Defs

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

Statistics

Metric	Count
Definitions `CancelCommMonoidWithZero`, `toCommMonoidWithZero`, `CancelMonoidWithZero`, `toMonoidWithZero`, `CommGroupWithZero`, `toCommMonoidWithZero`, `toDiv`, `toGroupWithZero`, `toInv`, `zpow`, `CommMonoidWithZero`, `toCommMonoid`, `toMonoidWithZero`, `toZero`, `toDiv`, `toDivInvMonoid`, `toInv`, `toMonoidWithZero`, `zpow`, `IsCancelMulZero`, `IsLeftCancelMulZero`, `IsRightCancelMulZero`, `toMonoid`, `toMulZeroOneClass`, `toSemigroupWithZero`, `toZero`, `MulDivCancelClass`, `MulZeroClass`, `toMul`, `toZero`, `MulZeroOneClass`, `toMulOneClass`, `toMulZeroClass`, `toZero`, `SemigroupWithZero`, `toMulZeroClass`, `toSemigroup`, `toZero`	38
Theorems `toIsLeftCancelMulZero`, `toIsCancelMulZero`, `div_eq_mul_inv`, `inv_zero`, `mul_inv_cancel`, `toNontrivial`, `zpow_neg'`, `zpow_succ'`, `zpow_zero'`, `mul_zero`, `zero_mul`, `div_eq_mul_inv`, `inv_zero`, `mul_inv_cancel`, `toMulDivCancelClass`, `toNontrivial`, `zpow_neg'`, `zpow_succ'`, `zpow_zero'`, `toIsLeftCancelMulZero`, `toIsRightCancelMulZero`, `mul_left_cancel_of_ne_zero`, `to_isCancelMulZero`, `to_isRightCancelMulZero`, `to_noZeroDivisors`, `mul_right_cancel_of_ne_zero`, `to_isCancelMulZero`, `to_isLeftCancelMulZero`, `to_noZeroDivisors`, `mul_zero`, `zero_mul`, `mul_div_cancel`, `mul_zero`, `zero_mul`, `mul_zero`, `zero_mul`, `eq_zero_or_eq_zero_of_mul_eq_zero`, `mul_zero`, `zero_mul`, `eq_zero_or_one_of_sq_eq_self`, `inv_zero`, `isCancelMulZero_iff`, `isCancelMulZero_iff_forall_isRegular`, `isLeftCancelMulZero_iff`, `isRightCancelMulZero_iff`, `mul_div_cancel_left₀`, `mul_div_cancel_right₀`, `mul_eq_mul_left_iff`, `mul_eq_mul_right_iff`, `mul_eq_zero`, `mul_eq_zero_comm`, `mul_eq_zero_iff_left`, `mul_eq_zero_iff_right`, `mul_eq_zero_of_left`, `mul_eq_zero_of_right`, `mul_inv_cancel_left₀`, `mul_inv_cancel_right₀`, `mul_inv_cancel₀`, `mul_left_cancel₀`, `mul_left_inj'`, `mul_left_injective₀`, `mul_ne_zero_comm`, `mul_ne_zero_iff`, `mul_ne_zero_iff_left`, `mul_ne_zero_iff_right`, `mul_right_cancel₀`, `mul_right_inj'`, `mul_right_injective₀`, `mul_self_eq_zero`, `mul_self_ne_zero`, `noZeroDivisors_iff`, `noZeroDivisors_iff_eq_zero_of_mul`, `noZeroDivisors_iff_left_eq_zero_of_mul`, `noZeroDivisors_iff_right_eq_zero_of_mul`, `pow_mul_apply_eq_pow_mul`, `zero_eq_mul`, `zero_eq_mul_self`, `zero_ne_mul_self`	78
Total	116

CancelCommMonoidWithZero

Definitions

Name	Category	Theorems
`toCommMonoidWithZero` 📖	CompOp	1 math math: `toIsLeftCancelMulZero`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`toIsLeftCancelMulZero` 📖	mathematical	—	`IsLeftCancelMulZero` `Semigroup.toMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `CommMonoidWithZero.toCommMonoid` `toCommMonoidWithZero` `CommMonoidWithZero.toZero`	—	—

CancelMonoidWithZero

Definitions

Name	Category	Theorems
`toMonoidWithZero` 📖	CompOp	1 math math: `toIsCancelMulZero`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`toIsCancelMulZero` 📖	mathematical	—	`IsCancelMulZero` `Semigroup.toMul` `Monoid.toSemigroup` `MonoidWithZero.toMonoid` `toMonoidWithZero` `MonoidWithZero.toZero`	—	—

CommGroupWithZero

Definitions

Name	Category	Theorems
`toCommMonoidWithZero` 📖	CompOp	53 math math: `ArithmeticFunction.vonMangoldt.residueClass_eq`, `coe_normUnit`, `HasProd.congr_cofinite₀`, `DirichletCharacter.LSeries_eulerProduct_tprod`, `mul_inv_cancel`, `DirichletCharacter.LSeries_modOne_eq`, `DirichletCharacter.LSeriesSummable_of_one_lt_re`, `DirichletCharacter.LSeries_twist_vonMangoldt_eq`, `DirichletCharacter.LFunction_eq_LSeries`, `DirichletCharacter.norm_LSeries_product_ge_one`, `DirichletCharacter.deriv_LFunction_eq_deriv_LSeries`, `DirichletCharacter.LFunction_changeLevel`, `DirichletCharacter.IsPrimitive.completedLFunction_one_sub`, `DirichletCharacter.norm_le_one`, `DirichletCharacter.mul_delta`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero`, `DirichletCharacter.unit_norm_eq_one`, `ArithmeticFunction.vonMangoldt.residueClass_apply`, `DirichletCharacter.LSeriesSummable_mul`, `DirichletCharacter.LSeries_changeLevel`, `DirichletCharacter.LSeries.mul_mu_eq_one`, `Char.card_pow_card`, `zpow_succ'`, `DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow`, `jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum`, `DirichletCharacter.LSeriesSummable_twist_vonMangoldt`, `DirichletCharacter.convolution_twist_vonMangoldt`, `DirichletCharacter.LSeriesSummable_iff`, `DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSum`, `DirichletCharacter.absicssaOfAbsConv_eq_one`, `MulChar.star_apply'`, `DirichletCharacter.norm_LFunction_product_ge_one`, `MulChar.inv_apply_eq_inv'`, `DirichletCharacter.LSeries_eulerProduct_hasProd`, `tsum_dirichletSummand`, `DirichletCharacter.LSeries_eulerProduct_exp_log`, `MulChar.star_eq_inv`, `ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq`, `div_eq_mul_inv`, `MulChar.inv_apply'`, `DirichletCharacter.not_LSeriesSummable_at_one`, `normalize_eq_one`, `inv_zero`, `DirichletCharacter.delta_mul`, `DirichletCharacter.convolution_mul_moebius`, `zpow_zero'`, `Units.mk0_prod`, `Multipliable.congr_cofinite₀`, `DirichletCharacter.modZero_eq_delta`, `DirichletCharacter.fourierTransform_eq_gaussSum_mulShift`, `Multipliable.tsum_congr_cofinite₀`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero`, `DirichletCharacter.LSeries_eulerProduct`
`toDiv` 📖	CompOp	1 math math: `div_eq_mul_inv`
`toGroupWithZero` 📖	CompOp	352 math math: `ArithmeticFunction.IsMultiplicative.pdiv`, `Valuation.mem_nhds_zero_iff`, `Valued.continuous_extension`, `Valuation.IsRankOneDiscrete.generator_lt_one`, `Valued.isOpen_closedball`, `RatFunc.liftMonoidWithZeroHom_apply`, `Set.preimage_const_mul_Ioi₀`, `le_mul_div_mul_left`, `Valuation.inversion_estimate'`, `WithVal.valueGroupOrderIso₀_symm_apply`, `Valuation.ltIdeal_le_leIdeal`, `mul_inv_eq_mul_inv_iff`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁`, `Valuation.isClopen_closedBall`, `HasProd.congr_cofinite₀`, `RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk`, `div_sq_cancel`, `Valued.extension_extends`, `WithVal.valueGroup_eq`, `Valuation.IsRankOneDiscrete.exists_generator_lt_one'`, `signHom_apply`, `le_div_iff₀'`, `NNReal.exists_lt_of_strictMono`, `RatFunc.exists_zpow_uniformizingPolynomial`, `Set.preimage_const_mul_Iio₀`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `WithZeroTopology.nhds_zero`, `Valuation.mem_ltIdeal_iff`, `WithVal.valueGroupOrderIso₀_restrict`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `Valuation.IsRankOneDiscrete.generator_mem_valueGroup`, `MonoidWithZeroHom.ValueGroup₀.monoidWithZeroHom_strictMono`, `WithVal.valueGroupOrderIso₀_apply`, `LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃`, `Set.preimage_const_mul_Ioo₀`, `Valued.toUniformSpace_eq`, `Valuation.instNontrivialSubtypeUnitsMemSubmonoidValueMonoidOfIsNontrivial`, `NumberField.HeightOneSpectrum.rankOne_hom'_def`, `WithVal.valueGroupEquiv_symm_apply`, `Valuation.restrict_eq_one_iff`, `Valuation.IsRankOneDiscrete.generator'_lt_one`, `WithZeroTopology.nhds_zero_of_units`, `ValuationSubring.mapOfLE_valuation_apply`, `lt_div_iff₀'`, `MonoidWithZeroHom.valueGroup.mk_mul`, `MonoidWithZeroHom.fst_mono`, `Valuation.IsEquiv.restrict`, `lt_inv_mul_iff₀'`, `RatFunc.liftMonoidWithZeroHom_apply_div'`, `Valuation.ltAddSubgroup_monotone`, `le_div_comm₀`, `Valuation.ltIdeal_v_le_of_mem`, `Mathlib.Tactic.FieldSimp.NF.eval_inv`, `Valued.isClopen_ball`, `ValuativeRel.ValueGroupWithZero.embed_strictMono`, `ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRel`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval`, `ValuativeRel.ValueGroupWithZero.mk_eq_div`, `lt_div_comm₀`, `Valuation.hasBasis_nhds_zero`, `div_mul_cancel_left₀`, `ValuativeExtension.mapValueGroupWithZero_mk`, `mul_div_mul_left_le`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁`, `Valuation.IsUniformizer.zpowers_eq_valueGroup`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `Valuation.restrict_le_iff`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_strictMono`, `Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval`, `Valued.is_topological_valuation`, `IsValuativeTopology.isOpen_ball`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero`, `Valuation.map_div`, `Valuation.restrict_eq_zero_iff`, `Valuation.restrict_eq_mk`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `div_le_comm₀`, `Valued.continuous_valuation`, `Valuation.restrict_lt_iff_lt_embedding`, `Set.preimage_const_mul_Ico₀`, `Valued.extension_eq_zero_iff`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `div_helper`, `ValuativeExtension.mapValueGroupWithZero_strictMono`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `IsValuativeTopology.isClopen_sphere`, `Mathlib.Tactic.FieldSimp.NF.pow_eq_eval`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero`, `OrderMonoidIso.withZeroUnits_symm_apply`, `MonoidWithZeroHom.inl_strictMono`, `inv_mul_eq_inv_mul_iff`, `Valuation.subgroups_basis`, `OrderMonoidIso.withZeroUnits_apply`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_eq_eval_of_eq_of_eq`, `Valued.isOpen_sphere`, `Valuation.restrict_le_iff_le_embedding`, `NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def`, `denselyOrdered_units_iff`, `OrderIso.withZeroUnits_symm_apply`, `Valuation.isEquiv_restrict`, `Valuation.nonempty_rankOne_iff_mulArchimedean`, `le_mul_inv_iff₀'`, `Valuation.RankOne.exists_val_lt`, `Mathlib.Tactic.FieldSimp.NF.zpow_eq_eval`, `Mathlib.Tactic.FieldSimp.NF.eval_zpow'`, `Valued.hasBasis_nhds_zero`, `Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup`, `SignType.pow_even`, `IsValuativeTopology.mem_nhds_iff'`, `mul_inv_lt_of_lt_mul₀`, `RatFunc.liftMonoidWithZeroHom_apply_div`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `instNontrivialUnitsOfDenselyOrdered`, `WithVal.strictMono_valueGroupOrderIso₀`, `SignType.castHom_apply`, `WithVal.strictMono_valueGroupOrderIso₀_symm`, `Valuation.IsUniformizer.val`, `ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq`, `ValuativeExtension.mapValueGroupWithZero_valuation`, `Set.preimage_const_mul_Ici₀`, `WithVal.valueGroupEquiv_apply`, `Polynomial.valuation_inv_monomial_eq_valuation_X_zpow`, `Valuation.RankOne.strictMono`, `ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀`, `Valued.coe_valuation_eq_rankOne_hom_comp_valuation`, `Polynomial.valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `Valued.isClosed_ball`, `Valuation.restrict_lt_one_iff`, `Valued.isClopen_sphere`, `div_mul_div_cancel₀'`, `LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ`, `Valued.isClosed_sphere`, `IsValuativeTopology.isClosed_closedBall`, `le_inv_mul_iff₀'`, `div_eq_div_iff`, `Polynomial.valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X`, `Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator`, `Mathlib.Tactic.FieldSimp.NF.eval_pow`, `Valuation.cauchy_iff`, `IsValuativeTopology.mem_nhds_zero_iff`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `Valuation.IsRankOneDiscrete.embedding_generator'`, `WithZeroTopology.isClosed_iff`, `WithZeroTopology.hasBasis_nhds_zero`, `div_eq_div_iff_div_eq_div'`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `ValuationSubring.monotone_mapOfLE`, `Valuation.restrict_inj`, `Valuation.ltSubmodule_monotone`, `SignType.zpow_even`, `ValuativeRel.RankLeOneStruct.strictMono`, `Valued.integer.mulArchimedean_mrange_of_isCompact_integer`, `Valuation.embedding_restrict`, `lt_mul_inv_iff₀'`, `mul_div_cancel_of_imp'`, `Valued.closure_coe_completion_v_lt`, `Valued.valuation_isClosedMap`, `WithZeroTopology.nhds_coe_units`, `MonoidWithZeroHom.ValueGroup₀.mk_eq_of_ne_zero`, `Valued.closure_coe_completion_v_mul_v_lt`, `Valued.cauchy_iff`, `Mathlib.Tactic.FieldSimp.list_prod_zpow'`, `mul_div_cancel₀`, `MonoidWithZeroHom.inr_mono`, `Valuation.extendToLocalization_mk'`, `Valuation.IsRankOneDiscrete.generator'_zpowers_eq_top`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `Valuation.restrict_pos_iff`, `IsValuativeTopology.isClopen_ball`, `IsValuativeTopology.hasBasis_nhds`, `Valuation.restrict_def`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₂`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons`, `IsValuativeTopology.hasBasis_nhds_zero`, `Matrix.ProjGenLinGroup.val_signDet_mk`, `Valuation.IsEquiv.orderMonoidIso_trans`, `WithVal.strictMono_valueGroupEquiv_symm`, `Matrix.ProjGenLinGroup.signDet_mk`, `Valuation.mem_ltAddSubgroup_iff`, `Set.preimage_const_mul_Icc₀`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroup`, `Valuation.isClosed_closedBall`, `RatFunc.liftMonoidWithZeroHom_injective`, `div_div_div_cancel_left'`, `IsValuativeTopology.isOpen_closedBall`, `LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ`, `Valuation.integer.v_irreducible_pos`, `Valuation.ltSubmodule_le_leSubmodule`, `Valuation.toTopologicalSpace_eq`, `ValuativeRel.exists_valuation_div_valuation_eq`, `Valuation.leIdeal_zero`, `Valuation.ltAddSubgroup_le_leAddSubgroup`, `LinearOrderedCommGroupWithZero.fst_comp_inl`, `inv_mul_lt_of_lt_mul₀`, `Polynomial.valuation_monomial_eq_valuation_X_pow`, `WithZeroTopology.isOpen_iff`, `WithZeroTopology.instContinuousMul`, `MonoidWithZeroHom.snd_mono`, `Valuation.IsUniformizer.val_pos`, `Valuation.isClopen_ball`, `div_le_div_iff₀`, `div_lt_iff₀'`, `Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div'`, `Set.preimage_const_mul_Ioc₀`, `sign_pow`, `Valuation.Integers.valuation_pos_iff_ne_zero`, `Valued.isOpen_closedBall`, `Valuation.instNontrivialSubtypeUnitsMemSubgroupValueGroupOfIsNontrivial`, `Valuation.hasBasis_nhds`, `RatFunc.valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_X`, `ValuativeRel.isNontrivial_iff_nontrivial_units`, `Valuation.ltSubmodule_v_le_of_mem`, `Valued.mem_nhds_zero`, `Valuation.RankLeOne.exists_val_lt`, `mul_eq_mul_of_div_eq_div`, `Valued.isOpen_ball`, `Valued.mem_nhds`, `div_lt_comm₀`, `Polynomial.valuation_aeval_monomial_eq_valuation_pow`, `Valuation.isOpen_ball`, `Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer`, `mul_div_cancel_left_of_imp`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `IsValuativeTopology.isClosed_ball`, `LinearOrderedCommGroupWithZero.fst_apply`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `Equiv.divLeft₀_apply`, `Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `mul_div_mul_left`, `Valuation.hasBasis_uniformity`, `Valued.toNormedField.norm_def`, `inv_mul_lt_iff₀'`, `Valuation.toUniformSpace_eq`, `Valuation.isOpen_sphere`, `Valuation.norm_def`, `exists_pow_lt₀`, `Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange`, `div_div_cancel₀`, `Valuation.exists_div_eq_of_unit`, `Valuation.restrict_le_one_iff`, `Valuation.isClosed_ball`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `WithZeroTopology.tendsto_units`, `OrderIso.withZeroUnits_apply`, `Valuation.leAddSubgroup_zero`, `WithZeroTopology.Iio_mem_nhds_zero`, `Valuation.IsEquiv.orderMonoidIso_eq_refl`, `divMonoidWithZeroHom_apply`, `Valuation.RankOne.zero_of_hom_zero`, `div_eq_div_of_div_eq_div`, `Valuation.IsEquiv.valueGroup₀Fun_zero`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `Valuation.Integers.valuation_irreducible_pos`, `MonoidWithZeroHom.inr_strictMono`, `Valuation.IsUniformizer.iff`, `Valued.hasBasis_uniformity`, `Equiv.divLeft₀_symm_apply`, `Valuation.mem_ltSubmodule_iff`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `SignType.pow_odd`, `Finset.sup_div₀`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg`, `Valuation.restrict_lt_iff`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `WithZeroTopology.tendsto_zero`, `Valued.isClosed_closedBall`, `Valuation.isOpen_closedBall`, `Valuation.coe_ltAddSubgroup`, `MonoidWithZeroHom.inl_mono`, `mul_inv_lt_iff₀'`, `div_lt_div_iff₀`, `Valuation.RankOne.isNontrivial_restrict`, `Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow`, `ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eq`, `ValuativeRel.restrict_lt_orderMonoidIso`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂`, `Valuation.norm_pos_iff_valuation_pos`, `pow_eq_pow_iff_of_coprime`, `div_div_cancel_left'`, `Units.mk0_prod`, `Units.zero_lt`, `Valuation.ltIdeal_mono`, `star_div₀`, `LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono`, `Valuation.restrict_exists_div_eq`, `Valuation.leSubmodule_zero`, `Units.mulArchimedean_iff`, `Valuation.IsEquiv.orderMonoidIso_spec`, `WithZeroTopology.singleton_mem_nhds_of_units`, `Valuation.RankOne.hom_eq_zero_iff`, `LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered`, `Multipliable.tsum_congr_cofinite₀`, `Valued.isClopen_closedBall`, `Valuation.RankOne.restrict_RankOne_hom_eq`, `div_le_iff₀'`, `LinearOrderedCommGroupWithZero.inl_apply`, `LinearOrderedCommGroupWithZero.inr_apply`, `SignType.coe_pow`, `WithVal.strictMono_valueGroupEquiv`, `IsValuativeTopology.mem_nhds_iff`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `SignType.coe_zpow`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zero`, `Valuation.RankLeOne.strictMono'`, `Mathlib.Tactic.FieldSimp.NF.eval_cons`, `denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units`, `Valuation.exists_setOf_restrict_le_iff`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono`, `WithZeroTopology.nhds_eq_update`, `Real.exists_lt_of_strictMono`, `Valuation.IsRankOneDiscrete.exists_generator_lt_one`, `IsValuativeTopology.isOpen_sphere`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃`, `ValuationSubring.mapOfLE_comp_valuation`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `pow_mem_range_pow_of_coprime`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero`, `MonoidWithZeroHom.ValueGroup₀.embedding_strictMono`, `div_mul_eq_mul_div₀`, `Valuation.IsRankOneDiscrete.generator_mem_range`, `Set.preimage_const_mul_Iic₀`, `IsValuativeTopology.isClopen_closedBall`, `Valuation.exists_div_eq_of_surjective`, `Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow`, `Valuation.mem_nhds_iff`, `Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange`, `Mathlib.Tactic.FieldSimp.NF.inv_eq_eval`, `Valuation.is_topological_valuation`, `Valuation.inversion_estimate`, `Valuation.isClopen_sphere`, `SignType.zpow_odd`, `Valuation.IsEquiv.orderMonoidIso_symm`, `WithZero.withZeroUnitsEquiv_strictMono`, `LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered`, `Valuation.isClosed_sphere`, `inv_mul_le_iff₀'`, `WithZeroTopology.hasBasis_nhds_units`, `instDenselyOrderedUnits`, `WithZeroTopology.instContinuousInv₀`, `Mathlib.Tactic.FieldSimp.NF.cons_zero_eq_div_of_eq_div`, `Valued.extensionValuation_toFun`, `Mathlib.Tactic.FieldSimp.mul_zpow'`, `mul_inv_le_iff₀'`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_of_pow_eq_zero`
`toInv` 📖	CompOp	4 math math: `mul_inv_cancel`, `zpow_neg'`, `div_eq_mul_inv`, `inv_zero`
`zpow` 📖	CompOp	3 math math: `zpow_succ'`, `zpow_neg'`, `zpow_zero'`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`div_eq_mul_inv` 📖	mathematical	—	`toDiv` `Semigroup.toMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `CommMonoidWithZero.toCommMonoid` `toCommMonoidWithZero` `toInv`	—	—
`inv_zero` 📖	mathematical	—	`toInv` `CommMonoidWithZero.toZero` `toCommMonoidWithZero`	—	—
`mul_inv_cancel` 📖	mathematical	—	`Semigroup.toMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `CommMonoidWithZero.toCommMonoid` `toCommMonoidWithZero` `toInv` `Monoid.toOne`	—	—
`toNontrivial` 📖	mathematical	—	`Nontrivial`	—	—
`zpow_neg'` 📖	mathematical	—	`zpow` `toInv`	—	—
`zpow_succ'` 📖	mathematical	—	`zpow` `Semigroup.toMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `CommMonoidWithZero.toCommMonoid` `toCommMonoidWithZero`	—	—
`zpow_zero'` 📖	mathematical	—	`zpow` `Monoid.toOne` `CommMonoid.toMonoid` `CommMonoidWithZero.toCommMonoid` `toCommMonoidWithZero`	—	—

