apply, LinearMap.GeneralLinearGroup.toLinearEquiv_inv, Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, LinearMap.BilinForm.isSymm_iff_flip, contMDiffAt_coordChangeL, Polynomial.sup_aeval_range_eq_top_of_isCoprime, Module.Basis.prod_apply, HasFDerivWithinAt.fun_sub, RootPairing.corootForm_apply_apply, LinearMap.flip_bijective_iff₁, HasStrictFDerivAt.rpow, PowerSeries.constantCoeff_comp_C, Polynomial.taylor_apply, InnerProductSpace.toDual_apply_apply, KaehlerDifferential.range_mapBaseChange, LinearMap.flip_bijective_iff₂, Algebra.SubmersivePresentation.sectionCotangent_eq_iff, Subring.map_id, Algebra.Extension.Cotangent.mk_eq_zero_iff, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.nonneg_iff_isPositive, MultilinearMap.fromDFinsuppEquiv_single, Rep.instIsTrivialCarrierVModuleCatOfCompLinearMapIdρ, Orientation.inner_rotation_pi_div_two_right, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, LinearMap.BilinForm.mem_dualSubmodule, LinearMap.range_dualMap_dual_eq_span_singleton, fderivWithin_fun_sub, coe_lpBCFₗᵢ, ContinuousAffineMap.norm_contLinear_le, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, LinearMap.det_toLin', CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Submodule.linearEquiv_det_reflection, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, fderivWithin_fun_mul', MvPolynomial.map_restrict_dom_evalₗ, Polynomial.iterate_derivative_comp_one_sub_X, LinearMap.mapMatrixModule_apply, Algebra.Presentation.differentials.surjective_hom₁, Trivialization.symmL_continuousLinearMapAt, ContinuousLinearMap.HasRightInverse.comp, ProbabilityTheory.IsGaussianProcess.comp_left, DirectSum.lmap_eq_map, ContinuousMap.evalCLM_apply, LinearPMap.apply_comp_inclusion, ProperCone.innerDual_singleton, DFinsupp.filterLinearMap_apply, Submodule.snd_map_snd, DirectSum.coe_congr_linearEquiv, CoalgHomClass.toSemilinearMapClass, Submodule.IsOrtho.map, LinearMap.ker_prod_ker_le_ker_coprod, TensorAlgebra.lift_comp_ι, LinearIsometryEquiv.comp_differentiableOn_iff, LieSubmodule.toEnd_comp_subtype_mem, LinearIsometryEquiv.comp_differentiableAt_iff, Matrix.Represents.zero, coe_toLexLinearEquiv, Submodule.coe_quotEquivOfEqBot_symm, LinearMap.range_toSpanSingleton, Submodule.map₂_map_right, Representation.norm_ofMulDistribMulAction_eq, CliffordAlgebra.submodule_comap_mul_reverse, Matrix.kroneckerMapBilinear_apply_apply, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, LaurentSeries.powerSeriesPart_coeff, ContDiffWithinAt.continuousLinearMap_comp, LinearMap.minpoly_dvd_charpoly, PowerBasis.trace_gen_eq_nextCoeff_minpoly, LinearEquiv.rTensor_pow, Ideal.pi_tensorProductMk_quotient_surjective, Matrix.rank_eq_finrank_range_toLin, MvPolynomial.rTensor_apply_tmul, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, ContinuousAlternatingMap.norm_ofSubsingleton, TensorProduct.AlgebraTensorModule.congr_mul, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', CliffordAlgebra.invOf_ι_mul_ι_mul_ι, Matrix.toLinearMapRight'_mul_apply, Submodule.toLinearMap_starProjection_eq_isComplProjection, CommRing.Pic.mk_eq_one_iff, hasStrictFDerivAt_finCons, InnerProductSpace.rankOne_def, MDifferentiableWithinAt.coordChangeL, Polynomial.degree_derivative_lt, Diffeomorph.mfderivToContinuousLinearEquiv_coe, BilinForm.toMatrix_comp, TensorProduct.nnnorm_map, MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_ne, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, IsLocalMinOn.hasFDerivWithinAt_nonneg, Orientation.oangle_rotation, CharacterModule.intSpanEquivQuotAddOrderOf_apply, Matrix.reindexLinearEquiv_one, LieAlgebra.ad_nilpotent_of_nilpotent, CliffordAlgebra.EvenHom.contract, Polynomial.derivative_natCast_mul, ContinuousLinearMap.coe_flipₗᵢ', AlgHom.mulLeftRight_apply, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, ModuleCat.mono_iff_injective, Module.Basis.linearCombination_dualBasis, Ideal.mapCotangent_toCotangent, PiTensorProduct.norm_eval_le_injectiveSeminorm, MeasureTheory.weightedSMul_null, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, FiniteDimensional.basisSingleton_repr_apply, SchwartzMap.convolution_apply, Submodule.sub_starProjection_mem_orthogonal, Module.Flat.iff_lTensor_preserves_injective_linearMap', contDiffOn_succ_iff_fderiv_of_isOpen, Algebra.Generators.Cotangent.surjective_map_ofComp, PointwiseConvergenceCLM.equivWeakDual_apply, DFinsupp.counit_comp_lsingle, ModuleCat.forget₂_obj, Subalgebra.linearEquivOp_apply_coe, Submodule.prodEquivOfIsCompl_symm_apply_fst_eq_zero, hasSum_jacobiTheta₂_term_fderiv, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, orthogonalBilin_innerₗ, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one, transpose_dualTensorHom, AffineMap.linearMap_vsub, ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, MvPolynomial.coeff_monomial_mul, LinearMap.coe_proj, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, Matrix.toLin_mul, ConvexOn.real_univ_sSup_of_countable_affine_eq, TensorProduct.AlgebraTensorModule.assoc_tmul, Rep.indResAdjunction_counit_app_hom_hom, FDRep.hom_hom_action_ρ, CliffordAlgebra.map_apply_ι, LinearMap.lTensor_neg, TensorAlgebra.ι_range_disjoint_one, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, FGModuleCat.FGModuleCatDual_obj, MvPolynomial.bind₂_id, CliffordAlgebra.submodule_map_pow_reverse, LinearEquiv.coe_prodUnique, Matrix.toLin_pow, Submodule.coe_tensorSpanEquivSpan_apply_tmul, Submodule.annihilator_map_mkQ_eq_colon, Module.Basis.equivFunL_symm_apply_repr, LieSubmodule.mem_baseChange_iff, Module.End.aeval_apply_of_hasEigenvector, LinearEquiv.baseChange_mul, Localization.localRingHom_id, QuadraticMap.associated_tmul, Submodule.FG.lTensor.directLimit_apply', TensorProduct.directSumLeft_tmul_lof, Algebra.Generators.H1Cotangent.exact_δ_map, fderiv_mul', LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, PowerSeries.coeff_invUnitsSub, PowerBasis.repr_gen_pow_isIntegral, Module.Free.linearMap, SemimoduleCat.hom_inv_apply, UniformSpace.Completion.norm_toComplL, SkewPolynomial.monomial_zero_one, ContinuousLinearMap.coe_projKerOfRightInverse_apply, fderivWithin_const_smul_of_field, ProbabilityTheory.covarianceBilin_comm, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Derivation.liftKaehlerDifferential_comp, Representation.FiniteCyclicGroup.coinvariantsKer_eq_range, Matrix.toLin_self, Rep.coindToInd_apply, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, Orientation.inner_rotation_pi_div_two_left, Module.Finite.linearMap, HasStrictFDerivAt.ccos, LinearMap.mulLeft_mul, ContinuousMap.toLp_def, groupHomology.mapCycles₁_comp_i_apply, CliffordAlgebra.ι_mul_ι_add_swap, kroneckerTMulLinearEquiv_one, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, DirectSum.lieAlgebraComponent_apply, AlternatingMap.ofSubsingleton_apply_apply, Submodule.dualCoannihilator_bot, VectorField.lieBracket_fmul_left, TensorProduct.AlgebraTensorModule.leftComm_symm_tmul, SheafOfModules.pushforwardCongr_hom_app_val_app, RootPairing.Hom.comp_weightMap_apply, Polynomial.valuation_inv_monomial_eq_valuation_X_zpow, Polynomial.sum_monomial_index, Module.DirectLimit.linearEquiv_of, Polynomial.derivativeFinsupp_derivative, HasFDerivAtFilter.sum, AdicCompletion.sumInv_comp_sum, SchwartzMap.integral_bilin_fourier_eq, fwdDiff_aux.shiftₗ_pow_apply, Complex.det_conjAe, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, HasFDerivWithinAt.lim, Orientation.oangle_rotation_self_left, Finsupp.lsum_single, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, KaehlerDifferential.ker_map, MvPolynomial.dvd_monomial_iff_exists, ContinuousLinearEquiv.contDiffPointwiseHolderAt, AlgCat.forget₂Module_preservesLimitsOfSize, LinearMap.BilinForm.neg_left, ModuleCat.comp_apply, ClosedSubmodule.orthogonal_eq_inter, PositiveLinearMap.toPreGNS_ofPreGNS, mulRightLinearMap_zero_eq_zero, AlgHom.toKerIsLocalization_apply, ContinuousMultilinearMap.prodL_apply, LinearMap.BilinForm.sum_repr_mul_repr_mul, Finsupp.linearEquivFunOnFinite_single, Module.Basis.mulOpposite_repr_op, Orientation.kahler_neg_orientation, TensorProduct.AlgebraTensorModule.rightComm_tmul, QuadraticForm.dualProdIsometry_invFun, PowerSeries.prod_monomial, ModuleCat.restrictScalarsCongr_hom_app, HasFDerivWithinAt.cexp, AdicCompletion.coe_eval, hasFDerivWithinAt_iff_hasDerivWithinAt, ProperCone.coe_comap, LinearMap.separatingLeft_toMatrix₂'_iff, LinearEquiv.transvections_subset_dilatransvections, Module.Basis.smulTower'_repr_mk, hasFTaylorSeriesUpToOn_succ_iff_right, fderiv_comp_fderivWithin, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, KaehlerDifferential.mapBaseChange_surjective, AffineMap.neg_linear, NonUnitalAlgHom.coe_Lmul, PowerSeries.coeff_succ_C, LinearMap.nondegenerate_iff_det_ne_zero, Polynomial.sum_monomial_eq, ContinuousLinearMap.toSpanSingleton_comp, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, TannakaDuality.FiniteGroup.leftRegular_apply, ContinuousMultilinearMap.norm_map_init_le, Module.FaithfullyFlat.iff_zero_iff_lTensor_zero, ContinuousMap.coeFnLinearMap_apply, ContinuousLinearMap.isIdempotentElem_toLinearMap_iff, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, AdicCompletion.coe_ofTensorProductEquivOfFiniteNoetherian, LeftInvariantDerivation.left_invariant'', groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CliffordAlgebra.contractLeft_contractLeft, MulOpposite.opContinuousLinearEquiv_symm_apply, TensorProduct.AlgebraTensorModule.assoc_symm_tmul, SchwartzMap.compCLMOfAntilipschitz_apply, LinearMap.pi_apply, TensorProduct.algebraMap_gradedMul, SchwartzMap.fourierInv_apply_eq, trace_eq_finrank_mul_minpoly_nextCoeff, PowerSeries.trunc_trunc_mul, SchwartzMap.smulRightCLM_apply_apply, Matrix.cramer_zero, Submodule.dualCoannihilator_top, hasEigenvector_toLin'_diagonal, LinearMap.lcomp_apply, LinearIsometryEquiv.conjStarAlgEquiv_refl, instIsLocalizedModuleFinsuppLinearMap, CurveIntegrable.fun_zero, Matrix.GeneralLinearGroup.toLin'_apply, LinearMap.mapMatrixModule_id_apply, Representation.apply_bijective, CategoryTheory.whiskering_linearYoneda, HasDerivAt.complexToReal_fderiv', IsBaseChange.lift_comp, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, MvPolynomial.mkDerivationₗ_monomial, hasStrictFDerivAt_iff_hasStrictDerivAt, Finsupp.counit_comp_lsingle, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ModuleCat.MonoidalCategory.rightUnitor_hom_apply, LinearMap.toMatrixAlgEquiv'_apply, LieAlgebra.ad_pow_lie, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, Submodule.FG.rTensor.directLimit_apply, VectorField.mpullback_apply, LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, Module.Dual.instIsReflecive, TensorProduct.directLimitLeft_rTensor_of, LinearMap.IsSymmetric.toSelfAdjoint_apply, TensorProduct.finsuppScalarRight_smul, MeasureTheory.Lp.constₗ_apply, Submodule.coe_continuous_linearProjOfClosedCompl, ContDiffWithinAt.continuousWithinAt_fderivWithin, fderiv_mem_iff, LinearMap.BilinForm.inf_orthogonal_self_le_ker_restrict, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, LinearMap.BilinForm.IsAlt.self_eq_zero, CliffordAlgebra.evenOdd_map_reverse, Polynomial.degree_derivative_eq, Polynomial.C_mul_monomial, MeasureTheory.aemeasurable_fderivWithin, LieModule.Cohomology.d₁₂_apply_coe_apply_apply, TopModuleCat.hom_zsmul, Matrix.reindexLinearEquiv_comp, Submodule.coe_orthogonalDecomposition, VectorField.lieBracket_eq, Orientation.map_eq_det_inv_smul, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, LinearMap.intrinsicStar_comp', ContinuousLinearMap.coe_restrict_scalarsL', HasDerivAt.complexToReal_fderiv, Polynomial.natDegree_hasseDeriv_le, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, ModuleCat.FilteredColimits.M.mk_map, ContinuousLinearMapWOT.isInducing_inducingFn, TensorProduct.lid_symm_apply, fderivWithin_fderivWithin_eq_of_eventuallyEq, groupCohomology.π_comp_H0Iso_hom_apply, LinearMap.sup_range_inl_inr, LinearEquiv.refl_trans, Submodule.map_unop_pow, IsTensorProduct.equiv_apply, Matrix.vecMulLinear_apply, DoubleCentralizer.star_fst, Matrix.toLinearMapₛₗ₂'_toMatrix', LinearMap.continuous_of_isContPerfPair, LinearMap.pi_eq_zero, ConvexCone.mem_map, Bialgebra.comul_algebraMap, LinearMap.toMatrix'_algebraMap, isNoetherian_linearMap, LieEquiv.right_inv, StrongDual.polarSubmodule_eq_polar, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, LinearMap.flip.instIsPerfPair, IsLocalizedModule.subsingleton_iff_ker_eq_top, ContinuousLinearMap.coe_inr, Matrix.cramer_reindex, Submodule.inclusionSpan_apply_coe, Module.End.coe_pow, Rep.resIndAdjunction_homEquiv_symm_apply, groupHomology.coe_mapCycles₂, finsuppTensorFinsupp_single, TensorProduct.counit_tmul, PiTensorProduct.liftEquiv_symm_apply, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, PiToModule.fromMatrix_apply_single_one, LocalizedModule.coe_map_eq, LinearIsometryEquiv.piLpCurry_apply, Representation.linHom_apply, MvPolynomial.sum_weightedHomogeneousComponent, RCLike.geometric_hahn_banach_point_point, Submodule.comap_subtype_self, Algebra.Extension.CotangentSpace.map_sub_map, TestFunction.coe_ofSupportedInLM, exteriorPower.oneEquiv_naturality, mfderivWithin_eventually_congr_set', QuadraticMap.associated_toQuadraticMap, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, ExteriorAlgebra.ι_range_disjoint_one, LinearMap.span_singleton_sup_ker_eq_top, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, MvPowerSeries.HasSubst.coeff_zero, LinearMap.dualMap_injective_iff, LinearMap.isPositive_natCast, RootPairing.bijOn_reflection_root, Algebra.normalizedTrace_eq_of_fininteDimensional, TensorProduct.toLinearEquiv_congrIsometry, LinearEquiv.instIsPerfPair, ContinuousLinearEquiv.prodComm_apply, CategoryTheory.whiskering_linearCoyoneda₂, IsLocalizedModule.mem_ker_iff, Module.DirectLimit.lift_comp_of, Module.Basis.equiv'_symm_apply, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, MeasureTheory.OuterMeasure.map_map, AlternatingMap.curryLeft_apply_toMultilinearMap, LieModule.isNilpotent_toEnd_of_isNilpotent₂, Polynomial.as_sum_range, Module.Basis.eval_range, hasFDerivAt_exp_smul_const', iteratedFDerivWithin_one_apply, SkewPolynomial.monomial_zero_right, LinearEquiv.comp_symm, QuadraticMap.IsometryEquiv.prodComm_invFun, ContinuousLinearMap.restrictScalars_add, MeasureTheory.SignedMeasure.re_toComplexMeasure, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, TemperedDistribution.smulLeftCLM_sub, groupHomology.H1π_comp_map_apply, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, Module.Basis.repr_reindex, BilinearForm.toMatrixAux_eq, CliffordAlgebra.contractLeft_ι_mul, QuadraticMap.two_nsmul_associated, ContinuousLinearEquiv.coe_prodCongr, TensorProduct.lid_tmul, RootPairing.rootForm_reflection_reflection_apply, Submodule.IsPrincipal.generator_submoduleImage_dvd_of_mem, LinearMap.dualPairing_nondegenerate, LieHom.lie_apply, LinearMap.isAdjointPair_one, Submodule.norm_subtypeL, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, CliffordAlgebra.comp_ι_sq_scalar, RootPairing.posRootForm_posForm_pos_of_ne_zero, LinearEquiv.withLpCongr_refl, Matrix.SeparatingLeft.toBilin, SemimoduleCat.hom_inv_leftUnitor, NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, Matrix.charpoly_toLin, Module.subsingletonEquiv_symm_apply, LinearMap.inr_injective, FGModuleCat.FGModuleCatCoevaluation_apply_one, Module.Basis.coe_sumCoords_eq_finsum, LinearMap.toMatrixOrthonormal_symm_apply, LinearEquiv.extendScalarsOfIsLocalization_symm_apply, Derivation.compAlgebraMapL_apply_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, LinearEquiv.congrLeft_apply, IsLocalizedModule.map_linearCombination, ContinuousLinearMap.IsStarNormal.orthogonal_range, DirectSum.congr_linearEquiv_toLinearMap, ContinuousLinearMap.aestronglyMeasurable_comp₂, LinearMap.BilinMap.baseChange_tmul, Module.Basis.algebraMapCoeffs_repr_apply_toFun, Module.Flat.eqLocus_lTensor_eq, Subspace.dualRestrict_leftInverse, QuadraticForm.tmul_tensorAssoc_apply, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, SchwartzMap.smulLeftCLM_const, TensorProduct.exists_finite_submodule_left_of_finite, hasStrictFDerivAt_piLp, StrongDual.dualPairing_apply, LinearMap.intrinsicStar_rTensor, IsLocalMinOn.hasFDerivWithinAt_eq_zero, HopfAlgebra.sum_antipode_mul_eq_smul, LinearMap.BilinForm.IsPosSemidef.add, LinearEquiv.piRing_symm_apply, MeasureTheory.OuterMeasure.restrict_empty, LinearEquiv.refl_symm, trace_eq_trace_adjoin, CliffordAlgebra.even.lift_ι, LinearMap.toMatrix_mulVec_repr, Module.charP_end, LinearMap.BilinForm.zero_left, CliffordAlgebra.ι_range_map_reverse, Submodule.IsCompl.projection_eq_self_iff, LinearMap.toMatrix_innerₛₗ_apply, TensorProduct.piRight_symm_apply, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem_ne, ContinuousMapZero.toContinuousMapCLM_apply, Module.Basis.ofIsLocalizedModule_apply, ContinuousAffineMap.sub_contLinear, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, KaehlerDifferential.map_surjective_of_surjective, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, LieModule.Cohomology.mem_twoCochain_iff, Submodule.mkQ_apply, PointwiseConvergenceCLM.equivWeakDual_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, Orientation.rightAngleRotation_map', TensorProduct.gradedComm_one, TensorProduct.toLinearEquiv_commIsometry, ProperCone.hyperplane_separation_point, LinearMap.BilinForm.isSymm_iff, fderiv_fun_sum, LinearMap.funLeft_injective_of_surjective, NumberField.mixedEmbedding.negAt_apply_isComplex, LinearMap.comap_codRestrict, IsLocalizedModule.pi, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, AffineMap.hasDerivAt, Matrix.toLin_apply_eq_zero_iff, LinearIsometry.coe_pow, Complex.hasFDerivAt_cpow, MvPolynomial.modMonomial_add_divMonomial, RootPairing.Equiv.weightEquiv_mul, StarConvex.linear_image, Orientation.inner_rotation_pi_div_two_left_smul, MonomialOrder.span_leadingTerm_eq_span_monomial', Submodule.norm_sq_eq_add_norm_sq_projection, TensorProduct.lTensorHomToHomLTensor_apply, LinearMap.extendTo𝕜'_apply_re, IsLocalizedModule.mapEquiv_apply, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, Algebra.PreSubmersivePresentation.jacobian_eq_det_aevalDifferential, tangentCoordChange_comp, Matrix.ker_mulVecLin_transpose_mul_self, Polynomial.det_taylorLinearEquiv_toLinearMap, PiTensorProduct.reindex_symm, IsTensorProduct.map_one, HasFDerivWithinAt.fun_neg, Matrix.nondegenerate_toBilin_iff, LinearIsometry.norm_iteratedFDeriv_comp_left, LinearEquiv.det_symm, Coalgebra.sum_counit_tmul_map_eq, LinearMap.range_toContinuousLinearMap, Ideal.exact_mulQuot_quotOfMul, MvPolynomial.decompose'_apply, WithCStarModule.linearEquiv_apply, LinearMap.BilinForm.isSymm_neg, Polynomial.mkDerivationEquiv_symm_apply, fderiv_const_smul_of_invertible, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, IsLocalMax.hasFDerivAt_eq_zero, ContinuousLinearEquiv.dimH_image, ContinuousLinearMap.norm_precompR_le, hasFDerivWithinAt_pow', LieModule.Weight.coe_toLinear_eq_zero_iff, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, Matrix.toLin'_reindex, LocalizedModule.subsingleton_iff_ker_eq_top, BialgHom.toAlgHom_toLinearMap, MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable, LinearMap.transvection.apply, PowerSeries.IsRestricted.isRestricted_iff, SemimoduleCat.hom_tensorHom, LinearMap.BilinForm.toDual_def, LinearMap.ker_toSpanSingleton_eq_bot_iff, CliffordAlgebra.contractRight_mul_algebraMap, Module.Relations.Solution.IsPresentation.uniq_var, MeasureTheory.OuterMeasure.map_ofFunction, ContinuousLinearMap.hasFDerivAtFilter, CliffordAlgebra.ι_range_map_involute, ContinuousLinearMap.isBoundedLinearMap_comp_right, WithLp.prodContinuousLinearEquiv_symm_apply_ofLp, ContinuousLinearEquiv.finTwoArrow_apply, PrimeSpectrum.BasicConstructibleSetData.map_id, Module.Basis.algebraMapCoeffs_repr_apply_apply, Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, MultilinearMap.domDomCongrLinearEquiv_apply, HasFDerivAt.iterate, Submodule.comm_trans_rTensorOne, groupHomology.π_comp_H0Iso_hom_apply, LinearMap.BilinForm.toMatrix'_compLeft, Matrix.toLinearMapₛₗ₂_apply, Submodule.starProjection_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, IsLocalizedModule.fromLocalizedModule_mk, Polynomial.monomial_mul_X, MeasureTheory.OuterMeasure.map_comap_of_surjective, MultilinearMap.freeDFinsuppEquiv_single, Finsupp.lcomapDomain_apply, LinearMap.mulRight_tmul, Polynomial.rootSet_derivative_subset_convexHull_rootSet, LineDeriv.laplacianCLM_eq_sum, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', VonNeumannAlgebra.mem_carrier, Polynomial.mapAlgHom_monomial, Finsupp.lhom_ext'_iff, groupCohomology.eq_d₀₁_comp_inv_apply, Submodule.card_quotient_mul_card_quotient, WeakDual.isSeqCompact_closedBall, LinearMap.BilinForm.dualBasis_repr_apply, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, MultilinearMap.map_add_sub_map_add_sub_linearDeriv, PiTensorProduct.liftEquiv_apply, MvPowerSeries.coeff_one, LinearMap.smul_lTensor, HasFDerivAt.cexp, Polynomial.iterate_derivative_X_pow_eq_natCast_mul, DoubleCentralizer.add_snd, MaximalSpectrum.mapPiLocalization_id, LinearMap.lsmul_injective, ModuleCat.MonoidalCategory.tensorLift_tmul, HasFDerivAt.ccos, MeasureTheory.norm_condExpInd_apply_le, Profinite.NobelingProof.Products.eval_πs_image', Submodule.factor_comp, LineDeriv.iteratedLineDerivOpCLM_apply, Module.IsReflexive.bijective_dual_eval', IsIsotypicOfType.linearEquiv_finsupp, fderivWithin_iteratedFDerivWithin, TensorProduct.intrinsicStar_map, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, Polynomial.natDegree_taylor, Unitization.sndHom_apply, WittVector.fromPadicInt_comp_toPadicInt_ext, ContinuousLinearMap.rayleighQuotient_add, Polynomial.degree_taylor, LinearMap.smulRight_apply_eq_zero_iff, LinearIsometry.toSpanSingleton_apply, span_range_eq_top_iff_surjective_fintypeLinearCombination, hasFDerivAt_iff_tendsto, Orientation.eq_rotation_self_iff, VonNeumannAlgebra.centralizer_centralizer, IsLocalizedModule.lift_comp, ContinuousMultilinearMap.piLinearEquiv_apply, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply, ExteriorAlgebra.liftAlternating_one, Complex.selfAdjointEquiv_apply, Subspace.flip_quotDualCoannihilatorToDual_bijective, LinearMap.isSelfAdjoint_iff', LinearIsometryEquiv.piLpCongrRight_single, Subspace.dual_finrank_eq, Derivation.commutator_coe_linear_map, ContinuousLinearMap.deriv_of_bilinear, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, linearIndepOn_iff_disjoint, Submodule.apply_mem_map₂, HasFDerivWithinAt.log, Valuation.comap_id, Orientation.areaForm'_apply, MvPolynomial.monomial_one_mul_cancel_left_iff, VectorBundleCore.coe_coordChange, pinGroup.conjAct_smul_ι_mem_range_ι, hasFDerivAtFilter_iff_hasDerivAtFilter, DirectSum.linearEquivFunOnFintype_lof, groupCohomology.cocycles₁_map_inv, Module.Basis.sumQuot_repr_inl_of_mem, Module.Basis.end_apply, Rep.freeLiftLEquiv_apply, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative_of_mem_nonZeroDivisors, HasFDerivAt.clog, Submodule.exists_fg_le_subset_range_rTensor_subtype, innerSLFlip_apply_apply, TensorPower.algebraMap₀_eq_smul_one, ContinuousLinearEquiv.mdifferentiableOn, Module.End.ringEquivEndFinsupp_apply_apply_apply, ContinuousLinearMap.nnnorm_holder_apply_apply_le, LinearMap.separatingLeft_iff_det_ne_zero, LinearMap.toSpanSingleton_smul, TensorProduct.rTensor_injective_of_forall_vanishesTrivially, PowerSeries.coeff_mk, Submodule.set_smul_eq_map, ModuleCat.hom_hom_leftUnitor, OrthogonalFamily.hasSum_linearIsometry, MvPolynomial.coe_basisMonomials, LinearMap.map_comp_rTensor, Polynomial.hasFDerivAt, MultilinearMap.curryMid_apply_apply, FractionalIdeal.canonicalEquiv_spanSingleton, PresheafOfModules.surjective_of_epi, DFinsupp.comul_comp_lapply, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_symm_apply, Distribution.mapCLM_apply, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FourierTransform.fourierCLE_apply, FormalMultilinearSeries.norm_compContinuousLinearMap_le, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, Module.End.isSemisimple_sub_algebraMap_iff, commute_mulLeftLinearMap_mulRightLinearMap, toKerIsLocalization_apply, LinearEquiv.symm_trans_self, Matrix.Nondegenerate.toBilin, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, PowerSeries.sub_const_eq_X_mul_shift, TensorProduct.finsuppScalarRight_apply_tmul_apply, SemimoduleCat.MonoidalCategory.tensorμ_apply, LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, Derivation.coe_comp, Algebra.TensorProduct.leftComm_toLinearEquiv, LinearMap.IsPositive.isSelfAdjoint, ModuleCat.adj_homEquiv, AlgEquiv.coe_symm_toLinearEquiv, ContinuousLinearMap.bilinear_hasTemperateGrowth, LinearMap.toMatrix'_apply, LinearMap.mem_span_iff_continuous_of_finite, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, LinearEquiv.baseChange_tmul, MvPolynomial.monomial_mem_pow_idealOfVars_iff, PiTensorProduct.ofDFinsuppEquiv_tprod_apply, DoubleCentralizer.norm_snd, QuadraticForm.tmul_tensorComm_apply, Module.Basis.repr_symm_single, Matrix.toLpLin_toLp, PowerSeries.coeff_largeSchroderSeries, Representation.finsuppToCoinvariants_single_mk, MvPowerSeries.coeff_mul_right_one_sub_of_lt_order, RingEquiv.moduleEndSelf_apply, ConvexOn.sSup_of_nat_affine_eq, apply_eq_dotProduct_toMatrix₂_mulVec, IsIdempotentElem.ker_toSpanSingleton_one_sub_eq_span, Polynomial.degreeLT.addLinearEquiv_apply, AlgHom.toLinearMap_injective, SchwartzMap.fourierTransformCLE_apply, Orthonormal.equiv_trans, Submodule.fst_orthogonalDecomposition_apply, LinearEquiv.mem_dilatransvections_iff_finrank, kroneckerLinearEquiv_symm_kronecker, Submodule.quotEquivOfEqBot_apply_mk, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, Rep.indToCoindAux_mul_fst, LinearEquiv.coe_toContinuousLinearEquiv', hasFDerivWithinAt_one, LinearMap.BilinForm.separatingRight_toMatrix_iff, RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict, MultilinearMap.freeDFinsuppEquiv_def, LinearMap.mulLeft_apply, map_equiv_traceDual, TensorProduct.finsuppLeft_apply, ModuleCat.hom_hom_rightUnitor, ContinuousLinearMap.toSpanSingletonLE_apply, MvPolynomial.irreducible_sumSMulX, LinearMap.comm_comp_lTensor_comp_comm_eq, RootPairing.Equiv.comp_weightMap_apply, ContinuousLinearEquiv.nhds, TensorProduct.mapBilinear_apply, Lagrange.eq_interpolate, Submodule.smul_starProjection_singleton, finsuppTensorFinsuppRid_symm_single_smul, Subalgebra.LinearDisjoint.trace_algebraMap, LightCondensed.forget_map_val_app, LinearEquiv.prodComm_apply, TensorProduct.prodRight_symm_tmul, MvPowerSeries.coeff_expand_smul, LinearEquiv.mapMatrix_refl, DoubleCentralizer.nnnorm_fst, Representation.IntertwiningMap.ext_iff, finsetBasisOfTopLeSpanOfCardEqFinrank_repr_apply, LinearEquiv.conj_apply, DFinsupp.mapRange.linearEquiv_apply, LinearMap.finiteDimensional', Module.Basis.toDual_range, ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, IsSemisimpleModule.exists_quotient_linearEquiv_submodule, Complex.equivRealProdLm_apply, Orientation.inner_comp_rightAngleRotation, PiTensorProduct.dualDistribInvOfBasis_apply, intervalIntegral.integral_hasStrictFDerivAt, Representation.asAlgebraHom_single_one, CStarAlgebra.linear_combination_nonneg, Polynomial.map_id, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, fderivWithin_mul_const', TensorProduct.gradedComm_symm, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Submodule.restrictScalarsEquiv_symm_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, ZMod.invDFT_def', LinearMap.quotientInfEquivSupQuotient_injective, linearIndependent_inl_union_inr', Complex.ofRealCLM_apply, ModuleCat.piIsoPi_inv_kernel_ι_apply, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, LinearEquiv.isPositive_symm_iff, Submodule.map₂_eq_span_image2, Polynomial.separable_def', ModuleCat.MonModuleEquivalenceAlgebra.functor_map_hom_apply, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Module.Basis.exists_opNNNorm_le, Rep.ihom_obj_ρ_apply, Module.Basis.restrictScalars_repr_apply, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, Matrix.ker_toLin_eq_bot, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, PiTensorProduct.mapL_mul, cfcHom_real_eq_restrict, FourierTransform.fourierInvₗ_apply, Polynomial.derivative_of_natDegree_zero, SpecialLinearGroup.det_coe, TensorProduct.AlgebraTensorModule.dualDistrib_apply, Representation.finsupp_single, LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left, ContinuousLinearMap.toLinearMap_innerSL_apply, Coalgebra.IsCocomm.comm_comp_comul, ModuleCat.ker_eq_bot_of_mono, RootPairing.Hom.coroot_coweightMap, CliffordAlgebra.GradedAlgebra.ι_apply, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, SchwartzMap.pderivCLM_apply, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, ContinuousLinearMap.isInvertible_equiv, Module.End.isUnit_iff, RootPairing.Equiv.weightEquiv_inv, hasFDerivAt_ofNat, CondensedMod.hom_naturality_apply, Finsupp.span_eq_range_linearCombination, Polynomial.toFinsuppIsoLinear_symm_apply_toFinsupp, Module.Basis.equivFunL_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, Submodule.dualAnnihilator_sup_eq, LieModule.Cohomology.d₁₂_apply_apply_ofTrivial, star_mul_self_add_self_mul_star, inner_map_complex, Finsupp.isCompl_range_lmapDomain_span, hasFDerivAt_list_prod_finRange', GradedTensorProduct.auxEquiv_mul, ContinuousMultilinearMap.apply_apply, Fintype.linearIndependent_iff'ₛ, QuadraticForm.tmul_tensorRId_apply, LinearMap.IsSymmetric.adjoint_eq, Trivialization.continuousLinearEquivAt_apply', BoundedContinuousFunction.probCharDual_zero, LinearMap.isPositive_sum, ContinuousMultilinearMap.flipLinear_apply_apply, Submodule.starProjection_norm_le, HasStrictFDerivAt.neg, DirectSum.congrLinearEquiv_toLinearMap, WeakDual.CharacterSpace.coe_toCLM, HahnSeries.ofPowerSeries_apply_coeff, MvPowerSeries.eval₂_eq_tsum, mfderiv_add, HasGradientAt.hasFDerivAt, TensorProduct.piRight_symm_single, Submodule.lTensorOne'_tmul, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, RootPairing.CoPolarizationIn_eq, Module.FinitePresentation.linearEquivMap_apply, LinearMap.range_inl, Submodule.equivOpposite_apply, LinearMap.hasDerivWithinAt, MvPowerSeries.homogeneousComponent_of_lt_order_eq_zero, MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination, CStarMatrix.toCLM_apply_single, Module.Relations.map_single, ModuleCat.lof_coprodIsoDirectSum_inv_apply, FourierTransform.fourierEquiv_symm_apply, Polynomial.Splits.taylor, pow_mulLeftLinearMap, LinearMap.BilinMap.isSymm_iff_eq_flip, MvPolynomial.rTensorAlgHom_toLinearMap, ContinuousLinearMap.coe_pi, Submodule.rTensorOne'_tmul_one, ContinuousLinearMap.comp_coprod, Submodule.inner_orthogonalProjection_eq_of_mem_right, Submodule.reflection_reflection, LinearMap.ker_domRestrict, AddEquiv.toNatLinearEquiv_trans, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, IsSelfAdjoint.spectrumRestricts, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, LinearMap.llcomp_apply', Submodule.dualCoannihilator_sup_eq, imaginaryPart.norm_le, AffineBasis.det_smul_coords_eq_cramer_coords, hasFTaylorSeriesUpTo_succ_nat_iff_right, LieModule.exists_forall_pow_toEnd_eq_zero, ModuleCat.Derivation.desc_d, LinearMap.BilinForm.zero_apply, Prod.comul_apply, hasFDerivWithinAt_zero, reesAlgebra.monomial_mem, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, Polynomial.lt_rootMultiplicity_iff_isRoot_iterate_derivative, Rep.finsuppTensorRight_hom_hom, Algebra.Extension.CotangentSpace.map_cotangentComplex, QuadraticModuleCat.forget₂_map_associator_hom, Nat.castRingHom_nat, HasFDerivWithinAt.norm_sq, MvPolynomial.coeff_sumSMulX, hasFDerivWithinAt_piLp, MeasureTheory.norm_weightedSMul_le, PresheafOfModules.injective_of_mono, lp.singleContinuousLinearMap_apply, Complex.restrictScalars_one_smulRight, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, ContinuousLinearMapWOT.isEmbedding_inducingFn, QuotSMulTop.equivQuotTensor_naturality, AddMonoidHom.coe_toNatLinearMap, LinearMap.smulRightₗ_apply, Submodule.rTensorOne'_tmul, PowerSeries.derivativeFun_coe, JacobsonNoether.exist_pow_eq_zero_of_le, LinearEquiv.coe_toAffineEquiv, CliffordAlgebra.reverse.map_mul, IsLocalizedModule.mapEquiv_symm_apply, QuadraticMap.isOrtho_polarBilin, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, MvPowerSeries.le_weightedOrder_subst, ModuleCat.free_ε_one, LinearMap.toMatrix'_symm, Polynomial.coeff_monomial, ProbabilityTheory.HasGaussianLaw.map, EuclideanGeometry.reflection_apply_of_mem, norm_fderiv_norm_rpow_le, ContinuousMultilinearMap.toContinuousLinearMap_apply, Module.symm_dualMap_evalEquiv, SeparationQuotient.exists_out_continuousLinearMap, Module.Invertible.rTensor_injective_iff, ContinuousLinearMap.one_apply, LinearMap.flip_mul, BialgEquiv.toLinearMap_ofAlgEquiv, StrongDual.dualPairing_separatingLeft, VectorFourier.fderiv_fourierIntegral, Finsupp.linearCombinationOn_range, Polynomial.splits_id_iff_splits, ProperCone.dual_singleton, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, AdicCompletion.of_bijective_iff, Algebra.TensorProduct.basisAux_tmul, groupCohomology.norm_ofAlgebraAutOnUnits_eq, VectorBundle.continuousOn_coordChange', TensorProduct.exists_finite_submodule_right_of_setFinite', Algebra.lsmul_injective, LinearMap.isPositive_linearIsometryEquiv_conj_iff, realPart_comp_subtype_selfAdjoint, MvPowerSeries.monomial_zero_eq_C_apply, TensorProduct.AlgebraTensorModule.map_add_left, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, Module.Basis.singleton_repr, ContinuousLinearMap.mfderiv_eq, RootPairing.algebraMap_rootFormIn, KaehlerDifferential.derivationQuotKerTotal_apply, InnerProductGeometry.norm_ofLp_crossProduct, AdicCompletion.transitionMap_comp_reduceModIdeal, MeasureTheory.integral_posConvolution, Orthonormal.linearIsometryEquiv_symm_apply_single_one, TensorProduct.AlgebraTensorModule.uncurry_apply, hasFDerivWithinAt_singleton, TensorProduct.map_comm, Module.DirectLimit.exists_of, Submodule.map_subtype_embedding_eq, ContinuousAffineMap.contLinear_eq_zero_iff_exists_const, LinearEquiv.coe_toContinuousLinearEquiv_symm', Pretrivialization.linearMapAt_apply, Submodule.le_linearEquiv_of_le_sSup, mulRightLinearMap_eq_zero_iff, SchwartzMap.fourierInv_lineDerivOp_eq, Differential.mapCoeffs_monomial, LinearEquiv.congr_trans_rTensor, IsStandardSmoothOfRelativeDimension.id, AlternatingMap.domCoprod'_apply, InnerProductSpace.harmonicAt_comp_CLE_iff, Bundle.RiemannianMetric.symm, Module.AEval.X_pow_smul_of, ExteriorAlgebra.ι_sq_zero, Submodule.exists_dual_map_eq_bot_of_lt_top, Polynomial.taylor_coeff_zero, MonomialOrder.monic_monomial, ModuleCat.imageIsoRange_hom_subtype_assoc, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, linearEquivIsoModuleIsoₛ_hom, PowerSeries.monomial_zero_eq_C, HasStrictFDerivAt.add, iteratedFDeriv_eq_equiv_comp, Submodule.reflection_inv, groupCohomology.mem_cocycles₂_iff, LinearMap.polyCharpolyAux_map_eq_charpoly, linear_isometry_complex, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, Submodule.LinearDisjoint.injective, DirectSum.lmap_surjective, Matrix.range_mulVecLin, Submodule.baseChange_eq_span, linearMap_toMatrix_mul_basis_toMatrix, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, TrivSqZeroExt.liftEquiv_apply, CliffordAlgebra.isUnit_ι_iff, LinearMap.mem_submoduleImage, Unitization.norm_eq_sup, LinearMap.add_compMultilinearMap, Submodule.dualCopairing_apply, iterateFrobenius_zero, LinearEquiv.toSpanNonzeroSingleton_apply, ProbabilityTheory.isGaussian_map, Matrix.kroneckerTMulAlgEquiv_symm_apply, ContinuousMap.toLp_norm_eq_toLp_norm_coe, Module.dualPairing_apply, LinearMap.iterateKer_coe, Polynomial.mul_eq_sum_sum, Submodule.comap_snd, MulOpposite.counit_def, PowerSeries.monomial_pow, mfderivWithin_comp_of_preimage_mem_nhdsWithin, Matrix.ofLp_toEuclideanCLM, Submodule.le_comap_mkQ, Polynomial.mkDerivationEquiv_apply, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Derivation.liftKaehlerDifferential_comp_D, LinearMap.IsPosSemidef.isNonneg, LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, Rep.resIndAdjunction_homEquiv_apply, CStarMatrix.toCLM_apply_eq_sum, TensorProduct.AlgebraTensorModule.coe_lTensor, LinearMap.BilinForm.isNonneg_zero, Submodule.span_algebraMap_image_of_tower, LinearMap.exact_smul_id_smul_top_mkQ, RootPairing.Equiv.coweightEquiv_mul, RootPairing.toPerfPair_flip_comp_coroot, Coalgebra.rTensor_counit_comp_comul, DFinsupp.linearEquivFunOnFintype_symm_apply, LinearMap.toMatrix_transpose_apply, LinearMap.BilinForm.IsSymm.sub, AffineIsometry.map_vsub, PiTensorProduct.mapL_comp, HasFDerivAt.ccosh, Submodule.norm_starProjection, CategoryTheory.HomOrthogonal.matrixDecompositionLinearEquiv_apply, Pi.basis_repr, MvPowerSeries.coeff_comp_monomial, PowerSeries.eq_X_pow_mul_shift_add_trunc, Matrix.kroneckerTMulStarAlgEquiv_apply, fderiv_cos, AffineMap.map_vectorSpan, PresheafOfModules.pushforward_obj_map_apply, Polynomial.iterate_derivative_C, FiniteDimensional.nonempty_continuousLinearEquiv_of_finrank_eq, MeasureTheory.weightedSMul_add_measure, Unitary.linearIsometryEquiv_coe_symm_apply, toMatrix_dualTensorHom, SemimoduleCat.homAddEquiv_apply, Submodule.eq_starProjection_of_mem_of_inner_eq_zero, Module.Presentation.ofLinearEquiv_toSolution, PowerSeries.trunc_trunc_of_le, ContDiff.comp_continuousLinearMap, MeasureTheory.Measure.map_conv_continuousLinearMap, PolynomialModule.comp_apply, exists_dual_vector, HasFDerivAt.abs_of_neg, LinearMap.BilinForm.nondegenerate_iff_ker_eq_bot, Orthonormal.map_equiv, MulOpposite.coe_opLinearEquiv_toLinearMap, MonomialOrder.sPolynomial_def, Submodule.ker_inclusion, hasFDerivWithinAt_comp_smul_smul_iff, AlgEquiv.symm_toAddEquiv, ContinuousLinearMap.coeLM_apply, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, groupHomology.d₂₁_comp_d₁₀_apply, fourierCoeff_toLp, Orientation.oangle_rotation_oangle_left, DirectSum.lmap_lof, IsLocalizedModule.mk'_cancel', ContinuousAlternatingMap.toContinuousMultilinearMapLinear_apply, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, exteriorPower.alternatingMapLinearEquiv_apply_ιMulti, ContinuousLinearMap.rayleighQuotient_le_norm, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Algebra.Generators.H1Cotangent.δAux_ofComp, Polynomial.taylor_X_pow, RootPairing.isCompl_rootSpan_ker_rootForm, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, CliffordAlgebra.changeForm_ι_mul_ι, groupHomology.mapCycles₂_comp_apply, Module.Relations.Quotient.linearMap_ext_iff, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, TensorProduct.AlgebraTensorModule.homTensorHomMap_apply, fderiv.snd, RootPairing.reflectionPerm_root, LinearMap.isPositive_toContinuousLinearMap_iff, OrthogonalFamily.summable_of_lp, ProbabilityTheory.IsGaussian.charFunDual_eq, Matrix.range_toLin', CommRing.Pic.mapRingHom_id, LinearIsometryEquiv.analyticWithinAt, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, LinearIsometryEquiv.toSpanUnitSingleton_apply, LinearMap.prodMapLinear_apply, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', fderivWithin_zero_of_notMem_closure, RootPairing.GeckConstruction.span_range_h_le_range_diagonal, Submodule.comap_subtype_eq_top, LinearEquiv.apply_smulCommClass, LinearIndependent.span_repr_eq, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, MeasureTheory.OuterMeasure.map_iSup, Submodule.map₂_span_singleton_eq_map_flip, LinearEquiv.finTwoArrow_apply, LinearMap.pi_apply_eq_sum_univ, Submodule.map_op_pow, curveIntegral_fun_add, RootPairing.rootForm_self_eq_zero_iff, ContinuousAffineMap.coe_contLinear_eq_linear, PerfectRing.lift_id_apply, RootPairing.corootSpan_mem_invtSubmodule_coreflection, iteratedDeriv_vcomp_three, VectorField.fderivWithin_apply_lieBracket_of_isSymmSndFDerivWithinAt, WithLp.coe_fstL, ModularFormClass.qExpansion_coeff, Submodule.prodEquivOfIsCompl_symm_apply, ZMod.dft_apply, ZMod.castHom_self, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, PiTensorProduct.piTensorHomMap_tprod_eq_map, Module.End.coe_mul, Rep.ofDistribMulAction_ρ_apply_apply, fderivWithin_fun_pow, RCLike.sqrt_map, LinearEquiv.skewProd_symm_apply, Submodule.injective_tensorToSpan, groupCohomology.d₀₁_ker_eq_invariants, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, Submodule.reflection_mul_reflection, MvPolynomial.as_sum, LinearMap.dualMap_apply', Submodule.Quotient.restrictScalarsEquiv_symm_mk, iteratedFDerivWithin_two_apply', LinearMap.mul_toMatrix', OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, Matrix.liftLinear_apply, HasStrictFDerivAt.arctan, curveIntegral_fun_neg, Rep.linearization_η_hom_apply, LinearMap.toMatrix₂_basisFun, LinearMap.det_eq_zero_iff_ker_ne_bot, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, MonomialOrder.leadingCoeff_monomial, Algebra.Presentation.differentials.comm₂₃', LinearMap.map_comp_lTensor, ContinuousLinearEquiv.symm_smul, HasFDerivAtFilter.const_smul, TensorProduct.LieModule.coe_liftLie_eq_lift_coe, ModuleCat.smulNatTrans_apply_app, rotationOf_rotation, LinearMap.BilinForm.separatingLeft_of_anisotropic, TopModuleCat.hom_id, exteriorPower.ιMultiDual_apply_ιMulti, InnerProductSpace.gramSchmidt_triangular, MvPolynomial.monomial_add_single, IsBaseChange.pi, Algebra.normalizedTrace_algebraMap_apply_eq_self, PiTensorProduct.lift_comp_reindex, ContinuousLinearMap.differentiable, QuadraticAlgebra.basis_repr_apply, IsLocalizedModule.lift_comp_iso, Submodule.starProjection_map_apply, IsMIntegralCurveAt.hasMFDerivAt, CliffordAlgebra.EquivEven.neg_v_mul_e0, pow_mulRightLinearMap, Submodule.natAbs_det_equiv, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, LinearMap.coe_prod, LinearMap.dualMap_bijective_iff, TensorPower.multilinearMapToDual_apply_tprod, HasFDerivAt.multiset_prod, HVertexOperator.of_coeff_coeff, CoalgHomClass.map_comp_comul, PiTensorProduct.map₂_tprod_tprod, LinearMap.star_eq_adjoint, AffineEquiv.coe_linear, skewAdjoint.negISMul_apply_coe, SemimoduleCat.hom_inv_associator, Polynomial.toFn_zero, LinearMap.instLieModule, IsLocalizedModule.mk'_one, Module.Basis.sum_dual_apply_smul_coord, LinearMap.compMultilinearMapₗ_apply, SpectrumRestricts.real_iff, Polynomial.ofFn_zero', TrivSqZeroExt.inrCLM_apply, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv, contDiffWithinAt_succ_iff_hasFDerivWithinAt', Matrix.mul_adjugate_apply, ContinuousLinearMap.range_smulRight_apply, Polynomial.derivative_C_mul_X, Submodule.LinearDisjoint.map, Subsemiring.map_id, IsLocalFrameOn.eventually_eq_sum_coeff_smul, LieDerivation.coe_zero_linearMap, LinearEquiv.conjRingEquiv_apply_apply, CliffordAlgebra.ι_range_comap_involute, LinearMap.toMatrix_smulBasis_right, Matrix.toLpLin_symm_id, Polynomial.eval_iterate_derivative_rootMultiplicity, contDiffOn_succ_iff_hasFDerivWithinAt, HasFDerivAt.mul_const, Submodule.map_subtype_span_singleton, Polynomial.lcoeff_apply, Polynomial.iterate_derivative_derivative_mul_X, Module.Basis.toDual_eq_repr, Polynomial.Chebyshev.add_one_mul_self_mul_T_eq_poly_in_T, Matrix.range_toLin_eq_top, Trivialization.coe_linearMapAt, AlternatingMap.curryLeft_zero, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LinearMap.coe_toAffineMap, Unitization.inrHom_apply, LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm, Module.Basis.baseChange_end, LinearAlgebra.FreeProduct.identify_one, TensorProduct.lid'_apply_tmul, Matrix.toLin_finTwoProd_apply, Submodule.mapQ_eq_factor, ModuleCat.forget_reflectsLimits, CliffordAlgebra.reverse_prod_map_ι, Rep.leftRegularHomEquiv_symm_apply, TannakaDuality.FiniteGroup.equivApp_hom, MeasureTheory.OuterMeasure.restrict_iSup, ModuleCat.uliftFunctorForgetIso_inv_app, FDRep.char_linHom, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, DoubleCentralizer.neg_toProd, FormalMultilinearSeries.radius_unshift, PowerSeries.coeff_exp, HVertexOperator.coeff_inj_iff, HasFPowerSeriesAt.fderiv_eq, LinearPMap.adjointDomainMkCLM_apply, Module.Basis.sum_repr_mul_repr, LinearMap.BilinForm.dualBasis_eq_iff, hasStrictFDerivAt_zero, Matrix.isPositive_toEuclideanLin_iff, ContDiffPointwiseHolderAt.continuousLinearMap_comp, RootPairing.coreflection_apply_self, ContinuousLinearMap.coe_restrictScalarsIsometry, Finsupp.linearCombination_apply, PointedCone.mem_map, ContinuousLinearMap.memLp_of_bilin, addMonoidEndRingEquivInt_apply, FreeAlgebra.toTensor_ι, ContinuousLinearMap.norm_inr, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, Polynomial.iterate_derivative_eq_zero, FourierTransform.fourierₗ_apply, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, AffineMap.map_vadd, LinearMap.uncurryMid_apply, Submodule.starProjection_bot, RootPairing.polarizationEquiv_apply, FiniteDimensional.nonempty_linearEquiv_iff_finrank_eq, DirectSum.linearMap_ext_iff, LinearIsometryEquiv.symm_trans_self, PerfectRing.liftAux_id_apply, Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent, iInter_halfSpaces_eq, Polynomial.hasseDeriv_coeff, ContinuousLinearEquiv.refl_apply, NumberField.integralBasis_repr_apply, Matrix.toBilin'Aux_single, ContinuousLinearMap.differentiableWithinAt, continuousMultilinearCurryFin0_apply, CStarMatrix.ofMatrix_eq_ofMatrixL, LieModule.lie_traceForm_eq_zero, geometric_hahn_banach_closed_compact, Module.Basis.det_map', EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, IsLocalizedModule.map_mk', PiTensorProduct.dualSeminorms_bounded, exteriorPower.pairingDual_ιMulti_ιMulti, LinearMap.lTensor_mul, Polynomial.derivative_rootMultiplicity_of_root_of_mem_nonZeroDivisors, LinearEquiv.isUnit_det', Polynomial.monomial_zero_one, HasFDerivWithinAt.mul_const', Polynomial.hasseDeriv_mul, HasDerivAt.comp_hasFDerivWithinAt_of_eq, ExteriorAlgebra.map_apply_ι, LinearMap.mul_toMatrix₂, PointwiseConvergenceCLM.coeLMₛₗ_apply, ProbabilityTheory.covarianceBilin_self_nonneg, Module.algebraMap_end_eq_smul_id, HasStrictFDerivAt.iterate, Orientation.rightAngleRotation_rightAngleRotation, Algebra.Extension.Cotangent.map_comp, PowerSeries.trunc_one_left, groupHomology.H2π_eq_iff, MonomialOrder.monic_monomial_one, MvPowerSeries.isHomogeneous_iff_eq_homogeneousComponent, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, Submodule.mulRightMap_eq_mulMap_comp, RootPairing.Equiv.coweightEquiv_inv, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, Module.Presentation.cokernel_var, ExteriorAlgebra.ι_leftInverse, ProbabilityTheory.integral_linearMap_gaussianReal, ContinuousLinearMap.compLeftContinuous_apply, TensorProduct.inner_assoc_assoc, ContinuousMultilinearMap.curryMidEquiv_apply, fderiv_const_mul, ApproximatesLinearOn.lipschitz_sub, kroneckerTMulLinearEquiv_mul, Algebra.trace_comp_trace_of_basis, QuadraticMap.discr_comp, Module.Basis.linearMap_repr_apply, exteriorPower.alternatingMapLinearEquiv_comp_ιMulti, MvPolynomial.monomial_eq_zero, differentialIdeal_le_fractionalIdeal_iff, HasStrictFDerivAt.continuousMultilinear_apply_const, AlgEquiv.toLinearMapHom_apply_apply, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, LinearMap.lsmul_eq_DistribMulAction_toLinearMap, toLinearMap_algebraMapCLM, groupHomology.H1AddEquivOfIsTrivial_single, Module.eval_apply_eq_zero_iff, MvPolynomial.eval_monomial, LaurentSeries.hasseDeriv_comp_coeff, LinearEquiv.baseChange_zpow, kroneckerTMulLinearEquiv_symm_kroneckerTMul, MvPolynomial.coeff_coe, MultilinearMap.curryFinFinset_apply_const, AdicCompletion.map_mk, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, RootPairing.bijOn_coreflection_coroot, ContinuousLinearMap.analyticOnNhd_bilinear, groupCohomology.mem_cocycles₁_iff, MultilinearMap.freeFinsuppEquiv_def, ContinuousLinearMap.reApplyInnerSelf_apply, imaginaryPart_realPart, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', TensorProduct.AlgebraTensorModule.map_eq, ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, Ideal.quotientToQuotientRangePowQuotSucc_surjective, ProbabilityTheory.indepFun_iff_charFunDual_prod', IsModuleTopology.continuous_bilinear_of_finite_left, fderiv_exp, LinearMap.lsum_single, DoubleCentralizer.algebraMap_snd, MvPolynomial.coeff_monomial_mul', PiTensorProduct.map_mul, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, groupHomology.range_d₁₀_eq_coinvariantsKer, PresheafOfModules.unitHomEquiv_apply_coe, Algebra.Generators.cotangentCompAwaySec_apply, LieModule.trace_comp_toEnd_genWeightSpace_eq, AffineMap.comp_linear, RingHomCompTriple.right_ids, MvPolynomial.monomial_mem_coeffsIn, ContinuousLinearMap.differentiableAt, LinearMap.IsProj.top, frobenius_comp_frobeniusEquiv_symm, LinearMap.nondegenerate_congr_iff, Rep.coindResAdjunction_homEquiv_apply, MulOpposite.toLinearEquiv_opLinearIsometryEquiv, fderiv_arctan, Matrix.sum_cramer_apply, TensorProduct.gradedMul_one, fderivWithin_const, ProbabilityTheory.covarianceBilinDual_self_eq_variance, Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff, RatFunc.laurentAux_algebraMap, MvPowerSeries.coeff_trunc', CliffordAlgebra.contractLeft_comm, DirectSum.ext_component_iff, CompactlySupportedContinuousMap.integralLinearMap_apply, LinearMap.le_def, ModuleCat.FreeMonoidal.εIso_inv_freeMk, PowerSeries.sub_const_eq_shift_mul_X, Module.End.smulLeft_apply, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, geometric_hahn_banach_open_open, ZMod.invDFT_apply', iteratedFDerivWithin_succ_apply_left, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, AdjoinRoot.modByMonicHom_mk, HasFDerivAtFilter.fun_const_smul, hasStrictFDerivAt_norm_sq, Submodule.finrank_map_le, Matrix.traceLinearMap_apply, Matrix.UnitaryGroup.coe_toGL, SpecialLinearGroup.coe_mul, FractionalIdeal.mem_dual, Submodule.starProjection_unit_singleton, Finset.weightedVSub_const_smul, LinearMap.toMatrix'_mul, SchwartzMap.fourier_evalCLM_eq, ContinuousLinearMap.toLinearMap_toSpanSingleton, LinearIsometryEquiv.ofTop_apply, Submodule.prodComm_trans_prodEquivOfIsCompl, LinearIsometryEquiv.comp_differentiableWithinAt_iff, MvPowerSeries.coeff_zero_mul_X, groupHomology.isoCycles₂_hom_comp_i_apply, IsBaseChange.end, LinearMap.coe_compMultilinearMap, Algebra.trace_self_apply, LinearMap.adjoint_toSpanSingleton, Module.End.lie_apply, LinearMap.lcomp_apply', DoubleCentralizer.one_snd, CliffordAlgebra.ofBaseChange_tmul_ι, mul_basis_toMatrix, PerfectRing.lift_self, LinearMap.GeneralLinearGroup.congrLinearEquiv_apply, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, Module.Basis.toDual_toDual, Finsupp.linearCombination_embDomain, IsLocalRing.ResidueField.map_id, CliffordAlgebra.reverse_reverse, Polynomial.iterate_derivative_X_pow_eq_smul, KaehlerDifferential.tensorKaehlerEquiv_left_inv, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, Module.dualProdDualEquivDual_apply_apply, Matrix.proj_comp_diagLinearMap, MvPowerSeries.coeff_inv_aux, trace_eq_sum_roots, contDiffOn_infty_iff_fderiv_of_isOpen, ContinuousLinearEquiv.trans_smul, RootPairing.zero_le_posForm, LinearMap.injective_iff_surjective, Submodule.quotientPi_apply, CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero, Submodule.rTensorOne_tmul, Polynomial.linearIndependent_powers_iff_aeval, fderivWithin_comp_of_eq, FiniteDimensional.nonempty_linearEquiv_of_finrank_eq, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, Polynomial.Chebyshev.derivative_U_eval_one, LinearMap.BilinForm.sub_apply, IsLocalizedModule.rTensor, LinearIsometryEquiv.withLpProdCongr_symm_apply, ContinuousLinearEquiv.analyticOn, LinearEquiv.conj_symm_conj, RingHomIsometric.ids, fderiv_pow_ring', LinearMap.toSpanSingleton_apply, QuasispectrumRestricts.real_iff, Rep.coinvariantsShortComplex_f, SheafOfModules.pushforwardCongr_inv_app_val_app, killingForm_apply_apply, LinearMap.inl_eq_prod, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, LinearMap.trace_id, LinearMap.toMatrix_algebraMap, LinearEquiv.coe_curry_symm, Algebra.trace_trace, TemperedDistribution.instLineDerivSMulReal, LinearMap.spectrum_toMatrix, AdicCompletion.ofAlgEquiv_apply, fderiv_natCast, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, PowerBasis.constr_pow_gen, Polynomial.monomial_one_eq_iff, LinearEquiv.refl_mem_dilatransvections, LaurentPolynomial.leval_apply, LinearMap.BilinForm.congr_refl, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, StandardEtalePresentation.toSubmersivePresentation_jacobian, SchwartzMap.evalCLM_apply_apply, LieSubalgebra.mem_engel_iff, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, IsBaseChange.equiv_symm_apply, Function.Exact.inr_fst, LinearMap.IsSymmetric.natCast, Orientation.rotation_eq_self_iff_angle_eq_zero, HasFDerivAtFilter.fun_sub, OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective, MvPowerSeries.coeff_weightedHomogeneousComponent, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ContinuousLinearMap.coe_pow, Module.Finite.of_isComplemented_domain, Matrix.isUnit_toLin_iff, Polynomial.degreeLT.addLinearEquiv_apply', fderiv_const, RootPairing.InvariantForm.apply_weylGroup_smul, Convex.linear_image, Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic, Matrix.uniqueLinearEquiv_apply, Representation.ofMulActionSelfAsModuleEquiv_apply, Submodule.singleton_smul, Subspace.quotAnnihilatorEquiv_apply, skewAdjointPart_comp_subtype_selfAdjoint, LinearMap.conjugate_apply, MeasureTheory.Measure.toTemperedDistribution_apply, ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, PowerSeries.HasSubst.monomial', ContinuousMultilinearMap.compContinuousLinearMap_apply, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, ModuleCat.RestrictionCoextensionAdj.unit'_app, Matrix.diagonal_toLin', LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, TensorPower.mul_one, Module.isTorsionBySet_iff_subseteq_ker_lsmul, ContinuousLinearEquiv.coe_refl, CStarMatrix.toCLM_apply, KaehlerDifferential.kerTotal_map, Polynomial.coeff_monomial_zero_mul, ContinuousLinearEquiv.hasFDerivWithinAt, Module.End.mem_genEigenspace_top, Submodule.coe_mulMap_comp_eq, Orientation.oangle_rotation_right, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, Bialgebra.counit_natCast, DoubleCentralizer.algebraMap_toProd, exteriorPower.oneEquiv_symm_apply, SeparationQuotient.mk_outCLM, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, TensorProduct.AlgebraTensorModule.curry_apply, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, ModuleCat.imageIsoRange_inv_image_ι, LinearMap.isPositive_self_comp_adjoint, QuadraticForm.tensorLId_symm_apply, Algebra.TensorProduct.mul_one, Coalgebra.counitCoalgHom_toLinearMap, IsAdjoinRootMonic.ext_elem_iff, Matrix.charpoly_toLin', LinearMap.BilinForm.toMatrix_symm, Lagrange.iterate_derivative_interpolate, Rep.ofMulActionSubsingletonIsoTrivial_inv_hom, fderivWithin.log, Polynomial.taylorAlgHom_apply, ContinuousLinearMap.norm_map_tail_le, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, LinearMap.BilinMap.toQuadraticMap_smul, LinearAlgebra.FreeProduct.