Documentation Verification Report

Nat

📁 Source: Mathlib/Algebra/GroupWithZero/Nat.lean

Statistics

Metric	Count
Definitions `instCommMonoidWithZero`, `instMonoidWithZero`, `instMulZeroClass`, `instMulZeroOneClass`, `instSemigroupWithZero`	5
Theorems `instIsCancelMulZero`, `instMulDivCancelClass`	2
Total	7

Nat

Definitions

Name	Category	Theorems
`instCommMonoidWithZero` 📖	CompOp	76 math math: `squarefree_and_prime_pow_iff_prime`, `Primes.prodNatEquiv_symm_apply`, `Ideal.absNorm_span_insert`, `factors_multiset_prod_of_irreducible`, `Cardinal.isPrimePow_iff`, `Pi.addOrderOf`, `IsPrimePow.dvd`, `FiniteField.isPrimePow_card`, `DihedralGroup.exponent`, `isPrimePow_iff_card_primeFactors_eq_one`, `two_le_radical_iff`, `prime_iff`, `Monoid.exponent_pi`, `isPrimePow_iff_factorization_eq_single`, `radical_pos`, `irreducible_iff_prime`, `isPrimePow_nat_iff`, `radical_eq_prod_primeFactors`, `Chebyshev.sum_PrimePow_eq_sum_sum`, `Prime.prime`, `Primes.prodNatEquiv_apply`, `disjoint_divisors_filter_isPrimePow`, `isPrimePow_nat_iff_bounded`, `gcd_eq_nat_gcd`, `AddMonoid.exponent_pi`, `Function.minimalPeriod_piMap_fintype`, `dvdNotUnit_setGcd_insert`, `AddMonoid.exponent_prod`, `instUniqueFactorizationMonoid`, `Int.radical_natCast`, `ArithmeticFunction.vonMangoldt_pos_iff`, `Monoid.lcm_orderOf_eq_exponent`, `Monoid.lcm_orderOf_dvd_exponent`, `Fintype.isPrimePow_card_of_field`, `isPrimePow_of_minFac_pow_factorization_eq`, `Equiv.Perm.lcm_cycleType`, `ArithmeticFunction.vonMangoldt_ne_zero_iff`, `isPrimePow_nat_iff_bounded_log`, `Fintype.nonempty_field_iff`, `factors_eq`, `radical_le_self_iff`, `Finset.lcm_eq_prod`, `sum_divisors_filter_squarefree`, `UnitAddCircle.mem_approxAddOrderOf_iff`, `Pi.orderOf`, `Primes.coe_prodNatEquiv_apply`, `ArithmeticFunction.carmichael_finset_lcm`, `ArithmeticFunction.cardDistinctFactors_eq_one_iff`, `Monoid.exponent_prod`, `isPrimePow_iff_unique_prime_dvd`, `exists_ordCompl_eq_one_iff_isPrimePow`, `lcm_eq_nat_lcm`, `ArithmeticFunction.carmichael_finset_prod`, `ArithmeticFunction.vonMangoldt_apply`, `instWfDvdMonoid`, `UniqueFactorizationMonoid.primeFactors_eq_natPrimeFactors`, `Prime.isPrimePow`, `AddMonoid.lcm_addOrderOf_eq_exponent`, `UnitAddCircle.mem_addWellApproximable_iff`, `ArithmeticFunction.vonMangoldt_eq_zero_iff`, `self_lt_radical_iff`, `isPrimePow_nat_iff_bounded_log_minFac`, `one_lt_radical_iff`, `ArithmeticFunction.carmichael_factorization`, `moebius_eq`, `Int.radical_natAbs_eq_radical`, `divisors_filter_squarefree`, `isPrimePow_pow_iff`, `radical_eq_one_iff`, `AddMonoid.lcm_addOrderOf_dvd_exponent`, `radical_le_one_iff`, `not_isPrimePow_iff_nontrivial_of_two_le`, `mul_divisors_filter_prime_pow`, `QuaternionGroup.exponent`, `isPrimePow_iff_minFac_pow_factorization_eq`, `charP_zero_or_prime_power`
`instMonoidWithZero` 📖	CompOp	28 math math: `DivisibleHull.archimedeanClassMk_mk_eq`, `DivisibleHull.mk_add_mk_left`, `DivisibleHull.instIsStrictOrderedModuleNNRat`, `PNat.equivNonZeroDivisorsNat_symm_apply_coe`, `DivisibleHull.coeAddMonoidHom_apply`, `DivisibleHull.instIsOrderedCancelAddMonoid`, `ArithmeticFunction.isMultiplicative_zeta`, `DivisibleHull.qsmul_def`, `ArithmeticFunction.isMultiplicative_pow`, `DivisibleHull.qsmul_of_nonneg`, `DivisibleHull.coeOrderAddMonoidHom_apply`, `DivisibleHull.nsmul_mk`, `ArithmeticFunction.isMultiplicative_sigma`, `MvPowerSeries.map_iterateFrobenius_expand`, `PNat.equivNonZeroDivisorsNat_apply_coe`, `DivisibleHull.mk_add_mk`, `DivisibleHull.archimedeanClassOrderIso_apply`, `DivisibleHull.zsmul_mk`, `DivisibleHull.neg_mk`, `DivisibleHull.qsmul_of_nonpos`, `DivisibleHull.archimedeanClassOrderIso_symm_apply`, `ArithmeticFunction.isMultiplicative_id`, `DivisibleHull.instIsStrictOrderedModuleRat`, `DivisibleHull.coe_add`, `DivisibleHull.mk_zero`, `DivisibleHull.zero_qsmul`, `instMulDivCancelClass`, `DivisibleHull.nnqsmul_mk`
`instMulZeroClass` 📖	CompOp	2426 math math: `Finset.map_nsmul_piAntidiag_univ`, `MvPolynomial.is_id`, `Finsupp.image_prodMap_embDomain_antidiagonal`, `MvPolynomial.pUnitAlgEquiv_symm_monomial`, `MvPowerSeries.coeff_zero_eq_constantCoeff_apply`, `MvPolynomial.funext_iff`, `MvPolynomial.eval_indicator_apply_eq_one`, `Height.logHeight_eval_ge`, `MvPolynomial.join₁_rename`, `MvPolynomial.vanishingIdeal_anti_mono`, `MvPolynomial.eval₂_mul_eq_zero_of_left`, `AlgebraicGeometry.AffineSpace.map_Spec_map`, `MvPolynomial.aeval_sum`, `Finsupp.sum_toMultiset`, `MvPolynomial.dvd_monomial_one_iff_exists`, `WittVector.bind₁_frobeniusPoly_wittPolynomial`, `MonomialOrder.le_degree_of_mem_support`, `Num.minFac_to_nat`, `LSeries.convolution_one_eq_convolution_zeta`, `Finsupp.finite_of_degree_le`, `IsAlgClosed.roots_eq_zero_iff_degree_nonpos`, `KaehlerDifferential.mvPolynomialBasis_apply`, `MvPowerSeries.WithPiTopology.tendsto_trunc_atTop`, `MvPolynomial.coeff_neg`, `MvPolynomial.support_sum`, `FirstOrder.Language.presburger.mul_not_definable`, `MonomialOrder.sPolynomial_leadingTerm_mul'`, `MvPolynomial.degrees_neg`, `ofDigits_eq_sum_mapIdx_aux`, `MvPolynomial.coe_C`, `Algebra.PreSubmersivePresentation.jacobiMatrix_naive`, `MvPolynomial.isJacobsonRing`, `MvPowerSeries.coeff_zero_eq_constantCoeff`, `MvPolynomial.support_mul`, `MvPolynomial.algHom_ext_iff`, `MonomialOrder.span_leadingTerm_sdiff_singleton_zero`, `MvPolynomial.map_bind₁`, `HahnSeries.instNoZeroDivisorsFinsuppNat`, `DFinsupp.toMultiset_sup`, `MvPolynomial.vars_sum_of_disjoint`, `MvPolynomial.totalDegree_monomial`, `Algebra.Generators.aeval_val_surjective`, `AlgebraicGeometry.AffineSpace.map_toSpecMvPoly_assoc`, `MvPolynomial.mul_X_divMonomial`, `ArithmeticFunction.sigma_pos`, `CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd`, `IsIsotypic.linearEquiv_fun`, `MvPolynomial.radical_le_vanishingIdeal_zeroLocus`, `wittPolynomial_zmod_self`, `coe_properDivisors_eq_prod_pow_lt_factorization`, `MvPolynomial.aeval_X_left`, `Prime.exists_orderOf_eq_pow_factorization_exponent`, `MvPolynomial.map_mapRange_eq_iff`, `MvPolynomial.map_comp_C`, `MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum`, `MvPolynomial.coeffs_add`, `MvPowerSeries.eq_iff_frequently_trunc'_eq`, `MvPolynomial.pUnitAlgEquiv_apply`, `Primes.prodNatEquiv_symm_apply`, `multiplicity_eq_factorization`, `MvPolynomial.eval₂Hom_X`, `factorization_eq_zero_of_not_dvd`, `MvPolynomial.toMvPowerSeries_uniformContinuous`, `MvPolynomial.exists_finset_rename`, `MonomialOrder.monic_X_sub_C`, `MvPolynomial.hom_C`, `IsPrimePow.exists_ordCompl_eq_one`, `AlgebraicIndependent.of_aeval`, `MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_same`, `EisensteinSeries.hasSum_e2Summand_symmetricIcc`, `MvPowerSeries.truncFinset_one`, `Polynomial.homogenize_map`, `MvPowerSeries.trunc'_trunc'`, `MvPolynomial.support_finSuccEquiv`, `Algebra.PreSubmersivePresentation.cotangentComplexAux_apply`, `MvPolynomial.rTensor_apply_tmul_apply`, `MvPolynomial.degrees_monomial`, `Submonoid.exists_finsupp_of_mem_closure_range`, `Prime.factorization_pos_of_dvd`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv`, `MvPolynomial.zero_divMonomial`, `Ideal.mem_span_iff_exists_isHomogeneous`, `MvPolynomial.coeff_divMonomial`, `WittVector.aeval_verschiebung_poly'`, `MonomialOrder.degree_add_of_ne`, `MvPolynomial.sum_def`, `MvPolynomial.rTensorAlgEquiv_apply`, `MvPolynomial.one_def`, `Algebra.Generators.H1Cotangent.δAux_mul`, `MvPowerSeries.coeff_mul_monomial`, `Algebra.Presentation.naive_toGenerators`, `Multiset.toFinsupp_add`, `MvPolynomial.mem_image_support_coeff_finSuccEquiv`, `MvPolynomial.mapEquiv_symm`, `Finsupp.toMultiset_strictMono`, `MvPolynomial.scalarRTensor_apply_monomial_tmul`, `ArithmeticFunction.cardFactors_pow`, `MvPolynomial.comapEquiv_symm_coe`, `MvPolynomial.homogeneousComponent_eq_zero'`, `WeierstrassCurve.Projective.eval_polynomial`, `factorization_prod_pow_eq_self_of_le_factorization`, `Matrix.charpoly.univ_map_map`, `ordCompl_le`, `MvPolynomial.eval₂_expand`, `MvPolynomial.isOpenMap_comap_C`, `MvPolynomial.weightedDegree_eq_zero_iff`, `MvPolynomial.universalFactorizationMap_comp_map`, `MvPolynomial.aeval_algebraMap_eq_zero_iff`, `MvPowerSeries.support_expand`, `multiplicative_factorization'`, `MonomialOrder.degree_monomial`, `MvPolynomial.coeff_X_mul'`, `IsPrimePow.minFac_pow_factorization_eq`, `factorization_prod_pow_eq_self`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_map`, `MvPolynomial.expand_X`, `Multiset.equivDFinsupp_symm_apply`, `algebraicIndependent_iff_ker_eq_bot`, `factorization_pow`, `MvPolynomial.IsSymmetric.map`, `Ideal.rank_prime_pow_ramificationIdx`, `sub_one_mul_sum_log_div_pow_eq_sub_sum_digits`, `ArithmeticFunction.carmichael_pow_of_prime_ne_two`, `MvPolynomial.derivation_eq_of_forall_mem_vars`, `Algebra.Generators.cotangentSpaceBasis_apply`, `Multiset.toDFinsupp_support`, `MvPolynomial.IsWeightedHomogeneous.pderiv`, `AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply`, `MvPolynomial.instIsReduced`, `MvPolynomial.X_pow_eq_monomial`, `MvPolynomial.isEmptyRingEquiv_apply`, `WittVector.ghostComponent_apply`, `MvPolynomial.ker_map`, `MvPolynomial.map_leftInverse`, `aeval_wittPolynomial`, `AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop`, `ArithmeticFunction.cardFactors_multiset_prod`, `MvPolynomial.aeval_range`, `MvPowerSeries.coeff_pow`, `KaehlerDifferential.mvPolynomialBasis_repr_D_X`, `MvPolynomial.optionEquivLeft_C`, `MvPolynomial.rename_rename`, `MonomialOrder.degree_X`, `MvPolynomial.iterToSum_sumToIter`, `constantCoeff_wittStructureRat`, `Algebra.Generators.toAlgHom_ofComp_localizationAway`, `MvPolynomial.leibniz_iff_X`, `MvPowerSeries.constantCoeff_subst`, `Polynomial.homogenize_smul`, `MvPolynomial.divMonomial_add_modMonomial`, `ArithmeticFunction.zeta_apply`, `MvPowerSeries.trunc'_expand_trunc'`, `AddCommMonCat.free_obj_coe`, `MvPolynomial.optionEquivLeft_X_some`, `MonomialOrder.leadingCoeff_eq_zero_iff`, `MvPolynomial.eval₂Hom_monomial`, `MvPolynomial.homogeneousComponent_of_mem`, `Polynomial.zero_le_degree_iff`, `MvPolynomial.aeval_X_left_apply`, `factorization_le_factorization_mul_left`, `Polynomial.toPowerSeries_toMvPowerSeries`, `MvPolynomial.le_vanishingIdeal_zeroLocus`, `MvPolynomial.homogeneousComponent_mem`, `MvPolynomial.pUnitAlgEquiv_symm_apply`, `MvPowerSeries.coeff_monomial_mul`, `MvPolynomial.expand_eq_zero`, `MvPowerSeries.exists_finsupp_eq_lexOrder_of_ne_zero`, `MvPowerSeries.coeff_X_pow`, `ArithmeticFunction.cardDistinctFactors_apply`, `Multiset.Nat.antidiagonalTuple_zero_right`, `WeierstrassCurve.Jacobian.baseChange_polynomialZ`, `MvPolynomial.support_monomial`, `Algebra.Presentation.localizationAway_relation`, `MvPolynomial.monomial_finsupp_sum_index`, `MvPolynomial.weightedHomogeneousSubmodule_mul`, `Ideal.span_pow_eq_map_homogeneousSubmodule`, `MvPolynomial.coeffs_mul_X`, `MvPolynomial.mul_def`, `MvPolynomial.natDegree_finSuccEquiv`, `Finsupp.prod_toMultiset`, `StandardEtalePresentation.toPresentation_algebra_smul`, `coe_divisors_eq_prod_pow_le_factorization`, `MvPolynomial.totalDegree_X_pow`, `Ideal.span_eq_map_homogeneousSubmodule`, `FirstOrder.Language.presburger.isSemilinearSet_boundedFormula_realize`, `Finsupp.toMultiset_zero`, `MvPolynomial.bind₂_comp_C`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C`, `MvPolynomial.eval₂_zero'_apply`, `MvPolynomial.image_comap_C_basicOpen`, `MvPowerSeries.X_pow_eq`, `MvPolynomial.degreeOf_C`, `WeierstrassCurve.Projective.polynomial_relation`, `Matrix.toMvPolynomial_add`, `LieAlgebra.Basis.borelLower_le_biSup`, `MvPolynomial.mem_support_iff`, `MvPolynomial.mvPolynomialEquivMvPolynomial_symm_apply`, `MvPolynomial.algHom_ext'_iff`, `IntermediateField.mem_adjoin_iff`, `AlgebraicIndependent.repr_ker`, `ArithmeticFunction.cardFactors_apply`, `MonomialOrder.leadingCoeff_mul_of_isRegular_right`, `chevalley_mvPolynomial_mvPolynomial`, `MvPolynomial.mem_range_map_iff_coeffs_subset`, `MvPolynomial.notMem_support_iff`, `MvPolynomial.aeval_X`, `MvPolynomial.comapEquiv_coe`, `MvPolynomial.vars_sub_of_disjoint`, `MvPolynomial.exists_dvd_map_of_isAlgebraic`, `Num.gcd_to_nat_aux`, `ofDigits_one`, `Polynomial.pUnitAlgEquiv_symm_toPowerSeries`, `MvPolynomial.scalarRTensor_apply_X_tmul_apply`, `factorization_eq_of_coprime_right`, `Num.of_to_nat'`, `Num.div_to_nat`, `factorization_mul_apply_of_coprime`, `Num.sub_to_nat`, `Num.succ'_to_nat`, `sub_one_mul_padicValNat_factorial`, `MvPowerSeries.ext_trunc'`, `MvPolynomial.smul_monomial`, `MvPolynomial.eval₂_pow`, `MvPolynomial.irreducible_mul_X_add`, `AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin`, `MvPowerSeries.LinearTopology.basis_le_iff`, `MonomialOrder.leadingCoeff_mul`, `MonomialOrder.degree_sub_le`, `prod_pow_