CommMonoidWithZero

Definitions

Name	Category	Theorems
`toCommMonoid` 📖	CompOp	180 math math: `WithTop.prod_lt_top`, `Associates.isAtom_iff`, `UniqueFactorizationMonoid.radical_prod`, `LinearOrderedCommGroupWithZero.mul_inv_cancel`, `HasProd.congr_cofinite₀`, `Associates.prime_pow_dvd_iff_le`, `Associates.le_of_count_ne_zero`, `WithZero.isOrderedMonoid`, `WithZero.mulArchimedean_iff`, `ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors`, `MulChar.toMonoidWithZeroHom_apply`, `Associates.factors_mul`, `CommGroupWithZero.mul_inv_cancel`, `coe_factor_orderIso_map_eq_one_iff`, `Associates.Prime.le_or_le`, `associatesEquivOfUniqueUnits_symm_apply`, `pow_image_of_prime_by_factor_orderIso_dvd`, `UniqueFactorizationMonoid.exists_prime_factors`, `Multiset.prod_eq_zero`, `Finset.emultiplicity_prod`, `UniqueFactorizationMonoid.induction_on_prime_power`, `DFinsupp.prod_eq_zero_iff`, `Localization.liftOn_zero`, `UniqueFactorizationMonoid.associated_finprod_pow_count`, `Submonoid.LocalizationMap.mk'_zero`, `one_le_finprod`, `LinearOrderedCommGroupWithZero.zpow_zero'`, `Finset.prod_le_prod`, `MulChar.mulEquivToUnitHom_apply`, `CancelCommMonoidWithZero.toIsLeftCancelMulZero`, `ValuativeRel.nonempty_orderIso_withZeroMul_int_iff`, `Associates.prod_le_prod_iff_le`, `Finset.prod_ite_zero`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero`, `Associates.instIsOrderedMonoid`, `UniqueFactorizationMonoid.factors_pow_count_prod`, `Associates.out_dvd_iff`, `Prime.not_dvd_finset_prod`, `ArithmeticFunction.IsMultiplicative.multiplicative_factorization`, `Multiset.prod_nonneg`, `zero_mul`, `Finset.lcm_dvd_prod`, `Multiset.le_prod_of_submultiplicative_on_pred_of_nonneg`, `Multiset.prod_map_lt_prod_map`, `Finset.le_prod_max_one`, `Multiset.prod_eq_zero_iff`, `Fintype.prod_ite_zero`, `Valuation.nonempty_rankOne_iff_mulArchimedean`, `UniqueFactorizationMonoid.prime_pow_coprime_prod_of_coprime_insert`, `MulChar.mulEquivToUnitHom_symm_apply`, `Finset.prod_le_one`, `UniqueFactorizationMonoid.normalizedFactors_prod_of_prime`, `ArithmeticFunction.IsMultiplicative.map_prod_of_prime`, `Submonoid.LocalizationMap.nonZeroDivisors_le_comap`, `LinearOrderedCommMonoidWithZero.toIsOrderedMonoid`, `Multiset.mem_le_prod_of_one_le`, `associatesNonZeroDivisorsEquiv_mk_mk`, `mulMonoidWithZeroHom_apply`, `Finset.associated_lcm_prod`, `associatesNonZeroDivisorsEquiv_symm_mk_mk`, `finprod_zero_le_one`, `Multiset.prod_map_nonneg`, `WithTop.prod_eq_top`, `Finset.prod_lt_prod`, `ArithmeticFunction.IsMultiplicative.prod_primeFactors`, `CommGroupWithZero.zpow_succ'`, `WfDvdMonoid.not_unit_iff_exists_factors_eq`, `Associates.prod_add`, `Associates.factors_le`, `MulChar.ringHomComp_inv`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator`, `Finsupp.prod_eq_zero_iff`, `Multiset.le_prod_of_submultiplicative_of_nonneg`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `hasProd_zero_of_exists_eq_zero`, `Valued.integer.mulArchimedean_mrange_of_isCompact_integer`, `finprod_le_finprod`, `Associates.instNoZeroDivisors`, `Submonoid.LocalizationMap.map_nonZeroDivisors_le`, `Multiset.prod_map_le_pow_card`, `ValuativeRel.isRankLeOne_iff_mulArchimedean`, `Multiset.prod_map_le_prod_map₀`, `ValuativeRel.instIsOrderedMonoidValueGroupWithZero`, `Finset.prod_lt_prod_of_nonempty`, `Associates.dvdNotUnit_iff_lt`, `Set.indicator_pi_one_apply`, `ArithmeticFunction.prodPrimeFactors_apply`, `WithTop.prod_eq_top_iff`, `Associates.prod_mono`, `UniqueFactorizationMonoid.radical_prod_dvd`, `Multiset.one_le_prod`, `Associates.exists_mem_multiset_le_of_prime`, `emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso`, `finprod_eq_zero`, `Finset.prod_eq_zero_iff`, `emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso`, `UniqueFactorizationMonoid.factors_prod`, `multipliable_of_exists_eq_zero`, `Associates.count_mul_of_coprime'`, `UniqueFactorizationMonoid.finprod_pow_count_eq_of_subsingleton_units`, `Finsupp.coe_sym2Mul`, `Submonoid.LocalizationMap.map_zero`, `Submonoid.instMonoidWithZeroHomClassLocalizationMap`, `Associates.sup_mul_inf`, `associatesEquivOfUniqueUnits_apply`, `Associates.le_of_mul_le_mul_left`, `tprod_of_exists_eq_zero`, `Associates.instIsCancelMulZero`, `UniqueFactorizationMonoid.prod_normalizedFactors`, `Finset.prod_pos`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `UniqueFactorizationMonoid.normalizedFactors_prod_eq`, `Associates.count_mul`, `CommGroupWithZero.div_eq_mul_inv`, `UniqueFactorizationMonoid.iff_exists_prime_factors`, `Finset.prod_boole`, `Finset.support_prod_subset`, `Finset.prod_eq_zero`, `ArithmeticFunction.IsMultiplicative.map_prod`, `MulChar.inv_apply'`, `UniqueFactorizationMonoid.multiplicative_prime_power`, `Finset.one_le_prod`, `IsPrimitiveRoot.zero`, `WfDvdMonoid.iff_wellFounded_associates`, `Associates.le_one_iff`, `Associates.out_mul`, `Finset.squarefree_prod_of_pairwise_isCoprime`, `Finset.prod_le_prod_of_subset_of_le_one`, `Fintype.prod_boole`, `LinearOrderedCommGroupWithZero.zpow_succ'`, `mul_zero`, `Multiset.one_le_prod_map`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `Associates.prime_pow_le_iff_le_bcount`, `factor_orderIso_map_one_eq_bot`, `prod_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `Associates.instCanonicallyOrderedMul`, `CommGroupWithZero.zpow_zero'`, `UniqueFactorizationMonoid.prod_normalizedFactors_eq`, `Associates.dvd_out_iff`, `WithZero.instMulArchimedean`, `Finset.prod_mono_set_of_one_le`, `map_prime_of_factor_orderIso`, `Units.mk0_prod`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe`, `Submonoid.LocalizationMap.lift₀_apply`, `WithBot.bot_lt_prod`, `WfDvdMonoid.wellFoundedLT_associates`, `Multipliable.congr_cofinite₀`, `WfDvdMonoid.exists_factors`, `LinearOrderedCommGroupWithZero.div_eq_mul_inv`, `Associates.count_mul_of_coprime`, `Units.mulArchimedean_iff`, `Multipliable.tsum_congr_cofinite₀`, `Associates.prod_le`, `Multiset.prod_primes_dvd`, `MulChar.map_zero`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero`, `Finset.prod_anti_set_of_le_one`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactors`, `DivisorChain.exists_chain_of_prime_pow`, `Multiset.prod_pos`, `Localization.mk_zero`, `MulChar.inv_apply`, `ValuativeRel.instMulArchimedeanValueGroupWithZeroOfIsRankLeOne`, `Prime.dvd_finset_prod_iff`, `Associates.prod_coe`, `Finset.prod_nonneg`, `Submonoid.LocalizationMap.lift₀_def`, `Finset.prod_primes_dvd`, `Finset.support_prod`, `UniqueFactorizationMonoid.normalizedFactors_multiset_prod`, `LinearOrderedCommMonoidWithZero.toPosMulStrictMono`, `Associates.le_zero`, `Submonoid.LocalizationMap.sec_zero_fst`, `mul_eq_mul_prime_prod`, `Finsupp.sym2_support_eq_preimage_support_mul`, `Finset.prod_le_prod_of_subset_of_one_le`
`toMonoidWithZero` 📖	CompOp	743 math math: `normalize_one`, `UniqueFactorizationMonoid.dvd_radical_iff`, `GCDMonoid.lcm_zero_right`, `Polynomial.degree_normalize`, `UniqueFactorizationMonoid.factors_one`, `Prime.irreducible`, `MulChar.equivToUnitHom_mul_apply`, `gcd_one_left'`, `UniqueFactorizationMonoid.squarefree_radical`, `Valuation.IsTrivialOn.valuation_algebraMap_le_one`, `Associates.dvd_count_pow`, `ofDual_toAdd_zero`, `Polynomial.coe_normUnit_of_ne_zero`, `CommGroupWithZero.coe_normUnit`, `Associates.isAtom_iff`, `Polynomial.roots_normalize`, `Valuation.FiniteField.algebraMap_le_one`, `Valuation.FiniteField.algebraMap_eq_one`, `lcm_dvd_lcm_mul_right`, `lcm_eq_zero_iff`, `Valuation.one_apply_lt_one_iff`, `normalize_dvd_iff`, `IsRelPrime.moebius_mul`, `Valuation.val_mrange_zero`, `exists_associated_mem_of_dvd_prod`, `Valuation.map_one_add_of_lt`, `Multiset.lcm_eq_zero_iff`, `UniqueFactorizationMonoid.moebius_one`, `Associates.prime_pow_dvd_iff_le`, `Valuation.mem_supp_iff`, `MulChar.toUnitHom_eq`, `Associates.le_of_count_ne_zero`, `Prime.isPrimal`, `mem_nonZeroDivisors_iff_left`, `Prime.associated_of_dvd`, `Valuation.isEquiv_map_self_of_strictMono`, `Associates.mk_out`, `gcd_dvd_gcd_mul_right`, `gcd_mul_lcm`, `UniqueFactorizationMonoid.exists_reduced_factors`, `normUnit_eq_one`, `factorization_pow`, `MulChar.map_one`, `ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff`, `MulChar.toMonoidWithZeroHom_apply`, `Associates.factors_mul`, `PUnit.norm_unit_eq`, `Associates.prod_top`, `WfDvdMonoid.isRelPrime_of_no_irreducible_factors`, `coe_factor_orderIso_map_eq_one_iff`, `gcd_mul_left`, `EReal.coe_ennreal_pow`, `Nat.factors_multiset_prod_of_irreducible`, `Valuation.IsTrivialOn.eq_one`, `Finset.gcd_empty`, `DirichletCharacter.changeLevel_def`, `gcd_greatest`, `UniqueFactorizationMonoid.primeFactors_zero`, `Valuation.toFun_eq_coe`, `Associates.Prime.le_or_le`, `associatesEquivOfUniqueUnits_symm_apply`, `MulChar.map_ringChar`, `pow_image_of_prime_by_factor_orderIso_dvd`, `UniqueFactorizationMonoid.exists_prime_factors`, `Finset.gcd_dvd`, `Multiset.prod_eq_zero`, `Finset.emultiplicity_prod`, `UniqueFactorizationMonoid.induction_on_prime_power`, `Associated.of_pow_associated_of_prime`, `GCDMonoid.toIsCancelMulZero`, `Associates.irreducible_mk`, `Associates.eq_pow_count_factors_of_dvd_pow`, `DFinsupp.prod_eq_zero_iff`, `le_zero_iff`, `Localization.liftOn_zero`, `IsRadical.of_dvd`, `prime_mul_iff`, `Prime.dvd_or_dvd`, `GCDMonoid.gcd_mul_lcm`, `normUnit_mul_normUnit`, `UniqueFactorizationMonoid.isRadical_radical`, `ValuationClass.toMonoidWithZeroHomClass`, `pow_injective_of_not_isUnit`, `normalize_eq_normalize`, `UniqueFactorizationMonoid.associated_finprod_pow_count`, `MulChar.inv_apply_eq_inv`, `prime_factors_irreducible`, `Prime.exists_mem_multiset_map_dvd`, `NormalizedGCDMonoid.normalize_lcm`, `FiniteMultiplicity.multiplicity_pow`, `Submonoid.LocalizationMap.mk'_zero`, `Associates.out_one`, `MulChar.one_apply_coe`, `UniqueFactorizationMonoid.factors_eq_singleton_of_irreducible`, `one_le_finprod`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefree`, `Associates.mk_dvdNotUnit_mk_iff`, `Int.normalize_of_nonneg`, `gcd_assoc'`, `gcd_dvd_gcd_mul_left_right`, `Finset.dvd_gcd`, `gcd_zero_right'`, `Int.normUnit_eq`, `UniqueFactorizationMonoid.normalizedFactors_zero`, `Prime.exists_mem_finset_dvd`, `List.one_le_prod`, `Valuation.IsEquiv.pos_iff`, `MulChar.mulEquivToUnitHom_apply`, `Dvd.dvd.lcm_left`, `gcd_mul_right'`, `Prime.dvd_mul`, `Multiset.lcm_singleton`, `emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactors`, `Polynomial.normUnit_content`, `Valuation.unit_map_eq`, `UniqueFactorizationMonoid.factors_pow`, `UniqueFactorizationMonoid.dvd_of_mem_normalizedFactors`, `Finset.gcd_eq_zero_iff`, `Finset.extract_gcd`, `NormalizationMonoid.normUnit_coe_units`, `Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd`, `Associates.pow_factors`, `dvd_lcm_right`, `lcm_dvd`, `Submonoid.LocalizationMap.subsingleton_iff`, `Finset.lcm_singleton`, `Associates.prod_le_prod_iff_le`, `Polynomial.Monic.normalize_eq_self`, `gcd_eq_normalize`, `FiniteMultiplicity.emultiplicity_self`, `not_prime_zero`, `UniqueFactorizationMonoid.primeFactors_pow'`, `Finset.prod_ite_zero`, `MonoidWithZero.coe_inverse`, `PowerSeries.normUnit_X`, `Prime.exists_mem_multiset_dvd`, `Prime.left_dvd_or_dvd_right_of_dvd_mul`, `Associates.instIsOrderedMonoid`, `UniqueFactorizationMonoid.exists_associated_prime_pow_of_unique_normalized_factor`, `UniqueFactorizationMonoid.factors_pow_count_prod`, `mul_dvd_mul_iff_right`, `Associates.out_dvd_iff`, `factorization_mul`, `Valuation.one_apply_of_ne_zero`, `UniqueFactorizationMonoid.exists_prime_iff`, `UniqueFactorizationMonoid.irreducible_iff_prime`, `Multiset.lcm_mono`, `Prime.not_dvd_finset_prod`, `isPrimePow_iff_pow_succ`, `ArithmeticFunction.IsMultiplicative.multiplicative_factorization`, `Multiset.prod_nonneg`, `OrderMonoidWithZeroHom.mul_comp`, `NormalizationMonoid.normUnit_zero`, `Associates.factorSetMem_eq_mem`, `UniqueFactorizationMonoid.normalize_normalized_factor`, `Associates.out_mk`, `Finset.lcm_dvd_prod`, `nonZeroDivisorsLeft_eq_right`, `normalize_eq_normalize_iff`, `prime_pow_iff`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `Associates.dvdNotUnit_of_lt`, `nonZeroDivisors_dvd_iff_dvd_coe`, `Associates.lcm_mk_mk`, `Associates.count_some`, `Associates.count_zero`, `DivisorChain.element_of_chain_not_isUnit_of_index_ne_zero`, `mul_left_mem_nonZeroDivisors_eq_zero_iff`, `Polynomial.leadingCoeff_normalize`, `Squarefree.gcd_right`, `lcm_eq_left_iff`, `Valuation.coe_coe`, `UniqueFactorizationMonoid.normalizedFactors_mul`, `ofAdd_bot`, `Valuation.IsEquiv.one_lt_iff_one_lt`, `UniqueFactorizationMonoid.factors_rel_of_associated`, `nonZeroDivisorsLeft_eq_nonZeroDivisors`, `powMonoidWithZeroHom_apply`, `Associates.factors_zero`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `UniqueFactorizationMonoid.factors_unique`, `UniqueFactorizationMonoid.normalizedFactors_one`, `MulChar.equivToUnitHom_symm_coe`, `dvd_and_not_dvd_iff`, `List.prod_map_lt_prod_map`, `UniqueFactorizationMonoid.normalizedFactors_pos`, `Prime.not_dvd_mul`, `Finset.le_prod_max_one`, `mem_nonZeroDivisors_iff_right`, `Multiset.prod_eq_zero_iff`, `Fintype.prod_ite_zero`, `lcm_mul_left`, `isUnit_gcd_one_right`, `lcm_comm'`, `isRadical_iff_squarefree_or_zero`, `UniqueFactorizationMonoid.primeFactors_one`, `Prime.not_dvd_one`, `UniqueFactorizationMonoid.prime_pow_coprime_prod_of_coprime_insert`, `Associates.one_or_eq_of_le_of_prime`, `MulChar.mulEquivToUnitHom_symm_apply`, `Finset.prod_le_one`, `dvd_of_lcm_left_dvd`, `ArithmeticFunction.IsMultiplicative.map_prod_of_prime`, `DirichletCharacter.Even.toUnitHom_eval_neg_one`, `Submonoid.LocalizationMap.nonZeroDivisors_le_comap`, `dvd_lcm_of_dvd_left`, `prime_pow_succ_dvd_mul`, `MulChar.pow_apply_coe`, `Associates.factors_subsingleton`, `MulChar.coe_mk`, `UniqueFactorizationMonoid.factors_pos`, `Finset.gcd_mul_left`, `Submonoid.LocalizationMap.noZeroDivisors`, `Finset.normalize_lcm`, `DirichletCharacter.toUnitHom_eq_char'`, `DirichletCharacter.changeLevel_toUnitHom`, `Associates.mem_factorSet_some`, `Valuation.toMonoidWithZeroHom_one`, `Associates.factors_mk`, `gcd_eq_zero_iff`, `IsMulTorsionFree.mk'`, `Associates.le_singleton_iff`, `associatesNonZeroDivisorsEquiv_mk_mk`, `mulMonoidWithZeroHom_apply`, `Multiset.extract_gcd'`, `Squarefree.gcd_left`, `Valuation.HasExtension.val_map_le_one_iff`, `Finset.associated_lcm_prod`, `mul_div_cancel_left₀`, `Nat.Primes.prodNatEquiv_apply`, `emultiplicity_pow_self`, `MulChar.eq_one_iff`, `Finset.gcd_eq_gcd_filter_ne_zero`, `Prime.not_isSquare`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right`, `associatesNonZeroDivisorsEquiv_symm_mk_mk`, `finprod_zero_le_one`, `Multiset.extract_gcd`, `Associates.dvd_of_mem_factors'`, `dvd_mul_gcd_of_dvd_mul`, `isRadical_iff_squarefree_of_ne_zero`, `UniqueFactorizationMonoid.normalizedFactorsEquiv_symm_apply`, `isRelPrime_zero_right`, `MulChar.restrict_ofUnitHom`, `Multiset.gcd_singleton`, `MulChar.val_neg_one_eq_one_of_odd_order`, `Multiset.prod_map_nonneg`, `Irreducible.isUnit_gcd_iff`, `mul_left_coe_nonZeroDivisors_eq_zero_iff`, `Associates.normalize_out`, `MulChar.coe_toMonoidHom`, `UniqueFactorizationMonoid.radical_of_prime`, `Valuation.map_add_le_max'`, `Polynomial.content_C_mul`, `Multiset.lcm_zero`, `Valuation.zero_iff`, `lcm_dvd_mul`, `ArithmeticFunction.IsMultiplicative.prod_primeFactors`, `gcd_one_left`, `MulCharClass.toMonoidHomClass`, `WfDvdMonoid.not_unit_iff_exists_factors_eq`, `GCDMonoid.dvd_gcd`, `Associates.prod_add`, `Associates.factors_le`, `UniqueFactorizationMonoid.multiplicative_of_coprime`, `Int.normalize_coe_nat`, `normalize_eq_zero`, `lcm_mul_right`, `Associated.of_mul_right`, `DivisorChain.isPrimePow_of_has_chain`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `factorization_zero`, `Polynomial.normalize_content`, `FiniteField.valuation_algebraMap_eq_one`, `ThreeGPFree.smul_set₀`, `Valuation.one_apply_eq_zero_iff`, `NormalizedGCDMonoid.normalize_gcd`, `Finsupp.prod_eq_zero_iff`, `normalize_gcd`, `Finsupp.support_sym2Mul_subset`, `normalize_apply`, `Valuation.apply_posSubmonoid_pos`, `Valuation.one_srel_iff`, `Associates.factors_prime_pow`, `exists_eq_pow_of_mul_eq_pow`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `Finset.gcd_mono`, `not_isRelPrime_zero_zero`, `dvd_mul_gcd_iff_dvd_mul`, `MulChar.pow_apply'`, `WfDvdMonoid.exists_irreducible_factor`, `UniqueFactorizationMonoid.primeFactors_mul_eq_union`, `UniqueFactorizationMonoid.primeFactors_mul_eq_disjUnion`, `List.prod_pos`, `Associates.count_pow`, `Finset.lcm_empty`, `Associates.reducible_notMem_factorSet`, `hasProd_zero_of_exists_eq_zero`, `Prime.dvd_prod_iff`, `Associates.factors_mono`, `Associates.factors_eq_some_iff_ne_zero`, `UniqueFactorizationMonoid.radical_associated`, `UniqueFactorizationMonoid.associated_iff_normalizedFactors_eq_normalizedFactors`, `Associates.map_subtype_coe_factors'`, `Valued.integer.mulArchimedean_mrange_of_isCompact_integer`, `lcm_assoc'`, `Padic.valuation_p_lt_one`, `Valuation.map_mul`, `not_isPrimePow_zero`, `UniqueFactorizationMonoid.primeFactors_pow`, `Squarefree.isRadical`, `UniqueFactorizationMonoid.radical_dvd_radical_iff_primeFactors_subset_primeFactors`, `DirichletCharacter.modOne_eq_one`, `normalize_coe_units`, `Associates.mem_factors'_iff_dvd`, `Submonoid.IsLocalizationMap.map_zero`, `WfDvdMonoid.max_power_factor`, `Nat.factors_eq`, `Valuation.one_apply_le_one`, `extract_gcd`, `gcd_one_right`, `gcd_mul_dvd_mul_gcd`, `UniqueFactorizationMonoid.dvd_of_dvd_mul_right_of_no_prime_factors`, `dvd_lcm_left`, `UniqueFactorizationMonoid.irreducible_of_factor`, `Associated.lcm`, `Valuation.map_one_sub_of_lt`, `lcm_dvd_iff`, `mk_mem_nonZeroDivisors_associates`, `Nat.sum_divisors_filter_squarefree`, `Associates.instNoZeroDivisors`, `Prime.dvd_finsuppProd_iff`, `lcm_dvd_lcm_mul_right_right`, `WfDvdMonoid.wfDvdMonoid_associates`, `Associates.mk_normalize`, `Prime.not_dvd_prod`, `Submonoid.LocalizationMap.map_nonZeroDivisors_le`, `Finset.dvd_gcd_iff`, `UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvd`, `Multiset.prod_map_le_pow_card`, `UniqueFactorizationMonoid.radical_one`, `UniqueFactorizationMonoid.radical_pow_dvd`, `Finset.lcm_dvd`, `MulChar.mul_apply`, `Prime.not_unit`, `Valuation.map_one`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_right`, `irreducible_iff_prime_of_exists_prime_factors`, `gcd_same`, `MulChar.ofUnitHom_eq`, `Associates.is_pow_of_dvd_count`, `Finset.extract_gcd'`, `gcd_zero_right`, `Valuation.one_vlt_iff`, `Associates.dvdNotUnit_iff_lt`, `divisor_closure_eq_closure`, `UniqueFactorizationMonoid.dvd_radical_iff_of_irreducible`, `MulChar.restrict_eq_one_iff`, `lcm_one_left`, `gcd_neg'`, `Set.indicator_pi_one_apply`, `multiplicity_pow_self`, `Valuation.one_vle_iff`, `lcm_eq_right_iff`, `ArithmeticFunction.prodPrimeFactors_apply`, `lcm_dvd_lcm_mul_left`, `Multiset.gcd_mono`, `Prime.finiteMultiplicity_mul`, `IsRadical.squarefree`, `IsPrimitiveRoot.injOn_pow_mul`, `Prime.pow_dvd_of_dvd_mul_right`, `Associates.mem_factorSet_top`, `Valuation.IsEquiv.eq_zero`, `Associates.prod_mono`, `Squarefree.dvd_of_squarefree_of_mul_dvd_mul_left`, `UniqueFactorizationMonoid.radical_prod_dvd`, `Associates.ufm`, `Prime.dvd_or_dvd_of_dvd_lcm`, `mul_eq_mul_prime_pow`, `UniqueFactorizationMonoid.radical_zero`, `prime_factors_unique`, `Int.normalize_of_nonpos`, `UniqueFactorizationMonoid.radical_pow`, `Multiset.one_le_prod`, `Associates.exists_mem_multiset_le_of_prime`, `emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso`, `gcd_mul_left'`, `MulChar.one_apply`, `FiniteMultiplicity.of_not_isUnit`, `finprod_eq_zero`, `Finset.prod_eq_zero_iff`, `emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso`, `Associates.out_eq_zero_iff`, `Prime.not_dvd_finsuppProd`, `Finset.gcd_singleton`, `WfDvdMonoid.max_power_factor'`, `normalize_lcm`, `UniqueFactorizationMonoid.factors_prod`, `Associates.mem_factors_iff_dvd`, `Associates.prime_mk`, `lcm_same`, `Prime.isRadical`, `Associates.count_mul_of_coprime'`, `Associates.factors_eq_top_iff_zero`, `irreducible_iff_prime_of_existsUnique_irreducible_factors`, `Valuation.map_apply`, `Polynomial.normalize_eq_self_iff_monic`, `UniqueFactorizationMonoid.finprod_pow_count_eq_of_subsingleton_units`, `Associates.count_factors_eq_find_of_dvd_pow`, `Finsupp.coe_sym2Mul`, `Associates.out_zero`, `Prime.dvd_pow_iff_dvd`, `coe_powMonoidWithZeroHom`, `isUnit_gcd_of_eq_mul_gcd`, `not_lt_zero'`, `Irreducible.normalizedFactors_pow`, `Submonoid.LocalizationMap.map_zero`, `Submonoid.instMonoidWithZeroHomClassLocalizationMap`, `Associates.sup_mul_inf`, `DvdNotUnit.isUnit_of_irreducible_right`, `associatesEquivOfUniqueUnits_apply`, `Valuation.toMonoidWithZeroHom_coe_eq_coe`, `Associates.le_of_mul_le_mul_left`, `Squarefree.dvd_of_squarefree_of_mul_dvd_mul_right`, `Valuation.srel_one_iff`, `GCDMonoid.lcm_zero_left`, `UniqueFactorizationMonoid.normalizedFactors_irreducible`, `Int.abs_eq_normalize`, `tprod_of_exists_eq_zero`, `Dvd.dvd.lcm_right`, `UniqueFactorizationMonoid.moebius_zero`, `Associates.instIsCancelMulZero`, `Multiset.dvd_gcd`, `dvd_of_lcm_right_dvd`, `ArithmeticFunction.IsMultiplicative.eq_iff_eq_on_prime_powers`, `Valuation.vle_one_iff`, `lcm_units_coe_left`, `gcd_dvd_gcd_mul_right_right`, `nonZeroDivisorsRight_eq_left`, `UniqueFactorizationMonoid.prod_normalizedFactors`, `Valuation.IsEquiv.one_le_iff_one_le`, `Finset.prod_pos`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `Finset.gcd_div_id_eq_one`, `gcd_zero_left`, `squarefree_mul_iff`, `Valuation.HasExtension.val_map_eq_one_iff`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors`, `Associates.irreducible_of_mem_factorSet`, `OrderMonoidWithZeroHom.coe_mul`, `UniqueFactorizationMonoid.radical_dvd_self`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_left`, `ofDual_toAdd_eq_top_iff`, `UniqueFactorizationMonoid.normalizedFactors_prod_eq`, `Associates.count_mul`, `multiplicity_mul`, `UniqueFactorizationMonoid.dvd_of_dvd_mul_left_of_no_prime_factors`, `UniqueFactorizationMonoid.iff_exists_prime_factors`, `UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors`, `Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer`, `not_irreducible_of_not_unit_dvdNotUnit`, `count_span_normalizedFactors_eq`, `Finset.prod_boole`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `finiteMultiplicity_mul_aux`, `Valuation.rel_one_iff`, `Finset.support_prod_subset`, `IsPrimal.mul`, `Associates.eq_pow_of_mul_eq_pow`, `gcd_one_right'`, `DivisorChain.second_of_chain_is_irreducible`, `Valuation.IsEquiv.eq_one_iff_eq_one`, `nonZeroDivisorsRight_eq_nonZeroDivisors`, `Finset.prod_eq_zero`, `ArithmeticFunction.IsMultiplicative.map_prod`, `dvd_lcm_of_dvd_right`, `gcd_mul_right`, `UniqueFactorizationMonoid.radical_of_isUnit`, `Associates.exists_prime_dvd_of_not_inf_one`, `UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors`, `exists_squarefree_dvd_pow_of_ne_zero`, `Valuation.vlt_one_iff`, `UniqueFactorizationMonoid.instIsMulTorsionFree`, `UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrime`, `not_isPrimePow_one`, `Associates.irreducible_iff_prime_iff`, `DvdNotUnit.not_unit`, `Polynomial.coe_normUnit`, `MulChar.ofRootOfUnity_spec`, `associated_of_factorization_eq`, `gcd_pow_left_dvd_pow_gcd`, `UniqueFactorizationMonoid.multiplicative_prime_power`, `gcd_isUnit_iff_isRelPrime`, `dvd_normalize_iff`, `Associated.of_mul_left`, `isUnit_gcd_one_left`, `associated_gcd_right_iff`, `Finset.one_le_prod`, `MulChar.map_nonunit`, `associated_normalize_iff`, `DirichletCharacter.apply_eq_toArithmeticFunction_apply`, `IsPrimitiveRoot.zero`, `Valuation.IsEquiv.le_one_iff_le_one`, `Multiset.normalize_lcm`, `DivisorChain.eq_pow_second_of_chain_of_has_chain`, `Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange`, `NormalizationMonoid.normUnit_mul`, `ArithmeticFunction.pmul_comm`, `zero_le'`, `MulChar.restrict_apply`, `WfDvdMonoid.iff_wellFounded_associates`, `dvd_prime_pow`, `Prime.not_dvd_lcm`, `Associates.le_one_iff`, `UniqueFactorizationMonoid.primeFactors_eq_empty_iff`, `Associates.out_mul`, `normUnit_one`, `IsRadical.dvd_radical`, `associated_gcd_left_iff`, `Finset.squarefree_prod_of_pairwise_isCoprime`, `exists_associated_pow_of_mul_eq_pow`, `LinearOrderedCommMonoidWithZero.toIsMulTorsionFree`, `lcm_dvd_lcm`, `DvdNotUnit.not_associated`, `Associates.count_ne_zero_iff_dvd`, `pow_dvd_of_mul_eq_pow`, `CommGroupWithZero.normalize_eq_one`, `mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors`, `UniqueFactorizationMonoid.normalizedFactors_pow`, `neg_gcd`, `Finset.lcm_mono_fun`, `Associates.FactorSet.coe_add`, `Prime.squarefree`, `Fintype.prod_boole`, `isPrimePow_def`, `Submonoid.LocalizationMap.isCancelMulZero`, `Ring.mul_inverse_rev`, `Valuation.HasExtension.mk_smul_mk`, `Finset.gcd_mul_right`, `Valuation.map_pow`, `UniqueFactorizationMonoid.radical_dvd_iff_primeFactors_subset`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff'`, `UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactors`, `FiniteMultiplicity.of_prime_left`, `EReal.coe_pow`, `Associates.eq_pow_find_of_dvd_irreducible_pow`, `MulChar.trivial_apply`, `Multiset.one_le_prod_map`, `Multiset.gcd_zero`, `zero_lt_iff`, `UniqueFactorizationMonoid.normalizedFactors_eq_zero_iff`, `gcd_comm'`, `UniqueFactorizationMonoid.irreducible_of_normalized_factor`, `not_prime_one`, `LinearOrderedCommMonoidWithZero.toMulPosStrictMono`, `emultiplicity_eq_zero_of_irreducible_ne`, `GCDMonoid.gcd_dvd_left`, `emultiplicity_pow`, `not_prime_pow`, `FiniteField.valuation_algebraMap_le_one`, `MulChar.coe_toUnitHom`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `DirichletCharacter.factorsThrough_iff_ker_unitsMap`, `pow_pos_iff`, `Associates.prime_pow_le_iff_le_bcount`, `factor_orderIso_map_one_eq_bot`, `List.prod_map_le_pow_length₀`, `UniqueFactorizationMonoid.radical_mul_dvd`, `prod_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `squarefree_iff_no_irreducibles`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_left`, `UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow`, `instDecompositionMonoidOfNonemptyGCDMonoid`, `dvd_gcd_mul_of_dvd_mul`, `MulCharClass.map_nonunit`, `Associates.mem_factors_of_dvd`, `Associates.instCanonicallyOrderedMul`, `DirichletCharacter.isMultiplicative_toArithmeticFunction`, `instIsCancelMulZero_1`, `FiniteMultiplicity.pow`, `Polynomial.content_C`, `MulChar.ofUnitHom_coe`, `UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors`, `Prime.dvd_of_dvd_pow`, `prime_dvd_prime_iff_eq`, `Multiset.gcd_dvd`, `bot_eq_zero''`, `UniqueFactorizationMonoid.prod_normalizedFactors_eq`, `Multiset.dvd_lcm`, `Associates.dvd_out_iff`, `UniqueFactorizationMonoid.dvd_of_mem_factors`, `Associates.out_injective`, `UniqueFactorizationMonoid.factors_zero`, `Valuation.HasExtension.val_map_lt_one_iff`, `UniqueFactorizationMonoid.radical_pow_of_prime`, `notMem_nonZeroDivisors_iff_left`, `map_prime_of_factor_orderIso`, `gcd_eq_left_iff`, `DirichletCharacter.Odd.toUnitHom_eval_neg_one`, `pow_dvd_pow_iff`, `Nat.divisors_filter_squarefree`, `lcm_dvd_lcm_mul_left_right`, `UniqueFactorizationMonoid.factors_mul`, `Valuation.coe_mk`, `Multiset.gcd_eq_zero_iff`, `irreducible_iff_prime`, `DirichletCharacter.map_zero'`, `Finsupp.sym2Mul_apply_mk`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe`, `OrderMonoidWithZeroHom.comp_mul`, `Submonoid.LocalizationMap.lift₀_apply`, `normalize_eq_one`, `Valuation.IsEquiv.lt_one_iff_lt_one`, `Associates.dvd_of_mem_factors`, `GCDMonoid.gcd_dvd_right`, `WfDvdMonoid.wellFoundedLT_associates`, `Multiset.lcm_dvd`, `Finset.lcm_dvd_iff`, `WfDvdMonoid.exists_factors`, `Associates.coprime_iff_inf_one`, `MonoidWithZero.inverse_apply`, `MulChar.map_nonunit'`, `associates_irreducible_iff_prime`, `Associates.count_mul_of_coprime`, `Valuation.one_apply_def`, `Finset.lcm_eq_zero_iff`, `Finset.lcm_mono`, `UniqueFactorizationMonoid.isRelPrime_iff_no_prime_factors`, `lcm_units_coe_right`, `gcd_greatest_associated`, `MulChar.coe_equivToUnitHom`, `gcd_pow_right_dvd_pow_gcd`, `Multiset.lcm_ne_zero_iff`, `Multiset.normalize_gcd`, `UniqueFactorizationMonoid.instDecompositionMonoid`, `emultiplicity_pow_self_of_prime`, `List.prod_map_le_prod_map₀`, `UniqueFactorizationMonoid.radical_dvd_radical`, `Polynomial.normUnit_X`, `dvd_gcd_mul_iff_dvd_mul`, `Associates.factors_self`, `IsPrimePow.pow`, `DivisorChain.element_of_chain_eq_pow_second_of_chain`, `Associates.prod_le`, `Multiset.prod_primes_dvd`, `DivisorChain.first_of_chain_isUnit`, `normalize_associated`, `MulChar.map_zero`, `Valuation.pos_iff`, `Irreducible.gcd_eq_one_iff`, `isRelPrime_zero_left`, `neg_gcd'`, `Finset.dvd_lcm`, `MulChar.coeToFun_mul`, `Polynomial.monic_normalize`, `Valuation.map_zero`, `multiplicity_self`, `ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply`, `isUnit_of_associated_mul`, `Multiset.gcd_map_mul`, `mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactors`, `DivisorChain.exists_chain_of_prime_pow`, `ofAdd_toDual_eq_zero_iff`, `Associates.factors_one`, `IsDedekindDomain.HeightOneSpectrum.associates_irreducible`, `notMem_nonZeroDivisors_iff_right`, `Finsupp.mem_sym2_support_of_mul_ne_zero`, `normalize_zero`, `UniqueFactorizationMonoid.radical_eq_one_iff`, `mul_mem_nonZeroDivisors`, `UniqueFactorizationMonoid.radical_mul`, `Multiset.prod_pos`, `Localization.mk_zero`, `gcd_neg`, `UniqueFactorizationMonoid.factors_eq_zero`, `threeGPFree_smul_set₀`, `UniqueFactorizationMonoid.toIsCancelMulZero`, `Associates.FactorSet.sup_add_inf_eq_add`, `MulChar.inv_apply`, `UniqueFactorizationMonoid.multiplicity_eq_count_normalizedFactors`, `gcd_zero_left'`, `UniqueFactorizationMonoid.zero_notMem_normalizedFactors`, `pow_inj_of_not_isUnit`, `lcm_eq_one_iff`, `IsPrimePow.not_unit`, `succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul`, `MulChar.apply_mem_rootsOfUnity`, `normalize_idem`, `UniqueFactorizationMonoid.radical_dvd_radical_iff_normalizedFactors_subset_normalizedFactors`, `Finset.normalize_gcd`, `lcm_eq_normalize`, `Associates.mem_factors'_of_dvd`, `Prime.dvd_finset_prod_iff`, `Associates.prod_coe`, `Associates.out_top`, `gcd_dvd_gcd_mul_left`, `Finset.prod_nonneg`, `DivisorChain.card_subset_divisors_le_length_of_chain`, `Prime.pow_dvd_of_dvd_mul_left`, `Associates.gcd_mk_mk`, `Submonoid.LocalizationMap.lift₀_def`, `Finset.prod_primes_dvd`, `emultiplicity_mul`, `Finset.support_prod`, `Int.nonneg_iff_normalize_eq_self`, `Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange`, `Associates.FactorSet.prod_eq_zero_iff`, `Associates.le_zero`, `Submonoid.LocalizationMap.sec_zero_fst`, `Associated.gcd`, `normalize_eq_normalize_iff_associated`, `factorization_one`, `Prime.dvd_prime_iff_associated`, `OrderMonoidWithZeroHom.mul_apply`, `PowerSeries.X_eq_normalizeX`, `mul_eq_mul_prime_prod`, `gcd_eq_right_iff`, `normalize_associated_iff`, `Valuation.one_rel_iff`, `Valuation.le_one_of_subsingleton`, `Polynomial.X_eq_normalize`, `Squarefree.dvd_pow_iff_dvd`, `UniqueFactorizationMonoid.exists_reduced_factors'`, `Associated.of_pow_associated_of_prime'`, `Polynomial.content_monomial`, `Finset.gcd_mono_fun`, `Polynomial.map_normalize`, `normalize_eq`, `gcd_dvd_gcd`, `multiplicity_pow_self_of_prime`, `Valuation.one_apply_eq_one_iff`, `Prime.dvd_lcm`, `FiniteMultiplicity.mul_iff`, `lcm_one_right`, `LinearOrderedCommMonoidWithZero.toZeroLeOneClass`, `List.prod_nonneg`, `UniqueFactorizationMonoid.exists_mem_factors_of_dvd`, `Finsupp.sym2_support_eq_preimage_support_mul`, `associated_normalize`, `Finset.gcd_div_eq_one`, `dvd_gcd_iff`
`toZero` 📖	CompOp	7 math math: `CancelCommMonoidWithZero.toIsLeftCancelMulZero`, `zero_mul`, `LinearOrderedCommMonoidWithZero.zero_le`, `LinearOrderedCommGroupWithZero.inv_zero`, `mul_zero`, `CommGroupWithZero.inv_zero`, `LinearOrderedCommMonoidWithZero.toPosMulStrictMono`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_zero` 📖	mathematical	—	`Semigroup.toMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `toCommMonoid` `toZero`	—	—
`zero_mul` 📖	mathematical	—	`Semigroup.toMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `toCommMonoid` `toZero`	—	—