ι_def, Representation.norm_comp_self, Matrix.toLinearMap₂'_toMatrix', Polynomial.pow_sub_dvd_iterate_derivative_pow, contMDiffOn_symm_coordChangeL, LinearMap.finrank_range_le, PiTensorProduct.ofFinsuppEquiv_apply, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, HasFDerivWithinAt.sinh, Module.DirectLimit.map_id, LinearMap.ker_snd, ContinuousAffineMap.map_vadd, rank_dual_eq_card_dual_of_aleph0_le_rank', RingCat.moduleCatRestrictScalarsPseudofunctor_mapId, Submodule.isIdempotentElemEquiv_apply_coe, ContinuousLinearMap.instStarModuleId, LinearEquiv.piCongrLeft'_symm_apply, TensorProduct.exists_finite_submodule_left_of_finite', Matrix.toLinearMapₛₗ₂'_apply, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, Polynomial.hasFDerivAt_aeval, ContinuousLinearMap.IsInvertible.comp, LinearEquiv.piCongrRight_symm, contMDiffAt_hom_bundle, TensorProduct.finsuppScalarRight_symm_apply_single, PolynomialModule.eval_lsingle, LinearIsometryEquiv.toLinearEquiv_lTensor, asBoolAlg_id, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply, IsLocalizedModule.map_apply, ContinuousLinearMap.compContinuousAlternatingMap_coe, ContinuousLinearMap.compContinuousMultilinearMap_coe, Module.End.genEigenspace_one, exists_dual_vector'', HasFDerivAt.continuousAlternatingMap_apply_const, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, ModuleCat.free_η_freeMk, Module.Flat.iff_lTensor_injective, RootPairing.RootPositiveForm.symm, Matrix.toLin'_pow, RootPairing.IsOrthogonal.reflection_apply_right, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, LinearMap.pi_ext_iff, PiTensorProduct.injectiveSeminorm_apply, Algebra.trace_eq_zero_of_not_exists_basis, ContinuousLinearMap.isBoundedLinearMap_comp_left, FormalMultilinearSeries.compContinuousLinearMap_applyComposition, Module.Basis.mem_span_image, IsSymmetricAlgebra.equiv_symm_apply, LinearIsometryEquiv.toLinearEquiv_smul, MeasureTheory.MemLp.continuousLinearMap_comp, PositiveLinearMap.toLinearMap_injective, ProbabilityTheory.IsGaussian.memLp_dual, LieModule.Cohomology.mem_twoCocycle_iff, LinearEquiv.symm_smul, CliffordAlgebra.ofBaseChangeAux_ι, Ideal.ker_tensorProductMk_quotient, norm_fderiv_iteratedFDeriv, MvPowerSeries.coeff_apply, rank_dual_eq_card_dual_of_aleph0_le_rank, curveIntegralFun_neg, Finset.affineCombination_apply, MulOpposite.opLinearEquiv_toAddEquiv, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, MeasureTheory.Lp.norm_constL_le, LinearEquiv.rTensor_symm_tmul, Submodule.annihilator_span_singleton, Bialgebra.comul_mul, Derivation.liftKaehlerDifferential_unique_iff, ProbabilityTheory.covarianceBilinDual_self_nonneg, conformalFactorAt_inner_eq_mul_inner', NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, PiTensorProduct.map_one, PowerSeries.constantCoeff_divXPowOrder, AffineMap.linear_surjective_iff, hasFDerivAt_pow, HasFDerivAt.log, LinearIsometryEquiv.analyticOn, LinearEquiv.transvections_pow_mono, Module.Basis.localizationLocalization_repr_algebraMap, LocallyConstant.comapₗ_apply_apply, TensorProduct.AlgebraTensorModule.mapBilinear_apply, LinearMap.BilinMap.toQuadraticMapLinearMap_apply, TemperedDistribution.fourier_lineDerivOp_eq, LinearIsometryEquiv.analyticAt, SemimoduleCat.MonoidalCategory.braiding_hom_apply, Matrix.toLinAlgEquiv'_apply, groupHomology.inhomogeneousChains.d_single, PowerSeries.monomial_eq_mk, IsLocalRing.ResidueField.map_id_apply, Complex.equivRealProdLm_symm_apply, Matrix.l2_opNNNorm_def, Polynomial.natDegree_derivative_le, hasMFDerivAt_const, ContinuousLinearEquiv.strictConvex_image, TensorProduct.piRightHom_tmul, MeasureTheory.charFunDual_map_const_add, LinearMap.lTensor_comm, RootPairing.rootForm_apply_apply, LieModule.traceForm_eq_zero_of_isTrivial, Trivialization.symm_coordChangeL, LinearEquiv.det_conj, Module.Basis.dualBasis_apply, LinearMap.apply_toPerfPair_flip, TensorProduct.quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, MeasureTheory.charFunDual_map_add_const, RootPairing.Equiv.weightHom_apply, MvPowerSeries.coeff_trunc, ModuleCat.exteriorPower.iso₁_hom_apply, ContinuousLinearMap.adjointAux_adjointAux, WithCStarModule.linearEquiv_symm_apply, HasStrictFDerivAt.const_sub, Complex.equivRealProdLm_symm_apply_im, HahnSeries.toPowerSeriesAlg_symm_apply_coeff, apply_eq_star_dotProduct_toMatrix₂_mulVec, tensorKaehlerQuotKerSqEquiv_tmul_D, MvPolynomial.mkDerivation_monomial, HopfAlgebra.mul_antipode_rTensor_comul, LinearMap.aeval_eq_aeval_mod_charpoly, LinearMap.toMatrix_mul, BialgHom.coe_toLinearMap, Subrepresentation.apply_mem_toSubmodule, fderiv_sub, Complex.coe_basisOneI_repr, Finsupp.linearCombination_single, realPart_I_smul, LinearMap.polar_gc, LinearMap.det_map, Orientation.rotation_trans, Module.Presentation.CokernelData.π_lift, TwoSidedIdeal.subtype_injective, TopModuleCat.freeMap_map, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, LinearMap.toMatrix₂_compl₁₂, LinearMap.BilinForm.IsSymm.smul, TensorProduct.tensorQuotientEquiv_apply_mk_tmul, RootPairing.Equiv.bijective_weightMap, LinearMap.hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, SemimoduleCat.MonoidalCategory.braiding_inv_apply, Matrix.minpoly_toLin', TensorProduct.exists_finite_submodule_of_finite, hasFDerivAt_single, Module.Basis.reindexFinsetRange_repr_self, QuadraticForm.tensorDistrib_tmul, AddEquiv.toIntLinearEquiv_symm, ContinuousLinearEquiv.coe_prodProdProdComm, selfAdjoint.realPart_unitarySelfAddISMul, IsLocalizedModule.linearEquiv_symm_apply, MeasureTheory.condExpL2_indicator_of_measurable, ExteriorAlgebra.ι_add_mul_swap, MvPolynomial.rename_monomial, RootPairing.iInf_ker_root'_eq, lift_rank_lt_rank_dual, Representation.coind'_apply_apply, ProbabilityTheory.covarianceBilin_real_self, LinearMap.eq_adjoint_iff, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, LinearMap.coprod_comp_prod, TensorProduct.map_one, GradedTensorProduct.mulHom_apply, LinearMap.toSpanSingleton_eq_zero_iff, PositiveLinearMap.gnsStarAlgHom_apply, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, BilinForm.toMatrix_compRight, Submodule.map_mul, ContDiffOn.continuousOn_fderivWithin_apply, Orthonormal.equiv_toLinearEquiv, LinearMap.BilinForm.nondegenerate_toMatrix'_iff, HasFDerivWithinAt.iterate, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, LinearMap.instIsStablyFiniteRingEnd, Polynomial.wronskianBilin_apply, Module.DirectLimit.linearEquiv_symm_mk, LinearMap.toMatrix₂_toLinearMap₂, MeasureTheory.condExp_ae_eq_condExpL1CLM, HasMFDerivWithinAt.sum, LinearMap.detAux_def', Orthonormal.inner_right_finsupp, MultilinearMap.fromDirectSumEquiv_lof, TensorProduct.directSumRight_tmul_lof, LinearMap.toMatrix_transpose_apply', MvPowerSeries.eq_zero_iff_forall_coeff_eq_zero_and, Submodule.IsPrincipal.generator_map_dvd_of_mem, CliffordAlgebra.changeForm_one, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, Submodule.closure_coe_iSup_map_single, BialgEquiv.map_mul', AffineIsometry.norm_map, LinearMap.norm_extendTo𝕜'_apply_sq, SpecialLinearGroup.coe_pow, CliffordAlgebra.lift_symm_apply, EuclideanSpace.basisFun_repr, Module.Invertible.rTensor_bijective_iff, Module.Basis.repr_symm_single_one, ImplicitFunctionData.hasStrictFDerivAt, ContinuousLinearMap.integral_comp_id_comm', Rep.diagonalOneIsoLeftRegular_inv_hom, ContinuousLinearMap.coprodEquivL_apply_apply, HasFTaylorSeriesUpToOn.hasFDerivAt, Submodule.linearEquiv_of_sSup_eq_top, DirectSum.algHom_ext'_iff, LinearMap.toMatrix'_intrinsicStar, MultilinearMap.domCoprod'_apply, RCLike.realLinearIsometryEquiv_symm_apply, LinearMap.BilinForm.congr_congr, BoundedContinuousFunction.coeFn_toLp, Submodule.linearMap_eq_iff_of_span_eq_top, ModuleCat.hom_inv_rightUnitor, LinearMap.finiteDimensional, Equiv.tensorProductAssoc_def, TrivSqZeroExt.inrHom_apply, LinearMap.isPosSemidef_zero, continuous_clm_apply, Matrix.compLinearEquiv_symm_apply, ContinuousLinearEquiv.skewProd_apply, ContinuousLinearMap.hasTemperateGrowth, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, LinearMap.map_rTensor, QuadraticForm.tensorComm_apply, Submodule.coe_isComplEquivProj_apply, PowerSeries.trunc_C, Orientation.oangle_sub_right_smul_rotation_pi_div_two, LinearIsometry.coe_toSpanSingleton, Submodule.prodEquivOfIsCompl_symm_apply_left, Algebra.PreSubmersivePresentation.aevalDifferential_single, cross_apply, MvPolynomial.isWeightedHomogeneous_monomial, LinearMap.isPositive_iff_complex, LinearEquiv.lieConj_apply, IsBaseChange.toDual_comp_apply, VectorFourier.fourierSMulRight_apply, LieModule.isNilpotent_toEnd_of_mem_rootSpace, IsBaseChange.linearMapLeftRightHom_toMatrix, Polynomial.sumIDeriv_apply, ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, DoubleCentralizer.pow_toProd, OrthonormalBasis.equiv_apply_euclideanSpace, RootPairing.PolarizationIn_apply, Submodule.injective_subtype, measurable_fderiv_apply_const, LinearMap.BilinForm.isAlt_zero, LinearMap.BilinForm.toMatrixAux_apply, Polynomial.sylvesterDeriv_updateRow, Submodule.linearProjOfIsCompl_isCompl_projection, MeasureTheory.OuterMeasure.comap_mono, PiTensorProduct.mapMultilinear_apply, Module.Flat.iff_rTensor_exact', TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, MeasureTheory.Measure.addHaar_image_linearMap, Submodule.quotientEquivOfIsCompl_apply_mk_coe, IsLocalFrameOn.coeff_apply_of_notMem, isSelfAdjoint_starProjection, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, VectorBundleCore.localTriv_coordChange_eq, LinearMap.BilinForm.isAdjointPair_iff_eq_of_nondegenerate, ContinuousMultilinearMap.uncurryRight_apply, LinearEquiv.snd_comp_prodComm, DirectSum.IsInternal.ofBijective_coeLinearMap_of_mem, Polynomial.dvd_derivative_iff, Polynomial.coeff_mul_monomial_zero, Submodule.map_inr, eventually_norm_symmL_trivializationAt_self_comp_lt, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, MeasureTheory.condExpL1CLM_indicatorConst, LinearEquiv.dualMap_symm, Submodule.localized'_eq_span, mfderivWithin_zero_of_not_mdifferentiableWithinAt, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, AdicCompletion.of_surjective, PiTensorProduct.dualDistrib_apply, Fintype.range_linearCombination, Submodule.linearProjOfIsCompl_comp_subtype, DFinsupp.lsum_single, Complex.orthonormalBasisOneI_repr_symm_apply, LinearEquiv.uniqueProd_symm_apply, CliffordAlgebraQuaternion.ofQuaternion_mk, Algebra.Generators.Cotangent.exact, PresheafOfModules.homMk_app, MeasureTheory.L1.nnnorm_Integral_le_one, HasFDerivAt.exp, Matrix.toLinOfInv_symm_apply, ContDiffWithinAt.laplacianWithin_CLM_comp_left, Manifold.riemannianEDist_def, ContinuousLinearEquiv.coe_neg, LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv', ModuleCat.hom_sum, LinearIsometry.norm_iteratedFDerivWithin_comp_left, HasFDerivAtFilter.isLittleO, LinearMap.toMatrix_smulRight, ModularFormClass.qExpansion_coeff_zero, curveIntegralFun_fun_zero, Polynomial.resultant_taylor, kroneckerTMulLinearEquiv_tmul, LinearEquiv.alternatingMapCongrRight_apply_apply, Submodule.comapMkQOrderEmbedding_eq, LinearMap.toMatrix₂Aux_eq, HasFDerivAt.fun_pow', Representation.averageMap_invariant, Matrix.represents_iff, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, imaginaryPart_apply_coe, ZSpan.map, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, IsModuleTopology.continuous_of_linearMap, LinearMap.pi_proj_comp, MvPolynomial.monomial_zero', LinearEquiv.extendScalarsOfIsLocalizationEquiv_apply, MultilinearMap.curryLeft_apply, LinearMap.rTensor_comp_comm, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, LinearMap.restrictScalars_add, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl, MeasureTheory.weightedSMul_smul, pinGroup.conjAct_smul_range_ι, MvPowerSeries.coeff_truncFun', LinearMap.lsmul_apply, HasMFDerivWithinAt.mul', MeasureTheory.integral_continuousLinearMap_prod, Submodule.coe_subtypeₗᵢ, Polynomial.degreeLT.addLinearEquiv_symm_apply_inr_basis, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, Submodule.IsCompl.projection_add_projection_eq_self, LieDerivation.toLinearMapLieHom_injective, fderivWithin_comp', Finsupp.counit_single, MvPolynomial.weightedHomogeneousComponent_directSum, Trivialization.continuousLinearMap_apply, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, ContinuousLinearMap.inverse_zero, TemperedDistribution.laplacian_eq_sum, Polynomial.natDegree_hasseDeriv, vecMulVecBilin_apply_apply, curveIntegralFun_def', NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, QuadraticForm.tmul_comp_tensorMap, isAdjointPair_toLinearMap₂', Orientation.areaForm_comp_rightAngleRotation, RootPairing.Equiv.coweightMap_coweightEquiv_symm, Module.Dual.baseChange_apply_tmul, Matrix.toLin'_apply', LinearMap.rTensor_baseChange, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, Representation.asModuleEquiv_symm_map_rho, AddMonoidAlgebra.mem_grade_iff', RootPairing.Base.toCoweightBasis_repr_coroot, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, LinearMap.isPairSelfAdjoint_equiv, LinearMap.toMatrix₂_symm, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, AdjoinRoot.powerBasisAux'_repr_symm_apply, Polynomial.Bivariate.swap_monomial_monomial, MvPowerSeries.coeff_prod, HasFDerivAtFilter.fun_add, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, Matrix.Represents.congr_fun, RootPairing.reflectionPerm_eq_reflectionPerm_iff_of_span, isLocalHom_id, ContinuousLinearMap.norm_extendTo𝕜'_bound, groupHomology.π_comp_H1Iso_hom_apply, TensorPower.toTensorAlgebra_gMul, ZMod.dft_comp_neg, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, Rep.coindIso_inv_hom_hom, TensorProduct.directSumLeft_symm_lof_tmul, Matrix.ker_toLin'_eq_bot_iff, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, LinearMap.isIdempotentElem_apply_one_iff, HasFDerivWithinAt.hasDerivWithinAt, Representation.ofModule_asModule_act, LinearMap.vecCons₂_apply, Finsupp.restrictDom_comp_subtype, Finsupp.lsum_apply, ModuleCat.hom_nsmul, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LinearMap.eval_charpoly, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, LinearMap.toMatrix'_toLinearMap₂', rTensor_mkQ, LieIdeal.coe_map_of_surjective, TensorPower.toTensorAlgebra_gOne, LinearIsometryEquiv.contDiffPointwiseHolderAt_left_comp, Derivation.llcomp_apply, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, HasGradientWithinAt.fderivWithin_apply, Submodule.map_le_isotypicComponent, Algebra.IsCentral.instContinuousLinearMap, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, MeasureTheory.integral_comp, Algebra.adjoin_inl_union_inr_eq_prod, TemperedDistribution.instContinuousLineDeriv, Basis.multilinearMap_apply_apply, LinearMap.BilinForm.toLin'Flip_apply, HasFDerivAtFilter.comp, TensorProduct.tensorQuotEquivQuotSMul_symm_mk, LinearMap.reduceModIdeal_apply, Finset.weightedVSubOfPoint_smul, LocalizedModule.lift_comp, LinearMap.charpoly_constantCoeff_eq_zero_iff, ContinuousLinearMap.restrictScalars_sub, RCLike.complexLinearIsometryEquiv_symm_apply, groupCohomology.map_id_comp_H0Iso_hom_apply, cfc_eq_cfcL_mkD, PolynomialModule.equivPolynomial_single, MvPolynomial.homogeneousComponent_apply, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, norm_derivWithin_eq_norm_fderivWithin, BilinForm.toMatrix_mul_basis_toMatrix, ModuleCat.forget_obj, LinearMap.convexOn, LinearMap.polar_weak_closed, Polynomial.toFn_comp_ofFn_eq_id, ContinuousLinearMap.le_def, MultilinearMap.dfinsuppFamilyₗ_apply, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, AffineMap.derivWithin, LieDerivation.lie_coe_lieDerivation_apply, contDiff_succ_iff_fderiv_apply, LinearMap.range_coprod, Rep.standardComplex.d_of, coe_lpPiLpₗᵢ, Module.Flat.tensorProduct_mapIncl_injective_of_left, SemimoduleCat.id_apply, imaginaryPart_comp_subtype_selfAdjoint, ContinuousLinearEquiv.smulLeft_apply_apply, iSupIndep.linearEquiv_apply, VectorBundleCore.localTriv_apply, QuadraticMap.half_moduleEnd_apply_eq_half_smul, Module.Basis.coe_finTwoProd_repr, AffineMap.add_linear, LinearMap.coe_snd, LinearIsometry.inr_apply, Polynomial.supNorm_monomial, groupHomology.chainsMap_id_f_hom_eq_mapRange, QuadraticForm.dualProdIsometry_toFun, Polynomial.derivative_comp, fderiv_ccos, TensorProduct.comm_trans_comm, Submodule.IsCompl.projection_ker, LinearMap.isPositive_zero, DoubleCentralizer.zero_fst, LinearMap.BilinForm.mul_toMatrix', MvPowerSeries.coeff_C_mul, MvPolynomial.divMonomial_mul_monomial, IsGroupLikeElem.antipode, LieModule.toEnd_lie, QuadraticForm.tensorAssoc_symm_apply, Coalgebra.coassoc, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, ContinuousLinearEquiv.toLinearEquiv_smul, Finsupp.linearCombination_unique, PiTensorProduct.isEmptyEquiv_symm_apply, PresheafOfModules.toPresheaf_map_app_apply, fderiv_update, DistribMulAction.toLinearEquiv_apply, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, TensorProduct.AlgebraTensorModule.map_add_right, CliffordAlgebra.reverse.commutes, LinearMap.map_mul_iff, PiTensorProduct.subsingletonEquiv_symm_apply', LinearEquiv.snd_comp_prodAssoc, extDerivWithin_apply_vectorField, PowerSeries.X_eq, ContinuousLinearMap.measurable_comp, Real.fourier_bilin_convolution_eq, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, TensorProduct.Algebra.linearMap_comp_mul', BoxIntegral.BoxAdditiveMap.toSMul_apply, SymmetricAlgebra.algHom_ext_iff, ProbabilityTheory.IsGaussian.map_rotation_eq_self, Finsupp.coe_lsum, LinearMap.toSpanSingleton_homothety, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, ContinuousLinearMap.hasFDerivWithinAt, fdifferential_comp, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, CStarMatrix.mul_entry_mul_eq_inner_toCLM, MvPolynomial.weightedHomogeneousComponent_finsupp, LinearIsometry.orthonormal_comp_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, LaurentSeries.hasseDeriv_coeff, Matrix.toLinearMap₂_symm, ContinuousLinearEquiv.prodUnique_symm_apply, Polynomial.gaussNorm_monomial, ExteriorAlgebra.toTrivSqZeroExt_ι, ContinuousLinearEquiv.refl_symm, AddMonoidHom.coe_toRatLinearMap, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, Module.Flat.iff_lTensor_injectiveₛ, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, SymmetricPower.range_mk, Finsupp.linearCombination_mapDomain, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, Span.finsupp_linearCombination_repr, ProbabilityTheory.covarianceOperator_inner, SymmetricAlgebra.equivMvPolynomial_symm_X, Subalgebra.map_toSubmodule, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_symm, LinearMap.sumOfConjugates_apply, InnerProductSpace.rankOne_def', ModuleCat.HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, ContDiff.fderiv_apply, ContinuousLinearMap.opNorm_mul_le, Polynomial.taylor_taylor, ContinuousLinearMap.uncurryLeft_norm, MeasureTheory.OuterMeasure.le_comap_map, RootPairing.Equiv.bijective_coweightMap, LinearMap.toMatrixAlgEquiv_symm, ContDiffWithinAt.fderivWithin', DirectSum.component.lof_self, LinearMap.toMatrixRight'_id, leibniz_cross, Orientation.inner_rightAngleRotation_left, HasFDerivAt.comp_hasDerivWithinAt, Filter.EventuallyEq.fderiv, HasFDerivWithinAt.multilinear_comp, lp.lsingle_apply, Polynomial.expand_monomial, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, LinearMap.lTensor_comp_rTensor, HVertexOperator.coeff_inj, MvPolynomial.prod_X_pow_eq_monomial, fderiv_apply_one_eq_deriv, Submodule.comap_map_mkQ, TensorProduct.rid_tmul, AffineMap.isOpenMap_linear_iff, CategoryTheory.Linear.homCongr_apply, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants, Submodule.coe_torsionBySet, Submodule.mem_dualCoannihilator, fwdDiff_aux.fwdDiffₗ_apply, LinearMap.minpoly_toMatrix, LinearMap.lTensor_zero, HasFTaylorSeriesUpToOn.compContinuousLinearMap, LinearMap.det_dualMap, hasFDerivAt_zero_of_eventually_const, PiToModule.fromEnd_apply_single_one, Finsupp.lapply_comp_lsingle_same, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top, MvPowerSeries.weightedHomogeneousComponent_mul_of_le_weightedOrder, Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one, Rep.indToCoindAux_mul_snd, ContDiffOn.continuousOn_fderivWithin, ModuleCat.FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, SchwartzMap.integral_sesq_fourierIntegral_eq, Submodule.norm_orthogonalProjection_apply, CharacterModule.homEquiv_symm_apply_apply_apply, CoalgHom.coe_linearMap_injective, ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier, contDiffAt_succ_iff_hasFDerivAt, fderivWithin_const_smul_of_invertible, ContinuousLinearMap.IsPositive.inner_nonneg_left, LinearMap.BilinForm.IsRefl.neg, MvPolynomial.constantCoeff_monomial, RootPairing.coroot_root_two, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, AffineEquiv.linearHom_apply, CliffordAlgebra.reverse_mem_evenOdd_iff, hasFDerivAt_const, HasFDerivAt.inner, PiTensorProduct.piTensorHomMapFun₂_smul, LinearMap.adjoint_lTensor, LieModule.Cohomology.add_apply_apply, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, SemimoduleCat.hom_zero, Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, LinearEquiv.smulOfNeZero_apply, LieModuleHom.ker_toSubmodule, fderiv_continuousMultilinear_apply_const_apply, LinearMap.slope_comp, MultilinearMap.map_add_eq_map_add_linearDeriv_add, multilinearCurryLeftEquiv_apply, LinearIsometryEquiv.coe_withLpProdUnique, MeasureTheory.Integrable.convolution_integrand, HasFDerivAtFilter.star, SchwartzMap.fourierTransformCLE_symm_apply, starL'_symm_apply, OrthonormalBasis.map_apply, CliffordAlgebra.evenToNeg_ι, ModuleCat.ExtendScalars.map_tmul, LinearMap.toMatrixOrthonormal_apply, MeasureTheory.condExpL1CLM_lpMeas, TensorProduct.AlgebraTensorModule.map_one, ContinuousLinearEquiv.unitsEquivAut_symm_apply, fderivWithin_exp, PiTensorProduct.tmulEquivDep_symm_apply, fwdDiff_aux.shiftₗ_apply, Submodule.rTensorOne_tmul_one, Submodule.isSymmetricProjection_starProjection, Representation.asAlgebraHom_of, ProbabilityTheory.HasGaussianLaw.map_fun, Submodule.eq_starProjection_of_mem_orthogonal, Submodule.toLinearMap_prodEquivOfIsCompl_symm, LinearMap.BilinMap.toQuadraticMap_list_sum, ContinuousLinearMap.mdifferentiableWithinAt, SeparatingDual.completeSpace_continuousLinearMap_iff, OrthogonalFamily.inner_sum, LinearMap.IsPositive.smul_of_nonneg, ProbabilityTheory.covarianceBilin_apply_pi, DFinsupp.comul_comp_lsingle, HasStrictFDerivAt.fun_sub, SchwartzMap.integral_bilinear_laplacian_right_eq_left, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, diffToIdealOfQuotientCompEq_apply, LinearMap.lTensor_comp_mk, Module.Basis.toDual_injective, ContinuousLinearMap.natCast_apply, ModuleCat.FilteredColimits.forget_reflectsFilteredColimits, IsAdjoinRootMonic.coeff_apply_lt, MultilinearMap.constLinearEquivOfIsEmpty_apply, HasFDerivAt.lim, LinearEquiv.finTwoArrow_symm_apply, LieModule.traceForm_eq_zero_if_mem_lcs_of_mem_ucs, LinearMap.map_mul_algebraMap, ContinuousLinearMap.isometry_mul, RootPairing.iInf_ker_coroot'_eq, Subspace.finrank_add_finrank_dualCoannihilator_eq, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', LinearMap.detAux_comp, CliffordAlgebra.map_comp_ι, ContinuousLinearMap.isOpen_injective, HopfAlgebra.counit_comp_antipode, PowerSeries.coeff_comp_monomial, LieHom.toFun_eq_coe, OrthonormalBasis.sum_repr_symm, Submodule.toLinearPMap_domain, HasFDerivAt.const_mul, LinearEquiv.toModuleIsoₛ_hom, DirectSum.IsInternal.collectedBasis_repr_of_mem_ne, AlternatingMap.compLinearMap_zero, Module.dualProdDualEquivDual_apply, MvPolynomial.divMonomial_monomial, Module.Basis.toMatrix_apply, realPart_surjective, StrongDual.toLpₗ_apply, LinearMap.id_moduleCat_comp, Orientation.kahler_apply_self, Module.Invertible.rTensorInv_leftInverse, RootPairing.Hom.weight_coweight_transpose_apply, Polynomial.derivative_sq, Module.End.invtSubmodule.map_subtype_mem_of_mem_invtSubmodule, MultilinearMap.curryFinFinset_symm_apply_const, KaehlerDifferential.mvPolynomialBasis_repr_apply, LinearMap.prodMapAlgHom_apply_apply, LinearMap.BilinForm.IsSymm.add, Module.End.eigenspace_def, IntermediateField.AdjoinSimple.trace_gen_eq_zero, HasStrictFDerivAt.continuousAlternatingMap_apply, ModuleCat.free_μ_freeMk_tmul_freeMk, ContinuousAffineMap.add_contLinear, ModuleCat.forget₂_obj_moduleCat_of, Module.Finite.range, Module.DualBases.eval_same, Orientation.inner_smul_rotation_pi_div_two_right, DoubleCentralizer.sub_toProd, MvPowerSeries.coeff_zero_one, ContinuousLinearMap.continuous_uncurry_of_multilinear, TensorProduct.forall_vanishesTrivially_iff_forall_rTensor_injective, Finsupp.sigmaFinsuppLEquivPiFinsupp_apply, Complex.conjCLE_nnorm, QuadraticForm.toDualProd_apply, tendsto_iff_forall_eval_tendsto_topDualPairing, Pi.orthonormalBasis.toBasis, HasStrictDerivAt.complexToReal_fderiv', LinearIsometry.map_starProjection, CategoryTheory.Iso.toLinearEquiv_apply, IsLocalFrameOn.coeff_apply_zero_at, SymmetricAlgebra.lift_comp_ι, Orientation.inner_mul_areaForm_sub', Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, RootPairing.CoPolarization_apply, ContinuousLinearMap.inr_apply, Module.End.one_apply, LinearMap.det_id, LinearMap.compLeft_apply, MeasureTheory.dist_convolution_le', ContinuousLinearEquiv.uniqueProd_apply, finsuppTensorFinsuppRid_single_tmul_single, AdicCompletion.sum_of, LinearIndependent.linearCombinationEquiv_symm_apply, Submodule.equivSubtypeMap_apply, LinearMap.isNilpotent_iff_charpoly, AlternatingMap.curryLeftLinearMap_apply, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero, HasFDerivWithinAt.rpow_const, SymmetricAlgebra.lift_ι, fderivWithin_multiset_prod, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, HasFDerivAt.mul, Module.DualBases.basis_repr_apply, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod, IsLocalRing.split_injective_iff_lTensor_residueField_injective, Algebra.Extension.Hom.mapKer_apply_coe, Module.preReflection_apply, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, SpecialLinearGroup.congr_linearEquiv_apply_apply, Algebra.toMatrix_lmul', Asymptotics.IsBigO.hasFDerivWithinAt, Submodule.isIdempotentElemEquiv_symm_apply_coe, LinearMap.continuous_of_nonzero_on_open, LieAlgebra.ad_apply, DFinsupp.sigmaCurryLEquiv_symm_apply, Polynomial.hasseDeriv_monomial, ConvexOn.real_univ_sSup_affine_eq, LieAlgebra.toEnd_pow_apply_mem, MeasureTheory.weightedSMul_union, PowerSeries.trunc_trunc_pow, PolynomialLaw.isCompat, PowerSeries.coeff_mul, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, Profinite.NobelingProof.πs_apply_apply, Module.Relations.Solution.isPresentation_iff, Module.Invertible.leftInverse_iff_rightInverse, LinearIsometry.coe_id, LinearIsometryEquiv.strictConvex_image, ContinuousLinearMap.toSpanSingleton_one, Module.DualBases.dual_lc, fderiv_add, AffineMap.homothety_linear, IsLocalDiffeomorph.mfderivToContinuousLinearEquiv_coe, DoubleCentralizer.nnnorm_fst_eq_snd, toWeakSpace_closedConvexHull_eq, LinearMap.apply_single, Algebra.Extension.contangentEquiv_tmul, Unitization.norm_def, LinearMap.BilinForm.isAlt_neg, Representation.IntertwiningMap.toLinearMap_apply, SheafOfModules.pushforwardComp_hom_app_val_app, DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSum, Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Submodule.reflection_map, LieModuleEquiv.coe_toLinearEquiv, MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_ne, Polynomial.derivativeFinsupp_map, Ideal.quotOfMul_surjective, Submodule.map₂_span_span, CochainComplex.HomComplex.δ_hom_apply, Pretrivialization.linearMapAt_symmₗ, LinearMap.isNilpotent_mulRight_iff, Submodule.det_reflection, LinearMap.BilinForm.ext_iff, ContinuousLinearMap.measurable_apply, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, SeparationQuotient.postcomp_mkCLM_surjective, Finsupp.llift_symm_apply, IsLocalizedModule.map_id, Orientation.kahler_rotation_left', fderivWithin_neg, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, PrimeSpectrum.comap_id, hasFDerivAtFilter_iff_isLittleOTVS, AffineMap.toConstProdLinearMap_apply, LinearMap.quotKerEquivRange_apply_mk, TensorProduct.finsuppScalarLeft_apply_tmul_apply, Matrix.ker_diagonal_toLin', ContinuousMultilinearMap.norm_ofSubsingleton_id_le, Polynomial.monomial_add, Algebra.Generators.cMulXSubOneCotangent_eq, ContinuousAlternatingMap.curryLeft_same, LinearMap.restrictScalars_neg, ContinuousMultilinearMap.curryRight_apply, TensorProduct.inner_comm_comm, CliffordAlgebraComplex.toComplex_ι, HasFDerivAtFilter.fst, Rep.linearization_obj_ρ, AdicCompletion.AdicCauchySequence.map_apply_coe, Rep.toCoinvariantsMkQ_hom, RootPairing.RootPositiveForm.two_mul_apply_root_root, MvPolynomial.isHomogeneous_monomial, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Polynomial.one_lt_rootMultiplicity_iff_isRoot_gcd, LinearEquiv.toModuleIsoₛ_inv, AddEquiv.coe_toLinearEquiv_symm, Ideal.toCotangent_apply, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContMDiffWithinAt.mfderivWithin, LinearMap.polyCharpolyAux_baseChange, Module.End.mem_iInf_maxGenEigenspace_iff, Polynomial.hasDerivWithinAt_aeval, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, groupHomology.isoCycles₁_hom_comp_i_apply, LinearMap.coe_rTensorHom, LinearMap.isLinearMap_of_compatibleSMul, Module.Basis.map_apply, LinearEquiv.trans_refl, HahnSeries.coeff_toPowerSeries, ContinuousLinearMap.extendTo𝕜_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, HasFDerivAt.sinh, LinearMap.baseChange_sub, Module.Basis.det_comp, Module.Basis.symmetricAlgebra_repr_apply, LinearEquiv.prodProdProdComm_apply, rotation_trans, DirectSum.single_eq_lof, Coalgebra.lift_lsmul_comp_counit_comp_comul, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, LinearMap.convOne_def, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_mem, Algebra.TensorProduct.opAlgEquiv_symm_apply, PowerSeries.coeff_smul, Polynomial.coeff_monomial_same, Module.AEval.of_symm_X_smul, LinearEquiv.sumPiEquivProdPi_symm_apply, HasFDerivAt.comp_hasDerivWithinAt_of_eq, PiLp.projₗ_apply, ProbabilityTheory.IsGaussian.integral_dual, LinearMap.range_prod_le, SheafOfModules.Presentation.map_relations_I, FGModuleCat.Iso.conj_eq_conj, TensorProduct.map_mul, Finsupp.supportedEquivFinsupp_symm_apply_coe_support_val, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', ModuleCat.instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, Module.End.isSemisimple_neg, Bialgebra.counit_mul, Complex.linearEquiv_det_conjAe, CurveIntegrable.fun_neg, Orientation.abs_areaForm_le, LieModule.traceForm_eq_sum_finrank_nsmul, ZLattice.exists_forall_abs_repr_le_norm, ContDiffWithinAt.laplacianWithin_CLM_comp_left_nhds, Matrix.toBilin'_apply, ContinuousLinearEquiv.neg_apply, AffineSubspace.map_direction, MultilinearMap.domDomCongrLinearEquiv'_apply, Pretrivialization.symmₗ_apply, mfderivWithin_const, fderivWithin_comp₃, LinearMap.det_restrictScalars, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, hasStrictFDerivAt_pow', Module.End.isSemisimple_zero, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, Submodule.linearMap_eq_iff_of_eq_span, CliffordAlgebra.changeForm_ι, Polynomial.hasStrictDerivAt_aeval, ContinuousLinearMap.applySMulCommClass, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, LieAlgebra.conj_ad_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, ContinuousLinearMap.norm_single, LinearMap.flip_injective_iff₂, VectorPrebundle.exists_coordChange, HasFDerivWithinAt.snd, MvPowerSeries.coeff_add_mul_monomial, DoubleCentralizer.one_fst, Matrix.adjugate_def, ContinuousLinearMap.norm_extendTo𝕜', RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn, RestrictScalars.lsmul_apply_apply, IsIntegralClosure.range_le_span_dualBasis, ModuleCat.imageIsoRange_inv_image_ι_assoc, LinearMap.compQuadraticMap_apply, StrongDual.polar_univ, isSimpleModule_iff_quot_maximal, LinearMap.toMatrix_prodMap, Matrix.toLin_apply, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero, groupCohomology.H1π_eq_zero_iff, fderivWithin_eventually_congr_set, Matrix.toLin'_one, groupHomology.H1AddEquivOfIsTrivial_symm_apply, LinearIsometry.coe_toAffineIsometry, PiTensorProduct.tmulEquivDep_apply, Polynomial.iterate_derivative_eq_zero_of_degree_lt, ContinuousLinearEquiv.unitsEquivAut_apply_symm, AdicCompletion.mk_surjective, Polynomial.toFinsuppIsoLinear_apply, MvPowerSeries.monomial_pow, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, ContDiffMapSupportedIn.postcompCLM_apply, TemperedDistribution.smulLeftCLM_add, ContinuousAlternatingMap.curryLeft_zero, IsContDiffImplicitAt.bijective, Submodule.eq_starProjection_of_mem_orthogonal', ProbabilityTheory.covarianceBilin_apply_basisFun, RootPairing.reflection_dualMap_eq_coreflection, Algebra.Extension.h1Cotangentι_ext_iff, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, Algebra.TensorProduct.linearEquivIncludeRange_symm_tmul, ContinuousAlternatingMap.restrictScalarsLI_apply, fderivWithin_fun_const, Complex.restrictScalars_toSpanSingleton, MultilinearMap.freeFinsuppEquiv_apply, MonoidAlgebra.domCongr_comp_lsingle, Orientation.normSq_kahler, Ideal.toCotangent_eq_zero, Finsupp.linearCombination_range, AlgEquiv.linearEquivConj_mulLeftRight, Module.Basis.constr_apply_fintype, ContinuousLinearEquiv.comp_right_differentiableOn_iff, OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective, UniformSpace.Completion.coe_toComplₗᵢ, HasFDerivWithinAt.clog, LinearMap.prod_ext_iff, hasGradientAt_iff_hasFDerivAt, DFinsupp.coprodMap_apply_single, LinearMap.IsSymmetric.invariant_orthogonalComplement_eigenspace, LinearEquiv.symm_conj_apply, algebraMapCLM_apply, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, TensorProduct.LieModule.lift_apply, Matrix.cramer_submatrix_equiv, curveIntegrable_neg_iff, MvPolynomial.decomposition.decompose'_apply, MultilinearMap.ofSubsingletonₗ_apply, Profinite.NobelingProof.GoodProducts.square_commutes, CliffordAlgebra.ι_mul_ι_add_swap_of_isOrtho, groupHomology.d₃₂_single_one_fst, Matrix.mulVecLin_submatrix, ContinuousLinearMap.snd_comp_prod, inhomogeneousCochains.d_hom_apply, Algebra.Generators.toKaehler_tmul_D, DFinsupp.lsum_symm_apply, LinearEquiv.restrictScalars_injective, ZMod.dft_dft, hasMFDerivWithinAt_const, iteratedFDeriv_one_apply, Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity, ContinuousLinearEquiv.iteratedFDeriv_comp_left, WithConv.linearEquiv_apply, PerfectRing.liftAux_id, AlgEquiv.coe_toLinearEquiv, PowerSeries.coeff_monomial_same, Submodule.mulRightMap_apply, LinearEquiv.conjAlgEquiv_apply_apply, Submodule.reflection_orthogonal, fderivWithin_comp_of_eq', hasFDerivAt_exp_smul_const_of_mem_ball, MultilinearMap.piFamilyₗ_apply, MultilinearMap.fromDirectSumEquiv_apply, fderiv_fun_mul', TrivSqZeroExt.liftEquivOfComm_apply, TensorProduct.isBaseChange, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, Rep.coind'_ext_iff, HasFDerivAt.const_smul, Polynomial.iterate_derivative_prod_X_sub_C, HasFDerivAt.hasLineDerivAt, LinearEquiv.algEquivOfRing_symm_apply, Module.Basis.SmithNormalForm.le_ker_coord_of_notMem_range, LieHom.quotKerEquivRange_invFun, Module.isTorsionBy_iff_mem_ker_lsmul, MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous, mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd, RingHomInvPair.comp_eq, NumberField.mixedEmbedding.negAt_symm, OrderRingHom.coe_ringHom_id, VectorFourier.contDiff_fourierIntegral, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, Matrix.reindexLinearEquiv_mul, LinearMap.concaveOn, Submodule.map₂_le, LieSubalgebra.coe_ofLe, iteratedFDeriv_succ_apply_right, LinearMap.eventually_isCompl_ker_pow_range_pow, LaurentPolynomial.comul_C, FormalMultilinearSeries.leftInv_coeff_one, LaurentSeries.hasseDeriv_single_add, LinearMap.IsSymmetric.smul, Submodule.isOpenMap_mkQ, MeasureTheory.Measure.mapₗ_apply_of_measurable, Module.Basis.smul_eq_map, Derivation.coeFn_coe, PiTensorProduct.mul_def, RootPairing.rootForm_self_sum_of_squares, finsuppLEquivDirectSum_single, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, Polynomial.opRingEquiv_symm_monomial, ContinuousLinearMap.hasMFDerivAt, Polynomial.toAddCircle_monomial_eq_smul_fourier, TensorProduct.assocIsometry_apply, Matrix.toLin_conjTranspose, mulRightLinearMap_apply, mdifferentiableOn_continuousLinearMapCoordChange, imaginaryPart_surjective, AdicCompletion.map_ext''_iff, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, Orthonormal.inner_finsupp_eq_sum_left, Submodule.quotientEquivOfIsCompl_symm_apply, MvPolynomial.map_monomial, PresheafOfModules.Elements.fromFreeYoneda_app_apply, fderiv_deriv, Finsupp.comul_single, HopfAlgebra.mul_antipode_rTensor_comul_apply, Representation.IntertwiningMap.toFun_injective, Module.Relations.Solution.IsPresentation.uniq_symm_var, MvPolynomial.monomial_mem_restrictSupport, DirectedSystem.lTensor, LinearMap.BilinForm.isRefl_neg, LinearEquiv.conj_conj_symm, IsBaseChange.iff_lift_unique, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, ModuleCat.HasColimit.coconePointSMul_apply, AlternatingMap.compLinearMap_assoc, Algebra.Extension.Cotangent.map_toInfinitesimal_bijective, QuadraticMap.canLift', GradedTensorProduct.auxEquiv_tmul, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, MulOpposite.opLinearIsometryEquiv_symm_apply, LinearIndependent.finsuppLinearCombination_injective, Ideal.cotangentEquivIdeal_apply, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, Submodule.IsPrincipal.map, LinearMap.det_eq_sign_charpoly_coeff, Module.End.eventually_disjoint_ker_pow_range_pow, ModuleCat.kernelIsoKer_hom_ker_subtype, Derivation.map_one_eq_zero', LinearIsometryEquiv.hasFDerivAt, Representation.ker_leftRegular_norm_eq, Finsupp.lapply_apply, Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_pow, ModuleCat.smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, MvPowerSeries.coeff_zero_X_mul, AdicCompletion.congr_symm_apply, ContinuousLinearMap.ker_prod, HasFDerivAtFilter.add, HasFDerivAt.lim_real, ModuleCat.hom_add, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, LinearEquiv.ofSubsingleton_apply, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, PointwiseConvergenceCLM.precomp_apply, TensorProduct.AlgebraTensorModule.lTensor_comp, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, LinearIsometryEquiv.rTensor_apply, Submodule.fst_map_fst, LinearIsometryEquiv.inner_map_map, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, Orientation.neg_rotation_pi_div_two, Algebra.Extension.H1Cotangent.val_add, PolynomialModule.equivPolynomialSelf_apply_eq, homTensorHomEquiv_toLinearMap, HasFDerivAt.rpow_const, Subspace.dualLift_of_mem, InnerProductSpace.isStarProjection_rankOne_self, ExteriorAlgebra.ιMulti_apply, LinearEquiv.coe_ofEq_apply, Polynomial.degreeLT.addLinearEquiv_symm_apply, SeparationQuotient.mk_comp_outCLM, coord_norm', RootPairing.algebraMap_posRootForm_posForm, Trivialization.apply_eq_prod_continuousLinearEquivAt, CliffordAlgebra.EquivEven.v_sq_scalar, HasFDerivWithinAt.comp, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, IsAdjoinRootMonic.coeff_injective, CharacterModule.dual_bijective_iff_bijective, ContinuousLinearMapWOT.ext_dual_iff, endVecAlgEquivMatrixEnd_apply_apply, LinearIsometry.integral_comp_comm, AffineMap.sub_linear, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Submodule.coe_torsionBy, MvPolynomial.homogeneousComponent_eq_zero, contDiff_clm_apply_iff, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, HasFPowerSeriesAt.hasFDerivAt, Submodule.dualAnnihilator_gc, StrictConvex.linearIsometry_preimage, OrthonormalBasis.measurePreserving_repr_symm, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Polynomial.coe_basisMonomials, MvPowerSeries.map_monomial, Rep.ofMulActionSubsingletonIsoTrivial_hom_hom, PowerSeries.trunc_apply, Ideal.quotientToQuotientRangePowQuotSucc_injective, groupCohomology.cocyclesMk₁_eq, AffineMap.toConstProdLinearMap_symm_apply, PiTensorProduct.ofDFinsuppEquiv_tprod_single, LinearMap.baseChange_neg, norm_fderiv_norm, SemimoduleCat.hom_injective, RootPairing.span_root'_eq_top, LinearEquiv.smul_apply, instInvertibleReprₛ, fderiv_comp, eventually_enorm_mfderiv_extChartAt_lt, AlgCat.forget₂_module_obj, DirectSum.decomposeLinearEquiv_apply, ContinuousLinearMap.restrictScalars_zero, EuclideanSpace.piLpCongrLeft_single, hasFDerivAt_exp_smul_const, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, ContinuousLinearMap.hasStrictFDerivAt, LinearMap.BilinForm.nondegenerate_congr_iff, NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subset, ContinuousLinearMap.instNontrivialId, LinearMap.aeval_self_charpoly, exteriorPower.alternatingMapLinearEquiv_comp, Matrix.trace_toLin'_eq, signedDist_linear_apply, Finset.weightedVSub_filter_of_ne, TensorProduct.gradedComm_of_zero_tmul, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, LocallyConstant.congrLeftₗ_symm_apply_apply, Matrix.toLin'OfInv_symm_apply, Orientation.rotation_eq_matrix_toLin, MeasureTheory.AEStronglyMeasurable.fourierSMulRight, ModuleCat.instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, oneTangentSpaceIcc_def, Finsupp.linearCombination_restrict, Algebra.Extension.H1Cotangent.val_smul, LinearMap.BilinForm.flip_apply, TrivSqZeroExt.inlCLM_apply, Algebra.Presentation.differentials.comm₁₂, RootPairing.orthogonal_corootSpan_eq, HasDerivAt.hasFDerivAt_equiv, SheafOfModules.relationsOfIsCokernelFree_I, PiTensorProduct.map_tprod, AlternatingMap.curryLeft_smul, Representation.isTrivial_def, HasStrictFDerivAt.const_rpow, Derivation.coe_sub_linearMap, Orientation.inner_rightAngleRotation_swap, Module.Basis.sumQuot_repr_inr_of_mem, MonomialOrder.sPolynomial_monomial_mul, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, IsGroupLikeElem.antipode_mul_cancel, Module.eval_ker, Finsupp.coe_lmapDomain, Module.Basis.sumCoords_self_apply, VertexOperator.ext_iff, ContinuousLinearMap.comp_analyticOn, Algebra.trace_localization, LinearIsometryEquiv.piLpCurry_symm_apply, Submodule.map_op_mul, AlternatingMap.domDomCongrₗ_toAddEquiv, Finset.weightedVSub_vadd, ModuleCat.MonoidalCategory.tensorμ_apply, AffineEquiv.ofLinearEquiv_apply, RootPairing.ker_rootForm_eq_dualAnnihilator, fderiv_finset_prod, Finsupp.lapply_comp_lsingle_of_ne, LinearMap.BilinForm.compRight_apply, SymmetricAlgebra.equivMvPolynomial_ι_apply, QuadraticAlgebra.linearEquivTuple_symm_apply, DirectSum.decomposeLinearEquiv_symm_comp_lof, Module.algebraMap_end_apply, Submodule.sup_dualAnnihilator_le_inf, hasStrictFDerivAt_list_prod_attach', rotationOf_coe, Module.Basis.repr_injective, LinearIsometryEquiv.coe_inv, AddCommGroup.DirectLimit.directedSystem, Module.FinitePresentation.linearEquivMapExtendScalars_apply, Polynomial.isNilpotent_monomial_iff, ContinuousLinearMap.fst_comp_inl, IsLocalizedModule.iso_symm_apply_aux, Polynomial.as_sum_range', IsBaseChange.endHom_apply, LinearMap.isSkewAdjoint_iff_neg_self_adjoint, LinearIndependent.fintypeLinearCombination_injective, NumberField.mixedEmbedding.volume_negAt_plusPart, HasFDerivAt.snd, AffineMap.vsub_linear, LinearMap.mulRight_zero_eq_zero, AdicCompletion.AdicCauchySequence.map_comp_apply, StrongDual.norm_toLpₗ_le, MvPolynomial.homogeneousComponent_zero, hasFDerivWithinAt_euclidean, Orientation.oangle_sub_left_smul_rotation_pi_div_two, ContinuousLinearEquiv.prodAssoc_apply, LinearIndependent.repr_range, DoubleCentralizer.sub_fst, LinearMap.polyCharpoly_eq_of_basis, PowerSeries.coeff_monomial, Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem, LinearMap.mul''_apply, Module.Basis.parallelepiped_eq_map, Polynomial.natDegree_monomial, selfAdjoint.realPart_coe, LinearEquiv.one_mem_dilatransvections, Module.Invertible.rTensorInv_injective, TensorProduct.AlgebraTensorModule.lTensor_mul, AddMonoidHom.coe_toIntLinearMap_ker, Rep.quotientToInvariantsFunctor_obj_V, TensorProduct.piScalarRight_symm_single, LinearEquiv.toLinearMap_smul, LinearMap.bijective_or_eq_zero, contDiffOn_clm_apply, LocallyConstant.ker_comapₗ, ContinuousLinearEquiv.det_coe_symm, Module.Basis.repr_apply_eq, Polynomial.factorial_mul_shiftedLegendre_eq, ContinuousLinearMap.restrictScalars_smul, SkewMonoidAlgebra.lhom_ext'_iff, ContinuousAlternatingMap.piLinearEquiv_symm_apply, fderiv_continuousAlternatingMap_apply_apply, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, MvPolynomial.monomial_left_injective, IsSemisimpleModule.exists_end_ringEquiv, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T, Module.End.mem_eigenspace_iff, Algebra.TensorProduct.one_mul, Submodule.starProjection_orthogonal, TensorPower.algebraMap₀_mul_algebraMap₀, Ideal.constr_basisSpanSingleton, IsAdjoinRootMonic.map_modByMonicHom, TrivSqZeroExt.sndHom_comp_map, PiTensorProduct.mapLMultilinear_apply_apply, TensorPower.gMul_def, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, ContinuousLinearMap.instNonnegSpectrumClassRealId, MeasureTheory.Measure.map_toOuterMeasure, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, HasStrictFDerivAt.cos, Function.Exact.iff_linearMap_rangeRestrict, Module.Flat.iff_rTensor_exact, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, LinearMap.restrictScalars_comp, LinearMap.mem_polar_singleton, MvPolynomial.monomial_sum_index, LinearMap.baseChange_zero, ContinuousLinearMap.uncurryMid_apply, Finsupp.linearCombination_comp, LinearEquiv.isUnit_det, hasFDerivAt_update, LinearMap.IsSymm.eq, SemimoduleCat.MonoidalCategory.associator_inv_apply, RootPairing.range_polarizationIn, isBoundedBilinearMap_apply, ContinuousLinearMap.fst_comp_inr, Polynomial.separable_def, Ring.DirectLimit.map_id, CliffordAlgebra.contractLeft_ι, LinearMap.polyCharpolyAux_map_aeval, MvPolynomial.monic_monomial_eq, MvPowerSeries.coeff_zero_iff, ProperCone.dual_flip_dual, KaehlerDifferential.map_surjective, RCLike.ofRealCLM_norm, Trivialization.coe_symmₗ, Pi.counit_coe_finsupp, TensorProduct.directSumLeft_tmul, ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse, Polynomial.iterate_derivative_smul, Complex.sqrt_map, HVertexOperator.ext_iff, Finset.weightedVSubOfPoint_apply_const, WithLp.sndₗ_apply, LinearIsometryEquiv.trans_refl, hasStrictFDerivAt_ringInverse, PowerSeries.coeff_X, KaehlerDifferential.map_compDer, Subspace.dualAnnihilator_iInf_eq, MvPolynomial.pderiv_monomial_single, Algebra.TensorProduct.piRightHom_one, Algebra.trace_eq_matrix_trace, LinearMap.pi_comp, LinearMap.prodMap_zero, ContDiffOn.continuousOn_fderiv_of_isOpen, LinearMap.liftBaseChange_tmul, ContinuousLinearMap.mul_apply', Submodule.mulMap_one_left_eq, Polynomial.sumIDeriv_X, Algebra.traceMatrix_of_basis, groupHomology.d₂₁_apply_mem_cycles₁, TrivSqZeroExt.map_comp_map, ContDiffOn.continuousLinearMap_comp, AlgEquiv.one_toLinearMap, HasFDerivAt.fun_sum, LinearEquiv.prodUnique_symm_apply, TensorProduct.quotTensorEquivQuotSMul_symm_mk, Algebra.trace_algebraMap_of_basis, Submodule.iSup_map_single, fderiv_zero_of_not_differentiableAt, Unitary.norm_map, AdicCompletion.of_ofLinearEquiv_symm, AdicCompletion.kerProj_of, Trivialization.coordChangeL_symm_apply, LieModule.traceForm_lieSubalgebra_mk_left, SpecialLinearGroup.toLinearEquiv_symm_apply, LinearMap.instStarModuleId, Submodule.starProjection_apply_mem, NumberField.inverse_basisMatrix_mulVec_eq_repr, LieDerivation.commutator_coe_linear_map, Finsupp.range_linearCombination, LieModule.Cohomology.smul_apply_apply, Polynomial.contentIdeal_monomial, groupCohomology.coboundariesToCocycles₂_apply, linearIndependent_iff_injective_fintypeLinearCombination, HahnSeries.coeff_toPowerSeries_symm, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, HasFDerivWithinAt.arsinh, InnerProductSpace.rankOne_comp_rankOne, TemperedDistribution.fourierTransform_apply, ContinuousLinearEquiv.rightInverse_hasRightInverse, Orientation.oangle_add_right_smul_rotation_pi_div_two, CliffordAlgebra.changeForm.neg_proof, Polynomial.injective_ofFn, HasStrictDerivAt.comp_hasStrictFDerivAt, HasDerivWithinAt.comp_hasFDerivWithinAt, Matrix.spectrum_toLin, TensorAlgebra.ι_leftInverse, ModuleCat.ihom_map_apply, geometric_hahn_banach_point_open, TestFunction.mkCLM_apply, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem, Submodule.quotDualCoannihilatorToDual_injective, Module.Basis.eval_injective, PowerSeries.IsWeierstrassDivisorAt.coeff_div, PolyEquivTensor.toFunBilinear_apply_apply, LinearMap.BilinForm.IsSymm.neg, LinearMap.mapMatrixModule_comp, LinearEquiv.apply_smulCommClass', Module.End.instSMulCommClass', LinearMap.toMatrix'_comp, Matrix.toLinearEquiv'_apply, LinearMap.isUnit_toMatrix'_iff, MvPowerSeries.map_id, Orientation.inner_smul_rotation_pi_div_two_left, Submodule.quotientPi_symm_apply, LinearMap.BilinForm.add_right, ModuleCat.ihom_coev_app, Matrix.toBilin_toMatrix, IsBaseChange.toDual_apply, BoxIntegral.hasIntegral_const, LinearMap.BilinForm.orthogonal_span_singleton_eq_toLin_ker, ZLattice.volume_image_eq_volume_div_covolume, Module.Relations.ker_toQuotient, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, RootPairing.reflection_apply_self, Module.AEval.mem_mapSubmodule_symm_apply, LinearIsometry.toLinearMap_rTensor, Real.map_linearMap_volume_pi_eq_smul_volume_pi, PolyEquivTensor.toFunLinear_tmul_apply, Module.jacobson_quotient_of_le, SemimoduleCat.MonoidalCategory.whiskerLeft_apply, ContinuousMap.toLp_injective, Finsupp.bilinearCombination_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, ContinuousAlternatingMap.compContinuousLinearMap_apply, TensorProduct.exists_finite_submodule_of_setFinite', groupCohomology.H2π_eq_zero_iff, MvPolynomial.DirectSum.coeLinearMap_eq_finsum, DoubleCentralizer.pow_fst, LinearMap.prodMap_map_prod, Matrix.nondegenerate_toLinearMap₂_iff, UniversalEnvelopingAlgebra.ι_apply, Polynomial.coeff_iterate_derivative, LinearMap.fst_apply, DFinsupp.ker_mapRangeLinearMap, LieHom.coe_toLinearMap, LaurentSeries.hasseDeriv_comp, Module.End.instIsScalarTower, Finsupp.apply_linearCombination, StrongDual.toLpₗ_of_not_memLp, isConformalMap_complex_linear_conj, LinearMap.zero_smulRight, PiTensorProduct.mapL_apply, Matrix.reindexLinearEquiv_apply, LinearMap.BilinForm.comp_congr, Module.Relations.Solution.IsPresentation.surjective_π, Matrix.cramer_subsingleton_apply, Euclidean.closedBall_eq_preimage, Matrix.toBilin'_comp, Matrix.isHermitian_iff_isSymmetric, MvPolynomial.support_monomial_subset, LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain, Subspace.dualRestrict_surjective, AffineEquiv.ofLinearEquiv_trans_ofLinearEquiv, MvPolynomial.monomial_mul, LieModule.toEnd_pow_lie, Module.compHom.toLinearMap_apply, RootPairing.InvariantForm.apply_eq_or_aux, KaehlerDifferential.kerTotal_mkQ_single_mul, MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrder, IsBaseChange.endHom_one, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, LinearEquiv.prodCongr_symm, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, SemimoduleCat.hom_bijective, DirectedSystem.rTensor, hasStrictFDerivAt_finset_prod, AdicCompletion.evalOneₐ_of, fderiv_fun_neg, Representation.norm_ofDistribMulAction_eq, Module.End.HasUnifEigenvector.apply_eq_smul, MultilinearMap.freeFinsuppEquiv_single, Submodule.ker_subtypeL, Algebra.Generators.H1Cotangent.exact_map_δ', ContinuousMapZero.evalCLM_apply, WeakBilin.coeFn_continuous, Lagrange.degree_interpolate_le, curveIntegral_zero, Polynomial.bernoulli_def, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Module.AEval.X_smul_of, Submodule.map₂_span_singleton_eq_map, Submodule.IsOrtho.comap_iff, Polynomial.derivative_eval₂_C, RingCat.ofHom_id, InnerProductSpace.rankOne_comp, Trivialization.mk_coordChangeL, MvPowerSeries.weightedOrder_eq_nat, Representation.averageMap_id, PiLp.basisFun_eq_pi_basisFun, HasDerivWithinAt.comp_hasFDerivAt, groupCohomology.H1π_comp_map_apply, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, StrongDual.mem_polarSubmodule, exists_dual_vector', LinearMap.proj_pi, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, LinearMap.intrinsicStar_id, Submodule.map₂_flip, Module.FaithfullyFlat.zero_iff_lTensor_zero, LocalizedModule.lift_mk, PowerSeries.as_tsum, LinearMap.lift_rank_range_add_rank_ker, CliffordAlgebra.invOf_ι, LinearMap.lTensor_bij_iff_rTensor_bij, Orientation.kahler_rightAngleRotation_left, Rep.leftRegularHom_hom_single, Submodule.mulMap_comm_of_commute, Submodule.fst_map_snd, CoalgEquiv.toLinearEquiv_toLinearMap, LinearMap.separatingLeft_congr_iff, Module.Basis.end_repr_symm_apply, MvPowerSeries.expand_monomial, TensorAlgebra.GradedAlgebra.