toEuclideanDomain đ | CompOp | 3040 mathmath: IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, Differential.logDeriv_prod, Pi.comul_eq_adjoint, LinearMap.det_toContinuousLinearMap, RatFunc.instFaithfulSMulPolynomialLaurentSeries, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, ContMDiffAt.coordChangeL, LinearMap.IsSymmetric.clm_adjoint_eq, RootPairing.nonempty_base, Polynomial.Gal.galActionHom_restrict, AffineSubspace.sOppSide_iff_exists_right, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, NumberField.basisMatrix_eq_embeddingsMatrixReindex, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, Polynomial.degree_normalize, minpoly_sub_algebraMap_splits, Lagrange.interpolate_one, Algebra.normalizedTrace_map, WeierstrassCurve.Affine.nonsingular_negAdd, MDifferentiable.coordChangeL, RatFunc.eval_mul, IsAlgClosed.roots_eq_zero_iff_degree_nonpos, Hyperreal.infinitePos_add_not_infiniteNeg, LieDerivation.IsKilling.ad_mem_ker_killingForm_ad_range_of_mem_orthogonal, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, IntermediateField.isSeparable_of_mem_isSeparable, Algebra.normalizedTrace_algebraMap_eq_id, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, Lagrange.eval_iterate_derivative_eq_sum, Emb.Cardinal.equivLim_coherence, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff, topDualPairing_isContPerfPair, InfiniteGalois.normal_iff_isGalois, RatFunc.liftMonoidWithZeroHom_apply, Lagrange.interpolate_eq_of_values_eq_on, IntermediateField.exists_algHom_adjoin_of_splits, mem_perfectClosure_iff_natSepDegree_eq_one, LeftInvariantDerivation.lift_zero, Irreducible.maximalIdeal_eq_setOf_le_v_coe, Polynomial.coe_normUnit_of_ne_zero, IntermediateField.aeval_gen_minpoly, IsUltrametricDist.isNonarchimedean_invariantExtension, MDifferentiableOn.clm_postcomp, WeierstrassCurve.Jacobian.Point.toAffineLift_neg, Matrix.rank_transpose, IsIntegralClosure.rank, integralClosure_le_span_dualBasis, HasCompactSupport.convolution_integrand_bound_left, Subfield.rank_comap, IsSepClosed.hasEnoughRootsOfUnity, RootPairing.GeckConstruction.instIsCartanSubalgebraSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra', WeierstrassCurve.Jacobian.nonsingular_iff_of_Y_eq_negY, LinearMap.adjoint_adjoint, quadraticChar_card_sqrts, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, FixedPoints.finrank_eq_card, IntermediateField.algHomEquivAlgHomOfSplits_symm_apply, minpoly.unique, IsPurelyInseparable.minpoly_natDegree_eq', AlgEquiv.coe_adjoinSingletonEquivAdjoinRootMinpoly_symm, ConjRootClass.mk_zero, RatFunc.num_div, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, LinearMap.toLinearMap_tracePositiveLinearMap, LieModule.Weight.IsZero.neg, LieDerivation.IsKilling.instIsKilling_range_ad, MeasureTheory.convolution_eq_right', IntermediateField.LinearDisjoint.linearIndependent_right', Orientation.ne_iff_eq_neg, Ideal.hasFiniteMulSupport_coe, ClassGroup.mk0_integralRep, SimpleGraph.lapMatrix_toLinearMapâ', NumberField.InfinitePlace.sum_mult_eq, RootPairing.coroot_eq_polarizationEquiv_apply_root, Ideal.exists_comap_galRestrict_eq, AlgebraicGeometry.pointOfClosedPoint_comp_assoc, NumberField.integralBasis_apply, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, IntermediateField.adjoin.finrank, ValuationSubring.integralClosure_algebraMap_injective, IsPurelyInseparable.minpoly_eq', AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegral, Polynomial.Gal.galActionHom_bijective_of_prime_degree', ContinuousLinearMap.continuous_det, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', LieAlgebra.IsKilling.restrict_killingForm_eq_sum, quadraticChar_card_card, FDRep.char_tensor, Lagrange.eval_interpolate_not_at_node', IntermediateField.algHomEquivAlgHomOfSplits_apply_apply, Lagrange.nodalWeight_eq_eval_nodal_erase_inv, Polynomial.Gal.smul_def, WeierstrassCurve.Jacobian.baseChange_add, IsGalois.card_aut_eq_finrank, AdjoinRoot.minpoly_root, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, Matrix.IsHermitian.det_abs, Algebra.normalizedTrace_surjective, Algebra.normalizedTrace_eq_of_finiteDimensional, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_eq_zero, MDifferentiableAt.cle_arrowCongr, LinearMap.isPositive_adjoint_comp_self, autAdjoinRootXPowSubCEquiv_root, LinearMap.IsSymmetric.isFinitelySemisimple, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, MulChar.exists_mulChar_orderOf, AffineSubspace.WOppSide.trans_wSameSide, ClassGroup.mk_eq_mk_of_coe_ideal, smoothSheafCommRing.nonunits_stalk, WeierstrassCurve.Jacobian.add_of_Y_ne', RatFunc.algEquivOfTranscendental_X, MulChar.exists_apply_eq_pow, RootPairing.GeckConstruction.instHasTrivialRadical, AffineSubspace.setOf_sSameSide_eq_image2, NumberField.canonicalEmbedding.latticeBasis_apply, NumberField.IsCMField.unitsComplexConj_torsion, RatFunc.num_div_dvd, SchwartzMap.pairing_apply_apply, minpoly.algEquiv_apply, Algebra.isInvariant_of_isGalois, Algebra.IsSeparable.of_equiv_equiv, WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_X, IsPurelyInseparable.elemExponent_min', jacobiSum_mem_algebraAdjoin_of_pow_eq_one, NumberField.norm_norm_le_norm_mul_house_pow, WeierstrassCurve.Jacobian.Point.toAffineLift_some, WeierstrassCurve.Jacobian.dblX_of_Z_ne_zero, ConjRootClass.aeval_minpoly_iff, Polynomial.Gal.restrict_smul, isConjRoot_iff_mem_minpoly_aroots, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, finrank_quotient_span_eq_natDegree_norm, root_X_pow_sub_C_eq_zero_iff, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, NumberField.RingOfIntegers.instIsIntegralClosureIntWithVal, Algebra.FormallySmooth.of_algebraicIndependent_of_isSeparable, Polynomial.idealX_span, RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, IsCovariantDerivativeOn.difference_apply, FiniteField.isSquare_neg_one_iff, FixedPoints.isSeparable, ClassGroup.Quot_mk_eq_mk, IntermediateField.isPurelyInseparable_iSup, WeierstrassCurve.Affine.Point.add_self_of_Y_ne, NumberField.IsCMField.equivInfinitePlace_symm_apply, Matrix.rank_add_rank_le_card_of_mul_eq_zero, Polynomial.Gal.galActionHom_injective, MeasureTheory.integral_fintype_prod_volume_eq_pow, AffineSubspace.SSameSide.not_sOppSide, ContMDiffCovariantDerivativeOn.affine_combination, LinearMap.orthogonal_ker, LinearMap.IsSymmetric.diagonalization_apply_self_apply, Matrix.isParabolic_iff_exists, WeierstrassCurve.Projective.comp_equiv_comp, MulChar.apply_mem_algebraAdjoin_of_pow_eq_one, FractionalIdeal.le_dual_iff, Ideal.ramificationIdx_le_finrank, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_pos, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, exteriorPower.ΚMulti_family_linearIndependent_field, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero, LieAlgebra.finrank_engel, RatFunc.num_one, Continuous.convolution_integrand_fst, Hyperreal.not_infinite_zero, WeierstrassCurve.HasAdditiveReduction.badReduction, AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iff, LaurentSeries.LaurentSeriesRingEquiv_def, Emb.Cardinal.directed_filtration, FirstOrder.Field.realize_genericMonicPolyHasRoot, isClosedEmbedding_cfcâAux, Lagrange.leadingCoeff_basis, LieModule.traceForm_eq_sum_finrank_nsmul', LeftInvariantDerivation.coe_derivation, FractionalIdeal.sup_mul_inf, Quaternion.coe_inv, minpoly_algebraMap_add_splits, FiniteField.isSquare_two_iff, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, LinearMap.adjoint_innerââ_apply, ContMDiffWithinAt.mfderivWithin_const, RatFunc.exists_zpow_uniformizingPolynomial, WeierstrassCurve.Jacobian.nonsingularLift_addMap, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContMDiffOn.clm_postcomp, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, LinearMap.adjoint_eq_toCLM_adjoint, minpoly.eq_iff_aeval_eq_zero, Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, QuasispectrumRestricts.cfcâ_eq_restrict, IsCyclotomicExtension.discr_odd_prime, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Valuation.norm_add_le, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, WeierstrassCurve.Projective.equiv_some_of_Z_ne_zero, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, FractionalIdeal.mul_inv_cancel_of_le_one, IsPurelyInseparable.insepDegree_eq, LeftInvariantDerivation.left_invariant', insepDegree_le_rank, RingHom.finite_iff_finiteType_of_isJacobsonRing, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Emb.Cardinal.filtration_succ, RatFunc.denom_one, Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, Hyperreal.not_infiniteNeg_add_infinitePos, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, isSepClosure_iff, IntermediateField.relfinrank_mul_finrank_top, LieAlgebra.IsKilling.rootSystem_coroot_apply, IsLocalRing.finrank_cotangentSpace_eq_zero, WittVector.RecursionMain.succNthVal_spec', LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, instIsTorsionFreeCyclotomicFieldOfIsDomainOfIsFractionRing, Matrix.spectrum_toLpLin, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, mdifferentiableOn_symm_coordChangeL, LieAlgebra.exists_isCartanSubalgebra_engel_of_finrank_le_card, NumberField.mixedEmbedding.mem_idealLattice, RatFunc.intDegree_div, sum_smul_minpolyDiv_eq_X_pow, RatFunc.denom_mul_dvd, SchwartzMap.bilinLeftCLM_apply, FunctionField.inftyValuation.X_inv, MeasureTheory.integral_fintype_prod_eq_prod, Hyperreal.epsilon_mul_omega, FiniteField.frobeniusAlgEquivOfAlgebraic_apply, Algebra.FormallyUnramified.of_isSeparable, minpoly.eq_of_irreducible, Valuation.IsRankOneDiscrete.valueGroupâ_equiv_withZeroMulInt_restrict_apply_of_surjective, PowerSeries.Unit_of_divided_by_X_pow_order_zero, InfiniteGalois.normalAutEquivQuotient_apply, IsPurelyInseparable.elemExponent_min, ArchimedeanClass.stdPart_zero, IsSeparable.of_algebra_isSeparable_of_isSeparable, Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_three, PowerSeries.maximalIdeal_eq_span_X, FixedPoints.minpoly.evalâ', WeierstrassCurve.Projective.dblU_smul, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, IsAlgClosure.of_exists_root, WeierstrassCurve.Jacobian.negAddY_eq, RootPairing.invtRootSubmodule.eq_span_root, NumberField.RingOfIntegers.mk_eq_mk, LieIdeal.reflectionPerm_mem_rootSet_iff, IntermediateField.isAlgebraic_tower_bot, IsSepClosed.exists_eq_mul_self, LieModule.Weight.IsNonZero.neg, Hyperreal.not_infinitePos_add_infiniteNeg, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, Normal.splits', instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, isConjRoot_iff_exists_algEquiv, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, IsPurelyInseparable.finInsepDegree_eq, IsPurelyInseparable.elemExponent_def', LaurentSeries.valuation_single_zpow, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, IntermediateField.algHomEquivAlgHomOfSplits_apply, Cubic.disc_eq_prod_three_roots, jacobiSum_mul_nontrivial, WeierstrassCurve.Projective.nonsingular_neg, WeierstrassCurve.ofJ_j, RatFunc.irreducible_min_polynomial_valuation_lt_one_and_ne_zero, Normal.minpoly_eq_iff_mem_orbit, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', IsLocalRing.instFiniteResidueField_1, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces, LieDerivation.IsKilling.exists_eq_ad, Subfield.relfinrank_mul_finrank_top, RootPairing.invtRootSubmodule.eq_top_iff, WeierstrassCurve.ofJ_1728_of_two_ne_zero, adjoinRootXPowSubCEquiv_symm_eq_root, WeierstrassCurve.Projective.Y_eq_iff', WeierstrassCurve.Projective.nonsingular_of_Z_ne_zero, Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff, contractLeft_assoc_coevaluation, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff, Lagrange.eval_interpolate_not_at_node, WeierstrassCurve.valuation_Î_aux_eq_of_isIntegral, Orientation.eq_or_eq_neg, Quaternion.coe_ratCast, NumberField.HeightOneSpectrum.rankOne_hom'_def, IntermediateField.relrank_mul_rank_top, IsGalois.card_fixingSubgroup_eq_finrank, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearMap.adjoint_id, LinearMap.coe_toContinuousLinearMap', Polynomial.SplittingFieldAux.algebraMap_succ, NumberField.natAbs_discr_eq_natAbs_discr_pow_mul_natAbs_discr_pow, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, ArchimedeanClass.FiniteResidueField.mk_eq_zero, NumberField.abs_discr_ge', WeierstrassCurve.Affine.CoordinateRing.XYIdeal_eqâ, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Matrix.mem_spectrum_iff_isRoot_charpoly, Submodule.one_le_traceDual_one, integralClosure.isIntegrallyClosedOfFiniteExtension, LieAlgebra.IsKilling.corootSpace_eq_bot_iff, SchwartzMap.laplacianCLM_eq, finSepDegree_mul_finInsepDegree, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, LinearIsometryEquiv.conjStarAlgEquiv_apply, RatFunc.IntermediateField.adjoin_X, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, IsPurelyInseparable.finrank_eq_pow, FractionalIdeal.coe_extendedHomâ_eq_span, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, mem_principal_ideals_iff, LinearMap.toMatrixOrthonormal_reindex, FunctionField.InftyValuation.map_zero', Polynomial.abc, MeasureTheory.ConvolutionExistsAt.integrable, LinearMap.ker_self_comp_adjoint, AffineSubspace.sOppSide_lineMap_left, ConjRootClass.rootSet_minpoly_eq_carrier, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, LocalSubring.isMax_iff, NumberField.abs_discr_ge, OnePoint.smul_infty_eq_self_iff, minpoly_neg_splits, isSeparable_algebraMap, Cubic.c_eq_three_roots, FractionalIdeal.divMod_zero_left, Algebra.normalizedTrace_comp_algHom, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, FractionalIdeal.count_finsuppProd, quadraticChar_two, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, IsPrimitiveRoot.subOneIntegralPowerBasis_gen, cfcâHom_nnreal_eq_restrict, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, IsAlgClosure.of_exist_roots, IntermediateField.normal_iff_forall_map_eq, MulChar.apply_mem_algebraAdjoin, IntermediateField.splits_of_mem_adjoin, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, WeierstrassCurve.Affine.Point.toClass_zero, LinearIndependent.rank_matrix, WeierstrassCurve.Jacobian.negY_of_Z_ne_zero, polynomialFunctions.starClosure_topologicalClosure, quadraticChar_isQuadratic, ConjRootClass.minpoly.map_eq_prod, finite_of_finite_type_of_isJacobsonRing, ContMDiffAt.clm_postcomp, Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_neg, ContMDiffWithinAt.clm_postcomp, WeierstrassCurve.Jacobian.addXYZ_of_X_eq, autAdjoinRootXPowSubCEquiv_symm_smul, smoothSheafCommRing.instLocalRing_stalk, Real.integrable_prod_sub, IsAlgClosed.card_roots_eq_natDegree, ContinuousLinearMap.eq_adjoint_iff, char_dvd_card_solutions_of_add_lt, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic, LinearMap.IsSymmetric.directSum_decompose_apply, FractionalIdeal.inv_le_inv_iff, LinearMap.IsSymmetric.splits_charpoly, IsPurelyInseparable.instOfHasExponent, Hyperreal.Infinitesimal.add, ContinuousLinearMap.IsPositive.smul_of_nonneg, LieModule.iSup_genWeightSpace_eq_top', WeierstrassCurve.Projective.add_of_Z_eq_zero, WeierstrassCurve.Projective.Point.toAffine_some, Matrix.IsHermitian.rank_eq_rank_diagonal, RatFunc.valuation_isEquiv_adic_of_valuation_X_le_one, IntermediateField.restrictScalars_normal, Polynomial.Gal.mapRoots_bijective, FractionalIdeal.instMulPosStrictMonoNonZeroDivisors, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, LieAlgebra.ad_isSemisimple_of_isSemisimple, FractionalIdeal.extendedHomâ_coeIdeal_eq_map, Polynomial.exists_monic_irreducible_factor, WeierstrassCurve.Jacobian.negAddY_of_X_eq, Polynomial.roots_degree_eq_one, IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation, RatFunc.eval_one, jacobiSum_trivial_trivial, WeierstrassCurve.Jacobian.addU_of_Z_eq_zero_right, LinearMap.IsPerfPair.of_injective, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, IsAlgClosed.instIsAlgClosure, FixedPoints.rank_le_card, Algebra.normalizedTrace_algebraMap, IsSelfAdjoint.adjoint_eq, Transcendental.of_tower_top, isPurelyInseparable_iff_fd_isPurelyInseparable, Hyperreal.InfiniteNeg.lt_zero, IntermediateField.LinearDisjoint.of_isField', RKHS.kernel_apply, spectrum_diagonal, LieModule.instIsTriangularizableSubtypeMemLieSubmodule_1, WeierstrassCurve.integralModel_bâ_eq, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, TensorProduct.adjoint_map, Matrix.linearIndependent_rows_of_invertible, VectorBundleCore.contMDiffOn_coordChange, PowerBasis.equivAdjoinSimple_symm_aeval, MDifferentiable.clm_postcomp, Orientation.map_eq_neg_iff_det_neg, LinearMap.ker_adjoint_comp_self, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, minpoly.coeff_zero_eq_zero, ContinuousLinearMap.isPositive_self_comp_adjoint, LinearMap.adjoint_toContinuousLinearMap, WeierstrassCurve.integralModel_Î_eq, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, Algebra.algebraMap_intNorm, algebraicClosure.normalClosure_eq_self, Matrix.IsHermitian.eigenvectorUnitary_col_eq, FractionalIdeal.inf_mul, LDL.lowerInv_eq_gramSchmidtBasis, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, IntermediateField.AdjoinDouble.normal_algebraicClosure, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, finrank_algHom, AffineSubspace.WSameSide.trans_wOppSide, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, LieAlgebra.IsKilling.apply_coroot_eq_cast', FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, NumberField.IsTotallyComplex.finrank, LinearMap.rank_diagonal, NumberField.RingOfIntegers.withValEquiv_symm_apply, LinearIsometryEquiv.adjoint_eq_symm, Algebra.FormallyEtale.of_isSeparable_aux, LieAlgebra.IsKilling.reflectRoot_isNonZero, Module.End.IsSemisimple.mul_of_commute, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, LinearMap.IsPositive.isPositive_smul_iff, Hyperreal.Infinite.mul, Polynomial.IsSplittingField.adjoin_rootSet, ContinuousLinearMap.finiteDimensional, Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn, AffineSubspace.sSameSide_iff_exists_left, LieAlgebra.IsKilling.chainLength_nsmul, RootPairing.restrictScalars_pairing, Cubic.discr_eq_prod_three_roots, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, IntermediateField.isAlgebraic_adjoin_iff_top, WeierstrassCurve.Projective.dblU_eq, MeasureTheory.integral_fintype_prod_eq_pow, LieAlgebra.InvariantForm.restrict_nondegenerate, IsPrimitiveRoot.powerBasis_dim, FGModuleCat.instFiniteHomModuleCatObjIsFG, WeierstrassCurve.Projective.Point.toAffineLift_of_Z_ne_zero, LieIdeal.toInvtRootSubmodule_mono, Algebra.IsAlgebraic.tower_top, NumberField.IsTotallyReal.finrank, algebraicClosure.isAlgebraic, Matrix.IsHermitian.eigenvalues_eq_eigenvalues_iff, NumberField.Units.coe_mul, Hyperreal.infinitePos_add_not_infinite, MDifferentiable.cle_arrowCongr, WeierstrassCurve.Projective.addY_of_X_eq, IsGalois.normalClosure, AlgEquiv.adjoinSingletonEquivAdjoinRootMinpoly_symm_toAlgHom, Lagrange.coeff_eq_sum, RatFunc.coe_X, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow', FiniteDimensional.mem_span_of_iInf_ker_le_ker, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, LinearMap.IsSymmetric.conj_adjoint, FractionalIdeal.count_coe_nonneg, FunctionField.inftyValuation.polynomial, IntermediateField.isAlgebraic_iff, RatFunc.Luroth.algEquiv_apply, IsAlgClosed.exists_evalâ_eq_zero_of_injective, AffineSubspace.wOppSide_iff_exists_wbtw, Subfield.relrank_mul_rank_top, WeierstrassCurve.toCharThreeNF_spec_of_bâ_ne_zero, ContinuousLinearMap.adjointAux_norm, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', MDifferentiable.clm_bundle_applyâ, IsSeparable.of_integral, FiniteField.cast_card_eq_zero, WeierstrassCurve.Projective.Point.toAffineAddEquiv_apply, LeftInvariantDerivation.lift_add, LinearMap.flip_injective_iffâ, WeierstrassCurve.Projective.addMap_of_Z_eq_zero_left, Pi.counit_eq_adjoint, LinearMap.toMatrixOrthonormal_apply_apply, WeierstrassCurve.Jacobian.add_of_Y_eq, Representation.card_inv_mul_sum_char_eq_finrank, VectorFourier.fourierIntegral_continuousLinearMap_apply, IntermediateField.finiteDimensional_iSup_of_finset, ValuationSubring.isMax_toLocalSubring, WeierstrassCurve.Projective.dblU_of_Z_eq_zero, Matrix.minpoly_dvd_charpoly, IntermediateField.LinearDisjoint.of_le, Lagrange.eq_interpolate_iff, Module.End.exists_eigenvalue, IsGaloisGroup.quotientMap, RatFunc.coe_coe, FiniteField.sum_pow_lt_card_sub_one, FractionalIdeal.instMulPosReflectLENonZeroDivisors, LinearMap.BilinForm.apply_dualBasis_left, LinearMap.toContinuousBilinearMap_apply, AffineSubspace.sOppSide_iff_exists_left, WeierstrassCurve.exists_isMinimal, IsNormalClosure.adjoin_rootSet, IntermediateField.LinearDisjoint.trace_algebraMap, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, NumberField.IsCMField.isQuadraticExtension, LaurentSeries.Cauchy.coeff_tendsto, Polynomial.valuation_of_mk, Module.End.IsSemisimple.add_of_commute, Emb.Cardinal.two_le_deg, MeasureTheory.integral_fin_nat_prod_volume_eq_prod, Polynomial.Gal.restrictDvd_def, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic, RootPairing.finrank_corootSpanIn_int, LeftInvariantDerivation.lift_smul, LinearIndependent.map_pow_expChar_pow_of_isSeparable', IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one, WeierstrassCurve.hasGoodReduction_iff, minpoly_algebraMap_sub_splits, NumberField.RingOfIntegers.coe_mk, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, IsCyclotomicExtension.Rat.discr_prime_pow', WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, HasMFDerivAt.smul, LinearMap.eq_adjoint_iff_basis_left, Representation.card_inv_mul_sum_char_mul_char_eq_finrank, MDifferentiableAt.clm_prodMap, Quaternion.inv_def, Matrix.ker_mulVecLin_conjTranspose_mul_self, Hyperreal.infinite_mul_of_not_infinitesimal_infinite, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, IntermediateField.isAlgebraic_adjoin_iff, IntermediateField.minpoly_gen, Emb.Cardinal.isLeast_leastExt, LaurentSeries.inducing_coe, isSplittingField_X_pow_sub_C_of_root_adjoin_eq_top, quadraticChar_dichotomy, Polynomial.exists_finset_of_splits, Cubic.splits_iff_card_roots, isSeparable_algebraMap, IsInertiaField.rank_left, isSeparable_neg, ContinuousLinearMap.holderâ_apply_apply, WeierstrassCurve.Projective.addY_of_Z_ne_zero, RatFunc.IntermediateField.isAlgebraic_X, LaurentSeries.continuous_coe, Polynomial.SplittingFieldAux.adjoin_rootSet, Differential.instDifferentialAlgebraAdjoinRoot, Matrix.IsHermitian.eigenvectorUnitary_mulVec, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, integralClosure.isDedekindDomain, IsSepClosedOfCharZero.isCyclotomicExtension, IsSepClosed.roots_eq_zero_iff, WeierstrassCurve.Projective.negAddY_of_X_eq, NumberField.IsCMField.orderOf_complexConj, MDifferentiableAt.clm_postcomp, Polynomial.nodup_aroots_iff_of_splits, WeierstrassCurve.Projective.Point.toAffineLift_neg, ArchimedeanClass.FiniteElement.val_add, AffineSubspace.SOppSide.not_wSameSide, Lagrange.interpolate_eq_sum, IsIdempotentElem.spectrum_subset, Polynomial.exists_aroots_norm_sub_lt_of_norm_coeff_sub_lt, IsSeparable.of_algHom, RatFunc.adicValuation_not_isEquiv_infty_valuation, normalClosure_eq_iSup_adjoin', MvPolynomial.rank_R, RatFunc.map_apply, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, AffineSubspace.wOppSide_self_iff, Matrix.rank_conjTranspose, NumberField.house_mul_le, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, Matrix.PosSemidef.det_sqrt, Hyperreal.archimdeanClassMk_coe, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, FiniteField.roots_X_pow_card_sub_X, IsCovariantDerivativeOn.torsion_self, IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one, quadraticCharFun_eq_zero_iff, Emb.Cardinal.succEquiv_coherence, MDifferentiableWithinAt.clm_bundle_applyâ, Algebra.discr_powerBasis_eq_norm, jacobiSum_one_nontrivial, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime_pow, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, Normal.splits, AffineSubspace.WSameSide.trans_sSameSide, Orientation.map_eq_iff_det_pos, IsIntegral.minpoly_splits_tower_top', IsPrimitiveRoot.norm_eq_neg_one_pow, Polynomial.factor_dvd_of_natDegree_ne_zero, LinearMap.flip_surjective_iffâ, coeSubmodule_differentIdeal, WeierstrassCurve.hasMultiplicativeReduction_iff, WeierstrassCurve.Projective.Point.toAffineLift_zero, minpoly.sub_algebraMap, Valued.integer.exists_norm_lt_one, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two, IntermediateField.relfinrank_top_right, Differential.logDeriv_prod_of_eq_zero, MeasureTheory.convolution_precompR_apply, WeierstrassCurve.Jacobian.Point.toAffine_neg, WeierstrassCurve.Projective.addXYZ_of_X_eq, PowerSeries.intValuation_eq_of_coe, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, AffineSubspace.WOppSide.trans_sOppSide, coeSubmodule_differentIdeal_fractionRing, FractionalIdeal.dual_eq_dual_mul_dual, FunctionField.instIsTrivialOnWithZeroMultiplicativeIntRatFuncInftyValuation, isConjRoot_iff_aeval_eq_zero, isAlgebraic_rat, rank_mul_sepDegree_of_isSeparable, WeierstrassCurve.Jacobian.comp_equiv_comp, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, WeierstrassCurve.Jacobian.Point.neg_point, LieAlgebra.Basis.linearIndepOn_root_baseSupp, Hyperreal.infinitePos_iff, FiniteField.algebraMap_trace_eq_sum_pow, IsAlgebraic.tower_top, RootPairing.coroot_mem_or_neg_mem_closure_of_root, LinearMap.isSymmetric_self_comp_adjoint, WeierstrassCurve.Affine.Point.add_of_X_ne, Quaternion.coe_zpow, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, solvableByRad.isSolvable, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, FractionalIdeal.count_finprod_coprime, AlgebraicGeometry.smooth_of_grpObj_of_isAlgClosed, IntermediateField.linearDisjoint_comm, IsDedekindDomain.HeightOneSpectrum.exists_primeCompl_mul_eq_or_mul_eq, WeierstrassCurve.Jacobian.equiv_zero_of_Z_eq_zero, FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed, Subspace.dualPairing_nondegenerate, Quaternion.imJ_nnratCast, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, IsGaloisGroup.of_fixedPoints_eq, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, Matrix.IsHermitian.charpoly_cfc_eq, MeasureTheory.ConvolutionExistsAt.integrable_swap, FDRep.instFiniteDimensionalHom, WeierstrassCurve.exists_variableChange_isCharTwoNF, MulChar.orderOf_dvd_card_sub_one, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, NumberField.RingOfIntegers.instIsTorsionFree_2, Algebra.discr_eq_discr_of_toMatrix_coeff_isIntegral, AlgebraicGeometry.instIsClosedImmersionLeftSchemeDiscretePUnitOneOverSpecOf, RootPairing.finrank_rootSpanIn_int, ContMDiffCovariantDerivativeOn.finite_affine_combination, LaurentSeries.val_le_one_iff_eq_coe, WeierstrassCurve.Projective.Point.toAffineLift_of_Z_eq_zero, WeierstrassCurve.integralModel_bâ_eq, OnePoint.smul_some_eq_ite, LinearMap.IsSymmetric.card_filter_eigenvalues_eq, LieIdeal.rootSpan_mem_invtRootSubmodule, Polynomial.dvd_C_mul, LieAlgebra.Basis.coroot_eq_h', Submodule.traceDual_top', IntermediateField.restrictRestrictAlgEquivMapHom_apply, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen_prime, Valued.extension_eq_zero_iff, Algebra.norm_eq_prod_embeddings, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, isAlgebraic_of_finite_intermediateField, LieAlgebra.InvariantForm.orthogonal_isCompl, IsPurelyInseparable.minpoly_eq, NumberField.canonicalEmbedding.integralBasis_repr_apply, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, AffineSubspace.SSameSide.not_wOppSide, LieSubalgebra.isNonZero_coe_root, IsCovariantDerivativeOn.smul_const, Ideal.sum_ramification_inertia, Polynomial.card_rootSet_eq_natDegree_iff_of_splits, FunctionField.classNumber_eq_one_iff, minpoly.degree_le, IsAlgClosed.card_roots_map_eq_natDegree_of_isUnit_leadingCoeff, FractionalIdeal.finprod_heightOneSpectrum_factorization, FractionalIdeal.one_le_dual_one, IsFractionRing.integerNormalization_eq_zero_iff, CSA.isSimple, quadraticCharFun_eq_one_of_char_two, LocalSubring.exists_le_valuationSubring, QuasispectrumRestricts.cfcâHom_eq_restrict, IntermediateField.adjoin.powerBasis_gen, WeierstrassCurve.Affine.slope_of_Y_ne, Algebra.FormallyUnramified.iff_isSeparable, iInf_valuationSubring_superset, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, Ideal.card_primesOverFinset_le_finrank, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, FGModuleCat.FGModuleCatEvaluation_apply, LieAlgebra.IsKilling.chainLength_zero, Module.End.map_genEigenrange_le, IntermediateField.normal_iff_normalClosure_le, IsPurelyInseparable.natSepDegree_eq_one, CovariantDerivative.torsion_apply, LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn, mem_perfectClosure_iff_pow_mem, Submodule.adjoint_subtypeL, IsCovariantDerivativeOn.torsion_antisymm, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, IntermediateField.relrank_top_right, coevaluation_apply_one, Emb.Cardinal.noMaxOrder_rank_toType, LinearMap.isSymmetric_adjoint_mul_self, WeierstrassCurve.Jacobian.Point.neg_def, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, WittVector.frobenius_frobeniusRotation, RatFunc.num_denom_add, Submodule.le_traceDual_traceDual, Subfield.finrank_comap, RatFunc.eq_C_of_minpolyX_coeff_eq_zero, WithAbs.tendsto_one_div_one_add_pow_nhds_one, GaloisField.finrank, Valued.integer.norm_irreducible_lt_one, MeasureTheory.convolution_def, WeierstrassCurve.Affine.slope_of_Y_ne', FunctionField.valuedFqtInfty.def, ContMDiffFiberwiseLinear.locality_auxâ, coe_toPrincipalIdeal, RatFunc.eval_X, AdjoinRoot.mul_div_root_cancel, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, MDifferentiableWithinAt.cle_arrowCongr, NumberField.RingOfIntegers.mk_mul_mk, MDifferentiableWithinAt.clm_precomp, Module.End.IsSemisimple.iSup_eigenspace_eq_top, ContMDiffVectorBundle.continuousLinearMap, Algebra.map_intNormAux, IsGaloisGroup.quotient, groupCohomology.isMulCoboundaryâ_of_isMulCocycleâ_of_aut_to_units, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', RatFunc.intDegree_inv, isSeparable_mul, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, IsSelfAdjoint.isClosed, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsNormalClosure.splits, FractionalIdeal.count_prod, Cubic.card_roots_of_disc_ne_zero, LaurentSeries.algebraMap_apply, DualNumber.maximalIdeal_eq_span_singleton_eps, IntermediateField.relfinrank_dvd_finrank_bot, quadraticChar_sum_zero, NumberField.Units.finrank_mul_regOfFamily_eq_det, Module.Basis.coe_constrL, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul, Module.End.IsSemisimple.sub_of_commute, IsDedekindDomain.selmerGroup.monotone, IsPrimitiveRoot.sub_one_norm_isPrimePow, isConjRoot_iff_eq_algebraMap, QuadraticForm.equivalent_weightedSumSquares_of_isAlgClosed, ContinuousLinearMap.IsPositive.conj_adjoint, minpoly.map_eq_of_isSeparable_of_isPurelyInseparable, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, normalClosure.restrictScalars_eq, IsDedekindDomain.HeightOneSpectrum.valuation_def, Module.End.hasUnifEigenvalue_iff_mem_spectrum, Cubic.card_roots_of_discr_ne_zero, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, IntermediateField.normal_iSup, LeftInvariantDerivation.evalAt_coe, FractionalIdeal.count_finprod, IsPrimitiveRoot.powerBasis_gen, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, LinearMap.adjoint_rTensor, WeierstrassCurve.Projective.Point.toAffineLift_some, NumberField.det_basisOfFractionalIdeal_eq_absNorm, ContMDiffOn.clm_precomp, ValuationSubring.toLocalSubring_injective, QuadraticForm.sigPos_add_sigNeg_add_radical, Valuation.Integers.isIntegrallyClosed_integers, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, FGModuleCat.instIsMonoidalClosedModuleCatIsFG, IsGaloisGroup.instSMulCommClassQuotientSubgroupSubtypeMemIntermediateField, Emb.cardinal_eq_of_isSeparable, IsAlgClosed.ringEquiv_of_equiv_of_char_eq, IntermediateField.AdjoinSimple.norm_gen_eq_one, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff, FixedPoints.finrank_le_card, LinearMap.adjoint_inner_right, InnerProductSpace.adjoint_rankOne, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, IntermediateField.instFiniteSubtypeMemBot, ArchimedeanClass.FiniteElement.mk_intCast, IntermediateField.isCyclotomicExtension_lcm_sup, Ideal.image_subset_nonunits_valuationSubring, IntermediateField.LinearDisjoint.linearIndependent_mul, AlgEquiv.card_le, Projectivization.cross_mk_of_cross_ne_zero, finrank_quotient_span_eq_natDegree, minpoly.frobenius_of_isSeparable, RatFunc.numDenom_div, IntermediateField.linearDisjoint_iff', ContMDiffOn.coordChangeL, integralClosure.isFractionRing_of_finite_extension, SchwartzMap.pairing_apply, NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def, IsSelfAdjoint.hasEigenvector_of_isMaxOn, IntermediateField.splits_iff_mem, mdifferentiableAt_hom_bundle, NumberField.RingOfIntegers.coe_eq_zero_iff, FractionalIdeal.mul_left_strictMono, spectralAlgNorm_mul, Matrix.det_map, AffineSubspace.wOppSide_iff_exists_left, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, isSeparable_add, Hyperreal.st_mul, algebraicClosure.isIntegralClosure, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, Algebra.normalizedTrace_intermediateField, RatFunc.num_C, minpoly.Irreducible.eq_minpoly, LinearMap.finrank_genEigenspace_le, cfcâAux_id, FunctionField.InftyValuation.map_add_le_max', LinearMap.IsSymmetric.diagonalization_symm_apply, minpoly.dvd_iff, WeierstrassCurve.Jacobian.map_add, Matrix.projVandermonde_apply_of_ne_zero, quadraticChar_eq_zero_iff, AdjoinRoot.coe_injective, OnePoint.map_smul, LieAlgebra.killingForm_apply_eq_zero_of_mem_rootSpace_of_add_ne_zero, Algebra.FormallyEtale.iff_isSeparable, IsNonarchimedeanLocalField.instIsRankLeOne, WeierstrassCurve.IsMinimal.val_Î_maximal, AffineSubspace.setOf_wOppSide_eq_image2, quadraticChar_zero, IsPrimitiveRoot.norm_eq_one, isNormalClosure_normalClosure, Polynomial.Irreducible.natDegree_dvd_finrank, FGModuleCat.instFiniteHom, WeierstrassCurve.Projective.negY_of_Z_ne_zero, Hyperreal.infinitePos_iff_infinite_and_pos, NumberField.IsCMField.complexConj_apply_apply, IntermediateField.finrank_eq_one_iff, LieAlgebra.mem_ker_killingForm_of_mem_rootSpace_of_forall_rootSpace_neg, LieAlgebra.cartan_sup_iSup_rootSpace_eq_top, LaurentSeries.exists_ratFunc_val_lt, ArchimedeanClass.FiniteElement.val_mul, WeierstrassCurve.Affine.addPolynomial_slope, AffineSubspace.wSameSide_and_wOppSide_iff, IsPrimitiveRoot.autToPow_injective, RatFunc.num_algebraMap, RatFunc.adjoin_X, LocalSubring.eq_iInf_of_isIntegrallyClosedIn, FractionalIdeal.extendedHomâ_injective, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', Matrix.GeneralLinearGroup.IsParabolic.pow, MeasureTheory.hasFDerivAt_convolution_right_with_param, ContMDiffAt.mfderiv_const, smoothSheafCommRing.isUnit_stalk_iff, Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, IntermediateField.finrank_lt_of_gt, NumberField.mixedEmbedding.span_idealLatticeBasis, ArchimedeanClass.stdPart_add, Lagrange.degree_interpolate_erase_lt, HasCompactSupport.hasFDerivAt_convolution_right, RootPairing.invtRootSubmodule.le_ker_coroot', FractionalIdeal.coe_dual, IntermediateField.exists_algHom_adjoin_of_splits_of_aeval, differentialIdeal_le_iff, Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff, mul_gaussSum_inv_eq_gaussSum, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, Quaternion.imI_nnratCast, AlgebraicIndependent.lift_reprField, Hyperreal.coe_nonneg, Hyperreal.infiniteNeg_mul_infiniteNeg, span_map_pow_expChar_pow_eq_top_of_isSeparable, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero, IntermediateField.isAlgebraic_adjoin, gcd_zero_eq, Quaternion.imK_nnratCast, LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute, FDRep.average_char_eq_finrank_invariants, LinearMap.IsSymmetric.adjoint_conj, instIsLiouvilleSubtypeMemIntermediateField, Polynomial.factor_dvd_of_degree_ne_zero, Algebra.adjoin.powerBasis_dim, IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, NumberField.IsCMField.coe_ringOfIntegersComplexConj, ContinuousLinearMap.adjoint_inner_left, PowerSeries.normalized_count_X_eq_of_coe, WeierstrassCurve.Jacobian.addX_of_Z_ne_zero, WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero, isQuotientCoveringMap_npow, RatFunc.eval_eq_zero_of_evalâ_denom_eq_zero, LaurentSeries.Cauchy.exists_lb_coeff_ne, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, AlgebraicGeometry.Scheme.residue_descResidueField, ConjRootClass.minpoly_mk, InnerProductSpace.AlgebraOfCoalgebra.mul_def, SeparableClosure.hasEnoughRootsOfUnity_pow, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq, ArchimedeanClass.FiniteElement.mk_mul_mk, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, Module.End.iSup_iInf_maxGenEigenspace_eq_top_of_forall_mapsTo, MulChar.apply_mem_rootsOfUnity_of_pow_eq_one, RatFunc.valuation_isEquiv_valuationIdeal_adic_of_valuation_X_le_one, WeierstrassCurve.HasGoodReduction.goodReduction, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, Polynomial.scaleRoots_evalâ_eq_zero_of_evalâ_div_eq_zero, IsTranscendenceBasis.isAlgebraic_field, RatFunc.Luroth.algEquiv_algebraMap, ArchimedeanClass.FiniteElement.mk_add_mk, RatFunc.num_dvd, Algebra.isAlgebraic_iff_isIntegral, minpoly.isIntegrallyClosed_eq_field_fractions, AlgebraicGeometry.Scheme.descResidueField_fromSpecResidueField, isPurelyInseparable_iff_pow_mem, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff, MDifferentiableOn.coordChangeL, quadraticCharFun_one, Lagrange.degree_interpolate_lt, FiniteField.norm_surjective, FractionalIdeal.canonicalEquiv_mk0, PowerBasis.equivAdjoinSimple_aeval, FiniteDimensional.of_subalgebra_toSubmodule, IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, NumberField.RingOfIntegers.mk_sub_mk, LinearIsometryEquiv.conjStarAlgEquiv_trans, traceForm_dualSubmodule_adjoin, FractionalIdeal.coe_dual_one, RootPairing.finrank_corootSpanIn, Polynomial.roots_C_mul_X_add_C, IsSepClosure.isSeparable, LinearMap.adjoint_comp_self_injective_iff, Module.End.IsSemisimple.pow, RatFunc.algEquivOfTranscendental_symm_gen, RatFunc.Luroth.generator_mem, Polynomial.Gal.instIsScalarTowerSplittingField, ContMDiffOn.cle_arrowCongr, isStronglyTranscendental_iff_of_field, LieDerivation.IsKilling.killingForm_restrict_range_ad, NumberField.IsCMField.equivInfinitePlace_apply, MDifferentiableOn.clm_prodMap, contMDiffAt_coordChangeL, IntermediateField.LinearDisjoint.of_le_right, AffineSubspace.SSameSide.trans_wOppSide, LinearMap.flip_bijective_iffâ, LinearMap.flip_bijective_iffâ, Hyperreal.coe_pos, ContinuousLinearMap.adjointAux_apply, eq_separableClosure_iff, MulChar.exists_mulChar_orderOf_eq_card_units, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, WeierstrassCurve.Affine.C_addPolynomial_slope, LinearMap.BilinForm.mem_dualSubmodule, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, Submodule.linearEquiv_det_reflection, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, IsCompactOperator.hasEigenvalue_or_mem_resolventSet, WeierstrassCurve.Jacobian.nonsingular_add, quadraticCharFun_mul, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, RingOfIntegers.norm_algebraMap, ConjRootClass.carrier_zero, LinearMap.minpoly_dvd_charpoly, spectralNorm_mul, PowerBasis.trace_gen_eq_nextCoeff_minpoly, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure, Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular, Matrix.cRank_diagonal, FunctionField.ringOfIntegers.instIsDomainSubtypeMemSubalgebraPolynomial, WeierstrassCurve.Affine.Point.map_injective, MDifferentiableWithinAt.coordChangeL, minpoly.degree_le_of_ne_zero, mem_algebraicClosure_iff, RatFunc.valuation_surjective, MDifferentiableAt.clm_bundle_applyâ, isConjRoot_iff_mem_minpoly_rootSet, NumberField.IsCMField.is_quadratic, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, WeierstrassCurve.exists_variableChange_isCharThreeNF, IntermediateField.normal_iff_forall_fieldRange_le, ArchimedeanClass.mk_sub_stdPart_pos, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Char.card_pow_card, Valuation.pow_Uniformizer_is_pow_generator, WeierstrassCurve.Affine.Point.add_self_of_Y_ne', Module.End.maxUnifEigenspaceIndex_le_finrank, IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one, isConjRoot_of_aeval_eq_zero, FiniteField.finrank_zmod_extension, PrincipalIdeals.normal, IsGalois.normalAutEquivQuotient_apply, IsGalois.normalBasis_apply, Submodule.IsLattice.inf, WeierstrassCurve.j_of_isCharTwoJEqZeroNF_of_char_two, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, NumberField.IsCMField.complexConj_apply_eq_self, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, Hyperreal.IsSt.add, Polynomial.valuation_inv_monomial_eq_valuation_X_zpow, RatFunc.num_zero, LieAlgebra.IsKilling.chainLength_neg, coeIdeal_differentIdeal, RootPairing.instIsBalanced, IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRing, IsPurelyInseparable.hasExponent_of_finiteDimensional, RatFunc.intDegree_mul, Algebra.norm_inv, LaurentSeries.exists_Polynomial_intValuation_lt, NumberField.rootDiscr_def, IntermediateField.LinearDisjoint.finrank_right_eq_finrank, QuadraticForm.equivalent_weightedSumSquares, Hyperreal.infiniteNeg_iff_infinite_and_neg, LeftInvariantDerivation.left_invariant'', Polynomial.SplittingFieldAux.scalar_tower', IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp, NumberField.house.exists_ne_zero_int_vec_house_le, FiniteField.algebraMap_norm_eq_pow, trace_eq_finrank_mul_minpoly_nextCoeff, gal_prod_isSolvable, LinearIsometryEquiv.conjStarAlgEquiv_refl, AffineSubspace.SSameSide.trans, Emb.Cardinal.strictMono_leastExt, IntermediateField.rank_adjoin_eq_one_iff, binomialSeries_apply, LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_sup, Orientation.map_eq_det_inv_smul, WeierstrassCurve.Projective.Point.neg_point, NumberField.house_sum_le_sum_house, QuadraticForm.finrank_radical_of_equiv_weightedSumSquares, IntermediateField.isAlgebraic_tower_top, NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, FractionalIdeal.inv_le_dual, Quaternion.normSq_inv, Algebra.TensorProduct.isField_of_isAlgebraic, IntermediateField.rank_top, transcendental_aeval_iff, Valuation.ideal_isPrincipal, Polynomial.valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X, Algebra.normalizedTrace_eq_of_fininteDimensional, ContMDiffOn.clm_comp, WeierstrassCurve.ofJ_1728_of_two_eq_zero, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, NumberField.HeightOneSpectrum.isNonarchimedean_adicAbv, NumberField.HeightOneSpectrum.adicAbv_add_le_max, fromTangentSpace_mfderiv_smul', FiniteField.isSquare_neg_two_iff, NumberField.mixedEmbedding.covolume_idealLattice, IntermediateField.finrank_eq_fixingSubgroup_index, Hyperreal.archimedeanClassMk_pos_of_tendsto, ArchimedeanClass.FiniteElement.val_sub, RatFunc.num_inv_dvd, FGModuleCat.FGModuleCatCoevaluation_apply_one, MvPolynomial.finrank_R, LinearMap.toMatrixOrthonormal_symm_apply, ContinuousLinearMap.aestronglyMeasurable_compâ, FiniteField.algebraMap_norm_eq_prod_pow, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero, SchwartzMap.smulLeftCLM_const, Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det, Lagrange.eval_basisDivisor_right, trace_eq_trace_adjoin, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Valuation.associated_of_isUniformizer, WeierstrassCurve.Jacobian.addY_of_Z_ne_zero, PowerSeries.X_inv, AdjoinRoot.coe_injective', IntermediateField.adjoin_root_eq_top, NumberField.RingOfIntegers.mk_add_mk, Matrix.ker_mulVecLin_transpose_mul_self, LinearMap.range_toContinuousLinearMap, Submodule.traceDual_le_span_map_traceDual, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, NumberField.Embeddings.card, IsAlgClosed.ringEquiv_of_equiv_of_charZero, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, InfiniteGalois.proj_adjoin_singleton_val, FractionalIdeal.le_inv_comm, Irreducible.exists_dvd_monic_irreducible_of_isIntegral, LieAlgebra.IsKilling.coroot_mem_corootSpace, quadraticChar_exists_neg_one', WeierstrassCurve.Jacobian.dblY_of_Z_ne_zero, IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank, Polynomial.rootSet_C_mul_X_pow, Matrix.eRank_diagonal, Representation.char_tensor, WeierstrassCurve.Projective.Point.toAffine_of_singular, WeakDual.isBounded_iff_isVonNBounded, NumberField.InfinitePlace.card_isUnramified, rank_mul_insepDegree_of_isPurelyInseparable, LocalSubring.map_maximalIdeal_eq_top_of_isMax, Matrix.det_eq_prod_roots_charpoly_of_splits, IsDecompositionField.algebraMap_ringEquiv_symm_apply, Subspace.flip_quotDualCoannihilatorToDual_bijective, LinearMap.isSelfAdjoint_iff', NumberField.IsCMField.complexEmbedding_complexConj, Orientation.areaForm'_apply, mem_perfectClosure_iff, WeierstrassCurve.baseChange_integralModel_eq, Subalgebra.algebraicClosure_eq_integralClosure, IntermediateField.exists_finset_of_mem_supr'', ContinuousLinearMap.nnnorm_holder_apply_apply_le, FiniteField.instFiniteExtension_1, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, PowerBasis.equivAdjoinSimple_gen, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, WeierstrassCurve.Jacobian.X_eq_iff, Emb.Cardinal.equivSucc_coherence, IsSepClosed.isCyclotomicExtension, ContinuousLinearMap.bilinear_hasTemperateGrowth, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, IntermediateField.finrank_top, LinearMap.mem_span_iff_continuous_of_finite, NumberField.CMExtension.equivMaximalRealSubfield_apply, FunctionField.ringOfIntegers.instIsIntegrallyClosedSubtypeMemSubalgebraPolynomial, Cubic.disc_ne_zero_iff_roots_