GroupWithZero

Definitions

Name	Category	Theorems
`toDiv` 📖	CompOp	1 math math: `div_eq_mul_inv`
`toDivInvMonoid` 📖	CompOp	493 math math: `div_le_one_of_le₀`, `div_mul_le_div_mul_of_div_le_div`, `half_lt_self`, `RatFunc.liftMonoidWithZeroHom_apply`, `ContMDiff.div₀`, `Set.preimage_const_mul_Ioi₀`, `div_le_of_le_mul₀`, `exists_nat_one_div_lt`, `le_mul_div_mul_left`, `Mathlib.Tactic.RingNF.nnrat_rawCast`, `MeasureTheory.StronglyMeasurable.div₀`, `max_div_div_right`, `hasSum_div_const_iff`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal`, `MeasureTheory.AEStronglyMeasurable.div₀`, `Ideal.hasFiniteMulSupport_coe`, `div_le_div₀`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁`, `zero_zpow`, `mul_div_mul_right`, `Set.preimage_mul_const_Icc₀`, `one_lt_zpow₀`, `HasProd.congr_cofinite₀`, `div_le_iff₀`, `Nat.cast_choose_eq_ascPochhammer_div`, `tendsto_const_div_atTop_nhds_zero_nat`, `RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk`, `div_sq_cancel`, `div_lt_self`, `IsAbsoluteValue.abv_div`, `eq_div_of_mul_eq`, `one_div_add_one_div`, `mul_div_mul_right_le`, `mul_inv_cancel_left₀`, `zpow_right_anti₀`, `Function.Antiperiodic.mul_const'`, `div_mul_cancel₀`, `cfc_map_div`, `one_div_pow_strictAnti`, `mul_div_cancel_of_invertible`, `le_div_iff₀'`, `continuousAt_zpow₀`, `zpow_one_sub_natCast₀`, `Unitary.coe_zpow`, `RatFunc.exists_zpow_uniformizingPolynomial`, `Set.preimage_const_mul_Iio₀`, `DirectLimit.zpow₀_def`, `Nonneg.mk_div_mk`, `Filter.NeBot.zero_div_nonneg`, `sum_div_card_sq_le_sum_sq_div_card`, `zpow_add_one₀`, `Commute.div_right`, `Nat.floor_div_natCast`, `div_le_div_of_nonneg_right`, `div_le_div_iff_of_pos_left`, `zpow_left_injOn₀`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃`, `NNRat.cast_def`, `div_div_self`, `Set.preimage_const_mul_Ioo₀`, `SemiconjBy.div_right`, `Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose`, `Filter.tendsto_div_const_atTop_iff_pos`, `FractionalIdeal.count_finsuppProd`, `ENNReal.orderIsoRpow_symm_apply`, `div_div_div_cancel_right₀`, `mul_inv_cancel₀`, `AntivaryOn.div_right₀`, `add_halves`, `Nat.one_div_le_one_div`, `zpow_right_inj₀`, `Finset.div_zero_subset`, `Filter.tendsto_div_const_atTop_of_pos`, `div_mul_cancel_of_imp`, `div_self_mul_self`, `lt_div_iff₀'`, `Function.Antiperiodic.div_inv`, `Nonneg.mk_zpow`, `half_pos`, `unitary.coe_div`, `Function.Periodic.mul_const'`, `lt_one_div`, `RatFunc.liftMonoidWithZeroHom_apply_div'`, `div_eq_one_iff_eq`, `lt_div_iff₀`, `Mathlib.Tactic.LinearCombination.div_lt_const`, `le_div_comm₀`, `ConjAct.toConjAct_zero`, `zpow_lt_zpow_right₀`, `unitary.coe_zpow`, `Int.self_le_zpow_clog`, `Finset.card_div_choose_le_card_shadow_div_choose`, `ValuativeRel.ValueGroupWithZero.mk_eq_div`, `NNRat.cast_div`, `lt_div_comm₀`, `one_le_zpow₀`, `ConjAct.smulCommClass₀`, `div_mul_cancel_left₀`, `mul_div_mul_left_le`, `MonovaryOn.div_right₀`, `one_div_strictAntiOn`, `tendsto_zpow_atTop_zero`, `ContMDiffAt.div₀`, `Finset.local_lubell_yamamoto_meshalkin_inequality_div`, `Commute.zpow_right₀`, `inv_zero`, `le_mul_div_mul_right`, `Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval`, `div_self_mul_self'`, `Nat.floor_div_ofNat`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero`, `Valuation.map_div`, `div_lt_div_iff_of_pos_right`, `one_div_neg`, `inv_mul_cancel_left₀`, `div_le_comm₀`, `Nat.cast_div_charZero`, `Quaternion.coe_zpow`, `FractionalIdeal.count_finprod_coprime`, `Set.preimage_const_mul_Ico₀`, `tendsto_one_div_add_atTop_nhds_zero_nat`, `summable_const_div_iff`, `one_lt_div`, `Int.zpow_le_iff_le_log`, `div_helper`, `Monovary.div_right₀`, `FractionalIdeal.finprod_heightOneSpectrum_factorization`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `Finset.sq_sum_div_le_sum_sq_div`, `IsSelfAdjoint.zpow₀`, `zero_div`, `zero_zpow_eq`, `zpow_natCast_sub_natCast₀`, `div_self_eq_one₀`, `Set.div_mem_centralizer₀`, `Mathlib.Meta.NormNum.isNat_zpow_pos`, `div_add'`, `ConjAct.smulCommClass₀'`, `FractionalIdeal.count_finprod`, `Function.Periodic.div_const`, `Commute.div_left`, `Filter.tendsto_zpow_atTop_atTop`, `Int.lt_zpow_iff_log_lt`, `zpow_le_zpow_iff_left₀`, `div_lt_div_of_pos_left`, `div_lt_div_iff_of_pos_left`, `zpow_le_zpow_iff_right_of_lt_one₀`, `zpow_lt_one_iff_right₀`, `ConjAct.ofConjAct_zero`, `div_nat_lt_self_of_pos_of_two_le`, `zpow_left_strictMonoOn₀`, `one_div_mul_add_mul_one_div_eq_one_div_add_one_div`, `Mathlib.Tactic.FieldSimp.NF.zpow_eq_eval`, `StrictMono.div_const`, `Mathlib.Meta.NormNum.isNNRat_zpow_pos`, `zpow_le_zpow_iff_right₀`, `AddCommGroup.mul_modEq_mul_left`, `Nat.one_div_cast_pos`, `one_div_lt`, `RatFunc.liftMonoidWithZeroHom_apply_div`, `Nat.cast_add_choose`, `one_le_zpow_iff_right_of_lt_one₀`, `add_thirds`, `div_two_lt_of_pos`, `hasSum_const_div_iff`, `zpow_add'`, `ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq`, `div_eq_of_eq_mul`, `le_div_self`, `Nat.floor_div_eq_div`, `SemiconjBy.zpow_right₀`, `tendsto_natCast_div_add_atTop`, `Int.zpow_pred_clog_lt_self`, `Commute.div_add_div`, `div_eq_iff_mul_eq`, `AddCommGroup.div_modEq_div`, `one_half_lt_one`, `Set.preimage_const_mul_Ici₀`, `one_div_nonneg`, `zpow_left_inj₀`, `Units.continuousOn_zpow₀_spectrum`, `mul_mul_div`, `Polynomial.valuation_inv_monomial_eq_valuation_X_zpow`, `RCLike.tendsto_add_mul_div_add_mul_atTop_nhds`, `zpow_sub₀`, `div_nonpos_of_nonpos_of_nonneg`, `Polynomial.eval_homogenize`, `Continuous.div₀`, `summable_div_const_iff`, `Filter.Tendsto.div`, `zero_zpow_eq_one₀`, `div_pos_iff_of_pos_right`, `continuousOn_div`, `zpow_le_one_iff_right₀`, `div_mul_div_cancel₀'`, `HasSum.div_const`, `div_eq_div_iff`, `ContinuousOn.div`, `Mathlib.Tactic.FieldSimp.zpow'_of_ne_zero_right`, `Commute.zpow_zpow_self₀`, `tsum_div_const`, `div_le_self`, `Mathlib.Meta.NormNum.IsNNRat.to_eq`, `Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg`, `div_le_div_iff_of_pos_right`, `NNRat.cast_zpow`, `one_le_zpow_iff_right₀`, `zpow_eq_zero_iff`, `Nat.choose_lt_pow_div`, `zpow_nonneg`, `Bound.div_lt_one_of_pos_of_lt`, `Finset.Nonempty.zero_div`, `toMulDivCancelClass`, `div_eq_div_iff_div_eq_div'`, `MeasureTheory.StronglyMeasurable.div`, `OrderIso.divRight₀_apply`, `div_lt_iff₀`, `geom_sum_of_lt_one`, `Set.preimage_mul_const_Ioo₀`, `Nat.cast_div_div_div_cancel_right`, `div_nonpos_of_nonneg_of_nonpos`, `zpow_lt_one₀`, `one_div_pow_lt_one_div_pow_of_lt`, `SignType.zpow_even`, `Quaternion.coe_div`, `div_self_le_one`, `Commute.zpow_self₀`, `zpow_le_zpow_right_of_le_one₀`, `mul_div_cancel_of_imp'`, `zpow_eq_one_iff_right₀`, `cfc_comp_zpow`, `add_div'`, `mul_inv_cancel_right₀`, `zpow_le_one_iff_right_of_lt_one₀`, `Filter.tendsto_div_const_iff`, `exists_mem_Ico_zpow`, `mul_one_div_cancel`, `mul_div_cancel₀`, `Finset.le_card_falling_div_choose`, `one_div_le_one_div`, `AntivaryOn.div_left₀`, `algebraMap.coe_div`, `ContinuousAt.div₀`, `zpow_pos`, `cfc_zpow`, `Set.preimage_mul_const_Iic₀`, `Continuous.div`, `AddCommGroup.mul_modEq_mul_right`, `Finset.zero_div_subset`, `half_lt_self_iff`, `div_nat_le_self_of_nonnneg`, `Finset.sum_div`, `Commute.zpow_left₀`, `Nat.cast_div`, `Int.zpow_log_le_self`, `Mathlib.Tactic.FieldSimp.zpow'_of_ne_zero_left`, `Finset.sum_card_slice_div_choose_le_one`, `one_div_le_one_div_of_le`, `tendsto_pow_neg_atTop`, `tendsto_add_mul_div_add_mul_atTop_nhds`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval₂`, `tendsto_one_div_atTop_nhds_zero_nat`, `div_le_one`, `Multiset.sum_map_div`, `Summable.const_div`, `Int.lt_zpow_succ_log_self`, `Ideal.finite_mulSupport_coe`, `exists_mem_Ioc_zpow`, `Set.preimage_const_mul_Icc₀`, `smul_zpow₀'`, `zpow_add₀`, `Mathlib.Tactic.FieldSimp.NF.div_eq_eval`, `Unitary.coe_div`, `div_add_one`, `div_div_div_cancel_left'`, `MonovaryOn.div_left₀`, `div_eq_iff`, `map_div₀`, `FractionalIdeal.count_zpow_self`, `Finset.cast_subConst`, `zpow_lt_zpow_iff_left₀`, `Finset.nnratCast_dens`, `zpow_lt_zpow_left₀`, `one_div_le`, `ValuativeRel.exists_valuation_div_valuation_eq`, `Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos`, `Function.support_div'`, `Set.preimage_mul_const_Ici₀`, `zpow_le_zpow_left₀`, `one_le_zpow_of_nonpos₀`, `one_half_pos`, `FractionalIdeal.count_neg_zpow`, `ContinuousAt.comp_div_cases`, `one_lt_zpow_of_neg₀`, `div_mul_cancel_of_invertible`, `half_le_self`, `div_add_div`, `ContinuousOn.zpow₀`, `Finset.cast_mulConst`, `Int.clog_zpow`, `div_lt_one`, `div_le_div_iff₀`, `div_lt_iff₀'`, `NNRat.cast_zpow_of_ne_zero`, `Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div'`, `Set.preimage_const_mul_Ioc₀`, `Nat.one_div_cast_nonneg`, `min_div_div_right`, `RatFunc.valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_X`, `Nat.cast_div_le`, `div_lt_div₀'`, `one_lt_zpow_iff_right₀`, `Mathlib.Tactic.Ring.div_congr`, `Nat.one_div_pos_of_nat`, `eq_div_iff_mul_eq`, `Set.preimage_mul_const_Ico₀`, `zpow_sub_one₀`, `NNReal.orderIsoRpow_symm_eq`, `zpow_lt_zpow_right_of_lt_one₀`, `zpow_right_injective₀`, `Continuous.comp_div_cases`, `div_lt_comm₀`, `ArithmeticFunction.pdiv_apply`, `Monovary.div_left₀`, `smul_div₀'`, `mul_div_cancel_left_of_imp`, `Int.le_zpow_iff_clog_le`, `zpow_lt_zpow_iff_right₀`, `one_div_pos`, `Set.Nonempty.div_zero`, `monotone_div_right_of_nonneg`, `div_add_same`, `Equiv.divLeft₀_apply`, `mem_segment_iff_div`, `Mathlib.Meta.NormNum.isNNRat_zpow_neg`, `one_div_lt_one_div`, `Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div`, `NNRat.cast_div_of_ne_zero`, `mul_div_mul_left`, `Filter.EventuallyEq.div_mul_cancel_atTop`, `zpow_neg_mul_zpow_self`, `Filter.Tendsto.atTop_div_const`, `Int.log_zpow`, `Mathlib.Tactic.LinearCombination.div_le_const`, `same_add_div`, `Nat.choose_le_pow_div`, `divp_mk0`, `ContinuousAt.div`, `div_div_cancel₀`, `geom₂_sum_of_lt`, `div_le_div_of_nonneg_left`, `DirectLimit.div₀_def`, `Antivary.div_right₀`, `Monotone.div_const`, `NNRat.cast_divNat_of_ne_zero`, `FractionalIdeal.count_zpow`, `Commute.div_eq_div_iff`, `div_eq_div_of_div_eq_div`, `Filter.Tendsto.zpow₀`, `zpow_lt_one_iff_right_of_lt_one₀`, `div_self_of_invertible`, `one_div_lt_one_div_of_lt`, `Int.zpow_lt_iff_lt_clog`, `strictMono_div_right_of_pos`, `Commute.self_zpow₀`, `zpow_one_add₀`, `Nonneg.coe_div`, `Equiv.divLeft₀_symm_apply`, `div_lt_div_of_pos_right`, `Finset.cast_divConst`, `zpow_le_zpow_right₀`, `one_add_div`, `ContinuousOn.div₀`, `Nat.pow_le_choose`, `invOf_div`, `div_mul_cancel_right₀`, `one_div_mul_cancel`, `div_pos`, `div_nonneg`, `Set.preimage_mul_const_Ioc₀`, `geom_sum_of_one_lt`, `Ideal.finprod_heightOneSpectrum_factorization_coe`, `Finset.sup_div₀`, `zpow_le_one₀`, `Mathlib.Meta.Positivity.zpow_zero_pos`, `Bound.one_lt_div_of_pos_of_lt`, `zpow_right_mono₀`, `Set.Nonempty.zero_div`, `one_le_div₀`, `Mathlib.Tactic.FieldSimp.zpow'_zero_eq_div`, `Filter.map_div_atTop_eq`, `zpow_natCast_sub_one₀`, `one_div_nonpos`, `map_zpow₀`, `mem_openSegment_iff_div`, `exists_zpow_btwn_of_lt_mul`, `Finset.expect_div`, `Commute.zpow_zpow₀`, `one_div_pow_le_one_div_pow_of_le`, `div_lt_div_iff₀`, `one_div_pow_anti`, `zpow_right_strictMono₀`, `ContMDiffWithinAt.div₀`, `Antivary.div_left₀`, `Set.zero_div_subset`, `IsSelfAdjoint.div`, `Nat.cast_choose`, `Set.div_zero_subset`, `ContinuousWithinAt.div`, `div_div_cancel_left'`, `Nonneg.coe_zpow`, `Mathlib.Tactic.Ring.div_pf`, `continuousOn_zpow₀`, `NNRat.cast_divNat`, `div_left_inj'`, `le_div_iff₀`, `star_div₀`, `one_le_div`, `one_lt_one_div`, `star_zpow₀`, `tsub_div`, `ContinuousAt.zpow₀`, `eq_div_iff`, `Multipliable.tsum_congr_cofinite₀`, `zpow_left_monoOn₀`, `pow_sum_div_card_le_sum_pow`, `div_le_iff₀'`, `Finset.Nonempty.div_zero`, `Finset.expect_eq_sum_div_card`, `Ideal.hasFiniteMulSupport_inv`, `Mathlib.Meta.NormNum.isNNRat_div`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `div_eq_zero_iff`, `SignType.coe_zpow`, `one_lt_zpow_iff_right_of_lt_one₀`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction`, `add_div_two_lt_right`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero`, `inv_mul_cancel₀`, `Finset.sup'_div₀`, `Summable.div_const`, `div_lt_one₀`, `ContinuousWithinAt.zpow₀`, `ArithmeticFunction.IsMultiplicative.map_div_of_coprime`, `zpow_lt_one_of_neg₀`, `zpow_lt_zpow_iff_right_of_lt_one₀`, `div_zero`, `Commute.inv_add_inv`, `mul_self_div_self`, `mul_div_cancel_of_imp`, `NNReal.tendsto_const_div_atTop_nhds_zero_nat`, `Mathlib.Tactic.LinearCombination.div_lt_const_weak`, `half_le_self_iff`, `div_mul_div_cancel₀`, `Mathlib.Meta.NormNum.isNat_zpow_neg`, `HasSum.const_div`, `Ideal.finite_mulSupport_inv`, `Commute.one_div_add_one_div`, `geom₂_sum_of_gt`, `zpow_le_one_of_nonpos₀`, `algebraMap.coe_zpow`, `one_le_one_div`, `div_self`, `Nat.one_div_lt_one_div`, `Finset.cast_addConst`, `div_mul_eq_mul_div₀`, `div_lt_div₀`, `le_one_div`, `Set.preimage_const_mul_Iic₀`, `Set.preimage_mul_const_Iio₀`, `one_lt_div₀`, `left_lt_add_div_two`, `Valuation.exists_div_eq_of_surjective`, `div_le_one₀`, `Set.preimage_mul_const_Ioi₀`, `ContMDiffOn.div₀`, `Filter.EventuallyEq.div_mul_cancel`, `Continuous.zpow₀`, `SignType.zpow_odd`, `inv_mul_cancel_right₀`, `FractionalIdeal.finprod_heightOneSpectrum_factorization'`, `Function.support_div`, `inv_add_inv`, `zpow_right_strictAnti₀`, `cfcUnits_zpow`, `add_div_eq_mul_add_div`, `add_div`, `Filter.NeBot.div_zero_nonneg`, `div_pos_iff_of_pos_left`, `Mathlib.Tactic.FieldSimp.NF.cons_zero_eq_div_of_eq_div`, `add_self_div_two`, `Equiv.divRight₀_apply`, `Fintype.expect_eq_sum_div_card`
`toInv` 📖	CompOp	4 math math: `div_eq_mul_inv`, `inv_zero`, `mul_inv_cancel`, `zpow_neg'`
`toMonoidWithZero` 📖	CompOp	872 math math: `Set.center_units_subset`, `AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀`, `ArithmeticFunction.IsMultiplicative.pdiv`, `Valuation.mem_nhds_zero_iff`, `div_eq_mul_inv`, `Valued.continuous_extension`, `Valuation.IsRankOneDiscrete.generator_lt_one`, `IsGaloisGroup.smul_mem_of_normal`, `unitsEquivNeZero_symm_apply`, `isHomeomorph_smul₀`, `Homeomorph.smulOfNeZero_symm_apply`, `Valued.isOpen_closedball`, `Subgroup.smul_mem_pointwise_smul_iff₀`, `interior_smul₀`, `RatFunc.liftMonoidWithZeroHom_apply`, `GrpWithZero.forget_map`, `Set.preimage_const_mul_Ioi₀`, `le_mul_div_mul_left`, `OrderMonoidIso.val_inv_unitsWithZero_symm_apply`, `Valuation.inversion_estimate'`, `Homeomorph.coe_mulRight₀`, `Set.image_mul_left_Iio`, `pow_sub_of_lt`, `mul_inv_cancel_of_invertible`, `neg_of_div_neg_right`, `WithVal.valueGroupOrderIso₀_symm_apply`, `Valuation.ltIdeal_le_leIdeal`, `inv_eq_zero`, `mul_inf₀`, `mul_inv_eq_mul_inv_iff`, `zero_zpow`, `Valuation.isClopen_closedBall`, `MeasurableEquiv.coe_smul₀`, `IsClosed.smul_of_ne_zero`, `mul_div_mul_right`, `Set.preimage_mul_const_Icc₀`, `HasProd.congr_cofinite₀`, `div_le_iff₀`, `Filter.smul_tendsto_smul_iff₀`, `support_comp_inv_smul₀`, `MonoidWithZeroHom.snd_comp_inl`, `absorbs_zero_iff`, `Nat.card_units`, `conj_pow₀`, `RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk`, `WithZero.withZeroUnitsEquiv_symm_apply_coe`, `div_sq_cancel`, `Submonoid.smul_mem_pointwise_smul_iff₀`, `Filter.mem_absorbing`, `smul_mem_nhds_smul₀`, `Valued.extension_extends`, `WithVal.valueGroup_eq`, `AffineSubspace.smul_mem_smul_iff₀`, `mul_div_mul_right_le`, `mul_inv_cancel_left₀`, `OrderIso.mulRight₀_symm_apply`, `OrderIso.smulRight_apply`, `mul_eq_of_eq_inv_mul₀`, `Set.natCard_smul_set₀`, `Commute.inv_right_iff₀`, `Submonoid.isUnit_iff_and`, `NumberField.RingOfIntegers.instSMulDistribClass`, `OrderIso.mulRight₀_symm`, `Set.inv_mem_centralizer₀`, `map_mul_left_nhds_one₀`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `div_mul_cancel₀`, `FiniteField.pow_card_sub_one_eq_one`, `IsClosed.smul₀`, `Valuation.IsRankOneDiscrete.exists_generator_lt_one'`, `inv_smul_smul₀`, `signHom_apply`, `mul_div_cancel_of_invertible`, `mul_inv_le_one`, `le_div_iff₀'`, `zpow_one_sub_natCast₀`, `Unitary.coe_zpow`, `NNReal.exists_lt_of_strictMono`, `isOpen_singleton_zero`, `Ring.inverse_eq_inv'`, `Set.preimage_const_mul_Iio₀`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `Filter.NeBot.zero_div_nonneg`, `WithZeroTopology.nhds_zero`, `inv_zero`, `Valuation.mem_ltIdeal_iff`, `measurableEmbedding_mulRight₀`, `Equiv.mulLeft₀_apply`, `WithVal.valueGroupOrderIso₀_restrict`, `isConj_iff₀`, `Set.image_mul_left_Ioi`, `zpow_add_one₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `Commute.div_right`, `Valuation.IsRankOneDiscrete.generator_mem_valueGroup`, `MonoidWithZeroHom.ValueGroup₀.monoidWithZeroHom_strictMono`, `WithVal.valueGroupOrderIso₀_apply`, `isClosedMap_smul_of_ne_zero`, `LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex`, `Set.mem_inv_smul_set_iff₀`, `Set.image_mul_right_Icc'`, `Set.preimage_smul_inv₀`, `Normal.minpoly_eq_iff_mem_orbit`, `zpow_left_injOn₀`, `Set.preimage_const_mul_Ioo₀`, `Set.smul_set_inter₀`, `Valued.toUniformSpace_eq`, `Valuation.instNontrivialSubtypeUnitsMemSubmonoidValueMonoidOfIsNontrivial`, `lowerBounds_smul_of_pos`, `Set.smul_set_subset_smul_set_iff₀`, `SemiconjBy.div_right`, `le_mul_inv_left`, `NumberField.HeightOneSpectrum.rankOne_hom'_def`, `WithVal.valueGroupEquiv_symm_apply`, `Valuation.restrict_eq_one_iff`, `instIsLocalHomOfMonoidWithZeroHomClassOfNontrivial`, `ENNReal.orderIsoRpow_symm_apply`, `Valuation.IsRankOneDiscrete.generator'_lt_one`, `SemiconjBy.inv_right₀`, `absorbent_univ`, `mul_inv_cancel₀`, `MonoidWithZeroHom.map_eq_zero_iff`, `WithZeroTopology.nhds_zero_of_units`, `Submonoid.pointwise_smul_le_pointwise_smul_iff₀`, `ValuationSubring.mapOfLE_valuation_apply`, `mul_eq_of_eq_mul_inv₀`, `inv_mul_le_of_le_mul₀`, `Finset.div_zero_subset`, `ValuationSubring.mem_inv_pointwise_smul_iff`, `mul_inv_cancel`, `div_mul_cancel_of_imp`, `Set.star_inv'`, `div_self_mul_self`, `lt_div_iff₀'`, `Filter.tendsto_mul_iff_of_ne_zero`, `unitary.coe_div`, `UniqueDiffWithinAt.smul`, `inv_le_one_iff₀`, `MonoidWithZeroHom.valueGroup.mk_mul`, `absorbs_inter`, `MonoidWithZeroHom.fst_mono`, `Valuation.IsEquiv.restrict`, `Subring.mem_pointwise_smul_iff_inv_smul_mem₀`, `lt_inv_mul_iff₀'`, `RatFunc.liftMonoidWithZeroHom_apply_div'`, `one_lt_inv_iff₀`, `lt_inv_smul_iff_of_pos`, `Valuation.ltAddSubgroup_monotone`, `lt_div_iff₀`, `ConjAct.toConjAct_zero`, `Finset.smul_finset_subset_smul_finset_iff₀`, `smul_uniformity₀`, `Valued.isClopen_ball`, `unitary.coe_zpow`, `ValuativeRel.ValueGroupWithZero.embed_strictMono`, `Set.image_mul_left_Icc'`, `inv_mul_lt_one₀`, `Ne.isUnit`, `ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRel`, `GrpWithZero.hom_comp`, `Equiv.mulLeft₀_symm_apply`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval`, `OrderIso.mulRight₀_apply`, `GrpWithZero.coe_id`, `Valuation.hasBasis_nhds_zero`, `inf_mul₀`, `div_mul_cancel_left₀`, `ValuativeExtension.mapValueGroupWithZero_mk`, `mul_div_mul_left_le`, `Subgroup.pointwise_smul_le_pointwise_smul_iff₀`, `Nonneg.inv_mk`, `Finset.smul_mem_smul_finset_iff₀`, `mul_eq_one_iff_inv_eq₀`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff`, `FiniteField.pow_card_pow`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁`, `Mathlib.Tactic.FieldSimp.NF.cons_pos`, `mul_inv_lt_iff₀`, `Valuation.IsUniformizer.zpowers_eq_valueGroup`, `OrderIso.smulRightDual_apply`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `Units.smul_mk0`, `Commute.zpow_right₀`, `closure_smul₀`, `Valuation.restrict_le_iff`, `inv_zero`, `smul_inv_smul₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_strictMono`, `le_mul_div_mul_right`, `closure_smul₀'`, `Set.smul_univ₀`, `Set.image_mul_right_Icc`, `div_self_mul_self'`, `Valued.is_topological_valuation`, `inv_mul_eq_iff_eq_mul₀`, `Bornology.isVonNBounded_iff_absorbing_le`, `Finset.smul_finset_univ₀`, `measurableEmbedding_const_smul₀`, `IsValuativeTopology.isOpen_ball`, `HasCompactMulSupport.comp_smul`, `eq_mul_inv_iff_mul_eq₀`, `Set.image_const_mul_Ioi_zero`, `one_div_neg`, `inv_mul_le_one`, `Valuation.restrict_eq_zero_iff`, `inv_mul_cancel_left₀`, `Valuation.restrict_eq_mk`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `lt_mul_inv_iff₀`, `Equiv.divRight₀_symm_apply`, `Valued.continuous_valuation`, `GrpWithZero.coe_comp`, `Set.smul_set_univ₀`, `inv_mul_le_one₀`, `Fintype.card_units`, `nhds_smul₀`, `ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem`, `le_inv_mul_right`, `Valuation.restrict_lt_iff_lt_embedding`, `Set.preimage_const_mul_Ico₀`, `zpow_zero'`, `OrderIso.divRight₀_symm_apply`, `Valued.extension_eq_zero_iff`, `OrderIso.mulLeft₀_apply`, `ValuationSubring.smul_mem_pointwise_smul_iff`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `pow_inv_comm₀`, `div_helper`, `Commute.inv_left_iff₀`, `Set.Finite.absorbs_sInter`, `ValuativeExtension.mapValueGroupWithZero_strictMono`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `IsValuativeTopology.isClopen_sphere`, `Mathlib.Tactic.FieldSimp.NF.pow_eq_eval`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero`, `inv_mul_lt_iff₀`, `IsSelfAdjoint.zpow₀`, `zero_div`, `OrderMonoidIso.withZeroUnits_symm_apply`, `eventually_cobounded_mapsTo`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_of_ne_zero`, `MonoidWithZeroHom.inl_strictMono`, `inv_mul_eq_inv_mul_iff`, `Absorbs.inter`, `Valuation.subgroups_basis`, `IsGaloisGroup.mulEquivCongr_apply_smul`, `OrderMonoidIso.withZeroUnits_apply`, `zero_zpow_eq`, `zpow_natCast_sub_natCast₀`, `Set.div_mem_centralizer₀`, `Submonoid.isUnit_iff_of_ne_zero`, `Ring.inverse_eq_inv`, `Valued.isOpen_sphere`, `Valuation.restrict_le_iff_le_embedding`, `Finset.sup'_mul₀`, `OrderMonoidIso.val_unitsWithZero_symm_apply`, `Homeomorph.smulOfNeZero_apply`, `MonoidWithZeroHom.valueMonoid_eq_valueGroup`, `instIsOpenUnitsOfContinuousInv₀OfT1Space`, `Function.Antiperiodic.const_inv_smul₀`, `Commute.div_left`, `NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def`, `denselyOrdered_units_iff`, `OrderIso.withZeroUnits_symm_apply`, `Valuation.isEquiv_restrict`, `Valuation.nonempty_rankOne_iff_mulArchimedean`, `mulLeft_bijective₀`, `le_mul_inv_iff₀'`, `mul_le_of_le_div₀`, `Set.smul_mem_smul_set_iff₀`, `ConjAct.ofConjAct_zero`, `Submonoid.le_pointwise_smul_iff₀`, `zpow_left_strictMonoOn₀`, `Valuation.RankOne.exists_val_lt`, `MonoidWithZeroHom.valueGroup_eq_range`, `Equiv.mulRight₀_apply`, `Valued.hasBasis_nhds_zero`, `Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup`, `GrpWithZero.Iso.mk_hom`, `absorbs_iInter`, `SignType.pow_even`, `IsValuativeTopology.mem_nhds_iff'`, `mul_inv_lt_of_lt_mul₀`, `RatFunc.liftMonoidWithZeroHom_apply_div`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `instNontrivialUnitsOfDenselyOrdered`, `Submonoid.pointwise_smul_le_iff₀`, `WithVal.strictMono_valueGroupOrderIso₀`, `MulPosReflectLE.of_posMulReflectLT_of_mulPosMono`, `SignType.castHom_apply`, `Set.inv_zero`, `WithVal.strictMono_valueGroupOrderIso₀_symm`, `OrderIso.smulRight_symm_apply`, `zpow_add'`, `Valuation.IsUniformizer.val`, `ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq`, `DilationEquiv.mulRight_symm_apply`, `inv_mul_mul_self`, `SemiconjBy.zpow_right₀`, `mul_inv_le_iff₀`, `Finset.smul_finset_subset_iff₀`, `div_eq_iff_mul_eq`, `nhds_translation_mul_inv₀`, `ValuativeExtension.mapValueGroupWithZero_valuation`, `Set.preimage_const_mul_Ici₀`, `WithVal.valueGroupEquiv_apply`, `one_div_nonneg`, `DilationEquiv.mulLeft_symm_apply`, `mul_mul_div`, `Subgroup.mem_inv_pointwise_smul_iff₀`, `instSMulDistribClassAlgEquiv`, `Valuation.RankOne.strictMono`, `set_smul_mem_nhds_zero_iff`, `inv_pos`, `inv_nonneg_of_nonneg`, `ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀`, `MonoidWithZeroHom.one_comp`, `Commute.inv_mul_eq_inv_mul_iff`, `Valued.coe_valuation_eq_rankOne_hom_comp_valuation`, `MonoidWithZeroHom.fst_comp_inl`, `mul_le_of_le_inv_mul₀`, `Polynomial.valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X`, `DilationEquiv.mulLeft_apply`, `Finset.smul_finset_symmDiff₀`, `div_nonpos_of_nonpos_of_nonneg`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_range_eq_top`, `eq_zero_of_zpow_eq_zero`, `Absorbs.iInter`, `Valued.isClosed_ball`, `AddSubgroup.pointwise_smul_le_iff₀`, `Valuation.restrict_lt_one_iff`, `MonoidWithZeroHom.one_apply_apply_eq`, `isUnit_of_mem_nonZeroDivisors`, `Set.univ_smul_nhds_zero`, `zero_zpow_eq_one₀`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `ContinuousInv₀.of_nhds_one`, `continuousOn_div`, `Valued.isClopen_sphere`, `div_mul_div_cancel₀'`, `Finset.inv_zero`, `MulPosReflectLT.toMulPosStrictMono`, `map_eq_zero`, `LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ`, `Valued.isClosed_sphere`, `IsValuativeTopology.isClosed_closedBall`, `Subsemiring.smul_mem_pointwise_smul_iff₀`, `le_inv_mul_iff₀'`, `zero_eq_inv`, `div_eq_div_iff`, `Polynomial.valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X`, `isUnit_iff_ne_zero`, `inv_neg''`, `Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator`, `Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe`, `Commute.zpow_zpow_self₀`, `Valuation.cauchy_iff`, `IsValuativeTopology.mem_nhds_zero_iff`, `mul_inv_le_one_of_le₀`, `IsSelfAdjoint.inv₀`, `Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `Set.image_mul_left_Ioc`, `continuousWithinAt_const_smul_iff₀`, `inv_mul_eq_one₀`, `Valuation.IsRankOneDiscrete.embedding_generator'`, `WithZeroTopology.isClosed_iff`, `zpow_eq_zero_iff`, `eq_inv_mul_iff_mul_eq₀`, `inv_lt_iff_one_lt_mul₀`, `WithZeroTopology.hasBasis_nhds_zero`, `zpow_nonneg`, `Submonoid.mem_inv_pointwise_smul_iff₀`, `UniqueDiffWithinAt.smul_iff`, `Finset.Nonempty.zero_div`, `MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit`, `continuousAt_const_smul_iff₀`, `toMulDivCancelClass`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `div_lt_iff₀`, `ValuationSubring.monotone_mapOfLE`, `one_le_inv_iff₀`, `Set.preimage_mul_const_Ioo₀`, `Finset.inv_smul_finset_distrib₀`, `div_nonpos_of_nonneg_of_nonpos`, `absorbs_iff_eventually_cobounded_mapsTo`, `Valuation.restrict_inj`, `Valuation.ltSubmodule_monotone`, `Filter.top_smul_nhds_zero`, `ValuativeRel.RankLeOneStruct.strictMono`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `Valued.integer.mulArchimedean_mrange_of_isCompact_integer`, `le_mul_inv_right`, `Valuation.embedding_restrict`, `Commute.zpow_self₀`, `DilationEquiv.mulRight_apply`, `AddSubmonoid.mem_inv_pointwise_smul_iff₀`, `lt_mul_inv_iff₀'`, `sup_mul₀`, `mul_div_cancel_of_imp'`, `Valued.closure_coe_completion_v_lt`, `Set.inv_smul_set_distrib₀`, `Valued.valuation_isClosedMap`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval`, `WithZeroTopology.nhds_coe_units`, `mul_inv_cancel_right₀`, `Set.image_mul_right_Ioo`, `Subsemiring.mem_inv_pointwise_smul_iff₀`, `MonoidWithZeroHom.ValueGroup₀.mk_eq_of_ne_zero`, `Valued.closure_coe_completion_v_mul_v_lt`, `continuousOn_const_smul_iff₀`, `smul_mem_nhds_smul_iff₀`, `Valued.cauchy_iff`, `mul_one_div_cancel`, `Mathlib.Tactic.FieldSimp.list_prod_zpow'`, `mul_div_cancel₀`, `Units.mk0_mul`, `Set.image_mul_left_Icc`, `mul_eq_one_iff_eq_inv₀`, `Right.inv_nonneg`, `MonoidWithZeroHom.inr_mono`, `Valuation.extendToLocalization_mk'`, `Homeomorph.mulLeft₀_symm_apply`, `Nat.card_eq_card_units_add_one`, `zpow_pos`, `inv_pos_of_pos`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `Valuation.IsRankOneDiscrete.generator'_zpowers_eq_top`, `Set.preimage_mul_const_Iic₀`, `MulAction.bijective₀`, `inv_smul_lt_iff_of_pos`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `Subring.le_pointwise_smul_iff₀`, `mul_inv_left_le`, `Finset.zero_div_subset`, `isOpenMap_smul₀`, `Units.mul_inv'`, `Subring.smul_mem_pointwise_smul_iff₀`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `Cardinal.mk_smul_set₀`, `inv_smul_le_iff_of_pos`, `Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe`, `Valuation.restrict_pos_iff`, `Commute.zpow_left₀`, `MonoidWithZeroHom.snd_inr`, `MonoidWithZeroHom.snd_inl_apply_of_ne_zero`, `IsValuativeTopology.isClopen_ball`, `IsValuativeTopology.hasBasis_nhds`, `WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv`, `mul_self_mul_inv`, `mul_le_of_le_mul_inv₀`, `Mathlib.Tactic.FieldSimp.zpow'_eq_zero_iff`, `Valuation.restrict_def`, `MonoidWithZeroHom.inl_injective`, `MulAction.surjective₀`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_surjective`, `Set.image_mul_left_Ico`, `lt_inv_mul_iff₀`, `mul_inv_right_le`, `Set.inv_Ioi₀`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons`, `IsValuativeTopology.hasBasis_nhds_zero`, `AddSubmonoid.smul_mem_pointwise_smul_iff₀`, `Matrix.ProjGenLinGroup.val_signDet_mk`, `Valuation.IsEquiv.orderMonoidIso_trans`, `WithVal.strictMono_valueGroupEquiv_symm`, `Commute.smul_right_iff₀`, `Matrix.ProjGenLinGroup.signDet_mk`, `Valuation.mem_ltAddSubgroup_iff`, `inv_smul_eq_iff₀`, `Set.preimage_const_mul_Icc₀`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroup`, `unitary.coe_inv`, `Valuation.isClosed_closedBall`, `Units.exists0'`, `smul_zpow₀'`, `dvd_iff`, `zpow_add₀`, `Function.support_inv`, `le_inv_mul_iff₀`, `Unitary.coe_div`, `antitoneOn_inv_pos`, `MeasurableSet.const_smul₀`, `RatFunc.liftMonoidWithZeroHom_injective`, `unitsEquivNeZero_apply_coe`, `Finset.inv_op_smul_finset_distrib₀`, `IsValuativeTopology.isOpen_closedBall`, `div_eq_iff`, `inv_nonneg`, `LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ`, `Valuation.integer.v_irreducible_pos`, `Valuation.ltSubmodule_le_leSubmodule`, `Submonoid.mem_nonunits_iff_or`, `Set.image_mul_right_Ioc`, `Valuation.toTopologicalSpace_eq`, `Function.Antiperiodic.const_smul₀`, `Finset.smul_univ₀'`, `SemiconjBy.inv_symm_left₀`, `Valuation.leIdeal_zero`, `inv_mul_left_le`, `Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos`, `Subring.pointwise_smul_le_iff₀`, `Function.support_div'`, `Valuation.ltAddSubgroup_le_leAddSubgroup`, `LinearOrderedCommGroupWithZero.fst_comp_inl`, `OrderIso.mulLeft₀_symm_apply`, `Subgroup.pointwise_smul_le_iff₀`, `Set.preimage_mul_const_Ici₀`, `inv_mul_lt_of_lt_mul₀`, `mul_right_surjective₀`, `mul_right_injective`, `Set.smul_set_sdiff₀`, `MeasurableSet.const_smul_of_ne_zero`, `Commute.pow_eq_pow_iff_of_coprime`, `IsCompactOperator.smul_iff₀`, `Polynomial.valuation_monomial_eq_valuation_X_pow`, `WithZeroTopology.isOpen_iff`, `inv_mul_le_iff₀`, `WithZeroTopology.instContinuousMul`, `div_mul_cancel_of_invertible`, `FiniteField.pow_card`, `MonoidWithZeroHom.snd_mono`, `Valuation.IsUniformizer.val_pos`, `Valuation.isClopen_ball`, `div_le_div_iff₀`, `Equiv.smulRight_symm_apply`, `div_lt_iff₀'`, `Set.preimage_const_mul_Ioc₀`, `sign_pow`, `Valuation.Integers.valuation_pos_iff_ne_zero`, `Valued.isOpen_closedBall`, `Valuation.instNontrivialSubtypeUnitsMemSubgroupValueGroupOfIsNontrivial`, `MonoidWithZeroHom.fst_apply_coe`, `MonoidWithZeroHom.fst_inl`, `MonoidWithZeroHom.fst_surjective`, `Valuation.hasBasis_nhds`, `isSimplyConnected_smul_set₀_iff`, `ValuativeRel.isNontrivial_iff_nontrivial_units`, `IsUnit.mk0`, `IsGaloisGroup.coe_quotient_smul`, `Valued.mem_nhds_zero`, `Valuation.RankLeOne.exists_val_lt`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀`, `mul_eq_mul_of_div_eq_div`, `Valued.isOpen_ball`, `one_le_inv_mul₀`, `tendsto_const_smul_iff₀`, `mulRight_bijective₀`, `Valued.mem_nhds`, `eq_div_iff_mul_eq`, `Set.preimage_mul_const_Ico₀`, `inv_pow_sub₀`, `zpow_sub_one₀`, `AddSubgroup.smul_mem_pointwise_smul_iff₀`, `NNReal.orderIsoRpow_symm_eq`, `MonoidWithZeroHom.snd_comp_inr`, `smul_inv₀`, `Polynomial.valuation_aeval_monomial_eq_valuation_pow`, `Valuation.isOpen_ball`, `ArithmeticFunction.pdiv_apply`, `Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer`, `ValuationSubring.coe_pointwise_smul`, `Units.exists_iff_ne_zero`, `Set.image_mul_left_Iic`, `mul_inv_eq_one₀`, `smul_div₀'`, `mul_div_cancel_left_of_imp`, `instIsCancelMulZero`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `MonoidWithZeroHom.inr_apply_unit`, `MonoidWithZeroHom.valueMonoid_eq_valueGroup'`, `IsValuativeTopology.isClosed_ball`, `one_div_pos`, `Set.Nonempty.div_zero`, `Right.inv_pos`, `inv_le_iff_one_le_mul₀`, `inv_pow_sub_of_lt`, `inv_lt_zero`, `inv_mul_right_le`, `le_mul_inv_iff₀`, `LinearOrderedCommGroupWithZero.fst_apply`, `map_mul_right_nhds₀`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `GrpWithZero.hom_id`, `MulAction.injective₀`, `Absorbs.biInter`, `inv_le_iff_one_le_mul₀'`, `IsOpen.smul₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `IsGaloisGroup.smul_eq_self`, `Submonoid.mem_nonunits_iff_of_ne_zero`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `mul_div_mul_left`, `Valuation.hasBasis_uniformity`, `inv_mul_cancel_of_invertible`, `zpow_neg_mul_zpow_self`, `Valued.toNormedField.norm_def`, `inv_mul_lt_iff₀'`, `IsSelfAdjoint.inv₀_iff`, `Units.isEmbedding_val₀`, `pow_sub₀`, `Subring.pointwise_smul_le_pointwise_smul_iff₀`, `Valuation.toUniformSpace_eq`, `punctured_nhds_smul₀`, `Valuation.isOpen_sphere`, `Valuation.norm_def`, `exists_pow_lt₀`, `Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange`, `inv_lt_iff_one_lt_mul₀'`, `nonZeroDivisorsEquivUnits_apply`, `divp_mk0`, `MonoidWithZeroHom.fst_inr_apply_of_ne_zero`, `Valuation.exists_div_eq_of_unit`, `zpow_succ'`, `map_mul_right_nhds_one₀`, `Valuation.restrict_le_one_iff`, `Valuation.isClosed_ball`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `eq_zero_of_one_div_eq_zero`, `orderOf_eq_zero_iff_eq_zero`, `Equiv.mulRight₀_symm_apply`, `WithZeroTopology.tendsto_units`, `ValuationSubring.mem_smul_pointwise_iff_exists`, `OrderIso.withZeroUnits_apply`, `Valuation.leAddSubgroup_zero`, `WithZeroTopology.Iio_mem_nhds_zero`, `mul_inv_eq_iff_eq_mul₀`, `Homeomorph.mulRight₀_symm_apply`, `Commute.div_eq_div_iff`, `Valuation.IsEquiv.orderMonoidIso_eq_refl`, `divMonoidWithZeroHom_apply`, `Valuation.RankOne.zero_of_hom_zero`, `Fintype.card_eq_card_units_add_one`, `nonZeroDivisorsEquivUnits_symm_apply_coe`, `MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀`, `Set.center_units_eq`, `Valuation.IsEquiv.valueGroup₀Fun_zero`, `WithZero.withZeroUnitsEquiv_symm_apply`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `Commute.self_zpow₀`, `Valuation.Integers.valuation_irreducible_pos`, `Set.preimage_smul₀`, `MonoidWithZeroHom.inr_strictMono`, `Valuation.IsUniformizer.iff`, `zpow_one_add₀`, `Valued.hasBasis_uniformity`, `Valuation.mem_ltSubmodule_iff`, `inv_mul_le_one_of_le₀`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `SignType.pow_odd`, `Set.image_mul_left_Ioo`, `Finset.inv_smul_mem_iff₀`, `invOf_eq_inv`, `Homeomorph.coe_mulLeft₀`, `invOf_div`, `div_mul_cancel_right₀`, `one_div_mul_cancel`, `div_pos`, `div_nonneg`, `Set.preimage_mul_const_Ioc₀`, `Finset.mul₀_sup'`, `AddSubgroup.mem_inv_pointwise_smul_iff₀`, `absorbent_iff_inv_smul`, `continuous_const_smul_iff₀`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `MeasurableEquiv.coe_mulLeft₀`, `OrderIso.mulLeft₀_symm`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg`, `Valuation.restrict_lt_iff`, `smul_pi₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `Finset.mem_inv_smul_finset_iff₀`, `Set.Nonempty.zero_div`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `bddBelow_smul_iff_of_pos`, `WithZeroTopology.tendsto_zero`, `IsLocalRing.ResidueField.residue_smul`, `Valued.isClosed_closedBall`, `Valuation.isOpen_closedBall`, `Valuation.coe_ltAddSubgroup`, `OrderIso.smulRightDual_symm_apply`, `inv_nonpos`, `MonoidWithZeroHom.inl_mono`, `Finset.subset_smul_finset_iff₀`, `mul_inv_lt_iff₀'`, `mul_left_injective`, `zpow_natCast_sub_one₀`, `Commute.mul_inv_eq_mul_inv_iff`, `Subsemiring.pointwise_smul_le_pointwise_smul_iff₀`, `one_div_nonpos`, `Set.image_mul_right_Ico`, `aestronglyMeasurable_const_smul_iff₀`, `bddAbove_smul_iff_of_pos`, `Commute.zpow_zpow₀`, `SubMulAction.smul_mem_iff`, `div_lt_div_iff₀`, `Valuation.RankOne.isNontrivial_restrict`, `Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow`, `ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eq`, `Absorbs.univ`, `Finset.smul_finset_inter₀`, `eq_inv_smul_iff₀`, `Commute.smul_left_iff₀`, `ValuativeRel.restrict_lt_orderMonoidIso`, `strictAntiOn_inv_pos`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂`, `Mathlib.Tactic.FieldSimp.zpow'_ofNat`, `Set.zero_div_subset`, `Finset.smul_finset_sdiff₀`, `Valuation.norm_pos_iff_valuation_pos`, `isClosedMap_smul₀`, `Commute.inv_right₀`, `Set.div_zero_subset`, `isLocalHom_of_exists_map_ne_one`, `pow_eq_pow_iff_of_coprime`, `Units.val_mk0`, `inv_lt_one_iff₀`, `WithZero.withZeroUnitsEquiv_apply`, `continuousOn_zpow₀`, `Units.mk0_prod`, `Units.zero_lt`, `Mathlib.Tactic.FieldSimp.zpow'_add`, `Valuation.ltIdeal_mono`, `ProbabilityTheory.gaussianPDFReal_mul`, `Subsemiring.pointwise_smul_le_iff₀`, `le_div_iff₀`, `star_div₀`, `ValuationSubring.smul_mem_pointwise_smul`, `Set.smul_set_subset_iff₀`, `star_zpow₀`, `Equiv.smulRight_apply`, `PosMulReflectLT.toPosMulStrictMono`, `mul_inv_le_of_le_mul₀`, `MonoidWithZeroHom.snd_apply_coe`, `Set.inv_Ioo_0_left`, `LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono`, `Set.Finite.absorbs_biInter`, `Units.exists0`, `Valuation.restrict_exists_div_eq`, `Valuation.leSubmodule_zero`, `eq_div_iff`, `Units.mulArchimedean_iff`, `Valuation.IsEquiv.orderMonoidIso_spec`, `WithZeroTopology.singleton_mem_nhds_of_units`, `Valuation.RankOne.hom_eq_zero_iff`, `eq_zero_or_unit`, `LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered`, `Multipliable.tsum_congr_cofinite₀`, `zpow_left_monoOn₀`, `Function.support_inv'`, `Valued.isClopen_closedBall`, `Valuation.RankOne.restrict_RankOne_hom_eq`, `div_le_iff₀'`, `Finset.Nonempty.div_zero`, `mul_left_surjective₀`, `LinearOrderedCommGroupWithZero.inl_apply`, `map_mul_left_nhds₀`, `OpenPartialHomeomorph.unitBallBall_symm_apply`, `AddSubgroup.le_pointwise_smul_iff₀`, `LinearOrderedCommGroupWithZero.inr_apply`, `Absorbs.sInter`, `mul_sup₀`, `SignType.coe_pow`, `WithVal.strictMono_valueGroupEquiv`, `AddSubmonoid.le_pointwise_smul_iff₀`, `mul_inv_mul_cancel`, `IsValuativeTopology.mem_nhds_iff`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `div_eq_zero_iff`, `SignType.coe_zpow`, `stronglyMeasurable_const_smul_iff₀`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `HasCompactSupport.comp_smul`, `inv_mul_cancel₀`, `Commute.inv_left₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zero`, `Valuation.RankLeOne.strictMono'`, `Mathlib.Tactic.FieldSimp.NF.eval_cons`, `ArithmeticFunction.IsMultiplicative.map_div_of_coprime`, `denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units`, `Set.smul_set_pi₀'`, `Subgroup.le_pointwise_smul_iff₀`, `div_zero`, `Valuation.exists_setOf_restrict_le_iff`, `mul_self_div_self`, `MonoidWithZeroHom.inr_injective`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono`, `Units.mk0_val`, `mul_div_cancel_of_imp`, `WithZeroTopology.nhds_eq_update`, `Real.exists_lt_of_strictMono`, `eq_mul_of_mul_inv_eq₀`, `MonoidWithZeroHom.commute_inl_inr`, `MonoidWithZeroHom.fst_comp_inr`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀`, `Mathlib.Tactic.FieldSimp.zero_zpow'`, `Valuation.IsRankOneDiscrete.exists_generator_lt_one`, `mulSupport_comp_inv_smul₀`, `OpenPartialHomeomorph.unitBallBall_apply`, `IsValuativeTopology.isOpen_sphere`, `div_mul_div_cancel₀`, `Set.mem_smul_set_iff_inv_smul_mem₀`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃`, `ValuationSubring.mapOfLE_comp_valuation`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `toNoZeroSMulDivisors`, `measurable_const_smul_iff₀`, `pow_mem_range_pow_of_coprime`, `Finset.smul_univ₀`, `Units.inv_mul'`, `noZeroDivisors`, `SemiconjBy.inv_symm_left_iff₀`, `Set.smul_univ₀'`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero`, `MonoidWithZeroHom.ValueGroup₀.embedding_strictMono`, `Set.smul_set_symmDiff₀`, `eq_mul_of_inv_mul_eq₀`, `Units.mk0_one`, `div_mul_eq_mul_div₀`, `Set.image_mul_left_Ici`, `Subring.mem_inv_pointwise_smul_iff₀`, `Valuation.IsRankOneDiscrete.generator_mem_range`, `Set.preimage_const_mul_Iic₀`, `neg_of_div_neg_left`, `le_inv_smul_iff_of_pos`, `Set.preimage_mul_const_Iio₀`, `IsValuativeTopology.isClopen_closedBall`, `Valuation.exists_div_eq_of_surjective`, `upperBounds_smul_of_pos`, `Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow`, `smul_inv₀'`, `Valuation.mem_nhds_iff`, `Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange`, `Set.preimage_mul_const_Ioi₀`, `Set.smul_set_pi₀`, `Filter.EventuallyEq.div_mul_cancel`, `MonoidWithZeroHom.inl_apply_unit`, `Valuation.is_topological_valuation`, `MonoidWithZeroHom.snd_surjective`, `Valuation.inversion_estimate`, `Valuation.isClopen_sphere`, `MeasurableEquiv.coe_mulRight₀`, `Unitary.coe_inv`, `Valuation.IsEquiv.orderMonoidIso_symm`, `star_inv₀`, `Set.inv_op_smul_set_distrib₀`, `inv_mul_cancel_right₀`, `WithZero.withZeroUnitsEquiv_strictMono`, `le_inv_mul_left`, `one_lt_inv_mul₀`, `LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered`, `Function.support_div`, `Set.subset_smul_set_iff₀`, `Valuation.isClosed_sphere`, `SemiconjBy.inv_right_iff₀`, `inv_mul_le_iff₀'`, `aemeasurable_const_smul_iff₀`, `WithZeroTopology.hasBasis_nhds_units`, `instDenselyOrderedUnits`, `AddSubmonoid.pointwise_smul_le_iff₀`, `cfcUnits_zpow`, `WithZeroTopology.instContinuousInv₀`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `Subsemiring.le_pointwise_smul_iff₀`, `Filter.NeBot.div_zero_nonneg`, `GrpWithZero.Iso.mk_inv`, `Valued.extensionValuation_toFun`, `Mathlib.Tactic.FieldSimp.mul_zpow'`, `mul_inv_le_iff₀'`, `measurableEmbedding_mulLeft₀`
`zpow` 📖	CompOp	3 math math: `zpow_zero'`, `zpow_neg'`, `zpow_succ'`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`div_eq_mul_inv` 📖	mathematical	—	`toDiv` `Semigroup.toMul` `Monoid.toSemigroup` `MonoidWithZero.toMonoid` `toMonoidWithZero` `toInv`	—	—
`inv_zero` 📖	mathematical	—	`toInv` `MonoidWithZero.toZero` `toMonoidWithZero`	—	—
`mul_inv_cancel` 📖	mathematical	—	`Semigroup.toMul` `Monoid.toSemigroup` `MonoidWithZero.toMonoid` `toMonoidWithZero` `toInv` `Monoid.toOne`	—	—
`toMulDivCancelClass` 📖	mathematical	—	`MulDivCancelClass` `toMonoidWithZero` `DivInvMonoid.toDiv` `toDivInvMonoid`	—	`div_eq_mul_inv` `mul_assoc` `mul_inv_cancel₀` `mul_one`
`toNontrivial` 📖	mathematical	—	`Nontrivial`	—	—
`zpow_neg'` 📖	mathematical	—	`zpow` `toInv`	—	—
`zpow_succ'` 📖	mathematical	—	`zpow` `Semigroup.toMul` `Monoid.toSemigroup` `MonoidWithZero.toMonoid` `toMonoidWithZero`	—	—
`zpow_zero'` 📖	mathematical	—	`zpow` `Monoid.toOne` `MonoidWithZero.toMonoid` `toMonoidWithZero`	—	—