ι_apply, LinearMap.GeneralLinearGroup.coe_ofLinearEquiv, LieSubmodule.coe_toEnd, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, LinearMap.continuous_of_finiteDimensional, HasFDerivAt.le_of_lip', Module.evalEquiv_apply, SchwartzMap.tsupport_smulLeftCLM_subset, Polynomial.lhom_ext'_iff, LinearMap.IsReflective.dvd_two_mul, HasMFDerivAt.sub, ContinuousLinearEquiv.prodComm_symm, CliffordAlgebra.contractRight_contractRight, InnerProductSpace.toMatrix_rankOne, HasFDerivWithinAt.continuousMultilinear_apply_const, TensorProduct.AlgebraTensorModule.map_mul, LinearMap.equivariantProjection_apply, QuadraticForm.tmul_tensorLId_apply, separate_convex_open_set, eventually_norm_symmL_trivializationAt_lt, LieAlgebra.InvariantForm.mem_orthogonal, cfcₙHom_real_eq_restrict, Coalgebra.Repr.convMul_apply, ClosedSubmodule.toSubmodule_comap, PeriodPair.latticeEquiv_symm_apply, MvPolynomial.rTensor_symm_apply_single, PowerSeries.derivative_coe, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, Complex.equivRealProdLm_symm_apply_re, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, ContinuousLinearEquiv.coe_uniqueProd, LinearMap.BilinMap.toQuadraticMap_multiset_sum, Module.Basis.equiv'_apply, LieModule.toEnd_apply_apply, hasFDerivAtFilter_finCons, MeasureTheory.ComplexMeasure.im_apply, LinearMap.IsPerfPair.bijective_right, PowerSeries.coeff_zero_eq_constantCoeff_apply, PiTensorProduct.liftIsometry_comp_mapL, CStarMatrix.reindexₗ_apply, CliffordAlgebra.star_ι, ContinuousLinearMap.pi_comp, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Polynomial.X_pow_mul_monomial, FractionalIdeal.den_mul_self_eq_num, QuadraticForm.tensorLId_apply, ModuleCat.hom_hom_associator, Matrix.ext_linearMap_iff, Representation.free_single_single, Submodule.isQuotientEquivQuotientPrime_iff, RCLike.geometric_hahn_banach_open, LinearMap.mul_toMatrix₂_mul, Submodule.map_smul', Polynomial.aeval_derivative_of_splits, span_eq_top_of_isLocalizedModule, LinearEquiv.coord_self, InnerProductSpace.isSymmetric_rankOne_self, Pretrivialization.linearMapAt_def_of_mem, MeasureTheory.OuterMeasure.isometryEquiv_map_mkMetric, MvPolynomial.pderiv_monomial, Algebra.trace_quotient_mk, CoalgCat.forget₂_obj, IsLocalization.bijective_linearMap_mul', ContinuousLinearMap.toSpanSingleton_comp_toSpanSingleton, TensorAlgebra.hom_ext_iff, ContinuousMap.coe_toLp, LinearMap.lTensor_comp_apply, Module.Basis.apply_eq_iff, RingEquiv.toRingHom_refl, Representation.IntertwiningMap.isIntertwining', Module.Flat.iff_forall_exists_factorization, skewAdjointPart_apply_coe, CliffordAlgebra.involute_ι, HasFDerivAt.sin, LinearMap.image_convexHull, fderiv_const_sub, continuousMultilinearCurryLeftEquiv_apply, ProbabilityTheory.HasGaussianLaw.map_equiv, tsupport_fderiv_subset, Orientation.abs_areaForm_of_orthogonal, exteriorPower.alternatingMapToDual_apply_ιMulti, Module.Basis.mk_coord_apply, continuous_selfAdjointPart, Polynomial.lsum_apply, FractionalIdeal.coe_map, sigmaFinsuppLequivDFinsupp_symm_apply, LinearMap.exact_zero_iff_injective, LinearIsometryEquiv.symm_rTensor, CoalgHom.coe_toLinearMap, LinearMap.isSymmetricProjection_iff, LinearMap.BilinForm.tensorDistribEquiv_tmul, innerₗ_apply_apply, Algebra.trace_surjective, HahnSeries.ofPowerSeriesAlg_apply_coeff, ContinuousAlternatingMap.ofSubsingleton_apply_apply, Module.Dual.lie_apply, LinearMap.coe_inl, HasMFDerivWithinAt.add, LinearMap.trace_tensorProduct', Algebra.Generators.toComp_toAlgHom_monomial, Module.Presentation.cokernel_G, Module.Relations.Solution.π_comp_map, MonoidAlgebra.GroupSMul.linearMap_apply, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, Submodule.annihilator_span, LinearMap.eq_adjoint_iff_basis, Module.Finite.exists_comp_eq_id_of_projective, RootPairing.polarizationEquiv_toLinearMap, LinearMap.IsReflective.coroot_apply_self, Representation.Coinvariants.mk_eq_zero, ContinuousLinearEquiv.prodAssoc_toLinearEquiv, HasFDerivAt.csin, TensorProduct.commIsometry_symm, isStarProjection_starProjection, precomp_compactConvergenceCLM_apply, TensorProduct.leftComm_symm_tmul, KaehlerDifferential.D_tensorProductTo, unitary.norm_map, Finsupp.domLCongr_symm, ContinuousLinearEquiv.fderiv, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Polynomial.derivative_pow, ContinuousAlternatingMap.restrictScalarsCLM_apply, RootPairing.coreflection_sq, ContMDiffWithinAt.mfderivWithin_apply, LinearEquiv.ofEq_symm, SchwartzMap.tsupport_fderivCLM_subset, Trivialization.symmₗ_linearMapAt, ContinuousLinearMap.isBigOTVS_comp, DFinsupp.coeFnLinearMap_apply, Algebra.Extension.toKaehler_surjective, ContinuousLinearEquiv.mdifferentiableWithinAt, LinearMap.det_eq_one_of_finrank_eq_zero, MonoidAlgebra.lhom_ext'_iff, hfdifferential_apply, Rep.finsuppTensorRight_inv_hom, TensorAlgebra.range_lift, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, ContinuousLinearEquiv.mdifferentiable, PiTensorProduct.one_mul, Submodule.IsCompl.projection_apply_eq_zero_iff, AlgEquiv.toLinearEquiv_toLinearMap, QuotSMulTop.equivQuotTensor_naturality_mk, Finset.weightedVSubOfPoint_eq_of_weights_eq, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree, Module.dual_rank_eq, Submodule.mulMap_eq_mul'_comp_mapIncl, DirectSum.decomposeLinearEquiv_symm_apply, ContinuousLinearMap.integral_comp_L1_comm, curveIntegralFun_add, Module.Flat.iff_lTensor_preserves_injective_linearMapₛ, Submodule.linearMap_eq_zero_iff_of_span_eq_top, CompactlySupportedContinuousMap.toNNRealLinear_apply, Polynomial.derivative_prod, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, LinearMap.rank_zero, LinearEquiv.isSymmetric_symm_iff, LinearMap.toMatrix'_id, setBasisOfTopLeSpanOfCardEqFinrank_repr_apply, bilinFormOfRealInner_orthogonal, LinearMap.polyCharpolyAux_coeff_eval, OrthonormalBasis.equiv_symm, HasFDerivAtFilter.snd, AffineMap.linear_eq_zero_iff_exists_const, AnalyticOnNhd.fderiv, Module.Invertible.lTensor_injective_iff, LinearMap.range_smul', WStarAlgebra.exists_predual, LinearEquiv.baseChange_inv, selfAdjointPartL_apply_coe, HasFDerivWithinAt.comp_hasDerivWithinAt, RootPairing.Equiv.coweightHom_op, weightedVSub_mem_vectorSpan, LocalizedModule.mul_by_divBy, EuclideanGeometry.inner_weightedVSub, Module.End.genEigenspace_zero_nat, Orientation.kahler_rotation_left, Representation.le_comap_invariants, LinearMap.exact_map_mkQ_range, HasFDerivWithinAt.sub, LindemannWeierstrass.integral_exp_mul_eval, HasFDerivAtFilter.fun_neg, LinearEquiv.coe_toContinuousLinearEquiv, PiTensorProduct.liftIsometry_symm_apply, Derivation.tensorProductTo_mul, ModularFormClass.hasSum_qExpansion_of_abs_lt, TensorProduct.assoc_tensor'', fderivWithin_continuousAlternatingMap_apply_apply, Matrix.toLinearMapₛₗ₂_symm, SchwartzMap.smulLeftCLM_neg, PowerSeries.coeff_map, contractLeft_apply, Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent, LinearIsometryEquiv.refl_trans, Algebra.Extension.Cotangent.mk_surjective, ContinuousLinearMap.opNNNorm_mul, Rep.ihom_obj_V_isAddCommGroup, Polynomial.valuation_monomial_eq_valuation_X_pow, Finsupp.disjoint_lsingle_lsingle, SemimoduleCat.Iso.conj_eq_conj, ContinuousLinearMap.ringInverse_eq_inverse, Complex.conjCLE_enorm, ContinuousLinearEquiv.comp_differentiableAt_iff, LinearMap.BilinMap.tensorDistrib_tmul, Trivialization.coe_coordChangeL', Projectivization.cross_mk, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, LinearMap.BilinForm.mul_toMatrix_mul, Polynomial.eval_sumIDeriv_of_pos, LinearMap.trace_transpose, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, MeasureTheory.charFunDual_eq_pi_iff, mfderiv_zero_of_not_mdifferentiableAt, MvPolynomial.dvd_monomial_mul_iff_exists, Trivialization.coe_linearMapAt_of_mem, CliffordAlgebra.reverse_comp_involute, MeasureTheory.aestronglyMeasurable_condExpL1CLM, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, WithCStarModule.map_top_submodule, Polynomial.mkDerivation_X, Submodule.mkQ_map_self, iteratedFDeriv_succ_eq_comp_right, LineDeriv.tensorLineDerivTwo_eq_lineDerivOp_lineDerivOp, ContinuousLinearEquiv.comp_hasFDerivAt_iff', Representation.invariants_eq_inter, Finsupp.linearCombination_comp_addSingleEquiv, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, QuadraticForm.comp_tensorRId_eq, ContinuousLinearMap.ofNat_apply, RootPairing.RootPositiveForm.isSymm_posForm, curveIntegralFun_sub, ContDiffMapSupportedIn.seminorm_apply, IsBaseChange.endHom_comp_apply, LinearMap.tripolar_eq_polar, LinearMap.BilinForm.toMatrix_mul_basis_toMatrix, inner_map_self_eq_zero, LinearMap.coe_single, OrthogonalFamily.eq_ite, AlgHom.toLinearMap_fromOpposite, LinearAlgebra.FreeProduct.rel_id, Matrix.toLinAlgEquiv_apply, AffineMap.linearHom_apply, TensorProduct.LieModule.toLinearMap_map, Module.Basis.coe_ofRepr, AdicCompletion.tensor_map_id_left_eq_map, ProperCone.coe_map, LinearMap.nondegenerate_toMatrix₂'_iff, Orientation.inner_sq_add_areaForm_sq, CoalgEquiv.symm_toLinearEquiv, TensorProduct.range_map_eq_span_tmul, Module.End.mem_invtSubmodule_symm_iff_le_map, LinearMap.BilinForm.toMatrix'_comp, Module.equiv_free_prod_directSum, Submodule.map_map₂, ContinuousLinearEquiv.prodProdProdComm_toLinearEquiv, VectorField.lieBracket_smul_left, ContinuousLinearMap.rotation_apply, ContinuousLinearMap.HasLeftInverse.comp, LieModule.exists_nontrivial_weightSpace_of_isSolvable, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, Algebra.Generators.CotangentSpace.exact, Algebra.Generators.H1Cotangent.δAux_X, DoubleCentralizer.algebraMap_fst, MonomialOrder.div_set, RCLike.reLm_coe, LinearMap.ker_dualMap_eq_dualCoannihilator_range, LinearMap.smul_compAlternatingMap, fderiv_continuousLinearEquiv_comp, MvPowerSeries.coeff_rescale, nnnorm_fderiv_norm_rpow_le, hasFDerivWithinAt_natCast, DFinsupp.lmk_apply, CharacterModule.dual_rTensor_conj_homEquiv, SchwartzMap.convolution_continuous_left, Submodule.IsCompl.projection_apply, ContinuousLinearMap.adjoint_toSpanSingleton, hasStrictFDerivAt_exp_zero_of_radius_pos, ContinuousLinearMap.toBilinForm_injective, TensorProduct.equivFinsuppOfBasisRight_apply, mulLinearMap_apply_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff, LinearIsometryEquiv.coe_one, LinearMap.intrinsicStar_mulLeft, CoalgEquiv.symm_toCoalgHom, ContinuousLinearMap.mfderivWithin_eq, ContinuousMultilinearMap.nnnorm_ofSubsingleton, Submodule.mulLeftMap_eq_mulMap_comp, CliffordAlgebra.changeForm_contractLeft, DividedPowers.IsSubDPIdeal.isDPMorphism, IsExposed.eq_inter_halfSpace, GroupLike.val_inv, ContDiffOn.fderivWithin, Submodule.map_pointwise_smul, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, IsLocalization.map_eq_toLinearMap_mapₐ, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, MvPowerSeries.WithPiTopology.hasSum_of_monomials_self, TangentBundle.symmL_model_space, triple_product_eq_det, LinearEquiv.dualMap_apply, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, TensorProduct.counit_def, LinearEquiv.nonempty_equiv_iff_lift_rank_eq, MeasureTheory.integrable_condExpL2_indicator, AdicCompletion.factor_eval_liftRingHom, QuadraticMap.coe_associatedHom, LinearMap.mem_selfAdjointSubmodule, groupHomology.isoCycles₂_inv_comp_iCycles_apply, ProbabilityTheory.isPosSemidef_covarianceBilinDual, ImplicitFunctionData.range_rightDeriv, tangentCoordChange_self, LinearMap.finrank_range_dualMap_eq_finrank_range, LinearIndependent.inl_union_inr, PointedCone.minTensorProduct_comm, fderiv_norm_smul, LinearMap.mulLeft_tmul, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, LinearMap.BilinForm.IsAlt.neg, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, ContinuousLinearMap.isEmbedding_restrictScalars, instRingHomIdId, LinearMap.extendScalarsOfSurjective_apply, ModuleCat.mkOfSMul_smul, HasFDerivAt.hasFDerivAt_norm_smul, Module.Basis.det_basis, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, LinearEquiv.funUnique_apply, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, TensorProduct.directSum_symm_lof_tmul, LinearEquiv.sumArrowLequivProdArrow_apply_fst, Module.bijective_dual_eval, LinearMap.isLinear, PowerSeries.coeff_one, Representation.norm_self_apply, Rep.coindResAdjunction_homEquiv_symm_apply, Module.End.eigenspace_div, HopfAlgebra.counit_antipode, Submodule.toLocalizedQuotient'_mk, fderivWithin_fun_add, coe_lpBCFₗᵢ_symm, range_mfderiv_coe_sphere, Finsupp.mapRange.linearMap_id, SemiRingCat.ofHom_id, PowerSeries.eq_shift_mul_X_add_const, Algebra.Extension.Hom.subToKer_apply_coe, coe_lpPiLpₗᵢ_symm, IsBoundedBilinearMap.toContinuousLinearMap_apply, LinearMap.comp_eq_id_comm, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Matrix.toLinearMapRight'_apply, LinearMap.BilinForm.toMatrix_mul, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, TopModuleCat.hom_sub, PowerSeries.coeff_prod, Submodule.reflection_eq_self_iff, HasFPowerSeriesWithinOnBall.fderivWithin_eq, jacobson_density, ContinuousLinearMap.proj_pi, MeasureTheory.weightedSMul_union', Module.FaithfullyFlat.tensorProduct_mk_injective, Polynomial.span_minpoly_eq_annihilator, ContinuousMultilinearMap.piₗᵢ_symm_apply, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, LinearMap.coprod_inl, AffineMap.zero_linear, Finset.weightedVSub_congr, AlgHom.coe_toContinuousLinearMap, hahnEmbedding_isOrderedModule_rat, LinearIsometry.comp_id, Polynomial.iterate_derivative_C_mul, AlgHomClass.toLinearMap_toAlgHom, AffineMap.restrict.linear_aux, LinearMap.nonUnitalAlgHom_comp_convMul_distrib, HasFDerivWithinAt.sqrt, ContinuousLinearMap.norm_id_le, Module.End.genEigenrange_nat, HasFDerivAt.le_of_lipschitz, LinearMap.map_codRestrict, Continuous.matrix_cramer, MonoidAlgebra.comul_single, PowerSeries.coeff_mul_X_pow', LinearMap.GeneralLinearGroup.coe_toLinearEquiv, CoalgEquiv.refl_toLinearEquiv, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, PolyEquivTensor.invFun_monomial, LinearEquiv.canLiftContinuousLinearEquiv, LieAlgebra.SpecialLinear.val_single, LinearMap.eventually_iInf_range_pow_eq, Matrix.ofLp_toEuclideanLin_apply, ContinuousLinearMap.smulRight_comp_smulRight, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', Matrix.toLinearMap₂_apply, AdicCompletion.of_inj, Finsupp.linearEquivFunOnFinite_apply, Real.hasFDerivAt_fourierIntegral, SchwartzMap.integralCLM_apply, linearEquiv_det_rotation, LieModule.isNilpotent_iff_forall, ExteriorAlgebra.map_surjective_iff, MvPolynomial.weightedHomogeneousComponent_eq_zero_of_notMem, ZLattice.abs_repr_lt_of_norm_lt, Polynomial.mkDerivation_one_eq_derivative, Complex.coe_selfAdjointEquiv, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, LinearMap.vecEmpty_apply, SpecialLinearGroup.toGeneralLinearGroup_injective, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, MultilinearMap.freeDFinsuppEquiv_apply, MeasureTheory.OuterMeasure.restrict_biInf, CliffordAlgebra.forall_mul_self_eq_iff, LinearMap.IsSymmetric.apply_eigenvectorBasis, HasStrictFDerivAt.hasStrictDerivAt, groupHomology.cyclesMk₂_eq, AffineMap.decomp, RootPairing.coroot_root_eq_pairing, FormalMultilinearSeries.radius_shift, Rep.coindVEquiv_apply_hom, LinearMap.compl₁₂_apply, CoalgHomClass.counit_comp, ContinuousLinearEquiv.comp_right_differentiableAt_iff, Representation.smul_tprod_one_asModule, LieModule.isNilpotent_toEnd_sub_algebraMap, rTensorHomEquivHomRTensor_toLinearMap, ConvexOn.real_univ_sSup_of_nat_affine_eq, IsBaseChange.ofEquiv, AdicCompletion.ofTensorProduct_tmul, fderivWithin_sqrt, fderivWithin_natCast, Polynomial.degreeLT.addLinearEquiv_symm_apply', Submodule.map_inl, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, ContinuousLinearMap.projKerOfRightInverse_comp_inv, Complex.conjCLE_apply, LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, KaehlerDifferential.kerTotal_mkQ_single_smul, LinearMap.intrinsicStar_lTensor, MultilinearMap.uncurryRight_apply, LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero, innerSLFlip_apply, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_is_extension, LinearIsometryEquiv.prodComm_symm_apply, ContinuousLinearEquiv.differentiableOn, MvPolynomial.rTensor_apply_monomial_tmul, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousLinearEquiv.hasStrictFDerivAt, CoalgEquiv.coe_symm_toLinearEquiv, CliffordAlgebraRing.ι_eq_zero, LinearMap.range_inr, Polynomial.iterate_derivative_mul_X_pow, AffineSubspace.linear_equivMapOfInjective, PiTensorProduct.piTensorHomMapFun₂_add, Matrix.mulVecBilin_apply, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, PowerSeries.coeff_zero_C, Submodule.ker_starProjection, Algebra.Generators.repr_CotangentSpaceMap, DirectSum.toModule_lof, ContinuousLinearEquiv.mfderiv_eq, LinearEquiv.congrQuadraticMap_symm_apply, Module.Basis.dualBasis_repr, groupHomology.H1π_eq_zero_iff, ContinuousLinearMap.toContinuousAddMonoidHom_restrictScalars, LinearMap.pi_ext'_iff, Trivialization.coe_continuousLinearEquivAt_eq, Algebra.normalizedTrace_minpoly, IsAdjoinRootMonic.modByMonicHom_root_pow, PiTensorProduct.mul_one, CategoryTheory.Abelian.Ext.bilinearCompOfLinear_apply_apply, AlternatingMap.uncurryFin_smul, PiTensorProduct.tmulEquiv_apply, BialgEquiv.trans_symm_apply, lieEquivMatrix'_symm_apply, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_divisionRing, ProbabilityTheory.covarianceBilin_real, MvPowerSeries.eq_zero_iff_forall_coeff_zero, Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr, LinearMap.compQuadraticMap'_apply, Projectivization.smul_def, Matrix.proj_diagonal, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', imaginaryPart_ofReal, QuadraticMap.Isometry.map_app', Module.Dual.baseChange_baseChange, separatingDual_iff_injective, fderivWithin_const_smul_field, LightCondMod.hom_naturality_apply, Module.Relations.Solution.IsPresentation.bijective, TensorProduct.dualDistribInvOfBasis_apply, Pi.comul_coe_finsupp, Polynomial.taylor_coeff_one, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, Hausdorffification.lift_comp_of, TopModuleCat.forget₂_TopCat_obj, LinearMap.map_smul₂, groupHomology.d₂₁_single_one_fst, RootPairing.root'_apply_apply_mem_of_mem_span, ContinuousLinearMap.measurable_coe, PowerSeries.forall_coeff_eq_zero, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, Euclidean.ball_eq_preimage, HasFDerivAt.fun_neg, Polynomial.sup_ker_aeval_le_ker_aeval_mul, ContinuousLinearMap.analyticOn, Polynomial.fderivWithin_aeval, RootPairing.Equiv.weightEquiv_one, fderiv_sinh, LinearMap.intrinsicStarModule, NNRealRMK.le_rieszMeasure_of_tsupport_subset, TensorProduct.lift_mk, WeierstrassCurve.VariableChange.map_id, MeasureTheory.L1.SimpleFunc.setToL1S_zero_left, hasFDerivAt_pow', dualTensorHom_prodMap_zero, MvPowerSeries.coeff_truncFun, PolyEquivTensor.toFunLinear_one_tmul_one, LinearEquiv.prodCongr_apply, MultilinearMap.comp_linearEquiv_eq_zero_iff, Smooth.id, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, LinearMap.comp_smul, Trivialization.continuousLinearEquivAt_symm_apply, LinearMap.range_liftBaseChange, NumberField.mixedEmbedding.stdBasis_apply_isReal, mdifferentiableOn_coordChangeL, Polynomial.fderivWithin, LinearMap.IsContPerfPair.bijective_right, HasFDerivWithinAt.const_cpow, PowerSeries.coeff_C, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, HahnSeries.coeff_toMvPowerSeries_symm, ZMod.completedLFunction_one_sub_odd, Polynomial.monomial_neg, Trivialization.coordChangeL_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, LinearMap.isUnit_toMatrix_iff, LinearMap.det_smul, Polynomial.hasDerivAt, HasFDerivAt.fun_add, HasFDerivAt.fst, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, TopModuleCat.hom_nsmul, PiTensorProduct.map_comp_reindex_symm, Subspace.dualEquivDual_def, AddMonoidAlgebra.lhom_ext'_iff, VectorPrebundle.mk_coordChange, ContinuousLinearMap.opNorm_lsmul_le, Module.Basis.linearCombination_repr, MvPolynomial.mkDerivationₗ_C, LinearMap.IsSymmetric.zero, TensorProduct.enorm_assoc, LocalizedModule.map_id, ContinuousMultilinearMap.ofSubsingleton_apply_toMultilinearMap, ContinuousLinearMap.toSpanSingleton_add, MvPowerSeries.isWeightedHomogeneous_weightedHomogeneousComponent, union_support_maximal_linearIndependent_eq_range_basis, NonUnitalAlgHom.comp_mul', OrthonormalBasis.repr_symm_single, ContinuousLinearMap.inverse_comp_equiv, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, TensorProduct.AlgebraTensorModule.rTensor_mul, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.curryMidLinearEquiv_apply, ProbabilityTheory.covarianceBilin_of_not_memLp, LinearMap.BilinForm.toMatrix_compLeft, Polynomial.monomial_zero_right, LinearMap.trace_eq_matrix_trace, TensorProduct.quotientTensorEquiv_apply_tmul_mk, RootPairing.polarizationEquiv_symm_apply_coroot, Module.FinitePresentation.out, BilinForm.toMatrix_apply, WeakDual.CharacterSpace.norm_le_norm_one, LinearEquiv.coe_rTensor_symm, Pretrivialization.linearEquivAt_apply, ContinuousAffineMap.vadd_contLinear, PolynomialModule.lsingle_apply, Algebra.SubmersivePresentation.cotangentComplexAux_surjective, LinearMap.continuous_on_pi, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, Representation.self_inv_apply, cfcL_integral, exteriorPower.zeroEquiv_ιMulti, MvPolynomial.ker_evalₗ, Polynomial.iterate_derivative_sub, BialgHom.map_mul', ContinuousMap.coeFn_toLp, LinearIsometryEquiv.withLpProdCongr_apply, Matrix.toBilin'_apply', Module.Basis.linearCombination_coord, LinearMap.BilinForm.IsSymm.polarization, Polynomial.signVariations_monomial, innerSL_apply_norm, LinearMap.surjective_comp_linearProjOfIsCompl, Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_ker, LinearMap.exact_subtype_ker_map, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, Derivation.map_aeval, IsSelfAdjoint.coe_selfAdjointPart_apply, Matrix.toLinearMap₂'_single, ExteriorAlgebra.liftAlternating_comp_ιMulti, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_symm_apply, CliffordAlgebra.toEven_ι, Algebra.Extension.H1Cotangent.map_apply_coe, ContinuousLinearMap.isPositive_def', HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, ContinuousLinearMap.coe_restrictScalarsL, LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero', Algebra.TensorProduct.mul_assoc, SemimoduleCat.hom_hom_associator, LinearMap.adjoint_inner_left, ContinuousLinearMap.fderivWithin, TensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse, LinearEquiv.piCurry_symm_apply, LinearMap.snd_prod, LocallyConstant.mapₗ_apply_apply, Polynomial.eval_eq_sum_degreeLTEquiv, Submodule.mulMap'_surjective, Polynomial.monomial_mul_X_pow, BoundedLatticeHom.asBoolRing_id, HasMFDerivAt.comp_hasMFDerivWithinAt, LinearMap.toMvPolynomial_comp, Module.Basis.toDual_apply, Submodule.subtypeL_apply, ContinuousAffineMap.coe_contLinear, PowerSeries.coeff_inv, AddMonoidHom.coe_toIntLinearMap_map, hasStrictFDerivAt_exp_zero, LinearMap.BilinForm.mul_toMatrix, ContinuousLinearMap.norm_compL_le, MvPowerSeries.coeff_expand_of_not_dvd, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, Module.Basis.tensorAlgebra_repr_apply, Submodule.map_unop_one, RingHomInvPair.ids, Orientation.oangle_map, ContMDiffVectorBundle.contMDiffOn_coordChangeL, aeval_derivative_mem_differentIdeal, MeasureTheory.Measure.addHaar_preimage_linearMap, Algebra.trace_eq_zero_of_not_isSeparable, Module.projective_def', Algebra.Generators.toKaehler_cotangentSpaceBasis, curveIntegral_eq_intervalIntegral_deriv, Filter.EventuallyEq.fderivWithin', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, ContinuousLinearMap.inCoordinates_eq, Polynomial.iterate_derivative_X_pow_eq_C_mul, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, IsAdjoinRootMonic.coeff_algebraMap, Subspace.dualLift_rightInverse, Representation.Coinvariants.mk_eq_iff, MvPowerSeries.coeff_zero_C, TensorProduct.rightComm_tmul, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, LinearMap.coprodEquiv_apply, QuadraticMap.associated_linMulLin, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, Polynomial.derivative_X_pow, ContDiffAt.continuousLinearMap_comp, Representation.isTrivial_apply, AffineMap.linear_bijective_iff, Rep.ihom_map_hom, Module.Basis.equivFun_apply, HasStrictFDerivAt.fun_neg, LinearMap.rTensor_map, Ideal.natAbs_det_equiv, dualTensorHomEquivOfBasis_toLinearMap, HasFDerivWithinAt.arctan, OrthogonalFamily.range_linearIsometry, QuadraticForm.associated_isSymm, IsBaseChange.dual, Polynomial.sumIDeriv_derivative, Module.apply_evalEquiv_symm_apply, TensorProduct.finsuppScalarLeft_apply_tmul, MvPowerSeries.coeff_monomial, Submodule.finrank_map_subtype_eq, HasStrictFDerivAt.sum, Submodule.IsCompl.projection_range, Submodule.coe_dualAnnihilator_span, MvPowerSeries.X_dvd_iff, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, TensorAlgebra.tprod_apply, HasCompactSupport.fderiv_apply, Submodule.ker_orthogonalProjection, Polynomial.X_mul_monomial, TensorProduct.directSumRight_tmul, fderiv_continuousMultilinear_apply_const, Orientation.kahler_mul, MvPowerSeries.coeff_C, TensorProduct.gradedComm_tmul_algebraMap, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, innerSL_real_flip, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', Lagrange.interpolate_eq_add_interpolate_erase, Submodule.reflection_map_apply, LinearMap.trace_conj', ProbabilityTheory.covarianceBilinDual_comm, Matrix.reindexLinearEquiv_symm, Module.Invertible.rTensor_surjective_iff, ModuleCat.piIsoPi_hom_ker_subtype_apply, StandardEtalePair.HasMap.isUnit_derivative_f, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', Matrix.SpecialLinearGroup.toLin'_to_linearMap, TwoSidedIdeal.coe_subtype, ModularFormClass.qExpansion_coeff_eq_circleIntegral, ProbabilityTheory.isGaussian_iff_charFunDual_eq, AffineIsometry.map_vadd, Module.Basis.mulOpposite_repr_eq, ModuleCat.reflectsColimitsOfShape, Module.Basis.coe_repr_symm, Representation.IsIntertwiningMap.isIntertwining, groupHomology.H1AddEquivOfIsTrivial_apply, ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, Module.Basis.smulTower'_repr, TensorProduct.congr_mul, ModuleCat.MonoidalCategory.whiskerRight_apply, TensorProduct.norm_lid, ContinuousLinearMap.norm_fst, LinearMap.mul_toMatrix₂'_mul, comp_id, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, HasFDerivWithinAt.rpow, SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, Module.Relations.toQuotient_map_apply, LinearMap.toMatrix₂'_mul, Rep.finsuppTensorLeft_inv_hom, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, LinearMap.snd_prodOfFinsuppNat, CliffordAlgebra.reverseEquiv_symm_apply, LinearMap.ofIsCompl_add, HasFPowerSeriesOnBall.hasFDerivAt, WittVector.toPadicInt_comp_fromPadicInt_ext, MeasureTheory.charFun_eq_charFunDual_toDualMap, Polynomial.aeval_sumIDeriv_eq_eval, ContinuousLinearMap.IsInvertible.inverse_comp_self, LieHom.range_toSubmodule, WithLp.linearEquiv_apply, AdicCompletion.transitionMap_map_pow, PowerSeries.coeff_expand_of_not_dvd, ModuleCat.free_δ_freeMk, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, TensorProduct.toLinearEquiv_assocIsometry, Submodule.FG.directedSystem, HasMFDerivAt.prod, LinearMap.rTensor_comp, fderivWithin_csin, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, Module.Projective.exists_dual_eq_one, IsCoprime.wronskian_eq_zero_iff, IsTensorProduct.lift_eq, LinearIndependent.of_isLocalizedModule, ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize, LinearMap.BilinForm.flip_flip, LinearMap.rTensor_zero, ContinuousMultilinearMap.curryMid_apply, Finsupp.LinearEquiv.finsuppUnique_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, ZLattice.volume_image_eq_volume_div_covolume', ProperCone.dual_dual_flip, LinearIsometryEquiv.withLpProdUnique_symm_apply, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, Algebra.trace_complex_apply, MvPowerSeries.homogeneousComponent_mul_of_le_order, PiTensorProduct.mapL_opNorm, Algebra.toMatrix_lsmul, flip_innerₗ, HasFDerivWithinAt.comp_hasDerivAt, AlgEquiv.moduleEndSelf_apply_apply, Submodule.fg_iff_exists_fin_linearMap, SchwartzMap.compCLM_apply, LinearEquiv.rTensor_trans_apply, LinearMap.mulRight_apply, toMatrix_innerSL_apply, Finset.weightedVSub_eq_linear_combination, OrthonormalBasis.equiv_apply_basis, LinearMap.intrinsicStar_single, Module.Basis.map_orientation_eq_det_inv_smul, isAssociatedPrime_iff_exists_injective_linearMap, intervalIntegral.fderivWithin_integral_of_tendsto_ae, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, hasStrictFDerivAt_one, Finsupp.linearCombination_fin_zero, ContinuousMap.toLp_comp_toContinuousMap, KaehlerDifferential.polynomial_D_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, MvPolynomial.support_sum_monomial_coeff, LinearMap.mulRight_eq_zero_iff, Matrix.separatingLeft_toLinearMap₂'_iff, Module.Relations.Solution.π_relation, DoubleCentralizer.mul_fst, TensorProduct.AlgebraTensorModule.map_smul_right, Localization.coe_algEquiv, LinearEquiv.inv_mem_dilatransvections_iff, Orientation.rightAngleRotation_trans_neg_orientation, QuadraticMap.exists_companion', PolynomialModule.eval_apply, exteriorPower.basis_repr_apply, Finsupp.linearEquivFunOnFinite_symm_single, LinearMap.rTensor_def, triple_product_permutation, ProbabilityTheory.HasGaussianLaw.map_equiv_fun, LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero', Polynomial.leval_apply, CoalgCat.forget₂_map, TensorProduct.rid_symm_apply, CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite_symm_apply, ContinuousLinearEquiv.leftInverse_hasLeftInverse, Submodule.prod_comap_inl, AlternatingMap.ofSubsingleton_symm_apply_apply, Module.Basis.toMatrix_update, LinearMap.intrinsicStar_smulRight, ContinuousLinearEquiv.comp_contDiffOn_iff, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, TensorPower.cast_tprod, PiLp.basis_toMatrix_basisFun_mul, PiTensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MDifferentiableAt.coordChangeL, Submodule.mk_quotientEquivOfIsCompl_apply, exists_derivative_mul_eq_and_isIntegral_coeff, Module.End.baseChangeHom_apply_apply, fderivWithin_continuousAlternatingMap_apply_const, groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂, PiTensorProduct.mul_tprod_tprod, Manifold.IsImmersionAt.target_subset_preimage_target, Polynomial.ofFn_degree_lt, Polynomial.taylor_monomial, MvPolynomial.weightedDecomposition.decompose'_eq, Submodule.prodEquivOfIsCompl_symm_apply_right, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, LinearMap.restrictScalars_zero, Submodule.coe_mapIic_apply, LinearMap.isProj_range_iff_isIdempotentElem, Rep.unit_iso_comm, Finsupp.linearCombination_equivMapDomain, BilinForm.toMatrix_mul, LinearMap.map_smul, Subspace.dualCopairing_nondegenerate, Module.End.instSMulCommClass, PrimeSpectrum.ConstructibleSetData.map_id, Module.finite_dual_iff, Rep.leftRegularHomEquiv_symm_single, Lagrange.interpolate_apply, Algebra.Generators.CotangentSpace.compEquiv_symm_inr, MultilinearMap.ofSubsingleton_symm_apply_apply, Submodule.map_liftQ, exists_lt_rieszContentAux_add_pos, ContinuousLinearMap.norm_restrictScalars, LinearMap.toMatrix_comp, Polynomial.valuation_aeval_monomial_eq_valuation_pow, Algebra.normalizedTrace_algebraMap_apply, LieSubmodule.toSubmodule_comap, LinearEquiv.prodProdProdComm_symm, LinearMap.add_compAlternatingMap, LinearMap.charpoly_one, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, Module.dual_projective, TensorProduct.AlgebraTensorModule.map_comp, CategoryTheory.NatTrans.appLinearMap_apply, ModularGroup.tendsto_lcRow0, ContinuousAlgEquiv.toContinuousLinearEquiv_toLinearEquiv_eq, Pretrivialization.continuousLinearMap_apply, PowerSeries.coeff_zero_eq_constantCoeff, LocallyConstant.congrLeftₗ_apply_apply, Polynomial.factorial_smul_hasseDeriv, Matrix.toLinAlgEquiv_self, SameRay.sameRay_map_iff, RootPairing.coreflection_apply, CliffordAlgebra.submodule_map_mul_reverse, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, DirectSum.sigmaLuncurry_apply, NormedSpace.sInter_polar_eq_closedBall, Module.Basis.coe_toDual_self, TemperedDistribution.instFourierInvSMul, RootPairing.RootPositiveForm.exists_pos_eq, ContinuousLinearMap.toContinuousAddMonoidHom_id, AddMonoidHom.coe_toIntLinearMap_range, FiniteField.minpoly_frobeniusAlgHom, PositiveLinearMap.ofPreGNS_toPreGNS, Polynomial.mem_ker_modByMonic, Matrix.separatingLeft_toBilin'_iff, Complex.imCLM_coe, Module.Basis.baseChange_repr_tmul, ModelWithCorners.transContinuousLinearEquiv_range, RingEquiv.coe_ringHom_refl, TensorProduct.nnnorm_assoc, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, Matrix.kroneckerAlgEquiv_symm_apply, Submodule.dualAnnihilator_top, Matrix.trace_toLin_eq, hasFDerivAt_natCast, Module.AEval'_def, ContinuousLinearMap.opNorm_mul_apply_le, TensorPower.cast_eq_cast, hasFDerivAt_intCast, LinearMap.inr_eq_prod, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, intervalIntegral.integral_hasFDerivWithinAt, ContinuousLinearMap.smul_def, LinearMap.toMatrix₂_mul_basis_toMatrix, ZSpan.repr_fract_apply, finsuppLEquivDirectSum_apply, ContinuousLinearMap.orthogonal_range, contDiff_one_iff_hasFDerivAt, MeasureTheory.charFunDual_prod', Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T, Matrix.Represents.add, Submodule.lipschitzWith_starProjection, LinearEquiv.ofTop_symm_apply, TensorProduct.AlgebraTensorModule.lift_apply, ContinuousLinearMap.isPositive_iff_complex, LinearIsometryEquiv.toMeasurableEquiv_symm, Module.End.IsSemisimple_smul, HasFDerivWithinAt.comp_hasFDerivAt_of_eq, LieAlgebra.IsKilling.rootSystem_pairing_apply, groupCohomology.cocyclesMk₂_eq, Module.Basis.toMatrix_eq_toMatrix_constr, Matrix.det_reindexLinearEquiv_self, Finset.weightedVSub_vadd_affineCombination, Rep.leftRegularTensorTrivialIsoFree_inv_hom, TensorProduct.comul_tmul, LinearMap.lcompₛₗ_apply, ProbabilityTheory.covarianceBilin_apply, Algebra.TensorProduct.basis_repr_symm_apply, ModuleCat.extendScalars_id_comp_assoc, DirectLimit.Module.hom_ext_iff, BoxIntegral.integralSum_sub_partitions, WithLp.coe_sndL, Polynomial.hasDerivAt_aeval, ContinuousLinearMap.comp_cpolynomialOn, HasFDerivAt.cos, ZMod.frobenius_zmod, DirectSum.lof_apply, LinearMap.polyCharpoly_map_eq_charpoly, HasFDerivAt.linear_multilinear_comp, Ideal.pi_mkQ_rTensor, MvPolynomial.coeffsIn_eq_span_monomial, IsBaseChange.basis_apply, Polynomial.aeval_root_derivative_of_splits, MeasureTheory.withDensitySMulLI_apply, LinearMap.BilinMap.toQuadraticMap_sum, IsBoundedBilinearMap.deriv_apply, Orthonormal.inner_finsupp_eq_zero, LinearMap.zero_compAlternatingMap, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, Algebra.Generators.ofComp_toAlgHom_monomial_sumElim, fderiv_zero, Submodule.mulLeftMap_apply_single, KaehlerDifferential.quotKerTotalEquiv_symm_apply, LinearEquiv.toFGModuleCatIso_hom, LaurentSeries.coeff_zero_of_lt_intValuation, Polynomial.iterate_derivative_neg, Submodule.mapQ_mkQ, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, finsuppTensorFinsuppLid_apply_apply, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, fderiv_comp', WittVector.toPadicInt_comp_fromPadicInt, ContinuousLinearEquiv.skewProd_symm_apply, MeasureTheory.convolutionExistsAt_iff_integrable_swap, Prod.comul_comp_fst, PiLp.hasFDerivAt_ofLp, TemperedDistribution.instFourierInvAdd, Matrix.mulVec_cramer, LinearMap.proj_comp_single, LinearIndependent.repr_ker, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_symm_tmul, AdicCompletion.of_injective, DirectSum.apply_eq_component, CliffordAlgebra.contractRight_one, ZLattice.comap_comp, PolyEquivTensor.toFunBilinear_apply_eq_smul, LinearMap.det_comp, LinearEquiv.smulOfNeZero_symm_apply, norm_iteratedFDeriv_one, LinearMap.ker_prod, LinearIsometryEquiv.comp_differentiable_iff, LinearEquiv.refl_apply, CliffordAlgebraDualNumber.equiv_ι, groupHomology.chainsMap_f_hom, MvPowerSeries.WithPiTopology.summable_iff_summable_coeff, MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, Polynomial.sum_taylor_eq, LinearMap.BilinForm.isSymm_def, Submodule.toLinearPMap_apply_aux, PiTensorProduct.lift_tprod, Matrix.toLinOfInv_apply, Polynomial.taylor_eval_sub, HasStrictFDerivAt.fun_const_smul, TensorProduct.lcurry_apply, TrivSqZeroExt.snd_map, LinearIsometryEquiv.coe_refl, Polynomial.derivative_prod_finset, HasFDerivAt.hasDerivAt, fderivWithin_const_smul, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, LinearMap.GeneralLinearGroup.congrLinearEquiv_symm, Submodule.mulMap_map_comp_eq, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, dualTensorHomEquivOfBasis_symm_cancel_left, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, ContinuousLinearMap.isPositive_iff, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, MvPolynomial.monomial_eq, LinearEquiv.trans_smul, TensorProduct.mapIsometry_apply, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, ContinuousMultilinearMap.compContinuousLinearMapL_apply, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, LinearMap.IsPerfPair.id, signedDist_apply_linear_apply, VectorBundleCore.inCoordinates_eq, ContinuousLinearMap.IsInvertible.inverse_apply_self, LinearMap.transvection.det, Module.Invertible.rTensorEquiv_symm_apply_apply, HasFDerivWithinAt.unique_on, Complex.selfAdjointEquiv_symm_apply, CliffordAlgebra.changeForm_algebraMap, QuaternionAlgebra.coe_basisOneIJK_repr, LaurentPolynomial.counit_C_mul_T, AlgHom.addHomMk_coe, TemperedDistribution.fourierInv_apply, TensorProduct.comul_def, VectorField.pullbackWithin_eq, ContinuousLinearMap.norm_bilinearRestrictScalars, QuadraticMap.IsometryEquiv.coe_toLinearEquiv, RootPairing.Equiv.weightHom_injective, Module.Flat.iff_lift_lsmul_comp_subtype_injective, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, LinearMap.BilinForm.comp_comp, TensorProduct.AlgebraTensorModule.congr_one, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Ideal.range_finsuppTotal, image_parallelepiped, Differential.deriv_aeval_eq, ContinuousLinearMap.norm_inl, Shrink.continuousLinearEquiv_symm_apply, ContinuousLinearMap.coeLMₛₗ_apply, LinearMap.IsSymmetric.sub, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, CliffordAlgebra.foldr'Aux_apply_apply, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, ContinuousLinearEquiv.comp_differentiable_iff, groupHomology.map_id_comp_H0Iso_hom_apply, Polynomial.hasseDeriv_C, Unitization.nnnorm_eq_sup, ModuleCat.extendScalars_id_comp, SchwartzMap.fourierTransformCLM_apply, RingCat.hom_id, Coalgebra.TensorProduct.lid_toLinearEquiv, mulRightLinearMap_mul, norm_deriv_eq_norm_fderiv, selfAdjointPart_apply_coe, CliffordAlgebra.reverse.map_one, Trivialization.symm_continuousLinearEquivAt_eq, Submodule.CoFG.ker, LinearEquiv.conj_id, AlgEquiv.moduleEndSelfOp_symm_apply, DFinsupp.linearEquivFunOnFintype_apply, Module.End.eigenspace_zero, Polynomial.coeff_list_sum, skewAdjointPartL_apply_coe, DoubleCentralizer.zero_toProd, IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite, AddEquiv.coe_symm_toNatLinearEquiv, groupHomology.cyclesMk₁_eq, finsuppLequivDFinsupp_apply_apply, Module.End.mem_invtSubmodule_iff_forall_mem_of_mem, minpoly_algEquiv_toLinearMap, Orientation.coe_basisRightAngleRotation, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, ContinuousLinearMap.inverse_of_not_isInvertible, Finset.weightedVSub_apply, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, HasFDerivAt.const_rpow, Polynomial.smeval_monomial, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, ContinuousLinearMap.nnnorm_smulRight_apply, Submodule.FG.lTensor.directLimit_apply, PowerSeries.X_pow_eq, PowerBasis.trace_gen_eq_sum_roots, LinearIsometryEquiv.smul_trans, Polynomial.eval_C_X_comp_eval₂_map_C_X, MeasureTheory.Lp.constL_apply, Matrix.toBilin'Aux_eq, SchwartzMap.fderivCLM_fourier_eq, TensorProduct.lift.equiv_symm_apply, MvPowerSeries.coeff_invOfUnit, Trivialization.linearMapAt_def_of_mem, SemimoduleCat.inv_hom_apply, LinearEquiv.det_mul_det_symm, withSeminorms_pi, addMonoidHomLequivNat_apply, Bundle.ContinuousRiemannianMetric.pos, ContinuousLinearEquiv.contDiffOn_comp_iff, Module.fgSystem.equiv_comp_of, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, MvPolynomial.esymm_eq_sum_monomial, Polynomial.homogenize_monomial_of_lt, TemperedDistribution.instLineDerivAdd, MeasureTheory.OuterMeasure.comap_boundedBy, Finset.weightedVSubOfPoint_eq_of_sum_eq_zero, SchwartzMap.derivCLM_apply, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, LinearMap.IsSymm.isRefl, LightCondensed.ihom_map_val_app, IsBaseChange.linearMapLeftRight, TensorProduct.toLinearMap_mapIsometry, MvPowerSeries.coeff_map, RCLike.map_nonneg_iff, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, LieDerivation.leibniz', Module.End.IsSemisimple_smul_iff, PowerSeries.monomial_eq_C_mul_X_pow, trace_quotient_eq_trace_localization_quotient, StandardEtalePair.cond, LieModuleHom.map_lie', LinearMap.id_semiModuleCat_comp, IsCoercive.continuousLinearEquivOfBilin_apply, LinearMap.toContinuousLinearMap₁_apply, VectorBundleCore.continuousOn_coordChange, AlternatingMap.curryLeft_compAlternatingMap, Submodule.range_inclusion, ContinuousLinearMap.projKerOfRightInverse_apply_idem, Orientation.volumeForm_zero_neg, Submodule.mem_traceDual, TemperedDistribution.fourierTransformCLM_apply, ContinuousLinearEquiv.fderivWithin, CategoryTheory.Linear.homCongr_symm_apply, LinearMap.comap_prod_prod, mfderiv_comp_apply, Submodule.mapHom_id, TopModuleCat.cokerπ_surjective, Unitary.inner_map_map, LinearMap.toMatrixAlgEquiv'_symm, ZMod.dft_const_mul, LinearMap.map_lTensor, MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc', TensorPower.one_mul, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, HasFDerivWithinAt.fun_sum, RootPairing.flip_toFun_apply, VectorField.lieBracketWithin_smul_right, ContinuousLinearMap.coe_proj, Algebra.normalizedTrace_trans_apply, Finsupp.domLCongr_apply, RootPairing.isFixedPt_reflection_of_isOrthogonal, fderiv_fun_const_smul, TensorProduct.enorm_map, PolynomialModule.eval_smul, Finset.weightedVSubOfPoint_const_smul, LinearEquiv.isScalarTower, Orientation.areaForm_map, Prod.comul_comp_snd, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, IsGroupLikeElem.counit_eq_one, Polynomial.derivative_sub, ModuleCat.FreeMonoidal.μIso_inv_freeMk, ModuleCat.uliftFunctor_map, LinearMap.derivWithin, Module.Basis.localizationLocalization_span, Bialgebra.counit_algebraMap, TensorProduct.mapOfCompatibleSMul_tmul, inner_gradientWithin_left, Rep.Action_ρ_eq_ρ, Rep.linearization_δ_hom, ContinuousLinearMap.adjoint_comp, LinearMap.coe_prodMap, Matrix.toPerfectPairing, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, Module.End.mem_genEigenspace_one, LieModule.toEnd_eq_zero_iff, Algebra.FormallySmooth.kerCotangentToTensor_injective_iff, tsupport_fderiv_apply_subset, isConformalMap_iff, MeasureTheory.OuterMeasure.map_id, Polynomial.hasStrictDerivAt, DistribSMul.toLinearMap_apply, Ideal.powQuotSuccInclusion_injective, IsConformalMap.comp, IsLocalRing.CotangentSpace.map_eq_top_iff, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, LinearMap.mapMatrix_id, MvPolynomial.weightedHomogeneousComponent_eq_zero, Submodule.smul_comap_le_comap_smul, LinearMap.update_apply, AlgebraicGeometry.StructureSheaf.comap_id_eq_map, LinearMap.charpoly_sub_smul, Pi.comul_comp_proj, LinearEquiv.congrRight₂_trans, Subspace.map_le_dualAnnihilator_dualAnnihilator, CliffordAlgebra.reverseOp_ι, LinearMap.surjective, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, LinearEquiv.conjRingEquiv_symm_apply_apply, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, ContinuousMultilinearMap.ofSubsingleton_apply_apply, LinearMap.BilinForm.isSymm_zero, contDiffOn_succ_iff_fderivWithin, Submodule.factor_comp_apply, NumberField.mixedEmbedding.commMap_apply_of_isReal, Finsupp.curryLinearEquiv_apply, ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_right, Algebra.norm_one_add_smul, TensorProduct.AlgebraTensorModule.rTensor_id, AffineMap.hasStrictDerivAt, Matrix.kroneckerTMulBilinear_apply, Submodule.AddMonoidHom.coe_toIntLinearMap_comap, groupCohomology.mapCocycles₁_comp_i_apply, LinearMap.BilinForm.orthogonal_top_eq_ker, TensorProduct.map_map_assoc, QuadraticMap.apply_linearCombination', InnerProductSpace.toLinearMap_rankOne, instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, Matrix.uniqueLinearEquiv_symm_apply, KaehlerDifferential.tensorProductTo_surjective, LinearMap.isClosed_or_dense_ker, ModuleCat.hom_zsmul, ContinuousLinearMap.adjointAux_inner_right, hasFDerivWithinAt_ofNat, Algebra.TensorProduct.linearEquivIncludeRange_symm_toLinearMap, LinearEquiv.sumArrowLequivProdArrow_apply_snd, MvPolynomial.totalDegree_monomial_le, PointedCone.maxTensorProduct_comm, Submodule.quotEquivOfEq_mk, HasMFDerivWithinAt.mul, Bundle.RiemannianMetric.pos, RootPairing.rootSpan_dualAnnihilator_map_eq_iInf_ker_root', SemimoduleCat.forget_map, TemperedDistribution.instLineDerivSMulComplex, OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv, ContinuousLinearEquiv.isOpen, PowerSeries.coeff_divXPowOrder, LinearMap.restrict_smul_one, HilbertBasis.repr_self, Module.End.mapsTo_maxGenEigenspace_of_comm, groupHomology.mapCycles₂_id_comp_apply, Algebra.norm_apply, Submodule.image2_subset_map₂, Polynomial.aroots_monomial, Coalgebra.rTensor_counit_comul, fderiv.fst, MeasureTheory.OuterMeasure.isometry_map_mkMetric, TensorProduct.commIsometry_apply, Algebra.norm_eq_zero_iff', Module.Basis.linearMap_apply_apply, ContinuousLinearEquiv.coe_toDiffeomorph, Rep.trivial_def, finsuppTensorFinsupp_symm_single, LinearMap.range_domRestrict, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Polynomial.det_taylorLinearEquiv, addMonoidHomLequivInt_symm_apply, PowerSeries.trunc_one, CliffordAlgebra.ι_mul_ι_comm_of_isOrtho, fderivWithin_sub, LinearMap.prodMap_smul, LinearMap.trace_tensorProduct, continuousMultilinearCurryRightEquiv_symm_apply', Polynomial.derivative_monomial_succ, comp_dualTensorHom, Polynomial.resultant_deriv, MeasureTheory.condExpInd_smul', LocalizedModule.lift_mk_one, Algebra.trace_quotient_eq_of_isDedekindDomain, QuadraticForm.dualProdProdIsometry_toFun, HasFDerivAt.arsinh, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, Algebra.Extension.h1Cotangentι_apply, DoubleCentralizer.norm_fst, Finsupp.linearCombination_linearCombination, Matrix.toLinearEquivRight'OfInv_apply, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, Submodule.coe_subtype, ContDiffWithinAt.fderivWithin, Submodule.mulMap_comp_lTensor, Module.Relations.Solution.IsPresentation.desc_comp_π, LinearEquiv.rank_map_eq, hasEigenvalue_toLin'_diagonal_iff, ContinuousLinearMap.prodL_apply, LinearEquiv.map_smul, StrongDual.zero_mem_polar, TensorProduct.congrIsometry_symm, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, ContDiffMapSupportedIn.structureMapLM_zero_injective, LinearMap.surjective_or_eq_zero, ContinuousLinearMapWOT.continuous_inducingFn, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, PowerSeries.ext_iff, Seminorm.comp_id, LinearEquiv.smul_id_of_finrank_eq_one_apply, MvPolynomial.constantCoeff_comp_C, ContinuousAlternatingMap.norm_ofSubsingleton_id, LinearMap.BilinForm.coe_injective, LinearIsometry.contDiff, RootPairing.algebraMap_coroot'In_apply, Algebra.Extension.cotangentComplex_injective_iff, LinearMap.toMatrix'_toLinearMapₛₗ₂', Complex.equivRealProdCLM_symm_apply_re, AdicCompletion.transitionMap_ideal_mk, LinearMap.BilinForm.smul_right, Trivialization.continuousLinearMapAt_symmL, AffineMap.continuous_linear_iff, LinearMap.isStarProjection_toContinuousLinearMap_iff, DirectSum.coeFnLinearMap_apply, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, idealFactorsFunOfQuotHom_id, LinearMap.linearEquiv_of_ne_zero, Manifold.pathELength_eq_lintegral_mfderiv_Icc, coe_id, PowerSeries.coeff_X_pow_self, HasFDerivAtFilter.isLittleOTVS, Module.Relations.Solution.IsPresentation.of_linearEquiv, Rep.MonoidalClosed.linearHomEquiv_hom, Representation.ofModule_asAlgebraHom_apply_apply, PowerSeries.trunc_succ, LinearMap.IsSymmetric.orthogonal_range, Matrix.toLpLin_mul, iteratedDerivWithin_eq_equiv_comp, Rep.invariantsAdjunction_homEquiv_apply_hom, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, TensorProduct.map_convMul_map, HasFDerivAt.const_sub, LinearMap.rTensor_exact_iff_lTensor_exact, MeasureTheory.charFunDual_eq_pi_iff', LinearMap.snd_comp_inr, MvPowerSeries.coeff_smul, ContinuousAffineMap.contLinear_map_vsub, LinearPMap.adjointDomainMkCLMExtend_apply, MvPolynomial.weightedHomogeneousComponent_C_mul, realPart_imaginaryPart, dimH_orthogonalProjection_le, Matrix.toLin'_submatrix, TensorProduct.gradedMul_algebraMap, QuaternionAlgebra.imJₗ_apply, IsAdjoinRootMonic.coeff_one, BoundedContinuousFunction.toLp_norm_le, Polynomial.monomial_one_right_eq_X_pow, iteratedFDerivWithin_two_apply, LinearMap.range_ofIsCompl, RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropic, fderiv_ccosh, LinearMap.det_conj, Derivation.compAEval_eq, instDiscreteTopologySubtypeMemSubmoduleIntComap, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, AlgEquiv.toLinearMap_apply, Matrix.separatingLeft_toLinearMap₂_iff, stdSimplex.image_linearMap, ModuleCat.localizedModuleMap_hom_apply, Derivation.tensorProductTo_tmul, Module.End.mem_maxGenEigenspace, DoubleCentralizer.coe_fst, Rep.hom_comm_apply, HasStrictFDerivAt.fun_smul, hasStrictFDerivAt_ofNat, ContinuousLinearMap.coprod_apply, Polynomial.hasseDeriv_apply_one, Finsupp.lift_symm_apply, AdicCompletion.transitionMap_map_mul, ContinuousLinearMap.coe_fst', ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, HasStrictFDerivAt.cpow, SheafOfModules.pushforwardNatTrans_app_val_app, Polynomial.aeval_endomorphism, Module.End.genEigenspace_div, ContDiffPointwiseHolderAt.fderiv, MvPowerSeries.coeff_zero_X, fderiv_fun_mul, Orientation.inner_rightAngleRotationAux₁_right, curveIntegral_fun_sub, LinearMap.ringLmapEquivSelf_apply, Submodule.re_inner_starProjection_nonneg, Module.Flat.iff_rTensor_preserves_injective_linearMapₛ, groupHomology.H2π_comp_map_apply, Matrix.toLin_toMatrix, LieModule.traceForm_genWeightSpace_eq, PiTensorProduct.lift_comp_map, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, TensorProduct.homTensorHomMap_apply, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, LinearMap.toSpanSingleton_convMul_toSpanSingleton, Submodule.lTensorOne_symm_apply, LinearMap.tensorEqLocus_tmul, LinearIsometryEquiv.mul_refl, exteriorPower.map_comp_ιMulti_family, ModularFormClass.qExpansion_isBigO, HasFDerivAt.pow', LaurentPolynomial.antipode_C, LieModule.traceForm_apply_apply, HasStrictFDerivAt.pow', cross_dot_cross, MvPolynomial.mul_monomial_mem_coeffsIn, LinearMap.toMatrix₂_apply, ModuleCat.Hom.hom₂_apply, AdicCompletion.sumEquivOfFintype_apply, OrthogonalFamily.sum_projection_of_mem_iSup, CategoryTheory.Iso.toIsometryEquiv_invFun, hasFDerivWithinAt_iff_hasGradientWithinAt, CurveIntegrable.smul, ConvexCone.map_map, LinearMap.iterateRange_coe, RootPairing.rootFormIn_self_smul_coroot, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, LinearEquiv.smul_def, Module.Basis.ext_elem_iff, AddEquiv.coe_toIntLinearEquiv, TopModuleCat.hom_smul, ContinuousLinearMap.hasFDerivAt_of_bilinear, ModuleCat.HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, ContinuousLinearMap.comp_lsmul_flip_apply, LocallyConvexSpace.induced, LinearMap.ker_compLeft, Submodule.tensorToSpan_apply_tmul, CliffordAlgebra.evenOdd_map_involute, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, ContinuousLinearEquiv.prodUnique_apply, LinearMap.adjoint_comp, contDiffOn_succ_iff_fderiv_apply, ModuleCat.forget₂_addCommGrp_additive, TensorProduct.gradedCommAux_comp_gradedCommAux, LinearMap.intrinsicStar_apply, RootPairing.Equiv.weightEquiv_symm_weightMap, FormalMultilinearSeries.ofScalars_comp_neg_id, PolynomialModule.comp_eval, LinearMap.ofIsCompl_left_apply, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, RootPairing.corootForm_self_smul_root, PiToModule.fromMatrix_apply, RootPairing.exists_form_eq_form_and_form_ne_zero, Submodule.isCompl_comap_subtype_of_isCompl_of_le, Polynomial.surjective_toFn, KaehlerDifferential.mvPolynomialBasis_repr_D, QuadraticForm.tensorAssoc_apply, LinearPMap.smul_graph, ProbabilityTheory.uncenteredCovarianceBilin_zero, HasStrictFDerivAt.multiset_prod, RootPairing.coroot'_reflection, ContinuousLinearMap.inverse_equiv_comp, OpenPartialHomeomorph.MDifferentiable.mfderiv_injective, LinearMap.toContPerfPair_apply, MonomialOrder.sPolynomial_monomial_mul', LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, LinearMap.IsPositive.inner_nonneg_right, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, HahnSeries.coeff_toMvPowerSeries, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, Module.AEval.of_aeval_smul, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, LinearMap.dualMap_apply, LieModule.Cohomology.twoCochain_val_apply, Lagrange.interpolate_empty, ContinuousAlternatingMap.curryLeft_add, LinearMap.isSelfAdjoint_iff_map_star, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, TensorAlgebra.ι_inj, bernsteinPolynomial.derivative_succ, LinearMap.dualMap_surjective_iff, multilinearCurryLeftEquiv_symm_apply, Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd, CliffordAlgebra.iSup_ι_range_eq_top, Algebra.SubmersivePresentation.aevalDifferentialEquiv_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, TensorProduct.tensorTensorTensorComm_trans_tensorTensorTensorComm, LinearIsometry.strictConvexSpace_range_iff, Submodule.starProjection_orthogonal_apply_eq_zero, groupCohomology.cochainsMap_f_hom, VectorFourier.fourierPowSMulRight_apply, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, MultilinearMap.piLinearMap_apply_apply_apply, extDeriv_apply_vectorField_of_pairwise_commute, finsuppTensorFinsuppRid_apply_apply, Module.Basis.repr_sum_self, HahnSeries.coeff.linearMap_apply, LinearEquiv.piFinTwo_apply, TensorProduct.toLinearMap_symm_lid, LinearIsometry.coe_mul, Matrix.linfty_opNorm_eq_opNorm, TensorAlgebra.