Defs

📁 Source: Mathlib/Algebra/Algebra/Defs.lean

Statistics

Metric	Count
Definitions algebraMap, cast, compHom, id, linearMap, ofModule, ofModule', toModule, toSMul, toAlgebra, toAlgebra', termη, «termη[_]», algebraMap, coeHTCT	15
Theorems algebraMap_eq_smul_one, algebraMap_eq_smul_one', algebraMap_self, algebraMap_self_apply, algebra_ext, algebra_ext_iff, coe_linearMap, commute_algebraMap_left, commute_algebraMap_right, commutes, commutes', compHom_algebraMap_apply, compHom_algebraMap_eq, compHom_smul_def, smul_eq_mul, left_comm, linearMap_apply, linearMap_self, mul_smul_comm, right_comm, smul_def, smul_def', smul_mul_assoc, subsingleton, right, algebraMap_toAlgebra, algebraMap_toAlgebra', smulOneHom_eq_algebraMap, smul_toAlgebra, smul_toAlgebra', coe_add, coe_mul, coe_natCast, coe_neg, coe_one, coe_pow, coe_smul, coe_smul', coe_sub, coe_zero, smul_algebraMap, toAlgebra_algebraMap	42
Total	57

Algebra

Definitions

Name	Category	Theorems
algebraMap 📖	CompOp	7 math math: SubmersivePresentation.ofSubsingleton_algebra_algebraMap, commutes', smul_def', PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, Generators.self_algebra_algebraMap
cast 📖	CompOp	33 math math: algebraMap.coe_one, algebraMap.coe_logDeriv, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, algebraMap.coe_sum, algebraMap.coe_eq_zero_iff, algebraMap.coe_inj, algebraMap.coe_deriv, algebraMap.coe_prod, IsFractionRing.coe_inj, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, div_eq_quo_add_sum_rem_div, algebraMap.lift_map_eq_zero_iff, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, algebraMap.coe_div, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, algebraMap.coe_smul', algebraMap.coe_mul, div_eq_quo_add_rem_div_add_rem_div, algebraMap.coe_sub, algebraMap.coe_smul, algebraMap.coe_zero, algebraMap.coe_pow, algebraMap.coe_natCast, algebraMap.coe_expect, algebraMap.coe_inv, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, algebraMap.coe_ratCast, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, algebraMap.coe_add, algebraMap.coe_zpow, algebraMap.coe_neg
compHom 📖	CompOp	3 math math: compHom_algebraMap_apply, compHom_smul_def, compHom_algebraMap_eq
id 📖	CompOp	5840 math math: AdicCompletion.of_surjective_iff, ArithmeticFunction.vonMangoldt.residueClass_eq, CommRingCat.tensorProd_map_right, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, MvPolynomial.pUnitAlgEquiv_symm_monomial, RatFunc.instFaithfulSMulPolynomialLaurentSeries, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_apply, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, Ideal.exists_pow_le_of_le_radical_of_fg_radical, MvPolynomial.join₁_rename, Polynomial.units_coeff_zero_smul, Ideal.toCotangent_to_quotient_square, LinearMap.isSymm_zero, KaehlerDifferential.kerCotangentToTensor_toCotangent, HasStrictFDerivAt.log, MvPolynomial.aeval_sum, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, WittVector.bind₁_frobeniusPoly_wittPolynomial, IsLocalizedModule.iso_symm_apply', range_ofId, exists_fg_and_mem_baseChange, CliffordAlgebra.contractRight_algebraMap_mul, LinearMap.restrictScalars_toMatrix, IsIntegrallyClosedIn.inst, MeasureTheory.Measure.MutuallySingular.smul_nnreal, CliffordAlgebra.toBaseChange_reverse, MeasureTheory.SMulInvariantMeasure.smul, RatFunc.laurent_injective, IntermediateField.extendScalars_toSubfield, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, Seminorm.isBounded_const, TensorAlgebra.ofDirectSum_of_tprod, LinearMap.apply_symm_toPerfPair_self, LinearMap.SeparatingRight.toMatrix₂', KaehlerDifferential.mvPolynomialBasis_apply, MeasureTheory.Measure.IsHaarMeasure.nnreal_smul, Matrix.toLinAlgEquiv_one, MeasureTheory.mulEquivHaarChar_smul_integral_map, PowerSeries.hasSum_aeval, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, minpoly.ToAdjoin.injective, SubmersivePresentation.cotangentComplexAux_injective, Bundle.ContMDiffRiemannianMetric.isVonNBounded, MeasureTheory.OuterMeasure.map_iInf, MonoidAlgebra.finiteType_of_fg, RatFunc.mk_def_of_ne, Polynomial.mem_aroots', Field.Emb.Cardinal.equivLim_coherence, MeasureTheory.ennreal_smul_extend, Ideal.Filtration.submodule_closure_single, InfiniteGalois.normal_iff_isGalois, Ideal.radical_sup, SymmetricAlgebra.lift_ι_apply, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, continuous_cfcₙHomSuperset_left, Generators.baseChange_val, SpectrumRestricts.nnreal_of_nonneg, cfcₙL_integral, RatFunc.ofFractionRing_mk', PreSubmersivePresentation.jacobiMatrix_naive, MeasureTheory.Measure.restrict_singleton, dot_self_cross, HasFDerivWithinAt.ccosh, Bundle.ContMDiffRiemannianMetric.contMDiff, CliffordAlgebra.contractRight_algebraMap, AddMonoidAlgebra.lift_apply', continuousOn_stereoToFun, ModularForm.smul_slash, MvPolynomial.algHom_ext_iff, MvPolynomial.map_bind₁, Matrix.toLin_kronecker, IntermediateField.exists_algHom_adjoin_of_splits, Matrix.toLin'_symm, MeasureTheory.Measure.isAddInvariant_eq_smul_of_compactSpace, QuaternionAlgebra.coe_mul_eq_smul, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right, Matrix.SeparatingLeft.toBilin', ProbabilityTheory.isGaussian_iff_gaussian_charFun, Generators.aeval_val_surjective, PowerSeries.constantCoeff_expand, Ideal.Filtration.submodule_eq_span_le_iff_stable_ge, norm_cfcₙHom, LinearMap.BilinForm.dualSubmoduleToDual_apply_apply, IntermediateField.aeval_gen_minpoly, RatFunc.mk_coe_def, AdjoinRoot.isAdjoinRoot_root_eq_root, LinearMap.IsPerfPair.restrict, Ideal.dvd_iff_le, CliffordAlgebra.contractRight_eq, OrthonormalBasis.orthogonalProjection_eq_sum, cfcₙHom_mono, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, LinearMap.toMatrixAlgEquiv'_mul, SymmetricAlgebra.rank_eq, strictConvexOn_iff_slope_strict_mono_adjacent, LinearMap.BilinForm.toMatrix_toBilin, polynomialFunctions.eq_adjoin_X, Presentation.differentials.comm₁₂_single, wittPolynomial_zmod_self, IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, MvPolynomial.aeval_X_left, RingHom.SurjectiveOnStalks.baseChange, Extension.Cotangent.span_eq_top_of_span_eq_ker, Polynomial.mem_lifts_iff_mem_alg, Polynomial.roots_expand, IntermediateField.LinearDisjoint.iff_inf_eq_bot, LinearMap.IsReflective.regular, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, MvPolynomial.pUnitAlgEquiv_apply, IntermediateField.normal_inf, LinearMap.BilinForm.dualSubmoduleToDual_injective, Polynomial.algEquivCMulXAddC_apply, HasFDerivWithinAt.ccos, Matrix.IsHermitian.isClosedEmbedding_cfcAux, Polynomial.coe_taylorAlgHom, Polynomial.transcendental, InnerProductSpace.toLinearIsometry_toDual, MeasureTheory.Measure.IsEverywherePos.smul_measure, AlgebraicIndependent.transcendental_adjoin_iff, AlgEquiv.coe_adjoinSingletonEquivAdjoinRootMinpoly_symm, LinearMap.exists_monic_and_aeval_eq_zero, HomogeneousIdeal.toIdeal_mul, PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, AddMonoidAlgebra.algHom_ext'_iff, RatFunc.num_div, algebraMap_self_apply, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, MvPolynomial.exists_finset_rename, LinearEquiv.flip_apply, Ideal.finite_setOf_absNorm_le₀, IsGalois.tower_top_intermediateField, Ideal.toCharacterSpace_apply_eq_zero_of_mem, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, hasFDerivAt_iff_hasGradientAt, NonUnitalIsometricContinuousFunctionalCalculus.isometric, PiTensorProduct.liftAlgHom_apply, IsAdicComplete.StrictMono.mk_liftRingHom, BilinForm.toMatrix_symm, TensorProduct.AlgebraTensorModule.leftComm_eq, cfcₙHom_apply_mem_elemental, ClassGroup.mk0_integralRep, Polynomial.expand_contract, AnalyticOn.aeval_polynomial, SimpleGraph.lapMatrix_toLinearMap₂', Quaternion.snd_imJ_dualNumberEquiv_symm, PowerBasis.exists_eq_aeval, Localization.algebraMap_injective_of_span_eq_top, tendsto_tsum_div_pow_atTop_integral, cardQuot_mul, MeasureTheory.Measure.ae_ennreal_smul_measure_eq, MvPolynomial.support_finSuccEquiv, NumberField.canonicalEmbedding.mem_span_latticeBasis, Polynomial.algebraMap_pi_eq_aeval, MeasureTheory.integral_smul_nnreal_measure, NumberField.integralBasis_apply, PreSubmersivePresentation.cotangentComplexAux_apply, Real.smul_map_volume_mul_right, InnerProductSpace.rankOne_one_left_eq_innerSL, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, Polynomial.Monic.free_quotient, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, StandardEtalePair.inv_aeval_X_g, IntermediateField.adjoin.finrank, ContinuousMap.abs_mem_subalgebra_closure, Ideal.span_singleton_mul_le_span_singleton_mul, Polynomial.expand_eq_sum, WittVector.aeval_verschiebung_poly', dotProductEquiv_symm_apply, PrimeSpectrum.residueField_specComap, PowerSeries.heval_C, MeasureTheory.Measure.IsAddHaarMeasure.smul, polynomial_smul_apply', HasStrictFDerivAt.csin, Matrix.separatingRight_toLinearMap₂'_iff, Polynomial.continuous_aeval, LinearMap.BilinForm.isSkewAdjoint_bracket, MvPolynomial.rTensorAlgEquiv_apply, ClassGroup.mk0_eq_mk0_iff, Complex.ofRealCLM_coe, Module.End.map_smul_of_iInf_genEigenspace_ne_bot, Generators.H1Cotangent.δAux_mul, AlgCat.hom_inv_associator, Presentation.naive_toGenerators, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, Complex.areaForm, Localization.epi', convex_iff_ordConnected, WeakDual.isCompact_polar, CliffordAlgebraComplex.ofComplex_conj, BialgCat.rightUnitor_def, HopfAlgCat.rightUnitor_def, Matrix.det_smul_inv_mulVec_eq_cramer, PowerSeries.le_order_subst_left', IsLocalization.coeSubmodule_mul, Matrix.pow_eq_aeval_mod_charpoly, Ideal.toCotangent_eq, MvPolynomial.mem_image_support_coeff_finSuccEquiv, WeierstrassCurve.Affine.CoordinateRing.smul, MeasureTheory.Measure.WeaklyRegular.smul_nnreal, ENNReal.nnreal_smul_lt_top, AdicCompletion.AdicCauchySequence.mk_eq_mk, PiTensorProduct.dualDistribEquivOfBasis_symm_apply, Ideal.absNorm_span_insert, FractionalIdeal.isPrincipal_of_isPrincipal_num, Polynomial.Gal.smul_def, Polynomial.derivWithin_aeval, AdjoinRoot.minpoly_root, MeasureTheory.Measure.rnDeriv_smul_right', LieSubmodule.lowerCentralSeries_tensor_eq_baseChange, MvPolynomial.comapEquiv_symm_coe, IntermediateField.extendScalars_sup, Module.End.HasEigenvalue.mem_spectrum, LieModule.toEnd_pow_apply_map, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, eval_minpolyDiv_self, MvPolynomial.eval₂_expand, Subspace.instModuleDualFiniteDimensional, normalizedTrace_eq_of_finiteDimensional, Polynomial.disjoint_ker_aeval_of_isCoprime, Ideal.squarefree_span_singleton, Ideal.iInf_pow_smul_eq_bot_of_isLocalRing, MvPolynomial.universalFactorizationMap_comp_map, MvPolynomial.aeval_algebraMap_eq_zero_iff, NumberField.FinitePlace.mk_apply, Polynomial.toAlgHom_taylorEquiv, ProbabilityTheory.covarianceBilinDual_apply', autAdjoinRootXPowSubCEquiv_root, MvPolynomial.isScalarTower_right, MvPowerSeries.support_expand, PolynomialModule.smul_def, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, IsAdjoinRoot.mem_ker_map, Polynomial.aroots_smul_nonzero, has_pointwise_sum_fourier_series_of_summable, AlgebraicGeometry.StructureSheaf.const_mul_rev, Ideal.relNorm_smul, LinearMap.IsPerfPair.bijective_left, Presentation.differentialsSolution_isPresentation, instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl, differentIdeal_eq_differentIdeal_mul_differentIdeal, concaveOn_iff_slope_anti_adjacent, FractionalIdeal.coeIdealHom_apply, LinearEquiv.coe_toLinearMap_flip, SeparableClosure.isSepClosed, MeasureTheory.convolution_mul, CommRing.Pic.mk_dual, AdicCompletion.map_val_apply, PowerSeries.coeff_expand_mul, RootPairing.GeckConstruction.instHasTrivialRadical, mem_reesAlgebra_iff_support, PreSubmersivePresentation.ofHasCoeffs_map, algebraMap_ofSubsemiring_apply, Matrix.spectrum_toEuclideanLin, Polynomial.aeval_algebraMap_apply_eq_algebraMap_eval, eval₂_minpolyDiv_self, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, MvPolynomial.expand_X, RatFunc.num_div_dvd, KaehlerDifferential.polynomialEquiv_symm, Ideal.exists_mem_span_singleton_map_residueField_eq, Submodule.instStrictConvexSpace, algebraicIndependent_iff_ker_eq_bot, AlgebraicIndependent.isTranscendenceBasis_iff_isAlgebraic, SymmetricAlgebra.isSymmetricAlgebra_ι, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply, Complex.real_algHom_eq_id_or_conj, LieAlgebra.Orthogonal.mem_so, Ideal.rank_prime_pow_ramificationIdx, IntermediateField.isScalarTower_mid', Polynomial.aeval_algebraMap_eq_zero_iff, SkewMonoidAlgebra.algHom_ext'_iff, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal, ConjRootClass.aeval_minpoly_iff, Matrix.coeff_charpoly_mem_ideal_pow, LinearMap.BilinForm.toMatrixAux_eq, PowerSeries.expand_subst, StrongDual.polarSubmodule_eq_setOf, Extension.H1Cotangent.equiv_apply, PowerSeries.expand_apply, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', Polynomial.contract_expand, LieModule.trace_toEnd_eq_zero_of_mem_lcs, Generators.cotangentSpaceBasis_apply, RootPairing.GeckConstruction.h_mem_cartanSubalgebra, Matrix.toLinearMap₂'_comp, SkewMonoidAlgebra.lift_apply', Asymptotics.isLittleOTVS_one, Submodule.mul_annihilator, MeasureTheory.OuterMeasure.comap_map, MvPolynomial.IsWeightedHomogeneous.pderiv, fderivWithin_csinh, RootPairing.root_coroot_two, normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity, WittVector.ghostComponent_apply, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, span_singleton_dvd_span_singleton_iff_dvd, Ideal.le_span_singleton_mul_iff, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, IsPushout.equiv_symm_algebraMap_left, LinearMap.toMatrix₂_mul, aeval_wittPolynomial, Ideal.ker_algebraMap_residueField, Matrix.lieConj_apply, Extension.H1Cotangent.map_id, RatFunc.laurent_X, NumberField.RingOfIntegers.instSMulDistribClass, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, ClassGroup.Quot_mk_eq_mk, LieAlgebra.Orthogonal.soIndefiniteEquiv_apply, WeakDual.isClosed_image_polar_of_mem_nhds, AdicCompletion.of_ofAlgEquiv_symm, AddCircle.volume_eq_smul_haarAddCircle, one_add_cpow_hasFPowerSeriesAt_zero, IsIntegral.tensorProduct, HasDerivAt.fun_finset_prod, LocalizedModule.restrictScalars_map_eq, LinearMap.polar_eq_iInter, ProbabilityTheory.covarianceBilinDual_apply, Real.strictConcaveOn_rpow, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, FormallyUnramified.inst, KaehlerDifferential.mvPolynomialBasis_repr_D_X, LinearEquiv.algEquivOfRing_apply, ConcaveOn.mul_convexOn', MvPolynomial.optionEquivLeft_C, MvPolynomial.rename_rename, Real.fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.toMatrixAlgEquiv_comp, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearMap.det_mulLeft, ProjectiveSpectrum.zeroLocus_mul_ideal, Module.rankAtStalk_eq, Subspace.dualLift_of_subtype, IsDedekindRing.toIsIntegralClosure, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, AlgebraicGeometry.StructureSheaf.const_self, Unitization.real_cfcₙ_eq_cfc_inr, Polynomial.sum_bernoulli, norm_eq_matrix_det, Localization.isFractionRing_range_mapToFractionRing, Representation.asAlgebraHom_single, AffineIsometryEquiv.ofTop_apply, deriv_fun_finset_prod, Generators.toAlgHom_ofComp_localizationAway, LieAlgebra.finrank_engel, skewAdjointLieSubalgebraEquiv_apply, CliffordAlgebraQuaternion.toQuaternion_star, Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free, MeasureTheory.Measure.measure_isMulLeftInvariant_eq_smul_of_ne_top, eval_det_add_X_smul, idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors, TensorProduct.toIntegralClosure_bijective_of_isLocalization, PowerSeries.derivative_exp, Polynomial.mem_rootSet_of_injective, OrthonormalBasis.toBasis_tensorProduct, LaurentSeries.LaurentSeriesRingEquiv_def, LipschitzWith.ae_lineDeriv_sum_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, CommRing.Pic.mapAlgebra_self, Subspace.dualRestrict_comp_dualLift, Orientation.areaForm_le, LinearMap.BilinForm.congr_apply, Polynomial.aeval_map_algebraMap, TensorAlgebra.toTrivSqZeroExt_ι, LieModule.traceForm_eq_sum_finrank_nsmul', MonoidAlgebra.algHom_ext'_iff, eval₂_minpolyDiv_of_eval₂_eq_zero, LinearMap.BilinForm.toMatrix_compRight, MeasureTheory.smul_le_stoppedValue_hittingBtwn, RatFunc.transcendental_X, innerSL_apply_apply, RootPairing.rootSpan_dualAnnihilator_le_ker_rootForm, MvPowerSeries.trunc'_expand_trunc', WeierstrassCurve.Projective.addY_smul, LinearMap.adjoint_innerₛₗ_apply, lmul_algebraMap, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, MvPolynomial.optionEquivLeft_X_some, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Submodule.dualQuotEquivDualAnnihilator_apply, Unitization.splitMul_apply, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, TensorAlgebra.ι_comp_lift, ContinuousLinearMap.toBilinForm_apply, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, MeasureTheory.Measure.ae_mem_finset_iff, MeasureTheory.FinMeasAdditive.smul_measure, minpoly.eq_iff_aeval_eq_zero, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, LinearMap.IsPosSemidef.add, PolyEquivTensor.right_inv, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, FormallySmooth.projective_kaehlerDifferential, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, MvPolynomial.aeval_X_left_apply, Associates.finite_factors, Polynomial.toPowerSeries_toMvPowerSeries, PolynomialModule.aeval_equivPolynomial, TensorAlgebra.adjoin_range_ι, Polynomial.algEquivOfCompEqX_symm, PowerSeries.order_expand, LeftInvariantDerivation.left_invariant', Presentation.differentials.comm₂₃, Polynomial.leadingCoeff_det_X_one_add_C, Ideal.comap_cotangentIdeal, MvPolynomial.pUnitAlgEquiv_symm_apply, Polynomial.quotientSpanXSubCAlgEquiv_symm_apply, QuasispectrumRestricts.nnreal_iff, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, MvPolynomial.expand_eq_zero, Field.Emb.Cardinal.filtration_succ, AlgebraicIndependent.transcendental_adjoin, LinearMap.IsReflective.smul_coroot, Unitization.algHom_ext'_iff, LieAlgebra.IsKilling.rootSystem_coroot_apply, instLiesOverFiberOfIsPrime, Polynomial.coeff_zero_of_isScalarTower, ProbabilityTheory.boolKernel_comp_measure, Metric.exists_forall_closedEBall_subset_aux₂, FreeAlgebra.lift_comp_ι, instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeComplFractionRing, Irreducible.natSepDegree_eq_one_iff_of_monic', CliffordAlgebraDualNumber.equiv_symm_eps, LinearMap.IsReflective.apply_self_mul_coroot_apply, MeasureTheory.OuterMeasure.restrict_trim, TensorAlgebra.toDirectSum_tensorPower_tprod, MonoidAlgebra.tensorEquiv.invFun_tmul, ProbabilityTheory.uncenteredCovarianceBilin_apply, Polynomial.rootMultiplicity_expand_pow, algebraicClosure.algebraicClosure_eq_bot, Module.End.spectrum_intrinsicStar, Polynomial.aeval_iterate_derivative_of_ge, KaehlerDifferential.cotangentComplexBaseChange_tmul, QuadraticAlgebra.algebraMap_inj, NumberField.FinitePlace.norm_def', MvPolynomial.weightedHomogeneousSubmodule_mul, cross_cross, Localization.mk_eq_mk', Matrix.separatingRight_toBilin_iff, Ideal.span_pow_eq_map_homogeneousSubmodule, Polynomial.derivative_expand, Matrix.spectrum_toLpLin, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, Ideal.span_singleton_mul_left_injective, Polynomial.aeval_fn_apply, AdicCompletion.instIsScalarTower_1, Module.Basis.repr_isUnitSMul, MvPolynomial.natDegree_finSuccEquiv, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Ideal.finite_setOf_absNorm_eq, NumberField.mixedEmbedding.mem_idealLattice, StandardEtalePresentation.toPresentation_algebra_smul, IsSymmetricAlgebra.equiv_apply, sum_smul_minpolyDiv_eq_X_pow, Submodule.quotDualCoannihilatorToDual_apply, Ideal.span_eq_map_homogeneousSubmodule, InnerProductSpace.toDual_symm_apply, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank, NumberField.Units.regOfFamily_eq_det, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, LinearMap.BilinForm.toMatrix'_symm, Module.End.isFinitelySemisimple_sub_algebraMap_iff, InfiniteGalois.normalAutEquivQuotient_apply, Submodule.dualPairing_apply, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', instIsFractionRing, LeftInvariantDerivation.left_invariant, MeasureTheory.Measure.haveLebesgueDecompositionSMul, AlgebraicGeometry.Scheme.zeroLocus_mul, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, Bundle.RiemannianMetric.isVonNBounded, MeasureTheory.tilted_neg_same', MeasureTheory.le_eLpNorm_of_bddBelow, WeierstrassCurve.Projective.dblU_smul, MvPolynomial.aevalTower_ofId, NumberField.FinitePlace.embedding_apply, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, ProbabilityTheory.sum_meas_smul_cond_fiber, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_eq_mk, MaximalSpectrum.toPiLocalization_apply_apply, QuadraticAlgebra.norm_algebraMap, IntermediateField.isAlgebraic_tower_bot, coe_algebraMap_ofSubring, Localization.algEquiv_apply, MeasureTheory.charFun_toDual_symm_eq_charFunDual, LieModule.instIsFaithfulMatrixForall, MvPolynomial.algHom_ext'_iff, Module.freeLocus_localization, LieSubalgebra.toEnd_eq, IntermediateField.mem_adjoin_iff, RatFunc.laurent_algebraMap, AlgebraicIndependent.repr_ker, MeasureTheory.condLExp_bot', Module.FinitePresentation.exists_notMem_bijective, Localization.algEquiv_mk', LinearMap.BilinForm.toMatrix'_apply, Module.Basis.dual_rank_eq, Localization.localRingHom_mk', Extension.formallySmooth_iff_split_injection, PowerBasis.quotientEquivQuotientMinpolyMap_apply, DoubleQuot.coe_quotLeftToQuotSupₐ, LSeriesSummable.smul, Differentiable.fderiv_norm_rpow, QuasiFiniteAt.baseChange, MvPolynomial.aeval_X, MvPolynomial.comapEquiv_coe, MeasureTheory.Measure.coe_nnreal_smul_apply, UnitAddTorus.mFourierSubalgebra_coe, LinearMap.BilinForm.SeparatingRight.toMatrix, AdicCompletion.incl_apply, AdicCompletion.map_ext'_iff, IntermediateField.botEquiv_symm, AlgCat.hom_inv_rightUnitor, Unitization.starAlgHom_ext_iff, AdicCompletion.ofTensorProduct_surjective_of_finite, MeasureTheory.Measure.comapₗ_eq_comap, LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero', Polynomial.pUnitAlgEquiv_symm_toPowerSeries, signedDist_right_congr, cross_self, LieAlgebra.lieCharacterEquivLinearDual_apply, Rep.to_Module_monoidAlgebra_map_aux, adjoinRootXPowSubCEquiv_symm_eq_root, CliffordAlgebra.contractRight_mul_ι, Ideal.iInf_pow_smul_eq_bot_of_le_jacobson, AdicCompletion.val_smul_eq_evalₐ_smul, FractionalIdeal.count_well_defined, Extension.h1Cotangentι_injective, ContinuousMap.toNNReal_neg_algebraMap, Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply, contractLeft_assoc_coevaluation, AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin, MeasureTheory.restrict_compl_sigmaFiniteSet, MeasureTheory.Measure.haarMeasure_unique, WeierstrassCurve.Projective.Point.toAffine_smul, Quaternion.snd_re_dualNumberEquiv_symm, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, instIsLocalizationAlgebraMapSubmonoidPrimeComplLocalization, PreSubmersivePresentation.cotangentComplexAux_zero_iff, Bialgebra.TensorProduct.counitAlgHom_def, Module.AEval.of_symm_smul, AlgebraicGeometry.Scheme.basic_open_isOpenImmersion, NumberField.RingOfIntegers.instIsFractionRing, Matrix.intrinsicStar_toLin', LieModule.isNilpotent_toEnd_genWeightSpace_zero, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, Ideal.range_cotangentToQuotientSquare, KaehlerDifferential.polynomialEquiv_D, MvPolynomial.optionEquivLeft_apply, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, MvPolynomial.instIsScalarTower, Polynomial.hilbertPoly_smul, CommRing.Pic.mul_eq_tensor, FormallySmooth.instFinitePresentationKaehlerDifferentialOfEssFiniteType, MvPolynomial.totalDegree_coeff_finSuccEquiv_add_le, Matrix.mem_spectrum_iff_isRoot_charpoly, NNReal.segment_eq_uIcc, Ideal.algebraMap_quotient_residueField_mk, MvPolynomial.map_comp_rename, IsLocalizedModule.iso_symm_apply, AlgebraicGeometry.localRingHom_comp_stalkIso_apply, MeasureTheory.condLExp_smul, smul_leftMulMatrix, MvPolynomial.ACounit_X, Real.vector_fourierIntegral_eq_integral_exp_smul, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, MvPolynomial.prime_rename_iff, starConvex_iff_ordConnected, Extension.CotangentSpace.map_id, PreSubmersivePresentation.baseChange_jacobian, LinearMap.toMatrixOrthonormal_reindex, bind₁_xInTermsOfW_wittPolynomial, Ideal.relNorm_mono, LinearMap.toMatrixAlgEquiv_toLinAlgEquiv, FractionalIdeal.absNorm_eq', finrank_quotient_span_eq_natDegree', UnitAddTorus.mFourierSubalgebra_closure_eq_top, MvPowerSeries.substAlgHom_X, Polynomial.cyclotomic_expand_eq_cyclotomic_mul, instIsScalarTowerAtPrimeFractionRing_1, polynomialFunctions_separatesPoints, QuadraticMap.toMatrix'_comp, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, ExteriorAlgebra.toTrivSqZeroExt_comp_map, fderivWithin_sinh, IsAdicComplete.mkQ_comp_lift, MeasureTheory.eLpNorm_smul_measure_of_ne_top', Localization.localRingHom_to_map, MvPolynomial.constantCoeff_rename, MeasureTheory.Measure.rnDeriv_smul_right, MeasureTheory.Measure.rnDeriv_smul_left_of_ne_top', SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, MvPowerSeries.continuous_aeval, CliffordAlgebra.equivBaseChange_symm_apply, PreSubmersivePresentation.jacobiMatrix_reindex, MeasureTheory.Measure.sum_smul_dirac, map_leftMulMatrix_localization, MeasureTheory.Measure.ae_mem_finset_iff_map_eq_sum_dirac, Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free, IsLocalizedModule.iso_apply_mk, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, IntermediateField.exists_algHom_of_adjoin_splits, KaehlerDifferential.kerToTensor_apply, matPolyEquiv_map_smul, Quaternion.imJ_fst_dualNumberEquiv, RatFunc.laurent_div, cfcₙHom_nnreal_eq_restrict, star_dotProduct_toMatrix₂_mulVec, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, RootPairing.root_coroot_eq_pairing, CliffordAlgebraQuaternion.toQuaternion_ofQuaternion, AlgebraicIndependent.iff_adjoin_image_compl, CommRingCat.free_map_coe, SubmersivePresentation.ofSubsingleton_algebra_algebraMap, IntermediateField.normal_iff_forall_map_eq, Presentation.differentials.hom₁_single, PowerSeries.derivative_inv', instIsLocalRingTensorProductResidueFieldOfIsLocalHomRingHomAlgebraMap, LocalizedModule.divBy_apply, Module.Basis.toMatrix_smul, MvPolynomial.killCompl_comp_rename, HasFDerivAt.norm_sq, MvPolynomial.supportedEquivMvPolynomial_symm_X, Ideal.iInf_mul, Ideal.relNorm_relNorm, skewAdjointLieSubalgebraEquiv_symm_apply, TrivSqZeroExt.fstHom_comp_map, Generators.exists_presentation_of_basis_cotangent, IntermediateField.extendScalars_injective, Bialgebra.counitBialgHom_apply, zero_prodMap_dualTensorHom, cfcHom_continuous, polynomialFunctions.starClosure_topologicalClosure, cfcL_apply, Ideal.mem_toCotangent_ker, innerₛₗ_apply_apply, Real.hasStrictFDerivAt_rpow_of_pos, WeierstrassCurve.Projective.addX_smul, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, Matrix.Represents.smul, TensorAlgebra.ι_def, MvPolynomial.pderiv_one, NumberField.Units.pos_at_place, AlgebraicGeometry.Scheme.IdealSheafData.ideal_mul, MvPowerSeries.coe_substAlgHom, MvPolynomial.mkDerivation_X, MvPolynomial.pderiv_mul, RootPairing.self_comp_coPolarization_eq_corootForm, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, Ideal.absNorm_pos_iff_mem_nonZeroDivisors, lmul_injective, SpectrumRestricts.nnreal_iff, Polynomial.aeval_sumIDeriv, Matrix.toBilin_symm, Generators.compLocalizationAwayAlgHom_toAlgHom_toComp, MeasureTheory.Measure.haarScalarFactor_smul, LinearMap.spectrum_toMatrix', autAdjoinRootXPowSubCEquiv_symm_smul, MeasureTheory.Measure.OuterRegular.smul_nnreal, LieModule.trace_toEnd_genWeightSpace, Bialgebra.counitAlgHom_apply, HasFDerivWithinAt.csin, Subalgebra.aeval_coe, Real.smul_map_diagonal_volume_pi, Ring.choose_eq_smul, matPolyEquiv_diagonal_X, RootPairing.span_coroot'_eq_top, MeasureTheory.Measure.map_fst_prod, Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_left, CliffordAlgebraComplex.ofComplex_toComplex, MvPolynomial.ACounit_surjective, toMatrix_rotation, instIsIntegrallyClosedInSubtypeMemSubringToSubringIntegralClosure, TensorProduct.piScalarRight_tmul, Ideal.Filtration.mem_submodule, AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap, Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top, MvPolynomial.supported_eq_adjoin_X, AlgHom.mulLeftRightMatrix.inv_comp, cfcHom_nonneg_iff, Submodule.dualCopairing_eq, CliffordAlgebraComplex.toComplex_comp_ofComplex, gelfandStarTransform_naturality, LinearMap.polar_singleton, LieModule.shiftedGenWeightSpace.toEnd_eq, toSubring_bot, segment_eq_uIcc, WeierstrassCurve.Projective.smul_equiv_smul, Ideal.liesOver_iff_dvd_map, WeierstrassCurve.Projective.add_of_Z_eq_zero, gelfandStarTransform_apply_apply, IntermediateField.restrictScalars_normal, WittVector.factorPowSucc_fontaineThetaModPPow_eq, Polynomial.aeval_iterate_derivative_self, IntermediateField.isScalarTower, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, BialgCat.associator_def, Polynomial.Gal.mapRoots_bijective, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, MvPolynomial.aeval_eq_eval, RootPairing.toLinearMap_apply_CoPolarization, MeasureTheory.Measure.const_comp, dot_cross_self, MonoidAlgebra.mem_adjoin_support, cfc_apply_mkD, NormedSpace.Dual.toWeakDual_continuous, WeierstrassCurve.Projective.dblXYZ_smul, PowerSeries.coeff_heval, Module.endTensorEndAlgHom_apply, Matrix.toLpLin_mul_same, MvPolynomial.aeval_ite_mem_eq_self, Submodule.quotDualCoannihilatorToDual_nondegenerate, signedDist_left_congr, cfcₙ_eq_cfcₙL_mkD, FormallySmooth.adjoin_of_algebraicIndependent, Matrix.det_updateRow_add_smul_self, instStarModuleNNRealReal, RootPairing.Hom.weight_coweight_transpose, ContinuousMultilinearMap.norm_smulRightL_le, TensorProduct.comm_comp_map_apply, MvPolynomial.eval₂Hom_C_id_eq_join₁, IsAlgClosed.instIsAlgClosure, PowerSeries.aeval_eq_sum, QuaternionAlgebra.smul_coe, isPurelyInseparable_iff_fd_isPurelyInseparable, PolyEquivTensor.toFunAlgHom_apply_tmul, PolynomialLaw.exists_lift', QuadraticForm.equivalent_signType_weighted_sum_squared, TrivSqZeroExt.fst_exp, openSegment_eq_Ioo, MeasureTheory.laverage_eq', IntermediateField.LinearDisjoint.of_isField', BialgCat.whiskerLeft_def, Representation.asAlgebraHom_def, HopfAlgCat.whiskerLeft_def, strictConvexOn_pow, MvPolynomial.pow_idealOfVars, spectrum_diagonal, Field.finInsepDegree_self, PolynomialLaw.toFun_eq_rTensor_φ_toFun', RootPairing.toPerfPair_comp_root, signedDist_triangle, MvPolynomial.comap_id, MeasureTheory.OuterMeasure.comap_iInf, IsDedekindDomain.HeightOneSpectrum.intValuationDef_if_neg, RootPairing.GeckConstruction.mem_ωConjLieSubmodule_iff, LinearMap.IsContPerfPair.bijective_left, NNReal.isBoundedSMul, MvPolynomial.eval_rename_prod_mk, AdjoinRoot.algHom_ext_iff, PowerBasis.equivAdjoinSimple_symm_aeval, TensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse, FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal, CliffordAlgebra.contractRight_comm, adjoin_monomial_eq_reesAlgebra, TrivSqZeroExt.map_inr, Unitization.starLift_symm_apply_apply, ofId_self, Ideal.absNorm_eq_pow_inertiaDeg', MvPolynomial.optionEquivRight_C, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, Module.End.instLieModule, Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, convexOn_univ_dist, AddMonoidAlgebra.mapDomainBialgHom_id, Unitization.starLift_apply_apply, Matrix.SeparatingLeft.toLinearMap₂', Ergodic.eq_smul_of_absolutelyContinuous, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial, IntermediateField.lift_adjoin_simple, Ideal.exists_pow_le_of_le_radical_of_fg, TensorProduct.dualDistrib_apply_comm, Polynomial.toAddCircle_X_pow_eq_fourier, idealFactorsFunOfQuotHom_comp, MvPolynomial.rename_msymm, MvPolynomial.comap_comp_apply, algebraicClosure.normalClosure_eq_self, AlgebraicIndependent.matroid_isBasis_iff, KaehlerDifferential.isLocalizedModule_of_isLocalizedModule, IsScalarTower.subsemiring, LieRinehartAlgebra.Hom.anchor_derivation, IntermediateField.AdjoinDouble.normal_algebraicClosure, IsStandardSmoothOfRelativeDimension.baseChange, ContinuousLinearMap.toSesqForm_apply_coe, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, signedDist_linear_apply_apply, MvPolynomial.eval₂Hom_C_eq_bind₁, Matrix.Nondegenerate.smul_iff, IsAlgebraic.tensorProduct, algebraMap_self, CliffordAlgebra.changeFormAux_changeFormAux, essSup_ennreal_smul_measure, LinearMap.BilinForm.nondegenerate_toMatrix_iff, Matrix.derivative_det_one_add_X_smul, Ideal.range_mul', QuadraticAlgebra.algebraMap_re, Subalgebra.mulMap_map_comp_eq, gelfandTransform_bijective, Polynomial.differentiableOn_aeval, PointedCone.subset_dual_dual, PreSubmersivePresentation.ofHasCoeffs_relation, QuadraticMap.discr_smul, Polynomial.mem_iff_eq_smul_annIdealGenerator, dotProductEquiv_apply_apply, MvPolynomial.degreeOf_coeff_finSuccEquiv, LinearMap.rank_diagonal, Subalgebra.algebra_isAlgebraic_bot_left_iff, NumberField.RingOfIntegers.withValEquiv_symm_apply, RootPairing.injOn_dualMap_subtype_span_root_coroot, MvPolynomial.mem_pow_idealOfVars_iff, RatFunc.liftMonoidWithZeroHom_apply_div', transcendental_iff_injective, fderivWithin_ccosh, AdjoinRoot.powerBasis'_gen, LinearMap.separatingRight_toMatrix₂'_iff, IsScalarTower.adjoin_range_toAlgHom, Matrix.toEuclideanLin_apply, AddMonoidAlgebra.mapRangeRingHom_comp_algebraMap, LieSubmodule.Quotient.toEnd_comp_mk', Quaternion.imI_fst_dualNumberEquiv, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, TensorProduct.toIntegralClosure_bijective_of_smooth, MvPolynomial.rename_id_apply, toMatrix_lmul_eq, VectorFourier.fourierPowSMulRight_eq_comp, EisensteinSeries.E2_slash_action, LinearMap.toMatrixAlgEquiv'_id, IsCyclotomicExtension.aeval_zeta, MvPowerSeries.expand_mul, isGeometricallyReduced_iff, cfcHom_isClosedEmbedding, Generators.liftBaseChange_injective_of_isLocalizationAway, Field.sepDegree_self, Quaternion.algebraMap_def, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, LieModule.instIsTriangularizableSubtypeEndMemLieSubalgebraRangeToEnd, Ideal.relNorm_top, UniformConvexOn.strictConvexOn, Orthonormal.basisTensorProduct, AlgebraicGeometry.Scheme.isOpenImmersion_SpecMap_localizationAway, algebraicClosure.isAlgebraic, HasFDerivAt.arctan, Polynomial.bernoulli_generating_function, NumberField.Units.coe_mul, MeasureTheory.Measure.InnerRegular.smul, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, QuadraticForm.tmul_tensorMap_apply, IsGalois.normalClosure, HopfAlgCat.tensorObj_instHopfAlgebra, MvPolynomial.nonempty_support_finSuccEquiv, FractionalIdeal.isUnit_num, AlgEquiv.adjoinSingletonEquivAdjoinRootMinpoly_symm_toAlgHom, Unitization.nnnorm_def, HasStrictFDerivAt.abs, RatFunc.coe_X, MeasureTheory.Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, MonoidAlgebra.lift_symm_apply, Ideal.gcd_eq_sup, QuaternionAlgebra.Basis.lift_smul, Extension.Cotangent.smul_eq_zero_of_mem, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow', Generators.cotangentSpaceBasis_repr_one_tmul, ediam_smul_le, FiniteDimensional.mem_span_of_iInf_ker_le_ker, Module.AEval'.X_smul_of, Matrix.det_updateRow_smul_left, AdjoinRoot.quotEquivQuotMap_symm_apply_mk, MvPolynomial.pderiv_rename, IsIntegrallyClosedIn.exists_algebraMap_eq_of_pow_mem_subalgebra, LieModule.mem_posFittingCompOf, Presentation.comp_relation_inr, FunctionField.inftyValuation.polynomial, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, Quaternion.normSq_smul, Ideal.relNorm_eq_pow_of_isPrime_isGalois, LocalizedModule.divBy_mul_by, Matrix.toBilin_apply, IntermediateField.isAlgebraic_iff, Ideal.absNorm_eq_pow_inertiaDeg_of_liesOver, LinearMap.toMatrix₂'_compl₁₂, QuadraticAlgebra.omega_mul_coe_mul_mk, PiTensorProduct.mapL_smul, AlgebraicGeometry.Scheme.instIsOpenImmersionMapOfHomAwayAlgebraMap, Ideal.mul_comm, RootPairing.flip_comp_polarization_eq_rootForm, cfcL_integrable, Ideal.absNorm_mem, Polynomial.derivative'_apply, AdjoinRoot.Minpoly.toAdjoin.surjective, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, RootPairing.GeckConstruction.cartanSubalgebra_eq_lieSpan, Representation.smul_ofModule_asModule, QuadraticAlgebra.algebraMap_dvd_iff, FreeAlgebra.instFree, Polynomial.aeval_X_pow, BoxIntegral.unitPartition.integralSum_eq_tsum_div, Ideal.map_mul, MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul', Matrix.inv_denom_smul_num, LinearMap.flip_injective_iff₁, Finsupp.linearCombination_one_tmul, Matrix.updateRow_eq_transvection, Polynomial.Bivariate.aveal_eq_map_swap, Ideal.isIdempotentElem_iff_eq_bot_or_top, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, AlgebraicIndependent.aeval_comp_repr, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.toMatrixOrthonormal_apply_apply, LocalizedModule.map_surjective, Ideal.sup_eq_top_iff_isCoprime, AdjoinRoot.powerBasis'_dim, Matrix.toLin'_mul_apply, Orientation.areaForm_to_volumeForm, LieModule.isNilpotent_range_toEnd_iff, MvPowerSeries.expand_substAlgHom, MeasureTheory.isProbabilityMeasureSMul, MeasureTheory.OuterMeasure.map_apply, IntermediateField.coe_inclusion, Nonneg.segment_eq_uIcc, QuadraticAlgebra.mul_coe_eq_smul, CliffordAlgebra.ofBaseChange_toBaseChange, PowerSeries.support_expand_subset, Polynomial.aevalTower_algebraMap, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, signedDist_le_dist, AffineSubspace.coe_subtypeₐᵢ, Extension.Cotangent.val_mk, Matrix.nondegenerate_toBilin'_iff, Polynomial.rootsExpandPowEquivRoots_apply, MvPolynomial.map_expand, NNReal.algebraMap_eq_coe, HasStrictFDerivAt.arsinh, LieAlgebra.rank_le_natTrailingDegree_charpoly_ad, LinearMap.trace_eq_contract_of_basis', PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, Matrix.det_smul, Polynomial.Bivariate.swap_apply, FractionRing.algebraMap_liftAlgebra, TensorProduct.AlgebraTensorModule.rightComm_eq, Matrix.minpoly_dvd_charpoly, QuadraticForm.tmul_comp_tensorComm, strictConvexOn_exp, LinearMap.BilinForm.congr_comp, LinearMap.toMatrixAlgEquiv_apply, MvPolynomial.map_aeval, cfcₙ_apply_mkD, HasFDerivWithinAt.exp, RatFunc.coe_coe, Field.finSepDegree_self, coe_algebraMap_ofSubsemiring, PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, CliffordAlgebra.foldr'Aux_foldr'Aux, integralClosure_idem, cfcₙHom_id, MvPolynomial.map_frobenius_expand, LindemannWeierstrass.exp_polynomial_approx, Basis.linearEquiv_dual_iff_finiteDimensional, Orientation.areaForm_neg_orientation, LinearMap.toMatrix'_toLin', tendsto_card_div_pow_atTop_volume, NumberField.FinitePlace.norm_embedding_eq, Polynomial.map_expand, Ideal.Quotient.algebraMap_eq, comp_ofId, MvPolynomial.renameEquiv_trans, QuadraticAlgebra.C_eq_algebraMap, LieAlgebra.Orthogonal.jb_transform, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, fderivWithin_sin, LinearMap.IsSymm.domRestrict, Polynomial.algEquivCMulXAddC_symm_eq, Polynomial.valuation_of_mk, IsLocalRing.exists_maximalIdeal_pow_le_of_finite_quotient, WeierstrassCurve.Projective.addXYZ_smul, TensorProduct.toMatrix_assoc, Subspace.finrank_dualCoannihilator_eq, AlgebraicIndependent.adjoin_iff_disjoint, Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap, MeasureTheory.Measure.comp_eq_sum_of_countable, Matrix.toLinearMap₂'_apply', Field.Emb.Cardinal.two_le_deg, LieSubmodule.lie_top_eq_of_span_sup_eq_top, Polynomial.Gal.restrictDvd_def, MvPolynomial.expand_monomial, MvPowerSeries.substAlgHom_eq_aeval, IsLocalization.self, SubmersivePresentation.basisKaehlerOfIsCompl_apply, Derivation.bracket_eq_fun, Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, Subring.integralClosure_subring_le_iff, MvPolynomial.expand_char, instIsPushoutFractionRingPolynomial_1, KaehlerDifferential.mapBaseChange_tmul, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, Complex.hasStrictFDerivAt_cpow', Matrix.det_one_add_smul, MonoidAlgebra.mapDomainBialgHom_comp, Real.fourier_iteratedFDeriv, WeierstrassCurve.Affine.CoordinateRing.instIsScalarTowerPolynomial, Polynomial.leadingCoeff_smul_integralNormalization, InnerProductSpace.toDualMap_apply_apply, LinearMap.exists_map_addHaar_eq_smul_addHaar, Ideal.ramificationIdx_ne_one_iff, Localization.AtPrime.eq_maximalIdeal_iff_comap_eq, MvPolynomial.map_rename, LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec, KaehlerDifferential.kerTotal_eq, IntermediateField.finInsepDegree_le_of_left_le, Ideal.toCotangent_range, MeasureTheory.addEquivAddHaarChar_smul_preimage, MvPowerSeries.hasSum_aeval, BoundedContinuousFunction.integral_const_sub, PowerSeries.derivativeFun_smul, PreSubmersivePresentation.ofHasCoeffs_σ', MvPolynomial.killCompl_C, Presentation.quotientEquiv_symm, MvPolynomial.eval₂_const_pUnitAlgEquiv_symm, Quaternion.inv_def, ProperCone.mem_dual, Subspace.finiteDimensional_quot_dualCoannihilator_iff, Matrix.toAlgEquiv_kroneckerStarAlgEquiv, MvPolynomial.eval_comp_toMvPolynomial, Generators.H1Cotangent.δAux_C, Generators.map_toComp_ker, MvPolynomial.support_finSuccEquiv_nonempty, signedDist_apply_apply, Generators.Hom.toExtensionHom_toAlgHom_apply, Ideal.prod_le_inf, Complex.liftAux_apply, Polynomial.Monic.quotient_isIntegral, PowerSeries.support_expand, MvPolynomial.bind₁_X_left, IntermediateField.minpoly_gen, MeasureTheory.OuterMeasure.restrict_iInf, MeasureTheory.OuterMeasure.comap_apply, LaurentSeries.inducing_coe, strictConcaveOn_log_Iio, WittVector.mk_pow_fontaineTheta, NonUnitalSubalgebra.unitization_injective, MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN, WeakDual.toStrongDual_inj, LieAlgebra.Orthogonal.indefiniteDiagonal_assoc, Polynomial.expand_eq_comp_X_pow, PowerSeries.smul_weierstrassDiv, strictConcaveOn_univ_of_deriv2_neg, MvPolynomial.sumAlgEquiv_comp_rename_inr, Ideal.adic_module_basis, TensorAlgebra.toDirectSum_ofDirectSum, FormallySmooth.iff_injective_cotangentComplexBaseChange_residueField, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, MvPolynomial.aevalTower_toAlgHom, CliffordAlgebra.toBaseChange_comp_ofBaseChange, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, IntermediateField.aeval_coe, Generators.ofComp_val, Orientation.areaForm_swap, MvPowerSeries.comp_aeval, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, IsGalois.self, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, MeasureTheory.Measure.discard_comp, LinearMap.isSymm_dualProd, Extension.subsingleton_h1Cotangent, AlgebraicIndependent.matroid_spanning_iff, LaurentSeries.continuous_coe, Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes, Bundle.ContinuousRiemannianMetric.symm, Differential.instDifferentialAlgebraAdjoinRoot, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, FreeAlgebra.star_algebraMap, fderiv.log, LocalizedModule.mem_ker_mkLinearMap_iff, Generators.exists_presentation_of_free_cotangent, openSegment_eq_Ioo', Subalgebra.range_isScalarTower_toAlgHom, MvPolynomial.X_mul_pderiv_monomial, IsSepClosedOfCharZero.isCyclotomicExtension, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType, Matrix.toLinAlgEquiv_mul, MvPolynomial.degree_optionEquivLeft, LinearMap.det_mulRight, Localization.algHom_ext_iff, Generators.naive_val, MeasureTheory.OuterMeasure.restrict_ofFunction, Polynomial.aeval_one, Module.AEval.instIsScalarTowerOrigPolynomial, IsLocalizedModule.fromLocalizedModule.bij, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, Extension.CotangentSpace.map_tmul, PowerSeries.le_order_subst_right', coe_innerSL_apply, cfcHom_le_iff, strongConcaveOn_zero, Polynomial.aeval_eq_zero_of_mem_rootSet, Ideal.absNorm_ne_zero_iff_mem_nonZeroDivisors, RatFunc.map_apply, Unitization.lift_symm_apply_apply, cfcHom_id, cross_anticomm, MeasureTheory.Measure.rnDeriv_smul_left_of_ne_top, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, KaehlerDifferential.polynomialEquiv_comp_D, MvPolynomial.coeff_expand_smul, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, KaehlerDifferential.span_range_map_derivation_of_isLocalization, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, Ideal.powQuotSuccInclusion_apply_coe, Generators.algebraMap_apply, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, ENNReal.instSMulPosMonoNNReal, instIsAbelianGalois, MeasureTheory.OuterMeasure.map_iInf_comap, CommRing.Pic.mk_tensor, range_cfcₙHom, LocalizedModule.equivTensorProduct_apply_mk, TensorProduct.lid_tmul, Field.Emb.Cardinal.succEquiv_coherence, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, MeasureTheory.FiniteMeasure.tendsto_iff_weakDual_tendsto, Submodule.isInternal_prime_power_torsion_of_is_torsion_by_ideal, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, IntermediateField.isScalarTower_bot, IsAdicComplete.of_liftRingHom, discr_powerBasis_eq_norm, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, convexOn_rpow_left, MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul, Localization.toLocalizationMap_eq_monoidOf, QuadraticForm.polarBilin_tmul, prod_mem_ideal_map_of_mem_conductor, LieModule.isNilpotent_toEnd_of_isNilpotent, Ideal.isIdempotentElem_iff_of_fg, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, LocalizedModule.map_injective, RootPairing.toLinearMap_apply_apply_Polarization, NonUnitalStarSubalgebra.unitization_range, Extension.H1Cotangent.val_zero, StrongDual.toWeakDual_inj, LinearMap.BilinForm.Nondegenerate.congr, IsAdic.hasBasis_nhds, Polynomial.expand_one, AlgebraicGeometry.Scheme.IdealSheafData.ideal_pow, MvPolynomial.expand_C, toRingHom_ofId, ProperCone.subset_dual_dual, SymmetricAlgebra.instModuleFree, IsAdicComplete.StrictMono.mk_comp_liftRingHom, LinearMap.flip_surjective_iff₁, TensorAlgebra.toExterior_ι, Matrix.inv_smul', NNReal.strictConcaveOn_sqrt, Generators.Hom.id_val, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, Polynomial.aeval_subalgebra_coe, Polynomial.separable_or, matPolyEquiv_coeff_apply_aux_1, WeierstrassCurve.Projective.addXYZ_of_X_eq, WeakDual.coe_toStrongDual, LinearMap.BilinForm.separatingLeft_toMatrix'_iff, FormallySmooth.iff_injective_lTensor_residueField, ZLattice.covolume.tendsto_card_div_pow, coeSubmodule_differentIdeal_fractionRing, Ideal.Fiber.lift_residueField_surjective, leftMulMatrix_injective, isConjRoot_iff_aeval_eq_zero, ContinuousMap.toNNReal_algebraMap, RatFunc.mk_eq_mk', Generators.compLocalizationAwayAlgHom_X_inl, MvPolynomial.optionEquivRight_X_none, Module.dual_finite, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, Polynomial.aeval_X_left_apply, MonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, MvPolynomial.rename_psum, spectrum.gelfandTransform_eq, LinearMap.trace_eq_contract, OrthonormalBasis.orthogonalProjection_apply_eq_sum, Generators.map_ofComp_ker, Seminorm.ball_smul, Even.strictConvexOn_pow, AddMonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst, NonUnitalSubalgebra.unitization_range, LieModule.LinearWeights.map_smul, CliffordAlgebra.changeFormAux_apply_apply, SkewMonoidAlgebra.lift_of, LocalizedModule.equivTensorProduct_symm_apply_tmul, RatFunc.mk_def, Ideal.relNorm_singleton, Complex.lift_apply, CliffordAlgebra.toBaseChange_comp_involute, SkewMonoidAlgebra.lift_single, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, solvableByRad.isSolvable, LieSubmodule.coe_map_toEnd_le, Module.FinitePresentation.linearEquivMap_symm_apply, MvPolynomial.expand_zero, exists_basis_of_pairing_ne_zero, IntermediateField.linearDisjoint_comm, Matrix.mem_spectrum_of_isRoot_charpoly, Matrix.isNilpotent_toLin'_iff, Bialgebra.TensorProduct.counit_eq_algHom_toLinearMap, Ideal.map_relNorm, Coalgebra.TensorProduct.lid_tmul, Polynomial.aeval_prod_apply, MvPolynomial.degreesLE_nsmul, RatFunc.mk_eq_div', SkewMonoidAlgebra.lift_apply, Module.AEval'.of_symm_X_smul, TensorAlgebra.equivFreeAlgebra_symm_ι, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, MeasureTheory.Measure.smul_measure_isAddInvariant_le_of_isCompact_closure, Bundle.ContinuousRiemannianMetric.continuous, LieModule.mem_genWeightSpace, Polynomial.aeval_add_of_sq_eq_zero, MvPolynomial.totalDegree_rename_le, Polynomial.Chebyshev.aeval_T, Polynomial.aeval_comp, LinearMap.detAux_def, Polynomial.deriv_aeval, hasGradientWithinAt_iff_hasFDerivWithinAt, MvPolynomial.coe_mapEquivMonic_comp', MeasureTheory.Measure.comapₗ_apply, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, MvPowerSeries.map_subst, Presentation.naive_relation, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, Matrix.permanent_updateRow_smul, LieRinehartRing.leibniz_mul_right, Real.smul_map_volume_mul_left, Ideal.span_singleton_mul_eq_span_singleton_mul, AddMonoidAlgebra.decomposeAux_coe, Polynomial.monic_mapAlg_iff, MeasureTheory.OuterMeasure.map_comap_le, matPolyEquiv_symm_apply_coeff, convexOn_dist, Matrix.toLinearEquiv'_symm_apply, IntermediateField.equivOfEq_symm, PiTensorProduct.constantBaseRingEquiv_symm, real_linearMap_map_smul_complex, LinearMap.BilinForm.mul_toMatrix'_mul, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ProbabilityTheory.covariance_smul_left, Ideal.inf_mul, LinearMap.toMatrixAlgEquiv_id, Ideal.isTorsionBySet_cotangent, algebraMap_intNorm_fractionRing, QuaternionAlgebra.algebraMap_injective, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, Seminorm.convexOn, IsFractionRing.self_iff_surjective, Polynomial.toMvPolynomial_eq_rename_comp, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_apply, HasDerivWithinAt.fun_finset_prod, Derivation.comp_aeval_eq, Extension.Cotangent.val_smul''', Polynomial.aeval_homogenize_X_one, MvPolynomial.adjoin_range_X, NormedSpace.smul_mem_polar, MeasureTheory.Measure.mapₗ_congr, IntermediateField.restrictRestrictAlgEquivMapHom_apply, WeakDual.CharacterSpace.continuousMapEval_bijective, instIsPushoutPolynomial_1, strictConcaveOn_sqrt_mul_log_Ioi, LieModule.Weight.coe_coe, AlgebraicGeometry.Scheme.ΓSpecIso_inv, InnerProductGeometry.norm_toLp_symm_crossProduct, Module.Invertible.algEquivOfRing_apply, dualTensorHom_apply, BilinForm.mul_toMatrix_mul, Ideal.sup_pow_add_le_pow_sup_pow, FractionalIdeal.coeIdeal_sup, MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, AddMonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure, TrivSqZeroExt.map_comp_inlAlgHom, Localization.epi, Polynomial.comap_taylorEquiv_degreeLT, Bialgebra.toLinearMap_counitAlgHom, QuadraticForm.tensorRId_symm_apply, Polynomial.ofReal_eval, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, Ideal.relNorm_le_comap, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, Ideal.algebraMap_residueField_surjective, Quaternion.fst_imK_dualNumberEquiv_symm, MeasureTheory.OuterMeasure.map_le_restrict_range, continuousMap_mem_polynomialFunctions_closure, MeasureTheory.Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, MeasureTheory.lpNorm_smul_measure_of_ne_zero, MvPolynomial.transcendental_polynomial_aeval_X_iff, PadicAlgCl.norm_extends, MvPolynomial.aeval_algebraMap_eq_zero_iff_of_injective, IsStandardSmoothOfRelativeDimension.iff_of_isStandardSmooth, AdicCompletion.mkₐ_apply_coe, Subalgebra.centralizer_coe_image_includeRight_eq_center_tensorProduct, FractionalIdeal.finprod_heightOneSpectrum_factorization, NormedSpace.inclusionInDoubleDual_norm_eq, Generators.algebraMap_eq, IntermediateField.fieldRange_comp_val, Polynomial.rootsExpandEquivRoots_apply, instPosMulStrictMonoIdeal, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, LinearAlgebra.FreeProduct.ι_apply, QuaternionAlgebra.imK_swapEquiv_symm_apply, Polynomial.aeval_prod, Ideal.pow_succ_lt_pow, IntermediateField.adjoin.powerBasis_gen, NonUnitalSubsemiring.unitization_apply, PowerBasis.leftMulMatrix, iInf_valuationSubring_superset, SubmersivePresentation.ofSubsingleton_relation, StandardEtalePair.equivMvPolynomialQuotient_symm_apply, NumberField.Units.regulator_eq_det, AlgCat.hom_hom_associator, logDeriv_eqOn_iff, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', cuspFunction_smul, Extension.Hom.comp_id, MvPolynomial.support_rename_of_injective, cfcₙHom_integral, Ideal.map_mk_comap_factorPow, IsSmoothAt.exists_isStandardEtale_mvPolynomial, MvPolynomial.comap_comp, IntermediateField.equivOfEq_rfl, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, CliffordAlgebra.changeForm_ι_mul, IsLocalizedModule.iso_symm_comp, MonoidAlgebra.scalarTensorEquiv_tmul, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, QuadraticForm.tensorAssoc_toLinearEquiv, TensorProduct.AlgebraTensorModule.rTensor_tensor, StarAlgHom.realContinuousMapOfNNReal_apply, Module.Ray.linearEquiv_smul_eq_map, MvPolynomial.eval_eq_eval_mv_eval', IntermediateField.normal_iff_normalClosure_le, MvPolynomial.ACounit_C, MeasureTheory.NullMeasurableSet.smul_measure, PreSubmersivePresentation.baseChange_toPresentation, TrivSqZeroExt.eq_smul_exp_of_ne_zero, AdicCompletion.isAdicCauchy_iff, ProbabilityTheory.setBernoulli_apply', Polynomial.expand_C, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply_mk, LinearMap.isAlt_iff_eq_neg_flip, RootPairing.corootSpan_map_flip_toPerfPair, LinearMap.toLinearMap_toContPerfPair, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, MvPolynomial.transcendental_supported_X_iff, Polynomial.aevalTower_toAlgHom, coevaluation_apply_one, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, gelfandStarTransform_symm_apply, ContinuousLinearMap.norm_smulRightL, MvPolynomial.optionEquivLeft_X_none, HomogeneousLocalization.val_awayMap, IsAdjoinRootMonic.map_modByMonic, IsBaseChange.transvection, LieSubalgebra.toEnd_mk, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, HahnSeries.instNontrivialSubalgebra, PowerSeries.substAlgHom_X, LinearMap.toBilin'Aux_toMatrixAux, MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, convexOn_univ_norm, MvPowerSeries.expand_one_apply, PrimeSpectrum.sup_vanishingIdeal_le, IsLocalRing.map_tensorProduct_mk_eq_top, Bialgebra.TensorProduct.comulAlgHom_def, AdjoinRoot.algebraMap_eq, MvPolynomial.degreeOf_rename_of_injective, LinearMap.toMatrix₂_compl₂, Polynomial.Monic.quotient_isIntegralElem, FormallySmooth.inst, MvPolynomial.degreesLE_add, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul', RatFunc.instIsFractionRingPolynomial, Polynomial.toAddCircle.integrable, MvPolynomial.exists_rename_eq_of_vars_subset_range, MvPolynomial.optionEquivRight_symm_apply, Ergodic.iff_mem_extremePoints_measure_univ_eq, PowerSeries.heval_apply, NumberField.Units.coe_coe, LinearMap.trace_eq_contract_apply, PiTensorProduct.constantBaseRingEquiv_tprod, FreeAlgebra.liftAux_eq, dualTensorHomEquivOfBasis_symm_cancel_right, spectrum.smul_mem_smul_iff, ProbabilityTheory.condVar_smul, linearMap_self, Matrix.toLpLin_symm_pow, Matrix.det_updateRow_sum_aux, Polynomial.mkDerivation_one_eq_derivative', PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_field, IsAdicComplete.of_lift, infEDist_smul₀, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', TensorAlgebra.lift_symm_apply, IsLocalization.instIsScalarTowerLocalizationAtPrime, MeasureTheory.instSFiniteHSMulENNRealMeasure, AddMonoidAlgebra.tensorEquiv.invFun_tmul, PowerSeries.expand_one_apply, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, hasFDerivAt_norm_rpow, Matrix.finite_spectrum, AlgebraicIndependent.sumElim_iff, CommRing.Pic.inv_eq_dual, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, Ideal.ResidueField.ringHom_ext_iff, Generators.Hom.aeval_val, NonUnitalSubring.unitization_apply, QuadraticModuleCat.instMonoidalCategory.tensorObj_form, IsDedekindDomain.HeightOneSpectrum.irreducible, LinearMap.IsPerfectCompl.isCompl_right, MeasureTheory.mulEquivHaarChar_smul_map, CoalgCat.tensorHom_def, Bialgebra.counitBialgHom_self, KaehlerDifferential.linearMapEquivDerivation_apply_apply, LinearMap.BilinForm.tensorDistribEquiv_toLinearMap, Field.absoluteGaloisGroup.commutator_closure_isNormal, Polynomial.aeval_pi_apply, LaurentSeries.algebraMap_apply, IsAdjoinRoot.map_repr, IntermediateField.relfinrank_dvd_finrank_bot, Polynomial.aevalTower_comp_algebraMap, IsGalois.sup_right, NumberField.Units.finrank_mul_regOfFamily_eq_det, TensorAlgebra.equivDirectSum_apply, Presentation.comp_aeval_relation_inl, AdjoinRoot.aeval_eq_of_algebra, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Matrix.linfty_opNNNorm_toMatrix, Real.concaveOn_rpow, MeasureTheory.OuterMeasure.isometry_comap_mkMetric, RatFunc.laurent_at_zero, KaehlerDifferential.tensorKaehlerEquivBase_tmul, WittVector.mulN_coeff, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul, MeasureTheory.OuterMeasure.map_comap, Matrix.isRepresentation.toEnd_represents, LSeries_smul, IsHausdorff.iInf_pow_smul, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, FormallySmooth.iff_subsingleton_and_projective, IsLocalizedModule.fromLocalizedModule.inj, Matrix.toEuclideanCLM_toLp, traceForm_toMatrix, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, WeakDual.CharacterSpace.homeoEval_naturality, signedDist_eq_zero_of_orthogonal, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq, KaehlerDifferential.isLocalizedModule_map, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, IntermediateField.adjoin_simple_adjoin_simple, ProbabilityTheory.covarianceBilin_zero, IsDedekindDomain.exists_forall_sub_mem_ideal, normalClosure.restrictScalars_eq, Module.End.hasUnifEigenvalue_iff_mem_spectrum, NumberField.InfinitePlace.isUnramified_self, contDiffOn_stereoToFun, cross_anticomm', WeierstrassCurve.Projective.negAddY_smul, LeftInvariantDerivation.evalAt_coe, FractionalIdeal.count_ne_zero, Ideal.span_singleton_mul_right_inj, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, toBilin'Aux_toMatrixAux, NumberField.det_basisOfFractionalIdeal_eq_absNorm, QuadraticAlgebra.lift_apply_apply, MeasureTheory.FiniteMeasure.map_fst_prod, MvPolynomial.pderiv_sumToIter, MvPolynomial.support_expand_subset, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, IntermediateField.AdjoinSimple.norm_gen_eq_one, MeasureTheory.isAddLeftInvariant_smul, HilbertBasis.hasSum_orthogonalProjection, LieModule.coe_genWeightSpaceOf_zero, Complex.hasStrictFDerivAt_cpow, TensorAlgebra.equivFreeAlgebra_ι_apply, BilinForm.dotProduct_toMatrix_mulVec, LinearMap.BilinForm.tensorDistrib_tmul, AdjoinRoot.mk_leftInverse, Polynomial.transcendental_X, IntermediateField.range_val, IntermediateField.instFiniteSubtypeMemBot, IntermediateField.isCyclotomicExtension_lcm_sup, Polynomial.differentiable_aeval, KaehlerDifferential.End_equiv_aux, Real.fourierIntegral_convergent_iff', Matrix.adjugate_adjugate, Projectivization.cross_mk_of_cross_ne_zero, MeasureTheory.Measure.ae_eq_or_eq_iff_map_eq_dirac_add_dirac, finrank_quotient_span_eq_natDegree, Unitization.splitMul_injective_of_clm_mul_injective, Matrix.toLpLin_one, Convex.toWeakSpace_closure, RatFunc.numDenom_div, Extension.instIsScalarTowerRing, IntermediateField.linearDisjoint_iff', Polynomial.roots_expand_map_frobenius, MvPolynomial.coeff_rename_embDomain, IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, Bundle.ContMDiffRiemannianMetric.symm, integralClosure.isFractionRing_of_finite_extension, IsLiouville.rfl, HasFDerivWithinAt.hasGradientWithinAt, charpoly_leftMulMatrix, Module.Invertible.instDual, IntermediateField.splits_iff_mem, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, Module.Basis.det_unitsSMul, NumberField.RingOfIntegers.coe_eq_zero_iff, Polynomial.aeval_X_left, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, TrivSqZeroExt.snd_exp, Matrix.inv_smul, Polynomial.map_under_lt_comap_of_weaklyQuasiFiniteAt, TensorProduct.toIntegralClosure_mvPolynomial_bijective, MvPolynomial.finSuccEquiv_coeff_coeff, MeasureTheory.Measure.Regular.smul, Ideal.index_pow_le, IntermediateField.extendScalars.orderIso_apply, MvPolynomial.rename_comp_expand, AlgebraicIndependent.adjoin_of_disjoint, MeasureTheory.Measure.hausdorffMeasure_smul₀, PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix, PowerSeries.substAlgHom_comp_substAlgHom, PreSubmersivePresentation.jacobiMatrix_apply, MeasureTheory.eLpNorm_one_smul_measure, HasFDerivWithinAt.cpow, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C', essFiniteType_cond_iff, SkewMonoidAlgebra.lift_unique, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, MvPolynomial.rename_esymm, StrongDual.toLp_of_not_memLp, Polynomial.roots_expand_image_frobenius, PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply, AffineSubspace.isometryEquivMap.toAffineMap_eq, algebraicClosure.isIntegralClosure, Ideal.surjectiveOnStalks_residueField, Quaternion.expSeries_odd_of_imaginary, AffineSubspace.signedInfDist_eq_signedDist_of_mem, TensorAlgebra.lift_ι_apply, HasStrictFDerivAt.const_cpow, MeasureTheory.OuterMeasure.restrict_univ, Extension.Cotangent.finite, Quaternion.smul_coe, KaehlerDifferential.linearMapEquivDerivation_symm_apply, HasFDerivWithinAt.csinh, normalizedTrace_intermediateField, TensorAlgebra.instModuleFree, LinearMap.BilinForm.tensorDistribEquiv_apply, MvPowerSeries.HasSubst.comp, AddMonoidAlgebra.lift_apply, KaehlerDifferential.span_range_derivation, Localization.algEquiv_mk, WeierstrassCurve.Projective.smul_eq, Generators.H1Cotangent.exact_map_δ, Matrix.piLp_ofLp_toEuclideanLin, Generators.H1Cotangent.δAux_monomial, LinearMap.BilinForm.toMatrix_apply, minpoly.dvd_iff, isIntegral_localization', MvPolynomial.pow_idealOfVars_eq_span, TrivSqZeroExt.map_comp_inrHom, RootPairing.reflectionPerm_coroot, NormedSpace.inclusionInDoubleDual_norm_le, RatFunc.smul_eq_C_mul, LieSubmodule.traceForm_eq_zero_of_isTrivial, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, LinearMap.dualProd_apply_apply, lieEquivMatrix'_apply, instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap, TensorAlgebra.rank_eq, Generators.CotangentSpace.compEquiv_symm_zero, TensorProduct.dualDistribEquivOfBasis_symm_apply, BilinForm.toMatrix_toBilin, TensorProduct.AlgebraTensorModule.congr_eq, Module.dual_free, HasFDerivAt.abs, WeakDual.isCompact_closedBall, LinearMap.IsPerfectCompl.flip_iff, LieModule.weight_vector_multiplication, NumberField.Units.norm, LinearMap.isSymm_def, Generators.toAlgHom_ofComp_surjective, Matrix.toPerfectPairing_apply_apply, isNormalClosure_normalClosure, Unitization.starMap_injective, MvPolynomial.bind₁_comp_bind₁, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, HasFDerivWithinAt.abs, MvPolynomial.commAlgEquiv_C, AdicCompletion.range_eval, InnerProductSpace.toDual_apply, Generators.Hom.algebraMap_toAlgHom', IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra, Ideal.Quotient.smul_top, Generators.cotangentSpaceBasis_repr_tmul, IntermediateField.finrank_eq_one_iff, RatFunc.laurent_laurent, IntermediateField.lift_top, LaurentSeries.exists_ratFunc_val_lt, LinearMap.IsPerfPair.compl₁₂, RingHom.SurjectiveOnStalks.tensorProductMap, Ideal.multiset_prod_span_singleton, NonUnitalAlgHom.toAlgHom_zero, LinearMap.minpoly_toMatrix', cfc_map_polynomial, LieSubalgebra.coe_ad_pow, RatFunc.num_algebraMap, Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, LinearMap.BilinForm.IsPosSemidef.smul, Seminorm.comp_smul, WeierstrassCurve.Projective.add_of_Z_eq_zero_left, AlgebraicGeometry.Spec_map_localization_isIso, HopfAlgCat.whiskerRight_def, FreeAlgebra.lift_ι_apply, MvPolynomial.commAlgEquiv_X, ProbabilityTheory.IsGaussian.charFun_eq', Derivation.instLieModule, ProbabilityTheory.covarianceBilinDual_eq_covariance, NumberField.RingOfIntegers.instIsLocalizationAlgebraMapSubmonoidIntNonZeroDivisors, FormalMultilinearSeries.coeff_ofScalars, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, Generators.Hom.comp_id, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, signedDist_zero, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, EMetric.exists_forall_closedBall_subset_aux₂, Polynomial.aevalTower_ofId, MeasureTheory.Measure.MutuallySingular.smul, CommAlgCat.lift_unop_hom, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, Subrepresentation.mem_asSubmodule'_iff, QuadraticForm.dualProd_apply, LinearMap.toMatrix₂_comp, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, NumberField.mixedEmbedding.span_idealLatticeBasis, Matrix.instFiniteSpectrum, MeasureTheory.SMul.sigmaFinite, Orthonormal.inner_left_right_finset, MvPolynomial.optionEquivRight_X_some, MeasureTheory.Measure.addHaarMeasure_unique, isometry_cfcₙHom, Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod, PrimeSpectrum.mem_image_comap_basicOpen, VonNeumannAlgebra.centralizer_centralizer', CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, MeasureTheory.isMulLeftInvariant_smul, MvPolynomial.aeval_expand, Unitization.starMap_id, ProbabilityTheory.covarianceBilinDual_zero, CoalgCat.associator_def, MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_innerRegular, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, isLocalizedModule_iff, AlgebraicIndependent.lift_reprField, Matrix.SeparatingRight.toLinearMap₂', Extension.Hom.sub_one_tmul, Polynomial.hilbertPoly_succ, Representation.asModuleEquiv_symm_map_smul, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, IntermediateField.isAlgebraic_adjoin, MvPolynomial.aeval_algebraMap_apply, id.smul_eq_mul, LieAlgebra.lieCharacterEquivLinearDual_symm_apply, PointedCone.mem_dual, Quaternion.imK_fst_dualNumberEquiv, IsAdjoinRoot.map_X, QuadraticForm.tensorRId_apply, InnerProductSpace.toDualMap_apply, gelfandTransform_map_star, QuadraticForm.comp_tensorLId_eq, SubmersivePresentation.linearIndependent_aeval_val_pderiv_relation, FDRep.average_char_eq_finrank_invariants, polynomialFunctions.starClosure_eq_adjoin_X, MvPolynomial.pderiv_X, instIsLiouvilleSubtypeMemIntermediateField, NumberField.mixedEmbedding.convexBodySumFun_smul, TensorProduct.lmulEquiv_eq_lidOfCompatibleSMul, KaehlerDifferential.exact_mapBaseChange_map, LinearMap.pow_eq_aeval_mod_charpoly, AffineIsometryEquiv.ofTop_symm_apply_coe, NumberField.mixedEmbedding.logMap_real_smul, LinearMap.tensorProductEnd_apply, Bialgebra.TensorProduct.assoc_tmul, fderivWithin_cos, Matrix.toLpLin_pow, PowerBasis.liftEquiv_symm_apply, KaehlerDifferential.tensorKaehlerEquiv_tmul, Module.AEval'.X_pow_smul_of, LinearMap.trace_eq_contract', RootPairing.toLinearMap_apply_PolarizationIn, Generators.H1Cotangent.δAux_toAlgHom, Matrix.kroneckerAlgEquiv_apply, LinearEquiv.symm_flip, fdifferential_apply, KaehlerDifferential.D_apply, MeasureTheory.OuterMeasure.map_iInf_le, IsSymmetricAlgebra.equiv_symm_comp, CliffordAlgebraComplex.ofComplex_I, SeparableClosure.hasEnoughRootsOfUnity_pow, LinearMap.BilinForm.separatingRight_toMatrix'_iff, Matrix.isUnit_toLin'_iff, cfcHom_integral, RatFunc.liftMonoidWithZeroHom_apply_div, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, AlgHom.IsArithFrobAt.localize_algebraMap, IsTranscendenceBasis.isAlgebraic_field, Subalgebra.mvPolynomial_aeval_coe, Submodule.dualCoannihilator_map_linearEquiv_flip, IsAdjoinRoot.adjoinRootAlgEquiv_apply_root, RootPairing.rootSpan_map_toPerfPair, RatFunc.num_dvd, innerₗ_apply, Polynomial.rootsExpandPowToRoots_apply, Ideal.ResidueField.liftₐ_comp_toAlgHom, TensorAlgebra.toClifford_ι, RootPairing.GeckConstruction.trace_toEnd_eq_zero, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, Matrix.toLin'_mul, fderivWithin_ccos, AdjoinRoot.Minpoly.coe_toAdjoin, Extension.Hom.id_toRingHom, PowerSeries.expand_smul, Real.ball_eq_openSegment, AddMonoidAlgebra.mapDomainBialgHom_apply, LinearMap.BilinForm.lieInvariant_iff, cfcₙHom_predicate, Ideal.eq_span_singleton_mul, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, Matrix.instLieModuleForall, LinearMap.BilinForm.dotProduct_toMatrix_mulVec, CliffordAlgebraQuaternion.equiv_apply, Quaternion.re_fst_dualNumberEquiv, HasStrictFDerivAt.clog, Module.End.rTensorAlgHom_apply_apply, Presentation.naive_relation_apply, Real.one_div_sub_hasFPowerSeriesOnBall_zero, Complex.liftAux_neg_I, norm_self, Seminorm.bound_of_continuous, FractionalIdeal.canonicalEquiv_mk0, PowerBasis.equivAdjoinSimple_aeval, PolynomialLaw.exists_lift, MeasureTheory.Measure.rnDeriv_smul_left', MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict, IntermediateField.extendScalars_adjoin, MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul', IntermediateField.isPurelyInseparable_tower_bot, MvPowerSeries.rescaleAlgHom_one, le_separableClosure_iff, LieModule.isFaithful_iff, Matrix.inv_def, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, AdicCompletion.transitionMap_comp_eval, Normal.algHomEquivAut_apply, Associates.le_singleton_iff, IsFractionRing.idem, AlgebraicIndependent.subalgebraAlgebraicClosure, Bundle.ContMDiffRiemannianMetric.pos, Matrix.permanent_updateCol_smul, AffineIsometryEquiv.ofEq_symm, HasStrictFDerivAt.sqrt, RatFunc.laurentAux_div, Matrix.ofLp_toLpLin, traceForm_dualSubmodule_adjoin, WittVector.mul_polyOfInterest_aux4, signedDist_triangle_left, ModularForm.instIsScalarTowerComplex, polyEquivTensor_symm_apply_tmul, MvPowerSeries.c_eq_algebraMap, AlgebraicGeometry.pullbackSpecIso_inv_fst'_assoc, IsContMDiffRiemannianBundle.exists_contMDiff, Nat.Partition.summable_genFun_term, Matrix.toBilin'_symm, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, MvPolynomial.rename_eval₂, MeasureTheory.Measure.pi_map_eval, Unitization.starLift_range, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some, HasDerivWithinAt.arsinh, RootPairing.corootSpan_dualAnnihilator_map_eq, NumberField.FinitePlace.norm_lt_one_iff_mem, IntermediateField.extendScalars_inf, MvPowerSeries.expand_eq_expand, Polynomial.Gal.instIsScalarTowerSplittingField, MeasureTheory.OuterMeasure.comap_top, AdjoinRoot.quotEquivQuotMap_apply, MvPowerSeries.substAlgHom_comp_substAlgHom_apply, IsAdjoinRootMonic.modByMonicHom_map, Ideal.finrank_prime_pow_ramificationIdx, Extension.CotangentSpace.map_toInfinitesimal_bijective, IsAzumaya.mulLeftRight_comp_congr, Ideal.le_pow_ramificationIdx, IntermediateField.botContinuousSMul, LinearMap.BilinForm.isSymm_iff_flip, MeasureTheory.isMulRightInvariant_smul, RatFunc.mk_eq_div, Polynomial.Bivariate.equivMvPolynomial_symm_X_0, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, Polynomial.sup_aeval_range_eq_top_of_isCoprime, AdjoinRoot.isAdjoinRoot_map_eq_mkₐ, MvPolynomial.finitePresentation_universalFactorizationMap, WeierstrassCurve.Projective.negY_smul, LinearMap.flip_bijective_iff₁, HasStrictFDerivAt.rpow, HopfAlgCat.associator_def, InnerProductSpace.toDual_apply_apply, KaehlerDifferential.range_mapBaseChange, LinearMap.flip_bijective_iff₂, Matrix.TransvectionStruct.toMatrix_reindexEquiv, SubmersivePresentation.sectionCotangent_eq_iff, Extension.Cotangent.mk_eq_zero_iff, ContinuousMap.sup_mem_closed_subalgebra, ContinuousLinearMap.adjointAux_apply, ContinuousFunctionalCalculus.exists_cfc_of_predicate, eq_separableClosure_iff, Generators.Hom.toExtensionHom_id, FiniteType.iff_quotient_mvPolynomial', LinearMap.det_toLin', Presentation.differentials.surjective_hom₁, ProperCone.innerDual_singleton, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, TensorAlgebra.lift_comp_ι, LieSubmodule.toEnd_comp_subtype_mem, MeasureTheory.eLpNorm'_smul_measure, MvPolynomial.tensorEquivSum_one_tmul_C, LinearMap.minpoly_dvd_charpoly, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, hasFDerivAt_list_prod', segment_eq_Icc', Polynomial.notMem_nonZeroDivisors_iff, MeasureTheory.eLpNorm_smul_measure_of_ne_top, InnerProductSpace.rankOne_def, CliffordAlgebraQuaternion.equiv_symm_apply, BilinForm.toMatrix_comp, AlgebraicGeometry.StructureSheaf.const_mul_cancel, LieAlgebra.ad_nilpotent_of_nilpotent, AlgHom.mulLeftRight_apply, TensorProduct.commRight_tmul, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero, Ideal.mapCotangent_toCotangent, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul, stereoToFun_apply, IntermediateField.normal_iff_forall_fieldRange_le, Generators.Cotangent.surjective_map_ofComp, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_regular, Polynomial.fderiv_aeval, transpose_dualTensorHom, Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom, Valuation.pow_Uniformizer_is_pow_generator, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, MeasureTheory.FinMeasAdditive.smul_measure_iff, Localization.mk_eq_mk'_apply, Ideal.exists_relNorm_eq_pow_of_isPrime, Polynomial.not_quasiFiniteAt, TensorAlgebra.ι_range_disjoint_one, MeasureTheory.Measure.map_eq_sum, MvPolynomial.eval₂Hom_rename, LieModule.rank_eq_natTrailingDegree, FGModuleCat.FGModuleCatDual_obj, IsAlgebraic.exists_nonzero_coeff_and_aeval_eq_zero, TensorProduct.lmul'_comp_map, LieSubmodule.mem_baseChange_iff, Module.End.aeval_apply_of_hasEigenvector, AdicCompletion.instIsHausdorff, PowerBasis.mem_span_pow', IsAzumaya.bij, QuasiFinite.baseChange, MvPowerSeries.rescaleAlgHom_mul, Generators.H1Cotangent.exact_δ_map, IsGalois.normalAutEquivQuotient_apply, Bialgebra.counitAlgHom_self, Ideal.mem_minimalPrimes_sup, Real.strictConvexOn_mul_log, IsDedekindDomain.map_differentIdeal_dvd_differentIdeal, ProbabilityTheory.covarianceBilin_comm, Derivation.liftKaehlerDifferential_comp, HasStrictFDerivAt.ccos, MvPolynomial.sumAlgEquiv_comp_rename_inl, Complex.det_conjAe, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, adjoin_singleton_eq_range_aeval, KaehlerDifferential.ker_map, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, ClosedSubmodule.orthogonal_eq_inter, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, LinearMap.BilinForm.sum_repr_mul_repr_mul, MvPolynomial.aeval_bind₁, MeasureTheory.Measure.rnDeriv_smul_right_of_ne_top', QuadraticForm.dualProdIsometry_invFun, AdicCompletion.coe_eval, Polynomial.isCoprime_expand, LinearMap.separatingLeft_toMatrix₂'_iff, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, CliffordAlgebraQuaternion.ofQuaternion_star, MonoidAlgebra.lift_unique, KaehlerDifferential.mapBaseChange_surjective, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, QuadraticForm.equivalent_weightedSumSquares, QuaternionAlgebra.lift_apply, AdicCompletion.coe_ofTensorProductEquivOfFiniteNoetherian, LeftInvariantDerivation.left_invariant'', CliffordAlgebra.contractLeft_contractLeft, Polynomial.SplittingFieldAux.scalar_tower', Subalgebra.centralizer_coe_map_includeRight_eq_center_tensorProduct, SchwartzMap.smulRightCLM_apply_apply, Submodule.dualCoannihilator_top, hasEigenvector_toLin'_diagonal, WeierstrassCurve.Projective.dblX_smul, MonoidAlgebra.tensorEquiv_symm_single, IntermediateField.rank_adjoin_eq_one_iff, taylor_mean_remainder, StrictMono.strictConvexOn_univ_of_deriv, LinearMap.toMatrixAlgEquiv'_apply, LieAlgebra.ad_pow_lie, Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin, Subalgebra.mem_saturation_iff, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, MvPolynomial.exists_fin_rename, RatFunc.liftOn_div, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, CoalgCat.whiskerRight_def, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, Orientation.map_eq_det_inv_smul, AdicCompletion.factorₐ_evalₐ_one, FormallySmooth.iff_of_surjective, cfc_def, MvPolynomial.optionEquivLeft_coeff_coeff, LinearMap.continuous_of_isContPerfPair, LinearMap.toMatrix'_algebraMap, IntermediateField.isAlgebraic_tower_top, EuclideanHalfSpace.convex, StrongDual.polarSubmodule_eq_polar, MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv, FiniteType.iff_quotient_freeAlgebra, LinearMap.flip.instIsPerfPair, Matrix.charpoly.optionEquivLeft_symm_univ_isHomogeneous, AlgCat.hom_hom_rightUnitor, instIsScalarTowerAtPrimeFractionRing, Complex.liftAux_I, LocalizedModule.coe_map_eq, Matrix.det_updateRow_sum, Extension.CotangentSpace.map_sub_map, IsStandardSmoothOfRelativeDimension.id, transcendental_aeval_iff, Ideal.exists_radical_pow_le_of_fg, Unitization.starMap_inl, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, fourierSubalgebra_separatesPoints, normalizedTrace_eq_of_fininteDimensional, LinearEquiv.instIsPerfPair, Polynomial.Splits.aeval_eq_prod_aroots, MvPolynomial.pderiv_def, MeasureTheory.OuterMeasure.map_map, LieModule.isNilpotent_toEnd_of_isNilpotent₂, MonoidAlgebra.lift_apply', Quaternion.exp_of_re_eq_zero, QuadraticAlgebra.coe_dvd_iff_dvd, Complex.one_add_cpow_hasFPowerSeriesAt_zero, Module.reflection_mul_reflection_pow, IsPreconnected.convex, MvPolynomial.mem_pow_idealOfVars_iff', MeasureTheory.integrable_smul_measure, BilinearForm.toMatrixAux_eq, CliffordAlgebra.contractLeft_ι_mul, MvPolynomial.mem_supported, Polynomial.expand_inj, NumberField.mixedEmbedding.covolume_idealLattice, FormallySmooth.instTensorProduct, IntermediateField.finrank_eq_fixingSubgroup_index, Commute.cfcₙHom, CliffordAlgebraQuaternion.toQuaternion_comp_ofQuaternion, WeierstrassCurve.Projective.addXYZ_neg, MvPolynomial.renameEquiv_apply, MvPowerSeries.expand_one, QuadraticAlgebra.mul_star, RootPairing.GeckConstruction.span_range_h'_eq_top, Submodule.norm_subtypeL, MvPolynomial.rename_esymmAlgHom, MeasureTheory.setLAverage_eq', Matrix.SeparatingLeft.toBilin, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, WeierstrassCurve.Projective.addZ_smul, ProbabilityTheory.Kernel.instIsIrreducibleHSMulENNRealMeasure, FGModuleCat.FGModuleCatCoevaluation_apply_one, AddMonoidAlgebra.finiteType_of_fg, LinearMap.toMatrixOrthonormal_symm_apply, Subrepresentation.submoduleSubrepresentationOrderIso_apply, segment_eq_Icc, MeasureTheory.nullMeasurableSet_smul_measure_iff, Subspace.dualRestrict_leftInverse, QuadraticForm.tmul_tensorAssoc_apply, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt, MvPolynomial.aeval_eq_zero, Polynomial.coeff_det_X_add_C_card, MvPolynomial.eval₂_cast_comp, StrongDual.dualPairing_apply, MeasureTheory.OuterMeasure.restrict_empty, PreSubmersivePresentation.naive_toPresentation, trace_eq_trace_adjoin, Ideal.Filtration.Stable.exists_pow_smul_eq_of_ge, Polynomial.quotientSpanXSubCAlgEquiv_mk, FormallyEtale.instTensorProduct, LinearMap.toMatrix_innerₛₗ_apply, MonoidAlgebra.mapDomainBialgHom_apply, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, KaehlerDifferential.map_surjective_of_surjective, PointwiseConvergenceCLM.equivWeakDual_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, adjoin_range_eq_range_freeAlgebra_lift, PadicAlgCl.instUniformContinuousConstSMulPadic, DoubleQuot.ker_quotQuotMk, NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm, QuadraticAlgebra.smul_C, Unitization.starMap_inr, Complex.hasFDerivAt_cpow, Polynomial.aeval_X_left_eq_map, Extension.Hom.toRingHom_algebraMap, IntermediateField.adjoin_root_eq_top, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, MvPolynomial.bind₁_C_right, BialgCat.tensorHom_def, MeasureTheory.Measure.toSignedMeasure_smul, Matrix.nondegenerate_toBilin_iff, Localization.AtPrime.mapPiEvalRingHom_comp_algebraMap, HasStrictDerivAt.fun_finset_prod, AdicCompletion.mk_ofAlgEquiv_symm, LSeriesHasSum.smul, Ideal.exact_mulQuot_quotOfMul, Complex.algHom_ext_iff, Ideal.span_singleton_nonZeroDivisors, Polynomial.mkDerivationEquiv_symm_apply, AdicCompletion.mk_smul_mk, Ideal.Cotangent.smul_eq_zero_of_mem, LieModule.Weight.coe_toLinear_eq_zero_iff, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, Matrix.toLin'_reindex, Quaternion.algebraMap_injective, LocalizedModule.subsingleton_iff_ker_eq_top, PowerSeries.smul_weierstrassMod, MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable, InfiniteGalois.proj_adjoin_singleton_val, LinearMap.BilinForm.toDual_def, CliffordAlgebra.contractRight_mul_algebraMap, MeasureTheory.OuterMeasure.map_ofFunction, Polynomial.expand_expand, IntermediateField.lift_inf, QuasiFinite.finite_fiber, Matrix.PosSemidef.toLinearMap₂'_zero_iff, Polynomial.Bivariate.swap_Y, LinearMap.BilinForm.toMatrix'_compLeft, IsLocalizedModule.fromLocalizedModule_mk, MeasureTheory.OuterMeasure.map_comap_of_surjective, MultilinearMap.freeDFinsuppEquiv_single, MvPolynomial.instIsLocalHomRingHomAlgebraMap, Polynomial.rootSet_derivative_subset_convexHull_rootSet, unramifiedLocus_eq_compl_support, VonNeumannAlgebra.mem_carrier, WittVector.bind₁_wittMulN_wittPolynomial, WeakDual.isSeqCompact_closedBall, PolynomialLaw.exists_range_φ_eq_of_fg, DoubleQuot.coe_quotQuotEquivQuotSupₐ, HasFDerivAt.ccos, AnalyticWithinAt.aeval_polynomial, Ideal.quotientMulEquivQuotientProd_snd, Unitization.algebraMap_eq_inl, Real.convexOn_log_Gamma, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, WeakDual.exists_countable_separating, Subspace.flip_quotDualCoannihilatorToDual_bijective, Subspace.dual_finrank_eq, Derivation.commutator_coe_linear_map, instFiniteH1CotangentOfFinitePresentationOfProjectiveKaehlerDifferential, HasFDerivWithinAt.log, Complex.range_liftAux, Orientation.areaForm'_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, MeasureTheory.hausdorffMeasure_lineMap_image, Ideal.dvd_bot, HasFDerivAt.clog, innerSLFlip_apply_apply, MvPolynomial.expand_one_apply, PadicAlgCl.spectralNorm_eq, IntermediateField.exists_algHom_of_splits, Polynomial.hasFDerivAt, Complex.liftAux_apply_I, intervalIntegral.integral_smul_measure, strictConvex_iff_convex, TensorProduct.isPushout, IntermediateField.extendScalars_self, signedDist_smul_of_pos, MvPolynomial.map_expand_pow_char, Module.rankAtStalk_eq_finrank_tensorProduct, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Module.End.isSemisimple_sub_algebraMap_iff, PowerBasis.equivAdjoinSimple_gen, MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, RatFunc.ofFractionRing_comp_algebraMap, Polynomial.aeval_apply_smul_mem_of_le_comap, Matrix.Nondegenerate.toBilin, WeakDual.CharacterSpace.toAlgHom_apply, LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero, Ideal.ResidueField.map_algebraMap, algebraMap_mk, ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule, infEdist_smul₀, Field.Emb.Cardinal.equivSucc_coherence, IsSepClosed.isCyclotomicExtension, LinearMap.toMatrix'_apply, LinearMap.mem_span_iff_continuous_of_finite, IsContinuousRiemannianBundle.exists_continuous, MvPolynomial.monomial_mem_pow_idealOfVars_iff, RatFunc.algebraMap_X, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_apply, QuadraticForm.tmul_tensorComm_apply, Matrix.toLpLin_toLp, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom_assoc, instDifferentialAlgebra, apply_eq_dotProduct_toMatrix₂_mulVec, Ideal.fst_comp_quotientMulEquivQuotientProd, Ideal.ResidueField.exists_smul_eq_tmul_one, AdjoinRoot.isAlgebraic_root, IsLocalization.at_units, MonomialOrder.degree_smul_le, minpoly.ker_aeval_eq_span_minpoly, LinearMap.BilinForm.separatingRight_toMatrix_iff, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, MultilinearMap.freeDFinsuppEquiv_def, map_equiv_traceDual, IntermediateField.restrictScalars_adjoin_eq_sup, Polynomial.Chebyshev.aeval_S, AnalyticOnNhd.aeval_mvPolynomial, LinearMap.BilinForm.SeparatingLeft.toMatrix', Polynomial.algebraMap_pi_self_eq_eval, NumberField.Units.mem_torsion, Polynomial.mem_annIdeal_iff_aeval_eq_zero, Subalgebra.LinearDisjoint.trace_algebraMap, FiniteGaloisIntermediateField.isGalois, MvPowerSeries.coeff_expand_smul, Polynomial.valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X, MeasureTheory.MemLp.smul_measure, PiTensorProduct.dualDistribInvOfBasis_apply, AlgebraicIndependent.isAlgebraic_adjoin_iff_of_matroid_isBasis, Matrix.isRepresentation.toEnd_exists_mem_ideal, instIsNoetherianRingSubtypePolynomialMemSubalgebraReesAlgebra, Representation.asAlgebraHom_single_one, Generators.Hom.toAlgHom_X, MvPolynomial.bind₁_rename, MeasureTheory.FiniteMeasure.instContinuousSMulNNReal, MvPolynomial.smulCommClass_right, Polynomial.C_eq_algebraMap, NonUnitalStarSubalgebra.unitization_injective, QuadraticForm.tensorLId_toLinearEquiv, Polynomial.mapAlg_eq_map, signedDist_lineMap_lineMap, NonUnitalStarSubalgebra.unitization_apply, IsAdic.hasBasis_nhds_zero, wittStructureRat_prop, IsPrimitiveRoot.minpoly_dvd_expand, InnerProductSpace.continuousLinearMapOfBilin_zero, Polynomial.eval_unique, MvPolynomial.degrees_rename, Localization.AtPrime.comap_maximalIdeal, Presentation.comp_relation, TensorProduct.AlgebraTensorModule.dualDistrib_apply, IntermediateField.Lifts.lt_iff, ContinuousLinearMap.toLinearMap_innerSL_apply, Polynomial.Bivariate.equivMvPolynomial_symm_C, UniformConvexOn.convexOn, LieSubalgebra.coe_incl', HahnSeries.C_eq_algebraMap, MvPowerSeries.aeval_coe, IntermediateField.extendScalars_le_iff, TensorProduct.toLinearEquiv_tensorTensorTensorComm, Polynomial.aeval_eq_smeval, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, MonoidAlgebra.mapRangeRingHom_comp_algebraMap, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, FractionRing.instIsFractionRing, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, Representation.isSimpleModule_iff_irreducible_ofModule, QuadraticForm.tmul_tensorRId_apply, MeasureTheory.Measure.ae_eq_or_eq_iff_eq_dirac_add_dirac, tendsto_integral_mul_one_add_inv_smul_sq_pow, WittVector.IsPoly.poly, Matrix.inv_adjugate, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, SymmetricAlgebra.algebraMap_eq_zero_iff, HasGradientAt.hasFDerivAt, Submodule.lTensorOne'_tmul, AddMonoidAlgebra.finiteType_iff_group_fg, IsCentral.self, Representation.instIsScalarTowerMonoidAlgebraAsModule, Module.FinitePresentation.linearEquivMap_apply, MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul, MeasureTheory.Measure.conv_smul_left, KaehlerDifferential.finite, MvPolynomial.finite_universalFactorizationMap, Real.fourier_fderiv, AdjoinRoot.isScalarTower_right, MvPolynomial.rTensorAlgHom_toLinearMap, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isOpen, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra', ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul', range_cfcₙ_eq_range_cfcₙHom, Matrix.det_one_add_X_smul, adjoin_mem_exists_aeval, QuaternionAlgebra.Basis.liftHom_apply, wittStructureRat_rec, ContinuousMap.adjoin_id_eq_span_one_union, signedDist_vadd_left_swap, coe_polyEquivTensor'_symm, ContinuousMap.AlgHom.closure_ker_inter, trace_self, Seminorm.const_isBounded, AffineBasis.det_smul_coords_eq_cramer_coords, Splits.algebraicClosure, PowerBasis.equivAdjoinSimple_symm_gen, LieModule.exists_forall_pow_toEnd_eq_zero, SeparableClosure.hasEnoughRootsOfUnity, reesAlgebra.monomial_mem, Unitization.starMap_surjective, Rep.finsuppTensorRight_hom_hom, Extension.CotangentSpace.map_cotangentComplex, MeasureTheory.Measure.isOpenPosMeasure_smul, HasFDerivWithinAt.norm_sq, Ideal.Filtration.inf_submodule, IntermediateField.coe_val, MvPolynomial.expand_eq_C, Polynomial.roots_expand_image_frobenius_subset, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, LinearMap.IsNonneg.smul, Submodule.rTensorOne'_tmul, Ideal.relNorm_algebraMap', Polynomial.SplittingField.splits, JacobsonNoether.exist_pow_eq_zero_of_le, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub, LinearMap.toMatrix'_symm, Module.End.IsSemisimple.aeval, RatFunc.smul_eq_C_smul, MvPowerSeries.trunc'_expand, MvPolynomial.universalFactorizationMapPresentation_map, WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_left, MeasureTheory.setAverage_eq', StrongDual.dualPairing_separatingLeft, ProperCone.dual_singleton, Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, MvPolynomial.coeff_rename_mapDomain, AdicCompletion.of_bijective_iff, norm_complex_eq, Matrix.reindexLieEquiv_apply, Real.doublingGamma_log_convex_Ioi, InnerProductGeometry.norm_ofLp_crossProduct, AdicCompletion.transitionMap_comp_reduceModIdeal, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', QuaternionAlgebra.Basis.k_self, MvPolynomial.algebraTensorAlgEquiv_symm_X, QuadraticAlgebra.norm_coe, Matrix.IsHermitian.cfcAux_apply, RatFunc.valuation_eq_LaurentSeries_valuation, MvPolynomial.expand_injective, ProbabilityTheory.Kernel.comp_discard', Bundle.RiemannianMetric.symm, MvPolynomial.support_coeff_finSuccEquiv, minpoly.aeval, Presentation.aeval_val_relation, AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule, strongConcaveOn_iff_convex, LieAlgebra.SpecialLinear.sl_bracket, NumberField.Units.coe_neg_one, MvPolynomial.expand_one, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, Unitization.norm_eq_sup, Submodule.dualCopairing_apply, IsStandardSmooth.baseChange, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, Polynomial.mkDerivationEquiv_apply, Derivation.liftKaehlerDifferential_comp_D, coe_polyEquivTensor', Unramified.baseChange, MvPolynomial.esymmAlgHom_fin_surjective, MvPolynomial.expand_inj, Polynomial.IsSplittingField.instIsTorsionFreeSplittingField, AlgebraicClosure.instIsAlgClosure, MonoidAlgebra.finiteType_iff_fg, PrimeSpectrum.residueField_comap, PowerSeries.instNontrivialSubalgebra, Ideal.mk_mem_cotangentIdeal, RootPairing.toPerfPair_flip_comp_coroot, RatFunc.map_apply_div, PadicInt.coe_adicCompletionIntegersEquiv_apply, Ideal.relNorm_int, IntermediateField.finrank_eq_finrank_subalgebra, HasFDerivAt.ccosh, MvPowerSeries.comp_subst_apply, MeasureTheory.Measure.instSMulCommClassDomMulActNNReal, fderiv_cos, LieSubmodule.toEnd_restrict_eq_toEnd, Matrix.reindexLieEquiv_symm, concaveOn_univ_of_deriv2_nonpos, ContinuousMap.sup_mem_subalgebra_closure, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', toMatrix_dualTensorHom, Ideal.absNorm_dvd_absNorm_of_le, TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_eq, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Complex.conjAe_coe, IntermediateField.restrictRestrictAlgEquivMapHom_injective, Generators.H1Cotangent.