pos_of_zero_notMem_support`, `Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff`, `AnalyticOnNhd.eval_linearMap'`, `ordCompl_dvd_ordCompl_iff_dvd`, `MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same`, `Sym.coe_equivNatSum_apply_apply`, `Num.toNat_injective`, `MvPolynomial.optionEquivLeft_apply`, `MvPolynomial.instIsScalarTower`, `MvPolynomial.bind₂_C_left`, `MvPolynomial.totalDegree_coeff_finSuccEquiv_add_le`, `Ideal.Factors.fact_ramificationIdx_neZero`, `Multiset.Icc_eq`, `MvPolynomial.map_comp_rename`, `Monoid.neZero_exponent_of_finite`, `MvPolynomial.ACounit_X`, `WittVector.mul_polyOfInterest_aux2`, `MvPolynomial.prime_rename_iff`, `ordProj_of_not_prime`, `Polynomial.eval_eq_div_eval_toTupleMvPolynomial`, `bind₁_xInTermsOfW_wittPolynomial`, `ArithmeticFunction.cardDistinctFactors_apply_prime_pow`, `WeierstrassCurve.Jacobian.eval_polynomialY`, `WithBot.add_eq_two_iff`, `MvPowerSeries.min_lexOrder_le`, `MvPolynomial.constantCoeff_rename`, `MvPolynomial.eval₂_prod`, `Algebra.PreSubmersivePresentation.jacobiMatrix_reindex`, `MvPolynomial.map_bind₂`, `Num.castNum_eq_bitwise`, `Finsupp.add_sub_single_one`, `MvPolynomial.iterToSum_C_X`, `AlgebraicClosure.maxIdeal.isMaximal`, `MvPolynomial.map_eval₂`, `pow_succ_factorization_not_dvd`, `MvPolynomial.eval_map`, `sum_le_ofDigits`, `CommRingCat.free_map_coe`, `Algebra.FinitePresentation.mvPolynomial_of_finitePresentation`, `Algebra.SubmersivePresentation.ofSubsingleton_algebra_algebraMap`, `modEq_digits_sum`, `MvPolynomial.killCompl_comp_rename`, `MvPolynomial.map_eval₂Hom`, `MvPolynomial.supportedEquivMvPolynomial_symm_X`, `Finsupp.Lex.single_strictAnti`, `MvPolynomial.pderiv_one`, `MvPolynomial.mkDerivation_X`, `MvPolynomial.pderiv_mul`, `Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp`, `Prime.factorization_pow`, `char_dvd_card_solutions_of_add_lt`, `MvPolynomial.comp_eval₂Hom`, `ArithmeticFunction.LSeries_zeta_mul_Lseries_moebius`, `MvPolynomial.ACounit_surjective`, `MvPolynomial.supported_eq_adjoin_X`, `MonomialOrder.degree_lt_iff`, `MvPolynomial.eval₂_zero`, `Polynomial.degree_list_prod`, `MvPolynomial.degreeOf_mul_le`, `MvPolynomial.degreeOf_sum_le`, `MvPolynomial.aeval_eq_eval`, `MvPolynomial.supDegree_esymmAlgHomMonomial`, `AddSubmonoid.mem_closure_range_iff`, `MvPolynomial.schwartz_zippel_totalDegree`, `ArithmeticFunction.sigma_apply`, `MvPolynomial.aeval_ite_mem_eq_self`, `MvPolynomial.support_sdiff_support_subset_support_add`, `Algebra.SubmersivePresentation.map_jacobianOfHasCoeffs`, `AddSubmonoid.exists_finsupp_of_mem_closure_range`, `FormalMultilinearSeries.id_apply_one'`, `MvPolynomial.IsWeightedHomogeneous.mul`, `MvPolynomial.eval₂Hom_C_id_eq_join₁`, `ArithmeticFunction.abscissaOfAbsConv_zeta`, `Finsupp.toMultiset_toFinsupp`, `MvPolynomial.eval_mem`, `PolynomialLaw.exists_lift'`, `ax_grothendieck_of_definable`, `Algebra.Generators.algebraMap_surjective`, `Partition.toFinsuppAntidiag_mem_finsuppAntidiag`, `MeasureTheory.upcrossingsBefore_zero'`, `MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt`, `MvPolynomial.pow_idealOfVars`, `MvPolynomial.join₂_comp_map`, `MvPolynomial.idealOfVars_eq_restrictSupportIdeal`, `PolynomialLaw.toFun_eq_rTensor_φ_toFun'`, `MvPolynomial.comap_id`, `Height.logHeight_eval_ge'`, `MvPolynomial.eval_rename_prod_mk`, `ArithmeticFunction.cardDistinctFactors_apply_prime`, `MvPolynomial.optionEquivRight_C`, `sub_one_mul_padicValNat_choose_eq_sub_sum_digits`, `MvPolynomial.monomial_zero`, `MvPolynomial.map_mvPolynomial_eq_eval₂`, `ZNum.gcd_to_nat`, `Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial`, `MonomialOrder.degree_reduce_lt`, `MvPolynomial.eval_eval₂`, `MvPolynomial.aevalTower_comp_C`, `MvPolynomial.totalDegree_eq`, `ArithmeticFunction.sigma_one_apply_prime_pow`, `MvPolynomial.rename_msymm`, `MvPolynomial.comap_comp_apply`, `MvPolynomial.eval₂_id`, `factorization_factorial`, `MvPolynomial.eval₂Hom_C_eq_bind₁`, `MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zero`, `MvPolynomial.X_mul_cancel_right_iff`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_relation`, `AddCommMonCat.free_map`, `MvPolynomial.degreeOf_coeff_finSuccEquiv`, `Multiset.toFinsupp_sum_eq`, `MvPolynomial.mem_pow_idealOfVars_iff`, `Multiset.toDFinsupp_apply`, `MvPolynomial.X_prime`, `minpoly.degree_pos`, `MvPolynomial.rename_id_apply`, `IsIsotypic.submodule_linearEquiv_fun`, `MvPolynomial.constantCoeff_C`, `MvPowerSeries.trunc_C`, `MvPolynomial.map_map`, `MvPolynomial.support_eq_empty`, `MonomialOrder.degree_mem_support_iff`, `List.sum_take_map_length_splitWrtComposition`, `Finset.map_nsmul_piAntidiag`, `Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg`, `MvPolynomial.eval₂Hom_comp_bind₂`, `ordCompl_div_of_dvd`, `MvPolynomial.degrees_def`, `MvPolynomial.coe_one`, `MvPolynomial.nonempty_support_finSuccEquiv`, `Polynomial.degree_list_prod_le`, `Algebra.Generators.cotangentSpaceBasis_repr_one_tmul`, `MvPolynomial.mvPolynomialEquivMvPolynomial_apply`, `MvPolynomial.pderiv_rename`, `Algebra.Presentation.comp_relation_inr`, `ofDigits_eq_sum_mapIdx`, `MvPolynomial.monomial_eq_monomial_iff`, `MvPolynomial.mem_vars`, `MonomialOrder.toSyn_strictMono`, `MvPowerSeries.coeff_X`, `LinearMap.nilRankAux_basis_indep`, `MonomialOrder.leadingTerm_zero`, `MvPolynomial.eval₂_mul_monomial`, `MvPolynomial.weightedHomogeneousComponent_zero`, `MvPolynomial.support_killCompl`, `AlgebraicIndependent.aeval_comp_repr`, `IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite`, `MonomialOrder.div_single`, `MvPolynomial.esymmAlgHomMonomial_single`, `MvPolynomial.homogeneousComponent_C_mul`, `MvPolynomial.IsHomogeneous.map`, `PowerSeries.support_expand_subset`, `MvPolynomial.map_expand`, `MonomialOrder.image_leadingTerm_sdiff_singleton_zero`, `Finsupp.card_toMultiset`, `RootPairing.Base.exists_root_eq_sum_nat_or_neg`, `MvPolynomial.map_aeval`, `MvPolynomial.instFree`, `Sym.coe_equivNatSum_symm_apply`, `MvPolynomial.map_frobenius_expand`, `MvPolynomial.coeffs_one`, `MvPolynomial.renameEquiv_trans`, `MvPolynomial.weightedDecomposition.decompose'_apply`, `Height.logHeight_eval_le'`, `FirstOrder.Ring.lift_genericPolyMap`, `ordCompl_dvd_ordCompl_of_dvd`, `MvPolynomial.coeffs_one_of_nontrivial`, `MvPolynomial.expand_monomial`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord`, `MvPolynomial.expand_char`, `MvPolynomial.monomial_mul_mem_coeffsIn`, `MvPolynomial.eval₂Hom_congr`, `Polynomial.degree_pos_of_root`, `WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero`, `MvPolynomial.map_rename`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc`, `MvPowerSeries.hasSum_aeval`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_σ'`, `MvPolynomial.killCompl_C`, `Algebra.Presentation.quotientEquiv_symm`, `MvPolynomial.eval₂_const_pUnitAlgEquiv_symm`, `MvPowerSeries.coeff_truncFinset_of_mem`, `MvPolynomial.eval_comp_toMvPolynomial`, `Algebra.Generators.H1Cotangent.δAux_C`, `Algebra.Generators.map_toComp_ker`, `MvPolynomial.support_finSuccEquiv_nonempty`, `Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply`, `MvPolynomial.eval₂_sum`, `PowerSeries.support_expand`, `MvPolynomial.bind₁_X_left`, `HahnSeries.toMvPowerSeries_symm_apply_coeff`, `MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero`, `three_dvd_iff`, `MvPolynomial.sumAlgEquiv_comp_rename_inr`, `factorization_mul`, `MvPolynomial.aevalTower_toAlgHom`, `Algebra.Generators.ofComp_val`, `instIsCancelMulZero`, `MvPolynomial.coe_eq_one_iff`, `Algebra.Presentation.map_relationOfHasCoeffs`, `LinearMap.polyCharpoly_coeff_isHomogeneous`, `isPrimePow_iff_factorization_eq_single`, `MvPolynomial.eval₂_map`, `MvPolynomial.X_mul_pderiv_monomial`, `MvPowerSeries.lexOrder_def_of_ne_zero`, `MonomialOrder.degree_add_le`, `MvPolynomial.degree_optionEquivLeft`, `MvPolynomial.mapAlgHom_id`, `Algebra.Generators.naive_val`, `MvPowerSeries.coeff_index_single_X`, `Num.castNum_shiftRight`, `MonomialOrder.leadingCoeff_prod_of_regular`, `MvPowerSeries.LinearTopology.mem_basis_iff`, `MvPowerSeries.subst_monomial`, `MvPolynomial.totalDegree_list_prod`, `Multiset.equivDFinsupp_apply`, `MvPolynomial.coeff_expand_smul`, `Algebra.Generators.algebraMap_apply`, `MvPolynomial.map_esymm`, `MvPolynomial.weightedHomogeneousComponent_eq_zero'`, `factorization_eq_card_pow_dvd_of_lt`, `MvPolynomial.IsHomogeneous.add`, `MvPolynomial.coe_eq_zero_iff`, `ArithmeticFunction.sigma_zero_apply`, `DFinsupp.toMultiset_single`, `MvPolynomial.expand_C`, `MvPowerSeries.trunc'_trunc'_pow`, `factorization_mul`, `MonomialOrder.eq_C_of_degree_eq_zero`, `MvPowerSeries.coeff_embDomain_rename`, `Polynomial.finsuppSum_homogenize_eq`, `instIsIntegralMvPolynomial`, `MvPolynomial.derivation_eq_zero_of_forall_mem_vars`, `MvPolynomial.coeffs_C`, `LieAlgebra.Basis.borelUpper_eq`, `Algebra.Generators.compLocalizationAwayAlgHom_X_inl`, `MvPolynomial.optionEquivRight_X_none`, `MvPolynomial.homogeneousComponent_isHomogeneous`, `MvPolynomial.rename_psum`, `Num.size_to_nat`, `Algebra.Generators.map_ofComp_ker`, `Finsupp.toMultiset_apply`, `MvPowerSeries.lexOrder_mul`, `ArithmeticFunction.cardDistinctFactors_eq_zero`, `WeierstrassCurve.Jacobian.polynomialY_eq`, `MvPolynomial.sum_homogeneousComponent`, `MvPolynomial.expand_zero`, `Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos`, `MvPolynomial.support_add`, `MonomialOrder.sPolynomial_self`, `MvPolynomial.degreesLE_nsmul`, `MvPolynomial.coe_monomial`, `ArithmeticFunction.IsMultiplicative.multiplicative_factorization`, `WeierstrassCurve.Jacobian.eval_polynomialX`, `MvPowerSeries.X_def`, `MvPolynomial.totalDegree_rename_le`, `MvPolynomial.C_apply`, `MonomialOrder.leadingCoeff_mul_of_right_mem_nonZeroDivisors`, `MvPolynomial.coe_mapEquivMonic_comp'`, `Algebra.Presentation.naive_relation`, `Finsupp.DegLex.single_lt_iff`, `sub_one_mul_padicValNat_choose_eq_sub_sum_digits'`, `WeierstrassCurve.Projective.eval_polynomialX`, `WeierstrassCurve.Projective.baseChange_polynomial`, `ordProj_dvd_ordProj_iff_dvd`, `Matrix.toMvPolynomial_map`, `MvPolynomial.single_eq_monomial`, `Polynomial.toMvPolynomial_eq_rename_comp`, `MvPowerSeries.trunc_one`, `DividedPowerAlgebra.dp_mul`, `MonomialOrder.le_degree`, `Polynomial.aeval_homogenize_X_one`, `MvPolynomial.adjoin_range_X`, `MvPolynomial.mul_X_mem_coeffsIn`, `ChevalleyThm.chevalley_mvPolynomialC`, `MvPolynomial.coeff_C`, `WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero`, `MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure`, `AddMonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure`, `MvPolynomial.bind₂_map`, `Finset.Nat.antidiagonalTuple_zero_right`, `MvPolynomial.totalDegree_mul_of_isDomain`, `Num.castNum_xor`, `exists_factorization_lt_of_lt`, `ArithmeticFunction.moebius_apply_of_squarefree`, `Finsupp.antidiagonal_single`, `MvPolynomial.X_dvd_X`, `MvPolynomial.transcendental_polynomial_aeval_X_iff`, `MvPolynomial.aeval_algebraMap_eq_zero_iff_of_injective`, `MvPolynomial.eval₂_neg`, `MvPolynomial.coeff_X`, `Algebra.Generators.algebraMap_eq`, `constantCoeff_wittStructureInt`, `Algebra.SubmersivePresentation.ofSubsingleton_relation`, `Finsupp.sub_add_single_one_cancel`, `StandardEtalePair.equivMvPolynomialQuotient_symm_apply`, `MonomialOrder.leadingTerm_monomial`, `MvPolynomial.X_mul_mem_coeffsIn`, `ordCompl_pow_mul_eq_self_iff`, `MvPolynomial.support_rename_of_injective`, `Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomial`, `MvPolynomial.comap_comp`, `MvPowerSeries.monomial_def`, `MvPolynomial.eval_ofNat`, `MonomialOrder.degree_mul_leadingTerm`, `Polynomial.abs_tendsto_atTop_iff`, `xInTermsOfW_eq`, `LinearMap.nilRank_eq_polyCharpoly_natTrailingDegree`, `MvPolynomial.eval_eq_eval_mv_eval'`, `factorization_eq_one_of_squarefree`, `MvPolynomial.IsHomogeneous.degree_eq_sum_deg_support`, `MvPolynomial.degrees_map_of_injective`, `MvPolynomial.ACounit_C`, `LinearMap.polyCharpoly_baseChange`, `MvPolynomial.eq_zero_of_eval_eq_zero`, `MvPolynomial.transcendental_supported_X_iff`, `Polynomial.homogenize_add`, `factorization_choose_prime_pow_add_factorization`, `MvPolynomial.vanishingIdeal_pointToPoint`, `MvPolynomial.optionEquivLeft_X_none`, `MvPowerSeries.coeff_trunc'_mul_trunc'_eq_coeff_mul`, `MvPolynomial.algebraicIndependent_polynomial_aeval_X`, `MvPowerSeries.le_lexOrder_iff`, `MvPowerSeries.expand_one_apply`, `MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring`, `MvPolynomial.degreeOf_rename_of_injective`, `MvPolynomial.degreesLE_add`, `MvPolynomial.exists_rename_eq_of_vars_subset_range`, `MonomialOrder.span_leadingTerm_eq_span_monomial`, `MvPolynomial.optionEquivRight_symm_apply`, `factorization_prod_apply`, `TensorPower.algebraMap₀_one`, `MvPolynomial.instIsPrimeVanishingIdealSingletonForallSet`, `MvPolynomial.eval₂Hom_zero_apply`, `Multiset.toFinsupp_union`, `MonomialOrder.span_leadingTerm_eq_span_monomial₀`, `Polynomial.degree_C`, `MvPolynomial.scalarRTensor_apply_tmul`, `MvPolynomial.degrees_C`, `MonomialOrder.degree_neg`, `properDivisors_eq_image_Iio_factorization_prod_pow`, `Real.log_nat_eq_sum_factorization`, `WeierstrassCurve.Jacobian.polynomial_relation`, `PowerSeries.expand_one_apply`, `LinearMap.polyCharpolyAux_map_eval`, `MvPolynomial.eval_prod`, `LinearMap.polyCharpoly_coeff_eq_zero_of_basis`, `MvPolynomial.C_mul_X_eq_monomial`, `Algebra.Generators.Hom.aeval_val`, `ArithmeticFunction.two_mul_carmichael_two_pow_of_three_le_eq_totient`, `Polynomial.MonicDegreeEq.freeMonic_coe`, `NumberField.Units.instNeZeroNatTorsionOrder`, `MvPowerSeries.coeff_index_single_self_X`, `DividedPowerAlgebra.natFactorial_mul_dp_eq`, `MvPolynomial.degreeOf_mul_eq`, `Algebra.Presentation.comp_aeval_relation_inl`, `MvPowerSeries.WithPiTopology.as_tsum`, `MvPolynomial.degreeOf_le_iff`, `MvPolynomial.C_0`, `WittVector.mulN_coeff`, `OrderedSemiring.toPosSMulMonoNat`, `MvPolynomial.bind₂_monomial`, `MvPolynomial.isUnit_iff_totalDegree_of_isReduced`, `MvPolynomial.totalDegree_finset_prod`, `MvPolynomial.monomialOneHom_apply`, `MvPolynomial.leadingCoeff_esymmAlgHomMonomial`, `factorization_one_right`, `Algebra.SubmersivePresentation.jacobianRelations_spec`, `MvPolynomial.pderiv_sumToIter`, `MvPolynomial.coeff_homogeneousComponent`, `MvPolynomial.support_expand_subset`, `ModEq.listSum_map`, `MonomialOrder.coeff_prod_sum_degree`, `MvPolynomial.totalDegree_C`, `LinearMap.toMvPolynomial_add`, `WeierstrassCurve.Projective.polynomialZ_eq`, `MonomialOrder.lex_lt_iff_of_unique`, `MvPolynomial.IsSymmetric.one`, `Num.to_of_nat`, `tsum_pow_div_one_sub_eq_tsum_sigma`, `Matrix.charpoly.univ_monic`, `MvPolynomial.totalDegree_pow`, `MvPolynomial.coeff_rename_embDomain`, `MvPolynomial.isUnit_iff`, `MvPolynomial.monomial_left_inj`, `Num.castNum_shiftLeft`, `MvPolynomial.X_dvd_monomial`, `MvPolynomial.coe_zero`, `MonomialOrder.degLex_le_iff`, `ArithmeticFunction.sigma_apply_prime_pow`, `TensorProduct.toIntegralClosure_mvPolynomial_bijective`, `MvPolynomial.finSuccEquiv_coeff_coeff`, `MvPolynomial.rename_comp_expand`, `Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix`, `Algebra.PreSubmersivePresentation.jacobiMatrix_apply`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C'`, `MvPowerSeries.monomial_zero_eq_C`, `Finsupp.multinomial_of_support_subset`, `MvPowerSeries.coeff_inv`, `MvPolynomial.coeff_C_mul`, `MvPolynomial.rename_esymm`, `MvPolynomial.IsHomogeneous.sub`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply`, `MvPolynomial.quotient_map_C_eq_zero`, `MvPolynomial.iterToSum_X`, `MvPolynomial.coeff_X_pow`, `MvPolynomial.C_mul_monomial`, `nine_dvd_iff`, `Algebra.Generators.H1Cotangent.δAux_monomial`, `MvPolynomial.vars_monomial`, `MvPolynomial.pow_idealOfVars_eq_span`, `ordProj_mul_ordCompl_eq_self`, `AnalyticOnNhd.eval_linearMap`, `MvPolynomial.IsHomogeneous.pow`, `pairwise_coprime_pow_primeFactors_factorization`, `MvPolynomial.IsWeightedHomogeneous.sum`, `Algebra.Generators.toAlgHom_ofComp_surjective`, `Num.of_to_nat`, `MvPolynomial.bind₁_comp_bind₁`, `MvPolynomial.commAlgEquiv_C`, `MvPolynomial.coeff_zero_C`, `ArithmeticFunction.LSeries_zeta_eq`, `Algebra.Generators.Hom.algebraMap_toAlgHom'`, `Algebra.FinitePresentation.ker_fg_of_mvPolynomial`, `Algebra.Generators.cotangentSpaceBasis_repr_tmul`, `MonomialOrder.monic_X_add_C`, `MvPolynomial.aevalTower_X`, `MvPolynomial.vars_sub_subset`, `MvPolynomial.bind₂_monomial_one`, `MvPolynomial.irreducible_of_forall_totalDegree_le`, `MvPolynomial.mem_support_notMem_vars_zero`, `MvPolynomial.commAlgEquiv_X`, `ArithmeticFunction.pow_carmichael`, `MvPolynomial.mapEquiv_apply`, `MvPolynomial.eval₂Hom_congr'`, `Matrix.charpoly.univ_coeff_eval₂Hom`, `ArithmeticFunction.cardFactors_pos_iff_one_lt`, `Polynomial.ofFinsupp_eq_one`, `Multiset.toFinsupp_inter`, `MvPolynomial.optionEquivRight_X_some`, `MonomialOrder.degree_le_iff`, `MvPolynomial.aeval_expand`, `AlgebraicIndependent.lift_reprField`, `MvPolynomial.instCharZero`, `CompositionAsSet.blocks_partial_sum`, `MvPolynomial.aeval_algebraMap_apply`, `ArithmeticFunction.zeta_mul_pow_eq_sigma`, `MvPolynomial.C_1`, `Real.logb_nat_eq_sum_factorization`, `MvPolynomial.eval₂Hom_X'`, `IsNonarchimedean.eval_mvPolynomial_le`, `MvPolynomial.eval₂_one`, `MvPolynomial.rTensor_apply_X_tmul`, `Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs`, `Algebra.SubmersivePresentation.linearIndependent_aeval_val_pderiv_relation`, `wittPolynomial_one`, `MvPolynomial.pderiv_X`, `Algebra.FiniteType.baseChangeAux_surj`, `MvPolynomial.eval₂_mul_eq_zero_of_right`, `isSumSq`, `MvPolynomial.eval_eq'`, `MvPolynomial.uniqueFactorizationMonoid`, `MvPolynomial.restrictSupport_univ`, `instPosSMulMonoNatOfIsOrderedAddMonoid`, `Finsupp.exists_le_degree_eq`, `Algebra.Generators.H1Cotangent.δAux_toAlgHom`, `MvPolynomial.eval₂_C`, `PosNum.pred'_to_nat`, `Subalgebra.mvPolynomial_aeval_coe`, `factorization_choose_le_one`, `IsLocalization.Away.mvPolynomialQuotientEquiv_apply`, `Prime.factorization`, `ArithmeticFunction.zeta_pos`, `Algebra.Presentation.naive_relation_apply`, `MvPolynomial.C_add`, `PolynomialLaw.exists_lift`, `LinearMap.toMvPolynomial_zero`, `Multiset.toFinsupp_apply`, `Module.rankAtStalk_eq_zero_iff_subsingleton`, `MvPolynomial.vars_eq_support_biUnion_support`, `MvPolynomial.isHomogeneous_C_mul_X`, `support_factorization`, `WittVector.mul_polyOfInterest_aux4`, `Polynomial.abs_tendsto_atBot_iff`, `MvPolynomial.rename_eval₂`, `MonomialOrder.support_leadingTerm'`, `MvPolynomial.eq_divMonomial_single`, `MvPolynomial.coeff_sum_X_pow_of_fintype`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some`, `MvPowerSeries.coeff_subst`, `MvPolynomial.coeff_smul`, `MvPowerSeries.expand_eq_expand`, `MvPolynomial.irreducible_of_disjoint_support`, `Algebra.Generators.localizationAway_σ`, `MvPolynomial.isWeightedHomogeneous_one`, `Ideal.finrank_prime_pow_ramificationIdx`, `ArithmeticFunction.zeta_mul_comm`, `MvPolynomial.mapAlgEquiv_apply`, `Polynomial.Bivariate.equivMvPolynomial_symm_X_0`, `MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval`, `dvd_ordCompl_of_dvd_not_dvd`, `MvPolynomial.finitePresentation_universalFactorizationMap`, `ArithmeticFunction.sigma_eq_zero`, `MvPolynomial.mapAlgEquiv_refl`, `WittVector.frobeniusPoly_zmod`, `MvPolynomial.totalDegree_multiset_prod`, `Finsupp.finite_of_nat_weight_le`, `MvPolynomial.eval_neg`, `Algebra.FiniteType.iff_quotient_mvPolynomial'`, `ArithmeticFunction.coe_mk`, `MvPolynomial.map_restrict_dom_evalₗ`, `MvPowerSeries.killCompl_monomial_embDomain`, `Polynomial.sum_eq_natDegree_of_mem_support_homogenize`, `Prime.dvd_iff_one_le_factorization`, `MvPolynomial.tensorEquivSum_one_tmul_C`, `MvPolynomial.eq_modMonomial_single_iff`, `ArithmeticFunction.carmichael_two_pow_of_le_two`, `eq_factorization_iff`, `Cubic.degree_of_d_ne_zero`, `MvPolynomial.rTensor_apply_tmul`, `MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_ne`, `MvPolynomial.IsSymmetric.mul`, `Finsupp.isLowerSet_range_embDomain`, `WeierstrassCurve.Jacobian.baseChange_polynomialY`, `MonomialOrder.Monic.pow`, `MonomialOrder.degree_mul_of_isRegular_right`, `MvPolynomial.map_ofNat`, `Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom`, `MvPolynomial.coeff_monomial_mul`, `Polynomial.degree_freeMonic`, `MvPolynomial.IsWeightedHomogeneous.add`, `MvPolynomial.eval₂Hom_rename`, `MvPolynomial.degreeOf_pow_eq`, `LieModule.rank_eq_natTrailingDegree`, `MvPolynomial.bind₂_id`, `MvPolynomial.X_mul_cancel_left_iff`, `WithBot.add_eq_one_iff`, `ArithmeticFunction.sigma_le_pow_succ`, `MvPolynomial.sumAlgEquiv_comp_rename_inl`, `MvPolynomial.dvd_monomial_iff_exists`, `WeierstrassCurve.Projective.baseChange_polynomialY`, `AlgebraicIndependent.aeval_of_algebraicIndependent`, `ArithmeticFunction.sigma_one_apply`, `MvPolynomial.aeval_bind₁`, `EisensteinSeries.hasSum_e2Summand_symmetricIco`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite`, `MonomialOrder.degree_sum_le`, `MonomialOrder.degree_mul_of_mul_leadingCoeff_ne_zero`, `MvPolynomial.X_dvd_mul_iff`, `MonomialOrder.leadingCoeff_pow_of_pow_leadingCoeff_ne_zero`, `MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sum`, `MvPolynomial.algebraMap_apply`, `MvPolynomial.mkDerivationₗ_monomial`, `Finsupp.le_weight`, `MvPolynomial.killCompl_monomial_eq_zero_of_not_subset`, `MvPolynomial.exists_fin_rename`, `LinearMap.toMvPolynomial_baseChange`, `EisensteinSeries.q_expansion_riemannZeta`, `Polynomial.ofFinsupp_one`, `MvPolynomial.optionEquivLeft_coeff_coeff`, `MonomialOrder.degree_subsingleton`, `MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv`, `Matrix.charpoly.optionEquivLeft_symm_univ_isHomogeneous`, `factorization_zero`, `ArithmeticFunction.cardFactors_eq_sum_factorization`, `Cardinal.mk_finsupp_nat`, `MvPolynomial.sum_weightedHomogeneousComponent`, `MvPolynomial.exists_degree_lt`, `MvPowerSeries.truncFinset_C`, `MvPolynomial.C_surjective`, `MvPolynomial.pderiv_def`, `MvPolynomial.isEmptyRingEquiv_symm_apply`, `MvPolynomial.finsupp_support_eq_support`, `ArithmeticFunction.convolution_vonMangoldt_zeta`, `AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord`, `DFinsupp.toMultiset_le_toMultiset`, `MonomialOrder.degree_leadingTerm_mul`, `MvPolynomial.hom_eq_hom`, `ceilRoot_def`, `MvPolynomial.mem_pow_idealOfVars_iff'`, `MvPolynomial.mem_supported`, `List.Nat.antidiagonalTuple_zero_right`, `Matrix.toMvPolynomial_zero`, `MvPolynomial.renameEquiv_apply`, `MvPowerSeries.expand_one`, `MvPolynomial.degrees_pow_le`, `Finsupp.DegLex.single_antitone`, `Finsupp.Lex.single_lt_iff`, `MvPolynomial.rename_esymmAlgHom`, `Num.castNum_or`, `dvd_iff_div_factorization_eq_tsub`, `List.IsZeckendorfRep.sum_fib_lt`, `MvPolynomial.ne_zero_iff`, `MvPolynomial.coeff_single_X`, `MvPolynomial.aeval_eq_zero`, `MvPolynomial.eval₂_cast_comp`, `Algebra.PreSubmersivePresentation.naive_toPresentation`, `Polynomial.eval_homogenize`, `MvPolynomial.modMonomial_add_divMonomial`, `MonomialOrder.span_leadingTerm_eq_span_monomial'`, `Finsupp.mem_toMultiset`, `ArithmeticFunction.sigma_pos_iff`, `MvPolynomial.bind₁_C_right`, `MvPolynomial.coe_coeffs_map`, `Polynomial.toTupleMvPolynomial_one_eq`, `MvPolynomial.decompose'_apply`, `MvPolynomial.rename_zero`, `ArithmeticFunction.sigma_one`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing`, `WithBot.add_eq_three_iff`, `MvPolynomial.instIsLocalHomRingHomAlgebraMap`, `WittVector.bind₁_wittMulN_wittPolynomial`, `MvPowerSeries.coeff_one`, `PolynomialLaw.exists_range_φ_eq_of_fg`, `Algebra.FinitePresentation.mvPolynomial`, `MvPowerSeries.truncFinset_map`, `MvPolynomial.coeff_single_X_pow`, `MvPolynomial.dvd_X_mul_iff`, `MonomialOrder.degree_X_sub_C`, `MvPolynomial.monomial_one_mul_cancel_left_iff`, `MvPolynomial.eq_zero_iff`, `MvPolynomial.aevalTower_C`, `TensorPower.algebraMap₀_eq_smul_one`, `MvPolynomial.expand_one_apply`, `MvPowerSeries.coeff_truncFinset_mul_truncFinset_eq_coeff_mul`, `MvPolynomial.coe_basisMonomials`, `exponent_eq_exponent_mul_factorization_of_prime_pow_eq_base_pow`, `MvPolynomial.map_expand_pow_char`, `xInTermsOfW_aux`, `Polynomial.degree_pos_of_ne_zero_of_nonunit`, `withBotSucc_zero`, `Algebra.Presentation.span_range_relation_eq_ker`, `MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero`, `MvPolynomial.mapRange_eq_map`, `MvPolynomial.monomial_mem_pow_idealOfVars_iff`, `MonomialOrder.degree_smul_le`, `LieAlgebra.Basis.iSupIndep_rootSpace`, `MvPolynomial.irreducible_sumSMulX`, `factorization_zero`, `AnalyticOnNhd.aeval_mvPolynomial`, `MvPolynomial.totalDegree_eq_zero_iff_eq_C`, `ArithmeticFunction.carmichael_two_pow_of_le_two_eq_totient`, `MvPowerSeries.coeff_expand_smul`, `Num.cast_to_nat`, `Algebra.Generators.Hom.toAlgHom_X`, `MvPolynomial.weightedTotalDegree_eq_zero_iff`, `MvPolynomial.bind₁_rename`, `MvPolynomial.degreeOf_sub_le`, `Irreducible.degree_pos`, `AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc`, `MvPolynomial.degreeOf_mul_X_eq_degreeOf_add_one_iff`, `wittStructureRat_prop`, `Partition.toFinsuppAntidiag_injective`, `WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero`, `MvPolynomial.degrees_rename`, `MvPolynomial.vars_neg`, `Algebra.Presentation.comp_relation`, `MvPolynomial.eval₂Hom_zero'`, `Polynomial.Bivariate.equivMvPolynomial_symm_C`, `Algebra.Generators.instIsScalarTowerRing`, `MvPowerSeries.aeval_coe`, `factorization_centralBinom_eq_zero_of_two_mul_lt`, `MvPowerSeries.truncFinset_monomial_eq_zero`, `MonomialOrder.toSyn_degree_mul_le`, `Polynomial.homogenize_X_pow`, `ArithmeticFunction.zeta_apply_ne`, `WittVector.IsPoly.poly`, `MvPolynomial.map_hsymm`, `Squarefree.natFactorization_le_one`, `MvPolynomial.monomial_le_degreeOf`, `Polynomial.Monic.degree_pos`, `MvPowerSeries.eval₂_eq_tsum`, `Multiset.toDFinsupp_replicate`, `MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination`, `MvPolynomial.finite_universalFactorizationMap`, `MvPolynomial.rTensorAlgHom_toLinearMap`, `ArithmeticFunction.natCoe_one`, `wittStructureRat_rec`, `WittVector.mul_polyOfInterest_vars`, `divisors_eq_map_attach_Iic_factorization_prod_pow`, `MvPolynomial.isRegular_prod_X`, `MvPolynomial.homogeneousSubmodule_zero`, `MvPolynomial.coeff_sumSMulX`, `MvPolynomial.expand_eq_C`, `Finsupp.multinomial_eq_of_support_subset`, `OrderedFinpartition.neZero_length`, `ArithmeticFunction.carmichael_dvd`, `MvPowerSeries.le_weightedOrder_subst`, `algebraicIndependent_iff`, `Finsupp.mapDomainEmbedding_apply`, `Multiset.uIcc_eq`, `MvPowerSeries.trunc'_expand`, `MvPolynomial.universalFactorizationMapPresentation_map`, `MvPolynomial.coeff_rename_mapDomain`, `factorization_choose_of_lt_three_mul`, `Num.castNum_ldiff`, `Finsupp.multinomial_update`, `MvPowerSeries.monomial_zero_eq_C_apply`, `MonomialOrder.degree_mul_le`, `MvPolynomial.restrictSupport_mono`, `Finsupp.count_toMultiset`, `MvPolynomial.algebraTensorAlgEquiv_symm_X`, `MvPolynomial.expand_injective`, `MvPolynomial.mem_restrictDegree`, `MvPolynomial.support_coeff_finSuccEquiv`, `MonomialOrder.monic_monomial`, `Algebra.Presentation.aeval_val_relation`, `LinearMap.polyCharpolyAux_map_eq_charpoly`, `MvPolynomial.totalDegree_neg`, `MvPolynomial.expand_one`, `ModEq.listSum_map_zero`, `MvPolynomial.degrees_map_le`, `MvPolynomial.esymmAlgHom_fin_surjective`, `MvPolynomial.expand_inj`, `Polynomial.toFinsupp_one`, `LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff`, `MvPolynomial.coeff_prod_X_pow`, `MvPolynomial.support_neg`, `ArithmeticFunction.cardDistinctFactors_prod`, `CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom`, `MvPolynomial.supDegree_esymm`, `factorization_lt`, `MvPolynomial.indicator_mem_restrictDegree`, `MvPolynomial.coeffsIn_mul`, `ordCompl_pow_mul_of_not_dvd`, `AlgebraicGeometry.AffineSpace.map_toSpecMvPoly`, `MvPolynomial.eval_eq`, `MvPowerSeries.rename_coe`, `MonomialOrder.sPolynomial_def`, `not_dvd_ordCompl`, `MvPolynomial.mk_eq_eval₂`, `MonomialOrder.sPolynomial_antisymm`, `Algebra.Generators.H1Cotangent.δAux_ofComp`, `MvPolynomial.restrictSupport_zero`, `factorization_lcm`, `MvPolynomial.killCompl_monomial_mapDomain`, `MonomialOrder.mem_nonZeroDivisors_of_leadingCoeff_mem_nonZeroDivisors`, `MonomialOrder.le_add_right`, `MvPolynomial.as_sum`, `MonomialOrder.degree_mul_of_left_mem_nonZeroDivisors`, `MvPolynomial.isUnit_iff_eq_C_of_isReduced`, `MonomialOrder.leadingCoeff_monomial`, `IsSemisimpleRing.exists_ringEquiv_pi_matrix_divisionRing`, `MvPolynomial.psum_zero`, `MvPolynomial.monomial_add_single`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none`, `MvPolynomial.le_coeffsIn_pow`, `MvPolynomial.supported_strictMono`, `MvPolynomial.IsWeightedHomogeneous.pow`, `MonomialOrder.degree_pow_le`, `MvPolynomial.eval_add`, `WeierstrassCurve.Projective.map_polynomialX`, `MvPolynomial.pointToPoint_zeroLocus_le`, `Num.succ_to_nat`, `Algebra.SubmersivePresentation.map_jacobianRelationsOfHasCoeffs`, `exists_integral_inj_algHom_of_quotient`, `MvPowerSeries.trunc_map`, `MvPolynomial.isNilpotent_iff`, `factorization_ceilRoot`, `MvPolynomial.instNoZeroDivisors`, `exists_finite_inj_algHom_of_fg`, `MvPolynomial.eval₂_eq'`, `MonomialOrder.monic_monomial_one`, `MvPolynomial.zeroLocus_bot`, `WeierstrassCurve.Jacobian.baseChange_polynomial`, `MvPolynomial.aeval_def`, `MvPolynomial.monomial_eq_zero`, `MvPolynomial.eval_monomial`, `MvPolynomial.eq_modMonomial_single`, `Relation.cutExpand_le_invImage_lex`, `MonomialOrder.degree_C`, `IsSimpleRing.exists_algEquiv_matrix_divisionRing_finite`, `MvPolynomial.coeff_monomial_mul'`, `MvPolynomial.monomial_mem_coeffsIn`, `MonomialOrder.toSyn_monotone`, `MvPolynomial.degrees_sub_le`, `ArithmeticFunction.sigma_eq_prod_primeFactors_sum_range_factorization_pow_mul`, `MvPolynomial.coe_eval₂Hom`, `MvPowerSeries.coeff_trunc'`, `MvPolynomial.vars_C_mul`, `MvPolynomial.coeff_zero_X`, `MonomialOrder.sPolynomial_left_zero`, `Polynomial.rootOfSplits'_eq_rootOfSplits`, `AbsoluteValue.eval_mvPolynomial_le`, `MvPowerSeries.coeff_zero_mul_X`, `Polynomial.degree_intCast_le`, `Behrend.sphere_zero_subset`, `Algebra.Generators.toAlgHom_ofComp_rename`, `MonomialOrder.support_leadingTerm`, `Algebra.FinitePresentation.iff`, `DividedPowerAlgebra.dp_zero`, `wittStructureRat_rec_aux`, `Polynomial.Bivariate.equivMvPolynomial_symm_X_1`, `PosNum.to_int_eq_succ_pred`, `MvPolynomial.eval₂_add`, `MonomialOrder.image_leadingTerm_insert_zero`, `WeierstrassCurve.Projective.eval_polynomialZ`, `MvPowerSeries.coeff_inv_aux`, `prod_pow_dvd_of_le_factorization`, `MvPolynomial.supported_mono`, `DFinsupp.toMultiset_toDFinsupp`, `Algebra.Generators.ker_localizationAway`, `Finsupp.DegLex.lt_iff`, `MonomialOrder.sPolynomial_decomposition`, `MonomialOrder.degLex_single_le_iff`, `MvPolynomial.constantCoeff_smul`, `MvPolynomial.totalDegree_expand`, `MvPolynomial.algHom_C`, `MvPolynomial.leadingCoeff_toLex_C`, `WithBot.lt_zero_iff`, `MvPolynomial.support_mul_X`, `PosNum.div'_to_nat`, `wittStructureInt_prop`, `MvPolynomial.eval_pow`, `TensorPower.mul_one`, `MvPolynomial.eval₂Hom_zero'_apply`, `MvPowerSeries.lexOrder_zero`, `MvPolynomial.psumPart_zero`, `Finsupp.degLex_def`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply`, `ArithmeticFunction.sum_Ioc_zeta`, `sum_digits_ofDigits_eq_sum`, `MvPolynomial.le_zeroLocus_iff_le_vanishingIdeal`, `MvPolynomial.support_esymm'`, `Finsupp.sum_id_lt_of_lt`, `dvd_iff_dvd_digits_sum`, `MonomialOrder.leadingCoeff_mul_of_left_mem_nonZeroDivisors`, `MvPolynomial.mkₐ_eq_aeval`, `MvPolynomial.derivation_C`, `MvPolynomial.mem_support_coeff_optionEquivLeft`, `Algebra.Presentation.fg_ker`, `Height.mulHeight_eval_ge`, `instIsAlgebraicMvPolynomialOfNoZeroDivisors`, `Polynomial.eval_X_toTupleMvPolynomial_zero_eq`, `MvPolynomial.dvd_smul_X_iff_exists`, `Algebra.Generators.σ_smul`, `MvPowerSeries.coeff_trunc`, `MvPolynomial.mem_supported_vars`, `Num.castNum_and`, `MvPolynomial.mkDerivation_monomial`, `MvPolynomial.degrees_sum_le`, `Algebra.Presentation.relation_mem_ker`, `Algebra.Generators.Hom.toExtensionHom_toRingHom`, `Finsupp.ofSupportFinite_fin_two_eq`, `MvPolynomial.schwartz_zippel_sup_sum`, `Algebra.Generators.comp_localizationAway_ker`, `MvPolynomial.mem_map_C_iff`, `MvPolynomial.rename_monomial`, `MvPolynomial.aeval_toMvPolynomial`, `MvPolynomial.mul_esymm_eq_sum`, `MvPolynomial.prime_C_iff`, `MvPolynomial.eval_mul`, `MvPolynomial.restrictScalars_restrictSupportIdeal`, `MvPolynomial.instFiniteSubtypeMemSubmoduleRestrictDegreeOfFinite`, `MvPolynomial.mem_restrictSupport_iff`, `MvPolynomial.degreesLE_zero`, `MvPolynomial.universalFactorizationMapPresentation_relation`, `MvPolynomial.aevalTower_comp_algebraMap`, `MvPolynomial.monic_esymm`, `MvPolynomial.eval₂_zero_apply`, `Algebra.PreSubmersivePresentation.aevalDifferential_single`, `Num.ofZNum_toNat`, `MvPolynomial.isWeightedHomogeneous_monomial`, `AlgebraicIndependent.algebraMap_aevalEquiv`, `MvPolynomial.isWeightedHomogeneous_zero`, `MonomialOrder.coeff_degree_eq_zero_iff`, `MvPolynomial.aeval_id_rename`, `Finsupp.sum_nsmul`, `Finsupp.toMultiset_add`, `primeFactorsList_count_eq`, `Multiset.toFinsupp_singleton`, `MvPolynomial.degreeOf_mul_X_self`, `MonomialOrder.monic_C_one`, `MvPolynomial.eq_C_of_isEmpty`, `MvPolynomial.coeff_one`, `MonomialOrder.sPolynomial_right_zero`, `WeierstrassCurve.Projective.polynomialX_eq`, `Algebra.adjoin_range_eq_range_aeval`, `Multiset.toFinsupp_symm_apply`, `MvPolynomial.monomial_zero'`, `setOf_pow_dvd_eq_Icc_factorization`, `Polynomial.homogenize_finsetSum`, `MvPolynomial.eval₂_sub`, `MvPolynomial.weightedHomogeneousComponent_directSum`, `Algebra.Generators.aeval_val_σ`, `MvPolynomial.msymm_zero`, `MvPolynomial.totalDegree_add`, `Polynomial.homogenize_C_mul`, `MvPowerSeries.coeff_prod`, `MvPowerSeries.exists_coeff_ne_zero_and_order`, `MvPolynomial.mem_zeroLocus_iff`, `factorization_choose'`, `MvPowerSeries.truncFinset_monomial`, `MvPolynomial.coe_add`, `TensorPower.toTensorAlgebra_gOne`, `DFinsupp.toMultiset_inf`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed`, `MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le`, `factorization_choose_le_log`, `MvPolynomial.modMonomial_X`, `MvPolynomial.homogeneousComponent_apply`, `factorization_eq_zero_of_not_prime`, `MvPolynomial.vars_prod`, `MonomialOrder.leadingCoeff_add_of_lt`, `MvPolynomial.eval_indicator_apply_eq_zero`, `MvPolynomial.sumToIter_iterToSum`, `ArithmeticFunction.carmichael_finset_lcm`, `MvPolynomial.divMonomial_mul_monomial`, `MvPolynomial.map_surjective_iff`, `AlgebraicIndependent.eq_zero_of_aeval_eq_zero`, `ArithmeticFunction.cardDistinctFactors_zero`, `constantCoeff_wittPolynomial`, `WeierstrassCurve.Projective.polynomialY_eq`, `MvPolynomial.aeval_eq_constantCoeff_of_vars`, `Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul`, `MvPolynomial.weightedHomogeneousComponent_finsupp`, `WeierstrassCurve.Projective.negDblY_eq`, `ArithmeticFunction.sigma_zero_apply_prime_pow`, `WithBot.one_le_iff_zero_lt`, `SymmetricAlgebra.equivMvPolynomial_symm_X`, `MvPolynomial.coeff_linearCombination_X_pow`, `MvPolynomial.expand_bind₁`, `MvPolynomial.map_injective_iff`, `MvPolynomial.linearIndependent_X`, `MvPolynomial.coeff_mul_X'`, `MvPolynomial.prod_X_pow_eq_monomial`, `IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite`, `twoPowSum_bitIndices`, `MvPolynomial.map_injective`, `MvPolynomial.constantCoeff_monomial`, `MvPolynomial.coeff_mul_X`, `MvPolynomial.smul_eval`, `Finsupp.multinomial_eq`, `MvPolynomial.eval₂Hom_zero`, `Polynomial.degree_one_le`, `MvPowerSeries.substAlgHom_coe`, `MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap`, `MvPolynomial.degrees_one`, `MvPolynomial.C_eq_zero`, `MvPolynomial.supDegree_toLex_C`, `WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero`, `MvPolynomial.coeff_rTensorAlgHom_tmul`, `MvPolynomial.aeval_zero`, `MvPolynomial.killCompl_rename_app`, `Icc_factorization_eq_pow_dvd`, `factorization_le_iff_dvd`, `Polynomial.tendsto_nhds_iff`, `MvPolynomial.mem_weightedHomogeneousSubmodule`, `MvPolynomial.hom_congr_vars`, `ordCompl_pos`, `MvPolynomial.comp_aeval`, `MvPolynomial.support_map_of_injective`, `MvPolynomial.constantCoeff_X`, `MvPolynomial.divMonomial_monomial`, `MvPolynomial.frobenius_zmod`, `KaehlerDifferential.mvPolynomialBasis_repr_apply`, `WittVector.frobeniusPolyAux_eq`, `MvPolynomial.optionEquivLeft_coeff_some_coeff_none`, `MvPowerSeries.coeff_zero_one`, `IntermediateField.mem_adjoin_range_iff`, `ordCompl_mul`, `DividedPowerAlgebra.mkAlgHom_surjective`, `WittVector.coeff_frobeniusFun`, `Composition.blocks_sum`, `ordProj_le`, `MvPolynomial.renameEquiv_refl`, `MvPolynomial.totalDegree_renameEquiv`, `Num.lt_to_nat`, `dvd_iff_exists_le_factorization`, `MvPolynomial.expand_mul`, `MvPolynomial.mem_coeffsIn`, `Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul`, `ArithmeticFunction.id_apply`, `AlgebraicGeometry.AffineSpace.map_SpecMap`, `WeierstrassCurve.Projective.baseChange_polynomialX`, `factorization_le_factorization_choose_add`, `MvPolynomial.isLocalHom_expand`, `MvPolynomial.exists_mem_support_not_dvd_of_forall_totalDegree_le`, `Polynomial.Bivariate.pderiv_zero_equivMvPolynomial`, `ArithmeticFunction.sigma_eq_one_iff`, `MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_ne`, `MvPolynomial.C_mul'`, `Num.ppred_to_nat`, `AlgebraicClosure.le_maxIdeal`, `MvPolynomial.isEmptyAlgEquiv_apply`, `MvPolynomial.bind₂_X_right`, `MvPolynomial.of_irreducible_expand`, `Algebra.Generators.cMulXSubOneCotangent_eq`, `DividedPowerAlgebra.submodule_span_prod_dp_eq_top`, `MvPolynomial.map_C`, `MvPolynomial.isHomogeneous_monomial`, `LinearMap.polyCharpolyAux_baseChange`, `Finsupp.prod_pow`, `Polynomial.Bivariate.equivMvPolynomial_X`, `Finsupp.sum_antidiagonal_swap`, `MvPolynomial.C_dvd_iff_dvd_coeff`, `MvPolynomial.pderiv_C_mul`, `Polynomial.homogenize_finsetProd`, `card_divisors`, `Module.Basis.symmetricAlgebra_repr_apply`, `MonomialOrder.degree_smul_of_isRegular`, `AlgebraicClosure.toSplittingField_coeff`, `MvPolynomial.eval₂_mul`, `Matrix.toMvPolynomial_eval_eq_apply`, `Prime.factorization_self`, `MvPolynomial.coe_pow`, `MvPowerSeries.coeff_add_mul_monomial`, `MonomialOrder.degree_one`, `MvPolynomial.natDegree_optionEquivLeft`, `Matrix