ι_eq_zero_iff, LinearMap.rTensor_comp_apply, RootPairing.Base.toWeightBasis_repr_root, ContinuousAlternatingMap.prodLIE_apply, MvPolynomial.C_mul_X_pow_eq_monomial, Rep.finsuppTensorLeft_hom_hom, mfderivWithin_eventually_congr_set, Finsupp.linearCombination_option, SMulMemClass.subtype_injective, DirectSum.range_lmap, LinearMap.mulLeftRight_apply, ContinuousLinearMap.coe_restrictScalars', Polynomial.iterate_derivative_X_sub_pow_self, Manifold.IsImmersionAtOfComplement.writtenInCharts, QuadraticMap.associated_sq, Polynomial.derivativeFinsupp_one, LinearIsometry.inl_apply, LinearMap.dualMap_def, MultilinearMap.coe_currySumEquiv, Algebra.leftMulMatrix_mulVec_repr, iSupIndep_iff_dfinsupp_lsum_injective, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, MvPowerSeries.order_monomial, LinearIsometryEquiv.comp_hasFDerivAt_iff', ExteriorAlgebra.map_apply_ιMulti, RootPairing.toPerfPair_conj_reflection, QuadraticMap.associated_comp, LinearMap.le_comap_isotypicComponent, norm_fderiv_le_of_lipschitzOn, ContinuousLinearMap.isBoundedLinearMap, LinearEquiv.ofSubsingleton_symm_apply, LinearMap.isSymmetric_iff_isSelfAdjoint, Finsupp.linearCombination_eq_fintype_linearCombination, MvPolynomial.weightedHomogeneousComponent_mem, KaehlerDifferential.ker_map_of_surjective, TensorProduct.tmul_of_gradedMul_of_tmul, CPolynomialOn.fderiv, Finsupp.supportedEquivFinsupp_symm_apply_coe, FourierTransform.fourierCLE_symm_apply, Dual.apply_one_mul_eq, NumberField.mixedEmbedding.normAtPlace_negAt, ContinuousLinearMap.coprod_comp_inr, PadicInt.mahlerEquiv_apply, CliffordAlgebra.submodule_comap_pow_reverse, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, Submodule.reflection_involutive, SchwartzMap.convolution_flip, QuadraticMap.associated_isOrtho, Lagrange.eq_interpolate_of_eval_eq, LinearEquiv.coe_lTensor_symm, LinearEquiv.toSpanNonzeroSingleton_one, Submodule.lTensorOne'_one_tmul, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, LinearMap.fst_comp_inl, AddMonoidAlgebra.mapRangeRingHom_id, Module.Basis.parallelepiped_map, IsLocalMaxOn.fderivWithin_eq_zero, LinearMap.mem_graph_iff, Matrix.cramer_one, MeasureTheory.charFunDual_dirac, CliffordAlgebra.contractLeft_mul_algebraMap, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, LinearMap.coe_quotientInfToSupQuotient, ContinuousLinearMap.precompCompactConvergenceCLM_apply, VectorPrebundle.continuousOn_coordChange, map_dualTensorHom, VectorField.mpullbackWithin_apply, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, Module.Basis.smulTower_repr_mk, Submodule.range_dualMap_mkQ_eq, Module.Basis.repr_support_subset_of_mem_span, Polynomial.taylor_zero, Subspace.dualLift_injective, Algebra.Generators.cotangentRestrict_mk, LinearMap.comp_id, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, LinearEquiv.prodAssoc_apply, ContinuousLinearMap.coe_snd', measurable_fderiv_with_param, IsLocalizedModule.lift_apply, Module.Relations.Solution.IsPresentation.postcomp_uniq, MultilinearMap.curryMidLinearEquiv_symm_apply, Polynomial.toMatrix_sylvesterMap, TensorProduct.exists_finite_submodule_right_of_finite, PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc, Finsupp.supportedEquivFinsupp_apply_support_val, LinearIsometryEquiv.reflections_generate_dim, GradedAlgebra.proj_apply, LinearMap.smulRightₗ_apply_apply, Representation.toCoinvariants_mk, Module.DualBases.finite, MvPolynomial.optionEquivLeft_monomial, Complex.isometryOfOrthonormal_apply, IsAdjoinRootMonic.modByMonicHom_root, GroupLike.val_inv_toUnits_apply, finsuppLequivDFinsupp_symm_apply, mfderiv_const, Bialgebra.comul_pow, IsConformalMap.smul, Algebra.TensorProduct.equivPiOfFiniteBasis_symm_apply, Finsupp.lsum_comp_lsingle, Shrink.continuousLinearEquiv_apply, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, Submodule.IsCompl.projection_eq_self_sub_projection, ContinuousLinearEquiv.smul_trans, AlternatingMap.uncurryFin_add, Algebra.Generators.cotangentRestrict_bijective_of_basis_kaehlerDifferential, TensorProduct.AlgebraTensorModule.lTensor_one, TensorProduct.finsuppRight_symm_apply_single, SchwartzMap.lineDerivOp_apply_eq_fderiv, CliffordAlgebra.toProd_one_tmul_ι, CoalgEquiv.trans_toLinearEquiv, Module.finrank_linearMap_self, TensorProduct.gradedComm_one_tmul, PositiveLinearMap.leftMulMapPreGNS_mul_eq_comp, conformalFactorAt_inner_eq_mul_inner, Matrix.separatingRight_toBilin'_iff, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, Derivation.coe_add_linearMap, AlgEquiv.moduleEndSelf_symm_apply, LinearEquiv.comm_trans_rTensor_trans_comm_eq, LinearMap.vecEmpty₂_apply, MvPowerSeries.substAlgHom_monomial, Trivialization.coe_coordChangeL, Polynomial.derivative_neg, Representation.IsTrivial.out, groupCohomology.π_comp_H2Iso_hom_apply, LinearIsometryEquiv.withLpProdUnique_apply, CoalgEquiv.trans_symm_apply, RootPairing.InvariantForm.apply_root_root_zero_iff, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, BoxIntegral.integral_const, TensorProduct.prodRight_tmul, LinearMap.transvection.of_left_eq_zero, LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, Matrix.toLin_finTwoProd, ModuleCat.HasLimit.lift_hom_apply, Polynomial.deriv, FormalMultilinearSeries.derivSeries_eq_zero, LinearIsometryEquiv.toContinuousLinearEquiv_refl, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Coalgebra.counitCoalgHom_apply, ContinuousLinearMap.differentiableOn, LinearMap.BilinForm.apply_toDual_symm_apply, MulOpposite.opLinearIsometryEquiv_apply, Module.Basis.flag_le_ker_coord_iff, LinearMap.range_compLeft, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_invariant, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, ContinuousLinearMap.isPositive_iff', qExpansion_mul_coeff_zero, CliffordAlgebra.even.lift.aux_apply, LinearIsometryEquiv.comp_hasFDerivAt_iff, CliffordAlgebra.toBaseChange_involute, LinearMap.IsProj.bot, Module.Basis.linearMap_repr_symm_apply, Derivation.coe_smul_linearMap, Matrix.toLinAlgEquiv'_toMatrixAlgEquiv', LinearEquiv.lieConj_symm, MeasureTheory.Measure.mapₗ_eq_zero_iff, LinearMap.funLeft_apply, ContinuousLinearMap.star_eq_adjoint, CliffordAlgebra.even.lift.aux_ι, Hausdorffification.lift_of, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, Complex.imCLM_nnnorm, LinearMap.BilinForm.neg_apply, LinearMap.ker_fst, RootPairing.rootForm_pos_of_ne_zero, ProperCone.mem_comap, Module.Basis.constr_basis, Submodule.comap_unop_pow, IsBaseChange.equiv_tmul, ContinuousMultilinearMap.curryLeft_apply, Module.End.ker_aeval_ring_hom'_unit_polynomial, Submodule.map_subtype_top, PowerSeries.trunc_coe_eq_self, LinearEquiv.charpoly_conj, AlgHom.toContinuousLinearMap_norm, instCharPLinearMapSubtypeMemSubringCenterId, ContDiffAt.laplacian_CLM_comp_left_nhds, Bialgebra.comul_one, LinearMap.tensorProduct_apply, LinearMap.BilinForm.isPosSemidef_zero, ModuleCat.homLinearEquiv_apply, Submodule.lipschitzWith_orthogonalProjection, Polynomial.hasseDeriv_natDegree_eq_C, Rep.coinvariantsTensorMk_apply, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, IsFractional.map, Orientation.inner_rightAngleRotation_right, HasFDerivAt.hasFDerivAt_norm_smul_neg, SpecialLinearGroup.toGeneralLinearGroup_toLinearEquiv_apply, QuaternionAlgebra.coe_linearEquivTuple, WeakBilin.eval_continuous, TopModuleCat.kerι_apply, fderiv_sqrt, QuotSMulTop.map_comp, ContinuousLinearEquiv.symm_trans_self, finsuppTensorFinsuppLid_single_tmul_single, ContinuousLinearMap.inverse_eq_ringInverse, ContinuousLinearMap.coe_prodMap', UniformSpace.Completion.coe_toComplL, LinearEquiv.nonempty_equiv_iff_rank_eq, LieModule.traceForm_apply_lie_apply, LinearMap.snd_surjective, Submodule.exists_fg_le_subset_range_rTensor_inclusion, Projectivization.cross_mk_of_ne, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, fderivWithin_list_prod', Algebra.tensorH1CotangentOfIsLocalization_toLinearMap, LinearEquiv.sumArrowLequivProdArrow_symm_apply_inl, Matrix.kroneckerTMulAlgEquiv_apply, RootPairing.reflection_inv, ProperCone.hyperplane_separation_of_notMem, LinearMap.single_apply, PrimeSpectrum.specComap_id, Module.End.genEigenspace_nat, LinearMap.continuous_of_isClosed_ker, Module.ker_algebraMap_end, ZSpan.map_fundamentalDomain, Rep.indMap_hom, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, PowerSeries.coeff_derivative, FormalMultilinearSeries.radius_le_radius_derivSeries, ContinuousAlternatingMap.curryLeftLI_apply, ContinuousLinearMap.prodEquiv_apply, endVecAlgEquivMatrixEnd_symm_apply_apply, LinearMap.det_zero'', ContinuousLinearMap.norm_single_le_one, Representation.coind_apply, CharacterModule.uncurry_apply, ContinuousLinearEquiv.smul_apply, Polynomial.derivative_C_mul_X_pow, AdicCompletion.of_bijective, iteratedFDerivWithin_zero_eq_comp, LinearMap.IsSymmetric.im_inner_apply_self, Polynomial.derivative_C, Rep.homEquiv_symm_apply_hom, HasFDerivWithinAt.fun_mul', ContinuousLinearMap.norm_compSL_le, MeasureTheory.norm_condExpInd_le, QuadraticMap.Ring.associated_pi, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, Submodule.ClosedComplemented.exists_submodule_equiv_prod, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, MvPolynomial.eval₂Hom_id_X_eq_join₂, LinearMap.nondegenerate_toMatrix₂_iff, LieEquiv.toLinearEquiv_injective, Matrix.trace_kroneckerMapBilinear, Polynomial.derivative_bernoulli_add_one, span_range_eq_top_iff_surjective_finsuppLinearCombination, FunOnFinite.linearMap_piSingle, AlgEquiv.linearEquivConj_mulRight, LinearMap.inl_apply, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, ModuleCat.extendScalarsComp_hom_app_one_tmul, Polynomial.hasseDeriv_apply, LinearMap.polar_isClosed, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Rep.invariantsFunctor_map_hom, ModuleCat.Iso.conj_eq_conj, fderiv_star, Polynomial.addSubmonoid_closure_setOf_eq_monomial, MeasureTheory.Measure.addHaar_preimage_linearEquiv, Module.Invertible.lTensor_surjective_iff, innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, ContinuousLinearMap.det_smulRight, RootPairing.rootSpan_mem_invtSubmodule_reflection, IsLocalization.algEquiv_symm_apply, Matrix.toLinAlgEquiv'_one, RootPairing.flip_toLinearMap, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, Polynomial.eval₂_derivative_of_splits, LinearPMap.vadd_apply, trace_eq_sum_embeddings, ContinuousLinearEquiv.hasFDerivAt, hasStrictFDerivAt_list_prod, Matrix.toLin_one, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, CliffordAlgebra.contractLeft_algebraMap_mul, PowerSeries.coeff_subst_finite, TensorAlgebra.mk_reindex_fin_cast, LinearMap.BilinForm.compLeft_apply, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Submodule.norm_starProjection_apply, Module.Finite.map, fderivWithin_continuousLinearEquiv_comp, DFinsupp.lapply_comp_lsingle_of_ne, contractRight_apply, cfc_eq_cfcL, LinearMap.trace_eq_contract_of_basis, CliffordAlgebra.reverseEquiv_apply, LinearMap.range_dualMap_le_dualAnnihilator_ker, PowerSeries.coeff_X_pow, Matrix.toLin_transpose, GradedTensorProduct.of_symm_of, Pretrivialization.continuousLinearMap_symm_apply, linearEquivIsoModuleIso_inv, stereographic_apply, MeasureTheory.inner_condExpL2_eq_inner_fun, Complex.toMatrix_conjAe, StrongDual.toLp_apply, OrthogonalFamily.norm_sum, MvPowerSeries.isHomogeneous_homogeneousComponent, Orientation.rotation_apply, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, LaurentPolynomial.counit_T, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, CoalgCat.toComon_map_hom, Submodule.finite_dualAnnihilator_iff, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, IsLocalMin.hasFDerivAt_eq_zero, Representation.leftRegular_norm_apply, BilinForm.mul_toMatrix, TensorProduct.liftAux.smul, inner_map_polarization, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, HasFDerivAtFilter.iterate, ModularFormClass.hasSum_qExpansion_of_norm_lt, Submodule.inner_starProjection_left_eq_right, PiLp.proj_apply, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, ContinuousLinearMap.normOneClass, ContMDiffAt.mfderiv, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, ContinuousLinearMap.IsPositive.spectrumRestricts, ContinuousLinearMap.snd_comp_inl, groupCohomology.π_comp_H1Iso_hom_apply, WeakSpace.coe_map, OrthonormalBasis.sum_repr, Representation.coinvariantsToFinsupp_mk_single, LinearMap.continuous_iff_isClosed_ker, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Submodule.reflection_mem_subspace_eq_self, Polynomial.sum_modByMonic_coeff, Orthonormal.mapLinearIsometryEquiv, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, Module.Relations.Solution.fromQuotient_comp_toQuotient, IsCoercive.ker_eq_bot, ContinuousLinearMap.ker_prod_ker_le_ker_coprod, Algebra.Generators.CotangentSpace.map_toComp_injective, LinearMap.rTensor_range, TensorProduct.mk_surjective, AdicCompletion.evalₐ_of, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Module.End.lTensorAlgHom_apply_apply, ContinuousLinearEquiv.analyticOnNhd, IsConformalMap.injective, PowerSeries.expand_monomial, fderivWithin_const_apply, Matrix.toLpLin_symm_comp, Module.Basis.SmithNormalForm.repr_comp_embedding_eq_smul, Polynomial.aeval_monomial, LinearIsometry.strictConvexSpace_range, Algebra.Extension.H1Cotangent.equivOfFormallySmooth_toLinearMap, MvPowerSeries.aeval_eq_sum, Representation.ind_mk, IntrinsicStar.StarHomClass.isSelfAdjoint, Module.Basis.toDual_linearCombination_right, Matrix.toLinearMapₛₗ₂_apply_basis, TensorProduct.exists_finite_submodule_right_of_finite', Module.Ray.map_apply, IsLocalRing.CotangentSpace.span_image_eq_top_iff, IsometryEquiv.coe_toRealLinearIsometryEquivOfMapZero_symm, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry, LaurentPolynomial.counit_C, MeasureTheory.condExpInd_disjoint_union_apply, LieAlgebra.ad_lie, fderivWithin_pow_ring', ContinuousLinearMap.analyticOn_uncurry_of_multilinear, qExpansion_coeff_unique, TensorProduct.tensorTensorTensorAssoc_symm_tmul, TensorProduct.finsuppLeft_apply_tmul, Polynomial.Chebyshev.iterate_derivative_T_eval_one, LinearEquiv.coord_apply_smul, FormalMultilinearSeries.compContinuousLinearMap_comp, PiTensorProduct.ofFinsuppEquiv'_apply_apply, LinearMap.toSeminorm_ball_zero, CliffordAlgebraRing.reverse_apply, Lagrange.eval_interpolate_at_node, LinearIsometryEquiv.hasFDerivWithinAt, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, RootPairing.restrictScalars_toLinearMap_apply_apply, MvPolynomial.divMonomial_monomial_mul, ExteriorAlgebra.hom_ext_iff, DFinsupp.counit_single, Submodule.fstL_comp_coe_orthogonalDecomposition, LocallyConstant.constₗ_apply_apply, ExteriorAlgebra.liftAlternating_algebraMap, Flat.id, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, LinearMap.ofIsCompl_right_apply, Orientation.kahler_apply_apply, LinearMap.det_zero', RCLike.imCLM_coe, Submodule.map_pow, LieHom.toLinearMap_comp, Module.Basis.ofZLatticeBasis_comap, isStarProjection_iff_eq_starProjection_range, groupHomology.d₂₁_single_one_snd, LinearMap.convMul_comp_coalgHom_distrib, ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv_apply, imaginaryPart_imaginaryPart, PowerSeries.coeff_subst', Orientation.inner_rightAngleRotationAux₁_left, LinearMap.GeneralLinearGroup.congrLinearEquiv_trans', TensorProduct.AlgebraTensorModule.map_tmul, Polynomial.sylvesterMap_apply_coe, LinearIsometryEquiv.symm_units_smul, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, LinearMap.toMatrix_toSpanSingleton, LinearEquiv.coe_inv_det, RootPairing.toPerfPair_flip_conj_coreflection, LinearMap.coprod_map_prod, IsHilbertSum.linearIsometryEquiv_symm_apply_single, PolynomialLaw.isCompat_apply', Module.Relations.Solution.IsPresentation.postcomp_uniq_symm, AffineIsometryEquiv.map_vadd, LinearMap.toMatrix₂_symm', VonNeumannAlgebra.mem_commutant_iff, MvPolynomial.sum_monomial_eq, exists_embedding_euclidean_of_compact, Complex.norm_fderiv_le_one_of_mapsTo_ball, Module.Invertible.bijective, UnitAddTorus.mFourierBasis_repr, Polynomial.degreeLT.addLinearEquiv_natAdd, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, ContinuousLinearMap.coe_id', TensorProduct.lidOfCompatibleSMul_tmul, Module.Invertible.lTensor_bijective_iff, LinearMap.toSeminorm_apply, LieModule.isNilpotent_iff_forall', LinearIsometryEquiv.toLinearIsometry_rTensor, IsLocalizedModule.fromLocalizedModule'_mk, VectorPrebundle.contMDiffOn_contMDiffCoordChange, riesz_extension, linearIndepOn_union_iff_quotient, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, Pi.comul_single, TrivSqZeroExt.sndHom_apply, MvPolynomial.degrees_monomial_eq, LinearMap.mulRight_toAddMonoidHom, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, Submodule.starProjection_minimal, QuadraticMap.IsometryEquiv.map_app', Coalgebra.coassoc_apply, TwoSidedIdeal.subtypeMop_apply, EuclideanGeometry.orthogonalProjection_linear, ContinuousLinearMap.contMDiffWithinAt, ZMod.invDFT_def, mulLeftLinearMap_zero_eq_zero, Coalgebra.TensorProduct.rid_toLinearEquiv, groupHomology.π_map_apply, PiTensorProduct.mapL_pow, LinearMap.rank_comp_le, LinearMap.continuous_of_isClosed_graph, DoubleCentralizer.natCast_toProd, pinGroup.involute_act_ι_mem_range_ι, LinearMap.GeneralLinearGroup.toLinearEquiv_mul, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, Module.End.mem_genEigenspace_nat, Submodule.inclusion_injective, Complex.conjCLE_norm, ContinuousLinearMap.dslope_comp, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, Submodule.le_comap_single_pi, ContinuousLinearMap.inl_apply, mdifferentiableAt_coordChangeL, ProbabilityTheory.variance_linearMap_gaussianReal, HopfAlgebra.mul_antipode_lTensor_comul_apply, MulOpposite.coe_opLinearEquiv, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Representation.coinvariantsFinsuppLEquiv_symm_apply, Submodule.mulMap_comp_map_inclusion, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, RootPairing.Equiv.reflection_smul, MvPolynomial.pUnitAlgEquiv_monomial, Subalgebra.linearEquivOp_symm_apply_coe, Submodule.orthogonalProjection_orthogonal_apply_eq_zero, conductor_mul_differentIdeal, Polynomial.support_derivativeFinsupp_subset_range, MvPolynomial.coeff_monomial, LinearMap.mulRight_mul, TensorProduct.equivFinsuppOfBasisRight_symm, MvPolynomial.coeff_mul_monomial, Polynomial.mapRingHom_id, CliffordAlgebraDualNumber.ι_mul_ι, CategoryTheory.Abelian.Ext.mk₀_linearEquiv₀_apply, Polynomial.ofFn_comp_toFn_eq_id_of_natDegree_lt, Polynomial.monomial_zero_left, groupHomology.d₃₂_single_one_snd, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, ContinuousLinearMap.HasLeftInverse.continuousLinearEquivalence_comp, LinearIsometryEquiv.piLpCongrLeft_single, Submodule.starProjection_mem_subspace_eq_self, MeasureTheory.BoundedContinuousFunction.inner_toLp, exteriorPower.basis_repr, ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, LinearEquiv.lTensor_trans_apply, ModuleCat.extendScalars_comp_id_assoc, MvPolynomial.mem_ideal_span_monomial_image_iff_dvd, HVertexOperator.compHahnSeries_coeff, LinearMap.liftBaseChange_comp, HahnSeries.map_smul, Submodule.ker_mkQ, DirectSum.congrLinearEquiv_toAddEquiv, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, IsSMulRegular.subsingleton_linearMap_iff, Subspace.dualAnnihilator_le_dualAnnihilator_iff, LieHom.map_lie', LinearMap.separatingRight_of_det_ne_zero, Bialgebra.counit_one, IsRegular.monomial, RootPairing.Equiv.weightEquiv_comp_toLin, ContinuousLinearMap.norm_id, groupHomology.π_comp_H2Iso_hom_apply, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, HasFDerivWithinAt.fun_pow', Equiv.toLinearEquiv_continuousLinearEquiv, Profinite.NobelingProof.CC_comp_zero, LieSubmodule.coe_toEnd_pow, RootPairing.InvariantForm.apply_eq_or, SeparationQuotient.isEmbedding_outCLM, Submodule.lTensorOne_tmul, SheafOfModules.relationsOfIsCokernelFree_s, instIsSimpleModuleSubtypeMemSubmoduleValSetSetOfNonemptyLinearEquivId, Matrix.Nondegenerate.toBilin', ContinuousLinearEquiv.prodProdProdComm_apply, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, ModuleCat.forget₂_reflectsLimits, ContDiff.contDiff_fderiv_apply, CliffordAlgebra.isUnit_ι_of_isUnit, FDRep.Iso.conj_ρ, LinearMap.isPositive_iff, TensorProduct.directLimitLeft_tmul_of, MeasureTheory.L1.norm_Integral_le_one, Lagrange.interpolate_poly_eq_self, ContinuousLinearMap.measurable_apply', Module.Relations.Solution.span_relation_le_ker_π, HasStrictFDerivAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.toSpanSingletonLE_symm_apply, VectorFourier.fourierIntegral_comp_add_right, NormedSpace.closedBall_inv_subset_polar_closedBall, LinearMap.isIntegral, ContDiffMapSupportedIn.postcompLM_apply, LinearMap.BilinForm.congr_trans, Polynomial.taylor_coeff, LinearMap.toMatrix_singleton, FDRep.of_ρ, LinearMap.BilinForm.toMatrix'_mul, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, Algebra.trace_prod_apply, MulOpposite.comul_def, Module.Flat.iff_rTensor_injectiveₛ, dotProductBilin_apply_apply, ContinuousLinearMap.norm_smulRightL_le, MvPolynomial.monomial_pow, TemperedDistribution.laplacian_apply_apply, Submodule.LinearDisjoint.val_mulMap_tmul, LaurentSeries.derivative_iterate, Algebra.trace_trace_of_basis, ModuleCat.forget₂PreservesColimitsOfShape, DoubleCentralizer.one_toProd, Submodule.mkQ_surjective, Module.Baer.ExtensionOf.le, Polynomial.taylor_inj, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, AddEquiv.coe_toNatLinearEquiv, LinearIsometryEquiv.symm_smul_apply, Polynomial.derivative_zero, Algebra.traceMatrix_of_basis_mulVec, SchwartzMap.tsupport_derivCLM_subset, HasFDerivAt.comp_semilinear, IsBaseChange.basis_repr_comp, MvPowerSeries.monomial_zero_one, Coalgebra.coassoc_symm, Module.Dual.finrank_ker_add_one_of_ne_zero, MvPowerSeries.monomial_one_eq, Algebra.Extension.Hom.sub_tmul, Rep.diagonalOneIsoLeftRegular_hom_hom, PowerSeries.IsRestricted.monomial, exteriorPower.alternatingMapLinearEquiv_symm_apply, OrthonormalBasis.coe_toBasis_repr_apply, Finsupp.mapDomain.toLinearMap_linearEquiv, FractionalIdeal.mem_canonicalEquiv_apply, MvPolynomial.eval₂_monomial, det_rotation, TensorProduct.lid'_symm_apply, SkewPolynomial.monomial_mul_monomial, PowerSeries.coeff_expand, MeasureTheory.integrable_continuousLinearMap_prod, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, LieModule.mem_genWeightSpaceOf, instIsStablyFiniteRingEndForallOfFinite, LinearEquiv.fst_comp_prodAssoc, PiLp.coe_symm_continuousLinearEquiv, ZLattice.normBound_spec, Rep.ihom_coev_app_hom, Algebra.map_intTraceAux, ModuleCat.biproductIsoPi_inv_comp_π_apply, QuadraticMap.apply_linearCombination, LinearIsometryEquiv.star_eq_symm, ContinuousLinearEquiv.dimH_preimage, ContinuousLinearMap.id_comp, LinearMap.toMatrix₂'_compl₂, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, LinearMap.restrictScalars₁₂_injective, ContDiffWithinAt.fderivWithin_right_apply, LaurentPolynomial.comul_C_mul_T, PiTensorProduct.map_reindex, Prod.comul_comp_inl, TensorPower.mul_algebraMap₀, AdicCompletion.factor_evalₐ_eq_eval, Profinite.NobelingProof.eval_eq_πJ, HasFDerivWithinAt.fun_add, PositiveLinearMap.toLinearMap_zero, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, Matrix.toLinAlgEquiv'_symm, Rep.leftRegularHomEquiv_apply, imaginaryPart_smul, OrthonormalBasis.coe_equiv_euclideanSpace, VectorFourier.fourierIntegral_probChar, fderivWithin_mul_const, hasFDerivAt_zero, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, LinearMap.IsSymm.add, ContinuousLinearEquiv.coe_prodUnique, PresheafOfModules.pushforward_obj_map_apply', Orientation.rightAngleRotation_map, VectorFourier.norm_fourierSMulRight_le, LinearMap.exists_extend, MeasureTheory.OuterMeasure.map_top_of_surjective, RootPairing.Hom.coroot_coweightMap_apply, Submodule.le_dualAnnihilator_iff_le_dualCoannihilator, ContinuousLinearMap.mul_def, Matrix.entryLinearMap_apply, fderivWithin.fst, HasFDerivAt.mul_const', ContinuousAlternatingMap.nnnorm_ofSubsingleton, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, LieAlgebra.IsKilling.traceForm_coroot, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, Polynomial.succ_signVariations_X_sub_C_mul_monomial, MeasureTheory.charFunDual_map, IsAdjoinRootMonic.coeff_apply_coe, HasFiniteFPowerSeriesOnBall.fderiv', TensorProduct.AlgebraTensorModule.curry_injective, Polynomial.derivative_X_add_C_sq, Module.Basis.mapCoeffs_repr, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative, PointedCone.mem_comap, LinearMap.lTensor_comp, AddMonoidHom.coe_toRealLinearMap, Submodule.orthogonalProjectionFn_eq, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, LieDerivation.coe_add_linearMap, LinearMap.BilinForm.comp_apply, LinearMap.rid_comp_lTensor, TensorProduct.nnnorm_comm, Polynomial.as_sum_support, ExteriorAlgebra.ιInv_comp_map, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, FDRep.char_dual, AlternatingMap.coe_compLinearMap, MvPolynomial.monomial_one_dvd_monomial_one, Ideal.cotangentEquivIdeal_symm_apply, Module.flat_iff, MultilinearMap.compLinearMap_apply, MeasureTheory.OuterMeasure.restrict_apply, LinearMap.smulRight_zero, Module.Basis.traceDual_repr_apply, ContinuousLinearMap.coe_fst, Polynomial.taylorLinearEquiv_symm, ContinuousAlternatingMap.toContinuousLinearMap_apply, TensorAlgebra.mk_reindex_cast, TemperedDistribution.lineDerivOp_apply_apply, MvPolynomial.mul_monomial_modMonomial, MeasureTheory.ComplexMeasure.re_apply, FormalMultilinearSeries.ofScalars_comp_neg, ContinuousLinearMap.pi_proj_comp, PiTensorProduct.lift.unique', Matrix.nondegenerate_toLinearMap₂'_iff, signedDist_apply, Algebra.SubmersivePresentation.sectionCotangent_comp, Unitization.norm_splitMul_snd_sq, LinearMap.separatingRight_toMatrix₂_iff, ContinuousLinearMap.IsPositive.conj_starProjection, RingEquiv.symm_comp, AdicCompletion.AdicCauchySequence.map_comp, DirectSum.IsInternal.ofBijective_coeLinearMap_of_ne, FGModuleCat.FGModuleCatEvaluation_apply', Polynomial.natTrailingDegree_monomial_le, ModuleCat.forget₂AddCommGroup_reflectsLimit, LieModule.traceForm_eq_sum_finrank_nsmul_mul, HasStrictFDerivAt.fun_pow', Matrix.SpecialLinearGroup.toLin'_injective, measurable_fderiv, Submodule.exists_fg_le_eq_rTensor_subtype, TensorProduct.piScalarRight_apply, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, CliffordAlgebra.lift_comp_ι, groupHomology.coe_mapCycles₁, NumberField.Units.logEmbeddingEquiv_apply, RootPairing.coreflection_same, LinearEquiv.lTensor_symm_tmul, Coalgebra.lTensor_counit_comp_comul, PowerSeries.eval₂_trunc_eq_sum_range, Orthonormal.comp_linearIsometryEquiv, SpecialLinearGroup.coe_toGeneralLinearGroup_apply, MulOpposite.opLinearEquiv_symm_toAddEquiv, TemperedDistribution.lineDerivOp_fourierInv_eq, AlternatingMap.curryLeft_compLinearMap, LieAlgebra.nilpotent_ad_of_nilpotent_algebra, Submodule.map_orthogonal, LinearMap.fst_eq_coprod, LinearMap.det_ring, HasStrictFDerivAt.comp, Polynomial.degreeLT.addLinearEquiv_symm_apply_inl_basis, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, ModuleCat.hom_inv_leftUnitor, SMulMemClass.subtype_apply, CliffordAlgebra.changeForm.associated_neg_proof, LinearMap.coe_det, DoubleCentralizer.natCast_snd, VonNeumannAlgebra.coe_commutant, Matrix.mulVecLin_reindex, PowerSeries.trunc_one_X, Module.Relations.toQuotient_relation, Polynomial.leval_coe_eq_smeval, TensorProduct.exists_finite_submodule_of_setFinite, LinearEquiv.baseChange_pow, TensorProduct.exists_finite_submodule_left_of_setFinite', HasFiniteFPowerSeriesOnBall.hasFDerivAt, LinearMap.BilinForm.neg_right, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, ProbabilityTheory.variance_dual_prod, CliffordAlgebra.ofEven_ι, exteriorPower.map_apply_ιMulti, ProbabilityTheory.isGaussian_map_equiv, LinearMap.ker_eq_bot_iff_range_eq_top, MvPolynomial.mkDerivationₗ_X, LinearMap.BilinForm.IsNonneg.smul, HasFDerivAt.hasGradientAt, Algebra.H1Cotangent.exact_map_δ, LinearMap.iSup_range_single_le_iInf_ker_proj, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, AlgEquiv.toLinearMap_ofBijective, HasStrictFDerivAt.sin, VectorBundleCore.coordChange_linear_comp, ContinuousAlternatingMap.alternatizeUncurryFin_add, QuadraticMap.Isometry.toLinearMap_injective, Module.End.isUnit_apply_inv_apply_of_isUnit, ContinuousLinearMap.isBigOTVS_fun_comp, LocallyConstant.coeFnₗ_apply, groupCohomology.d₀₁_comp_d₁₂_apply, Module.Basis.ofZLatticeComap_repr_apply, MvPowerSeries.monomial_eq, LinearMap.BilinForm.linMulLin_compLeft, Algebra.Generators.Hom.toAlgHom_monomial, Finset.sum_smul_vsub_const_eq_weightedVSub, Algebra.normalizedTrace_algebraMap_of_lifts, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, realPart_apply_coe, QuotSMulTop.map_apply_mk, LinearMap.IsSymmetric.conj_inner_sym, ContinuousLinearMap.coe_inl, Algebra.Generators.H1Cotangent.δ_comp_equiv, HasFDerivWithinAt.const_rpow, ModuleCat.free_map_apply, Matrix.cramer_smul, Matrix.represents_iff', MeasureTheory.Measure.restrictₗ_apply, AlternatingMap.domDomCongrₗ_symm_apply, Module.projective_def, Submodule.dualAnnihilator_bot, TensorProduct.gradedCommAux_lof_tmul, Representation.linHom.mem_invariants_iff_comm, CliffordAlgebra.submodule_map_reverse_eq_comap, Matrix.UnitaryGroup.toLin'_mul, LinearMap.algHom_comp_convMul_distrib, rotation_symm, CoalgHom.toLinearMap_eq_coe, LinearMap.disjoint_single_single, Module.End.ringEquivEndFinsupp_apply_apply_support, ContinuousLinearMap.extendTo𝕜'_apply, CompletelyPositiveMap.map_cstarMatrix_nonneg', fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, LinearMap.BilinForm.linMulLin_apply, ContinuousMultilinearMap.norm_ofSubsingleton, DFinsupp.lapply_apply, ContinuousLinearMap.isAdjointPair_inner, LinearMap.eventually_codisjoint_ker_pow_range_pow, TensorProduct.directLimitLeft_symm_of_tmul, Representation.IntertwiningMap.isIntertwining, LinearMap.coe_smulRight, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, groupHomology.mapCycles₂_comp_i_apply, VectorFourier.norm_fourierPowSMulRight_le, Orientation.map_apply, TensorProduct.norm_map, RootPairing.Equiv.id_weightMap_apply, PolynomialModule.monomial_smul_apply, Complex.equivRealProdCLM_symm_apply_im, ContinuousLinearMap.coe_le_coe_iff, PiTensorProduct.mapMonoidHom_apply, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, AdicCompletion.eval_of, RootPairing.corootSpan_dualAnnihilator_le_ker_rootForm, ContinuousLinearEquiv.analyticWithinAt, PowerSeries.coeff_succ_X_mul, LinearMap.pi_zero, LinearMap.toMvPolynomial_eval_eq_apply, LinearMap.mk₂'_apply, LinearEquiv.coe_one, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, IsLocalizedModule.map_comp, Real.hasFDerivAt_fourierChar_neg_bilinear_right, Module.Dual.eval_naturality, LinearMap.BilinForm.comp_symmCompOfNondegenerate_apply, HVertexOperator.coeff_comp, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, LinearIsometryEquiv.differentiableAt, MvPowerSeries.coeff_monomial_ne, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, LinearIsometryEquiv.differentiable, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ModuleCat.ofHom₂_hom_apply_hom, AdicCompletion.map_zero, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, PerfectRing.liftEquiv_id, Unitization.splitMul_injective, groupHomology.boundariesToCycles₂_apply, LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot, Polynomial.logMahlerMeasure_monomial, Function.ExtendByZero.linearMap_apply, PowerSeries.trunc_trunc, Module.Basis.toMatrix_transpose_apply, Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousLinearMap.smulRight_comp, cfcₙ_eq_cfcₙL, DoubleCentralizer.sub_snd, AdicCompletion.component_sumInv, Algebra.normalizedTrace_trans, LinearMap.trace_conj, ModelWithCorners.coe_transContinuousLinearEquiv, Submodule.map_range_rTensor_subtype_lid, QuadraticMap.Isometry.tmul_apply, LinearIsometry.withLpProdMap_apply, ContDiffOn.comp_continuousLinearMap, VectorFourier.norm_fourierSMulRight, FiniteDimensional.instSubtypeMemSubmoduleMap, isSMulRegular_on_quot_iff_lsmul_comap_eq, Rep.freeLift_hom, Polynomial.rootSet_monomial, ContinuousLinearEquiv.coord_norm', nonempty_linearEquiv_of_lift_rank_eq, LinearEquiv.coe_ofTop_symm_apply, Ideal.coe_torsionOf, LinearEquiv.baseChange_symm, ContinuousLinearMap.smulRight_one_one, ContinuousLinearMap.nnnorm_id, fderivWithin_continuousAlternatingMap_apply, LinearMap.mul'_tensor, LinearMap.map_smul_of_tower, Polynomial.monomial_left_inj, RatFunc.taylor_mem_nonZeroDivisors, IsBaseChange.comp, LinearMap.toSpanSingleton_zero, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, LinearMap.BilinForm.congr_fun, jacobi_cross, CliffordAlgebra.toBaseChange_ι, Polynomial.newtonMap_apply, LinearMap.separatingLeft_toMatrix₂_iff, hom_chart, Module.map_eval_injective, HVertexOperator.coeff_apply_apply, ContinuousLinearMap.isPositive_zero, ContinuousLinearMap.toUniformConvergenceCLM_continuous, hasStrictFDerivAt_inv', CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix, AdicCompletion.evalₐ_mk, Module.Basis.toDualFlip_apply, LinearMap.toSpanSingleton_one, RootPairing.EmbeddedG2.twoShortAddLongRoot_shortRoot, LinearMap.mem_span_iff_bound, cfcₙL_apply, TensorProduct.comm_tmul, Representation.asModuleEquiv_map_smul, Set.Finite.convexHull_eq_image, Submodule.mapHom_apply, Submodule.fstEquiv_symm_apply_coe, CoalgEquivClass.toSemilinearEquivClass, AdicCompletion.piEquivOfFintype_apply, MvPolynomial.monomial_sum_one, Algebra.algebraMap_intTrace, MulOpposite.opContinuousLinearEquiv_apply, hasFDerivAt_exp_smul_const_of_mem_ball', CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, MeasureTheory.Lp.toTemperedDistribution_apply, TensorProduct.dualDistrib_apply, SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, AlternatingMap.uncurryFin_apply, TemperedDistribution.smulLeftCLM_const, LinearIsometryEquiv.withLpProdComm_apply, hasFDerivAtFilter_natCast, SchwartzMap.smulLeftCLM_apply_apply, LinearMap.lTensor_pow, LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal, LinearEquiv.det_coe_symm, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, Module.Basis.ofZLatticeBasis_repr_apply, groupHomology.d₁₀_single_inv, HasMFDerivAt.sum, groupHomology.mkH1OfIsTrivial_apply, LinearEquiv.neg_apply, groupCohomology.π_map_apply, Rep.indToCoindAux_snd_mul_inv, CliffordAlgebra.ι_mem_evenOdd_one, Representation.ofMulDistribMulAction_apply_apply, MeasureTheory.charFunDual_pi, HopfAlgebra.mul_antipode_lTensor_comul, fromModuleCatToModuleCatLinearEquiv_apply, LinearMap.BilinForm.IsAlt.sub, Finsupp.span_single_image, SchwartzMap.fourier_fderivCLM_eq, ModuleCat.hom_sub, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, DirectSum.linearEquivFunOnFintype_symm_single, ContinuousLinearMap.integral_comp_id_comm, LinearPMap.vadd_domain, LinearMap.BilinForm.toMatrix'_toBilin', hasStrictFDerivAt_exp_smul_const, Fintype.linearCombination_apply_single, LinearEquiv.symm_smul_apply, Trivialization.apply_symm_apply_eq_coordChangeL, SimplexCategory.coe_toTopMap, AlgHom.toRingHom_toAddMonoidHom, isSimpleModule_iff_toSpanSingleton_surjective, LinearMap.rTensor_neg, SchwartzMap.fourier_convolution_apply, AlternatingMap.compLinearMap_apply, Complex.hasStrictFDerivAt_log_real, Fintype.linearCombination_apply, LinearMap.GeneralLinearGroup.congrLinearEquiv_trans, MeasureTheory.SimpleFunc.setToSimpleFunc_const', neg_cross, IsIsotypic.linearEquiv_finsupp, Projectivization.generalLinearGroup_smul_def, Rep.res_obj_ρ, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, LinearAlgebra.FreeProduct.lift_apply, LocalizedModule.map_mk, PowerBasis.liftEquiv'_symm_apply_apply, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, PiTensorProduct.lift_comp_reindex_symm, CoalgEquiv.toLinearEquiv_eq_coe, PiTensorProduct.map_update_smul, Polynomial.natDegree_iterate_derivative, Submodule.starProjection_le_starProjection_iff, CommRingCat.hom_id, Module.exists_surjective_quotient_of_finite, QuadraticMap.separatingLeft_of_anisotropic, PiTensorProduct.ofDFinsuppEquiv_symm_single_tprod, CliffordAlgebra.evenOdd_comap_reverse, Pi.comul_coe_dFinsupp, MultilinearMap.linearDeriv_apply, LieAlgebra.mem_zeroRootSubalgebra, TemperedDistribution.smulLeftCLM_sum, Submodule.linearProjOfIsCompl_range, PowerBasis.constr_pow_mul, ModuleCat.extendScalars_comp_id, HasStrictFDerivAt.mul, ContinuousLinearMap.analyticOnNhd, PolynomialLaw.isCompat_apply, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, HahnEmbedding.Partial.eval_eq_truncLT, AddMonoidHom.coe_toIntLinearMap, IsLocalMaxOn.hasFDerivWithinAt_eq_zero, Module.End.ker_pow_le_ker_pow_finrank, StrongDual.coe_toWeakDual, jacobiTheta₂_fderiv_undef, Orientation.oangle_rotation_self_right, LinearMap.det_toMatrix', LinearMap.GeneralLinearGroup.ofLinearEquiv_mul, Matrix.separatingLeft_toBilin_iff, Module.End.apply_isScalarTower, TensorProduct.congr_pow, PresheafOfModules.freeYonedaEquiv_comp, ModuleCat.forget₂AddCommGroup_preservesLimit, WeakDual.toStrongDual_apply, FormalMultilinearSeries.radius_rightInv_pos_of_radius_pos_aux2, ContinuousLinearEquiv.uniqueDiffOn_image_iff, Submodule.equivOpposite_symm_apply, LinearIsometryEquiv.withLpProdAssoc_apply, SMulMemClass.coe_subtype, LinearMap.eq_adjoint_iff_basis_right, Module.Basis.ofIsLocalizedModule_span, Submodule.prod_map_fst, ContinuousLinearMap.hasMFDerivWithinAt, Real.differentiable_fourierChar_neg_bilinear_left, Polynomial.eval_add_of_sq_eq_zero, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, CharacterModule.intSpanEquivQuotAddOrderOf_apply_self, Polynomial.derivative_X_add_C_pow, Module.Finite.exists_fin', LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebra, MeasureTheory.OuterMeasure.map_top, LinearMap.toMatrixAlgEquiv_apply', IsLocalizedModule.eq_iff_exists, LinearMap.lTensor_map, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, trace_eq_sum_automorphisms, Matrix.toLin'OfInv_apply, MvPowerSeries.coeff_subst_finite, MonomialOrder.div, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Basis.equivFun_symm_single, continuousMultilinearCurryLeftEquiv_symm_apply, Profinite.NobelingProof.injective_πs, MultilinearMap.toLinearMap_apply, IsModuleTopology.continuous_bilinear_of_finite_right, mulLeftLinearMap_eq_zero_iff, fderivWithin_add, AffineEquiv.linear_ofBijective, TensorProduct.map_map_comp_assoc_symm_eq, LineDeriv.lineDerivOpCLM_apply, Rep.ihom_obj_V_isModule, Finsupp.linearCombination_surjective, TensorProduct.tensorQuotEquivQuotSMul_comp_mk, LinearMap.existsUnique_eq_smul_id_of_finrank_eq_one, geometric_hahn_banach_closed_point, AdicCompletion.ofTensorProduct_naturality, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, LinearMap.BilinForm.isOrtho_def, ContinuousMultilinearMap.smulRightL_apply, ContinuousLinearMap.coe_prodMap, ContinuousLinearMap.contDiff, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, MvPolynomial.scalarRTensor_symm_apply_single, FractionalIdeal.equivNum_apply, TemperedDistribution.instContinuousFourierInv, DFinsupp.mapRange.linearMap_apply, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, LinearMap.rank_add_le, Representation.smul_one_tprod_asModule, Polynomial.natDegree_monomial_eq, ContinuousLinearMap.instBorelSpace, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, ModuleCat.FreeMonoidal.εIso_hom_one, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, innerₛₗ_apply_coe, ContinuousLinearMap.toSpanSingleton_smul', fderiv_csinh, Finsupp.lsingle_range_le_ker_lapply, SemimoduleCat.ofHom_comp, MultilinearMap.constLinearEquivOfIsEmpty_symm_apply, LinearMap.comp_id_semiModuleCat, Module.End.natCast_apply, AlternatingMap.domLCongr_trans, toWeakSpaceCLM_eq_toWeakSpace, ContinuousLinearMap.coprod_comp_inl, TensorProduct.equivFinsuppOfBasisLeft_apply, HasStrictFDerivAt.fun_add, IsLocalMinOn.fderivWithin_nonneg, CharacterModule.dual_surjective_iff_injective, Module.Basis.prod_repr_inr, instExpCharLinearMapSubtypeMemSubringCenterId, Complex.reCLM_norm, MulOpposite.toContinuousLinearEquiv_opLinearIsometryEquiv, ContinuousLinearMap.norm_snd_le, Polynomial.iterate_derivative_mul, LinearMap.BilinMap.toQuadraticMap_apply, Finsupp.range_lmapDomain, LinearEquiv.pow_apply, Polynomial.aeval_iterate_derivative_of_lt, Rep.freeLift_hom_single_single, Trivialization.linearMapAt_def_of_notMem, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, RootPairing.rootSpan_dualAnnihilator_map_eq, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, LinearIsometryEquiv.toLinearIsometry_lTensor, LinearMap.BilinForm.Nondegenerate.toMatrix', Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, fderiv_of_notMem_tsupport, RootPairing.Equiv.inv_coweightMap, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, AlternatingMap.domLCongr_apply, TensorProduct.comm_comp_comm_assoc, LinearMap.isSymm_iff_basis, Submodule.map_comap_subtype, MvPolynomial.weightedHomogeneousComponent_of_mem, Module.Basis.constr_self, hasStrictFDerivAt_const, ContinuousLinearMap.contMDiffOn, Polynomial.derivative_map, VonNeumannAlgebra.instStarMemClass, Finsupp.linearCombination_comp_lmapDomain, LinearMap.toMatrix_basis_equiv, Matrix.UnitaryGroup.toGL_one, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, contMDiffOn_coordChangeL, WithCStarModule.equivL_symm_apply, LinearMap.restrictScalars₁₂_apply_apply, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Finsupp.mem_span_image_iff_linearCombination, Matrix.reindexLinearEquiv_comp_apply, ExteriorAlgebra.ι_range_map_map, Coalgebra.TensorProduct.map_toLinearMap, ModuleCat.mono_iff_ker_eq_bot, Derivation.coe_zero_linearMap, TensorProduct.comm_comp_comm, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ, LinearIsometryEquiv.one_def, Submodule.comap_unop_one, Module.evalEquiv_toLinearMap, MvPowerSeries.order_eq_nat, exteriorPower.map_comp, LinearEquiv.rTensor_trans_lTensor, LinearMap.CompatibleSMul.map_smul, LinearMap.charpoly_zero, ContinuousLinearMap.opNorm_mulLeftRight_le, Module.End.mul_apply, MultilinearMap.compLinearMapMultilinear_apply, MvPolynomial.irreducible_sumSMulXSMulY, LinearEquiv.toAddEquiv_toNatLinearEquiv, CategoryTheory.Abelian.Ext.linearEquiv₀_symm_apply, DoubleCentralizer.intCast_fst, PointwiseConvergenceCLM.evalCLM_apply, HasFDerivAt.sqrt, LieModule.traceForm_apply_eq_zero_of_mem_lcs_of_mem_center, Submodule.map_toAddSubgroup, groupHomology.π_comp_H1Iso_inv_apply, topDualPairing_apply, LinearMap.trace_prodMap', ProperCone.comap_comap, AlgHom.linearMapMk_toAddHom, AddMonoidHom.coe_toZModLinearMap, lift_rank_range_le, SemimoduleCat.hom_hom_leftUnitor, MvPowerSeries.IsWeightedHomogeneous.coeff_eq_zero, LinearMap.quotientInfEquivSupQuotient_symm_apply_left, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, PowerSeries.coeff_C_mul, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, TensorProduct.AlgebraTensorModule.lift_tmul, PowerSeries.X_pow_dvd_iff, exteriorPower.ιMultiDual_apply_nondiag, MvPolynomial.mem_ideal_span_monomial_image, Polynomial.iterate_derivative_intCast_mul, Polynomial.taylor_mem_degreeLT, Polynomial.leadingCoeff_monomial, AddMonoidAlgebra.antipode_single, IsLocalizedModule.fromLocalizedModule.surj, ContDiffMapSupportedIn.structureMapCLM_zero_injective, Lagrange.eval_nodal_derivative_eval_node_eq, LinearMap.dualMap_comp_dualMap, Submodule.exists_dual_map_eq_bot_of_notMem, Finset.weightedVSub_subtype_eq_filter, LinearIsometryEquiv.prodComm_apply, TemperedDistribution.fourier_apply, Matrix.SeparatingRight.toBilin', RCLike.iInter_halfSpaces_eq, SemimoduleCat.hom_comp, Matrix.kroneckerTMul_assoc, LinearMap.lflip_symm, LinearMap.bijective_of_ne_zero, IsAdjoinRootMonic.coeff_apply_le, ContinuousMultilinearMap.piₗᵢ_apply, Module.Basis.traceDual_powerBasis_eq, LinearMap.ltoFun_apply, Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range, CliffordAlgebra.EquivEven.reverse_v, Polynomial.card_support_le_one_iff_monomial, LinearEquiv.coe_prodCongr, Orientation.areaForm_rightAngleRotation_right, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, LinearMap.convMul_apply, Module.End.smulLeft_eq, MeasureTheory.setIntegral_condExpL1CLM, Algebra.injective_lift_lsmul, MvPowerSeries.coeff_mul_left_one_sub_of_lt_order, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, Profinite.NobelingProof.coe_πs', groupCohomology.isoCocycles₂_hom_comp_i_apply, AdicCompletion.ofLinearEquiv_apply, Polynomial.coeff_mul_monomial, Algebra.algebraMap_intTrace_fractionRing, PiTensorProduct.map_comp_reindex_eq, TensorProduct.lift_compr₂, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, KaehlerDifferential.range_kerCotangentToTensor, IsLocalMin.fderiv_eq_zero, norm_iteratedFDerivWithin_fderivWithin, LaurentPolynomial.trunc_C_mul_T, ProperCone.hyperplane_separation, Module.Basis.map_addHaar, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, ModuleCat.hom_bijective, AffineIsometryEquiv.norm_map, LinearMap.compBilinForm_apply_apply, ContinuousLinearMap.cpolynomialOn, LinearMap.lid_comp_rTensor, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, DualNumber.algHom_ext'_iff, Rep.diagonalHomEquiv_apply, LinearMap.coe_toContinuousLinearMap_symm, Matrix.range_diagonal, Submodule.mulMap_op, ZMod.completedLFunction_one_sub_even, HasFDerivWithinAt.finset_prod, LinearMap.prod_apply, LinearIsometry.toLinearIsometryEquiv_apply, AdicCompletion.mk_apply_coe, hasStrictFDerivAt_list_prod', Prod.counit_apply, LinearPMap.graph_map_fst_eq_domain, AddEquiv.toNatLinearEquiv_symm, Module.Relations.toQuotient_map, continuousMultilinearCurryFin1_symm_apply, LinearMap.BilinForm.Nondegenerate.ker_eq_bot, Polynomial.derivative_natCast, Trivialization.symmL_apply, Module.End.ofNat_apply, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, ContinuousLinearMap.coe_mul, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, StrongDual.mem_polar_iff, LieModule.Cohomology.mem_twoCocycle_iff_of_trivial, IsTensorProduct.equiv_toLinearMap, TwoSidedIdeal.subtypeMop_injective, Submodule.orthogonal_eq_inter, groupHomology.d₂₁_single, Finsupp.mapDomain.linearEquiv_symm, ContinuousLinearMap.mdifferentiableOn, Matrix.piLinearEquiv_symm_apply, IsSymmetricAlgebra.comp_equiv, MeasureTheory.eLpNorm_condExpL2_le, LieModule.iterate_toEnd_mem_lowerCentralSeries, PadicInt.mahlerEquiv_symm_apply, LinearMap.extendScalarsOfIsLocalizationEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Orientation.inner_smul_rotation_pi_div_two_smul_left, Prod.comul_comp_inr, IsSelfAdjoint.coe_realPart, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, Module.Flat.tensorProduct_mapIncl_injective_of_right, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, SchwartzMap.coe_apply, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, LinearMap.proj_surjective, mulLeftLinearMap_apply, Module.Basis.constr_def, TensorProduct.lift_mk_compr₂ₛₗ, ContinuousLinearEquiv.coord_self, SheafOfModules.Presentation.IsFinite.finite_relations, IsLocalRing.map_mkQ_eq_top, SemimoduleCat.hom_add, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, cardinalMk_algHom, LinearIsometryEquiv.mul_def, LinearMap.trace_comp_comm, KaehlerDifferential.map_D, Polynomial.hasseDeriv_X, LinearMap.ofIsCompl_subtype_zero_eq, RCLike.geometric_hahn_banach_compact_closed, addMonoidEndRingEquivInt_symm_apply, SchwartzMap.smulLeftCLM_ofReal, HasStrictFDerivAt.ccosh, LinearMap.pow_mulLeft, extDerivWithin_apply, Derivation.liftKaehlerDifferential_apply, LinearMap.range_smulRight_apply, Rep.freeLiftLEquiv_symm_apply, Finsupp.comul_comp_lsingle, MvPolynomial.coeff_weightedHomogeneousComponent, realPart_smul, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_apply, RootPairing.Hom.weightMap_mul, LinearEquiv.finrank_map_eq, BilinForm.toMatrix_compLeft, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, LinearMap.IsPositive.adjoint_eq, groupHomology.eq_d₂₁_comp_inv_apply, Trivialization.prod_apply', PowerSeries.order_eq, Submodule.map_subtype_range_inclusion, Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace, fderivWithin_zero_of_not_differentiableWithinAt, Algebra.coe_lmul_eq_mul, StarHomClass.isSelfAdjoint, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, ContinuousLinearMap.prodₗ_apply, ContinuousLinearEquiv.comp_fderivWithin, Polynomial.derivative_bernoulli, ContinuousLinearMap.coprodEquiv_symm_apply, iteratedDeriv_vcomp_two, AdicCompletion.congr_apply, ContinuousLinearEquiv.coord_norm, PiTensorProduct.map_update_add, LinearMap.compl₂_id, Module.Basis.toDual_apply_left, LinearMap.nilRank_le_natTrailingDegree_charpoly, LinearMap.toPerfPair_apply, fderiv_norm_rpow, ExteriorAlgebra.comp_ι_sq_zero, LinearMap.id_comp, KaehlerDifferential.DLinearMap_apply, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, HasStrictFDerivAt.cosh, CategoryTheory.whiskering_linearYoneda₂, MeasureTheory.L1.integral_eq', QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar, LinearIsometryEquiv.map_smul, LinearMap.toMatrix₂'_comp, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, Module.End.invtSubmodule.zero, LieHom.ker_toSubmodule, MvPolynomial.rTensor_apply, LinearEquiv.congrQuadraticMap_apply, mulLeftLinearMap_mul, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, RootPairing.IsOrthogonal.coreflection_apply_left, Matrix.toLinearMap₂_apply_basis, Polynomial.ofFn_coeff_eq_val_of_lt, Finset.weightedVSubOfPoint_erase, isStarProjection_iff_eq_starProjection, IsAdjoinRootMonic.coeff_root, LinearEquiv.conjAlgEquiv_surjective, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, LinearEquiv.smul_trans, Matrix.coe_ofLinearEquiv_symm, TensorProduct.ext_iff, MvPolynomial.disjoint_support_monomial, TensorProduct.lift_comp_comm_eq, CliffordAlgebra.ofProd_ι_mk, Orientation.inner_smul_rotation_pi_div_two_smul_right, RCLike.geometric_hahn_banach_point_closed, Submodule.ker_inr, MvPowerSeries.monomial_mul_monomial, LinearMap.IsSymmetricProjection.le_iff_range_le_range, Module.DualBases.lc_def, ModuleCat.MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, AffineBasis.coord_smul, Module.exists_ker_toSpanSingleton_eq_annihilator, CliffordAlgebra.GradedAlgebra.lift_ι_eq, PolynomialModule.monomial_smul_lsingle, VonNeumannAlgebra.instSubringClass, TensorPower.toTensorAlgebra_galgebra_toFun, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Submodule.linearProjOfIsCompl_ker, VectorField.fderivWithin_apply_lieBracket, ContinuousAffineMap.vsub_contLinear, TensorProduct.Algebra.moduleAux_apply, fderivWithin_pow, ContinuousLinearMap.continuousConstSMul_apply, Rep.indToCoindAux_of_not_rel, VectorPrebundle.coordChange_apply, LinearEquiv.lift_rank_map_eq, PowerSeries.coeff_zero_X_mul, LinearMap.not_hasEigenvalue_zero_tfae, EuclideanGeometry.orthogonalProjection_apply, LinearMap.toMatrix_pow, TensorProduct.map_range_eq_span_tmul, MvPolynomial.aeval_monomial, hasFDerivAt_exp_zero_of_radius_pos, LinearMap.exact_iff, groupHomology.cyclesMk₀_eq, RootPairing.disjoint_rootSpan_ker_rootForm, Module.FinitePresentation.isLocalizedModule_mapExtendScalars, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, fderivWithin_fun_const_smul, CommSemiring.counit_apply, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Rep.applyAsHom_hom, Module.Projective.iff_split, NNRealRMK.integral_rieszMeasure, Module.Relations.Solution.IsPresentation.exact, fwdDiff_aux.coe_fwdDiffₗ_pow, ContinuousLinearEquiv.strictConvex_preimage, Complex.rightAngleRotation, ExteriorAlgebra.ι_mul_prod_list, LinearMap.BilinMap.polarBilin_toQuadraticMap, IsBaseChange.linearMapLeftRightHom_apply, Algebra.trace_apply, ContinuousLinearMap.hasDerivWithinAt, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, TensorAlgebra.toDirectSum_ι, FormalMultilinearSeries.derivSeries_apply_diag, ModuleCat.forget_map, LinearMap.coprodEquiv_symm_apply, NormedSpace.polar_closedBall, CompactlySupportedContinuousMap.monotone_of_nnreal, Submodule.norm_orthogonalProjection, TensorProduct.AlgebraTensorModule.congr_trans, LinearMap.BilinForm.toMatrix_comp, LinearEquiv.map_mem_invtSubmodule_iff, AnalyticAt.fderiv, ExteriorAlgebra.