δAux_ofComp, IsAdicComplete.of_comp_lift, RootPairing.reflectionPerm_root, QuaternionAlgebra.lift_symm_apply, Matrix.range_toLin', Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, ContinuousMapZero.nonUnitalStarAlgHom_precomp_apply, LieModule.IsFaithful.injective_toEnd, RootPairing.GeckConstruction.span_range_h_le_range_diagonal, Ideal.isOpen_pow_of_isMaximal, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, MeasureTheory.OuterMeasure.map_iSup, QuaternionAlgebra.re_swapEquiv_symm_apply, Quaternion.fst_imJ_dualNumberEquiv_symm, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure, PiTensorProduct.singleAlgHom_apply, Height.mulHeight_smul_eq_mulHeight, AlgCat.hom_inv_leftUnitor, MeasureTheory.Integrable.to_average, LinearMap.mul_toMatrix', signedDist_vadd_right, HasStrictFDerivAt.arctan, NumberField.Ideal.tendsto_norm_le_div_atTop₀, NumberField.isFinitePlace_iff, Presentation.instHasCoeffsSubtypeMemSubalgebraAdjoin, Transcendental.algebraicClosure, ENNReal.nnreal_smul_lt_top_iff, Polynomial.int_eval₂_eq, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, Presentation.differentials.comm₂₃', hasSum_sq_fourierCoeffOn, inr_comp_cfcₙHom_eq_cfcₙAux, AdjoinRoot.liftAlgHom_eq_algHom, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, Ideal.Quotient.alg_map_eq, convexOn_descPochhammer_eval, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, IsAdjoinRoot.algEquiv_def, TensorPower.multilinearMapToDual_apply_tprod, Polynomial.Monic.finite_adjoinRoot, MvPolynomial.supported_strictMono, Ideal.Filtration.Stable.exists_pow_smul_eq, MeasureTheory.tilted_const', Polynomial.Bivariate.swap_X, MvPolynomial.pointToPoint_zeroLocus_le, RatFunc.liftRingHom_apply_div', Matrix.toLpLin_symm_id, AdicCompletion.smul_mk, MonoidAlgebra.exists_finset_adjoin_eq_top, Real.concaveOn_negMulLog, IntermediateField.finrank_adjoin_eq_one_iff, Ring.instIsSeparableFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, FreeLieAlgebra.universalEnvelopingEquivFreeAlgebra_apply, exists_integral_inj_algHom_of_quotient, MeasureTheory.OuterMeasure.restrict_iSup, Extension.Cotangent.val_smul', IntermediateField.normal_iff_forall_map_le', Matrix.isPositive_toEuclideanLin_iff, padic_polynomial_dist, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, FractionalIdeal.coeIdeal_mul, MeasureTheory.OuterMeasure.instIsCentralScalar, TensorAlgebra.ofDirectSum_toDirectSum, IntermediateField.normal_iff_forall_fieldRange_eq, Polynomial.aeval_conj, StarAlgHom.ofId_apply, Ideal.le_mul_of_no_prime_factors, ProbabilityTheory.hasFPowerSeriesAt_mgf, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_essFiniteType, FreeAlgebra.toTensor_ι, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, MeasureTheory.smul_le_stoppedValue_hitting, instIsAbelianGaloisSubtypeMemIntermediateField_1, NumberField.integralBasis_repr_apply, exists_finite_inj_algHom_of_fg, LocalizedModule.smul'_mk, ContinuousMap.inf_mem_subalgebra_closure, exteriorPower.pairingDual_ιMulti_ιMulti, Polynomial.algEquivAevalNegX_symm_apply, LinearMap.mul_toMatrix₂, ProbabilityTheory.covarianceBilin_self_nonneg, mem_skewAdjointMatricesLieSubalgebra, Extension.Cotangent.map_comp, BialgHomClass.counitAlgHom_comp, MeasureTheory.Measure.isMulInvariant_eq_smul_of_compactSpace, Submodule.mulRightMap_eq_mulMap_comp, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, IsScalarTower.subalgebra, Localization.algEquiv_symm_mk', MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, TensorProduct.AlgebraTensorModule.rid_eq_rid, IsAdjoinRoot.adjoinRootAlgEquiv_apply_eq_map, MvPolynomial.aeval_def, Matrix.lieConj_symm_apply, MeasureTheory.measure_eq_div_smul, EuclideanQuadrant.convex, QuadraticMap.discr_comp, ContinuousMap.inf_mem_closed_subalgebra, RatFunc.liftRingHom_ofFractionRing_algebraMap, IntermediateField.finrank_bot, Int.absNorm_under_mem, AdicCompletion.map_mk, Polynomial.hermite_eq_deriv_gaussian', MultilinearMap.freeFinsuppEquiv_def, localizedModuleIsLocalizedModule, TensorProduct.AlgebraTensorModule.map_eq, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, fderiv_exp, DoubleCentralizer.algebraMap_snd, WeakDual.polar_def, Polynomial.aeval_smul, Generators.cotangentCompAwaySec_apply, LieModule.trace_comp_toEnd_genWeightSpace_eq, WittVector.ker_map_le_ker_mk_comp_ghostComponent, Bialgebra.TensorProduct.rid_toAlgEquiv, fderiv_arctan, ProbabilityTheory.covarianceBilinDual_self_eq_variance, RatFunc.laurentAux_algebraMap, QuadraticForm.tensorComm_toLinearEquiv, CliffordAlgebra.contractLeft_comm, AddMonoidAlgebra.lift_single, InfiniteGalois.restrict_fixedField, AdjoinRoot.modByMonicHom_mk, Orientation.areaForm_comp_linearIsometryEquiv, hasStrictFDerivAt_norm_sq, Ideal.Filtration.submodule_span_single, QuadraticAlgebra.coe_norm_eq_mul_star, IsLocalization.Away.quotient_of_isIdempotentElem, Matrix.dualNumberEquiv_symm_apply, LinearMap.toMatrix'_mul, TensorProduct.productMap_eq_comp_map, RatFunc.algebraMap_eq_C, AdjoinRoot.isAdjoinRootMonic_toAdjoinRoot, trace_self_apply, LinearMap.adjoint_toSpanSingleton, CliffordAlgebra.ofBaseChange_tmul_ι, Generators.toAlgHom_ofComp_rename, DualNumber.exp_eps, wittStructureRat_rec_aux, Polynomial.Bivariate.equivMvPolynomial_symm_X_1, IntermediateField.sepDegree_bot, EssFiniteType.isLocalization, WittVector.fontaineThetaModPPow_teichmuller, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, KaehlerDifferential.tensorKaehlerEquiv_left_inv, Module.dualProdDualEquivDual_apply_apply, factorPowSucc.isUnit_of_isUnit_image, QuadraticModuleCat.toIsometry_hom_leftUnitor, Matrix.matPolyEquiv_charmatrix, TensorProduct.rid_tmul, MvPolynomial.supported_mono, normalizedTrace_self, PowerBasis.mem_span_pow, Submodule.rTensorOne_tmul, Polynomial.aeval_def, RatFunc.algebraMap_apply_div, RatFunc.div_smul, MonomialOrder.sPolynomial_decomposition, CommRing.Pic.mapAlgebra_self_apply, Polynomial.aeval_mul, MvPolynomial.totalDegree_expand, RootPairing.GeckConstruction.instIsIrreducible, killingForm_apply_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, MvPolynomial.algHom_C, LinearMap.toMatrix_algebraMap, QuadraticModuleCat.toIsometry_hom_rightUnitor, LinearMap.spectrum_toMatrix, AdicCompletion.ofAlgEquiv_apply, Ideal.hasBasis_nhds_zero_adic, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, AddMonoidAlgebra.lift_symm_apply, LinearMap.BilinForm.congr_refl, StandardEtalePresentation.toSubmersivePresentation_jacobian, LieSubalgebra.mem_engel_iff, IsAlgClosed.exists_aeval_eq_zero_of_injective, norm_eq_norm_adjoin, wittStructureInt_prop, pushoutDesc_apply, Polynomial.expand_eq_zero, IsSelfAdjoint.sq_spectrumRestricts, QuadraticAlgebra.algebraMap_eq, Ideal.isCancelMulZero, TensorProduct.cancelBaseChange_tmul, NumberField.FinitePlace.coe_apply, Polynomial.differentiableAt_aeval, Subspace.quotAnnihilatorEquiv_apply, Unitization.mem_spectrum_inr_of_not_isUnit, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, MeasureTheory.Measure.smul_absolutelyContinuous, PowerSeries.derivative_invOf, PadicAlgCl.isAlgebraic, WeakDual.CharacterSpace.compContinuousMap_apply, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, Ideal.spanNorm_eq, Matrix.diagonal_toLin', Matrix.adjugate_smul, IntermediateField.restrictScalars_bot_eq_self, FractionalIdeal.absNorm_eq, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, QuadraticForm.tensorLId_symm_apply, Matrix.charpoly_toLin', Quaternion.fst_imI_dualNumberEquiv_symm, LinearMap.BilinForm.toMatrix_symm, fderivWithin.log, AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply, Polynomial.taylorAlgHom_apply, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, MeasureTheory.JordanDecomposition.smul_posPart, AlgebraicClosure.Monics.splits_finsetProd, AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_app, AlgCat.free_obj, HasFDerivWithinAt.sinh, Real.convexOn_Gamma, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, edist_smul₀, Polynomial.hasFDerivAt_aeval, continuous_cfcHomSuperset_left, ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smul, IsAdjoinRoot.lift_map, WeierstrassCurve.Projective.dblXYZ_of_Z_eq_zero, AlgCat.hom_hom_leftUnitor, Ideal.relNorm_algebraMap, Extension.H1Cotangent.equivOfFormallySmooth_apply, Ideal.spanNorm_mul, Matrix.toLin'_pow, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, Polynomial.algEquivOfCompEqX_symm_apply, IsSymmetricAlgebra.equiv_symm_apply, LinearIsometryEquiv.toLinearEquiv_smul, MvPowerSeries.instNontrivialSubalgebraOfNonempty, rank_dual_eq_card_dual_of_aleph0_le_rank, Unitization.lift_range, CommAlgCat.tensorHom_hom, LinearMap.BilinForm.SeparatingLeft.toMatrix, Polynomial.aeval_eq_prod_aroots_sub_of_monic_of_splits, instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient, Derivation.liftKaehlerDifferential_unique_iff, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, MvPolynomial.derivation_C, ProbabilityTheory.covarianceBilinDual_self_nonneg, MvPolynomial.mem_support_coeff_optionEquivLeft, HasFDerivAt.log, Polynomial.Bivariate.swap_C_C, QuadraticMap.basisRepr_eq_of_iIsOrtho, RatFunc.liftRingHom_apply_div, Derivation.liftKaehlerDifferential_D, Matrix.toLinAlgEquiv'_apply, Matrix.l2_opNNNorm_def, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, cfcₙHom_isClosedEmbedding, MeasureTheory.Measure.smul_finite, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure, MvPolynomial.dvd_smul_X_iff_exists, LinearMap.apply_toPerfPair_flip, MvPolynomial.mem_supported_vars, AlgebraicIndependent.option_iff_transcendental, apply_eq_star_dotProduct_toMatrix₂_mulVec, tensorKaehlerQuotKerSqEquiv_tmul_D, MvPolynomial.mkDerivation_monomial, LinearMap.aeval_eq_aeval_mod_charpoly, Complex.coe_basisOneI_repr, Localization.algEquiv_symm_mk, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, LinearMap.polar_gc, LieSubmodule.lie_baseChange, LinearMap.toMatrix₂_compl₁₂, LinearMap.hasEigenvalue_zero_tfae, Matrix.minpoly_toLin', Generators.Hom.toExtensionHom_toRingHom, QuadraticForm.tensorDistrib_tmul, signedDist_lineMap_left, Generators.comp_localizationAway_ker, Matrix.nonsing_inv_apply, Polynomial.algEquivAevalXAddC_symm_apply, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left, MvPolynomial.rename_monomial, RootPairing.iInf_ker_root'_eq, lift_rank_lt_rank_dual, MvPolynomial.aeval_toMvPolynomial, MeasureTheory.FiniteMeasure.smul_testAgainstNN_apply, ProbabilityTheory.covarianceBilin_real_self, WittVector.exists_frobenius_solution_fractionRing, NumberField.mixedEmbedding.norm_smul, WittVector.ghostComponentModPPow_teichmuller_coeff, PositiveLinearMap.gnsStarAlgHom_apply, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, LieModule.toEnd_eq_iff, BilinForm.toMatrix_compRight, LinearMap.BilinForm.nondegenerate_toMatrix'_iff, Polynomial.wronskianBilin_apply, AdjoinRoot.coe_mkₐ, smulTower_leftMulMatrix, MvPolynomial.restrictScalars_restrictSupportIdeal, IntermediateField.finrank_sup_le, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePos, TensorAlgebra.algebraMap_eq_one_iff, AlgCat.hom_whiskerLeft, Ideal.iSup_iInf_eq_top_iff_pairwise, Differential.instDifferentialAlgebraSubtypeMemIntermediateField_1, Complex.lintegral_comp_polarCoord_symm, Ideal.isCoprime_tfae, WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right, MvPowerSeries.expand_subst, Ideal.relNorm_eq_bot_iff, LinearMap.toMatrix'_intrinsicStar, LinearMap.BilinForm.congr_congr, RatFunc.algebraMap_C, MvPolynomial.universalFactorizationMapPresentation_relation, IntermediateField.adjoinRootEquivAdjoin_apply_root, LinearMap.isPosSemidef_zero, AnalyticAt.aeval_polynomial, Extension.Cotangent.map_id, IntermediateField.normalClosureOperator_apply, MvPolynomial.aevalTower_comp_algebraMap, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, QuadraticForm.tensorComm_apply, AffineSubspace.isometryEquivMap.coe_apply, MeasureTheory.eLpNorm_le_of_ae_enorm_bound, QuadraticAlgebra.lift_symm_apply_coe, MeasureTheory.Measure.nnreal_smul_coe_apply, Polynomial.Monic.mem_rootSet, PreSubmersivePresentation.aevalDifferential_single, cross_apply, AlgebraicIndependent.algebraMap_aevalEquiv, spectrum.map_polynomial_aeval_of_nonempty, cfcₙHom_le_iff, LinearEquiv.lieConj_apply, IsBaseChange.toDual_comp_apply, VectorFourier.fourierSMulRight_apply, LieModule.isNilpotent_toEnd_of_mem_rootSpace, AdjoinRoot.Minpoly.coe_toAdjoin_mk_X, MvPolynomial.aeval_id_rename, AlternatingMap.eq_smul_basis_det, LinearMap.BilinForm.toMatrixAux_apply, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, MeasureTheory.OuterMeasure.comap_mono, StrongConcaveOn.strictConcaveOn, WeierstrassCurve.Projective.smul_fin3, RatFunc.instIsScalarTowerPolynomial, MeasureTheory.Measure.ae_ennreal_smul_measure_iff, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, Real.closedBall_eq_segment, IsPrimitiveRoot.not_coprime_norm_of_mk_eq_one, Seminorm.closedBall_smul, IntermediateField.rank_bot, NumberField.FinitePlace.norm_def_int, AdicCompletion.of_surjective, Polynomial.expand_zero, PiTensorProduct.dualDistrib_apply, TrivSqZeroExt.exp_def, CliffordAlgebraQuaternion.ofQuaternion_mk, derivWithin_comp_mul_left, Generators.Cotangent.exact, HasFDerivAt.exp, Polynomial.roots_expand_pow_map_iterateFrobenius_le, LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv', instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Matrix.adjugate_adjugate', Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, adjoin_range_eq_range_aeval, HahnSeries.binomial_power, le_restrictScalars_separableClosure, signedDist_anticomm, MeasureTheory.Measure.addHaarScalarFactor_smul_smul, PowerBasis.equivOfMinpoly_aeval, MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg, LieDerivation.toLinearMapLieHom_injective, Ideal.card_norm_le_eq_card_norm_le_add_one, WeierstrassCurve.Projective.neg_of_Z_ne_zero, PointedContMDiffMap.instIsScalarTowerSomeENatTop, RootPairing.GeckConstruction.ωConjLieSubmodule_eq_top_iff, Generators.aeval_val_σ, QuadraticForm.tmul_comp_tensorMap, Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx, isAdjointPair_toLinearMap₂', Orientation.areaForm_comp_rightAngleRotation, Module.Dual.baseChange_apply_tmul, Matrix.toLin'_apply', Polynomial.aevalTower_id, MeasureTheory.IsFiniteMeasure.average, IntermediateField.instIsScalarTowerSubtypeMem_1, AdjoinRoot.powerBasisAux'_repr_symm_apply, Polynomial.Bivariate.swap_monomial_monomial, instIsIntegrallyClosedInSubtypeMemSubalgebraIntegralClosure, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, TensorPower.toTensorAlgebra_gMul, MvPolynomial.mem_zeroLocus_iff, MeasureTheory.hausdorffMeasure_homothety_image, Matrix.ker_toLin'_eq_bot_iff, Polynomial.rootMultiplicity_expand, BialgCat.whiskerRight_def, Localization.mk_one_eq_algebraMap, Representation.ofModule_asModule_act, NonUnitalSubalgebra.unitization_apply, MeasureTheory.Measure.absolutelyContinuous_smul, IsAzumaya.coe_tensorEquivEnd, cardQuot_pow_of_prime, AdicCompletion.Ideal.mk_eq_mk, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LinearMap.eval_charpoly, Ideal.IsPrime.mul_le, TensorPower.toTensorAlgebra_gOne, LinearMap.BilinForm.toLin'Flip_apply, IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed, MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le, UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal, ofId_apply, cfc_eq_cfcL_mkD, MeasureTheory.count_withDensity, dvd_differentIdeal_iff, IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d, BilinForm.toMatrix_mul_basis_toMatrix, exteriorPower.pairingDual_apply_apply_eq_one, LinearMap.polar_weak_closed, Real.convex_iff_isPreconnected, AdjoinRoot.quotEquivQuotMap_apply_mk, WeakDual.isClosed_closedBall, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, InformationTheory.convexOn_klFun, HasDerivAt.arsinh, Unitization.lift_symm_apply, Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free, algebraMap_ofSubring, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, NumberField.RingOfIntegers.withValEquiv_apply, Polynomial.Bivariate.swap_map_C, QuadraticForm.dualProdIsometry_toFun, fderiv_ccos, LinearMap.BilinForm.mul_toMatrix', IntermediateField.finrank_bot_mul_relfinrank, LieModule.toEnd_lie, transcendental_iff_ker_eq_bot, QuadraticForm.tensorAssoc_symm_apply, MonoidAlgebra.tensorEquiv_tmul, MvPolynomial.aeval_eq_constantCoeff_of_vars, Presentation.tensorModelOfHasCoeffsEquiv_tmul, TensorProduct.Algebra.linearMap_comp_mul', SymmetricAlgebra.algHom_ext_iff, isPurelyInseparable_self, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, Smooth.baseChange, fdifferential_comp, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, AddMonoidAlgebra.lift_of, MeasureTheory.Measure.smul_measure_isMulInvariant_le_of_isCompact_closure, Module.End.isRoot_of_hasEigenvalue, ExteriorAlgebra.toTrivSqZeroExt_ι, DividedPowers.isSubDPIdeal_sup, Polynomial.expand_X, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, QuaternionAlgebra.coe_starAe, QuadraticForm.equivalent_sum_squares, QuaternionAlgebra.imI_swapEquiv_symm_apply, Submodule.torsionBy.mk_ideal_smul, SymmetricAlgebra.equivMvPolynomial_symm_X, Extension.H1Cotangent.equivOfFormallySmooth_symm, InnerProductSpace.rankOne_def', MeasureTheory.OuterMeasure.le_comap_map, LinearMap.toMatrixAlgEquiv_symm, MeasureTheory.pdf.IsUniform.pdf_eq, Polynomial.eval_C_X_eval₂_map_C_X, MvPolynomial.expand_bind₁, CliffordAlgebra.toBaseChange_ofBaseChange, leibniz_cross, Orientation.inner_rightAngleRotation_left, minpoly.isIntegrallyClosed_dvd_iff, SkewMonoidAlgebra.lift_unique', CliffordAlgebraComplex.equiv_symm_apply, Polynomial.expand_monomial, cfcHomSuperset_apply, MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isEverywherePos, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul, LinearMap.minpoly_toMatrix, MeasureTheory.IsFiniteMeasureOnCompacts.smul_nnreal, matrixEquivTensor_apply_single, IntermediateField.finiteDimensional_adjoin, RootPairing.coroot_root_two, MvPolynomial.smul_eval, QuadraticModuleCat.toIsometry_inv_rightUnitor, PiTensorProduct.piTensorHomMapFun₂_smul, MvPowerSeries.substAlgHom_coe, Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂, IntermediateField.lift_injective, PadicComplex.instIsScalarTowerPadicPadicAlgCl, TensorProduct.cancelBaseChange_symm_tmul, matPolyEquiv_map_C, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, Quaternion.im_exp, LinearMap.toMatrixOrthonormal_apply, PowerSeries.map_subst, MvPolynomial.coeff_rTensorAlgHom_tmul, fderivWithin_exp, Representation.asAlgebraHom_of, Ideal.prod_mem_prod, MvPolynomial.aeval_zero, cfcₙHom_eq_cfcₙ_extend, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, range_cfc_eq_range_cfcHom, MeasureTheory.Measure.exists_sum_smul_dirac, leftMulMatrix_complex, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_measurableSet, ProbabilityTheory.covarianceBilin_apply_pi, KaehlerDifferential.isBaseChange, MvPolynomial.killCompl_rename_app, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, NormedRing.algEquivComplexOfComplete_symm_apply, Ideal.Filtration.stable_iff_exists_pow_smul_eq_of_ge, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, FormallyEtale.Algebra.FormallyEtale.iff_of_surjective, RootPairing.iInf_ker_coroot'_eq, Polynomial.mul_scaleRoots, Subspace.finrank_add_finrank_dualCoannihilator_eq, Matrix.IsHermitian.spectrum_eq_image_range, MvPowerSeries.rescale_homogeneous_eq_smul, IsAdicComplete.ofAlgEquiv_comp_liftRingHom, IntermediateField.coe_extendScalars, MvPolynomial.comp_aeval, NumberField.RingOfIntegers.coe_injective, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, Module.dualProdDualEquivDual_apply, MvPolynomial.frobenius_zmod, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, StrongDual.toLpₗ_apply, PowerSeries.expand_C, WeierstrassCurve.Projective.add_of_Z_eq_zero_right, RootPairing.Hom.weight_coweight_transpose_apply, KaehlerDifferential.mvPolynomialBasis_repr_apply, LinearMap.prodMapAlgHom_apply_apply, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, Polynomial.Monic.finite_quotient, IntermediateField.AdjoinSimple.trace_gen_eq_zero, integralClosure.isFractionRing_of_algebraic, MvPolynomial.optionEquivLeft_coeff_some_coeff_none, MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero, FreeAlgebra.rank_eq, MatrixEquivTensor.invFun_smul, IntermediateField.mem_adjoin_range_iff, UniformConcaveOn.concaveOn, QuadraticForm.toDualProd_apply, RatFunc.liftAlgHom_apply_div, tendsto_iff_forall_eval_tendsto_topDualPairing, LinearMap.IsNonneg.nonneg, SymmetricAlgebra.lift_comp_ι, Orientation.inner_mul_areaForm_sub', Polynomial.roots_smul_nonzero, WittVector.coeff_frobeniusFun, instLiesOverResidueFieldBotIdeal, MeasureTheory.measureReal_ennreal_smul_apply, HasFDerivWithinAt.rpow_const, SymmetricAlgebra.lift_ι, MvPolynomial.renameEquiv_refl, adjoin_eq_exists_aeval, IsLocalRing.split_injective_iff_lTensor_residueField_injective, MvPolynomial.totalDegree_renameEquiv, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, QuaternionAlgebra.hom_ext_iff, toMatrix_lmul', LieAlgebra.ad_apply, MvPolynomial.expand_mul, FreeAlgebra.algebraMap_inj, idealFactorsEquivOfQuotEquiv_symm, LieAlgebra.toEnd_pow_apply_mem, LaurentPolynomial.C_eq_algebraMap, Presentation.tensorModelOfHasCoeffsHom_tmul, Generators.toComp_toAlgHom, Localization.monoidOf_eq_algebraMap, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, CommAlgCat.whiskerLeft_hom, Ideal.sup_mul_inf, MvPolynomial.isLocalHom_expand, Ioo_subset_openSegment, toWeakSpace_closedConvexHull_eq, Extension.contangentEquiv_tmul, Unitization.norm_def, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul, Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Ideal.quotOfMul_surjective, MvPolynomial.C_mul', Polynomial.mem_roots_iff_aeval_eq_zero, MvPolynomial.isEmptyAlgEquiv_apply, LieAlgebra.lieCharacter_apply_of_mem_derived, ClassGroup.mk_mk0, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, AlgebraicIndepOn.insert_iff, IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt, MeasureTheory.Measure.InnerRegularWRT.smul, PowerSeries.C_eq_algebraMap, IntermediateField.finSepDegree_adjoin_simple_le_finrank, Polynomial.map_restriction, Matrix.ker_diagonal_toLin', FreeAlgebra.ι_comp_lift, CliffordAlgebraComplex.toComplex_ι, Ideal.toCotangent_apply, Polynomial.IsSplittingField.splittingField, Polynomial.Bivariate.equivMvPolynomial_X, Polynomial.hasDerivWithinAt_aeval, RootPairing.GeckConstruction.cartanSubalgebra_le_lieAlgebra, Quaternion.coe_mul_eq_smul, Ideal.snd_comp_quotientMulEquivQuotientProd, Ideal.isDomain, Polynomial.isEisensteinAt_iff, MvPolynomial.pderiv_C_mul, HasFDerivAt.sinh, Module.Basis.symmetricAlgebra_repr_apply, MeasureTheory.Measure.comap_smul, NumberField.absNorm_differentIdeal, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_mem, MeasureTheory.condLExp_smul_le, reesAlgebra.fg, ContinuousAlgHom.ext_ring_iff, DoubleQuot.ker_quotLeftToQuotSup, IntermediateField.card_algHom_adjoin_integral, MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct, Polynomial.aeval_coe_eq_smeval, MonomialOrder.degree_smul_of_isRegular, WeierstrassCurve.Projective.negDblY_smul, exists_etale_isIdempotentElem_forall_liesOver_eq, matrixEquivTensor_apply_symm, Polynomial.IsMonicOfDegree.aeval_add, MonoidAlgebra.finiteType_iff_group_fg, uniformConcaveOn_zero, ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring, Complex.linearEquiv_det_conjAe, Orientation.abs_areaForm_le, AffineSubspace.subtypeₐᵢ_linear, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, Matrix.toBilin'_apply, NumberField.RingOfIntegers.isIntegral_coe, IntermediateField.relrank_dvd_rank_bot, Ideal.finite_mulSupport_coe, Polynomial.hasStrictDerivAt_aeval, LieAlgebra.conj_ad_apply, LinearMap.flip_injective_iff₂, LieSubmodule.tmul_mem_baseChange_of_mem, QuadraticForm.tensorRId_toLinearEquiv, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, PrimeSpectrum.zeroLocus_mul, MvPolynomial.natDegree_optionEquivLeft, RestrictScalars.lsmul_apply_apply, Polynomial.aeval_algebraMap_eq_zero_iff_of_injective, ContinuousMapZero.toContinuousMapHom_toNNReal, IsLocalRing.ResidueField.algebraMap_eq, StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_x, Ideal.absNorm_top, Matrix.toLin'_one, NumberField.Units.complexEmbedding_apply, Ideal.absNorm_apply, AdicCompletion.mk_surjective, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply, LSeriesSummable.smul_iff, Complex.instStarModuleReal, QuadraticAlgebra.smul_coe, Ideal.absNorm_pos_of_nonZeroDivisors, signedDist_neg, PiTensorProduct.algHom_ext_iff, ProbabilityTheory.covarianceBilin_apply_basisFun, RootPairing.reflection_dualMap_eq_coreflection, MvPowerSeries.expand_comp_substAlgHom, Generators.self_algebra_smul, Polynomial.natSepDegree_smul_nonzero, Extension.h1Cotangentι_ext_iff, MultilinearMap.freeFinsuppEquiv_apply, AddMonoidAlgebra.exists_finset_adjoin_eq_top, PowerSeries.subst_coe, Smooth.exists_subalgebra_finiteType, MatrixEquivTensor.left_inv, Ideal.toCotangent_eq_zero, IntermediateField.AdjoinPair.algebraMap_gen₁, NumberField.fractionalIdeal_rank, HasFDerivWithinAt.clog, hasGradientAt_iff_hasFDerivAt, RatFunc.denom_div, Ideal.Filtration.pow_smul_le_pow_smul, MvPolynomial.restrictSupport_nsmul, WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, Generators.toKaehler_tmul_D, MeasureTheory.IsFiniteMeasureOnCompacts.smul, MvPolynomial.mem_support_finSuccEquiv, Quaternion.imJ_snd_dualNumberEquiv, smulTower_leftMulMatrix_algebraMap_ne, minpoly.aeval_algHom, cfcₙHom_map_quasispectrum, CoalgCat.MonoidalCategoryAux.counit_tensorObj, MeasureTheory.count_withDensity', TrivSqZeroExt.liftEquivOfComm_apply, Polynomial.monic_expand_iff, LinearEquiv.algEquivOfRing_symm_apply, Module.End.finite_spectrum, eval_det, Polynomial.natSepDegree_expand, IsDedekindDomain.inf_prime_pow_eq_prod, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, MeasureTheory.Measure.map_right_mul_eq_modularCharacterFun_smul, MeasureTheory.Measure.mapₗ_apply_of_measurable, RootPairing.GeckConstruction.instIsTriangularizableSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra'Forall, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, CommAlgCat.whiskerRight_hom, instIsPushoutPolynomial, CliffordAlgebra.toBaseChange_comp_reverseOp, AdicCompletion.map_ext''_iff, cfcHom_nnreal_eq_restrict, Ideal.isCoprime_iff_exists, Matrix.IsHermitian.spectral_theorem, Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, algebraicIndependent_iff_injective_aeval, RootPairing.GeckConstruction.diagonal_elim_mem_span_h_iff, MvPolynomial.aeval_map_algebraMap, MeasureTheory.addEquivAddHaarChar_smul_map, Generators.Hom.toAlgHom_C, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, IntermediateField.LinearDisjoint.of_inf_eq_bot, RatFunc.intDegree_polynomial, PrimeSpectrum.zeroLocus_smul_of_isUnit, Extension.Cotangent.map_toInfinitesimal_bijective, Ideal.cotangentEquivIdeal_apply, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, Tactic.ComputeAsymptotics.Majorized.smul, RatFunc.v_def, MvPolynomial.rename_comp_toMvPolynomial, strictConvexOn_rpow, Etale.exists_subalgebra_fg, signedDist_vsub_self_rev, exists_maximalIdeal_pow_eq_of_principal, Extension.H1Cotangent.val_add, PolynomialModule.equivPolynomialSelf_apply_eq, RootPairing.GeckConstruction.ωConj_invFun, MvPolynomial.finSuccEquiv_comp_C_eq_C, NumberField.Units.coe_pow, HasFDerivAt.rpow_const, Subspace.dualLift_of_mem, coord_norm', FreeAlgebra.adjoin_range_ι, MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, Quaternion.snd_imK_dualNumberEquiv_symm, LaurentSeries.LaurentSeries_coe, TensorAlgebra.toDirectSum_comp_ofDirectSum, MvPolynomial.coeToMvPowerSeries.algHom_apply, WeakDual.isClosed_polar, MeasureTheory.OuterMeasure.le_smul_caratheodory, KaehlerDifferential.submodule_span_range_eq_ideal, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal', IsAdjoinRoot.adjoinRootAlgEquiv_apply_mk, spec_cfcₙAux, RootPairing.span_root'_eq_top, Ideal.minimalPrimes_map_of_surjective, AlgebraicIndependent.liftAlgHom_comp_reprField, UniformConcaveOn.strictConcaveOn, Generators.toExtendScalars_val, MvPolynomial.rename_rightInverse, Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply, TensorProduct.map_range, IntermediateField.finrank_top', LinearMap.BilinForm.nondegenerate_congr_iff, LinearMap.aeval_self_charpoly, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_top, Matrix.trace_toLin'_eq, Measurable.smul_measure, signedDist_linear_apply, Ideal.adic_basis, Real.isBoundedSMul, LaurentSeries.powerSeries_ext_subring, Extension.H1Cotangent.val_smul, LinearMap.BilinForm.flip_apply, Presentation.differentials.comm₁₂, cfcHom_eq_cfc_extend, HasStrictFDerivAt.const_rpow, IntermediateField.inclusion_self, NumberField.Units.abs_det_eq_abs_det, IntermediateField.lift_bot, RootPairing.ker_rootForm_eq_dualAnnihilator, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, MvPolynomial.finSuccEquiv_eq, SymmetricAlgebra.equivMvPolynomial_ι_apply, LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank, MeasureTheory.isMulLeftInvariant_smul_nnreal, AddMonoidAlgebra.lift_unique', Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsLocalizedModule.iso_symm_apply_aux, norm_complex_apply, IntermediateField.normalClosure_of_normal, StrongDual.norm_toLpₗ_le, LinearMap.polyCharpoly_eq_of_basis, Extension.Cotangent.mk_eq_mk_iff_sub_mem, LieAlgebra.rootSpace_comap_eq_genWeightSpace, isAlgebraic_iff_exists_isTranscendenceBasis_subset, TensorProduct.map_comp_includeRight, spectrum.subset_polynomial_aeval, PowerSeries.expand_mul, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, MvPolynomial.bind₁_comp_rename, Ideal.constr_basisSpanSingleton, IsAdjoinRootMonic.map_modByMonicHom, ClassGroup.mk_eq_mk, TrivSqZeroExt.sndHom_comp_map, MeasureTheory.Measure.map_toOuterMeasure, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, HasStrictFDerivAt.cos, Subalgebra.tmul_mem_baseChange, LinearMap.mem_polar_singleton, signedDist_self, LinearMap.IsSymm.eq, MeasureTheory.condLExp_bot_ae_eq, RootPairing.range_polarizationIn, InfiniteGalois.isOpen_iff_finite, Localization.isLocalization, Smooth.exists_finiteType, Unitization.nnreal_cfcₙ_eq_cfc_inr, CliffordAlgebra.contractLeft_ι, LinearMap.polyCharpolyAux_map_aeval, dvd_differentIdeal_of_not_isSeparable, ProperCone.dual_flip_dual, KaehlerDifferential.map_surjective, isSplittingField_AdjoinRoot_X_pow_sub_C, MvPolynomial.image_support_finSuccEquiv, KaehlerDifferential.map_compDer, MvPolynomial.pderiv_monomial_single, trace_eq_matrix_trace, signedDist_vsub_self, IsConjRoot.aeval_eq_zero, PowerSeries.IsWeierstrassDivisorAt.mod_smul, traceMatrix_of_basis, Polynomial.Bivariate.aevalAeval_swap, Field.Emb.Cardinal.deg_lt_aleph0, TrivSqZeroExt.map_comp_map, MvPolynomial.eval₂_rename, AlgebraicIndependent.aeval_repr, Bialgebra.counitBialgHom_toCoalgHom, MeasureTheory.SignedMeasure.rnDeriv_smul, MvPolynomial.support_expand, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, AdjoinRoot.liftHom_eq_algHom, MeasureTheory.instIsProbabilityMeasureHAddMeasureHSMulNNRealToNNRealSymm, AdicCompletion.of_ofLinearEquiv_symm, IsPushout.equiv_tmul, AdicCompletion.kerProj_of, SubmersivePresentation.free_kaehlerDifferential, MeasureTheory.hausdorffMeasure_smul_right_image, NumberField.inverse_basisMatrix_mulVec_eq_repr, LieDerivation.commutator_coe_linear_map, signedDist_smul, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LieModule.Cohomology.smul_apply_apply, RatFunc.denom_div_dvd, HasFDerivWithinAt.arsinh, Ideal.iInf_pow_eq_bot_of_isLocalRing, AddMonoidAlgebra.tensorEquiv_tmul, matPolyEquiv_symm_C, Matrix.spectrum_toLin, TensorAlgebra.ι_leftInverse, IntermediateField.relfinrank_bot_left, FiniteType.iff_quotient_freeAlgebra', NumberField.RingOfIntegers.instIsIntegralClosureInt, LaurentPolynomial.invert_symm, IsPushout.tensorProduct_tensorProduct, Submodule.quotDualCoannihilatorToDual_injective, Polynomial.Bivariate.equivMvPolynomial_C_X, PowerSeries.expand_mul_eq_comp, PolyEquivTensor.toFunBilinear_apply_apply, Unitization.starLift_apply, MeasureTheory.laverage_union_mem_segment, SpectrumRestricts.starAlgHom_apply, LinearMap.toMatrix'_comp, Matrix.toLinearEquiv'_apply, LinearMap.isUnit_toMatrix'_iff, BialgCat.tensorObj_def, MvPolynomial.IsSymmetric.rename, MvPolynomial.IsHomogeneous.aeval, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, RatFunc.laurent_C, CommAlgCat.associator_inv_hom, AnalyticAt.hasFPowerSeriesAt, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, Matrix.toBilin_toMatrix, IsBaseChange.toDual_apply, Int.absNorm_under_dvd_absNorm, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, Polynomial.Gal.splits_in_splittingField_of_comp, Module.AEval.mem_mapSubmodule_symm_apply, Real.map_linearMap_volume_pi_eq_smul_volume_pi, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, NumberField.Units.coe_injective, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, UniversalEnvelopingAlgebra.ι_apply, StrongDual.toLpₗ_of_not_memLp, LinearMap.BilinForm.comp_congr, Matrix.toBilin'_comp, Matrix.isHermitian_iff_isSymmetric, cfcₙHomSuperset_id, LieModule.toEnd_pow_lie, Polynomial.algHom_ext_iff, Polynomial.coeToPowerSeries.algHom_apply, Asymptotics.Filter.Tendsto.isBigOTVS_one, AdicCompletion.evalOneₐ_of, NumberField.Units.coe_one, MultilinearMap.freeFinsuppEquiv_single, Generators.H1Cotangent.exact_map_δ', WeakBilin.coeFn_continuous, IntermediateField.le_extendScalars_iff, FormallySmooth.iff_split_surjection, LaurentSeries.powerSeriesRingEquiv_coe_apply, LinearMap.lift_lsmul_mul_eq_lsmul_lift_lsmul, StrongDual.mem_polarSubmodule, IsAdjoinRoot.adjoinRootAlgEquiv_symm_apply_root, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, Unitization.starMap_comp, ClassGroup.equivPic_symm_apply, minpoly.ofSubring, IsAdicComplete.StrictMono.of_comp_lift, MvPowerSeries.expand_monomial, UnitAddTorus.hasSum_mFourier_series_of_summable, TensorAlgebra.GradedAlgebra.ι_apply, LieSubmodule.coe_toEnd, hasDerivWithinAt_comp_mul_left_smul_iff, adjoin_top, MvPolynomial.aeval_bind₂, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, MvPolynomial.rename_bind₁, Real.fourierIntegral_fderiv, LinearMap.IsReflective.dvd_two_mul, IntermediateField.extendScalars.orderIso_symm_apply_coe, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, CliffordAlgebra.contractRight_contractRight, QuadraticForm.tmul_tensorLId_apply, MeasureTheory.Measure.measure_isAddLeftInvariant_eq_vadd_of_ne_top, PowerSeries.derivative_coe, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, MvPolynomial.pderiv_X_of_ne, LieModule.toEnd_apply_apply, MvPolynomial.renameSymmetricSubalgebra_symm_apply_coe, LinearMap.IsPerfPair.bijective_right, Generators.Hom.toAlgHom_comp_apply, MvPolynomial.degree_finSuccEquiv, Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial, Polynomial.roots_expand_pow_map_iterateFrobenius, UnitAddTorus.mFourierSubalgebra_separatesPoints, QuadraticForm.tensorLId_apply, Monotone.convexOn_univ_of_deriv, MvPowerSeries.order_expand, LinearMap.mul_toMatrix₂_mul, MvPolynomial.nonempty_support_optionEquivLeft, aemeasurable_smul_measure_iff, MeasureTheory.OuterMeasure.isometryEquiv_map_mkMetric, Polynomial.map_expand_pow_char, MvPolynomial.pderiv_monomial, Complex.coe_algebraMap, FinitePresentation.self, TensorAlgebra.hom_ext_iff, Commute.cfcHom, WeierstrassCurve.Projective.add_smul_equiv, instIsTorsionFreeLocalizationAlgebraMapSubmonoidPrimeCompl, mem_skewAdjointMatricesLieSubalgebra_unit_smul, HasFDerivAt.sin, Orientation.abs_areaForm_of_orthogonal, exteriorPower.alternatingMapToDual_apply_ιMulti, IsNoetherianRing.isNilpotent_nilradical, LinearMap.BilinForm.tensorDistribEquiv_tmul, bind₁_rename_expand_wittPolynomial, innerₗ_apply_apply, adjoin_eq_range, IsLocalization.exists_smul_mem_of_mem_adjoin, Generators.toComp_toAlgHom_monomial, instEssFiniteTypeResidueField, MeasureTheory.isAddRightInvariant_smul, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, Polynomial.coeff_expand_mul, MvPowerSeries.map_iterateFrobenius_expand, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, HasFDerivAt.csin, LieModule.commute_toEnd_of_mem_center_right, ProbabilityTheory.mgf_smul_left, KaehlerDifferential.D_tensorProductTo, MvPolynomial.rename_injective, NumberField.mixedEmbedding.unitSMul_smul, IntermediateField.inclusion_injective, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, AdjoinRoot.isIntegral_root', Differential.instDifferentialAlgebraSubtypeMemIntermediateField, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, IsDedekindDomain.HeightOneSpectrum.intValuation_def, Ideal.IsPrime.pow_le_iff, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, Extension.toKaehler_surjective, hfdifferential_apply, Rep.finsuppTensorRight_inv_hom, IntermediateField.LinearDisjoint.bot_right, TensorAlgebra.range_lift, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, Ideal.ResidueField.algHom_ext_iff, SymmetricAlgebra.algebraMap_eq_one_iff, MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree, Module.dual_rank_eq, SubmersivePresentation.aeval_jacobianOfHasCoeffs, MeasureTheory.Measure.mul_addHaarScalarFactor_smul, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, MeasureTheory.Measure.map_addHaar_smul, Polynomial.isSplittingField_C, LinearMap.toMatrix'_id, TensorProduct.algEquivIncludeRange_toAlgHom, WStarAlgebra.exists_predual, AddMonoidAlgebra.tensorEquiv_symm_single, not_irreducible_expand, AlgebraicClosure.Monics.map_eq_prod, AddMonoidAlgebra.lift_of', LieModule.toEnd_baseChange, MvPolynomial.coe_smul, LocalizedModule.mul_by_divBy, nnnorm_cfcₙHom, ModularFormClass.hasSum_qExpansion_of_abs_lt, contractLeft_apply, adjoinRootXPowSubCEquiv_root, IntermediateField.normal_iff_forall_map_le, Projectivization.cross_mk, Polynomial.expand_mul, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, LinearMap.BilinForm.mul_toMatrix_mul, LinearMap.trace_transpose, MeasureTheory.Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, MvPolynomial.killCompl_map, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, Polynomial.aeval_continuousMap_apply, IsLocalization.Away.tensor, Localization.subalgebra.isFractionRing, Polynomial.mkDerivation_X, Polynomial.coe_aeval_mk_apply, PowerSeries.heval_X, NormedRing.algEquivComplexOfComplete_apply, FiniteType.iff_quotient_mvPolynomial, separableClosure.isAlgebraic, localization_unit_isIso, QuadraticForm.comp_tensorRId_eq, PowerSeries.comp_aeval, HopfAlgCat.tensorHom_def, TrivSqZeroExt.algebraMap_eq_inl, LinearMap.tripolar_eq_polar, LinearMap.BilinForm.toMatrix_mul_basis_toMatrix, ContinuousMap.subsingleton_subalgebra, LinearAlgebra.FreeProduct.rel_id, RootPairing.GeckConstruction.f_lie_v_ne, FreeAlgebra.lift_unique, Matrix.toLinAlgEquiv_apply, AdicCompletion.tensor_map_id_left_eq_map, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, LinearMap.nondegenerate_toMatrix₂'_iff, Orientation.inner_sq_add_areaForm_sq, cfc_apply, signedDist_smul_of_neg, MeasureTheory.inv_measure_univ_smul_eq_self, LinearMap.BilinForm.toMatrix'_comp, NNReal.instMeasurableSMul₂ENNReal, IsAdicComplete.mk_liftRingHom, instIsScalarTowerCyclotomicField, Generators.CotangentSpace.exact, Polynomial.coeff_zero_eq_aeval_zero, Generators.H1Cotangent.δAux_X, DoubleCentralizer.algebraMap_fst, Polynomial.derivation_ext_iff, MvPolynomial.aeval_eq_bind₁, WeierstrassCurve.Projective.add_smul_of_not_equiv, MvPolynomial.support_optionEquivLeft, Real.hasFPowerSeriesOnBall_linear_zero, Ideal.coprime_of_no_prime_ge, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, quasispectrumRestricts_iff_spectrumRestricts_inr, CliffordAlgebra.changeForm_contractLeft, Ideal.ResidueField.lift_algebraMap, MeasureTheory.Measure.isMulLeftInvariant_eq_smul, MvPolynomial.dvd_X_iff_exists, IntermediateField.rank_eq_one_iff, MvPolynomial.finSuccEquiv_X_succ, MonoidAlgebra.scalarTensorEquiv_symm_single, triple_product_eq_det, MvPolynomial.aeval_ofNat, AddMonoidAlgebra.mem_adjoin_support, IsGaloisGroup.intermediateField, essFiniteType_iff_exists_subalgebra, TensorAlgebra.algebraMap_inj, smulTower_leftMulMatrix_algebraMap, ProbabilityTheory.isPosSemidef_covarianceBilinDual, HasStrictDerivAt.arsinh, WeierstrassCurve.Affine.Point.toClass_some, LinearMap.IsNonneg.add, fderiv_norm_smul, LocalizedModule.map_exact, LSeries.term_smul_apply, Matrix.det_smul_adjugate_adjugate, TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, Presentation.aeval_val_relationOfHasCoeffs, HasFDerivAt.hasFDerivAt_norm_smul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, RootPairing.GeckConstruction.ωConj_toFun, cfc_polynomial, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, polynomial_expand_eq, Module.End.eigenspace_div, MvPolynomial.expand_comp_bind₁, CuspForm.instIsScalarTowerComplex, Ideal.span_singleton_mul_right_mono, SubmersivePresentation.aeval_invJacobianOfHasCoeffs, Extension.Hom.subToKer_apply_coe, AlgEquiv.restrictNormalHom_id, NNReal.segment_eq_Icc, LinearMap.BilinForm.toMatrix_mul, Field.insepDegree_self, CoalgCat.whiskerLeft_def, MvPolynomial.aeval_injective_iff_of_isEmpty, RootPairing.GeckConstruction.e_lie_v_ne, Polynomial.span_minpoly_eq_annihilator, Polynomial.toFinsuppIsoAlg_symm_apply_toFinsupp, Generators.ofComp_kerCompPreimage, MvPolynomial.X_mem_supported, Unitization.fstHom_apply, AlgHom.coe_toContinuousLinearMap, SubmersivePresentation.basisCotangent_localizationAway_apply, HasFDerivWithinAt.sqrt, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Ideal.finite_factors, MvPolynomial.esymmAlgHom_fin_injective, FormallyUnramified.base_change, PolyEquivTensor.invFun_monomial, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, LieAlgebra.SpecialLinear.val_single, Matrix.ofLp_toEuclideanLin_apply, Polynomial.coe_expand, Real.one_add_rpow_hasFPowerSeriesAt_zero, spectralNorm.eq_of_normalClosure', signedDist_vadd_right_swap, AdicCompletion.of_inj, Ideal.Factors.finrank_pow_ramificationIdx, MvPolynomial.aeval_comp_bind₁, NumberField.exists_ideal_in_class_of_norm_le, LieModule.isNilpotent_iff_forall, polynomialFunctions_coe, Polynomial.mkDerivation_one_eq_derivative, Ideal.quotientMulEquivQuotientProd_fst, MultilinearMap.freeDFinsuppEquiv_apply, MeasureTheory.OuterMeasure.restrict_biInf, QuaternionAlgebra.Basis.i_self, CliffordAlgebra.forall_mul_self_eq_iff, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, MeasureTheory.VAddInvariantMeasure.vadd_nnreal, TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf_app, RootPairing.coroot_root_eq_pairing, Polynomial.fourierCoeff_toAddCircle_natCast, LieModule.isNilpotent_toEnd_sub_algebraMap, mem_span_of_iInf_ker_le_ker, IsBaseChange.ofEquiv, AdicCompletion.ofTensorProduct_tmul, fderivWithin_sqrt, isClosedEmbedding_cfcₙHom_of_cfcHom, QuadraticAlgebra.algHom_ext_iff, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, spectrum.map_polynomial_aeval_of_degree_pos, ContinuousMap.spectrum_eq_range, LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero, innerSLFlip_apply, MvPolynomial.eval₂_const_pUnitAlgEquiv, WeakDual.ker_isMaximal, Generators.repr_CotangentSpaceMap, MonoidAlgebra.lift_apply, normalizedTrace_minpoly, Ideal.mem_iInf_smul_pow_eq_bot_iff, lieEquivMatrix'_symm_apply, InnerProductSpace.toContinuousLinearMap_toDualMap, separableClosure.isSepClosure, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, Polynomial.annIdealGenerator_aeval_eq_zero, LieSubalgebra.instIsNoetherianSubtypeMem, IsLocalization.instIsScalarTowerAtPrimeFractionRing, InfiniteGalois.toAlgEquivAux_eq_liftNormal, Matrix.proj_diagonal, MeasureTheory.Measure.IsHaarMeasure.smul, Module.Dual.baseChange_baseChange, separatingDual_iff_injective, minpoly.eq_X_sub_C', TensorProduct.dualDistribInvOfBasis_apply, MeasureTheory.Measure.InnerRegular.smul_nnreal, Ideal.Filtration.pow_smul_le, MonoidAlgebra.lift_mapRangeRingHom_algebraMap, isNilpotent_tensor_residueField_iff, MvPolynomial.pderiv_pow, Polynomial.toContinuousMapAlgHom_apply, IsSelfAdjoint.commute_cfcₙHom, Rat.ringOfIntegersEquiv_apply_coe, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, Polynomial.algebraMap_hahnSeries_apply, BialgHomClass.map_comp_comulAlgHom, Polynomial.sup_ker_aeval_le_ker_aeval_mul, Polynomial.fderivWithin_aeval, fderiv_sinh, strictConvex_iff_ordConnected, Ergodic.iff_mem_extremePoints, IntermediateField.normalClosure_def'', MeasureTheory.HasFiniteIntegral.smul_measure, QuasispectrumRestricts.nonUnitalStarAlgHom_apply, dualTensorHom_prodMap_zero, MvPolynomial.aeval_esymm_eq_multiset_esymm, Ideal.rank_pow_quot_aux, MvPolynomial.supported_le_supported_iff, NumberField.Ideal.tendsto_norm_le_div_atTop, extremePoints_doublyStochastic, Unitization.starMap_apply, CliffordAlgebraComplex.equiv_apply, Function.Periodic.cuspFunction_smul, LieAlgebra.Orthogonal.jd_transform, Polynomial.fderivWithin, LinearMap.IsContPerfPair.bijective_right, HasFDerivWithinAt.const_cpow, MeasureTheory.JordanDecomposition.smul_negPart, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, WeierstrassCurve.Projective.addU_smul, Subfield.relrank_eq_rank_of_le, Subspace.dualEquivDual_def, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', MvPolynomial.eval_rename, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, IntermediateField.relfinrank_eq_finrank_of_le, LocalizedModule.map_id, IsLocalization.tmul_mk', ProbabilityTheory.covarianceBilin_of_not_memLp, StandardEtalePresentation.toPresentation_σ', LinearMap.BilinForm.toMatrix_compLeft, FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal, BilinForm.toMatrix_apply, WeakDual.CharacterSpace.norm_le_norm_one, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, KaehlerDifferential.isLocalizedModule, SubmersivePresentation.cotangentComplexAux_surjective, CommRingCat.coproductCoconeIsColimit_desc, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, Matrix.linfty_opNorm_toMatrix, IntermediateField.minpoly_eq, cfcL_integral, witt_structure_prop, not_dvd_differentIdeal_iff, AdjoinRoot.powerBasis_dim, Matrix.toBilin'_apply', innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, MeasureTheory.isAddRightInvariant_smul_nnreal, Derivation.map_aeval, Matrix.det_updateCol_smul, Matrix.det_updateCol_sum, matPolyEquiv_eval_eq_map, RootPairing.GeckConstruction.h_mem_lieAlgebra, Extension.H1Cotangent.map_apply_coe, NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate, LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero', Polynomial.Splits.aeval_eq_prod_aroots_of_monic, TensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse, PolyEquivTensor.left_inv, IntermediateField.isSplittingField_iff, CliffordAlgebra.equivBaseChange_apply, LinearMap.toMvPolynomial_comp, MeasureTheory.Measure.mconv_smul_right, MeasureTheory.SMulInvariantMeasure.smul_nnreal, Complex.lift_symm_apply_coe, matPolyEquiv_coeff_apply, LocalizedModule.instIsScalarTower, LinearMap.BilinForm.mul_toMatrix, restrictScalars_adjoin, MvPowerSeries.coeff_expand_of_not_dvd, MeasureTheory.mulEquivHaarChar_smul_preimage, Module.Basis.tensorAlgebra_repr_apply, FreeAlgebra.lift_symm_apply, MvPolynomial.IsHomogeneous.rename_isHomogeneous_iff, Polynomial.aeval_neg, MvPolynomial.vars_bind₁, Ideal.count_associates_eq, WittVector.bind₁_verschiebungPoly_wittPolynomial, aeval_derivative_mem_differentIdeal, Generators.toKaehler_cotangentSpaceBasis, Presentation.instFinitePresentationModelOfHasCoeffsOfFinite, PowerSeries.map_expand, Polynomial.taylorEquiv_symm, NumberField.RingOfIntegers.coe_eq_algebraMap, normalizedTrace_eq_of_finiteDimensional_apply, AdicCompletion.surjective_evalₐ, Subspace.dualLift_rightInverse, MvPowerSeries.rescaleAlgHom_apply, Matrix.charpoly_vecMulVec, DualNumber.algHom_ext_iff, IntermediateField.topEquiv_symm_apply_coe, QuadraticMap.associated_linMulLin, RatFunc.liftOn'_div, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, FiniteGaloisIntermediateField.adjoin_val, AdjoinRoot.noZeroSMulDivisors_of_prime_of_degree_ne_zero, StarAlgHom.realContinuousMapOfNNReal_injective, MvPowerSeries.HasSubst.smul, Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map, MvPolynomial.optionEquivRight_apply, LieAlgebra.rank_le_finrank_engel, Ideal.natAbs_det_equiv, dualTensorHomEquivOfBasis_toLinearMap, Polynomial.coeff_expand, HasFDerivWithinAt.arctan, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity, MvPolynomial.finSuccEquiv_apply, algebraMap_ofSubsemiring, AlgCat.free_map, IsBaseChange.dual, NumberField.mixedEmbedding.convexBodyLT_convex, IsUnramifiedAtInfinitePlaces.id, MeasureTheory.Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Polynomial.rootsExpandToRoots_apply, TensorAlgebra.tprod_apply, NumberField.mem_span_integralBasis, derivWithin_fun_finset_prod, tsum_sq_fourierCoeffOn, WeierstrassCurve.Projective.add_of_Y_eq, Ideal.FG.isNilpotent_iff_le_nilradical, ProbabilityTheory.covarianceBilinDual_comm, Transcendental.subalgebraAlgebraicClosure, Module.mem_support_iff_nontrivial_residueField_tensorProduct, StandardEtalePair.HasMap.isUnit_derivative_f, Matrix.SpecialLinearGroup.toLin'_to_linearMap, IntermediateField.adjoin_eq_range_algebraMap_adjoin, MvPolynomial.tensorEquivSum_X_tmul_X, Ideal.map_algebraMap_eq_finset_prod_pow, PreTilt.exists_smodEq_untiltAux, HasDerivWithinAt.finset_prod, QuaternionAlgebra.Basis.j_self, LinearMap.mul_toMatrix₂'_mul, HasFDerivWithinAt.rpow, LinearMap.toMatrix₂'_mul, ProbabilityTheory.covariance_smul_right, Rep.finsuppTensorLeft_inv_hom, Polynomial.leadingCoeff_expand, Ideal.absNorm_eq_one_iff, MvPolynomial.comp_aeval_apply, MeasureTheory.charFun_eq_charFunDual_toDualMap, IntermediateField.rank_top', Presentation.relation_comp_localizationAway_inl, Polynomial.aeval_sumIDeriv_eq_eval, IntermediateField.isAlgebraic_adjoin_simple, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NormedAlgebra.Real.nonempty_algEquiv_or, QuadraticAlgebra.mul_C_eq_smul, WittVector.coeff_select, AdicCompletion.transitionMap_map_pow, PowerSeries.coeff_expand_of_not_dvd, cfcHom_isStrictlyPositive_iff, Extension.Cotangent.val_smul, Polynomial.expand_eq_C, fderivWithin_csin, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, MvPolynomial.aeval_unique, LinearMap.BilinForm.flip_flip, Polynomial.aeval_C, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, ProperCone.dual_dual_flip, PowerBasis.exists_eq_aeval', trace_complex_apply, IntermediateField.AdjoinSimple.normal_algebraicClosure, toMatrix_lsmul, flip_innerₗ, Quaternion.coe_starAe, toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, Module.Basis.map_orientation_eq_det_inv_smul, convex_setOf_holderWith, Polynomial.aeval_eq_prod_aroots_sub_of_splits, SubmersivePresentation.basisKaehler_apply, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, KaehlerDifferential.polynomial_D_apply, Ideal.rank_pow_quot, AlgebraicGeometry.StructureSheaf.algebraMap_germ, MvPolynomial.bind₁_bind₁, one_add_rpow_hasFPowerSeriesAt_zero, TensorProduct.toIntegralClosure_injective_of_flat, Ideal.subtype_isoBaseOfIsPrincipal_eq_mul, IntermediateField.normal_iff_forall_map_eq', Matrix.separatingLeft_toLinearMap₂'_iff, WeierstrassCurve.Projective.equation_smul, Localization.coe_algEquiv, AdicCompletion.mk_ofAlgEquiv_symm_eq_evalOneₐ, triple_product_permutation, LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero', MvPolynomial.algebraTensorAlgEquiv_symm_map, IntermediateField.intermediateFieldMap_apply_coe, Subalgebra.rangeS_algebraMap, IntermediateField.topEquiv_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, Bialgebra.TensorProduct.lid_toAlgEquiv, PiTensorProduct.dualDistrib_dualDistribInvOfBasis_right_inverse, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, Module.End.baseChangeHom_apply_apply, MvPolynomial.rename_polynomial_aeval_X, WeierstrassCurve.Projective.add_of_X_ne, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, convexOn_pow, MvPolynomial.coeff_expand_of_not_dvd, MeasureTheory.Measure.prod_smul_right, Matrix.isRepresentation.toEnd_surjective, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply, BilinForm.toMatrix_mul, IntermediateField.exists_algHom_adjoin_of_splits', Polynomial.comp_eq_aeval, Module.finite_dual_iff, Real.strictConcaveOn_sqrt, QuaternionAlgebra.imJ_swapEquiv_symm_apply, Generators.CotangentSpace.compEquiv_symm_inr, Generators.Hom.equivAlgHom_symm_apply_val, isArtinianRing_iff_isNilpotent_maximalIdeal, Polynomial.valuation_aeval_monomial_eq_valuation_pow, MvPolynomial.tensorEquivSum_C_tmul_one, normalizedTrace_def, signedDist_vadd_left, Module.dual_projective, MvPolynomial.map_iterateFrobenius_expand, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, Matrix.toLinAlgEquiv_self, NumberField.Units.coe_zpow, Polynomial.toMvPolynomial_X, NumberField.mem_span_basisOfFractionalIdeal, Submodule.exists_isInternal_prime_power_torsion, Ideal.radical_pow, MvPowerSeries.rescale_eq_subst, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, MeasureTheory.JordanDecomposition.real_smul_posPart_neg, ExistsContDiffBumpBase.w_def, FiniteField.minpoly_frobeniusAlgHom, Matrix.separatingLeft_toBilin'_iff, Matrix.kroneckerAlgEquiv_symm_apply, Matrix.coeff_det_one_add_X_smul_one, MvPowerSeries.coe_aeval, Module.AEval'_def, RatFunc.mk_def_of_mem, MeasureTheory.OuterMeasure.smul_boundedBy, DoubleCentralizer.coe_eq_algebraMap, MvPolynomial.sumAlgEquiv_apply, Coalgebra.TensorProduct.assoc_tmul, IntermediateField.AdjoinSimple.isIntegral_gen, Polynomial.aeval_ofReal, cfc_apply_pi, AddMonoidAlgebra.algHom_ext_iff, LieAlgebra.IsKilling.rootSystem_pairing_apply, Generators.ker_comp_eq_sup, InformationTheory.strictConvexOn_klFun, MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_regular, TensorProduct.comul_tmul, ProbabilityTheory.covarianceBilin_apply, Polynomial.hasDerivAt_aeval, ediam_smul₀, Polynomial.coe_algebraMap_eq_CC, HasFDerivAt.cos, Localization.subalgebra.isFractionRing_ofField, AlgebraicGeometry.StructureSheaf.const_mul_cancel', ContinuousMapZero.toContinuousMapHom_apply, IntermediateField.exists_lt_finrank_of_infinite_dimensional, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, Generators.ofComp_toAlgHom_monomial_sumElim, Polynomial.Chebyshev.aeval_C, NonUnitalSubring.unitization_range, deriv_finset_prod, KaehlerDifferential.quotKerTotalEquiv_symm_apply, ContinuousMap.comp_attachBound_mem_closure, adjoin_restrictScalars, Polynomial.aeval_eq_sum_range, PreTilt.untiltAux_smodEq_untiltFun, polyEquivTensor_apply, MvPolynomial.exists_finset_rename₂, FreeLieAlgebra.universalEnvelopingEquivFreeAlgebra_symm_apply, AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk, Matrix.mulVec_cramer, LaurentPolynomial.invert_apply, AdicCompletion.of_injective, CliffordAlgebra.contractRight_one, LSeries.mul_delta_eq_smul_delta, MvPolynomial.algebraMap_eq, MeasureTheory.Measure.WeaklyRegular.smul, MvPolynomial.algebraicIndependent_X, MvPolynomial.eval_toMvPolynomial, CliffordAlgebraDualNumber.equiv_ι, MeasureTheory.laverage_mem_openSegment_compl_self, Presentation.algebraTensorAlgEquiv_symm_relation, MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict, Generators.aeval_val_eq_zero, IsAlgebraic.isNormalClosure_normalClosure, MeasureTheory.measure_eq_sub_vadd, LocalizedModule.algebraMap_mk, Polynomial.Chebyshev.aeval_U, TrivSqZeroExt.snd_map, Polynomial.algebraMap_hahnSeries_injective, instFiniteResidueField, IntermediateField.isPurelyInseparable_bot, minpoly.equivAdjoin_toAlgHom, Ideal.span_singleton_mem_isPrincipalSubmonoid, IsHausdorff.eq_iff_smodEq, dualTensorHomEquivOfBasis_symm_cancel_left, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span, MvPolynomial.esymmAlgHom_apply, LaurentSeries.valuation_coe_ratFunc, DividedPowers.dpow_smul_right, Module.End.hasEigenvalue_iff_isRoot, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, LinearMap.IsPerfPair.id, signedDist_apply_linear_apply, IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure, TensorProduct.comul_def, MvPolynomial.aeval_eq_eval₂Hom, Matrix.IsHermitian.cfcAux_id, WeierstrassCurve.Projective.add_of_Y_ne', DoubleQuot.coe_quotQuotToQuotSupₐ, ContinuousMap.adjoin_id_eq_span_one_add, TensorProduct.Algebra.TensorProduct.commRight_symm_tmul, MvPolynomial.rename_prod_mk_eval₂, MvPowerSeries.HasSubst.smul_X, Differential.deriv_aeval_eq, AlgebraicIndependent.aevalEquivField_apply_coe, MvPolynomial.IsSymmetric.smul, CliffordAlgebra.foldr'Aux_apply_apply, WeierstrassCurve.Projective.neg_of_Z_eq_zero, MvPolynomial.aeval_C, ProbabilityTheory.covarianceBilin_map, MeasureTheory.Measure.OuterRegular.smul, BoundedContinuousFunction.integral_add_const, IsTranscendenceBasis.mvPolynomial, Subalgebra.LinearDisjoint.basisOfBasisLeft_apply, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assoc, NonUnitalAlgHom.toAlgHom_apply, Unitization.nnnorm_eq_sup, MvPowerSeries.map_frobenius_expand, AffineSubspace.signedInfDist_singleton, Coalgebra.TensorProduct.lid_toLinearEquiv, RootPairing.pairingIn_eq_add_of_root_eq_smul_add_smul, IntermediateField.LinearDisjoint.exists_field_of_isDomain, instIsStandardOpenImmersionTensorProduct, MvPolynomial.toMvPowerSeries_pUnitAlgEquiv, MvPolynomial.pderiv_map, WeierstrassCurve.Projective.dblY_smul, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, Polynomial.derivation_C, minpoly_algEquiv_toLinearMap, HasFDerivAt.const_rpow, one_add_cpow_hasFPowerSeriesOnBall_zero, Surreal.dyadicMap_apply, Polynomial.natDegree_det_X_add_C_le, Polynomial.eval_C_X_comp_eval₂_map_C_X, RingHom.Finite.tensorProductMap, AdjoinRoot.algHom_subsingleton, Matrix.toBilin'Aux_eq, Bundle.ContinuousRiemannianMetric.pos, MvPolynomial.aeval_comp_expand, Generators.naive_σ, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct, AlgebraicIndependent.aevalEquiv_apply_coe, MeasureTheory.OuterMeasure.comap_boundedBy, FormalMultilinearSeries.ofScalars_smul, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', Matrix.toLin_finTwoProd_toContinuousLinearMap, HomogeneousLocalization.Away.eventually_smul_mem, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, StrictAnti.strictConcaveOn_univ_of_deriv, hasSum_fourier_series_of_summable, NumberField.FinitePlace.norm_eq_one_iff_notMem, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', Etale.baseChange, IsCoercive.continuousLinearEquivOfBilin_apply, MvPolynomial.rename_C, Ideal.map_eq_iff_sup_ker_eq_of_surjective, Nat.Partition.summable_genFun_term', IntermediateField.finiteDimensional_left, AffineSubspace.subtypeₐᵢ_linearIsometry, LinearMap.toMatrixAlgEquiv'_symm, MvPowerSeries.expand_X, instIsPushout_1, MeasureTheory.FiniteMeasure.map_smul, MvPowerSeries.map_expand, RootPairing.flip_toFun_apply, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, Extension.Hom.sub_aux, FractionalIdeal.instPosMulReflectLEIdealOfIsDedekindDomain, StandardEtalePresentation.aeval_val_equivMvPolynomial, Orientation.areaForm_map, instIsPushoutFractionRingPolynomial, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_tmul, Polynomial.mem_rootSet', MeasureTheory.average_eq', Matrix.toPerfectPairing, LieModule.toEnd_eq_zero_iff, FormallySmooth.kerCotangentToTensor_injective_iff, LaurentSeries.valuation_compare, MeasureTheory.OuterMeasure.map_id, KaehlerDifferential.derivationTensorProduct_algebraMap, PowerSeries.HasSubst.comp, Ideal.isUnit_iff, Ideal.powQuotSuccInclusion_injective, le_perfectClosure_iff, perfectClosure.isAlgebraic, IsLocalRing.CotangentSpace.map_eq_top_iff, cfcHomSuperset_id, MvPolynomial.aevalTower_comp_toAlgHom, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, MeasureTheory.tilted_zero', IntermediateField.isSeparable_sup, NumberField.mixedEmbedding.logMap_real, MvPolynomial.restrictSupport_add, IsLocalRing.isOpen_maximalIdeal_pow, Polynomial.Bivariate.swap_C, TensorProduct.lTensor_ker, FiniteGaloisIntermediateField.finiteDimensional, Ideal.le_comap_pow, Ideal.prod_span, AlgHom.map_coe_real_complex, InnerProductSpace.toLinearMap_rankOne, Ideal.associatesEquivIsPrincipal_mul, KaehlerDifferential.tensorProductTo_surjective, RatFunc.algebraMap_apply, Seminorm.finset_sup_smul, Bundle.RiemannianMetric.pos, Submodule.isInternal_prime_power_torsion, RootPairing.rootSpan_dualAnnihilator_map_eq_iInf_ker_root', MvPolynomial.IsHomogeneous.rename_isHomogeneous, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, ExteriorAlgebra.algebraMap_leftInverse, norm_apply, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, MeasureTheory.OuterMeasure.isometry_map_mkMetric, WittVector.polyOfInterest_vars_eq, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, convexOn_exp, Seminorm.isBounded_sup, Ideal.iInf_pow_eq_bot_of_isDomain, LinearMap.trace_tensorProduct, comp_dualTensorHom, NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero, QuadraticForm.dualProdProdIsometry_toFun, HasFDerivAt.arsinh, Extension.h1Cotangentι_apply, IsAdjoinRoot.algebraMap_apply, hasEigenvalue_toLin'_diagonal_iff, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, IsLocalizedModule.mk_eq_mk', strictConvexOn_univ_of_deriv2_pos, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, Coalgebra.TensorProduct.assoc_symm_tmul, StandardEtalePair.aeval_X_g_mul_mk_X, MvPolynomial.pderiv_inr_universalFactorizationMap_X, Matrix.det_updateCol_add_smul_self, Extension.cotangentComplex_injective_iff, PowerSeries.algebraMap_eq, MeasureTheory.addEquivAddHaarChar_smul_eq_comap, Submodule.smul_torsionBy, TrivSqZeroExt.fst_map, AdicCompletion.transitionMap_ideal_mk, idealFactorsFunOfQuotHom_id, Transcendental.aeval, MvPolynomial.sumAlgEquiv_symm_apply, MvPowerSeries.constantCoeff_expand, Representation.ofModule_asAlgebraHom_apply_apply, Matrix.toLpLin_mul, TensorProduct.map_convMul_map, instMulPosStrictMonoIdeal, QuasispectrumRestricts.nnreal_of_nonneg, TensorAlgebra.equivDirectSum_symm_apply, InfiniteGalois.restrictNormalHom_continuous, MvPolynomial.eval₂_pUnitAlgEquiv_symm, Matrix.toLin'_submatrix, Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE, ClassGroup.exists_mk0_eq_mk0, QuaternionAlgebra.re_swapEquiv_apply, fderiv_ccosh, Localization.instFaithfulSMulAtPrimeOfNoZeroDivisors, Module.End.isIntegral, Derivation.compAEval_eq, LaurentSeries.tendsto_valuation, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, IsGaloisGroup.subgroup, PowerSeries.continuous_aeval, IsIntegral.tmul, Ideal.finite_quotient_pow, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, AdicCompletion.transitionMap_map_mul, Generators.ker_eq_ker_aeval_val, HasStrictFDerivAt.cpow, Polynomial.aeval_endomorphism, MvPolynomial.instIsPushout_1, IntermediateField.fixedField.isScalarTower, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAux₁_right, IsGalois.of_separable_splitting_field_aux, IntermediateField.coe_equivMap_apply, AlgebraicClosure.isAlgebraic, AddMonoidAlgebra.mapDomainBialgHom_comp, RatFunc.transcendental, IntermediateField.mem_adjoin_simple_iff, Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, LieModule.traceForm_apply_apply, MeasureTheory.mulEquivHaarChar_smul_eq_comap, cross_dot_cross, RatFunc.mk_one, AddMonoidAlgebra.scalarTensorEquiv_symm_single, hasFDerivWithinAt_iff_hasGradientWithinAt, PowerSeries.heval_unit, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, IsLocalRing.exists_maximalIdeal_pow_le_of_isArtinianRing_quotient, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra, MvPolynomial.supported_empty, MvPolynomial.C_mem_pow_idealOfVars_iff, cfcₙHom_continuous, krullTopology_mem_nhds_one_iff, RatFunc.algebraMap_injective, SymmetricAlgebra.algHom_surjective, AlgebraicIndependent.option_iff, Generators.toExtension_algebra₁, signedDist_right_lineMap, baseChange_lmul, KaehlerDifferential.mvPolynomialBasis_repr_D, QuadraticForm.tensorAssoc_apply, ProbabilityTheory.uncenteredCovarianceBilin_zero, WeakDual.gelfandTransform_apply_apply, LinearMap.toContPerfPair_apply, LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, Polynomial.expand_contract', Module.AEval.of_aeval_smul, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, InformationTheory.convexOn_Ioi_klFun, mem_ideal_map_adjoin, LaurentSeries.coe_range_dense, lintegral_comp_polarCoord_symm, Ideal.finprod_count, Polynomial.mem_aroots, AlgebraicGeometry.ΓSpec.toSpecΓ_of, RootPairing.instIsValuedIn, MvPolynomial.pderiv_eq_zero_of_notMem_vars, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous, TensorAlgebra.ι_inj, MeasureTheory.Measure.comp_smul, ClassGroup.mk0_surjective, ZMod.expand_card, AlgebraicGeometry.StructureSheaf.toOpen_germ, LinearIsometry.strictConvexSpace_range_iff, VectorFourier.fourierPowSMulRight_apply, cfcₙHomSuperset_continuous, TensorAlgebra.ι_eq_zero_iff, MvPolynomial.aeval_C_comp_left, CoalgCat.MonoidalCategoryAux.comul_tensorObj, MvPolynomial.transcendental_X, MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_innerRegular, Rep.finsuppTensorLeft_hom_hom, MeasureTheory.JordanDecomposition.real_smul_negPart_neg, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, QuadraticMap.associated_sq, IsAdjoinRoot.map_self, leftMulMatrix_mulVec_repr, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, RootPairing.toPerfPair_conj_reflection, KaehlerDifferential.ker_map_of_surjective, Norm.Transitivity.mul_auxMat_toSquareBlock_eq, Ergodic.mem_extremePoints_measure_univ_eq, MvPolynomial.degrees_rename_of_injective, PolynomialLaw.range_φ, MeasureTheory.Measure.map_const, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, H1Cotangent.isLocalizedModule, TensorProduct.lift_comp_includeRight', cfcₙ_apply_pi, AlternatingMap.measure_def, Polynomial.toFinsuppIsoAlg_apply, MeasureTheory.maximal_ineq, strictConcaveOn_sin_Icc, CliffordAlgebra.contractLeft_mul_algebraMap, map_dualTensorHom, AlgebraicIndependent.matroid_closure_eq, LinearMap.isSymmetric_iff_sesqForm, AddMonoidAlgebra.finiteType_iff_fg, Subspace.dualLift_injective, Generators.cotangentRestrict_mk, minpoly.coe_equivAdjoin, MeasureTheory.dirac_withDensity', AlgebraicIndependent.integralClosure, convexOn_univ_of_deriv2_nonneg, krullTopology_mem_nhds_one_iff_of_normal, MvPolynomial.optionEquivLeft_monomial, RatFunc.ofFractionRing_eq, Matrix.dualNumberEquiv_apply, Matrix.separatingRight_toBilin'_iff, Ideal.finite_setOf_absNorm_le, LieModule.maxGenEigenSpace_toEnd_eq_top, MvPowerSeries.substAlgHom_monomial, Orientation.areaForm_map_complex, NumberField.mixedEmbedding.normAtPlace_smul, Ideal.mul_mem_mul_rev, Polynomial.aeval_algEquiv, Matrix.toLin_finTwoProd, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, LinearMap.BilinForm.apply_toDual_symm_apply, TensorProduct.quotIdealMapEquivTensorQuot_mk, Unitization.instStarModule, CliffordAlgebra.toBaseChange_involute, SubmersivePresentation.ofSubsingleton_algebra_smul, support_subset_support_matPolyEquiv, Matrix.toLinAlgEquiv'_toMatrixAlgEquiv', NonUnitalSubsemiring.unitization_range, LinearEquiv.lieConj_symm, MeasureTheory.Measure.mapₗ_eq_zero_iff, Polynomial.algEquivAevalNegX_apply, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, LieAlgebra.rank_eq_natTrailingDegree, WittVector.bind₁_onePoly_wittPolynomial, Real.map_volume_mul_right, adjoin_eq_range_freeAlgebra_lift, WeierstrassCurve.Projective.neg_smul, Module.End.ker_aeval_ring_hom'_unit_polynomial, lmul_isUnit_iff, MeasureTheory.Measure.haarScalarFactor_smul_smul, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, LinearMap.tensorProduct_apply, Ideal.pow_right_strictAnti, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, MvPolynomial.optionEquivLeft_symm_apply, RatFunc.denom_algebraMap, exteriorPower.pairingDual_apply_apply_eq_one_zero, Polynomial.hasFDerivWithinAt_aeval, Orientation.inner_rightAngleRotation_right, MeasureTheory.Measure.rnDeriv_smul_left, fourierSubalgebra_closure_eq_top, WeakBilin.eval_continuous, fderiv_sqrt, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, QuadraticAlgebra.algebraMap_dvd_iff_dvd, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Polynomial.contDiff_aeval, Projectivization.cross_mk_of_ne, tensorH1CotangentOfIsLocalization_toLinearMap, FreeLieAlgebra.instIsCentralScalar, IsAdjoinRoot.ofAlgEquiv_map_apply, isSeparable_self, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, RatFunc.liftRingHom_comp_algebraMap, Ideal.exists_mem_pow_notMem_pow_succ, Unitization.complex_cfcₙ_eq_cfc_inr, Module.ker_algebraMap_end, MvPolynomial.algebraTensorAlgEquiv_tmul, PowerSeries.coeff_derivative, separableClosure.isSeparable, matPolyEquiv_symm_map_eval, MonoidAlgebra.single_eq_algebraMap_mul_of, Real.nonempty_algEquiv_or, mem_reesAlgebra_iff, AdicCompletion.of_bijective, Bialgebra.TensorProduct.assoc_toCoalgEquiv, MvPolynomial.mem_support_coeff_finSuccEquiv, QuadraticAlgebra.mk_eq_add_smul_omega, Generators.aeval_val_σ', Polynomial.mem_rootSet, AdjoinRoot.minpoly_powerBasis_gen, AdjoinRoot.aeval_algHom_eq_zero, Generators.Hom.toAlgHom_id, Generators.Hom.comp_val, AlgHom.ker_kerSquareLift, PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable, MvPolynomial.instIsPushout, LinearMap.polar_isClosed, innerₛₗ_apply, LieAlgebra.mem_corootSpace', ContinuousLinearMap.det_smulRight, Polynomial.map_under_lt_comap_of_quasiFiniteAt, Ideal.mem_isPrincipalSubmonoid_iff, Matrix.toLinAlgEquiv'_one, innerSL_apply, AlgebraicGeometry.Scheme.affineOpenCoverOfSpanRangeEqTop_f, CliffordAlgebra.contractLeft_algebraMap_mul, IntermediateField.adjoin.finiteDimensional, IntermediateField.botEquiv_def, MvPolynomial.comap_apply, le_algebraicClosure_iff, IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_count, Quaternion.re_snd_dualNumberEquiv, contractRight_apply, cfc_eq_cfcL, LinearMap.trace_eq_contract_of_basis, HomogeneousLocalization.den_smul_val, FreeAlgebra.algebraMap_eq_one_iff, IsAdjoinRoot.map_eq_zero_iff, IntermediateField.adjoin_adjoin_comm, MvPolynomial.vars_rename, TrivSqZeroExt.algebraMap_eq_inlHom, stereographic_apply, Complex.toMatrix_conjAe, StrongDual.toLp_apply, Ideal.isCoprime_span_singleton_iff, AlgebraicIndependent.algebraicClosure, WittVector.bind₁_zero_wittPolynomial, BilinForm.mul_toMatrix, FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eq, ModularFormClass.hasSum_qExpansion_of_norm_lt, FDRep.char_orthonormal, Polynomial.exists_separable_of_irreducible, ContinuousLinearMap.IsPositive.spectrumRestricts, IsTranscendenceBasis.mvPolynomial', Module.End.IsSemisimple.minpoly_squarefree, Polynomial.roots_expand_image_iterateFrobenius, IntermediateField.val_mk, ENNReal.smul_toNNReal, MatrixEquivTensor.right_inv, StieltjesFunction.measure_smul, ClassGroup.exists_min, NumberField.RingOfIntegers.instIsScalarTower, Valuation.HasExtension.id, Generators.CotangentSpace.map_toComp_injective, AdicCompletion.evalₐ_of, Module.End.lTensorAlgHom_apply_apply, RatFunc.num_mul_eq_mul_denom_iff, PowerSeries.expand_monomial, IntermediateField.rank_sup_le, IsLocalization.tensor, Matrix.toLpLin_symm_comp, Module.Basis.SmithNormalForm.repr_comp_embedding_eq_smul, IntermediateField.LinearDisjoint.self_right, Polynomial.aeval_monomial, LinearIsometry.strictConvexSpace_range, Extension.H1Cotangent.equivOfFormallySmooth_toLinearMap, MvPowerSeries.aeval_eq_sum, Polynomial.eval_map_algebraMap, IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, IsLocalRing.CotangentSpace.span_image_eq_top_iff, LieAlgebra.ad_lie, AdjoinRoot.quotEquivQuotMap_symm_apply, isPrecomplete_iff, polynomialFunctions.topologicalClosure, Unitization.lift_range_le, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.RingOfIntegers.instIsScalarTower_1, StandardEtalePresentation.toPresentation_val, Polynomial.algEquivOfCompEqX_apply, NumberField.toNNReal_valued_eq_adicAbv, StrongConvexOn.strictConvexOn, Orientation.kahler_apply_apply, NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMap, matPolyEquiv_eval, MeasureTheory.FiniteMeasure.toWeakDualBCNN_continuous, TensorProduct.rid_toLinearEquiv, Orientation.inner_rightAngleRotationAux₁_left, Polynomial.mem_rootSet_of_ne, Polynomial.mapAlg_comp, Quaternion.mul_coe_eq_smul, Bialgebra.TensorProduct.lid_toCoalgEquiv, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, RootPairing.toPerfPair_flip_conj_coreflection, WittVector.exists_frobenius_solution_fractionRing_aux, IsAdjoinRoot.aeval_root_self, strictConvexOn_zpow, Module.Invertible.bijective, Polynomial.aeval_eq_sum_range', MvPolynomial.rename_comp_bind₁, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, AlgEquiv.restrictNormalHom_apply, LieModule.isNilpotent_iff_forall', InfiniteGalois.mk_toAlgEquivAux, Polynomial.expand_char, IsLocalizedModule.fromLocalizedModule'_mk, Orientation.areaForm_apply_self, MvPolynomial.aeval_id_eq_join₁, AlgebraicGeometry.pullbackSpecIso_hom_fst'_assoc, Polynomial.aeval_zero, instIsAbelianGaloisSubtypeMemIntermediateField, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, MvPolynomial.rename_X, Real.differentiable_fourierChar_neg_bilinear_right, Matrix.det_updateRow_smul, SymmetricAlgebra.algebraMap_leftInverse, CoalgCat.rightUnitor_def, Ideal.isCoprime_iff_add, MeasureTheory.Integrable.smul_measure, LeftInvariantDerivation.evalAt_mul, LinearMap.Nondegenerate.toMatrix₂', cfcHom_predicate, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.smul_mem, MvPolynomial.pUnitAlgEquiv_monomial, FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm, Generators.compLocalizationAwayAlgHom_relation_eq_zero, conductor_mul_differentIdeal, LSeries.delta_mul_eq_smul_delta, AffineSubspace.signedInfDist_def, WeakDual.CharacterSpace.continuousMapEval_apply_apply, QuadraticAlgebra.coe_mem_nonZeroDivisors_iff, WeierstrassCurve.Projective.add_smul_of_equiv, Localization.localRingHom_bijective_of_saturated_inf_eq_top, Bialgebra.TensorProduct.rid_symm_apply, IntermediateField.inclusion_inclusion, exists_extension_norm_eq, Module.AEval.annihilator_top_eq_ker_aeval, IsStandardSmooth.free_kaehlerDifferential, Ideal.eq_prime_pow_mul_coprime, mvPolynomial, ProjectiveSpectrum.zeroLocus_sup_ideal, RatFunc.liftAlgHom_apply_div', LieSubmodule.coe_toEnd_pow, Module.Basis.orientation_unitsSMul, Submodule.lTensorOne_tmul, Matrix.Nondegenerate.toBilin', Polynomial.roots_expand_pow_image_iterateFrobenius_subset, IntermediateField.extendScalars_restrictScalars, FractionalIdeal.map_canonicalEquiv_mk0, VectorFourier.fourierIntegral_comp_add_right, LinearMap.isIntegral, MeasureTheory.Measure.Regular.smul_nnreal, MvPolynomial.comap_id_apply, MeasureTheory.convolution_mul_swap, LinearMap.BilinForm.congr_trans, LinearMap.isNonneg_def, LinearMap.BilinForm.toMatrix'_mul, MvPolynomial.aeval_one_tmul, minpoly.eq_iff_aeval_minpoly_eq_zero, signedDist_lineMap_right, ContinuousLinearMap.norm_smulRightL_le, CliffordAlgebraQuaternion.ofQuaternion_comp_toQuaternion, Polynomial.algEquivCMulXAddC_symm_apply, PowerSeries.derivative_subst, TensorAlgebra.algebraMap_leftInverse, Ideal.absNorm_eq_pow_inertiaDeg, MeasureTheory.isZeroOrProbabilityMeasureSMul, MvPowerSeries.IsNilpotent_subst, Extension.Hom.sub_tmul, LieAlgebra.isNilpotent_range_ad_iff, AlgebraicGeometry.pullbackSpecIso_inv_fst', MvPolynomial.smul_eq_C_mul, PowerSeries.coeff_expand, IsAdicComplete.mk_lift, LieModule.mem_genWeightSpaceOf, Real.strictConcave_binEntropy, AdicCompletion.evalOneₐ_surjective, IsAlgebraic.tmul, LinearMap.toMatrix₂'_compl₂, IntermediateField.mem_extendScalars, MeasureTheory.isLocallyFiniteMeasureSMulNNReal, RatFunc.liftRingHom_algebraMap, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, DualNumber.exp_smul_eps, Polynomial.IsMonicOfDegree.aeval_sub, HopfAlgCat.leftUnitor_def, TensorProduct.comm_comp_map, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, MvPolynomial.finSuccEquiv_rename_finSuccEquiv, TrivSqZeroExt.map_inl, PowerSeries.coe_aeval, Matrix.toLinAlgEquiv'_symm, MvPolynomial.rename_expand, Quaternion.snd_imI_dualNumberEquiv_symm, CliffordAlgebraComplex.toComplex_involute, Ideal.mul_iInf, VectorFourier.fourierIntegral_probChar, MvPolynomial.homogeneousSubmodule_one_pow, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, LinearMap.IsSymm.add, SubmersivePresentation.rank_kaehlerDifferential, ContinuousMap.polynomial_comp_attachBound, VectorFourier.norm_fourierSMulRight_le, Polynomial.expand_eval, MeasureTheory.OuterMeasure.map_top_of_surjective, PowerSeries.le_order_subst_right, Ideal.spanNorm_mul_spanNorm_le, derivWithin_finset_prod, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, MonomialOrder.degree_smul, AdicCompletion.evalₐ_comp_liftRingHom, isAlgebraic_iff_not_injective, MvPolynomial.IsHomogeneous.sum_X_mul_pderiv, norm_cfcHom, MvPolynomial.derivation_C_mul, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, LieAlgebra.IsKilling.traceForm_coroot, Matrix.toLinearEquiv_kroneckerAlgEquiv, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, InfiniteGalois.proj_of_le, Ideal.Factors.finiteDimensional_quotient_pow, Submodule.span_eq_top_of_ne_zero, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, CliffordAlgebraComplex.toComplex_ofComplex, MvPolynomial.aeval_sumElim_pderiv_inl, MeasureTheory.isFiniteMeasureSMulNNReal, FDRep.char_dual, Matrix.det_sum_smul_le, Ideal.cotangentEquivIdeal_symm_apply, MeasureTheory.Integrable.smul_measure_nnreal, FiniteField.expand_card, MeasureTheory.OuterMeasure.restrict_apply, RatFunc.mk_one', Ideal.finprod_heightOneSpectrum_factorization_coe, AnalyticAt.aeval_mvPolynomial, MvPolynomial.tensorEquivSum_one_tmul_X, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow, Polynomial.coeff_expand_mul', Polynomial.differentiableWithinAt_aeval, Matrix.nondegenerate_toLinearMap₂'_iff, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, SubmersivePresentation.sectionCotangent_comp, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, MeasureTheory.condLExp_smul', UnitAddTorus.hasSum_mFourier_series_apply_of_summable, FGModuleCat.FGModuleCatEvaluation_apply', WeakDual.CharacterSpace.equivAlgHom_coe, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, AdjoinRoot.aeval_eq, subsingleton_id, exists_etale_isIdempotentElem_forall_liesOver_eq_aux, formallySmooth_iff, MvPowerSeries.comp_subst, Polynomial.coeff_zero_eq_aeval_zero', PowerSeries.expand_one, KaehlerDifferential.isBaseChange_of_formallyEtale, IsLocalizedModule.map_units, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, IsLocalization.adjoin_inv, LieAlgebra.nilpotent_ad_of_nilpotent_algebra, MvPolynomial.supported_univ, IntermediateField.relrank_eq_rank_of_le, Derivation.commutator_apply, MvPolynomial.isSymmetric_rename, strictConcaveOn_log_Ioi, MeasureTheory.withDensity_smul_measure, LinearMap.BilinForm.IsNonneg.smul, IntermediateField.lift_adjoin, Ideal.le_pow_of_le_ramificationIdx, HasFDerivAt.hasGradientAt, H1Cotangent.exact_map_δ, NumberField.basisOfFractionalIdeal_apply, HasStrictFDerivAt.sin, CliffordAlgebra.ofBaseChange_tmul_one, MeasureTheory.restrict_compl_sigmaFiniteSetWRT, Subalgebra.isAlgebraic_bot_iff, AlgebraicIndependent.iff_adjoin_image, MvPowerSeries.monomial_eq, Polynomial.roots_expand_pow, signedDist_eq_dist_iff_vsub_mem_span, MvPolynomial.universalFactorizationMap_freeMonic, AnalyticOnNhd.aeval_polynomial, Generators.Hom.toAlgHom_monomial, Bialgebra.subsingleton_to_ring, Ideal.span_singleton_mul_right_injective, LieModule.instIsFaithfulEnd, Generators.H1Cotangent.