IsCancelMulZero

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`toIsLeftCancelMulZero` 📖	mathematical	—	`IsLeftCancelMulZero`	—	—
`toIsRightCancelMulZero` 📖	mathematical	—	`IsRightCancelMulZero`	—	—

IsLeftCancelMulZero

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_left_cancel_of_ne_zero` 📖	mathematical	—	`IsLeftRegular`	—	—
`to_isCancelMulZero` 📖	mathematical	—	`IsCancelMulZero` `CommMagma.toMul`	—	`to_isRightCancelMulZero`
`to_isRightCancelMulZero` 📖	mathematical	—	`IsRightCancelMulZero` `CommMagma.toMul`	—	`mul_left_cancel₀` `mul_comm`
`to_noZeroDivisors` 📖	mathematical	—	`NoZeroDivisors` `MulZeroClass.toMul` `MulZeroClass.toZero`	—	`mul_left_cancel₀` `MulZeroClass.mul_zero`

IsRightCancelMulZero

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_right_cancel_of_ne_zero` 📖	mathematical	—	`IsRightRegular`	—	—
`to_isCancelMulZero` 📖	mathematical	—	`IsCancelMulZero` `CommMagma.toMul`	—	`to_isLeftCancelMulZero`
`to_isLeftCancelMulZero` 📖	mathematical	—	`IsLeftCancelMulZero` `CommMagma.toMul`	—	`mul_right_cancel₀` `mul_comm`
`to_noZeroDivisors` 📖	mathematical	—	`NoZeroDivisors` `MulZeroClass.toMul` `MulZeroClass.toZero`	—	`mul_right_cancel₀` `MulZeroClass.zero_mul`