ιMulti_succ_curryLeft, LinearMap.mul'_comm, Matrix.SpecialLinearGroup.toLin'_symm_apply, ContinuousLinearMap.IsInvertible.self_comp_inverse, Submodule.map_neg, ContinuousLinearEquiv.differentiableWithinAt, ContinuousLinearMap.coe_eq_id, DirectSum.lmap_of, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, AddMonoidAlgebra.mapDomainRingHom_id, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapId, fderiv_comp_smul, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, Finset.weightedVSub_sdiff_sub, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, IsExposed.eq_inter_halfSpace', QuadraticAlgebra.det_toLinearMap_eq_norm, ContinuousLinearMap.opNorm_lsmul, CoalgHomClass.map_comp_comul_apply, ExteriorAlgebra.leftInverse_map_iff, LinearIsometry.toLinearMap_lTensor, IsLocalizedModule.map_integerMultiple, Submodule.comap_smul', Module.Basis.reindexFinsetRange_repr, coe_innerₛₗ_apply, ProbabilityTheory.covarianceBilinDual_of_not_memLp, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange, Coalgebra.Repr.eq, Algebra.Generators.CotangentSpace.fst_compEquiv_apply, PiLp.hasStrictFDerivAt_ofLp, fderivWithin_arctan, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, LinearMap.lTensor_comp_map, Module.Basis.continuous_coe_repr, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, TensorProduct.finsuppScalarLeft_apply, MonomialOrder.degree_monomial_le, LinearMap.trace_comp_cycle, NumberField.InfinitePlace.comap_id, curveIntegral_add, LinearMap.intrinsicStar_comp, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, Submodule.lTensorOne_one_tmul, ModularGroup.lcRow0_apply, PowerSeries.WithPiTopology.tendsto_trunc_atTop, Algebra.FormallyUnramified.comp_sec, MulOpposite.coe_opLinearEquiv_symm_toLinearMap, Module.Basis.smulTower_repr, RingEquiv.toRingHom_comp_symm_toRingHom, HasFTaylorSeriesUpTo.zero_eq', TopModuleCat.hom_comp, TensorProduct.assoc_tensor, ContinuousLinearMap.prod_apply, Module.Basis.toDual_apply_right, MvPowerSeries.rescale_one, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, ContinuousLinearEquiv.analyticAt, LinearMap.trace_comp_cycle', IsLinearMap.mk'_apply, MvPolynomial.coeff_mul_monomial', Submodule.dualAnnihilator_map_linearEquiv_flip_symm, LinearMap.toMatrix'_one, Representation.dual_apply, LieAlgebra.SpecialLinear.val_singleSubSingle, AffineEquiv.map_vadd', InnerProductSpace.continuousLinearMapOfBilin_apply, lipschitzGroup.involute_act_ι_mem_range_ι, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, Polynomial.monomial_natDegree_leadingCoeff_eq_self, AdicCompletion.transitionMap_comp_eval_apply, Finsupp.linearCombination_comapDomain, NormedSpace.double_dual_bound, Module.DualBases.coeffs_apply, AdicCompletion.of_injective_iff, PowerSeries.rescale_one, MonoidAlgebra.mapRangeRingHom_id, Matrix.cstar_norm_def, Submodule.baseChange_span, AlternatingMap.domDomCongrₗ_apply, MeasureTheory.convolution_eq_swap, LinearMap.BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, Module.Basis.det_smul_mk_coord_eq_det_update, Module.surjective_piEquiv_apply_iff, ModelWithCorners.coe_transContinuousLinearEquiv_symm, LinearMap.transvection.congr, fderivWithin_def, UniformCauchySeqOnFilter.one_smulRight, Submodule.le_prod_iff, Real.zero_at_infty_vector_fourierIntegral, ContDiff.fderiv_right, PowerSeries.coeff_C_mul_X_pow, Submodule.dualAnnihilator_iSup_eq, LinearPMap.coe_vadd, ContinuousMultilinearMap.curryFinFinset_symm_apply, Submodule.map₂_map_map, VectorField.mlieBracketWithin_apply, LieAlgebra.isNilpotent_iff_forall, SchwartzMap.smulLeftCLM_apply, IsLocalizedModule.of_linearEquiv, Submodule.dualAnnihilator_eq_bot_iff, TensorAlgebra.lift_unique, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, TensorProduct.quotTensorEquivQuotSMul_comp_mk, ContinuousLinearEquiv.comp_contDiff_iff, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, fderiv_csin, bernsteinPolynomial.derivative_zero, ContinuousLinearMap.norm_snd, ZSpan.repr_floor_apply, PointedCone.mem_maxTensorProduct, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, Polynomial.iterate_derivative_map, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, Polynomial.sumIDeriv_apply_of_le, Coalgebra.TensorProduct.assoc_toLinearEquiv, LinearEquiv.dualMap_refl, MeasureTheory.condExpIndSMul_ae_eq_smul, Rep.indResHomEquiv_apply_hom, LinearEquiv.automorphismGroup.toLinearMapMonoidHom_apply, ContinuousLinearMap.iteratedFDeriv_comp_right, QuadraticMap.exists_companion, DirectSum.lmap_injective, LinearMap.BilinForm.IsAlt.add, cross_cross_eq_smul_sub_smul', Quaternion.linearIsometryEquivTuple_apply, rank_lt_rank_dual, norm_fderiv_le_of_lip', ModuleCat.homAddEquiv_apply, Module.Basis.repr_symm_apply, Module.fgSystem.instDirectedSystemSubtypeSubmoduleFGMemValCoeLinearMapId, isNoetherian_range, Finsupp.apply_linearCombination_id, QuadraticForm.tmul_comp_tensorAssoc, Submodule.linearProjOfIsCompl_apply_eq_zero_iff, Polynomial.Bivariate.pderiv_one_equivMvPolynomial, TensorProduct.rTensorHomToHomRTensor_apply, Module.Dual.congr_apply_apply, LieAlgebra.IsKilling.span_weight_eq_top, PresheafOfModules.ofPresheaf_map, LinearMap.comp_coprod, Algebra.coe_linearMap, TensorProduct.fromDirectLimit_of_tmul, PiTensorProduct.ofDirectSumEquiv_tprod_apply, Polynomial.support_monomial', fderiv_cosh, ContinuousLinearEquiv.self_trans_symm, LinearMap.tensorKerEquiv_apply, basis_toMatrix_mul_linearMap_toMatrix, LieModule.traceForm_flip, support_fderiv_subset, HasStrictFDerivAt.fun_mul, AlternatingMap.alternatizeUncurryFin_smul, ContDiff.continuousLinearMap_comp, LinearMap.toMatrixₛₗ₂'_apply, Representation.dualTensorHom_comm, ContinuousLinearMap.precomp_apply, ContinuousLinearMap.norm_holderL_le, ModuleCat.span_rightExact, hasFDerivWithinAt_pow, LinearMap.baseChange_tmul, MvPolynomial.lcoeff_apply, CommRingCat.KaehlerDifferential.ext_iff, LinearMap.transvection.baseChange, contDiff_infty_iff_fderiv, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, LinearMap.range_codRestrict, LinearMap.polar_mem_iff, Submodule.mem_biSup_iff_exists_dfinsupp, LinearMap.IsContPerfPair.continuous_uncurry, LinearEquiv.one_eq_refl, Module.Basis.tensorProduct_repr_tmul_apply, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Module.Basis.coe_ofEquivFun, PolynomialLaw.ground_apply, Matrix.toLinearMapRight'_one, Module.injective_iff, MvPolynomial.restrictSupport_eq_span, PiLp.continuousLinearEquiv_apply, curveIntegral_sub, cfcₙL_integrable, isSMulRegular_iff_ker_lsmul_eq_bot, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, HasFDerivWithinAt.mul', LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt, LinearEquiv.coe_uniqueProd, Polynomial.taylor_X, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem_of_analyticOn, PointedCone.dual_flip_dual_dual_flip, QuadraticForm.associated_tmul, groupCohomology.cocyclesMk₀_eq, HasGradientAt.fderiv_apply, differentiableWithinAt_complex_iff_differentiableWithinAt_real, ContinuousLinearMap.comp_analyticOnNhd, LinearEquiv.alternatingMapCongrRight_symm_apply_apply, ModN.instModuleFinite, TemperedDistribution.derivCLM_apply_apply, WithLp.linearEquiv_symm_apply, LieEquiv.left_inv, ModuleCat.endRingEquiv_apply, MultilinearMap.curryFinFinset_symm_apply, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, Submodule.range_subtype, LinearMap.rTensor_add, CharacterModule.dual_zero, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, Pretrivialization.symmₗ_linearMapAt, HasStrictFDerivAt.sinh, bernsteinPolynomial.iterate_derivative_at_0, LinearMap.toMatrixAlgEquiv_reindexRange, Matrix.GeneralLinearGroup.map_id, Submodule.one_eq_range, ContinuousLinearMap.precomp_uniformConvergenceCLM_apply, LinearEquiv.lTensor_refl_apply, PowerSeries.coeff_X_pow_mul', Basis.piTensorProduct_repr_tprod_apply, RootPairing.toLinearMap_apply_apply_mem_range_algebraMap, TensorProduct.star_map_apply_eq_map_intrinsicStar, Matrix.cramer_transpose_apply, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, Module.Invertible.rightCancelEquiv_comp_rTensor_comp_symm, MvPowerSeries.WithPiTopology.tendsto_iff_coeff_tendsto, Submodule.subtype_injective, DirectSum.toModule.unique, Orientation.norm_kahler, CliffordAlgebra.evenOdd_comap_involute, ModuleCat.HasColimit.reflectsColimit, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, HasFDerivAt.cpow, Finset.weightedVSub_indicator_subset, Module.Relations.Solution.π_comp_map_apply, PresheafOfModules.naturality_apply, Submodule.dualRestrict_apply, Polynomial.hasFDerivWithinAt, Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, LinearEquiv.inv_mem_transvections_iff, TrivSqZeroExt.liftEquiv_symm_apply_coe, TensorProduct.one_gradedMul, ContinuousLinearMap.coe_pi', HasMFDerivWithinAt.comp, Complex.isometryOfOrthonormal_symm_apply, IsLocalizedModule.map_iso_commute, LinearIsometryEquiv.inv_def, Module.Basis.sum_equivFun, Module.End.mem_genEigenspace, Submodule.comap_op_one, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, WithLp.coe_symm_linearEquiv, Pi.counit_comp_single, Algebra.coe_trace_int, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, groupHomology.single_mem_cycles₂_iff, LieModule.traceForm_apply_lie_apply', MeasureTheory.weightedSMul_smul_measure, LinearEquiv.rTensor_trans, TensorProduct.finsuppScalarLeft_symm_apply_single, MvPowerSeries.isWeightedHomogeneous_iff_eq_weightedHomogeneousComponent, VectorField.lieBracket_smul_right, MeasureTheory.OuterMeasure.restrict_mono, Module.Finite.exists_fin_quot_equiv, TensorProduct.piScalarRightHom_tmul, LinearMap.hasDerivAtFilter, Submodule.topologicalClosure_iSup_map_single, intervalIntegral.integral_hasFDerivAt, Submodule.comapSubtypeEquivOfLe_apply_coe, DFinsupp.lapply_comp_lsingle_same, AddMonoidHom.toIntLinearMap_injective, LinearMap.flip_surjective_iff₂, RootPairing.range_weylGroup_weightHom, Module.Basis.repr_smul', CurveIntegrable.sub, InnerProductSpace.HarmonicAt.comp_CLM, RootPairing.RootPositiveForm.algebraMap_posForm, lmap_finsuppLEquivDirectSum_eq, Orientation.inner_rightAngleRotation_self, AlgHom.id_toRingHom, LinearMap.lsum_piSingle, HasFiniteFPowerSeriesOnBall.fderiv_eq, Bialgebra.counit_pow, Submodule.liftQ_mkQ, CategoryTheory.Abelian.Ext.homLinearEquiv_symm_apply, Algebra.TensorProduct.equivPiOfFiniteBasis_apply, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, IsBaseChange.linearMapRight, Algebra.SubmersivePresentation.cotangentComplex_injective, Finsupp.ker_lsingle, Module.Projective.out, LinearMap.rTensor_pow, LinearMap.span_singleton_eq_range, ContinuousLinearEquiv.comp_contDiffAt_iff, Submodule.dualAnnihilator_eq_bot_iff', Module.Basis.constr_range, LinearMap.ker_lsmul, ContinuousLinearMap.smulRight_apply, Module.Basis.repr_unitsSMul, Module.compHom.toLinearEquiv_symm_apply, InnerProductSpace.laplacian_CLE_comp_left, coe_addMonoidHom_id, LinearEquiv.entryLinearMap_comp_mapMatrix, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, PiTensorProduct.mapL_add, PiTensorProduct.mul_comm, fderiv_fun_const, RootPairing.reflection_apply, ContinuousLinearMap.analyticAt_bilinear, inner_gradient_left, FormalMultilinearSeries.compContinuousLinearMap_apply, TensorProduct.piRight_apply, Matrix.toLpLin_apply, Representation.ind_apply, eventually_norm_trivializationAt_lt, TensorProduct.congrIsometry_apply, Submodule.starProjection_comp_starProjection_of_le, ZMod.dft_eq_fourier, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', PolynomialModule.eval_map', ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', HasFDerivWithinAt.comp_hasDerivAt_of_eq, HasFPowerSeriesAt.hasStrictFDerivAt, Matrix.entryLinearMap_toAddHom, DirectSum.isInternal_biSup_submodule_of_iSupIndep, Polynomial.iterate_derivative_one, contDiffOn_fderivWithin_apply, LinearEquiv.baseChange_one, Ideal.Quotient.factor_eq, PowerSeries.coeff_pow, QuadraticMap.linMulLin_comp, trace_eq_sum_embeddings_gen, ZMod.dft_odd_iff, Matrix.toLin'_apply, Representation.isIntertwiningMap_iff, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, Equiv.tensorProductComm_def, CliffordAlgebra.contractRight_ι, QuotSMulTop.map_id, LinearMap.ker_le_range_iff, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, ModuleCat.extendScalarsId_inv_app_apply, Polynomial.natDegree_derivative_lt, ContinuousLinearMap.pi_zero, LinearEquiv.det_refl, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, Ideal.map_toCotangent_ker, isSMulRegular_on_quot_iff_lsmul_comap_le, LinearMap.proj_comp_single_ne, Submodule.map_op_one, LieAlgebra.isNilpotent_ad_of_isNilpotent, innerSL_apply_coe, Submodule.map_dualCoannihilator_linearEquiv_flip, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, Module.Basis.constr_apply, fderivWithin_mul', MeasureTheory.eLpNorm_le_eLpNorm_fderiv, HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, TensorProduct.map_pow, LinearMap.ofIsCompl_zero, LinearEquiv.piCongrLeft'_apply, LinearMap.coprod_comp_inl_inr, ContinuousLinearMap.isPositive_one, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eq_poly_in_U, PowerSeries.coeff_one_pow, Trivialization.linearMapAt_apply, LieModule.Weight.toLinear_neg, ContinuousLinearMap.isPositive_sum, ContinuousLinearEquiv.prodCongr_apply, StrongDual.polar_singleton, Module.Flat.iff_rTensor_preserves_injective_linearMap', DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, DFinsupp.lsum_apply_apply, RatFunc.algebraMap_monomial, LinearMap.rTensor_smul, MvPowerSeries.monomial_smul_const, PowerSeries.coeff_mul_X_pow, exteriorPower.ιMulti_family_span, HasStrictFDerivAt.inner, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, Representation.self_comp_norm, ModuleCat.hom_comp, ModuleCat.MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, HasMFDerivAt.comp, TensorProduct.toLinearMap_symm_rid, RingHomCompTriple.ids, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, Submodule.smul_top_le_comap_smul_top, TensorProduct.assoc_tensor', Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero, HasStrictDerivAt.hasStrictFDerivAt_equiv, MeasureTheory.ContinuousMap.inner_toLp, Submodule.toLocalized'_apply_coe, Rep.diagonalSuccIsoFree_hom_hom_single, IsTensorProduct.map_mul, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, ConvexOn.real_sSup_of_nat_affine_eq, IsSymmetricAlgebra.equiv_toAlgHom, Polynomial.taylor_pow, skewAdjoint.I_smul_neg_I, Derivation.linearEquiv_coe_comp, Module.Dual.instLieModule, Finsupp.linearCombination_eq_fintype_linearCombination_apply, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, ProbabilityTheory.isPositive_covarianceOperator, GradedTensorProduct.of_one, MeasureTheory.dominatedFinMeasAdditive_weightedSMul, LinearEquiv.lTensor_trans_rTensor, Polynomial.smul_X_eq_monomial, Matrix.compLinearEquiv_apply, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, Module.Projective.iff_split', TensorProduct.AlgebraTensorModule.coe_rTensor, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, SemimoduleCat.ofHom_apply, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, SpecialLinearGroup.baseChange_apply_coe, HasFDerivAt.cosh, exists_continuousLinearEquiv_fderiv_symm_eq, QuadraticMap.tensorDistrib_tmul, Subspace.map_dualCoannihilator, FormalMultilinearSeries.rightInv_coeff, Submodule.ker_liftQ, Complex.map_isometryOfOrthonormal, Polynomial.one_lt_rootMultiplicity_iff_isRoot, ModuleCat.hom_neg, Polynomial.monomial_sub, LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero, TemperedDistribution.fourierTransformInv_apply, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, MeasureTheory.AEStronglyMeasurable.convolution_integrand', Polynomial.coeff_monomial_succ, Module.Basis.dvd_coord_smul, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, AddEquiv.coe_toLinearEquiv, CharacterModule.homEquiv_apply_apply, LinearMap.isSymmetric_iff_inner_map_self_real, ExteriorAlgebra.GradedAlgebra.ι_apply, mfderiv_neg, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, PowerSeries.trunc_sub, Algebra.SubmersivePresentation.basisCotangent_apply, Rep.ihom_obj_ρ, Submodule.linearProjOfIsCompl_surjective, hasFDerivWithinAt_of_subsingleton, LinearMap.exists_extend_of_notMem, MvPowerSeries.hasSum_eval₂, LinearMap.BilinForm.Nondegenerate.toMatrix, ContinuousLinearMap.IsInvertible.self_apply_inverse, RootPairing.isCompl_corootSpan_ker_corootForm, ContinuousLinearMap.coe_smulRight, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, ContinuousLinearMap.isOpenMap_of_ne_zero, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, Finset.weightedVSubOfPoint_subtype_eq_filter, ContinuousLinearMap.integral_comp_comm, LinearMap.comp_ker_subtype, hasFDerivWithinAt_iff_tendsto, Submodule.IsCompl.projection_isIdempotentElem, LinearMap.dualCoannihilator_range_eq_ker_flip, Submodule.mulMap_range, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, PowerSeries.IsWeierstrassDivisorAt.seq_one, weightedVSub_mem_vectorSpan_pair, QuadraticMap.associated_flip, AlgEquiv.toLinearEquiv_injective, Algebra.trace_eq_of_equiv_equiv, LinearMap.BilinForm.congr_symm, Nat.Partition.coeff_genFun, TensorProduct.tensorQuotientEquiv_symm_apply_tmul_mk, Polynomial.degree_monomial, strongRankCondition_iff_succ, Matrix.l2_opNorm_def, PowerSeries.map_id, mem_finsuppAffineCoords_iff_linearCombination, Algebra.kerTensorProductMapIdToAlgHomEquiv_symm_apply, exteriorPower.oneEquiv_ιMulti, Rep.free_ext_iff, GradedTensorProduct.symm_of_of, ContinuousLinearMap.coe_toContinuousAffineMap, Representation.inv_self_apply, LinearMap.toMatrixAlgEquiv_mul, PresheafOfModules.toSheafify_app_apply, signedDist_apply_linear, LinearMap.detAux_id, EuclideanGeometry.Sphere.secondInter_map, Module.End.invtSubmodule.comp, LinearIsometryEquiv.refl_mul, OrthogonalFamily.linearIsometry_apply, MeasureTheory.OuterMeasure.comap_iSup, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, Module.End.iterate_succ, TensorProduct.lift_mk_compr₂, ContinuousLinearMapWOT.continuous_dual_apply, Algebra.Extension.Cotangent.map_mk, RootPairing.CoPolarizationIn_apply, PowerSeries.trunc_derivativeFun, LinearAlgebra.FreeProduct.lof_map_one, ContinuousLinearMap.iteratedFDeriv_comp_left, Submodule.LinearDisjoint.linearIndependent_left_of_flat, LinearMap.BilinForm.baseChange_tmul, Submodule.orthogonalProjection_eq_zero_iff, LinearIsometryEquiv.piLpCongrLeft_symm, ContinuousLinearMap.holderL_apply_apply, Module.Basis.repr_eq_iff', linearDepOn_iff', StrongDual.mem_polar_singleton, Algebra.Extension.CotangentSpace.map_comp, LinearMap.toLinearMap_toPerfPair, LeftInvariantDerivation.toFun_eq_coe, Complex.reCLM_enorm, AdicCompletion.eval_surjective, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, MeasureTheory.condExpInd_empty, RootPairing.coroot_reflectionPerm, Profinite.NobelingProof.GoodProducts.max_eq_eval, Polynomial.sylveserMap_comp_adjSylvester, LieAlgebra.IsKilling.ker_killingForm_eq_bot, MeasureTheory.condExpL1CLM_smul, Matrix.entryLinearMap_toAddMonoidHom, isConformalMap_const_smul, WithCStarModule.equivL_apply, RootPairing.corootSpan_dualAnnihilator_map_eq_iInf_ker_coroot', LinearMap.toSpanSingleton_injective, MeasureTheory.AEStronglyMeasurable.convolution_integrand, LinearMap.BilinForm.isSymm_iff_basis, Complex.norm_fderiv_le_div_of_mapsTo_ball, ConvexOn.comp_linearMap, norm_innerSL_le, TensorProduct.gradedComm_of_tmul_of, Representation.apply_eq_of_coe_eq, PowerBasis.constr_pow_aeval, VectorFourier.hasFDerivAt_fourierChar_smul, HasStrictFDerivAt.sub, ModuleCat.ofHom_apply, Module.End.ringEquivEndFinsupp_symm_apply_apply, HasStrictFDerivAt.csinh, Submodule.map_le_localized₀, ContinuousLinearMap.IsInvertible.injective, ContinuousLinearMap.comp_fst_add_comp_snd, fderiv_const_smul_of_field, Finsupp.supportedEquivFinsupp_symm_apply_coe_apply, HasFDerivWithinAt.cos, LinearMap.ker_single, ContinuousLinearMap.IsPositive.isSelfAdjoint, PowerSeries.coeff_subst_finite', Submodule.orthogonalProjection_starProjection_of_le, QuadraticMap.Isometry.coe_toLinearMap, Real.exists_extension_norm_eq, PowerSeries.HasSubst.monomial, ContinuousLinearMap.isInvertible_equiv_comp, RootPairing.root_coroot'_eq_pairing, CliffordAlgebra.EvenHom.contract_mid, continuousMultilinearCurryRightEquiv_apply, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, hasStrictFDerivAt_intCast, LinearMap.finrank_range_add_finrank_ker, LinearMap.baseChange_mul, Submodule.IsCompl.projection_apply_mem, LinearMap.det_toMatrix, exteriorPower.toTensorPower_apply_ιMulti, Submodule.coe_orthogonalProjection_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, Submodule.starProjection_coe_eq_isCompl_projection, IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv_coe, HasFDerivAt.neg, Algebra.traceForm_toMatrix_powerBasis, algebraMapCLM_toLinearMap, Matrix.minpoly_toLin, ModuleCat.kernelIsoKer_inv_kernel_ι, LieDerivation.coeFn_coe, basis_toMatrix_mul, PowerSeries.trunc_map, MeasureTheory.OuterMeasure.map_biInf_comap, Module.End.HasEigenvector.pow_apply, AffineMap.image_vsub_image, ContinuousLinearEquiv.smulLeft_apply_toLinearEquiv, ContDiffMapSupportedIn.structureMapLM_zero_apply, iSupIndep_range_lsingle, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, Polynomial.ker_modByMonicHom, LinearMap.BilinForm.isAdjointPairLeftAdjointOfNondegenerate, LinearMap.injective_iff_antilipschitz, CoalgHom.coe_toAddMonoidHom, SemimoduleCat.homLinearEquiv_symm_apply, ContinuousLinearEquiv.iteratedFDerivWithin_comp_left, SeparationQuotient.mkCLM_apply, AffineMap.deriv, Matrix.toLin'_toMatrix', ContinuousAlternatingMap.prodLIE_symm_apply, fderiv_comp_deriv_of_eq, LinearEquiv.funCongrLeft_comp, AlternatingMap.alternatizeUncurryFinLM_apply, LinearMap.compMultilinearMap_apply, LinearMap.det_toLin, RootPairing.coroot'_reflectionPerm, LinearMap.injective_or_eq_zero, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, LinearMap.det_eq_one_of_subsingleton, Module.Basis.det_map, ProbabilityTheory.covarianceBilinDual_of_not_memLp', ModuleCat.restrictScalarsCongr_inv_app, LieModule.shiftedGenWeightSpace.shift_symm_apply, CliffordAlgebra.ι_range_comap_reverse, LinearMap.posSemidef_toMatrix_iff, Representation.linHom.invariantsEquivRepHom_apply_hom, PowerSeries.coeff_coe_trunc_of_lt, Matrix.coe_ofLinearEquiv, Prod.counit_comp_inl, ContDiff.fderiv, Submodule.starProjection_apply_eq_zero_iff, Function.Exact.inl_snd, Algebra.Extension.exact_cotangentComplex_toKaehler, instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation, fderiv_list_prod', SchwartzMap.fourier_convolution, LinearMap.trace_mul_cycle', HasMFDerivWithinAt.prod, Polynomial.isMonicOfDegree_monomial_one, AnalyticOnNhd.eval_continuousLinearMap', Submodule.iInf_comap_proj, MonoidAlgebra.counit_single, fderivWithin_comp_smul, Orientation.rotation_symm_apply, ZMod.LFunction_dft, groupCohomology.H1InfRes_f, PowerSeries.trunc_zero', MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, Module.Basis.norm_repr_le_norm, Pretrivialization.coe_linearMapAt_of_mem, LinearIsometryEquiv.withLpUniqueProd_apply, QuadraticMap.Isometry.toLinearMap_comp, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Module.Flat.iff_rTensor_injective', LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero', LinearEquiv.smul_refl, HasMFDerivAt.mul', Module.Basis.coord_unitsSMul, ContinuousLinearMap.flipₗᵢ_symm, FractionalIdeal.trace_mem_dual_one, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, LinearMap.BilinForm.sum_apply, MvPolynomial.scalarRTensor_apply_tmul_apply, ModuleCat.imageIsoRange_hom_subtype_apply, skewAdjointPart_comp_subtype_skewAdjoint, Module.Basis.mem_span_repr_support, Derivation.compAEval_apply, Pi.basisFun_repr, PowerSeries.coeff_mul_prod_one_sub_of_lt_order, LinearIsometryEquiv.coe_mul, HasFDerivAt.star_star, LinearMap.comp_id_moduleCat, RootPairing.InvariantForm.apply_eq_or_of_apply_ne, Algebra.leftMulMatrix_eq_repr_mul, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, IsLocalizedModule.mk'_cancel, Algebra.trace_comp_trace, QuadraticMap.associated_isSymm, TopModuleCat.hom_neg, Polynomial.hasseDeriv_eq_zero_of_lt_natDegree, exists_continuousLinearEquiv_fderivWithin_symm_eq, continuous_skewAdjointPart, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply, Polynomial.ofFn_coeff_eq_zero_of_ge, TensorProduct.directLimitRight_symm_of_tmul, Module.End.mem_invtSubmodule_iff_map_le, FGModuleCat.Iso.conj_hom_eq_conj, Finsupp.finsuppProdLEquiv_symm_apply_apply, AdicCompletion.transitionMap_map_one, RootPairing.InvariantForm.two_mul_apply_root_root, HasGradientWithinAt.hasFDerivWithinAt, Module.Basis.toDual_eq_equivFun, MeasureTheory.OuterMeasure.restrict_iInf_restrict, FormalMultilinearSeries.rightInv_coeff_one, FourierTransform.fourierCLM_apply, ContinuousAffineMap.zero_contLinear, hasFDerivAt_exp, RootPairing.isOrthogonal_comm, Matrix.derivative_det_one_add_X_smul_aux, MvPolynomial.coeffsIn_le, TensorProduct.toMatrix_comm, Module.Basis.sum_repr, LinearMap.lTensor_add, Polynomial.trailingDegree_monomial, PiTensorProduct.map_pow, ContinuousLinearMap.range_coprod, Pi.orthonormalBasis_repr, fderiv_continuousAlternatingMap_apply_const_apply, MonomialOrder.C_mul_leadingCoeff_monomial_degree, RootPairing.coreflection_apply_coroot, ZMod.dft_const_smul, RootPairing.Equiv.coweightHom_toLinearMap, Polynomial.coe_taylorEquiv, Finsupp.lmapDomain_disjoint_ker, Polynomial.hasDerivWithinAt, ModuleCat.epi_iff_range_eq_top, Finsupp.supportedEquivFinsupp_apply_apply, Submodule.map_one, fwdDiff_aux.coe_fwdDiffₗ, SpecialLinearGroup.coe_div, TensorAlgebra.ι_eq_algebraMap_iff, ZSpan.mem_fundamentalDomain, ContinuousLinearMap.coe_id, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, InnerProductGeometry.IsConformalMap.preserves_angle, LinearMap.BilinMap.toQuadraticMap_neg, LinearMap.map_algebraMap_mul, dualTensorHomEquivOfBasis_apply, NormedSpace.Dual.coe_toWeakDual, ModuleCat.forget₂AddCommGroupIsEquivalence, LinearMap.polar_mem, LinearMap.toMatrix₂'_apply, ApproximatesLinearOn.lipschitzOnWith, Submodule.FG.rTensor.directLimit_apply', norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, LieDerivation.toFun_eq_coe, Module.End.genEigenspace_le_smul, IsAdjoinRootMonic.liftPolyₗ_apply, LinearMap.isAdjointPair_inner, ModuleCat.monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, IsLocalizedModule.mk'_eq_zero, LinearMap.IsPositive.adjoint_conj, Module.Flat.injective_characterModule_iff_rTensor_preserves_injective_linearMap, HahnSeries.toPowerSeries_symm_apply_coeff, ContinuousLinearMap.norm_holder_apply_apply_le, SemimoduleCat.hom_smul, Module.Basis.toMatrix_mulVec_repr, ClosedSubmodule.coe_comap, PowerSeries.trunc_derivative, LieModule.Cohomology.d₂₃_comp_d₁₂, TensorProduct.assoc_symm_tmul, LinearMap.isPositive_one, ContinuousLinearEquiv.prodAssoc_symm_apply, Subspace.quotDualCoannihilatorToDual_bijective, Algebra.Generators.comp_σ, IsSelfAdjoint.imaginaryPart, id_comp, LinearMap.prodMap_mul, groupHomology.single_mem_cycles₁_iff, LinearMap.ker_tensorProductMk, CliffordAlgebraQuaternion.toQuaternion_ι, AdicCompletion.sumEquivOfFintype_symm_apply, SpecialLinearGroup.congr_linearEquiv_trans, LinearMap.IsPerfectCompl.flip, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, groupHomology.d₂₁_single_ρ_add_single_inv_mul, Algebra.Generators.CotangentSpace.map_ofComp_surjective, bernsteinPolynomial.derivative_succ_aux, MvPowerSeries.monomial_smul_eq, LinearMap.ker_dualMap_eq_dualAnnihilator_range, LaurentSeries.coeff_coe_powerSeries, fderivWithin_sum, Ideal.toCotangent_surjective, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, PiTensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse, Orientation.rotation_oangle_eq_iff_norm_eq, Matrix.kroneckerStarAlgEquiv_apply, lTensor_mkQ, AlgHom.equalizer_toSubmodule, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, BoundedContinuousFunction.range_toLp, CategoryTheory.InducedCategory.homLinearEquiv_symm_apply_hom, Submodule.norm_subtypeL_le, LinearEquiv.trans_dualMap_symm_flip, LinearMap.lTensor_inj_iff_rTensor_inj, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, TensorProduct.comm_symm_tmul, fderivWithin_pow_ring, fderiv_const_smul, LinearMap.BilinForm.separatingLeft_toMatrix_iff, IsSemisimpleModule.range, hasFDerivAtFilter_pi', LinearMap.trace_comp_comm', ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap, measurable_fderiv_apply_const_with_param, Polynomial.derivative_X_sub_C, CharacterModule.dual_apply, MvPolynomial.finsum_weightedHomogeneousComponent, TensorProduct.sum_tmul_basis_left_injective, fderivWithin_comp, MvPowerSeries.order_monomial_of_ne_zero, LinearMap.quotientInfEquivSupQuotient_symm_apply_right, LinearEquiv.toModuleIso_hom, AlgEquiv.toLinearEquiv_trans, exteriorPower.zeroEquiv_symm_apply, LinearIsometryEquiv.symm_lTensor, WithLp.fstL_apply, ZMod.dft_smul_const, ContinuousLinearMap.coe_ofIsClosedGraph, finsetBasisOfLinearIndependentOfCardEqFinrank_repr_apply, Module.torsion_by_prime_power_decomposition, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, Module.AEval.mem_mapSubmodule_apply, NumberField.mixedEmbedding.norm_negAt, DoubleCentralizer.toProdHom_apply, LinearMap.GeneralLinearGroup.coeFn_generalLinearEquiv, SpecialLinearGroup.toLinearEquiv_injective, LinearMap.comm_comp_rTensor_comp_comm_eq, TensorProduct.equivFinsuppOfBasisRight_symm_apply, DoubleCentralizer.mul_snd, QuadraticForm.associated_baseChange, HasFDerivWithinAt.comp_hasFDerivAt, Real.volume_preserving_transvectionStruct, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, ModuleCat.hom_injective, MeasureTheory.L1.integral_eq, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, continuousOn_clm_apply, HahnEmbedding.Partial.apply_of_mem_stratum, KaehlerDifferential.map_liftBaseChange_smul, ContinuousAlternatingMap.piLinearEquiv_apply, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, LinearMap.range_smul, LinearEquiv.self_trans_symm, ModularFormClass.hasSum_qExpansion, MeasureTheory.OuterMeasure.map_ofFunction_le, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Matrix.toLpLinAlgEquiv_symm_apply, RootPairing.Equiv.coweightHom_apply, HasFDerivAt.fun_mul', MvPowerSeries.IsHomogeneous.coeff_eq_zero, Matrix.toBilin'_toMatrix', ContinuousMultilinearMap.toMultilinearMapLinear_apply, qExpansion_coeff_isBigO_of_norm_isBigO, Module.Basis.algebraMapCoeffs_repr, Rep.linearization_map_hom_single, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, AdicCompletion.eval_apply, LinearMap.trace_baseChange, Submodule.sndEquiv_apply, HasStrictFDerivAt.continuousMultilinearMap_apply, LinearEquiv.multilinearMapCongrLeft_apply, LinearMap.lTensor_tensor, MeasureTheory.weightedSMul_zero_measure, CliffordAlgebra.contractLeftAux_apply_apply, LieEquiv.ofBijective_invFun, LinearPMap.adjointAux_inner, HasStrictFDerivAt.mul_const, IsGroupLikeElem.mul_antipode_cancel, CategoryTheory.preadditiveCoyoneda_obj, PowerSeries.coeff_one_mul, Submodule.sndEquiv_symm_apply_coe, Algebra.idealMap_apply_coe, AlternatingMap.domLCongr_symm, Matrix.toLinearMapₛₗ₂_toMatrix₂, Submodule.comapSubtypeEquivOfLe_symm_apply, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, LinearMap.BilinForm.IsAlt.smul, LaurentPolynomial.comul_C_mul_T_self, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, ContinuousLinearMap.IsInvertible.inverse_comp_apply_of_left, ContinuousLinearMap.opNNNorm_mul_apply, fderivInnerCLM_apply, Module.Basis.coord_apply, CliffordAlgebra.contractLeft_one, eventually_norm_mfderiv_extChartAt_lt, le_comap_range_rTensor, ContinuousMultilinearMap.curryFinFinset_apply, groupHomology.eq_d₁₀_comp_inv_apply, MultilinearMap.domCoprodDep'_apply, LinearMap.IsPerfPair.flip, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, TensorProduct.map_id, Rep.ihom_obj_V_carrier, LinearMap.toMatrix'_mulVec, RootPairing.EmbeddedG2.threeShortAddLongRoot_longRoot, TensorProduct.AlgebraTensorModule.rightComm_symm, LinearEquiv.toFGModuleCatIso_inv, RootPairing.ker_corootForm_eq_dualAnnihilator, MvPowerSeries.coeff_eq_zero_of_lt_lexOrder, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, Submodule.le_traceDual_iff_map_le_one, ModuleCat.semilinearMapAddEquiv_apply, Subspace.dualAnnihilator_inf_eq, VertexOperator.coeff_eq_ncoeff, LinearMap.lsum_symm_apply, Module.Basis.mem_span_iff_repr_mem, PowerSeries.monomial_zero_eq_C_apply, ModuleCat.CoextendScalars.map'_hom_apply_apply, Module.Basis.SmithNormalForm.repr_eq_zero_of_notMem_range, IsBaseChange.toDualBaseChange_tmul, IsLocalizedModule.map_LocalizedModules, Matrix.SeparatingLeft.toLinearMap₂, Submodule.coe_subtypeL, Module.Relations.Solution.IsPresentation.ker_π, KaehlerDifferential.quotKerTotalEquiv_apply, Coalgebra.comm_comp_comul, Rep.coindIso_hom_hom_hom, Polynomial.card_roots_toFinset_le_derivative, ULift.moduleEquiv_apply, MvPowerSeries.coeff_mul_of_add_lexOrder, Representation.mem_invtSubmodule, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, VectorBundleCore.coordChange_comp, AffineMap.linear_eqOn_vectorSpan, KaehlerDifferential.kerTotal_map', ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, SchwartzMap.denseRange_toLpCLM, TensorProduct.instDirectedSystemCoeLinearMapIdLTensor, SchwartzMap.toZeroAtInftyCLM_apply, ContinuousLinearMap.coe_prod, hasEigenvector_toLin_diagonal, Rep.leftRegularTensorTrivialIsoFree_hom_hom, LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero, mfderiv_comp_mfderivWithin_of_eq, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, Module.Basis.coord_equivFun_symm, mdifferentiableWithinAt_hom_bundle, Module.rank_linearMap_self, Polynomial.iterate_derivative_sum, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, RootPairing.reflection_reflectionPerm, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, quotient_prod_linearEquiv, isConformalMap_iff_is_complex_or_conj_linear, DirectSum.toLieAlgebra_apply, ZMod.dft_def, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, SemimoduleCat.hom_sum, CStarMatrix.mapₙₐ_apply, groupHomology.H0π_comp_H0Iso_hom_apply, ContinuousLinearMap.apply_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, Rep.barComplex.d_single, dotProduct_toMatrix₂_mulVec, Algebra.Generators.CotangentSpace.fst_compEquiv, IsTensorProduct.map_comp, ConvexCone.comap_comap, hasFDerivAt_pi', Matrix.entryLinearMap_eq_comp, ModuleCat.freeDesc_apply, Algebra.Extension.CotangentSpace.map_comp_apply, LinearMap.compAlternatingMapₗ_apply, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, Module.End.exists_isNilpotent_isSemisimple, MvPolynomial.linearMap_ext_iff, LinearMap.associated_det_comp_equiv, Ideal.map_includeLeft_eq, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, LieModule.range_traceForm_le_span_weight, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, RatFunc.laurentAux_ofFractionRing_mk, LinearMap.graph_eq_ker_coprod, FDRep.hom_action_ρ, Rep.mono_iff_injective, MeasureTheory.OuterMeasure.map_sup, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, Submodule.mem_graph_toLinearPMap, Profinite.NobelingProof.Products.eval_πs_image, LinearMap.le_rank_iff_exists_linearIndependent_finset, HVertexOperator.comp_apply, TensorProduct.gradedComm_gradedMul, IsSymmSndFDerivWithinAt.eq, CurveIntegrable.add, PiTensorProduct.mapLMultilinear_opNorm, fderivWithin_restrictScalars_comp, DirectSum.toAddMonoidHom_lmap, IsLocalExtr.hasFDerivAt_eq_zero, Matrix.diagonal_comp_single, LinearMap.canLiftContinuousLinearMap, SemimoduleCat.comp_apply, LinearMap.inr_map_mul, LinearIsometryEquiv.differentiableOn, RCLike.geometric_hahn_banach_closed_compact, FDRep.dualTensorIsoLinHom_hom_hom, ModuleCat.homEquiv_extendScalarsId, ContinuousLinearMap.instModuleFinite, fderivWithin_fun_sum, LinearMap.rank_finset_sum_le, MeasureTheory.charFunDual_eq_prod_iff', ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, inner_gradient_right, Algebra.Generators.H1Cotangent.equiv_apply, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, ModuleCat.ExtendScalars.hom_ext_iff, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, TensorPower.toTensorAlgebra_tprod, MvPolynomial.monomial_single_add, InnerProductSpace.laplacianWithin_CLE_comp_left, LinearMap.IsPerfectCompl.isCompl_left, Real.fourierIntegral_iteratedFDeriv, Algebra.Extension.CotangentSpace.map_comp_cotangentComplex, LinearMap.toMatrixAlgEquiv_transpose_apply, LinearEquiv.rTensor_tmul, groupCohomology.coe_mapCocycles₂, Orthonormal.equiv_apply, Submodule.Quotient.restrictScalarsEquiv_mk, CoalgEquiv.right_inv, Submodule.orthogonalProjection_norm_le, HasFDerivAt.mul', DoubleCentralizer.intCast_toProd, Module.Basis.repr_self, TensorProduct.rightComm_def, LinearMap.toSpanSingleton_isIdempotentElem_iff, MultilinearMap.compLinearMapₗ_apply, LinearMap.quotientInfEquivSupQuotient_surjective, AdicCompletion.piEquivFin_apply, Polynomial.coeff_coe, Orientation.rightAngleRotation_neg_orientation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, Orientation.rotationAux_apply, MvPolynomial.monomial_one_mul_cancel_right_iff, Fin.consEquivL_symm_apply, Polynomial.sumIDeriv_apply_of_lt, Submodule.map_dualAnnihilator_linearEquiv_flip_symm, fderiv_single, LinearMap.separatingLeft_of_det_ne_zero, Polynomial.erase_monomial, IsBaseChange.lift_eq, LinearPMap.graph_map_snd_eq_range, NormedSpace.Dual.toWeakDual_inj, MvPowerSeries.coeff_eq_zero_of_lt_weightedOrder, LinearMap.const_apply, IsLocalizedModule.lift_iso, SpecialLinearGroup.coe_dualMap, TensorProduct.finsuppRight_apply_tmul_apply, Shrink.linearEquiv_apply, TensorProduct.directSumRight_symm_lof_tmul, ModuleCat.toKernelSubobject_arrow, Polynomial.homogenizeLM_apply, LinearIsometryEquiv.withLpUniqueProd_symm_apply, Submodule.orthogonalProjection_orthogonal, LinearMap.isNilpotent_mulLeft_iff, Polynomial.degree_derivative_le, Module.Basis.SmithNormalForm.coord_apply_embedding_eq_smul_coord, LinearMap.surjective_comp_subtype_of_isComplemented, CategoryTheory.Iso.toLinearMap_toLinearEquiv, MvPolynomial.degreeOf_monomial_eq, Finsupp.linearCombination_zero, IsBaseChange.endHom_comp, Module.End.eigenspace_aeval_polynomial_degree_1, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, hasFDerivAt_list_prod_attach', Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, Ideal.comap_id, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, Polynomial.derivative_one, Polynomial.taylorLinearEquiv_apply_coe, LinearEquiv.symm_prodComm, LinearEquiv.lTensor_trans, TemperedDistribution.fourierTransformInvCLM_apply, MeasureTheory.norm_condExpL2_le_one, ContinuousLinearEquiv.mdifferentiableAt, PowerSeries.natDegree_trunc_lt, HasCompactSupport.convolution_integrand_bound_right, LinearMap.comp_compMultilinearMap, MeasureTheory.OuterMeasure.comap_ofFunction, FinitePresentation.id, LinearMap.traceAux_def, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, LinearMap.surjective_of_ne_zero, Condensed.instAB4CondensedMod, MultilinearMap.fromDFinsuppEquiv_symm_apply, CategoryTheory.Linear.rightComp_apply, Module.Flat.iff_lTensor_injective', fderivWithin_mem_iff, SkewPolynomial.smul_monomial, groupCohomology.H1π_eq_iff, ContinuousLinearEquiv.piCongrRight_symm_apply, IsLocalization.map_id_mk', NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, Algebra.leftMulMatrix_apply, Complex.imLm_coe, PiTensorProduct.congr_tprod, Polynomial.Chebyshev.derivative_T_eval_one, DifferentiableAt.lineDeriv_eq_fderiv, Module.DirectLimit.hom_ext_iff, OrthonormalBasis.repr_reindex, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, MeasureTheory.condExpL2_comp_continuousLinearMap, Polynomial.taylor_C, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, AdicCompletion.ofLinearEquiv_symm_of, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, Subspace.isCompl_dualAnnihilator, LinearMap.BilinForm.toMatrix'_compRight, isBoundedBilinearMap_smulRight, TensorProduct.finsuppRight_apply_tmul, MultilinearMap.compLinearMap_assoc, inCoordinates_tangent_bundle_core_model_space, LocalizedModule.mkLinearMap_apply, LinearEquiv.ofTop_apply, LinearIsometryEquiv.differentiableWithinAt, Polynomial.derivative_apply, Submodule.mulMap_comp_rTensor, PowerSeries.trunc_X, Module.subsingletonEquiv_apply, Algebra.Extension.Cotangent.ker_mk, linearEquivIsoModuleIsoₛ_inv, HopfAlgebra.antipode_one, LinearMap.toAddMonoidHom_mulRight, Algebra.normalizedTrace_self_apply, AnalyticOnNhd.eval_continuousLinearMap, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, HasDerivWithinAt.comp_hasFDerivAt_of_eq, ContinuousLinearMap.adjoint_innerSL_apply, Polynomial.degreeLT.basis_repr, IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_end, HasFDerivAt.rpow, ZLattice.coe_comap, LieModuleEquiv.right_inv, Submodule.IsOrtho.comap, hasFDerivAt_iff_isLittleO_nhds_zero, Submodule.map_div, Module.Basis.eval_ker, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, LinearIsometry.submoduleMap_apply_coe, OrthogonalFamily.inner_right_fintype, nonempty_linearEquiv_of_rank_eq, AffineMap.vectorSpan_image_eq_submodule_map, Pi.counit_single, ContDiffMapSupportedIn.structureMapLM_apply, ExteriorAlgebra.liftAlternating_ι, ContinuousLinearMap.circleAverage_comp_comm, TensorProduct.AlgebraTensorModule.lcurry_apply, trace_adjoinSimpleGen, TensorProduct.comm_trans_rid, ContinuousLinearMap.coprodEquivL_symm_apply, Polynomial.monomial_comp, VectorPrebundle.contMDiffCoordChange_apply, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, AlternatingMap.compLinearEquiv_eq_zero_iff, Matrix.SeparatingRight.toBilin, TwoSidedIdeal.subtype_apply, LieModule.coe_maxTrivLinearMapEquivLieModuleHom, fderivWithin_fun_mul, Module.Basis.repr_reindex_apply, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Module.End.algebraMap_isUnit_inv_apply_eq_iff, EuclideanGeometry.reflection_apply, continuousOn_coordChange, HasCompactSupport.convolution_integrand_bound_right_of_subset, LinearIsometryEquiv.comp_fderiv', LinearPMap.adjoint_apply_of_dense, ContinuousLinearEquiv.prodComm_toLinearEquiv, RootPairing.range_polarizationIn_le_span_coroot, CliffordAlgebra.contractLeftAux_contractLeftAux, LinearEquiv.coe_toLinearMap_one, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, DoubleCentralizer.smul_snd, lipschitzGroup.conjAct_smul_range_ι, DirectSum.lmap_eq_iff, groupHomology.H0π_comp_map_apply, MvPowerSeries.monomial_eq', Matrix.transposeLinearEquiv_apply, Subspace.comap_dualAnnihilator_dualAnnihilator, Complex.det_conjLIE, ContinuousLinearEquiv.coe_funUnique_symm, LinearMap.toMatrix_apply, RootPairing.ker_polarization_eq_ker_rootForm, ContinuousLinearMap.integral_id_map, PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, linearDepOn_iff'ₛ, PiTensorProduct.map_range_eq_span_tprod, BoundedContinuousFunction.toLp_denseRange, AlgHom.coe_toAddMonoidHom, SemimoduleCat.forget₂_obj, LinearMap.intrinsicStar_eq_comp, LinearMap.baseChange_add, MeasureTheory.condExpL2_const_inner, RootPairing.mapsTo_coreflection_coroot, ContinuousLinearMap.HasRightInverse.surjective, NumberField.house.basis_repr_norm_le_const_mul_house, LinearPMap.toFun_eq_coe, LinearMap.IsSymmetric.intCast, Polynomial.ofFn_natDegree_lt, MvPolynomial.weightedHomogeneousComponent_apply, CliffordAlgebra.EquivEven.involute_v, Module.erange_coe, Submodule.map_subtype_le, TensorProduct.toMatrix_map, Matrix.toLinAlgEquiv_toMatrixAlgEquiv, IsCoercive.isClosed_range, Matrix.rank_vecMulVec, RCLike.realLinearIsometryEquiv_apply, LinearMap.continuous_uncurry_of_isContPerfPair, TemperedDistribution.laplacianCLM_apply, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, AdicCompletion.map_of, ContinuousLinearMap.toWOT_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, contMDiffWithinAt_hom_bundle, PolynomialModule.hom_ext_iff, ContinuousLinearMap.one_def, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, PowerSeries.coeff_X_pow_mul, ContinuousLinearEquiv.piCongrRight_apply, LinearMap.finiteDimensional_range, LinearEquiv.lTensor_mul, mem_contMDiffFiberwiseLinear_iff, RootPairing.polarization_apply_eq_zero_iff, curveIntegralFun_def, Submodule.le_dualCoannihilator_dualAnnihilator, MvPolynomial.range_evalᵢ, Submodule.coe_prodEquivOfClosedCompl, IsLocalizedModule.mk'_eq_iff, ContinuousLinearMap.ext_ring_iff, Polynomial.monomial_mul_monomial, TensorProduct.exists_of_fg, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, ContinuousLinearMap.intervalIntegral_comp_comm, PowerSeries.coeff_zero_mul_X, Submodule.comap_liftQ, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_longRoot, groupHomology.π_comp_H2Iso_inv_apply, TannakaDuality.FiniteGroup.rightRegular_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, PositiveLinearMap.toLinearMap_nsmul, Orientation.areaForm_rightAngleRotation_left, MvPowerSeries.coeff_mul_C, HasFDerivAt.smul, LinearMap.BilinForm.restrict_apply, ContinuousLinearMap.contMDiffAt, IsSymmetricAlgebra.lift_comp_linearMap, isOpen_setOf_nat_le_rank, HasFDerivWithinAt.sin, Algebra.H1Cotangent.exact_δ_mapBaseChange, Matrix.toLinAlgEquiv_symm, DirectSum.range_coeLinearMap, LaurentPolynomial.antipode_C_mul_T, SchwartzMap.smulLeftCLM_smul, DFinsupp.lhom_ext'_iff, CurveIntegrable.neg, LinearMap.rTensor_mul, LinearMap.map_finsupp_linearCombination, AlternatingMap.toMultilinearMapLM_apply, Module.FinitePresentation.exists_basis_localizedModule_powers, DoubleCentralizer.coe_snd, LinearIsometry.angle_map, LinearMap.snd_apply, PolynomialModule.map_single, HasStrictFDerivAt.exp, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, NumberField.mixedEmbedding.disjoint_negAt_plusPart, Algebra.SubmersivePresentation.cotangentEquiv_apply, IsSimpleModule.ker_toSpanSingleton_isMaximal, MeasureTheory.integral_convolution, LinearMap.toMatrix_id_eq_basis_toMatrix, contractLeft_assoc_coevaluation', Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, DirectSum.lequivProdDirectSum_symm_apply, Finsupp.range_restrictDom, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, RCLike.imCLM_apply, LinearMap.toMatrixAlgEquiv_transpose_apply', TensorProduct.dualDistribEquivOfBasis_apply_apply, RootPairing.root_reflectionPerm, fderiv_sin, Polynomial.mkDerivation_apply, LinearMap.baseChangeHom_apply, Module.Relations.Solution.π_single, ContinuousLinearEquiv.piFinTwo_symm_apply, Finsupp.lmapDomain_apply, Polynomial.coeff_monomial_mul, linearIndepOn_iff_linearCombinationOnₛ, LinearMap.toMatrixRight'_comp, OrthonormalBasis.tensorProduct_repr_tmul_apply, Trivialization.coordChangeL_apply', ContinuousLinearEquiv.coe_refl', Derivation.evalAt_apply, ContinuousLinearEquiv.ofSubmodule'_toContinuousLinearMap, SemimoduleCat.forget₂_map, PositiveLinearMap.preGNS_norm_sq, LinearMap.rank_range_add_rank_ker, ContinuousMultilinearMap.norm_curryMid, Matrix.kroneckerStarAlgEquiv_symm_apply, ConvexOn.univ_sSup_of_nat_affine_eq, CommSemiring.comul_apply, Algebra.Generators.H1Cotangent.δ_map, Module.dualProdDualEquivDual_symm_apply, AlternatingMap.curryLeft_add, BialgHom.map_one', ModuleCat.restrictScalarsComp'App_inv_apply, ContinuousLinearEquiv.comp_right_differentiable_iff, Perfection.frobenius_pthRoot, LinearMap.uncurryLeft_apply, InnerProductGeometry.ConformalAt.preserves_angle, LinearMap.trace_map, AdicCompletion.of_apply, TensorProduct.assocIsometry_symm_apply, Submodule.starProjection_tendsto_closure_iSup, hasFDerivAt_exp_of_mem_ball, ContinuousLinearMap.comp_id, domain_mvt, CliffordAlgebra.reverse_ι, norm_iteratedFDeriv_fderiv, MeasureTheory.Lp.toTemperedDistribution_smul_eq, Fin.consLinearEquiv_symm_apply, CliffordAlgebra.reverse_involutive, Submodule.reflection_mem_subspace_orthogonalComplement_eq_neg, NormedSpace.dual_def, LinearMap.IsSymmetric.add, FDRep.endRingEquiv_comp_ρ, HasFDerivAtFilter.hasDerivAtFilter, Finsupp.domLCongr_single, Module.FinitePresentation.isLocalizedModule_map, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, TensorProduct.inner_map_map, RCLike.geometric_hahn_banach_open_open, SpecialLinearGroup.toLinearEquiv_to_linearMap, ContinuousAlternatingMap.ofSubsingleton_symm_apply_apply, Submodule.comap_unop_mul, Submodule.disjoint_iff_comap_eq_bot, LinearMap.lTensor_tmul, groupHomology.mem_cycles₁_iff, Module.instFinitePolynomialAEval', LinearMap.lTensor_def, const_smul_mfderiv, fderiv_norm_sq, LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm, LaurentSeries.hasseDeriv_single, LinearMap.applyₗ_apply_apply, LinearMap.dualProd.toQuadraticForm, 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ContinuousLinearMapWOT.ext_inner_iff, Module.compHom.toLinearEquiv_apply, groupHomology.chainsMap_f, ContinuousLinearMap.coeFn_ofIsClosedGraph, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd', SheafOfModules.unitHomEquiv_apply_coe, Submodule.comap_subtype_le_iff, Continuous.fderiv_one, PowerSeries.order_eq_nat, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, CategoryTheory.preadditiveYonedaObj_map, IsTensorProduct.map_eq, PolynomialModule.eval_single, IsLocalMinOn.fderivWithin_eq_zero, RCLike.geometric_hahn_banach_open_point, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, Polynomial.aeval_sumIDeriv_of_pos, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, MvPolynomial.monomial_mul_modMonomial, DirectSum.gMulLHom_apply_apply, MvPolynomial.constantCoeff_comp_algebraMap, LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly, Submodule.mem_iff_norm_starProjection, SpecialLinearGroup.toLinearEquiv_apply, 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unitary.linearIsometryEquiv_coe_apply, AdicCompletion.ofAlgEquiv_symm_of, Derivation.apply_aeval_eq, LieSubalgebra.ad_comp_incl_eq, Trivialization.coordChangeL_prod, PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_mem, PrimeSpectrum.BasicConstructibleSetData.map_id', PowerSeries.trunc_derivative', ContinuousLinearMap.IsInvertible.inverse_apply_eq, Ideal.mulQuot_injective, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, kroneckerLinearEquiv_tmul, ConvexCone.mem_comap, LieAlgebra.killingForm_of_equiv_apply, AlgEquiv.toLinearEquiv_apply, MvPolynomial.rTensorAlgHom_apply_eq, mfderivWithin_comp_of_eq