.charpoly.univ_coeff_isHomogeneous`, `MvPolynomial.isHomogeneous_one`, `ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial`, `WittVector.constantCoeff_wittMul`, `ArithmeticFunction.sigma_mono`, `MvPolynomial.totalDegree_eq_zero_iff`, `MvPowerSeries.monomial_pow`, `AlgebraicGeometry.AffineSpace.SpecIso_inv_over_assoc`, `Algebra.Generators.self_algebra_smul`, `ordProj_dvd_ordProj_of_dvd`, `MvPolynomial.decomposition.decompose'_apply`, `MvPolynomial.restrictSupport_nsmul`, `Algebra.Generators.toKaehler_tmul_D`, `MvPolynomial.mem_support_finSuccEquiv`, `ModEq.listSum_zero`, `MvPolynomial.psum_one`, `MvPolynomial.mem_degreesLE`, `MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous`, `MvPolynomial.isNoetherianRing_fin`, `Polynomial.degree_one`, `MvPolynomial.X_dvd_iff_modMonomial_eq_zero`, `Finsupp.coe_orderIsoMultiset_symm`, `MvPolynomial.funext_set_iff`, `MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing`, `Sylow.card_eq_multiplicity`, `MvPolynomial.X_mul_divMonomial`, `MvPolynomial.map_monomial`, `MvPolynomial.monomial_mem_restrictSupport`, `algebraicIndependent_iff_injective_aeval`, `Num.bit_to_nat`, `MvPolynomial.vars_map_of_injective`, `MvPolynomial.aeval_map_algebraMap`, `Algebra.Generators.Hom.toAlgHom_C`, `PosNum.mod'_to_nat`, `MvPowerSeries.coeff_zero_X_mul`, `MvPolynomial.rename_comp_toMvPolynomial`, `Height.mulHeightBound_eq`, `MvPolynomial.comap_C_surjective`, `MvPolynomial.finSuccEquiv_comp_C_eq_C`, `MvPolynomial.esymmAlgHom_zero`, `MvPolynomial.homogeneousComponent_eq_zero`, `Iio_factorization_prod_pow_injective`, `factorization_centralBinom_of_two_mul_self_lt_three_mul`, `MvPolynomial.eval₂_eta`, `MvPolynomial.coeToMvPowerSeries.algHom_apply`, `Finsupp.DegLex.single_le_iff`, `Polynomial.degree_zero_le`, `Polynomial.Monic.degree_pos_of_not_isUnit`, `MvPolynomial.degreeOf_eq_sup`, `AlgebraicIndependent.liftAlgHom_comp_reprField`, `DividedPowerAlgebra.algHom_ext_iff`, `MvPolynomial.rename_rightInverse`, `char_dvd_card_solutions`, `Algebra.SubmersivePresentation.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs`, `WeierstrassCurve.Jacobian.polynomialZ_eq`, `MonomialOrder.sPolynomial_monomial_mul`, `MvPolynomial.hsymmPart_zero`, `MvPolynomial.eval₂Hom_map_hom`, `MvPolynomial.isRegular_X`, `MvPolynomial.mem_homogeneousSubmodule`, `Polynomial.isBoundedUnder_abs_atBot_iff`, `MvPolynomial.finSuccEquiv_eq`, `char_dvd_card_solutions_of_sum_lt`, `SymmetricAlgebra.equivMvPolynomial_ι_apply`, `ordCompl_self_pow_mul`, `RingHom.IsStandardSmooth.exists_etale_mvPolynomial`, `MvPolynomial.homogeneousComponent_zero`, `LinearMap.polyCharpoly_eq_of_basis`, `MvPolynomial.ker_eval₂Hom_universalFactorizationMap`, `MvPolynomial.monomial_left_injective`, `IsSemisimpleModule.exists_end_ringEquiv`, `MvPolynomial.bind₁_comp_rename`, `MvPolynomial.coeff_map`, `MonomialOrder.degree_le_degree_of_support_subset`, `MvPolynomial.monomial_sum_index`, `MonomialOrder.degree_eq_zero_iff_totalDegree_eq_zero`, `MvPolynomial.degrees_prod_le`, `LinearMap.polyCharpolyAux_map_aeval`, `Matrix.mvPolynomialX_mapMatrix_eval`, `MvPolynomial.monic_monomial_eq`, `MvPolynomial.image_support_finSuccEquiv`, `MvPolynomial.support_nonempty`, `AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply`, `MvPolynomial.pderiv_monomial_single`, `MvPolynomial.degreeOf_prod_eq`, `MvPolynomial.eval₂_rename`, `AlgebraicIndependent.aeval_repr`, `Polynomial.degree_pos_of_not_isUnit_of_dvd_monic`, `MvPolynomial.support_expand`, `MonomialOrder.degree_eq_zero_iff`, `MonomialOrder.degree_mem_support`, `MvPolynomial.add_divMonomial`, `MvPolynomial.instFiniteSubtypeMemSubmoduleRestrictTotalDegreeOfFinite`, `Polynomial.Bivariate.equivMvPolynomial_C_X`, `factorization_one`, `MvPolynomial.IsSymmetric.rename`, `MvPolynomial.IsHomogeneous.aeval`, `MvPolynomial.isEmptyRingEquiv_symm_toRingHom`, `MonomialOrder.leadingTerm_C`, `MvPolynomial.DirectSum.coeLinearMap_eq_finsum`, `Finsupp.antidiagonal_zero`, `TensorPower.list_prod_gradedMonoid_mk_single`, `EisensteinSeries.E_qExpansion_coeff`, `WittVector.mul_polyOfInterest_aux1`, `MvPolynomial.support_monomial_subset`, `MvPolynomial.monomial_mul`, `MonomialOrder.toSyn_eq_zero_iff`, `MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse`, `PNat.mk_ofNat`, `MvPowerSeries.weightedOrder_eq_nat`, `ArithmeticFunction.carmichael_dvd_totient`, `Height.mulHeight_eval_le`, `MvPowerSeries.totalDegree_trunc'`, `MvPowerSeries.expand_monomial`, `ArithmeticFunction.cardDistinctFactors_eq_one_iff`, `FirstOrder.Ring.MvPolynomialSupportLEEquiv_symm_apply_coeff`, `MvPolynomial.aeval_bind₂`, `MvPolynomial.rename_bind₁`, `MvPolynomial.support_X_pow`, `MvPolynomial.rTensor_symm_apply_single`, `MvPolynomial.pderiv_X_of_ne`, `MvPolynomial.prod_X_add_C_coeff`, `MvPolynomial.renameSymmetricSubalgebra_symm_apply_coe`, `MvPolynomial.IsSymmetric.zero`, `Algebra.Generators.Hom.toAlgHom_comp_apply`, `MvPolynomial.degree_finSuccEquiv`, `Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial`, `MvPolynomial.isNoetherianRing_fin_0`, `MvPolynomial.nonempty_support_optionEquivLeft`, `MvPolynomial.pderiv_monomial`, `Polynomial.toFinsupp_eq_one`, `MvPolynomial.isRegular_X_pow`, `Polynomial.mem_closure_X_union_C`, `prod_pow_primeFactors_factorization`, `bind₁_rename_expand_wittPolynomial`, `Algebra.adjoin_eq_range`, `MvPolynomial.degrees_add_le`, `MvPolynomial.mapAlgEquiv_symm`, `Algebra.Generators.toComp_toAlgHom_monomial`, `MvPolynomial.counit_surjective`, `DFinsupp.toMultiset_injective`, `MvPolynomial.rename_injective`, `Multiset.toFinsupp_zero`, `MvPolynomial.isHomogeneous_zero`, `IsSemisimpleModule.exists_end_algEquiv`, `MvPolynomial.degrees_mul_le`, `WeierstrassCurve.Projective.negDblY_eq'`, `MvPolynomial.quotient_mk_comp_C_injective`, `MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree`, `MonomialOrder.leadingCoeff_neg`, `Algebra.SubmersivePresentation.aeval_jacobianOfHasCoeffs`, `Affine.Simplex.faceOpposite_point_eq_point_succAbove`, `Multiset.toFinsupp_toMultiset`, `LinearMap.polyCharpolyAux_coeff_eval`, `MvPolynomial.esymmAlgHomMonomial_single_one`, `AlgebraicClosure.Monics.map_eq_prod`, `MvPolynomial.coe_smul`, `MonomialOrder.degree_prod_le`, `MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt`, `MvPolynomial.map_rightInverse`, `MvPolynomial.finrank_eq_zero`, `MvPolynomial.dvd_monomial_mul_iff_exists`, `MvPolynomial.killCompl_map`, `MonomialOrder.span_leadingTerm_insert_zero`, `Algebra.FiniteType.iff_quotient_mvPolynomial`, `MeasureTheory.upcrossingsBefore_eq_sum`, `Finsupp.DegLex.isStrictOrder`, `Algebra.Generators.H1Cotangent.δAux_X`, `MonomialOrder.div_set`, `MvPolynomial.aeval_eq_bind₁`, `MvPolynomial.support_optionEquivLeft`, `MvPowerSeries.coeff_rescale`, `ZNum.abs_to_nat`, `EisensteinSeries.q_expansion_bernoulli`, `LSeries.one_convolution_eq_zeta_convolution`, `MvPolynomial.X_mul_modMonomial`, `MvPolynomial.degreeOf_pow_le`, `MvPolynomial.dvd_X_iff_exists`, `tsum_prod_pow_eq_tsum_sigma`, `MvPowerSeries.WithPiTopology.hasSum_of_monomials_self`, `MvPolynomial.finSuccEquiv_X_succ`, `MvPolynomial.aeval_ofNat`, `MonomialOrder.degree_zero`, `Algebra.Presentation.aeval_val_relationOfHasCoeffs`, `MvPolynomial.eval₂Hom_eq_zero`, `sum_zeckendorf_fib`, `MvPolynomial.instCharP`, `ordProj_self_pow`, `MvPolynomial.expand_comp_bind₁`, `MvPolynomial.mapAlgEquiv_trans`, `MonomialOrder.leadingCoeff_C`, `IsAddTorsionFree.to_noZeroSMulDivisors_nat`, `Algebra.SubmersivePresentation.aeval_invJacobianOfHasCoeffs`, `exists_ordCompl_eq_one_iff_isPrimePow`, `MvPolynomial.ker_mapAlgHom`, `Finsupp.degree_preimage_nsmul`, `factorization_le_factorization_mul_right`, `MvPolynomial.aeval_injective_iff_of_isEmpty`, `MvPolynomial.support_one`, `WittVector.constantCoeff_wittAdd`, `Algebra.Generators.ofComp_kerCompPreimage`, `MvPolynomial.X_mem_supported`, `multinomial_single`, `MvPolynomial.coeff_zero`, `MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder`, `prod_factorization_eq_prod_primeFactors`, `MvPolynomial.eval_sub`, `factorization_eq_zero_iff_remainder`, `MvPolynomial.mem_restrictDegree_iff_sup`, `MvPolynomial.esymmAlgHom_fin_injective`, `MvPolynomial.aeval_comp_bind₁`, `MvPolynomial.hsymm_one`, `Prime.pow_dvd_iff_dvd_ordProj`, `MvPolynomial.weightedHomogeneousComponent_eq_zero_of_notMem`, `Height.logHeight_eval_le`, `ArithmeticFunction.LSeries_zeta_eq_riemannZeta`, `prod_pow_factorization_eq_self`, `MvPolynomial.totalDegree_sub`, `Polynomial.degree_eq_zero_of_isUnit`, `Polynomial.monic_freeMonic`, `MvPolynomial.rTensor_apply_monomial_tmul`, `MvPolynomial.IsWeightedHomogeneous.prod`, `ordCompl_div_pow_of_dvd`, `MvPolynomial.eval₂_const_pUnitAlgEquiv`, `Algebra.Generators.repr_CotangentSpaceMap`, `DividedPowerAlgebra.dp_sum_smul`, `IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_divisionRing`, `MonomialOrder.degLex_lt_iff`, `MvPolynomial.coeff_X'`, `MvPolynomial.pderiv_pow`, `constantCoeff_wittStructureRat_zero`, `WeierstrassCurve.Jacobian.map_polynomialZ`, `Field.instNeZeroFinSepDegree`, `MvPolynomial.aeval_esymm_eq_multiset_esymm`, `MvPolynomial.supported_le_supported_iff`, `MvPolynomial.totalDegree_zero`, `MonomialOrder.coeff_pow_nsmul_degree`, `Num.dvd_to_nat`, `WithBot.lt_one_iff_le_zero`, `MvPolynomial.bind₂_C_right`, `MvPowerSeries.algebraMap_apply'`, `MvPolynomial.constantCoeff_eq`, `LinearMap.toMvPolynomial_constantCoeff`, `HahnSeries.coeff_toMvPowerSeries_symm`, `WeierstrassCurve.Projective.map_polynomialZ`, `MvPolynomial.eval_rename`, `MvPolynomial.mkDerivationₗ_C`, `MvPolynomial.vars_one`, `StandardEtalePresentation.toPresentation_σ'`, `MvPolynomial.totalDegree_finsetSum_le`, `MvPolynomial.weightedTotalDegree_piSingle`, `factorization_eq_primeFactorsList_multiset`, `MvPolynomial.isIntegral_iff_isIntegral_coeff`, `witt_structure_prop`, `factorization_floorRoot`, `MvPolynomial.map_surjective`, `Matrix.toLinearMap₂'_single`, `MvPolynomial.degreeOf_one`, `MvPolynomial.coe_eval₂AlgHom`, `WittVector.constantCoeff_wittNSMul`, `LinearMap.toMvPolynomial_comp`, `MvPolynomial.eval₂Hom_eq_bind₂`, `floorRoot_def`, `MvPolynomial.IsHomogeneous.rename_isHomogeneous_iff`, `MvPolynomial.vars_bind₁`, `MonomialOrder.leadingCoeff_pow`, `WittVector.bind₁_verschiebungPoly_wittPolynomial`, `MvPolynomial.prod_C_add_X_eq_sum_esymm`, `Algebra.Presentation.instFinitePresentationModelOfHasCoeffsOfFinite`, `MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero_of_le_card`, `MvPolynomial.eval₂_map_comp_C`, `MonomialOrder.degree_pow`, `MvPowerSeries.coeff_zero_C`, `MvPolynomial.support_smul_eq`, `MvPolynomial.optionEquivRight_apply`, `MvPolynomial.finSuccEquiv_apply`, `MvPowerSeries.coeff_monomial`, `MvPolynomial.vanishingIdeal_empty`, `MvPowerSeries.coeff_C`, `MvPolynomial.C_eq_coe_nat`, `MvPolynomial.tensorEquivSum_X_tmul_X`, `MvPolynomial.comp_aeval_apply`, `MvPolynomial.vars_mul`, `prod_factorization_pow_eq_self`, `Algebra.Presentation.relation_comp_localizationAway_inl`, `MvPolynomial.bind₂_comp_bind₂`, `WittVector.coeff_select`, `Finsupp.toFinset_toMultiset`, `MvPolynomial.aeval_unique`, `WeierstrassCurve.Jacobian.baseChange_polynomialX`, `dvd_prod_pow_of_factorization_le`, `ArithmeticFunction.carmichael_finset_prod`, `DividedPowerAlgebra.dp_def`, `SchwartzMap.schwartzSeminormFamily_apply_zero`, `MvPolynomial.coeff_rTensorAlgHom_monomial_tmul`, `MvPolynomial.bind₁_bind₁`, `MvPolynomial.support_sum_monomial_coeff`, `MvPolynomial.degreeOf_mul_C_le`, `MvPolynomial.mem_coeffsIn_iff_coeffs_subset`, `MvPolynomial.esymmAlgHomMonomial_add`, `Polynomial.isBoundedUnder_abs_atTop_iff`, `MvPolynomial.algebraTensorAlgEquiv_symm_map`, `neZero_totient`, `MvPolynomial.coeff_sub`, `MvPolynomial.rename_polynomial_aeval_X`, `MvPolynomial.weightedDecomposition.decompose'_eq`, `MvPolynomial.degrees_mul_eq`, `MvPolynomial.coeff_expand_of_not_dvd`, `MvPowerSeries.lexOrder_eq_top_iff_eq_zero`, `DividedPowerAlgebra.dp_sum`, `Algebra.Generators.Hom.equivAlgHom_symm_apply_val`, `MvPolynomial.isHomogeneous_C_mul_X_pow`, `MvPolynomial.tensorEquivSum_C_tmul_one`, `MvPolynomial.map_iterateFrobenius_expand`, `MvPolynomial.vars_pow`, `Finsupp.Lex.single_antitone`, `Polynomial.toMvPolynomial_X`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop`, `MvPolynomial.hsymm_zero`, `MvPolynomial.sumAlgEquiv_apply`, `Algebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one`, `Multiset.toFinsupp_eq_iff`, `ArithmeticFunction.LSeriesSummable_zeta_iff`, `Algebra.Generators.ker_comp_eq_sup`, `MvPolynomial.degreeOf_C_mul_le`, `algebraicIndependent_subtype`, `LinearMap.polyCharpoly_map_eq_charpoly`, `MonomialOrder.degree_add_eq_right_of_lt`, `MvPolynomial.coeffsIn_eq_span_monomial`, `MvPolynomial.sumToIter_Xr`, `LinearMap.polyCharpoly_monic`, `Polynomial.natDegree_freeMonic`, `Algebra.Generators.ofComp_toAlgHom_monomial_sumElim`, `MvPolynomial.exists_finset_rename₂`, `ArithmeticFunction.cardDistinctFactors_mul`, `Matrix.charpoly.univ_natDegree`, `WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero`, `MvPolynomial.algebraMap_eq`, `MvPolynomial.algebraicIndependent_X`, `MvPolynomial.eval_toMvPolynomial`, `Algebra.Presentation.algebraTensorAlgEquiv_symm_relation`, `Algebra.Generators.aeval_val_eq_zero`, `MvPolynomial.coeffsIn_pow`, `MvPolynomial.sum_C`, `MvPolynomial.totalDegree_one`, `MvPolynomial.esymmAlgHom_apply`, `MvPolynomial.monomial_eq`, `MvPolynomial.homogeneousSubmodule_eq_finsupp_supported`, `MvPolynomial.aeval_eq_eval₂Hom`, `factorizationEquiv_symm_apply_coe`, `totient_eq_prod_factorization`, `MvPolynomial.vars_C`, `MvPolynomial.rename_prod_mk_eval₂`, `factorization_div`, `AlgebraicIndependent.aevalEquivField_apply_coe`, `MvPolynomial.IsSymmetric.smul`, `MvPolynomial.aeval_C`, `MvPolynomial.support_map_subset`, `IsTranscendenceBasis.mvPolynomial`, `factorization_choose_eq_zero_of_lt`, `centralBinom_factorization_small`, `MvPolynomial.toMvPowerSeries_pUnitAlgEquiv`, `MvPolynomial.transcendental_polynomial_aeval_X`, `MvPolynomial.pderiv_map`, `IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite`, `prod_pow_factorization_choose`, `WeierstrassCurve.Jacobian.eval_polynomial`, `MvPowerSeries.coeff_invOfUnit`, `MvPolynomial.aeval_comp_expand`, `Algebra.Generators.naive_σ`, `AlgebraicIndependent.aevalEquiv_apply_coe`, `MvPolynomial.esymm_eq_sum_monomial`, `Polynomial.homogenize_monomial_of_lt`, `WittVector.wittMul_zero`, `MvPolynomial.rename_C`, `Finsupp.toMultiset_sum`, `MvPolynomial.HomogeneousSubmodule.gradedMonoid`, `ArithmeticFunction.mul_zeta_apply`, `FirstOrder.realize_genericPolyMapSurjOnOfInjOn`, `TensorPower.gOne_def`, `MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc'`, `TensorPower.one_mul`, `Multiset.toDFinsupp_injective`, `factorization_prime_le_iff_dvd`, `CompositionAsSet.blocks_sum`, `MvPolynomial.eval₂_mul_C`, `MonomialOrder.degree_lt_of_left_ne_zero_of_degree_mul_lt`, `StandardEtalePresentation.aeval_val_equivMvPolynomial`, `AddAction.minimalPeriod_pos`, `sum_divisors`, `MvPolynomial.instFiniteOfIsEmpty`, `prod_primeFactors_prod_factorization`, `MvPolynomial.C_neg`, `MvPolynomial.weightedHomogeneousComponent_eq_zero`, `MvPolynomial.aevalTower_comp_toAlgHom`, `MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection`, `ArithmeticFunction.cardFactors_zero`, `MvPolynomial.coeToMvPowerSeries.ringHom_apply`, `MvPolynomial.restrictSupport_add`, `MvPolynomial.eval₂_X_pow`, `MvPolynomial.zeroLocus_span`, `MvPolynomial.instIsCancelMulZeroOfIsCancelAdd`, `MvPolynomial.coeffs_map`, `MvPolynomial.totalDegree_monomial_le`, `factorization_pow_self`, `MvPowerSeries.totalDegree_truncFinset`, `MvPolynomial.IsHomogeneous.rename_isHomogeneous`, `WittVector.polyOfInterest_vars_eq`, `IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end`, `Polynomial.degree_le_zero_iff`, `WeierstrassCurve.Jacobian.map_polynomial`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom`, `MvPolynomial.mapEquiv_trans`, `MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop`, `MvPolynomial.isNoetherianRing`, `MvPolynomial.constantCoeff_comp_C`, `MvPolynomial.pderiv_inr_universalFactorizationMap_X`, `MvPolynomial.degrees_zero`, `MvPolynomial.IsHomogeneous.mul`, `MvPolynomial.sumAlgEquiv_symm_apply`, `MvPolynomial.eval₂_comp`, `MvPolynomial.weightedHomogeneousComponent_C_mul`, `MonomialOrder.leadingCoeff_zero`, `digit_sum_le`, `MvPolynomial.eval₂_pUnitAlgEquiv_symm`, `Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul`, `factorizationEquiv_apply`, `Submonoid.mem_closure_range_iff`, `WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero`, `MvPolynomial.dvd_C_iff_exists`, `Algebra.Generators.ker_eq_ker_aeval_val`, `MvPolynomial.instIsPushout_1`, `MvPowerSeries.coeff_zero_X`, `WittVector.wittNeg_zero`, `Algebra.Generators.ker_ofAlgHom`, `MvPolynomial.mul_monomial_mem_coeffsIn`, `MvPolynomial.IsHomogeneous.sum`, `Multiset.toDFinsupp_le_toDFinsupp`, `MvPolynomial.supported_empty`, `MvPolynomial.C_mem_pow_idealOfVars_iff`, `Multiset.toDFinsupp_toMultiset`, `Polynomial.isUnit_iff_degree_eq_zero`, `Polynomial.degree_pos_of_aeval_root`, `instIsAlgebraicMvPolynomialOfNoZeroDivisors_1`, `ArithmeticFunction.cardDistinctFactors_one`, `MvPolynomial.esymmPart_zero`, `Algebra.Generators.toExtension_algebra₁`, `KaehlerDifferential.mvPolynomialBasis_repr_D`, `ArithmeticFunction.carmichael_eq_exponent'`, `MonomialOrder.sPolynomial_monomial_mul'`, `HahnSeries.coeff_toMvPowerSeries`, `MvPolynomial.pderiv_eq_zero_of_notMem_vars`, `Multiset.toDFinsupp_singleton`, `WittVector.map_frobeniusPoly`, `factorization_eq_card_pow_dvd`, `MvPolynomial.sum_eval_eq_zero`, `MvPolynomial.support_divMonomial`, `CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq`, `MvPolynomial.le_degrees_add_right`, `MvPolynomial.weightedTotalDegree'_zero`, `WittVector.constantCoeff_wittZSMul`, `WeierstrassCurve.Jacobian.polynomialX_eq`, `MvPolynomial.aeval_C_comp_left`, `MvPolynomial.transcendental_X`, `MvPolynomial.msymm_one`, `MvPolynomial.C_mul_X_pow_eq_monomial`, `MvPolynomial.totalDegree_mul`, `factorization_eq_count`, `factorization_factorial_mul_succ`, `MvPolynomial.weightedHomogeneousComponent_mem`, `PosNum.divMod_to_nat_aux`, `MvPolynomial.degrees_rename_of_injective`, `sub_one_mul_sum_div_pow_eq_sub_sum_digits`, `PolynomialLaw.range_φ`, `MvPolynomial.coeff_add`, `OrderedFinpartition.neZero_partSize`, `MvPolynomial.psum_eq_mul_esymm_sub_sum`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight`, `MvPolynomial.eval_C`, `MvPolynomial.IsWeightedHomogeneous.C_mul`, `MvPolynomial.mapAlgHom_apply`, `MvPolynomial.support_zero`, `Algebra.Generators.cotangentRestrict_mk`, `factorization_ordCompl`, `EisensteinSeries.G2_eq_tsum_cexp`, `MvPolynomial.optionEquivLeft_monomial`, `multiplicative_factorization`, `MvPolynomial.rename_eq_zero_iff_of_injective`, `MvPowerSeries.substAlgHom_monomial`, `Polynomial.coeff_homogenize`, `Algebra.Generators.H1Cotangent.δ_eq_δAux`, `Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat`, `IsSimpleRing.exists_ringEquiv_matrix_divisionRing`, `Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul`, `MonomialOrder.leadingCoeff_mul_of_isRegular_left`, `KaehlerDifferential.mvPolynomialBasis_repr_comp_D`, `LieAlgebra.rank_eq_natTrailingDegree`, `WittVector.bind₁_onePoly_wittPolynomial`, `map_wittPolynomial`, `MvPowerSeries.coeff_truncFinset_eq_zero`, `StandardEtalePresentation.toPresentation_algebra_algebraMap_apply`, `MvPolynomial.optionEquivLeft_symm_apply`, `MvPolynomial.exists_coeff_ne_zero`, `factorizationEquiv_inv_apply`, `ArithmeticFunction.LSeriesHasSum_zeta`, `LieAlgebra.Basis.borelUpper_le_biSup`, `MvPolynomial.isLocalization_C_mk'`, `PosNum.divMod_to_nat`, `MvPolynomial.algebraTensorAlgEquiv_tmul`, `MvPolynomial.vars_map`, `tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow`, `MvPolynomial.mem_support_coeff_finSuccEquiv`, `factorization_eq_zero_iff'`, `MvPolynomial.homogeneousSubmodule_one_eq_span_X`, `Algebra.Generators.aeval_val_σ'`, `MvPolynomial.support_sub`, `WittVector.wittOne_zero_eq_one`, `MvPolynomial.eval₂Hom_id_X_eq_join₂`, `Algebra.Generators.Hom.toAlgHom_id`, `Algebra.Generators.Hom.comp_val`, `MvPolynomial.degreeOf_C_mul`, `MvPolynomial.instIsPushout`, `MvPolynomial.C_injective`, `ArithmeticFunction.cardDistinctFactors_pos`, `MvPolynomial.C_mul`, `CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst`, `MvPolynomial.esymm_eq_multiset_esymm`, `ArithmeticFunction.pow_apply`, `MvPolynomial.comap_apply`, `AlgebraicGeometry.AffineSpace.over_over`, `Polynomial.abs_isBoundedUnder_iff`, `MvPolynomial.vars_rename`, `MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars`, `WittVector.bind₁_zero_wittPolynomial`, `Finsupp.weight_sub_single_add`, `IsTranscendenceBasis.mvPolynomial'`, `MvPowerSeries.coeff_killCompl`, `MvPolynomial.totalDegree_finset_sum`, `ArithmeticFunction.carmichael_eq_exponent`, `MonomialOrder.lex_lt_iff`, `sub_one_mul_factorization_factorial`, `MvPowerSeries.aeval_eq_sum`, `Polynomial.natDegree_eq_zero_iff_degree_le_zero`, `AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp`, `MvPolynomial.support_esymm''`, `MvPolynomial.isLocalization`, `MvPolynomial.instExpChar`, `MvPolynomial.divMonomial_monomial_mul`, `StandardEtalePresentation.toPresentation_val`, `AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly`, `MonomialOrder.notMem_support_of_degree_lt`, `MvPolynomial.instIsCancelAddOfIsLeftCancelAdd`, `ordProj_dvd`, `Num.cmp_to_nat`, `MvPolynomial.divMonomial_zero`, `MvPolynomial.sum_monomial_eq`, `MvPolynomial.rename_comp_bind₁`, `MvPolynomial.degrees_monomial_eq`, `WithBot.add_eq_zero_iff`, `MvPolynomial.zeroLocus_top`, `FirstOrder.Language.presburger.definable₁_iff_ultimately_periodic`, `MvPolynomial.aeval_id_eq_join₁`, `MvPolynomial.rename_X`, `Num.to_nat_to_int`, `MvPolynomial.IsSymmetric.C`, `MvPolynomial.pUnitAlgEquiv_monomial`, `Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero`, `MvPolynomial.le_totalDegree`, `MvPolynomial.coeff_monomial`, `MvPolynomial.coeff_mul_monomial`, `Polynomial.homogenize_sub`, `MvPolynomial.eval₂_eq`, `MvPolynomial.degreeOf_zero`, `Associates.count_reducible`, `MvPolynomial.ringHom_ext'_iff`, `MvPolynomial.mem_ideal_span_monomial_image_iff_dvd`, `MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero`, `Algebra.mvPolynomial`, `Num.ofZNum'_toNat`, `IsRegular.monomial`, `Matrix.charpoly.univ_map_eval₂Hom`, `MonomialOrder.leadingCoeff_prod_of_mem_nonZeroDivisors`, `MvPolynomial.comap_id_apply`, `MvPolynomial.aeval_one_tmul`, `Algebra.SubmersivePresentation.ofSubsingleton_σ'`, `factorization_def`, `MvPolynomial.monomial_pow`, `Finsupp.prod_antidiagonal_swap`, `MvPolynomial.divMonomial_add_modMonomial_single`, `MvPolynomial.eval_sum`, `MonomialOrder.degree_prod`, `MvPowerSeries.monomial_zero_one`, `MvPowerSeries.monomial_one_eq`, `MvPolynomial.degreeOf_sub_lt`, `ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomial`, `ArithmeticFunction.cardFactors_eq_zero_iff_eq_zero_or_one`, `MvPolynomial.smul_eq_C_mul`, `MvPolynomial.eval₂_monomial`, `coprime_ordCompl`, `MvPolynomial.counitNat_C`, `Polynomial.degree_leadingCoeff_inv`, `MvPolynomial.finSuccEquiv_rename_finSuccEquiv`, `Prime.pow_dvd_iff_le_factorization`, `Algebra.Presentation.HasCoeffs.relation_mem_range_map`, `MvPolynomial.rename_expand`, `MvPolynomial.homogeneousSubmodule_one_pow`, `MvPolynomial.coeff_mapRange`, `Algebra.Generators.fg_ker_of_finitePresentation`, `Finsupp.Colex.single_le_iff`, `MvPolynomial.prod_X_pow`, `MvPolynomial.universalFactorizationMapPresentation_algebra_smul`, `MonomialOrder.degree_smul`, `Algebra.FiniteType.instMvPolynomialOfFinite`, `MvPolynomial.IsHomogeneous.sum_X_mul_pderiv`, `MvPolynomial.derivation_C_mul`, `LieAlgebra.Basis.borelLower_eq`, `MvPolynomial.aeval_sumElim_pderiv_inl`, `MvPolynomial.monomial_one_dvd_monomial_one`, `AnalyticAt.aeval_mvPolynomial`, `MvPolynomial.mul_monomial_modMonomial`, `MvPolynomial.eval₂_natCast`, `MvPolynomial.tensorEquivSum_one_tmul_X`, `factorization_factorial_le_div_pred`, `LinearMap.polyCharpoly_coeff_eq_zero_iff_of_basis`, `MvPolynomial.iterToSum_C_C`, `MvPolynomial.mapEquiv_refl`, `MvPolynomial.totalDegree_sub_C_le`, `IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing`, `MvPolynomial.coeffAddMonoidHom_apply`, `sum_sum_digits_eq`, `MvPolynomial.coeff_X_mul`, `PowerSeries.expand_one`, `MvPolynomial.supported_univ`, `MvPolynomial.isSymmetric_rename`, `Polynomial.degree_pos_of_irreducible`, `MvPolynomial.one_coeffsIn`, `MvPolynomial.mkDerivationₗ_X`, `MvPolynomial.eval₂_C_mk_eq_zero`, `MvPolynomial.mem_degrees`, `MvPowerSeries.monomial_eq`, `MvPolynomial.universalFactorizationMap_freeMonic`, `ArithmeticFunction.cardFactors_eq_one_iff_prime`, `Algebra.Generators.Hom.toAlgHom_monomial`, `Polynomial.homogenize_zero`, `MvPolynomial.le_degrees_add_left`, `Finsupp.DegLex.wellFoundedLT`, `MonomialOrder.sPolynomial_mem_ideal`, `MvPolynomial.mem_ideal_of_coeff_mem_ideal`, `MvPolynomial.irreducible_of_totalDegree_eq_one`, `MvPolynomial.universalFactorizationMapPresentation_val`, `MvPolynomial.rename_comp_rename`, `MonomialOrder.leadingCoeff_sub_of_lt`, `HahnSeries.toMvPowerSeries_apply`, `MvPolynomial.coe_expand`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero`, `modEq_three_digits_sum`, `MvPolynomial.aeval_sumElim`, `MvPolynomial.universalFactorizationMapPresentation_σ'`, `Multiset.toDFinsupp_inter`, `MvPolynomial.aeval_comp_rename`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing_finite`, `LinearMap.toMvPolynomial_eval_eq_apply`, `KaehlerDifferential.mvPolynomialBasis_repr_symm_single`, `Num.natSize_to_nat`, `Num.le_to_nat`, `MvPolynomial.mem_symmetricSubalgebra`, `MonomialOrder.degree_mul_of_isRegular_left`, `IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed`, `MvPolynomial.support_rename_killCompl_subset`, `dvd_ordProj_of_dvd`, `factorization_pow`, `Cubic.degree_of_d_ne_zero'`, `MvPolynomial.eval₂_rename_prod_mk`, `properDivisors_eq_map_attach_Iio_factorization_prod_pow`, `AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe`, `Finsupp.DegLex.le_iff`, `Algebra.IsAlgebraic.rank_fractionRing_mvPolynomial`, `ordProj_pos`, `MvPolynomial.coeff_linearCombination_X_pow_of_fintype`, `MvPolynomial.mapAlgHom_coe_ringHom`, `MvPolynomial.monomial_sum_one`, `Fin.instNeZeroNatHSubVal_mathlib`, `MvPowerSeries.truncFinset_truncFinset`, `bind₁_wittPolynomial_xInTermsOfW`, `ordCompl_eq_self_iff_zero_or_not_dvd`, `MvPolynomial.schwartz_zippel_sum_degreeOf`, `MvPolynomial.isHomogeneous_C`, `prod_primeFactors_invOn_squarefree`, `MulAction.minimalPeriod_pos`, `Algebra.FinitePresentation.out`, `ordProj_mul`, `factorization_eq_zero_of_remainder`, `MvPolynomial.rename_leftInverse`, `MvPolynomial.totalDegree_smul_le`, `MvPowerSeries.support_truncFinset_subset`, `ArithmeticFunction.sum_Ioc_sigma0_eq_sum_div`, `MonomialOrder.Monic.mul`, `ax_grothendieck_of_locally_finite`, `MvPowerSeries.coeff_truncFinset`, `Algebra.FiniteType.iff_quotient_mvPolynomial''`, `Algebra.Presentation.quotientEquiv_mk`, `Finsupp.toMultiset_single`, `MvPolynomial.esymmAlgHom_fin_bijective`, `MvPolynomial.esymmAlgEquiv_apply`, `AddMonoid.neZero_exponent_of_finite`, `Polynomial.homogenize_C`, `MvPolynomial.eval₂AlgHom_X`, `MvPolynomial.mem_vanishingIdeal_iff`, `MonomialOrder.degree_add_of_lt`, `MvPolynomial.mem_vanishingIdeal_singleton_iff`, `MvPowerSeries.coeff_subst_finite`, `MonomialOrder.div`, `MvPolynomial.weightedTotalDegree'_eq_bot_iff`, `AlgebraicGeometry.AffineSpace.SpecIso_inv_over`, `WittVector.mul_polyOfInterest_aux5`, `Multiset.toDFinsupp_lt_toDFinsupp`, `MvPolynomial.scalarRTensor_symm_apply_single`, `MvPolynomial.expand_zmod`, `ArithmeticFunction.natCoe_apply`, `MonomialOrder.lex_le_iff`, `MvPolynomial.aeval_zero'`, `Multiset.toDFinsupp_union`, `MvPolynomial.weightedTotalDegree_rename_of_injective`, `MvPolynomial.range_mapAlgHom`, `MvPolynomial.counit_C`, `MvPolynomial.weightedHomogeneousComponent_of_mem`, `ArithmeticFunction.carmichael_mul`, `WeierstrassCurve.Projective.baseChange_polynomialZ`, `MvPolynomial.IsHomogeneous.prod`, `MvPowerSeries.order_eq_nat`, `factorization_choose_prime_pow`, `Polynomial.degree_cyclotomic_pos`, `MvPolynomial.irreducible_sumSMulXSMulY`, `MvPolynomial.counitNat_X`, `MonomialOrder.degree_sPolynomial_le`, `Polynomial.degree_pos_of_eval₂_root`, `MonomialOrder.degree_X_add_C`, `MvPolynomial.eval₂Hom_bind₂`, `MvPolynomial.mem_ideal_span_monomial_image`, `ArithmeticFunction.carmichael_factorization`, `MvPolynomial.rename_toMvPolynomial`, `MvPolynomial.aeval_rename`, `MonomialOrder.Monic.add_of_lt`, `WittVector.bind₁_frobeniusPolyRat_wittPolynomial`, `MvPolynomial.optionEquivLeft_symm_C_X`, `MvPolynomial.mul_X_modMonomial`, `Num.mod_to_nat`, `factorization_choose`, `Num.to_nat_inj`, `MvPolynomial.bind₂_bind₂`, `Cubic.degree_of_c_eq_zero`, `MvPolynomial.IsSymmetric.antitone_supDegree`, `WittVector.aeval_verschiebungPoly`, `MvPolynomial.eval₂Hom_bind₁`, `cast_list_sum`, `Module.rankAtStalk_eq_zero_of_subsingleton`, `Polynomial.homogenize_X`, `MvPolynomial.finSuccEquiv_X_zero`, `MvPolynomial.isJacobsonRing_MvPolynomial_fin`, `Num.gcd_to_nat`, `MvPolynomial.degreeOf_prod_le`, `MonomialOrder.monic_one`, `MvPolynomial.degreeOf_eq_natDegree`, `MvPowerSeries.support_expand_subset`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_degree`, `MvPolynomial.coeff_weightedHomogeneousComponent`, `WeierstrassCurve.Projective.dblX_eq`, `MonomialOrder.coeff_mul_of_degree_add`, `Num.castNum_testBit`, `Algebra.Presentation.baseChange_relation`, `MonomialOrder.degree_sub_leadingTerm_lt_degree`, `ArithmeticFunction.cardFactors_mul`, `MonomialOrder.coeff_sPolynomial_sup_eq_zero`, `MonomialOrder.sPolynomial_mem_sup_ideal`, `MvPolynomial.esymm_zero`, `MvPolynomial.rTensor_apply`, `ax_grothendieck_univ`, `MvPolynomial.C_mem_coeffsIn`, `MvPolynomial.bind₁_X_right`, `MvPolynomial.coeff_rename_eq_zero`, `MvPolynomial.disjoint_support_monomial`, `MvPowerSeries.monomial_mul_monomial`, `MonomialOrder.coeff_mul_of_add_of_degree_le`, `Num.size_eq_natSize`, `MvPolynomial.join₂_map`, `ArithmeticFunction.natCoe_mul`, `MvPolynomial.eval₂Hom_C_left`, `MvPolynomial.transcendental_supported_polynomial_aeval_X_iff`, `MvPolynomial.aeval_monomial`, `Polynomial.homogenize_eq_zero_iff`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over`, `StandardEtalePresentation.toPresentation_relation`, `DividedPowerAlgebra.dp_smul`, `MvPolynomial.leadingCoeff_toLex`, `Polynomial.toMvPolynomial_injective`, `modEq_nine_digits_sum`, `Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix`, `factorization_eq_zero_iff`, `MvPolynomial.coeff_eval_eq_eval_coeff`, `MvPolynomial.C_pow`, `LinearMap.polyCharpoly_natDegree`, `MvPolynomial.coeffs_C_subset`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_val`, `MvPolynomial.IsSymmetric.add`, `MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRing`, `MonomialOrder.degree_mul`, `MonomialOrder.degree_monomial_le`, `MvPolynomial.C_sub`, `Algebra.Generators.self_algebra_algebraMap`, `MvPolynomial.esymm_eq_sum_subtype`, `Finsupp.toMultiset_sup`, `Polynomial.natDegree_pos_iff_degree_pos`, `ArithmeticFunction.zeta_eq_zero`, `MvPolynomial.coeff_mul_monomial'`, `MonomialOrder.Monic.prod`, `MvPolynomial.ringKrullDim_of_isNoetherianRing`, `MvPowerSeries.lexOrder_le_of_coeff_ne_zero`, `DFinsupp.toMultiset_inj`, `MvPolynomial.pderiv_X_self`, `MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse`, `WittVector.mul_polyOfInterest_aux3`, `Prime.exists_addOrderOf_eq_pow_padic_val_nat_add_exponent`, `card_pair_lcm_eq`, `WittVector.verschiebungPoly_zero`, `MvPolynomial.pderiv_C`, `factorization_eq_zero_of_non_prime`, `MonomialOrder.degLex_single_lt_iff`, `MvPowerSeries.trunc'_one`, `MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix`, `MvPolynomial.modMonomial_add_divMonomial_single`, `constantCoeff_xInTermsOfW`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_smul`, `MvPolynomial.C_dvd_iff_zmod`, `Num.mul_to_nat`, `MvRatFunc.rank_eq_max_lift`, `MvPolynomial.aeval_prod`, `MvPolynomial.homogeneousSubmodule_mul`, `MonomialOrder.leadingCoeff_one`, `Matrix.toMvPolynomial_mul`, `Polynomial.Bivariate.pderiv_one_equivMvPolynomial`, `WittVector.wittOne_pos_eq_zero`, `Height.mulHeight_eval_le'`, `MvPolynomial.IsHomogeneous.neg`, `MvPowerSeries.trunc_C_mul`, `MvPolynomial.exists_restrict_to_vars`, `MvPolynomial.lcoeff_apply`, `wittStructureInt_rename`, `WittVector.constantCoeff_wittNeg`, `algebraicIndependent_comp_subtype`, `map_wittStructureInt`, `MvPolynomial.algebraTensorAlgEquiv_symm_monomial`, `Finsupp.Colex.single_lt_iff`, `MvPolynomial.restrictSupport_eq_span`, `prod_pow_factorization_centralBinom`, `MonomialOrder.degree_sub_LTerm_lt`, `MvPolynomial.constantCoeff_comp_map`, `Finsupp.sub_single_one_add`, `FirstOrder.Ring.mvPolynomial_zeroLocus_definable`, `MvPolynomial.rank_eq`, `MvPolynomial.vars_add_subset`, `MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq`, `MvPolynomial.aevalTower_algebraMap`, `ArithmeticFunction.cardFactors_one`, `MvPolynomial.optionEquivLeft_elim_eval`, `MvPolynomial.esymm_one`, `MvPolynomial.optionEquivLeft_symm_X`, `SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial`, `MvPolynomial.renameEquiv_symm`, `MvPolynomial.eval₂Hom_C`, `DFinsupp.toMultiset_lt_toMultiset`, `MvPolynomial.counitNat_surjective`, `Finsupp.DegLex.monotone_degree`, `MvPolynomial.support_symmDiff_support_subset_support_add`, `ArithmeticFunction.zeta_mul_apply`, `MvPolynomial.isEmptyRingEquiv_eq_coeff_zero`, `MvPolynomial.sumToIter_C`, `MvPolynomial.mem_coeffs_iff`, `MvPolynomial.X_divMonomial`, `Height.mulHeight_eval_ge'`, `WeierstrassCurve.Projective.dblX_eq'`, `MvPolynomial.eval_expand`, `RingHom.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial`, `StrictOrderedSemiring.toPosSMulStrictMonoNat`, `MvPolynomial.aeval_comp_toMvPolynomial`, `ordCompl_dvd`, `MvPolynomial.divMonomial_add`, `MvPolynomial.finrank_eq_one`, `MvPolynomial.supportedEquivMvPolynomial_symm_C`, `MvPowerSeries.monomial_smul_const`, `Matrix.toMvPolynomial_constantCoeff`, `MvPowerSeries.trunc'_map`, `Cubic.degree_of_c_eq_zero'`, `MvPolynomial.derivation_eqOn_supported`, `MvPolynomial.killCompl_monomial_eq_monomial_comapDomain_of_subset`, `MvPolynomial.eval₂AlgHom_apply`, `MvPolynomial.tensorEquivSum_X_tmul_one`, `MvPolynomial.instIsMaximalVanishingIdealSingletonForallSet`, `factorization_eq_zero_of_lt`, `MvPolynomial.C_inj`, `MvPolynomial.expand_mul_eq_comp`, `WeierstrassCurve.Jacobian.map_polynomialY`, `Finsupp.Lex.single_le_iff`, `MvPolynomial.IsHomogeneous.eval₂`, `MvPolynomial.eval₂_pUnitAlgEquiv`, `MvPolynomial.eval_X`, `MvPowerSeries.hasSum_eval₂`, `Ideal.mem_span_pow_iff_exists_isHomogeneous`, `MvPolynomial.killCompl_monomial`, `Polynomial.map_map_freeMonic`, `MonomialOrder.degree_prod_of_regular`, `Partition.coeff_genFun`, `MvPolynomial.supported_eq_range_rename`, `factorization_gcd`, `MvPolynomial.trdeg_of_isDomain`, `ArithmeticFunction.carmichael_lcm`, `WeierstrassCurve.Projective.dblY_of_Y_eq'`, `MvPolynomial.support_esymm`, `MvPolynomial.IsHomogeneous.C_mul`, `MvPolynomial.rename_hsymm`, `MonomialOrder.sPolynomial_decomposition'`, `PosNum.to_nat_eq_succ_pred`, `MvPolynomial.constantCoeff_map`, `MvPolynomial.transcendental_supported_X`, `MvPolynomial.degrees_add_of_disjoint`, `IsLinearSet.definable`, `DividedPowerAlgebra.dp_add`, `MvPolynomial.aeval_natDegree_le`, `AnalyticOnNhd.eval_continuousLinearMap'`, `MvPolynomial.degreeOf_neg`, `MvPolynomial.scalarRTensor_apply_tmul_apply`, `MvPolynomial.optionEquivLeft_symm_C_C`, `MvPowerSeries.le_lexOrder_mul`, `WithBot.coe_nonneg`, `C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum`, `Algebra.Generators.Hom.algebraMap_toAlgHom`, `MvPolynomial.IsSymmetric.sub`, `MvPolynomial.coeffsIn_le`, `MonomialOrder.C_mul_leadingCoeff_monomial_degree`, `WittVector.coeff_frobenius`, `MvPolynomial.degreeOf_mul_X_of_ne`, `ArithmeticFunction.cardFactors_apply_prime`, `Finsupp.nsmul_single_one_image`, `Function.locallyFinsuppWithin.single_pos_nat_one`, `Finsupp.DegLex.lt_def`, `Algebra.Generators.comp_σ`, `AnalyticOnNhd.eval_mvPolynomial`, `MvPolynomial.support_smul`, `MvPowerSeries.monomial_smul_eq`, `MvPowerSeries.truncFinset_apply`, `Finsupp.sum_eq_one_iff`, `DividedPowerAlgebra.dp_null_of_ne_zero`, `WeierstrassCurve.Projective.map_polynomialY`, `MvPolynomial.tensorEquivSum_C_tmul_C`, `MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous`, `MvPolynomial.finsum_weightedHomogeneousComponent`, `Algebra.Presentation.instFinitePresentationQuotientOfFinite`, `WeierstrassCurve.Projective.map_polynomial`, `WittVector.wittSub_zero`, `ArithmeticFunction.sigma_eq_sum_div`, `DividedPowerAlgebra.mkRingHom_C`, `MvPolynomial.eval₂_assoc`, `MvPolynomial.instIsDomainOfIsCancelAdd`, `MvPowerSeries.subst_coe`, `MvPolynomial.coeff_zero_one`, `MvPolynomial.mapEquivMonic_symm_map_algebraMap`, `MvPolynomial.support_X`, `WittVector.wittZero_eq_zero`, `MvPolynomial.coe_aeval_eq_eval`, `factorization_inj`, `Finsupp.toMultiset_sum_single`, `WeierstrassCurve.Projective.eval_polynomialY`, `factorization_prod`, `Multiset.toFinsupp_support`, `DividedPowerAlgebra.prod_dp`, `exists_integral_inj_algHom_of_fg`, `MvPolynomial.coeff_rename_ne_zero`, `MvPowerSeries.coeff_mul_of_add_lexOrder`, `Num.pred_to_nat`, `MvPolynomial.instIsLocalHomRingHomC`, `MvPolynomial.eval₂_eq_eval_map`, `MvPolynomial.coeff_add_pow`, `Finsupp.weight_eq_zero_iff_eq_zero`, `Finsupp.toMultiset_map`, `MvPolynomial.weightedTotalDegree_zero`, `Matrix.charpoly.univ_coeff_card`, `Polynomial.Bivariate.equivMvPolynomial_C_C`, `MonomialOrder.degree_sub_of_lt`, `DividedPowerAlgebra.mkAlgHom_C`, `MvPolynomial.isWeightedHomogeneous_C`, `MvPolynomial.linearMap_ext_iff`, `FirstOrder.Language.presburger.term_realize_eq_add_dotProduct`, `MvPolynomial.map_X`, `PerfectClosure.mk_zero`, `MvPolynomial.eval_assoc`, `MvPolynomial.monomial_single_add`, `ax_grothendieck_zeroLocus`, `wittPolynomial_eq_sum_C_mul_X_pow`, `Polynomial.homogenize_one`, `MvPolynomial.support_X_mul`, `MvPolynomial.coeffs_zero`, `MvPolynomial.monomial_one_mul_cancel_right_iff`, `MonomialOrder.degree_mul'`, `constantCoeff_wittStructureInt_zero`, `Polynomial.homogenizeLM_apply`, `Algebra.Generators.ker_naive`, `MvPolynomial.degreeOf_monomial_eq`, `MvPolynomial.vanishingIdeal_zeroLocus_eq_radical`, `bitIndices_twoPowsum`, `factorization_mul_of_coprime`, `Multiset.toFinsupp_strictMono`, `Polynomial.homogenize_mul`, `MonomialOrder.degree_sPolynomial_lt_sup_degree`, `MonomialOrder.leadingTerm_eq_zero_iff`, `instFreeMvPolynomialKaehlerDifferential`, `isPrimePow_iff_minFac_pow_factorization_eq`, `ArithmeticFunction.cardFactors_apply_prime_pow`, `MvPolynomial.hom_bind₁`, `WeierstrassCurve.Jacobian.map_polynomialX`, `MvPolynomial.coeff_expand_zero`, `MvPolynomial.C_dvd_iff_map_hom_eq_zero`, `MvPolynomial.IsSymmetric.neg`, `Finsupp.toMultiset_inf`, `IsSimpleRing.exists_algEquiv_matrix_divisionRing`, `support_factorization`, `rank_mvPolynomial_mvPolynomial`, `AnalyticOnNhd.eval_continuousLinearMap`, `MvPowerSeries.LinearTopology.hasBasis_nhds_zero`, `Polynomial.Monic.degree_le_zero_iff_eq_one`, `WeierstrassCurve.Jacobian.eval_polynomialZ`, `FirstOrder.Language.presburger.isSemilinearSet_formula_realize_semilinear`, `IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_end`, `MvPolynomial.vars_sum_subset`, `MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton`, `Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial`, `ordCompl_self_pow`, `MvPolynomial.degreeOf_add_le`, `Matrix.mvPolynomialX_mapMatrix_aeval`, `MvPolynomial.algebraMap_def`, `IsSemilinearSet.definable`, `MonomialOrder.leadingCoeff_mul_of_mul_leadingCoeff_ne_zero`, `MvPolynomial.support_C`, `MvPolynomial.supported_eq_vars_subset`, `MvPolynomial.coeffs_X_mul`, `MvPowerSeries.monomial_eq'`, `DividedPowerAlgebra.embed_def`, `MonomialOrder.degree_sub_leadingTerm_lt_iff`, `MvPolynomial.IsHomogeneous.coeff_isHomogeneous_of_optionEquivLeft_symm`, `MvPolynomial.eval₂_comp_right`, `factorization_zero_right`, `MvPolynomial.weightedHomogeneousComponent_apply`, `Polynomial.aeval_homogenize_of_eq_one`, `pow_factorization_choose_le`, `Finsupp.coe_orderIsoMultiset`, `MonomialOrder.degree_mul_of_right_mem_nonZeroDivisors`, `factorization_le_of_le_pow`, `MvPolynomial.map_eval`, `MonomialOrder.degree_sub_leadingTerm_le`, `Field.instNeZeroFinInsepDegree`, `Polynomial.homogenize_dvd`, `MvPolynomial.rename_eq`, `MvPolynomial.rank_eq_lift`, `Prime.sub_one_mul_multiplicity_factorial`, `Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det`, `MvPolynomial.totalDegree_coeff_optionEquivLeft_le`, `Finsupp.lt_wf`, `MvPolynomial.derivation_ext_iff`, `MvPolynomial.coeff_mul`, `MvPolynomial.eval₂Hom_smul`, `WittVector.wittAdd_zero`, `Finsupp.DegLex.single_strictAnti`, `MvPolynomial.mapEquivMonic_symm_map`, `ringKrullDim_mvPolynomial_of_isEmpty`, `MvPolynomial.IsHomogeneous.pderiv`, `MvPolynomial.mem_ideal_span_X_image`, `FirstOrder.Language.presburger.definable_iff_isSemilinearSet`, `char_dvd_card_solutions_of_fintype_sum_lt`, `MvPolynomial.mem_restrictTotalDegree`, `MvPolynomial.vars_0`, `Polynomial.homogenize_neg`, `MvPolynomial.isHomogeneous_X_pow`, `MvPolynomial.vars_add_of_disjoint`, `MvPolynomial.restrictTotalDegree_le_restrictDegree`, `factorization_eq_of_coprime_left`, `factorization_one`, `Algebra.SubmersivePresentation.basisDeriv_apply`, `MvPolynomial.bind₁_monomial`, `LinearMap.polyCharpoly_coeff_eval`, `MvPolynomial.induction_on_monomial`, `MvPolynomial.degreeOf_lt_iff`, `MonomialOrder.degree_smul_of_mem_nonZeroDivisors`, `Multiset.toDFinsupp_inj`, `MvPolynomial.coe_coeffsIn`, `MvPolynomial.coe_mul`, `MvPolynomial.mem_image_comap_C_basicOpen`, `MvPolynomial.continuous_eval`, `Algebra.Presentation.mem_ker_naive`, `MvPolynomial.C_eq_smul_one`, `MvPowerSeries.coeff_mul`, `MvPolynomial.coeff_killCompl`, `MvPolynomial.vars_monomial_single`, `MvPolynomial.evalₗ_apply`, `Polynomial.degree_natCast_le`, `Polynomial.degree_coe_units`, `Finsupp.Colex.single_strictMono`, `Polynomial.natDegree_list_prod_le`, `MvPolynomial.esymmAlgHom_surjective`, `Iic_factorization_prod_pow_injective`, `MvPolynomial.aevalTower_ofNat`, `MvPolynomial.killCompl_monomial_eq_zero_of_notMem_range`, `MvPolynomial.monomial_modMonomial`, `MvPolynomial.WeightedHomogeneousSubmodule.gradedMonoid`, `instPosSMulStrictMonoNatOfIsOrderedAddMonoid`, `MvPolynomial.esymmAlgEquiv_symm_apply`, `MvPowerSeries.lexOrder_mul_ge`, `ArithmeticFunction.carmichael_two_pow_of_ne_two`, `instIsPushoutFractionRingMvPolynomial_1`, `MvPolynomial.rename_surjective`, `Finsupp.toMultiset_eq_iff`, `ArithmeticFunction.toFun_eq`, `MvPolynomial.map_id`, `MvPowerSeries.coeff_add_monomial_mul`, `MvPolynomial.eval₂Hom_comp_expand`, `Polynomial.toMvPolynomial_C`, `MonomialOrder.degree_sub_LTerm_le`, `factorization_le_factorization_of_dvd_right`, `ordCompl_of_not_prime`, `MonomialOrder.lex_le_iff_of_unique`, `MonomialOrder.sPolynomial_mul_monomial`, `MonomialOrder.degree_prod_of_mem_nonZeroDivisors`, `Algebra.Generators.toExtension_commRing`, `factorization_factorial_mul`, `ArithmeticFunction.cardDistinctFactors_eq_cardFactors_iff_squarefree`, `MvPowerSeries.trunc'_C`, `MvPowerSeries.prod_monomial`, `MonomialOrder.degree_pow_of_pow_leadingCoeff_ne_zero`, `Algebra.Generators.Hom.equivAlgHom_apply_coe`, `MvPolynomial.decomposition.decompose'_eq`, `Algebra.Generators.C_mul_X_sub_one_mem_ker`, `MvPolynomial.universalFactorizationMapPresentation_jacobian`, `MvPowerSeries.prod_smul_X_eq_smul_monomial_one`, `DividedPowerAlgebra.dp_eq_mkRingHom`, `MonomialOrder.sPolynomial_leadingTerm_mul`, `Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap`, `squarefree_iff_factorization_le_one`, `MvPolynomial.esymmAlgHom_injective`, `MvPolynomial.coeff_sum`, `MvPowerSeries.trunc'_C_mul`, `MvPolynomial.commAlgEquiv_C_X`, `MvPolynomial.expand_zero_apply`, `Polynomial.homogenize_monomial`, `List.sum_fixedLengthDigits_sum`, `Finsupp.DegLex.wellFounded`, `MvPowerSeries.truncFinset_truncFinset_pow`, `WeierstrassCurve.Projective.negDblY_of_Y_eq'`, `Polynomial.coeff_freeMonic`, `MonomialOrder.degree_sPolynomial`, `Num.add_to_nat`, `Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap'`, `MvPolynomial.renameSymmetricSubalgebra_apply_coe`, `Polynomial.degree_C_le`, `Algebra.FinitePresentation.iff_quotient_mvPolynomial'`, `MvPolynomial.monomial_dvd_monomial`, `MonomialOrder.degree_X_le_single`, `MvPolynomial.coe_mapEquivMonic_comp`, `MvPolynomial.eq_zero_of_eval_zero_at_prod_finset`, `MvPolynomial.transcendental_supported_polynomial_aeval_X`, `card_finMulAntidiag_of_squarefree`, `instIsPushoutFractionRingMvPolynomial`, `Height.max_mulHeightBound_zero_one_eq_one`, `MvPolynomial.monomial_mul_modMonomial`, `MvPolynomial.eval_polynomial_eval_finSuccEquiv`, `MvPolynomial.constantCoeff_comp_algebraMap`, `MvPolynomial.sumToIter_Xl`, `LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly`, `Finsupp.image_pow_eq_finsuppProd_image`, `DividedPowerAlgebra.dp_null`, `MvPolynomial.pderiv_inl_universalFactorizationMap_X`, `WittVector.constantCoeff_wittSub`, `divisors_eq_image_Iic_factorization_prod_pow`, `zeckendorf_sum_fib`, `MvPolynomial.counit_X`, `MvPolynomial.instFaithfulSMul`, `MvPolynomial.rename_id`, `MvPolynomial.eval₂Hom_comp_C`, `factorization_factorial_eq_zero_of_lt`, `Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val`, `MvPolynomial.idealOfVars_fg`, `MvPolynomial.rTensorAlgHom_apply_eq`, `List.getElem_splitWrtCompositionAux`
`instMulZeroOneClass` 📖	CompOp	130 math math: `Cardinal.toNat_ofENat`, `Cardinal.toNat_surjective`, `Cardinal.toNat_ofNat`, `Ideal.finite_setOf_absNorm_le₀`, `Ideal.absNorm_span_insert`, `summable_riemannZetaSummand`, `Cardinal.toNat_eq_iff`, `Cardinal.toNat_congr`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst`, `NumberField.FinitePlace.norm_def'`, `Ideal.finite_setOf_absNorm_eq`, `NumberField.HeightOneSpectrum.NumberField.toNNReal_valued_eq_adicAbv`, `Cardinal.toNat_mul`, `NumberField.HeightOneSpectrum.rankOne_hom'_def`, `FractionalIdeal.absNorm_eq'`, `Ideal.absNorm_pos_iff_mem_nonZeroDivisors`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le`, `Ideal.absNorm_eq_pow_inertiaDeg'`, `Cardinal.toNat_apply_of_aleph0_le`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion`, `Ideal.absNorm_eq_pow_inertiaDeg_of_liesOver`, `Ideal.absNorm_mem`, `EulerProduct.eulerProduct_completely_multiplicative`, `Matrix.cRank_toNat_eq_rank`, `NumberField.HeightOneSpectrum.adicAbv_def`, `Cardinal.cast_toNat_eq_iff_lt_aleph0`, `Matrix.cRank_toNat_eq_finrank`, `Cardinal.toNat_monotoneOn`, `Cardinal.mk_toNat_eq_card`, `Ring.HasFiniteQuotients.finite_absNorm_heightOneSpectrum_le`, `NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def`, `Ring.HasFiniteQuotients.finite_absNorm_le`, `NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow`, `EulerProduct.eulerProduct_completely_multiplicative_tprod`, `NumberField.FinitePlace.IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm`, `ENat.coe_toNatHom`, `tsum_riemannZetaSummand`, `Cardinal.toNat_rightInverse`, `Cardinal.toNat_strictMonoOn`, `Ideal.relNorm_int`, `Cardinal.toNat_le_toNat`, `Ideal.absNorm_dvd_absNorm_of_le`, `NumberField.Ideal.tendsto_norm_le_div_atTop₀`, `Cardinal.toNat_lt_iff_lt_of_lt_aleph0`, `NumberField.HeightOneSpectrum.embedding_mul_absNorm`, `Int.absNorm_under_mem`, `Cardinal.toNat_lift`, `EulerProduct.eulerProduct_completely_multiplicative_hasProd`, `ENat.toNatHom_apply`, `FractionalIdeal.absNorm_eq`, `summable_dirichletSummand`, `Cardinal.toNat_eq_one`, `Cardinal.toNat_toENat`, `IsPrimitiveRoot.not_coprime_norm_of_mk_eq_one`, `NumberField.FinitePlace.norm_def_int`, `Ideal.card_norm_le_eq_card_norm_le_add_one`, `IntermediateField.relfinrank_eq_toNat_relrank`, `Subfield.relfinrank_eq_toNat_relrank`, `Cardinal.mk_toNat_of_infinite`, `Cardinal.toNat_eq_iff_of_lt_aleph0`, `NumberField.absNorm_differentIdeal`, `Ideal.absNorm_top`, `Ideal.absNorm_apply`, `Ideal.absNorm_pos_of_nonZeroDivisors`, `Cardinal.cast_toNat_of_aleph0_le`, `Cardinal.toNat_le_iff_of_lt_aleph0`, `Cardinal.toNat_inj_of_lt_aleph0`, `Int.absNorm_under_dvd_absNorm`, `Cardinal.toNat_injOn`, `Int.natAbsHom_apply`, `NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm`, `Cardinal.toNat_le_iff_le_of_lt_aleph0`, `tsum_dirichletSummand`, `NumberField.exists_ideal_in_class_of_norm_le`, `NumberField.Ideal.tendsto_norm_le_div_atTop`, `Cardinal.toNat_eq_one_iff_unique`, `Ideal.natAbs_det_equiv`, `Ideal.absNorm_eq_one_iff`, `NumberField.torsionOrder_dvd_absNorm_sub_one`, `NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal`, `Cardinal.toNat_lt_toNat`, `EulerProduct.one_sub_inv_eq_geometric_of_summable_norm`, `Cardinal.cast_toNat_of_lt_aleph0`, `Cardinal.toNat_eq_zero`, `Field.finSepDegree_eq`, `Ideal.finite_setOf_absNorm_le`, `Ideal.span_singleton_absNorm`, `Field.finInsepDegree_def'`, `NumberField.HeightOneSpectrum.NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def`, `FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm`, `Ideal.absNorm_eq_pow_inertiaDeg`, `NumberField.HeightOneSpectrum.one_lt_absNorm`, `Ideal.absNorm_eq_zero_iff`, `IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one`, `Cardinal.aleph0_toNat`, `MonoidWithZeroHom.ext_nat_iff`, `Cardinal.toNat_natCast`, `Ideal.absNorm_bot`, `NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop`, `Cardinal.toNat_apply_of_lt_aleph0`, `Int.ideal_span_absNorm_eq_self`, `Cardinal.toNat_lift_add_lift`, `Cardinal.toNat_pos`, `NumberField.HeightOneSpectrum.toNNReal_valued_eq_adicAbv`, `NumberField.FinitePlace.norm_embedding'`, `Cardinal.toNat_add`, `Ideal.absNorm_relNorm`, `Int.absNorm_under_eq_sInf`, `Ideal.absNorm_span_singleton`, `FractionalIdeal.coeIdeal_absNorm`, `Ideal.absNorm_algebraMap`, `Int.cast_mem_ideal_iff`, `Ideal.span_singleton_absNorm_le`, `Ideal.natAbs_det_basis_change`, `NumberField.HeightOneSpectrum.one_lt_absNorm_nnreal`, `Ideal.ringChar_quot`, `Int.liesOver_span_absNorm`, `Cardinal.zero_toNat`, `NumberField.FinitePlace.norm_embedding_int`, `MonoidWithZeroHomClass.ext_nnrat_iff`, `Cardinal.aleph_toNat`, `Cardinal.natCast_toNat_le`, `absNorm_under_prime`, `MonoidWithZeroHom.ENatMap_apply`, `NumberField.FinitePlace.norm_def`, `EulerProduct.exp_tsum_primes_log_eq_tsum`, `Cardinal.toNat_eq_ofNat`, `Cardinal.one_toNat`, `Cardinal.continuum_toNat`, `Ideal.absNorm_dvd_norm_of_mem`
`instSemigroupWithZero` 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`instIsCancelMulZero` 📖	mathematical	—	`IsCancelMulZero` `MulZeroClass.toZero` `instMulZeroClass`	—	—
`instMulDivCancelClass` 📖	mathematical	—	`MulDivCancelClass` `instMonoidWithZero`	—	—

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