MonoidWithZero

Definitions

Name	Category	Theorems
`toMonoid` 📖	CompOp	13506 math math: `AnalyticWithinAt.const_smul`, `AdicCompletion.of_surjective_iff`, `unitary.spectrum.unitary_conjugate`, `MultilinearMap.map_piecewise_smul`, `Set.center_units_subset`, `AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀`, `Unitary.openPartialHomeomorph_source`, `withSeminorms_iff_mem_nhds_isVonNBounded`, `SchwartzMap.norm_toLp_le_seminorm`, `IsUnit.cfcRpow`, `Matrix.l2_opNorm_toEuclideanCLM`, `IsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one`, `GradedRing.toGradedMonoid`, `DFinsupp.coprodMap_apply`, `FiniteField.Extension.frob_apply`, `WeierstrassCurve.b₂_of_char_three`, `LinearMap.det_toContinuousLinearMap`, `HasDerivAt.fun_neg`, `LieSubmodule.coe_smul`, `OreLocalization.left_distrib`, `Polynomial.rightInverse_ofMultiset_roots`, `SubMulAction.zero_mem`, `isUnit_cfc_iff`, `units_inv_smul`, `LieAlgebra.IsKilling.rootSystem_toLinearMap_apply`, `TestFunction.lineDerivCLM_apply_of_le`, `absorbent_iff_eventually_nhdsNE_zero`, `Finset.sum_pow_eq_sum_piAntidiag`, `LeftPreLieAlgebra.toSMulCommClass`, `CategoryTheory.ShortComplex.opcyclesMap_smul`, `StarConvex.preimage_add_right`, `pow_expChar_pow_inj_of_pNilradical_eq_bot`, `iteratedDeriv_scomp_two`, `HasDerivAt.isLittleO`, `Polynomial.units_coeff_zero_smul`, `MvPowerSeries.hasSubst_def`, `LinearMap.IsSymmetric.clm_adjoint_eq`, `Finset.expect_ite_mem`, `ContinuousLinearMap.rayleigh_smul`, `NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply'`, `Valuation.mem_nhds_zero_iff`, `Ideal.toCotangent_to_quotient_square`, `LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm`, `sub_pow_eq_mul_pow_sub_pow_div_char_of_commute`, `GroupWithZero.div_eq_mul_inv`, `ContinuousMap.toLp_inj`, `Real.hasDerivAt_fourier`, `InnerProductSpace.Core.inner_smul_right`, `AffineSpace.asymptoticNhds_smul`, `Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe`, `CStarRing.norm_mul_coe_unitary`, `ContinuousMultilinearMap.map_piecewise_smul`, `Polynomial.isUnit_C_add_X_mul_iff`, `WeierstrassCurve.j_of_char_two`, `spectrum.inv_mem_iff`, `LinearIsometryEquiv.strictConvex_preimage`, `Polynomial.natDegree_mul_X_pow`, `WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero`, `isUnit_cfc`, `TemperedDistribution.lineDerivOpCLM_eq`, `NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'`, `MvPolynomial.dvd_monomial_one_iff_exists`, `IsLocalizedModule.iso_symm_apply'`, `Module.Finite.instLocalizationLocalizedModule`, `Commute.geom_sum₂_succ_eq`, `vsub_midpoint`, `WithZero.logOrderIso_apply`, `Polynomial.degreeLT.addLinearEquiv_symm_apply_inr`, `LinearMap.restrictScalars_toMatrix`, `Valuation.IsRankOneDiscrete.generator_lt_one`, `DiffContOnCl.smul`, `MeasureTheory.Lp.toTemperedDistributionCLM_apply`, `nhds_hasBasis_absConvex_open`, `IsLocalization.mul_add_inv_left`, `fderiv_iteratedFDeriv`, `fun_meromorphicOrderAt_pow_id_sub_const`, `Matrix.discr_conj`, `PrimeSpectrum.basicOpen_pow`, `HasStrictDerivAt.fun_pow'`, `ConvexCone.convex`, `Convex.translate_preimage_right`, `RootPairing.rootForm_self_smul_coroot`, `CochainComplex.HomComplex.δ_units_smul`, `ZMod.isUnit_iff_coprime`, `FormalMultilinearSeries.comp_rightInv_aux1`, `NNReal.pow_arith_mean_le_arith_mean_pow`, `Complex.cos_eq_tsum`, `exists_rat_pow_btwn`, `unitsEquivNeZero_symm_apply`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_refl`, `Seminorm.isBounded_const`, `TensorAlgebra.ofDirectSum_of_tprod`, `cfcₙ_def`, `PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective`, `LinearMap.mkContinuous₂_norm_le'`, `AffineMap.lineMap_apply_module`, `Prime.irreducible`, `AlgebraicGeometry.Proj.awayMap_awayToSection_assoc`, `LinearMap.SeparatingRight.toMatrix₂'`, `isHomeomorph_smul₀`, `IsSelfAdjoint.sq_nonneg`, `HasDerivWithinAt.clog_real`, `ContinuousMultilinearMap.norm_mkPiRing`, `Matrix.toLinAlgEquiv_one`, `Finsupp.linearCombination_apply_of_mem_supported`, `ContinuousLinearMap.derivWithin_of_bilinear`, `Perfection.pthRoot_frobenius`, `WeierstrassCurve.c₄_of_char_three`, `Rat.RingOfIntegers.isUnit_iff`, `PowerSeries.hasSum_aeval`, `IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots`, `Homeomorph.smulOfNeZero_symm_apply`, `Submodule.mem_colon_span_singleton`, `ConvexOn.smul''`, `NonUnitalStarSubalgebra.topologicalClosure_map_le`, `ZMod.irreducible_of_dvd_cyclotomic_of_natDegree`, `StrictConcaveOn.sub`, `Valued.isOpen_closedball`, `Matrix.GeneralLinearGroup.det_scalar`, `Polynomial.degree_pow_le_of_le`, `HasDerivWithinAt.clm_comp`, `SchwartzMap.lineDerivOpCLM_eq`, `PointedCone.toConvexCone_closure_pointed`, `Subgroup.smul_mem_pointwise_smul_iff₀`, `DivisibleHull.archimedeanClassMk_mk_eq`, `Polynomial.X_pow_mul_assoc_C`, `AddChar.card_addChar_le`, `IsCoprime.pow_left`, `HasDerivWithinAt.congr_of_mem`, `pow_eq_neg_pow_iff`, `LinearEquiv.congrRight₂_refl`, `Field.Emb.Cardinal.equivLim_coherence`, `Units.divp_sub`, `Convex.neg`, `InfiniteGalois.normal_iff_isGalois`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective`, `iSupIndep.dfinsupp_lsum_injective`, `MulChar.equivToUnitHom_mul_apply`, `SymmetricAlgebra.lift_ι_apply`, `EulerSine.integral_cos_mul_cos_pow`, `Height.logHeight₁_pow`, `continuous_cfcₙHomSuperset_left`, `interior_smul₀`, `ConvexOn.mul_concaveOn'`, `hasDerivWithinAt_Iio_iff_Iic`, `gcd_one_left'`, `LinearMap.BilinForm.isOrtho_smul_right`, `HasStrictFDerivAt.fun_mul'`, `unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `Derivation.apply_eval_eq`, `sq_lt_one_iff₀`, `LinearMap.mkContinuous₂_apply`, `Polynomial.monic_X_pow`, `Polynomial.leadingCoeff_mul_X_pow`, `ModularGroup.SLOnGLPos_smul_apply`, `Module.End.exp_mul_of_derivation`, `AffineMap.hasStrictDerivAt_lineMap`, `ContinuousLinearMap.isPositive_iff_eq_sum_rankOne`, `AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf`, `dot_self_cross`, `Bundle.ContMDiffRiemannianMetric.contMDiff`, `ExteriorAlgebra.isLocalHom_algebraMap`, `Complex.one_add_tan_sq_mul_cos_sq_eq_one`, `InnerProductSpace.isPositive_rankOne_self`, `ModularForm.smul_slash`, `AffineMap.lineMap_vsub_left`, `DFinsupp.lsum_lsingle`, `MonoidAlgebra.liftMagma_apply_apply`, `Mathlib.Tactic.Ring.mul_pp_pf_overlap`, `MonoidWithZeroHom.mem_valueGroup`, `ValuativeRel.pow_vle_pow_of_vle_one`, `MeasureTheory.condExpL1_smul`, `UniqueFactorizationMonoid.squarefree_radical`, `Seminorm.absorbent_closedBall_zero`, `Matrix.toLin_kronecker`, `ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable`, `IntermediateField.exists_algHom_adjoin_of_splits`, `LinearMap.ortho_smul_right`, `Matrix.toLin'_symm`, `ModuleCat.FilteredColimits.colimit_smul_mk_eq`, `ContinuousLinearEquiv.unitsEquiv_apply`, `Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_right`, `ordinaryHypergeometric_sum_eq`, `Unitary.conjStarAlgAut_trans_conjStarAlgAut`, `Associates.dvd_count_pow`, `AlgEquiv.moduleEndSelfOp_apply_apply`, `Polynomial.derivative_X_sq`, `Matrix.SeparatingLeft.toBilin'`, `ZMod.isCyclic_units_iff_of_odd`, `MeasureTheory.Lp.instIsScalarTower`, `hasSum_geometric_of_norm_lt_one`, `Polynomial.coe_normUnit_of_ne_zero`, `ContinuousLinearMap.mulLeftRight_isBoundedBilinear`, `QuadraticMap.smul_toBilin`, `NNReal.rpow_sub_intCast`, `Ideal.Filtration.submodule_eq_span_le_iff_stable_ge`, `Polynomial.separable_X_pow_sub_C_unit`, `CategoryTheory.ShortComplex.homologyMap_smul`, `ProbabilityTheory.gaussianReal_map_const_mul`, `norm_cfcₙHom`, `Algebra.TensorProduct.instSMulCommClassTensorProduct`, `Module.Basis.mem_submodule_iff`, `WeierstrassCurve.Jacobian.negAddY_of_Z_eq_zero_left`, `HasFDerivWithinAt.continuousMultilinearMap_apply`, `Polynomial.smeval_monomial_mul`, `IntermediateField.aeval_gen_minpoly`, `NNReal.tsum_geometric`, `RootPairing.pairing_smul_root_eq_of_not_linearIndependent`, `Unitary.toLinearMap_mulRight`, `ENNReal.pow_right_strictMono`, `MDifferentiableOn.clm_postcomp`, `OrthonormalBasis.orthogonalProjection_eq_sum`, `cfcₙHom_mono`, `hasDerivWithinAt_ofNat`, `cfc_pow`, `IsNilpotent.isUnit_exp`, `RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root`, `quasispectrum_eq_spectrum_union`, `ContinuousLinearMap.analyticWithinAt_bilinear`, `Complex.restrictScalars_one_smulRight'`, `LinearMap.toMatrixAlgEquiv'_mul`, `Matrix.GLPos.coe_neg_apply`, `orderOf_lt_card`, `OrderMonoidIso.val_inv_unitsWithZero_symm_apply`, `Seminorm.bound_of_shell`, `SymmetricAlgebra.rank_eq`, `Algebra.norm_algebraMap_of_basis`, `Matrix.kroneckerTMulStarAlgEquiv_symm_apply`, `CommGroupWithZero.coe_normUnit`, `Matrix.frobeniusIsBoundedSMul`, `HasCompactSupport.convolution_integrand_bound_left`, `LinearMap.BilinForm.toMatrix_toBilin`, `Associates.isAtom_iff`, `WithZero.val_expOrderIso_apply`, `ContinuousLinearMap.compSL_apply`, `ContinuousLinearMap.continuous₂`, `ValuativeRel.pow_rel_pow_of_rel_one`, `LinearMap.IsSymmetric.inner_map_polarization`, `QuaternionAlgebra.coe_pow`, `WeierstrassCurve.Jacobian.dblX_of_Y_eq`, `ValuationSubring.coe_mem_principalUnitGroup_iff`, `CategoryTheory.Functor.mapExtLinearMap_toAddMonoidHom`, `AdicCompletion.algebraMap_apply`, `HasDerivAt.const_sub`, `Subgroup.adjoinNegOne_eq_self_iff`, `hasDerivWithinAt_add_const_iff`, `LinearOrder.strictConcaveOn_of_lt`, `LinearMap.coe_toSeminorm`, `FormalMultilinearSeries.comp_partialSum`, `SameRay.nonneg_smul_left`, `Convex.intrinsicClosure`, `Real.sSup_smul_of_nonpos`, `pow_sub_of_lt`, `OreLocalization.cardinalMk`, `pow_le_pow_iff_right_of_lt_one₀`, `AdicCompletion.mk_zero_of`, `NonUnitalStarSubalgebra.instSMulMemClass`, `CStarRing.norm_unitary_smul`, `Module.mem_annihilator`, `Matrix.SeparatingRight.toLinearMap₂`, `quadraticChar_card_sqrts`, `AnalyticOnNhd.smul`, `IntermediateField.LinearDisjoint.iff_inf_eq_bot`, `HasDerivAtFilter.sum`, `RootPairing.linearIndepOn_root_baseOf'`, `Ideal.Cotangent.lift_comp_toCotangent`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply`, `IntermediateField.normal_inf`, `PolyEquivTensor.toFunBilinear_apply_eq_sum`, `Rep.MonoidalClosed.linearHomEquiv_symm_hom`, `binomialSeries_eq_ordinaryHypergeometricSeries`, `ENNReal.toNNReal_pow`, `Polynomial.lcoeff_comp_mapAlgHom_eq`, `Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub`, `IntermediateField.algHomEquivAlgHomOfSplits_symm_apply`, `StarAddMonoid.toStarModuleNNRat`, `StarAlgEquiv.ofLeftInverse'_apply`, `LaurentPolynomial.mk'_one_X_pow`, `Ideal.tensorCotangentEquiv_tmul`, `Ideal.pow_multiset_sum_mem_span_pow`, `ZMod.pow_card_sub_one`, `SchwartzMap.integral_sesq_fourier_fourier`, `selfZPow_of_nonpos`, `Bornology.isVonNBounded_iff_tendsto_smallSets_nhds`, `Asymptotics.IsBigOTVS.congr'`, `Submodule.isScalarTower`, `PowerSeries.IsRestricted.smul`, `Module.support_quotient`, `GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I`, `LinearMap.exists_monic_and_aeval_eq_zero`, `PadicInt.lift_sub_val_mem_span`, `WithSeminorms.image_isVonNBounded_iff_seminorm_bounded`, `Filter.IsBoundedUnder.smul_tendsto_zero`, `tendsto_const_mul_pow_nhds_iff'`, `WithVal.valueGroupOrderIso₀_symm_apply`, `Valuation.ltIdeal_le_leIdeal`, `Matrix.SpecialLinearGroup.map_mapGL`, `DividedPowers.RatAlgebra.dpow_eq_inv_fact_smul`, `WithZero.logEquiv_symm`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `HasDerivWithinAt.Iio_of_Iic`, `RootPairing.Polarization_apply`, `PolynomialModule.comp_single`, `hasStrictDerivAt_intCast`, `Complex.cos_three_mul`, `Balanced.smul_mem_iff`, `sub_pow_expChar_pow_of_commute`, `Complex.linearEquiv_det_conjLIE`, `Polynomial.coeff_X_pow_mul'`, `isSMulRegular_iff_mem_nonZeroSMulDivisors`, `MeasureTheory.convolution_eq_right'`, `Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `EisensteinSeries.hasSum_e2Summand_symmetricIcc`, `NonUnitalIsometricContinuousFunctionalCalculus.isometric`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn`, `MeasureTheory.eLpNormEssSup_const_smul`, `BilinForm.toMatrix_symm`, `TensorProduct.AlgebraTensorModule.leftComm_eq`, `PowerSeries.constantCoeff_subst`, `sq_eq_one_iff`, `ValuativeRel.pow_rel_pow`, `Asymptotics.isBigO_const_smul_right`, `cfcₙHom_apply_mem_elemental`, `Ideal.hasFiniteMulSupport_coe`, `ClassGroup.mk0_integralRep`, `Polynomial.one_add_X_pow_sub_X_pow`, `NonUnitalStarAlgHom.coe_codRestrict`, `CategoryTheory.Linear.instMonoHSMulHomOfInvertible`, `SimpleGraph.lapMatrix_toLinearMap₂'`, `curveIntegral_smul`, `InnerProductSpace.volume_closedBall_of_dim_even`, `FormalMultilinearSeries.ofScalars_apply_eq'`, `LocalizedModule.subsingleton_iff_disjoint`, `Quaternion.snd_imJ_dualNumberEquiv_symm`, `LinearMap.pow_mulRight`, `AddDissociated.randomisation`, `IntervalIntegrable.smul_continuousOn`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1`, `FixedPoints.minpoly.irreducible`, `Polynomial.eq_cyclotomic_iff`, `MultilinearMap.map_update_smul`, `GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I`, `RootPairing.coroot_eq_polarizationEquiv_apply_root`, `ZMod.unitsMap_surjective`, `derivWithin_smul`, `Real.fderiv_fourierIntegral`, `Valuation.isClopen_closedBall`, `hasStrictFDerivAt_list_prod_finRange'`, `MeasurableEquiv.coe_smul₀`, `MeasureTheory.integral_smul_nnreal_measure`, `ContinuousMultilinearMap.map_smul_univ`, `MeasureTheory.taylor_charFun_two`, `MeasureTheory.condExp_bilin_of_stronglyMeasurable_left`, `ENNReal.exists_inv_two_pow_lt`, `IsLocalization.Away.algebraMap_isUnit_iff`, `Ideal.IsTwoSided.pow_succ`, `Polynomial.smeval_commute`, `MvPolynomial.rTensor_apply_tmul_apply`, `InnerProductSpace.rankOne_one_left_eq_innerSL`, `Submodule.le_annihilator_iff`, `PeriodPair.hasSumLocallyUniformly_weierstrassP`, `IsClosed.smul_of_ne_zero`, `LinearIndependent.pair_add_smul_right_iff`, `StandardEtalePair.inv_aeval_X_g`, `IntermediateField.adjoin.finrank`, `Seminorm.le_finset_sup_apply`, `WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF_of_char_three`, `Matrix.isUnit_of_right_inverse`, `Asymptotics.IsThetaTVS.trans_isBigOTVS`, `Mathlib.Tactic.Module.NF.eval_algebraMap`, `IsPurelyInseparable.minpoly_eq'`, `FormalMultilinearSeries.smul_apply`, `Matrix.GeneralLinearGroup.map_det`, `LaurentPolynomial.mk'_mul_T`, `NonUnitalCStarAlgebra.toStarModule`, `Polynomial.expand_eq_sum`, `Complex.circleTransformDeriv_eq`, `NumberField.Units.logEmbedding_fundSystem`, `LinearMap.IsSymmetric.restrictScalars`, `Mathlib.Tactic.Ring.pow_one`, `Seminorm.norm_sub_map_le_sub`, `emultiplicity_sub_of_gt`, `bddBelow_smul_iff_of_neg`, `Matrix.GeneralLinearGroup.val_mkOfDetNeZero`, `StrongDual.norm_extendRCLike`, `IsBaseChange.comp_iff`, `addMonoidHomLequivNat_symm_apply`, `HasFiniteFPowerSeriesAt.neg`, `TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_symm`, `Submodule.mem_ideal_smul_span_iff_exists_sum`, `Matrix.separatingRight_toLinearMap₂'_iff`, `LinearMap.baseChange_smul`, `FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero`, `LinearMap.BilinForm.isSkewAdjoint_bracket`, `Balanced.smul_congr`, `MvPolynomial.rTensorAlgEquiv_apply`, `ContinuousLinearMap.smulRight_one_eq_toSpanSingleton`, `Algebra.Generators.H1Cotangent.δAux_mul`, `AffineMap.lineMap_linear`, `Pi.image_update_openSegment`, `AlgCat.hom_inv_associator`, `ContinuousLinearMap.map_add_add`, `X_pow_sub_C_splits_of_isPrimitiveRoot`, `LieAlgebra.IsKilling.restrict_killingForm_eq_sum`, `SeminormFamily.basisSets_smul_right`, `HasFDerivWithinAt.pow`, `Antivary.smul_add_smul_le_smul_add_smul`, `AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι_assoc`, `AddSubgroup.zero_smul`, `MeromorphicOn.divisor_fun_smul`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `Bornology.IsVonNBounded.of_sub_left`, `Matrix.SpecialLinearGroup.continuous_toGL`, `Matrix.pow_eq_aeval_mod_charpoly`, `FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite`, `HasDerivWithinAt.div_const`, `IntermediateField.algHomEquivAlgHomOfSplits_apply_apply`, `Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point`, `Unitization.inrNonUnitalAlgHom_toFun`, `Ideal.toCotangent_eq`, `exists_associated_mem_of_dvd_prod`, `Subsemiring.coe_pow`, `Polynomial.resultant_X_add_C_right`, `AdicCompletion.AdicCauchySequence.mk_eq_mk`, `Real.hasDerivAt_sigmoid`, `MeasureTheory.IntegrableOn.continuousOn_smul`, `Polynomial.pow_rootMultiplicity_dvd`, `taylorWithinEval_hasDerivAt_Ioo`, `AlternatingMap.map_vecCons_smul`, `NonUnitalSubalgebraClass.coe_subtype`, `ContDiffMapSupportedIn.seminorm_monoLM_eq`, `MulSemiringAction.toRingHom_apply`, `fderivWithin_fun_smul`, `dvd_sub_pow_of_dvd_sub`, `ContinuousMultilinearMap.norm_iteratedFDerivComponent_le`, `Finset.weightedVSubOfPoint_apply`, `PowerSeries.coeff_rescale`, `X_pow_sub_C_eq_prod`, `HasDerivWithinAt.congr_mono`, `ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap`, `complexOfReal_hasDerivWithinAt`, `ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff`, `MvPolynomial.scalarRTensor_apply_monomial_tmul`, `Real.fourierIntegralInv_eq'`, `AffineMap.hasDerivAtFilter`, `NNRat.num_pow`, `ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply`, `Subgroup.instHasDetOneRangeSpecialLinearGroupGeneralLinearGroupMapGL`, `LinearIndependent.pair_add_smul_left_iff`, `Module.End.HasEigenvalue.mem_spectrum`, `QuadraticMap.canLift`, `LieModule.toEnd_pow_apply_map`, `StrictConvex.is_linear_image`, `WeierstrassCurve.Projective.eval_polynomial`, `Associates.prime_pow_dvd_iff_le`, `IntermediateField.coe_algebraMap_over_bot`, `IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic`, `MulChar.toUnitHom_eq`, `fderivWithin_fderivWithin_eq_of_mem_nhdsWithin`, `Matrix.toLinearMapRight'_mul`, `RingTheory.Sequence.isWeaklyRegular_cons_iff'`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm`, `SlashInvariantForm.slash_action_eq'`, `MeasureTheory.VectorMeasure.coe_smul`, `Finset.sum_smul`, `MvPolynomial.eval₂_expand`, `hasDerivAt_integral_of_dominated_loc_of_lip`, `NumberField.Units.instNonemptySubtypeUnitsRingOfIntegersMemSubgroupTorsion`, `ModularForm.mul_slash`, `ProbabilityTheory.gaussianReal_const_mul`, `ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds`, `Matrix.one_div_pow`, `finsuppTensorFinsupp_apply`, `WeierstrassCurve.c_relation`, `Submodule.smul_eq_map₂`, `Convex.smul_preimage`, `AntivaryOn.sum_smul_lt_sum_comp_perm_smul_iff`, `ZMod.LFunction_stdAddChar_eq_expZeta`, `Submodule.toConvexCone_inf`, `Polynomial.disjoint_ker_aeval_of_isCoprime`, `Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular`, `Filter.smul_tendsto_smul_iff₀`, `Ideal.squarefree_span_singleton`, `ContDiffOn.smul_const`, `Ideal.iInf_pow_smul_eq_bot_of_isLocalRing`, `MvPolynomial.universalFactorizationMap_comp_map`, `Module.Basis.equivFun_symm_apply`, `CFC.inv_nonneg`, `MDifferentiableAt.cle_arrowCongr`, `IsUnit.isStrictlyPositive_star_right_conjugate_iff`, `WithLp.prod_nndist_eq_of_L2`, `Absorbs.eventually_nhds_zero`, `Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_pow`, `autAdjoinRootXPowSubCEquiv_root`, `Associates.le_of_count_ne_zero`, `MvPowerSeries.subst_pow`, `MonoidAlgebra.isLocalHom_algebraMap`, `splits_X_pow_sub_one_of_X_pow_sub_C`, `AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul'`, `Polynomial.resultant_one_right`, `PolynomialModule.smul_def`, `Seminorm.bot_eq_zero`, `geom_series_mul_shift`, `CoalgHom.coe_addMonoidHom_injective`, `cfcₙHom_of_cfcHom_injective`, `Mathlib.Tactic.Ring.single_pow`, `Complex.integral_boundary_rect_eq_zero_of_differentiableOn`, `Submodule.isInternal_prime_power_torsion_of_pid`, `ContinuousLinearMap.continuousSMul`, `IsFractionRing.nonZeroDivisors_eq_isUnit`, `PowerSeries.invOneSubPow_zero`, `SModEq.pow_pow_add_one`, `Ideal.IsHomogeneous.iff_exists`, `hasFTaylorSeriesUpToOn_top_iff_right`, `isReduced_of_injective`, `support_comp_inv_smul₀`, `Module.End.isNilpotent_restrict_genEigenspace_nat`, `Seminorm.smul_comp`, `MonoidWithZeroHom.snd_comp_inl`, `add_pow_expChar_pow_of_commute`, `CochainComplex.HomComplex.Cocycle.coe_smul`, `ConvexCone.mem_positive`, `LinearIsometry.map_smul`, `Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `ClassGroup.mk_eq_mk_of_coe_ideal`, `UpperHalfPlane.instContinuousSMulGL2R`, `MeasureTheory.Lp.const_smul_mem_Lp`, `RootPairing.reflectionPerm_eq_iff_smul_root`, `smoothSheafCommRing.nonunits_stalk`, `IsBaseChange.finsuppPow`, `Prime.associated_of_dvd`, `strictConvex_Iic`, `spectrum.of_inv₀_mem`, `Matrix.separatingRight_toLinearMap₂_iff`, `WeierstrassCurve.Jacobian.add_of_Y_ne'`, `Matrix.isUnit_det_zpow_iff`, `RatFunc.algEquivOfTranscendental_X`, `arithGeom_eq'`, `AddSubgroupClass.coe_zmod_smul`, `absorbs_zero_iff`, `IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable'`, `MulChar.exists_apply_eq_pow`, `AdicCompletion.map_val_apply`, `Matrix.SpecialLinearGroup.coeToGL_det`, `ConvexOn.smul`, `Ideal.mul_le_right`, `Module.End.HasUnifEigenvector.pow_apply`, `expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul`, `Nat.card_units`, `Polynomial.isPrimitive_iff_isUnit_of_C_dvd`, `PeriodPair.derivWeierstrassPExcept_sub`, `Associates.mk_out`, `AffineSubspace.setOf_sSameSide_eq_image2`, `NumberField.Units.fun_eq_repr`, `ContinuousMultilinearMap.analyticAt_uncurry_of_linear`, `intervalIntegral.integral_hasDerivWithinAt_right`, `isLittleO_exp_neg_mul_sq_cocompact`, `Matrix.spectrum_toEuclideanLin`, `Bornology.isVonNBounded_add_of_nonempty`, `Polynomial.support_trinomial`, `Monotone.quasiconcaveOn`, `Perfection.mk_comp_teichmuller₀`, `Matrix.iSup_eigenspace_toLin'_diagonal_eq_top`, `NumberField.IsCMField.unitsComplexConj_torsion`, `FormalMultilinearSeries.radius_pi_eq_iInf`, `MvPolynomial.expand_X`, `Polynomial.divX_X_pow`, `GroupWithZero.conj_pow₀`, `ProperCone.convex`, `JacobsonNoether.exists_pow_mem_center_of_inseparable'`, `gcd_mul_lcm`, `KaehlerDifferential.polynomialEquiv_symm`, `Derivation.coe_to_linearMap_comp`, `UniqueFactorizationMonoid.exists_reduced_factors`, `HurwitzZeta.cosZeta_two_mul_nat'`, `addMonoidHomLequivInt_apply`, `SchwartzMap.pairing_apply_apply`, `PadicInt.val_mkUnits`, `Submodule.instStrictConvexSpace`, `InnerProductSpace.isIdempotentElem_rankOne_self`, `AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk`, `norm_iteratedFDerivWithin_smul_le`, `normUnit_eq_one`, `Units.mulLeftLinearEquiv_trans_mulLeftLinearEquiv`, `SymmetricAlgebra.isSymmetricAlgebra_ι`, `factorization_pow`, `Submodule.tensorEquivSpan_apply_tmul`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply`, `Matrix.cstar_nnnorm_def`, `minpoly.algEquiv_apply`, `IsLprojection.Lnorm`, `AddCommGroup.intIsScalarTower`, `IsPrimitiveRoot.isRoot`, `NonUnitalSubalgebra.instIsScalarTower'`, `Ideal.smul_top_eq_map`, `LineDifferentiableWithinAt.smul`, `IsPurelyInseparable.elemExponent_min'`, `egauge_prod_mk`, `Differentiable.clm_comp`, `parallelogram_law_with_nnnorm`, `PreTilt.valAux_eq`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv`, `hasSum_choose_mul_geometric_of_norm_lt_one`, `intervalIntegral.integral_hasFDerivAt_of_tendsto_ae`, `MeasureTheory.LocallyIntegrable.integrable_smul_right_of_hasCompactSupport`, `Polynomial.cyclotomic_six`, `AlgHom.coe_addMonoidHom_injective`, `summableLocallyUniformlyOn_iteratedDerivWithin_cexp`, `IsLocalization.Away.algebraMap_pow_isUnit`, `WithZero.withZeroUnitsEquiv_symm_apply_coe`, `IntermediateField.isScalarTower_mid'`, `div_sq_cancel`, `Submonoid.smul_mem_pointwise_smul_iff₀`, `LinearEquiv.congrRight_symm`, `WeierstrassCurve.Jacobian.Point.toAffineLift_some`, `VitaliFamily.withDensity_le_mul`, `tsum_coe_mul_geometric_of_norm_lt_one'`, `LinearMap.mapMatrixLinear_apply`, `WeierstrassCurve.Jacobian.dblX_of_Z_ne_zero`, `Filter.mem_absorbing`, `TensorProduct.CompatibleSMul.of_algebraMap_surjective`, `Matrix.GeneralLinearGroup.map_comp_apply`, `IsPrimitiveRoot.isRoot_of_dvd`, `LinearMap.BilinForm.toMatrixAux_eq`, `CliffordAlgebra.ι_mul_ι_mul_invOf_ι`, `smul_mem_nhds_smul₀`, `Orientation.linearEquiv_det_rotation`, `IsScalarTower.to_smulCommClass'`, `ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars`, `hasDerivWithinAt_Ioi_iff_Ici`, `ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto`, `PowerSeries.expand_apply`, `NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd`, `KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul'`, `HasStrictDerivAt.pow`, `one_le_pow_mul_abs_eval_div`, `IsExposed.isExtreme`, `ContinuousLinearMap.isUniformEmbedding_restrictScalars`, `LieModule.trace_toEnd_eq_zero_of_mem_lcs`, `DividedPowers.factorial_mul_dpow_eq_pow`, `CliffordAlgebra.involute_prod_map_ι`, `CFC.sq_sqrt`, `RingTheory.Sequence.isWeaklyRegular_cons_iff`, `Unitary.conjStarAlgAut_symm`, `ConvexCone.canLift`, `hasDerivWithinAt_taylorWithinEval`, `Matrix.toLinearMap₂'_comp`, `Function.HasTemperateGrowth.fun_pow`, `map_ratCast_smul`, `FormalMultilinearSeries.changeOriginSeriesTerm_apply`, `DirectLimit.Module.of_f`, `AffineSubspace.smul_mem_smul_iff₀`, `CharP.isUnit_ofNat_iff`, `Asymptotics.isLittleOTVS_one`, `Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U`, `kroneckerTMulAlgEquiv_symm_single_tmul`, `Polynomial.cyclotomic.irreducible`, `Cubic.of_a_eq_zero'`, `not_isUnit_prime_of_dvd_card`, `UpperHalfPlane.re_smul`, `ZMod.orderOf_one_add_mul_prime`, `Seminorm.finset_sup_apply`, `HasDerivAt.hasDerivWithinAt`, `LinearEquiv.transvection.det_eq_one`, `ContinuousLinearMap.hasDerivAtFilter`, `Module.isTorsionBySet_quotient_set_smul`, `pow_four_add_four_mul_pow_four'`, `WeierstrassCurve.ΨSq_even`, `span_fourier_closure_eq_top`, `Real.fourierIntegral_eq`, `NNReal.pow_antitone_exp`, `ModularForm.eta_q_eq_pow`, `root_X_pow_sub_C_eq_zero_iff`, `MvPolynomial.instIsReduced`, `OrderIso.mulRight₀_symm_apply`, `MvPolynomial.X_pow_eq_monomial`, `normalizedFactorsEquivOfQuotEquiv_emultiplicity_eq_emultiplicity`, `OrderIso.smulRight_apply`, `add_pow_char_pow`, `IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen`, `ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall`, `HasDerivWithinAt.fun_div`, `intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right`, `IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin`, `TrivSqZeroExt.isNilpotent_iff_isNilpotent_fst`, `Submonoid.isUnit_iff_and`, `LinearMap.llcomp_apply`, `CategoryTheory.ShortComplex.Homotopy.smul_h₁`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec`, `LinearMap.toMatrix₂_mul`, `StarConvex.affine_preimage`, `aeval_wittPolynomial`, `AffineEquiv.coe_homothetyUnitsMulHom_eq_homothetyHom_coe`, `HasFPowerSeriesOnBall.add`, `LinearEquiv.det_trans`, `OnePoint.isBoundedAt_iff_exists_SL2Z`, `LinearMap.BilinForm.smul_left_of_tower`, `HasDerivWithinAt.complexToReal_fderiv'`, `Subgroup.instHasDetOneMapSpecialLinearGroupGeneralLinearGroupToGL`, `Algebra.Extension.H1Cotangent.map_id`, `Matrix.isUnit_det_of_invertible`, `circleIntegral_def_Icc`, `mdifferentiableAt_iff_localFrame_coeff`, `convexJoin_singletons`, `Polynomial.leadingCoeff_quadratic`, `pow_pos`, `LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply`, `setIntegral_withDensity_eq_setIntegral_smul₀`, `sub_pow_expChar_of_commute`, `Complex.hasSum_taylorSeries_of_entire`, `ContinuousMap.toLp_denseRange`, `IsCovariantDerivativeOn.difference_apply`, `Multiset.prod_X_sub_X_eq_sum_esymm`, `ContinuousLinearMap.toContinuousAddMonoidHom_add`, `ClassGroup.Quot_mk_eq_mk`, `PowerSeries.trunc_X_pow_self_mul`, `Polynomial.eraseLead_X_pow`, `Bornology.isVonNBounded_add_self`, `Finset.exists_eq_pow_of_mul_eq_pow_of_coprime`, `AdicCompletion.of_ofAlgEquiv_symm`, `IsArtinianRing.isUnit_of_mem_nonZeroDivisors`, `ZLattice.covolume_eq_det_inv`, `Seminorm.ball_smul_closedBall`, `IntermediateField.isPurelyInseparable_iSup`, `ContinuousLinearMap.integral_apply`, `CochainComplex.HomComplex.Cochain.leftShift_smul`, `WeierstrassCurve.Projective.nonsingularLift_some`, `segment_inter_subset_endpoint_of_linearIndependent_sub`, `Unitary.mem_pathComponentOne_iff`, `Units.toLinearMap_mulRightLinearEquiv`, `IsPrimitiveRoot.minpoly_dvd_pow_mod`, `HasDerivAt.fun_finset_prod`, `LocalizedModule.restrictScalars_map_eq`, `QuadraticAlgebra.C_pow`, `spectrum.inv₀_mem_iff`, `circleIntegrable_iff`, `Matrix.SpecialLinearGroup.toGLPos_injective`, `PolynomialModule.map_smul`, `MvPowerSeries.coeff_pow`, `Polynomial.resultant_add_left_deg`, `SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left`, `LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `convex_iff_sum_mem`, `ConcaveOn.mul_convexOn'`, `Complex.tsum_exp_neg_mul_int_sq`, `PowerBasis.repr_pow_isIntegral`, `Subring.instSMulCommClassSubtypeMemCenter`, `CharTwo.CommRing.sq_injective`, `NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded`, `ZMod.units_pow_card_sub_one_eq_one`, `MeasureTheory.integral_fintype_prod_volume_eq_pow`, `FiniteField.pow_card_sub_one_eq_one`, `LinearMap.tensorKer_tmul`, `ContMDiffCovariantDerivativeOn.affine_combination`, `UpperHalfPlane.analyticAt_smul`, `WithSeminorms.mem_nhds_iff`, `WithZero.coe_unitsWithZeroEquiv_eq_units_val`, `LinearMap.toMatrixAlgEquiv_comp`, `Convex.vadd`, `IsUnit.natCast_factorial_of_le`, `Polynomial.degree_quadratic_lt`, `LinearMap.IsSymmetric.diagonalization_apply_self_apply`, `Matrix.isParabolic_iff_exists`, `Module.rankAtStalk_eq`, `TensorProduct.sum_tmul_basis_right_injective`, `LinearMap.extendScalarsOfIsLocalization_apply`, `Submodule.mem_colon'`, `Memℓp.const_smul`, `Polynomial.irreducible_of_mirror`, `StrictConvex.diff_interior_subset_extremePoints`, `Real.fourier_continuousLinearMap_apply`, `MeasureTheory.iteratedDeriv_charFun_zero`, `DirectSum.of_smul`, `FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField`, `Unitization.real_cfcₙ_eq_cfc_inr`, `PadicInt.appr_spec`, `neg_smul`, `IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow`, `fderivWithin_fun_pow'`, `AlgebraicGeometry.Scheme.mem_basicOpen'`, `Associates.factors_mul`, `Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly`, `intervalIntegral.fderiv_integral_of_tendsto_ae`, `Units.val_cfcRpow`, `ZMod.invDFT_apply`, `WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero`, `SMulPosReflectLE_iff_smulPosReflectLT`, `Polynomial.cyclotomic_dvd_geom_sum_of_dvd`, `Convex.combo_interior_closure_mem_interior`, `CliffordAlgebra.isUnit_of_isUnit_ι`, `Representation.asAlgebraHom_single`, `NormedSpace.isBounded_iff_subset_smul_ball`, `AffineIsometryEquiv.ofTop_apply`, `AddValuation.map_pow`, `Valuation.IsRankOneDiscrete.exists_generator_lt_one'`, `HasFDerivWithinAt.clm_apply`, `Balanced.sub`, `LieAlgebra.finrank_engel`, `one_div_pow_strictAnti`, `skewAdjointLieSubalgebraEquiv_apply`, `hasFPowerSeriesOnBall_pi_iff`, `inv_smul_smul₀`, `analyticOnNhd_inverse`, `UpperHalfPlane.instSMulInvariantMeasureGeneralLinearGroupFinOfNatNatRealVolume`, `imaginaryPart_I_smul`, `Polynomial.natSepDegree_pow`, `Units.nhds`, `ZMod.charpoly_pow_card`, `UpperHalfPlane.deriv_smul`, `PUnit.norm_unit_eq`, `Asymptotics.IsBigOWith.pow`, `Continuous.convolution_integrand_fst`, `Associates.prod_top`, `ContinuousAlternatingMap.vecCons_smul`, `MDifferentiableOn.smul_const_section`, `ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries`, `Module.Ray.neg_units_smul`, `MvPolynomial.leibniz_iff_X`, `WfDvdMonoid.isRelPrime_of_no_irreducible_factors`, `DilationEquiv.smulTorsor_symm_apply`, `ContDiffMapSupportedIn.structureMapCLM_apply`, `iteratedFDerivWithin_succ_eq_comp_right`, `OrthonormalBasis.toBasis_tensorProduct`, `Convex.convex_remove_iff_notMem_convexHull_remove`, `PowerSeries.invOneSubPow_inv_eq_one_sub_pow`, `Representation.freeLift_single_single`, `ConvexOn.lt_left_of_right_lt'`, `HasFPowerSeriesWithinAt.const_smul`, `norm_smul_inv_norm'`, `Polynomial.not_isUnit_of_natDegree_pos`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen`, `FractionalIdeal.fg_unit`, `WeierstrassCurve.ofJNe0Or1728_Δ`, `SchwartzMap.lineDerivOp_fourier_eq`, `AlgebraicGeometry.Proj.pow_apply`, `MvPowerSeries.constantCoeff_subst`, `AddChar.expect_ne_zero_iff_eq_zero`, `LinearMap.BilinForm.congr_apply`, `diam_smul₀`, `Seminorm.uniformContinuous_of_forall`, `geom_sum_alternating_of_le_neg_one`, `IsCusp.smul_of_mem`, `isClosedEmbedding_cfcₙAux`, `Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar`, `TensorAlgebra.toTrivSqZeroExt_ι`, `abs_smul`, `Polynomial.degree_pow_le`, `Polynomial.homogenize_smul`, `AddChar.wInner_cWeight_self`, `LieModule.traceForm_eq_sum_finrank_nsmul'`, `zpow_one_sub_natCast₀`, `HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq`, `IsNilpotent.isUnit_sub_one`, `Module.Flat.localizedModule`, `LinearMap.BilinForm.toMatrix_compRight`, `coe_factor_orderIso_map_eq_one_iff`, `SpecialLinearGroup.coe_zpow`, `NonUnitalAlgHom.range_comp_le_range`, `HasFPowerSeriesWithinOnBall.restrictScalars`, `NormedSpace.isVonNBounded_iff`, `segment_translate_preimage`, `IsCyclic.val_mulAutMulEquiv_apply`, `convexHull_eq_iInter`, `Unitary.coe_zpow`, `Polynomial.IsMonicOfDegree.natDegree_sub_X_pow`, `SeminormFamily.filter_eq_iInf`, `LinearMap.rTensor_smul_action`, `WeierstrassCurve.ψ₂_sq`, `toMul_uzpow`, `aemeasurable_smul_const`, `WeierstrassCurve.Projective.addY_smul`, `SchwartzMap.integral_bilin_fourierInv_eq`, `TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars`, `NNReal.exists_lt_of_strictMono`, `Algebra.lmul_algebraMap`, `HasFTaylorSeriesUpTo.hasFDerivAt`, `TensorProduct.AlgebraTensorModule.rid_tmul`, `ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap`, `EReal.coe_ennreal_pow`, `KaehlerDifferential.tensorKaehlerEquiv_symm_D_tmul`, `CongruenceSubgroup.exists_Gamma_le_conj'`, `SpecialLinearGroup.toLinearEquiv_symm_to_linearMap`, `UpperHalfPlane.tendsto_smul_atImInfty`, `Bornology.IsVonNBounded.of_neg`, `tsum_geometric_encode_lt_top`, `Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv`, `Nat.factors_multiset_prod_of_irreducible`, `Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap`, `PolynomialModule.comp_smul`, `Unitization.splitMul_apply`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst`, `geom₂_sum`, `GaussianFourier.integral_cexp_neg_mul_sq_norm`, `ContMDiffOn.clm_postcomp`, `Polynomial.monic_X_pow_add_C`, `unitsNonZeroDivisorsEquiv_apply`, `spectrum.units_smul_resolvent_self`, `inner_eq_norm_mul_iff`, `AddAut.mulRight_symm_apply`, `TensorAlgebra.