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instFunLike 📖 | CompOp | 4788 mathmath: IsLocalization.algebraMap_apply_eq_map_map_submonoid, WeierstrassCurve.Jacobian.map_addX, Polynomial.mul_div_eq_iff_isRoot, DFinsupp.coprodMap_apply, Complex.norm_conj, MvPowerSeries.coeff_zero_eq_constantCoeff_apply, MvPolynomial.funext_iff, MvPolynomial.eval_indicator_apply_eq_one, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, IsAlgebraic.exists_nonzero_dvd, IsLocalization.localization_localization_isLocalization_of_has_all_units, PresheafOfModules.Monoidal.tensorObj_obj, CommSemiRingCat.forget_obj, MvPowerSeries.hasSubst_def, WeierstrassCurve.Projective.map_dblZ, Polynomial.not_ker_le_map_C_of_surjective_of_quasiFiniteAt, KaehlerDifferential.kerCotangentToTensor_toCotangent, RCLike.conj_re, Polynomial.isUnit_C_add_X_mul_iff, PrimeSpectrum.closure_range_comap, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Polynomial.isMonicOfDegree_X_add_one, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, Polynomial.natDegree_mul_leadingCoeff_inv, minpoly_sub_algebraMap_splits, CliffordAlgebra.contractRight_algebraMap_mul, Complex.log_conj_eq_ite, smoothSheafCommRing.ι_forgetStalk_inv, Orientation.kahler_map_complex, Ideal.Quotient.exists_algHom_fixedPoint_quotient_under, IsDedekindDomain.differentIdeal_dvd_map_differentIdeal, Polynomial.ker_mapRingHom, NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, AlgebraicGeometry.SurjectiveOnStalks.eq_stalkwise, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst_assoc, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, IsLocalization.map_radical, Language.map_kstar, ValuationRing.mem_integer_iff, RootPairing.RootPositiveForm.algebraMap_rootLength, LaurentPolynomial.degree_C_mul_T_ite, MeasureTheory.lpNorm_conj, RingTheory.Sequence.isWeaklyRegular_map_algebraMap_iff, WeierstrassCurve.Projective.map_neg, Polynomial.X_pow_mul_assoc_C, CommRingCat.forget₂Ring_preservesLimitsOfSize, WittVector.ghostMap.bijective_of_invertible, Polynomial.separable_X_add_C, Polynomial.map_dickson, Polynomial.mahlerMeasure_const, Algebra.RingHom.adjoin_algebraMap_apply, LinearMap.BilinForm.dualSubmoduleParing_spec, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, CommRingCat.KaehlerDifferential.map_d, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, MvPolynomial.coe_C, ker_evalRingHom, Algebra.idealMap_eq_ofEq_comp_toLocalized₀, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, MvPowerSeries.coeff_zero_eq_constantCoeff, CliffordAlgebra.contractRight_algebraMap, ExteriorAlgebra.isLocalHom_algebraMap, coe_iterateFrobenius_mul, AddMonoidAlgebra.lift_apply', ModularForm.smul_slash, WeierstrassCurve.map_a₂, Polynomial.eq_C_of_derivative_eq_zero, MvPolynomial.map_bind₁, jacobiTheta₂_conj, GaussianInt.toComplex_mul, Orthonormal.inner_left_finsupp, Valuation.IsTrivialOn.valuation_algebraMap_le_one, Polynomial.derivative_X_sq, cfc_le_algebraMap_iff, Polynomial.coe_normUnit_of_ne_zero, PowerSeries.constantCoeff_expand, Subsemiring.coe_subtype, Polynomial.separable_X_pow_sub_C_unit, CommSemiRingCat.hom_inv_apply, Polynomial.splits_iff_exists_multiset, CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd, IsIntegrallyClosed.exists_algebraMap_eq_of_isIntegral_pow, ValuationSubring.mem_comap, Algebra.norm_algebraMap_of_basis, derivationToSquareZeroOfLift_apply, Complex.sinh_conj, Polynomial.toLaurent_eq_zero, CategoryTheory.Functor.mapExtLinearMap_toAddMonoidHom, IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, MvPolynomial.map_mapRange_eq_iff, IsLocalRing.ResidueField.algebraMap_residue, exists_isIdempotentElem_eq_of_ker_isNilpotent, RootPairing.linearIndepOn_root_baseOf', taylorWithin_succ, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, PolyEquivTensor.toFunBilinear_apply_eq_sum, Valuation.FiniteField.algebraMap_le_one, Polynomial.algEquivCMulXAddC_apply, Polynomial.mul_divByMonic_eq_iff_isRoot, IsUltrametricDist.algNormOfAlgEquiv_extends, Valuation.FiniteField.algebraMap_eq_one, CommRingCat.instFullRingCatForget₂RingHomCarrierCarrier, galRestrict_symm_algebraMap_apply, NumberField.InfinitePlace.norm_embedding_of_isReal, Polynomial.monic_X_sub_C, PadicInt.lift_sub_val_mem_span, MvPolynomial.eval₂Hom_X, RatFunc.num_div, Algebra.algebraMap_self_apply, Subring.coe_subtype, MonomialOrder.monic_X_sub_C, MvPolynomial.hom_C, RingCat.FilteredColimits.instPreservesFilteredColimitsAddCommGrpCatForget₂RingHomCarrierAddMonoidHomCarrier, Valuation.HasExtension.val_map_le_iff, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, quasispectrum.algebraMap_mem, CommRingCat.forget_preservesLimitsOfSize, IntermediateField.LinearDisjoint.linearIndependent_right', IsAdicComplete.StrictMono.mk_liftRingHom, PowerSeries.constantCoeff_subst, ExteriorAlgebra.ι_eq_algebraMap_iff, Matrix.scalar_inj, Submodule.algebraMap_mem, Polynomial.homogenize_map, CommRingCat.forgetReflectIsos, BoolRing.hasForgetToBoolAlg_forget₂_obj_coe, Subring.coe_comap, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, AlgebraicGeometry.RingedSpace.basicOpen_res, Localization.algebraMap_injective_of_span_eq_top, Complex.lim_conj, PowerSeries.coeff_mul_C, LocalSubring.range_toSubring, Polynomial.algebraMap_pi_eq_aeval, NumberField.integralBasis_apply, IsLocalization.Away.algebraMap_isUnit_iff, Polynomial.ker_evalRingHom, StandardEtalePair.inv_aeval_X_g, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, Polynomial.eval₂_intCastRingHom_X, IsIntegrallyClosedIn.isIntegral_iff, ValuationSubring.integralClosure_algebraMap_injective, Ideal.mem_span_iff_exists_isHomogeneous, IsPurelyInseparable.minpoly_eq', CommRingCat.closure_range_union_range_eq_top_of_isPushout, IntermediateField.algebraMap_mem, Matrix.GeneralLinearGroup.map_det, LaurentPolynomial.mk'_mul_T, Polynomial.expand_eq_sum, IsLocalization.AtPrime.liesOver_map_of_liesOver, Polynomial.root_X_sub_C, PowerSeries.heval_C, Algebra.Norm.Transitivity.polyToMatrix_cornerAddX, RingHomInvPair.comp_apply_eq₂, Matrix.scalar_comm, frobeniusEquiv_apply, NumberField.mixedEmbedding.convexBodyLT'_mem, Complex.kahler, X_pow_sub_C_splits_of_isPrimitiveRoot, Complex.areaForm, Complex.re_eq_add_conj, Differential.implicitDeriv_C, CliffordAlgebraComplex.ofComplex_conj, AlgHom.coe_toRingHom, Pi.algebraMap_apply, WittVector.coeff_truncate, GaussianInt.intCast_im, WeierstrassCurve.VariableChange.map_s, IntermediateField.algHomEquivAlgHomOfSplits_apply_apply, IsIntegralElem.map, WeierstrassCurve.Affine.CoordinateRing.smul, Polynomial.resultant_X_add_C_right, Polynomial.pow_rootMultiplicity_dvd, IsLocalization.minimalPrimes_map, MulSemiringAction.toRingHom_apply, AlgebraicGeometry.surjectiveOnStalks_iff, AdjoinRoot.minpoly_root, PowerSeries.coeff_rescale, X_pow_sub_C_eq_prod, PositiveLinearMap.apply_le_of_isSelfAdjoint, WeierstrassCurve.Projective.eval_polynomial, IntermediateField.coe_algebraMap_over_bot, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_apply_mk, Polynomial.rootMultiplicity_eq_rootMultiplicity, RingTheory.Sequence.isWeaklyRegular_cons_iff', NumberField.isCoprime_differentIdeal_of_isCoprime_discr, WittVector.mapFun.zero, WithAbs.algebraMap_left_apply, RootPairing.Base.algebraMap_cartanMatrixIn_apply, MvPolynomial.aeval_algebraMap_eq_zero_iff, NumberField.FinitePlace.mk_apply, instRingHomClass, BoundedContinuousFunction.algebraMap_apply, MonoidAlgebra.isLocalHom_algebraMap, coe_frobeniusEquiv_symm_comp_coe_frobenius, spectrumRestricts_iff, GaussianInt.toComplex_def', CoalgHom.coe_addMonoidHom_injective, Algebra.adjoin_algebraMap_image_union_eq_adjoin_adjoin, HahnSeries.C_injective, Ideal.map_ofList, IsLocalization.mk'_spec_mk, IsLocalization.AtPrime.coe_orderIsoOfPrime_apply_coe, differentIdeal_eq_differentIdeal_mul_differentIdeal, RingCon.ker_apply, smoothSheafCommRing.nonunits_stalk, star_apply, FractionalIdeal.coeIdealHom_apply, qExpansionRingHom_apply, AlgHom.ker_coe, Polynomial.derivative_C_mul, Algebra.algebraMap_ofSubsemiring_apply, Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval, NumberField.canonicalEmbedding.latticeBasis_apply, Polynomial.support_trinomial, WittVector.constantCoeff_surjective, IsLocalRing.ker_residue, PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_X_mem, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_symm_mk, PerfectClosure.mk_mul_mk, RatFunc.num_div_dvd, FractionalIdeal.coeIdeal_span_singleton, Ideal.exists_mem_span_singleton_map_residueField_eq, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, algebraicIndependent_iff_ker_eq_bot, MonoidAlgebra.mapRangeRingHom_single, IsBaseChange.basis_repr_comp_apply, NumberField.InfinitePlace.le_iff_le, Ideal.smul_top_eq_map, PreTilt.valAux_eq, MvPolynomial.IsSymmetric.map, AlgHom.coe_addMonoidHom_injective, Polynomial.Chebyshev.algebraMap_eval_U, IsLocalization.Away.algebraMap_pow_isUnit, NumberField.norm_norm_le_norm_mul_house_pow, Polynomial.rootMultiplicity_eq_natTrailingDegree, Polynomial.aeval_algebraMap_eq_zero_iff, Ideal.algebraMap_quotient_injective, Algebra.algebraMap_eq_smul_one', PolynomialModule.eval_map, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Matrix.det_det, IsLocalization.coeSubmodule_span, SkewMonoidAlgebra.lift_apply', RCLike.star_def, DirectLimit.Module.of_f, Polynomial.div_def, rangeRestrict_surjective, Cubic.of_a_eq_zero', WittVector.mapFun.nsmul, Polynomial.C_inj, MvPolynomial.isEmptyRingEquiv_apply, WittVector.ghostComponent_apply, MvPowerSeries.rescaleUnit, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ_symm, MvPolynomial.ker_map, Polynomial.prod_X_sub_C_nextCoeff, Algebra.IsPushout.equiv_symm_algebraMap_left, Polynomial.mem_roots_sub_C', WittVector.ghostComponent_verschiebungFun, Ideal.ker_algebraMap_residueField, Polynomial.Monic.leadingCoeff_C_mul, SemiRingCat.inv_hom_apply, RatFunc.laurent_X, Ideal.mem_leadingCoeffNth_zero, Polynomial.leadingCoeff_quadratic, Multiset.prod_X_sub_X_eq_sum_esymm, ContinuousLinearMap.toContinuousAddMonoidHom_add, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, Polynomial.coeffList_C_mul, Polynomial.support_C_mul_X, IsIntegrallyClosed.isIntegral_iff, RCLike.algebraMap_eq_ofReal, NumberField.IsCMField.equivInfinitePlace_symm_apply, SemiRingCat.comp_apply, Polynomial.nnqsmul_eq_C_mul, DividedPowers.IsDPMorphism.ideal_comp, Polynomial.leadingCoeff_C_mul_of_isUnit, CFC.exists_pos_algebraMap_le_iff, RCLike.inner_apply', AlgebraicGeometry.isIso_SpecMap_iff, IsLocalization.to_map_eq_zero_iff, Polynomial.aroots_X_sub_C, Complex.conj_inv, Polynomial.fiberEquivQuotient_tmul, Localization.AtPrime.mapPiEvalRingHom_bijective, NNReal.coe_toRealHom, MvPolynomial.optionEquivLeft_C, NumberField.InfinitePlace.isometry_embedding, Polynomial.degree_quadratic_lt, Matrix.isParabolic_iff_exists, IntermediateField.coe_bot, Ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem, WeierstrassCurve.Projective.comp_equiv_comp, WeierstrassCurve.Affine.CoordinateRing.basis_one, ValuativeExtension.srel_iff_srel, AlgebraicGeometry.Scheme.mem_basicOpen', NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, MvPolynomial.iterToSum_sumToIter, Polynomial.C_mul_X_eq_monomial, Algebra.Generators.toAlgHom_ofComp_localizationAway, eval_det_add_X_smul, PadicComplex.coe_eq, Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq, TensorProduct.piScalarRight_symm_algebraMap, RCLike.sub_conj, NumberField.mem_maximalRealSubfield_iff, rangeS_eq_top, LaurentSeries.LaurentSeriesRingEquiv_def, Polynomial.logMahlerMeasure_C_mul, WittVector.mapFun.add, MvPowerSeries.constantCoeff_subst, StarSubalgebra.range_le, Polynomial.C_1, Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar, Ideal.map_fst_prod, eval₂_minpolyDiv_of_eval₂_eq_zero, CommRingCat.id_apply, Bijective.respectsIso, PowerSeries.algebraMap_apply'', minpoly_algebraMap_add_splits, map_neg, Complex.star_def, WeierstrassCurve.ψ₂_sq, Algebra.lmul_algebraMap, EuclideanSpace.inner_single_left, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, MvPolynomial.optionEquivLeft_X_some, Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap, Unitization.splitMul_apply, Polynomial.monic_X_pow_add_C, Polynomial.monic_multisetProd_X_sub_C, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, MvPolynomial.eval₂Hom_monomial, Matrix.charpoly_map, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, Valuation.IsTrivialOn.eq_one, DoubleCentralizer.nnnorm_def', IsArtinianRing.localization_surjective, frobenius_one, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, WeierstrassCurve.Jacobian.map_dblX, PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_isPrime, Polynomial.leadingCoeff_det_X_one_add_C, Ideal.comap_cotangentIdeal, WittVector.frobeniusEquiv_symm_apply, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, Complex.nndist_self_conj, faithfulSMul_iff_algebraMap_injective, NumberField.mixedEmbedding.norm_eq_norm, TopCommRingCat.instReflectsIsomorphismsTopCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier, DoubleQuot.coe_quotQuotMkₐ, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_apply, BoolAlg.hasForgetToBoolRing_forget₂_obj_carrier, Polynomial.coeff_zero_of_isScalarTower, X_pow_sub_C_irreducible_iff_of_odd, Subring.coe_inclusion, WeierstrassCurve.Jacobian.baseChange_polynomialZ, Polynomial.zero_notMem_multiset_map_X_sub_C, Polynomial.card_roots_sub_C', Irreducible.natSepDegree_eq_one_iff_of_monic', IsLocalization.surj, Algebra.Presentation.localizationAway_relation, Polynomial.coeff_map, MeasureTheory.charFun_neg, MvPolynomial.monomial_finsupp_sum_index, KaehlerDifferential.cotangentComplexBaseChange_tmul, Polynomial.eq_C_of_degree_eq_zero, QuadraticAlgebra.algebraMap_inj, NumberField.FinitePlace.norm_def', IsPRadical.pow_mem, quasispectrumRestricts_iff, IsLocalRing.instIsLocalHomRingHomOfNontrivial, IsBaseChange.of_fintype_basis_eq, QuasispectrumRestricts.rightInvOn, Polynomial.nextCoeffUp_C_eq_zero, X_pow_sub_C_irreducible_of_odd, Polynomial.derivative_pow_succ, IsLocalization.algEquivOfAlgEquiv_eq, Circle.ofConjDivSelf_coe, IsLocalRing.finrank_quotient_map, NumberField.mixedEmbedding.mem_idealLattice, smoothSheafCommRing.ι_evalHom_apply, StandardEtalePresentation.toPresentation_algebra_smul, cyclotomicCharacter.toZModPow, BoxIntegral.unitPartition.mem_smul_span_iff, Ideal.comap_map_eq_self_of_faithfullyFlat, InnerProductSpace.Core.inner_smul_left, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, minpoly.eq_of_irreducible, RingCat.Colimits.cocone_naturality_components, Ideal.quotient_map_C_eq_zero, LinearMap.toAddMonoidHom_mulLeft, cfc_apply_one, Module.End.isFinitelySemisimple_sub_algebraMap_iff, PrimeSpectrum.denseRange_comap_iff_ker_le_nilRadical, Polynomial.natDegree_X_pow_sub_C, UpperHalfPlane.specialLinearGroup_apply, RCLike.conj_nat_cast, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', IsLocalization.algEquiv_apply, SemilinearMapClass.toMulActionSemiHomClass, PowerSeries.degree_weierstrassMod_lt, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C, MvPolynomial.eval₂_zero'_apply, Polynomial.eval₂_hom, CategoryTheory.Linear.smulOfRingMorphism_smul_eq', NumberField.FinitePlace.embedding_apply, mapMatrix_apply, Complex.conjLIE_apply, Polynomial.roots_C_mul_X_pow, Circle.starRingEnd_addChar, MvPolynomial.degreeOf_C, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mk, Valuation.Integers.isPrincipal_iff_exists_isGreatest, MaximalSpectrum.toPiLocalization_apply_apply, QuadraticAlgebra.norm_algebraMap, MvPowerSeries.mapAlgHom_apply, WeierstrassCurve.Projective.polynomial_relation, IsLocalization.mk'_tmul, surjective_of_tmul_eq_tmul_of_finite, WeierstrassCurve.Jacobian.map_negDblY, TruncatedWittVector.iInf_ker_truncate, Algebra.coe_algebraMap_ofSubring, Localization.algEquiv_apply, RingCon.comap_bot, Complex.cosh_conj, RatFunc.laurent_algebraMap, AlgebraicIndependent.repr_ker, AlgebraicGeometry.SpecMap_preimage_basicOpen, Polynomial.iterate_derivative_eq_factorial_smul_sum, HahnSeries.ofPowerSeries_X_pow, CommRingCat.mkUnder_ext_iff, AlgHom.IsArithFrobAt.mk_apply, Ideal.map_mk_comap_factor, Polynomial.iterate_derivative_X_add_pow, MvPolynomial.mem_range_map_iff_coeffs_subset, PowerBasis.quotientEquivQuotientMinpolyMap_apply, DoubleQuot.coe_quotLeftToQuotSupₐ, RCLike.re_add_im_ax, PreInnerProductSpace.Core.smul_left, WeierstrassCurve.Projective.map_negAddY, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, Matrix.map_swap, Complex.oangle, AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, NumberField.InfiniteAdeleRing.algebraMap_apply, Algebra.injective_of_transcendental, IntermediateField.botEquiv_symm, Ideal.quotientInfToPiQuotient_inj, MvPolynomial.exists_dvd_map_of_isAlgebraic, Cubic.disc_eq_prod_three_roots, NumberField.Units.dirichletUnitTheorem.seq_decreasing, smoothSheafCommRing.eval_germ, Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center, Polynomial.degree_C_mul_of_isUnit, UpperHalfPlane.σ_sq, frobenius_natCast, MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, WittVector.map_teichmuller, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', PreTilt.coeff_pow_p, RestrictScalars.ringEquiv_algebraMap, Matrix.blockDiagonal'RingHom_apply, RCLike.is_real_TFAE, Polynomial.degree_mul_leadingCoeff_inv, PerfectClosure.frobenius_mk, ContinuousMap.toNNReal_neg_algebraMap, Submodule.quotientPi_aux.map_smul, mem_fieldRange_self, Polynomial.eq_prod_roots_of_splits, Polynomial.map_injective_iff, Polynomial.eq_prod_roots_of_monic_of_splits_id, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, Ideal.torsionMapQuot_apply, AnalyticOnNhd.eval_linearMap', Algebra.adjoin_singleton_algebraMap, inner_gradientWithin_right, Algebra.TensorProduct.algebraMap_apply, IsLocalization.Away.sec_spec, Ideal.Quotient.algEquivOfEqMap_apply, InnerProductSpace.smul_left, MvPowerSeries.map_algebraMap_eq_subst_X, Ideal.Quotient.factor_mk, IsLocalization.mem_span_map, MvPolynomial.optionEquivLeft_apply, minpoly_algHom_toLinearMap, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, Set.algebraMap_mem_centralizer, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₂, Ideal.Factors.fact_ramificationIdx_neZero, CommRingCat.forget₂CommSemiRing_preservesLimitsOfSize, Polynomial.prime_C_iff, Ideal.algebraMap_quotient_residueField_mk, AdjoinRoot.mk_surjective, PowerSeries.coeff_ne_zero_C, Field.localization_map_bijective, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, WittVector.map_coeff, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, Matrix.mem_range_scalar_iff_commute_transvectionStruct, IsLocalization.isUnit_comp, RingCat.forget₂AddCommGroup_preservesLimits, FractionalIdeal.coe_extendedHomₐ_eq_span, IsIntegralClosure.algebraMap_lift, HomogeneousLocalization.range_awayMapAux_subset, Algebra.IsPushout.cancelBaseChange_symm_tmul, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, IsCyclotomicExtension.isCyclotomicExtension_zero_iff, conjneg_conj, CommAlgCat.forget₂_commRingCat_obj, WeierstrassCurve.Jacobian.eval_polynomialY, Ideal.quotientInfToPiQuotient_surj, id_apply, DirectLimit.Module.lift_of, WeierstrassCurve.Affine.CoordinateRing.coe_basis, SemilinearMapClass.distribMulActionSemiHomClass, Polynomial.natSepDegree_X_sub_C_pow, inner_smul_left_eq_star_smul, IsLocalization.algEquivOfAlgEquiv_apply, RCLike.mul_conj, Polynomial.isMonicOfDegree_two_iff', Polynomial.not_isRoot_C, algebraMapCLM_coe, RCLike.norm_conj, MvPolynomial.constantCoeff_rename, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_comap_ideal, Multiset.prod_X_add_C_coeff, Valuation.Integers.exists_of_le_one, CommRingCat.forget_obj, Ideal.map_spanIntNorm, MvPolynomial.map_bind₂, Polynomial.natDegree_C_add, Algebra.map_leftMulMatrix_localization, Field.isSeparable_algebraMap, Cubic.c_eq_three_roots, QuotientMapQuotient.isNoetherian, PowerSeries.mapAlgHom_apply, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, PresheafOfModules.Derivation.d_map, IsLocalizedModule.iso_apply_mk, Polynomial.C_mul', Polynomial.eraseLead_add_C_mul_X_pow, KaehlerDifferential.kerToTensor_apply, AlgEquiv.prodQuotientOfIsIdempotentElem_apply, RatFunc.laurent_div, CFC.negPart_algebraMap, MvPolynomial.iterToSum_C_X, FractionalIdeal.coe_mem_one, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, MvPolynomial.map_eval₂, MvPolynomial.eval_map, AlgebraicGeometry.ValuativeCriterion.Existence.instIsLocalHomCarrierRingHomHomHomCommRingCat, Polynomial.isMonicOfDegree_X_sub_one, WittVector.mapFun.one, CommRingCat.free_map_coe, coe_monoidHom_id, IsLocalization.AtPrime.comap_map_eq_map, Algebra.Generators.defaultHom_val, MvPolynomial.map_eval₂Hom, DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv, AlgebraNorm.extends_norm, LinearMap.sum_repr_mul_repr_mulₛₗ, IsScalarTower.coe_toAlgHom', Ideal.map_under_le_under_map, ConjRootClass.minpoly.map_eq_prod, Valuation.Integers.valuation_irreducible_lt_one, TruncatedWittVector.truncate_wittVector_truncate, NumberField.Units.pos_at_place, map_rat_algebraMap, algebraMap_le_of_le_spectrum, ExteriorAlgebra.algebraMap_inj, PowerSeries.rescale_X, Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, map_preNormEDS, Polynomial.sumIDeriv_C, char_dvd_card_solutions_of_add_lt, NumberField.InfinitePlace.comap_apply, MvPolynomial.comp_eval₂Hom, Ideal.height_eq_height_add_of_liesOver_of_hasGoingDown, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Polynomial.roots_C_mul, Algebra.mem_adjoin_iff, AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap, IsFractionRing.mk'_eq_div, Polynomial.coeff_divByMonic_X_sub_C_rec, Ideal.Quotient.tower_quotient_map_quotient, GaussianInt.toComplex_def₂, SetSemiring.imageHom_def, Ideal.liesOver_iff_dvd_map, Localization.localRingHom_injective_of_primesOver_eq_singleton, Complex.isCauSeq_conj, Ring.DirectLimit.congr_symm_apply_of, PowerSeries.coe_add, WittVector.factorPowSucc_fontaineThetaModPPow_eq, HasDerivAt.hasGradientAt, RingCat.forget₂_map, Ideal.Quotient.factor_comp_apply, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, RootPairing.RootPositiveForm.zero_lt_posForm_iff, MvPolynomial.aeval_eq_eval, PowerSeries.catalanSeries_constantCoeff, FractionalIdeal.extendedHomₐ_coeIdeal_eq_map, MvPolynomial.schwartz_zippel_totalDegree, IsLocalization.smul_mk'_self, Polynomial.leadingCoeff_X_pow_add_C, Ring.ordFrac_eq_ord, Ideal.comap_map_eq_self_iff_of_isPrime, Polynomial.eval_C, Matrix.charmatrix_apply_eq, IsGalois.mem_range_algebraMap_iff_fixed, Lagrange.nodal_insert_eq_nodal, Algebra.SubmersivePresentation.map_jacobianOfHasCoeffs, Localization.mk_algebraMap, Polynomial.mapAlgHom_eq_eval₂AlgHom'_CAlgHom, MvPolynomial.eval₂Hom_C_id_eq_join₁, Algebra.dvd_algebraMap_intNorm_self, map_complEDS', Polynomial.count_map_roots, WeierstrassCurve.map_c₆, PrimeSpectrum.vanishingIdeal_range_comap, PolyEquivTensor.toFunAlgHom_apply_tmul, MvPolynomial.eval_mem, LinearMap.toMatrix_baseChange, Algebra.Generators.algebraMap_surjective, LocallyConstant.comapRingHom_apply_apply, Ideal.spanIntNorm_localization, IsLocalization.Away.algebraMap_surjective_of_isIdempotentElem, Polynomial.eval_divByMonic_eq_trailingCoeff_comp, Polynomial.algebraMap_apply, Valuation.Integers.map_le_one, Algebra.isInvariant_iff, RingCat.inv_hom_apply, MvPolynomial.eval_rename_prod_mk, jacobiTheta₂'_conj, RingEquiv.ofHomInv_symm_apply, map_matrix_mul, MvPolynomial.optionEquivRight_C, Ideal.isPrime_map_of_isLocalizationAtPrime, Valuation.HasExtension.val_map_eq_iff, Pi.evalRingHom_apply, WeierstrassCurve.Affine.map_addY, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, ExteriorAlgebra.algebraMap_eq_one_iff, MvPolynomial.map_mvPolynomial_eq_eval₂, Polynomial.monomial_mul_C, Unitization.starLift_apply_apply, WeierstrassCurve.integralModel_Δ_eq, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, MvPolynomial.eval_eval₂, IsLocalization.mk'_mul_cancel_left, Polynomial.trunc_toLaurent, Algebra.traceMatrix_localizationLocalization, Algebra.algebraMap_intNorm, rangeSRestrict_surjective, WittVector.iterate_verschiebung_mul, LaurentSeries.ofPowerSeries_powerSeriesPart, MvPolynomial.eval₂_id, Polynomial.scaleRoots_eval₂_mul, toRatAlgHom_apply, Polynomial.as_sum_range_C_mul_X_pow', AlgebraicGeometry.Scheme.exists_germ_injective, LaurentSeries.single_order_mul_powerSeriesPart, coe_algebraMapCLM, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk, Complex.cos_conj, Matrix.derivative_det_one_add_X_smul, Polynomial.integralNormalization_C, Polynomial.rootMultiplicity_X_sub_C_pow, QuadraticAlgebra.algebraMap_re, Polynomial.resultant_X_sub_C_right, CliffordAlgebra.ι_mul_ι_comm, Module.associatedPrimes.preimage_comap_associatedPrimes_eq_associatedPrimes_of_isLocalizedModule, IsLocalRing.residue_eq_zero_iff, MvPowerSeries.isUnit_iff_constantCoeff, RatFunc.liftMonoidWithZeroHom_apply_div', GaussianInt.toComplex_div_re, bijective_iterateFrobenius, HahnSeries.embDomainRingHom_apply, nnnorm_algebraMap_nnreal, Complex.conj_rootsOfUnity, ker_rangeRestrict, algebraMap_pos, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, WithAbs.equiv_algebraMap_apply, LocallyConstant.evalRingHom_apply, WittVector.mapFun.sub, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd_assoc, Polynomial.update_eq_add_sub_coeff, RootPairing.restrictScalars_pairing, Polynomial.monic_finprod_X_sub_C, Polynomial.degree_C_mul_of_mul_ne_zero, Cubic.discr_eq_prod_three_roots, Ideal.jacobson_bot_polynomial_le_sInf_map_maximal, MvPolynomial.constantCoeff_C, MvPowerSeries.smul_eq_C_mul, AlgebraicGeometry.Scheme.Hom.toImage_app_injective, CliffordAlgebra.ι_sq_scalar, Quaternion.algebraMap_def, Algebra.intTrace_eq_of_isLocalization, Real.Polynomial.isRoot_cos_pi_div_five, Polynomial.coe_C, mem_range, MvPowerSeries.trunc_C, NumberField.mixedEmbedding.convexBodyLT_mem, Zsqrtd.hom_ext_iff, WeierstrassCurve.Affine.C_addPolynomial, Ideal.Quotient.factorₐ_apply_mk, MvPolynomial.map_map, AlgebraicGeometry.Scheme.IdealSheafData.ideal_le_ker_glueDataObjι, OrderRingHom.coe_coe_ringHom, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe, Algebra.trace_algebraMap, Module.Basis.repr_algebraMap, Polynomial.bernoulli_generating_function, NumberField.Units.coe_mul, PEquiv.map_toMatrix, LinearMap.det_baseChange, Polynomial.natDegree_finset_prod_X_sub_C_eq_card, RCLike.conjCLE_apply, Polynomial.support_C_mul_X', congr_fun, Ideal.Quotient.instIsPrimeQuotientMapRingHomAlgebraMapMkOfLiesOver, ValuationSubring.subtype_injective, RatFunc.coe_X, NumberField.InfinitePlace.comp_of_comap_eq, IsPurelyInseparable.iterateFrobenius_algebraMap, IsUltrametricDist.invariantExtension_extends, CFC.rpow_algebraMap, Polynomial.eval₂_ofFinsupp, WittVector.frobenius_isPoly, Polynomial.eval₂_monomial, AdjoinRoot.smul_mk, PowerSeries.map_cos, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, Orthonormal.inner_left_fintype, PowerSeries.coeff_coe, IsIntegrallyClosedIn.exists_algebraMap_eq_of_pow_mem_subalgebra, Polynomial.coe_compRingHom_apply, MonoidHom.map_iterate_frobenius, FunctionField.inftyValuation.polynomial, AdjoinRoot.liftAlgHom_of, Polynomial.pow_rootMultiplicity_not_dvd, Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative, LocalizedModule.divBy_mul_by, IsFractionRing.algHom_commutes, IsLocalRing.basisQuotient_repr, AdjoinRoot.evalEval_apply, QuadraticAlgebra.omega_mul_coe_mul_mk, PowerSeries.constantCoeff_X, Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero, LinearEquiv.det_baseChange, algebraicIndependent_empty_iff, Algebra.FormallyUnramified.iff_map_maximalIdeal_eq, DoubleCentralizer.norm_def', Module.End.ringHomEndFinsupp_apply_apply, BoolAlg.hasForgetToBoolRing_forget₂_map, Polynomial.constantCoeff_apply, QuadraticAlgebra.algebraMap_dvd_iff, algebra_compatible_smul, IsLocalization.comap_map_of_isPrime_disjoint, AlgHom.commutes', Algebra.compHom_algebraMap_apply, span_eq_top_localization_localization, IsFractionRing.injective, MvPolynomial.eval₂_mul_monomial, MvPolynomial.weightedHomogeneousComponent_zero, instIsLocalHomAtPrimeRingHomAlgebraMap, Complex.isometry_conj, Polynomial.Bivariate.aveal_eq_map_swap, Polynomial.le_trailingDegree_C, WithLp.unitization_algebraMap, Polynomial.eval_natCast_map, Ideal.FG.map, Polynomial.integralNormalization_aeval_eq_zero, RatFunc.coe_mapRingHom_eq_coe_map, MvPolynomial.esymmAlgHomMonomial_single, MvPolynomial.homogeneousComponent_C_mul, AlgEquiv.quotientBot_mk, LaurentPolynomial.eval₂_C_mul_T, LaurentSeries.coe_algebraMap, Polynomial.toLaurent_C_mul_T, PadicInt.algebraMap_apply, Complex.summable_conj, UpperHalfPlane.denom_cocycle_σ, MvPolynomial.IsHomogeneous.map, Polynomial.aevalTower_algebraMap, MvPolynomial.map_expand, Algebra.Norm.Transitivity.comp_det_mul_pow, NNReal.algebraMap_eq_coe, Complex.log_inv_eq_ite, Algebra.traceMatrix_of_matrix_vecMul, RingEquiv.quotientBot_symm_mk, HomogeneousLocalization.awayMap_mk, Polynomial.Bivariate.swap_apply, DifferentialAlgebra.deriv_algebraMap, MvPolynomial.map_aeval, IsLocalization.AtPrime.inertiaDeg_map_eq_inertiaDeg, Matrix.center_eq_range, RatFunc.coe_coe, Algebra.coe_algebraMap_ofSubsemiring, Ideal.quotEquivOfEq_mk, WeierstrassCurve.Jacobian.map_negY, Algebra.TensorProduct.basis_repr_tmul, rangeS_toSubmonoid, AlgebraicGeometry.stalkwise_SpecMap_iff, MvPolynomial.map_frobenius_expand, Valuation.Integers.le_of_dvd, NumberField.FinitePlace.norm_embedding_eq, WittVector.mapFun.pow, Ideal.injective_quotient_le_comap_map, Polynomial.C_eq_zero, Polynomial.dvd_comp_X_add_C_iff, IntermediateField.LinearDisjoint.trace_algebraMap, Polynomial.separable_X_pow_sub_C, Int.coe_castRingHom, QuadraticAlgebra.C_eq_algebraMap, ValuativeExtension.mapValueGroupWithZero_mk, LinearMap.range_toAddSubmonoid, Ideal.comap_of_equiv, Polynomial.dvd_comp_C_mul_X_add_C_iff, PowerSeries.isUnit_iff_constantCoeff, AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion, Ideal.Quotient.algebraMap_quotient_map_quotient, FirstOrder.Ring.lift_genericPolyMap, WittVector.truncate_surjective, PresheafOfModules.Derivation.postcomp_d_apply, RingCat.forget_map_apply, Complex.mul_conj', RootPairing.exists_ge_zero_eq_rootForm, norm_algebraMap_nnreal, SkewPolynomial.φ_iterate_apply, Algebra.mem_bot, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, PresheafOfModules.Derivation.d_one, Polynomial.X_pow_sub_one_splits, injective_frobenius, MvPolynomial.expand_char, Polynomial.coeff_C_ne_zero, Polynomial.isMonicOfDegree_add_add_two, Algebra.right_comm, Polynomial.degree_X_pow_add_C, ExteriorAlgebra.algebraMap_eq_zero_iff, Matrix.det_one_add_smul, minpoly_algebraMap_sub_splits, PreTilt.mk_comp_untilt_eq_coeff_zero, PowerSeries.WithPiTopology.continuous_constantCoeff, MvPolynomial.eval₂Hom_congr, Polynomial.Monic.comp_X_sub_C, Rat.coe_castHom, ZMod.ringHom_rightInverse, DoubleQuot.quotQuotEquivComm_comp_quotQuotMk, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, Localization.AtPrime.eq_maximalIdeal_iff_comap_eq, MvPolynomial.map_rename, PrimeSpectrum.toPiLocalization_surjective_of_discreteTopology, Polynomial.hom_eval₂, IsFractionRing.surjective_iff_isField, Algebra.PreSubmersivePresentation.ofHasCoeffs_σ', MvPolynomial.killCompl_C, Algebra.Presentation.quotientEquiv_symm, FractionalIdeal.mem_coeSubmodule, AddMonoidAlgebra.singleZeroRingHom_apply, LaurentPolynomial.algebraMap_apply, DoubleQuot.quotQuotEquivComm_quotQuotMk, AlgebraicGeometry.StructureSheaf.comap_const, frobenius_mul, Algebra.Generators.H1Cotangent.δAux_C, Polynomial.degree_X_sub_C, Polynomial.iterate_derivative_X_sub_pow, algebraMap_strictMono, Polynomial.support_trinomial', Complex.liftAux_apply, TensorProduct.gradedComm_algebraMap_tmul, CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker_aux, RingEquiv.toNonUnitalRingHom_commutes, Polynomial.C_0, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_apply_coe_asIdeal, LaurentSeries.inducing_coe, WittVector.mk_pow_fontaineTheta, FirstOrder.Ring.realize_termOfFreeCommRing, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, Ideal.ker_Pi_Quotient_mk, FirstOrder.Field.lift_genericMonicPoly, NumberField.exists_conjugate_one_le_norm, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map, Polynomial.exists_finset_of_splits, boolRingCatEquivBoolAlg_functor, toAddMonoidHom_eq_coe, map_preNormEDS', Algebra.QuasiFiniteAt.exists_fg_and_exists_notMem_and_awayMap_bijective, NumberField.InfinitePlace.norm_embedding_eq, Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd, PowerSeries.coe_smul, isSeparable_algebraMap, PreTilt.coeff_frobeniusEquiv_symm, FreeAbelianGroup.liftMonoid_coe_addMonoidHom, Algebra.Generators.ofComp_val, MvPowerSeries.comp_aeval, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, Algebra.Presentation.map_relationOfHasCoeffs, LaurentSeries.continuous_coe, Matrix.charpoly_of_upperTriangular, algebraMap_apply, IsLocalRing.instIsLocalHomResidueFieldRingHomResidue, LinearMap.convOne_apply, Valuation.HasExtension.val_map_lt_iff, MonoidAlgebra.coe_algebraMap, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, FreeAlgebra.star_algebraMap, MvPolynomial.eval₂_map, AddMonoidAlgebra.mapRangeRingHom_single, Polynomial.irreducible_mul_leadingCoeff_inv, PresheafOfModules.Derivation.d_mul, iterateFrobenius_one_apply, GaussianInt.toComplex_injective, MulOpposite.algebraMap_apply, IsSepClosed.roots_eq_zero_iff, IsIntegrallyClosedIn.exists_algebraMap_eq_of_isIntegral_pow, Algebra.Generators.naive_val, Ideal.Quotient.factorₐ_apply, comap_ker, Ideal.map_id, gal_X_pow_sub_C_isSolvable, Lagrange.interpolate_eq_sum, MonoidAlgebra.mapDomain_algebraMap, StarSubalgebra.mem_bot, Module.AEval.C_smul, Algebra.Extension.CotangentSpace.map_tmul, Orientation.kahler_swap, MulChar.ringHomComp_apply, Polynomial.sum_C_index, element_smul_restrictScalars, Matrix.charmatrix_apply_ne, CommSemiRingCat.ofHom_apply, MvPowerSeries.subst_monomial, RatFunc.map_apply, coe_coe, IsFractionRing.coe_liftAlgHom, Polynomial.le_rootMultiplicity_map, toMonoidHom_eq_coe, coe_rangeSRestrict, MvPowerSeries.le_weightedOrder_map, Ideal.powQuotSuccInclusion_apply_coe, Algebra.Generators.algebraMap_apply, IsLocalization.map_eq_zero_iff, Subalgebra.algebraMap_mk, toIntAlgHom_apply, IsBaseChange.endHom_toMatrix, MvPolynomial.map_esymm, WeierstrassCurve.Affine.map_linePolynomial, IsAdicComplete.of_liftRingHom, Polynomial.natTrailingDegree_C, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Complex.UnitDisc.coe_conj, Polynomial.X_mul_C, Module.IsTorsionBySet.mk_smul, IsLocalization.mapFrameHom_apply, Derivation.mapCoeffs_C, DirectSum.algebraMap_toAddMonoid_hom, AlgebraicGeometry.StructureSheaf.comap_apply, Polynomial.coeff_C_mul_X, Polynomial.leadingCoeff_cubic, Polynomial.map_monomial, Polynomial.resultant_C_zero_right, Polynomial.natDegree_eq_one, MvPolynomial.expand_C, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, ModuleCat.smul_naturality, CharP.ker_intAlgebraMap_eq_span, LaurentPolynomial.smeval_C_mul, IsLocalization.map_inf, PadicInt.ext_of_toZModPow, MonomialOrder.eq_C_of_degree_eq_zero, minpoly.sub_algebraMap, WeierstrassCurve.φ_three, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, AdjoinRoot.mk_eq_mk, MvPolynomial.coeffs_C, UniformSpace.Completion.map_smul_eq_mul_coe, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, Polynomial.C_eq_natCast, FractionalIdeal.dual_eq_dual_mul_dual, ContinuousMap.toNNReal_algebraMap, IsLocalization.isMaximal_iff_isMaximal_disjoint, AlgebraicGeometry.IsAffineOpen.ideal_le_iff, Polynomial.derivative_X_sub_C_sq, AlgebraicGeometry.stalkToFiberRingHom_homogeneousLocalizationToStalk, Matrix.charpoly_sub_scalar, Algebra.Generators.compLocalizationAwayAlgHom_X_inl, WeierstrassCurve.Jacobian.comp_equiv_comp, MvPolynomial.optionEquivRight_X_none, PreInnerProductSpace.Core.conj_inner_symm, Polynomial.smul_eq_C_mul, FiniteField.algebraMap_trace_eq_sum_pow, Algebra.coe_bot, Polynomial.opRingEquiv_op_C, RatFunc.mk_def, Submodule.factor_eq_factor, Polynomial.C_eq_intCast, Ideal.IsDedekindDomain.ramificationIdx_eq_normalizedFactors_count, Perfection.coeff_map, Polynomial.degree_C_lt_degree_C_mul_X, Polynomial.aroots_C_mul, WeierstrassCurve.Jacobian.polynomialY_eq, Polynomial.isUnit_iff, RingTheory.Sequence.IsWeaklyRegular.of_flat, WeierstrassCurve.Jacobian.map_dblZ, ContinuousMap.spectrum_eq_preimage_range, PowerSeries.map_constantCoeff_le_self_of_X_mem, Polynomial.roots_X_pow_char_pow_sub_C_pow, Module.Basis.localizationLocalization_apply, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, Algebra.TensorProduct.right_algebraMap_apply, Localization.map_isUnit_of_le, FreeCommRing.lift_of, Multiset.prod_X_sub_C_dvd_iff_le_roots, Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRing, Ideal.map_relNorm, Polynomial.leadingCoeff_mul_prod_normalizedFactors, RatFunc.mk_eq_div', IsLocalization.coe_liftAlgHom, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, WeierstrassCurve.Jacobian.eval_polynomialX, Matrix.IsHermitian.charpoly_cfc_eq, Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero, MvPolynomial.C_apply, Ideal.localized'_eq_map, Bialgebra.algebraMap_injective, IsLocalization.mk'_eq_mul_mk'_one, IsLocalization.ringEquivOfRingEquiv_symm_apply, MvPowerSeries.map_subst, HahnSeries.map_C, Polynomial.nextCoeff_C_mul_X_add_C, Polynomial.toLaurent_injective, LaurentSeries.val_le_one_iff_eq_coe, WeierstrassCurve.Projective.eval_polynomialX, PowerSeries.constantCoeff_invUnitsSub, PiTensorProduct.constantBaseRingEquiv_symm, Polynomial.scaleRoots_eval₂_eq_zero, WeierstrassCurve.Projective.baseChange_polynomial, continuous_algebraMap, Algebra.algebraMap_intNorm_fractionRing, QuaternionAlgebra.algebraMap_injective, Polynomial.prod_multiset_root_eq_finset_root, Polynomial.dvd_C_mul, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.Hom.germ_stalkMap_apply, Matrix.toMvPolynomial_map, IsFractionRing.self_iff_surjective, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, AlgebraicGeometry.Scheme.preimage_basicOpen_top, IsLocalization.AtPrime.exists_algebraMap_quot_eq_of_mem_quot, spectrum.algebraMap_mem_iff, CStarAlgebra.nnnorm_le_iff_of_nonneg, Matrix.SpecialLinearGroup.map_apply_coe, Algebra.Extension.Cotangent.val_smul''', Polynomial.X_pow_sub_C_separable_iff, CFC.spectrum_algebraMap_eq, map_complEDS₂, Algebra.norm_eq_prod_embeddings, AlgCat.forget₂Ring_preservesLimitsOfSize, IsPurelyInseparable.minpoly_eq, NumberField.canonicalEmbedding.integralBasis_repr_apply, mem_range_self, Module.Invertible.algEquivOfRing_apply, Polynomial.nextCoeff_mul_C, Polynomial.coeff_X_sub_C_mul, WeierstrassCurve.Affine.CoordinateRing.mk_ψ, MvPolynomial.coeff_C, Cubic.of_a_eq_zero, Polynomial.comp_C_mul_X_eq_zero_iff, Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed, Polynomial.modByMonic_eq_zero_iff_quotient_eq_zero, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_app, gal_X_pow_sub_C_isSolvable_aux, MvPolynomial.bind₂_map, Module.Basis.norm_smul, Bijective.isStableUnderBaseChange, Polynomial.degree_quadratic, WittVector.frobenius_bijective, Ideal.relNorm_le_comap, SpectrumRestricts.algebraMap_image, SemiRingCat.forget₂Mon_preservesLimitsOfSize, PowerSeries.rescale_rescale, ContinuousMap.coeFnRingHom_apply, SubsemiringClass.subtype_injective, Ideal.algebraMap_residueField_surjective, RingHomIsometric.enorm_map, PadicAlgCl.norm_extends, coe_rangeRestrictField, Polynomial.monic_X_pow_sub_C, AdicCompletion.mkₐ_apply_coe, AlgebraicGeometry.Scheme.germToFunctionField_injective, Algebra.FormallyUnramified.isField_quotient_map_maximalIdeal, Complex.Gamma_conj, UpperHalfPlane.σ_mul, compLeft_apply, Polynomial.leadingCoeff_linear, CommRingCat.instIsRightAdjointCommMonCatForget₂RingHomCarrierMonoidHomCarrier, AdjoinRoot.coe_mapAlgHom, Polynomial.rootMultiplicity_eq_natFind_of_ne_zero, Polynomial.isMonicOfDegree_two_iff, IsLocalization.Away.instMapRingHomPowersOfCoe, NumberField.ComplexEmbedding.IsConj.eq, Polynomial.C_mul_X_pow_eq_monomial, Polynomial.nextCoeff_X_add_C, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, PrimeSpectrum.toPiLocalization_not_surjective_of_infinite, NumberField.Units.regulator_eq_det, DividedPowers.isSubDPIdeal_map, PrimeSpectrum.preimage_comap_zeroLocus, PowerSeries.coe_mul, Ideal.map_mk_comap_factorPow, IsIntegralClosure.isIntegral_iff, PowerSeries.trunc_mul_C, MvPolynomial.eval_ofNat, RingCon.ker_comp, PresheafOfModules.map_smul, xInTermsOfW_eq, Polynomial.eq_X_add_C_of_degree_le_one, Complex.dist_self_conj, RCLike.conj_ofReal, MvPolynomial.eval_eq_eval_mv_eval', RootPairing.exists_value, Module.comap_annihilator, PerfectRing.comp_lift_apply, MvPolynomial.ACounit_C, PowerSeries.IsWeierstrassDivisionAt.degree_lt, Polynomial.expand_C, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, Polynomial.logMahlerMeasure_X_sub_C, RootPairing.RootPositiveForm.exists_eq, NumberField.AdeleRing.algebraMap_snd_apply, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, IsSelfAdjoint.neg_algebraMap_norm_le_self, PresheafOfModules.Monoidal.tensorObj_map_tmul, Ideal.map_mk_eq_bot_of_le, Polynomial.C_mem_lifts, MatrixEquivTensor.toFunBilinear_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, WittVector.frobenius_frobeniusRotation, HomogeneousLocalization.val_awayMap, PowerSeries.rescale_zero_apply, RCLike.conjLIE_apply, MonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, LaurentPolynomial.degree_C_mul_T, Subalgebra.algebraMap_def, Polynomial.natDegree_mul_leadingCoeff_self_inv, Localization.awayMap_surjective_iff, Module.End.intCast_def, IsLocalRing.residue_def, RCLike.conj_mul, Polynomial.CAlgHom_apply, PerfectRing.bijective_frobenius, WeierstrassCurve.coe_map_Δ', Polynomial.trailingDegree_C_mul_X_pow, Polynomial.Monic.quotient_isIntegralElem, Subring.comap_map_eq, PowerSeries.IsWeierstrassFactorizationAt.natDegree_eq_toNat_order_map_of_ne_top, NormedAlgebra.exists_isMinOn_norm_sub_smul, Polynomial.X_pow_sub_one_eq_prod, Polynomial.prod_multiset_X_sub_C_dvd, Pi.ker_ringHom, WeierstrassCurve.map_b₈, Polynomial.degree_cubic_lt, AdjoinRoot.mul_div_root_cancel, NumberField.Units.coe_coe, Polynomial.eq_X_add_C_of_natDegree_le_one, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, GradedRing.projZeroRingHom'_apply_coe, AlgebraicGeometry.Scheme.Hom.app_surjective, TrivSqZeroExt.algebraMap_eq_inl', fourier_neg', FunctionField.algebraMap_injective, MvPowerSeries.LinearTopology.isTopologicallyNilpotent_iff_constantCoeff, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, MvPolynomial.eval₂Hom_zero_apply, Polynomial.degree_C, FreeCommRing.hom_ext_iff, Cubic.of_b_eq_zero, Algebra.IsCentral.baseField_essentially_unique, PowerSeries.coe_sub, Algebra.map_intNormAux, MvPolynomial.degrees_C, Polynomial.derivative_X_add_C, smoothSheafCommRing.forgetStalk_inv_comp_eval_assoc, MvPowerSeries.constantCoeff_invOfUnit, Algebra.norm_localization, IsLocalization.liftAlgHom_apply, Algebra.mul_sub_algebraMap_commutes, WeierstrassCurve.Jacobian.polynomial_relation, PrimeSpectrum.basicOpen_le_basicOpen_iff_algebraMap_isUnit, PrimeSpectrum.specComap_asIdeal, IsBaseChange.det_endHom, ContinuousLinearMap.toLinearMapRingHom_apply, IsLocalization.injective, AlgEquiv.commutes, AddMonoidAlgebra.mapRangeRingHom_apply, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, MvPolynomial.eval_prod, RingCon.mk'_surjective, AddValuation.comap_supp, MvPolynomial.C_mul_X_eq_monomial, MatrixEquivTensor.invFun_algebraMap, Algebra.Generators.Hom.aeval_val, ext_iff, Polynomial.ofFinsupp_algebraMap, RingQuot.idealQuotientToRingQuot_apply, spectrum.resolvent_eq, LaurentSeries.algebraMap_apply, Ideal.height_le_height_add_of_liesOver, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial, NumberField.Units.finrank_mul_regOfFamily_eq_det, Algebra.Presentation.comp_aeval_relation_inl, AdjoinRoot.aeval_eq_of_algebra, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', Algebra.commutes', MvPolynomial.C_0, MvPowerSeries.constantCoeff_inv, UpperHalfPlane.norm_σ, FreeRing.map_of, LaurentPolynomial.smeval_C, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, Polynomial.support_binomial', isConjRoot_iff_eq_algebraMap, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.invApp_app_apply, CategoryTheory.Linear.smulOfRingMorphism_smul_eq, IsLocalization.mk'_spec', MvPolynomial.bind₂_monomial, minpoly.IsIntegrallyClosed.isIntegral_iff_leadingCoeff_dvd, algebraMap_galRestrict_apply, AddMonoidAlgebra.isLocalHom_singleZeroRingHom, Polynomial.cyclotomic_eq_prod_X_sub_primitiveRoots, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, CFC.posPart_algebraMap_nnreal, WeierstrassCurve.Projective.map_negDblY, Polynomial.X_add_C_scaleRoots, Matrix.toLin_scalar, Polynomial.resultant_C_right, Polynomial.splits_C, Polynomial.Splits.comp_X_sub_C, WeierstrassCurve.Ψ_ofNat, FractionalIdeal.count_ne_zero, RCLike.conj_conj, MvPolynomial.pderiv_sumToIter, TopCommRingCat.forgetToTopCatTopologicalRing, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, Ideal.height_le_height_add_one_of_mem, PowerSeries.le_order_map, PowerSeries.aeval_unique, AdjoinRoot.mk_leftInverse, MvPolynomial.totalDegree_C, PerfectRing.lift_lift_apply, Polynomial.natDegree_C_mul_X, RingEquiv.quotientBot_mk, smoothSheafCommRing.forgetStalk_inv_comp_eval, Ideal.image_subset_nonunits_valuationSubring, KaehlerDifferential.End_equiv_aux, AddMonoidAlgebra.ringHom_ext'_iff, WeierstrassCurve.Projective.polynomialZ_eq, Polynomial.comp_C, WeierstrassCurve.map_a₄, Polynomial.coeff_mul_X_sub_C, SubsemiringClass.coe_subtype, PowerSeries.rescale_mk, FractionalIdeal.mem_one_iff, RingCat.forget₂SemiRing_preservesLimitsOfSize, Complex.normSq_add, Algebra.smul_def', minpoly.frobenius_of_isSeparable, RatFunc.numDenom_div, Ideal.disjoint_map_primeCompl_iff_comap_le, Polynomial.roots_expand_map_frobenius, CStarMatrix.algebraMap_apply, RCLike.re_eq_norm_of_mul_conj, IsIntegralClosure.algebraMap_injective, PowerSeries.constantCoeff_surj, IsLocalization.Away.map_injective_iff, Polynomial.natDegree_X_add_C, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, CommSemiRingCat.forgetReflectIsos, Polynomial.map_taylor, NumberField.RingOfIntegers.coe_eq_zero_iff, AlgebraicGeometry.Scheme.ker_of_isAffine, Polynomial.map_under_lt_comap_of_weaklyQuasiFiniteAt, LaurentPolynomial.degree_C, MvPowerSeries.constantCoeff_C, Polynomial.support_C, SemiRingCat.forget_preservesLimitsOfSize, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C', Algebra.essFiniteType_cond_iff, MvPowerSeries.monomial_zero_eq_C, MvPowerSeries.coeff_inv, RCLike.conj_eq_iff_re, MvPolynomial.coeff_C_mul, LaurentPolynomial.eval₂_T, Polynomial.roots_expand_image_frobenius, Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, MvPolynomial.quotient_map_C_eq_zero, MvPolynomial.iterToSum_X, IsLocalization.mk'_mem_iff, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Submodule.span_singleton_algebraMap_of_isUnit, MvPolynomial.C_mul_monomial, PowerSeries.exp_mul_exp_neg_eq_one, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap, AddMonoidAlgebra.isLocalHom_algebraMap, ClassGroup.mkMMem_surjective, Polynomial.height_map_C, Algebra.Extension.algebraMap_surjective, RatFunc.num_C, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, WeierstrassCurve.Jacobian.map_add, MonoidAlgebra.coe_mapRangeRingHom, isIntegral_localization', Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic, AdjoinRoot.coe_injective, OnePoint.map_smul, RatFunc.smul_eq_C_mul, PowerBasis.constr_pow_algebraMap, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, Polynomial.roots_C_mul_X_sub_C_of_IsUnit, AnalyticOnNhd.eval_linearMap, isStrictlyPositive_algebraMap, Module.Basis.algebraMap_injective, Algebra.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap, RingTheory.Sequence.IsRegular.of_faithfullyFlat, PerfectClosure.mk_add_mk, Polynomial.leadingCoeff_map_eq_of_isUnit_leadingCoeff, LaurentPolynomial.C_apply, galLift_algebraMap_apply, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk, Polynomial.derivative_X_pow_succ, NumberField.Units.norm, LinearMap.isSymm_def, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, Polynomial.eq_C_of_natDegree_le_zero, MvPolynomial.commAlgEquiv_C, MvPolynomial.coeff_zero_C, Polynomial.monic_X_add_C, Polynomial.logMahlerMeasure_X_add_C, ContinuousLinearMap.toContinuousAddMonoidHom_zero, IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra, smoothSheafCommRing.forgetStalk_inv_comp_eval_apply, SemilinearMapClass.map_smul_inv, Algebra.FinitePresentation.ker_fg_of_mvPolynomial, IsLocalization.finsetIntegerMultiple_image, Algebra.norm_eq_iff, MonomialOrder.monic_X_add_C, Polynomial.aevalTower_C, MonoidAlgebra.isLocalHom_singleOneRingHom, LaurentSeries.exists_ratFunc_val_lt, PowerSeries.constantCoeff_one, Ideal.under_map_of_isLocalizationAtPrime, WeierstrassCurve.Affine.addPolynomial_slope, Ideal.comp_quotientMap_eq_of_comp_eq, Polynomial.coeff_C_mul, Ideal.Quotient.eq_zero_iff_dvd, RatFunc.num_algebraMap, Ideal.mem_of_liesOver, Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, FractionalIdeal.extendedHomₐ_injective, MvPolynomial.bind₂_monomial_one, map_one, MonoidHom.iterate_map_frobenius, MvPolynomial.commAlgEquiv_X, Algebra.pushoutDesc_right, PowerSeries.map_sin, smoothSheafCommRing.isUnit_stalk_iff, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, Polynomial.rootMultiplicity_eq_nat_find_of_nonzero, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero, IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le, MvPolynomial.mapEquiv_apply, MvPolynomial.eval₂Hom_congr', Polynomial.derivative_X_sub_C_pow, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, Matrix.charpoly.univ_coeff_eval₂Hom, Module.Quotient.mk_smul_mk, IsPurelyInseparable.surjective_algebraMap_of_isSeparable, Polynomial.natDegree_C_mul_eq_of_mul_eq_one, Bijective.ofLocalizationSpan, PrimeSpectrum.mem_image_comap_basicOpen, Polynomial.eraseLead_C_mul_X, PowerSeries.derivativeFun_C, IsLocalization.AtPrime.comap_maximalIdeal, DirectSum.toAlgebra_apply, WithAbs.algebraMap_right_apply, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, Polynomial.natDegree_C, TensorProduct.gradedComm_algebraMap, Complex.inv_cpow_eq_ite', liftOfDerivationToSquareZero_mk_apply, isLocalizedModule_iff, AlgebraicIndependent.lift_reprField, ValuativeExtension.vlt_iff_vlt, RCLike.conj_I_ax, Polynomial.ker_constantCoeff, Representation.asModuleEquiv_symm_map_smul, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PowerSeries.constantCoeff_invOfUnit, MvPolynomial.aeval_algebraMap_apply, IsLocalization.Away.awayToAwayLeft_eq, Polynomial.constantCoeff_coe, MvPolynomial.C_1, MvPolynomial.eval₂Hom_X', Ideal.Factors.isScalarTower, Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs, wittPolynomial_one, Polynomial.toLaurent_comp_C, IsField.localization_map_bijective, Polynomial.IsRoot.mul_div_eq, contraction_of_isPowMul, Polynomial.sum_C_mul_X_pow_eq, DifferentiableAt.conj_conj, MvPolynomial.eval_eq', isStronglyTranscendental_mk_radical_conductor, RootPairing.toLinearMap_apply_PolarizationIn, Field.DirectLimit.nontrivial, Polynomial.as_sum_support_C_mul_X_pow, Algebra.Generators.comp_val, DirectSum.algebraMap_apply, nnnorm_algebraMap, Algebra.adjoin_eq_ring_closure, MvPolynomial.eval₂_C, DividedPowers.isDPMorphism_iff, RatFunc.liftMonoidWithZeroHom_apply_div, Submodule.span_algebraMap_image, Polynomial.degree_quadratic_le, Polynomial.eq_quadratic_of_degree_le_two, AlgHom.IsArithFrobAt.localize_algebraMap, WeierstrassCurve.φ_one, AlgebraicGeometry.RingedSpace.res_zero, RatFunc.num_dvd, Polynomial.divX_eq_zero_iff, minpoly.isIntegrallyClosed_eq_field_fractions, IsLocalization.algebraMap_mem_map_algebraMap_iff, CommRingCat.instIsLocalHomCarrierObjWalkingParallelPairFunctorConstPtEqualizerForkZeroParallelPairRingHomHomι, Ideal.Quotient.mk_singleton_self, MulSemiringAction.charpoly_eq_prod_smul, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, AdjoinRoot.mk_eq_zero, FiniteField.frobeniusAlgEquiv_symm_apply, Polynomial.card_support_eq, ContinuousMap.compStarAlgHom_comp, IsLocalization.Away.tensorRight, frobenius_sub, AddMonoidAlgebra.coe_algebraMap, Polynomial.leadingCoeff_pow_X_add_C, Algebra.linearMap_apply, isIntegralElem_map, MvPolynomial.C_add, NNRat.coe_castHom, HahnSeries.embDomainRingHom_C, Polynomial.coeff_map_eq_comp, WeierstrassCurve.Jacobian.map_addZ, PowerSeries.C_injective, RootPairing.algebraMap_coxeterWeightIn, IsDedekindDomain.primesOverEquivPrimesOver_apply, algebraMap_monotone, Polynomial.cauchyBound_C, LinearMap.ker_toAddSubmonoid, DifferentiableAt.comp_ringHom, MvPolynomial.isHomogeneous_C_mul_X, RatFunc.laurentAux_div, polyEquivTensor_symm_apply_tmul, Polynomial.roots_C_mul_X_add_C, Polynomial.natDegree_C_mul_le, RootPairing.coroot'_apply_apply_mem_of_mem_span, ContinuousLinearMap.toContinuousAddMonoidHom_comp, Ideal.quotientToQuotientRangePowQuotSucc_mk, Ideal.IsMaximal.comap_piEvalRingHom, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, PadicInt.toZModPow_ofIntSeq_of_pow_dvd_sub, integral_conj, Polynomial.leadingCoeff_X_pow_sub_C, PowerSeries.eq_X_mul_shift_add_const, LaurentPolynomial.mk'_eq, CommRingCat.forget_map, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, NumberField.FinitePlace.norm_lt_one_iff_mem, Module.support_of_algebra, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, WeierstrassCurve.map_a₆, IsIntegrallyClosedIn.algebraMap_eq_of_integral, Algebra.Generators.localizationAway_σ, AdjoinRoot.quotEquivQuotMap_apply, MvPowerSeries.constantCoeff_smul, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, IsLocalization.Away.awayToAwayRight_eq, UnitAddTorus.mFourier_neg, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, LinearIndependent.localization_localization, Ideal.le_pow_ramificationIdx, RatFunc.mk_eq_div, MvPolynomial.mapAlgEquiv_apply, IsAdjoinRoot.lift_root, Polynomial.Bivariate.equivMvPolynomial_symm_X_0, toMonoidWithZeroHom_eq_coe, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, Algebra.adjoin_insert_algebraMap, Valuation.HasExtension.val_map_le_one_iff, smoothSheafCommRing.evalHom_germ, Polynomial.taylor_apply, WittVector.frobeniusPoly_zmod, Polynomial.natDegree_C_mul_of_mul_ne_zero, PresheafOfModules.Derivation.congr_d, WeierstrassCurve.Affine.C_addPolynomial_slope, MvPolynomial.eval_neg, Complex.normSq_sub, GaussianInt.toComplex_im_div, Polynomial.Splits.eq_prod_roots, algebraMap_isometry, frobenius_zero, RCLike.add_conj, Polynomial.evalEvalRingHom_apply, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, RCLike.ofReal_re_ax, RingOfIntegers.norm_algebraMap, map_iterate_frobenius, MvPowerSeries.HasSubst.const_coeff, MvPolynomial.tensorEquivSum_one_tmul_C, PowerSeries.exp_mul_exp_eq_exp_add, IsLocalization.height_map_of_disjoint, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, Ideal.quotientKerAlgEquivOfRightInverse_symm_apply, RCLike.im_eq_conj_sub, ValuationRing.isFractionRing_iff, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, RingEquiv.symm_toRingHom_apply_toRingHom_apply, WittVector.pow_dvd_ghostComponent_of_dvd_coeff, Polynomial.div_wf_lemma, Matrix.charmatrix_fromBlocks, PowerBasis.exists_smodEq, OreLocalization.numeratorRingHom_apply, CliffordAlgebra.EvenHom.contract, RCLike.conj_im_ax, AlgHom.ker_coe_equiv, Polynomial.eq_X_add_C_of_degree_eq_one, IsFractionRing.mk'_num_den', NumberField.RingOfIntegers.ker_algebraMap_eq_bot, WeierstrassCurve.Jacobian.baseChange_polynomialY, PrimeSpectrum.preimage_specComap_zeroLocus, PowerSeries.evalNegHom_X, IsLocalization.Away.commutes, IsLocalization.isPrime_iff_isPrime_disjoint, ValuativeExtension.mapValueGroupWithZero_valuation, MvPolynomial.map_ofNat, Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, inner_self_conj, Polynomial.mahlerMeasure_C_mul_X_add_C, MvPolynomial.eval₂Hom_rename, Algebra.bijective_algebraMap_iff, SemiRingCat.FilteredColimits.forget₂Mon_preservesFilteredColimits, Perfection.coeff_mk, Subring.subtype_injective, Localization.localRingHom_id, WittVector.mapFun.mul, Ideal.Quotient.mk_bijective_iff_eq_bot, Subring.mem_map, Ring.DirectLimit.congr_apply_of, Circle.coe_inv_eq_conj, Polynomial.eq_C_of_natDegree_eq_zero, CliffordAlgebra.ι_mul_ι_add_swap, IsLocalization.AtPrime.to_map_mem_maximal_iff, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, Polynomial.smeval_C, Complex.sub_conj, KaehlerDifferential.ker_map, DividedPowers.DPMorphism.dpow_comp, Algebra.FormallySmooth.mk_lift, WeierstrassCurve.Projective.baseChange_polynomialY, mem_span_C_coeff, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, AlgHom.toKerIsLocalization_apply, SetLike.GradeZero.algebraMap_apply, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, Orientation.kahler_neg_orientation, IsFractionRing.to_map_eq_zero_iff, Polynomial.X_mul_divX_add, IsFractionRing.div_surjective, Complex.conj_im, cfc_add_const, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, isometry, conj_trivial, Matrix.GeneralLinearGroup.fixpointPolynomial_eq_zero_iff, Polynomial.card_support_binomial, PowerSeries.coeff_succ_C, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C', HomogeneousLocalization.awayMapₐ_apply, IsLocalization.mk'_algebraMap_eq_mk', LinearEquiv.map_smulₛₗ, IsLocalization.toLocalizationMap_apply, TensorProduct.algebraMap_gradedMul, FiniteField.algebraMap_norm_eq_pow, PerfectClosure.of_apply, MvPolynomial.algebraMap_apply, Ideal.mem_quotient_iff_mem, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, SubMulAction.algebraMap_mem, IsLocalization.Away.map_surjective_iff, LinearMap.IsSymmetric.toSelfAdjoint_apply, RatFunc.liftOn_div, Polynomial.Splits.comp_X_add_C, RCLike.conj_div, WeierstrassCurve.map_b₆, QuotientRing.isOpenMap_coe, RingCat.FilteredColimits.forget_preservesFilteredColimits, LinearMap.toMvPolynomial_baseChange, IsLocalization.bot_lt_comap_prime, RingHomIsometric.nnnorm_map, Polynomial.C_mul_monomial, AdicCompletion.factorₐ_evalₐ_one, HasDerivAtFilter.hasGradientAtFilter, RootPairing.algebraMap_pairingIn, HahnSeries.algebraMap_apply, IsFractionRing.ringEquivOfRingEquiv_algebraMap, Bialgebra.comul_algebraMap, ZMod.castHom_apply, LinearMap.toMatrix'_algebraMap, Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one, TensorProduct.tensorQuotEquivQuotSMul_tmul_mk, QuotientRing.isQuotientMap_coe_coe, Polynomial.separable_X_pow_sub_C', Algebra.IsAlgebraic.algHomEquivAlgHomOfSplits_apply_apply, algebraMap_smul, RCLike.summable_conj, AlgebraicGeometry.Scheme.Hom.ker_apply, Ideal.quotientKerAlgEquivOfRightInverse_apply, IsLocalization.localization_localization_surj, IsLocalization.map_comap, IsLocalization.algEquiv_comp_algebraMap_apply, RingCon.lift_surjective_iff, IsLocalization.AtPrime.liesOver_comap_of_liesOver, MvPolynomial.C_surjective, AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersion, Unitization.starMap_inl, IsHausdorff.map_algebraMap_iff, Polynomial.Splits.aeval_eq_prod_aroots, MvPolynomial.isEmptyRingEquiv_symm_apply, MonoidAlgebra.lift_apply', AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, functions_ext_iff, Polynomial.toLaurent_apply, RingQuot.eq_lift_comp_mkRingHom, QuadraticAlgebra.coe_dvd_iff_dvd, PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map, Representation.IntertwiningMap.algebraMap_apply, Matrix.mem_range_scalar_iff_commute_single, IsPerfectClosure.ker_eq, PreTilt.coeff_frobenius, QuadraticAlgebra.mul_star, PerfectRing.lift_comp_lift_apply, NumberField.place_apply, RootPairing.isValuedIn_iff_mem_range, CliffordAlgebra.comp_ι_sq_scalar, Polynomial.natDegree_mul_C_eq_of_mul_eq_one, Ideal.Quotient.mk_span_range, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_assoc, Derivation.compAlgebraMapL_apply_apply, isLocalization_iff, Polynomial.content_C_mul, Polynomial.Splits.eq_X_sub_C_of_single_root, TruncatedWittVector.commutes_symm', FiniteField.algebraMap_norm_eq_prod_pow, TruncatedWittVector.truncate_truncate, Polynomial.coeff_det_X_add_C_card, WittVector.mapFun.zsmul, MvPowerSeries.constantCoeff_zero, Polynomial.eval_homogenize, Polynomial.quotientSpanXSubCAlgEquiv_mk, AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen, IsLocalization.iff_map_piEvalRingHom, Cubic.of_c_eq_zero', Complex.continuous_conj, Zsqrtd.lift_symm_apply_coe, Localization.mapPiEvalRingHom_bijective, DoubleQuot.ker_quotQuotMk, PadicInt.Coe.ringHom_apply, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ_apply, AdjoinRoot.coe_injective', iterateFrobenius_inj, RingOfIntegers.not_dvd_exponent_iff, Submodule.setLike.coe_galgebra_toFun, Lagrange.X_sub_C_dvd_nodal, Algebra.Extension.Hom.toRingHom_algebraMap, IsLocalization.algebraMap_isUnit_iff, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, MvPolynomial.bind₁_C_right, UpperHalfPlane.