δ_comp_equiv, HasFDerivWithinAt.const_rpow, Matrix.cramer_smul, MeasureTheory.Measure.restrictₗ_apply, Ideal.pow_lt_self, QuaternionAlgebra.algebraMap_eq, MvPolynomial.universalFactorizationMapPresentation_val, MvPolynomial.rename_comp_rename, Ideal.absNorm_eq_zero_iff, AdjoinRoot.adjoinRoot_eq_top, MvPolynomial.coe_expand, IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one, LocalizedModule.smul_eq_iff_of_mem, Polynomial.contract_mul_expand, fderivWithin_cosh, QuaternionAlgebra.Basis.range_liftHom, ContinuousLinearMap.isAdjointPair_inner, Polynomial.algEquivAevalXAddC_apply, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, IntermediateField.extendScalars_top, VectorFourier.norm_fourierPowSMulRight_le, MvPolynomial.aeval_sumElim, MvPolynomial.universalFactorizationMapPresentation_σ', Polynomial.map_frobenius_expand, AdicCompletion.eval_of, FractionalIdeal.finite_factors', RootPairing.corootSpan_dualAnnihilator_le_ker_rootForm, CommAlgCat.associator_hom_hom, MvPolynomial.aeval_comp_rename, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, MeasureTheory.Measure.InnerRegularCompactLTTop.smul_nnreal, IsPushout.equiv_symm_algebraMap_right, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, MeasureTheory.OuterMeasure.mkMetric_smul, MeasureTheory.Measure.ennreal_smul_eq_zero, RatFunc.isScalarTower_liftAlgebra, Unitization.splitMul_injective, QuadraticAlgebra.algebraMap_norm_eq_mul_star, IntermediateField.rank_eq_rank_subalgebra, MvPolynomial.mem_symmetricSubalgebra, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Nonneg.Icc_subset_segment, idealFactorsFunOfQuotHom_coe_coe, AddMonoidAlgebra.decomposeAux_single, IsLocalization.isLocalization_atPrime_localization_atPrime, cfcₙ_eq_cfcₙL, RingOfIntegers.algebraMap_norm_algebraMap, Bialgebra.TensorProduct.rid_tmul, IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed, QuadraticMap.Isometry.tmul_apply, convex_setOf_holderOnWith, VectorFourier.norm_fourierSMulRight, WeakDual.CharacterSpace.instAlgHomClass, MeasureTheory.FiniteMeasure.isEmbedding_toWeakDualBCNN, Norm.Transitivity.auxMat_toSquareBlock_ne, ContinuousLinearEquiv.coord_norm', matPolyEquiv_symm_X, HahnSeries.coeff_toOrderTopSubOnePos_pow, exists_bijective_map_powers, Subalgebra.setRange_algebraMap, MvPolynomial.eval₂_rename_prod_mk, IsLocalizedModule.iso_localizedModule_eq_refl, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, jacobi_cross, FractionRing.isScalarTower_liftAlgebra, Polynomial.aeval_pi, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, CoalgCat.tensorObj_instCoalgebra, CliffordAlgebra.toBaseChange_ι, Polynomial.newtonMap_apply, Derivation.apply_aeval_eq', SymmetricAlgebra.algebraMap_inj, IntermediateField.lift_sup, AdicCompletion.evalₐ_mk, Bialgebra.TensorProduct.lid_tmul, LinearMap.mem_span_iff_bound, cfcₙL_apply, Representation.asModuleEquiv_map_smul, QuaternionAlgebra.coe_algebraMap, PadicAlgCl.coe_eq, instIsStandardEtale, Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct, bind₁_wittPolynomial_xInTermsOfW, TensorProduct.dualDistrib_apply, NumberField.FinitePlace.isFinitePlace, cfcHomSuperset_continuous, MeasureTheory.Measure.IsEverywherePos.smul_measure_nnreal, Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicity, strongConvexOn_iff_convex, normalClosure.normal, strongConvexOn_zero, IsStandardSmooth.iff_exists_basis_kaehlerDifferential, Subalgebra.algebraMap_apply, count_associates_factors_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, LinearMap.BilinForm.toMatrix'_toBilin', Polynomial.coe_aeval_eq_eval, DoubleQuot.quotQuotEquivComm_mk_mk, FinitePresentation.out, Matrix.aeval_self_charpoly, Ideal.multiset_prod_le_inf, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, MvPolynomial.rename_leftInverse, MeasureTheory.withDensity_smul, neg_cross, Complex.adjoin_I, MeasureTheory.Measure.haveLebesgueDecompositionSMulRight, LinearAlgebra.FreeProduct.lift_apply, LocalizedModule.map_mk, AffineSubspace.isometryEquivMap.apply_symm_apply, PiTensorProduct.map_update_smul, LSeries.term_smul, integralClosure.isIntegralClosure, IsAdicComplete.StrictMono.of_lift, LieModule.coe_lcs_range_toEnd_eq, LieModule.toEnd_module_end, IntermediateField.adjoin_adjoin_left, AdicCompletion.evalₐ_mkₐ, LieAlgebra.mem_zeroRootSubalgebra, FiniteType.iff_quotient_mvPolynomial'', RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, instIsScalarTowerLocalizationAlgebraMapSubmonoid, Irreducible.maximalIdeal_pow_eq_closedBall_pow, Presentation.quotientEquiv_mk, Polynomial.smul_modByMonic, MvPolynomial.esymmAlgHom_fin_bijective, StrongDual.coe_toWeakDual, LinearMap.det_toMatrix', LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, IsAdjoinRoot.algEquiv_map, Matrix.separatingLeft_toBilin_iff, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, WeakDual.toStrongDual_apply, Module.Basis.toMatrix_reindex', LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, ContinuousMap.elemental_id_eq_top, instFiniteTypeSubtypePolynomialMemSubalgebraReesAlgebraOfIsNoetherianRing, IsLocalRing.subsingleton_tensorProduct, MvPolynomial.esymmAlgEquiv_apply, Real.differentiable_fourierChar_neg_bilinear_left, Unitization.starLift_range_le, PowerSeries.aeval_coe, Antitone.concaveOn_univ_of_deriv, LaurentSeries.ratfuncAdicComplRingEquiv_apply, MeasureTheory.OuterMeasure.map_top, Nat.Partition.hasProd_genFun, LinearMap.toMatrixAlgEquiv_apply', MvPolynomial.mem_vanishingIdeal_iff, is_ideal_adic_pow, instContainConstants, MvPolynomial.mem_vanishingIdeal_singleton_iff, gelfandTransform_isometry, Quaternion.coe_ofComplex, Ideal.count_associates_eq', WeakDual.CharacterSpace.compContinuousMap_comp, MeasureTheory.Measure.IsAddHaarMeasure.nnreal_smul, HasStrictDerivAt.finset_prod, MonoidAlgebra.lift_def, AdicCompletion.ofTensorProduct_naturality, separableClosure_le_iff, solvableByRad.isIntegral, ContinuousMultilinearMap.smulRightL_apply, polynomialFunctions_closure_eq_top', Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, MvPolynomial.expand_zmod, PowerSeries.coeff_heval_zero, IsAzumaya.id, innerₛₗ_apply_coe, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, fderiv_csinh, Polynomial.Monic.expand, LieSubalgebra.instIsScalarTowerSubtypeMem, MeasureTheory.Measure.compProd_smul_left, MeasureTheory.Measure.mul_haarScalarFactor_smul, ClassGroup.equiv_mk0, MvPolynomial.aeval_zero', NumberField.RingOfIntegers.map_mk, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, PowerSeries.IsWeierstrassFactorizationAt.smul, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, MvPolynomial.weightedTotalDegree_rename_of_injective, QuadraticModuleCat.toIsometry_inv_leftUnitor, Polynomial.aeval_iterate_derivative_of_lt, RootPairing.rootSpan_dualAnnihilator_map_eq, Ideal.absNorm_bot, ContinuousMapZero.toNNReal_neg_smul, LinearMap.BilinForm.Nondegenerate.toMatrix', DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, Representation.is_simple_module_iff_irreducible_ofModule, Subalgebra.LinearDisjoint.norm_algebraMap, Ideal.relNorm_apply, LinearMap.isSymm_iff_basis, RingHom.locally_iff_finite, IntermediateField.insepDegree_bot, QuaternionAlgebra.mul_coe_eq_smul, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_measurableSet, IntermediateField.equivOfEq_apply, NormedAlgebra.Complex.nonempty_algEquiv, NumberField.mixedEmbedding.convexBodySum_convex, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, ContinuousMap.polynomial_comp_attachBound_mem, PowerSeries.substAlgHom_coe, range_cfcHom, HasFDerivAt.sqrt, LieAlgebra.ExtendScalars.instLieModule, topDualPairing_apply, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, LinearMap.toSeminormFamily_apply, HasFDerivAt.csinh, Module.End.mem_spectrum_iff_isRoot_charpoly, Ideal.mem_span_singleton_mul, Subrepresentation.mem_ofSubmodule_iff, AddMonoidAlgebra.decomposeAux_eq_decompose, IsLocalizedModule.fromLocalizedModule.surj, MeasureTheory.laverage_union_mem_openSegment, MvPolynomial.rename_toMvPolynomial, MeasureTheory.llr_smul_right, Matrix.SeparatingRight.toBilin', Polynomial.natDegree_expand, MvPolynomial.aeval_rename, CStarAlgebra.nonneg_TFAE, LinearMap.compQuadraticMap_polarBilin, adjoin_union_eq_adjoin_adjoin, nnnorm_cfcHom, Module.Basis.traceDual_powerBasis_eq, SubmersivePresentation.sectionCotangent_zero_of_notMem_range, Localization.localRingHom_bijective_of_not_conductor_le, Orientation.areaForm_rightAngleRotation_right, WittVector.bind₁_frobeniusPolyRat_wittPolynomial, MvPolynomial.optionEquivLeft_symm_C_X, Presentation.id_dimension, BilinForm.apply_eq_dotProduct_toMatrix_mulVec, IsAlgClosed.nonempty_algEquiv_or_of_finrank_eq_two, AdicCompletion.ofLinearEquiv_apply, algebraMap_intTrace_fractionRing, WeakDual.CharacterSpace.equivAlgHom_symm_coe, KaehlerDifferential.range_kerCotangentToTensor, Ideal.isIdempotentElem_iff_eq_bot_or_top_of_isLocalRing, IntermediateField.fieldRange_val, IsTranscendenceBasis.isAlgebraic, IntermediateField.liftAlgEquiv_apply, Polynomial.aeval_pi_apply₂, Matrix.range_diagonal, Unitization.lift_apply_apply, AdicCompletion.mk_apply_coe, RatFunc.num_div_denom, Submodule.torsionBySet.mk_smul, PowerSeries.derivative_C, Quaternion.hasSum_expSeries_of_imaginary, WittVector.aeval_verschiebungPoly, FixedPoints.smulCommClass', separableClosure_le_separableClosure_iff, Submodule.orthogonal_eq_inter, NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply, MvPolynomial.eval₂Hom_bind₁, PowerSeries.IsWeierstrassDivisorAt.div_smul, IsSymmetricAlgebra.comp_equiv, LieModule.iterate_toEnd_mem_lowerCentralSeries, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, BialgHom.ext_of_ring_iff, sup_eq_prod_inf_factors, MvPolynomial.finSuccEquiv_X_zero, CliffordAlgebraComplex.ofComplex_comp_toComplex, UniformOnFun.continuousSMul_submodule_of_image_bounded, MvPolynomial.degreeOf_eq_natDegree, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, MeasureTheory.integrable_average, MvPowerSeries.support_expand_subset, LinearMap.trace_comp_comm, KaehlerDifferential.map_D, RootPairing.pairing_eq_add_of_root_eq_smul_add_smul, HasStrictFDerivAt.ccosh, Derivation.liftKaehlerDifferential_apply, Generators.instFreeCotangentSpaceToExtension, QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff, BilinForm.toMatrix_compLeft, Polynomial.aeval_mem_adjoin_singleton, MeasureTheory.lpNorm_smul_measure_of_ne_top, PowerSeries.expand_X, Ideal.iInf_pow_smul_eq_bot_of_isTorsionFree, coe_lmul_eq_mul, Presentation.baseChange_relation, Height.logHeight_smul_eq_logHeight, ContinuousLinearEquiv.coord_norm, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, LinearMap.toPerfPair_apply, fderiv_norm_rpow, HasDerivAt.finset_prod, Int.ideal_span_absNorm_eq_self, MonomialOrder.sPolynomial_mem_sup_ideal, KaehlerDifferential.DLinearMap_apply, HasStrictFDerivAt.cosh, RootPairing.GeckConstruction.f_mem_lieAlgebra, LieAlgebra.lieCharacter_apply_lie, FinitePresentation.baseChange, Polynomial.toAddCircle_X_eq_fourier_one, TensorProduct.lmul''_eq_lid_comp_mapOfCompatibleSMul, MeasureTheory.lpMeasToLpTrim_smul, LieRinehartAlgebra.instDerivation, LinearMap.toMatrix₂'_comp, Ideal.multiset_prod_eq_bot, localization_unit_isIso', LinearEquiv.conjAlgEquiv_surjective, LinearPMap.mem_adjoint_domain_iff, MvPolynomial.bind₁_X_right, MvPolynomial.coeff_rename_eq_zero, Module.End.hasEigenvalue_iff_mem_spectrum, Polynomial.tendsto_abv_aeval_atTop, TensorPower.toTensorAlgebra_galgebra_toFun, normalizedTrace_eq_of_fininteDimensional_apply, PowerSeries.HasSubst.smul, AddMonoidAlgebra.lift_unique, MvPolynomial.eval₂Hom_C_left, Ideal.mul_inf, LinearMap.not_hasEigenvalue_zero_tfae, MvPolynomial.transcendental_supported_polynomial_aeval_X_iff, MeasureTheory.Measure.mconv_smul_left, TensorAlgebra.algebraMap_eq_zero_iff, MvPolynomial.aeval_monomial, separableClosure.separableClosure_eq_bot, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, IntermediateField.rank_bot_mul_relrank, Ideal.relNorm_bot, AddMonoidAlgebra.lift_def, Ideal.norm_mem_relNorm, ContinuousMapZero.elemental_eq_top, LieDerivation.coe_ad_apply_eq_ad_apply, StandardEtalePresentation.toPresentation_relation, ContinuousMapZero.adjoin_id_dense, Polynomial.cyclotomic_expand_eq_cyclotomic, Ideal.prod_span_singleton, trace_apply, Polynomial.toMvPolynomial_injective, TensorAlgebra.toDirectSum_ι, MeasureTheory.JordanDecomposition.real_smul_negPart_nonneg, SubmersivePresentation.free_cotangent, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, Submodule.norm_orthogonalProjection, LinearMap.BilinForm.toMatrix_comp, Matrix.SpecialLinearGroup.toLin'_symm_apply, ClassGroup.mk0_eq_mk0_inv_iff, spectrum.unit_smul_eq_smul, ContinuousMapZero.toNNReal_smul, QuadraticAlgebra.coe_algebraMap, QuadraticAlgebra.det_toLinearMap_eq_norm, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one, QuaternionAlgebra.imJ_swapEquiv_apply, PreSubmersivePresentation.ofHasCoeffs_val, PrimeSpectrum.zeroLocus_sup, coe_innerₛₗ_apply, LieAlgebra.lieCharacter_apply_lie', ProbabilityTheory.covarianceBilinDual_of_not_memLp, FormallySmooth.iff_injective_cotangentComplexBaseChange, Generators.CotangentSpace.fst_compEquiv_apply, fderivWithin_arctan, TemperedDistribution.smulLeftCLM_smul, Pi.constAlgHom_eq_algebra_ofId, TrivSqZeroExt.instIsScalarTower, Generators.self_algebra_algebraMap, IsAlgClosed.isAlgClosure_of_transcendence_basis, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, RootPairing.GeckConstruction.e_mem_lieAlgebra, IsFractionRing.self_iff_nonZeroDivisors_le_isUnit, FormallyUnramified.comp_sec, Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe, Complex.ofRealAm_coe, MeasureTheory.charFun_map_eq_charFunDual_smul, AlgCat.hom_tensorHom, AlgebraicGeometry.pullbackSpecIso_hom_fst', PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, IsDedekindDomain.exists_representative_mod_finset, Submodule.dualAnnihilator_map_linearEquiv_flip_symm, LinearMap.toMatrix'_one, Representation.dual_apply, LieAlgebra.SpecialLinear.val_singleSubSingle, MeasureTheory.eLpNorm_smul_measure_of_ne_zero, InnerProductSpace.continuousLinearMapOfBilin_apply, smulTower_leftMulMatrix_algebraMap_eq, AlgebraicGeometry.StructureSheaf.instAwayObjOppositeOpensCarrierTopValStructureSheafInTypeOpBasicOpen, NormedSpace.double_dual_bound, Even.convexOn_pow, AdicCompletion.of_injective_iff, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, MvPolynomial.pderiv_X_self, Polynomial.aeval_algHom_apply, Polynomial.coe_toLaurentAlg, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, QuaternionAlgebra.imI_swapEquiv_apply, Module.Basis.det_smul_mk_coord_eq_det_update, WittVector.mul_polyOfInterest_aux3, Matrix.invOf_eq, PowerSeries.IsWeierstrassDivisionAt.smul, Real.zero_at_infty_vector_fourierIntegral, Unitization.starLift_symm_apply, MvPolynomial.pderiv_C, BialgCat.leftUnitor_def, LieAlgebra.isNilpotent_iff_forall, algebraMapSubmonoid_self, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix, TensorAlgebra.lift_unique, IntermediateField.finiteDimensional_map, Bialgebra.TensorProduct.lid_symm_apply, LieAlgebra.ad_ker_eq_bot_of_hasTrivialRadical, RatFunc.toFractionRingRingEquiv_symm_eq, Bialgebra.TensorProduct.rid_toCoalgEquiv, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, PreSubmersivePresentation.ofHasCoeffs_algebra_smul, AddMonoidAlgebra.scalarTensorEquiv_tmul, fderiv_csin, Polynomial.shiftedLegendre_eval_symm, PointedCone.mem_maxTensorProduct, MvRatFunc.rank_eq_max_lift, MvPolynomial.aeval_prod, WeakDual.isSeqCompact_polar, Coalgebra.TensorProduct.assoc_toLinearEquiv, MvPolynomial.homogeneousSubmodule_mul, IsCyclotomicExtension.union_right, NumberField.Units.finrank_mul_regulator_eq_det, spectrum.smul_eq_smul, Ideal.IsHomogeneous.mul, IsLocalization.ideal_eq_iInf_comap_map_away, cross_cross_eq_smul_sub_smul', MeasureTheory.isMulRightInvariant_smul_nnreal, rank_lt_rank_dual, RatFunc.aeval_X_left_eq_algebraMap, Matrix.toMvPolynomial_mul, QuadraticForm.tmul_comp_tensorAssoc, Polynomial.Bivariate.pderiv_one_equivMvPolynomial, Module.Dual.congr_apply_apply, LieAlgebra.IsKilling.span_weight_eq_top, Polynomial.residueFieldMapCAlgEquiv_symm_X, MeasureTheory.Measure.instIsCentralScalar, WeierstrassCurve.Projective.smul_fin3_ext, fderiv_cosh, Ideal.spanNorm_mul_of_bot_or_top, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, Representation.dualTensorHom_comm, algebraMap_ofSubring_apply, AdicCompletion.eval_lift_apply, MvPolynomial.exists_restrict_to_vars, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, wittStructureInt_rename, LinearMap.transvection.baseChange, LinearMap.polar_mem_iff, LinearMap.IsContPerfPair.continuous_uncurry, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, skewAdjointMatricesLieSubalgebraEquiv_apply, PolynomialLaw.ground_apply, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, cfcₙL_integrable, Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace, LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe, Subring.isIntegrallyClosedIn_iff, IntermediateField.normalClosure_le_iff_of_normal, PointedCone.dual_flip_dual_dual_flip, instIsPushout, EssFiniteType.cond, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, ProbabilityTheory.mgf_smul_measure, MeasureTheory.isAddLeftInvariant_smul_nnreal, AlgHom.fieldRange_of_normal, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, HasStrictFDerivAt.sinh, LinearMap.toMatrixAlgEquiv_reindexRange, IntermediateField.Lifts.eq_iff, MeasureTheory.Measure.map_right_add_eq_addModularCharacterFun_vadd, IsStandardSmoothOfRelativeDimension.rank_kaehlerDifferential, RootPairing.toLinearMap_apply_apply_mem_range_algebraMap, Ideal.absNorm_relNorm, abs_signedDist_le_dist, ClassGroup.equivPic_apply, NumberField.FinitePlace.norm_le_one, HasFDerivAt.cpow, MvPolynomial.aevalTower_algebraMap, Submodule.mem_div_iff_smul_subset, WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq, NumberField.Units.sum_mult_mul_log, Polynomial.hasFDerivWithinAt, WeierstrassCurve.Projective.add_of_Y_ne, Real.hasStrictFDerivAt_rpow_of_neg, MvPolynomial.optionEquivLeft_elim_eval, FormallySmooth.polynomial, MvPolynomial.optionEquivLeft_symm_X, IsLocalizedModule.map_iso_commute, Subalgebra.LinearDisjoint.leftMulMatrix_basisOfBasisRight_algebraMap, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, MeasureTheory.weightedSMul_smul_measure, MvPolynomial.renameEquiv_symm, MeasureTheory.OuterMeasure.restrict_mono, TensorAlgebra.ofDirectSum_comp_toDirectSum, Int.absNorm_under_eq_sInf, QuadraticForm.tensorComm_symm, Ideal.algebraMap_residueField_eq_zero, LinearMap.flip_surjective_iff₂, Ideal.absNorm_span_singleton, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, Polynomial.expand_aeval, PowerSeries.substAlgHom_comp_substAlgHom_apply, Extension.Hom.id_comp, PowerSeries.weierstrassUnit_smul, FormallyEtale.iff_of_surjective, cfcHom_mono, smoothLocus_eq_compl_support_inter, RCLike.ofRealCLM_coe, IsBaseChange.linearMapRight, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, SubmersivePresentation.cotangentComplex_injective, IntermediateField.normalClosure_map_eq, IsometricContinuousFunctionalCalculus.isometric, MeasureTheory.hausdorffMeasure_homothety_preimage, FractionalIdeal.coeIdeal_absNorm, Module.Basis.repr_unitsSMul, instIsStandardEtaleTensorProduct, matPolyEquiv_coeff_apply_aux_2, Matrix.toLpLin_apply, MeasureTheory.OuterMeasure.smul_dirac_apply, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, IntermediateField.relrank_bot_left, Polynomial.aeval_natCast, ProbabilityTheory.IsGaussian.charFunDual_eq', AlgHom.kerSquareLift_mk, Ideal.dvd_span_singleton, Polynomial.aevalTower_comp_toAlgHom, Polynomial.preimage_eval_singleton, TensorProduct.piScalarRight_tmul_apply, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, MvPolynomial.eval_expand, Matrix.toLin'_apply, CliffordAlgebra.contractRight_ι, LaurentSeries.mem_integers_of_powerSeries, Unitization.algebraMap_eq_inlRingHom, spectrum.units_smul_resolvent, Ideal.map_toCotangent_ker, WeaklyQuasiFiniteAt.baseChange, Ideal.absNorm_algebraMap, Ideal.isCoprime_iff_codisjoint, LieAlgebra.isNilpotent_ad_of_isNilpotent, MvPolynomial.aeval_comp_toMvPolynomial, innerSL_apply_coe, TensorProduct.lidOfCompatibleSMul_tmul, Polynomial.aeval_algHom, Polynomial.coe_aevalAeval_eq_evalEval, Submodule.map_dualCoannihilator_linearEquiv_flip, MvPolynomial.supportedEquivMvPolynomial_symm_C, Polynomial.IsSplittingField.IsScalarTower.splits, PowerBasis.aeval_minpolyGen, MeasureTheory.VAddInvariantMeasure.vadd, LieModule.Weight.toLinear_neg, Ideal.map_pointwise_smul, Polynomial.coe_aeval_eq_evalRingHom, RatFunc.algebraMap_monomial, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, TensorProduct.isPushout', Matrix.det_updateCol_smul_left, MvPowerSeries.monomial_smul_const, AdjoinRoot.coe_algHomOfDvd, MeasureTheory.FiniteMeasure.map_snd_prod, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, LinearMap.BilinForm.SeparatingRight.toMatrix', ENNReal.instMeasurableSMulNNReal, RatFunc.denom_dvd, IntermediateField.isPurelyInseparable_tower_top, instFreeCotangentToExtensionUnitLocalizationAway, AlgebraicGeometry.StructureSheaf.toOpen_res, Polynomial.toLaurentAlg_apply, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', IsSymmetricAlgebra.equiv_toAlgHom, IsAdicComplete.mk_comp_liftRingHom, Polynomial.Monic.free_adjoinRoot, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, MvPolynomial.tensorEquivSum_X_tmul_one, MvPolynomial.instIsMaximalVanishingIdealSingletonForallSet, Submodule.dualQuotEquivDualAnnihilator_symm_apply_mk, Complex.coe_basisOneI, LieSubmodule.coe_baseChange, WeakDual.CharacterSpace.exists_apply_eq_zero, CoalgCat.leftUnitor_def, HasFDerivAt.cosh, IntermediateField.le_normalClosure, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, MeasureTheory.eLpNorm_smul_measure_of_ne_zero', Subspace.map_dualCoannihilator, MvPolynomial.expand_mul_eq_comp, instIsLocalizationAlgebraMapSubmonoid, Subalgebra.LinearDisjoint.adjoin_rank_eq_rank_right, Polynomial.not_weaklyQuasiFiniteAt, Int.cast_mem_ideal_iff, LieAlgebra.Extension.twoCocycleOf_coe_coe, LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, FDRep.scalar_product_char_eq_finrank_equivariant, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, cfcₙHom_of_cfcHom_map_quasispectrum, Ideal.isCoprime_iff_sup_eq, MvPolynomial.eval₂_pUnitAlgEquiv, Ideal.relNorm_map_algEquiv, IntermediateField.equivOfEq_trans, WeakDual.CharacterSpace.compContinuousMap_id, MeasureTheory.OuterMeasure.mkMetric_nnreal_smul, WeierstrassCurve.Affine.CoordinateRing.map_smul, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, convexOn_zpow, SubmersivePresentation.basisCotangent_apply, LinearMap.BilinForm.Nondegenerate.toMatrix, AdicCompletion.tensor_map_id_left_injective_of_injective, MvPowerSeries.expand_mul_eq_comp, Ideal.le_comap_mul, Ideal.mem_span_pow_iff_exists_isHomogeneous, emultiplicity_eq_emultiplicity_span, IntermediateField.normalClosure_def', IsDedekindDomain.exists_sup_span_eq, AlgCat.hom_whiskerRight, LinearMap.BilinForm.congr_symm, TensorProduct.map_bijective, MeasureTheory.withDensity_const, matPolyEquiv_smul_one, autAdjoinRootXPowSubC_root, Matrix.l2_opNorm_def, spectrum.map_polynomial_aeval, IsLocalization.tensorProduct_tensorProduct, MvPolynomial.supported_eq_range_rename, kerTensorProductMapIdToAlgHomEquiv_symm_apply, DoubleQuot.quotLeftToQuotSupₐ_toRingHom, LinearMap.toMatrixAlgEquiv_mul, signedDist_apply_linear, IsArtinianRing.isNilpotent_nilradical, Ideal.ResidueField.liftₐ_algebraMap, MeasureTheory.OuterMeasure.comap_iSup, WeierstrassCurve.Projective.comp_smul, matrixEquivTensor_apply, MvPolynomial.trdeg_of_isDomain, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, Extension.Cotangent.map_mk, MatrixEquivTensor.toFunAlgHom_apply, EssFiniteType.of_id, Extension.CotangentSpace.map_comp, LinearMap.toLinearMap_toPerfPair, PowerSeries.heval_mul, AdicCompletion.eval_surjective, Unitization.quasispectrum_eq_spectrum_inr, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, cardQuot_mul_of_coprime, Polynomial.toAddCircle_C_eq_smul_fourier_zero, RootPairing.corootSpan_dualAnnihilator_map_eq_iInf_ker_coroot', isAdic_iff, MeasureTheory.Measure.singularPart_smul_right, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, norm_innerSL_le, QuasiFinite.instIsArtinianRingFiber, polynomialFunctions_closure_eq_top, AffineSubspace.subtypeₐᵢ_toAffineMap, VectorFourier.hasFDerivAt_fourierChar_smul, IntermediateField.mem_restrict, Ideal.iInf_pow_smul_eq_bot_of_noZeroSMulDivisors, MvPolynomial.aevalTower_id, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, strictConcaveOn_cos_Icc, HasStrictFDerivAt.csinh, MvPowerSeries.comp_substAlgHom, MeasureTheory.OuterMeasure.smul_ofFunction, Pi.constRingHom_eq_algebraMap, Quaternion.hom_ext_iff, IsFractionRing.self_iff_nonZeroDivisors_eq_isUnit, RootPairing.invtSubmodule_reflection_of_invtSubmodule_coreflection, HasFDerivWithinAt.cos, cfcₙHomSuperset_apply, Polynomial.isLocalHom_expand, Real.exists_extension_norm_eq, cfcₙ_apply, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm, NumberField.Units.dirichletUnitTheorem.exists_unit, LaurentPolynomial.toLaurent_reverse, traceForm_toMatrix_powerBasis, Matrix.minpoly_toLin, MvPolynomial.rename_hsymm, normal_self, MeasureTheory.OuterMeasure.map_biInf_comap, MonomialOrder.sPolynomial_decomposition', RCLike.ofRealAm_coe, MvPowerSeries.subst_self, Polynomial.ker_modByMonicHom, Ideal.span_singleton_absNorm_le, SkewMonoidAlgebra.lift_def, Ideal.isCoprime_of_isMaximal, Ideal.Factors.piQuotientEquiv_mk, Matrix.toLin'_toMatrix', ENNReal.instPosSMulStrictMonoNNReal, MvPolynomial.transcendental_supported_X, PowerSeries.smul_inv, IntermediateField.LinearDisjoint.isDomain, ProbabilityTheory.covarianceBilinDual_of_not_memLp', Ideal.finprod_not_dvd, Extension.exact_cotangentComplex_toKaehler, Ideal.natAbs_det_basis_change, instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation, MvPolynomial.aeval_natDegree_le, TensorProduct.lid_toLinearEquiv, Matrix.isIntegral, MeasureTheory.FiniteMeasure.coe_toWeakDualBCNN, QuadraticAlgebra.omega_mul_omega_eq_add, IntermediateField.finrank_dvd_of_le_right, LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero', AdjoinRoot.minpoly_powerBasis_gen_of_monic, qExpansion_smul, MvPolynomial.optionEquivLeft_symm_C_C, Matrix.Represents.algebraMap, Derivation.compAEval_apply, IsLocalRing.finite_quotient_iff, FiniteType.baseChange, Matrix.adjugate_mul, C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum, cfcHom_eq_of_isStarNormal, matPolyEquiv_eq_X_pow_sub_C, leftMulMatrix_eq_repr_mul, Generators.Hom.algebraMap_toAlgHom, ENNReal.toReal_smul, HasGradientWithinAt.hasFDerivWithinAt, MeasureTheory.OuterMeasure.restrict_iInf_restrict, LinearMap.SeparatingLeft.toMatrix₂', LinearMap.isNonneg_zero, Matrix.derivative_det_one_add_X_smul_aux, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, TensorProduct.toMatrix_comm, Bialgebra.mul_compr₂_counit, ContinuousMapZero.coe_toContinuousMapHom, MeasureTheory.eLpNormEssSup_ennreal_smul_measure, TensorProduct.lid_symm_apply, Polynomial.coe_taylorEquiv, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, WittVector.coeff_frobenius, TensorAlgebra.ι_eq_algebraMap_iff, Ergodic.mem_extremePoints, IntermediateField.finrank_le_of_le_right, dualTensorHomEquivOfBasis_apply, NormedSpace.Dual.coe_toWeakDual, LinearMap.polar_mem, NumberField.RingOfIntegers.instIsIntegralClosure, Matrix.aeval_eq_aeval_mod_charpoly, ClassGroup.integralRep_mem_nonZeroDivisors, LinearMap.isAdjointPair_inner, ModuleCat.monoidalClosed_pre_app, Polynomial.aeval_algebraMap_apply, NNReal.strictConcaveOn_rpow, Polynomial.Gal.card_of_separable, PowerSeries.trunc_derivative, MeasureTheory.Measure.isAddLeftInvariant_eq_smul, Generators.basisCotangentAway_apply, Subspace.quotDualCoannihilatorToDual_bijective, Generators.comp_σ, CliffordAlgebraQuaternion.toQuaternion_ι, LieSubmodule.baseChange_top, Ideal.ringChar_quot, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, LinearMap.IsPerfectCompl.flip, Unitization.lift_apply, ProbabilityTheory.setBernoulli_apply, Generators.CotangentSpace.map_ofComp_surjective, Ideal.toCotangent_surjective, edist_smul_le, PiTensorProduct.dualDistrib_dualDistribInvOfBasis_left_inverse, Matrix.kroneckerStarAlgEquiv_apply, LieModule.commute_toEnd_of_mem_center_left, Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂, Submodule.norm_subtypeL_le, LinearEquiv.trans_dualMap_symm_flip, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, Ideal.cotangentIdeal_square, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, Polynomial.mul_contentIdeal_le_radical_contentIdeal_mul, IsDedekindDomain.HeightOneSpectrum.associates_irreducible, isGalois_bot, LinearMap.BilinForm.separatingLeft_toMatrix_iff, MvPolynomial.tensorEquivSum_C_tmul_C, MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, IsAzumaya.matrix, Polynomial.IsDistinguishedAt.algEquivQuotient_apply, IntermediateField.intermediateFieldMap_symm_apply_coe, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, exteriorPower.zeroEquiv_symm_apply, Module.AEval.mem_mapSubmodule_apply, cfcHom_map_spectrum, AlgebraicGeometry.structureSheafInType.smul_apply, Presentation.instFinitePresentationQuotientOfFinite, NumberField.mixedEmbedding.norm_unit, ProbabilityTheory.Kernel.const_comp, Real.volume_preserving_transvectionStruct, ContinuousLinearMap.smulRightL_apply_apply, Representation.asAlgebraHom_mem_of_forall_mem, MvPowerSeries.subst_coe, Quaternion.coe_real_complex_mul, KaehlerDifferential.map_liftBaseChange_smul, ModularFormClass.hasSum_qExpansion, MeasureTheory.OuterMeasure.map_ofFunction_le, Matrix.toLpLinAlgEquiv_symm_apply, Matrix.toBilin'_toMatrix', MvPolynomial.mapEquivMonic_symm_map_algebraMap, WeierstrassCurve.Projective.neg_smul_equiv, LieAlgebra.ad_ker_eq_self_module_ker, minpoly.ker_eval, MeasureTheory.integrable_inv_smul_measure, Generators.Hom.id_comp, Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, AdicCompletion.eval_apply, Polynomial.SplittingField.adjoin_rootSet, MvPolynomial.coe_aeval_eq_eval, FreeAlgebra.hom_ext_iff, Submodule.instSMulCommClassSubtypeMemTorsion', Ideal.map_pow, CliffordAlgebra.contractLeftAux_apply_apply, IsSepClosure.self_of_isSepClosed, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, Int.liesOver_span_absNorm, LinearIsometryEquiv.toContinuousLinearEquiv_smul, IsLocalization.coeSubmodule_sup, AlgebraicGeometry.localRingHom_comp_stalkIso, CliffordAlgebra.ofBaseChange_comp_toBaseChange, Localization.AtPrime.map_eq_maximalIdeal, Real.convexOn_mul_log, Subalgebra.range_algebraMap, isGalois_iff_isGalois_bot, CliffordAlgebra.contractLeft_one, LinearMap.IsPerfPair.flip, FreeAlgebra.algebraMap_leftInverse, LinearMap.toMatrix'_mulVec, AlgebraicIndependent.iff_transcendental_adjoin_image, RootPairing.ker_corootForm_eq_dualAnnihilator, ProbabilityTheory.variance_smul, LaurentPolynomial.invert_C, exists_integral_inj_algHom_of_fg, IsBaseChange.toDualBaseChange_tmul, AlgHom.eq_piEvalAlgHom, IsLocalizedModule.map_LocalizedModules, KaehlerDifferential.quotKerTotalEquiv_apply, Field.insepDegree_le_of_left_le, IntermediateField.finiteDimensional_adjoin_pair, Polynomial.map_aeval_eq_aeval_map, MvPowerSeries.smul_inv, MeasureTheory.integral_smul_measure, summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, Ideal.finite_mulSupport_inv, Polynomial.adjoin_X, Real.strictConcaveOn_negMulLog, MvPowerSeries.substAlgHom_apply, IsDedekindDomain.quotientEquivPiFactors_mk, IntermediateField.normal_sup, IntermediateField.coe_algebraMap_apply, LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero, cfcₙHom_nonneg_iff, Bialgebra.TensorProduct.assoc_symm_tmul, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, NumberField.IsCMField.complexConj_torsion, Polynomial.residueFieldMapCAlgEquiv_algebraMap, Surreal.dyadicMap_apply_pow, Module.AEval.annihilator_eq_ker_aeval, Polynomial.Bivariate.equivMvPolynomial_C_C, FreeAlgebra.algebraMap_eq_zero_iff, dotProduct_toMatrix₂_mulVec, Generators.CotangentSpace.fst_compEquiv, Extension.CotangentSpace.map_comp_apply, Module.End.exists_isNilpotent_isSemisimple, Nat.Partition.multipliable_genFun, AdicCompletion.flat_of_isNoetherian, LieModule.range_traceForm_le_span_weight, separableClosure.isGalois, Localization.awayMap_awayMap_surjective, MeasureTheory.OuterMeasure.map_sup, isTranscendenceBasis_iff_algebraicIndependent_isAlgebraic, Polynomial.aeval_add, Module.End.HasUnifEigenvalue.mem_spectrum, Polynomial.instIsLocalHomRingHomAlgebraMap, Polynomial.continuousOn_aeval, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, MvPowerSeries.substAlgHom_comp_substAlgHom, Bialgebra.TensorProduct.assoc_toAlgEquiv, Polynomial.aeval_sub, Matrix.diagonal_comp_single, FDRep.dualTensorIsoLinHom_hom_hom, IsTranscendenceBasis.polynomial, Generators.H1Cotangent.equiv_apply, TensorPower.toTensorAlgebra_tprod, TensorProduct.rid_symm_apply, LinearMap.IsPerfectCompl.isCompl_left, Real.fourierIntegral_iteratedFDeriv, IntermediateField.restrictScalars_adjoin, HahnSeries.SummableFamily.powerSeriesFamily_smul, ax_grothendieck_zeroLocus, Extension.CotangentSpace.map_comp_cotangentComplex, LinearMap.toMatrixAlgEquiv_transpose_apply, Coalgebra.TensorProduct.lid_symm_apply, Submodule.orthogonalProjection_norm_le, DividedPowers.dpow_smul, IsAdjoinRoot.map_surjective, IntermediateField.finrank_adjoin_simple_eq_one_iff, FractionalIdeal.coe_mk0, ClassGroup.mk_def, Submodule.map_dualAnnihilator_linearEquiv_flip_symm, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, Quaternion.fst_re_dualNumberEquiv_symm, Polynomial.continuousAt_aeval, IsSepClosed.exists_aeval_eq_zero, PowerSeries.derivative_inv, NormedSpace.Dual.toWeakDual_inj, SpecialLinearGroup.coe_dualMap, integralClosure.mem_lifts_of_monic_of_dvd_map, MeasureTheory.Measure.conv_smul_right, PrimeSpectrum.zeroLocus_pow, IntermediateField.isSeparable_tower_top, continuousFunctionalCalculus_map_id, Module.Basis.SmithNormalForm.coord_apply_embedding_eq_smul_coord, Generators.ker_naive, Module.End.eigenspace_aeval_polynomial_degree_1, inv_eq_of_aeval_divX_ne_zero, exists_eq_sum_perm_of_mem_doublyStochastic, Polynomial.exists_monic_aeval_eq_zero_forall_mem_of_mem_map, Quaternion.imI_snd_dualNumberEquiv, one_add_rpow_hasFPowerSeriesOnBall_zero, Polynomial.taylorLinearEquiv_apply_coe, MeasureTheory.Measure.addHaarScalarFactor_smul, MeasureTheory.norm_condExpL2_le_one, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, MonoidAlgebra.mapDomainBialgHom_id, MvPowerSeries.HasSubst.expand, MeasureTheory.OuterMeasure.comap_ofFunction, PowerSeries.derivativeFun_mul, LinearMap.mem_span_iff_continuous, Ideal.Fiber.exists_smul_eq_one_tmul, leftMulMatrix_apply, PowerSeries.coe_substAlgHom, instFreeMvPolynomialKaehlerDifferential, FractionRing.mk_eq_div, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom, Ideal.mapHom_apply, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, WeierstrassCurve.Affine.CoordinateRing.basis_apply, AdicCompletion.ofLinearEquiv_symm_of, MvPolynomial.hom_bind₁, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, LinearMap.BilinForm.toMatrix'_compRight, Ideal.hasBasis_nhds_adic, MvPolynomial.coeff_expand_zero, isBoundedBilinearMap_smulRight, Ideal.relNorm_eq_pow_of_isMaximal, DoubleQuot.coe_liftSupQuotQuotMkₐ, QuaternionAlgebra.imK_swapEquiv_apply, EssFiniteType.baseChange, LocalizedModule.mkLinearMap_apply, MeasureTheory.withDensity_smul', IntermediateField.finiteDimensional_sup, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Extension.Cotangent.ker_mk, IntermediateField.Lifts.le_iff, normalizedTrace_self_apply, Polynomial.aeval_X, Real.rpowIntegrand₀₁_eqOn_mul_rpowIntegrand₀₁_one, WeierstrassCurve.Affine.Point.toClass_apply, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, ContinuousLinearMap.adjoint_innerSL_apply, HasFDerivAt.rpow, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul, polyEquivTensor_symm_apply_tmul_eq_smul, Extension.Hom.toAlgHom_id, MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton, RatFunc.map_apply_div_ne_zero, IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial, trace_adjoinSimpleGen, PowerSeries.derivative_X, AdjoinRoot.mkₐ_toRingHom, Matrix.mvPolynomialX_mapMatrix_aeval, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', Matrix.SeparatingRight.toBilin, Polynomial.IsEisensteinAt.notMem, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, AlgEquiv.eq_linearEquivConjAlgEquiv, IsAdjoinRoot.algEquiv_apply_map, IntermediateField.normal_iff_normalClosure_eq, IntermediateField.rank_adjoin_simple_eq_one_iff, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, CliffordAlgebra.contractLeftAux_contractLeftAux, Module.reflection_mul_reflection_zpow, MvPolynomial.supported_eq_vars_subset, Polynomial.roots_expand_map_frobenius_le, IntermediateField.AdjoinPair.algebraMap_gen₂, AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective, PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, MeasureTheory.llr_smul_left, AdicCompletion.evalₐ_liftRingHom, PrimeSpectrum.nontrivial_iff_mem_rangeComap, NumberField.house.basis_repr_norm_le_const_mul_house, IsAdicComplete.StrictMono.mkQ_comp_lift, SpectrumRestricts.nnreal_iff_nnnorm, TensorProduct.toMatrix_map, Matrix.toLinAlgEquiv_toMatrixAlgEquiv, ProbabilityTheory.convex_integrableExpSet, Matrix.rank_vecMulVec, LinearMap.continuous_uncurry_of_isContPerfPair, Real.strictConcaveOn_qaryEntropy, Polynomial.aeval_homogenize_of_eq_one, LieAlgebra.IsKilling.rootSystem_root_apply, Nat.absNorm_under_prime, MonoidAlgebra.lift_single, AdicCompletion.map_of, NumberField.IsCMField.Units.complexConj_eq_self_iff, Polynomial.toContinuousMapOnAlgHom_apply, IntermediateField.isIntegral_iff, AdjoinRoot.isIntegral_root, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, Matrix.permanent_smul, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, IsAdjoinRoot.ker_map, WeierstrassCurve.Projective.smul_equiv, ContinuousLinearMap.norm_smulRightL_apply, Submodule.torsionBy.mk_smul, MeasureTheory.Measure.map_snd_prod, Extension.Hom.toAlgHom_apply, Orientation.areaForm_rightAngleRotation_left, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, LaurentPolynomial.invert_comp_C, MvPolynomial.rename_eq, Transcendental.integralClosure, HasFDerivWithinAt.sin, H1Cotangent.exact_δ_mapBaseChange, Matrix.toLinAlgEquiv_symm, SchwartzMap.smulLeftCLM_smul, MvPolynomial.totalDegree_coeff_optionEquivLeft_le, MeasureTheory.Measure.singularPart_smul, Module.FinitePresentation.exists_basis_localizedModule_powers, PowerSeries.weierstrassDistinguished_smul, HasStrictFDerivAt.exp, MvPolynomial.derivation_ext_iff, botEquiv_symm_apply, SubmersivePresentation.cotangentEquiv_apply, contractLeft_assoc_coevaluation', FractionalIdeal.coeIdeal_pow, fderiv_norm_sq_apply, AddMonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure, separableClosure.normalClosure_eq_self, LinearMap.toMatrixAlgEquiv_transpose_apply', TensorProduct.dualDistribEquivOfBasis_apply_apply, fderiv_sin, Polynomial.mkDerivation_apply, cfcHom_apply_mem_elemental, FractionalIdeal.count_coe, LieSubalgebra.instIsArtinianSubtypeMem, convexOn_rpow, Matrix.kroneckerStarAlgEquiv_symm_apply, Generators.H1Cotangent.δ_map, Ideal.radical_mul, MvPolynomial.mapEquivMonic_symm_map, Module.dualProdDualEquivDual_symm_apply, MvPolynomial.IsHomogeneous.pderiv, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, Localization.AtPrime.mapPiEvalRingHom_algebraMap_apply, IntermediateField.adjoin.powerBasis_dim, AdicCompletion.of_apply, WittVector.ghostComponentModPPow_map_mk, TensorProduct.AlgebraTensorModule.assoc_eq, LinearMap.exists_map_addHaar_eq_smul_addHaar', Quaternion.exp_eq, PreSubmersivePresentation.baseChange_ring, NormedSpace.dual_def, Nat.Partition.genFun_eq_tprod, QuadraticMap.toMatrix'_smul, IsGalois.of_fixedField_normal_subgroup, Module.instFinitePolynomialAEval', Polynomial.residueFieldMapCAlgEquiv_symm_C, fderiv_norm_sq, exists_mem_doublyStochastic_eq_smul_iff, Seminorm.smul_le_smul, LinearMap.dualProd.toQuadraticForm, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, MeasureTheory.addEquivAddHaarChar_smul_integral_map, WeakDual.CharacterSpace.instStarHomClass, MeasureTheory.Measure.rnDeriv_smul_right_of_ne_top, IntermediateField.AdjoinSimple.algebraMap_gen, SubmersivePresentation.basisDeriv_apply, MvPolynomial.bind₁_monomial, MeasureTheory.OuterMeasure.map_mono, Extension.Cotangent.map_sub_map, Matrix.toBilin_comp, IntermediateField.isPurelyInseparable_sup, PiTensorProduct.instIsScalarTower, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, NumberField.FinitePlace.norm_def, KaehlerDifferential.mulActionBaseChange_smul_tmul, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, Rat.ringOfIntegersWithValEquiv_apply, IntermediateField.splits_of_splits, MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto, FormallySmooth.iff_split_injection, MeasureTheory.Measure.InnerRegularCompactLTTop.smul, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, Ideal.Filtration.submodule_fg_iff_stable, MeasureTheory.OuterMeasure.restrict_le_self, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', MonomialOrder.degree_smul_of_mem_nonZeroDivisors, IsAdicComplete.StrictMono.mk_lift, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, Ideal.relNorm_comap_algEquiv, UniversalEnvelopingAlgebra.lift_ι_apply', ContinuousLinearMap.innerSL_apply_comp, Matrix.SpecialLinearGroup.toLin'_apply, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, ContinuousLinearMap.toSesqForm_apply_norm_le, Smooth.exists_subalgebra_fg, Presentation.mem_ker_naive, MvPolynomial.C_eq_smul_one, PowerSeries.le_order_subst_left, Polynomial.algEquivAevalXAddC_symm, QuadraticAlgebra.coe_dvd_iff, etaleLocus_eq_compl_support, AdjoinRoot.powerBasis_gen, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, IsAlgClosed.exists_aeval_eq_zero, ModuleCat.ihom_ev_app, TensorProduct.adjoin_one_tmul_image_eq_top, Polynomial.expand_injective, LieModule.Weight.instLinearMapClass, Polynomial.coeff_det_X_add_C_zero, TrivSqZeroExt.eq_smul_exp_of_invertible, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, MvPolynomial.esymmAlgHom_surjective, LieModule.Weight.hasEigenvalueAt, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, PointedCone.dual_dual_flip_dual, Ideal.exists_pow_inf_eq_pow_smul, NumberField.mixedEmbedding.convexBodyLT'_convex, TrivSqZeroExt.map_id, Submodule.flip_quotDualCoannihilatorToDual_injective, Extension.H1Cotangent.map_comp, LieRinehartAlgebra.instLieRinehartRingDerivation, instFinitePresentationKaehlerDifferentialOfFinitePresentation, Bundle.ContinuousRiemannianMetric.isVonNBounded, Extension.cotangentComplex_mk, IsLocalizedModule.fromLocalizedModule'_smul, Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct, Subspace.dualPairing_eq, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal, Complex.conjCLE_coe, QuadraticForm.dualProdProdIsometry_invFun, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, MvPolynomial.esymmAlgEquiv_symm_apply, Matrix.Nondegenerate.toLinearMap₂', Subrepresentation.submoduleSubrepresentationOrderIso_symm_apply, Polynomial.map_iterateFrobenius_expand, AlgHom.mulLeftRightMatrix.comp_inv, AdicCompletion.eval_comp_of, Orientation.inner_mul_areaForm_sub, Ideal.to_quotient_square_comp_toCotangent, RatFunc.algebraMap_comp_C, instIsPushoutFractionRingMvPolynomial_1, MvPolynomial.rename_surjective, Icc_subset_segment, KaehlerDifferential.linearCombination_surjective, uniformConvexOn_zero, MeasureTheory.measureReal_nnreal_smul_apply, RatFunc.ofFractionRing_algebraMap, Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂, LieAlgebra.Orthogonal.pd_inv, Ideal.le_comap_pow_ramificationIdx, QuadraticAlgebra.algebraMap_im, Polynomial.eval₂_algebraMap_X, separableClosure.isPurelyInseparable, MvPolynomial.eval₂Hom_comp_expand, LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul, MvPowerSeries.expand_C, Polynomial.toMvPolynomial_C, LinearMap.toMatrixAlgEquiv'_comp, signedDist_vadd_vadd, Ideal.Factors.piQuotientEquiv_map, Nonneg.segment_eq_Icc, instIsStandardOpenImmersionAway, IsStandardSmoothOfRelativeDimension.exists_subalgebra_fg, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_emultiplicity, LieModule.rank_le_natTrailingDegree_charpoly_ad, Presentation.baseChange_toGenerators, derivationQuotKerSq_mk, HasFDerivAt.const_cpow, Subspace.dualEquivDual_apply, LieSubalgebra.coe_ad, IsFractionRing.self_iff_bijective, Polynomial.SplittingField.instNormal, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, HasFDerivWithinAt.cosh, MeasureTheory.Measure.prod_smul_left, Module.Dual.congr_symm_apply_apply, NNReal.Icc_subset_segment, LieModule.toEnd_matrix, Matrix.det_smul_inv_vecMul_eq_cramer_transpose, Generators.Hom.equivAlgHom_apply_coe, LieModule.Weight.toLinear_apply, MvPolynomial.universalFactorizationMapPresentation_jacobian, PointedCone.dual_singleton, Complex.exp_bound_sq, convexOn_norm, Matrix.mul_adjugate, TensorPower.pairingDual_tprod_tprod, Polynomial.add_scaleRoots_of_natDegree_eq, MonoidAlgebra.lift_of, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap, LaurentPolynomial.invert_T, cfc_comp_polynomial, NNReal.concaveOn_rpow, isometry_cfcHom, IntermediateField.adjoin_rootSet_isSplittingField, IsLocalizedModule.iso_mk_one, IntermediateField.nonempty_algHom_adjoin_of_splits, MeasureTheory.Measure.haveLebesgueDecompositionSMul', IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, QuadraticModuleCat.hom_hom_associator, MvPolynomial.esymmAlgHom_injective, Polynomial.C_smul_derivation_apply, HasStrictFDerivAt.rpow_const, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, MvPolynomial.commAlgEquiv_C_X, MvPolynomial.expand_zero_apply, LieModule.toEnd_pow_comp_lieHom, ProbabilityTheory.setBernoulli_eq_map, Polynomial.expand_pow, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', Ideal.span_singleton_mul_le_iff, Polynomial.map_taylorEquiv_degreeLT, WeierstrassCurve.Projective.nonsingular_smul, PowerBasis.liftEquiv_apply_coe, LinearMap.flip.instIsContPerfPair, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, QuadraticAlgebra.algebraMap_injective, IsAzumaya.AlgHom.mulLeftRight_bij, Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap', Matrix.toBilin'_single, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, perfectClosure.isPurelyInseparable, Polynomial.algebraMap_eq, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, MeasureTheory.Measure.bind_const, LinearMap.separatingLeft_dualProd, Polynomial.valuation_X_eq_neg_one, Localization.coe_algEquiv_symm, MvPolynomial.renameSymmetricSubalgebra_apply_coe, IntermediateField.isSeparable_adjoin_iff_isSeparable, TensorProduct.includeRight_lid, MeasureTheory.OuterMeasure.isometryEquiv_comap_mkMetric, FinitePresentation.iff_quotient_mvPolynomial', LieAlgebra.SpecialLinear.sl_non_abelian, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, IsAdjoinRootMonic.modByMonic_repr_map, Polynomial.trdeg_of_isDomain, Quaternion.imK_snd_dualNumberEquiv, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, prod_galRestrict_eq_norm, AdicCompletion.eval_lift, PowerSeries.derivative_pow, MvPolynomial.coe_mapEquivMonic_comp, Ideal.absNorm_dvd_norm_of_mem, instIsPushoutFractionRingMvPolynomial, WeierstrassCurve.Affine.Point.map_id, LaurentPolynomial.involutive_invert, Polynomial.aeval_sumIDeriv_of_pos, MvPolynomial.eval_polynomial_eval_finSuccEquiv, MvPolynomial.constantCoeff_comp_algebraMap, Polynomial.continuousWithinAt_aeval, CliffordAlgebraQuaternion.ofQuaternion_toQuaternion, IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure, MvPolynomial.pderiv_inl_universalFactorizationMap_X, Extension.H1Cotangent.map_toInfinitesimal_bijective, convexOn_iff_slope_mono_adjacent, Extension.Cotangent.val_smul'', SkewMonoidAlgebra.lift_symm_apply, QuadraticModuleCat.hom_inv_associator, LieSubmodule.baseChange_bot, Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra, LeftInvariantDerivation.evalAt_apply, MonoidAlgebra.lift_unique', MvPolynomial.rename_id, MeasureTheory.dirac_withDensity, Real.map_volume_mul_left, Localization.algEquiv_symm_apply, CliffordAlgebra.contractLeft_algebraMap, Matrix.spectrum_toLin', LinearMap.dualAnnihilator_ker_eq_range_flip, AdicCompletion.ofAlgEquiv_symm_of, Derivation.apply_aeval_eq, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, LieSubalgebra.ad_comp_incl_eq, IntermediateField.extendScalars_le_extendScalars_iff, Presentation.tensorModelOfHasCoeffsInv_aeval_val, PowerSeries.trunc_derivative', instFormallyUnramifiedResidueField, Ideal.cotangent_subsingleton_iff, Ideal.mulQuot_injective, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isOpen, RatFunc.toFractionRing_eq, WeierstrassCurve.Projective.dblZ_smul, MvPolynomial.rTensorAlgHom_apply_eq
linearMap 📖	CompOp	45 math math: normalizedTrace_algebraMap_eq_id, idealMap_eq_ofEq_comp_toLocalized₀, PolynomialModule.aeval_equivPolynomial, normalizedTrace_algebraMap, Pi.counit_eq_adjoint, IsLocalizedModule.map_linearMap_of_isLocalization, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Ideal.localized'_eq_map, linearMap_self, LinearMap.toSpanSingleton_one_eq_algebraLinearMap, Submodule.span_algebraMap_image, IsLocalization.mk'_eq_mk', linearMap_apply, KaehlerDifferential.ker_map, IsLocalizedModule.map_linearCombination, instIsLocalizedModuleLinearMapOfIsLocalization, Submodule.span_algebraMap_image_of_tower, toLinearMap_algebraMapCLM, Ideal.localized₀_eq_restrictScalars_map, KaehlerDifferential.kerTotal_map, HopfAlgebra.mul_antipode_rTensor_comul, TensorProduct.Algebra.linearMap_comp_mul', LinearMap.toSpanSingleton_eq_algebra_linearMap, LinearMap.convOne_def, IsIntegralClosure.range_le_span_dualBasis, FractionalIdeal.den_mul_self_eq_num, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, CliffordAlgebra.forall_mul_self_eq_iff, RootPairing.root'_apply_apply_mem_of_mem_span, isLocalizedModule_iff_isLocalization', KaehlerDifferential.ker_map_of_surjective, LinearMap.restrictScalarsField_apply_apply, IsBaseChange.basis_repr_comp, IsBaseChange.linearMap, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, HopfAlgebra.mul_antipode_lTensor_comul, coe_linearMap, Submodule.one_eq_range, LinearMap.IsPerfPair.restrictScalars_of_field, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, algebraMapCLM_toLinearMap, Submodule.localized'_smul, KaehlerDifferential.kerTotal_map', ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_one, Submodule.restrictScalars_localized'_smul
ofModule 📖	CompOp	—
ofModule' 📖	CompOp	—
toModule 📖	CompOp	2859 math math: CommRingCat.tensorProd_map_right, Field.FiniteDimensional.of_exists_primitive_element, CliffordAlgebra.unop_reverseOp, CliffordAlgebra.ι_range_map_map, IsSymmetricAlgebra.lift_eq, TensorProduct.congr_trans, KaehlerDifferential.kerCotangentToTensor_toCotangent, NumberField.basisMatrix_eq_embeddingsMatrixReindex, exists_fg_and_mem_baseChange, CliffordAlgebra.contractRight_algebraMap_mul, LinearMap.restrictScalars_toMatrix, normalizedTrace_map, CliffordAlgebra.toBaseChange_reverse, AlgHom.coe_toLinearMap, FormallyUnramified.one_tmul_mul_elem, Subalgebra.mulMap_comm, TensorAlgebra.ofDirectSum_of_tprod, Bialgebra.comulAlgHom_apply, KaehlerDifferential.mvPolynomialBasis_apply, AlgEquivClass.toLinearEquivClass, Submodule.rTensorOne_symm_apply, Bialgebra.comul_natCast, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, NonUnitalAlgebra.adjoin_le_algebra_adjoin, LinearMap.baseChange_eq_ltensor, normalizedTrace_algebraMap_eq_id, Submodule.mul_one, InfiniteGalois.normal_iff_isGalois, SymmetricAlgebra.lift_ι_apply, Generators.baseChange_val, Ideal.comap_fiberIsoOfBijectiveResidueField_apply, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, idealMap_eq_ofEq_comp_toLocalized₀, CliffordAlgebra.contractRight_algebraMap, IntermediateField.exists_algHom_adjoin_of_splits, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right, ordinaryHypergeometric_sum_eq, AlgEquiv.moduleEndSelfOp_apply_apply, Ideal.selfBasis_def, TensorProduct.instSMulCommClassTensorProduct, TensorProduct.lift_comp_includeLeft, IntermediateField.aeval_gen_minpoly, CliffordAlgebra.contractRight_eq, quasispectrum_eq_spectrum_union, SymmetricAlgebra.rank_eq, IsIntegralClosure.rank, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, AddMonoidAlgebra.domCongr_comp_lsingle, derivationToSquareZeroOfLift_apply, Presentation.differentials.comm₁₂_single, RingHom.SurjectiveOnStalks.baseChange, spectrum_subset_quasispectrum, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, PolyEquivTensor.toFunBilinear_apply_eq_sum, binomialSeries_eq_ordinaryHypergeometricSeries, Polynomial.lcoeff_comp_mapAlgHom_eq, ExteriorAlgebra.GradedAlgebra.liftι_eq, TensorProduct.intCast_def', GradedTensorProduct.hom_ext_iff, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, HopfAlgCat.of_comul, ExteriorAlgebra.ι_eq_algebraMap_iff, TensorProduct.prodRight_tmul_fst, Submodule.algebraMap_mem, FormalMultilinearSeries.ofScalars_apply_eq', AddDissociated.randomisation, CFC.abs_eq_cfc_norm, NumberField.InfinitePlace.sum_mult_eq, NumberField.integralBasis_apply, Ideal.finrank_eq_finrank, CFC.sqrt_eq_one_iff', CFC.posPart_one, MvPolynomial.rTensor_apply_tmul_apply, FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero, Subalgebra.toSubmodule_injective, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, IntermediateField.adjoin.finrank, exteriorPower.basis_apply, CliffordAlgebraQuaternion.j_quaternionBasis, NormedSpace.expSeries_summable_of_mem_ball, FractionalIdeal.fg_of_isUnit, ExteriorAlgebra.ι_inj, Ideal.exists_smith_normal_form, LinearMap.baseChange_smul, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, MvPolynomial.rTensorAlgEquiv_apply, Generators.H1Cotangent.δAux_mul, AlgCat.hom_inv_associator, CliffordAlgebra.changeForm_comp_changeForm, CliffordAlgebra.mul_ι_mul_ι_of_isOrtho, CliffordAlgebra.foldl_prod_map_ι, BialgCat.rightUnitor_def, exteriorPower.linearMap_ext_iff, TrivSqZeroExt.lift_inlAlgHom_inrHom, HopfAlgCat.rightUnitor_def, IsLocalization.coeSubmodule_mul, Module.Flat.toAlgebra_injective, Submodule.mulMap_tmul, FractionalIdeal.isPrincipal_of_isPrincipal_num, IsGalois.card_aut_eq_finrank, TensorProduct.includeLeft_map_center_le, MultilinearMap.mkPiAlgebra_apply, Submodule.comm_trans_lTensorOne, LaurentPolynomial.comul_T, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, normalizedTrace_surjective, normalizedTrace_eq_of_finiteDimensional, MvPolynomial.universalFactorizationMap_comp_map, CommRingCat.pushoutCocone_pt, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, CFC.posPart_natCast, IsFractionRing.coeSubmodule_strictMono, NumberField.canonicalEmbedding.latticeBasis_apply, LinearMap.BilinMap.baseChange_isSymm, KaehlerDifferential.polynomialEquiv_symm, Derivation.coe_to_linearMap_comp, Subalgebra.LinearDisjoint.include_range, LocalizedModule.smul'_mul, Submodule.tensorEquivSpan_apply_tmul, minpoly.algEquiv_apply, LinearMap.baseChange_comp, Ideal.smul_top_eq_map, LinearEquiv.coe_baseChange, AlgHom.coe_addMonoidHom_injective, Ideal.rank_prime_pow_ramificationIdx, NumberField.norm_norm_le_norm_mul_house_pow, IntermediateField.isScalarTower_mid', BialgHom.coe_coalgHom_injective, Submodule.LinearDisjoint.bot_right, Submodule.coe_mapAlgEquiv_symm_apply, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, commBialgCatEquivComonCommAlgCat_unitIso_inv_app, Extension.H1Cotangent.equiv_apply, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', CommAlgCat.braiding_hom_hom, Generators.cotangentSpaceBasis_apply, CliffordAlgebra.involute_prod_map_ι, IsLocalization.coeSubmodule_span, IsAdjoinRootMonic.coeff_apply, CFC.sq_sqrt, BialgEquiv.toHopfAlgIso_refl, Submodule.LinearDisjoint.not_linearIndependent_pair_of_flat_left, ExteriorAlgebra.lift_symm_apply, finrank_quotient_span_eq_natDegree_norm, BialgEquiv.toBialgIso_refl, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, Submodule.mul_comm, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, IsPushout.equiv_symm_algebraMap_left, Bialgebra.TensorProduct.map_toAlgHom, DirectSum.decomposeAlgEquiv_symm_apply, Extension.H1Cotangent.map_id, AlgHom.comp_toLinearMap, IsCyclotomicExtension.finite, ContinuousAlgEquiv.toContinuousLinearMap_toContinuousLinearEquiv_eq, IsIntegral.tensorProduct, CliffordAlgebra.even.lift.aux_mul, LocalizedModule.restrictScalars_map_eq, GradedTensorProduct.tmul_zero_coe_mul_coe_tmul, KaehlerDifferential.mvPolynomialBasis_repr_D_X, Polynomial.fiberEquivQuotient_tmul, exteriorPower.coe_basis, Module.rankAtStalk_eq, TensorProduct.congr_symm_apply, Ideal.ramificationIdx_le_finrank, WeierstrassCurve.Affine.CoordinateRing.basis_one, Submodule.mulMap_one_right_eq, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, exteriorPower.ιMulti_family_linearIndependent_field, Submodule.comap_op_mul, PolynomialLaw.factorsThrough_toFunLifted_π, TensorProduct.toIntegralClosure_bijective_of_isLocalization, traceForm_nondegenerate_tfae, TensorProduct.piScalarRight_symm_algebraMap, trace_eq_of_ringEquiv, FractionalIdeal.fg_unit, Field.Emb.Cardinal.directed_filtration, CategoryTheory.Iso.toHopfAlgEquiv_trans, TensorProduct.mapOfCompatibleSMul_surjective, TensorAlgebra.toTrivSqZeroExt_ι, RCLike.norm_expect_le, lmul_algebraMap, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, TensorAlgebra.ι_comp_lift, IsPushout.cancelBaseChange_tmul, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, ContinuousMultilinearMap.mkPiAlgebra_apply, IsCyclotomicExtension.discr_odd_prime, Ring.instIsTorsionFreeNormalClosure, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, FractionalIdeal.coeIdeal_fg, PolyEquivTensor.right_inv, exteriorPower.basis_repr_ne, IsPurelyInseparable.insepDegree_eq, AddMonoidAlgebra.mapDomainNonUnitalAlgHom_apply, PolynomialModule.aeval_equivPolynomial, TensorAlgebra.adjoin_range_ι, LeftInvariantDerivation.left_invariant', Field.insepDegree_le_rank, Presentation.differentials.comm₂₃, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, FormallyUnramified.lmul_elem, DualNumber.range_lift, Unitization.algHom_ext'_iff, CliffordAlgebraDualNumber.equiv_symm_eps, TensorAlgebra.toDirectSum_tensorPower_tprod, MonoidAlgebra.tensorEquiv.invFun_tmul, ExteriorAlgebra.ιMulti_span_fixedDegree, MonoidAlgebra.antipode_single, KaehlerDifferential.cotangentComplexBaseChange_tmul, Module.Invertible.instTensorProduct_1, Ideal.span_pow_eq_map_homogeneousSubmodule, instIsTorsionFreeCyclotomicFieldOfIsDomainOfIsFractionRing, AlgebraicGeometry.diagonal_SpecMap, ExteriorAlgebra.ι_eq_zero_iff, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, Submodule.comap_op_pow, IsLocalRing.finrank_quotient_map, IsSymmetricAlgebra.equiv_apply, Complex.re_balance, Submodule.mul_one_div_le_one, Ideal.span_eq_map_homogeneousSubmodule, WeakDual.CharacterSpace.apply_mem_spectrum, InfiniteGalois.normalAutEquivQuotient_apply, LeftInvariantDerivation.left_invariant, FractionalIdeal.isFractional_div_of_ne_zero, FormallyUnramified.isOpenImmersion_SpecMap_lmul, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, IsAlgClosure.of_exists_root, LinearMap.baseChange_baseChange, IsAdjoinRootMonic.finrank, AlgEquiv.linearEquivConj_mulLeft, Subalgebra.LinearDisjoint.linearIndependent_mul_of_flat_left, TensorProduct.prodRight_symm_tmul, TensorProduct.tensorTensorTensorComm_symm, IsLocalization.mk'_tmul, IntermediateField.isAlgebraic_tower_bot, CFC.sqrt_rpow, MvPolynomial.algHom_ext'_iff, LinearAlgebra.FreeProduct.mul_injections, Module.FinitePresentation.exists_notMem_bijective, IsPurelyInseparable.finInsepDegree_eq, Extension.formallySmooth_iff_split_injection, TensorProduct.map_comp, UnitAddTorus.mFourierSubalgebra_coe, IntermediateField.botEquiv_symm, AlgCat.hom_inv_rightUnitor, Unitization.starAlgHom_ext_iff, ZMod.dft_mul_const, CliffordAlgebra.contractRight_mul_ι, Submodule.LinearDisjoint.op, CliffordAlgebra.op_reverse, Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct, Field.FiniteDimensional.of_finite_intermediateField, Complex.im_expect, Ideal.inertiaDeg_algebraMap, Bialgebra.TensorProduct.counitAlgHom_def, CliffordAlgebra.reverse_involute_commute, TensorProduct.algebraMap_apply, exteriorPower.ιMulti_family_span_fixedDegree_of_span, KaehlerDifferential.polynomialEquiv_D, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, hasStrictFDerivAt_exp_smul_const_of_mem_ball', NumberField.abs_discr_ge', Submodule.one_le_traceDual_one, Submodule.span_pow, Field.finSepDegree_mul_finInsepDegree, ExteriorAlgebra.liftAlternating_ι_mul, FractionalIdeal.coe_le_coe, smul_leftMulMatrix, Module.rank_baseChange, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, IsPurelyInseparable.finrank_eq_pow, FractionalIdeal.coe_extendedHomₐ_eq_span, Extension.CotangentSpace.map_id, PreSubmersivePresentation.baseChange_jacobian, IsPushout.cancelBaseChange_symm_tmul, CliffordAlgebra.foldr_mul, TensorProduct.piRightHom_mul, WeierstrassCurve.Affine.CoordinateRing.coe_basis, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, algebraMapCLM_coe, Submodule.val_mulMap'_tmul, CliffordAlgebra.equivBaseChange_symm_apply, Module.FaithfullyFlat.instTensorProduct, Smooth.flat, QuotientMapQuotient.isNoetherian, exteriorPower.alternatingMapLinearEquiv_ιMulti, normalizedTrace_comp_algHom, IntermediateField.exists_algHom_of_adjoin_splits, KaehlerDifferential.kerToTensor_apply, CFC.negPart_algebraMap, AlgebraicGeometry.structureSheafInType.mul_apply, IsAlgClosure.of_exist_roots, TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange, IntermediateField.normal_iff_forall_map_eq, instIsLocalRingTensorProductResidueFieldOfIsLocalHomRingHomAlgebraMap, FractionalIdeal.coe_inf, Module.Basis.toMatrix_smul, RingHom.SurjectiveOnStalks.exists_mul_eq_tmul, BialgCat.of_counit, Bialgebra.counitBialgHom_apply, cfcL_apply, TensorProduct.basis_apply, TensorAlgebra.ι_def, LinearMap.liftBaseChange_one_tmul, finite_of_finite_type_of_isJacobsonRing, RCLike.ofReal_balance, lmul_injective, Submodule.one_mem_div, Bialgebra.counitAlgHom_apply, traceMatrix_apply, Ring.choose_eq_smul, toMatrix_rotation, Subalgebra.mulMap_toLinearMap, NumberField.RingOfIntegers.instIsTorsionFree_1, TensorProduct.piScalarRight_tmul, KaehlerDifferential.isScalarTower', AlgHom.mulLeftRightMatrix.inv_comp, Derivation.linearEquiv_coe_to_linearMap_comp, instFiniteResidueFieldOfQuasiFiniteAt, gelfandStarTransform_apply_apply, IntermediateField.restrictScalars_normal, IntermediateField.isScalarTower, BialgCat.associator_def, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, SubmodulesRingBasis.toRing_subgroups_basis, CommBialgCat.id_apply, FormalMultilinearSeries.ofScalars_apply_eq, CliffordAlgebra.toProd_ι_tmul_one, FormallySmooth.adjoin_of_algebraicIndependent, TensorProduct.comm_comp_map_apply, IsAlgClosed.instIsAlgClosure, CliffordAlgebra.changeForm_self_apply, normalizedTrace_algebraMap, isPurelyInseparable_iff_fd_isPurelyInseparable, PolyEquivTensor.toFunAlgHom_apply_tmul, Submonoid.adjoin_eq_span_of_eq_span, WeaklyQuasiFiniteAt.finite_residueField, PolynomialLaw.exists_lift', LinearMap.toMatrix_baseChange, RCLike.ofReal_comp_balance, ContinuousMultilinearMap.norm_mkPiAlgebra_le, Submodule.ker_unitsToPic, BialgCat.whiskerLeft_def, HopfAlgCat.whiskerLeft_def, coeff_minpolyDiv_sub_pow_mem_span, PolynomialLaw.toFun_eq_rTensor_φ_toFun', ContinuousAlgEquiv.toContinuousLinearEquiv_symm, trace_eq_of_algEquiv, PowerBasis.equivAdjoinSimple_symm_aeval, CliffordAlgebra.contractRight_comm, Unitization.starLift_symm_apply_apply, NumberField.instFiniteDimensional, CliffordAlgebra.EquivEven.reverse_e0, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, PowerBasis.map_basis, QuasiFinite.iff_of_isArtinianRing, Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, AddMonoidAlgebra.mapDomainBialgHom_id, Unitization.starLift_apply_apply, IntermediateField.lift_adjoin_simple, traceMatrix_localizationLocalization, ExteriorAlgebra.liftAlternating_comp, algebraicClosure.normalClosure_eq_self, isIntegral_trace, HopfAlgCat.of_counit, IntermediateField.AdjoinDouble.normal_algebraicClosure, IsStandardSmoothOfRelativeDimension.baseChange, Subalgebra.inclusion.isScalarTower_left, coe_algebraMapCLM, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, finrank_algHom, TensorProduct.assoc_tmul, IsAlgebraic.tensorProduct, CliffordAlgebra.changeFormAux_changeFormAux, exteriorPower.ιMulti_span_of_span, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, Subalgebra.comm_trans_rTensorBot, Subalgebra.mulMap_map_comp_eq, CliffordAlgebra.ι_mul_ι_comm, gelfandTransform_bijective, NormedSpace.expSeries_apply_eq_div', NumberField.IsTotallyComplex.finrank, FractionalIdeal.isNoetherian_coeIdeal, AlgEquiv.pow_toLinearMap, KaehlerDifferential.ideal_fg, TensorProduct.map_tmul, TensorProduct.flip_mk_surjective, TensorProduct.toIntegralClosure_bijective_of_smooth, toMatrix_lmul_eq, AlgEquiv.toLinearEquiv_toOpposite, instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, adjoin_span, isGeometricallyReduced_iff, CliffordAlgebra.ι_sq_scalar, Generators.liftBaseChange_injective_of_isLocalizationAway, StarAlgebra.adjoin_nonUnitalStarSubalgebra, intTrace_eq_of_isLocalization, BialgHom.coe_linearMap_injective, exteriorPower.alternatingMapLinearEquiv_symm_map, NumberField.IsTotallyReal.finrank, algebraicClosure.isAlgebraic, trace_algebraMap, Submodule.le_div_iff_mul_le, LinearMap.det_baseChange, exteriorPower.instFree, isBoundedBilinearMap_mul, Submodule.mulMap_comm, IsGalois.normalClosure, FractionalIdeal.isFractional_span_iff, TensorProduct.algEquivIncludeRange_symm_tmul, ExteriorAlgebra.ιMulti_succ_apply, IsUnit.cfcSqrt, Generators.cotangentSpaceBasis_repr_one_tmul, BialgEquiv.refl_symm_apply, IsFractional.inf_right, commBialgCatEquivComonCommAlgCat_unitIso_hom_app, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, TensorProduct.leftComm_tmul, RCLike.wInner_cWeight_eq_expect, IsLocalRing.basisQuotient_repr, IntermediateField.isAlgebraic_iff, MonoidAlgebra.coe_liftNCAlgHom, LocalizedModule.mk_mul_mk, LinearEquiv.det_baseChange, DualNumber.lift_apply_eps, cfcL_integrable, TensorProduct.includeRight_apply, FreeAlgebra.instFree, KaehlerDifferential.instIsScalarTowerTensorProduct, ContinuousAlgEquiv.refl_toContinuousLinearEquiv, CommRingCat.pushoutCocone_inl, CommBialgCat.isoEquivBialgEquiv_apply, Finsupp.linearCombination_one_tmul, ExteriorAlgebra.map_comp_ι, FormalMultilinearSeries.ofScalars_eq_zero, ExteriorAlgebra.ιMulti_span, FormalMultilinearSeries.ofScalars_apply_zero, LocalizedModule.map_surjective, FractionalIdeal.inv_nonzero, IsLocalizedModule.map_linearMap_of_isLocalization, CliffordAlgebra.EquivEven.ι_eq_v_add_smul_e0, IntermediateField.coe_inclusion, CliffordAlgebra.ofBaseChange_toBaseChange, span_le_adjoin, MonoidAlgebra.instIsPushout, HopfAlgCat.Hom.toBialgHom_injective, CliffordAlgebra.foldl_one, Submodule.linearDisjoint_iff, QuadraticForm.polarBilin_baseChange, traceForm_apply, PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, CliffordAlgebra.foldl_mul, GradedTensorProduct.auxEquiv_one, TensorProduct.basis_repr_tmul, CliffordAlgebra.changeFormEquiv_symm, BialgEquivClass.toCoalgEquivClass, Module.finite_iff_isArtinianRing, HopfAlgCat.forget_reflects_isos, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, ContinuousAlgHom.coe_toContinuousLinearMap, AlgHom.toLinearMap_toOpposite, Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap, Field.Emb.Cardinal.two_le_deg, Submodule.mem_div_iff_forall_mul_mem, ExteriorAlgebra.map_comp_ιMulti, exteriorPower.ιMultiDual_apply_diag, SubmersivePresentation.basisKaehlerOfIsCompl_apply, CommBialgCat.ofHom_comp, Polynomial.X_pow_smul_rTensor_monomial, TensorProduct.linearEquivIncludeRange_toLinearMap, FractionalIdeal.div_of_ne_zero, retractionOfSectionOfKerSqZero_comp_kerToTensor, instIsPushoutFractionRingPolynomial_1, KaehlerDifferential.mapBaseChange_tmul, MonoidAlgebra.mapDomainBialgHom_comp, CategoryTheory.Iso.toBialgEquiv_refl, IsCyclotomicExtension.Rat.discr_prime_pow', ExteriorAlgebra.ιMulti_zero_apply, KaehlerDifferential.kerTotal_eq, ContinuousAlgEquiv.trans_toContinuousLinearEquiv, MatrixEquivTensor.invFun_add, LinearMap.baseChange_one, PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks, FractionalIdeal.mem_coeSubmodule, Bialgebra.TensorProduct.map_toCoalgHom, Generators.H1Cotangent.δAux_C, Generators.Hom.toExtensionHom_toAlgHom_apply, NoZeroSMulDivisors.iff_faithfulSMul, CliffordAlgebra.star_def', IntermediateField.minpoly_gen, Field.Emb.Cardinal.isLeast_leastExt, NonUnitalSubalgebra.unitization_injective, IsAdjoinRootMonic.basis_repr, TrivSqZeroExt.fst_expSeries, ContinuousMultilinearMap.mkPiAlgebraFin_apply, Submodule.instSMulCommClass, GradedTensorProduct.tmul_coe_mul_one_tmul, MvPolynomial.sumAlgEquiv_comp_rename_inr, QuasiFiniteAt.exists_fg_and_exists_notMem_and_awayMap_bijective, FormallySmooth.iff_injective_cotangentComplexBaseChange_residueField, FractionalIdeal.coe_pow, IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective, MvPolynomial.aevalTower_toAlgHom, CliffordAlgebra.toBaseChange_comp_ofBaseChange, Subalgebra.mem_toSubmodule, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, HopfAlgebra.sum_mul_antipode_eq_smul, Extension.subsingleton_h1Cotangent, TensorProduct.basisAux_map_smul, LinearMap.convOne_apply, PolynomialLaw.smul_def, traceMatrix_reindex, Subalgebra.range_isScalarTower_toAlgHom, AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType, Localization.algHom_ext_iff, BialgCat.forget_reflects_isos, Extension.CotangentSpace.map_tmul, PiTensorProduct.tprod_prod, Unitization.lift_symm_apply_apply, BialgEquiv.toCoalgEquiv_eq_coe, KaehlerDifferential.polynomialEquiv_comp_D, GradedTensorProduct.tmul_coe_mul_coe_tmul, KaehlerDifferential.span_range_map_derivation_of_isLocalization, Ideal.powQuotSuccInclusion_apply_coe, LaurentPolynomial.antipode_T, PowerBasis.finrank, TensorProduct.lid_tmul, Field.Emb.Cardinal.succEquiv_coherence, TrivSqZeroExt.algHom_ext'_iff, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, discr_powerBasis_eq_norm, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, toSubmodule_bot, LocalizedModule.map_injective, NonUnitalStarSubalgebra.unitization_range, Extension.H1Cotangent.val_zero, CliffordAlgebra.foldr_prod_map_ι, Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv, IsPrimitiveRoot.norm_eq_neg_one_pow, TensorProduct.tensorTensorTensorComm_symm_tmul, SymmetricAlgebra.instModuleFree, directSumGAlgebra_toFun_apply, KaehlerDifferential.mulActionBaseChange_smul_add, TensorProduct.Algebra.smul_def, TensorAlgebra.toExterior_ι, coeSubmodule_differentIdeal, Submodule.LinearDisjoint.not_linearIndependent_pair_of_flat_right, AlgEquiv.trans_toLinearMap, ExteriorAlgebra.liftAlternatingEquiv_symm_apply, Derivation.toFun_eq_coe, TensorProduct.includeLeft_apply, Submodule.map_unop_mul, FormallySmooth.iff_injective_lTensor_residueField, coeSubmodule_differentIdeal_fractionRing, Ideal.Fiber.lift_residueField_surjective, Field.rank_mul_sepDegree_of_isSeparable, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, MonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, spectrum.gelfandTransform_eq, AddMonoidAlgebra.mapDomainBialgHom_mapDomainBialgHom, NonUnitalSubalgebra.unitization_range, FiniteField.algebraMap_trace_eq_sum_pow, CliffordAlgebra.changeFormAux_apply_apply, Module.comap_freeLocus_le, CliffordAlgebra.toBaseChange_comp_involute, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, Derivation.coe_neg_linearMap, FormalMultilinearSeries.ofScalars_series_of_subsingleton, solvableByRad.isSolvable, IsEpi.injective_lift_mul, Unitization.quasispectrum_inr_eq, IntermediateField.linearDisjoint_comm, Module.Basis.localizationLocalization_apply, TensorProduct.right_algebraMap_apply, Bialgebra.TensorProduct.counit_eq_algHom_toLinearMap, CliffordAlgebra.reverse_involute, TensorAlgebra.equivFreeAlgebra_symm_ι, NormedSpace.norm_expSeries_summable, ExteriorAlgebra.GradedAlgebra.ι_sq_zero, NormedSpace.expSeries_sum_eq, BialgCat.Hom.toBialgHom_injective, Ideal.localized'_eq_map, FiniteField.instIsScalarTowerZModExtension, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, CliffordAlgebra.star_def, NumberField.RingOfIntegers.instIsTorsionFree_2, sInf_toSubmodule, Submodule.mul_mem_smul_iff, FormalMultilinearSeries.ofScalars_add, ExteriorAlgebra.lift_comp_ι, IntermediateField.equivOfEq_symm, CliffordAlgebra.evenOdd.gradedMonoid, CFC.sqrt_eq_rpow, Module.FaithfullyFlat.of_comap_surjective, CliffordAlgebraQuaternion.k_quaternionBasis, Submodule.traceDual_top', IntermediateField.restrictRestrictAlgEquivMapHom_apply, instIsPushoutPolynomial_1, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, LinearMap.baseChange_pow, NumberField.canonicalEmbedding.integralBasis_repr_apply, CommRingCat.pushoutCocone_inr, CliffordAlgebra.involute_mem_evenOdd_iff, Polynomial.comap_taylorEquiv_degreeLT, Bialgebra.toLinearMap_counitAlgHom, TensorProduct.Algebra.exists_of_fg, Ideal.map_includeRight_eq, TensorProduct.includeLeft_bijective, Ideal.sum_ramification_inertia, AlgebraicGeometry.pullbackSpecIso_inv_snd, AlgHom.comp_mul', minpoly.degree_le, Subalgebra.centralizer_coe_image_includeRight_eq_center_tensorProduct, IntermediateField.fieldRange_comp_val, LinearAlgebra.FreeProduct.ι_apply, IntermediateField.adjoin.powerBasis_gen, Module.Basis.traceDual_def, FractionalIdeal.fractional_div_of_nonzero, ExteriorAlgebra.liftAlternating_ιMulti, Ideal.card_primesOverFinset_le_finrank, AlgCat.hom_hom_associator, Extension.Hom.comp_id, linearIndependent_algHom_toLinearMap', IntermediateField.equivOfEq_rfl, CliffordAlgebra.changeForm_ι_mul, MonoidAlgebra.scalarTensorEquiv_tmul, finite_of_algHom_finiteType_of_isJacobsonRing, IntermediateField.normal_iff_normalClosure_le, PreSubmersivePresentation.baseChange_toPresentation, Submodule.span_mul_span, LinearMap.iterateFrobenius_def, LinearMap.polyCharpoly_baseChange, CliffordAlgebra.changeForm_self, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Module.Basis.trace_traceDual_mul, Polynomial.aevalTower_toAlgHom, CliffordAlgebraQuaternion.i_quaternionBasis, MatrixEquivTensor.toFunBilinear_apply, Field.Emb.Cardinal.noMaxOrder_rank_toType, Submodule.le_traceDual_traceDual, IsBaseChange.transvection, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, instFiniteResidueFieldOfFormallyUnramified, CommBialgCat.forget₂_commAlgCat_obj, PadicInt.coe_addChar_of_value_at_one, lipschitzGroup.conjAct_smul_ι_mem_range_ι, Subalgebra.finrank_toSubmodule, IsLocalRing.map_tensorProduct_mk_eq_top, Bialgebra.TensorProduct.comulAlgHom_def, GaloisField.finrank, IsLocalization.coeSubmodule_mono, ExteriorAlgebra.liftAlternatingEquiv_apply, HopfAlgCat.MonoidalCategory.inducingFunctorData_εIso, Module.Invertible.embAlgebra_injective, spinGroup.units_involute_act_eq_conjAct, AlgHomClass.linearMapClass, PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_field, IsLocalization.tensorProduct_isLocalizedModule, TensorAlgebra.lift_symm_apply, TensorProduct.map_ker, Subalgebra.isIdempotentElem_toSubmodule, AddMonoidAlgebra.tensorEquiv.invFun_tmul, Complex.re_comp_balance, Submodule.mem_smul_iff_inv_mul_mem, Module.finite_of_isSemisimpleRing, TensorProduct.includeRight_map_center_le, MatrixEquivTensor.invFun_algebraMap, TensorProduct.productMap_left_apply, TensorProduct.instSMulCommClassTensorProduct_1, TensorProduct.algebraMap_eq_includeRight, Bialgebra.counitBialgHom_self, Submodule.surjective_tensorToSpan, CommRingCat.coproductCocone_inl, PolyEquivTensor.toFunLinear_mul_tmul_mul, IsAdjoinRootMonic.finite, FractionalIdeal.coe_nsmul, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, IntermediateField.relfinrank_dvd_finrank_bot, IsIntegral.finite, NumberField.Units.finrank_mul_regOfFamily_eq_det, KaehlerDifferential.tensorKaehlerEquivBase_tmul, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, span_coeff_minpolyDiv, FormalMultilinearSeries.ofScalars_sub, IsCyclotomicExtension.finite_of_singleton, NormedSpace.expSeries_hasSum_exp, ContinuousAlgEquiv.toContinuousLinearEquiv_apply, AlgebraicGeometry.pullbackSpecIso_hom_base, PowerBasis.coe_basis, traceForm_toMatrix, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, IsLocalization.coeSubmodule_bot, IsFractional.mul, KaehlerDifferential.isLocalizedModule_map, DualNumber.lift_inlAlgHom_eps, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, TensorProduct.productMap_left, IntermediateField.adjoin_simple_adjoin_simple, RingHom.smulOneHom_eq_algebraMap, CFC.posPart_algebraMap_nnreal, spinGroup.conjAct_smul_ι_mem_range_ι, LeftInvariantDerivation.evalAt_coe, TensorProduct.includeLeftRingHom_comp_algebraMap, hasStrictFDerivAt_exp_smul_const', GradedTensorProduct.auxEquiv_symm_one, FractionalIdeal.coe_natCast, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, NumberField.det_basisOfFractionalIdeal_eq_absNorm, GradedTensorProduct.auxEquiv_comm, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, Field.Emb.cardinal_eq_of_isSeparable, Subalgebra.isScalarTower_right, IntermediateField.AdjoinSimple.norm_gen_eq_one, TensorAlgebra.equivFreeAlgebra_ι_apply, TensorProduct.productMap_apply_tmul, LinearMap.BilinForm.tensorDistrib_tmul, AdjoinRoot.mk_leftInverse, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, CliffordAlgebra.coe_toEven_reverse_involute, IntermediateField.range_val, IntermediateField.instFiniteSubtypeMemBot, IntermediateField.isCyclotomicExtension_lcm_sup, QuadraticForm.baseChange_tmul, PolynomialLaw.toFun_add_apply, KaehlerDifferential.End_equiv_aux, AlgEquiv.card_le, Module.Basis.trace_mul_traceDual, AddChar.expect_apply_eq_zero_iff_ne_zero, CliffordAlgebra.ι_mul_ι_mul_ι, Extension.instIsScalarTowerRing, Complex.ofReal_balance, IntermediateField.linearDisjoint_iff', IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, top_toSubmodule, AlgHom.coe_tensorEqualizer, Submodule.one_le_one_div, IntermediateField.splits_iff_mem, CliffordAlgebra.EvenHom.compr₂_bilin, LinearMap.toSpanSingleton_one_eq_algebraLinearMap, TensorProduct.toIntegralClosure_mvPolynomial_bijective, spinGroup.involute_act_ι_mem_range_ι, PowerSeries.substAlgHom_comp_substAlgHom, Module.rankAtStalk_baseChange, CliffordAlgebra.reverse_comp_reverse, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_apply, exteriorPower.finrank_eq, TensorProduct.lmul'_apply_tmul, Quaternion.expSeries_odd_of_imaginary, linearIndependent_algHom_toLinearMap, TensorAlgebra.lift_ι_apply, CommBialgCat.bialgEquivOfIso_apply, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, Submodule.span_singleton_algebraMap_of_isUnit, normalizedTrace_intermediateField, TensorAlgebra.instModuleFree, LinearMap.BilinForm.tensorDistribEquiv_apply, KaehlerDifferential.span_range_derivation, linearIndependent_toLinearMap, Generators.H1Cotangent.exact_map_δ, Generators.H1Cotangent.δAux_monomial, trace_isNilpotent_of_isNilpotent, TrivSqZeroExt.map_comp_inrHom, CliffordAlgebra.adjoin_range_ι, CliffordAlgebra.changeFormEquiv_apply, PowerBasis.constr_pow_algebraMap, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, TensorProduct.includeLeft_injective, TensorAlgebra.rank_eq, Generators.CotangentSpace.compEquiv_symm_zero, AlgHom.toLinearMap_apply, spinGroup.conjAct_smul_range_ι, CliffordAlgebra.EquivEven.neg_e0_mul_v, isNormalClosure_normalClosure, AlgHom.toNonUnitalAlgHom_eq_coe, CFC.sqrt_eq_one_iff, CategoryTheory.Iso.toBialgEquiv_trans, Generators.cotangentSpaceBasis_repr_tmul, IntermediateField.finrank_eq_one_iff, IntermediateField.lift_top, RingHom.SurjectiveOnStalks.tensorProductMap, BialgCat.of_comul, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Derivation.leibniz', ordinaryHypergeometricSeries_apply_eq', HopfAlgCat.whiskerRight_def, Submodule.LinearDisjoint.one_left, CliffordAlgebra.range_ι_le_evenOdd_one, Generators.Hom.comp_id, LinearMap.liftBaseChangeEquiv_symm_apply, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, CommAlgCat.lift_unop_hom, WeaklyQuasiFiniteAt.finite_locoalization, TensorProduct.equivFinsuppOfBasis_apply, exteriorPower.map_apply_ιMulti_family, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, instFiniteOfIsQuadraticExtension, isNilpotent_trace_of_isNilpotent, ExteriorAlgebra.