ι_comp_lift`, `Seminorm.restrictScalars_closedBall`, `MvPolynomial.eval₂Hom_monomial`, `smulPosMono_iff_smulPosStrictMono`, `iteratedDerivWithin_comp_two`, `Polynomial.derivative_pow_eq_zero`, `tendsto_smul_comp_nat_floor_of_tendsto_mul`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `LinearMap.adjoint_eq_toCLM_adjoint`, `Quaternion.normSq_natCast`, `Asymptotics.IsLittleOTVS.tendsto_div`, `Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor`, `DirectSum.instIsCentralScalar`, `IsCyclotomicExtension.discr_odd_prime`, `Polynomial.toFinsupp_pow`, `WeierstrassCurve.b₈_of_char_two`, `fwdDiff_iter_pow_eq_zero_of_lt`, `LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem`, `Seminorm.bddAbove_range_iff`, `AntivaryOn.sub_smul_sub_nonpos`, `NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm`, `Module.Basis.basis_singleton_iff`, `convex_iff_pairwise_pos`, `NormedSpace.image_isVonNBounded_iff`, `Matrix.trace_units_conj`, `DirichletCharacter.changeLevel_def`, `VectorField.mpullbackWithin_smul`, `ContinuousMap.range_toLp`, `eqOn_dslope_sub_smul`, `Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div`, `IsLocalizedModule.exists_subsingleton_away`, `convex_Iic`, `Associates.finite_factors`, `AddMonoidAlgebra.mapDomainNonUnitalAlgHom_apply`, `Seminorm.closedBall_iSup`, `Differentiable.fun_smul`, `TensorAlgebra.adjoin_range_ι`, `Subbimodule.smul_mem'`, `selfAdjoint.expUnitaryPathToOne_apply`, `TemperedDistribution.fourierMultiplierCLM_smul`, `Ideal.comap_cotangentIdeal`, `NormedRing.inverse_add_norm_diff_nth_order`, `hasDerivAt_bernoulliFun`, `Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single`, `Unitary.continuousOn_argSelfAdjoint`, `LinearMap.det_zero`, `ENNReal.iSup_pow_of_ne_zero`, `hasSum_one_div_nat_pow_mul_fourier`, `NumberField.mixedEmbedding.norm_unit_smul`, `derivWithin_fderivWithin`, `Matrix.toLinearMap₂_toMatrix₂`, `pow_add_pow_le`, `two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even`, `WithLp.isBoundedSMulSeminormedAddCommGroupToProd`, `InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois`, `Submodule.smul_mem_span_smul`, `selfZPow_pow_sub`, `Field.Emb.Cardinal.filtration_succ`, `deriv_fun_pow'`, `Ideal.span_singleton_eq_span_singleton`, `Matrix.isNilpotent_transpose_iff`, `Module.isTorsionBySet_quotient_ideal_smul`, `IsSelfAdjoint.smul_mem_skewAdjoint`, `Set.unit_eq`, `DualNumber.range_lift`, `StarConvex.add_smul_mem`, `Unitization.algHom_ext'_iff`, `QuotSMulTop.equivTensorQuot_naturality`, `ZMod.isCyclic_units_two_mul_iff_of_odd`, `LieAlgebra.IsKilling.rootSystem_coroot_apply`, `StrictConvexOn.neg`, `PowerSeries.eq_divided_by_X_pow_order_Iff_Unit`, `Affine.Simplex.centroid_eq_smul_sum_vsub_vadd`, `geom_sum₂_self`, `GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace`, `X_pow_sub_C_irreducible_iff_of_odd`, `MultilinearMap.mkContinuousMultilinear_apply`, `Polynomial.coeff_one_add_X_pow`, `MvPowerSeries.coeff_X_pow`, `Valuation.mem_ltIdeal_iff`, `MvPowerSeries.X_pow_mul`, `WittVector.RecursionMain.succNthVal_spec'`, `NNReal.sqrt_le_iff_le_sq`, `SlashInvariantForm.quotientFunc_mk`, `PosSMulReflectLE_iff_posSMulReflectLT`, `CliffordAlgebraDualNumber.equiv_symm_eps`, `Monovary.sum_smul_comp_perm_le_sum_smul`, `TensorAlgebra.toDirectSum_tensorPower_tprod`, `WeierstrassCurve.variableChange_a₁`, `emultiplicity_add_eq_min`, `Polynomial.rootMultiplicity_expand_pow`, `StrongDual.norm_extendRCLike_bound`, `TemperedDistribution.lineDerivOp_fourier_eq`, `Module.End.spectrum_intrinsicStar`, `Polynomial.irreducible_of_monic`, `Equiv.mulLeft₀_apply`, `WeakFEPair.symm_Λ₀_eq`, `WeierstrassCurve.Jacobian.addY_neg`, `Module.Flat.ker_lTensor_eq`, `ModularForm.SL_slash`, `Fin.sum_neg_one_pow`, `selfAdjoint.norm_sq_expUnitary_sub_one`, `KaehlerDifferential.cotangentComplexBaseChange_tmul`, `CongruenceSubgroup.conjGL_coe`, `LinearMap.isSelfAdjoint_toContinuousLinearMap_iff`, `WeierstrassCurve.Projective.addY_of_X_eq'`, `SpecialLinearGroup.mem_center_iff_spec`, `sq_lt_sq₀`, `IsPRadical.pow_mem`, `Associates.Prime.le_or_le`, `cross_cross`, `Seminorm.smul_inf`, `DividedPowers.OfInvertibleFactorial.dpow_apply`, `Matrix.separatingRight_toBilin_iff`, `Submodule.Quotient.instIsBoundedSMul`, `Polynomial.derivative_expand`, `associatesEquivOfUniqueUnits_symm_apply`, `Polynomial.degree_pow`, `IsLocalRing.instIsLocalHomRingHomOfNontrivial`, `AddChar.sum_mulShift`, `Matrix.spectrum_toLpLin`, `HasDerivAt.comp_ofReal`, `WithVal.valueGroupOrderIso₀_restrict`, `tangentConeAt_nonempty_of_properSpace`, `GroupWithZero.isConj_iff₀`, `X_pow_sub_C_irreducible_of_odd`, `Polynomial.derivative_pow_succ`, `AdicCompletion.instIsScalarTower_1`, `convexJoin_singleton_left`, `ProbabilityTheory.hasDerivAt_integral_pow_mul_exp`, `ContinuousLinearMap.opNorm_lsmul_apply_le`, `ContDiffMapSupportedIn.fderivLM_eq_of_scalars`, `Polynomial.coeff_pow_eq_ite_of_natDegree_le_of_le`, `AnalyticAt.fun_const_smul`, `Module.Basis.repr_isUnitSMul`, `sum_div_card_sq_le_sum_sq_div_card`, `HurwitzZeta.cosZeta_two_mul_nat`, `Submodule.ideal_span_singleton_smul`, `Continuous.integral_hasStrictDerivAt`, `tsum_choose_mul_geometric_of_norm_lt_one'`, `LinearMap.ofIsCompl_smul`, `OrthonormalBasis.orthogonalProjection_eq_sum_rankOne`, `Cardinal.sum_zero_pow`, `AlgebraicGeometry.Proj.basicOpenIsoAway_hom`, `two_mul_le_add_sq`, `pow_image_of_prime_by_factor_orderIso_dvd`, `NumberField.mixedEmbedding.mem_idealLattice`, `fderiv_clm_comp`, `IsSymmetricAlgebra.equiv_apply`, `sum_smul_minpolyDiv_eq_X_pow`, `cyclotomicCharacter.toZModPow`, `StrictConcaveOn.sub_convexOn`, `Submodule.top_eq_ofList_cons_smul_iff`, `UpperHalfPlane.im_smul_eq_div_normSq`, `ContDiff.pow`, `smulMonoidWithZeroHom_apply`, `SemimoduleCat.MonoidalCategory.rightUnitor_hom_apply`, `Complex.val_UnitI`, `MvPolynomial.totalDegree_X_pow`, `mdifferentiableWithinAt_smul_const_section`, `InnerProductSpace.Core.inner_smul_left`, `SchwartzMap.bilinLeftCLM_apply`, `AlternatingMap.smulRight_apply`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_zero`, `IsConformalMap.is_complex_or_conj_linear`, `Bornology.isVonNBounded_pi_iff`, `fderiv_continuousAlternatingMap_apply_const`, `NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne`, `LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank`, `OreLocalization.universalHom_apply`, `emultiplicity_add_of_gt`, `NumberField.Units.regOfFamily_eq_det`, `ContinuousLinearMap.nhds_zero_eq_of_basis`, `HasGradientAt.hasDerivAt'`, `OreLocalization.nsmul_eq_nsmul`, `Fintype.expect_dite_eq`, `Module.Basis.isScalarTower_of_nonempty`, `LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian`, `Matrix.isHyperbolic_conj_iff`, `DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `LinearMap.toAddMonoidHom_mulLeft`, `PowerSeries.Unit_of_divided_by_X_pow_order_zero`, `LinearMap.BilinForm.toMatrix'_symm`, `iteratedDeriv_pow`, `Matrix.ProjGenLinGroup.mk_scalar`, `Module.End.isFinitelySemisimple_sub_algebraMap_iff`, `hasSum_coe_mul_geometric_of_norm_lt_one'`, `Prod.image_mk_openSegment_left`, `InfiniteGalois.normalAutEquivQuotient_apply`, `IsPurelyInseparable.elemExponent_min`, `Polynomial.natDegree_X_pow_sub_C`, `AffineMap.hasDerivWithinAt`, `IsLocalization.mk'_pow`, `Submodule.starProjection_singleton`, `TrivSqZeroExt.inv_inl`, `HasDerivAt.clm_apply`, `Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_three`, `SemilinearMapClass.toMulActionSemiHomClass`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal`, `NonUnitalAlgHom.coe_lmul_eq_mul`, `MvPowerSeries.commute_X_pow`, `TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_symm_apply_mk_tmul`, `ContDiffMapSupportedIn.seminorm_fderivLM_le`, `WeierstrassCurve.variableChange_Δ'`, `add_pow_prime_pow_eq`, `riemannZeta_two`, `Cardinal.sum_pow_le_max_aleph0`, `LinearMap.tensorEqLocusEquiv_apply`, `toMatrix_distrib_mul_action_toLinearMap`, `IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg`, `PerfectionMap.map_eq_map`, `LinearMap.IsRefl.ker_flip_eq_bot`, `RKHS.coe_smul`, `vadd_right_mem_affineSpan_pair`, `mul_apply_eq_zero`, `Polynomial.isNilpotent_X_mul_iff`, `ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le`, `IsNilpotent.isNilpotent_exp_sub_one`, `ContDiffMapSupportedIn.seminorm_fderivLM_top`, `tsum_coe_mul_geometric_of_norm_lt_one`, `WeierstrassCurve.Projective.dblU_smul`, `Convex.affine_image`, `NormedSpace.toIsBoundedSMul`, `FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax`, `Fintype.mem_span_image_iff_exists_fun`, `MvPowerSeries.X_pow_eq`, `WeierstrassCurve.Jacobian.negAddY_eq`, `Polynomial.irreducible_comp`, `QuasispectrumRestricts.nonUnitalStarAlgHom_id`, `HasFPowerSeriesAt.neg`, `pinGroup.val_inv_toUnits_apply`, `Valuation.IsRankOneDiscrete.generator_mem_valueGroup`, `IsLocalRing.isUnit_or_isUnit_one_sub_self`, `UniqueFactorizationMonoid.exists_prime_factors`, `MonoidWithZeroHom.ValueGroup₀.monoidWithZeroHom_strictMono`, `Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux`, `Seminorm.continuous_of_forall'`, `Complex.hasStrictDerivAt_tan`, `Polynomial.roots_C_mul_X_pow`, `WithVal.valueGroupOrderIso₀_apply`, `tsum_geometric_lt_top`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal`, `QuadraticAlgebra.norm_algebraMap`, `LieIdeal.reflectionPerm_mem_rootSet_iff`, `curveIntegralFun_smul`, `Algebra.TensorProduct.tensorTensorTensorComm_symm`, `addInvariantVectorField_smul`, `Matrix.GeneralLinearGroup.map_inv_mul_map`, `intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivWithinAt`, `IntermediateField.isAlgebraic_tower_bot`, `VertexOperator.of_coeff_apply_coeff`, `Submodule.sup_eq_sup_smul_of_le_smul_of_le_jacobson`, `neg_strictConvexOn_iff`, `Module.Basis.smul_eq_zero`, `smul_lt_smul_of_neg_left`, `Polynomial.IsDistinguishedAt.map_eq_X_pow`, `ENNReal.mulRightOrderIso_symm_apply`, `LieAlgebra.Basis.borelLower_le_biSup`, `egauge_ball_le_of_one_lt_norm`, `Units.symm_mulLeftLinearEquiv`, `fourierIntegral_gaussian_innerProductSpace'`, `Polynomial.dickson_two_zero`, `CategoryTheory.Quotient.Linear.smul_eq`, `isUnit_iff_notMem_of_isAdicComplete_maximal`, `Module.Basis.isUnit_det`, `MvPolynomial.algHom_ext'_iff`, `Module.freeLocus_localization`, `LaurentPolynomial.mk'_one_X`, `Polynomial.natDegree_smul`, `MonovaryOn.sum_smul_comp_perm_le_sum_smul`, `isClosedMap_smul_of_ne_zero`, `hasDerivWithinAt_iff_isLittleO`, `LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex`, `CategoryTheory.Mat.equivalenceSingleObjInverse_obj_obj`, `TensorPower.gMul_eq_coe_linearMap`, `GeneralSchauderBasis.proj_apply`, `hasStrictFDerivAt_iff_isLittleOTVS`, `CStarMatrix.mapₗ_reindexₐ`, `LieSubalgebra.toEnd_eq`, `Matrix.charpoly_units_conj'`, `derivWithin_fun_const_smul_field`, `Polynomial.iterate_derivative_eq_factorial_smul_sum`, `Module.FinitePresentation.exists_notMem_bijective`, `ContinuousLinearEquiv.toCompactConvergenceCLM_apply`, `HahnSeries.ofPowerSeries_X_pow`, `Set.mem_inv_smul_set_iff₀`, `LinearMap.BilinForm.IsRefl.groupSMul`, `LinearMap.BilinForm.toMatrix'_apply`, `Submodule.mem_smul_span_singleton`, `RingPreordering.pow_two_mem`, `AlgHom.IsArithFrobAt.mk_apply`, `WittVector.factorPowSucc_comp_fontaineThetaModPPow`, `Set.unitEquivUnitsInteger_symm_apply_coe`, `Polynomial.iterate_derivative_X_add_pow`, `Finsupp.sum_smul_index_linearMap'`, `MeasureTheory.IntegrableOn.smul_continuousOn`, `PadicInt.norm_p_pow`, `fourier_gaussian_pi'`, `Finset.emultiplicity_prod`, `ContinuousAlternatingMap.piLIE_apply_apply`, `Set.preimage_smul_inv₀`, `Cardinal.mk_vector`, `AffineSubspace.wOppSide_smul_vsub_vadd_left`, `ContinuousLinearMap.applySMulCommClass'`, `PreInnerProductSpace.Core.smul_left`, `inv_intCast_smul_eq`, `extremePoints_prod`, `WeierstrassCurve.ΨSq_odd`, `IsPurelyInseparable.elemExponent_def'`, `lintegral_fderiv_lineMap_eq_edist`, `NormedSpace.isUnit_exp_of_mem_ball`, `TemperedDistribution.smulLeftCLM_compL_smulLeftCLM`, `LinearMap.BilinForm.SeparatingRight.toMatrix`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_left`, `AdicCompletion.incl_apply`, `IntermediateField.algHomEquivAlgHomOfSplits_apply`, `balancedCoreAux_maximal`, `hasDerivWithinAt_zero`, `AdicCompletion.map_ext'_iff`, `HahnSeries.single_pow`, `HasStrictDerivAt.pow'`, `TestFunction.monoCLM_eq_zero`, `UniqueFactorizationMonoid.induction_on_prime_power`, `CategoryTheory.Abelian.Ext.smul_hom`, `IntermediateField.botEquiv_symm`, `AlgCat.hom_inv_rightUnitor`, `coe_convexAddSubmonoid`, `TopologicalGroup.IsSES.integral_inducedMeasure`, `Unitization.starAlgHom_ext_iff`, `Cubic.disc_eq_prod_three_roots`, `iteratedDerivWithin_tsum_cexp_eq`, `LinearMap.nondegenerate_toLinearMap₂'_of_det_ne_zero'`, `hasDerivAt_star_conj_iff`, `AbsolutelyContinuousOnInterval.const_smul`, `ContDiffAt.hasStrictDerivAt`, `ENNReal.smul_def`, `Polynomial.eval₂_X_pow`, `Seminorm.neg_ball`, `RatFunc.irreducible_min_polynomial_valuation_lt_one_and_ne_zero`, `TrivSqZeroExt.inv_one`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective`, `jacobiTheta₂_functional_equation`, `MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent`, `LinearEquiv.congrRight₂_apply`, `Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero'`, `Associated.of_pow_associated_of_prime`, `FormalMultilinearSeries.hasSum_of_finite`, `cross_self`, `PreTilt.coeff_pow_p`, `LieAlgebra.of_smul`, `Rep.to_Module_monoidAlgebra_map_aux`, `adjoinRootXPowSubCEquiv_symm_eq_root`, `SpecialLinearGroup.mem_center_iff`, `Ideal.iInf_pow_smul_eq_bot_of_le_jacobson`, `StrictConcaveOn.translate_right`, `hasDerivAtFilter_ofNat`, `Asymptotics.IsBigO.smul`, `ZMod.unitsMap_self`, `exists_associated_pow_of_associated_pow_mul`, `CategoryTheory.Mat.instFaithfulMat_SingleObjMulOppositeEquivalenceSingleObjInverse`, `WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF`, `AdicCompletion.val_smul_eq_evalₐ_smul`, `iteratedDeriv_comp_const_mul`, `instStarModuleNNRealOfReal`, `VectorField.mlieBracket_smul_left`, `Matrix.Nondegenerate.toLinearMap₂`, `ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one`, `Ideal.pow_eq_zero_of_mem`, `FractionalIdeal.count_well_defined`, `Seminorm.continuous'`, `TensorProduct.gradedMul_assoc`, `MvPolynomial.eval₂_pow`, `Set.smul_set_inter₀`, `Valued.toUniformSpace_eq`, `PerfectClosure.frobenius_mk`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₃`, `curveIntegrable_smul_iff`, `Complex.hasSum_taylorSeries_on_ball`, `Submodule.mem_span_image_iff_exists_fun`, `Subalgebra.centralizer_coe_map_includeLeft_eq_center_tensorProduct`, `WeierstrassCurve.Jacobian.addZ_smul`, `Valuation.instNontrivialSubtypeUnitsMemSubmonoidValueMonoidOfIsNontrivial`, `QuadraticMap.map_smul_of_tower`, `Asymptotics.IsBigOTVS.add`, `NormedSpace.exp_series_hasSum_exp'`, `Complex.cosh_three_mul`, `MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff`, `MvPolynomial.irreducible_mul_X_add`, `HasFPowerSeriesOnBall.restrictScalars`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply`, `smul_nonneg_iff_neg_imp_nonpos`, `GaussianFourier.integral_cexp_neg_mul_sq_norm_add`, `IsPurelyInseparable.hasExponent_iff`, `StrictConcaveOn.inf`, `Perfection.coeff_iterate_symm_frobeniusEquiv`, `norm_cexp_neg_mul_sq`, `integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1`, `ContinuousLinearMap.isometry_mul_flip`, `Cardinal.mk_list_eq_sum_pow`, `UpperHalfPlane.num_neg`, `ExpChar.pow_prime_pow_mul_eq_one_iff`, `Quaternion.snd_re_dualNumberEquiv_symm`, `Ideal.torsionMapQuot_apply`, `LinearMap.injective_compr₂_of_injective`, `ZSpan.smul`, `Set.smul_set_subset_smul_set_iff₀`, `ContinuousMultilinearMap.piLinearEquiv_symm_apply`, `HasStrictFDerivAt.mul'`, `Module.AEval.of_symm_smul`, `isPowMul_spectralNorm_of_finiteDimensional_normal`, `Mathlib.Tactic.Module.NF.eval_neg`, `Module.Ray.units_smul_of_neg`, `Matrix.intrinsicStar_toLin'`, `fderiv_fun_pow`, `LieModule.isNilpotent_toEnd_genWeightSpace_zero`, `HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt`, `ValuationSubring.valuation_unit`, `AlgebraicGeometry.StructureSheaf.const_add`, `NumberField.HeightOneSpectrum.rankOne_hom'_def`, `LocalizedModule.mk_add_mk`, `Polynomial.dvd_iterate_derivative_pow`, `IsLocalization.Away.sec_spec`, `Associates.irreducible_mk`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective`, `HasStrictFDerivAt.comp_hasStrictDerivAt`, `Ideal.range_cotangentToQuotientSquare`, `ContinuousLinearMap.adjoint_id`, `Ideal.Filtration.smul_le`, `InnerProductSpace.smul_left`, `ClosedSubmodule.inf_orthogonal`, `LinearMap.coe_toContinuousLinearMap'`, `ContDiffWithinAt.fun_smul`, `balanced_ball_zero`, `HasFDerivWithinAt.linear_multilinear_comp`, `Associates.eq_pow_count_factors_of_dvd_pow`, `AdicCompletion.exists_smodEq_pow_smul_top_and_smodEq_pow_add_one_smul_top`, `emultiplicity_zero_eq_zero_of_ne_zero`, `iteratedFDerivWithin_succ_eq_comp_left`, `UpperHalfPlane.moebius_im`, `summable_norm_mul_geometric_of_norm_lt_one`, `Module.supportDim_add_length_eq_supportDim_of_isRegular`, `isGalois_iff_isGalois_top`, `minpoly_algHom_toLinearMap`, `ModularForm.prod_slash`, `NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe`, `Commute.isNilpotent_mul_left`, `ConvexCone.coe_zero`, `CharacterModule.smul_apply`, `MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart`, `Module.Free.instFaithfulSMulOfNontrivial`, `contDiffOn_iff_continuousOn_differentiableOn`, `CommRing.Pic.mul_eq_tensor`, `Complex.isQuotientCoveringMap_npow`, `IsNilpotent.neg`, `hasFDerivWithinAt_comp_smul_iff_smul`, `ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint`, `convexJoin_segments`, `ClosedSubmodule.instSMulMemClass`, `Submodule.comap_le_comap_smul`, `sub_sq`, `sum_cauchyPowerSeries_eq_integral`, `SchwartzMap.laplacianCLM_eq`, `fderiv_fun_smul`, `CStarModule.innerSL_apply`, `NNReal.pow_rpow_inv_natCast`, `IsLocalizedModule.iso_symm_apply`, `intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDerivAt`, `QuadraticMap.toBilinHom_apply`, `MeromorphicOn.fun_smul`, `monomial_has_deriv_aux`, `ContinuousLinearMap.hasDerivWithinAt_of_bilinear`, `Matrix.det_succ_row`, `LieRinehartAlgebra.LieRinehartRing.leibniz_smul_right`, `TensorProduct.AlgebraTensorModule.rightComm_symm_tmul`, `exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional`, `LinearMap.tensorKer_coe`, `LinearIsometryEquiv.conjStarAlgEquiv_apply`, `MeasureTheory.smul_convolution`, `Bundle.ContinuousLinearMap.vectorBundle`, `Real.vector_fourierIntegral_eq_integral_exp_smul`, `FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1`, `WittVector.mul_polyOfInterest_aux2`, `VectorField.mlieBracketWithin_const_smul_right`, `HasDerivWithinAt.sub`, `PadicInt.mahlerTerm_apply`, `IsLocalization.isUnit_comp`, `Algebra.Extension.CotangentSpace.map_id`, `Ideal.span_pow_eq_top`, `HomogeneousLocalization.range_awayMapAux_subset`, `mem_principal_ideals_iff`, `LinearMap.toMatrixOrthonormal_reindex`, `Polynomial.pow_comp`, `AlternatingMap.map_update_smul`, `LinearMap.toMatrixAlgEquiv_toLinAlgEquiv`, `autEquivZmod_symm_apply_natCast`, `WithLp.smul_snd`, `MeasureTheory.ConvolutionExistsAt.integrable`, `Fintype.linearIndependent_iff'`, `Complex.taylorSeries_eq_of_entire`, `HurwitzZeta.evenKernel_def`, `HasStrictFDerivAt.pow`, `egauge_add_add_le`, `HVertexOperator.coeff_isPWOsupport`, `WeierstrassCurve.Jacobian.eval_polynomialY`, `LinearMap.charpoly_nilpotent_tfae`, `exists_pos_right_iff_sameRay`, `WithVal.valueGroupEquiv_symm_apply`, `QuadraticMap.associated_eq_self_apply`, `pow_mul_eq_zero_of_le`, `DirectLimit.Module.lift_of`, `subgroup_units_cyclic`, `Bound.le_self_pow_of_pos`, `QuadraticMap.toMatrix'_comp`, `SemilinearMapClass.distribMulActionSemiHomClass`, `Real.fourier_real_eq_integral_exp_smul`, `Units.inv_eq_self_iff`, `HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap`, `FiniteGaloisIntermediateField.mem_fixingSubgroup_iff`, `Monotone.quasilinearOn`, `euler_four_squares`, `pow_nonneg`, `CStarAlgebra.pow_nonneg`, `Polynomial.map_sub_roots_sprod_eq_prod_map_eval`, `Asymptotics.IsBigOWith.const_smul_self`, `Polynomial.natSepDegree_X_sub_C_pow`, `PMF.binomial_apply_zero`, `Asymptotics.isLittleOTVS_prodMk_left`, `ExteriorAlgebra.toTrivSqZeroExt_comp_map`, `AntivaryOn.sum_comp_perm_smul_eq_sum_smul_iff`, `inner_smul_left_eq_star_smul`, `BoundedContinuousFunction.toContinuousMapLinearMap_apply`, `nndist_smul₀`, `Polynomial.resultant_zero_right`, `IsAdicComplete.mkQ_comp_lift`, `RCLike.mul_conj`, `Polynomial.isMonicOfDegree_two_iff'`, `Module.exists_smul_eq_zero_and_mk_eq`, `IsRadical.of_dvd`, `Module.basicOpen_subset_freeLocus_iff`, `Asymptotics.IsBigOTVS.comp_tendsto`, `ValueDistribution.logCounting_pow_top`, `AlgebraicGeometry.exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isCompact`, `OnePoint.smul_infty_eq_self_iff`, `TensorProduct.quotTensorEquivQuotSMul_comp_mkQ_rTensor`, `Matrix.GeneralLinearGroup.coe_toLin`, `NonUnitalSubalgebra.inclusion_mk`, `Submodule.span_smul_eq_of_isUnit`, `exists_pow_btwn_of_lt_mul`, `WithSeminorms.continuousSMul`, `Matrix.adjugate_fin_succ_eq_det_submatrix`, `PreTilt.instPerfectRing`, `IsSl2Triple.lie_lie_smul_f`, `LinearMap.ortho_smul_left`, `hasLineDerivAt_iff_isLittleO_nhds_zero`, `SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix`, `prime_mul_iff`, `deriv.scomp_of_eq`, `ContinuousMultilinearMap.mkPiRing_apply`, `LinearEquiv.conjAlgEquiv_ext_iff'`, `hasDerivAt_of_hasDerivAt_of_ne`, `LinearMap.lTensor_smul`, `smul_unitClosedBall`, `im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four`, `AddMonoidHom.coe_smul'`, `Finset.subConst_le_addConst_sq`, `TestFunction.continuous_iff_continuous_comp`, `CongruenceSubgroup.strictPeriods_Gamma0`, `Valuation.restrict_eq_one_iff`, `Ideal.IsPrime.pow_mem_iff_mem`, `HasFiniteFPowerSeriesOnBall.sum`, `Quaternion.coe_pow`, `Ring.map_multichoose`, `MeasureTheory.L1.integral_smul`, `Distribution.IsVanishingOn.smulLeftCLM`, `Matrix.exists_right_inverse_iff_isUnit`, `ContinuousLinearMap.smulRight_one_pow`, `Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one`, `Polynomial.IsUnitTrinomial.irreducible_of_coprime`, `ContinuousLinearMap.opNorm_mul_flip_apply`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars`, `inv_natCast_smul_eq`, `DifferentiableOn.smul_const`, `IsLocalizedModule.iso_apply_mk`, `NonUnitalSubalgebra.topologicalClosure_map_le`, `Polynomial.eraseLead_add_C_mul_X_pow`, `instIsLocalHomOfMonoidWithZeroHomClassOfNontrivial`, `IntermediateField.exists_algHom_of_adjoin_splits`, `GCDMonoid.gcd_mul_lcm`, `Quaternion.imJ_fst_dualNumberEquiv`, `Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzCone`, `ENNReal.tendsto_pow_atTop_nhds_zero_iff`, `InnerProductSpace.inner_left_rankOne_apply`, `Commute.add_pow_add_eq_zero_of_pow_eq_zero`, `cfcₙHom_nnreal_eq_restrict`, `star_dotProduct_toMatrix₂_mulVec`, `TestFunction.toBoundedContinuousFunctionCLM_apply`, `minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C`, `MeasureTheory.Lp.instFourierInvSMul`, `AlgebraicGeometry.ValuativeCriterion.Existence.instIsLocalHomCarrierRingHomHomHomCommRingCat`, `SpecialLinearGroup.coe_one`, `CochainComplex.HomComplex.Cocycle.coe_units_smul`, `normUnit_mul_normUnit`, `TensorProduct.AlgebraTensorModule.lTensor_comp_cancelBaseChange`, `ModularForm.discriminant_bounded_factor`, `NNReal.rpow_natCast`, `summable_norm_mul_geometric_of_norm_lt_one'`, `Bornology.isVonNBounded_neg`, `PadicInt.norm_units`, `SchwartzMap.fderivCLM_apply`, `Polynomial.degreeLT.basis_val`, `hasStrictDerivAt_abs_pos`, `WithTop.pow_right_strictMono`, `IntermediateField.normal_iff_forall_map_eq`, `ContinuousLinearMap.smul_compLp`, `Associates.instNontrivial`, `Matrix.det_le`, `difference_quotients_converge_uniformly`, `PowerSeries.derivative_inv'`, `hasDerivWithinAt_abs_pos`, `WeierstrassCurve.Jacobian.negY_eq`, `HasDerivWithinAt.sub_const`, `LocalizedModule.divBy_apply`, `ContinuousLinearMap.norm_extendTo𝕜`, `TensorProduct.AlgebraTensorModule.lTensor_id`, `WeierstrassCurve.ofJNe0Or1728_c₄`, `LocalizedModule.lift'_smul`, `ModularForm.norm_eq_zero_iff`, `HasSum.hasSum_at_zero`, `Valuation.IsRankOneDiscrete.generator'_lt_one`, `UniqueFactorizationMonoid.isRadical_radical`, `cfcₙHom_mem_elemental`, `Seminorm.continuousAt_zero_of_forall'`, `HasFPowerSeriesAt.add`, `WeierstrassCurve.Jacobian.negY_of_Z_ne_zero`, `OreLocalization.nontrivial`, `DivisibleHull.mk_add_mk_left`, `lineDifferentiableAt_smul_iff`, `skewAdjointLieSubalgebraEquiv_symm_apply`, `Algebra.zariskisMainProperty_iff`, `TrivSqZeroExt.fstHom_comp_map`, `ContinuousAlternatingMap.curryLeft_smul`, `derivWithin.scomp_of_eq`, `fderiv_const_smul_field`, `absorbent_univ`, `pow_eq_zero_iff`, `ArchimedeanClass.mk_pow`, `WeierstrassCurve.b_relation_of_char_two`, `Matrix.conjTranspose_natCast_smul`, `LinearMap.sum_repr_mul_repr_mulₛₗ`, `cfcₙ_map_pi`, `ContinuousLinearMap.hasBasis_nhds_zero`, `ZMod.val_unit'`, `Complex.norm_pow`, `Ideal.mul_sup_eq_of_coprime_right`, `Bornology.IsVonNBounded.of_add_right`, `Polynomial.reverse_mul_X_pow`, `tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support`, `Matrix.diagonal_pow`, `HasFDerivAtFilter.isBigOTVS_sub`, `Ideal.mem_toCotangent_ker`, `TensorProduct.AlgebraTensorModule.rTensor_one`, `antideriv_bernoulliFun`, `CochainComplex.HomComplex.Cochain.units_smul_comp`, `hasFDerivWithinAt_inv`, `WeierstrassCurve.Projective.addX_smul`, `hasSum_nat_jacobiTheta`, `WithZeroTopology.nhds_zero_of_units`, `Matrix.Represents.smul`, `Seminorm.ball_mem_nhds`, `eventually_nhds_norm_smul_sub_lt`, `MonoidWithZeroHom.coe_one`, `geom_sum_two`, `CentroidHom.smul_def`, `NumberField.Units.pos_at_place`, `DoubleCentralizer.pow_snd`, `TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM`, `Units.divp_add`, `Module.IsTorsionFree.isSMulRegular`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn`, `ContMDiffAt.clm_postcomp`, `TensorProduct.zero_smul`, `Algebra.lmul_injective`, `norm_pow`, `QuadraticMap.associated_rightInverse`, `IsMulTorsionFree.pow_right_inj₀`, `Module.associatedPrimes.mem_associatePrimes_localizedModule_atPrime_of_mem_associated_primes`, `scalarSMulCLE_symm_apply`, `Real.fourier_deriv`, `RightPreLieAlgebra.toIsScalarTower`, `ContMDiffWithinAt.clm_postcomp`, `iteratedDeriv_scomp_three`, `Real.toNNReal_pow`, `fderiv_fun_pow'`, `hasDerivWithinAt_pi`, `Matrix.toBilin_symm`, `Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp`, `LinearMap.spectrum_toMatrix'`, `autAdjoinRootXPowSubCEquiv_symm_smul`, `pow_injective_of_not_isUnit`, `Polynomial.Monic.natDegree_pow`, `LieModule.trace_toEnd_genWeightSpace`, `Real.integrable_prod_sub`, `NormedSpace.isVonNBounded_ball`, `locallyConvexSpace_iff`, `MDifferentiable.smul`, `NumberField.Embeddings.pow_eq_one_of_norm_le_one`, `Real.smul_map_diagonal_volume_pi`, `strictConvex_Icc`, `DirichletCharacter.norm_LSeries_product_ge_one`, `antivary_iff_smul_rearrangement`, `iterateFrobeniusEquiv_def`, `Ring.choose_eq_smul`, `norm_smul_inv_norm`, `LinearMap.smulRight_id`, `ContinuousLinearMap.eq_adjoint_iff`, `PairReduction.card_pairSetSeq_le_logSizeRadius_mul`, `PeriodPair.hasSum_derivWeierstrassPExcept`, `ConcaveOn.smul_convexOn'`, `IsLocalizedModule.mk'_eq_zero'`, `IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable`, `NonUnitalSubalgebra.inclusion_right`, `WeierstrassCurve.Jacobian.negAddY_of_Z_eq_zero_right`, `toMatrix_rotation`, `tangentConeAt_univ`, `UniqueFactorizationMonoid.associated_finprod_pow_count`, `PiTensorProduct.toDualContinuousMultilinearMap_apply_apply`, `NNReal.sqrt_sq`, `SubMulAction.neg_mem`, `IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic`, `Nat.Partition.tendsto_order_genFun_term_atTop_nhds_top`, `Submonoid.pointwise_smul_le_pointwise_smul_iff₀`, `prime_factors_irreducible`, `ContinuousLinearMap.toSpanSingleton_apply`, `ConcaveOn.add_const`, `Polynomial.resultant_comm`, `FreeNonUnitalNonAssocAlgebra.of_comp_lift`, `smul_vsub_rev_vadd_mem_affineSpan_pair`, `KaehlerDifferential.isScalarTower'`, `IsArtinianRing.isUnit_of_nonZeroDivisor_of_isIntegral'`, `ZMod.stdAddChar_coe`, `Submodule.mem_torsion_iff`, `Matrix.GeneralLinearGroup.isParabolic_conj_iff`, `derivWithin.scomp`, `ZMod.trace_pow_card`, `AlgHom.mulLeftRightMatrix.inv_comp`, `gal_X_pow_isSolvable`, `Subfield.splits_bot`, `DifferentiableOn.circleIntegral_sub_inv_smul`, `Derivation.linearEquiv_coe_to_linearMap_comp`, `Submodule.sum_smul_mem`, `ValueDistribution.proximity_pow_zero`, `Prod.segment_subset`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le`, `smul_nonpos_iff`, `NonUnitalStarAlgHom.map_cfcₙ`, `Polynomial.monic_X_pow_add`, `HasFPowerSeriesAt.comp`, `le_comap_range_lTensor`, `HasFDerivAt.continuousMultilinear_apply_const`, `EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection`, `HasFDerivWithinAt.continuousAlternatingMap_apply`, `ContinuousLinearMap.IsPositive.smul_of_nonneg`, `PadicInt.irreducible_p`, `ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀`, `InnerProductSpace.rankOne_apply`, `Convex.combo_eq_smul_sub_add`, `EuclideanSpace.nndist_eq`, `ConcaveOn.smul_convexOn`, `Module.End.HasUnifEigenvalue.isNilpotent_of_isNilpotent`, `LieModule.shiftedGenWeightSpace.toEnd_eq`, `Unitary.coe_linearIsometryEquiv_apply`, `FormalMultilinearSeries.sum_of_finite`, `MeromorphicOn.divisor_pow`, `RingTheory.Sequence.isRegular_cons_iff`, `ModularForm.prod_slash_sum_weights`, `WeierstrassCurve.Projective.add_of_Z_eq_zero`, `Ideal.finsuppTotal_apply_eq_of_fintype`, `ConcaveOn.comp_linearMap`, `MeasureTheory.convolution_tendsto_right`, `IsPrimitiveRoot.prod_one_sub_pow_eq_order`, `ContinuousLinearEquiv.map_smul`, `extremePoints_pi`, `IntermediateField.restrictScalars_normal`, `WittVector.factorPowSucc_fontaineThetaModPPow_eq`, `Submodule.reflection_singleton_apply`, `IntermediateField.isScalarTower`, `HasFTaylorSeriesUpToOn.zero_eq'`, `Ring.add_choose_eq`, `inv_pow_le_inv_pow_of_le`, `KaehlerDifferential.quotKerTotalEquiv_symm_comp_D`, `pow_eq_zero_of_le`, `Asymptotics.IsLittleOTVS.trans_isThetaTVS`, `Fintype.expect_ite_eq`, `MultilinearMap.map_insertNth_smul`, `IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply`, `LieAlgebra.ad_isSemisimple_of_isSemisimple`, `NNReal.summable_geometric`, `QuotSMulTop.equivTensorQuot_naturality_mk`, `Commute.pow_add_mul_le_add_pow_of_sq_nonneg`, `FiniteMultiplicity.multiplicity_pow`, `SchwartzMap.compCLMOfContinuousLinearEquiv_apply`, `ENNReal.pow_lt_top_iff`, `inv_pow_anti`, `Complex.instPathConnectedSpaceUnits`, `IsLocalRing.map_mkQ_eq`, `FormalMultilinearSeries.ofScalars_apply_eq`, `dot_cross_self`, `MvPolynomial.schwartz_zippel_totalDegree`, `Matrix.IsSymm.pow`, `Polynomial.leadingCoeff_X_pow_add_C`, `Polynomial.exists_monic_irreducible_factor`, `WeierstrassCurve.Jacobian.negAddY_of_X_eq`, `NonUnitalSubalgebra.topologicalClosure_map`, `smulMemClass`, `HasStrictDerivAt.clm_comp`, `IsPrimitiveRoot.pow_sub_one_eq_geom_sum_mul_geom_sum_inv_mul_pow_sub_one`, `WeierstrassCurve.Projective.dblXYZ_smul`, `LieModule.Cohomology.twoCochain_alt`, `PiLp.isBoundedSMulSeminormedAddCommGroupToPi`, `Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence`, `WeierstrassCurve.Projective.Point.zero_point`, `Module.endTensorEndAlgHom_apply`, `inv_intCast_smul_comm`, `Polynomial.smeval_X_pow`, `Matrix.toLpLin_mul_same`, `PowerSeries.isUnit_exp`, `ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator`, `ProbabilityTheory.HasSubgaussianMGF.const_mul`, `sum_eight_sq_mul_sum_eight_sq`, `NumberField.mixedEmbedding.convexBodyLT_volume`, `Matrix.isHyperbolic_conj'_iff`, `deriv_fun_inv''`, `ModularGroup.coe_apply_complex`, `Algebra.FormallySmooth.adjoin_of_algebraicIndependent`, `MeasureTheory.convolution_integrand_bound_right_of_le_of_subset`, `ContinuousMap.toLp_norm_le`, `Ideal.bot_pow`, `contMDiffOn_localFrame_coeff`, `ContDiffMapSupportedIn.monoLM_apply`, `GroupWithZero.mul_inv_cancel`, `HasDerivWithinAt.Iic_of_Iio`, `ContinuousMultilinearMap.norm_smulRightL_le`, `HasSummableGeomSeries.summable_geometric_of_norm_lt_one`, `TensorProduct.coe_directSumRight'`, `tsum_geometric_of_norm_lt_one`, `Algebra.TensorProduct.comm_comp_map_apply`, `Multiset.sum_smul_sum`, `balancedCore_nonempty_iff`, `StrictConvex.affine_image`, `WeakFEPair.h_feq`, `derivWithin_clm_comp`, `Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective`, `Function.support_pow`, `LinearMap.ker_restrictScalars`, `Antitone.convex_le`, `ContinuousLinearMap.precompL_apply`, `Seminorm.closedBall_smul_ball`, `egauge_univ`, `NNReal.le_sqrt_iff_sq_le`, `PowerSeries.aeval_eq_sum`, `Algebra.normalizedTrace_algebraMap`, `Subalgebra.coe_pointwise_smul`, `IsSelfAdjoint.adjoint_eq`, `LaurentPolynomial.T_pow`, `Antitone.quasiconvexOn`, `Submodule.smul_mem'`, `HahnSeries.SummableFamily.binomialFamily_apply_of_orderTop_nonpos`, `isPurelyInseparable_iff_fd_isPurelyInseparable`, `Submodule.mem_ideal_smul_span_iff_exists_sum'`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc`, `inv_pow_strictAnti`, `Matrix.charpoly_natCast`, `pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum`, `Asymptotics.IsLittleOTVS.prodMk`, `TrivSqZeroExt.fst_exp`, `Ideal.FG.pow`, `DirectSum.mk_smul`, `Perfection.coeff_toMonoidHom`, `HasDerivWithinAt.clm_apply`, `SchwartzMap.integral_fourierInv_smul_eq`, `DifferentiableAt.hasDerivAt`, `IntermediateField.LinearDisjoint.of_isField'`, `Submodule.ker_unitsToPic`, `MonovaryOn.sum_comp_perm_smul_le_sum_smul`, `Set.Ioc.coe_pow`, `SlashInvariantForm.quotientFunc_smul`, `OrderDual.instIsStrictOrderedModule`, `RootPairing.coroot_eq_smul_coroot_iff`, `Representation.asAlgebraHom_def`, `Finpartition.IsEquipartition.card_biUnion_offDiag_le`, `Mathlib.Tactic.Ring.mul_pf_left`, `dvd_geom_sum₂_iff_of_dvd_sub`, `coeff_minpolyDiv_sub_pow_mem_span`, `instIsReducedZModOfFactSquarefreeNat`, `RKHS.kernel_apply`, `HasDerivAt.finCons`, `Seminorm.bound_of_continuous_normedSpace`, `unitary.spectrum.unitary_conjugate'`, `Complex.volume_sum_rpow_le`, `Perfection.coe_pthRoot_eq_symm_frobeniusEquiv`, `Commute.geom_sum₂_mul`, `add_pow_expChar_pow`, `Associates.out_one`, `spectrum.pow_mem_pow`, `HasDerivAtFilter.add`, `IsDedekindDomain.HeightOneSpectrum.intValuationDef_if_neg`, `UniqueFactorizationMonoid.factors_eq_singleton_of_irreducible`, `exists_nonneg_left_iff_sameRay`, `Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub`, `Polynomial.eval_divByMonic_eq_trailingCoeff_comp`, `LinearMap.BilinForm.isOrtho_smul_left`, `FormalMultilinearSeries.radius_le_smul`, `PowerBasis.equivAdjoinSimple_symm_aeval`, `edist_le_of_edist_le_geometric_of_tendsto`, `MDifferentiable.clm_postcomp`, `ModularForm.levelOne_neg_weight_rank_zero`, `Ideal.pow_sup_eq_top`, `IsRelPrime.neg_left`, `Ring.jacobson_smul_top_le`, `IsArtinian.exists_pow_succ_smul_dvd`, `TrivSqZeroExt.map_inr`, `Unitization.starLift_symm_apply_apply`, `WeierstrassCurve.Jacobian.Y_eq_of_equiv`, `PiLp.nnnorm_eq_of_L2`, `AntivaryOn.smul_add_smul_le_smul_add_smul`, `WeierstrassCurve.j_of_char_three`, `CharTwo.multiset_sum_sq`, `NonUnitalSubalgebra.prod_inf_prod`, `intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right`, `MeasureTheory.VectorMeasure.smul_apply`, `Subgroup.IsArithmetic.is_commensurable`, `Subgroup.IsArithmetic.inter`, `Matrix.isElliptic_conj'_iff`, `InfiniteGalois.toAlgEquivAux_eq_proj_of_mem`, `Module.End.instLieModule`, `CStarMatrix.toCLM_injective`, `biUnion_associatedPrimes_eq_compl_regular`, `WithZero.coe_expEquiv_apply`, `Asymptotics.IsLittleOTVS.insert`, `Algebra.Extension.lTensor_cotangentComplex_eq_cotangentComplexBaseChange`, `MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right`, `Complex.integral_circleTransform`, `ContinuousLinearMap.isPositive_self_comp_adjoint`, `iteratedDeriv_scomp_eq_sum_orderedFinpartition`, `Polynomial.Monic.geom_sum'`, `Unitization.starLift_apply_apply`, `HasFPowerSeriesOnBall.hasSum_iteratedFDeriv`, `unitary.coe_div`, `Polynomial.IsPrimitive.isUnit_iff_isUnit_map_of_injective`, `ModularGroup.sl_moeb`, `LinearMap.adjoint_toContinuousLinearMap`, `Polynomial.X_pow_eq_monomial`, `Matrix.SeparatingLeft.toLinearMap₂'`, `Matrix.GeneralLinearGroup.center_eq_range_scalar`, `X_pow_sub_C_irreducible_iff_forall_prime_of_odd`, `irreducible_pow_sup_of_ge`, `hasDerivAt_iff_isLittleO`, `IntermediateField.lift_adjoin_simple`, `LinearMap.rTensor_comp_flip_mk`, `Polynomial.not_isUnit_of_degree_pos_of_isReduced`, `Absorbs.eventually_nhdsNE_zero`, `Polynomial.toAddCircle_X_pow_eq_fourier`, `Unitization.sqrt_inr`, `UniqueDiffWithinAt.smul`, `TopModuleCat.continuousSMul`, `OreLocalization.nonempty_oreSet_iff_of_noZeroDivisors`, `Unitary.linearIsometryEquiv_coe_apply`, `LocallyConvexSpace.convex_basis_zero`, `algebraicClosure.normalClosure_eq_self`, `NormedSpace.isBounded_iff_subset_smul_closedBall`, `contMDiffOn_baseSet_iff_localFrame_coeff`, `Metric.PiNatEmbed.edist_def`, `AddChar.sum_eq_ite`, `KaehlerDifferential.isLocalizedModule_of_isLocalizedModule`, `MonoidWithZeroHom.valueGroup.mk_mul`, `hasFPowerSeriesAt_const`, `IntermediateField.AdjoinDouble.normal_algebraicClosure`, `Polynomial.scaleRoots_eval₂_mul`, `HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap`, `ZMod.isCyclic_units_one`, `UniformOnFun.continuousSMul_induced_of_image_bounded`, `Subalgebra.inclusion.isScalarTower_left`, `Polynomial.as_sum_range_C_mul_X_pow'`, `HasFPowerSeriesOnBall.const_smul`, `ContinuousLinearMap.toSesqForm_apply_coe`, `IsPurelyInseparable.exists_pow_mem_range_tensorProduct`, `Finsupp.linearCombination_smul`, `Submodule.comap_smul_top_of_surjective`, `ConcaveOn.smul''`, `Algebra.TensorProduct.assoc_tmul`, `FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius`, `HurwitzZeta.oddKernel_def'`, `SpecialLinearGroup.mem_range_toGeneralLinearGroup_iff`, `CFC.abs_coe_unitary`, `neg_one_smul`, `absorbs_inter`, `Fintype.bilinearCombination_apply_single`, `MonoidWithZeroHom.fst_mono`, `Submodule.pow_smul_top_le`, `Complex.