σ_num, MvPolynomial.coe_coeffs_map, Subring.coe_map, Complex.conj_cpow, Localization.AtPrime.mapPiEvalRingHom_comp_algebraMap, TrivSqZeroExt.inlHom_apply, Polynomial.roots_X_sub_C, AdicCompletion.mk_ofAlgEquiv_symm, Submodule.traceDual_le_span_map_traceDual, AlgebraicGeometry.LocallyRingedSpace.stalkMap_inv_hom_apply, AdicCompletion.mk_smul_mk, Polynomial.isUnit_C, Valuation.Integers.hom_inj, Quaternion.algebraMap_injective, PowerSeries.exp_pow_sum, CliffordAlgebra.contractRight_mul_algebraMap, WeierstrassCurve.C_Ψ₂Sq, IsLocalization.ringEquivOfRingEquiv_eq_map, Polynomial.Chebyshev.algebraMap_eval_C, AdjoinRoot.smul_of, Polynomial.natDegree_quadratic_le, Polynomial.Bivariate.swap_Y, Polynomial.rootSet_C_mul_X_pow, PreTilt.coeff_iterate_frobeniusEquiv_symm, Matrix.toLinearMapₛₗ₂_apply, cfc_apply_zero, IsLocalizedModule.fromLocalizedModule_mk, MvPolynomial.instIsLocalHomRingHomAlgebraMap, AlgebraicGeometry.Scheme.stalkSpecializes_stalkMap_apply, IsLocalRing.ResidueField.mapEquiv_apply, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PowerSeries.one_le_order_iff_constCoeff_eq_zero, WeierstrassCurve.Jacobian.map_dblXYZ, DoubleQuot.coe_quotQuotEquivQuotSupₐ, Ideal.quotientMulEquivQuotientProd_snd, MvPowerSeries.C_inv, Unitization.algebraMap_eq_inl, WittVector.mem_ker_truncate, Polynomial.le_rootMultiplicity_iff, LocalSubring.map_maximalIdeal_eq_top_of_isMax, WittVector.fromPadicInt_comp_toPadicInt_ext, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, CommSemiRingCat.forget₂SemiRing_preservesLimits, MonomialOrder.degree_X_sub_C, NumberField.IsCMField.complexEmbedding_complexConj, sum_embeddings_eq_finrank_mul, Subfield.coe_comap, MvPolynomial.aevalTower_C, IsFractionRing.closure_range_algebraMap, Ideal.isPrime_map_quotientMk_of_isPrime, CommRingCat.HomTopology.isClosedEmbedding_hom, Polynomial.support_C_subset, algebraMap_lt_algebraMap, Complex.inv_cpow_eq_ite, FractionalIdeal.canonicalEquiv_spanSingleton, Cubic.of_b_eq_zero', Pi.constRingHom_apply, WeierstrassCurve.Affine.derivative_addPolynomial_slope, MvPolynomial.map_expand_pow_char, isLocalHom_of_comp, Polynomial.support_C_mul_X_pow', Module.End.isSemisimple_sub_algebraMap_iff, xInTermsOfW_aux, RatFunc.ofFractionRing_comp_algebraMap, Polynomial.eq_C_content_mul_primPart, PowerSeries.sub_const_eq_X_mul_shift, CommSemiRingCat.forget_preservesLimits, algebraMap_mk, MvPolynomial.mapRange_eq_map, RestrictedProduct.evalRingHom_apply, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, Polynomial.rootMultiplicity_mul_X_sub_C_pow, WittVector.ghostComponent_frobeniusFun, RatFunc.algebraMap_X, Ideal.Quotient.stabilizerHom_apply, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_apply, NumberField.CMExtension.equivMaximalRealSubfield_apply, IsLocalization.Away.isUnit_of_dvd, apply_eq_dotProduct_toMatrix₂_mulVec, Ideal.map_evalRingHom_pi, PowerSeries.constantCoeff_C, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal, CommRingCat.hom_inv_apply, ENat.toENNRealRingHom_apply, RatFunc.intDegree_C, HomogeneousLocalization.awayMap_fromZeroRingHom, IsIntegralClosure.algebraMap_injective', Polynomial.algebraMap_pi_self_eq_eval, MvPolynomial.totalDegree_eq_zero_iff_eq_C, Polynomial.eval₂_at_natCast, NumberField.Units.mem_torsion, AlgebraicIndependent.algebraMap_injective, Subalgebra.LinearDisjoint.trace_algebraMap, ContinuousLinearMap.map_smulₛₗ, Polynomial.card_support_eq', UpperHalfPlane.coe_smul, Complex.inv_def, RingEquiv.ofHomInv_apply, AlgebraicGeometry.Scheme.zeroLocus_map, Polynomial.scaleRoots_aeval_eq_zero, Polynomial.C_eq_algebraMap, PowerSeries.constantCoeff_inv, Polynomial.map_roots_le, Subalgebra.coe_algebraMap, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, Module.toCentroidHom_apply_toFun, MonoidAlgebra.ringHom_ext_iff, NonUnitalStarSubalgebra.unitization_apply, Matrix.projVandermonde_map, Module.Basis.restrictScalars_repr_apply, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, Orthonormal.inner_finsupp_eq_sum_right, IsLocalization.sec_spec', CliffordAlgebra.foldr'_algebraMap, Localization.AtPrime.comap_maximalIdeal, Finset.prod_X_add_C_coeff, Polynomial.Bivariate.equivMvPolynomial_symm_C, IsLocalization.minimalPrimes_comap, AlgebraicGeometry.Scheme.Hom.ideal_ker_le, Polynomial.divX_mul_X_add, AlgebraicGeometry.AffineSpace.comp_homOfVector, Subfield.subtype_apply, Polynomial.Splits.roots_map, RootPairing.isValuedIn_iff, Complex.arg_conj, inner_map_complex, Polynomial.natSepDegree_X_pow_char_pow_sub_C, LaurentPolynomial.algebraMap_X_pow, MvPolynomial.map_hsymm, FractionalIdeal.extendedHomₐ_eq_zero_iff, SymmetricAlgebra.algebraMap_eq_zero_iff, HahnSeries.ofPowerSeries_apply_coeff, Submodule.lTensorOne'_tmul, UniformSpace.Completion.continuous_coeRingHom, GaussianInt.toComplex_add, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, Polynomial.coeffList_C, IsLocalization.mk'_add_eq_iff_add_mul_eq_mul, Polynomial.eval_intCast_map, IsIntegralClosure.algebraMap_equiv, DirectSum.decompose_symm_algebraMap, Matrix.det_one_add_X_smul, RingEquiv.ofRingHom_symm_apply, IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime, coe_fst, wittStructureRat_rec, Algebra.compHom_smul_def, AlgebraicGeometry.germ_injective_of_isIntegral, Ideal.Quotient.torsionBy_eq_span_singleton, AddMonoidHom.coe_fn_mkRingHomOfMulSelfOfTwoNeZero, pi_bijective_of_isIdempotentElem, Algebra.isUnramifiedAt_iff_map_eq, WeierstrassCurve.Jacobian.map_addY, CFC.abs_algebraMap, MvPolynomial.expand_eq_C, Polynomial.roots_expand_image_frobenius_subset, Submodule.rTensorOne'_tmul, Ideal.relNorm_algebraMap', RingCon.lift_bijective_iff, AlgebraicGeometry.isClosedImmersion_iff_isAffineHom, Polynomial.comp_eq_zero_iff, RatFunc.smul_eq_C_smul, PowerSeries.invUnitsSub_mul_sub, AnalyticAt.harmonicAt_conj, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, exists_root_adjoin_eq_top_of_isCyclic, existsUnique_isIdempotentElem_eq_of_ker_isNilpotent, Algebra.TensorProduct.basisAux_tmul, AlgebraicGeometry.AffineSpace.hom_ext_iff, groupCohomology.norm_ofAlgebraAutOnUnits_eq, CommRingCat.forget₂CommSemiRing_preservesLimits, IsLocalization.isPrime_of_isPrime_disjoint, DividedPowers.IsDPMorphism.map_dpow, MvPowerSeries.monomial_zero_eq_C_apply, ValuativeExtension.vle_iff_vle, RootPairing.algebraMap_rootFormIn, ModP.preVal_mk, QuadraticAlgebra.norm_coe, map_closureS, Localization.localAlgHom_apply, RatFunc.valuation_eq_LaurentSeries_valuation, FractionalIdeal.extendedHomₐ_eq_one_iff, GaussianInt.toComplex_sub, Polynomial.integralNormalization_eval₂_eq_zero, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen, Perfection.coeff_iterate_frobenius, bijective_algebraMap_of_linearEquiv, Polynomial.degree_X_pow_sub_C, SkewMonoidAlgebra.coe_algebraMap, PowerSeries.monomial_zero_eq_C, isIntegral_algebraMap, NumberField.Units.coe_neg_one, FractionalIdeal.mem_coeIdeal, Matrix.SpecialLinearGroup.scalar_eq_coe_self_center, PrimeSpectrum.toPiLocalization_bijective, Ideal.map_quotient_self, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Valuation.comap_supp, Unitization.norm_eq_sup, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_lt', Algebra.discr_of_matrix_mulVec, IsLocalization.mk'_mem_map_algebraMap_iff, SemiRingCat.FilteredColimits.forget_preservesFilteredColimits, MvPolynomial.degrees_map_le, Ideal.IsIntegralClosure.comap_lt_comap, Ideal.Quotient.exists_algEquiv_fixedPoint_quotient_under, LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, AlgEquiv.toUnder_inv_right_apply, Perfection.map_apply_coe, Irreducible.natSepDegree_eq_one_iff_of_monic, Polynomial.natDegree_X_pow_add_C, Matrix.scalar_commute, Submodule.span_algebraMap_image_of_tower, Ideal.mk_mem_cotangentIdeal, isLocalHom_comp, RatFunc.map_apply_div, AlgebraicGeometry.Scheme.basicOpen_res_eq, GaussianInt.toComplex_star, Polynomial.divX_C_mul, MvPowerSeries.comp_subst_apply, FreeCommRing.lift_comp_of, Polynomial.iterate_derivative_C, SkewMonoidAlgebra.liftNC_one, WeierstrassCurve.Affine.map_slope, NormedSpace.algebraMap_exp_comm, MvPolynomial.eval_eq, FreeRing.hom_ext_iff, cfc_le_algebraMap, Polynomial.degree_mul_leadingCoeff_self_inv, Polynomial.mahlerMeasure_X_add_C, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, AlgebraicGeometry.Scheme.Hom.stalkFunctor_toImage_injective, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Complex.conjAe_coe, RingHomInvPair.comp_apply_eq, AlgebraicGeometry.Scheme.image_basicOpen, map_sub, IsLocalRing.ResidueField.map_map, IsLocalization.algEquivOfAlgEquiv_eq_map, Polynomial.taylor_X_pow, GaussianInt.toComplex_def, CliffordAlgebra.changeForm_ι_mul_ι, AlgebraicGeometry.LocallyRingedSpace.Hom.prop, TopCat.Presheaf.SubmonoidPresheaf.map, AlgebraicGeometry.SurjectiveOnStalks.surj_on_stalks, IsLocalRing.exists_surjective_of_not_isLocalRing, IsLocalization.map_integerMultiple, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, LaurentPolynomial.algebraMap_eq_toLaurent, Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zero, PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, PowerSeries.map_eq_zero, AlgEquivClass.commutes, Differential.mapCoeffs_C, spectrum.preimage_algebraMap, PerfectRing.lift_id_apply, Algebra.FinitePresentation.ker_fG_of_surjective, Polynomial.comp_C_mul_X_coeff, smul_algebraMap, starRingEnd_apply, Ideal.spanRank_map_le, MvPolynomial.isUnit_iff_eq_C_of_isReduced, Complex.conj_mul', gal_C_isSolvable, Ideal.spanFinrank_map_le_of_fg, Polynomial.resultant_X_sub_C_pow_left, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, ModuleCat.smulNatTrans_apply_app, Algebra.normalizedTrace_algebraMap_apply_eq_self, algebraMap_le_cfc, Subalgebra.algebraMap_mem', HahnSeries.ofPowerSeries_X, CommRingCat.commMon_forget₂_obj_coe, Polynomial.toLaurent_X_pow, StarSubalgebra.coe_bot, Complex.sin_conj, GaussianInt.to_real_re, Polynomial.derivative_C_mul_X, CommRingCat.toAlgHom_apply, Polynomial.Bivariate.swap_X, MvPolynomial.eval_add, WeierstrassCurve.Projective.map_polynomialX, AdjoinRoot.lift_mk, Polynomial.eval_iterate_derivative_rootMultiplicity, Algebra.SubmersivePresentation.map_jacobianRelationsOfHasCoeffs, WeierstrassCurve.Affine.CoordinateRing.map_mk, Polynomial.Splits.X_add_C, LocallyConstant.mapRingHom_apply_apply, AlgebraicGeometry.SurjectiveOnStalks.stalkMap_surjective, IsLocalRing.ResidueField.map_residue, RingCat.forget_preservesLimitsOfSize, MvPowerSeries.trunc_map, isIntegralElem_leadingCoeff_mul, Polynomial.degree_C_lt, algebraMap_comp_intCast, PowerSeries.coeff_exp, Complex.conj_eq_iff_re, IsSelfAdjoint.algebraMap, Localization.mapToFractionRing_apply, coe_frobeniusEquiv, Polynomial.aeval_conj, StarAlgHom.ofId_apply, Polynomial.nextCoeff_C_eq_zero, CommRingCat.HomTopology.isEmbedding_hom, PerfectRing.liftAux_id_apply, RCLike.re_eq_add_conj, NumberField.integralBasis_repr_apply, Matrix.scalarAlgHom_apply, Polynomial.degree_C_mul_X_pow_le, Polynomial.separable_prod_X_sub_C_iff', RingCon.coe_algebraMap, Polynomial.le_trailingDegree_C_mul_X_pow, AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_hom_eq_germ_apply, Polynomial.map_mapRingHom_evalEval, PowerSeries.spanFinrank_eq_spanFinrank_map_constantCoeff_of_X_notMem_of_fg_of_isPrime, AdjoinRoot.root_isInv, MvPolynomial.eval₂_eq', Module.algebraMap_end_eq_smul_id, LocallyConstant.constRingHom_apply, PowerSeries.trunc_one_left, LaurentSeries.coe_X_compare, WeierstrassCurve.Jacobian.baseChange_polynomial, IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, codomain_trivial_iff_map_one_eq_zero, WittVector.IsPoly.map, Polynomial.coeff_mul_C, MvPolynomial.eval_monomial, PrimeSpectrum.sigmaToPi_asIdeal, MonomialOrder.degree_C, RingCat.ofHom_apply, Ideal.quotientToQuotientRangePowQuotSucc_surjective, smoothSheafCommRing.ι_forgetStalk_inv_apply, DoubleCentralizer.algebraMap_snd, Polynomial.rootMultiplicity_C, WittVector.ker_map_le_ker_mk_comp_ghostComponent, Polynomial.eq_prod_roots_of_splits_id, RCLike.wInner_const_left, Valuation.Integers.dvdNotUnit_iff_lt, Ideal.le_comap_of_ramificationIdx_ne_zero, RatFunc.laurentAux_algebraMap, RCLike.wInner_cWeight_const_left, MvPolynomial.coe_eval₂Hom, MvPolynomial.vars_C_mul, Polynomial.coeff_C, PowerSeries.sub_const_eq_shift_mul_X, Algebra.algebraMapSubmonoid_le_comap, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, AdjoinRoot.modByMonicHom_mk, QuadraticAlgebra.coe_norm_eq_mul_star, Ideal.localized₀_eq_restrictScalars_map, Algebra.intNorm_eq_of_isLocalization, Algebra.Generators.toAlgHom_ofComp_rename, DirectSum.decompose_algebraMap, Valuation.Integers.valuation_unit, Polynomial.natDegree_X_sub_C, IsLocalization.localization_localization_map_units, IsLocalization.Away.mul_invSelf, WeierstrassCurve.Affine.CoordinateRing.mk_φ, wittStructureRat_rec_aux, WittVector.fontaineThetaModPPow_teichmuller, WeierstrassCurve.Projective.eval_polynomialZ, trace_eq_sum_roots, Matrix.matPolyEquiv_charmatrix, Polynomial.natDegree_C_mul, NumberField.canonicalEmbedding.nnnorm_eq, CliffordAlgebra.foldl_algebraMap, Submodule.rTensorOne_tmul, Algebra.Generators.ker_localizationAway, Polynomial.card_support_eq_three, RatFunc.algebraMap_apply_div, algebraMap_memℓp_infty, FractionalIdeal.mem_coeIdeal_of_mem, spectrum.mem_resolventSet_iff, AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst, Algebra.WeaklyQuasiFiniteAt.comap_algEquiv, RatFunc.div_smul, MvPolynomial.constantCoeff_smul, HahnSeries.C_zero, IntermediateField.algebraMap_apply, MvPolynomial.algHom_C, LinearMap.toMatrix_algebraMap, IsAlgClosure.equivOfEquiv_symm_algebraMap, MvPolynomial.leadingCoeff_toLex_C, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, Ideal.Quotient.factor_surjective, Polynomial.resultant_X_sub_C_pow_right, RCLike.inner_apply, IsSelfAdjoint.conj_eq, WittVector.iterate_frobenius_coeff, Polynomial.smeval_C_mul, Complex.conj_cpow_eq_ite, PerfectionMap.map_map, Polynomial.X_sub_C_dvd_sub_C_eval, MvPolynomial.eval_pow, QuadraticAlgebra.algebraMap_eq, Algebra.discr_of_matrix_vecMul, RingCon.coe_quotientKerEquivRangeS_mk, WeierstrassCurve.Ψ_three, Subsemiring.comap_toSubmonoid, Polynomial.prime_X_sub_C, Matrix.Module.scalar_smul, IntermediateField.LinearDisjoint.norm_algebraMap, MvPolynomial.eval₂Hom_zero'_apply, PowerSeries.coe_zero, FractionalIdeal.exists_mem_algebraMap_eq, Polynomial.eval₂_def, DoubleCentralizer.algebraMap_toProd, PowerSeries.IsWeierstrassDivisorAt.isUnit_shift, RatFunc.eval_C, RingTheory.Sequence.isWeaklyRegular_append_iff', Valuation.supp_quot, RCLike.hasSum_conj, Lagrange.iterate_derivative_interpolate, Ideal.ideal_prod_eq, PowerSeries.map_X, injective, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, CommRingCat.forgetToRingCat_obj, WeierstrassCurve.Projective.map_addY, Ideal.map_snd_prod, CommRingCat.Colimits.cocone_naturality_components, isSMulRegular_algebraMap_iff, iterateFrobenius_def, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, UniformSpace.Completion.algebraMap_def, Matrix.toLinearMapₛₗ₂'_apply, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, IntermediateField.adjoin.range_algebraMap_subset, IsAdjoinRoot.lift_map, Ideal.relNorm_algebraMap, AlgebraicGeometry.Scheme.evaluation_naturality_apply, Polynomial.C_sub, LaurentPolynomial.single_eq_C, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, OrthogonalIdempotents.surjective_pi, Polynomial.roots_X_pow_char_sub_C_pow, mem_rangeS, PrimeSpectrum.discreteTopology_iff_toPiLocalization_surjective, rangeS_top_iff_surjective, Complex.normSq_conj, Valuation.HasExtension.val_algebraMap, WeierstrassCurve.VariableChange.map_t, DividedPowers.DPMorphism.toRingHom_apply, Subfield.coe_subtype, MvPolynomial.derivation_C, PowerSeries.constantCoeff_divXPowOrder, Matrix.submonoidCenter_eq_scalar_map, IsLocalization.isLocalization_of_submonoid_le, Polynomial.Bivariate.swap_C_C, Module.Basis.localizationLocalization_repr_algebraMap, Ideal.Quotient.eq_zero_iff_mem, ValuationSubring.algebraMap_apply, AdjoinRoot.liftAlgHom_mk, IsLocalRing.ResidueField.map_id_apply, MvPolynomial.dvd_smul_X_iff_exists, PowerSeries.inv_eq_zero, tensorKaehlerQuotKerSqEquiv_tmul_D, smoothSheafCommRing.eval_surjective, Complex.add_conj, WeierstrassCurve.Projective.map_dblY, Zsqrtd.lift_apply_apply, LinearMap.hasEigenvalue_zero_tfae, Polynomial.iterate_derivative_eq_sum, Complex.tanh_conj, AlgebraicGeometry.Scheme.residue_surjective, Ideal.finrank_quotient_map, MvPolynomial.schwartz_zippel_sup_sum, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, MvPolynomial.mem_map_C_iff, Polynomial.algEquivAevalXAddC_symm_apply, FractionalIdeal.coeSubmoduleHom_apply, contraction_of_isPowMul_of_boundedWrt, MvPolynomial.prime_C_iff, derivationToSquareZeroEquivLift_symm_apply_apply_coe, Polynomial.isMaximal_comap_C_of_isJacobsonRing, WittVector.ghostComponentModPPow_teichmuller_coeff, Polynomial.nextCoeff_X_sub_C, LaurentSeries.exists_powerSeries_of_memIntegers, Polynomial.natDegree_C_mul_X_pow, MvPolynomial.eval_mul, AdjoinRoot.coe_mkₐ, Ideal.Quotient.algEquivOfEqComap_apply, Ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff, TensorAlgebra.algebraMap_eq_one_iff, WittVector.iterate_verschiebung_iterate_frobenius, GaussianInt.to_real_im, LinearMap.norm_extendTo𝕜'_apply_sq, DirectLimit.Ring.of_f, ENNReal.coe_ofNNRealHom, Ideal.quotEquivOfEq_eq_factor, Polynomial.dvd_mul_leadingCoeff_inv, galRestrictHom_symm_algebraMap_apply, RatFunc.algebraMap_C, Polynomial.C_mul_X_pow_eq_self, MvPowerSeries.map_toSubring, MvPolynomial.universalFactorizationMapPresentation_relation, coe_frobenius_comp_coe_frobeniusEquiv_symm, IsLocalization.isLocalization_isLocalization_atPrime_isLocalization, Polynomial.degree_X_sub_C_le, PowerSeries.trunc_C, Polynomial.eval₂_at_intCast, Ideal.quotientKerAlgEquivOfSurjective_apply, Matrix.mem_range_scalar_iff_commute_single', MvPolynomial.eval₂_zero_apply, GaussianInt.toComplex_re_div, AlgebraicIndependent.algebraMap_aevalEquiv, Valuation.comap_apply, IsBaseChange.toDual_comp_apply, toFun_eq_coe, IsBaseChange.linearMapLeftRightHom_toMatrix, AdjoinRoot.Minpoly.coe_toAdjoin_mk_X, IsLocalization.mk'_eq_iff_eq, LinearIsometry.map_smulₛₗ, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, Algebra.algebraMap_eq_smul_one, IsConjRoot.add_algebraMap, ContinuousLinearMap.toContinuousAddMonoidHom_injective, smoothSheafCommRing.forgetStalk_hom_comp_evalHom, Polynomial.degree_C_mul_X_le, Module.isTorsionFree_iff_algebraMap_injective, NumberField.FinitePlace.norm_def_int, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom, IsAdjoinRoot.lift_algebraMap, Module.Invertible.toModuleEnd_bijective, UpperHalfPlane.J_smul, WittVector.verschiebung_mul_frobenius, MvPolynomial.eq_C_of_isEmpty, Polynomial.expand_zero, IsLocalization.injectiveₛ, CliffordAlgebraQuaternion.ofQuaternion_mk, Polynomial.eraseLead_C_mul_X_pow, PerfectRing.lift_comp_lift_apply_eq_self, Polynomial.roots_expand_pow_map_iterateFrobenius_le, WittVector.coeff_frobenius_charP, Polynomial.Monic.natSepDegree_eq_one_iff, Polynomial.trailingDegree_C, GaussianInt.toComplex_re, WeierstrassCurve.Projective.polynomialX_eq, Subsemiring.mem_comap, PowerSeries.WithPiTopology.continuous_C, Ring.DirectLimit.ringEquiv_of, CommRingCat.FilteredColimits.forget_preservesFilteredColimits, MulSemiringActionHom.coe_fn_coe, Module.End.natCast_def, MvPolynomial.monomial_zero', X_pow_sub_C_irreducible_of_prime, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, Polynomial.roots_multiset_prod_X_sub_C, PowerSeries.coe_C, PrimeSpectrum.mem_range_comap_iff, ZMod.ringHom_map_cast, Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx, Polynomial.eval_one_map, AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes_apply, Set.up_image, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, IntermediateField.adjoin.algebraMap_mem, prod_bijective_of_isIdempotentElem, Polynomial.homogenize_C_mul, IsLocalRing.exists_factor_valuationRing, AdjoinRoot.powerBasisAux'_repr_symm_apply, spectrum.add_singleton_eq, MvPowerSeries.map_eq_zero, isLocalHom_id, Matrix.algebraMap_eq_diagonal, IsLocalHom.of_specComap_surjective, Localization.mk_one_eq_algebraMap, Polynomial.contract_C, NonUnitalSubalgebra.unitization_apply, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, Polynomial.sylvester_map_map, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, AdicCompletion.Ideal.mk_eq_mk, Matrix.charpoly_fin_two, LinearMap.eval_charpoly, Algebra.mul_sub_algebraMap_pow_commutes, RCLike.conj_tsum, coe_one, ZMod.ringHom_surjective, AddChar.starComp_apply, Polynomial.separable_prod_X_sub_C_iff, Polynomial.resultant_C_left, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, Algebra.ofId_apply, Polynomial.natDegree_mul_C_of_isUnit, Polynomial.dickson_add_two, surjective_algebraMap_of_linearMap, FreeRing.lift_comp_of, AdjoinRoot.quotEquivQuotMap_apply_mk, WeierstrassCurve.Projective.map_dblU, PowerSeries.coe_neg, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Derivation.map_algebraMap, MvPolynomial.eval_indicator_apply_eq_zero, Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd, Polynomial.Bivariate.swap_map_C, MvPolynomial.sumToIter_iterToSum, Polynomial.Monic.eq_X_add_C, MvPowerSeries.coeff_C_mul, Perfection.ext_iff, MvPolynomial.map_surjective_iff, Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_snd, LaurentPolynomial.eval₂_C_mul_T_neg_n, constantCoeff_wittPolynomial, WeierstrassCurve.Affine.CoordinateRing.mk_Ψ_sq, Ideal.comap_map_quotientMk, surjective_iff_epi_and_finite, CliffordAlgebra.reverse.commutes, AlgebraicGeometry.Scheme.map_basicOpen, IsLocalization.nonZeroDivisors_le_comap, WeierstrassCurve.Projective.polynomialY_eq, MvPolynomial.aeval_eq_constantCoeff_of_vars, Polynomial.eq_C_of_degree_le_zero, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, SemiRingCat.forgetReflectIsos, WittVector.ghostMap_apply, GaussianInt.toComplex_inj, WeierstrassCurve.Projective.negDblY_eq, Algebra.norm_eq_prod_automorphisms, PresheafOfModules.Derivation'.d_app, Ideal.minimalPrimes_eq_comap, MvPowerSeries.constantCoeff_toSubring, MulChar.starComp_apply, Submodule.torsionBy.mk_ideal_smul, RCLike.wInner_const_right, SetLike.algebraMap_mem_graded, Matrix.sub_scalar_sq_eq_disc, AddMonoidAlgebra.coe_mapRangeRingHom, Polynomial.contentIdeal_C, Ideal.Quotient.mkₐ_ker, Polynomial.eval_C_X_eval₂_map_C_X, MvPolynomial.map_injective_iff, PowerSeries.gaussNorm_C, SetLike.GradeZero.coe_algebraMap, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, Polynomial.supNorm_C, SetSemiring.down_imageHom, OrthogonalIdempotents.lift_of_isNilpotent_ker, Complex.cot_conj, DividedPowers.DPMorphism.ideal_comp, Bijective.containsIdentities, FaithfullyFlat.codescendsAlong_surjective, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, MvPolynomial.constantCoeff_monomial, MvPolynomial.smul_eval, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, AlgebraicGeometry.StructureSheaf.const_algebraMap, Subsemiring.inclusion_injective, Ideal.Quotient.mk_surjective, RCLike.conj_eq_iff_real, DividedPowers.isDPMorphism_def, DirectSum.toSemiring_apply, matPolyEquiv_map_C, WittVector.ghostComponent_verschiebung, PowerSeries.map_subst, MvPolynomial.C_eq_zero, MvPolynomial.supDegree_toLex_C, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, smoothSheafCommRing.ι_forgetStalk_inv_assoc, Polynomial.card_roots_X_pow_sub_C, NumberField.InfinitePlace.embedding_of_isReal_apply, MvPolynomial.aeval_zero, Ideal.Quotient.eq, Ideal.quotientEquivAlgOfEq_mk, Valuation.HasExtension.instIsLocalHomValuationInteger, sclosure_preimage_le, PresheafOfModules.map_comp, IsScalarTower.algebraMap_smul, IsLocalization.mk'_eq_iff_eq_mul, Algebra.Norm.Transitivity.eval_zero_comp_det, MvPowerSeries.algebraMap_apply'', IsLocalization.coe_toLocalizationMap, LinearMap.map_mul_algebraMap, Ideal.comap_surjective_of_faithfullyFlat, MvPowerSeries.rescale_homogeneous_eq_smul, surjectiveOnStalks_iff_forall_maximal', IsFractionRing.mk'_mk_eq_div, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, NumberField.RingOfIntegers.coe_injective, Language.map_map, MvPolynomial.constantCoeff_X, MvPolynomial.frobenius_zmod, PowerSeries.expand_C, Polynomial.derivative_sq, Polynomial.leadingCoeff_C_mul_X_pow, WittVector.frobeniusPolyAux_eq, Polynomial.mem_roots_sub_C, Orthonormal.inner_left_sum, algebraMap_le_iff_le_spectrum, PowerSeries.map_algebraMap_eq_subst_X, RatFunc.liftAlgHom_apply_div, Subring.closure_preimage_le, CyclotomicRing.adjoin_algebra_injective, Polynomial.isMaximal_comap_C_of_isMaximal, Polynomial.not_isUnit_X_add_C, Polynomial.degree_cubic, ModuleCat.Derivation.d_map, Polynomial.natSepDegree_C_mul, UpperHalfPlane.petersson_symm, Algebra.Extension.Hom.mapKer_apply_coe, StarSubalgebra.algebraMap_mem, FreeAlgebra.algebraMap_inj, PrimeSpectrum.range_comap_snd, LaurentPolynomial.C_eq_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, Localization.monoidOf_eq_algebraMap, PowerSeries.constantCoeff_largeSchroderSeries, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, IsLocalization.toInvSubmonoid_mul, WeierstrassCurve.Projective.baseChange_polynomialX, ExteriorAlgebra.isUnit_algebraMap, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom, CommRingCat.ofHom_apply, GradedTensorProduct.algebraMap_def', WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul, MvPolynomial.C_mul', Polynomial.cyclotomic.eval_apply, frobenius_neg, PerfectionMap.comp_equiv, MvPolynomial.isEmptyAlgEquiv_apply, IsPRadical.ker_le, MvPolynomial.bind₂_X_right, Ideal.Quotient.factor_ker, IsLocalization.scaleRoots_commonDenom_mem_lifts, IsSepClosed.algebraMap_surjective, PowerSeries.C_eq_algebraMap, Algebra.Generators.cMulXSubOneCotangent_eq, MvPolynomial.map_C, Polynomial.eval₂_at_one, spectrum.singleton_add_eq, UpperHalfPlane.σ_ofReal, TruncatedWittVector.truncate_surjective, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, AlgebraicGeometry.isOpenImmersion_eq_inf, Polynomial.resultant_X_add_C_left, gal_X_sub_C_isSolvable, boolRingCatEquivBoolAlg_inverse, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap, PrimeSpectrum.piLocalizationToMaximal_surjective, MvPolynomial.C_dvd_iff_dvd_coeff, Algebra.IsInvariant.isInvariant, iterate_map_frobenius, isIntegrallyClosedIn_iff, MvPolynomial.pderiv_C_mul, Filter.Germ.coe_coeRingHom, TwoSidedIdeal.comap_comap, map_iterate_frobeniusEquiv_symm, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eq₁, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap_1, IsLocalization.AtPrime.map_eq_maximalIdeal, DoubleQuot.ker_quotLeftToQuotSup, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, matrixEquivTensor_apply_symm, Polynomial.IsMonicOfDegree.aeval_add, Polynomial.natDegree_multiset_prod_X_sub_C_eq_card, CommSemiRingCat.FilteredColimits.forget_preservesFilteredColimits, NumberField.RingOfIntegers.isIntegral_coe, Matrix.toMvPolynomial_eval_eq_apply, Polynomial.C_dvd_iff_dvd_coeff, IsAdjoinRoot.lift_self_apply, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, RestrictScalars.ringEquiv_map_smul, LaurentPolynomial.single_eq_C_mul_T, Ideal.under_def, AlgHom.toUnder_right, AddMonoidAlgebra.mapDomain_algebraMap, Polynomial.Splits.C_mul_X_pow, Ideal.Factors.liesOver, WittVector.constantCoeff_wittMul, AlgHom.liftNormal_commutes, spectrum.singleton_sub_eq, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, AlgebraicGeometry.instIsZariskiLocalAtTargetStalkwiseBijectiveCoeRingHom, map_mulVec, IsAdicComplete.mk_liftAlgHom, op_symm_apply_apply, CStarAlgebra.mul_star_le_algebraMap_norm_sq, Polynomial.exists_eq_X_add_C_of_natDegree_le_one, Algebra.Generators.self_algebra_smul, MvPowerSeries.map_map, Matrix.charpoly_coeff_eq_prod_coeff_of_le, AdjoinRoot.Polynomial.quotQuotEquivComm_mk, Ideal.quotientInfEquivQuotientProd_snd, IsLocalization.toLocalizationMap_toMonoidHom, IntermediateField.AdjoinPair.algebraMap_gen₁, RatFunc.denom_div, algebraMapCLM_apply, WeierstrassCurve.coe_inv_map_Δ', Polynomial.opRingEquiv_symm_C_mul_X_pow, Polynomial.eval_map_apply, ker_coe_toRingHom, PowerSeries.invOfUnit_eq, DirectSum.coeRingHom_of, IsIntegralClosure.algebraMap_mk', WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, BoundedLatticeHom.asBoolRing_apply, PrimeSpectrum.preimage_comap_zeroLocus_aux, ValuationRing.of_integers, Polynomial.contentIdeal_map_eq_map_contentIdeal, Algebra.smulTower_leftMulMatrix_algebraMap_ne, PerfectRing.liftAux_id, quasispectrum.algebraMap_mem_iff, IsDiscreteValuationRing.exists_lift_of_le_one, Polynomial.iterate_derivative_prod_X_sub_C, CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, Polynomial.signVariations_eraseLead_mul_X_sub_C, IsLocalization.AtPrime.isMaximal_map, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, Valuation.HasExtension.algebraMap_mem_valuationSubring, eval_det, Polynomial.dvd_content_iff_C_dvd, NoZeroSMulDivisors.iff_algebraMap_injective, cfc_const, LaurentPolynomial.comul_C, NumberField.InfinitePlace.denseRange_algebraMap_pi, Polynomial.coeff_C_succ, algebraMap_injective_of_field_isFractionRing, MvPolynomial.funext_set_iff, map_adjugate, IsLocalization.algEquivOfAlgEquiv_symm_apply, Algebra.commute_algebraMap_left, Complex.inner, WittVector.map_verschiebung, Polynomial.separable_C, coe_iterateFrobenius, WittVector.verschiebung_frobenius, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Orthonormal.inner_finsupp_eq_sum_left, MvPolynomial.map_monomial, QuasispectrumRestricts.algebraMap_image, Polynomial.instIsLocalHomRingHomC, HopfAlgebra.mul_antipode_rTensor_comul_apply, BoolRing.hasForgetToBoolAlg_forget₂_map, AddMonoidAlgebra.liftNC_smul, MvPowerSeries.rescale_rescale, Ring.DirectLimit.quotientMk_of, AlgEquiv.toUnder_hom_right_apply, MvPolynomial.aeval_map_algebraMap, Algebra.Generators.Hom.toAlgHom_C, NumberField.RingOfIntegers.mapRingHom_apply, ModuleCat.HasColimit.coconePointSMul_apply, RatFunc.intDegree_polynomial, LaurentPolynomial.eval₂_C, cfc_eval_C, Polynomial.mahlerMeasure_X_sub_C, RCLike.continuous_conj, Ideal.comap_map_mk, minpoly.add_algebraMap, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, Polynomial.not_ker_le_map_C_of_surjective_of_weaklyQuasiFiniteAt, AlgebraicGeometry.Scheme.stalkMap_hom_inv_apply, iterate_frobenius, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, PowerSeries.map_invUnitsSub, IsLocalization.lift_id, Ideal.isPrime_map_C_of_isPrime, Matrix.GeneralLinearGroup.mem_center_iff_val_eq_scalar, CommRingCat.HomTopology.continuous_apply, Polynomial.div_eq_quo_add_rem_div, norm_algebraMap, UpperHalfPlane.coe_J_smul, ContinuousLinearMap.toContinuousAddMonoidHom_inj, NumberField.Units.coe_pow, IsPurelyInseparable.algebraMap_elemReduct_eq', MulSemiringAction.charpoly_eq, RootPairing.algebraMap_posRootForm_posForm, DoubleQuot.coe_quotQuotEquivQuotOfLEₐ, MvPolynomial.esymmAlgHom_zero, CliffordAlgebra.EquivEven.v_sq_scalar, LaurentSeries.LaurentSeries_coe, MvPowerSeries.map_monomial, MvPolynomial.coeToMvPowerSeries.algHom_apply, Ideal.quotientToQuotientRangePowQuotSucc_injective, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope, IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk, Algebra.idealMap_isLocalizedModule, Polynomial.isMonicOfDegree_one_iff, PrimeSpectrum.closure_image_comap_zeroLocus, root_X_pow_sub_C_pow, mem_rangeS_self, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, PerfectionMap.comp_symm_equiv, NumberField.conj_basisMatrix, char_dvd_card_solutions, coe_fieldRange, CommSemiRingCat.comp_apply, AlgebraicGeometry.Scheme.basicOpen_appLE, Mathlib.Tactic.ComputeDegree.natDegree_C_le, AlgHom.coe_ideal_map, WeierstrassCurve.Jacobian.polynomialZ_eq, NumberField.Units.abs_det_eq_abs_det, rangeRestrictFieldEquiv_apply_symm_apply, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, MvPolynomial.eval₂Hom_map_hom, LaurentPolynomial.eval₂_toLaurent, IsPurelyInseparable.algebraMap_iterateFrobenius, AlgebraicGeometry.Scheme.Hom.stalkSpecializes_stalkMap_apply, Polynomial.coe_mapRingHom, CommSemiRingCat.id_apply, Polynomial.C_mul_dvd, AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap', Algebra.trace_localization, MvPolynomial.finSuccEquiv_eq, char_dvd_card_solutions_of_sum_lt, Algebra.adjoin_eq_adjoin_union, CommRingCat.forget_map_apply, Module.algebraMap_end_apply, MvPowerSeries.isUnit_constantCoeff, PowerSeries.constantCoeff_divXPowOrder_eq_zero_iff, MvPolynomial.homogeneousComponent_zero, FractionalIdeal.exists_ne_zero_mem_isInteger, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, Algebra.discr_powerBasis_eq_prod, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, Matrix.mem_range_scalar_of_commute_single, NumberField.InfinitePlace.isometry_embedding_of_isReal, Matrix.scalar_comm_iff, Polynomial.C_comp, pNilradical_le_ker_of_perfectRing, MvPolynomial.coeff_map, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, OrthogonalIdempotents.map, MvPolynomial.monomial_sum_index, Polynomial.div_C, LinearMap.IsSymm.eq, spectralNorm_extends, InfiniteGalois.mem_range_algebraMap_iff_fixed, Algebra.Smooth.exists_finiteType, ContinuousLinearEquiv.map_smulₛₗ, Ring.DirectLimit.map_id, CliffordAlgebra.contractLeft_ι, Matrix.mvPolynomialX_mapMatrix_eval, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero, Polynomial.comp_one, IsLocalization.mem_localizationLocalizationSubmodule, Ideal.mem_map_C_iff, RingHomIsometric.norm_map, isLocalHom_of_isIso, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, PadicInt.ker_toZModPow, Polynomial.sumIDeriv_X, WeierstrassCurve.Δ_integral_of_isIntegral, map_zero, Algebra.trace_algebraMap_of_basis, WittVector.fontaineTheta_teichmuller, CommRingCat.forget₂Ring_preservesLimits, Algebra.IsPushout.equiv_tmul, NumberField.inverse_basisMatrix_mulVec_eq_repr, CStarAlgebra.norm_le_iff_le_algebraMap, Polynomial.dvd_C_mul_X_sub_one_pow_add_one, RatFunc.denom_div_dvd, MonomialOrder.degree_eq_zero_iff, Polynomial.rootSet_C, matPolyEquiv_symm_C, RingCat.forgetReflectIsos, Polynomial.eval₂_at_zero, Polynomial.toFinsupp_algebraMap, injective_respectsIso, PowerSeries.constantCoeff_zero, Polynomial.Bivariate.equivMvPolynomial_C_X, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Polynomial.lifts_iff_coeff_lifts, Prod.algebraMap_apply, Polynomial.natDegree_mul_C_eq_of_mul_ne_zero, StarSubalgebra.range_subset, Polynomial.coe_compRingHom, NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iff, DividedPowers.isSubDPIdeal_ker, RatFunc.laurent_C, Polynomial.ofMultiset_apply, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, toNatAlgHom_coe, kerLift_injective, DifferentiableAt.comp_semilinear₁, MonomialOrder.leadingTerm_C, ContinuousLinearMap.comp_smulₛₗ, NumberField.Units.coe_injective, CFC.log_smul', Ideal.comap_lt_comap_of_integral_mem_sdiff, Cubic.prod_X_sub_C_eq, PowerSeries.fg_iff_of_isPrime, MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse, Module.compHom.toLinearMap_apply, Polynomial.coeToPowerSeries.algHom_apply, AdicCompletion.evalOneₐ_of, AlgebraicGeometry.LocallyRingedSpace.stalkMap_germ_apply, Polynomial.rootMultiplicity_eq_multiplicity, NumberField.Units.coe_one, WittVector.truncate_lift, spectralAlgNorm_extends, CommSemiRingCat.forget_map, Algebra.IsCentral.mem_center_iff, AlgebraicGeometry.stalkwise_Spec_map_iff, Algebra.FormallySmooth.iff_split_surjection, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Subring.mem_closure_image_of, LaurentSeries.powerSeriesRingEquiv_coe_apply, Ideal.Quotient.mk_out, Polynomial.multiset_prod_X_sub_C_nextCoeff, frobenius_def, Polynomial.C_div, Subring.integralClosure_le_iff, IsLocalization'.toIsLocalizationMap, AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι_app, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, MvPolynomial.aeval_bind₂, NumberField.IsCMField.mem_realUnits_iff, CentroidHom.toEndRingHom_apply, Polynomial.Chebyshev.algebraMap_eval_T, Lagrange.nodal_eq_mul_nodal_erase, map_iterateFrobenius, map_det, CFC.abs_algebraMap_nnreal, WittVector.ghostComponent_zero_verschiebung, Polynomial.divX_C_mul_X_pow, Submodule.mker_spanSingleton, MvPolynomial.prod_X_add_C_coeff, PowerSeries.coeff_zero_eq_constantCoeff_apply, RingQuot.mkRingHom_surjective, SeparationQuotient.mk_algebraMap, DirectSum.toSemiring_of, MvPowerSeries.inv_eq_zero, Polynomial.roots_expand_pow_map_iterateFrobenius, bijective_algebraMap_of_linearMap, LaurentPolynomial.toLaurent_support, RCLike.conj_wInner_symm, Algebra.trace_quotient_mk, IsSMulRegular.of_flat_of_isBaseChange, Complex.coe_algebraMap, CommRingCat.equalizer_ι_isLocalHom', NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo', WeierstrassCurve.ψ_three, surjective_frobenius, GradedTensorProduct.includeLeftRingHom_apply, IsCoprime.map, Algebra.surjective_algebraMap_iff, Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk, LaurentSeries.powerSeriesEquivSubring_apply, MvPolynomial.counit_surjective, MvPowerSeries.map_iterateFrobenius_expand, Polynomial.eval_zero_map, NumberField.mixedEmbedding.unitSMul_smul, RingCon.kerLift_injective, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Subring.mem_comap, Polynomial.nextCoeff_map_eq, Polynomial.derivative_pow, CommRingCat.FilteredColimits.forget₂Ring_preservesFilteredColimits, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, AlgebraicIndependent.sumElim_comp, Polynomial.C_ofNat, Polynomial.reverse_add_C, AlgebraicGeometry.stalkMap_toStalk_apply, Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree, WeierstrassCurve.Projective.negDblY_eq', MvPolynomial.quotient_mk_comp_C_injective, SymmetricAlgebra.algebraMap_eq_one_iff, injective_nat, Polynomial.isSplittingField_C, LinearMap.polyCharpolyAux_coeff_eval, IsIntegral.map_of_comp_eq, AlgebraicClosure.Monics.map_eq_prod, coe_snd, liftOfDerivationToSquareZero_apply, LocalizedModule.mul_by_divBy, AlgHomClass.commutes, Orientation.kahler_rotation_left, minpoly.dvd_map_of_isScalarTower', AlgebraicGeometry.Scheme.stalkMap_germ_apply, Ring.DirectLimit.map_comp, Polynomial.isLocalization, SemiRingCat.ofHom_apply, PowerSeries.coeff_map, GaussianInt.intCast_real_norm, SemiRingCat.hom_inv_apply, Ideal.map_of_equiv, PowerSeries.eval₂_C, ContinuousLinearMap.toContinuousAddMonoidHom_neg, WeierstrassCurve.Affine.map_negAddY, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, surjective_of_epi_of_finite, PowerSeries.constantCoeff_smul, NumberField.AdeleRing.algebraMap_injective, MvPolynomial.killCompl_map, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map, IsFractionRing.algEquivOfAlgEquiv_algebraMap, IsAlgClosed.algebraMap_bijective_of_isIntegral, IsLocalization.Away.tensor, IsLocalization.orderIsoOfPrime_symm_apply_coe, Complex.hasSum_conj, IsScalarTower.of_compHom, NormedRing.algEquivComplexOfComplete_apply, Polynomial.dickson_one_one_eq_chebyshev_T, AdjoinRoot.coe_liftAlgHom, IsLocalization.sec_spec, Polynomial.leadingCoeff_mul_C_of_isUnit, PowerSeries.comp_aeval, FunctionField.ringOfIntegers.algebraMap_injective, TrivSqZeroExt.algebraMap_eq_inl, Ideal.isMaximal_comap_of_isIntegral_of_isMaximal, AlgebraicGeometry.Scheme.coprodPresheafObjIso_hom_fst, IsAdicComplete.mk_liftRingHom, DoubleCentralizer.algebraMap_fst, MvPowerSeries.coeff_rescale, spectrum.mem_iff, OrderRingHom.coe_ringHom_apply, rootOfSplitsXPowSubC_pow, UpperHalfPlane.coe_specialLinearGroup_apply, Polynomial.not_isUnit_X_sub_C, Ideal.map_map, MvPolynomial.dvd_X_iff_exists, IsLocalization.surj_of_gcd_domain, MvPolynomial.finSuccEquiv_X_succ, WittVector.StandardOneDimIsocrystal.frobenius_apply, Polynomial.card_support_eq_two, TensorAlgebra.algebraMap_inj, AdicCompletion.factor_eval_liftRingHom, MvPowerSeries.constantCoeff_one, Algebra.smulTower_leftMulMatrix_algebraMap, CStarAlgebra.star_mul_le_algebraMap_norm_sq, Algebra.TensorProduct.tmul_one_eq_one_tmul, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, ModuleCat.mkOfSMul_smul, IsIntegral.quotient, RCLike.nnnorm_conj, MvPolynomial.eval₂Hom_eq_zero, GradedTensorProduct.algebraMap_def, Ideal.map_eq_submodule_map, IsLocalization.map_units_map_submonoid, Polynomial.eq_mul_leadingCoeff_of_monic_of_dvd_of_natDegree_le, Module.End.eigenspace_div, MonomialOrder.leadingCoeff_C, PowerSeries.constantCoeff_mk, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_obj, PowerSeries.eq_shift_mul_X_add_const, iterateFrobeniusEquiv_apply, Algebra.Extension.Hom.subToKer_apply_coe, spectrum.add_mem_add_iff, MvPolynomial.ker_mapAlgHom, Ideal.comap_map_eq_self_of_isMaximal, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, Polynomial.chebyshev_T_eq_dickson_one_one, ModuleCat.restrictScalars.smul_def, MvPolynomial.aeval_injective_iff_of_isEmpty, AlgebraicGeometry.StructureSheaf.comapₗ_const, Polynomial.resultant_map_map, WittVector.constantCoeff_wittAdd, TopCat.Presheaf.restrictOpenCommRingCat_apply, RCLike.wInner_one_const_right, GaussianInt.toComplex_im, Matrix.diagonalRingHom_apply, FaithfulSMul.algebraMap_injective, CommSemiRingCat.FilteredColimits.forget₂SemiRing_preservesFilteredColimits, GaussianInt.im_toComplex, HomogeneousLocalization.val_awayMap_eq_aux, Polynomial.iterate_derivative_C_mul, FreeRing.lift_of, MvPolynomial.eval_sub, IsLocalization.disjoint_comap_iff, Polynomial.reflect_C_mul_X_pow, Algebra.commute_algebraMap_right, Polynomial.card_support_eq_one, MonoidHom.map_iterateFrobenius, spectralNorm.eq_of_normalClosure', Ideal.Factors.finrank_pow_ramificationIdx, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, NumberField.mixedEmbedding.normAtPlace_apply, IsPRadical.comap_pNilradical, Polynomial.aroots_C_mul_X_pow, DividedPowers.Quotient.isDPMorphism, Ideal.quotientMulEquivQuotientProd_fst, Matrix.charpoly_sub_diagonal_degree_lt, CliffordAlgebra.forall_mul_self_eq_iff, Complex.dist_conj_conj, IsAlgClosure.equivOfEquiv_algebraMap, Subring.subtype_apply, Polynomial.leadingCoeff_C_mul_X, Polynomial.map_smul, nnnorm_algebraMap', LieModule.isNilpotent_toEnd_sub_algebraMap, RootPairing.IsValuedIn.exists_value, continuous_algebraMap_iff_smul, RCLike.norm_sq_re_conj_add, Complex.conjCLE_apply, Polynomial.constantCoeff_surjective, scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero, Polynomial.eraseLead_C, Polynomial.Splits.X_sub_C, PresheafOfModules.Derivation.d_app, Polynomial.isUnit_primPart_C, PowerSeries.coeff_zero_C, IsLocalRing.isLocalHom_iff_comap_closedPoint, Complex.arg_conj_coe_angle, ContinuousLinearMap.toContinuousAddMonoidHom_restrictScalars, HomogeneousLocalization.val_awayMap_mk, Complex.nndist_conj_self, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C, IsSMulRegular.of_isLocalization, PrimeSpectrum.comap_basicOpen, IsLocalization.eq_iff_eq, ZMod.ker_intCastRingHom, minpoly.eq_X_sub_C', MonoidAlgebra.lift_mapRangeRingHom_algebraMap, Set.algebraMap_mem_center, isNilpotent_tensor_residueField_iff, LinearEquiv.isSMulRegular_congr', constantCoeff_wittStructureRat_zero, Rat.ringOfIntegersEquiv_apply_coe, Polynomial.algebraMap_hahnSeries_apply, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, WeierstrassCurve.Jacobian.map_polynomialZ, Matrix.eval_charpoly, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, WeierstrassCurve.Projective.map_addXYZ, IsIntegrallyClosed.algebraMap_eq_of_integral, Algebra.weaklyQuasiFiniteAt_iff, injective_stableUnderComposition, Ideal.rank_pow_quot_aux, MeasureTheory.SimpleFunc.const_algebraMap, UpperHalfPlane.cosh_half_dist, Unitization.starMap_apply, Valuation.Integers.valuation_pos_iff_ne_zero, MvPolynomial.bind₂_C_right, RCLike.conj_im, MvPowerSeries.algebraMap_apply', PowerSeries.coeff_C, MvPolynomial.constantCoeff_eq, LinearMap.toMvPolynomial_constantCoeff, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, Ideal.Quotient.mkₐ_eq_mk, WeierstrassCurve.Projective.map_polynomialZ, FaithfulSMul.algebraMap_eq_one_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', MvPolynomial.eval_rename, Ideal.rootsOfUnityMapQuot_apply, Polynomial.Monic.comp_X_add_C, Ideal.IntegralClosure.comap_lt_comap, MvPolynomial.mkDerivationₗ_C, AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map, RCLike.conj_I, Polynomial.divX_C, coeff_minpolyDiv, IsLocalization.tmul_mk', NumberField.canonicalEmbedding.norm_le_iff, StandardEtalePresentation.toPresentation_σ', Submodule.mem_one, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, witt_structure_prop, Subsemiring.map_toSubmonoid, Ideal.map_comap_of_equiv, smul_def, Polynomial.Monic.C_dvd_iff_isUnit, bijective_frobenius, rangeRestrictField_bijective, map_nonunit, Polynomial.monic_mul_C_of_leadingCoeff_mul_eq_one, Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity, surjective_stableUnderComposition, Algebra.Presentation.coeffs_subset_range, AdjoinRoot.map_root, Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le, Polynomial.nextCoeff_map_of_leadingCoeff_ne_zero, MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zero, Polynomial.natSepDegree_C, IsIntegrallyClosed.eq_map_mul_C_of_dvd, Ideal.smul_restrictScalars, matPolyEquiv_eval_eq_map, Polynomial.monic_mul_leadingCoeff_inv, Polynomial.eq_X_sub_C_of_splits_of_single_root, AlgebraicGeometry.RingedSpace.basicOpen_res_eq, Ideal.mem_primesOver_iff_mem_normalizedFactors, WittVector.constantCoeff_wittNSMul, Polynomial.card_support_C_mul_X_pow_le_one, AlgebraicGeometry.Spec_zeroLocus, PowerSeries.coeff_inv, AlgEquiv.restrictNormal_commutes, ValuationSubring.coe_comap, PerfectClosure.mk_eq_iff, Polynomial.discr_C, NumberField.mixedEmbedding_injective, PowerSeries.rescale_injective, Polynomial.coeToPowerSeries.ringHom_apply, Polynomial.support_C_mul_X_pow, MvPolynomial.prod_C_add_X_eq_sum_esymm, spectrum.algebraMap_eq_of_mem, Polynomial.modByMonic_X_sub_C_eq_C_eval, PresheafOfModules.Monoidal.tensorHom_app, Polynomial.binomial_eq_binomial, RCLike.inv_def, DividedPowers.IsDPMorphism.dpow_comp, PowerSeries.map_expand, NumberField.RingOfIntegers.coe_eq_algebraMap, Valuation.HasExtension.val_map_eq_one_iff, Polynomial.iterate_derivative_X_pow_eq_C_mul, IsAdjoinRootMonic.coeff_algebraMap, RingCat.instFullSemiRingCatForget₂RingHomCarrierCarrier, MvPolynomial.eval₂_map_comp_C, Matrix.GeneralLinearGroup.coe_map_mul_map_inv, MvPowerSeries.rescaleAlgHom_apply, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map, MvPowerSeries.coeff_zero_C, RatFunc.liftOn'_div, Polynomial.derivative_X_pow, MvPolynomial.optionEquivRight_apply, MvPolynomial.finSuccEquiv_apply, Subfield.closure_preimage_le, IsPerfectClosure.equiv_comp_apply, Polynomial.degree_C_mul, UpperHalfPlane.exp_half_dist, Polynomial.Splits.map_roots, HomogeneousLocalization.awayMapAux_mk, MvPowerSeries.coeff_C, Polynomial.gaussNorm_C, TensorProduct.gradedComm_tmul_algebraMap, MvPolynomial.C_eq_coe_nat, SubalgebraClass.coe_algebraMap, Polynomial.Splits.eq_prod_roots_of_monic, Subalgebra.lTensorBot_tmul, IntermediateField.adjoin_eq_range_algebraMap_adjoin, RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChange, WittVector.quotientPEquiv_mk, AdjoinRoot.mk_X, Ideal.map_algebraMap_eq_finset_prod_pow, IsLocalization.injective_iff_map_algebraMap_eq, CommRingCat.inv_hom_apply, cfc_const_add, Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent, WittVector.toPadicInt_comp_fromPadicInt_ext, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_snd, fourier_neg, Polynomial.leadingCoeff_X_sub_C, RatFunc.denom_C, IsLocalization.mk'_one, Polynomial.expand_eq_C, RatFunc.num_div_dvd', WeierstrassCurve.Jacobian.baseChange_polynomialX, WeierstrassCurve.Φ_two, CyclotomicRing.algebraBase_injective, Polynomial.aeval_C, Polynomial.Monic.roots_map_of_card_eq_natDegree, Polynomial.aeval_eq_prod_aroots_sub_of_splits, Complex.conj_re, Ideal.rank_pow_quot, spectrum.add_mem_iff, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2, LaurentSeries.powerSeriesEquivSubring_coe_apply, WeierstrassCurve.Jacobian.Equation.map, MvPolynomial.degreeOf_mul_C_le, Polynomial.toLaurent_inj, PerfectClosure.r_iff, AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, PresheafOfModules.Derivation'.app_apply, CommRingCat.comp_apply, MvPolynomial.algebraTensorAlgEquiv_symm_map, MvPowerSeries.map.isLocalHom, Ideal.map_height_le_one_of_mem_minimalPrimes, Complex.im_eq_sub_conj, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, Polynomial.taylor_monomial, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, WittVector.map_eq_zero_iff, AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleCarrierStalkAbPresheafOpensCarrierTopModuleStructurePresheafPrimeComplAsIdealToStalkₗ, Algebra.Extension.Hom.algebraMap_toRingHom, Lagrange.interpolate_apply, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Polynomial.C_mul, MvPolynomial.isHomogeneous_C_mul_X_pow, Algebra.normalizedTrace_algebraMap_apply, MvPolynomial.tensorEquivSum_C_tmul_one, Polynomial.natDegree_X_sub_C_le, Polynomial.splits_X_sub_C_mul_iff, AlgebraicGeometry.basicOpen_eq_of_affine', MvPolynomial.map_iterateFrobenius_expand, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, PowerSeries.coeff_zero_eq_constantCoeff, NumberField.Units.coe_zpow, MvPowerSeries.constantCoeff_map, GaussianInt.toComplex_neg, Algebra.Extension.tensorCotangentInvFun_smul_mk, instIsPrincipalMapRingHom, MvPowerSeries.rescale_eq_subst, RootPairing.RootPositiveForm.exists_pos_eq, ContinuousLinearMap.toContinuousAddMonoidHom_id, PowerSeries.coe_X, Rat.int_algebraMap_injective, Polynomial.dickson_of_two_le, Ring.DirectLimit.ringEquiv_symm_mk, Matrix.coeff_det_one_add_X_smul_one, AlgebraicGeometry.LocallyRingedSpace.stalkSpecializes_stalkMap_apply, AlgebraicGeometry.Spec.coe_toTop_map_hom_apply_asIdeal, DoubleCentralizer.coe_eq_algebraMap, MvPolynomial.sumAlgEquiv_apply, Differential.logDeriv_algebraMap, Polynomial.degree_add_degree_leadingCoeff_inv, ContinuousLinearMap.toContinuousAddMonoidHom_sub, RootPairing.algebraMap_pairingIn', Module.Finite.toModuleEnd_moduleEnd_surjective, MvPolynomial.degreeOf_C_mul_le, Polynomial.trinomial_def, LinearEquiv.isWeaklyRegular_congr', DirectLimit.Module.hom_ext_iff, smoothSheafCommRing.ι_forgetStalk_hom_apply, Polynomial.coe_algebraMap_eq_CC, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, selfZPow_natCast, AlgebraicGeometry.stalkToFiberRingHom_germ, MvPolynomial.sumToIter_Xr, Polynomial.X_sub_C_scaleRoots, DirectSum.ringHom_ext'_iff, Complex.conj_ofNat, Ideal.quotientKerAlgEquivOfSurjective_symm_apply, mem_coeSubmodule_conductor, Module.toModuleEnd_apply, Polynomial.resultant_C_zero_left, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, conjnegRingHom_apply, Polynomial.C_eq_or_isOpenQuotientMap_eval, RingTheory.Sequence.IsWeaklyRegular.of_flat_of_isBaseChange, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, RatFunc.C_injective, TopCat.Sheaf.objSupIsoProdEqLocus_inv_eq_iff, MvPolynomial.eval_toMvPolynomial, Ideal.quotientKerAlgEquivOfSurjective_mk, MonoidAlgebra.singleOneRingHom_apply, FractionalIdeal.one_le_extendedHomₐ_iff, Polynomial.sum_taylor_eq, Subalgebra.range_subset, Nat.coe_castRingHom, UnitAddTorus.hasSum_prod_mFourierCoeff, MvPolynomial.sum_C, LocalizedModule.algebraMap_mk, Ideal.mem_quotient_iff_mem_sup, Polynomial.algebraMap_hahnSeries_injective, NumberField.mixedEmbedding.latticeBasis_apply, AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen, MvPowerSeries.constantCoeff_X, IsLocalRing.isLocalHom_residue, smoothSheafCommRing.