nodup, LinearMap.coe_toContinuousLinearMap, minpoly.ker_aeval_eq_span_minpoly, Matrix.rank_eq_finrank_span_row, map_equiv_traceDual, RatFunc.intDegree_C, gcd_eq_of_ne, FractionalIdeal.count_maximal_coprime, Lagrange.eq_interpolate, FiniteGaloisIntermediateField.isGalois, separableClosure.eq_top_iff, IsBilinearMap.toContinuousBilinearMap_apply, Valued.integer.norm_le_one, LieAlgebra.IsKilling.apply_coroot_eq_cast, contMDiffOn_continuousLinearMapCoordChange, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, minpoly.eq_of_irreducible_of_monic, IntermediateField.LinearDisjoint.finrank_left_eq_finrank, IntermediateField.Lifts.lt_iff, IsCyclotomicExtension.Rat.discr_prime_pow_ne_two', FunctionField.InftyValuation.map_one', IsAlgClosure.equivOfEquiv_comp_algebraMap, Subfield.roots_X_pow_char_sub_X_bot, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, finrank_of_isSplittingField_X_pow_sub_C, Algebra.isSeparable_tower_top_of_isSeparable, LinearMap.IsSymmetric.adjoint_eq, FractionalIdeal.extendedHomâ_eq_zero_iff, minpoly.isRadical, minpoly.unique_of_degree_le_degree_minpoly, LaurentSeries.Cauchy.coeff_support_bddBelow, FractionalIdeal.divMod_zero_of_not_le, WeierstrassCurve.Affine.Y_eq_of_X_eq, RootPairing.GeckConstruction.basis_A_eq, WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero, Subfield.relfinrank_top_right, Lagrange.leadingCoeff_eq_sum, RatFunc.num_denom_mul, RatFunc.Luroth.generator_ne_C, Matrix.trace_eq_sum_roots_charpoly, ContinuousMap.adjoin_id_eq_span_one_union, IsSl2Triple.h_eq_coroot, Splits.algebraicClosure, PowerBasis.equivAdjoinSimple_symm_gen, IsCovariantDerivativeOn.leibniz, SeparableClosure.hasEnoughRootsOfUnity, LieIdeal.restr_eq_iSup_sl2SubmoduleOfRoot, RatFunc.intDegree_add_le, AffineSubspace.WSameSide.not_sOppSide, minpoly.prime, LieDerivation.IsKilling.ad_mem_orthogonal_of_mem_orthogonal, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, LinearMap.tracePositiveLinearMap_apply, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne, MDifferentiableAt.clm_comp, WeierstrassCurve.Projective.equiv_of_Z_eq_zero, Module.End.IsSemisimple.aeval, NumberField.FinitePlace.add_le, exists_root_adjoin_eq_top_of_isCyclic, LinearMap.IsSymmetric.isSymmetric_smul_iff, LieAlgebra.hasTrivialRadical_of_isIrreducible_of_isFaithful, groupCohomology.norm_ofAlgebraAutOnUnits_eq, WeierstrassCurve.toCharTwoJNeZeroNF_spec, LieAlgebra.IsKilling.isSimple_iff_isIrreducible, WittVector.exists_eq_pow_p_mul', Matrix.IsHermitian.roots_charpoly_eq_eigenvalues, Matrix.IsHermitian.cfcAux_apply, RatFunc.valuation_eq_LaurentSeries_valuation, FractionalIdeal.extendedHomâ_eq_one_iff, Matrix.IsHermitian.splits_charpoly, LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, RatFunc.finrank_eq_max_natDegree, LieAlgebra.lieIdeal_eq_iSup_inf_genWeightSpace, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, WeierstrassCurve.Projective.addZ_eq, AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero, Matrix.rank_transpose_mul_self, isPurelyInseparable_iff_natSepDegree_eq_one, RatFunc.liftRingHom_apply, AlgebraicClosure.instIsAlgClosure, NumberField.InfinitePlace.card_isUnramified_compl, integralClosure.isNoetherianRing, IntermediateField.finrank_eq_finrank_subalgebra, IntermediateField.finrank_eq_one_iff_eq_top, QuadraticForm.sigNeg_weightedSumSquares, Algebra.Transcendental.rank_eq_cardinalMk, IsDecompositionField.rank_right, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', LinearPMap.adjoint_isClosed, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', WeierstrassCurve.Affine.map_slope, quadraticChar_neg_two, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, LinearMap.IsSymmetric.hasEigenvalue_eigenvalues, IntermediateField.restrictRestrictAlgEquivMapHom_injective, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, OrthonormalBasis.det_to_matrix_orthonormalBasis, exists_jacobiSum_eq_neg_one_add, RootPairing.isCompl_rootSpan_ker_rootForm, LinearMap.isPositive_toContinuousLinearMap_iff, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', LieModule.Weight.isZero_neg, Submodule.inf_iSup_genEigenspace, Cubic.splits_iff_roots_eq_three, WeierstrassCurve.exists_variableChange_of_j_eq, IsCyclotomicExtension.discr_prime_pow_ne_two, WeierstrassCurve.Jacobian.Point.toAffineLift_add, Transcendental.algebraicClosure, RootPairing.invtRootSubmodule.eq_bot_iff, inr_comp_cfcâHom_eq_cfcâAux, FGModuleCat.ihom_obj, IntermediateField.LinearDisjoint.finrank_sup, Algebra.normalizedTrace_algebraMap_apply_eq_self, WeierstrassCurve.Jacobian.addMap_of_Z_eq_zero_right, Module.End.IsSemisimple.of_mem_adjoin_pair, LinearMap.star_eq_adjoint, isNonarchimedean_spectralNorm, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, IsFractionRing.liftAlgHom_fieldRange_eq_of_range_eq, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', IntermediateField.finrank_adjoin_eq_one_iff, WittVector.isDiscreteValuationRing, exists_integral_inj_algHom_of_quotient, FDRep.char_linHom, IntermediateField.normal_iff_forall_map_le', Submodule.restrictScalars_traceDual, LinearMap.BilinForm.dualBasis_eq_iff, NumberField.RingOfIntegers.rank, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos, ContinuousLinearMap.memLp_of_bilin, IntermediateField.normal_iff_forall_fieldRange_eq, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_essFiniteType, Differential.differentialAlgebraFiniteDimensional, Differential.logDeriv_one, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, RootPairing.polarizationEquiv_apply, ContinuousLinearMap.isometry_iff_adjoint_comp_self, NumberField.integralBasis_repr_apply, AlgebraicGeometry.Scheme.Hom.genericPoint_mem_smoothLocus_of_perfectField, exists_finite_inj_algHom_of_fg, WithAbs.instIsSeparable_1, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, Polynomial.separable_prod_X_sub_C_iff', finSepDegree_le_finrank, RootPairing.linearIndepOn_root_baseOf, FractionalIdeal.dual_mul_self, ArchimedeanClass.stdPart_add_eq_right, IsIntegrallyClosed.iInf, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, FunctionField.InftyValuation.map_mul', LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, IsSelfAdjoint.conj_adjoint, differentialIdeal_le_fractionalIdeal_iff, IntermediateField.finrank_bot, WeierstrassCurve.Projective.nonsingularLift_addMap, IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero, Quaternion.coe_div, isSeparable_inv, Polynomial.exists_roots_norm_sub_lt_of_norm_coeff_sub_lt, LieIdeal.mem_rootSet_of_mem_rootSpan, AffineSubspace.WOppSide.trans, WeierstrassCurve.Jacobian.addX_of_X_eq, Hyperreal.IsSt.mul, LieIdeal.rootSet_apply_coroot_eq_zero_of_notMem_rootSet, AlgHom.natCard_of_splits, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, WeierstrassCurve.Affine.Point.add_def, instIsDecompositionFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupStabilizerIdealOfIsGalois, FractionalIdeal.mem_dual, Matrix.linearIndependent_cols_iff_isUnit, Polynomial.rootOfSplits'_eq_rootOfSplits, LinearMap.adjoint_toSpanSingleton, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesâ, Polynomial.IsSplittingField.adjoin_rootSet', IntermediateField.sepDegree_bot, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, WeakDual.withSeminorms, trace_eq_sum_roots, WeierstrassCurve.Jacobian.Point.toAffineAddEquiv_apply, Algebra.normalizedTrace_self, RatFunc.algebraMap_apply_div, jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum, Module.End.IsSemisimple.of_mem_adjoin_singleton, RatFunc.Luroth.eq_adjoin_generator, RootPairing.GeckConstruction.instIsIrreducible, IsAlgClosure.equivOfEquiv_symm_algebraMap, RatFunc.minpolyX_aeval_X, AlgHom.card_of_powerBasis, Differential.logDeriv_mul, RatFunc.algEquivOfTranscendental_symm_aeval, IsAlgClosed.exists_aeval_eq_zero_of_injective, Algebra.norm_eq_norm_adjoin, WeierstrassCurve.Projective.addU_of_Z_eq_zero_left, ContMDiffWithinAt.clm_bundle_applyâ, Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic, IsLiouville.isLiouville, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, LinearMap.re_inner_adjoint_mul_self_nonneg, LieIdeal.restr_inf_cartan_eq_biSup_corootSubmodule, IntermediateField.LinearDisjoint.norm_algebraMap, LinearMap.isPositive_self_comp_adjoint, RatFunc.eval_C, ContinuousLinearMap.ker_self_comp_adjoint, WeierstrassCurve.Projective.negDblY_of_Z_ne_zero, Lagrange.iterate_derivative_interpolate, instIsIntegrallyClosed, finSepDegree_eq_finrank_of_isSeparable, PowerBasis.toMatrix_isIntegral, AlgebraicGeometry.pointOfClosedPoint_apply, AlgebraicClosure.Monics.splits_finsetProd, contMDiffOn_symm_coordChangeL, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two', Hyperreal.infinitePos_mul_infiniteNeg, ContinuousLinearMap.instStarModuleId, Algebra.FormallyEtale.iff_formallyUnramified_of_field, contMDiffAt_hom_bundle, LinearIsometry.adjoint_comp_self', FractionalIdeal.dual_involutive, PowerSeries.zero_inv, Algebra.adjoin.powerBasis_gen, WeierstrassCurve.Affine.Point.map_baseChange, Matrix.trace_eq_sum_roots_charpoly_of_splits, NumberField.RingOfIntegers.mk_zero, AffineSubspace.SOppSide.trans_sSameSide, rank_dual_eq_card_dual_of_aleph0_le_rank, WittVector.irreducible, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, groupCohomology.exists_mul_galRestrict_of_norm_eq_one, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, Matrix.l2_opNNNorm_def, IntermediateField.isAlgebraic_adjoin_pair, PowerSeries.inv_eq_zero, RatFunc.faithfulSMul, ContinuousLinearMap.adjointAux_adjointAux, Normal.isIntegral, RatFunc.num_X, isIdempotentElem_iff_quasispectrum_subset, LinearMap.det_map, AffineSubspace.WSameSide.trans, Hyperreal.infiniteNeg_mul_infinitePos, WeierstrassCurve.Projective.Point.toAffine_neg, LinearMap.hasEigenvalue_zero_tfae, AffineSubspace.wSameSide_iff_exists_left, Ideal.finrank_quotient_map, ContMDiffAt.clm_precomp, lift_rank_lt_rank_dual, AffineSubspace.SSameSide.trans_wSameSide, LinearMap.eq_adjoint_iff, WittVector.exists_frobenius_solution_fractionRing, Polynomial.valuation_le_one_of_valuation_X_le_one, NumberField.mixedEmbedding.norm_smul, Algebra.discr_mul_isIntegral_mem_adjoin, LaurentSeries.exists_powerSeries_of_memIntegers, LaurentSeries.continuous_coe', IntermediateField.finrank_sup_le, Differential.instDifferentialAlgebraSubtypeMemIntermediateField_1, isConjRoot_zero_iff_eq_zero, WeierstrassCurve.Affine.addY_sub_negY_addY, ConjRootClass.mk_eq_zero_iff, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, IntermediateField.adjoinRootEquivAdjoin_apply_root, LinearMap.finiteDimensional, MDifferentiable.clm_prodMap, isAlgebraic_of_adjoin_eq_adjoin, InnerProductSpace.gramSchmidtOrthonormalBasis_det, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, LaurentSeries.Cauchy.exists_lb_eventual_support, LieModule.isNilpotent_toEnd_of_mem_rootSpace, ContinuousLinearMap.isSelfAdjoint_iff', Emb.Cardinal.eq_bot_of_not_nonempty, MeasureTheory.euclideanHausdorffMeasure_homothety_image, Submodule.le_traceDual, IsConjRoot.add_algebraMap, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, IsDecompositionField.rank_left, WeierstrassCurve.Affine.Point.add_of_Y_ne, IntermediateField.rank_bot, FiniteField.exists_nonsquare, IsNonarchimedeanLocalField.instCompactSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, MeasureTheory.euclideanHausdorffMeasure_homothety_preimage, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Valuation.valuationSubring_isPrincipalIdealRing, IsAlgClosed.card_aroots_eq_natDegree, le_restrictScalars_separableClosure, FractionalIdeal.dual_eq_mul_inv, Submodule.IsLattice.finrank_of_pi, WeierstrassCurve.Jacobian.Point.toAffine_add, MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero, LinearMap.IsSymmetric.directSum_isInternal_of_commute, WeierstrassCurve.Projective.neg_of_Z_ne_zero, WeierstrassCurve.hasAdditiveReduction_iff, NumberField.RingOfIntegers.instIsTorsionFree, FractionalIdeal.dual_div_dual, contDiffOn_fderiv_coord_change, IsLocalRing.exists_factor_valuationRing, RatFunc.num_eq_zero_iff, Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero, QuadraticForm.sigPos_of_equiv_weightedSumSquares, MvPolynomial.mem_zeroLocus_iff, MeasureTheory.hausdorffMeasure_homothety_image, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, FractionalIdeal.count_mul, AddChar.PrimitiveAddChar.prim, FractionalIdeal.dual_zero, Polynomial.separable_prod_X_sub_C_iff, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, WeierstrassCurve.HasAdditiveReduction.additiveReduction, WeierstrassCurve.Projective.map_dblU, AlgebraicGeometry.ValuativeCommSq.commSq, MvPolynomial.eval_indicator_apply_eq_zero, NumberField.RingOfIntegers.withValEquiv_apply, IntermediateField.finrank_bot_mul_relfinrank, LieAlgebra.exists_isCartanSubalgebra_engel, FiniteField.Matrix.charpoly_pow_card, PowerSeries.hasUnitMulPowIrreducibleFactorization, RatFunc.irreducible_minpolyX, minpoly.dvd_map_of_isScalarTower, ValuationSubring.isIntegral_of_mem_ringOfIntegers', IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two, WeierstrassCurve.Projective.negDblY_eq, Algebra.norm_eq_prod_automorphisms, ContinuousLinearMap.lpPairing_eq_integral, lift_rank_mul_lift_insepDegree_of_isPurelyInseparable, IntermediateField.LinearDisjoint.of_basis_right, Matrix.sub_scalar_sq_eq_disc, Polynomial.Splits.dvd_iff_roots_le_roots, CyclotomicField.instIsCyclotomicExtensionSingletonNatSetOfCharZero, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, Submodule.IsLattice.rank_of_pi, Matrix.rank_self_mul_conjTranspose, IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic, Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, Matrix.IsHermitian.eigenvectorUnitary_apply, natDegree_radical_le, FiniteField.trace_pow_card, FractionalIdeal.count_pow, ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero, IsUltrametricDist.algNormOfAlgEquiv_apply, IntermediateField.bot_eq_top_iff_finrank_eq_one, SchwartzMap.fourierMultiplierCLM_const, IntermediateField.finiteDimensional_adjoin, IntermediateField.isTranscendenceBasis_adjoin_iff, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, LinearMap.adjoint_lTensor, IsDecompositionField.algebraMap_ringEquiv_apply, MeasureTheory.Integrable.convolution_integrand, RatFunc.intDegree_add, WeierstrassCurve.Jacobian.Point.add_point, LinearMap.toMatrixOrthonormal_apply, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, Matrix.IsHermitian.det_eq_prod_eigenvalues, LinearMap.IsPositive.smul_of_nonneg, cfcâAux_injective, LieAlgebra.IsKilling.biSup_corootSpace_eq_top, Hyperreal.infinite_iff, IsPRadical.isPurelyInseparable, Algebra.IsUnramifiedAt.not_minpoly_sq_dvd, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, RatFunc.Luroth.algEquiv_X, Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff, Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eq, Hyperreal.Infinitesimal.mul, Submodule.le_traceDual_comm, Algebra.FormallySmooth.of_algebraicIndependent, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, one_mem_inv_coe_ideal, RatFunc.valuation_isEquiv_infty_or_adic, IntermediateField.AdjoinSimple.trace_gen_eq_zero, integralClosure.isFractionRing_of_algebraic, Valued.integer.coe_span_singleton_eq_closedBall, ArchimedeanClass.FiniteElement.val_zero, isIdempotentElem_iff_spectrum_subset, Module.End.det_eq_prod_roots_charpoly_of_splits, MeasureTheory.dist_convolution_le', isQuotientCoveringMap_zpow, WeierstrassCurve.integralModel_câ_eq, WeierstrassCurve.Projective.addX_eq, LinearMap.singularValues_fin, LinearMap.sq_singularValues_of_lt, LieIdeal.isCompl_killingCompl, CovariantDerivative.torsion_eq_zero_iff, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, MDifferentiableOn.cle_arrowCongr, RatFunc.denom_X, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, toWeakSpace_closedConvexHull_eq, ExteriorAlgebra.map_injective_field, IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow, IntermediateField.relrank_dvd_rank_top_of_le, ContMDiff.clm_bundle_applyâ, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_neg_mul, RatFunc.natDegree_minpolyX, IsSeparable.tower_bot, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, WeierstrassCurve.Projective.addMap_of_Y_eq, LaurentSeries.Cauchy.eventually_mem_nhds, WeierstrassCurve.Affine.Point.add_of_Y_eq, LinearMap.IsSymmetric.direct_sum_isInternal, Submodule.det_reflection, ClassGroup.mk_mk0, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, RatFunc.irreducible_minpolyX', IntermediateField.finSepDegree_adjoin_simple_le_finrank, IsAlgClosed.card_aroots_eq_natDegree_of_leadingCoeff_ne_zero, LieIdeal.mem_rootSet, ContMDiffWithinAt.mfderivWithin, LieAlgebra.InvariantForm.restrict_orthogonal_nondegenerate, FractionalIdeal.coe_ideal_mul_inv, exists_primitive_element_iff_finite_intermediateField, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Hyperreal.coe_eq_zero, QuadraticForm.sigPos_weightedSumSquares, WeierstrassCurve.Jacobian.Point.toAffine_some, isSolvable_gal_minpoly, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two, IntermediateField.card_algHom_adjoin_integral, WeierstrassCurve.integralModel_câ_eq, Emb.Cardinal.filtration_apply, IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducible, ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, WeierstrassCurve.Projective.Y_eq_iff, IntermediateField.relrank_dvd_rank_bot, Ideal.finite_mulSupport_coe, algebraicClosure_toSubalgebra, LinearMap.flip_injective_iffâ, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, IsPrimitiveRoot.subOnePowerBasis_dim, LieAlgebra.IsKilling.instSemisimple, IsIntegralClosure.range_le_span_dualBasis, IsPrimitiveRoot.subOnePowerBasis_gen, Lagrange.eval_basis_of_ne, MDifferentiableAt.clm_precomp, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne', OnePoint.smul_infty_eq_ite, ClassGroup.mk_eq_one_iff, IntermediateField.AdjoinPair.algebraMap_genâ, NumberField.fractionalIdeal_rank, WeierstrassCurve.Projective.Point.neg_def, RatFunc.denom_div, LinearMap.finrank_range_adjoint, gaussSum_pow_eq_prod_jacobiSum_aux, LieDerivation.IsKilling.rangeAdOrthogonal_carrier, Polynomial.IsSplittingField.IsScalarTower.isAlgebraic, WeierstrassCurve.Projective.nonsingular_add, WeierstrassCurve.Affine.Point.map_map, doublyStochastic_eq_convexHull_permMatrix, LinearMap.sq_singularValues_fin, AffineSubspace.sSameSide_lineMap_right, Module.End.finite_spectrum, LaurentSeries.valuation_LaurentSeries_equal_extension, ContinuousLinearMap.adjoint_comp_self_injective_iff, LinearMap.IsSymmetric.smul, IsPrimitiveRoot.norm_eq_one_of_linearly_ordered, AffineSubspace.WOppSide.not_sSameSide, IsAlgClosed.exists_evalâ_eq_zero, Matrix.toLin_conjTranspose, mdifferentiableOn_continuousLinearMapCoordChange, FixedPoints.toAlgAut_surjective, LinearMap.range_adjoint_comp_self, Matrix.IsHermitian.spectral_theorem, isIntegral_discr_mul_of_mem_traceDual, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, IsPurelyInseparable.minpoly_natDegree_eq, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, IntermediateField.LinearDisjoint.of_inf_eq_bot, RatFunc.intDegree_polynomial, PowerBasis.ofAdjoinEqTop_gen, toPrincipalIdeal_eq_iff, minpoly.map_algebraMap, WeierstrassCurve.isMinimal_iff, exteriorPower.map_injective_field, Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_pow, RatFunc.v_def, RingOfIntegers.coe_norm, minpoly.add_algebraMap, RatFunc.instCharZero, Subfield.relrank_dvd_rank_top_of_le, divRadical_dvd_wronskian_right, ArchimedeanClass.FiniteResidueField.mk_ne_zero, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, contDiff_clm_apply_iff, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope, Hyperreal.coe_zero, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal', spec_cfcâAux, Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero, root_X_pow_sub_C_pow, AlgebraicIndependent.liftAlgHom_comp_reprField, Subalgebra.finiteDimensional_toSubmodule, NumberField.RingOfIntegers.mk_one, Algebra.IsSeparable.finSepDegree_eq, FixedPoints.isIntegral, IntermediateField.finrank_top', char_dvd_card_solutions, WeierstrassCurve.Projective.baseChange_add, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_top, NumberField.IsCMField.unitsMulComplexConjInv_apply, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, RootPairing.orthogonal_corootSpan_eq, AffineSubspace.sOppSide_lineMap_right, PowerSeries.instIsDiscreteValuationRing, FractionalIdeal.dual_le_dual, Polynomial.C_mul_dvd, RootPairing.ker_rootForm_eq_dualAnnihilator, char_dvd_card_solutions_of_sum_lt, ContinuousLinearMap.self_comp_adjoint_injective_iff, IsPrimitiveRoot.norm_pow_sub_one_two, IntermediateField.normalClosure_of_normal, Quaternion.imK_ratCast, IsInertiaField.rank_right, Algebra.FormallyUnramified.isSeparable, Algebra.discr_powerBasis_eq_prod, Polynomial.mem_iff_annIdealGenerator_dvd, Polynomial.card_rootSet_eq_natDegree, contDiffOn_clm_apply, AffineSubspace.SOppSide.trans, FDRep.char_one, ContinuousLinearEquiv.det_coe_symm, FunctionField.ringOfIntegers.instIsDedekindDomainSubtypeMemSubalgebraPolynomialOfIsSeparableRatFunc, Algebra.IsAlgebraic.isNormalClosure_iff, ClassGroup.mk_eq_mk, RatFunc.minpolyX_eq_zero_iff, ContinuousLinearMap.evalL_apply, jacobiSum_nontrivial_inv, WeierstrassCurve.integralModel_bâ_eq, InfiniteGalois.isOpen_iff_finite, RootPairing.restrictScalars_coe_root, isSplittingField_AdjoinRoot_X_pow_sub_C, FractionalIdeal.count_zpow_self, WeierstrassCurve.integralModel_bâ_eq, IsPurelyInseparable.trans, Matrix.IsHermitian.eigenvectorUnitary_coe, WeierstrassCurve.Jacobian.nonsingular_neg, minpoly.eq_of_root, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, ValuationSubring.isIntegral_of_mem_ringOfIntegers, IntermediateField.isSplittingField_iSup, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, Emb.Cardinal.deg_lt_aleph0, fromTangentSpace_mfderiv_smul, WeierstrassCurve.Î_integral_of_isIntegral, Valued.integer.isDiscreteValuationRing_of_compactSpace, LinearMap.instStarModuleId, NumberField.inverse_basisMatrix_mulVec_eq_repr, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, RatFunc.denom_div_dvd, IntermediateField.relfinrank_bot_left, NumberField.RingOfIntegers.instIsIntegralClosureInt, Matrix.PosSemidef.det_nonneg, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Differential.logDeriv_zero, Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg, RatFunc.eval_add, ConjRootClass.exists_mem_carrier_add_eq_zero, AffineSubspace.SOppSide.not_sSameSide, RootPairing.eq_baseOf_of_linearIndepOn_of_mem_or_neg_mem_closure, FunctionField.inftyValuation.X_zpow, RatFunc.rank_ratFunc_ratFunc, WeierstrassCurve.exists_isIntegral, WittVector.RecursionMain.succNthVal_spec, LieIdeal.rootSpace_le_of_apply_coroot_ne_zero, Matrix.PosSemidef.inv_sqrt, WeierstrassCurve.Jacobian.addMap_of_Z_eq_zero_left, Valued.integer.norm_unit, Lagrange.degree_interpolate_le, IntermediateField.LinearDisjoint.rank_sup, AlgebraicGeometry.Scheme.default_asIdeal, WeierstrassCurve.Affine.nonsingular_add, InnerProductSpace.rankOne_comp, LaurentSeries.powerSeriesRingEquiv_coe_apply, RatFunc.transcendental_of_ne_C, LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute, minpoly.ofSubring, IntermediateField.rank_sup_le_of_isAlgebraic, Polynomial.normalize_eq_self_iff_monic, IsNonarchimedeanLocalField.instIsDiscrete, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, MDifferentiableWithinAt.clm_comp, cfcâHom_real_eq_restrict, normal_iff, ConjRootClass.nodup_aroots_minpoly, AlgHom.card, MDifferentiableOn.clm_comp, IsAlgClosure.equivOfEquiv_symm_comp_algebraMap, Quaternion.im_nnratCast, FiniteDimensional.finiteDimensional_subalgebra, Module.End.isSemisimple_of_squarefree_aeval_eq_zero, WeierstrassCurve.Projective.addMap_of_Z_eq_zero_right, FractionalIdeal.smul_mem_dual_one, Matrix.rank_diagonal, NumberField.InfinitePlace.isReal_comap_iff, Hyperreal.infiniteNeg_add_infiniteNeg, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_mono, LaurentSeries.powerSeriesEquivSubring_apply, WeierstrassCurve.Projective.nonsingular_iff_of_Z_ne_zero, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, RootPairing.polarizationEquiv_toLinearMap, AffineSubspace.SOppSide.trans_wSameSide, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, ContMDiffAt.clm_prodMap, ArchimedeanClass.FiniteElement.val_one, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbvDef, LocalSubring.mem_of_isMax_of_isIntegral, IsGaloisGroup.subgroup_iff, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, WeierstrassCurve.Jacobian.add_of_X_ne, LinearMap.det_eq_one_of_finrank_eq_zero, FDRep.simple_iff_end_is_rank_one, IntermediateField.LinearDisjoint.bot_right, MvPolynomial.quotient_mk_comp_C_injective, FractionalIdeal.count_neg_zpow, FunctionField.inftyValuation.X, quadraticChar_eq_one_of_char_two, AlgebraicClosure.Monics.map_eq_prod, primitive_element_iff_minpoly_degree_eq, WeierstrassCurve.Jacobian.Y_eq_iff', minpoly.dvd_map_of_isScalarTower', WeierstrassCurve.Jacobian.isUnit_dblZ_of_Y_ne', IsPurelyInseparable.tower_bot, RootPairing.IsIrreducible.mk', adjoinRootXPowSubCEquiv_root, IsSepClosed.hasEnoughRootsOfUnity_pow, Polynomial.valuation_monomial_eq_valuation_X_pow, Projectivization.orthogonal_mk, Polynomial.Gal.galAction_isPretransitive, IntermediateField.normal_iff_forall_map_le, Projectivization.cross_mk, MeasureTheory.integral_fin_nat_prod_eq_prod, WeierstrassCurve.Projective.Point.toAffine_of_Z_ne_zero, LieAlgebra.IsKilling.root_apply_coroot, FractionalIdeal.divMod_zero_right, Submodule.eq_iSup_inf_genEigenspace, IsSeparable.tower_top, AffineSubspace.WSameSide.trans_sOppSide, Quaternion.imJ_ratCast, Polynomial.factor_dvd_of_not_isUnit, separableClosure.isAlgebraic, IsAlgClosed.card_roots_map_eq_natDegree_of_injective, IsAlgClosure.ofAlgebraic, Hyperreal.not_infinite_add, FunctionField.ringOfIntegers.algebraMap_injective, sepDegree_mul_insepDegree, AffineSubspace.sSameSide_smul_vsub_vadd_right, LieAlgebra.IsKilling.coroot_neg, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, RatFunc.denom_inv_dvd, LieModule.exists_nontrivial_weightSpace_of_isSolvable, instIsScalarTowerCyclotomicField, RatFunc.setOf_polynomial_valuation_lt_one_and_ne_zero_nonempty, isGalois_iff, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, gaussSum_mul_gaussSum_pow_orderOf_sub_one, isPurelyInseparable_iff_perfectClosure_eq_top, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, AlgHom.card_le, IntermediateField.rank_eq_one_iff, Algebra.isSeparable_tower_bot_of_isSeparable, IsGaloisGroup.intermediateField, WeierstrassCurve.Affine.Point.toClass_some, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, bilinearIteratedFDerivWithinTwo_eq_iteratedFDeriv, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, Module.End.eigenspace_div, Affine.Simplex.sOppSide_affineSpan_faceOpposite_of_pos_of_neg, LieAlgebra.InvariantForm.orthogonal_isCompl_toSubmodule, WeierstrassCurve.Projective.X_eq_iff, WeierstrassCurve.ofJ_ne_0_ne_1728, spectralNorm.eq_of_normalClosure, FunctionField.inftyValuedFqt.def, Polynomial.span_minpoly_eq_annihilator, IntermediateField.LinearDisjoint.linearIndependent_right, NumberField.Embeddings.coeff_bdd_of_norm_le, Subfield.relrank_top_right, LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul, ContinuousLinearMap.ker_adjoint_comp_self, isSeparable_sub, SchwartzMap.pairing_continuous_left, IsDedekindDomain.selmerGroup.fromUnit_ker, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, spectralNorm.eq_of_normalClosure', NumberField.exists_ideal_in_class_of_norm_le, RootPairing.root_mem_submodule_iff_of_add_mem_invtSubmodule, IsCovariantDerivativeOn.add_one_form, AffineSubspace.sOppSide_pointReflection, LieAlgebra.IsKilling.eq_zero_of_apply_eq_zero_of_mem_corootSpace, algebraicClosure.eq_top_iff, IsAlgClosure.equivOfEquiv_algebraMap, mem_span_of_iInf_ker_le_ker, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, Valued.integer.exists_nnnorm_lt_one, WeierstrassCurve.ofJ_0_of_three_eq_zero, WeierstrassCurve.toCharThreeNF_spec, IntermediateField.finrank_fixedField_eq_card, WeierstrassCurve.Projective.dblY_of_Z_ne_zero, Algebra.normalizedTrace_minpoly, separableClosure.isSepClosure, IntermediateField.finrank_comap, InfiniteGalois.toAlgEquivAux_eq_liftNormal, Hyperreal.isSt_iff, separatingDual_iff_injective, minpoly.eq_X_sub_C', Valued.integer.properSpace_iff_compactSpace_integer, Differential.logDeriv_pow, ProbabilityTheory.iIndepFun.integral_prod_eq_prod_integral, primitive_element_iff_minpoly_natDegree_eq, FractionalIdeal.mul_inf, IntermediateField.normalClosure_def'', QuasispectrumRestricts.nonUnitalStarAlgHom_apply, Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint, extremePoints_doublyStochastic, LinearIsometryEquiv.symm_conjStarAlgEquiv, mdifferentiableOn_coordChangeL, RatFunc.num_mul_dvd, IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, WeierstrassCurve.Projective.addU_smul, Subfield.relrank_eq_rank_of_le, WeierstrassCurve.Affine.Point.toClass_injective, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', LieAlgebra.Basis.cartanMatrix_base_eq, Emb.Cardinal.strictMono_filtration, quadraticChar_sq_one, IntermediateField.relfinrank_eq_finrank_of_le, RatFunc.valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_X, LieAlgebra.IsKilling.biSup_corootSubmodule_eq_cartan, RootPairing.polarizationEquiv_symm_apply_coroot, WeierstrassCurve.Affine.Point.add_some, LinearIndependent.map_pow_expChar_pow_of_isSeparable, IntermediateField.isSeparable_tower_bot, FiniteField.isSquare_iff, IntermediateField.minpoly_eq, RatFunc.instExpChar, RatFunc.valuation_isEquiv_adic_of_not_isEquiv_infty, MvPolynomial.ker_evalâ, AdjoinRoot.powerBasis_dim, isNonarchimedean_spectralNorm_of_finiteDimensional_normal, RootPairing.linearIndepOn_coroot_iff, Real.fourier_bilin_convolution_eq_integral, isConjRoot_zero_iff_eq_zero', IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, IsAlgClosure.separable, LinearMap.adjoint_inner_left, IntermediateField.isSplittingField_iff, ArchimedeanClass.FiniteElement.mk_zero, PowerSeries.coeff_inv, IsSepClosed.exists_evalâ_eq_zero_of_injective, AddChar.IsPrimitive.of_ne_one, Matrix.vecMul_injective_iff_isUnit, ContMDiffVectorBundle.contMDiffOn_coordChangeL, WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval, sepDegree_eq_of_isPurelyInseparable_of_isSeparable, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Hyperreal.infinite_mul_of_infinite_not_infinitesimal, IsPurelyInseparable.pow_mem, Valuation.valuationSubring_not_isField, FiniteGaloisIntermediateField.adjoin_val, isPurelyInseparable_iff_finSepDegree_eq_one, LieAlgebra.rank_le_finrank_engel, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, FixedPoints.linearIndependent_smul_of_linearIndependent, ConjRootClass.aroots_minpoly_eq_carrier_val, NumberField.mem_span_integralBasis, quadraticCharFun_eq_pow_of_char_ne_two, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, Lagrange.interpolate_eq_add_interpolate_erase, ArchimedeanClass.FiniteResidueField.instArchimedean, WeierstrassCurve.Projective.add_of_Y_eq, Ideal.coe_smul_primesOver_eq_map_galRestrict, Quaternion.normSq_zpow, FractionalIdeal.count_zero, Polynomial.resultant_eq_prod_roots_sub, Quaternion.coe_nnratCast, NumberField.RingOfIntegers.mapRingEquiv_apply, WeierstrassCurve.Affine.slope_of_Y_eq, LieDerivation.IsKilling.range_ad_eq_top, Algebra.discr_isUnit_of_basis, IntermediateField.rank_top', NumberField.IsCMField.exists_isConj, NumberField.RingOfIntegers.neg_mk, IntermediateField.isAlgebraic_adjoin_simple, FractionalIdeal.le_one_of_extendedHomâ_le_one, CovariantDerivative.torsion_antisymm, RatFunc.denom_C, isPurelyInseparable_of_finSepDegree_eq_one, WeierstrassCurve.Projective.Point.toAffineLift_add, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, RatFunc.num_div_dvd', WeierstrassCurve.Projective.negAddY_eq, RingHom.finite_of_algHom_finiteType_of_isJacobsonRing, LaurentSeries.coeff_zero_of_lt_valuation, IntermediateField.AdjoinSimple.normal_algebraicClosure, LaurentSeries.powerSeriesEquivSubring_coe_apply, IntermediateField.normal_iff_forall_map_eq', ContMDiff.clm_postcomp, FractionalIdeal.count_one, RatFunc.Luroth.generator_eq_zero, WeierstrassCurve.Jacobian.addX_eq, WeierstrassCurve.Jacobian.Point.toAffine_smul, LieModule.iSup_genWeightSpace_eq_top, MDifferentiableAt.coordChangeL, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, WeierstrassCurve.Projective.add_of_X_ne, RootPairing.eq_baseOf_iff, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, IntermediateField.LinearDisjoint.symm, IntermediateField.exists_algHom_adjoin_of_splits', Subspace.dualCopairing_nondegenerate, FixedPoints.toAlgHom_bijective, LieAlgebra.IsKilling.eq_neg_or_eq_of_eq_smul, LieAlgebra.lieIdeal_eq_inf_cartan_sup_biSup_inf_rootSpace, Lagrange.interpolate_apply, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Algebra.normalizedTrace_algebraMap_apply, FiniteField.isSquare_odd_prime_iff, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, Ideal.FinrankQuotientMap.span_eq_top, MDifferentiableWithinAt.clm_postcomp, Valuation.norm_eq_zero, RatFunc.eval_zero, NumberField.mem_span_basisOfFractionalIdeal, IsNonarchimedeanLocalField.isCompact_closedBall, FiniteField.minpoly_frobeniusAlgHom, IsAlgebraic.isIntegral, ContMDiff.clm_prodMap, AffineSubspace.sSameSide_iff_exists_right, FiniteField.natCard_algHom_of_finrank_dvd, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, WeierstrassCurve.Jacobian.addU_of_Z_eq_zero_left, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, IntermediateField.AdjoinSimple.isIntegral_gen, RatFunc.instCharP, ContinuousLinearMap.orthogonal_range, IsGaloisGroup.fixedPoints, perfectField_iff_isSeparable_algebraicClosure, RatFunc.natDegree_num_le_natDegree_minpolyX, Module.End.IsSemisimple_smul, LieAlgebra.IsKilling.rootSystem_pairing_apply, LieAlgebra.IsKilling.chainTopCoeff_zero_right, AlgHom.natCard_of_powerBasis, quadraticChar_odd_prime, ConjRootClass.carrier_eq_mk_aroots_minpoly, LaurentSeries.instLaurentSeriesComplete, IntermediateField.exists_lt_finrank_of_infinite_dimensional, IntermediateField.adjoin_rank_le_of_isAlgebraic, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, LaurentSeries.coeff_zero_of_lt_intValuation, IsDedekindDomain.selmerGroup.fromUnitLift_injective, ContinuousLinearMap.spectralRadius_eq_nnnorm, MeasureTheory.convolutionExistsAt_iff_integrable_swap, Algebra.FormallyEtale.iff_exists_algEquiv_prod, Hyperreal.omega_pos, WeierstrassCurve.Projective.baseChange_dblU, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, IntermediateField.normal_iInf, FractionalIdeal.one_le_extendedHomâ_iff, Algebra.IsAlgebraic.isNormalClosure_normalClosure, Module.End.generalized_eigenvec_disjoint_range_ker, IntermediateField.isPurelyInseparable_bot, NumberField.mixedEmbedding.latticeBasis_apply, mem_algebraicClosure_iff', Hyperreal.coe_add, Polynomial.mem_normalizedFactors_iff, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, FiniteField.sum_pow_units, LaurentSeries.valuation_surjective, LaurentSeries.valuation_coe_ratFunc, Hyperreal.archimedeanClassMk_omega_neg, WeierstrassCurve.Projective.add_of_Y_ne', AlgebraicGeometry.finite_appTop_of_universallyClosed, cfcâAux_mem_range_inr, WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero, ContinuousMap.adjoin_id_eq_span_one_add, Hyperreal.archimedeanClassMk_coe_nonneg, minpolyDiv_eq_of_isIntegrallyClosed, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, Normal.toIsAlgebraic, Polynomial.Gal.galActionHom_bijective_of_prime_degree, IsSelfAdjoint.hasEigenvector_of_isMinOn, AlgebraicIndependent.aevalEquivField_apply_coe, ProbabilityTheory.covarianceBilin_map, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, IntermediateField.LinearDisjoint.exists_field_of_isDomain, FractionalIdeal.dual_inv, WittVector.RecursionMain.root_exists, Ideal.factors_span_eq, minpoly_algEquiv_toLinearMap, AffineSubspace.wSameSide_iff_exists_right, Subfield.relfinrank_dvd_finrank_top_of_le, Matrix.vecMul_injective_of_invertible, PowerBasis.trace_gen_eq_sum_roots, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff, minpoly.natSepDegree_eq_one_iff_pow_mem, IsAlgClosed.card_roots_map_eq_natDegree_of_leadingCoeff_ne_zero, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, Matrix.toLin_finTwoProd_toContinuousLinearMap, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, Module.End.IsSemisimple_smul_iff, Valuation.exists_pow_Uniformizer, minpoly.zero, FractionalIdeal.divMod_spec, Submodule.mem_traceDual, IntermediateField.finiteDimensional_left, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, IntermediateField.finiteDimensional_iSup_of_finite, MDifferentiableOn.clm_precomp, minpoly.one, Algebra.normalizedTrace_trans_apply, LinearMap.IsSymmetric.det_eq_prod_eigenvalues, Matrix.finiteDimensional, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, ContinuousLinearMap.adjoint_comp, LaurentSeries.valuation_compare, isConjRoot_iff_orbitRel, AlgebraicClosure.instIsScalarTower, Hyperreal.tendsto_atBot_iff, le_perfectClosure_iff, perfectClosure.isAlgebraic, Orientation.someBasis_orientation, NumberField.IsCMField.complexConj_eq_self_iff, AffineSubspace.sSameSide_lineMap_left, FractionalIdeal.not_inv_le_one_of_ne_bot, LieAlgebra.IsKilling.coroot_eq_zero_iff, IntermediateField.isSeparable_sup, FiniteGaloisIntermediateField.finiteDimensional, ClassGroup.isPrincipal_coeSubmodule_of_isUnit, PowerSeries.ker_coeff_eq_max_ideal, minpoly.neg, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, ContinuousLinearMap.adjointAux_inner_right, RatFunc.Luroth.adjoin_generator_le, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, ContMDiffAt.clm_bundle_applyâ, IsSepClosure.isAlgClosure_of_perfectField_top, FractionalIdeal.dual_eq_zero_iff, IntermediateField.relfinrank_dvd_finrank_top_of_le, IsDedekindDomain.exists_add_spanSingleton_mul_eq, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, Hyperreal.infinitesimal_iff, finSepDegree_dvd_finrank, LinearMap.isStarProjection_toContinuousLinearMap_iff, RatFunc.liftAlgHom_apply, Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesâ, exists_linearIndependent_algEquiv_apply, Polynomial.roots_C_mul_X_sub_C, InfiniteGalois.restrictNormalHom_continuous, RatFunc.Luroth.transcendental_generator, Algebra.IsSeparable.sepDegree_eq, IntermediateField.isAlgebraic_iSup, RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropic, LaurentSeries.tendsto_valuation, Submodule.traceDual_bot, IsGaloisGroup.subgroup, normalClosure_eq_iSup_adjoin, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, Algebra.FormallySmooth.of_perfectField, Polynomial.natSepDegree_eq_of_isAlgClosed, isSepClosed_iff_isPurelyInseparable_algebraicClosure, NumberField.abs_discr_ge_of_isTotallyComplex, FiniteField.bijective_frobeniusAlgHom_pow, Module.End.genEigenspace_div, Differential.logDeriv_eq_zero, IsGalois.of_separable_splitting_field_aux, WeierstrassCurve.Projective.negMap_of_Z_eq_zero, WeierstrassCurve.Projective.Point.add_def, IntermediateField.LinearDisjoint.isField_of_isAlgebraic', AlgebraicClosure.isAlgebraic, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, IsCyclotomicExtension.Rat.cyclotomicRing_isIntegralClosure_of_prime, Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, LieAlgebra.IsKilling.finrank_rootSpace_eq_one, IntermediateField.finrank_le_of_le_left, IntermediateField.finInsepDegree_bot, LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic, LinearMap.adjoint_comp, krullTopology_mem_nhds_one_iff, IsFractionRing.isAlgebraic_iff, FiniteField.unitsMap_norm_surjective, gaussSum_pow_eq_prod_jacobiSum, quadraticChar_sq_one', IsPurelyInseparable.minpoly_eq_X_sub_C_pow, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, ArchimedeanClass.mk_sub_pos_iff, Matrix.posDef_inv_iff, FractionalIdeal.instPosMulStrictMonoNonZeroDivisors, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, Valued.integer.mem_iff, Lagrange.interpolate_empty, LaurentSeries.coe_range_dense, WeierstrassCurve.Projective.addMap_of_Z_ne_zero, WeierstrassCurve.Projective.equiv_zero_of_Z_eq_zero, TensorialAt.mkHomâ_apply, Emb.Cardinal.iSup_adjoin_eq_top, WeierstrassCurve.Affine.Point.add_self_of_Y_eq, WeierstrassCurve.Affine.Point.map_some, MvPolynomial.sum_eval_eq_zero, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', RatFunc.finrank_ratFunc_ratFunc, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero, JacobsonNoether.exists_separable_and_not_isCentral', LieAlgebra.IsKilling.chainBotCoeff_of_eq_zsmul_add, Polynomial.Splits.dvd_of_roots_le_roots, PowerSeries.intValuation_X, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, span_flip_eq_top_iff_linearIndependent, LieAlgebra.IsKilling.chainLength_zero_right, AlgebraicGeometry.Proj.valuativeCriterion_existence_aux, Matrix.det_eq_prod_roots_charpoly, LieAlgebra.IsKilling.chainLength_smul, Module.End.HasUnifEigenvalue.of_mem_spectrum, Hyperreal.not_infinite_mul, IsCyclotomicExtension.Rat.finrank, WeierstrassCurve.Jacobian.nonsingularLift_negMap, SchwartzMap.convolution_flip, Lagrange.eq_interpolate_of_eval_eq, Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, Hyperreal.infinitesimal_zero, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, ContinuousLinearMap.IsPositive.adjoint_conj, IntermediateField.isSeparable_iSup, PerfectClosure.instPerfectField, krullTopology_mem_nhds_one_iff_of_normal, RootPairing.isIrreducible_iff_invtRootSubmodule, Irreducible.maximalIdeal_eq_closedBall, IntermediateField.finrank_bot', WeierstrassCurve.Projective.Point.toAffine_add, IsGalois.integral, ContMDiffCovariantDerivativeOn.contMDiff, IsPurelyInseparable.elemExponent_le_exponent, Module.End.HasEigenvalue.of_mem_spectrum, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, ConjRootClass.mk_def, IsUnramifiedAtInfinitePlaces.card_infinitePlace, CyclotomicRing.instIsTorsionFreeCyclotomicField, WeierstrassCurve.Jacobian.Point.toAffineLift_zero, Algebra.FormallyEtale.of_isSeparable, RatFunc.denom_algebraMap, ContMDiffWithinAt.coordChangeL, mem_adjoin_of_smul_prime_pow_smul_of_minpoly_isEisensteinAt, AffineSubspace.SSameSide.trans_sOppSide, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, LinearMap.isSymmetric_adjoint_comp_self, Subfield.lift_rank_comap, Projectivization.cross_mk_of_ne, Algebra.isSeparable_self, ProperCone.hyperplane_separation_of_notMem, Module.End.trace_eq_sum_roots_charpoly_of_splits, AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectField, Module.End.mem_invtSubmodule_adjoint_iff, FractionalIdeal.count_zpow, NumberField.house_nat_mul, separableClosure.isSeparable, minpoly.natDegree_le, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, LinearMap.restrictScalarsField_apply_apply, IsNonarchimedeanLocalField.toIsValuativeTopology, CyclotomicField.isCyclotomicExtension, PowerBasis.ofAdjoinEqTop_dim, FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc, WeierstrassCurve.Affine.baseChange_slope, RatFunc.isAlgebraic_adjoin_simple_X', WittVector.isUnit_of_coeff_zero_ne_zero, RatFunc.valuation_isEquiv_inftyValuation_of_one_lt_valuation_X, IsAlgClosed.card_aroots_eq_natDegree_of_isUnit_leadingCoeff, AdjoinRoot.minpoly_powerBasis_gen, WeierstrassCurve.Jacobian.addY_of_X_eq, LieDerivation.IsKilling.ad_apply_eq_zero_iff, ContMDiffFiberwiseLinear.locality_auxâ, LinearMap.range_self_comp_adjoint, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, Algebra.norm_eq_prod_roots, Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_pos, Lagrange.sum_basis, Valued.integer.isUnit_iff_norm_eq_one, IntermediateField.adjoin.finiteDimensional, le_algebraicClosure_iff, IsConjRoot.of_isScalarTower, IsSelfAdjoint.hasEigenvector_of_isLocalExtrOn, AlgebraicIndependent.algebraicClosure, IsConjRoot.neg, Valued.integer.isPrincipalIdealRing_of_compactSpace, FDRep.char_orthonormal, ContMDiffAt.mfderiv, Module.End.IsSemisimple.minpoly_squarefree, RatFunc.intDegree_one, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv, WeierstrassCurve.Projective.equiv_of_X_eq_of_Y_eq, RatFunc.eq_C_iff, WeierstrassCurve.ofJ_0_of_two_eq_zero, RatFunc.num_mul_eq_mul_denom_iff, IntermediateField.rank_sup_le, algNormFromConst_def, IntermediateField.LinearDisjoint.self_right, LieAlgebra.IsKilling.lieIdealOrderIso_right_inv, CSA.fin_dim, AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv_assoc, finSepDegree_eq_finrank_iff, Lagrange.eval_interpolate_at_node, RootPairing.restrictScalars_toLinearMap_apply_apply, LinearMap.finrank_maxGenEigenspace_zero_eq, FractionalIdeal.count_pow_self, isAlgebraic_solvableByRad, LaurentSeries.comparePkg_eq_extension, quadraticChar_apply, FiniteDimensional.exists_is_basis_integral, LinearMap.IsSymmetric.roots_charpoly_eq_eigenvalues, IsSelfAdjoint.adjoint_conj, WittVector.exists_frobenius_solution_fractionRing_aux, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, IsIntegral.mem_range_algebraMap_of_minpoly_splits, AlgEquiv.restrictNormalHom_apply, InfiniteGalois.mk_toAlgEquivAux, Normal.out, VectorPrebundle.contMDiffOn_contMDiffCoordChange, LeftInvariantDerivation.toDerivation_injective, WeierstrassCurve.Jacobian.Point.toAffine_zero, WeierstrassCurve.Affine.Point.add_of_Y_ne', instIsAbelianGaloisSubtypeMemIntermediateField, minpoly.dvd, IsCovariantDerivativeOn.torsion_apply_eq_extend, FixedPoints.minpoly_eq_minpoly, algebraicClosure.isAlgClosure, IsPurelyInseparable.of_injective_comp_algebraMap, mdifferentiableAt_coordChangeL, Quaternion.im_ratCast, AlgebraicGeometry.geometrically_iff_of_commRing_of_isClosedUnderIsomorphisms, jacobiSum_mul_jacobiSum_inv, RatFunc.single_zpow, Emb.Cardinal.adjoin_image_leastExt, ContinuousLinearMap.adjoint_inner_right, WeierstrassCurve.Affine.Point.add_of_X_ne', LaurentSeries.valuation_def, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic, Representation.char_linHom, FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, MeasureTheory.integral_fintype_prod_volume_eq_prod, AddChar.FiniteField.primitiveChar_to_Complex_isPrimitive, WeierstrassCurve.Jacobian.equiv_of_X_eq_of_Y_eq, isAlgebraic_of_isFractionRing, QuadraticForm.radical_weightedSumSquares, WeierstrassCurve.Jacobian.negDblY_of_Z_ne_zero, Lagrange.interpolate_poly_eq_self, FractionalIdeal.map_canonicalEquiv_mk0, FiniteField.nonempty_algHom_iff_finrank_dvd, FiniteField.isSquare_of_char_two, CovariantDerivative.torsion_self, minpoly.eq_iff_aeval_minpoly_eq_zero, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, Algebra.discr_powerBasis_eq_prod'', FractionalIdeal.count_inv, IsPrimitiveRoot.coe_toInteger, IsCyclotomicExtension.norm_zeta_eq_one, ArchimedeanClass.stdPart_add_eq_left, FunctionField.inftyValuation.C, IsAlgClosed.roots_eq_zero_iff, LieAlgebra.IsKilling.coe_invtSubmoduleToLieIdeal_eq_iSup, Algebra.map_intTraceAux, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, integralClosure.isDedekindDomain_fractionRing, NumberField.house_add_le, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, Polynomial.coeff_eq_esymm_roots_of_splits, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, NumberField.mixedEmbedding.norm_real, Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, continuous_cfcâAux, isAlgClosure_iff, RatFunc.C_minpolyX, LieAlgebra.IsKilling.traceForm_coroot, WeierstrassCurve.Jacobian.addU_smul, InfiniteGalois.proj_of_le, WeierstrassCurve.toCharTwoNF_spec, ClassGroup.mk_eq_one_of_coe_ideal, WittVector.RecursionBase.solution_spec', AlgebraicGeometry.pullback_of_geometrically', Cubic.eq_sum_three_roots, WeierstrassCurve.Affine.equation_negAdd, FDRep.char_dual, RootPairing.finrank_rootSpanIn, Valuation.IsUniformizer.is_generator, Ideal.finprod_heightOneSpectrum_factorization_coe, quadraticChar_neg_one_iff_not_isSquare, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, CyclotomicField.instIsCyclotomicExtensionSingletonNatSetOfNat, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, FGModuleCat.FGModuleCatEvaluation_apply', LieModule.traceForm_eq_sum_finrank_nsmul_mul, ProbabilityTheory.iIndepFun.integral_fun_prod_eq_prod_integral, NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, Polynomial.nodup_roots_iff_of_splits, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, LinearMap.IsSymmetric.charpoly_eq, toPrincipalIdeal_def, LieAlgebra.IsKilling.coroot_zero, FractionalIdeal.count_mul', quadraticChar_eq_pow_of_char_ne_two, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, IntermediateField.relrank_eq_rank_of_le, WeierstrassCurve.Projective.map_add, mfderiv_smul, FractionalIdeal.dual_inv_le, NumberField.basisOfFractionalIdeal_apply, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, IsIntegral.inv, LaurentSeries.uniformContinuous_coeff, Algebra.normalizedTrace_algebraMap_of_lifts, LinearIsometryEquiv.toMatrix_mem_unitaryGroup, LieAlgebra.IsKilling.chainBotCoeff_zero_right, LieModule.Weight.isNonZero_neg, ContMDiffWithinAt.clm_prodMap, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, LinearMap.IsSymmetric.LinearMap.IsSymmetric.directSum_isInternal_of_pairwise_commute, WeierstrassCurve.Projective.Point.add_point, LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdeal, IsNonarchimedeanLocalField.instCompatibleValueGroupWithZeroV, ContinuousLinearMap.isAdjointPair_inner, WeierstrassCurve.Projective.Point.toAffine_of_Z_eq_zero, WeierstrassCurve.IsIntegral.integral, IntermediateField.algebraicIndependent_adjoin_iff, WeierstrassCurve.Jacobian.Point.add_def, mem_separableClosure_iff, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, IsFractionRing.comap_isAlgebraic_iff, Cubic.discr_ne_zero_iff_roots_nodup, LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot, IntermediateField.rank_eq_rank_subalgebra, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, quadraticChar_eq_pow_of_char_ne_two', LieAlgebra.Basis.root_mem_or_mem_neg, Algebra.normalizedTrace_trans, RingOfIntegers.algebraMap_norm_algebraMap, WeierstrassCurve.Jacobian.Y_eq_iff, lift_rank_mul_lift_sepDegree_of_isSeparable, autEquivRootsOfUnity_apply_rootOfSplit, bijective_rangeRestrict_comp_of_valuationRing, IsPurelyInseparable.iterateFrobeniusââ_algebraMap, isSeparable_iff_finInsepDegree_eq_one, Submodule.IsLattice.of_rank_le, Polynomial.rootSet_monomial, LieAlgebra.IsKilling.chainTopCoeff_of_eq_zsmul_add, IntermediateField.LinearDisjoint.of_finrank_sup, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, Submodule.traceDual_span_of_basis, Algebra.discr_powerBasis_eq_prod', Polynomial.X_sub_C_mul_removeFactor, IsInertiaField.algebraMap_ringEquiv_apply, Algebra.algebraMap_intTrace, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, LieAlgebra.InvariantForm.isSemisimple_of_nondegenerate, IsInertiaField.rank_decompositionField, LinearEquiv.det_coe_symm, WeierstrassCurve.j_of_isShortNF_of_char_three, normalClosure.normal, Representation.char_orthonormal, WeierstrassCurve.Jacobian.Point.toAffineLift_eq, Ideal.inertiaDeg_le_finrank, RatFunc.valuation_eq_valuation_uniformizingPolynomial_pow_of_valuation_X_le_one, FixedPoints.toAlgAut_bijective, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, SchwartzMap.fourier_convolution_apply, LinearMap.IsPerfPair.of_injective', Polynomial.cyclotomic'_splits, IsCyclotomicExtension.fromZetaAut_spec, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, Ideal.exist_integer_multiples_notMem, Irreducible.maximalIdeal_pow_eq_closedBall_pow, Polynomial.annIdealGenerator_eq_minpoly, Valued.integer.totallyBounded_iff_finite_residueField, divRadical_dvd_wronskian_left, Module.End.iSup_maxGenEigenspace_eq_top, AlgebraicGeometry.Scheme.residue_descResidueField_assoc, LieAlgebra.IsKilling.restr_invtSubmoduleToLieIdeal_eq_iSup, instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C', LieAlgebra.IsKilling.rootSpace_two_smul, LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, LinearMap.eq_adjoint_iff_basis_right, Algebra.PowerBasis.norm_gen_eq_prod_roots, MDifferentiable.clm_precomp, IsPurelyInseparable.iterateFrobeniusââ_algebraMap_base, MDifferentiable.clm_comp, Hyperreal.InfinitePos.pos, WeierstrassCurve.Affine.Point.toClass_eq_zero, LaurentSeries.ratfuncAdicComplRingEquiv_apply, ContMDiff.clm_comp, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, MvPolynomial.mem_vanishingIdeal_iff, MvPolynomial.mem_vanishingIdeal_singleton_iff, AffineSubspace.SOppSide.trans_wOppSide, Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map, WeierstrassCurve.Jacobian.Point.toAffineAddEquiv_symm_apply, IsFractionRing.liftAlgHom_fieldRange, IntermediateField.LinearDisjoint.linearIndependent_mul', IsIdempotentElem.quasispectrum_subset, NumberField.InfinitePlace.LiesOver.instLiesOverRealValAbsoluteValueExistsRingHomComplexEqPlaceMkOfLiesOver, WeierstrassCurve.Jacobian.isUnit_dblZ_of_Y_ne, separableClosure_le_iff, solvableByRad.isIntegral, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, Submodule.le_traceDual_mul_iff, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, ArchimedeanClass.stdPart_mul, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, RatFunc.intDegree_X, LaurentSeries.Cauchy.coeff_eventually_equal, ClassGroup.equiv_mk0, NumberField.RingOfIntegers.map_mk, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, Valuation.Uniformizer.is_generator, LinearMap.orthogonal_range, WeierstrassCurve.Projective.Point.toAffine_zero, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, IntermediateField.insepDegree_bot, LinearMap.singularValues_of_lt, CovariantDerivative.torsion_apply_eq_extend, contMDiffOn_coordChangeL, IntermediateField.rank_bot', ProbabilityTheory.iIndepFun.integral_fun_prod_comp, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, quadraticChar_neg_one, Algebra.norm_algebraMap, Hyperreal.infiniteNeg_mul_of_not_infinitesimal_neg_infinitePos, Polynomial.rootSet_X_pow, AffineSubspace.wOppSide_iff_exists_right, RatFunc.denom_add_dvd, Module.End.mem_spectrum_iff_isRoot_charpoly, RatFunc.valuation_uniformizingPolynomial_lt_one, NumberField.IsCMField.infinitePlace_complexConj, Matrix.IsHermitian.rank_eq_card_non_zero_eigs, Polynomial.rootSet_prod, IntermediateField.isAlgebraic_adjoin_iff_bot, NumberField.ComplexEmbedding.isReal_comp_iff, ContMDiffWithinAt.clm_precomp, NumberField.house_prod_le, LinearMap.coe_toContinuousLinearMap_symm, IntermediateField.LinearDisjoint.of_basis_mul, RatFunc.num_div_denom, FractionalIdeal.count_self, Module.End.genEigenspace_restrict_eq_top, separableClosure_le_separableClosure_iff, Subring.eq_iInf_of_isIntegrallyClosedIn, AffineSubspace.sOppSide_smul_vsub_vadd_left, Module.End.iSup_iInf_maxGenEigenspace_eq_top_of_iSup_maxGenEigenspace_eq_top_of_commute, IsGaloisGroup.card_eq_finrank, Quaternion.re_ratCast, ProbabilityTheory.iIndepFun.integral_prod_comp, FixedPoints.coe_algebraMap, cardinalMk_algHom, IsGalois.tfae, WeierstrassCurve.Projective.dblX_eq, LinearMap.IsPositive.adjoint_eq, IntermediateField.transcendental_adjoin_iff, minpoly_add_algebraMap_splits, Emb.Cardinal.iSup_filtration, Cubic.d_eq_three_roots, RootPairing.isRootSystem_mk'', FractionalIdeal.inv_le_comm, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, WeierstrassCurve.Projective.addX_of_Z_ne_zero, Module.End.IsSemisimple.eq_zero_iff_forall_eigenvalue, minpoly.iterateFrobenius_of_isSeparable, ContinuousLinearMap.norm_adjoint_comp_self, spectralNorm_zero, RootPairing.rootSpan_eq_top_iff, Module.End.hasEigenvalue_iff_mem_spectrum, ContMDiff.clm_precomp, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, FractionalIdeal.dual_injective, IntermediateField.rank_comap, LieIdeal.corootSubmodule_le, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, LinearMap.not_hasEigenvalue_zero_tfae, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, NumberField.FinitePlace.instNonarchimedeanHomClassReal, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, IntermediateField.rank_bot_mul_relrank, ContinuousMapZero.elemental_eq_top, ContMDiffOn.clm_prodMap, ContinuousMapZero.adjoin_id_dense, LieModule.instIsTriangularizableOfIsAlgClosed, NumberField.totalWeight_eq_finrank, IntermediateField.fg_top_iff, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C, Hyperreal.infinitePos_mul_of_not_infinitesimal_neg_infiniteNeg, LeftInvariantDerivation.commutator_coe_derivation, IsCyclotomicExtension.Rat.discr_odd_prime', ContMDiffWithinAt.clm_comp, WeierstrassCurve.toCharThreeNF_spec_of_bâ_eq_zero, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, Hyperreal.coe_mul, Matrix.trace_map, Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange, instIsInertiaFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupInertiaOfIsGalois, IsAlgClosed.isAlgClosure_of_transcendence_basis, AffineSubspace.setOf_sOppSide_eq_image2, NumberField.coe_discr, LinearMap.finrank_maxGenEigenspace_eq, MulChar.apply_mem_rootsOfUnity_orderOf, Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg, Algebra.FormallyEtale.of_formallyUnramified_of_field, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, MeasureTheory.convolution_eq_swap, IsTranscendenceBasis.lift_rank_eq_max_lift, IntermediateField.finiteDimensional_map, minpoly.degree_dvd, IntermediateField.LinearDisjoint.isField_of_forall, FractionalIdeal.self_mul_dual, MvRatFunc.rank_eq_max_lift, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly_of_splits, WeakDual.seminormFamily_apply, NumberField.Units.finrank_mul_regulator_eq_det, RatFunc.algEquivOfTranscendental_algebraMap, WeierstrassCurve.Affine.Point.xRep_eq_xRep_iff, linearIndependent_pow, rank_lt_rank_dual, ClassGroup.mk_canonicalEquiv, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, IntermediateField.LinearDisjoint.isDomain', LieAlgebra.InvariantForm.atomistic, Polynomial.IsSplittingField.adjoin_rootSet_eq_range, IntermediateField.lift_rank_comap, ContinuousLinearMap.norm_holderL_le, AffineSubspace.not_sOppSide_self, Sbtw.sOppSide_of_notMem_of_mem, Algebra.IsSeparable.of_algHom, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, CSA.isCentral, WeierstrassCurve.ofJ_0_of_three_ne_zero, IsAdjoinRoot.primitive_element_root, quadraticCharFun_zero, Matrix.IsHermitian.charpoly_eq, RatFunc.associated_num_inv, IntermediateField.normalClosure_le_iff_of_normal, FiniteField.orderOf_frobeniusAlgHom, eq_zero_of_map_spectralNorm_eq_zero, LinearIndependent.map_of_isPurelyInseparable_of_isSeparable, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, AffineSubspace.setOf_wSameSide_eq_image2, AlgHom.fieldRange_of_normal, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, ContinuousLinearMap.finite_dimensional_eigenspace, IntermediateField.Lifts.eq_iff, Module.End.genEigenspace_le_genEigenspace_finrank, WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq, WeierstrassCurve.Projective.add_of_Y_ne, Differential.logDeriv_multisetProd, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, WeierstrassCurve.Projective.Point.toAffineAddEquiv_symm_apply, IsCovariantDerivativeOn.affine_combination, Emb.Cardinal.adjoin_basis_eq_top, Algebra.coe_trace_int, WeierstrassCurve.HasMultiplicativeReduction.badReduction, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, Hyperreal.infiniteNeg_add_not_infinitePos, LinearMap.flip_surjective_iffâ, LinearMap.self_comp_adjoint_injective_iff, FractionalIdeal.adjoinIntegral_eq_one_of_isUnit, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, Valued.integer.norm_coe_unit, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IntermediateField.normalClosure_map_eq, MeasureTheory.hausdorffMeasure_homothety_preimage, WeierstrassCurve.j_of_isShortNF, WithAbs.instIsSeparable, IsNonarchimedeanLocalField.toIsNontrivial, QuadraticForm.sigPos_add_finrank_le_of_nonpos, Polynomial.natSepDegree_eq_of_splits, LieAlgebra.Basis.coe_linearMap_baseSupp', WeierstrassCurve.Jacobian.equiv_of_Z_eq_zero, FractionalIdeal.count_maximal, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, IntermediateField.relrank_bot_left, WeierstrassCurve.Affine.Point.X_eq_iff, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, LaurentSeries.mem_integers_of_powerSeries, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AlgHom.card_of_splits, IsConjRoot.sub_algebraMap, LaurentSeries.Cauchy.exists_lb_support, IsCovariantDerivativeOn.torsion_apply, RingOfIntegers.coe_algebraMap_norm, Ring.instIsIntegralClosureNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, AffineSubspace.sSameSide_smul_vsub_vadd_left, LaurentSeries.instIsFractionRingPowerSeries, NumberField.mixedEmbedding.convexBodySum_volume, LieModule.Weight.toLinear_neg, WeierstrassCurve.Affine.Point.map_zero, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, RatFunc.isAlgebraic_adjoin_simple_X, WeierstrassCurve.Projective.negAddY_of_Z_ne_zero, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, Hyperreal.infinitePos_add_infinitePos, RatFunc.denom_dvd, IntermediateField.isPurelyInseparable_tower_top, Algebra.Etale.iff_exists_algEquiv_prod, LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commute, LinearMap.toMatrix_adjoint, LieDerivation.IsKilling.killingForm_restrict_range_ad_nondegenerate, IntermediateField.le_normalClosure, LaurentSeries.eq_coeff_of_valuation_sub_lt, LinearMap.IsPerfPair.restrictScalars_of_field, IsPrimitiveRoot.norm_of_cyclotomic_irreducible, TensorialAt.mkHomâ_apply_eq_extend, MeasureTheory.AEStronglyMeasurable.convolution_integrand', FDRep.scalar_product_char_eq_finrank_equivariant, RootPairing.isCompl_corootSpan_ker_corootForm, WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq, WeierstrassCurve.Jacobian.equation_of_Z_ne_zero, WeierstrassCurve.Projective.dblX_of_Z_ne_zero, ContinuousLinearMap.isPositive_adjoint_comp_self, IsNonarchimedeanLocalField.instCompleteSpaceSubtypeMemSubringIntegerValueGroupWithZeroValuation, IntermediateField.normalClosure_def', LinearMap.im_inner_adjoint_mul_self_eq_zero, ValuationSubring.algebraMap_injective, WittVector.isocrystal_classification, autAdjoinRootXPowSubC_root, Matrix.l2_opNorm_def, Ideal.hasFiniteMulSupport_inv, Algebra.discr_isIntegral, AffineSubspace.wOppSide_pointReflection, AffineSubspace.WOppSide.trans_sSameSide, Algebra.isIntegral_norm, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, ContinuousLinearMap.holderL_apply_apply, WeierstrassCurve.isIntegral_iff, RatFunc.single_inv, LeftInvariantDerivation.toFun_eq_coe, sepDegree_le_rank, Cubic.b_eq_three_roots, Hyperreal.infiniteNeg_iff, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, quadraticChar_eq_neg_one_iff_not_one, MeasureTheory.AEStronglyMeasurable.convolution_integrand, Subalgebra.SeparatesPoints.rclike_to_real, RatFunc.intDegree_neg, ContMDiffWithinAt.cle_arrowCongr, perfectClosure.perfectRing, AlgebraicGeometry.pointEquivClosedPoint_symm_apply_coe, LieModule.eq_iSup_inf_genWeightSpace, Algebra.norm_eq_prod_embeddings_gen, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, Matrix.linearIndependent_cols_of_invertible, LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero, PerfectClosure.mk_inv, RatFunc.uniformizingPolynomial_isUniformizer, Polynomial.monic_normalize, Polynomial.map_dvd_map', ArchimedeanClass.FiniteElement.mk_natCast, IntermediateField.LinearDisjoint.isDomain, WeierstrassCurve.Jacobian.Point.toAffine_of_singular, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_eq_zero, SchwartzMap.fourier_convolution, gcd_eq, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, IsInertiaField.algebraMap_ringEquiv_symm_apply, IntermediateField.finrank_dvd_of_le_right, FractionalIdeal.trace_mem_dual_one, AdjoinRoot.minpoly_powerBasis_gen_of_monic, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, gaussSum_mul_gaussSum_eq_card, IsGalois.splits, WeierstrassCurve.instIsEllipticOfJ, Quaternion.normSq_div, Polynomial.resultant_eq_zero_iff, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, Matrix.PosDef.det_pos, IntermediateField.finrank_le_of_le_right, NumberField.RingOfIntegers.instIsIntegralClosure, LinearMap.isAdjointPair_inner, LinearMap.IsPositive.adjoint_conj, RatFunc.natDegree_denom_le_natDegree_minpolyX, ContinuousLinearMap.norm_holder_apply_apply_le, isAlgebraic_iff_isIntegral, Subspace.quotDualCoannihilatorToDual_bijective, IsIntegral.minpoly_splits_tower_top, Hyperreal.infinitePos_mul_infinitePos, Matrix.sub_scalar_sq_eq_discr, Algebra.IsAlgebraic.isPurelyInseparable_of_isSepClosed, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, isGalois_bot, LieAlgebra.Basis.coe_baseSupportEquiv_apply, Polynomial.irreducible_iff_lt_natDegree_lt, IntermediateField.finrank_dvd_of_le_left, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, Algebra.prod_embeddings_eq_finrank_pow, IsSepClosure.separable, FiniteField.card_algHom_of_finrank_dvd, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, Matrix.mulVec_injective_of_invertible, MDifferentiableWithinAt.clm_prodMap, ContMDiffAt.clm_comp, minpoly.eq_X_sub_C, Polynomial.SplittingField.adjoin_rootSet, isSplittingField_iff_intermediateField, WeierstrassCurve.j_of_isCharTwoJNeZeroNF_of_char_two, Polynomial.eval_gcd_eq_zero, WeierstrassCurve.Projective.nonsingular_iff_of_Y_eq_negY, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, Lagrange.nodal_erase_eq_nodal_div, AbsoluteValue.isEquiv_iff_isHomeomorph, Emb.cardinal_eq_two_pow_rank, Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splits, RootPairing.ker_corootForm_eq_dualAnnihilator, NumberField.RingOfIntegers.mapRingEquiv_symm_apply, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic, Submodule.le_traceDual_iff_map_le_one, exists_integral_inj_algHom_of_fg, FunctionField.inftyValuation_apply, IsGalois.separable, FiniteField.algebraMap_norm_eq_pow_sum, WeierstrassCurve.Jacobian.addMap_of_Y_eq, NumberField.instIsAlgebraicSubtypeMemSubfield, IntermediateField.finiteDimensional_adjoin_pair, LinearMap.IsSymmetric.hasEigenvector_eigenvectorBasis, Ideal.finite_mulSupport_inv, WeierstrassCurve.Projective.dblY_of_Y_eq, IntermediateField.normal_sup, IsAlgClosed.associated_iff_roots_eq_roots, IsPrimitiveRoot.norm_sub_one_two, WeierstrassCurve.Affine.Point.eq_or_eq_neg_of_xRep_eq_xRep, mdifferentiableWithinAt_hom_bundle, NumberField.IsCMField.complexConj_torsion, IsAlgClosed.exists_eq_mul_self, Submodule.traceDual_top, Module.End.exists_isNilpotent_isSemisimple, Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff, LieModule.range_traceForm_le_span_weight, separableClosure.isGalois, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, IsGalois.to_isSeparable, Quaternion.normSq_ratCast, FDRep.dualTensorIsoLinHom_hom_hom, WeierstrassCurve.Jacobian.isUnit_addZ_of_X_ne, LieAlgebra.IsKilling.corootSpace_zero_eq_bot, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, LaurentSeries.exists_ratFunc_eq_v, MvPolynomial.instFiniteDimensionalROfFinite, IntermediateField.finiteDimensional_iSup_of_finset', FixedPoints.minpoly.evalâ, WeierstrassCurve.Jacobian.isUnit_dblU_of_Y_eq, IntermediateField.finrank_adjoin_simple_eq_one_iff, FractionalIdeal.coe_mk0, ClassGroup.mk_def, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, IntermediateField.LinearDisjoint.map, IsSepClosed.exists_aeval_eq_zero, gaussSum_sq, SchwartzMap.fourierMultiplierCLM_smul, integralClosure.mem_lifts_of_monic_of_dvd_map, IsSeparable.of_equiv_equiv, IntermediateField.isSeparable_tower_top, LinearMap.finrank_eigenspace_le, Algebra.finite_of_essFiniteType_of_isAlgebraic, Module.End.eigenspace_aeval_polynomial_degree_1, exists_eq_sum_perm_of_mem_doublyStochastic, Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, minpoly.map_eq_of_equiv_equiv, RatFunc.algEquivOfTranscendental_apply, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, ConjRootClass.carrier_neg, HasCompactSupport.convolution_integrand_bound_right, isIntegral_of_mem_solvableByRad, QuadraticAlgebra.norm_eq_zero_iff_eq_zero, IsFractionRing.ideal_span_singleton_map_subset, normalClosure.is_finiteDimensional, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, Algebra.IsSeparable.trans, LieIdeal.root_apply_eq_zero_of_notMem_rootSet, IntermediateField.finiteDimensional_sup, AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed, ContMDiffAt.cle_arrowCongr, IntermediateField.Lifts.le_iff, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, separableClosure.eq_bot_iff, Algebra.normalizedTrace_self_apply, ConjRootClass.mk_eq_mk, WeierstrassCurve.Affine.Point.toClass_apply, Polynomial.normalizedFactors_cyclotomic_card, ContinuousLinearMap.adjoint_innerSL_apply, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Valuation.coeff_zero_minpoly, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, trace_adjoinSimpleGen, jacobiSum_one_one, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, IntermediateField.normal_iff_normalClosure_eq, HasCompactSupport.convolution_integrand_bound_right_of_subset, LaurentSeries.uniformContinuous_withVal_equiv, IntermediateField.rank_adjoin_simple_eq_one_iff, Matrix.rank_conjTranspose_mul_self, IsSepClosed.exists_evalâ_eq_zero, isDedekindDomainInv_iff, IntermediateField.AdjoinPair.algebraMap_genâ, Hyperreal.st_add, irreducible_X_pow_sub_C_of_root_adjoin_eq_top, NumberField.house.basis_repr_norm_le_const_mul_house, ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero, cyclotomicCharacter.continuous, FractionalIdeal.zero_divMod, Valued.integer.exists_norm_coe_lt_one, notMem_iff_exists_ne_and_isConjRoot, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, ContinuousLinearMap.toWOT_apply, Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map, IntermediateField.isIntegral_iff, contMDiffWithinAt_hom_bundle, AdjoinRoot.isIntegral_root, mem_contMDiffFiberwiseLinear_iff, RatFunc.denom_zero, IntermediateField.LinearDisjoint.isField_of_isAlgebraic, MvPolynomial.range_evalᾢ, FractionalIdeal.mul_right_strictMono, LieAlgebra.IsKilling.coe_coroot_mem_corootSubmodule, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, RatFunc.associated_denom_inv, SchwartzMap.smulLeftCLM_smul, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, LieAlgebra.IsKilling.lieIdeal_eq_inf_cartan_sup_biSup_rootSpace, WeierstrassCurve.Projective.isUnit_addZ_of_X_ne, MeasureTheory.integral_convolution, contractLeft_assoc_coevaluation', separableClosure.normalClosure_eq_self, Algebra.IsAlgebraic.isSeparable_of_perfectField, FractionalIdeal.count_coe, LinearMap.IsSymmetric.sort_roots_charpoly_eq_eigenvalues, IsAlgClosed.dvd_iff_roots_le_roots, Derivation.evalAt_apply, FractionalIdeal.le_dual_inv_aux, WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, IntermediateField.adjoin.powerBasis_dim, mod_eq, LaurentSeries.valuation_X_pow, char_dvd_card_solutions_of_fintype_sum_lt, IsCyclotomicExtension.isSeparable, isConjRoot_iff_eq_algebraMap', IsCyclotomicExtension.autEquivPow_symm_apply, quadraticChar_one_iff_isSquare, IsGalois.of_fixedField_normal_subgroup, quadraticChar_exists_neg_one, const_smul_mfderiv, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, IntermediateField.essFiniteType_iff, FractionalIdeal.instPosMulReflectLENonZeroDivisors, Emb.cardinal_separableClosure, HasMFDerivAt.const_smul, IsCovariantDerivativeOn.finite_affine_combination, Lagrange.interpolate_singleton, LieModule.Weight.coe_neg, WeierstrassCurve.Projective.Point.toAffineLift_eq, IntermediateField.isPurelyInseparable_sup, mem_adjoin_of_smul_prime_smul_of_minpoly_isEisensteinAt, SimpleGraph.lapMatrix_toLinearMapâ'_apply'_eq_zero_iff_forall_adj, Rat.ringOfIntegersWithValEquiv_apply, IntermediateField.splits_of_splits, MDifferentiableOn.clm_bundle_applyâ, ClassGroup.equiv_mk, RootPairing.orthogonal_rootSpan_eq, ArchimedeanClass.FiniteElement.ext_iff, WeierstrassCurve.Jacobian.nonsingular_iff_of_Z_ne_zero, ContinuousLinearMap.innerSL_apply_comp, Algebra.IsSeparable.of_integral, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, Matrix.mulVec_injective_iff_isUnit, ContinuousLinearMap.coeFn_holder, RatFunc.intDegree_zero, FractionalIdeal.extendedHomâ_le_one_iff, AdjoinRoot.powerBasis_gen, ContMDiff.cle_arrowCongr, WeierstrassCurve.HasMultiplicativeReduction.multiplicativeReduction, IsDedekindDomain.selmerGroup.valuation_ker_eq, IsAlgClosed.exists_aeval_eq_zero, ContMDiffOn.clm_bundle_applyâ, LinearMap.adjoint_id, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, FiniteField.finrank_extension, Matrix.linearIndependent_rows_iff_isUnit, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, Quaternion.re_nnratCast, FDRep.simple_iff_char_is_norm_one, FractionalIdeal.finprod_heightOneSpectrum_factorization', IsPurelyInseparable.algebraMap_iterateFrobeniusââ, AlgebraicGeometry.geometrically_iff_of_isClosedUnderIsomorphisms, Subspace.dualPairing_eq, WeierstrassCurve.ofJ_1728_of_three_eq_zero, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_mul_XYIdeal, Matrix.PosDef.inv, NumberField.InfinitePlace.unramifedPlacesOver_ncard_add_eq_finrank, Polynomial.map_normalize, WeierstrassCurve.Projective.addU_of_Z_eq_zero_right, ContMDiff.coordChangeL, IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow', RatFunc.eval_algebraMap, Hyperreal.infiniteNeg_add_not_infinite, IsCyclotomicExtension.autEquivPow_apply, IsPurelyInseparable.elemExponent_def, IsCyclotomicExtension.discr_prime_pow, WeierstrassCurve.Jacobian.add_of_Y_ne, separableClosure.isPurelyInseparable, ContinuousLinearMap.orthogonal_ker, WeierstrassCurve.Projective.negDblY_of_Y_eq, FixedPoints.minpoly.of_evalâ, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, Hyperreal.epsilon_pos, LinearMap.BilinForm.apply_dualBasis_right, FunctionField.ringOfIntegers.not_isField, FractionalIdeal.exists_notMem_one_of_ne_bot, Hyperreal.archimedeanClassMk_epsilon_pos, AlgebraicGeometry.pointOfClosedPoint_comp, IntermediateField.finite_of_fg_of_isAlgebraic, minpoly.isIntegrallyClosed_eq_field_fractions', isCyclic_tfae, Algebra.IsAlgebraic.isIntegral, RatFunc.Luroth.generator_spec, LinearMap.IsPositive.conj_adjoint, LinearMap.ker_toContinuousLinearMap, WeierstrassCurve.Projective.nonsingularLift_negMap, Valued.integer.norm_irreducible_pos, Lagrange.nodalWeight_eq_eval_derivative_nodal, IntermediateField.adjoin_rootSet_isSplittingField, IntermediateField.nonempty_algHom_adjoin_of_splits, IntermediateField.finSepDegree_bot, Hyperreal.tendsto_atTop_iff, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', AlgebraicGeometry.pullback_of_geometrically, RatFunc.num_denom_neg, ArchimedeanClass.FiniteElement.mk_sub_mk, IsCyclotomicExtension.discr_prime_pow_ne_two', IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, IntermediateField.LinearDisjoint.linearIndependent_left, LinearMap.IsSymmetric.eigenvalues_eq_eigenvalues_iff, perfectClosure.isPurelyInseparable, Polynomial.valuation_X_eq_neg_one, QuadraticForm.sigNeg_of_equiv_weightedSumSquares, IntermediateField.isSeparable_adjoin_iff_isSeparable, Lagrange.eval_basis_not_at_node, FDRep.finrank_hom_simple_simple, AffineSubspace.sOppSide_smul_vsub_vadd_right, prod_galRestrict_eq_norm, Quaternion.imI_ratCast, IsDedekindDomain.HeightOneSpectrum.exists_primeCompl_mul_eq_of_integer, WeierstrassCurve.Affine.Point.map_id, WeierstrassCurve.Projective.equation_of_Z_ne_zero, WeierstrassCurve.Affine.equation_add, RootPairing.baseOf_root_eq_baseOf_coroot, LieAlgebra.engel_isBot_of_isMin, autEquivRootsOfUnity_smul, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff, LinearMap.IsSymmetric.eigenvectorBasis_def, KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk_symm_apply_eq_span, LinearMap.dualAnnihilator_ker_eq_range_flip, Matrix.rank_self_mul_transpose, LinearIsometry.adjoint_comp_self, IsPurelyInseparable.tower_top
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