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq`, `ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear`, `LinearMap.BilinForm.nondegenerate_toMatrix_iff`, `Subring.mem_pointwise_smul_iff_inv_smul_mem₀`, `Associates.mk_dvdNotUnit_mk_iff`, `FormalMultilinearSeries.radius_compNeg`, `spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div`, `Fintype.expect_ite_zero`, `LinearMap.toMatrixₛₗ₂'_symm`, `NormedAddGroupHom.smul_apply`, `Odd.pow_nonneg_iff`, `Polynomial.rootMultiplicity_X_sub_C_pow`, `IsBoundedBilinearMap.smul_left`, `Polynomial.resultant_X_sub_C_right`, `Matrix.kroneckerTMul_mem_unitary`, `quasispectrum.mem_iff_of_isUnit`, `MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zero`, `NormedSpace.expSeries_apply_eq_div'`, `SchwartzMap.integral_bilin_fourierIntegral_eq`, `Module.equiv_directSum_of_isTorsion`, `PowerSeries.binomialSeries_coeff`, `TopologicalGroup.IsSES.pushforward_def`, `fourier_gaussian_innerProductSpace`, `SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM`, `QuadraticMap.discr_smul`, `Real.fourierIntegral_continuousMultilinearMap_apply`, `MvPowerSeries.isUnit_iff_constantCoeff`, `LinearMap.rank_diagonal`, `StrictConcaveOn.lt_map_sum`, `MonotoneOn.convex_ge`, `HomogeneousLocalization.Away.adjoin_mk_prod_pow_eq_top`, `IsRelPrime.add_mul_left_right`, `QuotSMulTop.map_comp_mkQ`, `NormedRing.inverse_one_sub_nth_order`, `Polynomial.aeval_pow_two_pow_dvd_aeval_iterate_newtonMap`, `HasStrictDerivAt.fun_sum`, `Matrix.isNilpotent_iff_forall_row`, `OnePoint.isZeroAt_iff_exists_SL2Z`, `Char.card_pow_char_pow`, `LinearIsometryEquiv.adjoint_eq_symm`, `smul_mem_closure_star_mul`, `extDeriv_fun_smul`, `VectorField.mpullback_const_smul_apply`, `ZMod.not_isUnit_of_mem_primeFactors`, `Even.pow_nonneg`, `Ideal.finsuppTotal_apply`, `IsLocalizedModule.exist_integer_multiples`, `ContinuousAlternatingMap.toAlternatingMap_curryLeft`, `IsRelPrime.add_mul_left_left`, `TensorProduct.flip_mk_surjective`, `Ideal.pow_sup_pow_eq_top`, `lt_inv_smul_iff_of_pos`, `Polynomial.isEquivalent_cobounded_leading_monomial`, `LinearMap.separatingRight_toMatrix₂'_iff`, `Finset.prod_sub`, `Complex.conj_rootsOfUnity`, `Matrix.toEuclideanLin_apply`, `StrictConvex.neg`, `WeierstrassCurve.b₈_of_isCharNeTwoNF`, `inner_self_eq_norm_sq_to_K`, `gcd_assoc'`, `LieSubmodule.Quotient.toEnd_comp_mk'`, `mem_rootsOfUnity_prime_pow_mul_iff'`, `Bornology.IsVonNBounded.image_multilinear'`, `Finset.expect_ite_zero`, `Submodule.biSup_eq_range_dfinsupp_lsum`, `Quaternion.imI_fst_dualNumberEquiv`, `HasDerivAt.congr_of_eventuallyEq`, `mem_tangentConeAt_of_pow_smul`, `FiniteField.coe_frobeniusAlgEquivOfAlgebraic`, `LinearMap.IsPositive.isPositive_smul_iff`, `analyticOrderAt_smul_eq_top_of_left`, `mem_openSegment_sub_add`, `VectorFourier.fourierPowSMulRight_eq_comp`, `LinearIsometryEquiv.trans_smul`, `Cubic.mem_roots_iff`, `IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable`, `Subgroup.instHasDetOneMinGeneralLinearGroup_1`, `Polynomial.isUnit_map`, `DirectSum.coe_of_mul_apply_aux`, `Polynomial.update_eq_add_sub_coeff`, `HasFPowerSeriesOnBall.tendsto_partialSum_prod`, `ContinuousLinearMap.hasFDerivWithinAt_of_bilinear`, `TensorProduct.tensorQuotEquivQuotSMul_comp_mkQ_lTensor`, `WithSeminorms.tendsto_nhds'`, `LinearMap.toMatrixAlgEquiv'_id`, `isAdjointPair_toLinearMap₂`, `Cubic.discr_eq_prod_three_roots`, `Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced`, `WeierstrassCurve.Projective.dblU_eq`, `ContinuousLinearMap.opNorm_mul`, `MvPowerSeries.smul_eq_C_mul`, `Algebra.isGeometricallyReduced_iff`, `Complex.mem_rootsOfUnity`, `LieModule.Cohomology.d₂₃_apply`, `MeasureTheory.integral_fintype_prod_eq_pow`, `Mathlib.Tactic.Ring.add_overlap_pf_zero`, `Algebra.Generators.liftBaseChange_injective_of_isLocalizationAway`, `Seminorm.pullback_apply`, `WeierstrassCurve.IsElliptic.isUnit`, `collinear_iff_of_mem`, `ContDiffMapSupportedIn.fderivCLM_apply_of_gt`, `TestFunction.fderivCLM_apply_of_le`, `IsReduced.pow_eq_zero_iff'`, `mul_neg_one_pow_eq_zero_iff`, `CuspForm.coe_trace`, `TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply`, `Real.Polynomial.isRoot_cos_pi_div_five`, `ContinuousAlternatingMap.constOfIsEmptyLIE_apply`, `Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_iInf`, `Ideal.rootsOfUnityMapQuot_injective`, `CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right`, `gcd_zero_right'`, `Seminorm.bddAbove_of_absorbent`, `LieModule.instIsTriangularizableSubtypeEndMemLieSubalgebraRangeToEnd`, `WeierstrassCurve.Projective.Point.toAffineLift_of_Z_ne_zero`, `LieIdeal.toInvtRootSubmodule_mono`, `Int.normUnit_eq`, `PowerSeries.coeff_subst`, `TemperedDistribution.smulLeftCLM_neg`, `Module.Dual.im_extendRCLike_apply`, `Orthonormal.basisTensorProduct`, `InnerProductSpace.Core.inner_smul_ofReal_right`, `Matrix.vandermonde_succ`, `Asymptotics.IsLittleO.pow`, `UpperHalfPlane.glPos_smul_def`, `AlgebraicGeometry.SpecToEquivOfLocalRing_apply_snd_coe`, `Valuation.ltAddSubgroup_monotone`, `egauge_zero_zero`, `algebraicClosure.isAlgebraic`, `AnalyticOn.pow`, `sum_pow_char_pow`, `NumberField.Units.coe_mul`, `IsFractionRing.exists_reduced_fraction`, `ZMod.isCyclic_units_iff`, `IsCusp.of_isFiniteRelIndex_conj`, `Finset.smul_finset_subset_smul_finset_iff₀`, `Units.index_posSubgroup`, `Matrix.conjTranspose_inv_intCast_smul`, `TestFunction.lineDerivOpCLM_eq_lineDerivCLM`, `MDifferentiable.cle_arrowCongr`, `Asymptotics.IsLittleOTVS.neg_right`, `QuadraticForm.tmul_tensorMap_apply`, `mem_rootsOfUnity_iff_mem_nthRoots`, `segment_subset_convexHull`, `HasSum.smul_eq`, `Units.symm_mulRightLinearEquiv`, `Polynomial.monic_of_isUnit_leadingCoeff_inv_smul`, `Polynomial.prod_cyclotomic_eq_X_pow_sub_one`, `HasFTaylorSeriesUpTo.fderiv_eq`, `Polynomial.eq_quo_mul_prod_pow_add_sum_rem_mul_prod_pow`, `PowerSeries.isUnit_divided_by_X_pow_order`, `IsGalois.normalClosure`, `HasDerivAt.fun_pow'`, `FractionalIdeal.isUnit_num`, `Unitization.nnnorm_def`, `LieModule.mem_weightSpace`, `instSMulCommClassMatrixFinOfNatNatProd`, `WeierstrassCurve.b₂_of_char_two`, `PowerSeries.le_order_smul`, `UpperHalfPlane.J_sq`, `IsUnit.cfcSqrt`, `CFC.continuousOn_log`, `IsPurelyInseparable.iterateFrobenius_algebraMap`, `AlgebraicGeometry.Proj.basicOpenToSpec_app_top`, `ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear`, `Matrix.liftLinear_singleLinearMap`, `sub_pow_eq_mul_pow_sub_pow_div_expChar`, `LieModule.Cohomology.d₁₂_apply_apply`, `Algebra.Extension.Cotangent.smul_eq_zero_of_mem`, `TestFunction.fderivCLM_ofSupportedIn`, `convexHull_toCone_eq_sInf`, `NonUnitalSubalgebra.prod_top`, `Polynomial.eval₂_ofFinsupp`, `IsArtinianRing.isUnit_iff_isRegular_of_mulOpposite`, `Polynomial.eval₂_monomial`, `ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson`, `ConcaveOn.inf`, `Finset.zero_mem_smul_finset_iff`, `smul_uniformity₀`, `LinearMap.smulRight_apply`, `HasFDerivAt.fun_smul`, `Matrix.charpoly_mul_comm_of_le`, `Module.AEval'.X_smul_of`, `Matrix.det_updateRow_smul_left`, `LinearMap.isUnit_iff_isUnit_det`, `Function.HasTemperateGrowth.toTemperedDistribution_apply`, `Complex.sin_bound`, `ContinuousLinearMap.flipMultilinear_apply_apply`, `ContinuousMultilinearMap.uncurrySum_apply`, `MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotent`, `one_lt_sq_iff₀`, `Orthonormal.inner_left_fintype`, `ENNReal.pow_rpow_inv_natCast`, `arithGeom_eq_add_sum`, `Valued.isClopen_ball`, `Height.mulHeight₁_pow`, `lie_smul`, `HasLineDerivAt.tendsto_slope_zero_right`, `LieModule.mem_posFittingCompOf`, `WeierstrassCurve.Affine.irreducible_polynomial`, `TensorProduct.AlgebraTensorModule.map_smul_left`, `Balanced.convexHull`, `NonUnitalStarAlgHom.range_comp_le_range`, `Complex.hasDerivAt_GammaIntegral`, `AntitoneOn.convex_le`, `CongruenceSubgroup.exists_Gamma_le_conj`, `fderiv_continuousAlternatingMapCompContinuousLinearMap`, `Polynomial.pow_rootMultiplicity_not_dvd`, `Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable`, `unitary.coe_zpow`, `Quaternion.normSq_smul`, `HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope`, `WeierstrassCurve.Jacobian.negAddY_neg`, `LocalizedModule.divBy_mul_by`, `IncidenceAlgebra.instIsScalarTower`, `Matrix.toBilin_apply`, `NumberField.mixedEmbedding.fundamentalCone.torsion_unitSMul_mem_integerSet`, `IntermediateField.isAlgebraic_iff`, `RatFunc.Luroth.algEquiv_apply`, `LinearMap.toMatrix₂'_compl₁₂`, `WeierstrassCurve.Affine.equation_iff'`, `LSeries_iteratedDeriv`, `ValuativeRel.ValueGroupWithZero.embed_strictMono`, `MonoidAlgebra.coe_liftNCAlgHom`, `PiTensorProduct.mapL_smul`, `Module.End.maxGenEigenspace_eq_maxGenEigenspace_zero`, `SchwartzMap.integral_sesq_fourier_eq`, `LinearEquiv.det_baseChange`, `DFinsupp.instSMulPosMono`, `DualNumber.lift_apply_eps`, `gaussSum_mul`, `modularCyclotomicCharacter.spec`, `Real.fderiv_fourier`, `CategoryTheory.ShortComplex.Homotopy.smul_h₂`, `LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle`, `Polynomial.natDegree_of_dvd_cyclotomic_of_irreducible`, `ContinuousLinearMap.adjointAux_norm`, `LinearMap.prodEquiv_apply`, `Representation.smul_ofModule_asModule`, `CStarMatrix.norm_def'`, `MulChar.mulEquivToUnitHom_apply`, `Matrix.det_units_conj'`, `MulActionWithZero.zero_smul`, `KaehlerDifferential.instIsScalarTowerTensorProduct`, `Polynomial.aeval_X_pow`, `algebra_compatible_smul`, `PeriodPair.ite_eq_one_sub_sq_mul_weierstrassP`, `AntitoneOn.convex_gt`, `MeasureTheory.Integrable.smul_bdd`, `MDifferentiable.clm_bundle_apply₂`, `Fintype.expect_dite_eq'`, `Ideal.map_mul`, `PowerSeries.eq_shift_mul_X_pow_add_trunc`, `isUnit_le_nonZeroDivisors`, `Polynomial.monomial_pow`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le`, `NonUnitalStarAlgHom.injective_codRestrict`, `Polynomial.coeff_mul_X_pow`, `MeasureTheory.convolution_smul`, `MeasureTheory.MemLp.integrable_enorm_pow'`, `TensorProduct.AlgebraTensorModule.restrictScalars_lTensor`, `neg_smul_neg`, `spectrum.zero_notMem_iff`, `MvPolynomial.eval₂_mul_monomial`, `hasDerivAtFilter_natCast`, `Submodule.map_smul''`, `Polynomial.isEquivalent_atTop_lead`, `LinearMap.flip_injective_iff₁`, `Finsupp.linearCombination_one_tmul`, `exists_add_pow_prime_pow_eq`, `WeierstrassCurve.Projective.addMap_of_Z_eq_zero_left`, `CategoryTheory.Linear.units_smul_comp`, `add_sq`, `meromorphicOrderAt_ne_top_iff`, `Ideal.mul_bot`, `spinGroup.units_mem_lipschitzGroup`, `intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip`, `ConvexCone.coe_map`, `WithLp.unitization_algebraMap`, `WeierstrassCurve.Jacobian.Point.fromAffine_some`, `HomogeneousLocalization.Away.map_map`, `HahnSeries.SummableFamily.hsum_smul_module`, `ContinuousAlternatingMap.instContinuousSMul`, `LinearMap.ker_smul'`, `DualNumber.inv_eps`, `LinearMap.toMatrixOrthonormal_apply_apply`, `LocalizedModule.map_surjective`, `IsLocalizedModule.map_linearMap_of_isLocalization`, `gcd_mul_right'`, `HasFDerivAt.restrictScalars`, `ContinuousLinearMap.hasStrictFDerivAt_of_bilinear`, `MvPolynomial.esymmAlgHomMonomial_single`, `Ne.isUnit`, `Matrix.toLin'_mul_apply`, `LaurentPolynomial.eval₂_C_mul_T`, `IsCoprime.pow_left_iff`, `Complex.taylorSeries_eq_on_ball'`, `SameRay.exists_eq_smul_add`, `CategoryTheory.Functor.Linear.map_smul`, `LieModule.isNilpotent_range_toEnd_iff`, `Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub`, `StrongFEPair.functional_equation`, `WeierstrassCurve.preΨ_odd`, `MonotoneOn.convex_le`, `fourierCoeff_bernoulli_eq`, `PerfectClosure.instPerfectRing`, `Matrix.coe_units_inv`, `Polynomial.resultant_X_pow_right`, `IntermediateField.coe_inclusion`, `ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRel`, `Matrix.toLinearMapₛₗ₂'_single`, `Mathlib.Tactic.Ring.mul_pow`, `LieAlgebra.bracket_ofTwoCocycle`, `Matrix.toLin'_hadamard`, `UpperHalfPlane.denom_cocycle_σ`, `VectorFourier.fourierIntegral_continuousLinearMap_apply`, `AnalyticAt.exists_eventuallyEq_sum_add_pow_mul`, `GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace`, `ContDiffOn.pow`, `LocalizedModule.mk_eq`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_apply`, `IsLinearMap.isLinearMap_smul'`, `WeierstrassCurve.b₈_of_isCharTwoJEqZeroNF_of_char_two`, `AffineSubspace.coe_subtypeₐᵢ`, `MonoidAlgebra.instIsPushout`, `Matrix.nondegenerate_toBilin'_iff`, `Polynomial.rootsExpandPowEquivRoots_apply`, `emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactors`, `Ideal.smul_eq_mul`, `Equiv.mulLeft₀_symm_apply`, `TensorProduct.AlgebraTensorModule.restrictScalars_curry`, `Algebra.Norm.Transitivity.comp_det_mul_pow`, `Polynomial.normUnit_content`, `IntermediateField.finiteDimensional_iSup_of_finset`, `HasFDerivAtFilter.isThetaTVS_sub`, `CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φH`, `LieAlgebra.rank_le_natTrailingDegree_charpoly_ad`, `MonotoneOn.quasiconvexOn`, `Subgroup.instIsArithmeticRangeSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGL`, `Matrix.det_smul`, `pow_two_nonneg`, `modularCyclotomicCharacter.toFun_spec'`, `HomogeneousLocalization.awayMap_mk`, `Matrix.SpecialLinearGroup.isClosedEmbedding_toGL`, `Polynomial.separable_X_pow_sub_C_of_irreducible`, `FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop`, `TensorProduct.AlgebraTensorModule.rightComm_eq`, `QuadraticForm.tmul_comp_tensorComm`, `LinearMap.BilinForm.congr_comp`, `NonUnitalSubalgebra.inclusion_self`, `LinearMap.toMatrixAlgEquiv_apply`, `IntermediateField.LinearDisjoint.of_le`, `Finset.mem_convexHull'`, `StarConvex.affine_image`, `cfcₙ_apply_mkD`, `LocalizedModule.lift'_mk`, `iteratedDeriv_smul_const`, `circleIntegral.integral_sub_inv_smul_sub_smul`, `Action.smul_hom`, `RingTheory.Sequence.isWeaklyRegular_iff_Fin`, `IsGaloisGroup.quotientMap`, `Polynomial.derivative_eval`, `OrderIso.mulRight₀_apply`, `EulerSine.integral_cos_mul_cos_pow_aux`, `HasStrictFDerivAt.list_prod'`, `FreeNonUnitalNonAssocAlgebra.lift_unique`, `CliffordAlgebra.foldr'Aux_foldr'Aux`, `FiniteField.sum_pow_lt_card_sub_one`, `SchwartzMap.fourier_lineDerivOp_eq`, `DifferentiableAt.smul`, `Valuation.unit_map_eq`, `HasFDerivWithinAt.isThetaTVS_sub`, `LieAdmissibleAlgebra.toSMulCommClass`, `LinearMap.isBigOTVS_rev_comp`, `cfcₙHom_id`, `AlgebraicGeometry.IsReduced.component_reduced`, `AddChar.wInner_cWeight_eq_zero_iff_ne`, `LinearMap.toContinuousBilinearMap_apply`, `Algebra.Extension.instIsScalarTowerH1CotangentOfCotangent`, `TemperedDistribution.instLineDerivLeftSMulReal`, `MvPolynomial.map_frobenius_expand`, `PrimeSpectrum.le_basicOpen_pow`, `Submodule.span_singleton_eq_top_iff`, `CStarMatrix.inner_toCLM_conjTranspose_left`, `RootPairing.reflection_apply_root'`, `LinearMap.toMatrix'_toLin'`, `geom_sum_pos_iff`, `affineSpan_eq_affineSpan_lineMap_units`, `hasStrictDerivAt_exp_smul_const`, `Submodule.FG.restrictScalars`, `PolynomialModule.monomial_smul_single`, `MeasureTheory.iteratedFDeriv_charFun`, `multiplicity_sub_of_gt`, `Derivation.leibniz_div`, `Subgroup.mem_adjoinNegOne_iff`, `NeZero.pow`, `UniqueFactorizationMonoid.factors_pow`, `IntermediateField.LinearDisjoint.trace_algebraMap`, `Polynomial.separable_X_pow_sub_C`, `Valuation.hasBasis_nhds_zero`, `Filter.EventuallyEq.ftaylorSeries`, `isBoundedBilinearMap_comp`, `StarConvex.smul_mem`, `NonUnitalSubalgebra.iSupLift_of_mem`, `instIsAbelianGaloisSubtypeMemIntermediateFieldBot`, `NormedSpace.exp_eq_tsum`, `lp.instIsCentralScalarPreLp`, `LinearMap.range_toAddSubmonoid`, `set_smul_sphere_zero`, `MeasureTheory.Integrable.essSup_smul`, `Polynomial.Monic.eq_X_pow_iff_natDegree_le_natTrailingDegree`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx`, `IsLocalRing.exists_maximalIdeal_pow_le_of_finite_quotient`, `NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply`, `SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv`, `WeierstrassCurve.Projective.addXYZ_smul`, `LinearMap.bijective_compr₂_of_equiv`, `Subgroup.pointwise_smul_le_pointwise_smul_iff₀`, `PowerSeries.isUnit_iff_constantCoeff`, `TensorProduct.toMatrix_assoc`, `CochainComplex.HomComplex.Cochain.rightUnshift_units_smul`, `Finset.smul_mem_smul_finset_iff₀`, `ContMDiff.smul`, `AdicCompletion.ofPowSMul_ofValEqZero`, `FormalMultilinearSeries.nnnorm_changeOrigin_le`, `Bialgebra.TensorProduct.comul_eq_algHom_toLinearMap`, `hasStrictDerivAt_add_const_iff`, `hasLineDerivWithinAt_smul_iff`, `Matrix.toLinearMap₂'_apply'`, `inrNonUnitalStarAlgHom_comp_cfcₙHom_eq_cfcₙAux`, `Perfection.mk_teichmuller`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff`, `Asymptotics.IsBigO.const_smul_left`, `PowerSeries.subst_pow`, `Asymptotics.IsTheta.smul`, `TemperedDistribution.fourierInv_lineDerivOp_eq`, `MDifferentiable.const_smul`, `LieSubmodule.lie_top_eq_of_span_sup_eq_top`, `TrivSqZeroExt.lift_comp_inrHom`, `FiniteField.pow_card_pow`, `Complex.mul_conj'`, `NNReal.instPosSMulStrictMono`, `Convex.openSegment_self_interior_subset_interior`, `Asymptotics.IsBigOTVS.neg_right`, `ModuleCat.smulShortComplex_X₃_isAddCommGroup`, `Submodule.span_smul_le`, `Unitary.tmul_mem`, `LeftInvariantDerivation.lift_smul`, `IsMIntegralCurveOn.hasDerivWithinAt`, `TensorProduct.quotTensorEquivQuotSMul_mk_one_tmul`, `IsLocalizedModule.mk'_add_mk'`, `Algebra.Extension.instIsScalarTowerRingTensorProductBaseChange`, `Polynomial.X_pow_smul_rTensor_monomial`, `FormalMultilinearSeries.rightInv_removeZero`, `ZMod.AddAutEquivUnits_symm_apply`, `Polynomial.X_pow_sub_one_splits`, `LinearIndependent.map_pow_expChar_pow_of_isSeparable'`, `arithGeom_zero_eq_mul_div'`, `geom_series_succ`, `MvPolynomial.expand_char`, `Asymptotics.isLittleO_pow_pow`, `IsLocalRing.mem_maximalIdeal`, `ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply`, `ClosedSubmodule.orthogonal_closure''`, `Polynomial.isMonicOfDegree_add_add_two`, `instIsPushoutFractionRingPolynomial_1`, `Unitary.mulRight_trans_mulRight`, `HasDerivWithinAt.comp`, `Asymptotics.isBigOWith_self_const_mul'`, `LinearMap.coe_lTensorHom`, `hasStrictDerivAt_exp_smul_const'`, `KaehlerDifferential.mapBaseChange_tmul`, `SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable`, `Polynomial.degree_X_pow_add_C`, `Module.DirectLimit.quotMk_of`, `Matrix.det_one_add_smul`, `Valuation.IsUniformizer.zpowers_eq_valueGroup`, `Polynomial.IsUnitTrinomial.irreducible_of_isCoprime`, `openSegment_translate_image`, `egauge_univ_pi`, `Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_eq`, `OrderIso.smulRightDual_apply`, `AffineSubspace.smul_vsub_vadd_mem`, `MeromorphicAt.fun_smul`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `Finset.sum_sq_le_sq_sum_of_nonneg`, `Real.fourier_iteratedFDeriv`, `Polynomial.disc_of_degree_eq_two`, `HasDerivAt.add`, `SchwartzMap.smulLeftCLM_real_smul`, `Units.smul_mk0`, `strictConvex_uIcc`, `one_geom_sum`, `WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero`, `Ideal.ramificationIdx_ne_one_iff`, `ENat.epow_natCast`, `HasMFDerivAt.smul`, `LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec`, `AddChar.sum_apply_eq_ite`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk`, `TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm`, `ContinuousLinearEquiv.unitsEquivAut_apply`, `HasStrictDerivAt.div`, `Polynomial.eval_pow`, `NormMulClass.toNormSMulClass_op`, `RootPairing.pairing_one_four_iff'`, `Complex.cpow_ofNat_mul'`, `MvPowerSeries.hasSum_aeval`, `ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply`, `NormalizationMonoid.normUnit_coe_units`, `tsum_geometric_le_of_norm_lt_one`, `Complex.cos_eq_iff_quadratic`, `MDifferentiableOn.smul`, `integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable`, `OreLocalization.zero_smul`, `MDifferentiableAt.clm_prodMap`, `TrivSqZeroExt.fst_invOf`, `ContinuousLinearMap.intrinsicStarModule`, `Associates.pow_factors`, `hasDerivAtFilter_zero`, `EuclideanDomain.div_pow`, `Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone`, `segment_subset_convexJoin`, `Matrix.toAlgEquiv_kroneckerStarAlgEquiv`, `StrictConvex.is_linear_preimage`, `Algebra.Generators.H1Cotangent.δAux_C`, `NormedAddGroupHom.isCentralScalar`, `Seminorm.map_eq_zero_of_norm_zero`, `smul_closedBall'`, `NormedSpace.exp_eq_tsum_div`, `Polynomial.iterate_derivative_X_sub_pow`, `ContinuousLinearMap.one_smulRight_eq_toSpanSingleton`, `Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply`, `spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul`, `Polynomial.support_trinomial'`, `QuadraticMap.associated_prod`, `ConvexCone.coe_comap`, `WithZero.expOrderIso_symm_apply`, `LinearOrder.strictConvexOn_of_lt`, `Convex.combo_interior_closure_subset_interior`, `Valuation.restrict_le_iff`, `LocalizedModule.mk_cancel`, `Module.add_smul`, `IntermediateField.minpoly_gen`, `MvPowerSeries.X_pow_dvd_iff`, `PresheafOfModules.Sheafify.map_smul_eq`, `Polynomial.Chebyshev.leadingCoeff_U_natCast`, `convex_iff_openSegment_subset`, `Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem`, `Matrix.PosSemidef.posDef_iff_isUnit`, `smul_inv_smul₀`, `Monotone.convex_ge`, `isSplittingField_X_pow_sub_C_of_root_adjoin_eq_top`, `UnitAddTorus.mFourierCoeff_toLp`, `NonUnitalSubalgebra.unitization_injective`, `Polynomial.irreducible_of_eisenstein_criterion`, `Submodule.coe_toConvexCone`, `PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision`, `LinearMap.toMatrix_transpose`, `Polynomial.expand_eq_comp_X_pow`, `PiCountable.min_edist_le_edist_pi`, `EuclideanSpace.volume_closedBall_fin_three`, `LinearMap.toMatrix₂_toLinearMapₛₗ₂`, `ContinuousLinearMap.uniformContinuous_restrictScalars`, `Matrix.isParabolic_conj'_iff`, `TensorProduct.finsuppLeft_smul'`, `MvPolynomial.sumAlgEquiv_comp_rename_inr`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_strictMono`, `Ideal.adic_module_basis`, `LieSubmodule.instSMulMemClass`, `TensorAlgebra.toDirectSum_ofDirectSum`, `SubmodulesBasis.smul`, `ContinuousLinearMap.mulLeftRight_apply`, `Polynomial.Chebyshev.T_two`, `mem_openSegment_translate`, `MDifferentiableAt.pow`, `PowerSeries.coe_smul`, `isModuleTopologyOfFiniteDimensional`, `IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective`, `MvPolynomial.aevalTower_toAlgHom`, `LinearMap.extendTo𝕜'_apply`, `LieAlgebra.ad_eq_lmul_left_sub_lmul_right`, `PeriodPair.hasSum_derivWeierstrassP`, `ENNReal.pow_le_pow_left`, `Differentiable.pow`, `curveIntegral_fun_smul`, `WeierstrassCurve.ΨSq_ofNat`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum`, `MonotoneOn.convex_gt`, `fromTangentSpace_mfderiv_smul_apply`, `PiCountable.edist_eq_tsum`, `Complex.sinh_three_mul`, `Polynomial.nthRootsFinset_toSet`, `Seminorm.ball_eq_emptyset`, `ArchimedeanClass.mk_le_mk_smul`, `dslope_sub_smul`, `AddChar.sum_eq_zero_iff_ne_zero`, `rescale_to_shell_semi_normed_zpow`, `WeierstrassCurve.Projective.addY_of_Z_eq_zero_left`, `closure_smul₀'`, `Perfection.teichmuller₀_spec`, `LinearMap.trace_smulRight`, `Algebra.TensorProduct.basisAux_map_smul`, `IsLocalRing.instIsLocalHomResidueFieldRingHomResidue`, `balancedCore_mem_nhds_zero`, `convexJoin_segment_singleton`, `SameRay.exists_eq_smul`, `pinGroup.val_toUnits_apply`, `DirectSum.instSMulCommClass`, `ContinuousMultilinearMap.curryRight_norm`, `AdicCompletion.factor_eval_eq_evalₐ`, `Associates.prod_le_prod_iff_le`, `hasDerivWithinAt_Iic_of_tendsto_deriv`, `CentroidHom.instSMulCommClass_2`, `mellin_hasDerivAt_of_isBigO_rpow`, `ContinuousLinearMap.analyticOn_bilinear`, `Set.smul_univ₀`, `IsLocalHom.of_surjective`, `deriv_fun_smul`, `Commute.sq_eq_sq_iff_eq_or_eq_neg`, `QuadraticAlgebra.norm_eq_one_iff_mem_unitary`, `ConvexCone.salient_strictlyPositive`, `iteratedFDeriv_comp_const_smul`, `Mathlib.Tactic.Ring.mul_pf_right`, `Subgroup.instIsArithmeticMapSpecialLinearGroupFinOfNatNatIntGeneralLinearGroupRealMapGLOfFiniteIndex`, `FiniteMultiplicity.emultiplicity_self`, `Pi.intrinsicStar_comul_commSemiring`, `LocalizedModule.mem_ker_mkLinearMap_iff`, `Matrix.det_kroneckerMapBilinear`, `HasStrictDerivAt.mul`, `Polynomial.irreducible_mul_leadingCoeff_inv`, `PresheafOfModules.Derivation.d_mul`, `iterateFrobenius_one_apply`, `ZMod.val_pow_le`, `PeriodPair.weierstrassP_bound`, `Bundle.Trivialization.eq_sum_localFrame_coeff_smul`, `IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_algebraMap`, `LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot`, `MeasureTheory.convolution_lsmul`, `QuadraticMap.map_smul`, `Valued.is_topological_valuation`, `Matrix.toLinAlgEquiv_mul`, `MDifferentiableAt.clm_postcomp`, `PeriodPair.hasSumLocallyUniformly_derivWeierstrassP`, `fderiv_continuousAlternatingMap_apply`, `SlashInvariantForm.coe_translate`, `TemperedDistribution.laplacian_eq_fourierMultiplierCLM`, `abs_nnqsmul`, `Localization.algHom_ext_iff`, `SeminormFamily.finset_sup_comp`, `Module.Dual.norm_extendRCLike_apply_sq`, `Submodule.mem_span_finset`, `Bornology.isVonNBounded_iff_absorbing_le`, `Module.AEval.instIsScalarTowerOrigPolynomial`, `IsLocalizedModule.fromLocalizedModule.bij`, `CategoryTheory.Pretriangulated.Triangle.smul_hom₂`, `gal_X_pow_sub_C_isSolvable`, `ContDiffMapSupportedIn.monoLM_eq_of_scalars`, `meromorphicNFOn_smul_iff_right_of_analyticOnNhd`, `Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap`, `UniqueFactorizationMonoid.primeFactors_pow'`, `Finset.smul_finset_univ₀`, `ringKrullDim_quotSMulTop_succ_eq_ringKrullDim`, `Module.AEval.C_smul`, `Algebra.Extension.CotangentSpace.map_tmul`, `Bornology.isVonNBounded_covers`, `hasDerivAt_abs_neg`, `measurableEmbedding_const_smul₀`, `Matrix.vecMulBilin_apply`, `IsValuativeTopology.isOpen_ball`, `element_smul_restrictScalars`, `integral_withDensity_eq_integral_smul`, `HasCompactMulSupport.comp_smul`, `MvPowerSeries.subst_monomial`, `Representation.ofMulAction_self_smul_eq_mul`, `emultiplicity_pow_sub_pow_of_prime`, `Matrix.instSMulCommClassForall_1`, `Unitization.lift_symm_apply_apply`, `convex_singleton`, `cross_anticomm`, `LinearMap.range_smulRight_apply_of_surjective`, `HasDerivAt.pow`, `Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splits`, `deriv_fderiv`, `PowerSeries.normUnit_X`, `RegularNormedAlgebra.isometry_mul'`, `Associated.pow_iff`, `convexJoin_singleton_segment`, `cauchyPowerSeries_apply`, `WeierstrassCurve.Jacobian.negAddY_of_X_eq'`, `KaehlerDifferential.span_range_map_derivation_of_isLocalization`, `LocalizedModule.equivTensorProduct_symm_apply_tmul_one`, `mem_smul_of_egauge_lt`, `Associates.instIsOrderedMonoid`, `Asymptotics.isBigO_pow_pow_cobounded_of_le`, `Rep.ihom_ev_app_hom`, `Polynomial.coeff_X_pow_mul`, `Unitary.spectrum_star_left_conjugate`, `edist_le_of_edist_le_geometric_two_of_tendsto`, `WeierstrassCurve.Projective.isUnit_dblU_of_Y_eq`, `WeierstrassCurve.b₆_of_char_three`, `UniqueFactorizationMonoid.exists_associated_prime_pow_of_unique_normalized_factor`, `Matrix.GeneralLinearGroup.upperRightHom_apply`, `FiniteField.roots_X_pow_card_sub_X`, `NumberField.mixedEmbedding.fundamentalCone.torsion_smul_mem_of_mem`, `ProbabilityTheory.setBernoulli_singleton`, `orderOf_zero`, `CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM`, `TemperedDistribution.instFourierSMul`, `Ideal.range_mul`, `CommRing.Pic.mk_tensor`, `integral_smul_const`, `IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eq'`, `range_cfcₙHom`, `LocalizedModule.equivTensorProduct_apply_mk`, `Field.Emb.Cardinal.succEquiv_coherence`, `cross_cross_eq_smul_sub_smul`, `Module.exists_nontrivial_relation_of_finrank_lt_card`, `Real.map_matrix_volume_pi_eq_smul_volume_pi`, `ZMod.pow_totient`, `NonUnitalStarSubalgebra.map_map`, `MDifferentiableWithinAt.clm_bundle_apply₂`, `TrivSqZeroExt.algHom_ext'_iff`, `add_pow_char`, `fun_meromorphicOrderAt_smul`, `IsDiscreteValuationRing.irreducible_of_span_eq_maximalIdeal`, `IsAdicComplete.of_liftRingHom`, `Algebra.discr_powerBasis_eq_norm`, `WeierstrassCurve.Jacobian.smul_fin3`, `TestFunction.limitCLM_apply`, `LinearMap.associated_det_of_eq_comp`, `MonoidWithZeroHom.one_apply_val_unit`, `Module.IsTorsionBySet.mk_smul`, `spinGroup.val_inv_toUnits_apply`, `hasDerivWithinAt_abs`, `Algebra.TensorProduct.linearMap_comp_rid`, `associated_of_dvd_dvd`, `hasFPowerSeriesOnBall_const`, `Complex.exp_nsmul`, `Subgroup.IsArithmetic.isCusp_iff_isCusp_SL2Z`, `QuadraticForm.polarBilin_tmul`, `tendsto_smoothingFun_comp`, `HasFDerivAt.clm_apply`, `openSegment_eq_image'`, `HasStrictDerivAt.const_mul`, `ContDiffMapSupportedIn.seminorm_le_iff`, `LieModule.isNilpotent_toEnd_of_isNilpotent`, `Fintype.sum_pow`, `Unitary.openPartialHomeomorph_symm_apply`, `LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful`, `Matrix.GeneralLinearGroup.val_mk''`, `UniqueFactorizationMonoid.factors_pow_count_prod`, `Valuation.restrict_eq_zero_iff`, `Cardinal.power_nat_le`, `ConcaveOn.convex_strict_hypograph`, `LocalizedModule.map_injective`, `norm_pow_le`, `ContinuousLinearMap.hasDerivAt`, `hasDerivAt_of_tendstoUniformly`, `NonUnitalStarSubalgebra.unitization_range`, `Polynomial.leadingCoeff_cubic`, `Polynomial.eval_X_pow`, `Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv`, `mul_neg_geom_sum`, `smul_nonpos_iff_pos_imp_nonpos`, `LinearMap.BilinForm.Nondegenerate.congr`, `Subfield.mem_bot_iff_pow_eq_self`, `Complex.cosh_sq_sub_sinh_sq`, `IsAdic.hasBasis_nhds`, `Algebra.Extension.tensorCotangentSpace_tmul_tmul`, `Polynomial.resultant_C_zero_right`, `IsPrimitiveRoot.norm_eq_neg_one_pow`, `Algebra.TensorProduct.tensorTensorTensorComm_symm_tmul`, `VectorFourier.hasFDerivAt_fourierIntegral`, `DiffContOnCl.circleIntegral_sub_inv_smul`, `PowerSeries.coeff_X_mul_largeSchroderSeriesSeries_sq`, `AlgebraicGeometry.RingedSpace.mem_top_basicOpen`, `MvPowerSeries.trunc'_trunc'_pow`, `Associates.out_dvd_iff`, `cfc_comp_pow`, `WeierstrassCurve.b₈_of_isCharTwoJEqZeroNF`, `HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq`, `TensorProduct.equivFinsuppOfBasisLeft_symm`, `SymmetricAlgebra.instModuleFree`, `KaehlerDifferential.mulActionBaseChange_smul_add`, `Submodule.comap_smul`, `ContractingWith.apriori_edist_iterate_efixedPoint_le'`, `TensorProduct.Algebra.smul_def`, `LinearMap.flip_surjective_iff₁`, `LinearMap.tensorEqLocus_coe`, `AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right_assoc`, `TensorAlgebra.toExterior_ι`, `LaurentPolynomial.smeval_C_mul`, `Matrix.inv_smul'`, `Seminorm.ball_norm_mul_subset`, `DirichletCharacter.unit_norm_eq_one`, `IsLocalizedModule.exist_integer_multiples_of_finset`, `Valuation.restrict_eq_mk`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `PairReduction.pow_logSizeRadius_le_card_le_logSizeRadius`, `Perfection.coeff_symm_frobeniusEquiv`, `List.sum_smul`, `AddMonoidAlgebra.Monic.pow`, `WeierstrassCurve.φ_three`, `ClosedSubmodule.inner_real_eq_re_inner`, `hasFDerivAt_ringInverse`, `Language.reverse_pow`, `Polynomial.separable_or`, `Polynomial.X_pow_mul_assoc`, `ContinuousMultilinearMap.opNorm_smul_le`, `Commute.pow_dvd_pow_of_add_pow_eq_zero`, `Function.HasTemperateGrowth.fun_smul`, `Filter.HasBasis.isLittleOTVS_iff`, `Matrix.toLinearMap₂'_apply`, `HasFDerivAt.continuousAlternatingMap_apply`, `MeasureTheory.convolution_precompR_apply`, `MonoidWithZeroHom.mem_valueMonoid`, `PolynomialModule.single_smul`, `SchwartzMap.compSubConstCLM_apply`, `Polynomial.degreeLT.addLinearEquiv_apply_fst`, `lTensorHomEquivHomLTensor_apply`, `LinearMap.BilinForm.separatingLeft_toMatrix'_iff`, `isCusp_SL2Z_iff'`, `IsNilpotent.exp_smul_eq_sum`, `MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc`, `VectorFourier.fourierIntegral_iteratedFDeriv`, `Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero`, `ModularGroup.lcRow0Extend_symm_apply`, `TopologicalAddGroup.IsSES.pushforward_apply_apply`, `rank_lt_rank_dual'`, `coeSubmodule_differentIdeal_fractionRing`, `WeierstrassCurve.toCharNeTwoNF_u`, `LieAlgebra.Basis.borelUpper_eq`, `QuotSMulTop.map_surjective`, `Ideal.Fiber.lift_residueField_surjective`, `Module.End.HasEigenvalue.pow`, `InformationTheory.hasDerivAt_klFun`, `isBaseChange_tensorProduct_map`, `Polynomial.coeff_X_pow`, `AddChar.sum_eq_card_of_eq_one`, `IsLocalizedModule.mk'_eq_mk'_iff`, `InnerProductSpace.nnnorm_rankOne`, `Polynomial.derivative_X_sub_C_sq`, `IsPrimitiveRoot.autToPow_eq_modularCyclotomicCharacter`, `Algebra.Generators.compLocalizationAwayAlgHom_X_inl`, `FreeLieAlgebra.liftAux_map_smul`, `FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin`, `Seminorm.closedBall_zero_eq_preimage_closedBall`, `spectrum.zero_mem_iff`, `MonotoneOn.quasilinearOn`, `fderiv_smul`, `Set.smul_set_univ₀`, `Finset.divConst_le_mulConst_sq`, `ArithmeticFunction.one_smul'`, `Polynomial.coeff_isUnit_isNilpotent_of_isUnit`, `OrthonormalBasis.orthogonalProjection_apply_eq_sum`, `ModularGroup.denom_apply`, `intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left`, `Filter.BoundedAtFilter.smul`, `FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard`, `Seminorm.ball_smul`, `LieAlgebra.Basis.linearIndepOn_root_baseSupp`, `Finpartition.IsEquipartition.card_interedges_sparsePairs_le`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst`, `IsPrimitiveRoot.minpoly_eq_pow_coprime`, `NonUnitalSubalgebra.unitization_range`, `LieModule.LinearWeights.map_smul`, `FiniteField.algebraMap_trace_eq_sum_pow`, `SemimoduleCat.Algebra.instIsScalarTowerCarrier`, `instIsOrderedModule`, `ModuleCat.CoextendScalars.smul_apply`, `UniqueFactorizationMonoid.exists_prime_iff`, `HasDerivAt.fun_pow`, `UniqueFactorizationMonoid.irreducible_iff_prime`, `OreLocalization.numeratorHom_inj`, `hasDerivAt_of_tendstoLocallyUniformlyOn`, `ZMod.not_isCyclic_units_of_mul_coprime`, `hasDerivAtFilter_iff_tendsto_slope`, `starConvex_compl_Ici`, `LocalizedModule.equivTensorProduct_symm_apply_tmul`, `Polynomial.Chebyshev.U_two`, `ContinuousLinearMap.norm_toSpanSingleton`, `FormalMultilinearSeries.continuousOn_of_finite`, `intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left`, `TensorProduct.finsuppScalarRight_apply_tmul`, `Submodule.topologicalClosure_map`, `Perfection.coeff_map`, `Submodule.toConvexCone_top`, `Representation.single_smul`, `WeierstrassCurve.Jacobian.polynomialY_eq`, `IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff`, `Polynomial.isUnit_iff`, `FormalMultilinearSeries.ofScalars_series_of_subsingleton`, `Fintype.card_units`, `ContinuousAlternatingMap.curryLeft_apply_apply`, `NormedSpace.isVonNBounded_closedBall`, `Polynomial.Splits.X_pow`, `ContinuousLinearMap.flip_smul`, `logDeriv_fun_pow`, `LieSubmodule.coe_map_toEnd_le`, `Module.FinitePresentation.linearEquivMap_symm_apply`, `HomogeneousLocalization.Away.map_id`, `ENNReal.rpow_natCast`, `WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero`, `ContDiffMapSupportedIn.coe_smul`, `HasDerivAtFilter.mono`, `PadicInt.mahlerSeries_apply`, `HahnSeries.SummableFamily.coe_powers`, `ValuativeRel.pow_vle_pow`, `Nat.card_units_zmod_lt_sub_one`, `nhds_smul₀`, `HasFDerivAt.isBigOTVS_sub`, `HasDerivWithinAt.fun_pow'`, `Polynomial.roots_X_pow_char_pow_sub_C_pow`, `LieModuleHom.coe_smul`, `IntermediateField.linearDisjoint_comm`, `Commute.geom_sum₂_mul_add`, `Module.Dual.extendRCLike_apply`, `PowerSeries.IsWeierstrassDivision.isUnit_of_map_ne_zero`, `isPrimePow_iff_pow_succ`, `HasCompactSupport.hasDerivAt_convolution_right`, `WeierstrassCurve.Jacobian.addY_smul`, `InnerProductSpace.isSymmetricProjection_rankOne_self`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe`, `Submodule.annihilator_mul`, `min_pow_dvd_add`, `IsCoprime.isUnit_of_dvd'`, `Localization.map_isUnit_of_le`, `Matrix.isNilpotent_toLin'_iff`, `HasFTaylorSeriesUpToOn.eventually_hasFDerivAt`, `Finset.affineCombination_eq_linear_combination`, `HasDerivWithinAt.const_add`, `SameRay.pos_smul_left`, `Coalgebra.TensorProduct.lid_tmul`, `HahnSeries.SummableFamily.co_support_zero`, `IsRelPrime.of_mul_add_right_left`, `MvPolynomial.degreesLE_nsmul`, `ENNReal.pow_lt_top`, `sq_add_mul_sq_mul_sq_add_mul_sq`, `Module.Basis.constrL_apply`, `complEDS₂_three`, `Module.AEval'.of_symm_X_smul`, `fourierIntegral_gaussian_pi`, `MeromorphicOn.divisor_fun_pow`, `differentiableWithinAt_pow`, `TensorAlgebra.equivFreeAlgebra_symm_ι`, `Commute.isNilpotent_sum`, `homTensorHomEquiv_apply`, `QuadraticMap.associated_apply`, `LieModule.mem_genWeightSpace`, `WeierstrassCurve.Jacobian.eval_polynomialX`, `NonUnitalSubalgebra.iSupLift_comp_inclusion`, `Polynomial.squarefree_cyclotomic`, `iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow`, `ExteriorAlgebra.GradedAlgebra.