ι_forgetStalk_hom_assoc, cyclotomicCharacter.toZModPow_toFun, LaurentSeries.valuation_coe_ratFunc, MvPolynomial.monomial_eq, Polynomial.isNilpotent_C_iff, CliffordAlgebra.star_algebraMap, Algebra.left_comm, Polynomial.disc_C, CliffordAlgebra.changeForm_algebraMap, LaurentPolynomial.counit_C_mul_T, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, MvPolynomial.aeval_eq_eval₂Hom, LinearMap.eqLocus_toAddSubmonoid, Algebra.TensorProduct.algebraMap_apply', GaussianInt.re_toComplex, DoubleQuot.coe_quotQuotToQuotSupₐ, Ideal.Quotient.norm_mk_lt, MvPolynomial.vars_C, Algebra.Extension.algebraMap_σ, Subsemiring.mem_map, Complex.ofRealHom_eq_coe, AlgebraicIndependent.aevalEquivField_apply_coe, ZMod.castHom_bijective, MvPolynomial.aeval_C, MvPolynomial.support_map_subset, IsSimpleRing.injective_ringHom_or_subsingleton_codomain, FreeAbelianGroup.liftMonoid_coe, Subalgebra.LinearDisjoint.basisOfBasisLeft_apply, NonUnitalAlgHom.toAlgHom_apply, Polynomial.hasseDeriv_C, AlgEquiv.quotientBot_symm_mk, frobenius_apply_frobeniusEquiv_symm, Unitization.nnnorm_eq_sup, Finsupp.sum_smul_index_semilinearMap', MvPowerSeries.map_frobenius_expand, IsLocalization.submonoid_map_le_is_unit, TruncatedWittVector.zmodEquivTrunc_apply, Perfection.coeff_pthRoot, Polynomial.natDegree_linear_le, algebraMap_mem, RingEquiv.ofRingHom_apply, coe_mk, IsLocalRing.basisQuotient_apply, RingHomCompTriple.comp_apply, MvPolynomial.pderiv_map, PowerSeries.exp_pow_eq_rescale_exp, Polynomial.derivation_C, minpoly_algEquiv_toLinearMap, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, CommRingCat.coyonedaUnique_inv_app_hom_apply, WeierstrassCurve.Jacobian.eval_polynomial, PowerBasis.trace_gen_eq_sum_roots, Polynomial.natDegree_det_X_add_C_le, Ideal.injective_algebraMap_quotient_residueField, Polynomial.eval_C_X_comp_eval₂_map_C_X, AdjoinRoot.algHom_subsingleton, spectralNorm.eq_of_tower, spectrum.scalar_eq, Complex.hasSum_conj', SubringClass.subtype_injective, Polynomial.toLaurent_one, NumberField.norm_embedding_le_house, AlgebraicGeometry.specTargetImageFactorization_app_injective, minpoly.root, Polynomial.mod_X_sub_C_eq_C_eval, MvPowerSeries.coeff_map, HomogeneousLocalization.Away.eventually_smul_mem, NumberField.FinitePlace.norm_eq_one_iff_notMem, AlgebraicGeometry.Scheme.IsGermInjectiveAt.cond, NumberField.canonicalEmbedding_injective, PowerSeries.monomial_eq_C_mul_X_pow, trace_quotient_eq_trace_localization_quotient, RingCat.forget₂SemiRing_preservesLimits, MvPolynomial.rename_C, Ideal.Quotient.mk_eq_mk_iff_sub_mem, WeierstrassCurve.Projective.map_dblXYZ, LinearMap.map_smulₛₗ, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, AlgHom.commutes, MvPowerSeries.map_expand, Algebra.Extension.Hom.sub_aux, MvPolynomial.eval₂_mul_C, StandardEtalePresentation.aeval_val_equivMvPolynomial, LaurentPolynomial.degree_C_ite, Perfection.coeff_frobeniusEquiv_symm, Polynomial.smul_C, Ideal.ker_quotientMap_mk, ULift.down_algebraMap, PowerBasis.exists_gen_dvd_sub, Bialgebra.counit_algebraMap, RCLike.conj_eq_iff_im, Complex.exp_conj, Algebra.discr_localizationLocalization, AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk, Padic.isUniformInducing_cast_withVal, KaehlerDifferential.derivationTensorProduct_algebraMap, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal', Pi.conj_apply, MvPolynomial.C_neg, Ideal.powQuotSuccInclusion_injective, SemiRingCat.forget₂AddCommMon_preservesLimits, Matrix.GeneralLinearGroup.val_map_apply, LinearMap.charpoly_sub_smul, LaurentPolynomial.eval₂_T_neg_n, IsLocalization.AtPrime.comap_map_of_isMaximal, IsAdjoinRoot.lift_algEquiv, MvPolynomial.coeToMvPowerSeries.ringHom_apply, WeierstrassCurve.Jacobian.map_negAddY, CommSemiRingCat.forget₂SemiRing_preservesLimitsOfSize, Polynomial.Bivariate.swap_C, IsFractionRing.num_mul_den_eq_num_iff_eq, Submodule.span_singleton_eq_one_iff, Algebra.RingHom.adjoin_algebraMap_surjective, PowerSeries.ker_coeff_eq_max_ideal, AlgHom.map_coe_real_complex, IsAlgebraic.exists_nonzero_eq_adjoin_mul, isDedekindRing_iff, MvPolynomial.coeffs_map, Polynomial.natSepDegree_X_sub_C, Polynomial.coe_normUnit, RatFunc.algebraMap_apply, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, WittVector.ghostComponent_frobenius, Perfection.lift_apply_apply_coe, ExteriorAlgebra.algebraMap_leftInverse, RCLike.conj_re_ax, smulOneHom_apply, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, spectralNorm.spectralMulAlgNorm_eq_of_mem_roots, IsLocalization.comap_map_of_isPrimary_disjoint, Algebra.trace_quotient_eq_of_isDedekindDomain, Polynomial.degree_le_zero_iff, PreTilt.coeff_iterate_frobenius, WeierstrassCurve.Jacobian.map_polynomial, HahnSeries.C_mul_eq_smul, GradedRing.projZeroRingHom'_surjective, Complex.conj_conj, AlgebraicGeometry.StructureSheaf.stalkAlgebra_map, Pi.ringHom_apply, IntermediateField.set_range_subset, IsAdjoinRoot.algebraMap_apply, Matrix.circulant_single, AdjoinRoot.lift_of, spectralValue_X_sub_C, StandardEtalePair.aeval_X_g_mul_mk_X, RootPairing.algebraMap_coroot'In_apply, AdicCompletion.transitionMap_ideal_mk, MvPolynomial.sumAlgEquiv_symm_apply, UpperHalfPlane.sinh_half_dist_add_dist, PrimeSpectrum.comap_asIdeal, coe_id, IsLocalization.map_units, MvPowerSeries.constantCoeff_expand, CommRingCat.equalizer_ι_isLocalHom, AlgebraicGeometry.Scheme.stalkMap_inv_hom_apply, MvPolynomial.eval₂_comp, Polynomial.roots_C_mul_X_sub_C, conjneg_apply, MvPolynomial.weightedHomogeneousComponent_C_mul, WeierstrassCurve.map_c₄, AlgEquiv.algebraMap_eq_apply, TensorProduct.gradedMul_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, SeparationQuotient.mkRingHom_apply, ClassGroup.exists_mk0_eq_mk0, IsStableUnderBaseChange.isLocalization_map, injective_algebraMap_of_linearMap, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, coe_comp, ker_coe_equiv, RingCat.comp_apply, LinearIsometry.im_apply_eq_im, isIntegralElem_localization_at_leadingCoeff, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, MvPolynomial.dvd_C_iff_exists, PowerSeries.map_C, AdjoinRoot.coe_mapAlgEquiv, range_eq_top, WeierstrassCurve.Affine.CoordinateRing.mk_ψ₂_sq, NumberField.mixedEmbedding.latticeBasis_repr_apply, LaurentPolynomial.antipode_C, Algebra.Generators.ker_ofAlgHom, Polynomial.rootMultiplicity_le_iff, NumberField.canonicalEmbedding.apply_at, Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zero, RingCon.kerLift_mk, AddMonoidAlgebra.liftNC_one, FreeCommRing.restriction_of, RatFunc.mk_one, AlgebraicGeometry.AffineSpace.reindex_appTop_coord, DirectSum.liftRingHom_symm_apply_coe, MvPolynomial.C_mem_pow_idealOfVars_iff, Complex.mul_conj, RatFunc.algebraMap_injective, Ideal.quotientInfToPiQuotient_mk', SubsemiringClass.subtype_apply, CommSemiRingCat.forget_preservesLimitsOfSize, isIntegrallyClosed_iff, Matrix.charmatrix_map, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalizedModule_of_mem, surjective_respectsIso, Polynomial.modByMonic_X, IsDedekindDomain.primesOverEquivPrimesOver_symm_apply, coe_monoidHom_injective, Complex.nndist_conj_comm, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, AlgEquiv.prodQuotientOfIsIdempotentElem_apply_fst, MonoidAlgebra.liftNC_smul, AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen, Ideal.Quotient.mk_eq_mk, DividedPowers.DPMorphism.coe_toRingHom, Algebra.mem_ideal_map_adjoin, LaurentSeries.coe_range_dense, X_pow_sub_C_irreducible_of_prime_pow, Algebra.algebraMap_intNorm_of_isGalois, NumberField.AdeleRing.algebraMap_fst_apply, Algebra.isEpi_iff_surjective_algebraMap_of_finite, Polynomial.integralNormalization_mul_C_leadingCoeff, WittVector.map_frobeniusPoly, RingCat.forget₂AddCommGroup_preservesLimitsOfSize, MvPolynomial.sum_eval_eq_zero, Ideal.exists_coeff_ne_zero_mem_comap_of_root_mem, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', WittVector.constantCoeff_wittZSMul, WeierstrassCurve.Jacobian.polynomialX_eq, IsLocalization.injective_iff_isRegular, MvPolynomial.aeval_C_comp_left, MvPolynomial.C_mul_X_pow_eq_monomial, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, Rat.int_algebraMap_surjective, PerfectionMap.surjective, Polynomial.iterate_derivative_X_sub_pow_self, Algebra.traceMatrix_of_matrix_mulVec, Complex.conj_natCast, FreeCommRing.map_of, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, Polynomial.X_dvd_sub_C, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, IsLocalization.mapₐ_coe, Polynomial.eval_mul_X_sub_C, AlgebraicGeometry.Proj.stalkIso'_germ, minpolyDiv_spec, Polynomial.leadingCoeff_map_of_leadingCoeff_ne_zero, SubringClass.subtype_apply, cyclotomicCharacter.spec, RingCon.lift_mk', Complex.nndist_conj_conj, Polynomial.reverse_C, restrict_apply, comp_apply, Polynomial.Splits.C_mul, Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, Polynomial.reflect_C, Polynomial.eval₂_C, TruncatedWittVector.coeff_truncate, CliffordAlgebra.contractLeft_mul_algebraMap, MvPolynomial.eval_C, MvPolynomial.IsWeightedHomogeneous.C_mul, Polynomial.comp_zero, map_geom_sum₂, Algebra.pushoutDesc_left, WeierstrassCurve.Projective.map_addU, AlgebraicGeometry.Scheme.mem_basicOpen_top, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, Polynomial.reflect_C_mul, SemiRingCat.forget_preservesLimits, CommRingCat.coyonedaUnique_hom_app_hom_apply, WittVector.mapFun.intCast, MvPowerSeries.substAlgHom_monomial, Orientation.areaForm_map_complex, RCLike.conj_to_real, Algebra.Presentation.HasCoeffs.coeffs_subset_range, Matrix.charpoly_inv, galLiftEquiv_algebraMap_apply, Ideal.instIsTwoSidedMapRingHomOfRingHomSurjective, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Complex.cpow_conj, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, WeierstrassCurve.map_b₄, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul, PowerSeries.rescale_neg_one_X, Polynomial.natDegree_sub_C, HahnSeries.C_one, prod_apply, PowerSeries.constantCoeff_exp, MaximalSpectrum.toPiLocalization_injective, GaussianInt.toComplex_zero, map_wittPolynomial, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Ideal.IsDedekindDomain.ramificationIdx_eq_factors_count, Ideal.minimalPrimes_comap_subset, RatFunc.denom_algebraMap, Polynomial.hasseDeriv_natDegree_eq_C, AlgebraicGeometry.LocallyRingedSpace.preimage_basicOpen, WeierstrassCurve.Jacobian.map_dblY, isLocalHom_of_le_jacobson_bot, QuadraticAlgebra.algebraMap_dvd_iff_dvd, map_field_closure, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Polynomial.as_sum_range_C_mul_X_pow, Submodule.IsPrincipal.contentIdeal_generator_dvd, RCLike.wInner_one_const_left, WeierstrassCurve.Projective.map_addX, MonoidAlgebra.ringHom_ext'_iff, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, PrimeSpectrum.BasicConstructibleSetData.map_f, Ideal.quotientInfToPiQuotient_mk, MvPowerSeries.algebraMap_apply, MvPolynomial.isLocalization_C_mk', FractionalIdeal.exists_eq_spanSingleton_mul, derivationToSquareZeroEquivLift_apply_coe_apply, IsLocalization.isMaximal_of_isMaximal_disjoint, Module.ker_algebraMap_end, Ideal.spanNorm_le_comap, MvPolynomial.algebraTensorAlgEquiv_tmul, matPolyEquiv_symm_map_eval, MonoidAlgebra.single_eq_algebraMap_mul_of, AdjoinRoot.quotMapOfEquivQuotMapCMapSpanMk_mk, WeierstrassCurve.Projective.map_addZ, MvPolynomial.vars_map, Polynomial.eval₂_at_apply, LinearMap.restrictScalarsField_apply_apply, Padic.coe_withValRingEquiv_symm, AlgebraicGeometry.Scheme.basicOpen_res, algebraMap_nonneg, Polynomial.derivative_C_mul_X_pow, RCLike.norm_sq_re_add_conj, Polynomial.signVariations_X_sub_C_mul_eraseLead_le, Polynomial.support_binomial, Polynomial.derivative_C, QuadraticAlgebra.mk_eq_add_smul_omega, Polynomial.roots_X_pow_char_sub_C, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, Polynomial.degree_mul_C_of_isUnit, AdjoinRoot.minpoly_powerBasis_gen, GradedRing.projZeroRingHom_apply, MvPolynomial.degreeOf_C_mul, AlgHom.ker_kerSquareLift, Polynomial.Chebyshev.algebraMap_eval_S, Matrix.GeneralLinearGroup.map_apply, MvPolynomial.C_injective, Algebra.norm_eq_prod_roots, AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv_apply, Polynomial.map_under_lt_comap_of_quasiFiniteAt, Valuation.HasExtension.mk_smul_mk, Polynomial.dickson_two_one_eq_chebyshev_U, IsLocalization.algEquiv_symm_apply, CFC.sqrt_algebraMap, MvPolynomial.C_mul, Ring.DirectLimit.exists_of, CFC.posPart_algebraMap, trace_eq_sum_embeddings, exists_integer_of_is_root_of_monic, Ideal.span_singleton_absNorm, CliffordAlgebra.contractLeft_algebraMap_mul, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1, coe_mul, IntermediateField.botEquiv_def, SemilinearEquivClass.map_smulₛₗ, liftOfDerivationToSquareZero_mk_apply', LaurentPolynomial.support_C_mul_T_of_ne_zero, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, Ideal.quotientInfEquivQuotientProd_fst, HomogeneousLocalization.den_smul_val, FreeAlgebra.algebraMap_eq_one_iff, Polynomial.C_mul_comp, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Complex.conj_eq_iff_real, WittVector.verschiebung_frobenius_comm, MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars, AlgebraicGeometry.germ_eq_zero_of_pow_mul_eq_zero, Ideal.map_comap_natCastRingHom_int, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, Polynomial.roots_expand_image_iterateFrobenius, AdjoinRoot.lift_root, IsLocalization.mk'_spec'_mk, WittVector.quotEquivOfEq_ghostComponentModPPow, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, RatFunc.eq_C_iff, AdicCompletion.evalₐ_of, RatFunc.num_mul_eq_mul_denom_iff, InnerProductSpaceable.innerProp, Polynomial.aeval_monomial, Equiv.algebraMap_def, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, Algebra.Norm.Transitivity.eval_zero_det_det, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, MvPolynomial.isLocalization, LaurentPolynomial.counit_C, IsTranscendenceBasis.sumElim_comp, AdjoinRoot.quotEquivQuotMap_symm_apply, Polynomial.bernoulli_one, HahnSeries.order_C, CompleteOrthogonalIdempotents.bijective_pi', SkewMonoidAlgebra.single_eq_algebraMap_mul_of, WeierstrassCurve.map_Δ', PowerSeries.isWeierstrassDivisionAt_iff, Valuation.Integers.valuation_irreducible_pos, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, StandardEtalePresentation.toPresentation_val, ExteriorAlgebra.liftAlternating_algebraMap, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, Ideal.isDomain_map_C_quotient, Polynomial.IsWeaklyEisensteinAt.map, RingEquiv.toRingHom_apply_symm_toRingHom_apply, matPolyEquiv_eval, RCLike.conj_inv, WittVector.exists_frobenius_solution_fractionRing_aux, Ideal.height_le_height_add_encard_of_subset, DirectLimit.Module.lift_apply, Ring.DirectLimit.Polynomial.exists_of, smoothSheafCommRing.ι_forgetStalk_hom, toIntAlgHom_coe, Polynomial.natDegree_mul_C_le, IsLocalizedModule.fromLocalizedModule'_mk, Complex.normSq_eq_conj_mul_self, Algebra.FormallyUnramified.map_maximalIdeal, ModularForm.slash_def, AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app_surjective, LinearMap.mulRight_toAddMonoidHom, AlgebraicGeometry.Scheme.preimage_zeroLocus, WittVector.iterate_verschiebung_mul_left, LinearMap.map_smul', Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, Subalgebra.algebraMap_mem, HopfAlgebra.mul_antipode_lTensor_comul_apply, LinearAlgebra.FreeProduct.lift_algebraMap, SymmetricAlgebra.algebraMap_leftInverse, Complex.conj_eq_iff_im, DividedPowers.Quotient.dpow_apply, isUnit_map, Algebra.adjoin_algebraMap, AlgEquiv.liftNormal_commutes, MvPolynomial.IsSymmetric.C, SubringClass.coe_subtype, ModP.v_p_lt_val, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, QuadraticAlgebra.coe_mem_nonZeroDivisors_iff, Localization.localRingHom_bijective_of_saturated_inf_eq_top, Polynomial.monomial_zero_left, LocalSubring.le_def, MvPolynomial.eval₂_eq, Ideal.Quotient.mk_eq_one_iff_sub_mem, Algebra.smul_def, PowerSeries.constantCoeff_toSubring, Polynomial.natDegree_mul_C, MeasureTheory.BoundedContinuousFunction.inner_toLp, MvPolynomial.ringHom_ext'_iff, Complex.dist_conj_comm, HahnSeries.map_smul, AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_mk, DividedPowers.isSubDPIdeal_map_of_isSubDPIdeal, RatFunc.liftAlgHom_apply_div', AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply, Submodule.lTensorOne_tmul, WeierstrassCurve.φ_four, Polynomial.roots_expand_pow_image_iterateFrobenius_subset, RingCon.coe_mk', IsLocalization.ringEquivOfRingEquiv_eq, PowerSeries.C_inv, surjectiveOnStalks_iff_of_isLocalHom, Polynomial.rootMultiplicity_X_sub_C_self, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, Polynomial.splits_X_sub_C, surjective, MvPolynomial.eval_sum, Complex.GammaIntegral_conj, spectralNorm_extends_of_finiteDimensional, Algebra.discr_powerBasis_eq_prod'', Polynomial.algEquivCMulXAddC_symm_apply, mem_fieldRange, TensorAlgebra.algebraMap_leftInverse, AlgebraicGeometry.Scheme.map_basicOpen_map, LocallyConstant.coe_algebraMap, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, Polynomial.opRingEquiv_symm_C, FractionalIdeal.mem_canonicalEquiv_apply, MvPolynomial.smul_eq_C_mul, FunctionField.inftyValuation.C, MvPolynomial.eval₂_monomial, SkewPolynomial.monomial_mul_monomial, MvPolynomial.counitNat_C, RCLike.enorm_conj, Ideal.quotientMap_injective, IntermediateField.adjoin_subset_adjoin_iff, IsAlgClosed.roots_eq_zero_iff, ContinuousMap.C_apply, PowerSeries.algebraMap_apply, Algebra.map_intTraceAux, Polynomial.natDegree_cubic, Polynomial.degree_leadingCoeff_inv, IsLocalization.mk'_mul_cancel_right, CommSemiRingCat.inv_hom_apply, LaurentPolynomial.comul_C_mul_T, IsLocalization.exists_integer_multiple', Polynomial.IsMonicOfDegree.aeval_sub, AdicCompletion.factor_evalₐ_eq_eval, IsLocalization.Away.surj, Algebra.Presentation.HasCoeffs.relation_mem_range_map, CliffordAlgebra.foldr_algebraMap, isStronglyTranscendental_mk_of_mem_minimalPrimes, CliffordAlgebraComplex.toComplex_involute, LaurentPolynomial.smeval_C_mul_T_n, RCLike.conjAe_coe, MaximalSpectrum.toPiLocalization_not_surjective_of_infinite, Valuation.Integers.isUnit_iff_valuation_eq_one, ModuleCat.restrictScalars.smul_def', NormedSpace.algebraMap_exp_comm_of_mem_ball, Polynomial.toFinsupp_C_mul_X_pow, Polynomial.logMahlerMeasure_const, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, Polynomial.natDegree_C_mul_of_isUnit, Polynomial.hermite_zero, Algebra.algebra_ext_iff, ZMod.castHom_injective, MvPolynomial.derivation_C_mul, Polynomial.dickson_two, Polynomial.succ_signVariations_X_sub_C_mul_monomial, Module.toAddMonoidEnd_apply_apply, Polynomial.derivative_X_add_C_sq, Ideal.Factors.finiteDimensional_quotient_pow, Cubic.eq_sum_three_roots, MvPolynomial.aeval_sumElim_pderiv_inl, WittVector.frobeniusEquiv_apply, RespectsIso.isLocalization_away_iff, RatFunc.mk_one', IsLocalization.isLocalization_algebraMapSubmonoid_map_algHom, AlgHom.map_algebraMap, Polynomial.comp_eq_sum_left, Polynomial.rootMultiplicity_X_sub_C, cfc_predicate_algebraMap, MvPolynomial.iterToSum_C_C, MvPolynomial.totalDegree_sub_C_le, WeierstrassCurve.Jacobian.map_dblU, AlgCat.forget₂Ring_preservesLimits, WeierstrassCurve.Projective.Equation.map, HahnSeries.ofPowerSeries_apply, AdjoinRoot.aeval_eq, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, ValuativeExtension.mapPosSubmonoid_apply_coe, MvPowerSeries.comp_subst, Polynomial.coeff_zero_eq_aeval_zero', PowerSeries.eval₂_trunc_eq_sum_range, Ideal.Quotient.liftₐ_apply, IsLocalizedModule.map_units, IsLocalization.adjoin_inv, WeierstrassCurve.Affine.Equation.map, WeierstrassCurve.Projective.map_add, RingCat.forget_preservesLimits, CliffordAlgebra.ofEven_ι, Polynomial.dvd_comp_X_sub_C_iff, AdjoinRoot.liftHom_of, LaurentPolynomial.leftInverse_trunc_toLaurent, Ideal.le_pow_of_le_ramificationIdx, CliffordAlgebra.ofBaseChange_tmul_one, WittVector.truncate_mk', Algebra.normalizedTrace_algebraMap_of_lifts, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, LinearMap.IsSymmetric.conj_inner_sym, SemiRingCat.forget_obj, Subsemiring.subtype_apply, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, PowerSeries.map_exp, QuaternionAlgebra.algebraMap_eq, Valuation.extendToLocalization_apply_map_apply, Localization.le_comap_primeCompl_iff, AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_map, algebraMap_mono, Polynomial.pow_mul_divByMonic_rootMultiplicity_eq, Localization.awayMap_injective_iff, PowerSeries.coe_one, Polynomial.algEquivAevalXAddC_apply, WeierstrassCurve.inv_map_Δ', Polynomial.leadingCoeff_C, MvPolynomial.aeval_sumElim, MvPolynomial.universalFactorizationMapPresentation_σ', jacobiSum_ringHomComp, isAlgebraic_algebraMap, Polynomial.leadingCoeff_map, LinearMap.toMvPolynomial_eval_eq_apply, IsLocalRing.ResidueField.residue_smul, AlgebraicGeometry.StructureSheaf.comap_basicOpen, Matrix.SpecialLinearGroup.coe_matrix_coe, Algebra.IsPushout.equiv_symm_algebraMap_right, Polynomial.eval₂_eq_sum_range, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, Derivation.compAlgebraMap_apply, QuadraticAlgebra.algebraMap_norm_eq_mul_star, AlgebraicGeometry.Scheme.mem_basicOpen'', WeierstrassCurve.Jacobian.map_addU, LaurentPolynomial.smul_eq_C_mul, Polynomial.cauchyBound_X_add_C, Polynomial.degree_cubic_le, IsLocalization.AtPrime.isUnit_to_map_iff, smul_toAlgebra, WeierstrassCurve.Ψ_four, IsLocalization.isLocalization_atPrime_localization_atPrime, map_mul, RingOfIntegers.algebraMap_norm_algebraMap, RCLike.ofReal_im_ax, bijective_rangeRestrict_comp_of_valuationRing, IsLocalization.Away.associated_sec_fst, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, IsLocalization.mul_toInvSubmonoid, IsLocalization.algebraMap_mk', RegularExpression.matches'_map, NumberField.InfinitePlace.eq_iff_eq, HurwitzZeta.jacobiTheta₂''_conj, Subalgebra.setRange_algebraMap, AlgebraicGeometry.specTargetImageRingHom_surjective, SemiRingCat.id_apply, map_normEDS, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, Polynomial.toLaurent_C_mul_eq, SymmetricAlgebra.algebraMap_inj, AdicCompletion.evalₐ_mk, PowerSeries.inv_eq_inv_aux, Submodule.mapHom_apply, Algebra.discr_powerBasis_eq_prod', QuaternionAlgebra.coe_algebraMap, PadicAlgCl.coe_eq, Polynomial.X_sub_C_mul_removeFactor, Algebra.algebraMap_intTrace, Polynomial.logMahlerMeasure_C_mul_X_add_C, fieldRange_eq_top_iff, Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicity, IsLocalization.mk'_eq_iff_eq', coe_monoidHom_mk, IsSimpleRing.iff_injective_ringHom, AlgebraicGeometry.basicOpen_eq_of_affine, Ideal.KerLift.map_smul, IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, congr_arg, IsLocalization.eq_mk'_of_mul_eq, MvPolynomial.schwartz_zippel_sum_degreeOf, MvPolynomial.isHomogeneous_C, Ideal.IsPrimary.comap, Algebra.IsIntegral.quotient, Subalgebra.algebraMap_apply, Cubic.eq_prod_three_roots, SpectrumRestricts.nnreal_iff_spectralRadius_le, Algebra.adjoin_res_eq_adjoin_res, PadicInt.ker_toZMod, DoubleQuot.quotQuotEquivComm_mk_mk, Algebra.FinitePresentation.out, AlgHom.toRingHom_toAddMonoidHom, dist_algebraMap, Multiset.prod_X_add_C_eq_sum_esymm, WittVector.IsPoly₂.map, MvPowerSeries.invOfUnit_eq, Polynomial.coeff_C_zero, AlgHom.IsArithFrobAt.restrict_mk, FaithfulSMul.ker_algebraMap_eq_bot, isLocalHom_of_iso, RCLike.wInner_cWeight_const_right, AdicCompletion.evalₐ_mkₐ, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, RCLike.inv_eq_conj, Ideal.Factors.isPrime, LaurentPolynomial.eval₂_T_n, Polynomial.exists_prod_multiset_X_sub_C_mul, Polynomial.degree_linear_le, Matrix.blockDiagonalRingHom_apply, SubMulAction.mem_one', PrimeSpectrum.piLocalizationToMaximal_bijective, Algebra.Presentation.quotientEquiv_mk, DirectSum.toSemiring_coe_addMonoidHom, IsSMulRegular.of_flat, ker_equiv_comp, toNatAlgHom_apply, Matrix.charmatrix_apply, IsLocalization.Away.mapₐ_apply, Algebra.PowerBasis.norm_gen_eq_prod_roots, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, Polynomial.derivative_X_add_C_pow, Polynomial.homogenize_C, map_add, Matrix.map_pow, le_algebraMap_of_spectrum_le, Polynomial.content_C, trace_eq_sum_automorphisms, UpperHalfPlane.σ_conj, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, surjective_localizationPreserves, IntermediateField.LinearDisjoint.linearIndependent_mul', IsTranscendenceBasis.algebraMap_comp, PrimeSpectrum.toPiLocalization_injective, quasispectrum.preimage_algebraMap, DoubleQuot.quotQuotEquivQuotOfLE_symm_comp_mk, MonoidAlgebra.lift_def, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, FractionalIdeal.equivNum_apply, coe_addMonoidHom_mk, Polynomial.splits_iff_exists_multiset', PowerSeries.coeff_heval_zero, Polynomial.toFinsupp_C_mul_X, PowerSeries.order_ne_zero_iff_constCoeff_eq_zero, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, CommRingCat.commMon_forget₂_map, IsLocalization.invertible_mk'_one_invOf, Algebra.algebraMapSubmonoid_powers, Polynomial.dvd_iff_isRoot, Perfection.coeff_iterate_frobeniusEquiv_symm, HahnSeries.ofPowerSeries_injective, MvPolynomial.aeval_zero', NumberField.RingOfIntegers.map_mk, IsAlgebraic.algebraMap, Zsqrtd.toReal_apply, Ideal.Quotient.quotient_ring_saturate, MvPolynomial.counit_C, DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, Subalgebra.LinearDisjoint.norm_algebraMap, Complex.conj_ofReal, Ideal.comap_fiberIsoOfBijectiveResidueField_symm, Polynomial.qsmul_eq_C_mul, IsPurelyInseparable.bijective_algebraMap_of_isSeparable, PerfectClosure.iterate_frobenius_mk, IsFractionRing.algEquiv_commutes, AlgebraicGeometry.isomorphisms_eq_stalkwise, IsStronglyTranscendental.iff_of_isLocalization, WeierstrassCurve.Projective.baseChange_polynomialZ, SpectrumRestricts.rightInvOn, Multiset.prod_X_add_C_coeff', norm_algebraMap', Polynomial.degree_linear_lt_degree_C_mul_X_sq, Polynomial.cauchyBound_X_sub_C, Polynomial.splits_of_exists_multiset, WeierstrassCurve.Jacobian.comp_smul, IsLocalization.mul_mk'_eq_mk'_of_mul, Algebra.norm_algebraMap, Polynomial.map_C, Submodule.map_toAddSubgroup, IsPurelyInseparable.algebraMap_elemReduct_eq, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, WittVector.ker_constantCoeff, Ideal.mk_ker, MvPolynomial.counitNat_X, CommRingCat.isLocalHom_comp, WeierstrassCurve.Affine.map_addPolynomial, PowerSeries.coeff_C_mul, OrthogonalIdempotents.lift_of_isNilpotent_ker_aux, MonomialOrder.degree_X_add_C, Polynomial.eval₂_at_ofNat, AddChar.map_neg_eq_conj, AdjoinRoot.map_of, MvPolynomial.eval₂Hom_bind₂, Polynomial.C_neg, IsLocalization.integerNormalization_spec, WeierstrassCurve.map_a₃, SkewMonoidAlgebra.ringHom_ext'_iff, EuclideanSpace.inner_single_right, Matrix.scalar_apply, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, Polynomial.ringHom_eval₂_intCastRingHom, Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent, Polynomial.prod_X_sub_C_coeff_card_pred, GradedTensorProduct.tmul_algebraMap_mul_coe_tmul, Localization.localRingHom_bijective_of_not_conductor_le, Ideal.height_le_height_add_spanFinrank_of_le, MvPolynomial.optionEquivLeft_symm_C_X, IsIntegral.algebraMap, Subsemiring.subtype_injective, Polynomial.not_irreducible_C, Polynomial.degree_quadratic_lt_degree_C_mul_X_cb, IsLocalization.eq_mk'_iff_mul_eq, Algebra.algebraMap_intTrace_fractionRing, Valuation.HasExtension.val_map_lt_one_iff, Polynomial.coeff_C_mul_X_pow, LaurentPolynomial.trunc_C_mul_T, Unitization.lift_apply_apply, MvPolynomial.bind₂_bind₂, AlgebraicGeometry.instIsQuasicoherentOpensCarrierCarrierCommRingCatSpecTilde, RatFunc.num_div_denom, Submodule.torsionBySet.mk_smul, ValuationSubring.subtype_apply, PowerSeries.derivative_C, mem_eqLocusField, LaurentPolynomial.support_C_mul_T, Zsqrtd.lift_injective, WeierstrassCurve.φ_two, MvPolynomial.eval₂Hom_bind₁, RCLike.normSq_add, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Polynomial.degree_C_mul_X, MvPolynomial.eval₂_comp_left, Ideal.under_map_eq_map_under, FractionalIdeal.den_mul_self_eq_num', Polynomial.comp_X_add_C_eq_zero_iff, MonomialOrder.monic_one, Polynomial.resultant_X_sub_C_left, isLocalization_iff_isLocalizationMap, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, KaehlerDifferential.map_D, instIsLocalHomZModRingHomOfIsLocalRingOfNontrivial, Algebra.adjoin_toSubsemiring, QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff, WeierstrassCurve.Projective.dblX_eq, Polynomial.toLaurent_X, Orientation.oangle_map_complex, Algebra.Presentation.baseChange_relation, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, minpoly_add_algebraMap_splits, Polynomial.scaleRoots_C, AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply, Cubic.d_eq_three_roots, SemiRingCat.forget₂AddCommMon_preservesLimitsOfSize, DoubleQuot.coe_quotQuotEquivCommₐ, AdjoinRoot.mk_self, PerfectRing.lift_comp_apply, minpoly.iterateFrobenius_of_isSeparable, WeierstrassCurve.map_a₁, MonoidWithZeroHomClass.ext_rat_iff, Complex.inv_eq_conj, MvPolynomial.C_mem_coeffsIn, ContMDiffMap.coeFnRingHom_apply, Polynomial.map_monic_eq_zero_iff, IsLocalization.mem_coeSubmodule, WeierstrassCurve.Affine.map_negY, map_dfinsuppSumAddHom, TensorPower.toTensorAlgebra_galgebra_toFun, MvPolynomial.join₂_map, Polynomial.degree_mul_C, LinearMap.not_hasEigenvalue_zero_tfae, TensorAlgebra.algebraMap_eq_zero_iff, MvPolynomial.aeval_monomial, Polynomial.div_C_mul, PowerSeries.X_dvd_iff, Subalgebra.range_le, Polynomial.resultant_C_mul_left, AddMonoidAlgebra.lift_def, Complex.conj_neg_I, WittVector.constantCoeff_apply, StandardEtalePresentation.toPresentation_relation, PowerSeries.invUnitsSub_mul_X, CauSeq.Completion.ofRatRingHom_apply, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, Polynomial.eval₂_eq_sum, isDedekindDomain_iff, Ideal.map_prodComm_prod, Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix, NumberField.InfiniteAdeleRing.denseRange_algebraMap, spectrum.algebraMap_mem, MvPolynomial.coeff_eval_eq_eval_coeff, HasDerivAt.conj_conj, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, MvPolynomial.C_pow, QuadraticAlgebra.coe_algebraMap, LinearMap.map_smul_inv, CharP.quotient_iff_le_ker_natCast, AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo, CFC.log_algebraMap, MvPolynomial.coeffs_C_subset, Algebra.PreSubmersivePresentation.ofHasCoeffs_val, Polynomial.eval₂_eq_sum_range', Polynomial.opRingEquiv_op_C_mul_X_pow, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk, AlgebraicGeometry.Scheme.basicOpen_restrict, AlgHom.toRingHom_toMonoidHom, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, TruncatedWittVector.commutes', Polynomial.eval₂_smul, MvPolynomial.C_sub, GradedTensorProduct.tmul_coe_mul_algebraMap_tmul, AlgebraicGeometry.IsAffineOpen.app_basicOpen_eq_away_map, HasGradientAt.hasDerivAt, UpperHalfPlane.denom_cocycle', Polynomial.roots_X_add_C, Subfield.mem_map, iterateFrobenius_add_apply, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, CommRingCat.forget_preservesLimits, IsDedekindDomain.exists_representative_mod_finset, Polynomial.map_surjective_iff, Matrix.mem_range_scalar_of_commute_transvectionStruct, MvPowerSeries.eval₂_C, Algebra.smulTower_leftMulMatrix_algebraMap_eq, HasDerivAt.comp_ringHom, AlgebraicGeometry.Scheme.preimage_basicOpen, AddMonoidHom.coe_addMonoidHom_mkRingHomOfMulSelfOfTwoNeZero, IntermediateField.adjoin_toSubfield, UpperHalfPlane.tanh_half_dist, MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse, Polynomial.coe_toLaurentAlg, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, PerfectClosure.eq_iff, MvPolynomial.pderiv_C, PowerSeries.coeff_C_mul_X_pow, Ideal.comap_coe, RCLike.conj_eq_re_sub_im, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, Ideal.quotient_mk_maps_eq, AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff, map_geom_sum, Submodule.map_toAddSubmonoid', constantCoeff_xInTermsOfW, coe_toSemilinearMap, MvPolynomial.C_dvd_iff_zmod, AlgebraicGeometry.Scheme.exists_le_and_germ_injective, Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero, isPRadical_iff, CFC.spectrum_algebraMap_subset, RingCat.hom_inv_apply, selfZPow_of_nonneg, NumberField.Units.finrank_mul_regulator_eq_det, coe_pow, IsLocalization.ringEquivOfRingEquiv_apply, IsLocalization.ideal_eq_iInf_comap_map_away, DoubleQuot.quotQuotEquivQuotOfLE_symm_mk, RatFunc.aeval_X_left_eq_algebraMap, Polynomial.base_mul_mem_lifts, Algebra.coe_linearMap, MonoidAlgebra.mapDomainRingHom_apply, op_apply_apply, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, Ideal.exists_notMem_dvd_algebraMap_of_primesOver_eq_singleton, isIntegral_quotientMap_iff, Submodule.map_mem_span_algebraMap_image, Algebra.algebraMap_ofSubring_apply, MvPowerSeries.trunc_C_mul, Ideal.coeff_zero_mem_comap_of_root_mem, IsLocalization.mem_map_algebraMap_iff, Algebra.algebraMap_pUnit, WittVector.constantCoeff_wittNeg, map_wittStructureInt, HahnSeries.C_apply, Algebra.IsIntegral.isLocalHom, exists_reduced_fraction', cfc_algebraMap, MvPowerSeries.map_X, Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, ringHom_monotone, AlgHom.restrictNormal_commutes, rangeRestrictFieldEquiv_apply_coe, Submodule.span.ringHom_apply, CommRingCat.forgetToRingCat_map_hom, IsLocalization.orderIsoOfPrime_apply_coe, Matrix.IsHermitian.charpoly_eq, PresheafOfModules.germ_ringCat_smul, Polynomial.taylor_X, RCLike.conj_ofNat, Polynomial.multiset_prod_X_sub_C_coeff_card_pred, Polynomial.Splits.roots_map_of_ne_zero, Module.Basis.norm_extends, SemiRingCat.forget₂_monCat_map, Polynomial.separable_X_sub_C, Algebra.EssFiniteType.cond, AlgebraicGeometry.Scheme.Hom.toImage_app, Polynomial.finiteMultiplicity_X_sub_C, IsLocalization.primeHeight_comap, NumberField.FinitePlace.norm_le_one, Complex.conj_tsum, MvPolynomial.aevalTower_algebraMap, WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq, Ring.le_comap_jacobson, NumberField.Units.sum_mult_mul_log, Bijective.stableUnderComposition, MvPolynomial.optionEquivLeft_elim_eval, Subfield.coe_map, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, MvPowerSeries.map_C, Subalgebra.LinearDisjoint.leftMulMatrix_basisOfBasisRight_algebraMap, Polynomial.leadingCoeff_X_add_C, Polynomial.degree_sum_fin_lt, Language.map_id, UpperHalfPlane.σ_mul_comm, PowerSeries.algebraMap_apply', HahnSeries.ofPowerSeries_C, NumberField.ComplexEmbedding.conjugate_coe_eq, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, exists_C_coeff_notMem, Ideal.algebraMap_residueField_eq_zero, MvPolynomial.eval₂Hom_C, Module.Basis.repr_smul', PowerSeries.coe_pow, Polynomial.ringHom_ext'_iff, RootPairing.RootPositiveForm.algebraMap_posForm, MvPolynomial.counitNat_surjective, Polynomial.irreducible_X_sub_C, NumberField.ComplexEmbedding.lift_algebraMap_apply, PreTilt.mk_untilt_eq_coeff_zero, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, LinearEquiv.isRegular_congr', PrimeSpectrum.range_comap_fst, AlgebraicGeometry.Scheme.Hom.stalkMap_inv_hom_apply, Polynomial.Monic.as_sum, coe_addMonoidHom_id, AlgEquiv.commutes', AlgHom.kerSquareLift_mk, MvPolynomial.sumToIter_C, AlgebraicGeometry.Scheme.image_zeroLocus, Polynomial.preimage_eval_singleton, WeierstrassCurve.Projective.dblX_eq', FaithfullyFlat.injective, trace_eq_sum_embeddings_gen, MvPolynomial.eval_expand, WeierstrassCurve.map_j, CliffordAlgebra.contractRight_ι, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, LaurentSeries.mem_integers_of_powerSeries, CompleteOrthogonalIdempotents.map, Ideal.bijective_algebraMap_quotient_residueField, AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen, IsConjRoot.sub_algebraMap, algebraMap_galRestrict'_apply, Ideal.absNorm_algebraMap, RingOfIntegers.coe_algebraMap_norm, WittVector.mk_fontaineTheta, Cubic.C_mul_prod_X_sub_C_eq, Polynomial.map_mapRingHom_eval_map_eval, AlgebraicGeometry.Proj.res_apply, Polynomial.toLaurent_C, Polynomial.eq_leadingCoeff_mul_of_monic_of_dvd_of_natDegree_le, PowerSeries.binomialSeries_constantCoeff, tendsto_algebraMap_cobounded, MvPolynomial.supportedEquivMvPolynomial_symm_C, AlgebraicGeometry.StructureSheaf.comapₗ_eq_localRingHom, tendsto_algebraMap_inv_atTop_nhds_zero_nat, PowerSeries.coeff_one_pow, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, coe_iterateFrobeniusEquiv, Ideal.map_pointwise_smul, RatFunc.algebraMap_monomial, IsPRadical.ker_le', AdjoinRoot.coe_algHomOfDvd, Subsemiring.coe_map, IsNilpotent.isUnit_quotient_mk_iff, Matrix.toMvPolynomial_constantCoeff, RatFunc.denom_dvd, PresheafOfModules.Sheafify.map_smul, surjective_isStableUnderBaseChange, Matrix.GeneralLinearGroup.coe_map_inv_mul_map, MvPowerSeries.trunc'_map, WittVector.ghostComponent_zero_verschiebungFun, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, RingCon.coe_liftₐ, Polynomial.toLaurentAlg_apply, dist_algebraMap', CategoryTheory.Linear.toCatCenter_apply_app, Complex.tan_conj, PowerSeries.smul_eq_C_mul, field_closure_preimage_le, Polynomial.irreducible_C_mul_X_add_C, Ideal.Quotient.norm_mk_le, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, PresheafOfModules.germ_smul, MonoidAlgebra.liftNC_one, Polynomial.succ_signVariations_le_X_sub_C_mul, Projectivization.map_mk, MvPolynomial.C_inj, RCLike.conj_smul, WeierstrassCurve.Jacobian.map_polynomialY, MvPowerSeries.rescale_zero_apply, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, surjectiveOnStalks_iff_forall_ideal, LinearMap.map_smulₛₗ₂, Polynomial.Splits.C, LinearMap.isSymmetric_iff_inner_map_self_real, LocalizedModule.algebraMap_mk', WeierstrassCurve.Affine.CoordinateRing.map_smul, MvPolynomial.eval_X, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, Ideal.mem_span_pow_iff_exists_isHomogeneous, AlgebraicGeometry.AffineSpace.map_appTop_coord, Subfield.subtype_injective, Polynomial.reverse_C_add, MonoidHom.map_frobenius, PowerSeries.IsWeierstrassDivisorAt.seq_one, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, Polynomial.natDegree_linear, ValuationSubring.algebraMap_injective, IsLocalization.bijective, IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomain, autAdjoinRootXPowSubC_root, AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr, Polynomial.toLaurent_C_mul_X_pow, PowerSeries.map_id, codomain_trivial_iff_range_trivial, FreeAbelianGroup.liftMonoid_symm_coe, RestrictScalars.addEquiv_symm_map_algebraMap_smul, WeierstrassCurve.map_Δ, Ideal.ResidueField.liftₐ_algebraMap, WeierstrassCurve.Projective.comp_smul, frobenius_add, IntermediateField.mem_bot, Ideal.isPrime_map_C_iff_isPrime, Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem, PrimeSpectrum.BasicConstructibleSetData.map_g, MatrixEquivTensor.toFunAlgHom_apply, mem_eqLocusS, Matrix.charpoly_diagonal, Cubic.b_eq_three_roots, LaurentPolynomial.eval₂_C_mul_T_n, Perfection.coeff_pow_p, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Polynomial.degree_add_C, Polynomial.toAddCircle_C_eq_smul_fourier_zero, Matrix.entryLinearMap_toAddMonoidHom, Polynomial.evalEval_C, Perfection.coeff_iterate_frobenius', IsFractionRing.num_mul_den_eq_num_iff_eq', IsLocalization.AtPrime.isPrime_map_of_liesOver, MvPowerSeries.comp_substAlgHom, Matrix.scalar_commute_iff, PowerSeries.rescale_neg_one_invOneSubPow, HahnSeries.algebraMap_apply', WeierstrassCurve.VariableChange.map_r, Algebra.norm_eq_prod_embeddings_gen, Polynomial.coe_eval₂RingHom, WeierstrassCurve.Projective.dblY_of_Y_eq', NumberField.Units.dirichletUnitTheorem.exists_unit, Polynomial.natDegree_pow_X_add_C, LaurentPolynomial.toLaurent_reverse, MeasureTheory.SimpleFunc.coe_algebraMap, IsScalarTower.algebraMap_apply, MvPolynomial.IsHomogeneous.C_mul, PowerSeries.trunc_map, Complex.UnitDisc.coe_star, Polynomial.natDegree_eq_zero, SkewMonoidAlgebra.lift_def, CoalgHom.coe_toAddMonoidHom, Ideal.Factors.piQuotientEquiv_mk, MvPolynomial.constantCoeff_map, Ideal.quotient_map_mkₐ, Algebra.QuasiFiniteAt.comap_algEquiv, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible, smoothSheafCommRing.forgetStalk_hom_comp_evalHom_apply, kerLift_mk, IsSelfAdjoint.le_algebraMap_norm_self, map_frobenius, Ideal.map_coe, IsLocalization.Away.integralClosure, Polynomial.IsUnitTrinomial.irreducible_aux1, Polynomial.roots_C_mul_X_add_C_of_IsUnit, LaurentSeries.X_order_mul_powerSeriesPart, AnalyticOnNhd.eval_continuousLinearMap', AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap, coe_prodMap, Polynomial.mirror_C, TopCat.Presheaf.submonoidPresheafOfStalk_obj, Polynomial.nextCoeff_map_eq_of_isUnit_leadingCoeff, IsAdjoinRoot.lift_algebraMap_apply, MvPolynomial.optionEquivLeft_symm_C_C, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalization_of_mem, Matrix.Represents.algebraMap, Cubic.of_c_eq_zero, PrimeSpectrum.maximalSpectrumToPiLocalization_surjective_of_discreteTopology, RingCat.id_apply, QuotientRing.isOpenQuotientMap_mk, matPolyEquiv_eq_X_pow_sub_C, Algebra.Generators.Hom.algebraMap_toAlgHom, Polynomial.coeff_divByMonic_X_sub_C, AdjoinRoot.liftHom_mk, Matrix.derivative_det_one_add_X_smul_aux, surjectiveOnStalks_iff_forall_maximal, Polynomial.degree_C_mul_X_pow, Polynomial.C_pow, Polynomial.C_add, RCLike.hasSum_conj', MonomialOrder.C_mul_leadingCoeff_monomial_degree, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, Polynomial.zero_notMem_multiset_map_X_add_C, WittVector.coeff_frobenius, TensorAlgebra.ι_eq_algebraMap_iff, AlgebraicGeometry.LocallyRingedSpace.stalkMap_hom_inv_apply, WeierstrassCurve.Affine.map_addX, LinearMap.map_algebraMap_mul, NumberField.RingOfIntegers.algebraMap.injective, InnerProductSpace.conj_inner_symm, Polynomial.mod_def, PadicInt.cast_toZModPow, isLocalHom_toRingHom, IsLocalization.algebraMap_pi_surjective_of_isLocalization, TwoSidedIdeal.ker_ringCon_mk', Polynomial.aeval_algebraMap_apply, Polynomial.polynomial_map_coe, AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_apply, IsLocalRing.local_hom_TFAE, Valuation.Integers.one_of_isUnit, AlgebraicGeometry.map_injective_of_isIntegral, Polynomial.leadingCoeff_divByMonic_X_sub_C, AnalyticOnNhd.eval_mvPolynomial, Polynomial.pairwise_coprime_X_sub_C, MvPowerSeries.monomial_smul_eq, LaurentSeries.coeff_coe_powerSeries, RingEquiv.coe_toRingHom, Matrix.sub_scalar_sq_eq_discr, AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, WeierstrassCurve.Projective.map_polynomialY, MvPolynomial.tensorEquivSum_C_tmul_C, Polynomial.derivative_X_sub_C, Subalgebra.rTensorBot_tmul, AlgebraicGeometry.Proj.stalkIso'_symm_mk, map_complEDS, IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdx, Module.End.ringHomEndFinsupp_surjective, map_dotProduct, WeierstrassCurve.Projective.map_polynomial, PiTensorProduct.algebraMap_apply, CommAlgCat.forget₂_commRingCat_map, RingCat.forget_obj, NumberField.mixedEmbedding.norm_unit, algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, LocallyConstant.coeFnRingHom_apply, RingTheory.Sequence.IsWeaklyRegular.of_isLocalization, Pi.algebraMap_def, RingCon.map_apply, Polynomial.aroots_C, coe_addMonoidHom_injective, Ring.DirectLimit.map_apply_of, minpoly.ker_eval, minpoly.eq_X_sub_C, Ideal.Quotient.mk_smul_mk_quotient_map_quotient, AlgebraicGeometry.Scheme.IdealSheafData.ideal_map_of_isAffineHom, WittVector.frobenius_verschiebung, LinearMap.trace_baseChange, Polynomial.roots_C, Matrix.charmatrix_diagonal, AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap, PowerSeries.coeff_one_mul, Algebra.idealMap_apply_coe, WeierstrassCurve.Projective.eval_polynomialY, AddValuation.supp_quot, LaurentPolynomial.comul_C_mul_T_self, FractionalIdeal.den_mem_inv, Lagrange.nodal_erase_eq_nodal_div, Localization.AtPrime.map_eq_maximalIdeal, Polynomial.monic_prod_X_sub_C, Complex.log_conj, RingTheory.Sequence.IsWeaklyRegular.of_isLocalizedModule, Polynomial.natDegree_cubic_le, FreeAlgebra.algebraMap_leftInverse, RingCat.FilteredColimits.forget₂SemiRing_preservesFilteredColimits, LaurentPolynomial.invert_C, WittVector.mapFun.natCast, Module.Basis.mem_span_iff_repr_mem, PowerSeries.monomial_zero_eq_C_apply, FiniteField.algebraMap_norm_eq_pow_sum, IsBaseChange.toDualBaseChange_tmul, Ideal.isMaximal_comap_of_isIntegral_of_isMaximal', Perfection.coeff_pow_p', IsLocalRing.ResidueField.lift_residue_apply, Polynomial.map_aeval_eq_aeval_map, PowerSeries.map_toSubring, IsDedekindDomain.quotientEquivPiFactors_mk, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, MvPolynomial.instIsLocalHomRingHomC, IntermediateField.coe_algebraMap_apply, QuasispectrumRestricts.left_inv, MvPolynomial.eval₂_eq_eval_map, ZMod.castHom_surjective, AdjoinRoot.coe_mapRingEquiv, AlgebraicGeometry.RingedSpace.mem_basicOpen, WeierstrassCurve.ψ_four, NumberField.IsCMField.complexConj_torsion, AlgebraicGeometry.Scheme.Hom.app_injective, AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_mk_of, spectrum.vadd_eq, Polynomial.Bivariate.equivMvPolynomial_C_C, FreeAlgebra.algebraMap_eq_zero_iff, dotProduct_toMatrix₂_mulVec, WeierstrassCurve.Ψ_odd, MvPolynomial.isWeightedHomogeneous_C, Polynomial.natDegree_quadratic, algebraMap_cobounded_le_cobounded, MvPolynomial.map_X, RatFunc.laurentAux_ofFractionRing_mk, Polynomial.natDegree_C_mul_X_pow_le, HasGradientAtFilter.hasDerivAtFilter, ContinuousLinearMap.map_smulₛₗ₂, Polynomial.instIsLocalHomRingHomAlgebraMap, MvPowerSeries.WithPiTopology.continuous_constantCoeff, Ring.DirectLimit.of_f, NumberField.InfinitePlace.apply, PowerSeries.IsRestricted.C, MeasureTheory.eLpNorm_conj, Module.Basis.toMatrix_map_vecMul, inner_gradient_right, Module.IsTorsionBy.mk_smul, MvPolynomial.eval_assoc, Algebra.commutes, RingTheory.Sequence.isRegular_cons_iff', ax_grothendieck_zeroLocus, Transcendental.linearIndependent_sub_inv, wittPolynomial_eq_sum_C_mul_X_pow, PowerSeries.isUnit_constantCoeff, Polynomial.card_roots_sub_C, IsLocalization.liesOver_of_isPrime_of_disjoint, WittVector.ghostComponent_teichmuller, Algebra.mem_algebraMapSubmonoid_of_mem, constantCoeff_wittStructureInt_zero, Complex.conj_I, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, inner_conj_symm, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, inv_eq_of_aeval_divX_ne_zero, Polynomial.lifts_iff_coeffs_subset_range, IsSMulRegular.of_isLocalizedModule, Ideal.comap_id, Polynomial.resultant_C_mul_right, MonoidWithZeroHomClass.ext_nnrat_iff, MvPowerSeries.aeval_unique, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, Polynomial.map_scaleRoots, ValuationSubring.coe_subtype, Polynomial.coe_evalEvalRingHom, Padic.isDenseInducing_cast_withVal, IsLocalization.map_id_mk', AddChar.inv_apply_eq_conj, WeierstrassCurve.Projective.map_negY, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, FractionRing.mk_eq_div, Polynomial.degree_linear, SemiRingCat.forget₂Mon_preservesLimits, Ideal.mapHom_apply, HasDerivAt.comp_semilinear, IsLocalization.surj₂, Polynomial.taylor_C, MvPolynomial.hom_bind₁, WeierstrassCurve.map_b₂, WeierstrassCurve.Jacobian.map_polynomialX, WeierstrassCurve.Jacobian.map_neg, CFC.log_smul, DoubleQuot.coe_liftSupQuotQuotMkₐ, Polynomial.derivative_apply, RingCon.lift_injective_iff, Polynomial.C_injective, HomogeneousLocalization.algebraMap_apply, LinearMap.toAddMonoidHom_mulRight, AnalyticOnNhd.eval_continuousLinearMap, Submodule.map_toAddSubmonoid, GaussianInt.toComplex_one, AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen, HomogeneousIdeal.toIdeal_irrelevant, IsStronglyTranscendental.of_isLocalization, WeierstrassCurve.Jacobian.eval_polynomialZ, AlgebraicGeometry.Scheme.localRingHom_comp_stalkIso_apply, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, RingOfIntegers.dvd_norm, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, Subalgebra.coe_valA', LaurentPolynomial.exists_T_pow, Polynomial.nextCoeff_C_mul, spectrum.sub_singleton_eq, iterateFrobenius_zero_apply, Valuation.coeff_zero_minpoly, SemiRingCat.forget_map, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, RatFunc.map_apply_div_ne_zero, RCLike.normSq_sub, Polynomial.self_sub_C_mul_X_pow, Polynomial.monomial_comp, algebraicIndependent_empty_type_iff, CommSemiRingCat.instFullSemiRingCatForget₂RingHomCarrierCarrier, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Polynomial.natDegree_add_C, Orthonormal.inner_sum, Ideal.comap_lt_comap_of_root_mem_sdiff, WeierstrassCurve.VariableChange.map_u, PreTilt.coeff_def, Polynomial.coe_evalRingHom, Polynomial.eval_C_mul, PadicInt.val_toZMod_eq_zmodRepr, starRingEnd_self_apply, RingHomSurjective.is_surjective, UpperHalfPlane.σ_denom, Polynomial.roots_map, Matrix.algebraMap_matrix_apply, MvPolynomial.support_C, Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range, MvPowerSeries.monomial_eq', Polynomial.roots_expand_map_frobenius_le, IsLocalization.height_comap, PerfectionMap.equiv_apply, IntermediateField.AdjoinPair.algebraMap_gen₂, DoubleQuot.quotQuotEquivQuotOfLE_comp_quotQuotMk, Polynomial.isCoprime_X_sub_C_of_isUnit_sub, PowerSeries.map.isLocalHom, IsLocalization.eq_iff_exists, AdicCompletion.evalₐ_liftRingHom, AlgHom.coe_toAddMonoidHom, MvPolynomial.eval₂_comp_right, PresheafOfModules.map_comp_assoc, IsLocalHom.of_comap_surjective, NumberField.house.basis_repr_norm_le_const_mul_house, Complex.dist_conj_self, SpectrumRestricts.nnreal_iff_nnnorm, Unitization.inlRingHom_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, HasDerivAt.star_conj, is_integral_localization_at_leadingCoeff, MvPolynomial.map_eval, GradedRing.coe_projZeroRingHom'_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Module.Basis.restrictScalars_toMatrix, InnerProductSpaceable.inner_.conj_symm, WittVector.truncate_liftFun, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Submodule.torsionBy.mk_smul, Algebra.Extension.Hom.toAlgHom_apply, MvPowerSeries.coeff_mul_C, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, LaurentPolynomial.invert_comp_C, Matrix.center_eq_scalar_image, IsLocalRing.residue_surjective, algebraMap_le_algebraMap, LaurentPolynomial.antipode_C_mul_T, PadicInt.toZMod_spec, Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det, Polynomial.signVariations_C_mul, WeierstrassCurve.Jacobian.map_addXYZ, Algebra.botEquiv_symm_apply, coe_rangeS, GaussianInt.normSq_div_sub_div_lt_one, RingQuot.mkRingHom_rel, AlgebraicGeometry.Scheme.zeroLocus_map_of_eq, RingCon.comap_eq, SemimoduleCat.forget₂_map, map_frobeniusEquiv_symm, RCLike.conj_neg_I, IsLocalization.Away.algebraMap_isUnit, Polynomial.IsRoot.map, Localization.AtPrime.mapPiEvalRingHom_algebraMap_apply, Ideal.pointwise_smul_def, WittVector.ghostComponentModPPow_map_mk, LaurentSeries.valuation_X_pow, LaurentPolynomial.degree_C_le, InnerProductSpace.Core.inner_conj_symm, char_dvd_card_solutions_of_fintype_sum_lt, isConjRoot_iff_eq_algebraMap', closure_preimage_le, Ideal.ramificationIdx_map_self_eq_one, MulAlgebraNorm.extends_norm, NumberField.house_eq_sup', GaussianInt.intCast_complex_norm, injective_int, coe_range, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, Ideal.comap_jacobson, GaussianInt.intCast_re, MvPolynomial.bind₁_monomial, Lagrange.interpolate_singleton, Polynomial.C_content_dvd, IsLocalization.mk'_spec, cyclotomicCharacter.toFun_spec, LinearMap.polyCharpoly_coeff_eval, NumberField.FinitePlace.norm_def, PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijective, AdjoinRoot.ringHom_ext_iff, NumberField.mixedEmbedding.convexBodySum_mem, Polynomial.coeff_X_add_C_pow, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, RootPairing.algebraMap_root'In_apply, Ideal.kerLiftAlg_mk, Polynomial.degree_linear_lt, PreTilt.coeff_iterate_frobenius', PerfectRing.lift_aux, CommRingCat.instIsRightAdjointForgetRingHomCarrier, MvPolynomial.continuous_eval, PowerSeries.trunc_C_mul, PadicInt.lift_self, FaithfullyFlat.codescendsAlong_bijective, MvPolynomial.C_eq_smul_one, QuadraticAlgebra.coe_dvd_iff, RingQuot.eq_liftAlgHom_comp_mkAlgHom, FractionalIdeal.extendedHomₐ_le_one_iff, MvPolynomial.evalₗ_apply, Ideal.pi_quotient_surjective, RestrictScalars.smul_def, coe_rangeRestrict, inner_smul_left, DoubleQuot.quotQuotEquivQuotOfLE_quotQuotMk, Polynomial.coeff_det_X_add_C_zero, iterateFrobenius_mul_apply, Polynomial.derivative_C_mul_X_sq, Lagrange.nodal_eq, Polynomial.derivativeFinsupp_C, SkewMonoidAlgebra.liftNC_smul, frobeniusEquiv_symm_apply_frobenius, Polynomial.card_support_trinomial, Valuation.HasExtension.algebraMap_injective, ULift.algebraMap_eq, AddMonoidAlgebra.mapDomainRingHom_apply, LinearMap.prodMapRingHom_apply, Polynomial.taylor_one, X_pow_sub_C_irreducible_iff_of_prime, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, Matrix.SpecialLinearGroup.mem_center_iff, surjective_localRingHom_iff, CompleteOrthogonalIdempotents.bijective_pi, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal, inv_eq_of_root_of_coeff_zero_ne_zero, IsScalarTower.toAlgHom_apply, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, AdjoinRoot.mk_C, Polynomial.roots_X_pow_char_pow_sub_C, map_vecMul, RatFunc.ofFractionRing_algebraMap, RatFunc.eval_algebraMap, LinearMap.mulLeft_toAddMonoidHom, MvPolynomial.map_id, CFC.eq_algebraMap_of_spectrum_subset_singleton, Ideal.le_comap_pow_ramificationIdx, QuadraticAlgebra.algebraMap_im, RCLike.normSq_conj, GaussianInt.toComplex_div_im, DoubleQuot.quotQuotEquivComm_symm, algebraMap_comp_natCast, le_algebraMap_iff_spectrum_le, MvPowerSeries.expand_C, Polynomial.toMvPolynomial_C, WittVector.mapFun.neg, mem_eqLocus, Ideal.Factors.piQuotientEquiv_map, ClassGroup.exists_mem_finsetApprox, Algebra.TensorProduct.includeLeftRingHom_apply, WeierstrassCurve.Projective.map_dblX, AlgebraicGeometry.IsAffineOpen.appLE_eq_away_map, spectrum.notMem_iff, algebraMap_star_comm, Polynomial.exists_mul_add_mul_eq_C_resultant, Matrix.charpoly_of_card_eq_two, Polynomial.eval_multiset_prod_X_sub_C_derivative, Polynomial.toFinsupp_C, AdjoinRoot.coe_ofAlgHom, AlgebraicGeometry.Scheme.Modules.map_smul, AlgebraicGeometry.RingedSpace.mem_basicOpen', Unitization.algebraMap_eq_inl_comp, map_closure, TensorProduct.quotTensorEquivQuotSMul_mk_tmul, RestrictScalars.addEquiv_map_smul, derivationQuotKerSq_mk, Subfield.mem_comap, IsFractionRing.self_iff_bijective, MvPowerSeries.trunc'_C, AdjoinRoot.of.injective_of_degree_ne_zero, Polynomial.X_sub_C_pow_dvd_iff, LaurentPolynomial.degree_C_mul_T_le, IsAlgClosed.ringHom_bijective_of_isIntegral, GaussianInt.toComplex_eq_zero, LinearIsometryEquiv.map_smulₛₗ, AlgebraicGeometry.Scheme.mem_basicOpen, FaithfullyFlat.codescendsAlong_injective, RingCat.forget_map, Matrix.charmatrix_zero, Algebra.Generators.C_mul_X_sub_one_mem_ker, Subsemiring.coe_comap, isCyclic_tfae, Polynomial.roots_prod_X_sub_C, Polynomial.integralNormalization_eval₂_leadingCoeff_mul, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, MonoidAlgebra.mapRangeRingHom_apply, SemiRingCat.forget₂_addCommMonCat_map, Polynomial.C_smul_derivation_apply, MvPowerSeries.trunc'_C_mul, MvPolynomial.commAlgEquiv_C_X, MvPolynomial.expand_zero_apply, ZMod.unitsMap_def, Polynomial.X_pow_mul_C, AdjoinRoot.evalEval_mk, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, Polynomial.degree_sub_C, DoubleCentralizer.toProdMulOppositeHom_apply, ModularForm.slash_apply, Module.Basis.ofIsLocalizedModule_repr_apply, Multiset.prod_X_sub_C_coeff, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.ofRestrict_invApp_apply, ContinuousLinearMap.algebraMap_apply, ker_rangeSRestrict, WeierstrassCurve.Projective.negDblY_of_Y_eq', DoubleQuot.quotQuotEquivComm_algebraMap, IsFractionRing.liftAlgHom_apply, QuadraticAlgebra.algebraMap_injective, Polynomial.degree_X_add_C, IsPRadical.pow_mem', MvPowerSeries.WithPiTopology.continuous_C, Polynomial.isMonicOfDegree_sub_add_two, TensorProduct.liftAux.smulₛₗ, FaithfulSMul.algebraMap_eq_zero_iff, WittVector.frobenius_zmodp, Ideal.Quotient.mk_algebraMap, surjective_ofLocalizationSpan, Perfection.coeff_frobenius, Polynomial.degree_C_le, Algebra.FinitePresentation.iff_quotient_mvPolynomial', CliffordAlgebra.even.lift.aux_algebraMap, prod_galRestrict_eq_norm, sum_conjneg, algebraMap_le_cfc_iff, AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHom, AlgebraicGeometry.IsAffineOpen.ideal_ext_iff, Algebra.PreSubmersivePresentation.localizationAway_jacobian, RingCon.lift_coe, Ideal.comap_comap, MvPolynomial.eval_polynomial_eval_finSuccEquiv, MvPolynomial.sumToIter_Xl, Polynomial.isIntegral_isLocalization_polynomial_quotient, frobenius_inj, AlgebraicGeometry.Scheme.Hom.stalkMap_surjective, IsLocalization.map_nonZeroDivisors_le, FreeCommRing.map_subtype_val_restriction, WittVector.constantCoeff_wittSub, Ideal.Quotient.algebraMap_mk_of_liesOver, ModuleCat.forget₂_map, asBoolAlg_toFun, MvPolynomial.counit_X, Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits, MvPowerSeries.le_order_map, UpperHalfPlane.petersson_slash, Localization.algEquiv_symm_apply, CliffordAlgebra.contractLeft_algebraMap, IsLocalization.coeSubmodule_span_singleton, RingQuot.ringQuotToIdealQuotient_apply, PerfectRing.lift_self_apply, Algebra.ZariskisMainProperty.exists_fg_and_exists_notMem_and_awayMap_bijective, map_pow, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, NNRat.coe_coeHom, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, AlgebraicGeometry.IsAffineOpen.mem_ideal_iff, Zsqrtd.toReal_injective
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