ιMulti_range, PrimeSpectrum.mem_image_comap_basicOpen, IntermediateField.exists_algHom_adjoin_of_splits_of_aeval, differentialIdeal_le_iff, CommRingCat.isPushout_tensorProduct, TensorProduct.opAlgEquiv_apply, Bialgebra.counit_surjective, PolynomialLaw.π_surjective, AlgebraicIndependent.lift_reprField, Extension.Hom.sub_one_tmul, cfcₙHom_eq_cfcₙHom_of_cfcHom, GradedAlgebra.proj_recompose, HopfAlgCat.MonoidalCategory.inducingFunctorData_μIso, LinearMap.BilinForm.IsSymm.baseChange, RingEquivClass.toLinearEquivClassRat, DualNumber.lift_smul, IntermediateField.isAlgebraic_adjoin, TensorProduct.equivFinsuppOfBasis_symm_apply, gelfandTransform_map_star, MvPolynomial.rTensor_apply_X_tmul, FiniteType.baseChangeAux_surj, instIsLiouvilleSubtypeMemIntermediateField, TensorProduct.lmulEquiv_eq_lidOfCompatibleSMul, KaehlerDifferential.exact_mapBaseChange_map, FormallySmooth.flat_of_algHom_of_isNoetherianRing, CommAlgCat.binaryCofan_pt, LinearMap.tensorProductEnd_apply, Bialgebra.TensorProduct.assoc_tmul, KaehlerDifferential.tensorKaehlerEquiv_tmul, AlgEquiv.toLinearEquiv_symm, Generators.H1Cotangent.δAux_toAlgHom, AlgEquiv.toLinearMap_injective, exteriorPower.zeroEquiv_naturality, FractionalIdeal.div_nonzero, fdifferential_apply, KaehlerDifferential.D_apply, CliffordAlgebra.EquivEven.e0_mul_v_mul_e0, IsSymmetricAlgebra.equiv_symm_comp, CliffordAlgebraComplex.ofComplex_I, HopfAlgCat.toBialgHom_comp, Submodule.span_algebraMap_image, BialgEquiv.invFun_eq_symm, Ideal.ResidueField.liftₐ_comp_toAlgHom, IsLocalization.mk'_eq_mk', BialgCat.forget₂_coalgebra_obj, TensorAlgebra.toClifford_ι, CliffordAlgebra.hom_ext_iff, FractionalIdeal.coeToSubmodule_eq_bot, Unitary.conjStarAlgAut_ext_iff', GroupLike.valMonoidHom_apply, AddMonoidAlgebra.mapDomainBialgHom_apply, IsLocalization.Away.tensorRight, linearMap_apply, ExteriorAlgebra.liftAlternating_apply_ιMulti, PowerBasis.equivAdjoinSimple_aeval, PolynomialLaw.exists_lift, rank_polynomial_polynomial, IntermediateField.isPurelyInseparable_tower_bot, CommRingCat.coproductCocone_inr, le_separableClosure_iff, exteriorPower.ιMulti_span_fixedDegree_of_span_eq_top, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, CommRing.Pic.mapAlgebra_apply, IsCyclotomicExtension.finrank, traceForm_dualSubmodule_adjoin, FractionalIdeal.adjoinIntegral_coe, FractionalIdeal.coe_dual_one, polyEquivTensor_symm_apply_tmul, AlgebraicGeometry.pullbackSpecIso_inv_fst'_assoc, Ideal.quotientToQuotientRangePowQuotSucc_mk, CliffordAlgebra.one_le_evenOdd_zero, Module.finite_of_isArtinianRing, Subalgebra.mul_toSubmodule, Unitization.starLift_range, adjoin_nonUnitalSubalgebra_eq_span, Module.support_of_algebra, IsAdjoinRootMonic.modByMonicHom_map, KaehlerDifferential.one_smul_sub_smul_one_mem_ideal, Ideal.finrank_prime_pow_ramificationIdx, Extension.CotangentSpace.map_toInfinitesimal_bijective, IsAzumaya.mulLeftRight_comp_congr, TensorProduct.algebraMap_def, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, HopfAlgCat.associator_def, IsFractional.sup, KaehlerDifferential.range_mapBaseChange, SubmersivePresentation.sectionCotangent_eq_iff, rank_le_of_surjective_injective, eq_separableClosure_iff, Generators.Hom.toExtensionHom_id, LinearMap.BilinForm.mem_dualSubmodule, TensorProduct.includeRight_injective, TensorAlgebra.lift_comp_ι, RingOfIntegers.norm_algebraMap, GradedTensorProduct.tmul_one_mul_coe_tmul, MvPolynomial.tensorEquivSum_one_tmul_C, CFC.abs_natCast, CliffordAlgebra.submodule_comap_mul_reverse, PowerBasis.trace_gen_eq_nextCoeff_minpoly, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, MvPolynomial.rTensor_apply_tmul, CliffordAlgebra.invOf_ι_mul_ι_mul_ι, CliffordAlgebra.EvenHom.contract, AlgHom.mulLeftRight_apply, TensorProduct.commRight_tmul, IntermediateField.normal_iff_forall_fieldRange_le, IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one, CliffordAlgebra.map_apply_ι, exteriorPower.ιMulti_apply_coe, TensorAlgebra.ι_range_disjoint_one, FiniteField.finrank_zmod_extension, CliffordAlgebra.submodule_map_pow_reverse, Submodule.coe_tensorSpanEquivSpan_apply_tmul, TensorProduct.lmul'_comp_map, LinearEquiv.baseChange_mul, PowerBasis.mem_span_pow', IsAzumaya.bij, QuasiFinite.baseChange, Generators.H1Cotangent.exact_δ_map, IsGalois.normalAutEquivQuotient_apply, PowerBasis.repr_gen_pow_isIntegral, IsGalois.normalBasis_apply, Generators.cotangentCompLocalizationAwayEquiv_symm_comp_inl, Derivation.liftKaehlerDifferential_comp, CliffordAlgebra.ι_mul_ι_add_swap, kroneckerTMulLinearEquiv_one, Complex.det_conjAe, ContinuousFunctionalCalculus.toNonUnital, KaehlerDifferential.ker_map, TensorProduct.lift_comp_includeRight, AlgHom.toKerIsLocalization_apply, IsAzumaya.toProjective, NonUnitalSubalgebra.coe_sub, KaehlerDifferential.mapBaseChange_surjective, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, IsLocalization.mk'_algebraMap_eq_mk', IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, LeftInvariantDerivation.left_invariant'', ordinaryHypergeometricSeries_apply_zero, CliffordAlgebra.contractLeft_contractLeft, PolynomialLaw.toFun_zero, Subalgebra.centralizer_coe_map_includeRight_eq_center_tensorProduct, trace_eq_finrank_mul_minpoly_nextCoeff, MonoidAlgebra.tensorEquiv_symm_single, NormedSpace.norm_expSeries_summable_of_mem_ball, Field.Emb.Cardinal.strictMono_leastExt, IntermediateField.rank_adjoin_eq_one_iff, GroupLike.val_one, binomialSeries_apply, SubMulAction.algebraMap_mem, LinearMap.toMvPolynomial_baseChange, CliffordAlgebra.evenOdd_map_reverse, TensorProduct.map_id, IsQuadraticExtension.finrank_eq_two', Submodule.map_unop_pow, rank_le_of_injective_injective, BialgEquiv.trans_apply, Bialgebra.comul_algebraMap, NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, AlgCat.hom_hom_rightUnitor, LocalizedModule.coe_map_eq, NonUnitalSubalgebra.toSubring_subtype, FractionalIdeal.isFractional_adjoin_integral, TensorProduct.isField_of_isAlgebraic, CyclotomicRing.instIsTorsionFreeOfIsDomainOfIsFractionRing, Extension.CotangentSpace.map_sub_map, exteriorPower.oneEquiv_naturality, ExteriorAlgebra.ι_range_disjoint_one, IsHausdorff.map_algebraMap_iff, normalizedTrace_eq_of_fininteDimensional, hasFDerivAt_exp_smul_const', FormalMultilinearSeries.ofScalars_norm_le, CliffordAlgebra.contractLeft_ι_mul, PolynomialLaw.zero_def, FormallySmooth.instTensorProduct, IntermediateField.finrank_eq_fixingSubgroup_index, FractionalIdeal.fg_of_isNoetherianRing, CliffordAlgebra.comp_ι_sq_scalar, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, isLocalizedModule_iff_isLocalization, mem_integralClosure_iff_mem_fg, IsLocalizedModule.map_linearCombination, LinearMap.BilinMap.baseChange_tmul, FiniteField.algebraMap_norm_eq_prod_pow, HopfAlgebra.sum_antipode_mul_eq_smul, addMonoidAlgebraAlgEquivDirectSum_symm_apply, trace_eq_trace_adjoin, CliffordAlgebra.even.lift_ι, CliffordAlgebra.ι_range_map_reverse, FormallyEtale.instTensorProduct, Module.instFiniteSubtypeMemIdealOfIsNoetherian, embeddingsMatrixReindex_eq_vandermonde, TensorProduct.congr_toLinearEquiv, MonoidAlgebra.mapDomainBialgHom_apply, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, Submodule.setLike.coe_galgebra_toFun, Extension.Hom.toRingHom_algebraMap, isPushout_iff, BialgCat.tensorHom_def, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, NumberField.Embeddings.card, TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul, FractionalIdeal.mul_generator_self_inv, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, BialgHom.toAlgHom_toLinearMap, InfiniteGalois.proj_adjoin_singleton_val, CliffordAlgebra.contractRight_mul_algebraMap, Submodule.baseChange_bot, IntermediateField.lift_inf, CommBialgCat.reflectsIsomorphisms_forget, CliffordAlgebra.ι_range_map_involute, QuasiFinite.finite_fiber, FractionalIdeal.coe_mk, Submodule.comm_trans_rTensorOne, QuasiFinite.instFiniteResidueField, BialgCat.forget₂_algebra_map, IsFractional.div_of_nonzero, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, instIsLocalizedModuleLinearMapOfIsLocalization, NumberField.InfinitePlace.card_isUnramified, NormedSpace.expSeries_apply_eq, Field.rank_mul_insepDegree_of_isPurelyInseparable, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, ExteriorAlgebra.liftAlternating_one, Derivation.commutator_coe_linear_map, sum_embeddings_eq_finrank_mul, TensorProduct.instFree, IsAlgebraic.instIsLocalizedModuleNonZeroDivisorsToLinearMapToAlgHom, pinGroup.conjAct_smul_ι_mem_range_ι, DirectSum.coeAlgHom_of, Submodule.prod_span, AlgebraicGeometry.StructureSheaf.const_one, IntermediateField.exists_algHom_of_splits, FiniteField.instFiniteExtension_1, TensorProduct.isPushout, Subalgebra.adjoin_eq_span_basis, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, PowerBasis.equivAdjoinSimple_gen, RingHom.toKerIsLocalization_apply, WeakDual.CharacterSpace.toAlgHom_apply, Derivation.coe_comp, TensorProduct.leftComm_toLinearEquiv, AlgEquiv.coe_symm_toLinearEquiv, CommBialgCat.inv_hom_apply, Field.Emb.Cardinal.equivSucc_coherence, LinearEquiv.baseChange_tmul, AlgHom.toLinearMap_injective, Ideal.ResidueField.exists_smul_eq_tmul_one, map_equiv_traceDual, IntermediateField.restrictScalars_adjoin_eq_sup, IsIntegralClosure.finite, BialgEquiv.toBialgIso_symm, Subalgebra.LinearDisjoint.trace_algebraMap, FiniteGaloisIntermediateField.isGalois, Submodule.mem_mul_span_singleton, NonUnitalStarSubalgebra.unitization_injective, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, NonUnitalStarSubalgebra.unitization_apply, NumberField.to_finiteDimensional, TensorProduct.congr_apply, cfcHom_real_eq_restrict, TensorProduct.AlgebraTensorModule.dualDistrib_apply, Submodule.prod_span_singleton, IntermediateField.Lifts.lt_iff, IsCyclotomicExtension.Rat.discr_prime_pow_ne_two', CliffordAlgebra.GradedAlgebra.ι_apply, IntermediateField.extendScalars_le_iff, TensorProduct.toLinearEquiv_tensorTensorTensorComm, Polynomial.aeval_eq_smeval, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Generators.snd_comp_cotangentCompLocalizationAwayEquiv, finrank_of_isSplittingField_X_pow_sub_C, GradedTensorProduct.auxEquiv_mul, Submodule.lTensorOne'_tmul, Submodule.equivOpposite_apply, HopfAlgCat.forget₂_bialgebra_obj, MvPolynomial.rTensorAlgHom_toLinearMap, Submodule.rTensorOne'_tmul_one, DirectSum.decompose_symm_algebraMap, FractionalIdeal.coe_add, coe_polyEquivTensor'_symm, baseChange_ext_iff, trace_self, Finset.expect_boole_mul', Splits.algebraicClosure, PowerBasis.equivAdjoinSimple_symm_gen, Subbimodule.coe_mk, Extension.CotangentSpace.map_cotangentComplex, CFC.abs_algebraMap, IntermediateField.coe_val, Submodule.rTensorOne'_tmul, Ideal.relNorm_algebraMap', CliffordAlgebra.reverse.map_mul, Localization.finite_of_primesOver_eq_singleton, Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, HomogeneousLocalization.Away.span_mk_prod_pow_eq_top, TensorProduct.basisAux_tmul, Submodule.projective_units, KaehlerDifferential.derivationQuotKerTotal_apply, MvPolynomial.algebraTensorAlgEquiv_symm_X, ExteriorAlgebra.ι_sq_zero, Subalgebra.mul_toSubmodule_le, instIsMonHomOppositeCommAlgCatOpOfHomToAlgHomBialgHom, isNoetherian_of_liesOver, Submodule.LinearDisjoint.injective, Submodule.baseChange_eq_span, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, TrivSqZeroExt.liftEquiv_apply, CliffordAlgebra.isUnit_ι_iff, RingHomClass.toLinearMapClassRat, IsStandardSmooth.baseChange, FractionalIdeal.isPrincipal_iff, Matrix.kroneckerTMulAlgEquiv_symm_apply, Quaternion.expSeries_even_of_imaginary, Derivation.liftKaehlerDifferential_comp_D, coe_polyEquivTensor', Module.Flat.instSubalgebraToSubmodule, Unramified.baseChange, Polynomial.IsSplittingField.instIsTorsionFreeSplittingField, AlgebraicClosure.instIsAlgClosure, IsStrictlyPositive.nnrpow, Submodule.span_algebraMap_image_of_tower, NumberField.InfinitePlace.card_isUnramified_compl, trace_prod, Submodule.coe_mapAlgEquiv_apply, Ideal.relNorm_int, IntermediateField.finrank_eq_finrank_subalgebra, MvPolynomial.coeffsIn_mul, Matrix.kroneckerTMulStarAlgEquiv_apply, FractionalIdeal.coe_inv_of_ne_zero, lift_rank_eq_of_equiv_equiv, Transcendental.rank_eq_cardinalMk, instFiniteResidueFieldOfIsUnramifiedAt, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, AddMonoidAlgebra.instIsPushout, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', TensorProduct.includeRight_bijective, NormedSpace.expSeries_apply_eq_div, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, AlgEquiv.symm_toAddEquiv, IntermediateField.restrictRestrictAlgEquivMapHom_injective, exteriorPower.alternatingMapLinearEquiv_apply_ιMulti, Generators.H1Cotangent.δAux_ofComp, CliffordAlgebra.changeForm_ι_mul_ι, FractionalIdeal.isNoetherian_zero, adjoin_toSubmodule_le, TensorProduct.nontrivial_of_algebraMap_injective_of_isDomain, PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks_aux, IsLocalization.coeSubmodule_le_coeSubmodule, Submodule.map_op_pow, Submodule.injective_tensorToSpan, IsCyclotomicExtension.discr_prime_pow_ne_two, PiTensorProduct.singleAlgHom_apply, AlgebraicGeometry.pullbackSpecIso_inv_fst, AlgCat.hom_inv_leftUnitor, Presentation.differentials.comm₂₃', NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, CommBialgCat.hom_inv_apply, exteriorPower.ιMultiDual_apply_ιMulti, normalizedTrace_algebraMap_apply_eq_self, Module.Finite.of_isLocalization, CliffordAlgebra.EquivEven.neg_v_mul_e0, PiTensorProduct.dualDistribEquivOfBasis_apply_apply, MvPolynomial.le_coeffsIn_pow, Polynomial.Monic.finite_adjoinRoot, Submodule.LinearDisjoint.map, module_finite_of_liesOver, CliffordAlgebra.ι_range_comap_involute, AddMonoidAlgebra.instIsPushout', Module.Basis.baseChange_end, LinearAlgebra.FreeProduct.identify_one, IntermediateField.finrank_adjoin_eq_one_iff, TensorProduct.lid'_apply_tmul, TensorProduct.liftEquiv_apply, CliffordAlgebra.reverse_prod_map_ι, KaehlerDifferential.instSMulCommClassTensorProduct_1, IsGaloisGroup.finiteDimensional, IntermediateField.normal_iff_forall_map_le', Submodule.restrictScalars_traceDual, FractionalIdeal.coe_one, NumberField.RingOfIntegers.rank, IntermediateField.normal_iff_forall_fieldRange_eq, Module.Basis.baseChange_apply, FreeAlgebra.toTensor_ι, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent, TensorProduct.not_isField_of_transcendental, NumberField.integralBasis_repr_apply, Field.finSepDegree_le_finrank, exteriorPower.ιMulti_family_eq_coe_comp, exteriorPower.pairingDual_ιMulti_ιMulti, ExteriorAlgebra.map_apply_ι, BialgHomClass.counitAlgHom_comp, BialgEquiv.toCoalgEquiv_toCoalgHom, TensorProduct.productMap_range, Submodule.mulRightMap_eq_mulMap_comp, TensorProduct.basis_repr_symm_apply', ExteriorAlgebra.ι_leftInverse, kroneckerTMulLinearEquiv_mul, trace_comp_trace_of_basis, exteriorPower.alternatingMapLinearEquiv_comp_ιMulti, differentialIdeal_le_fractionalIdeal_iff, AlgEquiv.toLinearMapHom_apply_apply, toLinearMap_algebraMapCLM, IntermediateField.finrank_bot, LinearEquiv.baseChange_zpow, Ideal.quotientToQuotientRangePowQuotSucc_surjective, NormedSpace.expSeries_apply_zero, Bialgebra.TensorProduct.rid_toAlgEquiv, RCLike.wInner_cWeight_const_left, CliffordAlgebra.contractLeft_comm, InfiniteGalois.restrict_fixedField, AlgHom.natCard_of_splits, AdjoinRoot.modByMonicHom_mk, FractionalIdeal.mem_dual, TensorProduct.productMap_eq_comp_map, trace_self_apply, Ideal.localized₀_eq_restrictScalars_map, CliffordAlgebra.ofBaseChange_tmul_ι, DirectSum.decompose_algebraMap, Submodule.mul_smul_mul_eq_smul_mul_smul, IntermediateField.sepDegree_bot, ContinuousMultilinearMap.norm_mkPiAlgebra, CliffordAlgebra.reverse_reverse, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, KaehlerDifferential.tensorKaehlerEquiv_left_inv, CategoryTheory.Iso.toBialgEquiv_symm, trace_eq_sum_roots, TensorProduct.rid_tmul, mem_quasispectrum_iff, normalizedTrace_self, CliffordAlgebra.foldl_algebraMap, CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero, PowerBasis.mem_span_pow, Submodule.rTensorOne_tmul, TensorProduct.lmul'_comp_includeRight, trace_trace, PowerBasis.constr_pow_gen, IsBaseChange.equiv_symm_apply, norm_eq_norm_adjoin, pushoutDesc_apply, AddChar.expect_eq_zero_iff_ne_zero, TensorProduct.cancelBaseChange_tmul, Submodule.singleton_smul, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, Submodule.unitsToPic_apply, TensorProduct.map_comp_id, KaehlerDifferential.kerTotal_map, IntermediateField.restrictScalars_bot_eq_self, Submodule.coe_mulMap_comp_eq, Complex.ofReal_comp_balance, functionField_iff, Bialgebra.counit_natCast, exteriorPower.oneEquiv_symm_apply, IsAdjoinRootMonic.ext_elem_iff, Module.FinitePresentation.iff_finitePresentation_of_finite, Polynomial.taylorAlgHom_apply, LinearAlgebra.FreeProduct.ι_def, Field.finSepDegree_eq_finrank_of_isSeparable, PowerBasis.toMatrix_isIntegral, Submodule.range_unitsToPic, traceForm_isSymm, AlgCat.hom_hom_leftUnitor, Ideal.relNorm_algebraMap, Extension.H1Cotangent.equivOfFormallySmooth_apply, IsUnit.cfcNNRpow, Submodule.spanSingleton_apply, TensorProduct.mk_one_injective_of_isScalarTower, FractionalIdeal.coe_mul, IsSymmetricAlgebra.equiv_symm_apply, CliffordAlgebra.ofBaseChangeAux_ι, Unitary.toAlgEquiv_conjStarAlgAut, BialgEquiv.toHopfAlgIso_symm, Unitization.lift_range, CommAlgCat.tensorHom_hom, PolynomialLaw.one_tmul_ground, inf_toSubmodule, Bialgebra.comul_mul, Derivation.liftKaehlerDifferential_unique_iff, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, CommAlgCat.coe_tensorObj, Module.Basis.localizationLocalization_repr_algebraMap, exteriorPower.map_comp_ιMulti, Derivation.liftKaehlerDifferential_D, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, Ideal.basisSpanSingleton_apply, instIsLocalizedModuleToLinearMapToAlgHomOfIsLocalizationAlgebraMapSubmonoid, tensorKaehlerQuotKerSqEquiv_tmul_D, HopfAlgebra.mul_antipode_rTensor_comul, PowerBasis.basis_eq_pow, BialgHom.coe_toLinearMap, Complex.coe_basisOneI_repr, FractionalIdeal.mul_def, ExteriorAlgebra.instGradedMonoidNatSubmoduleExteriorPower, Ideal.finrank_quotient_map, FormallyUnramified.one_tmul_sub_tmul_one_mul_elem, QuadraticForm.tensorDistrib_tmul, ExteriorAlgebra.ι_add_mul_swap, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left, FractionalIdeal.coeSubmoduleHom_apply, derivationToSquareZeroEquivLift_symm_apply_apply_coe, NumberField.mixedEmbedding.norm_smul, GradedTensorProduct.mulHom_apply, Submodule.map_mul, discr_mul_isIntegral_mem_adjoin, CliffordAlgebra.foldr_ι, smulTower_leftMulMatrix, IntermediateField.finrank_sup_le, PolyEquivTensor.invFun_add, AlgCat.hom_whiskerLeft, CliffordAlgebra.changeForm_one, ordinaryHypergeometricSeries_apply_eq, BialgEquiv.map_mul', CliffordAlgebra.lift_symm_apply, Ring.instFiniteNormalClosure, DirectSum.algHom_ext'_iff, MvPolynomial.universalFactorizationMapPresentation_relation, IntermediateField.adjoinRootEquivAdjoin_apply_root, Extension.Cotangent.map_id, TensorProduct.congr_refl, Module.FaithfullyFlat.of_flat_of_isLocalHom, Subbimodule.coe_toSubbimoduleInt, Module.Flat.linearIndependent_one_tmul, IsBaseChange.toDual_comp_apply, finrank_eq_of_equiv_equiv, CliffordAlgebra.foldl_ι, Submodule.le_traceDual, Subalgebra.linearDisjoint_iff, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, GroupLike.val_mul, IsFractional.pow, Module.isTorsionFree_iff_algebraMap_injective, IntermediateField.rank_bot, IsPushout.out, CliffordAlgebraQuaternion.ofQuaternion_mk, Generators.Cotangent.exact, IsFractionRing.coeSubmodule_le_coeSubmodule, CommBialgCat.isoEquivBialgEquiv_symm_apply, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, le_restrictScalars_separableClosure, CategoryTheory.Iso.toHopfAlgEquiv_symm, AddMonoidAlgebra.coe_liftNCAlgHom, RingHom.finite_algebraMap, Submodule.IsLattice.finrank_of_pi, pinGroup.conjAct_smul_range_ι, CliffordAlgebra.foldl_reverse, Module.Dual.baseChange_apply_tmul, LinearMap.rTensor_baseChange, NumberField.RingOfIntegers.instIsTorsionFree, IsPushout.cancelBaseChangeAux_symm_tmul, IsStrictlyPositive.sqrt, IntermediateField.instIsScalarTowerSubtypeMem_1, AdjoinRoot.powerBasisAux'_repr_symm_apply, TensorProduct.map_surjective, TensorPower.toTensorAlgebra_gMul, BialgCat.whiskerRight_def, NonUnitalSubalgebra.unitization_apply, IsAzumaya.coe_tensorEquivEnd, AlgHom.tensorEqualizerEquiv_apply, DualNumber.lift_apply_apply, Complex.im_balance, TensorPower.toTensorAlgebra_gOne, Complex.ofReal_expect, adjoin_inl_union_inr_eq_prod, cfc_eq_cfcL_mkD, PolynomialModule.equivPolynomial_single, instIsTorsionFreeLocalizationAlgebraMapSubmonoidPrimeCompl_1, exteriorPower.pairingDual_apply_apply_eq_one, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, Unitization.lift_symm_apply, CommAlgCat.binaryCofan_inl, IntermediateField.finrank_bot_mul_relfinrank, PolynomialLaw.add_def_apply, MonoidAlgebra.tensorEquiv_tmul, Module.mem_freeLocus_iff_tensor, CliffordAlgebra.reverse.commutes, Presentation.tensorModelOfHasCoeffsEquiv_tmul, TensorProduct.Algebra.linearMap_comp_mul', SymmetricAlgebra.algHom_ext_iff, Smooth.baseChange, fdifferential_comp, CliffordAlgebra.foldr_one, ExteriorAlgebra.toTrivSqZeroExt_ι, Submodule.unitsQuotEquivRelPic_symm_apply, Field.lift_rank_mul_lift_insepDegree_of_isPurelyInseparable, SymmetricAlgebra.equivMvPolynomial_symm_X, SetLike.algebraMap_mem_graded, Subalgebra.map_toSubmodule, TensorProduct.comm_comp_includeRight, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, Submodule.IsLattice.rank_of_pi, CliffordAlgebra.toBaseChange_ofBaseChange, SetLike.GradeZero.coe_algebraMap, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, BialgHom.coe_toCoalgHom, IsCyclotomicExtension.finiteDimensional, IntermediateField.bot_eq_top_iff_finrank_eq_one, Submodule.tmul_mem_baseChange_of_mem, matrixEquivTensor_apply_single, IntermediateField.finiteDimensional_adjoin, CliffordAlgebra.reverse_mem_evenOdd_iff, AlgebraicGeometry.StructureSheaf.const_algebraMap, IntermediateField.lift_injective, TensorProduct.cancelBaseChange_symm_tmul, CliffordAlgebra.evenToNeg_ι, MvPolynomial.coeff_rTensorAlgHom_tmul, Submodule.rTensorOne_tmul_one, CFC.sqrt_sq, TensorProduct.comm_comp_includeLeft, Subbimodule.coe_toSubbimoduleNat, diffToIdealOfQuotientCompEq_apply, AlgHom.instNonUnitalAlgHomClassOfAlgHomClass, KaehlerDifferential.instSMulCommClassTensorProduct, IsAdjoinRootMonic.coeff_apply_lt, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, LinearMap.map_mul_algebraMap, CliffordAlgebra.map_comp_ι, Submodule.le_traceDual_comm, HopfAlgebra.counit_comp_antipode, Submodule.mem_span_singleton_mul, CFC.rpow_sqrt_nnreal, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, Module.Flat.baseChange, KaehlerDifferential.mvPolynomialBasis_repr_apply, IntermediateField.AdjoinSimple.trace_gen_eq_zero, FreeAlgebra.rank_eq, MatrixEquivTensor.invFun_smul, SymmetricAlgebra.lift_comp_ι, Submodule.span_range_natDegree_eq_adjoin, SymmetricAlgebra.lift_ι, IsLocalRing.split_injective_iff_lTensor_residueField_injective, lift_rank_le_of_injective_injective, Extension.Hom.mapKer_apply_coe, toMatrix_lmul', Presentation.tensorModelOfHasCoeffsHom_tmul, adjoin_nonUnitalSubalgebra, PolynomialLaw.isCompat, CommAlgCat.whiskerLeft_hom, Extension.contangentEquiv_tmul, Subalgebra.coe_smul, PolynomialLaw.add_def, LinearMap.isNilpotent_mulRight_iff, LinearMap.toSpanSingleton_eq_algebra_linearMap, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, WeakDual.CharacterSpace.eq_set_map_one_map_mul, IntermediateField.finSepDegree_adjoin_simple_le_finrank, FractionalIdeal.isPrincipal_inv, FractionalIdeal.coeToSet_coeToSubmodule, CliffordAlgebraComplex.toComplex_ι, NormedSpace.expSeries_apply_eq', LinearMap.polyCharpolyAux_baseChange, Subalgebra.LinearDisjoint.linearIndependent_mul_of_flat, TensorProduct.assoc_toLinearEquiv, LinearMap.baseChange_sub, Module.Basis.symmetricAlgebra_repr_apply, LinearMap.convOne_def, TensorProduct.assoc_symm_tmul, TensorProduct.opAlgEquiv_symm_apply, IntermediateField.card_algHom_adjoin_integral, BialgHom.id_toCoalgHom, Polynomial.aeval_coe_eq_smeval, Field.Emb.Cardinal.filtration_apply, exists_etale_isIdempotentElem_forall_liesOver_eq, matrixEquivTensor_apply_symm, Bialgebra.counit_mul, Complex.linearEquiv_det_conjAe, IntermediateField.relrank_dvd_rank_bot, CliffordAlgebra.changeForm_ι, IsAlgebraic.finrank_of_isFractionRing, Subalgebra.bot_eq_top_iff_finrank_eq_one, RestrictScalars.ringEquiv_map_smul, Bialgebra.TensorProduct.map_tmul, PolynomialLaw.toFun_smul, CliffordAlgebra.foldr_reverse, PiTensorProduct.algHom_ext_iff, DualNumber.coe_lift_symm_apply, Extension.h1Cotangentι_ext_iff, TensorProduct.linearEquivIncludeRange_symm_tmul, MonoidAlgebra.domCongr_comp_lsingle, TensorProduct.algEquivIncludeRange_tmul, Smooth.exists_subalgebra_finiteType, MatrixEquivTensor.left_inv, ClassGroup.mk_eq_one_iff, AlgEquiv.linearEquivConj_mulLeftRight, exteriorPower.ιMulti_family_span_of_span, NumberField.fractionalIdeal_rank, algebraMapCLM_apply, CliffordAlgebra.ι_mul_ι_add_swap_of_isOrtho, Generators.toKaehler_tmul_D, smulTower_leftMulMatrix_algebraMap_ne, AlgEquiv.coe_toLinearEquiv, hasFDerivAt_exp_smul_const_of_mem_ball, TrivSqZeroExt.liftEquivOfComm_apply, TensorProduct.isBaseChange, isGroupLikeElem_unitsInv, LinearEquiv.algEquivOfRing_symm_apply, NormedSpace.expSeries_sum_eq_rat, iInf_toSubmodule, NoZeroSMulDivisors.iff_algebraMap_injective, fourierSubalgebra_coe, Derivation.coeFn_coe, instFlatAtPrime, NumberField.finite_of_discr_bdd, CommAlgCat.whiskerRight_hom, instIsPushoutPolynomial, Submodule.linearDisjoint_op, CliffordAlgebra.toBaseChange_comp_reverseOp, MonoidAlgebra.instIsPushout', cfcHom_nnreal_eq_restrict, HopfAlgebra.mul_antipode_rTensor_comul_apply, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, IntermediateField.LinearDisjoint.of_inf_eq_bot, Extension.Cotangent.map_toInfinitesimal_bijective, GradedTensorProduct.auxEquiv_tmul, KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange, Derivation.map_one_eq_zero', exteriorPower.map_injective_field, Etale.exists_subalgebra_fg, NormedSpace.exp_def, Extension.H1Cotangent.val_add, PolynomialModule.equivPolynomialSelf_apply_eq, ExteriorAlgebra.ιMulti_apply, CliffordAlgebra.EquivEven.v_sq_scalar, IsAdjoinRootMonic.coeff_injective, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, Basis.mem_ideal_iff', Ideal.quotientToQuotientRangePowQuotSucc_injective, KaehlerDifferential.submodule_span_range_eq_ideal, idealMap_isLocalizedModule, LinearMap.baseChange_neg, AlgebraicGeometry.pullbackSpecIso_inv_snd_assoc, AlgebraicIndependent.liftAlgHom_comp_reprField, AlgCat.forget₂_module_obj, Finset.expect_boole_mul, Subalgebra.finiteDimensional_toSubmodule, hasFDerivAt_exp_smul_const, Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply, TensorProduct.map_range, Field.Algebra.IsSeparable.finSepDegree_eq, IntermediateField.finrank_top', IsQuadraticExtension.finrank_eq_two, exteriorPower.alternatingMapLinearEquiv_comp, TensorProduct.tmul_pow, Extension.H1Cotangent.val_smul, Presentation.differentials.comm₁₂, Subalgebra.isScalarTower_mid, Derivation.coe_sub_linearMap, IntermediateField.inclusion_self, Valuation.HasExtension.instIsTorsionFreeInteger, Complex.im_comp_balance, IntermediateField.lift_bot, FractionalIdeal.eq_spanSingleton_of_principal, trace_localization, Submodule.map_op_mul, SymmetricAlgebra.equivMvPolynomial_ι_apply, exteriorPower.basis_coord, Subalgebra.toSubmodule_toSubalgebra, Module.FinitePresentation.linearEquivMapExtendScalars_apply, IsBaseChange.endHom_apply, FractionalIdeal.mem_span_mul_finite_of_mem_mul, GroupLike.val_toUnits_apply, IntermediateField.normalClosure_of_normal, LinearMap.mul''_apply, discr_powerBasis_eq_prod, TensorProduct.map_comp_includeRight, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, LocalizedModule.mk_mul_mk', Ideal.constr_basisSpanSingleton, IsAdjoinRootMonic.map_modByMonicHom, TrivSqZeroExt.sndHom_comp_map, Polynomial.coeff_divModByMonicAux_mem_span_pow_mul_span, ContinuousLinearMap.instNonnegSpectrumClassRealId, Subalgebra.tmul_mem_baseChange, LinearMap.baseChange_zero, Localization.instIsTorsionFreeAtPrimeAlgebraMapSubmonoidPrimeComplOfIsDomain, CommAlgCat.braiding_inv_hom, InfiniteGalois.isOpen_iff_finite, Smooth.exists_finiteType, CliffordAlgebra.contractLeft_ι, exteriorPower.presentation_relation, adjoin_union_coe_submodule, LinearMap.polyCharpolyAux_map_aeval, BialgEquiv.symm_toCoalgEquiv, Real.rank_rat_real, KaehlerDifferential.map_compDer, TensorProduct.piRightHom_one, trace_eq_matrix_trace, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, LinearMap.liftBaseChange_tmul, Submodule.mulMap_one_left_eq, traceMatrix_of_basis, Field.Emb.Cardinal.deg_lt_aleph0, AlgEquiv.one_toLinearMap, Bialgebra.counitBialgHom_toCoalgHom, trace_algebraMap_of_basis, IsPushout.equiv_tmul, HopfAlgCat.toBialgHom_id, NumberField.inverse_basisMatrix_mulVec_eq_repr, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, AddMonoidAlgebra.tensorEquiv_tmul, MultilinearMap.mkPiAlgebraFin_apply, TensorAlgebra.ι_leftInverse, IntermediateField.relfinrank_bot_left, NNReal.coe_expect, PolyEquivTensor.toFunBilinear_apply_apply, Unitization.starLift_apply, Module.Basis.traceDual_involutive, BialgCat.tensorObj_def, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_mul, CFC.abs_ofNat, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, CommAlgCat.associator_inv_hom, IsBaseChange.toDual_apply, PolyEquivTensor.toFunLinear_tmul_apply, CFC.negPart_one, RatFunc.rank_ratFunc_ratFunc, UniversalEnvelopingAlgebra.ι_apply, Module.FaithfullyFlat.one_tmul_eq_zero_iff, TensorProduct.tensorTensorTensorComm_toLinearEquiv, Generators.H1Cotangent.exact_map_δ', AlgebraicGeometry.pullbackSpecIso_inv_fst_assoc, IntermediateField.le_extendScalars_iff, ClassGroup.equivPic_symm_apply, CliffordAlgebra.invOf_ι, TensorProduct.ext_iff, fg_adjoin_of_finite, TensorAlgebra.GradedAlgebra.ι_apply, CliffordAlgebra.contractRight_contractRight, Module.isTorsionFree_iff_faithfulSMul, CFC.abs_algebraMap_nnreal, MvPolynomial.rTensor_symm_apply_single, AlgHom.card, Submodule.mker_spanSingleton, CliffordAlgebra.star_ι, exteriorPower.instFinite, FractionalIdeal.den_mul_self_eq_num, RCLike.ofReal_expect, trace_quotient_mk, IsLocalization.bijective_linearMap_mul', TensorAlgebra.hom_ext_iff, CliffordAlgebra.involute_ι, exteriorPower.alternatingMapToDual_apply_ιMulti, FractionalIdeal.coe_map, instFiniteAtPrimeLocalizationAlgebraMapSubmonoidPrimeCompl, trace_surjective, KaehlerDifferential.D_tensorProductTo, IntermediateField.inclusion_injective, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, adjoin_eq_span, Submodule.nat_power_gradedMonoid, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, Extension.toKaehler_surjective, hfdifferential_apply, IntermediateField.LinearDisjoint.bot_right, TensorAlgebra.range_lift, IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective, AlgEquiv.toLinearEquiv_toLinearMap, Ideal.ResidueField.algHom_ext_iff, Submodule.mulMap_eq_mul'_comp_mapIncl, NumberField.RingOfIntegers.extension_isNoetherian, CliffordAlgebra.even_toSubmodule, TensorProduct.algEquivIncludeRange_toAlgHom, AddMonoidAlgebra.tensorEquiv_symm_single, Field.primitive_element_iff_minpoly_degree_eq, LinearEquiv.baseChange_inv, liftOfDerivationToSquareZero_apply, toSubmodule_eq_top, Derivation.tensorProductTo_mul, IntermediateField.normal_iff_forall_map_le, CliffordAlgebra.reverse_comp_involute, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, ValuationSubring.ofPrime_scalar_tower, IsLocalization.Away.tensor, BialgHom.toCoalgHom_apply, separableClosure.isAlgebraic, IsAlgClosure.ofAlgebraic, HopfAlgCat.tensorHom_def, Field.sepDegree_mul_insepDegree, FractionalIdeal.isNoetherian_iff, AlgHom.toLinearMap_fromOpposite, LinearAlgebra.FreeProduct.rel_id, SubmodulesRingBasis.leftMul, DirectSum.decomposeAlgEquiv_apply, DualNumber.range_inlAlgHom_sup_adjoin_eps, Submodule.smul_one_eq_span, PolynomialLaw.toFun_add, Generators.CotangentSpace.exact, Generators.H1Cotangent.δAux_X, TensorProduct.comm_symm_tmul, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, BialgEquiv.trans_toCoalgEquiv, AlgHom.card_le, Submodule.mulLeftMap_eq_mulMap_comp, CliffordAlgebra.changeForm_contractLeft, GroupLike.val_inv, IsAlgebraic.isBaseChange_of_isFractionRing, FractionalIdeal.isFractional_span_singleton, IsLocalization.map_eq_toLinearMap_mapₐ, IntermediateField.rank_eq_one_iff, MonoidAlgebra.scalarTensorEquiv_symm_single, TensorProduct.counit_def, smulTower_leftMulMatrix_algebraMap, TensorProduct.tmul_one_eq_one_tmul, Subbimodule.coe_toSubmodule, TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, instFiniteFractionRingLocalizationAlgebraMapSubmonoidNonZeroDivisors, cfc_comp_norm, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, CFC.abs_intCast, HopfAlgebra.counit_antipode, Extension.Hom.subToKer_apply_coe, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, spectralNorm.eq_of_normalClosure, Module.FaithfullyFlat.tensorProduct_mk_injective, NumberField.Embeddings.coeff_bdd_of_norm_le, Subalgebra.pi_toSubsemiring, IsIntegral.mem_span_pow, AlgHomClass.toLinearMap_toAlgHom, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, FractionalIdeal.coe_sup, PiTensorProduct.tprod_noncommProd, FormallyUnramified.base_change, PolyEquivTensor.invFun_monomial, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, spectralNorm.eq_of_normalClosure', Ideal.Factors.finrank_pow_ramificationIdx, NumberField.exists_ideal_in_class_of_norm_le, CliffordAlgebra.forall_mul_self_eq_iff, CliffordAlgebra.even.lift_symm_apply_bilin, isClosedEmbedding_cfcₙHom_of_cfcHom, Submodule.LinearDisjoint.rank_le_one_of_flat_of_self, PolynomialLaw.neg_def, KaehlerDifferential.kerTotal_mkQ_single_smul, MvPolynomial.rTensor_apply_monomial_tmul, CommBialgCat.comp_apply, Submodule.instInvertibleSubtypeMemVal, CliffordAlgebraRing.ι_eq_zero, HahnSeries.SummableFamily.binomialFamily_apply, WeakDual.ker_isMaximal, Generators.repr_CotangentSpaceMap, Subbimodule.coe_toSubmodule', AlgebraicIndependent.linearIndependent, normalizedTrace_minpoly, IsAdjoinRootMonic.modByMonicHom_root_pow, BialgEquiv.trans_symm_apply, separableClosure.isSepClosure, InfiniteGalois.toAlgEquivAux_eq_liftNormal, Module.Dual.baseChange_baseChange, CommSemiring.antipode_eq_id, isNilpotent_tensor_residueField_iff, RootPairing.root'_apply_apply_mem_of_mem_span, Field.primitive_element_iff_minpoly_natDegree_eq, BialgHomClass.map_comp_comulAlgHom, IntermediateField.normalClosure_def'', QuasispectrumRestricts.nonUnitalStarAlgHom_apply, Ideal.rank_pow_quot_aux, PolyEquivTensor.toFunLinear_one_tmul_one, rank_eq_of_equiv_equiv, LinearMap.range_liftBaseChange, BialgCat.MonoidalCategory.inducingFunctorData_μIso, SubmodulesRingBasis.inter, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Field.Emb.Cardinal.strictMono_filtration, LocalizedModule.map_id, IsLocalization.tmul_mk', Submodule.mem_one, IntermediateField.isSeparable_tower_bot, CommRingCat.coproductCoconeIsColimit_desc, IntermediateField.minpoly_eq, cfcL_integral, exteriorPower.zeroEquiv_ιMulti, TensorProduct.piRight_tmul, BialgHom.map_mul', AlgebraicGeometry.pullbackSpecIso_hom_fst, ExteriorAlgebra.liftAlternating_comp_ιMulti, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, CliffordAlgebra.toEven_ι, Extension.H1Cotangent.map_apply_coe, FractionalIdeal.coe_inv_of_nonzero, PolyEquivTensor.left_inv, IntermediateField.isSplittingField_iff, CliffordAlgebra.equivBaseChange_apply, Submodule.mulMap'_surjective, Module.Basis.tensorAlgebra_repr_apply, Submodule.map_unop_one, AlgCat.instMonoidalCategory.tensorObj_carrier, trace_eq_zero_of_not_isSeparable, Generators.toKaehler_cotangentSpaceBasis, Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparable, normalizedTrace_eq_of_finiteDimensional_apply, IsAdjoinRootMonic.coeff_algebraMap, IntermediateField.topEquiv_symm_apply_coe, FiniteGaloisIntermediateField.adjoin_val, AdjoinRoot.noZeroSMulDivisors_of_prime_of_degree_ne_zero, FractionalIdeal.spanFinset_coe, QuadraticForm.associated_isSymm, IsBaseChange.dual, TensorAlgebra.tprod_apply, NumberField.mem_span_integralBasis, Module.mem_support_iff_nontrivial_residueField_tensorProduct, CommBialgCat.bialgEquivOfIso_symm_apply, MvPolynomial.tensorEquivSum_X_tmul_X, isLocalizedModule_iff_isLocalization', discr_isUnit_of_basis, CliffordAlgebra.reverseEquiv_symm_apply, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, trace_complex_apply, IntermediateField.AdjoinSimple.normal_algebraicClosure, toMatrix_lsmul, AlgEquiv.moduleEndSelf_apply_apply, exteriorPower.map_injective, SubmersivePresentation.basisKaehler_apply, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, KaehlerDifferential.polynomial_D_apply, Ideal.rank_pow_quot, TensorProduct.toIntegralClosure_injective_of_flat, StarAlgHom.coe_toNonUnitalStarAlgHom, IntermediateField.normal_iff_forall_map_eq', LinearEquiv.dilatransvection.baseChange, exteriorPower.basis_repr_apply, MvPolynomial.algebraTensorAlgEquiv_symm_map, IntermediateField.intermediateFieldMap_apply_coe, IntermediateField.topEquiv_apply, TensorProduct.productMap_right_apply, Bialgebra.TensorProduct.lid_toAlgEquiv, Module.Finite.of_equiv_equiv, CFC.spectrum_abs, Module.End.baseChangeHom_apply_apply, isBoundedBilinearMap_smul, IntermediateField.exists_algHom_adjoin_of_splits', exteriorPower.presentation_R, Generators.CotangentSpace.compEquiv_symm_inr, normalizedTrace_algebraMap_apply, IsLocalRing.ResidueField.finite_of_module_finite, MvPolynomial.tensorEquivSum_C_tmul_one, normalizedTrace_def, ContinuousAlgEquiv.toContinuousLinearEquiv_toLinearEquiv_eq, Submodule.pow_eq_span_pow_set, BialgCat.toBialgHom_id, CliffordAlgebra.submodule_map_mul_reverse, NumberField.mem_span_basisOfFractionalIdeal, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, Subbimodule.coe_baseChange, FiniteField.minpoly_frobeniusAlgHom, Module.Basis.baseChange_repr_tmul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, Subalgebra.coe_pi, IntermediateField.AdjoinSimple.isIntegral_gen, Submodule.instIsOrderedRing, Basis.mem_ideal_iff, GradedTensorProduct.tmul_coe_mul_zero_coe_tmul, TensorProduct.basis_repr_symm_apply, ordinaryHypergeometricSeries_eq_zero_iff, KaehlerDifferential.quotKerTotalEquiv_symm_apply, NumberField.mixedEmbedding.logMap_apply, mem_coeSubmodule_conductor, polyEquivTensor_apply, CliffordAlgebra.evenOdd_mul_le, MonoidAlgebra.mapDomainNonUnitalAlgHom_apply, CliffordAlgebra.contractRight_one, PolyEquivTensor.toFunBilinear_apply_eq_smul, CliffordAlgebraDualNumber.equiv_ι, Presentation.algebraTensorAlgEquiv_symm_relation, IsAlgebraic.isNormalClosure_normalClosure, MvPolynomial.coeffsIn_pow, LocalizedModule.algebraMap_mk, FractionalIdeal.isPrincipal.of_finite_maximals_of_inv, instFiniteResidueField, IntermediateField.isPurelyInseparable_bot, NumberField.mixedEmbedding.latticeBasis_apply, Submodule.le_div_iff, PowerBasis.finite, IsAlgebraic.lift_rank_of_isFractionRing, Submodule.mulMap_map_comp_eq, GradedTensorProduct.comm_coe_tmul_coe, TensorProduct.right_isScalarTower, CliffordAlgebra.changeForm_algebraMap, AlgHom.addHomMk_coe, TensorProduct.algebraMap_apply', TensorProduct.Algebra.TensorProduct.commRight_symm_tmul, IsLocalizedModule.mkOfAlgebra, AlgebraicIndependent.aevalEquivField_apply_coe, CliffordAlgebra.foldr'Aux_apply_apply, CategoryTheory.Iso.toHopfAlgEquiv_refl, NonUnitalAlgHom.toAlgHom_apply, IntermediateField.LinearDisjoint.exists_field_of_isDomain, CliffordAlgebra.reverse.map_one, instIsStandardOpenImmersionTensorProduct, IsLocalRing.basisQuotient_apply, AlgEquiv.moduleEndSelfOp_symm_apply, TensorProduct.lift_tmul, minpoly_algEquiv_toLinearMap, NonUnitalAlgebra.to_subring_eq_top, TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, PowerBasis.trace_gen_eq_sum_roots, RingHom.Finite.tensorProductMap, Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct, FractionalIdeal.mul_def', FormalMultilinearSeries.ofScalars_smul, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, IsLocalization.mapExtendScalars_eq_toLinearMap_mapₐ, Etale.baseChange, trace_quotient_eq_trace_localization_quotient, Module.Flat.instSubtypeMemSubmoduleSubmoduleAlgebra, Submodule.mem_traceDual, IntermediateField.finiteDimensional_left, Submodule.mapHom_id, ZMod.dft_const_mul, cardinalMk_algHom_le_rank, Ideal.inertiaDeg_bot, NonUnitalAlgebra.toNonUnitalSubring_eq_top, instIsPushout_1, HopfAlgCat.forget₂_bialgebra_map, Extension.Hom.sub_aux, normalizedTrace_trans_apply, IsAlgebraic.rank_fractionRing, instIsPushoutFractionRingPolynomial, Module.Basis.localizationLocalization_span, Bialgebra.counit_algebraMap, discr_localizationLocalization, FormallySmooth.kerCotangentToTensor_injective_iff, instFiniteLocalizationAlgebraMapSubmonoidPrimeCompl, KaehlerDifferential.derivationTensorProduct_algebraMap, RingHomClass.toLinearMapClassNNRat, AlgebraicClosure.instIsScalarTower, Ideal.powQuotSuccInclusion_injective, le_perfectClosure_iff, perfectClosure.isAlgebraic, MvPolynomial.aevalTower_comp_toAlgHom, CliffordAlgebra.reverseOp_ι, IntermediateField.isSeparable_sup, TensorProduct.lTensor_ker, Submodule.span_singleton_eq_one_iff, FiniteGaloisIntermediateField.finiteDimensional, ClassGroup.isPrincipal_coeSubmodule_of_isUnit, norm_one_add_smul, KaehlerDifferential.tensorProductTo_surjective, TensorProduct.linearEquivIncludeRange_symm_toLinearMap, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, norm_apply, norm_eq_zero_iff', IntermediateField.coe_smul, CliffordAlgebra.ι_mul_ι_comm_of_isOrtho, CFC.sqrt_eq_cfc, NormedSpace.expSeries_sum_eq_div, trace_quotient_eq_of_isDedekindDomain, IsSepClosure.isAlgClosure_of_perfectField_top, Extension.h1Cotangentι_apply, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, Module.IsTorsionFree.of_isLocalization, IsLocalizedModule.map_injective_iff_localizedModuleMap_injective, MvPolynomial.pderiv_inr_universalFactorizationMap_X, Extension.cotangentComplex_injective_iff, Field.finSepDegree_dvd_finrank, TensorProduct.tensorTensorTensorComm_tmul, AlgHom.toLinearMap_id, RingHom.faithfullyFlat_algebraMap_iff, Ring.instFiniteNormalClosure_1, exists_linearIndependent_algEquiv_apply, InfiniteGalois.restrictNormalHom_continuous, IsSeparable.sepDegree_eq, Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, IsAdjoinRootMonic.coeff_one, Submodule.traceDual_bot, AlgEquiv.toLinearMap_apply, IsIntegral.tmul, Derivation.tensorProductTo_tmul, derivationOfSectionOfKerSqZero_apply_coe, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, Ideal.card_stabilizer_eq_card_inertia_mul_finrank, NumberField.abs_discr_ge_of_isTotallyComplex, MvPolynomial.instIsPushout_1, FiniteField.bijective_frobeniusAlgHom_pow, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, IsGalois.of_separable_splitting_field_aux, IntermediateField.coe_equivMap_apply, AddMonoidAlgebra.mapDomainBialgHom_comp, NumberField.mixedEmbedding.latticeBasis_repr_apply, IsGalois.finiteDimensional_of_finite, Submodule.lTensorOne_symm_apply, exteriorPower.map_comp_ιMulti_family, LaurentPolynomial.antipode_C, Submodule.mul_eq_map₂, AddMonoidAlgebra.scalarTensorEquiv_symm_single, IntermediateField.finInsepDegree_bot, Submodule.tensorToSpan_apply_tmul, CliffordAlgebra.evenOdd_map_involute, krullTopology_mem_nhds_one_iff, CFC.abs_sq, exteriorPower.map_id, FormalMultilinearSeries.ofScalars_comp_neg_id, baseChange_lmul, KaehlerDifferential.mvPolynomialBasis_repr_D, WeakDual.gelfandTransform_apply_apply, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, CommBialgCat.isoMk_hom, WeierstrassCurve.Affine.CoordinateRing.basis_zero, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, Field.Emb.Cardinal.iSup_adjoin_eq_top, TensorAlgebra.ι_inj, CliffordAlgebra.iSup_ι_range_eq_top, RatFunc.finrank_ratFunc_ratFunc, NormedSpace.expSeries_eq_expSeries_rat, TensorAlgebra.ι_eq_zero_iff, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, leftMulMatrix_mulVec_repr, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, ExteriorAlgebra.map_apply_ιMulti, KaehlerDifferential.ker_map_of_surjective, traceForm_nondegenerate, IsCyclotomicExtension.Rat.finrank, CliffordAlgebra.submodule_comap_pow_reverse, Submodule.lTensorOne'_one_tmul, Module.finite_iff_krullDimLE_zero, H1Cotangent.isLocalizedModule, TensorProduct.lift_comp_includeRight', CliffordAlgebra.contractLeft_mul_algebraMap, CommBialgCat.forget_obj, PolynomialLaw.smul_def_apply, GradedAlgebra.proj_apply, krullTopology_mem_nhds_one_iff_of_normal, FractionalIdeal.mem_coe, IsAdjoinRootMonic.modByMonicHom_root, GroupLike.val_inv_toUnits_apply, Bialgebra.comul_pow, TensorProduct.equivPiOfFiniteBasis_symm_apply, IntermediateField.finrank_bot', CliffordAlgebra.toProd_one_tmul_ι, FractionalIdeal.coeToSubmodule_injective, Derivation.coe_add_linearMap, AlgEquiv.moduleEndSelf_symm_apply, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, TensorProduct.quotIdealMapEquivTensorQuot_mk, CliffordAlgebra.even.lift.aux_apply, CliffordAlgebra.toBaseChange_involute, Derivation.coe_smul_linearMap, NumberField.mixedEmbedding.finrank, CliffordAlgebra.even.lift.aux_ι, IsUnramifiedAtInfinitePlaces.card_infinitePlace, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, CyclotomicRing.instIsTorsionFreeCyclotomicField, Submodule.comap_unop_pow, PolynomialLaw.toFun_neg, IsBaseChange.equiv_tmul, BialgEquiv.toBialgIso_trans, lmul_isUnit_iff, Bialgebra.comul_one, LinearMap.tensorProduct_apply, exteriorPower.pairingDual_apply_apply_eq_one_zero, IsFractional.map, Generators.snd_cotangentCompLocalizationAwayEquiv, CStarAlgebra.isStrictlyPositive_TFAE, AlgebraicGeometry.pullbackSpecIso_hom_base_assoc, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, tensorH1CotangentOfIsLocalization_toLinearMap, Matrix.kroneckerTMulAlgEquiv_apply, derivationToSquareZeroEquivLift_apply_coe_apply, CommBialgCat.ofHom_apply, StarSubalgebra.one_mem_toNonUnitalStarSubalgebra, MvPolynomial.algebraTensorAlgEquiv_tmul, tmul_comm, TensorProduct.comm_tmul, separableClosure.isSeparable, minpoly.natDegree_le, LinearMap.restrictScalarsField_apply_apply, Bialgebra.TensorProduct.assoc_toCoalgEquiv, FractionalIdeal.abs_det_basis_change, LinearMap.frobenius_def, AlgEquiv.linearEquivConj_mulRight, AlgCat.forget₂_module_map, PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable, MvPolynomial.instIsPushout, CFC.sqrt_algebraMap, Subalgebra.coe_toSubmodule, CFC.posPart_algebraMap, trace_eq_sum_embeddings, CliffordAlgebra.contractLeft_algebraMap_mul, IntermediateField.adjoin.finiteDimensional, CFC.sqrt_one, IntermediateField.botEquiv_def, liftOfDerivationToSquareZero_mk_apply', le_algebraicClosure_iff, IsLocalization.tensorRight, cfc_eq_cfcL, CliffordAlgebra.reverseEquiv_apply, subalgebra_top_finrank_eq_submodule_top_finrank, IntermediateField.adjoin_adjoin_comm, GradedTensorProduct.of_symm_of, Submodule.span_singleton_mul, KaehlerDifferential.span_range_eq_ideal, Complex.toMatrix_conjAe, LaurentPolynomial.counit_T, TensorProduct.lmul'_comp_includeLeft, IntermediateField.val_mk, ContinuousLinearMap.toSpanSingleton_one_eq_algebraMapCLM, MatrixEquivTensor.right_inv, Generators.CotangentSpace.map_toComp_injective, TensorProduct.mk_surjective, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, IntermediateField.rank_sup_le, IsLocalization.tensor, IntermediateField.LinearDisjoint.self_right, Extension.H1Cotangent.equivOfFormallySmooth_toLinearMap, CSA.fin_dim, FormalMultilinearSeries.ofScalars_series_eq_zero, Field.finSepDegree_eq_finrank_iff, Unitization.lift_range_le, PrimeSpectrum.continuous_tensorProductTo, TensorProduct.opAlgEquiv_tmul, CliffordAlgebraRing.reverse_apply, ExteriorAlgebra.hom_ext_iff, ExteriorAlgebra.liftAlternating_algebraMap, Submodule.map_pow, FiniteDimensional.exists_is_basis_integral, TensorProduct.rid_toLinearEquiv, Bialgebra.TensorProduct.lid_toCoalgEquiv, PolynomialLaw.isCompat_apply', FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, Units.submodule_isFractional, AlgEquiv.restrictNormalHom_apply, InfiniteGalois.mk_toAlgEquivAux, AlgebraicGeometry.pullbackSpecIso_hom_fst'_assoc, instIsAbelianGaloisSubtypeMemIntermediateField, IsLocalization.flat, IsAlgebraic.rank_of_isFractionRing, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, pinGroup.involute_act_ι_mem_range_ι, Module.Flat.iff_flat_tensorProduct, HopfAlgebra.mul_antipode_lTensor_comul_apply, LeftInvariantDerivation.evalAt_mul, RingHom.flat_algebraMap_iff, BialgCat.forget₂_coalgebra_map, FractionalIdeal.coe_spanSingleton, CliffordAlgebraDualNumber.ι_mul_ι, Bialgebra.TensorProduct.rid_symm_apply, IntermediateField.inclusion_inclusion, Field.Emb.Cardinal.adjoin_image_leastExt, exteriorPower.basis_repr, LinearMap.liftBaseChange_comp, MatrixEquivTensor.invFun_zero, TensorProduct.algEquivIncludeRange_symm_toAlgHom, Bialgebra.counit_one, BialgEquiv.toHopfAlgIso_trans, Submodule.LinearDisjoint.one_right, FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, Submodule.lTensorOne_tmul, HopfAlgCat.tensorObj_carrier, CliffordAlgebra.isUnit_ι_of_isUnit, NonUnitalSubalgebra.coe_neg, IntermediateField.extendScalars_restrictScalars, NonnegSpectrumClass.of_spectrum_nonneg, FiniteField.nonempty_algHom_iff_finrank_dvd, MvPolynomial.aeval_one_tmul, trace_prod_apply, Subalgebra.comm_trans_lTensorBot, quasispectrumRestricts_iff_spectrumRestricts, Submodule.LinearDisjoint.val_mulMap_tmul, trace_trace_of_basis, discr_powerBasis_eq_prod'', traceMatrix_of_basis_mulVec, IsBaseChange.basis_repr_comp, CFC.sqrt_rpow_nnreal, Extension.Hom.sub_tmul, exteriorPower.alternatingMapLinearEquiv_symm_apply, AlgebraicGeometry.pullbackSpecIso_inv_fst', TensorProduct.lid'_symm_apply, IsAlgebraic.tmul, map_intTraceAux, instFreeSubtypeMemIdealOfFiniteOfIsTorsionFree, HopfAlgCat.leftUnitor_def, TensorProduct.comm_comp_map, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, CliffordAlgebra.foldr_algebraMap, NumberField.mixedEmbedding.norm_real, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, IsLocalizedModule.mk'_mul_mk', Subalgebra.restrictScalars_toSubmodule, isAlgClosure_iff, AdjoinRoot.powerBasisAux'_repr_apply_to_fun, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, IsAdjoinRootMonic.coeff_apply_coe, InfiniteGalois.proj_of_le, StarAlgebra.adjoin_eq_span, Ideal.Factors.finiteDimensional_quotient_pow, PolynomialLaw.comp_toFun', Submodule.mul_eq_span_mul_set, ExteriorAlgebra.ιInv_comp_map, Module.Basis.traceDual_repr_apply, FormalMultilinearSeries.ofScalars_comp_neg, Complex.rank_rat_complex, MvPolynomial.tensorEquivSum_one_tmul_X, SubmersivePresentation.sectionCotangent_comp, FractionalIdeal.val_eq_coe, Matrix.det_kroneckerTMul, CommAlgCat.binaryCofan_inr, FractionalIdeal.isNoetherian, CliffordAlgebra.lift_comp_ι, exists_etale_isIdempotentElem_forall_liesOver_eq_aux, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, KaehlerDifferential.isBaseChange_of_formallyEtale, Complex.re_expect, Submodule.iSup_eq_toSubmodule_range, LinearEquiv.baseChange_pow, CliffordAlgebra.ofEven_ι, exteriorPower.map_apply_ιMulti, IntermediateField.lift_adjoin, H1Cotangent.exact_map_δ, NumberField.basisOfFractionalIdeal_apply, AlgEquiv.toLinearMap_ofBijective, CliffordAlgebra.ofBaseChange_tmul_one, MvPolynomial.universalFactorizationMap_freeMonic, normalizedTrace_algebraMap_of_lifts, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, Submodule.mulExact_unitsMap_spanSingleton_unitsToPic, Bialgebra.subsingleton_to_ring, Generators.H1Cotangent.δ_comp_equiv, MultilinearMap.mkPiAlgebraFin_apply_const, PolynomialLaw.id_apply', DualNumber.lift_apply_inl, CliffordAlgebra.submodule_map_reverse_eq_comap, TensorProduct.prodRight_tmul, LinearMap.algHom_comp_convMul_distrib, BialgEquiv.toBialgIso_hom, TensorProduct.prodRight_tmul_snd, AlgebraicGeometry.diagonal_Spec_map, MvPolynomial.universalFactorizationMapPresentation_σ', IsBaseChange.linearMap, TensorProduct.map_restrictScalars_comp_includeRight, CommAlgCat.associator_hom_hom, Submodule.setSemiring_smul_def, KaehlerDifferential.mvPolynomialBasis_repr_symm_single, TensorProduct.liftEquiv_symm_apply_coe, commBialgCatEquivComonCommAlgCat_inverse_map_unop_hom, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, IsPushout.equiv_symm_algebraMap_right, IntermediateField.rank_eq_rank_subalgebra, FormalMultilinearSeries.ofScalars_series_injective, BialgCat.toBialgHom_comp, normalizedTrace_trans, DualNumber.lift_op_smul, Bialgebra.TensorProduct.rid_tmul, Field.lift_rank_mul_lift_sepDegree_of_isSeparable, autEquivRootsOfUnity_apply_rootOfSplit, WeakDual.CharacterSpace.instAlgHomClass, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, LinearEquiv.baseChange_symm, Ideal.Quotient.finite_of_isInvariant, exists_bijective_map_powers, IsFractional.nsmul, AlgHom.toEnd_apply, IsLocalization.map_linearMap_eq_toLinearMap_mapₐ, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, CliffordAlgebra.toBaseChange_ι, IsAlgebraic.rank_fractionRing_mvPolynomial, IsIntegral.fg_adjoin_singleton, IntermediateField.lift_sup, Bialgebra.TensorProduct.lid_tmul, Submodule.mapHom_apply, discr_powerBasis_eq_prod', algebraMap_intTrace, hasFDerivAt_exp_smul_const_of_mem_ball', Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct, FractionalIdeal.isPrincipal, normalClosure.normal, CliffordAlgebra.ι_mem_evenOdd_one, IsLocalization.span_invSubmonoid, IsAzumaya.toFinite, quasispectrum_eq_spectrum_union_zero, Ideal.inertiaDeg_le_finrank, FractionalIdeal.spanSingleton_def, IsStandardSmooth.iff_exists_basis_kaehlerDifferential, HopfAlgebra.mul_antipode_lTensor_comul, CliffordAlgebraComplex.reverse_eq_id, CFC.nnrpow_eq_rpow, hasStrictFDerivAt_exp_smul_const, AlgHom.toRingHom_toAddMonoidHom, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, LinearAlgebra.FreeProduct.lift_apply, LocalizedModule.map_mk, PowerBasis.liftEquiv'_symm_apply_apply, CliffordAlgebra.evenOdd_comap_reverse, instIsTorsionFreeLocalizationAlgebraMapSubmonoidPrimeCompl_2, IntermediateField.adjoin_adjoin_left, RCLike.wInner_cWeight_const_right, Finset.expect_div, PowerBasis.constr_pow_mul, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, IsLocalization.coeSubmodule_strictMono, PolynomialLaw.isCompat_apply, Ideal.ncard_primesOver_mul_card_inertia_mul_finrank, SubMulAction.mem_one', CategoryTheory.Iso.toBialgEquiv_toBialgHom, TensorProduct.includeRight_surjective, IntermediateField.normalClosure_mono, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, Submodule.equivOpposite_symm_apply, NumberField.mixedEmbedding.euclidean.finrank, IsLocalRing.subsingleton_tensorProduct, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, MeasureTheory.lpNorm_expect_le, Unitization.starLift_range_le, IsFractionRing.coeSubmodule_isPrincipal, TensorProduct.lmul'_toLinearMap, card_algHom_le_finrank, trace_eq_sum_automorphisms, gelfandTransform_isometry, Submodule.coe_mapAlgHom_apply, AlgHom.toKerIsLocalization_isLocalizedModule, Polynomial.instFiniteUniversalFactorizationRing, solvableByRad.isIntegral, Submodule.le_traceDual_mul_iff, FractionalIdeal.equivNum_apply, GroupLike.val_pow, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, ExteriorAlgebra.lhom_ext_iff, CommBialgCat.isoMk_inv, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, TensorProduct.nontrivial_of_algebraMap_injective_of_flat_right, MvPolynomial.range_mapAlgHom, Submodule.instSMulCommClass_1, IntermediateField.insepDegree_bot, Ideal.comap_fiberIsoOfBijectiveResidueField_symm, Generators.cotangentCompLocalizationAwayEquiv_symm_inl, IntermediateField.equivOfEq_apply, Generators.cotangentCompLocalizationAwayEquiv_symm_inr, ExteriorAlgebra.ι_range_map_map, CommBialgCat.forget_map, Derivation.coe_zero_linearMap, Submodule.baseChange_top, IntermediateField.rank_bot', Module.Flat.top_mul_submoduleAlgebra, Submodule.comap_unop_one, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, exteriorPower.map_comp, CommBialgCat.ofHom_id, norm_algebraMap, DualNumber.lift_comp_inlHom, AlgHom.linearMapMk_toAddHom, exteriorPower.ιMultiDual_apply_nondiag, CFC.abs_one, RingHom.SurjectiveOnStalks.baseChange', AddMonoidAlgebra.antipode_single, TensorProduct.antipode_def, exteriorPower.presentation_var, Bialgebra.toLinearMap_comulAlgHom, IsAdjoinRootMonic.coeff_apply_le, Module.Basis.traceDual_powerBasis_eq, SubmersivePresentation.sectionCotangent_zero_of_notMem_range, CliffordAlgebra.EquivEven.reverse_v, GradedTensorProduct.tmul_algebraMap_mul_coe_tmul, injective_lift_lsmul, CommBialgCat.forget₂_commAlgCat_map, algebraMap_intTrace_fractionRing, KaehlerDifferential.range_kerCotangentToTensor, IntermediateField.fieldRange_val, LinearMap.compBilinForm_apply_apply, IntermediateField.liftAlgEquiv_apply, DualNumber.algHom_ext'_iff, Submodule.mulMap_op, Unitization.lift_apply_apply, Quaternion.hasSum_expSeries_of_imaginary, separableClosure_le_separableClosure_iff, IsSymmetricAlgebra.comp_equiv, IsGaloisGroup.card_eq_finrank, BialgHom.ext_of_ring_iff, cardinalMk_algHom, KaehlerDifferential.map_D, Derivation.liftKaehlerDifferential_apply, Generators.instFreeCotangentSpaceToExtension, IsGalois.tfae, KaehlerDifferential.instIsScalarTowerTensorProduct_1, coe_lmul_eq_mul, Presentation.baseChange_relation, FiniteDimensional.subalgebra_toSubmodule, ExteriorAlgebra.comp_ι_sq_zero, exteriorPower.map_surjective, KaehlerDifferential.DLinearMap_apply, FinitePresentation.baseChange, TensorProduct.lmul''_eq_lid_comp_mapOfCompatibleSMul, MvPolynomial.rTensor_apply, TensorProduct.productMap_right, IsAdjoinRootMonic.coeff_root, Subalgebra.LinearDisjoint.linearIndependent_mul_of_flat_right, Pi.evalStarAlgHom_apply, CliffordAlgebra.ofProd_ι_mk, IsLocalization.mem_coeSubmodule, BialgEquiv.toHopfAlgIso_hom, CliffordAlgebra.GradedAlgebra.lift_ι_eq, TensorPower.toTensorAlgebra_galgebra_toFun, normalizedTrace_eq_of_fininteDimensional_apply, TensorProduct.Algebra.moduleAux_apply, IntermediateField.rank_bot_mul_relrank, IsLocalRing.instFiniteResidueField, ordinaryHypergeometricSeries_eq_zero_of_neg_nat, ExteriorAlgebra.ι_mul_prod_list, IsBaseChange.linearMapLeftRightHom_apply, trace_apply, IsCyclotomicExtension.Rat.discr_odd_prime', TensorAlgebra.toDirectSum_ι, Module.Finite.base_change, Smooth.flat_of_isNoetherianRing, ExteriorAlgebra.ιMulti_succ_curryLeft, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, IsGroupLikeElem.one, FormallySmooth.iff_injective_cotangentComplexBaseChange, exteriorPower.presentation_G, Generators.CotangentSpace.fst_compEquiv_apply, GradedTensorProduct.tmul_coe_mul_algebraMap_tmul, Submodule.lTensorOne_one_tmul, FormallyUnramified.comp_sec, NumberField.coe_discr, AlgCat.hom_tensorHom, AlgebraicGeometry.pullbackSpecIso_hom_fst', PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, smulTower_leftMulMatrix_algebraMap_eq, Localization.flat, lipschitzGroup.involute_act_ι_mem_range_ι, LocalizedModule.mul_smul', Submodule.baseChange_span, CategoryTheory.Iso.toHopfAlgEquiv_toBialgHom, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, CFC.isUnit_nnrpow_iff, Unitization.starLift_symm_apply, BialgCat.leftUnitor_def, IsTranscendenceBasis.lift_rank_eq_max_lift, TensorAlgebra.lift_unique, IntermediateField.finiteDimensional_map, BialgHomClass.toCoalgHomClass, Bialgebra.TensorProduct.lid_symm_apply, minpoly.degree_dvd, Bialgebra.TensorProduct.rid_toCoalgEquiv, AddMonoidAlgebra.scalarTensorEquiv_tmul, NumberField.Units.finrank_mul_regulator_eq_det, IsPrimitiveRoot.lcm_totient_le_finrank, ModuleCat.MonModuleEquivalenceAlgebra.inverse_map_hom, linearIndependent_pow, FractionalIdeal.coe_div, IsSepClosure.isAlgClosure_of_perfectField, coe_linearMap, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, BialgEquiv.refl_toCoalgEquiv, LinearMap.baseChange_tmul, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, Real.compact_inner_le_weight_mul_Lp_of_nonneg, IsFractionRing.coeSubmodule_injective, LinearMap.transvection.baseChange, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, exteriorPower.ιMulti_family_linearIndependent_ofBasis, PolynomialLaw.ground_apply, Submodule.span.ringHom_apply, IntermediateField.normalClosure_le_iff_of_normal, FiniteField.orderOf_frobeniusAlgHom, instIsPushout, AlgHom.fieldRange_of_normal, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, TensorProduct.ringHom_ext_iff, Submodule.one_eq_range, IntermediateField.Lifts.eq_iff, AlgEquiv.toLinearEquiv_refl, ClassGroup.equivPic_apply, algebraMap.coe_expect, CliffordAlgebra.evenOdd_comap_involute, Submodule.mem_div_iff_smul_subset, TrivSqZeroExt.liftEquiv_symm_apply_coe, Field.Emb.Cardinal.adjoin_basis_eq_top, Submodule.comap_op_one, Module.Finite.of_quasiFinite, coe_trace_int, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, TensorProduct.toLinearMap_map, GradedAlgebra.mem_support_iff, TensorProduct.adjoin_tmul_eq_top, Module.Basis.repr_smul', Subalgebra.pointwise_smul_toSubmodule, Bialgebra.counit_pow, Bialgebra.mul_compr₂_comul, TensorProduct.equivPiOfFiniteBasis_apply, SubmersivePresentation.cotangentComplex_injective, IntermediateField.normalClosure_map_eq, BialgCat.forget₂_algebra_obj, instIsStandardEtaleTensorProduct, PiTensorProduct.mul_comm, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, IntermediateField.relrank_bot_left, Polynomial.aevalTower_comp_toAlgHom, TensorProduct.map_id_comp, LinearEquiv.baseChange_one, TensorProduct.piScalarRight_tmul_apply, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, trace_eq_sum_embeddings_gen, CliffordAlgebra.contractRight_ι, AlgHom.card_of_splits, Ideal.absNorm_algebraMap, Submodule.map_op_one, TensorProduct.lidOfCompatibleSMul_tmul, IsLocalization.coeSubmodule_fg, NumberField.mixedEmbedding.convexBodySum_volume, KaehlerDifferential.mulActionBaseChange_smul_zero, TensorProduct.isPushout', exteriorPower.ιMulti_family_span, Etale.iff_exists_algEquiv_prod, Subalgebra.prod_toSubmodule, Submodule.mul_def, exteriorPower.ιMulti_span_fixedDegree, finite_iff_isIntegral_and_finiteType, IsSymmetricAlgebra.equiv_toAlgHom, Derivation.linearEquiv_coe_comp, GradedTensorProduct.of_one, Polynomial.Monic.free_adjoinRoot, MvPolynomial.tensorEquivSum_X_tmul_one, Complex.coe_basisOneI, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, Finset.expect_eq_sum_div_card, SpecialLinearGroup.baseChange_apply_coe, IntermediateField.le_normalClosure, LinearMap.IsPerfPair.restrictScalars_of_field, TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι, NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoin, CliffordAlgebraRing.reverse_eq_id, cfcₙHom_of_cfcHom_map_quasispectrum, ExteriorAlgebra.GradedAlgebra.ι_apply, IntermediateField.equivOfEq_trans, LocalizedModule.algebraMap_mk', AlgebraicGeometry.pullbackSpecIso_hom_snd, AlgebraicGeometry.StructureSheaf.const_mul, IntermediateField.normalClosure_def', Submodule.mulMap_range, AlgCat.hom_whiskerRight, AlgEquiv.toLinearEquiv_injective, trace_eq_of_equiv_equiv, WeakDual.CharacterSpace.isClosed, TensorProduct.map_bijective, kerTensorProductMapIdToAlgHomEquiv_symm_apply, exteriorPower.oneEquiv_ιMulti, TensorProduct.nontrivial_of_algebraMap_injective_of_flat_left, GradedTensorProduct.symm_of_of, matrixEquivTensor_apply, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, Extension.Cotangent.map_mk, MatrixEquivTensor.toFunAlgHom_apply, LinearAlgebra.FreeProduct.lof_map_one, LinearMap.BilinForm.baseChange_tmul, AddChar.expect_apply_eq_ite, Extension.CotangentSpace.map_comp, LeftInvariantDerivation.toFun_eq_coe, Field.sepDegree_le_rank, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, PowerBasis.constr_pow_aeval, exteriorPower.ιMulti_span, IntermediateField.mem_restrict, CommBialgCat.hom_id, TensorProduct.opAlgEquiv_symm_tmul, IsLocalization.coeSubmodule_isPrincipal, CliffordAlgebra.EvenHom.contract_mid, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, LinearMap.baseChange_mul, exteriorPower.toTensorPower_apply_ιMulti, traceForm_toMatrix_powerBasis, algebraMapCLM_toLinearMap, IsLocalization.coeSubmodule_top, FractionalIdeal.mem_extended_iff, addMonoidAlgebraAlgEquivDirectSum_apply, IntermediateField.LinearDisjoint.isDomain, CliffordAlgebra.ι_range_comap_reverse, commBialgCatEquivComonCommAlgCat_counitIso_hom_app, FormallyUnramified.finite_of_free, Submodule.localized'_smul, Extension.exact_cotangentComplex_toKaehler, instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation, BialgEquiv.toHopfAlgIso_inv, TensorProduct.lid_toLinearEquiv, Module.Basis.norm_repr_le_norm, LinearMap.baseChange_id, IntermediateField.finrank_dvd_of_le_right, FractionalIdeal.trace_mem_dual_one, CommBialgCat.hom_comp, IsIntegralClosure.module_free, FiniteType.baseChange, leftMulMatrix_eq_repr_mul, trace_comp_trace, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, isEpi_iff_forall_one_tmul_eq, Module.finrank_baseChange, SubmodulesRingBasis.mul, PolynomialLaw.toFun_comp, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, Bialgebra.mul_compr₂_counit, TensorProduct.lid_symm_apply, Polynomial.coe_taylorEquiv, Submodule.map_one, commBialgCatEquivComonCommAlgCat_functor_map_unop_hom, TensorAlgebra.ι_eq_algebraMap_iff, IntermediateField.finrank_le_of_le_right, LinearMap.map_algebraMap_mul, CliffordAlgebra.evenOdd_isCompl, IsAdjoinRootMonic.liftPolyₗ_apply, Polynomial.Gal.card_of_separable, lift_rank_le_of_surjective_injective, Subalgebra.bot_eq_top_iff_rank_eq_one, CliffordAlgebraQuaternion.toQuaternion_ι, Unitization.lift_apply, Generators.CotangentSpace.map_ofComp_surjective, AlgHom.equalizer_toSubmodule, TensorProduct.leftComm_symm_tmul, isGalois_bot, MvPolynomial.tensorEquivSum_C_tmul_C, AlgEquiv.toLinearEquiv_trans, IntermediateField.intermediateFieldMap_symm_apply_coe, exteriorPower.zeroEquiv_symm_apply, PiTensorProduct.algebraMap_apply, prod_embeddings_eq_finrank_pow, QuadraticForm.associated_baseChange, KaehlerDifferential.map_liftBaseChange_smul, Subalgebra.pi_toSubmodule, Matrix.toLpLinAlgEquiv_symm_apply, Module.FaithfullyFlat.of_specComap_surjective, IsQuadraticExtension.toFree, Generators.Hom.id_comp, Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, LinearMap.trace_baseChange, CliffordAlgebra.contractLeftAux_apply_apply, RingHom.toKerIsLocalization_isLocalizedModule, idealMap_apply_coe, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, IsLocalization.coeSubmodule_sup, CliffordAlgebra.ofBaseChange_comp_toBaseChange, CliffordAlgebra.contractLeft_one, BialgCat.MonoidalCategory.inducingFunctorData_εIso, TensorProduct.congr_symm, Submodule.le_traceDual_iff_map_le_one, FormallyUnramified.iff_exists_tensorProduct, FiniteField.algebraMap_norm_eq_pow_sum, IsBaseChange.toDualBaseChange_tmul, IntermediateField.finiteDimensional_adjoin_pair, instFiniteDimensionalFractionRingOfFinite, TensorProduct.comm_toLinearEquiv, KaehlerDifferential.kerTotal_map', Submodule.mulExact_unitsToPic_mapAlgebra, IntermediateField.normal_sup, IntermediateField.coe_algebraMap_apply, Bialgebra.TensorProduct.assoc_symm_tmul, Submodule.LinearDisjoint.bot_left, Submodule.traceDual_top, Generators.CotangentSpace.fst_compEquiv, Extension.CotangentSpace.map_comp_apply, Ideal.map_includeLeft_eq, separableClosure.isGalois, PolynomialLaw.one_tmul_ground_apply', IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, MvPowerSeries.substAlgHom_comp_substAlgHom, Bialgebra.TensorProduct.assoc_toAlgEquiv, Module.Basis.toMatrix_map_vecMul, Generators.H1Cotangent.equiv_apply, TensorPower.toTensorAlgebra_tprod, TensorProduct.rid_symm_apply, IntermediateField.restrictScalars_adjoin, HahnSeries.SummableFamily.powerSeriesFamily_smul, Extension.CotangentSpace.map_comp_cotangentComplex, TensorProduct.rTensor_ker, Transcendental.linearIndependent_sub_inv, isGroupLikeElem_iff_of_mul_eq_one, IntermediateField.finrank_adjoin_simple_eq_one_iff, TensorProduct.map_comp_includeLeft, Submodule.LinearDisjoint.rank_inf_le_one_of_flat_right, IsAlgebraic.rank_fractionRing_polynomial, Subalgebra.LinearDisjoint.isDomain_of_injective, LinearMap.isNilpotent_mulLeft_iff, finite_of_essFiniteType_of_isAlgebraic, Polynomial.taylorLinearEquiv_apply_coe, MonoidAlgebra.mapDomainBialgHom_id, TensorProduct.mapOfCompatibleSMul_tmul, Ideal.Fiber.exists_smul_eq_one_tmul, leftMulMatrix_apply, LinearMap.charpoly_baseChange, normalClosure.is_finiteDimensional, WeierstrassCurve.Affine.CoordinateRing.basis_apply, FormalMultilinearSeries.ofScalars_norm_eq_mul, EssFiniteType.baseChange, NormedSpace.expSeries_hasSum_exp_of_mem_ball, IntermediateField.finiteDimensional_sup, IntermediateField.Lifts.le_iff, HopfAlgebra.antipode_one, normalizedTrace_self_apply, rank_mvPolynomial_mvPolynomial, CommRingCat.coproductCocone_ι, Submodule.map_div, polyEquivTensor_symm_apply_tmul_eq_smul, Extension.Hom.toAlgHom_id, Submodule.LinearDisjoint.rank_inf_le_one_of_flat_left, ExteriorAlgebra.liftAlternating_ι, trace_adjoinSimpleGen, Subalgebra.one_mem_toNonUnitalSubalgebra, AlgebraicGeometry.pullbackSpecIso_hom_fst_assoc, IntermediateField.normal_iff_normalClosure_eq, IntermediateField.rank_adjoin_simple_eq_one_iff, CliffordAlgebra.contractLeftAux_contractLeftAux, lipschitzGroup.conjAct_smul_range_ι, AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective, AlgHom.coe_toAddMonoidHom, LinearMap.baseChange_add, PrimeSpectrum.nontrivial_iff_mem_rangeComap, NumberField.house.basis_repr_norm_le_const_mul_house, exteriorPower.ιMulti_family_apply_coe, CliffordAlgebra.EquivEven.involute_v, Submodule.mem_traceDual_iff_isIntegral, IsIntegralClosure.isNoetherian, IntermediateField.isIntegral_iff, Subalgebra.rank_toSubmodule, commBialgCatEquivComonCommAlgCat_counitIso_inv_app, Extension.Hom.toAlgHom_apply, TensorProduct.comm_symm, IsSymmetricAlgebra.lift_comp_linearMap, H1Cotangent.exact_δ_mapBaseChange, IsLocalization.coeSubmodule_injective, LaurentPolynomial.antipode_C_mul_T, KaehlerDifferential.instIsScalarTowerTensorProduct_2, Subalgebra.fg_bot_toSubmodule, separableClosure.normalClosure_eq_self, LinearMap.baseChangeHom_apply, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_one, Derivation.evalAt_apply, TrivSqZeroExt.snd_expSeries_of_smul_comm, AddChar.expect_eq_ite, Generators.H1Cotangent.δ_map, BialgHom.map_one', ContinuousMultilinearMap.norm_mkPiAlgebraFin, IntermediateField.adjoin.powerBasis_dim, Submodule.ker_unitsMap_spanSingleton, CliffordAlgebra.reverse_ι, PreSubmersivePresentation.baseChange_ring, CliffordAlgebra.reverse_involutive, IsGalois.of_fixedField_normal_subgroup, TensorProduct.lift_includeLeft_includeRight, Submodule.comap_unop_mul, Complex.nonempty_linearEquiv_real, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, Module.finite_of_surjective_of_ker_le_nilradical, CliffordAlgebra.submodule_map_involute_eq_comap, Complex.ofReal_choose, Extension.Cotangent.map_sub_map, IntermediateField.isPurelyInseparable_sup, CliffordAlgebra.changeForm_changeForm, KaehlerDifferential.mulActionBaseChange_smul_tmul, IntermediateField.splits_of_splits, FormallySmooth.iff_split_injection, Subalgebra.rank_top, UniversalEnvelopingAlgebra.lift_ι_apply', TensorProduct.linearEquivIncludeRange_tmul, NonnegSpectrumClass.iff_spectrum_nonneg, Smooth.exists_subalgebra_fg, Module.Flat.instInvertibleSubtypeMemSubmoduleSubmoduleAlgebra, BialgHom.comp_toCoalgHom, TensorProduct.includeLeft_surjective, TensorProduct.adjoin_one_tmul_image_eq_top, PolynomialLaw.isCompat', FiniteField.finrank_extension, exteriorPower.basis_repr_self, GradedTensorProduct.of_symm_one, Extension.cotangentComplex_mk, Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, subalgebra_top_rank_eq_submodule_top_rank, AlgHom.mulLeftRightMatrix.comp_inv, retractionOfSectionOfKerSqZero_tmul_D, instIsPushoutFractionRingMvPolynomial_1, Submodule.fg_unit, KaehlerDifferential.linearCombination_surjective, IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow', Submodule.restrictScalars_localized'_smul, FractionalIdeal.inv_of_ne_zero, Module.Basis.traceDual_injective, FormalMultilinearSeries.ofScalars_norm, Module.Basis.baseChange_linearMap, IsCyclotomicExtension.discr_prime_pow, IsAdjoinRootMonic.coeff_root_pow, LinearEquiv.baseChange_trans, TensorProduct.includeLeftRingHom_apply, FaithfulSMul.to_isTorsionFree, IsStandardSmoothOfRelativeDimension.exists_subalgebra_fg, FractionalIdeal.coe_zero, Presentation.baseChange_toGenerators, Submodule.unitsQuotEquivRelPic_apply_coe, derivationQuotKerSq_mk, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, CFC.isUnit_sqrt_iff, CliffordAlgebra.even.lift.aux_one, MvPolynomial.universalFactorizationMapPresentation_jacobian, BialgEquiv.toBialgIso_inv, IntermediateField.finite_of_fg_of_isAlgebraic, Submodule.instIsScalarTower, Polynomial.IsSplittingField.finiteDimensional, CliffordAlgebra.ι_mul_ι_mul_of_isOrtho, IntermediateField.adjoin_rootSet_isSplittingField, IntermediateField.nonempty_algHom_adjoin_of_splits, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, hasStrictFDerivAt_exp_smul_const_of_mem_ball, Polynomial.map_taylorEquiv_degreeLT, FractionalIdeal.coe_extended_eq_span, IsAdjoinRootMonic.basis_one, IsCyclotomicExtension.discr_prime_pow_ne_two', IsAzumaya.AlgHom.mulLeftRight_bij, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, perfectClosure.isPurelyInseparable, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, Module.FinitePresentation.of_finite_of_finitePresentation, IntermediateField.isSeparable_adjoin_iff_isSeparable, TensorProduct.includeRight_lid, CliffordAlgebra.even.lift.aux_algebraMap, CliffordAlgebraComplex.reverse_apply, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, prod_galRestrict_eq_norm, Module.Basis.traceDual_eq_iff, discr_reindex, NormedSpace.exp_eq_expSeries_sum, instFinitePresentationTensorProduct, instIsPushoutFractionRingMvPolynomial, CFC.rpow_sqrt, IsAdjoinRootMonic.basis_apply, MvPolynomial.pderiv_inl_universalFactorizationMap_X, Extension.H1Cotangent.map_toInfinitesimal_bijective, autEquivRootsOfUnity_smul, Extension.Cotangent.val_smul'', LeftInvariantDerivation.evalAt_apply, CliffordAlgebra.contractLeft_algebraMap, IsLocalization.coeSubmodule_span_singleton, TensorProduct.closure_range_union_range_eq_top, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, ZariskisMainProperty.exists_fg_and_exists_notMem_and_awayMap_bijective, Presentation.tensorModelOfHasCoeffsInv_aeval_val, Fintype.expect_eq_sum_div_card, AlgEquiv.toLinearEquiv_apply, AlgebraicGeometry.pullbackSpecIso_hom_snd_assoc, MvPolynomial.rTensorAlgHom_apply_eq
toSMul 📖	CompOp	2379 math math: AdicCompletion.of_surjective_iff, ArithmeticFunction.vonMangoldt.residueClass_eq, Matrix.l2_opNorm_toEuclideanCLM, RatFunc.instFaithfulSMulPolynomialLaurentSeries, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, Polynomial.units_coeff_zero_smul, Ideal.Quotient.isScalarTower, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', LinearMap.restrictScalars_toMatrix, MeasureTheory.Measure.MutuallySingular.smul_nnreal, MeasureTheory.SMulInvariantMeasure.smul, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, Seminorm.isBounded_const, MeasureTheory.Measure.IsHaarMeasure.nnreal_smul, Matrix.toLinAlgEquiv_one, MeasureTheory.mulEquivHaarChar_smul_integral_map, PowerSeries.hasSum_aeval, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, IntermediateField.finInsepDegree_top, Field.Emb.Cardinal.equivLim_coherence, MeasureTheory.ennreal_smul_extend, InfiniteGalois.normal_iff_isGalois, PowerSeries.IsWeierstrassFactorizationAt.algEquivQuotient_symm_apply, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, idealMap_eq_ofEq_comp_toLocalized₀, MeasureTheory.Measure.restrict_singleton, AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf, ModularForm.smul_slash, IntermediateField.exists_algHom_adjoin_of_splits, MeasureTheory.Measure.isAddInvariant_eq_smul_of_compactSpace, QuaternionAlgebra.coe_mul_eq_smul, ordinaryHypergeometric_sum_eq, AlgEquiv.moduleEndSelfOp_apply_apply, Ideal.selfBasis_def, TensorProduct.instSMulCommClassTensorProduct, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', IntermediateField.aeval_gen_minpoly, OrthonormalBasis.orthogonalProjection_eq_sum, StarAlgEquiv.ofInjective_symm_apply, LinearMap.toMatrixAlgEquiv'_mul, strictConvexOn_iff_slope_strict_mono_adjacent, AdicCompletion.mk_zero_of, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, Polynomial.lcoeff_comp_mapAlgHom_eq, MeasureTheory.Measure.IsEverywherePos.smul_measure, NumberField.RingOfIntegers.inst_isScalarTower, LinearMap.exists_monic_and_aeval_eq_zero, DividedPowers.RatAlgebra.dpow_eq_inv_fact_smul, Ideal.toCharacterSpace_apply_eq_zero_of_mem, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, PowerSeries.constantCoeff_subst, FormalMultilinearSeries.ofScalars_apply_eq', tendsto_tsum_div_pow_atTop_integral, MeasureTheory.Measure.ae_ennreal_smul_measure_eq, MeasureTheory.integral_smul_nnreal_measure, Ideal.finrank_eq_finrank, Real.smul_map_volume_mul_right, Polynomial.Monic.free_quotient, IntermediateField.adjoin.finrank, LinearMap.IsSymmetric.restrictScalars, Ideal.exists_smith_normal_form, IsBaseChange.comp_iff, MeasureTheory.Measure.IsAddHaarMeasure.smul, LinearMap.BilinForm.isSkewAdjoint_bracket, Module.End.map_smul_of_iInf_genEigenspace_ne_bot, ContinuousAlternatingMap.isEmbedding_restrictScalars, convex_iff_ordConnected, WeakDual.isCompact_polar, TrivSqZeroExt.lift_inlAlgHom_inrHom, Matrix.det_smul_inv_mulVec_eq_cramer, Rat.instSMulCommClass, MeasureTheory.Measure.WeaklyRegular.smul_nnreal, ENNReal.nnreal_smul_lt_top, MeasureTheory.Measure.rnDeriv_smul_right', Module.End.HasEigenvalue.mem_spectrum, LieModule.toEnd_pow_apply_map, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, ModularForm.mul_slash, Polynomial.disjoint_ker_aeval_of_isCoprime, MvPolynomial.universalFactorizationMap_comp_map, MvPolynomial.isScalarTower_right, BoundedContinuousFunction.algebraMap_apply, mul_smul_comm, PolynomialModule.smul_def, Polynomial.aroots_smul_nonzero, has_pointwise_sum_fourier_series_of_summable, instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl, IsBaseChange.finsuppPow, concaveOn_iff_slope_anti_adjacent, IsLocalization.smul_mem_finsetIntegerMultiple_span, Matrix.spectrum_toEuclideanLin, Derivation.coe_to_linearMap_comp, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply, Ideal.smul_top_eq_map, IntermediateField.isScalarTower_mid', Extension.H1Cotangent.equiv_apply, algebraMap_eq_smul_one', KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul', ContinuousLinearMap.isUniformEmbedding_restrictScalars, LieModule.trace_toEnd_eq_zero_of_mem_lcs, CliffordAlgebra.involute_prod_map_ι, Asymptotics.isLittleOTVS_one, finrank_quotient_span_eq_natDegree_norm, FractionRing.instIsScalarTower, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, LinearMap.BilinForm.smul_left_of_tower, NumberField.RingOfIntegers.instSMulDistribClass, WeakDual.isClosed_image_polar_of_mem_nhds, AdicCompletion.of_ofAlgEquiv_symm, AddCircle.volume_eq_smul_haarAddCircle, FaithfulSMul.of_field_isFractionRing, ContinuousLinearMap.integral_apply, HasDerivAt.fun_finset_prod, LocalizedModule.restrictScalars_map_eq, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, Real.strictConcaveOn_rpow, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, ConcaveOn.mul_convexOn', LinearMap.toMatrixAlgEquiv_comp, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LinearMap.extendScalarsOfIsLocalization_apply, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, Polynomial.sum_bernoulli, Submodule.FG.restrictScalars_of_surjective, Representation.asAlgebraHom_single, AffineIsometryEquiv.ofTop_apply, deriv_fun_finset_prod, LieAlgebra.finrank_engel, skewAdjointLieSubalgebraEquiv_apply, MeasureTheory.Measure.measure_isMulLeftInvariant_eq_smul_of_ne_top, eval_det_add_X_smul, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, QuaternionAlgebra.Basis.i_mul_i, MvPowerSeries.constantCoeff_subst, TensorAlgebra.toTrivSqZeroExt_ι, to_smulCommClass, IntermediateField.lift_insepDegree_bot', MeasureTheory.smul_le_stoppedValue_hittingBtwn, HasFPowerSeriesWithinOnBall.restrictScalars, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, WeierstrassCurve.Projective.addY_smul, instIsScalarTowerPolynomial_1, lmul_algebraMap, KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Unitization.splitMul_apply, spectrum.units_smul_resolvent_self, MeasureTheory.Measure.ae_mem_finset_iff, continuousSMul_of_algebraMap, MeasureTheory.FinMeasAdditive.smul_measure, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, selfAdjoint.expUnitaryPathToOne_apply, Polynomial.leadingCoeff_det_X_one_add_C, faithfulSMul_iff_algebraMap_injective, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, StarSubalgebra.smulMemClass, LieAlgebra.IsKilling.rootSystem_coroot_apply, ProbabilityTheory.boolKernel_comp_measure, Metric.exists_forall_closedEBall_subset_aux₂, instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeComplFractionRing, Module.End.spectrum_intrinsicStar, MulAlgebraNorm.extends_norm', Matrix.spectrum_toLpLin, AdicCompletion.instIsScalarTower_1, Module.Basis.repr_isUnitSMul, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, StandardEtalePresentation.toPresentation_algebra_smul, sum_smul_minpolyDiv_eq_X_pow, SchwartzMap.bilinLeftCLM_apply, LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, Module.End.isFinitelySemisimple_sub_algebraMap_iff, InfiniteGalois.normalAutEquivQuotient_apply, MeasureTheory.Measure.haveLebesgueDecompositionSMul, MeasureTheory.tilted_neg_same', MeasureTheory.le_eLpNorm_of_bddBelow, WeierstrassCurve.Projective.dblU_smul, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, ProbabilityTheory.sum_meas_smul_cond_fiber, IntermediateField.isAlgebraic_tower_bot, QuaternionAlgebra.Basis.k_mul_i, IsGaloisGroup.fixedPoints_top, MvPolynomial.algHom_ext'_iff, LieSubalgebra.toEnd_eq, MeasureTheory.condLExp_bot', LSeriesSummable.smul, MeasureTheory.Measure.coe_nnreal_smul_apply, UnitAddTorus.mFourierSubalgebra_coe, AdicCompletion.incl_apply, AdicCompletion.map_ext'_iff, IntermediateField.botEquiv_symm, AdicCompletion.ofTensorProduct_surjective_of_finite, Rep.to_Module_monoidAlgebra_map_aux, CliffordAlgebra.contractRight_mul_ι, FormallyUnramified.finite_of_free_aux, IsScalarTower.right, Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, IsLocalization.lift_mem_adjoin_finsetIntegerMultiple, MeasureTheory.restrict_compl_sigmaFiniteSet, MeasureTheory.Measure.haarMeasure_unique, WeierstrassCurve.Projective.Point.toAffine_smul, LieModule.isNilpotent_toEnd_genWeightSpace_zero, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, ModularForm.prod_slash, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, MvPolynomial.instIsScalarTower, Polynomial.hilbertPoly_smul, NNReal.segment_eq_uIcc, SchwartzMap.laplacianCLM_eq, MeasureTheory.condLExp_smul, StarAlgEquiv.restrictScalars_symm_apply, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, starConvex_iff_ordConnected, LinearMap.toMatrixOrthonormal_reindex, LinearMap.toMatrixAlgEquiv_toLinAlgEquiv, autEquivZmod_symm_apply_natCast, finrank_quotient_span_eq_natDegree', PowerSeries.HasSubst.smul', Ideal.Quotient.instFaithfulSMul, UnitAddTorus.mFourierSubalgebra_closure_eq_top, NNRat.instSMulCommClass', instIsScalarTowerAtPrimeFractionRing_1, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, ExteriorAlgebra.toTrivSqZeroExt_comp_map, inner_smul_left_eq_star_smul, MeasureTheory.eLpNorm_smul_measure_of_ne_top', MeasureTheory.Measure.rnDeriv_smul_right, MeasureTheory.Measure.rnDeriv_smul_left_of_ne_top', LinearEquiv.conjAlgEquiv_ext_iff', MeasureTheory.Measure.sum_smul_dirac, MeasureTheory.Measure.ae_mem_finset_iff_map_eq_sum_dirac, LinearMap.ker_localizedMap_eq_localized'_ker, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, IsLocalizedModule.iso_apply_mk, IntermediateField.exists_algHom_of_adjoin_splits, matPolyEquiv_map_smul, IsAlgebraic.exists_integral_multiples, StarAlgEquiv.coe_toAlgEquiv, IntermediateField.normal_iff_forall_map_eq, RingHom.SurjectiveOnStalks.exists_mul_eq_tmul, skewAdjointLieSubalgebraEquiv_symm_apply, TrivSqZeroExt.fstHom_comp_map, polynomialFunctions.starClosure_topologicalClosure, WeierstrassCurve.Projective.addX_smul, Matrix.Represents.smul, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, lmul_injective, MeasureTheory.Measure.haarScalarFactor_smul, LinearMap.spectrum_toMatrix', MeasureTheory.Measure.OuterRegular.smul_nnreal, LieModule.trace_toEnd_genWeightSpace, Real.smul_map_diagonal_volume_pi, Ring.choose_eq_smul, MeasureTheory.Measure.map_fst_prod, IsCentral.instEnd, RCLike.smul_re, TensorProduct.piScalarRight_tmul, instIsScalarTowerAtPrimeLocalizationAlgebraMapSubmonoidPrimeCompl, Ideal.Quotient.tower_quotient_map_quotient, Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top, AlgHom.mulLeftRightMatrix.inv_comp, Derivation.linearEquiv_coe_to_linearMap_comp, Ring.instFaithfulSMulNormalClosure, gelfandStarTransform_naturality, LieModule.shiftedGenWeightSpace.toEnd_eq, segment_eq_uIcc, WeierstrassCurve.Projective.smul_equiv_smul, ModularForm.prod_slash_sum_weights, WeierstrassCurve.Projective.add_of_Z_eq_zero, gelfandStarTransform_apply_apply, IntermediateField.restrictScalars_normal, IntermediateField.isScalarTower, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, SetLike.Homogeneous.smul, FormalMultilinearSeries.ofScalars_apply_eq, MeasureTheory.Measure.const_comp, IsLocalization.smul_mk'_self, NormedSpace.Dual.toWeakDual_continuous, WeierstrassCurve.Projective.dblXYZ_smul, Module.endTensorEndAlgHom_apply, QuaternionAlgebra.Basis.j_mul_j, FormallySmooth.adjoin_of_algebraicIndependent, Matrix.det_updateRow_add_smul_self, instStarModuleNNRealReal, PowerSeries.aeval_eq_sum, QuaternionAlgebra.smul_coe, isPurelyInseparable_iff_fd_isPurelyInseparable, TrivSqZeroExt.fst_exp, openSegment_eq_Ioo, MeasureTheory.laverage_eq', IntermediateField.LinearDisjoint.of_isField', Representation.asAlgebraHom_def, strictConvexOn_pow, NNReal.isBoundedSMul, AlgebraicGeometry.functionField_isScalarTower, PowerBasis.equivAdjoinSimple_symm_aeval, TrivSqZeroExt.map_inr, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, Module.End.instLieModule, convexOn_univ_dist, Ergodic.eq_smul_of_absolutelyContinuous, IntermediateField.lift_adjoin_simple, algebraicClosure.normalClosure_eq_self, KaehlerDifferential.isLocalizedModule_of_isLocalizedModule, IsScalarTower.subsemiring, IntermediateField.AdjoinDouble.normal_algebraicClosure, Matrix.Nondegenerate.smul_iff, CliffordAlgebra.changeFormAux_changeFormAux, essSup_ennreal_smul_measure, Matrix.derivative_det_one_add_X_smul, Subalgebra.mulMap_map_comp_eq, gelfandTransform_bijective, Polynomial.mem_iff_eq_smul_annIdealGenerator, LieSubmodule.Quotient.toEnd_comp_mk', StarAlgEquiv.ofInjective_apply, EisensteinSeries.E2_slash_action, LinearMap.toMatrixAlgEquiv'_id, instIsScalarTowerAtPrimeLocalizationAlgebraMapSubmonoidPrimeComplFractionRing, AlgebraNormClass.map_smul_eq_mul, LieModule.instIsTriangularizableSubtypeEndMemLieSubalgebraRangeToEnd, PowerSeries.coeff_subst, UniformConvexOn.strictConvexOn, algebraicClosure.isAlgebraic, Polynomial.bernoulli_generating_function, MeasureTheory.Measure.InnerRegular.smul, IsGalois.normalClosure, FractionalIdeal.isFractional_span_iff, ContinuousAlgHom.map_smul, Unitization.nnnorm_def, MeasureTheory.Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, UpperHalfPlane.coe_pos_real_smul, QuaternionAlgebra.Basis.lift_smul, ediam_smul_le, Module.AEval'.X_smul_of, Matrix.det_updateRow_smul_left, LieModule.mem_posFittingCompOf, Quaternion.normSq_smul, LocalizedModule.divBy_mul_by, IntermediateField.isAlgebraic_iff, Complex.starConvex_ofReal_slitPlane, StarAlgEquiv.toAlgEquiv_injective, IsLocalization.isInteger_smul, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, RCLike.toIsStrictOrderedModule, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', KaehlerDifferential.instIsScalarTowerTensorProduct, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul', TensorProduct.AlgebraTensorModule.restrictScalars_lTensor, Matrix.inv_denom_smul_num, Matrix.updateRow_eq_transvection, SpectrumRestricts.smul_of_nonneg, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, FormalMultilinearSeries.ofScalars_apply_zero, LinearMap.toMatrixOrthonormal_apply_apply, HasFDerivAt.restrictScalars, CliffordAlgebra.EquivEven.ι_eq_v_add_smul_e0, IntermediateField.instSMulMemClass, LieModule.isNilpotent_range_toEnd_iff, MeasureTheory.isProbabilityMeasureSMul, IntermediateField.coe_inclusion, Nonneg.segment_eq_uIcc, QuadraticAlgebra.mul_coe_eq_smul, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, AffineSubspace.coe_subtypeₐᵢ, MonoidAlgebra.instIsPushout, TensorProduct.AlgebraTensorModule.restrictScalars_curry, LieAlgebra.rank_le_natTrailingDegree_charpoly_ad, Matrix.det_smul, strictConvexOn_exp, LinearMap.toMatrixAlgEquiv_apply, CliffordAlgebra.foldr'Aux_foldr'Aux, SchwartzMap.fourier_lineDerivOp_eq, Complex.starConvex_one_slitPlane, Extension.instIsScalarTowerH1CotangentOfCotangent, tendsto_card_div_pow_atTop_volume, hasStrictDerivAt_exp_smul_const, LieAlgebra.Orthogonal.jb_transform, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, NormedSpace.exp_eq_tsum, PowerSeries.binomialSeries_add, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, WeierstrassCurve.Projective.addXYZ_smul, TensorProduct.toMatrix_assoc, Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap, MeasureTheory.Measure.comp_eq_sum_of_countable, LieSubmodule.lie_top_eq_of_span_sup_eq_top, TrivSqZeroExt.lift_comp_inrHom, instIsPushoutFractionRingPolynomial_1, hasStrictDerivAt_exp_smul_const', Matrix.det_one_add_smul, WeierstrassCurve.Affine.CoordinateRing.instIsScalarTowerPolynomial, SchwartzMap.smulLeftCLM_real_smul, Polynomial.leadingCoeff_smul_integralNormalization, LinearMap.exists_map_addHaar_eq_smul_addHaar, MeasureTheory.addEquivAddHaarChar_smul_preimage, MvPowerSeries.hasSum_aeval, BoundedContinuousFunction.integral_const_sub, PowerSeries.derivativeFun_smul, Quaternion.inv_def, IsLocalization.smul_mk', spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, IsBaseChange.directSumPow, NoZeroSMulDivisors.iff_faithfulSMul, Complex.liftAux_apply, DiscreteTopology.instContinuousSMul, IntermediateField.minpoly_gen, strictConcaveOn_log_Iio, MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN, WeakDual.toStrongDual_inj, PowerSeries.smul_weierstrassDiv, strictConcaveOn_univ_of_deriv2_neg, ContinuousLinearMap.uniformContinuous_restrictScalars, MvPolynomial.sumAlgEquiv_comp_rename_inr, MvPolynomial.aevalTower_toAlgHom, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, IntermediateField.aeval_coe, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, MeasureTheory.Measure.discard_comp, HopfAlgebra.sum_mul_antipode_eq_smul, algebraMap_apply, AdicCompletion.factor_eval_eq_evalₐ, openSegment_eq_Ioo', AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType, Matrix.toLinAlgEquiv_mul, IsIntegral.exists_multiple_integral_of_isLocalization, Localization.algHom_ext_iff, Module.AEval.instIsScalarTowerOrigPolynomial, element_smul_restrictScalars, strongConcaveOn_zero, IsLocalization.surj'', MeasureTheory.Measure.rnDeriv_smul_left_of_ne_top, KaehlerDifferential.polynomialEquiv_comp_D, Ideal.powQuotSuccInclusion_apply_coe, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, ENNReal.instSMulPosMonoNNReal, IsLocalization.integerNormalization_map_to_map, TensorProduct.lid_tmul, Field.Emb.Cardinal.succEquiv_coherence, cross_cross_eq_smul_sub_smul, Real.map_matrix_volume_pi_eq_smul_volume_pi, TrivSqZeroExt.algHom_ext'_iff, MeasureTheory.FiniteMeasure.tendsto_iff_weakDual_tendsto, IntermediateField.isScalarTower_bot, IsAdicComplete.of_liftRingHom, PowerSeries.binomialSeries_zero, convexOn_rpow_left, MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul, LieModule.isNilpotent_toEnd_of_isNilpotent, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, polynomialFunctions.starClosure_le_equalizer, Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv, convex_halfSpace_re_le, KaehlerDifferential.mulActionBaseChange_smul_add, Matrix.inv_smul', NNReal.strictConcaveOn_sqrt, MeasureTheory.convolution_precompR_apply, WeierstrassCurve.Projective.addXYZ_of_X_eq, WeakDual.coe_toStrongDual, UniformSpace.Completion.map_smul_eq_mul_coe, ZLattice.covolume.tendsto_card_div_pow, coeSubmodule_differentIdeal_fractionRing, Ideal.Fiber.lift_residueField_surjective, isBaseChange_tensorProduct_map, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, spectrum.gelfandTransform_eq, OrthonormalBasis.orthogonalProjection_apply_eq_sum, Seminorm.ball_smul, Even.strictConvexOn_pow, LieModule.LinearWeights.map_smul, SemimoduleCat.Algebra.instIsScalarTowerCarrier, LocalizedModule.equivTensorProduct_symm_apply_tmul, Presentation.instIsScalarTowerCore, SkewMonoidAlgebra.lift_single, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, solvableByRad.isSolvable, LieSubmodule.coe_map_toEnd_le, IntermediateField.linearDisjoint_comm, SkewMonoidAlgebra.lift_apply, Module.AEval'.of_symm_X_smul, StarAlgEquiv.toAlgEquiv_symm, MeasureTheory.Measure.smul_measure_isAddInvariant_le_of_isCompact_closure, LieModule.mem_genWeightSpace, NormedSpace.expSeries_sum_eq, LinearMap.detAux_def, FiniteField.instIsScalarTowerZModExtension, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, Matrix.permanent_updateRow_smul, MvPowerSeries.WithPiTopology.instContinuousSMul, LieRinehartRing.leibniz_mul_right, Real.smul_map_volume_mul_left, convexOn_dist, IntermediateField.equivOfEq_symm, real_linearMap_map_smul_complex, ProbabilityTheory.covariance_smul_left, LinearMap.toMatrixAlgEquiv_id, Seminorm.convexOn, HasDerivWithinAt.fun_finset_prod, Submodule.traceDual_top', IntermediateField.restrictRestrictAlgEquivMapHom_apply, WeakDual.CharacterSpace.continuousMapEval_bijective, instIsPushoutPolynomial_1, strictConcaveOn_sqrt_mul_log_Ioi, TrivSqZeroExt.map_comp_inlAlgHom, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, Ideal.map_includeRight_eq, MeasureTheory.Measure.measure_preimage_isAddLeftInvariant_eq_smul_of_hasCompactSupport, MeasureTheory.lpNorm_smul_measure_of_ne_zero, IntermediateField.fieldRange_comp_val, SchwartzMap.smulLeftCLM_sum, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, FractionRing.instIsScalarTower_1, IntermediateField.adjoin.powerBasis_gen, logDeriv_eqOn_iff, cuspFunction_smul, IsSmoothAt.exists_isStandardEtale_mvPolynomial, IntermediateField.equivOfEq_rfl, MonoidAlgebra.scalarTensorEquiv_tmul, QuadraticForm.tensorAssoc_toLinearEquiv, TensorProduct.AlgebraTensorModule.rTensor_tensor, Module.Ray.linearEquiv_smul_eq_map, IntermediateField.normal_iff_normalClosure_le, MeasureTheory.NullMeasurableSet.smul_measure, TrivSqZeroExt.eq_smul_exp_of_ne_zero, ContinuousAlternatingMap.norm_restrictScalars, ProbabilityTheory.setBernoulli_apply', ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, Polynomial.aevalTower_toAlgHom, Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul, gelfandStarTransform_symm_apply, LieSubalgebra.toEnd_mk, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, convexOn_univ_norm, Bialgebra.TensorProduct.comulAlgHom_def, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul', Ergodic.iff_mem_extremePoints_measure_univ_eq, spectrum.smul_mem_smul_iff, ProbabilityTheory.condVar_smul, Submodule.le_spanRank_restrictScalars, Matrix.det_updateRow_sum_aux, IsAdicComplete.of_lift, infEDist_smul₀, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', ContinuousLinearMap.continuous_restrictScalars, IsLocalization.instIsScalarTowerLocalizationAtPrime, MeasureTheory.instSFiniteHSMulENNRealMeasure, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, TensorProduct.instSMulCommClassTensorProduct_1, MeasureTheory.mulEquivHaarChar_smul_map, IntermediateField.relfinrank_dvd_finrank_bot, Real.concaveOn_rpow, KaehlerDifferential.tensorKaehlerEquivBase_tmul, Matrix.isRepresentation.toEnd_represents, LSeries_smul, multiple_mem_adjoin_of_mem_localization_adjoin, IsAlgebraic.smul, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, Submodule.isLocalizedModule, Matrix.toEuclideanCLM_toLp, KaehlerDifferential.tensorKaehlerEquivBase_symm_apply, WeakDual.CharacterSpace.homeoEval_naturality, StarAlgEquiv.toAlgEquiv_refl, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, IntermediateField.adjoin_simple_adjoin_simple, Module.End.hasUnifEigenvalue_iff_mem_spectrum, contDiffOn_stereoToFun, WeierstrassCurve.Projective.negAddY_smul, hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, QuadraticAlgebra.lift_apply_apply, convex_halfSpace_im_gt, MeasureTheory.FiniteMeasure.map_fst_prod, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, IntermediateField.AdjoinSimple.norm_gen_eq_one, MeasureTheory.isAddLeftInvariant_smul, IsFractionRing.instFaithfulSMul, HilbertBasis.hasSum_orthogonalProjection, LieModule.coe_genWeightSpaceOf_zero, LinearMap.BilinForm.tensorDistrib_tmul, IntermediateField.range_val, IntermediateField.instFiniteSubtypeMemBot, IntermediateField.isCyclotomicExtension_lcm_sup, QuadraticForm.baseChange_tmul, KaehlerDifferential.End_equiv_aux, Matrix.adjugate_adjugate, MeasureTheory.Measure.ae_eq_or_eq_iff_map_eq_dirac_add_dirac, finrank_quotient_span_eq_natDegree, Unitization.splitMul_injective_of_clm_mul_injective, PreSubmersivePresentation.comp_jacobian_eq_jacobian_smul_jacobian, Convex.toWeakSpace_closure, smul_def', Extension.instIsScalarTowerRing, IntermediateField.linearDisjoint_iff', IsGaloisGroup.fixedPoints_fixingSubgroup, SchwartzMap.pairing_apply, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, IntermediateField.splits_iff_mem, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, AffineIsometryEquiv.coe_ofEq_apply, TrivSqZeroExt.snd_exp, Matrix.inv_smul, MeasureTheory.Measure.Regular.smul, MeasureTheory.Measure.hausdorffMeasure_smul₀, RatFunc.instIsScalarTowerOfPolynomial_1, PowerSeries.substAlgHom_comp_substAlgHom, MeasureTheory.eLpNorm_one_smul_measure, SkewMonoidAlgebra.lift_unique, AffineSubspace.isometryEquivMap.toAffineMap_eq, Quaternion.expSeries_odd_of_imaginary, Quaternion.smul_coe, normalizedTrace_intermediateField, LinearMap.BilinForm.smul_right_of_tower, AddMonoidAlgebra.lift_apply, NormedSpace.norm_expSeries_summable_of_mem_ball', WeierstrassCurve.Projective.smul_eq, TrivSqZeroExt.map_comp_inrHom, RatFunc.smul_eq_C_mul, LieSubmodule.traceForm_eq_zero_of_isTrivial, lieEquivMatrix'_apply, instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap, Generators.CotangentSpace.compEquiv_symm_zero, LieRinehartAlgebra.toIsScalarTower, Extension.instIsScalarTowerCotangent, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, WeakDual.isCompact_closedBall, LieModule.weight_vector_multiplication, isNormalClosure_normalClosure, PointedContMDiffMap.smul_def, AdicCompletion.range_eval, IsLocalization.finsetIntegerMultiple_image, IntermediateField.finrank_eq_one_iff, IntermediateField.lift_top, LinearMap.minpoly_toMatrix', LieSubalgebra.coe_ad_pow, Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, Seminorm.comp_smul, WeierstrassCurve.Projective.add_of_Z_eq_zero_left, ordinaryHypergeometricSeries_apply_eq', AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, MeasureTheory.hasFDerivAt_convolution_right_with_param, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, EMetric.exists_forall_closedBall_subset_aux₂, exists_isIntegral_leadingCoeff_pow_smul_sub_of_isIntegralElem_of_mul_mem_range, MeasureTheory.Measure.MutuallySingular.smul, MeasureTheory.SMul.sigmaFinite, Orthonormal.inner_left_right_finset, IntermediateField.insepDegree_bot', MeasureTheory.Measure.addHaarMeasure_unique, HasCompactSupport.hasFDerivAt_convolution_right, VonNeumannAlgebra.centralizer_centralizer', CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, IntermediateField.exists_algHom_adjoin_of_splits_of_aeval, differentialIdeal_le_iff, MeasureTheory.isMulLeftInvariant_smul, TensorProduct.opAlgEquiv_apply, Extension.isScalarTower, MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_innerRegular, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, isLocalizedModule_iff, AlgebraicIndependent.lift_reprField, Extension.Hom.sub_one_tmul, Polynomial.hilbertPoly_succ, IntermediateField.isAlgebraic_adjoin, IsAlgebraic.exists_integral_multiple, id.smul_eq_mul, IsLocalRing.ResidueField.instIsScalarTower_1, Ideal.Factors.isScalarTower, gelfandTransform_map_star, FDRep.average_char_eq_finrank_invariants, polynomialFunctions.starClosure_eq_adjoin_X, instIsLiouvilleSubtypeMemIntermediateField, NumberField.mixedEmbedding.convexBodySumFun_smul, TensorProduct.lmulEquiv_eq_lidOfCompatibleSMul, LinearMap.pow_eq_aeval_mod_charpoly, AffineIsometryEquiv.ofTop_symm_apply_coe, NumberField.mixedEmbedding.logMap_real_smul, LinearMap.tensorProductEnd_apply, Bialgebra.TensorProduct.assoc_tmul, KaehlerDifferential.tensorKaehlerEquiv_tmul, Module.AEval'.X_pow_smul_of, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, QuaternionAlgebra.Basis.j_mul_k, Ideal.ResidueField.liftₐ_comp_toAlgHom, RootPairing.GeckConstruction.trace_toEnd_eq_zero, PowerSeries.HasSubst.smul_X', Unitary.conjStarAlgAut_ext_iff', PowerSeries.expand_smul, Real.ball_eq_openSegment, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, Module.End.rTensorAlgHom_apply_apply, Seminorm.bound_of_continuous, PowerBasis.equivAdjoinSimple_aeval, MeasureTheory.Measure.rnDeriv_smul_left', MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul', IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, DifferentiableAt.fderiv_restrictScalars, LieModule.isFaithful_iff, Matrix.inv_def, Module.FaithfullyFlat.faithfulSMul, AdicCompletion.transitionMap_comp_eval, selfAdjoint.unitarySelfAddISMul_coe, Matrix.permanent_updateCol_smul, AffineIsometryEquiv.ofEq_symm, IsScalarTower.Algebra.ext_iff, ModularForm.instIsScalarTowerComplex, AlgebraNorm.smul', Ideal.quotientToQuotientRangePowQuotSucc_mk, Nat.Partition.summable_genFun_term, MeasureTheory.Measure.pi_map_eval, HasDerivWithinAt.arsinh, MvPowerSeries.coeff_subst, Polynomial.Gal.instIsScalarTowerSplittingField, IsAzumaya.mulLeftRight_comp_congr, IntermediateField.botContinuousSMul, MeasureTheory.isMulRightInvariant_smul, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, Polynomial.sup_aeval_range_eq_top_of_isCoprime, WeierstrassCurve.Projective.negY_smul, eq_separableClosure_iff, Submodule.spanRank_restrictScalars_eq, LieSubmodule.toEnd_comp_subtype_mem, MeasureTheory.eLpNorm'_smul_measure, instIsScalarTowerPolynomial, LinearMap.minpoly_dvd_charpoly, PowerSeries.IsWeierstrassDivisorAt.mod'_mk_eq_mod, hasFDerivAt_list_prod', segment_eq_Icc', Polynomial.notMem_nonZeroDivisors_iff, hasFDerivAt_integral_of_dominated_loc_of_lip', MeasureTheory.eLpNorm_smul_measure_of_ne_top, Rat.instSMulCommClass', LieAlgebra.ad_nilpotent_of_nilpotent, AlgHom.mulLeftRight_apply, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul, stereoToFun_apply, IntermediateField.normal_iff_forall_fieldRange_le, autEquivZmod_symm_apply_intCast, PointwiseConvergenceCLM.equivWeakDual_apply, MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_regular, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, MeasureTheory.FinMeasAdditive.smul_measure_iff, MeasureTheory.Measure.map_eq_sum, LieModule.rank_eq_natTrailingDegree, Submodule.fg_restrictScalars, Module.End.aeval_apply_of_hasEigenvector, AdicCompletion.instIsHausdorff, IsAzumaya.bij, IsGalois.normalAutEquivQuotient_apply, Real.strictConvexOn_mul_log, Derivation.liftKaehlerDifferential_comp, instSMulDistribClassAlgEquiv, KaehlerDifferential.ker_map, TensorProduct.lift_comp_includeRight, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, AlgHom.toKerIsLocalization_apply, LinearMap.BilinForm.sum_repr_mul_repr_mul, MeasureTheory.Measure.rnDeriv_smul_right_of_ne_top', AdicCompletion.coe_eval, MonoidAlgebra.lift_unique, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, AdicCompletion.coe_ofTensorProductEquivOfFiniteNoetherian, Polynomial.SplittingFieldAux.scalar_tower', SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', WeierstrassCurve.Projective.dblX_smul, IntermediateField.rank_adjoin_eq_one_iff, IsBaseChange.lift_comp, taylor_mean_remainder, StrictMono.strictConvexOn_univ_of_deriv, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, LinearMap.toMatrixAlgEquiv'_apply, LieAlgebra.ad_pow_lie, binomialSeries_apply, Subalgebra.mem_saturation_iff, SubMulAction.algebraMap_mem, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, ContinuousLinearMap.coe_restrict_scalarsL', LinearMap.toMatrix'_algebraMap, EuclideanHalfSpace.convex, instIsScalarTowerAtPrimeFractionRing, TensorProduct.counit_tmul, Matrix.det_updateRow_sum, Extension.CotangentSpace.map_sub_map, inner_smul_real_right, fourierSubalgebra_separatesPoints, LieModule.isNilpotent_toEnd_of_isNilpotent₂, hasFDerivAt_exp_smul_const', ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, Quaternion.exp_of_re_eq_zero, IsPreconnected.convex, MeasureTheory.integrable_smul_measure, CliffordAlgebra.contractLeft_ι_mul, PolynomialModule.isScalarTower', IntermediateField.finrank_eq_fixingSubgroup_index, WeierstrassCurve.Projective.addXYZ_neg, RootPairing.GeckConstruction.span_range_h'_eq_top, Submodule.norm_subtypeL, MeasureTheory.setLAverage_eq', WeierstrassCurve.Projective.addZ_smul, ProbabilityTheory.Kernel.instIsIrreducibleHSMulENNRealMeasure, LinearMap.toMatrixOrthonormal_symm_apply, segment_eq_Icc, MeasureTheory.nullMeasurableSet_smul_measure_iff, QuadraticForm.tmul_tensorAssoc_apply, Polynomial.coeff_det_X_add_C_card, SchwartzMap.smulLeftCLM_const, HopfAlgebra.sum_antipode_mul_eq_smul, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, Module.instFiniteSubtypeMemIdealOfIsNoetherian, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, PointwiseConvergenceCLM.equivWeakDual_symm_apply, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of, QuadraticAlgebra.smul_C, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, MeasureTheory.Measure.toSignedMeasure_smul, HasStrictDerivAt.fun_finset_prod, LSeriesHasSum.smul, IsGaloisGroup.fixingSubgroup_fixedPoints, PowerSeries.smul_weierstrassMod, InfiniteGalois.proj_adjoin_singleton_val, IntermediateField.lift_inf, convex_halfSpace_im_lt, exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂, IsLocalizedModule.fromLocalizedModule_mk, VonNeumannAlgebra.mem_carrier, WeakDual.isSeqCompact_closedBall, NormedSpace.expSeries_apply_eq, Real.convexOn_log_Gamma, AdicCompletion.ofTensorProduct_bijective_of_finite_of_isNoetherian, WeakDual.exists_countable_separating, Derivation.commutator_coe_linear_map, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, IntermediateField.smul_mem, MeasureTheory.hausdorffMeasure_lineMap_image, CliffordAlgebra.star_smul, IntermediateField.exists_algHom_of_splits, intervalIntegral.integral_smul_measure, strictConvex_iff_convex, TensorProduct.isPushout, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Module.End.isSemisimple_sub_algebraMap_iff, PowerBasis.equivAdjoinSimple_gen, Polynomial.aeval_apply_smul_mem_of_le_comap, RingHom.toKerIsLocalization_apply, Derivation.coe_comp, ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule, infEdist_smul₀, Field.Emb.Cardinal.equivSucc_coherence, MonomialOrder.degree_smul_le, IsDedekindDomain.FiniteAdeleRing.instIsScalarTower, map_equiv_traceDual, IntermediateField.restrictScalars_adjoin_eq_sup, FiniteGaloisIntermediateField.isGalois, MeasureTheory.MemLp.smul_measure, Matrix.isRepresentation.toEnd_exists_mem_ideal, Representation.asAlgebraHom_single_one, MeasureTheory.FiniteMeasure.instContinuousSMulNNReal, MvPolynomial.smulCommClass_right, Polynomial.smul_mem_lifts, HomogeneousLocalization.instIsScalarTowerSubtypeMemOfNatLocalization, IsLocalization.smul_bijective, cfcHom_real_eq_restrict, TensorProduct.AlgebraTensorModule.dualDistrib_apply, IntermediateField.Lifts.lt_iff, IsLocalization.map_smul, UniformConvexOn.convexOn, Generators.instIsScalarTowerRing, LieSubalgebra.coe_incl', IntermediateField.extendScalars_le_iff, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, IsLocalization.exists_isIntegral_smul_of_isIntegral_map, MeasureTheory.Measure.ae_eq_or_eq_iff_eq_dirac_add_dirac, tendsto_integral_mul_one_add_inv_smul_sq_pow, Matrix.inv_adjugate, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, Submodule.lTensorOne'_tmul, Representation.instIsScalarTowerMonoidAlgebraAsModule, MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul, MeasureTheory.Measure.conv_smul_left, AdjoinRoot.isScalarTower_right, IsStrictlyPositive.smul, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isOpen, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul', Matrix.det_one_add_X_smul, ContinuousMap.adjoin_id_eq_span_one_union, compHom_smul_def, IsGaloisGroup.fixedPoints_bot, Seminorm.const_isBounded, AffineBasis.det_smul_coords_eq_cramer_coords, Splits.algebraicClosure, PowerBasis.equivAdjoinSimple_symm_gen, LieModule.exists_forall_pow_toEnd_eq_zero, MeasureTheory.Measure.isOpenPosMeasure_smul, IntermediateField.coe_val, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Submodule.rTensorOne'_tmul, JacobsonNoether.exist_pow_eq_zero_of_le, Module.End.IsSemisimple.aeval, RatFunc.smul_eq_C_smul, WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_left, MeasureTheory.setAverage_eq', StrongDual.dualPairing_separatingLeft, AdicCompletion.of_bijective_iff, lsmul_injective, Real.doublingGamma_log_convex_Ioi, KaehlerDifferential.derivationQuotKerTotal_apply, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, MonoidAlgebra.isScalarTower_monoidAlgebra, ProbabilityTheory.Kernel.comp_discard', strongConcaveOn_iff_convex, IsIntegral.smul, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, Unitization.norm_eq_sup, Matrix.kroneckerTMulAlgEquiv_symm_apply, Matrix.ofLp_toEuclideanCLM, HasStrictFDerivAt.restrictScalars, IntermediateField.finrank_eq_finrank_subalgebra, MeasureTheory.Measure.instSMulCommClassDomMulActNNReal, LieSubmodule.toEnd_restrict_eq_toEnd, ordinaryHypergeometric_eq_tsum, concaveOn_univ_of_deriv2_nonpos, hasDerivAt_exp_smul_const, AddMonoidAlgebra.instIsPushout, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', IsAlgebraic.exists_smul_eq_mul, CliffordAlgebra.instSMulCommClass, IntermediateField.restrictRestrictAlgEquivMapHom_injective, IsAdicComplete.of_comp_lift, IsLocalization.map_integerMultiple, LieModule.IsFaithful.injective_toEnd, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure, Height.mulHeight_smul_eq_mulHeight, MeasureTheory.Integrable.to_average, ENNReal.nnreal_smul_lt_top_iff, AdicCompletion.ofTensorProduct_bijective_of_pi_of_fintype, hasSum_sq_fourierCoeffOn, convexOn_descPochhammer_eval, RCLike.smul_im, RatFunc.instIsScalarTowerOfIsDomainOfPolynomial, MeasureTheory.tilted_const', AddMonoidAlgebra.instIsPushout', Real.concaveOn_negMulLog, IntermediateField.finrank_adjoin_eq_one_iff, KaehlerDifferential.instSMulCommClassTensorProduct_1, IntermediateField.normal_iff_forall_map_le', Submodule.restrictScalars_traceDual, ContinuousLinearMap.coe_restrictScalarsIsometry, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, MeasureTheory.OuterMeasure.instIsCentralScalar, IntermediateField.normal_iff_forall_fieldRange_eq, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, MeasureTheory.smul_le_stoppedValue_hitting, LocalizedModule.smul'_mk, CommCStarAlgebra.toStarModule, Extension.Cotangent.map_comp, MeasureTheory.Measure.isMulInvariant_eq_smul_of_compactSpace, Submodule.mulRightMap_eq_mulMap_comp, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, IsScalarTower.subalgebra, MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, MeasureTheory.measure_eq_div_smul, IsBaseChange.prodMap, EuclideanQuadrant.convex, trace_comp_trace_of_basis, IsLocalizedModule.toLocalizedQuotient', differentialIdeal_le_fractionalIdeal_iff, IntermediateField.finrank_bot, AdicCompletion.map_mk, MultilinearMap.freeFinsuppEquiv_def, Ideal.quotientToQuotientRangePowQuotSucc_surjective, DoubleCentralizer.algebraMap_snd, WeakDual.polar_def, LieModule.trace_comp_toEnd_genWeightSpace_eq, RCLike.wInner_const_left, AddMonoidAlgebra.lift_single, InfiniteGalois.restrict_fixedField, FormalMultilinearSeries.ofScalarsSum_zero, IsBaseChange.end, Ideal.localized₀_eq_restrictScalars_map, IntermediateField.sepDegree_bot, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, KaehlerDifferential.tensorKaehlerEquiv_left_inv, TensorProduct.rid_tmul, Submodule.rTensorOne_tmul, MonomialOrder.sPolynomial_decomposition, killingForm_apply_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, LinearMap.toMatrix_algebraMap, LinearMap.spectrum_toMatrix, AdicCompletion.ofAlgEquiv_apply, IntermediateField.finInsepDegree_bot', WithVal.instIsScalarTower_1, LieSubalgebra.mem_engel_iff, norm_eq_norm_adjoin, TensorProduct.cancelBaseChange_tmul, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, MeasureTheory.Measure.smul_absolutelyContinuous, WeakDual.CharacterSpace.compContinuousMap_apply, Matrix.adjugate_smul, KaehlerDifferential.kerTotal_map, IntermediateField.restrictScalars_bot_eq_self, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, DoubleCentralizer.algebraMap_toProd, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, MeasureTheory.JordanDecomposition.smul_posPart, instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient, HasFPowerSeriesAt.restrictScalars, Real.convexOn_Gamma, edist_smul₀, ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smul, WeierstrassCurve.Projective.dblXYZ_of_Z_eq_zero, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, ContDiffAt.restrictScalars_iteratedFDeriv, LinearIsometryEquiv.toLinearEquiv_smul, Valuation.HasExtension.instIsScalarTower_valuationSubring', CliffordAlgebra.ofBaseChangeAux_ι, Unitary.toAlgEquiv_conjStarAlgAut, IsScalarTower.of_algebraMap_eq', instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient, Derivation.liftKaehlerDifferential_unique_iff, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, Derivation.liftKaehlerDifferential_D, Matrix.toLinAlgEquiv'_apply, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, MeasureTheory.Measure.smul_finite, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure, MvPolynomial.dvd_smul_X_iff_exists, Generators.σ_smul, Ideal.basisSpanSingleton_apply, CyclotomicRing.instIsScalarTowerCyclotomicField, RatFunc.faithfulSMul, LinearMap.aeval_eq_aeval_mod_charpoly, FractionalIdeal.mem_spanSingleton, LinearMap.hasEigenvalue_zero_tfae, Matrix.minpoly_toLin', DivisionRing.continuousConstSMul_rat, QuadraticForm.tensorDistrib_tmul, Matrix.nonsing_inv_apply, Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left, MeasureTheory.FiniteMeasure.smul_testAgainstNN_apply, derivationToSquareZeroEquivLift_symm_apply_apply_coe, NumberField.mixedEmbedding.norm_smul, PositiveLinearMap.gnsStarAlgHom_apply, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, LieModule.toEnd_eq_iff, discr_mul_isIntegral_mem_adjoin, MvPolynomial.restrictScalars_restrictSupportIdeal, IntermediateField.finrank_sup_le, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePos, Complex.lintegral_comp_polarCoord_symm, ordinaryHypergeometricSeries_apply_eq, WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, IntermediateField.adjoinRootEquivAdjoin_apply_root, IntermediateField.normalClosureOperator_apply, AffineSubspace.isometryEquivMap.coe_apply, MeasureTheory.eLpNorm_le_of_ae_enorm_bound, QuadraticAlgebra.lift_symm_apply_coe, MeasureTheory.Measure.nnreal_smul_coe_apply, LinearEquiv.lieConj_apply, LieModule.isNilpotent_toEnd_of_mem_rootSpace, HasFDerivWithinAt.restrictScalars, algebraMap_eq_smul_one, StrongConcaveOn.strictConcaveOn, WeierstrassCurve.Projective.smul_fin3, StarAlgEquiv.toAlgEquiv_trans, RatFunc.instIsScalarTowerPolynomial, MeasureTheory.Measure.ae_ennreal_smul_measure_iff, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, Real.closedBall_eq_segment, Seminorm.closedBall_smul, IntermediateField.rank_bot, Real.isScalarTower, differentiableWithinAt_iff_restrictScalars, AdicCompletion.of_surjective, TrivSqZeroExt.exp_def, CliffordAlgebraQuaternion.ofQuaternion_mk, derivWithin_comp_mul_left, LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv', instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Matrix.adjugate_adjugate', RCLike.ofReal_alg, le_restrictScalars_separableClosure, MeasureTheory.Measure.addHaarScalarFactor_smul_smul, SchwartzMap.smulLeftCLM_add, MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg, Module.IsTorsionFree.to_faithfulSMul, TensorProduct.AlgebraTensorModule.restrictScalars_rTensor, LieDerivation.toLinearMapLieHom_injective, WeierstrassCurve.Projective.neg_of_Z_ne_zero, PointedContMDiffMap.instIsScalarTowerSomeENatTop, Module.Dual.baseChange_apply_tmul, FormalMultilinearSeries.ofScalarsSum_eq_tsum, MeasureTheory.IsFiniteMeasure.average, IntermediateField.instIsScalarTowerSubtypeMem_1, MeasureTheory.hausdorffMeasure_homothety_image, ContinuousMultilinearMap.integral_apply, MeasureTheory.Measure.absolutelyContinuous_smul, IsAzumaya.coe_tensorEquivEnd, spectralNorm_smul, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, LinearMap.eval_charpoly, IsCentral.instContinuousLinearMap, tsirelson_inequality, MeasureTheory.count_withDensity, Real.convex_iff_isPreconnected, WeakDual.isClosed_closedBall, InformationTheory.convexOn_klFun, HasDerivAt.arsinh, IntermediateField.finrank_bot_mul_relfinrank, LieModule.toEnd_lie, QuadraticForm.tensorAssoc_symm_apply, MonoidAlgebra.tensorEquiv_tmul, Presentation.tensorModelOfHasCoeffsEquiv_tmul, IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAt, MeasureTheory.Measure.smul_measure_isMulInvariant_le_of_isCompact_closure, Module.End.isRoot_of_hasEigenvalue, ExteriorAlgebra.toTrivSqZeroExt_ι, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, Submodule.torsionBy.mk_ideal_smul, RCLike.wInner_const_right, LinearMap.toMatrixAlgEquiv_symm, MeasureTheory.pdf.IsUniform.pdf_eq, MeasureTheory.FiniteMeasure.toMeasure_normalize_eq_of_nonzero, MeasureTheory.Measure.measure_isAddHaarMeasure_eq_smul_of_isEverywherePos, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, LinearMap.minpoly_toMatrix, MeasureTheory.IsFiniteMeasureOnCompacts.smul_nnreal, ContinuousAlternatingMap.continuous_restrictScalars, IntermediateField.finiteDimensional_adjoin, MvPolynomial.smul_eval, IntermediateField.lift_injective, PadicComplex.instIsScalarTowerPadicPadicAlgCl, Quaternion.im_exp, LinearMap.toMatrixOrthonormal_apply, Representation.asAlgebraHom_of, convex_halfSpace_re_ge, MeasureTheory.Measure.exists_sum_smul_dirac, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_measurableSet, KaehlerDifferential.isBaseChange, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, diffToIdealOfQuotientCompEq_apply, KaehlerDifferential.instSMulCommClassTensorProduct, Polynomial.mul_scaleRoots, MvPowerSeries.rescale_homogeneous_eq_smul, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, DifferentiableWithinAt.restrictScalars_fderivWithin, WeierstrassCurve.Projective.add_of_Z_eq_zero_right, LinearMap.prodMapAlgHom_apply_apply, Polynomial.Monic.finite_quotient, IntermediateField.AdjoinSimple.trace_gen_eq_zero, IntermediateField.lift_sepDegree_bot', MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero, UniformConcaveOn.concaveOn, NormedSpace.norm_expSeries_summable', Polynomial.roots_smul_nonzero, MeasureTheory.measureReal_ennreal_smul_apply, Extension.Hom.mapKer_apply_coe, toMatrix_lmul', LieAlgebra.ad_apply, LieAlgebra.toEnd_pow_apply_mem, Presentation.tensorModelOfHasCoeffsHom_tmul, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, Ioo_subset_openSegment, toWeakSpace_closedConvexHull_eq, Unitization.norm_def, MvPolynomial.C_mul', selfAdjoint.star_coe_unitarySelfAddISMul, MeasureTheory.Measure.InnerRegularWRT.smul, IntermediateField.finSepDegree_adjoin_simple_le_finrank, Subalgebra.smul_mem, CliffordAlgebraComplex.toComplex_ι, NormedSpace.expSeries_apply_eq', convex_halfSpace_im_ge, Quaternion.coe_mul_eq_smul, Ideal.Quotient.isScalarTower_of_liesOver, MeasureTheory.Measure.comap_smul, TensorProduct.opAlgEquiv_symm_apply, MeasureTheory.condLExp_smul_le, IntermediateField.card_algHom_adjoin_integral, MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct, MonomialOrder.degree_smul_of_isRegular, WeierstrassCurve.Projective.negDblY_smul, uniformConcaveOn_zero, AffineSubspace.subtypeₐᵢ_linear, IntermediateField.relrank_dvd_rank_bot, LinearMap.det_restrictScalars, LieAlgebra.conj_ad_apply, RestrictScalars.ringEquiv_map_smul, NNRat.instSMulCommClass, RestrictScalars.lsmul_apply_apply, convex_halfSpace_re_lt, AdicCompletion.mk_surjective, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply, LSeriesSummable.smul_iff, Complex.instStarModuleReal, QuadraticAlgebra.smul_coe, Generators.self_algebra_smul, Polynomial.natSepDegree_smul_nonzero, StarAlgEquiv.coe_symm_toAlgEquiv, ContinuousAlternatingMap.restrictScalarsLI_apply, QuaternionAlgebra.Basis.k_mul_k, MeasureTheory.IsFiniteMeasureOnCompacts.smul, MeasureTheory.count_withDensity', TrivSqZeroExt.liftEquivOfComm_apply, TensorProduct.isBaseChange, Module.End.finite_spectrum, fourierSubalgebra_coe, MeasureTheory.Measure.map_right_mul_eq_modularCharacterFun_smul, Polynomial.toAddCircle_monomial_eq_smul_fourier, NumberField.finite_of_discr_bdd, RCLike.instStarModuleReal, instIsPushoutPolynomial, CliffordAlgebra.toBaseChange_comp_reverseOp, AdicCompletion.map_ext''_iff, MonoidAlgebra.instIsPushout', cfcHom_nnreal_eq_restrict, Matrix.IsHermitian.spectral_theorem, isIntegral_discr_mul_of_mem_traceDual, MeasureTheory.addEquivAddHaarChar_smul_map, IsBaseChange.iff_lift_unique, IntermediateField.LinearDisjoint.of_inf_eq_bot, PrimeSpectrum.zeroLocus_smul_of_isUnit, Tactic.ComputeAsymptotics.Majorized.smul, strictConvexOn_rpow, coord_norm', endVecAlgEquivMatrixEnd_apply_apply, MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN, Basis.mem_ideal_iff', Ideal.quotientToQuotientRangePowQuotSucc_injective, WeakDual.isClosed_polar, MeasureTheory.OuterMeasure.le_smul_caratheodory, idealMap_isLocalizedModule, AlgebraicIndependent.liftAlgHom_comp_reprField, UniformConcaveOn.strictConcaveOn, hasFDerivAt_exp_smul_const, exists_leadingCoeff_pow_smul_mem_radical_conductor, IntermediateField.finrank_top', LinearMap.aeval_self_charpoly, Measurable.smul_measure, Real.isBoundedSMul, IsLocalization.smul_mk'_one, PolynomialModule.instIsScalarTower, IntermediateField.inclusion_self, IntermediateField.lift_bot, LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank, MeasureTheory.isMulLeftInvariant_smul_nnreal, IntermediateField.normalClosure_of_normal, HasFPowerSeriesWithinAt.restrictScalars, LieAlgebra.rootSpace_comap_eq_genWeightSpace, Ideal.constr_basisSpanSingleton, TrivSqZeroExt.sndHom_comp_map, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, MeasureTheory.condLExp_bot_ae_eq, InfiniteGalois.isOpen_iff_finite, MulAlgebraNormClass.toSeminormClass, KaehlerDifferential.map_compDer, PowerSeries.IsWeierstrassDivisorAt.mod_smul, TrivSqZeroExt.map_comp_map, MeasureTheory.SignedMeasure.rnDeriv_smul, MeasureTheory.instIsProbabilityMeasureHAddMeasureHSMulNNRealToNNRealSymm, AdicCompletion.of_ofLinearEquiv_symm, AdicCompletion.kerProj_of, MeasureTheory.hausdorffMeasure_smul_right_image, LieDerivation.commutator_coe_linear_map, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LieModule.Cohomology.smul_apply_apply, AddMonoidAlgebra.tensorEquiv_tmul, Matrix.spectrum_toLin, IntermediateField.relfinrank_bot_left, IsPushout.tensorProduct_tensorProduct, MeasureTheory.laverage_union_mem_segment, Module.AEval.mem_mapSubmodule_symm_apply, Real.map_linearMap_volume_pi_eq_smul_volume_pi, CFC.log_smul', CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, isConformalMap_complex_linear_conj, TrivSqZeroExt.instL1IsBoundedSMul, LieModule.toEnd_pow_lie, Asymptotics.Filter.Tendsto.isBigOTVS_one, MulAlgebraNormClass.map_smul_eq_mul, AdicCompletion.evalOneₐ_of, IntermediateField.le_extendScalars_iff, StarAlgEquiv.restrictScalars_apply, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, RatFunc.instIsScalarTowerOfPolynomial, TensorProduct.ext_iff, IsAdicComplete.StrictMono.of_comp_lift, UnitAddTorus.hasSum_mFourier_series_of_summable, LieSubmodule.coe_toEnd, hasDerivWithinAt_comp_mul_left_smul_iff, pow_smul_mem_adjoin_smul, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, SchwartzMap.tsupport_smulLeftCLM_subset, Extension.instIsScalarTowerRing_1, IntermediateField.extendScalars.orderIso_symm_apply_coe, cfcₙHom_real_eq_restrict, MeasureTheory.Measure.measure_isAddLeftInvariant_eq_vadd_of_ne_top, Module.isTorsionFree_iff_faithfulSMul, Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule, Subalgebra.instSMulMemClass, LieModule.toEnd_apply_apply, UnitAddTorus.mFourierSubalgebra_separatesPoints, Monotone.convexOn_univ_of_deriv, aemeasurable_smul_measure_iff, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, FractionalIdeal.smul_mem_dual_one, WeierstrassCurve.Projective.add_smul_equiv, mem_skewAdjointMatricesLieSubalgebra_unit_smul, Presentation.instFaithfulSMulCore, IsLocalization.exists_smul_mem_of_mem_adjoin, MeasureTheory.isAddRightInvariant_smul, IntermediateField.sepDegree_bot', Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, LieModule.commute_toEnd_of_mem_center_right, ProbabilityTheory.mgf_smul_left, KaehlerDifferential.D_tensorProductTo, IntermediateField.inclusion_injective, Polynomial.IsDistinguishedAt.algEquivQuotient_symm_apply, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, ContinuousAlternatingMap.restrictScalarsCLM_apply, IsSemisimpleModule.exists_end_algEquiv, IntermediateField.LinearDisjoint.bot_right, Ideal.ResidueField.algHom_ext_iff, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, RingHom.smul_toAlgebra', MeasureTheory.Measure.mul_addHaarScalarFactor_smul, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, MeasureTheory.Measure.map_addHaar_smul, TensorProduct.algEquivIncludeRange_toAlgHom, ContinuousLinearMap.intervalIntegral_apply, LieModule.toEnd_baseChange, MvPolynomial.coe_smul, liftOfDerivationToSquareZero_apply, LocalizedModule.mul_by_divBy, LindemannWeierstrass.integral_exp_mul_eval, ModularFormClass.hasSum_qExpansion_of_abs_lt, SchwartzMap.smulLeftCLM_neg, IntermediateField.normal_iff_forall_map_le, RestrictScalars.addEquiv_symm_map_smul_smul, AdicCompletion.mk_smul_top_ofAlgEquiv_symm, MeasureTheory.Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, spectrum.differentiableOn_inverse_one_sub_smul, IsLocalization.exist_integer_multiples_of_finset, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, ValuationSubring.ofPrime_scalar_tower, IsScalarTower.of_compHom, separableClosure.isAlgebraic, TrivSqZeroExt.algebraMap_eq_inl, IsAlgebraic.iff_exists_smul_integral, RootPairing.GeckConstruction.f_lie_v_ne, Matrix.toLinAlgEquiv_apply, AdicCompletion.tensor_map_id_left_eq_map, MeasureTheory.inv_measure_univ_smul_eq_self, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, NNReal.instMeasurableSMul₂ENNReal, instIsScalarTowerCyclotomicField, Generators.CotangentSpace.exact, DoubleCentralizer.algebraMap_fst, WeierstrassCurve.Projective.add_smul_of_not_equiv, inner_smul_real_left, MeasureTheory.Measure.isMulLeftInvariant_eq_smul, StarSubalgebra.starModule, MvPolynomial.dvd_X_iff_exists, IsLocalization.map_eq_toLinearMap_mapₐ, IntermediateField.rank_eq_one_iff, AdicCompletion.factor_eval_liftRingHom, HasStrictDerivAt.arsinh, LSeries.term_smul_apply, ContinuousLinearMap.isEmbedding_restrictScalars, Matrix.det_smul_adjugate_adjugate, TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, IsLocalization.exist_integer_multiples_of_finite, Module.End.eigenspace_div, Submodule.toLocalizedQuotient'_mk, CuspForm.instIsScalarTowerComplex, Extension.Hom.subToKer_apply_coe, NNReal.segment_eq_Icc, spectralNorm.eq_of_normalClosure, RootPairing.GeckConstruction.e_lie_v_ne, Polynomial.span_minpoly_eq_annihilator, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, IsAlgebraic.exists_smul_eq_mul, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, SchwartzMap.pairing_continuous_left, LieAlgebra.SpecialLinear.val_single, spectralNorm.eq_of_normalClosure', AdicCompletion.of_inj, SchwartzMap.integralCLM_apply, LieModule.isNilpotent_iff_forall, MeasureTheory.VAddInvariantMeasure.vadd_nnreal, LieModule.isNilpotent_toEnd_sub_algebraMap, AdicCompletion.ofTensorProduct_tmul, continuous_algebraMap_iff_smul, KaehlerDifferential.kerTotal_mkQ_single_smul, MonoidAlgebra.lift_apply, normalizedTrace_minpoly, lieEquivMatrix'_symm_apply, separableClosure.isSepClosure, LieSubalgebra.instIsNoetherianSubtypeMem, IsLocalization.instIsScalarTowerAtPrimeFractionRing, InfiniteGalois.toAlgEquivAux_eq_liftNormal, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, MeasureTheory.Measure.IsHaarMeasure.smul, MeasureTheory.Measure.InnerRegular.smul_nnreal, isNilpotent_tensor_residueField_iff, Ring.instIsScalarTowerNormalClosure, IsLocalizedModule.isScalarTower_module, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, Localization.AtPrime.instIsScalarTower_1, Polynomial.sup_ker_aeval_le_ker_aeval_mul, strictConvex_iff_ordConnected, Ergodic.iff_mem_extremePoints, IntermediateField.normalClosure_def'', MeasureTheory.HasFiniteIntegral.smul_measure, Ideal.rank_pow_quot_aux, extremePoints_doublyStochastic, SchwartzMap.lineDerivOp_fourierInv_eq, Function.Periodic.cuspFunction_smul, LieAlgebra.Orthogonal.jd_transform, MeasureTheory.JordanDecomposition.smul_negPart, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, WeierstrassCurve.Projective.addU_smul, Localization.AtPrime.instIsScalarTower, Subfield.relrank_eq_rank_of_le, WeakDual.CharacterSpace.norm_le_norm_one, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, KaehlerDifferential.isLocalizedModule, IntermediateField.minpoly_eq, MeasureTheory.isAddRightInvariant_smul_nnreal, Matrix.det_updateCol_smul, Ideal.smul_restrictScalars, Matrix.det_updateCol_sum, Extension.H1Cotangent.map_apply_coe, ContinuousLinearMap.coe_restrictScalarsL, IntermediateField.isSplittingField_iff, MeasureTheory.Measure.mconv_smul_right, exists_integral_multiples, MeasureTheory.SMulInvariantMeasure.smul_nnreal, LocalizedModule.instIsScalarTower, MeasureTheory.mulEquivHaarChar_smul_preimage, EssFiniteType.aux, normalizedTrace_eq_of_finiteDimensional_apply, Matrix.charpoly_vecMulVec, IntermediateField.topEquiv_symm_apply_coe, FiniteGaloisIntermediateField.adjoin_val, MvPowerSeries.HasSubst.smul, LieAlgebra.rank_le_finrank_engel, IsBaseChange.dual, NumberField.mixedEmbedding.convexBodyLT_convex, MeasureTheory.Measure.measure_preimage_isMulLeftInvariant_eq_smul_of_hasCompactSupport, RestrictScalars.isScalarTower, derivWithin_fun_finset_prod, tsum_sq_fourierCoeffOn, WeierstrassCurve.Projective.add_of_Y_eq, Subalgebra.lTensorBot_tmul, HasDerivWithinAt.finset_prod, ProbabilityTheory.covariance_smul_right, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, QuadraticAlgebra.mul_C_eq_smul, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, IntermediateField.AdjoinSimple.normal_algebraicClosure, toMatrix_lsmul, AlgEquiv.moduleEndSelf_apply_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, convex_setOf_holderWith, Ideal.rank_pow_quot, IntermediateField.normal_iff_forall_map_eq', WeierstrassCurve.Projective.equation_smul, TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent, IntermediateField.intermediateFieldMap_apply_coe, IntermediateField.topEquiv_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, Module.End.baseChangeHom_apply_apply, WeierstrassCurve.Projective.add_of_X_ne, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, convexOn_pow, MeasureTheory.Measure.prod_smul_right, Matrix.isRepresentation.toEnd_surjective, IntermediateField.exists_algHom_adjoin_of_splits', Real.strictConcaveOn_sqrt, Generators.CotangentSpace.compEquiv_symm_inr, ContinuousLinearMap.norm_restrictScalars, normalizedTrace_def, NormedAlgebra.norm_smul_le, Matrix.toLinAlgEquiv_self, instFaithfulSMul_1, MvPowerSeries.rescale_eq_subst, MeasureTheory.JordanDecomposition.real_smul_posPart_neg, ExistsContDiffBumpBase.w_def, FiniteField.minpoly_frobeniusAlgHom, instSMulCommClass, Module.Basis.baseChange_repr_tmul, Matrix.coeff_det_one_add_X_smul_one, Homeomorph.compStarAlgEquiv'_apply, Module.AEval'_def, MeasureTheory.OuterMeasure.smul_boundedBy, Coalgebra.TensorProduct.assoc_tmul, IntermediateField.AdjoinSimple.isIntegral_gen, Basis.mem_ideal_iff, TensorProduct.AlgebraTensorModule.lift_apply, LieAlgebra.IsKilling.rootSystem_pairing_apply, InformationTheory.strictConvexOn_klFun, MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_regular, ediam_smul₀, IntermediateField.exists_lt_finrank_of_infinite_dimensional, deriv_finset_prod, KaehlerDifferential.quotKerTotalEquiv_symm_apply, Polynomial.aeval_eq_sum_range, Matrix.mulVec_cramer, AdicCompletion.of_injective, LSeries.mul_delta_eq_smul_delta, MeasureTheory.Measure.WeaklyRegular.smul, CliffordAlgebraDualNumber.equiv_ι, MeasureTheory.laverage_mem_openSegment_compl_self, IsAlgebraic.isNormalClosure_normalClosure, MeasureTheory.measure_eq_sub_vadd, TrivSqZeroExt.snd_map, IntermediateField.isPurelyInseparable_bot, DividedPowers.dpow_smul_right, Module.End.hasEigenvalue_iff_isRoot, IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure, TensorProduct.right_isScalarTower, TensorProduct.comul_def, WeierstrassCurve.Projective.add_of_Y_ne', ContinuousMap.adjoin_id_eq_span_one_add, MvPowerSeries.HasSubst.smul_X, AlgebraicIndependent.aevalEquivField_apply_coe, MvPolynomial.IsSymmetric.smul, WeierstrassCurve.Projective.neg_of_Z_eq_zero, RCLike.real_smul_ofReal, MeasureTheory.Measure.OuterRegular.smul, BoundedContinuousFunction.integral_add_const, Unitization.nnnorm_eq_sup, RootPairing.pairingIn_eq_add_of_root_eq_smul_add_smul, IntermediateField.LinearDisjoint.exists_field_of_isDomain, IsScalarTower.of_algebraMap_eq, AlgEquiv.moduleEndSelfOp_symm_apply, TensorProduct.directSumRight'_restrict, WeierstrassCurve.Projective.dblY_smul, IsAzumaya.toFaithfulSMul, minpoly_algEquiv_toLinearMap, Polynomial.natDegree_det_X_add_C_le, SchwartzMap.fderivCLM_fourier_eq, StarSubalgebra.smul_mem, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct, instIsScalarTowerTensorAlgebra, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, IsBaseChange.linearMapLeftRight, HomogeneousLocalization.Away.eventually_smul_mem, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, StrictAnti.strictConcaveOn_univ_of_deriv, hasSum_fourier_series_of_summable, smul_mul_assoc, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', StarAlgEquiv.ofAlgEquiv_apply, Nat.Partition.summable_genFun_term', IntermediateField.finiteDimensional_left, AffineSubspace.subtypeₐᵢ_linearIsometry, LinearMap.toMatrixAlgEquiv'_symm, MeasureTheory.FiniteMeasure.map_smul, AlgebraNorm.extends_norm', instIsPushoutFractionRingPolynomial, MeasureTheory.average_eq', LieModule.toEnd_eq_zero_iff, KaehlerDifferential.derivationTensorProduct_algebraMap, AlgebraicClosure.instIsScalarTower, Ideal.powQuotSuccInclusion_injective, le_perfectClosure_iff, perfectClosure.isAlgebraic, MvPolynomial.aevalTower_comp_toAlgHom, AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_apply, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, MeasureTheory.tilted_zero', IntermediateField.isSeparable_sup, NumberField.mixedEmbedding.logMap_real, FiniteGaloisIntermediateField.finiteDimensional, norm_one_add_smul, KaehlerDifferential.tensorProductTo_surjective, Seminorm.finset_sup_smul, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, norm_apply, instFaithfulSMulPolynomial, convexOn_exp, Seminorm.isBounded_sup, Ring.instFaithfulSMulSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, exists_leadingCoeff_pow_smul_mem_conductor, strictConvexOn_univ_of_deriv2_pos, Coalgebra.TensorProduct.assoc_symm_tmul, Complex.log_eq_integral, Matrix.det_updateCol_add_smul_self, MeasureTheory.addEquivAddHaarChar_smul_eq_comap, Submodule.smul_torsionBy, TrivSqZeroExt.fst_map, Representation.ofModule_asAlgebraHom_apply_apply, RingQuot.Rel.smul, InfiniteGalois.restrictNormalHom_continuous, Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, Localization.instFaithfulSMulAtPrimeOfNoZeroDivisors, Module.End.isIntegral, IsLocalRing.ResidueField.instIsScalarTower, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, IsGaloisGroup.subgroup, derivationOfSectionOfKerSqZero_apply_coe, instIsScalarTowerQuotientIdealResidueField, Polynomial.aeval_endomorphism, MvPolynomial.instIsPushout_1, IntermediateField.fixedField.isScalarTower, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, IsGalois.of_separable_splitting_field_aux, IntermediateField.coe_equivMap_apply, Derivation.map_smul, Matrix.isRepresentation.eq_toEnd_of_represents, LieModule.traceForm_apply_apply, MeasureTheory.mulEquivHaarChar_smul_eq_comap, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra, krullTopology_mem_nhds_one_iff, baseChange_lmul, KaehlerDifferential.mvPolynomialBasis_repr_D, QuadraticForm.tensorAssoc_apply, WeakDual.gelfandTransform_apply_apply, LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, VonNeumannAlgebra.coe_toStarSubalgebra, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, InformationTheory.convexOn_Ioi_klFun, hasFDerivAt_integral_of_dominated_of_fderiv_le, lintegral_comp_polarCoord_symm, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous, MeasureTheory.Measure.comp_smul, LinearIsometry.strictConvexSpace_range_iff, MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_innerRegular, IsIntegrallyClosed.minpoly_smul, MeasureTheory.JordanDecomposition.real_smul_negPart_neg, TrivSqZeroExt.liftEquivOfComm_symm_apply_coe, Norm.Transitivity.mul_auxMat_toSquareBlock_eq, Ergodic.mem_extremePoints_measure_univ_eq, MeasureTheory.Measure.map_const, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, AlternatingMap.measure_def, MeasureTheory.maximal_ineq, strictConcaveOn_sin_Icc, MeasureTheory.dirac_withDensity', convexOn_univ_of_deriv2_nonneg, krullTopology_mem_nhds_one_iff_of_normal, LieModule.maxGenEigenSpace_toEnd_eq_top, AlgEquiv.moduleEndSelf_symm_apply, LinearMap.restrictScalars_extendScalarsOfIsLocalization, NumberField.mixedEmbedding.normAtPlace_smul, Unitization.instStarModule, SubmersivePresentation.ofSubsingleton_algebra_smul, Matrix.toLinAlgEquiv'_toMatrixAlgEquiv', LinearEquiv.lieConj_symm, FractionalIdeal.spanSingleton_eq_spanSingleton, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, LieAlgebra.rank_eq_natTrailingDegree, Real.map_volume_mul_right, WeierstrassCurve.Projective.neg_smul, Module.End.ker_aeval_ring_hom'_unit_polynomial, lmul_isUnit_iff, MeasureTheory.Measure.haarScalarFactor_smul_smul, IsLocalization.AtPrime.faithfulSMul, QuaternionAlgebra.Basis.j_mul_i, MeasureTheory.Measure.rnDeriv_smul_left, fourierSubalgebra_closure_eq_top, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, ModularForm.prod_fintype_slash, FreeLieAlgebra.instIsCentralScalar, Matrix.kroneckerTMulAlgEquiv_apply, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, derivationToSquareZeroEquivLift_apply_coe_apply, Module.ker_algebraMap_end, MvPolynomial.algebraTensorAlgEquiv_tmul, separableClosure.isSeparable, endVecAlgEquivMatrixEnd_symm_apply_apply, LinearMap.restrictScalarsField_apply_apply, AdicCompletion.of_bijective, Bialgebra.TensorProduct.assoc_toCoalgEquiv, Complex.starConvex_slitPlane, QuadraticAlgebra.mk_eq_add_smul_omega, RCLike.nnnorm_nnqsmul, MvPolynomial.instIsPushout, LieAlgebra.mem_corootSpace', Valuation.HasExtension.mk_smul_mk, Matrix.toLinAlgEquiv'_one, IntermediateField.adjoin.finiteDimensional, PowerSeries.coeff_subst_finite, IntermediateField.botEquiv_def, liftOfDerivationToSquareZero_mk_apply', le_algebraicClosure_iff, HomogeneousLocalization.den_smul_val, IntermediateField.adjoin_adjoin_comm, IsLocalization.exists_integer_multiple, TrivSqZeroExt.algebraMap_eq_inlHom, stereographic_apply, RingQuot.smul_quot, FormallySmooth.exists_adicCompletionEvalOneₐ_comp_eq, ModularFormClass.hasSum_qExpansion_of_norm_lt, FDRep.char_orthonormal, IntermediateField.finSepDegree_bot', Module.End.IsSemisimple.minpoly_squarefree, IntermediateField.val_mk, ENNReal.smul_toNNReal, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, StieltjesFunction.measure_smul, NumberField.RingOfIntegers.instIsScalarTower, Generators.CotangentSpace.map_toComp_injective, AdicCompletion.evalₐ_of, Module.End.lTensorAlgHom_apply_apply, IntermediateField.rank_sup_le, Module.Basis.SmithNormalForm.repr_comp_embedding_eq_smul, LinearIsometry.strictConvexSpace_range, MvPowerSeries.aeval_eq_sum, LieAlgebra.ad_lie, TensorProduct.opAlgEquiv_tmul, NumberField.RingOfIntegers.instIsScalarTower_1, inner_smul_left_eq_smul, StrongConvexOn.strictConvexOn, Orientation.kahler_apply_apply, StarAlgEquiv.restrictScalars_injective, MeasureTheory.FiniteMeasure.toWeakDualBCNN_continuous, PowerSeries.coeff_subst', Quaternion.mul_coe_eq_smul, strictConvexOn_zpow, Polynomial.aeval_eq_sum_range', FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, AlgEquiv.restrictNormalHom_apply, LieModule.isNilpotent_iff_forall', InfiniteGalois.mk_toAlgEquivAux, IsLocalizedModule.fromLocalizedModule'_mk, instIsAbelianGaloisSubtypeMemIntermediateField, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, FormalMultilinearSeries.ofScalars_sum_eq, Matrix.det_updateRow_smul, MeasureTheory.Integrable.smul_measure, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.smul_mem, LSeries.delta_mul_eq_smul_delta, WeakDual.CharacterSpace.continuousMapEval_apply_apply, WeierstrassCurve.Projective.add_smul_of_equiv, IntermediateField.inclusion_inclusion, smul_def, exists_extension_norm_eq, LinearMap.liftBaseChange_comp, LieSubmodule.coe_toEnd_pow, Submodule.lTensorOne_tmul, IntermediateField.extendScalars_restrictScalars, LinearMap.isIntegral, MeasureTheory.Measure.Regular.smul_nnreal, differentiableAt_iff_restrictScalars, MeasureTheory.isZeroOrProbabilityMeasureSMul, SchwartzMap.tsupport_derivCLM_subset, Extension.Hom.sub_tmul, LieAlgebra.isNilpotent_range_ad_iff, MvPolynomial.smul_eq_C_mul, Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul, inner_smul_right_eq_smul, LieModule.mem_genWeightSpaceOf, Real.strictConcave_binEntropy, MeasureTheory.isLocallyFiniteMeasureSMulNNReal, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, DualNumber.exp_smul_eps, AdicCompletion.factor_evalₐ_eq_eval, instFreeSubtypeMemIdealOfFiniteOfIsTorsionFree, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, TrivSqZeroExt.map_inl, Matrix.toLinAlgEquiv'_symm, Subalgebra.restrictScalars_toSubmodule, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, derivWithin_finset_prod, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, MonomialOrder.degree_smul, LieAlgebra.IsKilling.traceForm_coroot, InfiniteGalois.proj_of_le, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, MeasureTheory.isFiniteMeasureSMulNNReal, Matrix.det_sum_smul_le, MeasureTheory.Integrable.smul_measure_nnreal, Unitization.norm_splitMul_snd_sq, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, MeasureTheory.condLExp_smul', UnitAddTorus.hasSum_mFourier_series_apply_of_summable, WeakDual.CharacterSpace.equivAlgHom_coe, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing, KaehlerDifferential.isBaseChange_of_formallyEtale, IsLocalizedModule.map_units, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, LieAlgebra.nilpotent_ad_of_nilpotent_algebra, strictConcaveOn_log_Ioi, MeasureTheory.withDensity_smul_measure, IntermediateField.lift_adjoin, MeasureTheory.restrict_compl_sigmaFiniteSetWRT, MvPowerSeries.monomial_eq, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, Generators.Hom.toAlgHom_monomial, LieModule.instIsFaithfulEnd, Matrix.cramer_smul, IsGaloisGroup.fixedPoints_le_of_le, norm_smul_one_eq_norm, isScalarTower_of_section_of_ker_sqZero, LocalizedModule.smul_eq_iff_of_mem, TensorProduct.map_restrictScalars_comp_includeRight, AdicCompletion.eval_of, cfc_comp_const_mul, MeasureTheory.Measure.InnerRegularCompactLTTop.smul_nnreal, PowerSeries.IsWeierstrassDivisorAt.mk_mod'_eq_self, MeasureTheory.OuterMeasure.mkMetric_smul, MeasureTheory.Measure.ennreal_smul_eq_zero, RatFunc.isScalarTower_liftAlgebra, Unitization.splitMul_injective, IntermediateField.rank_eq_rank_subalgebra, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Nonneg.Icc_subset_segment, RingHom.smul_toAlgebra, normalizedTrace_trans, Bialgebra.TensorProduct.rid_tmul, convex_setOf_holderOnWith, MeasureTheory.FiniteMeasure.isEmbedding_toWeakDualBCNN, Norm.Transitivity.auxMat_toSquareBlock_ne, ContinuousLinearEquiv.coord_norm', Extension.σ_smul, HahnSeries.coeff_toOrderTopSubOnePos_pow, IsBaseChange.comp, FractionRing.isScalarTower_liftAlgebra, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, IntermediateField.lift_sup, AdicCompletion.evalₐ_mk, Bialgebra.TensorProduct.lid_tmul, LinearMap.mem_span_iff_bound, Representation.asModuleEquiv_map_smul, Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct, SchwartzMap.smulLeftCLM_sub, MeasureTheory.Measure.IsEverywherePos.smul_measure_nnreal, IsScalarTower.subalgebra', SchwartzMap.smulLeftCLM_apply_apply, strongConvexOn_iff_convex, normalClosure.normal, Ideal.KerLift.map_smul, strongConvexOn_zero, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, hasStrictFDerivAt_exp_smul_const, MeasureTheory.withDensity_smul, MeasureTheory.Measure.haveLebesgueDecompositionSMulRight, AffineSubspace.isometryEquivMap.apply_symm_apply, LSeries.term_smul, IsAdicComplete.StrictMono.of_lift, LieModule.coe_lcs_range_toEnd_eq, LieModule.toEnd_module_end, IntermediateField.adjoin_adjoin_left, LieAlgebra.mem_zeroRootSubalgebra, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, instIsScalarTowerLocalizationAlgebraMapSubmonoid, SubMulAction.mem_one', Polynomial.smul_modByMonic, LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, WeakDual.toStrongDual_apply, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, ContinuousMap.elemental_id_eq_top, Antitone.concaveOn_univ_of_deriv, Nat.Partition.hasProd_genFun, LinearMap.toMatrixAlgEquiv_apply', gelfandTransform_isometry, NormedSpace.exp_eq_tsum_rat, MvPowerSeries.coeff_subst_finite, hasDerivAt_exp_smul_const', WeakDual.CharacterSpace.compContinuousMap_comp, MeasureTheory.Measure.IsAddHaarMeasure.nnreal_smul, HasStrictDerivAt.finset_prod, AlgHom.toKerIsLocalization_isLocalizedModule, AdicCompletion.ofTensorProduct_naturality, solvableByRad.isIntegral, FractionalIdeal.equivNum_apply, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, LieSubalgebra.instIsScalarTowerSubtypeMem, MeasureTheory.Measure.compProd_smul_left, MeasureTheory.Measure.mul_haarScalarFactor_smul, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, PowerSeries.IsWeierstrassFactorizationAt.smul, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, IntermediateField.insepDegree_bot, QuaternionAlgebra.mul_coe_eq_smul, MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure_of_measurableSet, IntermediateField.equivOfEq_apply, Homeomorph.compStarAlgEquiv'_symm_apply, NumberField.mixedEmbedding.convexBodySum_convex, convex_halfSpace_im_le, ProbabilityTheory.variance_smul', Module.End.mem_spectrum_iff_isRoot_charpoly, IsLocalization.integerNormalization_spec, MeasureTheory.laverage_union_mem_openSegment, MeasureTheory.llr_smul_right, cfc_const_mul_id, IntermediateField.isAlgebraic_adjoin_iff_bot, injective_lift_lsmul, AdicCompletion.ofLinearEquiv_apply, WeakDual.CharacterSpace.equivAlgHom_symm_coe, KaehlerDifferential.range_kerCotangentToTensor, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, AdicCompletion.mk_apply_coe, Submodule.torsionBySet.mk_smul, IntermediateField.insepDegree_top, Quaternion.hasSum_expSeries_of_imaginary, FixedPoints.smulCommClass', separableClosure_le_separableClosure_iff, PowerSeries.IsWeierstrassDivisorAt.div_smul, LieModule.iterate_toEnd_mem_lowerCentralSeries, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, MvPowerSeries.subst_smul, UniformOnFun.continuousSMul_submodule_of_image_bounded, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, MeasureTheory.integrable_average, RootPairing.pairing_eq_add_of_root_eq_smul_add_smul, SchwartzMap.smulLeftCLM_ofReal, KaehlerDifferential.instIsScalarTowerTensorProduct_1, MeasureTheory.lpNorm_smul_measure_of_ne_top, coe_lmul_eq_mul, Height.logHeight_smul_eq_logHeight, ContinuousLinearEquiv.coord_norm, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, HasDerivAt.finset_prod, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, TensorProduct.lmul''_eq_lid_comp_mapOfCompatibleSMul, MeasureTheory.lpMeasToLpTrim_smul, MvPolynomial.rTensor_apply, Matrix.PosSemidef.smul, LinearEquiv.conjAlgEquiv_surjective, Module.End.hasEigenvalue_iff_mem_spectrum, normalizedTrace_eq_of_fininteDimensional_apply, PowerSeries.HasSubst.smul, AddMonoidAlgebra.lift_unique, NormedSpace.expSeries_hasSum_exp_of_mem_ball', LinearMap.not_hasEigenvalue_zero_tfae, MeasureTheory.Measure.mconv_smul_left, IntermediateField.rank_bot_mul_relrank, LieDerivation.coe_ad_apply_eq_ad_apply, trace_apply, MeasureTheory.JordanDecomposition.real_smul_negPart_nonneg, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, Submodule.norm_orthogonalProjection, spectrum.unit_smul_eq_smul, Valuation.HasExtension.instIsScalarTower_valuationSubring, TemperedDistribution.smulLeftCLM_smul, Extension.instIsScalarTowerRing_2, TrivSqZeroExt.instIsScalarTower, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, FormallyUnramified.comp_sec, PowerSeries.subst_smul, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, LieAlgebra.SpecialLinear.val_singleSubSingle, MeasureTheory.eLpNorm_smul_measure_of_ne_zero, Even.convexOn_pow, AdicCompletion.of_injective_iff, Matrix.cstar_norm_def, CStarAlgebra.toStarModule, Matrix.invOf_eq, isConformalMap_complex_linear, PowerSeries.IsWeierstrassDivisionAt.smul, Real.zero_at_infty_vector_fourierIntegral, LieAlgebra.isNilpotent_iff_forall, SchwartzMap.smulLeftCLM_apply, IntermediateField.finiteDimensional_map, LieAlgebra.ad_ker_eq_bot_of_hasTrivialRadical, PreSubmersivePresentation.ofHasCoeffs_algebra_smul, AddMonoidAlgebra.scalarTensorEquiv_tmul, WeakDual.isSeqCompact_polar, Coalgebra.TensorProduct.assoc_toLinearEquiv, spectrum.smul_eq_smul, ContinuousAlternatingMap.uniformContinuous_restrictScalars, cross_cross_eq_smul_sub_smul', MeasureTheory.isMulRightInvariant_smul_nnreal, QuadraticForm.tmul_comp_tensorAssoc, MeasureTheory.Measure.instIsCentralScalar, IntermediateField.finSepDegree_top, WeierstrassCurve.Projective.smul_fin3_ext, CliffordAlgebra.instIsScalarTower, AdicCompletion.eval_lift_apply, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, Module.Basis.tensorProduct_repr_tmul_apply, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, IntermediateField.normalClosure_le_iff_of_normal, TemperedDistribution.derivCLM_apply_apply, ProbabilityTheory.mgf_smul_measure, MeasureTheory.isAddLeftInvariant_smul_nnreal, AlgHom.fieldRange_of_normal, LinearMap.toMatrixAlgEquiv_reindexRange, IntermediateField.Lifts.eq_iff, MeasureTheory.Measure.map_right_add_eq_addModularCharacterFun_vadd, Submodule.mem_div_iff_smul_subset, PowerSeries.binomialSeries_nat, WeierstrassCurve.Projective.add_of_Y_ne, IsLocalization.exist_integer_multiples, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, MeasureTheory.weightedSMul_smul_measure, HasFDerivAtFilter.restrictScalars, PowerSeries.weierstrassUnit_smul, IsBaseChange.linearMapRight, IntermediateField.normalClosure_map_eq, MeasureTheory.hausdorffMeasure_homothety_preimage, Module.Basis.repr_unitsSMul, MeasureTheory.OuterMeasure.smul_dirac_apply, IntermediateField.relrank_bot_left, Polynomial.aevalTower_comp_toAlgHom, Submodule.restrictScalars_localized', convex_halfSpace_re_gt, TensorProduct.piScalarRight_tmul_apply, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, IsAlgebraic.faithfulSMul_tower_top, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, spectrum.units_smul_resolvent, LieAlgebra.isNilpotent_ad_of_isNilpotent, TensorProduct.lidOfCompatibleSMul_tmul, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, PowerSeries.binomialSeries_constantCoeff, KaehlerDifferential.mulActionBaseChange_smul_zero, IsLocalization.localization_isScalarTower_of_submonoid_le, MeasureTheory.VAddInvariantMeasure.vadd, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, TensorProduct.isPushout', Matrix.det_updateCol_smul_left, MvPowerSeries.monomial_smul_const, MeasureTheory.FiniteMeasure.map_snd_prod, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, ENNReal.instMeasurableSMulNNReal, Submodule.toLocalized'_apply_coe, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', Derivation.linearEquiv_coe_comp, TensorProduct.AlgebraTensorModule.coe_rTensor, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, WeakDual.CharacterSpace.exists_apply_eq_zero, IntermediateField.le_normalClosure, RCLike.conj_smul, LinearMap.IsPerfPair.restrictScalars_of_field, MeasureTheory.eLpNorm_smul_measure_of_ne_zero', FDRep.scalar_product_char_eq_finrank_equivariant, IntermediateField.equivOfEq_trans, WeakDual.CharacterSpace.compContinuousMap_id, MeasureTheory.OuterMeasure.mkMetric_nnreal_smul, convexOn_zpow, AdicCompletion.tensor_map_id_left_injective_of_injective, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, IntermediateField.normalClosure_def', NormedSpace.expSeries_summable_of_mem_ball', Matrix.IsHermitian.mulVec_eigenvectorBasis, MeasureTheory.withDensity_const, matPolyEquiv_smul_one, LinearMap.toMatrixAlgEquiv_mul, WeierstrassCurve.Projective.comp_smul, ModuleCat.isScalarTower_of_algebra_moduleCat, FractionRing.instFaithfulSMul, LinearMap.BilinForm.baseChange_tmul, Extension.CotangentSpace.map_comp, AdicCompletion.eval_surjective, Polynomial.toAddCircle_C_eq_smul_fourier_zero, ModuleCat.Algebra.instIsScalarTowerCarrier, IsScalarTower.of_algebraMap_smul, MeasureTheory.Measure.singularPart_smul_right, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, AffineSubspace.subtypeₐᵢ_toAffineMap, BoundedContinuousFunction.separatesPoints_charPoly, IntermediateField.mem_restrict, strictConcaveOn_cos_Icc, IsBaseChange.finitePow, MeasureTheory.OuterMeasure.smul_ofFunction, TensorProduct.opAlgEquiv_symm_tmul, CStarAlgebra.exists_sum_four_unitary, PowerSeries.coeff_subst_finite', Real.exists_extension_norm_eq, CliffordAlgebra.EvenHom.contract_mid, RCLike.real_smul_eq_coe_mul, Matrix.minpoly_toLin, MonomialOrder.sPolynomial_decomposition', Polynomial.ker_modByMonicHom, ENNReal.instPosSMulStrictMonoNNReal, Matrix.PosDef.smul, PowerSeries.smul_inv, IntermediateField.LinearDisjoint.isDomain, SchwartzMap.fourier_convolution, Complex.log_inv_eq_integral, instSMulCommClassTensorAlgebra, MeasureTheory.FiniteMeasure.coe_toWeakDualBCNN, QuadraticAlgebra.omega_mul_omega_eq_add, IntermediateField.finrank_dvd_of_le_right, qExpansion_smul, Matrix.Represents.algebraMap, Matrix.adjugate_mul, cfcHom_eq_of_isStarNormal, trace_comp_trace, PowerSeries.HasSubst.smul_X, ENNReal.toReal_smul, Matrix.derivative_det_one_add_X_smul_aux, MeasureTheory.eLpNormEssSup_ennreal_smul_measure, Ergodic.mem_extremePoints, IntermediateField.finrank_le_of_le_right, NNReal.strictConcaveOn_rpow, MeasureTheory.Measure.isAddLeftInvariant_eq_smul, ProbabilityTheory.setBernoulli_apply, instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl_1, edist_smul_le, Matrix.kroneckerStarAlgEquiv_apply, LieModule.commute_toEnd_of_mem_center_left, Submodule.norm_subtypeL_le, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, isGalois_bot, MvPolynomial.tensorEquivSum_C_tmul_C, Subalgebra.rTensorBot_tmul, IntermediateField.intermediateFieldMap_symm_apply_coe, exteriorPower.zeroEquiv_symm_apply, Module.AEval.mem_mapSubmodule_apply, AlgebraicGeometry.structureSheafInType.smul_apply, isIntegral_leadingCoeff_smul, ProbabilityTheory.Kernel.const_comp, Representation.asAlgebraHom_mem_of_forall_mem, Quaternion.coe_real_complex_mul, KaehlerDifferential.map_liftBaseChange_smul, ModularFormClass.hasSum_qExpansion, Matrix.toLpLinAlgEquiv_symm_apply, WeierstrassCurve.Projective.neg_smul_equiv, LieAlgebra.ad_ker_eq_self_module_ker, MeasureTheory.integrable_inv_smul_measure, Ideal.Quotient.mk_smul_mk_quotient_map_quotient, Generators.H1Cotangent.map_comp_cotangentComplex_baseChange, AdicCompletion.eval_apply, Submodule.instSMulCommClassSubtypeMemTorsion', RingHom.toKerIsLocalization_isLocalizedModule, idealMap_apply_coe, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, LinearIsometryEquiv.toContinuousLinearEquiv_smul, Real.convexOn_mul_log, StarAlgEquiv.ofAlgEquiv_symm, ProbabilityTheory.variance_smul, Submodule.le_traceDual_iff_map_le_one, AlgebraNormClass.toSeminormClass, IntermediateField.finiteDimensional_adjoin_pair, IsLocalRing.instIsScalarTowerResidueField, MvPowerSeries.smul_inv, MeasureTheory.integral_smul_measure, summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, Real.strictConcaveOn_negMulLog, KaehlerDifferential.kerTotal_map', IntermediateField.normal_sup, IntermediateField.coe_algebraMap_apply, Bialgebra.TensorProduct.assoc_symm_tmul, HasFTaylorSeriesUpToOn.restrictScalars, Module.End.exists_isNilpotent_isSemisimple, Nat.Partition.multipliable_genFun, AdicCompletion.flat_of_isNoetherian, Ideal.map_includeLeft_eq, separableClosure.isGalois, Module.End.HasUnifEigenvalue.mem_spectrum, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, fderivWithin_restrictScalars_comp, MvPowerSeries.substAlgHom_comp_substAlgHom, Bialgebra.TensorProduct.assoc_toAlgEquiv, Generators.H1Cotangent.equiv_apply, IntermediateField.restrictScalars_adjoin, HahnSeries.SummableFamily.powerSeriesFamily_smul, Extension.CotangentSpace.map_comp_cotangentComplex, LinearMap.toMatrixAlgEquiv_transpose_apply, Submodule.orthogonalProjection_norm_le, DividedPowers.dpow_smul, IntermediateField.finrank_adjoin_simple_eq_one_iff, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, MeasureTheory.Measure.conv_smul_right, continuousFunctionalCalculus_map_id, IsBaseChange.endHom_comp, Module.End.eigenspace_aeval_polynomial_degree_1, exists_eq_sum_perm_of_mem_doublyStochastic, MeasureTheory.Measure.addHaarScalarFactor_smul, MeasureTheory.norm_condExpL2_le_one, PowerSeries.derivativeFun_mul, leftMulMatrix_apply, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, AdicCompletion.ofLinearEquiv_symm_of, CFC.log_smul, MeasureTheory.withDensity_smul', IntermediateField.finiteDimensional_sup, Extension.Cotangent.ker_mk, IntermediateField.Lifts.le_iff, Real.rpowIntegrand₀₁_eqOn_mul_rpowIntegrand₀₁_one, IsGaloisGroup.commutes, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul, trace_adjoinSimpleGen, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', AlgEquiv.eq_linearEquivConjAlgEquiv, IntermediateField.normal_iff_normalClosure_eq, IntermediateField.rank_adjoin_simple_eq_one_iff, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, CliffordAlgebra.contractLeftAux_contractLeftAux, RCLike.wInner_cWeight_eq_smul_wInner_one, MeasureTheory.llr_smul_left, Unitary.path_apply, Unitary.conjStarAlgAut_ext_iff, Matrix.toLinAlgEquiv_toMatrixAlgEquiv, ProbabilityTheory.convex_integrableExpSet, Real.strictConcaveOn_qaryEntropy, LieAlgebra.IsKilling.rootSystem_root_apply, MonoidAlgebra.lift_single, AdicCompletion.map_of, QuaternionAlgebra.Basis.k_mul_j, IntermediateField.isIntegral_iff, Matrix.permanent_smul, WeierstrassCurve.Projective.smul_equiv, Submodule.torsionBy.mk_smul, MeasureTheory.Measure.map_snd_prod, Matrix.toLinAlgEquiv_symm, SchwartzMap.smulLeftCLM_smul, MeasureTheory.Measure.singularPart_smul, KaehlerDifferential.instIsScalarTowerTensorProduct_2, PowerSeries.weierstrassDistinguished_smul, separableClosure.normalClosure_eq_self, LinearMap.toMatrixAlgEquiv_transpose_apply', IsScalarTower.of_algHom, LieSubalgebra.instIsArtinianSubtypeMem, NNRat.instContinuousSMulRatReal, convexOn_rpow, Matrix.kroneckerStarAlgEquiv_symm_apply, IntermediateField.adjoin.powerBasis_dim, AdicCompletion.of_apply, IsLocalization.smul_toInvSubmonoid, LinearMap.exists_map_addHaar_eq_smul_addHaar', MulAlgebraNorm.smul', Quaternion.exp_eq, Nat.Partition.genFun_eq_tprod, QuadraticMap.toMatrix'_smul, IsGalois.of_fixedField_normal_subgroup, TensorProduct.lift_includeLeft_includeRight, Module.instFinitePolynomialAEval', cfc_const_mul, exists_mem_doublyStochastic_eq_smul_iff, Seminorm.smul_le_smul, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, MeasureTheory.addEquivAddHaarChar_smul_integral_map, WeakDual.CharacterSpace.instStarHomClass, MeasureTheory.Measure.rnDeriv_smul_right_of_ne_top, IntermediateField.isPurelyInseparable_sup, PiTensorProduct.instIsScalarTower, MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure_of_innerRegularCompactLTTop, KaehlerDifferential.mulActionBaseChange_smul_tmul, IntermediateField.splits_of_splits, MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto, MeasureTheory.Measure.InnerRegularCompactLTTop.smul, Module.End.mem_subalgebraCenter_iff, MonomialOrder.degree_smul_of_mem_nonZeroDivisors, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, MvPolynomial.C_eq_smul_one, lsmul_coe, QuaternionAlgebra.Basis.i_mul_k, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, Polynomial.coeff_det_X_add_C_zero, TrivSqZeroExt.eq_smul_exp_of_invertible, LieModule.Weight.hasEigenvalueAt, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, HasCompactSupport.hasFDerivAt_convolution_left, NumberField.mixedEmbedding.convexBodyLT'_convex, TrivSqZeroExt.map_id, Extension.H1Cotangent.map_comp, selfAdjoint.expUnitary_coe, IsBaseChange.linearMapLeftRightHom_comp, IsLocalizedModule.fromLocalizedModule'_smul, TemperedDistribution.smulLeftCLM_apply_apply, ClassGroup.exists_mem_finset_approx', RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, AlgHom.mulLeftRightMatrix.comp_inv, AdicCompletion.eval_comp_of, instIsPushoutFractionRingMvPolynomial_1, Icc_subset_segment, uniformConvexOn_zero, MeasureTheory.measureReal_nnreal_smul_apply, Submodule.restrictScalars_localized'_smul, LieAlgebra.Orthogonal.pd_inv, LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul, LinearMap.toMatrixAlgEquiv'_comp, ClassGroup.exists_mem_finsetApprox, Nonneg.segment_eq_Icc, LieModule.rank_le_natTrailingDegree_charpoly_ad, hasFDerivAt_integral_of_dominated_loc_of_lip, LieSubalgebra.coe_ad, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, MeasureTheory.Measure.prod_smul_left, NNReal.Icc_subset_segment, LieModule.toEnd_matrix, Matrix.det_smul_inv_vecMul_eq_cramer_transpose, Complex.exp_bound_sq, convexOn_norm, Matrix.mul_adjugate, MvPowerSeries.prod_smul_X_eq_smul_monomial_one, Polynomial.add_scaleRoots_of_natDegree_eq, NNReal.concaveOn_rpow, IntermediateField.adjoin_rootSet_isSplittingField, IntermediateField.nonempty_algHom_adjoin_of_splits, MeasureTheory.Measure.haveLebesgueDecompositionSMul', IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, QuadraticModuleCat.hom_hom_associator, RCLike.norm_nnqsmul, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, LieModule.toEnd_pow_comp_lieHom, ProbabilityTheory.setBernoulli_eq_map, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', WeierstrassCurve.Projective.nonsingular_smul, IsAzumaya.AlgHom.mulLeftRight_bij, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, perfectClosure.isPurelyInseparable, MeasureTheory.Measure.bind_const, AddMonoidAlgebra.vaddAssocClass_addMonoidAlgebra, LinearEquiv.conjAlgEquiv_ext_iff, Submodule.restrictScalars_span, IntermediateField.isSeparable_adjoin_iff_isSeparable, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, IntermediateField.sepDegree_top, AdicCompletion.eval_lift, instIsPushoutFractionRingMvPolynomial, Valuation.HasExtension.instIsScalarTowerInteger, Valuation.HasExtension.val_smul, IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure, convexOn_iff_slope_mono_adjacent, QuadraticModuleCat.hom_inv_associator, MvPolynomial.instFaithfulSMul, MeasureTheory.dirac_withDensity, Real.map_volume_mul_left, Matrix.spectrum_toLin', AdicCompletion.ofAlgEquiv_symm_of, LieSubalgebra.ad_comp_incl_eq, Presentation.tensorModelOfHasCoeffsInv_aeval_val, MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isOpen, WeierstrassCurve.Projective.dblZ_smul

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
algebraMap_eq_smul_one 📖	mathematical	—	DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap toSMul AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	mul_one smul_def
algebraMap_eq_smul_one' 📖	mathematical	—	DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap toSMul AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne	—	algebraMap_eq_smul_one
algebraMap_self 📖	mathematical	—	algebraMap CommSemiring.toSemiring id RingHom.id Semiring.toNonAssocSemiring	—	—
algebraMap_self_apply 📖	mathematical	—	DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap id	—	—
algebra_ext 📖	—	DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	—	DFunLike.ext smul_def'
algebra_ext_iff 📖	mathematical	—	DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	algebra_ext
coe_linearMap 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule toModule LinearMap.instFunLike linearMap RingHom RingHom.instFunLike algebraMap	—	—
commute_algebraMap_left 📖	mathematical	—	Commute Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	commutes
commute_algebraMap_right 📖	mathematical	—	Commute Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	commutes
commutes 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	commutes'
commutes' 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	—
compHom_algebraMap_apply 📖	mathematical	—	DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap compHom	—	—
compHom_algebraMap_eq 📖	mathematical	—	algebraMap compHom RingHom.comp Semiring.toNonAssocSemiring CommSemiring.toSemiring	—	—
compHom_smul_def 📖	mathematical	—	toSMul compHom DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike	—	—
left_comm 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	mul_assoc commutes
linearMap_apply 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toModule toModule LinearMap.instFunLike linearMap RingHom RingHom.instFunLike algebraMap	—	—
linearMap_self 📖	mathematical	—	linearMap CommSemiring.toSemiring id LinearMap.id NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Semiring.toModule	—	—
mul_smul_comm 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring toSMul	—	smul_def left_comm
right_comm 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	mul_assoc commutes
smul_def 📖	mathematical	—	toSMul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	smul_def'
smul_def' 📖	mathematical	—	toSMul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	—
smul_mul_assoc 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring toSMul	—	smul_mul_assoc IsScalarTower.right
subsingleton 📖	—	—	—	—	RingHom.codomain_trivial

Algebra.id

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
smul_eq_mul 📖	mathematical	—	Algebra.toSMul CommSemiring.toSemiring Algebra.id Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring	—	—

IsScalarTower

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
right 📖	mathematical	—	IsScalarTower Algebra.toSMul SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoidWithOne.toAddMonoid AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne Semiring.toNonAssocSemiring DistribSMul.toSMulZeroClass instDistribSMul NonAssocSemiring.toNonUnitalNonAssocSemiring	—	smul_eq_mul Algebra.smul_def mul_assoc

RingHom

Definitions

Name	Category	Theorems
toAlgebra 📖	CompOp	42 math math: AlgebraicGeometry.IsAffineOpen.isLocalization_of_eq_basicOpen, IsStandardOpenImmersion.toAlgebra, IsLocalization.isLocalization_iff_of_ringEquiv, AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage, IsLocalization.isLocalization_iff_of_base_ringEquiv, FormallySmooth.toAlgebra, AlgebraicGeometry.Scheme.Hom.ι_toNormalization, Algebra.SubmersivePresentation.ofSubsingleton_relation, IsStandardSmoothOfRelativeDimension.toAlgebra, IsFractionRing.isFractionRing_iff_of_base_ringEquiv, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, AlgebraicGeometry.formallySmooth_stalkMap_iff, IsLocalization.away_snd, AlgebraicGeometry.Scheme.AffineZariskiSite.coequifibered_iff_forall_isLocalizationAway, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, MvPolynomial.universalFactorizationMapPresentation_map, Etale.toAlgebra, MvPolynomial.universalFactorizationMapPresentation_relation, IsStandardSmooth.toAlgebra, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, AlgebraicGeometry.Scheme.IdealSheafData.isLocalization_away, QuasiFinite.toAlgebra, IsLocalization.isLocalization_of_base_ringEquiv, AlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, HomogeneousLocalization.Away.isLocalization_mul, Algebra.Extension.Hom.sub_aux, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, algebraMap_toAlgebra, MvPolynomial.universalFactorizationMapPresentation_val, isScalarTower_of_section_of_ker_sqZero, MvPolynomial.universalFactorizationMapPresentation_σ', smul_toAlgebra, IsLocalization.away_fst, Smooth.toAlgebra, MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix, AlgebraicGeometry.Scheme.Hom.normalizationObjIso_hom_val, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, IsScalarTower.of_algHom, toAlgebra_algebraMap, MvPolynomial.universalFactorizationMapPresentation_jacobian
toAlgebra' 📖	CompOp	2 math math: algebraMap_toAlgebra', smul_toAlgebra'

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
algebraMap_toAlgebra 📖	mathematical	—	algebraMap CommSemiring.toSemiring toAlgebra	—	—
algebraMap_toAlgebra' 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring instFunLike	algebraMap toAlgebra'	—	—
smulOneHom_eq_algebraMap 📖	mathematical	—	smulOneHom CommSemiring.toSemiring Semiring.toNonAssocSemiring Algebra.toModule IsScalarTower.right algebraMap	—	ext IsScalarTower.right Algebra.algebraMap_eq_smul_one
smul_toAlgebra 📖	mathematical	—	Algebra.toSMul CommSemiring.toSemiring toAlgebra Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom instFunLike	—	—
smul_toAlgebra' 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DFunLike.coe RingHom CommSemiring.toSemiring instFunLike	Algebra.toSMul toAlgebra'	—	—

RingTheory.LinearMap

Definitions

Name	Category	Theorems
termη 📖	CompOp	—
«termη[_]» 📖	CompOp	—

(root)

Definitions

Name	Category	Theorems
algebraMap 📖	CompOp	1832 math math: RingHom.essFiniteType_algebraMap, IsLocalization.algebraMap_apply_eq_map_map_submonoid, IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, IsAlgebraic.exists_nonzero_dvd, IsLocalization.localization_localization_isLocalization_of_has_all_units, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply', KaehlerDifferential.kerCotangentToTensor_toCotangent, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, CliffordAlgebra.contractRight_algebraMap_mul, Ideal.Quotient.exists_algHom_fixedPoint_quotient_under, AlgebraicGeometry.IsPreimmersion.of_isLocalization, IsDedekindDomain.differentIdeal_dvd_map_differentIdeal, IsLocalization.map_radical, ValuationRing.mem_integer_iff, RootPairing.RootPositiveForm.algebraMap_rootLength, RingTheory.Sequence.isWeaklyRegular_map_algebraMap_iff, Algebra.RingHom.adjoin_algebraMap_apply, IsLocalization.lift_algebraMap_eq_algebraMap, LinearMap.BilinForm.dualSubmoduleParing_spec, Algebra.idealMap_eq_ofEq_comp_toLocalized₀, CliffordAlgebra.contractRight_algebraMap, ExteriorAlgebra.isLocalHom_algebraMap, AddMonoidAlgebra.lift_apply', Valuation.IsTrivialOn.valuation_algebraMap_le_one, RingHom.finiteType_algebraMap, cfc_le_algebraMap_iff, IsIntegrallyClosed.exists_algebraMap_eq_of_isIntegral_pow, Algebra.norm_algebraMap_of_basis, derivationToSquareZeroOfLift_apply, IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply, IsLocalRing.ResidueField.algebraMap_residue, IntermediateField.fieldRange_le, Polynomial.mem_lifts_iff_mem_alg, PolyEquivTensor.toFunBilinear_apply_eq_sum, Valuation.FiniteField.algebraMap_le_one, IsUltrametricDist.algNormOfAlgEquiv_extends, Valuation.FiniteField.algebraMap_eq_one, galRestrict_symm_algebraMap_apply, Matrix.SpecialLinearGroup.map_mapGL, RatFunc.num_div, Algebra.algebraMap_self_apply, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, Valuation.HasExtension.val_map_le_iff, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentation, quasispectrum.algebraMap_mem, IntermediateField.LinearDisjoint.linearIndependent_right', ExteriorAlgebra.ι_eq_algebraMap_iff, Submodule.algebraMap_mem, CStarAlgebra.mem_Icc_algebraMap_iff_norm_le, Localization.algebraMap_injective_of_span_eq_top, NumberField.canonicalEmbedding.mem_span_latticeBasis, Polynomial.algebraMap_pi_eq_aeval, NumberField.integralBasis_apply, IsLocalization.Away.algebraMap_isUnit_iff, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, IsIntegrallyClosedIn.isIntegral_iff, ValuationSubring.integralClosure_algebraMap_injective, IntermediateField.algebraMap_mem, IsLocalization.AtPrime.liesOver_map_of_liesOver, PrimeSpectrum.residueField_specComap, Localization.epi', Pi.algebraMap_apply, PrimeSpectrum.localization_specComap_range, 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IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, RootPairing.RootPositiveForm.zero_lt_posForm_iff, FractionalIdeal.extendedHomₐ_coeIdeal_eq_map, IsLocalization.smul_mk'_self, Ring.ordFrac_eq_ord, IsGalois.mem_range_algebraMap_iff_fixed, Algebra.SubmersivePresentation.map_jacobianOfHasCoeffs, Localization.mk_algebraMap, Algebra.dvd_algebraMap_intNorm_self, PolyEquivTensor.toFunAlgHom_apply_tmul, LinearMap.toMatrix_baseChange, Algebra.Generators.algebraMap_surjective, Ideal.spanIntNorm_localization, IsLocalization.Away.algebraMap_surjective_of_isIdempotentElem, Polynomial.algebraMap_apply, Valuation.Integers.map_le_one, Algebra.isInvariant_iff, Ideal.isPrime_map_of_isLocalizationAtPrime, Valuation.HasExtension.val_map_eq_iff, Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange, ExteriorAlgebra.algebraMap_eq_one_iff, Unitization.starLift_apply_apply, WeierstrassCurve.integralModel_Δ_eq, IsLocalization.mk'_mul_cancel_left, Algebra.traceMatrix_localizationLocalization, Algebra.algebraMap_intNorm, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_snd, IsLocalization.lift_comp, coe_algebraMapCLM, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, Algebra.algebraMap_self, QuadraticAlgebra.algebraMap_re, CliffordAlgebra.ι_mul_ι_comm, Module.associatedPrimes.preimage_comap_associatedPrimes_eq_associatedPrimes_of_isLocalizedModule, RatFunc.liftMonoidWithZeroHom_apply_div', nnnorm_algebraMap_nnreal, AddMonoidAlgebra.mapRangeRingHom_comp_algebraMap, algebraMap_pos, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, PrimeSpectrum.comap_surjective_of_faithfullyFlat, WithAbs.equiv_algebraMap_apply, RootPairing.restrictScalars_pairing, CliffordAlgebra.ι_sq_scalar, Quaternion.algebraMap_def, Algebra.intTrace_eq_of_isLocalization, AlgebraicGeometry.StructureSheaf.to_basicOpen_epi, AlgebraicGeometry.Scheme.isOpenImmersion_SpecMap_localizationAway, Algebra.trace_algebraMap, Module.Basis.repr_algebraMap, NumberField.Units.coe_mul, LinearMap.det_baseChange, Ideal.Quotient.instIsPrimeQuotientMapRingHomAlgebraMapMkOfLiesOver, RatFunc.coe_X, IsPurelyInseparable.iterateFrobenius_algebraMap, IsUltrametricDist.invariantExtension_extends, CFC.rpow_algebraMap, IsLocalization.isLocalization_iff_of_base_ringEquiv, IsIntegrallyClosedIn.exists_algebraMap_eq_of_pow_mem_subalgebra, ValuationRing.range_algebraMap_eq, FunctionField.inftyValuation.polynomial, LocalizedModule.divBy_mul_by, IsFractionRing.algHom_commutes, IsLocalRing.basisQuotient_repr, QuadraticAlgebra.omega_mul_coe_mul_mk, Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero, LinearEquiv.det_baseChange, AlgebraicGeometry.Scheme.instIsOpenImmersionMapOfHomAwayAlgebraMap, algebraicIndependent_empty_iff, Algebra.FormallyUnramified.iff_map_maximalIdeal_eq, QuadraticAlgebra.algebraMap_dvd_iff, algebra_compatible_smul, IsLocalization.comap_map_of_isPrime_disjoint, CommRingCat.pushoutCocone_inl, 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Valuation.HasExtension.val_map_lt_iff, MonoidAlgebra.coe_algebraMap, FreeAlgebra.star_algebraMap, MulOpposite.algebraMap_apply, IsIntegrallyClosedIn.exists_algebraMap_eq_of_isIntegral_pow, MonoidAlgebra.mapDomain_algebraMap, StarSubalgebra.mem_bot, Algebra.Extension.CotangentSpace.map_tmul, IsCyclotomicExtension.Rat.ramificationIdx_eq_of_prime, element_smul_restrictScalars, RingHom.locally_iff_isLocalization, MvPowerSeries.subst_monomial, RatFunc.map_apply, Ideal.powQuotSuccInclusion_apply_coe, Algebra.Generators.algebraMap_apply, IsLocalization.map_eq_zero_iff, Subalgebra.algebraMap_mk, IsLocalization.integerNormalization_map_to_map, IsBaseChange.endHom_toMatrix, IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right_assoc, HopfAlgebra.sum_mul_antipode_eq_algebraMap_counit, PowerBasis.quotientEquivQuotientMinpolyMap_apply_mk, Polynomial.algebraMap_def, IsLocalization.mapFrameHom_apply, 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Module.Basis.algebraMap_injective, Algebra.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap, RingTheory.Sequence.IsRegular.of_faithfullyFlat, galLift_algebraMap_apply, NumberField.Units.norm, CommRing.Pic.mapRingHom_algebraMap, IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra, IsLocalization.finsetIntegerMultiple_image, Algebra.norm_eq_iff, LaurentSeries.exists_ratFunc_val_lt, Ideal.under_map_of_isLocalizationAtPrime, IsFractionRing.isFractionRing_iff_of_base_ringEquiv, RatFunc.num_algebraMap, Ideal.mem_of_liesOver, Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat, AlgebraicGeometry.Spec_map_localization_isIso, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux, Algebra.pushoutDesc_right, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le, AlgebraicGeometry.StructureSheaf.algebraMap_self_map, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, IsPurelyInseparable.surjective_algebraMap_of_isSeparable, PrimeSpectrum.mem_image_comap_basicOpen, IsLocalization.AtPrime.comap_maximalIdeal, WithAbs.algebraMap_right_apply, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, TensorProduct.gradedComm_algebraMap, CommRingCat.isPushout_tensorProduct, IsLocalization.isUnit_piRingHom_algebraMap_comp_piEvalRingHom, liftOfDerivationToSquareZero_mk_apply, isLocalizedModule_iff, ValuativeExtension.vlt_iff_vlt, Representation.asModuleEquiv_symm_map_smul, MvPolynomial.aeval_algebraMap_apply, IsLocalization.Away.awayToAwayLeft_eq, IsCyclotomicExtension.splits_cyclotomic, Ideal.Factors.isScalarTower, Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs, IsField.localization_map_bijective, IsLocalization.map_comp, CommRingCat.mkUnder_hom, RootPairing.toLinearMap_apply_PolarizationIn, Algebra.Generators.comp_val, DirectSum.algebraMap_apply, nnnorm_algebraMap, Algebra.adjoin_eq_ring_closure, RatFunc.liftMonoidWithZeroHom_apply_div, Submodule.span_algebraMap_image, AlgHom.IsArithFrobAt.localize_algebraMap, RatFunc.num_dvd, minpoly.isIntegrallyClosed_eq_field_fractions, IsLocalization.algebraMap_mem_map_algebraMap_iff, isPurelyInseparable_iff_pow_mem, AbsoluteValue.LiesOver.comp_eq', IsLocalization.Away.tensorRight, AddMonoidAlgebra.coe_algebraMap, Algebra.linearMap_apply, Polynomial.exists_dvd_map_of_isAlgebraic, Module.support_subset_preimage_comap, RootPairing.algebraMap_coxeterWeightIn, IsDedekindDomain.primesOverEquivPrimesOver_apply, RingHom.formallyEtale_algebraMap, algebraMap_monotone, RatFunc.laurentAux_div, polyEquivTensor_symm_apply_tmul, RootPairing.coroot'_apply_apply_mem_of_mem_span, MvPowerSeries.c_eq_algebraMap, AlgebraicGeometry.pullbackSpecIso_inv_fst'_assoc, Ideal.quotientToQuotientRangePowQuotSucc_mk, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, Module.support_of_algebra, IsIntegrallyClosedIn.algebraMap_eq_of_integral, CommRingCat.isPushout_of_isPushout, Ideal.finrank_prime_pow_ramificationIdx, IsLocalization.Away.awayToAwayRight_eq, LinearIndependent.localization_localization, Algebra.TensorProduct.algebraMap_def, NumberField.IsCMField.equivInfinitePlace_apply, RatFunc.mk_eq_div, Algebra.adjoin_insert_algebraMap, Valuation.HasExtension.val_map_le_one_iff, IsLocalization.map_eq, algebraMap_isometry, AlgebraicGeometry.StructureSheaf.toOpen_comp_comap_assoc, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, RCLike.ofReal_re_ax, RingOfIntegers.norm_algebraMap, MvPolynomial.tensorEquivSum_one_tmul_C, IsLocalization.height_map_of_disjoint, ValuationRing.isFractionRing_iff, PowerBasis.exists_smodEq, CliffordAlgebra.EvenHom.contract, IsFractionRing.mk'_num_den', NumberField.RingOfIntegers.ker_algebraMap_eq_bot, RingHom.formallyUnramified_algebraMap, IsLocalization.Away.commutes, IsLocalization.isPrime_iff_isPrime_disjoint, ValuativeExtension.mapValueGroupWithZero_valuation, Algebra.bijective_algebraMap_iff, Polynomial.Separable.map_irreducible_of_isPurelyInseparable, CliffordAlgebra.ι_mul_ι_add_swap, IsLocalization.AtPrime.to_map_mem_maximal_iff, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, KaehlerDifferential.ker_map, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, SetLike.GradeZero.algebraMap_apply, IsFractionRing.to_map_eq_zero_iff, Algebra.QuasiFinite.iff_finite_comap_preimage_singleton, IsFractionRing.div_surjective, cfc_add_const, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, IsLocalization.mk'_algebraMap_eq_mk', IsLocalization.toLocalizationMap_apply, TensorProduct.algebraMap_gradedMul, FiniteField.algebraMap_norm_eq_pow, MvPolynomial.algebraMap_apply, RingHom.algebraMap_toAlgebra', SubMulAction.algebraMap_mem, RatFunc.liftOn_div, LinearMap.toMvPolynomial_baseChange, IsLocalization.bot_lt_comap_prime, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AlgHom.comp_algebraMap_of_tower, NumberField.InfinitePlace.LiesOver.comap_eq, RootPairing.algebraMap_pairingIn, HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat, HahnSeries.algebraMap_apply, IsFractionRing.ringEquivOfRingEquiv_algebraMap, Bialgebra.comul_algebraMap, LinearMap.toMatrix'_algebraMap, algebraMap_smul, Subfield.algebraMap_ofSubfield, IsLocalization.localization_localization_surj, IsCyclotomicExtension.splits_X_pow_sub_one, IsLocalization.map_comap, IsLocalization.algEquiv_comp_algebraMap_apply, IsLocalization.AtPrime.liesOver_comap_of_liesOver, Unitization.starMap_inl, IsHausdorff.map_algebraMap_iff, MonoidAlgebra.lift_apply', QuadraticAlgebra.coe_dvd_iff_dvd, Representation.IntertwiningMap.algebraMap_apply, QuadraticAlgebra.mul_star, RootPairing.isValuedIn_iff_mem_range, CliffordAlgebra.comp_ι_sq_scalar, Derivation.compAlgebraMapL_apply_apply, isLocalization_iff, FiniteField.algebraMap_norm_eq_prod_pow, Subfield.bot_eq_of_zMod_algebra, IsScalarTower.coe_toAlgHom, RingOfIntegers.not_dvd_exponent_iff, Submodule.setLike.coe_galgebra_toFun, Polynomial.aeval_X_left_eq_map, Algebra.Extension.Hom.toRingHom_algebraMap, IsLocalization.algebraMap_isUnit_iff, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, Localization.AtPrime.mapPiEvalRingHom_comp_algebraMap, Submodule.traceDual_le_span_map_traceDual, Valuation.Integers.hom_inj, Quaternion.algebraMap_injective, PowerSeries.exp_pow_sum, Irreducible.exists_dvd_monic_irreducible_of_isIntegral, CliffordAlgebra.contractRight_mul_algebraMap, Polynomial.Chebyshev.algebraMap_eval_C, cfc_apply_zero, IsLocalizedModule.fromLocalizedModule_mk, MvPolynomial.instIsLocalHomRingHomAlgebraMap, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, NumberField.InfinitePlace.isRamified_iff, Unitization.algebraMap_eq_inl, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, sum_embeddings_eq_finrank_mul, mem_perfectClosure_iff, IsFractionRing.closure_range_algebraMap, algebraMap_lt_algebraMap, Ideal.ramificationIdx_map_eq, IsPurelyInseparable.exponent_def', hasSum_one_div_nat_pow_mul_cos, Polynomial.IsSplittingField.splits, Module.End.isSemisimple_sub_algebraMap_iff, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, RatFunc.ofFractionRing_comp_algebraMap, RingHom.toKerIsLocalization_apply, ValuativeExtension.compatible_comap, Ideal.ResidueField.map_algebraMap, algebraMap_mk, Polynomial.IsSplittingField.splits', RatFunc.algebraMap_X, Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_apply, NumberField.InfinitePlace.IsRamified.isReal, NumberField.CMExtension.equivMaximalRealSubfield_apply, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom_assoc, Algebra.quasiFiniteAt_iff_isOpen_singleton_fiber, PrimeSpectrum.specComap_surjective_of_faithfullyFlat, IsLocalization.Away.isUnit_of_dvd, IsIntegralClosure.algebraMap_injective', Polynomial.algebraMap_pi_self_eq_eval, NumberField.Units.mem_torsion, AlgebraicIndependent.algebraMap_injective, Subalgebra.LinearDisjoint.trace_algebraMap, Polynomial.scaleRoots_aeval_eq_zero, Polynomial.C_eq_algebraMap, Subalgebra.coe_algebraMap, Polynomial.mapAlg_eq_map, NonUnitalStarSubalgebra.unitization_apply, Algebra.smoothLocus_comap_of_isLocalization, Module.Basis.restrictScalars_repr_apply, IsLocalization.sec_spec', CliffordAlgebra.foldr'_algebraMap, Polynomial.eval_unique, Localization.AtPrime.comap_maximalIdeal, NumberField.ComplexEmbedding.IsConj.isReal_comp, IsLocalization.minimalPrimes_comap, IsAlgClosure.equivOfEquiv_comp_algebraMap, HahnSeries.C_eq_algebraMap, MonoidAlgebra.mapRangeRingHom_comp_algebraMap, RootPairing.isValuedIn_iff, LaurentPolynomial.algebraMap_X_pow, SymmetricAlgebra.algebraMap_eq_zero_iff, Submodule.lTensorOne'_tmul, IsLocalization.mk'_add_eq_iff_add_mul_eq_mul, IsIntegralClosure.algebraMap_equiv, DirectSum.decompose_symm_algebraMap, IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime, CommRingCat.epi_iff_tmul_eq_tmul, Algebra.isUnramifiedAt_iff_map_eq, CFC.abs_algebraMap, Submodule.rTensorOne'_tmul, Ideal.relNorm_algebraMap', Polynomial.SplittingField.splits, Algebra.QuasiFinite.finite_comap_preimage, Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex, exists_root_adjoin_eq_top_of_isCyclic, Algebra.TensorProduct.basisAux_tmul, groupCohomology.norm_ofAlgebraAutOnUnits_eq, Polynomial.UniversalFactorizationRing.monicDegreeEq_coe, IsLocalization.isPrime_of_isPrime_disjoint, ValuativeExtension.vle_iff_vle, RootPairing.algebraMap_rootFormIn, ModP.preVal_mk, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', QuadraticAlgebra.norm_coe, RatFunc.valuation_eq_LaurentSeries_valuation, bijective_algebraMap_of_linearEquiv, SkewMonoidAlgebra.coe_algebraMap, mem_range_of_deriv_eq_zero, isIntegral_algebraMap, NumberField.Units.coe_neg_one, FractionalIdeal.mem_coeIdeal, tensorKaehlerQuotKerSqEquiv_symm_tmul_D, Unitization.norm_eq_sup, Algebra.discr_of_matrix_mulVec, IsLocalization.mk'_mem_map_algebraMap_iff, Ideal.IsIntegralClosure.comap_lt_comap, Ideal.Quotient.exists_algEquiv_fixedPoint_quotient_under, PrimeSpectrum.residueField_comap, Submodule.span_algebraMap_image_of_tower, RatFunc.map_apply_div, AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom, NormedSpace.algebraMap_exp_comm, cfc_le_algebraMap, IsDedekindDomain.primesOverEquivPrimesOver_ramificationIdx_eq, NumberField.mixedEmbedding.logMap_eq_logEmbedding, CliffordAlgebra.changeForm_ι_mul_ι, IsLocalization.map_integerMultiple, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, LaurentPolynomial.algebraMap_eq_toLaurent, AlgEquivClass.commutes, spectrum.preimage_algebraMap, AlgebraicGeometry.pullbackSpecIso_inv_fst, smul_algebraMap, Polynomial.int_eval₂_eq, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, Ideal.Quotient.alg_map_eq, RingHom.formallySmooth_algebraMap, Algebra.normalizedTrace_algebraMap_apply_eq_self, algebraMap_le_cfc, Subalgebra.algebraMap_mem', NumberField.InfinitePlace.IsUnramified.eq, StarSubalgebra.coe_bot, RatFunc.liftRingHom_apply_div', Algebra.SubmersivePresentation.map_jacobianRelationsOfHasCoeffs, algebraMap_comp_intCast, PowerSeries.coeff_exp, IsSelfAdjoint.algebraMap, Localization.mapToFractionRing_apply, StarAlgHom.ofId_apply, CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right_assoc, IsLocalization.lift_of_comp, NumberField.integralBasis_repr_apply, RingCon.coe_algebraMap, FiniteField.splits_X_pow_nat_card_sub_X, Module.algebraMap_end_eq_smul_id, MvPolynomial.aeval_def, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, CommRingCat.epi_iff_epi, RatFunc.liftRingHom_ofFractionRing_algebraMap, ConjRootClass.splits_minpoly, Module.rankAtStalk_tensorProduct_of_isScalarTower, DoubleCentralizer.algebraMap_snd, Valuation.Integers.dvdNotUnit_iff_lt, RatFunc.laurentAux_algebraMap, QuadraticAlgebra.coe_norm_eq_mul_star, FractionalIdeal.mem_dual, RatFunc.algebraMap_eq_C, Ideal.localized₀_eq_restrictScalars_map, Algebra.intNorm_eq_of_isLocalization, Algebra.Generators.toAlgHom_ofComp_rename, DirectSum.decompose_algebraMap, Valuation.Integers.valuation_unit, IsLocalization.localization_localization_map_units, IsLocalization.Away.mul_invSelf, minpoly.mem_range_of_degree_eq_one, CliffordAlgebra.foldl_algebraMap, Submodule.rTensorOne_tmul, Polynomial.aeval_def, RatFunc.algebraMap_apply_div, algebraMap_memℓp_infty, FractionalIdeal.mem_coeIdeal_of_mem, spectrum.mem_resolventSet_iff, RatFunc.div_smul, IntermediateField.algebraMap_apply, MvPolynomial.algHom_C, LinearMap.toMatrix_algebraMap, IsAlgClosure.equivOfEquiv_symm_algebraMap, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, QuadraticAlgebra.algebraMap_eq, Algebra.discr_of_matrix_vecMul, IntermediateField.LinearDisjoint.norm_algebraMap, FractionalIdeal.exists_mem_algebraMap_eq, DoubleCentralizer.algebraMap_toProd, isSMulRegular_algebraMap_iff, AlgebraicClosure.Monics.splits_finsetProd, UniformSpace.Completion.algebraMap_def, Algebra.isUnramifiedAt_iff_of_isDedekindDomain, IntermediateField.adjoin.range_algebraMap_subset, Ideal.relNorm_algebraMap, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, IsLocalization.Away.lift_eq, Valuation.HasExtension.val_algebraMap, IsLocalization.isLocalization_of_submonoid_le, Module.Basis.localizationLocalization_repr_algebraMap, RatFunc.liftRingHom_apply_div, ValuationSubring.algebraMap_apply, tensorKaehlerQuotKerSqEquiv_tmul_D, Ideal.finrank_quotient_map, HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat, derivationToSquareZeroEquivLift_symm_apply_apply_coe, TensorAlgebra.algebraMap_eq_one_iff, NumberField.InfinitePlace.IsRamified.comap_embedding, NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq, galRestrictHom_symm_algebraMap_apply, RatFunc.algebraMap_C, MvPolynomial.aevalTower_comp_algebraMap, IsLocalization.isLocalization_isLocalization_atPrime_isLocalization, Unitization.algebraMap_eq_inlRingHom_comp, AlgebraicIndependent.algebraMap_aevalEquiv, IsBaseChange.toDual_comp_apply, IsBaseChange.linearMapLeftRightHom_toMatrix, IsLocalization.mk'_eq_iff_eq, CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, Algebra.algebraMap_eq_smul_one, IsConjRoot.add_algebraMap, Module.isTorsionFree_iff_algebraMap_injective, IsAdjoinRoot.lift_algebraMap, IsLocalization.injectiveₛ, CliffordAlgebraQuaternion.ofQuaternion_mk, HurwitzZeta.sinZeta_two_mul_nat_add_one', IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, RingHom.finite_algebraMap, IsLocalization.epi, Ideal.Quotient.algebraMap_quotient_pow_ramificationIdx, Subalgebra.algebraMap_eq, Algebra.IsPushout.cancelBaseChangeAux_symm_tmul, IntermediateField.adjoin.algebraMap_mem, spectrum.add_singleton_eq, Matrix.algebraMap_eq_diagonal, Localization.mk_one_eq_algebraMap, NonUnitalSubalgebra.unitization_apply, IsLocalization.AtPrime.equivQuotMaximalIdeal_apply_mk, LinearMap.eval_charpoly, Algebra.mul_sub_algebraMap_pow_commutes, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, Algebra.ofId_apply, surjective_algebraMap_of_linearMap, AlgebraicGeometry.ValuativeCommSq.commSq, Algebra.algebraMap_ofSubring, Subfield.bot_eq_of_charZero, PowerBasis.quotientEquivQuotientMinpolyMap_symm_apply, Derivation.map_algebraMap, Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree, CliffordAlgebra.reverse.commutes, IsLocalization.nonZeroDivisors_le_comap, MvPolynomial.aeval_eq_constantCoeff_of_vars, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul, Polynomial.eq_mul_mul_of_aroots_quadratic_eq_pair, CommRingCat.isPushout_iff_isPushout, minpoly.dvd_map_of_isScalarTower, Algebra.norm_eq_prod_automorphisms, SetLike.algebraMap_mem_graded, Polynomial.eval_C_X_eval₂_map_C_X, SetLike.GradeZero.coe_algebraMap, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, AlgebraicGeometry.StructureSheaf.const_algebraMap, MvPolynomial.aeval_zero, Valuation.HasExtension.instIsLocalHomValuationInteger, IsScalarTower.algebraMap_smul, IsLocalization.mk'_eq_iff_eq_mul, Algebra.IsUnramifiedAt.not_minpoly_sq_dvd, MvPowerSeries.algebraMap_apply'', CommRingCat.pushout_inl_tensorProdObjIsoPushoutObj_inv_right, IsLocalization.coe_toLocalizationMap, LinearMap.map_mul_algebraMap, Ideal.comap_surjective_of_faithfullyFlat, StarSubalgebra.rangeS_le, Ideal.ramificationIdxIn_eq_ramificationIdx, IsFractionRing.mk'_mk_eq_div, NumberField.RingOfIntegers.coe_injective, algebraMap_le_iff_le_spectrum, PowerSeries.map_algebraMap_eq_subst_X, RatFunc.liftAlgHom_apply_div, CyclotomicRing.adjoin_algebra_injective, Ideal.exists_ltSeries_of_hasGoingDown, StarSubalgebra.algebraMap_mem, FreeAlgebra.algebraMap_inj, LaurentPolynomial.C_eq_algebraMap, Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, Localization.monoidOf_eq_algebraMap, IsLocalization.AtPrime.algebraMap_equivQuotMaximalIdeal_symm_apply, IsLocalization.toInvSubmonoid_mul, ExteriorAlgebra.isUnit_algebraMap, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, GradedTensorProduct.algebraMap_def', IsSepClosed.algebraMap_surjective, PowerSeries.C_eq_algebraMap, Polynomial.map_restriction, spectrum.singleton_add_eq, LinearMap.polyCharpolyAux_baseChange, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap, Algebra.IsInvariant.isInvariant, isIntegrallyClosedIn_iff, IsLocalization.Away.instHMulAwayCoeRingHomAlgebraMap_1, IsLocalization.AtPrime.map_eq_maximalIdeal, matrixEquivTensor_apply_symm, AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero, NumberField.RingOfIntegers.isIntegral_coe, IsAdjoinRoot.lift_self_apply, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, RestrictScalars.ringEquiv_map_smul, Ideal.under_def, AddMonoidAlgebra.mapDomain_algebraMap, IsLocalRing.ResidueField.algebraMap_eq, Ideal.Factors.liesOver, AlgHom.liftNormal_commutes, spectrum.singleton_sub_eq, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, CStarAlgebra.mul_star_le_algebraMap_norm_sq, IsLocalization.toLocalizationMap_toMonoidHom, IntermediateField.AdjoinPair.algebraMap_gen₁, RatFunc.denom_div, algebraMapCLM_apply, IsIntegralClosure.algebraMap_mk', ValuationRing.of_integers, Algebra.smulTower_leftMulMatrix_algebraMap_ne, NumberField.InfinitePlace.not_isUnramified_iff, quasispectrum.algebraMap_mem_iff, NumberField.InfinitePlace.isUnramified_iff, IsDiscreteValuationRing.exists_lift_of_le_one, IsLocalization.AtPrime.isMaximal_map, Valuation.HasExtension.algebraMap_mem_valuationSubring, NoZeroSMulDivisors.iff_algebraMap_injective, cfc_const, NumberField.InfinitePlace.denseRange_algebraMap_pi, algebraMap_injective_of_field_isFractionRing, Algebra.commute_algebraMap_left, QuasispectrumRestricts.algebraMap_image, HopfAlgebra.mul_antipode_rTensor_comul_apply, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, MvPolynomial.aeval_map_algebraMap, Algebra.Generators.Hom.toAlgHom_C, RatFunc.intDegree_polynomial, RingHom.isStandardSmoothOfRelativeDimension_algebraMap, cfc_eval_C, minpoly.add_algebraMap, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, IsLocalization.lift_id, Polynomial.div_eq_quo_add_rem_div, norm_algebraMap, NumberField.Units.coe_pow, IsPurelyInseparable.algebraMap_elemReduct_eq', RootPairing.algebraMap_posRootForm_posForm, CliffordAlgebra.EquivEven.v_sq_scalar, LaurentSeries.LaurentSeries_coe, MvPolynomial.coeToMvPowerSeries.algHom_apply, Algebra.idealMap_isLocalizedModule, AlgebraicGeometry.pullbackSpecIso_inv_snd_assoc, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, HomogeneousLocalization.algebraMap_eq, NumberField.Units.abs_det_eq_abs_det, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, IsPurelyInseparable.algebraMap_iterateFrobenius, Algebra.trace_localization, Algebra.adjoin_eq_adjoin_union, Module.algebraMap_end_apply, FractionalIdeal.exists_ne_zero_mem_isInteger, IsLocalization.isLocalization_of_base_ringEquiv, Algebra.discr_powerBasis_eq_prod, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, Algebra.IsAlgebraic.isNormalClosure_iff, spectralNorm_extends, InfiniteGalois.mem_range_algebraMap_iff_fixed, Algebra.Smooth.exists_finiteType, CliffordAlgebra.contractLeft_ι, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero, IsLocalization.mem_localizationLocalizationSubmodule, WeierstrassCurve.Δ_integral_of_isIntegral, Algebra.trace_algebraMap_of_basis, Algebra.IsPushout.equiv_tmul, NumberField.inverse_basisMatrix_mulVec_eq_repr, CStarAlgebra.norm_le_iff_le_algebraMap, RatFunc.denom_div_dvd, Polynomial.toFinsupp_algebraMap, Prod.algebraMap_apply, StarSubalgebra.range_subset, NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iff, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, Polynomial.Gal.splits_in_splittingField_of_comp, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, NumberField.Units.coe_injective, CFC.log_smul', Ideal.comap_lt_comap_of_integral_mem_sdiff, Polynomial.coeToPowerSeries.algHom_apply, NumberField.Units.coe_one, spectralAlgNorm_extends, Algebra.IsCentral.mem_center_iff, AlgebraicGeometry.pullbackSpecIso_inv_fst_assoc, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Subring.integralClosure_le_iff, IsLocalization'.toIsLocalizationMap, minpoly.ofSubring, AbsoluteValue.LiesOver.comp_eq, NumberField.IsCMField.mem_realUnits_iff, Polynomial.Chebyshev.algebraMap_eval_T, IsFractionRing.injective_comp_algebraMap, normal_iff, CFC.abs_algebraMap_nnreal, Submodule.mker_spanSingleton, SeparationQuotient.mk_algebraMap, bijective_algebraMap_of_linearMap, RingHom.quasiFinite_algebraMap, IsAlgClosure.equivOfEquiv_symm_comp_algebraMap, Algebra.trace_quotient_mk, IsSMulRegular.of_flat_of_isBaseChange, Complex.coe_algebraMap, Algebra.surjective_algebraMap_iff, NumberField.mixedEmbedding.unitSMul_smul, AlgebraicGeometry.Scheme.Hom.fromNormalization_app_assoc, PrimeSpectrum.localization_comap_injective, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, AlgebraicIndependent.sumElim_comp, SymmetricAlgebra.algebraMap_eq_one_iff, AlgebraicClosure.Monics.map_eq_prod, liftOfDerivationToSquareZero_apply, LocalizedModule.mul_by_divBy, AlgHomClass.commutes, minpoly.dvd_map_of_isScalarTower', NumberField.AdeleRing.algebraMap_injective, IsLocalization.algEquiv_comp_algebraMap, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, IsFractionRing.algEquivOfAlgEquiv_algebraMap, IsAlgClosed.algebraMap_bijective_of_isIntegral, IsLocalization.Away.tensor, IsLocalization.orderIsoOfPrime_symm_apply_coe, IsScalarTower.of_compHom, NormedRing.algEquivComplexOfComplete_apply, localization_unit_isIso, IsLocalization.sec_spec, FunctionField.ringOfIntegers.algebraMap_injective, TrivSqZeroExt.algebraMap_eq_inl, Ideal.isMaximal_comap_of_isIntegral_of_isMaximal, AlgebraicGeometry.Scheme.toOpen_eq, DoubleCentralizer.algebraMap_fst, spectrum.mem_iff, NumberField.ComplexEmbedding.Extension.comp_eq, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, rootOfSplitsXPowSubC_pow, UpperHalfPlane.coe_specialLinearGroup_apply, Ideal.ResidueField.lift_algebraMap, IsLocalization.surj_of_gcd_domain, FiniteField.splits_X_pow_card_sub_X, TensorAlgebra.algebraMap_inj, Algebra.smulTower_leftMulMatrix_algebraMap, CStarAlgebra.star_mul_le_algebraMap_norm_sq, Algebra.TensorProduct.tmul_one_eq_one_tmul, Algebra.TensorProduct.quotIdealMapEquivTensorQuot_symm_tmul, GradedTensorProduct.algebraMap_def, IsLocalization.map_units_map_submonoid, Module.End.eigenspace_div, spectrum.add_mem_add_iff, ascPochhammer_eval_comp, IsLocalRing.quotient_span_eq_top_iff_span_eq_top, MvPolynomial.aeval_injective_iff_of_isEmpty, HurwitzZeta.sinZeta_two_mul_nat_add_one, FaithfulSMul.algebraMap_injective, IsLocalization.disjoint_comap_iff, Algebra.commute_algebraMap_right, spectralNorm.eq_of_normalClosure', Ideal.Factors.finrank_pow_ramificationIdx, NumberField.ComplexEmbedding.lift_comp_algebraMap, isPurelyInseparable_iff, CliffordAlgebra.forall_mul_self_eq_iff, AlgebraicGeometry.StructureSheaf.algebraMap_germ_assoc, TopCat.Presheaf.SubmonoidPresheaf.toLocalizationPresheaf_app, IsAlgClosure.equivOfEquiv_algebraMap, nnnorm_algebraMap', LieModule.isNilpotent_toEnd_sub_algebraMap, RingHom.etale_algebraMap, RootPairing.IsValuedIn.exists_value, continuous_algebraMap_iff_smul, Valuation.HasExtension.val_isEquiv_comap, MonoidAlgebra.algebraMap_def, scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, IsSMulRegular.of_isLocalization, IsLocalization.eq_iff_eq, Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComap, MonoidAlgebra.lift_mapRangeRingHom_algebraMap, Set.algebraMap_mem_center, isNilpotent_tensor_residueField_iff, Rat.ringOfIntegersEquiv_apply_coe, Polynomial.algebraMap_hahnSeries_apply, IsIntegrallyClosed.algebraMap_eq_of_integral, Algebra.weaklyQuasiFiniteAt_iff, MeasureTheory.SimpleFunc.const_algebraMap, Unitization.starMap_apply, Valuation.Integers.valuation_pos_iff_ne_zero, MvPowerSeries.algebraMap_apply', FaithfulSMul.algebraMap_eq_one_iff, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Ideal.IntegralClosure.comap_lt_comap, coeff_minpolyDiv, IsLocalization.tmul_mk', Submodule.mem_one, Ideal.ramificationIdx_eq_of_isGalois, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, AlgebraicGeometry.pullbackSpecIso_hom_fst, Algebra.Presentation.coeffs_subset_range, Ideal.smul_restrictScalars, minpoly.degree_eq_one_iff, Ideal.mem_primesOver_iff_mem_normalizedFactors, IntermediateField.isSplittingField_iff, AlgEquiv.restrictNormal_commutes, NumberField.InfinitePlace.comap_mk_lift, IntermediateField.bot_toSubfield, spectrum.algebraMap_eq_of_mem, NumberField.RingOfIntegers.coe_eq_algebraMap, Valuation.HasExtension.val_map_eq_one_iff, IsAdjoinRootMonic.coeff_algebraMap, IsPurelyInseparable.pow_mem, RatFunc.liftOn'_div, Algebra.algebraMap_ofSubsemiring, NumberField.mem_span_integralBasis, TensorProduct.gradedComm_tmul_algebraMap, SubalgebraClass.coe_algebraMap, CommRingCat.tensorProdIsoPushout_app, Subalgebra.lTensorBot_tmul, IntermediateField.adjoin_eq_range_algebraMap_adjoin, RingTheory.Sequence.IsRegular.of_faithfullyFlat_of_isBaseChange, Ideal.map_algebraMap_eq_finset_prod_pow, IsLocalization.injective_iff_map_algebraMap_eq, cfc_const_add, Polynomial.aeval_sumIDeriv_eq_eval, IsLocalization.mk'_one, CyclotomicRing.algebraBase_injective, Polynomial.aeval_C, AlgebraicGeometry.StructureSheaf.algebraMap_germ, spectrum.add_mem_iff, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_2, Algebra.QuasiFinite.finite_comap_preimage_singleton, MvPolynomial.algebraTensorAlgEquiv_symm_map, Subalgebra.rangeS_algebraMap, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, Algebra.Extension.Hom.algebraMap_toRingHom, Polynomial.SplittingFieldAux.splits, Algebra.normalizedTrace_algebraMap_apply, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, NumberField.Units.coe_zpow, RootPairing.RootPositiveForm.exists_pos_eq, Rat.int_algebraMap_injective, MvPowerSeries.coe_aeval, DoubleCentralizer.coe_eq_algebraMap, Differential.logDeriv_algebraMap, RootPairing.algebraMap_pairingIn', IsLocalization.ker_map, Polynomial.coe_algebraMap_eq_CC, selfZPow_natCast, RingHom.IsStandardOpenImmersion.algebraMap, IsScalarTower.algebraMap_eq, IsLocalization.integerNormalization_eval₂_eq_zero, mem_coeSubmodule_conductor, RingTheory.Sequence.IsWeaklyRegular.of_flat_of_isBaseChange, PolyEquivTensor.toFunBilinear_apply_eq_smul, MvPolynomial.algebraMap_eq, Subalgebra.range_subset, LocalizedModule.algebraMap_mk, Polynomial.algebraMap_hahnSeries_injective, LaurentSeries.valuation_coe_ratFunc, CliffordAlgebra.star_algebraMap, Algebra.left_comm, CliffordAlgebra.changeForm_algebraMap, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, MvPolynomial.aeval_eq_eval₂Hom, Algebra.TensorProduct.algebraMap_apply', Algebra.Extension.algebraMap_σ, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, MvPolynomial.aeval_C, Subalgebra.LinearDisjoint.basisOfBasisLeft_apply, NonUnitalAlgHom.toAlgHom_apply, Unitization.nnnorm_eq_sup, IsLocalization.submonoid_map_le_is_unit, algebraMap_mem, IsLocalRing.basisQuotient_apply, AlgebraicGeometry.isIso_SpecMap_stakMap_localization, hasSum_one_div_nat_pow_mul_sin, Ideal.injective_algebraMap_quotient_residueField, Polynomial.eval_C_X_comp_eval₂_map_C_X, minpoly.natSepDegree_eq_one_iff_pow_mem, spectralNorm.eq_of_tower, spectrum.scalar_eq, localizationAlgebraMap_def, minpoly.root, HomogeneousLocalization.Away.eventually_smul_mem, trace_quotient_eq_trace_localization_quotient, Submodule.mem_traceDual, NumberField.InfinitePlace.LiesOver.mk_embedding_comp, AlgHom.commutes, Algebra.Extension.Hom.sub_aux, ULift.down_algebraMap, PowerBasis.exists_gen_dvd_sub, Bialgebra.counit_algebraMap, Algebra.discr_localizationLocalization, KaehlerDifferential.derivationTensorProduct_algebraMap, Ideal.powQuotSuccInclusion_injective, IsLocalization.AtPrime.comap_map_of_isMaximal, IsFractionRing.num_mul_den_eq_num_iff_eq, Submodule.span_singleton_eq_one_iff, Algebra.RingHom.adjoin_algebraMap_surjective, AlgHom.map_coe_real_complex, IsAlgebraic.exists_nonzero_eq_adjoin_mul, isDedekindRing_iff, RatFunc.algebraMap_apply, ExteriorAlgebra.algebraMap_leftInverse, spectralNorm.spectralMulAlgNorm_eq_of_mem_roots, IsLocalization.comap_map_of_isPrimary_disjoint, Algebra.trace_quotient_eq_of_isDedekindDomain, RingHom.finitePresentation_algebraMap, AlgebraicGeometry.StructureSheaf.stalkAlgebra_map, IntermediateField.set_range_subset, IsAdjoinRoot.algebraMap_apply, RootPairing.algebraMap_coroot'In_apply, PowerSeries.algebraMap_eq, IsLocalization.map_units, RingHom.faithfullyFlat_algebraMap_iff, AlgEquiv.algebraMap_eq_apply, TensorProduct.gradedMul_algebraMap, ClassGroup.exists_mk0_eq_mk0, injective_algebraMap_of_linearMap, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, RingHom.isIntegralElem_localization_at_leadingCoeff, RatFunc.mk_one, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, IsPurelyInseparable.exponent_min, RatFunc.algebraMap_injective, isIntegrallyClosed_iff, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalizedModule_of_mem, IsDedekindDomain.primesOverEquivPrimesOver_symm_apply, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, Algebra.mem_ideal_map_adjoin, LaurentSeries.coe_range_dense, Algebra.algebraMap_intNorm_of_isGalois, NumberField.AdeleRing.algebraMap_fst_apply, Algebra.isEpi_iff_surjective_algebraMap_of_finite, AlgebraicGeometry.ΓSpec.toSpecΓ_of, AlgebraicGeometry.StructureSheaf.toOpen_germ, IsLocalization.injective_iff_isRegular, Rat.int_algebraMap_surjective, Algebra.traceMatrix_of_matrix_mulVec, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal, minpolyDiv_spec, IsAdjoinRoot.coe_liftHom, CliffordAlgebra.contractLeft_mul_algebraMap, RingHom.isStandardSmooth_algebraMap, Algebra.pushoutDesc_left, IsCyclotomicExtension.Rat.ramificationIdx_of_not_dvd, MvPowerSeries.substAlgHom_monomial, Algebra.Presentation.HasCoeffs.coeffs_subset_range, galLiftEquiv_algebraMap_apply, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Polynomial.eval₂_pow', Algebra.TensorProduct.quotIdealMapEquivTensorQuot_mk, PrimeSpectrum.range_comap_algebraMap_localization_compl_eq_range_comap_quotientMk, StandardEtalePresentation.toPresentation_algebra_algebraMap_apply, RatFunc.denom_algebraMap, IsLocalization.lift_injective_iff, AlgebraicGeometry.pullbackSpecIso_hom_base_assoc, QuadraticAlgebra.algebraMap_dvd_iff_dvd, MvPowerSeries.algebraMap_apply, RatFunc.liftRingHom_comp_algebraMap, 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, MonoidAlgebra.single_eq_algebraMap_mul_of, algebraMap_nonneg, QuadraticAlgebra.mk_eq_add_smul_omega, Algebra.QuasiFinite.isDiscrete_comap_preimage, Polynomial.Chebyshev.algebraMap_eval_S, Valuation.HasExtension.mk_smul_mk, CFC.sqrt_algebraMap, CFC.posPart_algebraMap, trace_eq_sum_embeddings, IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvd, AlgebraicGeometry.Scheme.affineOpenCoverOfSpanRangeEqTop_f, exists_integer_of_is_root_of_monic, Ideal.span_singleton_absNorm, CliffordAlgebra.contractLeft_algebraMap_mul, PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1, IntermediateField.botEquiv_def, liftOfDerivationToSquareZero_mk_apply', HomogeneousLocalization.den_smul_val, FreeAlgebra.algebraMap_eq_one_iff, TrivSqZeroExt.algebraMap_eq_inlHom, RootPairing.RootPositiveForm.algebraMap_apply_eq_form_iff, Ideal.quotientMap_algebraMap, IsLocalization.mk'_spec'_mk, IsPurelyInseparable.hasExponent_iff', RatFunc.num_mul_eq_mul_denom_iff, Polynomial.aeval_monomial, Equiv.algebraMap_def, Polynomial.eval_map_algebraMap, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, IsTranscendenceBasis.sumElim_comp, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, Valuation.Integers.valuation_irreducible_pos, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply, ExteriorAlgebra.liftAlternating_algebraMap, Polynomial.isIntegrallyClosed_iff', AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, WittVector.exists_frobenius_solution_fractionRing_aux, Normal.out, IsLocalizedModule.fromLocalizedModule'_mk, Algebra.FormallyUnramified.map_maximalIdeal, AlgebraicGeometry.pullbackSpecIso_hom_fst'_assoc, Subalgebra.algebraMap_mem, HopfAlgebra.mul_antipode_lTensor_comul_apply, LinearAlgebra.FreeProduct.lift_algebraMap, SymmetricAlgebra.algebraMap_leftInverse, Algebra.adjoin_algebraMap, AlgEquiv.liftNormal_commutes, RingHom.flat_algebraMap_iff, ModP.v_p_lt_val, AlgebraicGeometry.geometrically_iff_of_commRing_of_isClosedUnderIsomorphisms, QuadraticAlgebra.coe_mem_nonZeroDivisors_iff, Localization.localRingHom_bijective_of_saturated_inf_eq_top, Algebra.smul_def, RatFunc.liftAlgHom_apply_div', Submodule.lTensorOne_tmul, IsLocalization.ringEquivOfRingEquiv_eq, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, spectralNorm_extends_of_finiteDimensional, Algebra.discr_powerBasis_eq_prod'', TensorAlgebra.algebraMap_leftInverse, LocallyConstant.coe_algebraMap, AlgebraicGeometry.pullbackSpecIso_inv_fst', IntermediateField.adjoin_subset_adjoin_iff, ContinuousMap.C_apply, PowerSeries.algebraMap_apply, Algebra.map_intTraceAux, RatFunc.liftRingHom_algebraMap, IsLocalization.mk'_mul_cancel_right, Polynomial.algHom_eval₂_algebraMap, IsLocalization.exists_integer_multiple', IsLocalization.Away.surj, minpoly.natDegree_eq_one_iff, Algebra.Presentation.HasCoeffs.relation_mem_range_map, PowerSeries.coe_aeval, CliffordAlgebra.foldr_algebraMap, Valuation.Integers.isUnit_iff_valuation_eq_one, Polynomial.UniversalCoprimeFactorizationRing.factor₁_mul_factor₂, NormedSpace.algebraMap_exp_comm_of_mem_ball, Algebra.algebra_ext_iff, RingHom.algebraMap_toAlgebra, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, Ideal.Factors.finiteDimensional_quotient_pow, algebraMap_int_eq, IsCyclotomicExtension.Rat.ramificationIdx_eq, RatFunc.mk_one', AlgHom.map_algebraMap, cfc_predicate_algebraMap, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, ValuativeExtension.mapPosSubmonoid_apply_coe, Polynomial.coeff_zero_eq_aeval_zero', IsLocalizedModule.map_units, CliffordAlgebra.ofEven_ι, AdjoinRoot.liftHom_of, CliffordAlgebra.ofBaseChange_tmul_one, MvPolynomial.universalFactorizationMap_freeMonic, HopfAlgebra.sum_antipode_mul_eq_algebraMap_counit, QuaternionAlgebra.algebraMap_eq, Valuation.extendToLocalization_apply_map_apply, algebraMap_mono, AlgebraicGeometry.diagonal_Spec_map, IsPurelyInseparable.exponent_min', MvPolynomial.aeval_sumElim, isAlgebraic_algebraMap, Algebra.IsPushout.equiv_symm_algebraMap_right, Derivation.compAlgebraMap_apply, NumberField.InfinitePlace.mem_orbit_iff, QuadraticAlgebra.algebraMap_norm_eq_mul_star, Matrix.SpecialLinearGroup.mapGL_coe_matrix, IsLocalization.AtPrime.isUnit_to_map_iff, NumberField.InfinitePlace.isUnramifiedIn_comap, Algebra.compHom_algebraMap_eq, IsLocalization.isLocalization_atPrime_localization_atPrime, RingOfIntegers.algebraMap_norm_algebraMap, RCLike.ofReal_im_ax, IsLocalization.Away.associated_sec_fst, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, IsLocalization.mul_toInvSubmonoid, IsLocalization.algebraMap_mk', Subalgebra.setRange_algebraMap, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, SymmetricAlgebra.algebraMap_inj, Algebra.discr_powerBasis_eq_prod', QuaternionAlgebra.coe_algebraMap, PadicAlgCl.coe_eq, Algebra.algebraMap_intTrace, PrimeSpectrum.instLiesOverAsIdealComapAlgebraMap, IsLocalization.mk'_eq_iff_eq', IsLocalization.AtPrime.equivQuotientMapMaximalIdeal_apply_mk, IsLocalization.eq_mk'_of_mul_eq, Algebra.IsIntegral.quotient, Subalgebra.algebraMap_apply, SpectrumRestricts.nnreal_iff_spectralRadius_le, Algebra.adjoin_res_eq_adjoin_res, DoubleQuot.quotQuotEquivComm_mk_mk, dist_algebraMap, FaithfulSMul.ker_algebraMap_eq_bot, Ideal.Factors.isPrime, SubMulAction.mem_one', Algebra.Presentation.quotientEquiv_mk, PrimeSpectrum.exists_image_comap_of_finite_of_free, IsSMulRegular.of_flat, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, le_algebraMap_of_spectrum_le, trace_eq_sum_automorphisms, Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map, IntermediateField.LinearDisjoint.linearIndependent_mul', IsTranscendenceBasis.algebraMap_comp, quasispectrum.preimage_algebraMap, MonoidAlgebra.lift_def, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, FractionalIdeal.equivNum_apply, IsLocalization.invertible_mk'_one_invOf, Algebra.algebraMapSubmonoid_powers, MvPolynomial.aeval_zero', NumberField.RingOfIntegers.map_mk, IsAlgebraic.algebraMap, Subalgebra.LinearDisjoint.norm_algebraMap, RingHom.locally_iff_finite, PrimeSpectrum.localization_specComap_injective, IsPurelyInseparable.bijective_algebraMap_of_isSeparable, IsFractionRing.algEquiv_commutes, IsStronglyTranscendental.iff_of_isLocalization, SpectrumRestricts.rightInvOn, norm_algebraMap', IsLocalization.mul_mk'_eq_mk'_of_mul, Algebra.norm_algebraMap, IsPurelyInseparable.algebraMap_elemReduct_eq, IsLocalization.integerNormalization_spec, GradedTensorProduct.tmul_algebraMap_mul_coe_tmul, Localization.localRingHom_bijective_of_not_conductor_le, IsIntegral.algebraMap, IsLocalization.eq_mk'_iff_mul_eq, Algebra.algebraMap_intTrace_fractionRing, Valuation.HasExtension.val_map_lt_one_iff, Unitization.lift_apply_apply, AlgebraicGeometry.IsOpenImmersion.of_isLocalization, RatFunc.num_div_denom, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Polynomial.cyclotomic_mahlerMeasure_eq_one, Ideal.under_map_eq_map_under, FixedPoints.coe_algebraMap, FractionalIdeal.den_mul_self_eq_num', isLocalization_iff_isLocalizationMap, KaehlerDifferential.map_D, Algebra.adjoin_toSubsemiring, QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff, Ideal.Quotient.mk_comp_algebraMap, Algebra.Presentation.baseChange_relation, NumberField.InfinitePlace.isUnramified_iff_mult_le, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, Subalgebra.mem_perfectClosure_iff, localization_unit_isIso', Polynomial.Monic.exists_splits_map, IsLocalization.mem_coeSubmodule, TensorPower.toTensorAlgebra_galgebra_toFun, TensorAlgebra.algebraMap_eq_zero_iff, MvPolynomial.aeval_monomial, Subalgebra.range_le, AddMonoidAlgebra.lift_def, isDedekindDomain_iff, NumberField.InfiniteAdeleRing.denseRange_algebraMap, spectrum.algebraMap_mem, QuadraticAlgebra.coe_algebraMap, CFC.log_algebraMap, GradedTensorProduct.tmul_coe_mul_algebraMap_tmul, AlgebraicGeometry.pullbackSpecIso_hom_fst', PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, Algebra.smulTower_leftMulMatrix_algebraMap_eq, IntermediateField.adjoin_toSubfield, KaehlerDifferential.tensorKaehlerEquiv_tmul_D, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero, CFC.spectrum_algebraMap_subset, IsPurelyInseparable.isPRadical, selfZPow_of_nonneg, NumberField.Units.finrank_mul_regulator_eq_det, IsLocalization.ideal_eq_iInf_comap_map_away, RatFunc.aeval_X_left_eq_algebraMap, Algebra.coe_linearMap, Polynomial.residueFieldMapCAlgEquiv_symm_X, ValuationRing.coe_equivInteger_apply, Ideal.exists_notMem_dvd_algebraMap_of_primesOver_eq_singleton, Submodule.map_mem_span_algebraMap_image, Algebra.algebraMap_ofSubring_apply, IsLocalization.mem_map_algebraMap_iff, Algebra.algebraMap_pUnit, Algebra.IsIntegral.isLocalHom, exists_reduced_fraction', cfc_algebraMap, PrimeSpectrum.localization_comap_range, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map, AlgHom.restrictNormal_commutes, IsLocalization.orderIsoOfPrime_apply_coe, StandardEtalePair.HasMap.map_algebraMap, Module.Basis.norm_extends, Algebra.EssFiniteType.cond, RootPairing.toLinearMap_apply_apply_mem_range_algebraMap, IsLocalization.primeHeight_comap, MvPolynomial.aevalTower_algebraMap, NumberField.Units.sum_mult_mul_log, Algebra.IsInvariant.charpoly_mem_lifts, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, RingHom.IsStandardSmoothOfRelativeDimension.algebraMap_isLocalizationAway, Subalgebra.LinearDisjoint.leftMulMatrix_basisOfBasisRight_algebraMap, RingHom.locally_iff_exists, PowerSeries.algebraMap_apply', Ideal.algebraMap_residueField_eq_zero, Module.Basis.repr_smul', AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec, RootPairing.RootPositiveForm.algebraMap_posForm, NumberField.ComplexEmbedding.lift_algebraMap_apply, AlgEquiv.commutes', CliffordAlgebra.contractRight_ι, Ideal.bijective_algebraMap_quotient_residueField, Polynomial.IsPrimitive.isUnit_iff_isUnit_map, Unitization.algebraMap_eq_inlRingHom, IsConjRoot.sub_algebraMap, algebraMap_galRestrict'_apply, Ideal.absNorm_algebraMap, RingOfIntegers.coe_algebraMap_norm, IsLocalization.surjective_piRingHom_algebraMap_comp_piEvalRingHom, tendsto_algebraMap_cobounded, MvPolynomial.supportedEquivMvPolynomial_symm_C, tendsto_algebraMap_inv_atTop_nhds_zero_nat, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, RatFunc.algebraMap_monomial, RatFunc.denom_dvd, AlgebraicGeometry.StructureSheaf.toOpen_res, dist_algebraMap', PrimeSpectrum.localization_comap_isEmbedding, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_spec_assoc, Ideal.quotientToQuotientRangePowQuotSuccAux_mk, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_spec, Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply, LocalizedModule.algebraMap_mk', AlgebraicGeometry.pullbackSpecIso_hom_snd, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, RingHom.surjectiveOnStalks_of_isLocalization, Polynomial.aroots_def, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, ValuationSubring.algebraMap_injective, matPolyEquiv_smul_one, RestrictScalars.addEquiv_symm_map_algebraMap_smul, Ideal.ResidueField.liftₐ_algebraMap, IsPurelyInseparable.exponent_def, IntermediateField.mem_bot, MatrixEquivTensor.toFunAlgHom_apply, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, IsFractionRing.num_mul_den_eq_num_iff_eq', IsLocalization.AtPrime.isPrime_map_of_liesOver, Pi.constRingHom_eq_algebraMap, MonoidAlgebra.mapDomainRingHom_comp_algebraMap, HahnSeries.algebraMap_apply', NumberField.Units.dirichletUnitTheorem.exists_unit, MeasureTheory.SimpleFunc.coe_algebraMap, IsScalarTower.algebraMap_apply, Polynomial.Gal.splits_ℚ_ℂ, SkewMonoidAlgebra.lift_def, Ideal.Factors.piQuotientEquiv_mk, IsSelfAdjoint.le_algebraMap_norm_self, IsLocalization.Away.integralClosure, Ideal.ramificationIdx_eq_of_isGaloisGroup, IsAdjoinRoot.lift_algebraMap_apply, RingTheory.Sequence.IsWeaklyRegular.isRegular_of_isLocalization_of_mem, NumberField.InfinitePlace.comap_surjective, Matrix.Represents.algebraMap, AlgebraicGeometry.StructureSheaf.algebraMap_pushforward_stalk, Algebra.Generators.Hom.algebraMap_toAlgHom, IsGalois.splits, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, Subalgebra.rangeS_le, TensorAlgebra.ι_eq_algebraMap_iff, LinearMap.map_algebraMap_mul, NumberField.RingOfIntegers.algebraMap.injective, IsLocalization.algebraMap_pi_surjective_of_isLocalization, Polynomial.aeval_algebraMap_apply, Valuation.Integers.one_of_isUnit, PrimeSpectrum.localization_away_comap_range, Subalgebra.rTensorBot_tmul, IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdx, PiTensorProduct.algebraMap_apply, NumberField.mixedEmbedding.norm_unit, algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, RingTheory.Sequence.IsWeaklyRegular.of_isLocalization, Pi.algebraMap_def, MvPolynomial.mapEquivMonic_symm_map_algebraMap, minpoly.eq_X_sub_C, Ideal.Quotient.mk_smul_mk_quotient_map_quotient, isSplittingField_iff_intermediateField, LinearMap.trace_baseChange, Algebra.idealMap_apply_coe, FractionalIdeal.den_mem_inv, Localization.AtPrime.map_eq_maximalIdeal, Subalgebra.range_algebraMap, RingTheory.Sequence.IsWeaklyRegular.of_isLocalizedModule, FreeAlgebra.algebraMap_leftInverse, Module.Basis.mem_span_iff_repr_mem, FiniteField.algebraMap_norm_eq_pow_sum, IsBaseChange.toDualBaseChange_tmul, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, IntermediateField.coe_algebraMap_apply, QuasispectrumRestricts.left_inv, NumberField.IsCMField.complexConj_torsion, Polynomial.residueFieldMapCAlgEquiv_algebraMap, spectrum.vadd_eq, FreeAlgebra.algebraMap_eq_zero_iff, algebraMap_cobounded_le_cobounded, Localization.awayMap_awayMap_surjective, Polynomial.instIsLocalHomRingHomAlgebraMap, Module.Basis.toMatrix_map_vecMul, Algebra.commutes, Transcendental.linearIndependent_sub_inv, IsLocalization.liesOver_of_isPrime_of_disjoint, Algebra.mem_algebraMapSubmonoid_of_mem, NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zero, inv_eq_of_aeval_divX_ne_zero, IsSMulRegular.of_isLocalizedModule, Polynomial.IsSplittingField.map, AlgebraicGeometry.StructureSheaf.algebraMap_germ_apply, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, FractionRing.mk_eq_div, AlgebraicGeometry.Scheme.Spec.residue_residueFieldIso_hom, LinearMap.charpoly_baseChange, IsLocalization.surj₂, CFC.log_smul, HomogeneousLocalization.algebraMap_apply, IsStronglyTranscendental.of_isLocalization, RingOfIntegers.dvd_norm, Differential.ContainConstants.mem_range_of_deriv_eq_zero, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, polyEquivTensor_symm_apply_tmul_eq_smul, spectrum.sub_singleton_eq, Valuation.coeff_zero_minpoly, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, RatFunc.map_apply_div_ne_zero, algebraicIndependent_empty_type_iff, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, MvPolynomial.algebraMap_def, AlgebraicGeometry.pullbackSpecIso_hom_fst_assoc, Matrix.algebraMap_matrix_apply, IsPurelyInseparable.inseparable, AlgebraicGeometry.Scheme.Hom.fromNormalization_app, Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one, IsLocalization.height_comap, IntermediateField.AdjoinPair.algebraMap_gen₂, IsLocalization.eq_iff_exists, PrimeSpectrum.nontrivial_iff_mem_rangeComap, NumberField.house.basis_repr_norm_le_const_mul_house, SpectrumRestricts.nnreal_iff_nnnorm, NumberField.IsCMField.Units.complexConj_eq_self_iff, Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map, is_integral_localization_at_leadingCoeff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Module.Basis.restrictScalars_toMatrix, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, algebraMap_le_algebraMap, Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det, Algebra.botEquiv_symm_apply, IsLocalization.Away.algebraMap_isUnit, Localization.AtPrime.mapPiEvalRingHom_algebraMap_apply, Submodule.ker_unitsMap_spanSingleton, isConjRoot_iff_eq_algebraMap', MulAlgebraNorm.extends_norm, Polynomial.residueFieldMapCAlgEquiv_symm_C, Matrix.algebraMap_eq_diagonalRingHom, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, IsLocalization.mk'_spec, RootPairing.algebraMap_root'In_apply, QuadraticAlgebra.coe_dvd_iff, RestrictScalars.smul_def, Polynomial.eval₂_comp', AlgebraicGeometry.ΓSpec.toSpecΓ_unop, Valuation.HasExtension.algebraMap_injective, ULift.algebraMap_eq, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, inv_eq_of_root_of_coeff_zero_ne_zero, IsScalarTower.toAlgHom_apply, NumberField.InfinitePlace.IsUnramified.comap, RatFunc.algebraMap_comp_C, toAlgebra_algebraMap, RatFunc.ofFractionRing_algebraMap, RatFunc.eval_algebraMap, CFC.eq_algebraMap_of_spectrum_subset_singleton, IsPurelyInseparable.elemExponent_def, QuadraticAlgebra.algebraMap_im, Polynomial.eval₂_algebraMap_X, algebraMap_comp_natCast, le_algebraMap_iff_spectrum_le, Ideal.Factors.piQuotientEquiv_map, ClassGroup.exists_mem_finsetApprox, spectrum.notMem_iff, algebraMap_star_comm, Unitization.algebraMap_eq_inl_comp, RestrictScalars.addEquiv_map_smul, derivationQuotKerSq_mk, IsFractionRing.self_iff_bijective, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, minpoly.isIntegrallyClosed_eq_field_fractions', isCyclic_tfae, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, IsFractionRing.lift_algebraMap, Module.Basis.ofIsLocalizedModule_repr_apply, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, AlgebraicGeometry.LocallyRingedSpace.toΓSpecCApp_iff, ContinuousLinearMap.algebraMap_apply, DoubleQuot.quotQuotEquivComm_algebraMap, QuadraticAlgebra.algebraMap_injective, Polynomial.algebraMap_eq, FaithfulSMul.algebraMap_eq_zero_iff, Ideal.Quotient.mk_algebraMap, CliffordAlgebra.even.lift.aux_algebraMap, prod_galRestrict_eq_norm, algebraMap_le_cfc_iff, IsLocalization.algebraMap_eq_map_map_submonoid, Algebra.PreSubmersivePresentation.localizationAway_jacobian, RingHom.smooth_algebraMap, MvPolynomial.constantCoeff_comp_algebraMap, IsLocalization.map_nonZeroDivisors_le, Ideal.Quotient.algebraMap_mk_of_liesOver, CliffordAlgebra.contractLeft_algebraMap, IsLocalization.coeSubmodule_span_singleton, CommRingCat.pushout_inr_tensorProdObjIsoPushoutObj_inv_right, KaehlerDifferential.kerTotal_mkQ_single_algebraMap, AlgebraicGeometry.pullbackSpecIso_hom_snd_assoc

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
smul_algebraMap 📖	mathematical	—	SemigroupAction.toSMul Monoid.toSemigroup MulAction.toSemigroupAction MulDistribMulAction.toMulAction MonoidWithZero.toMonoid Semiring.toMonoidWithZero DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring RingHom.instFunLike algebraMap	—	Algebra.algebraMap_eq_smul_one SMulCommClass.smul_comm MulDistribMulAction.smul_one
toAlgebra_algebraMap 📖	mathematical	—	RingHom.toAlgebra algebraMap CommSemiring.toSemiring	—	Algebra.algebra_ext

algebraMap

Definitions

Name	Category	Theorems
coeHTCT 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe_add 📖	mathematical	—	Algebra.cast Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring CommSemiring.toSemiring	—	map_add AddMonoidHomClass.toAddHomClass RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass
coe_mul 📖	mathematical	—	Algebra.cast Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring CommSemiring.toSemiring	—	map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass RingHom.instRingHomClass
coe_natCast 📖	mathematical	—	Algebra.cast AddMonoidWithOne.toNatCast AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne Semiring.toNonAssocSemiring CommSemiring.toSemiring	—	map_natCast RingHom.instRingHomClass
coe_neg 📖	mathematical	—	Algebra.cast CommRing.toCommSemiring Ring.toSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing	—	map_neg RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass
coe_one 📖	mathematical	—	Algebra.cast AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne Semiring.toNonAssocSemiring CommSemiring.toSemiring	—	map_one MonoidHomClass.toOneHomClass MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass RingHom.instRingHomClass
coe_pow 📖	mathematical	—	Algebra.cast Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring	—	map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass RingHom.instRingHomClass
coe_smul 📖	mathematical	—	Algebra.cast	—	Algebra.algebraMap_eq_smul_one smul_assoc
coe_smul' 📖	mathematical	—	Algebra.cast SemigroupAction.toSMul Monoid.toSemigroup MulAction.toSemigroupAction MulDistribMulAction.toMulAction MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	Algebra.algebraMap_eq_smul_one SMulDistribClass.smul_distrib_smul MulDistribMulAction.smul_one
coe_sub 📖	mathematical	—	Algebra.cast CommRing.toCommSemiring Ring.toSemiring SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing	—	map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass
coe_zero 📖	mathematical	—	Algebra.cast MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring CommSemiring.toSemiring	—	map_zero MonoidWithZeroHomClass.toZeroHomClass RingHomClass.toMonoidWithZeroHomClass RingHom.instRingHomClass

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