ι_sq_zero`, `ModuleFilterBasis.smul_right`, `inv_pow_lt_inv_pow_of_lt`, `MeasureTheory.ConvolutionExistsAt.integrable_swap`, `isPowMul_spectralNorm`, `NormedSpace.expSeries_sum_eq`, `DifferentiableWithinAt.fun_pow`, `DirectSum.coe_of_mul_apply_add`, `CFC.rpow_neg`, `NumberField.Units.map_complexEmbedding_torsion`, `norm_inner_eq_norm_iff`, `TensorProduct.mk_apply`, `Complex.tendsto_pow_exp_of_isLittleO_sub_add_div`, `IsLocalizedModule.finsetIntegerMultiple_image`, `Real.circleAverage_eq_circleIntegral`, `HasFiniteFPowerSeriesOnBall.eq_partialSum`, `image_openSegment`, `Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left`, `WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF`, `hasDerivAt_tsum_of_isPreconnected`, `subset_balancedCore`, `Submodule.mul_mem_smul_iff`, `lt_self_pow₀`, `FormalMultilinearSeries.ofScalars_add`, `Polynomial.Chebyshev.S_sq_add_S_sq`, `Valuation.restrict_lt_iff_lt_embedding`, `ContMDiffCovariantDerivativeOn.finite_affine_combination`, `RCLike.im_ofReal_pow`, `FloorSemiring.tendsto_pow_div_factorial_atTop`, `Polynomial.splits_pow`, `NumberField.Units.span_basisOfIsMaxRank`, `GroupWithZero.zpow_zero'`, `Matrix.toLinearEquiv'_symm_apply`, `UpperHalfPlane.isPretransitiveGL2R`, `IntermediateField.equivOfEq_symm`, `LinearIsometryEquiv.smul_apply`, `CliffordAlgebra.evenOdd.gradedMonoid`, `WeierstrassCurve.Projective.eval_polynomialX`, `convexOn_iff_forall_pos`, `PowerSeries.constantCoeff_invUnitsSub`, `Algebra.TensorProduct.ext_ring_iff`, `inner_eq_norm_mul_iff_div`, `AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd_assoc`, `convex_Ico`, `Submodule.topologicalClosure_eq_self`, `Submodule.smul_subset_smul`, `SameRay.nonneg_smul_right`, `LinearMap.hasStrictDerivAt`, `WeierstrassCurve.Projective.Point.toAffineLift_of_Z_eq_zero`, `real_linearMap_map_smul_complex`, `Commute.pow_dvd_pow_of_sub_pow_eq_zero`, `LinearMap.BilinForm.mul_toMatrix'_mul`, `OnePoint.smul_some_eq_ite`, `NormalizationMonoid.normUnit_zero`, `ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul`, `RingHom.ker_isRadical_iff_reduced_of_surjective`, `Matrix.GeneralLinearGroup.continuous_det`, `LieIdeal.rootSpan_mem_invtRootSubmodule`, `AffineMap.hasDerivAt_lineMap`, `LinearMap.toMatrixAlgEquiv_id`, `exists_associated_pow_of_mul_eq_pow'`, `IsRelPrime.mul_add_right_left`, `DirectSum.ofPow`, `fderivWithin_continuousAlternatingMap_apply_const_apply`, `Polynomial.X_pow_sub_one_dvd_prod_cyclotomic`, `WeakDual.CharacterSpace.instNonUnitalAlgHomClass`, `Polynomial.prod_multiset_root_eq_finset_root`, `ratCast_smul_eq`, `IsRelPrime.neg_neg`, `Polynomial.iterate_derivative_derivative_mul_X_sq`, `LieAlgebra.Basis.coroot_eq_h'`, `WeierstrassCurve.Jacobian.nonsingularLift_iff`, `Associates.factorSetMem_eq_mem`, `MeasureTheory.integral_smul`, `Seminorm.convexOn`, `PowerSeries.mk_add_choose_mul_one_sub_pow_eq_one`, `Polynomial.Monic.irreducible_iff_lt_natDegree_lt`, `Associates.out_mk`, `Summable.tendsto_alternating_series_tsum`, `Complex.cos_eq_tsum'`, `mellinInv_eq_fourierIntegralInv`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_const`, `isStrictlyPositive_add`, `ContDiffAt.pow`, `Polynomial.ofFinsupp_pow`, `HasDerivWithinAt.fun_finset_prod`, `Monovary.pow_right₀`, `Convex.semilinear_image`, `Derivation.comp_aeval_eq`, `Algebra.Extension.Cotangent.val_smul'''`, `Polynomial.X_pow_sub_C_separable_iff`, `IsUnit.natCast_factorial_of_lt`, `sq_le_sq`, `HasDerivWithinAt.norm_sq`, `CStarModule.inner_smul_right_complex`, `IsPrimitiveRoot.coe_autToPow_apply`, `HasGradientAtFilter.hasDerivAtFilter'`, `IntermediateField.restrictRestrictAlgEquivMapHom_apply`, `instIsPushoutPolynomial_1`, `WeierstrassCurve.variableChange_b₈`, `NumberField.Units.logEmbeddingQuot_apply`, `Valued.extension_eq_zero_iff`, `OrderIso.mulLeft₀_apply`, `IsIntegral.isUnit`, `IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one`, `MonomialOrder.isUnit_leadingCoeff`, `IsPurelyInseparable.minpoly_eq`, `Seminorm.balanced_closedBall_zero`, `Int.cast_pow`, `Polynomial.scaleRoots_eval₂_mul_of_commute`, `InnerProductGeometry.norm_toLp_symm_crossProduct`, `Finset.pluennecke_ruzsa_inequality_nsmul_add`, `zmod_smul_mem`, `dualTensorHom_apply`, `Cubic.of_a_eq_zero`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `BilinForm.mul_toMatrix_mul`, `LinearEquiv.mem_fixedSubmodule_transvection_iff`, `NonUnitalStarSubalgebra.val_inclusion`, `WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero`, `NonUnitalAlgebra.range_id`, `Matrix.isUnits_det_units`, `ContMDiffAt.smul`, `Mathlib.Tactic.Module.NF.add_eq_eval₃`, `TrivSqZeroExt.map_comp_inlAlgHom`, `gal_X_pow_sub_C_isSolvable_aux`, `Polynomial.UniversalFactorizationRing.jacobian_resentation`, `intervalIntegral.integral_hasDerivWithinAt_left`, `instIsCyclicUnitsWithZero`, `GeneralSchauderBasis.expansion`, `QuadraticForm.tensorRId_symm_apply`, `pow_inv_comm₀`, `dvd_pow_pow_sub_self_of_dvd`, `ofNat_smul_eq_nsmul`, `HasFPowerSeriesOnBall.fderiv_eq`, `Finsupp.weight_single`, `Polynomial.degree_quadratic`, `Seminorm.coe_restrictScalars`, `strictConvex_closedBall`, `NumberField.Units.basisOfIsMaxRank_apply`, `Units.toLinearMap_mulLeftLinearEquiv`, `Module.Invertible.rTensorEquiv_apply_apply`, `NormedSpace.toNormSMulClass`, `lTensorHomEquivHomLTensor_toLinearMap`, `Finset.sum_smul_const_vsub_eq_vsub_affineCombination`, `Ideal.bot_mul`, `Quaternion.fst_imK_dualNumberEquiv_symm`, `midpoint_eq_smul_add`, `abs_pow_eq_one`, `AlgebraicGeometry.Proj.SpecMap_awayMap_awayι_assoc`, `IsCovariantDerivativeOn.smul_const`, `Matrix.ProjGenLinGroup.lift_mk`, `Asymptotics.IsLittleOTVS.zero`, `gaussSum_frob`, `Polynomial.monic_X_pow_sub_C`, `Subalgebra.centralizer_coe_image_includeRight_eq_center_tensorProduct`, `LinearMap.det_toLpLin`, `FractionalIdeal.finprod_heightOneSpectrum_factorization`, `Module.FinitePresentation.exists_lift_of_isLocalizedModule`, `HasDerivAtFilter.fun_add`, `WeierstrassCurve.Projective.isUnit_Y_of_Z_eq_zero`, `AffineMap.left_vsub_lineMap`, `IntermediateField.fieldRange_comp_val`, `Polynomial.rootsExpandEquivRoots_apply`, `NNReal.rpow_sub_natCast`, `NonUnitalClosedEmbeddingContinuousFunctionalCalculus.isClosedEmbedding`, `abs_neg_one_pow`, `PowerSeries.coeff_invOfUnit`, `SchwartzMap.smulLeftCLM_sum`, `Matrix.toLinearMap₂_compl₁₂`, `midpoint_sub_right`, `Set.Finite.absorbs_sInter`, `IsRealClosed.exists_eq_pow_of_nonneg`, `Submodule.smul_mem_span_smul_of_mem`, `sq_le`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_trans`, `LinearAlgebra.FreeProduct.ι_apply`, `WeierstrassCurve.Projective.negAddY_eq'`, `UpperHalfPlane.σ_mul`, `Units.map_neg`, `multiplicity_addValuation_apply`, `PadicInt.continuous_choose`, `Submodule.coe_span_smul`, `RingOfIntegers.isUnit_norm_of_isGalois`, `FiniteField.exists_forall_apply_eq_pow`, `CFC.sqrt_map_prod`, `AffineMap.hasDerivWithinAt_lineMap`, `Polynomial.rootMultiplicity_eq_natFind_of_ne_zero`, `Asymptotics.IsLittleOTVS.congr_left`, `IntermediateField.adjoin.powerBasis_gen`, `WeierstrassCurve.Affine.slope_of_Y_ne`, `Polynomial.isMonicOfDegree_two_iff`, `IsLocalization.Away.instMapRingHomPowersOfCoe`, `Asymptotics.SuperpolynomialDecay.param_pow_mul`, `Polynomial.C_mul_X_pow_eq_monomial`, `ContinuousLinearMap.fderiv_of_bilinear`, `TestFunction.coe_smul`, `SkewMonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `NumberField.Units.regulator_eq_det`, `AlgCat.hom_hom_associator`, `prime_pow_iff`, `Algebra.Extension.Hom.comp_id`, `cfcₙHom_integral`, `unitary.linearIsometryEquiv_coe_symm_apply`, `Ideal.map_mk_comap_factorPow`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `IntermediateField.equivOfEq_rfl`, `Seminorm.gaugeSeminorm_ball`, `ContinuousLinearMap.nnnorm_toSpanSingleton`, `ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos`, `emultiplicity_pow_prime_pow_sub_pow_prime_pow`, `ContinuousAlternatingMap.alternatizeUncurryFin_smul`, `AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst`, `IsLocalizedModule.iso_symm_comp`, `PresheafOfModules.map_smul`, `fderiv_mul_const'`, `tendsto_integral_exp_smul_cocompact`, `Complex.UnitDisc.coe_pow`, `QuadraticForm.tensorAssoc_toLinearEquiv`, `xInTermsOfW_eq`, `Matrix.linftyOpIsBoundedSMul`, `TensorProduct.AlgebraTensorModule.rTensor_tensor`, `Complex.hasDerivAt_Gammaℝ_one`, `NonUnitalAlgHom.subsingleton`, `Matrix.toLinearMapₛₗ₂'_symm`, `ContDiffMapSupportedIn.monoCLM_eq_of_scalars`, `WeierstrassCurve.c₄_of_isCharThreeJNeZeroNF`, `sub_pow_char_pow_of_commute`, `Module.Ray.linearEquiv_smul_eq_map`, `CStarAlgebra.isStrictlyPositive_iff_exists_isUnit_and_isSelfAdjoint_and_eq_mul_self`, `Asymptotics.isLittleOTVS_fun_neg_left`, `TestFunction.postcompCLM_apply`, `Submodule.mem_annihilator'`, `hasDerivAt_iff_tendsto_slope_left_right`, `BoundedContinuousFunction.instStarModule`, `IntermediateField.normal_iff_normalClosure_le`, `DualNumber.fst_eq_zero_iff_eps_dvd`, `SzemerediRegularity.mul_sq_le_sum_sq`, `AlgebraicGeometry.Proj.awayι_comp_map_assoc`, `Polynomial.isUnit_iff'`, `Finset.sq_sum_div_le_sum_sq_div`, `HasFTaylorSeriesUpToOn.hasFDerivWithinAt`, `TrivSqZeroExt.eq_smul_exp_of_ne_zero`, `WeierstrassCurve.preΨ'_even`, `Asymptotics.isBigOTVS_iff_smallSets`, `Derivation.leibniz_inv`, `Real.fourierIntegral_continuousLinearMap_apply`, `pow_left_inj₀`, `smul_left_inj`, `WeierstrassCurve.j_eq_zero_iff'`, `AdicCompletion.isAdicCauchy_iff`, `mem_perfectClosure_iff_pow_mem`, `LinearMap.iterateFrobenius_def`, `Associates.dvdNotUnit_of_lt`, `LinearMap.isAlt_iff_eq_neg_flip`, `multiplicity_neg`, `Mathlib.Tactic.FieldSimp.NF.pow_eq_eval`, `Submodule.adjoint_subtypeL`, `TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf`, `multiset_sum_pow_char_pow`, `Associates.lcm_mk_mk`, `TensorProduct.AlgebraTensorModule.rTensor_comp`, `NumberField.mixedEmbedding.fundamentalDomain_idealLattice`, `Mathlib.Tactic.LinearCombination.smul_lt_const`, `ConvexOn.sub`, `Polynomial.aevalTower_toAlgHom`, `HasDerivAtFilter.sub`, `midpoint_mem_openSegment`, `Ideal.disjoint_powers_iff_notMem`, `gauge_norm_smul`, `Associates.count_some`, `Associates.count_zero`, `MatrixEquivTensor.toFunBilinear_apply`, `PairReduction.card_le_logSizeRadius_le_pow_logSizeRadius`, `InnerProductSpace.Core.cauchy_schwarz_aux`, `Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul`, `ContinuousLinearMap.opNorm_mul_apply`, `gelfandStarTransform_symm_apply`, `JacobsonNoether.exists_pow_mem_center_of_inseparable`, `HahnSeries.isUnit_of_isUnit_leadingCoeff_AddUnitOrder`, `ContinuousLinearMap.norm_smulRightL`, `wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg`, `DivisorChain.element_of_chain_not_isUnit_of_index_ne_zero`, `TrivSqZeroExt.inl_mul_inr`, `mul_neg_geom_series`, `IsNilpotent.smul`, `HomogeneousLocalization.val_awayMap`, `riemannZeta_four`, `Asymptotics.IsBigOWith.const_smul_left`, `PowerSeries.commute_X_pow`, `LieSubalgebra.toEnd_mk`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1`, `LinearMap.piApply_apply`, `Ideal.mul_left_self_sup`, `unitSphereToUnits_apply_coe`, `deriv_fun_div`, `LinearMap.toBilin'Aux_toMatrixAux`, `WithAbs.tendsto_one_div_one_add_pow_nhds_one`, `PadicInt.coe_addChar_of_value_at_one`, `MeasureTheory.FiniteMeasure.self_eq_mass_smul_normalize`, `lipschitzGroup.conjAct_smul_ι_mem_range_ι`, `Complex.cos_two_mul`, `LieAlgebra.Basis.symm_baseSupp`, `PosSMulMono.nnrat_of_rat`, `Valued.tendsto_zero_pow_of_le_exp_neg_one`, `IsLocalRing.map_tensorProduct_mk_eq_top`, `sub_mem_pNilradical_iff_pow_expChar_pow_eq`, `HasFDerivWithinAt.fun_smul`, `Bialgebra.TensorProduct.comulAlgHom_def`, `AffineMap.lineMap_vsub_right`, `Localization.awayMap_surjective_iff`, `WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm`, `Module.End.intCast_def`, `Submodule.exists_isTorsionBy`, `OrderMonoidIso.withZeroUnits_symm_apply`, `Unitary.expUnitary_eq_mul_inv`, `MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring`, `RCLike.conj_mul`, `ZMod.dft_comp_unitMul`, `WeierstrassCurve.coe_map_Δ'`, `Commute.exists_add_pow_prime_pow_eq`, `strictAnti_smul_left`, `MeasureTheory.convolution_def`, `WeierstrassCurve.Affine.slope_of_Y_ne'`, `LinearMap.toMatrix₂_compl₂`, `Even.pow_of_ne_zero`, `Polynomial.trailingDegree_C_mul_X_pow`, `ContinuousMultilinearMap.curryLeft_norm`, `Seminorm.ball_zero_eq_preimage_ball`, `lp.norm_const_smul`, `finsuppTensorFinsuppLid_symm_single_smul`, `ContinuousLinearMap.compContinuousMultilinearMapL_apply`, `Polynomial.Splits.coeff_zero_eq_prod_roots_of_monic`, `Polynomial.X_pow_sub_one_eq_prod`, `Module.reflection_mul_reflection_pow_apply`, `eventually_cobounded_mapsTo`, `WeierstrassCurve.VariableChange.mul_def`, `DFinsupp.sum_mapRange_index.linearMap`, `HasDerivAtFilter.iterate`, `CategoryTheory.Abelian.Ext.mk₀_smul`, `InnerProductSpace.trace_rankOne`, `coe_toPrincipalIdeal`, `NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_smul_coe`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_of_ne_zero`, `AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap`, `MonoidWithZeroHom.inl_strictMono`, `Polynomial.degree_cubic_lt`, `mulRightLinearMap_eq_mulRight`, `rTensorHomEquivHomRTensor_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp`, `IntermediateField.continuousSMul`, `IsCyclotomicExtension.Rat.inertiaDegIn_of_not_dvd`, `NumberField.Units.coe_coe`, `minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow`, `MDifferentiableWithinAt.cle_arrowCongr`, `Balanced.add`, `Subgroup.commensurable_adjoinNegOne_self`, `sq_pos_of_neg`, `ConvexOn.openSegment_subset_strict_epigraph`, `CStarModule.inner_smul_left_complex`, `MvPowerSeries.LinearTopology.isTopologicallyNilpotent_iff_constantCoeff`, `HasFPowerSeriesWithinOnBall.prod`, `units_smul_eq_self_iff`, `MDifferentiableWithinAt.clm_precomp`, `Squarefree.gcd_right`, `WithZero.expEquiv_symm`, `spectrum.smul_mem_smul_iff`, `instFiniteMonoidHomUnits`, `smul_add_smul_lt_smul_add_smul`, `HasDerivAt.fun_add`, `SchwartzMap.fourierMultiplierCLM_sum`, `HasDerivAt.neg`, `Nat.Partition.hasProd_powerSeriesMk_card_countRestricted`, `ContMDiffVectorBundle.continuousLinearMap`, `DFinsupp.mapRange_smul`, `Matrix.toLpLin_symm_pow`, `Set.coe_unit`, `Module.End.HasEigenvalue.isNilpotent_of_isNilpotent`, `DenseRange.topologicalClosure_map_submodule`, `Prod.image_mk_segment_left`, `Polynomial.coeff_zero_eq_leadingCoeff_mul_prod_roots_of_splits`, `Matrix.isBoundedSMul`, `HasDerivAt.star`, `spinGroup.units_involute_act_eq_conjAct`, `MvPolynomial.scalarRTensor_apply_tmul`, `TensorProduct.prodLeft_tmul`, `Matrix.conjTranspose_inv_natCast_smul`, `IsGaloisGroup.quotient`, `ZMod.natCast_pow_eq_zero_of_le`, `WeierstrassCurve.Δ_of_char_three`, `PowerSeries.mk_one_pow_eq_mk_choose_add`, `groupCohomology.isMulCoboundary₁_of_isMulCocycle₁_of_aut_to_units`, `ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply`, `IsAdicComplete.of_lift`, `Polynomial.natTrailingDegree_mul_X_pow`, `IsLocalization.tensorProduct_isLocalizedModule`, `Polynomial.smeval_smul`, `Matrix.PosDef.isUnit`, `Convex.combo_self_interior_subset_interior`, `infEDist_smul₀`, `LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton'`, `MvPowerSeries.constantCoeff_invOfUnit`, `Bornology.IsVonNBounded.neg`, `ContinuousLinearMap.continuous_restrictScalars`, `UniqueDiffWithinAt.dense_tangentConeAt`, `hasStrictDerivAt_const_add_iff`, `TensorAlgebra.lift_symm_apply`, `WeierstrassCurve.Jacobian.dblZ_smul`, `RootPairing.EmbeddedG2.twoShortAddLongRoot_eq`, `smul_add_smul_le_smul_add_smul`, `AlgebraicGeometry.RingedSpace.basicOpen_pow`, `Finset.centerMass_insert`, `isBoundedBilinearMap_compMultilinear`, `Asymptotics.IsBigOTVS.fun_add`, `AnalyticAt.smul`, `hasLineDerivAt_smul_iff`, `VectorField.lieBracket_const_smul_left`, `SameRay.sameRay_nonneg_smul_left`, `Polynomial.IsPrimitive.irreducible_of_irreducible_map_of_injective`, `LinearIndependent.pair_smul_iff`, `Absorbs.inter`, `neg_convexOn_iff`, `SimpContFract.determinant`, `pow_le_pow_left₀`, `PrimeSpectrum.basicOpen_le_basicOpen_iff_algebraMap_isUnit`, `Valuation.subgroups_basis`, `ENNReal.smul_top`, `Complex.cos_add_sin_mul_I_pow`, `Submodule.mem_smul_iff_inv_mul_mem`, `ContinuousLinearMap.compL_apply`, `DirichletCharacter.mulEquiv_units`, `OrderMonoidIso.withZeroUnits_apply`, `ContinuousLinearMap.lsmul_flip_inj`, `SpecialLinearGroup.coe_inv`, `Polynomial.resultant_eq_prod_eval`, `Matrix.toLinearMapₛₗ₂'_aux_eq`, `ContinuousAlternatingMap.map_piecewise_smul`, `RingHom.IsIntegral.isLocalHom`, `mellinInv_eq_fourierInv`, `WeierstrassCurve.Jacobian.add_smul_of_not_equiv`, `units_smul_eq_neg_iff`, `Complex.cos_two_mul_eq_one_sub`, `HasFPowerSeriesOnBall.uniform_geometric_approx`, `TrivSqZeroExt.isNilpotent_inr`, `unitary.norm_sub_eq`, `Matrix.isUnit_fromBlocks_zero₂₁`, `Polynomial.isUnit_of_isUnit_leadingCoeff_of_isUnit_map`, `Module.End.algebraMap_isUnit_inv_apply_eq_iff'`, `NumberField.Units.instFiniteIntAdditiveUnitsRingOfIntegers`, `FiniteField.forall_pow_eq_one_iff`, `IsDedekindDomain.HeightOneSpectrum.irreducible`, `ContDiffMapSupportedIn.structureMapLM_eq_of_scalars`, `Algebra.TensorProduct.instSMulCommClassTensorProduct_1`, `sub_sq_comm`, `ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM`, `Real.fibRec_charPoly_eq`, `LinearMap.BilinForm.tensorDistribEquiv_toLinearMap`, `Matrix.charpoly_zero`, `Convex.strictConvex`, `IsSl2Triple.mem_toLieSubalgebra_iff`, `Matrix.pow_apply_nonneg`, `ModuleCat.MonoidalCategory.leftUnitor_hom_apply`, `HasDerivAtFilter.const_smul`, `Submodule.mem_torsionBySet_iff`, `spectrum.resolvent_eq`, `IntermediateField.relfinrank_dvd_finrank_bot`, `zpow_natCast_sub_natCast₀`, `Asymptotics.isBigOTVS_fun_neg_left`, `GradedAlgHom.includeRight_apply`, `Valued.tendsto_zero_pow_of_v_lt_one`, `LipschitzWith.pow_end`, `WeierstrassCurve.Projective.isUnit_addU_of_Y_ne`, `TensorProduct.directSumRight_comp_rTensor`, `card_units_lt`, `UniqueFactorizationMonoid.factors_rel_of_associated`, `fourier_gaussian_innerProductSpace'`, `DividedPowerAlgebra.natFactorial_mul_dp_eq`, `sub_smul`, `VectorFourier.fourierIntegral_const_smul`, `HasFPowerSeriesWithinAt.fderivWithin_eq`, `NumberField.Units.finrank_mul_regOfFamily_eq_det`, `TensorAlgebra.equivDirectSum_apply`, `ContDiffBump.convolution_tendsto_right`, `IsUnit.natCast_factorial_iff_of_charP`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff'`, `Matrix.linfty_opNNNorm_toMatrix`, `Mathlib.Tactic.Ring.zero_pow`, `inCoordinates_apply_eq₂`, `Asymptotics.isBigOTVS_fun_neg_right`, `IsNilpotent.not_isUnit`, `CompactlySupportedContinuousMap.instSMulCommClass`, `KaehlerDifferential.tensorKaehlerEquivBase_tmul`, `Real.fourier_real_eq`, `WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul`, `Matrix.isRepresentation.toEnd_represents`, `MeasureTheory.setToFun_smul`, `FormalMultilinearSeries.id_comp'`, `Seminorm.rescale_to_shell_zpow`, `mdifferentiableOn_localFrame_coeff`, `IsDedekindDomain.selmerGroup.monotone`, `FormalMultilinearSeries.ofScalars_sub`, `IsHausdorff.iInf_pow_smul`, `Valuation.mem_unitGroup_iff`, `Asymptotics.IsEquivalent.smul`, `LieModule.exists_genWeightSpace_le_ker_of_isNoetherian`, `Submonoid.isUnit_iff_of_ne_zero`, `Polynomial.support_binomial'`, `MeasureTheory.volume_sum_rpow_lt`, `MeromorphicOn.meromorphicTrailingCoeffAt_extract_zeros_poles`, `ContinuousMultilinearMap.range_toUniformOnFun`, `Subgroup.strictWidthInfty_eq_one_of_T_mem`, `PowerBasis.coe_basis`, `QuadraticMap.toQuadraticMap_associated`, `QuadraticForm.equivalent_weightedSumSquares_of_isAlgClosed`, `FormalMultilinearSeries.hasSum`, `hasDerivAt_abs_rpow`, `Convex.openSegment_interior_self_subset_interior`, `ContinuousLinearMap.IsPositive.conj_adjoint`, `ContinuousLinearMap.flip_apply`, `derivWithin_fun_div`, `IsLocalizedModule.fromLocalizedModule.inj`, `derivWithin_inv`, `Matrix.toEuclideanCLM_toLp`, `PiTensorProduct.liftAux.smul`, `Algebra.traceForm_toMatrix`, `Seminorm.smul_closedBall_zero`, `powMonoidWithZeroHom_apply`, `MvPolynomial.isUnit_iff_totalDegree_of_isReduced`, `AddMonoidAlgebra.isLocalHom_singleZeroRingHom`, `HasDerivAt.comp`, `Seminorm.balanced_ball_zero`, `Matrix.isUnit_nonsing_inv_det_iff`, `hasSum_fourier_series_L2`, `KaehlerDifferential.isLocalizedModule_map`, `MvPowerSeries.le_weightedOrder_pow`, `DualNumber.lift_inlAlgHom_eps`, `Valuation.restrict_le_iff_le_embedding`, `DifferentiableWithinAt.hasDerivWithinAt`, `isSMulRegular_submodule_iff_right_eq_zero_of_smul`, `IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure`, `NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis`, `Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNil`, `Associates.factors_zero`, `Polynomial.roots_pow`, `IntermediateField.adjoin_simple_adjoin_simple`, `Commute.add_pow_prime_pow_eq`, `mem_openSegment_of_ne_left_right`, `analyticOrderAt_centeredMonomial`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `Height.mulHeight_pow`, `HasFPowerSeriesOnBall.sum`, `Real.tendsto_integral_gaussian_smul'`, `Module.End.hasUnifEigenvalue_iff_mem_spectrum`, `HasFDerivAt.comp_hasDerivAt`, `Mathlib.Tactic.Module.NF.eq_cons_const`, `Real.hasFDerivAt_fourier`, `LinearOrder.convexOn_of_lt`, `val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe`, `cross_anticomm'`, `HasDerivWithinAt.mul`, `absorbs_iff_eventually_nhdsNE_zero`, `IsCompactOperator.antilipschitz_of_not_hasEigenvalue`, `UniqueFactorizationMonoid.factors_unique`, `spinGroup.conjAct_smul_ι_mem_range_ι`, `Matrix.toLin_scalar`, `Polynomial.resultant_C_right`, `WeierstrassCurve.Projective.negAddY_smul`, `Antitone.convex_lt`, `CategoryTheory.ShortComplex.Homotopy.smul_h₀`, `MulChar.equivToUnitHom_symm_coe`, `ENNReal.instIsScalarTowerNNReal`, `Units.instIsManifoldModelWithCornersSelf`, `IntermediateField.normal_iSup`, `Unitary.coe_symm_linearIsometryEquiv_apply`, `selfAdjoint.expUnitary_zero`, `fderiv_inverse`, `smul_sphere'`, `SchwartzMap.smulLeftCLM_fun_neg`, `ClosedSubmodule.mulI_sup`, `FractionalIdeal.count_ne_zero`, `deriv_pow`, `Algebra.SubmersivePresentation.jacobianRelations_spec`, `two_smul`, `IsRealClosed.exists_eq_pow_of_odd`, `toBilin'Aux_toMatrixAux`, `PiLp.instNormSMulClass`, `WeierstrassCurve.Projective.Point.toAffineLift_some`, `NumberField.det_basisOfFractionalIdeal_eq_absNorm`, `map_pow_le_pow`, `Pi.intrinsicStar_comul`, `AlgebraicGeometry.exists_eq_pow_mul_of_is_compact_of_quasi_separated_space_aux`, `MeasureTheory.FiniteMeasure.map_fst_prod`, `ContMDiffOn.clm_precomp`, `CharP.orderOf_eq_two_iff`, `CategoryTheory.ShortComplex.Homotopy.smul_h₃`, `add_pow_eq_mul_pow_add_pow_div_char_of_commute`, `DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap`, `contDiffOn_nat_iff_continuousOn_differentiableOn`, `FractionalIdeal.spanSingleton_pow`, `Module.Basis.isScalarTower_finsupp`, `IntermediateField.restrictRestrictAlgEquivMapHom_surjective`, `isPowMul_smoothingFun`, `Ideal.FG.mul`, `CategoryTheory.ShortComplex.cyclesMap_smul`, `TensorProduct.finsuppLeft_symm_apply_single`, `IsGaloisGroup.instSMulCommClassQuotientSubgroupSubtypeMemIntermediateField`, `Subalgebra.isScalarTower_right`, `IntermediateField.AdjoinSimple.norm_gen_eq_one`, `GaussianFourier.integrable_cexp_neg_mul_sum_add`, `HilbertBasis.hasSum_orthogonalProjection`, `ContinuousLinearMap.bilinearRestrictScalars_apply_apply`, `LieModule.coe_genWeightSpaceOf_zero`, `ContinuousLinearMap.isUnit_of_forall_le_norm_inner_map`, `Submodule.smul_coe_torsionBy`, `OrderMonoidIso.val_unitsWithZero_symm_apply`, `Fintype.not_linearIndependent_iffₛ`, `TensorAlgebra.equivFreeAlgebra_ι_apply`, `BilinForm.dotProduct_toMatrix_mulVec`, `InnerProductSpace.adjoint_rankOne`, `FormalMultilinearSeries.compAlongComposition_nnnorm`, `DihedralGroup.oddCommuteEquiv_symm_apply`, `UniqueFactorizationMonoid.normalizedFactors_pos`, `Homeomorph.smulOfNeZero_apply`, `LinearMap.BilinForm.tensorDistrib_tmul`, `map_nnrat_smul`, `DirectSum.coe_mul_of_apply_of_not_le`, `IntermediateField.range_val`, `monovaryOn_iff_forall_smul_nonneg`, `IntermediateField.instFiniteSubtypeMemBot`, `TrivSqZeroExt.mul_left_eq_one`, `Algebra.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot`, `MonoidWithZeroHom.valueMonoid_eq_valueGroup`, `instIsOpenUnitsOfContinuousInv₀OfT1Space`, `TensorProduct.AlgebraTensorModule.mk_apply`, `StrictConvexOn.translate_left`, `IntermediateField.isCyclotomicExtension_lcm_sup`, `analyticAt_smul`, `Seminorm.restrictScalars_ball`, `Filter.EventuallyEq.hasDerivAt_iff`, `LinearMap.trace_transpose'`, `fderiv_pow`, `LieAlgebra.Basis.baseSupp_apply_smul_f`, `InnerProductSpace.rankOne_eq_zero`, `Complex.exp_nsmul'`, `egauge_le_one`, `KaehlerDifferential.End_equiv_aux`, `DirectSum.decompose_symm_one`, `Real.fourierIntegral_convergent_iff'`, `WeierstrassCurve.Projective.polynomialZ_eq`, `fderivWithin_continuousMultilinear_apply_const_apply`, `LieModuleHom.smul_apply`, `Matrix.adjugate_adjugate`, `Projectivization.cross_mk_of_cross_ne_zero`, `Cardinal.mk_univ_quaternionAlgebra`, `Submodule.mem_annihilator`, `hasDerivAt_deriv_iff`, `Polynomial.disc_of_degree_eq_three`, `Unitization.splitMul_injective_of_clm_mul_injective`, `RCLike.mul_wInner_left`, `Seminorm.continuous`, `Matrix.toLpLin_one`, `PowerSeries.rescale_mk`, `Function.Antiperiodic.const_inv_smul₀`, `Unitary.instLocPathConnectedSpace`, `IsPurelyInseparable.HasExponent.has_exponent`, `AddChar.expect_apply_eq_zero_iff_ne_zero`, `StrictConvexOn.translate_right`, `CliffordAlgebra.ι_mul_ι_mul_ι`, `ContinuousAlternatingMap.norm_curryLeft`, `PowerSeries.HasSubst.X_pow`, `Polynomial.eval_monomial_one_add_sub`, `ContinuousMap.isUnit_iff_forall_isUnit`, `Algebra.Extension.instIsScalarTowerRing`, `Module.End.HasEigenvector.apply_eq_smul`, `Monovary.pow_left₀`, `WeierstrassCurve.Projective.negDblY_of_Z_eq_zero`, `tsum_pow_div_one_sub_eq_tsum_sigma`, `IntermediateField.linearDisjoint_iff'`, `MvPolynomial.totalDegree_pow`, `CFC.nnrpow_map_pi`, `UpperHalfPlane.volume_def`, `inner_map_polarization'`, `Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct`, `HasStrictDerivAt.clog_real`, `MvPolynomial.isUnit_iff`, `selfAdjoint.nnnorm_pow_two_pow`, `Polynomial.map_pow`, `Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal`, `hasDerivAt_of_hasDerivAt_of_ne'`, `gal_X_pow_sub_one_isSolvable`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `LieDerivation.ofGradingSum_of`, `InnerProductSpace.inner_right_rankOne_apply`, `Units.divp_add_divp`, `HilbertBasis.hasSum_repr`, `ContDiff.differentiable_iteratedFDeriv`, `PowerSeries.largeSchroderSeries_eq_one_add_X_mul_largeSchroderSeries_add_X_mul_largeSchroderSeries_sq`, `IsLocalization.Away.map_injective_iff`, `SchwartzMap.pairing_apply`, `CategoryTheory.Mat.instEssSurjMat_SingleObjMulOppositeEquivalenceSingleObjInverse`, `Module.Dual.transpose_apply`, `HasFDerivAt.pow`, `QuadraticMap.polar_smul_left_of_tower`, `NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def`, `ContinuousLinearMapWOT.smul_apply`, `MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt`, `spectrum.eventually_isUnit_resolvent`, `Asymptotics.isBigOTVS_iff_isBigO`, `IntermediateField.splits_iff_mem`, `Subgroup.negOne_mem_adjoinNegOne`, `LinearMap.isPosSemidef_iff_posSemidef_toMatrix`, `NNReal.rpow_add_natCast'`, `MonovaryOn.pow_right₀`, `Asymptotics.IsLittleO.smul`, `setIntegral_withDensity_eq_setIntegral_smul₀'`, `LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval`, `Finpartition.IsEquipartition.sum_nonUniforms_lt'`, `Module.Basis.det_unitsSMul`, `Bornology.isVonNBounded_sub_of_nonempty`, `WithLp.prod_edist_eq_of_L2`, `ENNReal.Tendsto.pow`, `AffineIsometryEquiv.coe_ofEq_apply`, `fderivWithin_continuousAlternatingMapCompContinuousLinearMap`, `subset_tangentConeAt_prod_right`, `TrivSqZeroExt.snd_exp`, `pow_succ_nonneg`, `WithSeminorms.isVonNBounded_iff_seminorm_bddAbove`, `MeasureTheory.condExpIndSMul_smul`, `fderivWithin_inv'`, `KaehlerDifferential.isScalarTower_of_tower`, `TannakaDuality.FiniteGroup.sumSMulInv_apply`, `TensorProduct.AlgebraTensorModule.rTensor_tmul`, `hasDerivAt_add_const_iff`, `not_disjoint_segment_convexHull_triple`, `hasDerivWithinAt_pow`, `exists_nat_pow_near_of_lt_one`, `Asymptotics.isLittleO_pow_id`, `MeasureTheory.Measure.hausdorffMeasure_smul₀`, `Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix`, `spinGroup.involute_act_ι_mem_range_ι`, `Padic.norm_p_pow`, `denselyOrdered_units_iff`, `isUnit_gcd_one_right`, `TensorProduct.prodLeft_symm_tmul`, `lcm_comm'`, `IntermediateField.LinearDisjoint.basisOfBasisLeft_apply`, `OrderIso.withZeroUnits_symm_apply`, `EisensteinSeries.G2_S_transform`, `Algebra.essFiniteType_cond_iff`, `isRadical_iff_squarefree_or_zero`, `geom_sum_lt`, `Monotone.ae_hasDerivAt`, `LaurentPolynomial.eval₂_T`, `MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left`, `star_natCast_smul`, `ContinuousLinearMap.fderivWithin_of_bilinear`, `AffineSubspace.isometryEquivMap.toAffineMap_eq`, `Valuation.nonempty_rankOne_iff_mulArchimedean`, `HasFPowerSeriesOnBall.compContinuousLinearMap`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff`, `TensorAlgebra.lift_ι_apply`, `lineMap_mem_openSegment`, `ZMod.cast_pow'`, `Polynomial.degreeLT.addLinearEquiv_apply_snd`, `PowerSeries.eval₂_eq_tsum`, `Fintype.sum_single_smul`, `Polynomial.natSepDegree_C_mul_X_sub_C_pow`, `unitSphereToUnits_injective`, `FiniteField.sum_subgroup_units_eq_zero`, `Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map`, `NNReal.sqrt_eq_iff_eq_sq`, `Complex.tendsto_one_add_div_pow_exp`, `MvPolynomial.coeff_X_pow`, `not_isNilpotent_one`, `QuadraticMap.associated_left_inverse`, `Algebra.normalizedTrace_intermediateField`, `gaugeSeminorm_ball_one`, `AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap`, `LinearMap.BilinForm.smul_right_of_tower`, `AddMonoidAlgebra.isLocalHom_algebraMap`, `TensorAlgebra.instModuleFree`, `ContinuousMultilinearMap.cons_smul`, `TensorProduct.tmul_eq_smul_one_tmul`, `DiffContOnCl.deriv_eq_smul_circleIntegral`, `Matrix.SpecialLinearGroup.mapGL_injective`, `EuclideanSpace.volume_closedBall_fin_two`, `ModularGroup.SL_to_GL_tower`, `LinearMap.BilinForm.tensorDistribEquiv_apply`, `ContinuousLinearMap.applyFaithfulSMul`, `DifferentiableOn.deriv_eq_smul_circleIntegral`, `ContDiffMapSupportedIn.uniformSpace_eq_iInf`, `NormedSpace.norm_expSeries_summable_of_mem_ball'`, `Filter.tendsto_const_mul_pow_atTop`, `WeierstrassCurve.Projective.smul_eq`, `spectrum.gelfand_formula`, `sq_le_one_iff₀`, `Matrix.piLp_ofLp_toEuclideanLin`, `Submodule.mem_span_singleton`, `iteratedFDerivWithin_smul_const_apply`, `tendsto_pow_atTop_nhds_zero_iff_norm_lt_one`, `cfcₙAux_id`, `Nonneg.val_unitsEquivPos_symm_apply_coe`, `Algebra.Generators.H1Cotangent.δAux_monomial`, `LinearMap.BilinForm.toMatrix_apply`, `UniqueFactorizationMonoid.prime_pow_coprime_prod_of_coprime_insert`, `WeierstrassCurve.Jacobian.dblY_of_Z_eq_zero`, `multiset_sum_pow_char`, `PiTensorProduct.liftIsometry_tprodL`, `Algebra.trace_isNilpotent_of_isNilpotent`, `ModularFormClass.one_mem_strictPeriods_SL2Z`, `Matrix.projVandermonde_apply_of_ne_zero`, `Submodule.eq_smul_of_le_smul_of_le_jacobson`, `Perfection.coeff_mapMonoidHom`, `VectorField.mpullback_smul_apply`, `IsNilpotent.charpoly_eq_X_pow_finrank`, `DualNumber.isNilpotent_iff_eps_dvd`, `OnePoint.map_smul`, `TrivSqZeroExt.map_comp_inrHom`, `RootPairing.reflectionPerm_coroot`, `NumberField.Units.complexEmbedding_injective`, `TensorProduct.map₂_apply_tmul`, `neg_one_pow_char`, `ValuationSubring.principalUnitGroup_le_principalUnitGroup`, `LieSubmodule.traceForm_eq_zero_of_isTrivial`, `PowerBasis.constr_pow_algebraMap`, `Polynomial.roots_C_mul_X_sub_C_of_IsUnit`, `Disjoint.exists_open_convexes`, `one_le_pow₀`, `UniformConvergenceCLM.continuousSMul`, `isStrictlyPositive_algebraMap`, `lieEquivMatrix'_apply`, `Matrix.det_sum_le`, `one_lt_pow_iff_of_nonneg`, `TensorAlgebra.rank_eq`, `Algebra.Generators.CotangentSpace.compEquiv_symm_zero`, `hasDerivWithinAt_one`, `BilinForm.toMatrix_toBilin`, `Associates.one_or_eq_of_le_of_prime`, `TensorProduct.AlgebraTensorModule.congr_eq`, `ConvexOn.smul_concaveOn'`, `MulChar.mulEquivToUnitHom_symm_apply`, `le_egauge_smul_left`, `sub_smul_slope_vadd`, `MvPolynomial.IsHomogeneous.pow`, `LieRinehartAlgebra.toIsScalarTower`, `HomogeneousLocalization.Away.map_comp`, `Algebra.Extension.instIsScalarTowerCotangent`, `Bundle.Trivialization.eventually_eq_localFrame_sum_coeff_smul`, `DualNumber.isMaximal_span_singleton_eps`, `HahnSeries.SummableFamily.smul_hsum`, `Matrix.ProjGenLinGroup.ker_mk`, `Seminorm.finset_sup_apply_lt`, `Polynomial.derivative_X_pow_succ`, `Polynomial.degree_X_pow_le`, `Convex.second_derivative_within_at_symmetric`, `geom_sum_inv`, `AffineSubspace.setOf_wOppSide_eq_image2`, `LieModule.weight_vector_multiplication`, `NumberField.Units.norm`, `pinGroup.mem_unitary`, `Commute.sub_sq`, `spinGroup.conjAct_smul_range_ι`, `Set.smul_mem_smul_set_iff₀`, `ConvexCone.isGenerating_bot`, `ModuleCat.Derivation.d_mul`, `isNormalClosure_normalClosure`, `VectorFourier.iteratedFDeriv_fourierIntegral`, `Unitization.starMap_injective`, `TestFunction.coe_ofSupportedInCLM`, `AlgHom.toNonUnitalAlgHom_eq_coe`, `MeasureTheory.Integrable.toL1_smul`, `SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux`, `ZMod.isUnit_inv`, `SpecialLinearGroup.congr_linearEquiv_coe_apply`, `LinearMap.BilinForm.IsRefl.smul`, `ContDiffBump.normed_convolution_eq_right`, `isClosedMap_pow`, `Odd.pow_neg_iff`, `Matrix.det_eq_sum_column_mul_submatrix_succAbove_succAbove_det`, `AdicCompletion.range_eval`, `InnerProductSpace.rankOne_eq_rankOne_iff_comm`, `realPart_add_I_smul_imaginaryPart`, `Complex.iteratedDeriv_odd_sin`, `ContinuousLinearMap.toContinuousAddMonoidHom_zero`, `Ideal.Quotient.smul_top`, `HasLineDerivAt.tendsto_slope_zero`, `Asymptotics.IsLittleOTVS.fst`, `Matrix.SpecialLinearGroup.mapGL_inj`, `SemilinearMapClass.map_smul_inv`, `HasDerivWithinAt.inner`, `LieDerivation.exp_map_apply`, `subset_tangentConeAt_prod_left`, `Submonoid.le_pointwise_smul_iff₀`, `WeierstrassCurve.variableChange_b₂`, `LocalizedModule.mk_cancel_common_left`, `Polynomial.resultant_dvd_leadingCoeff_pow`, `strictConvex_Ioo`, `IntermediateField.finrank_eq_one_iff`, `ContinuousLinearMap.holder_smul_left`, `ValuationRing.unique_irreducible`, `ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear`, `IntermediateField.lift_top`, `Perfection.instCharP`, `ContinuousLinearMap.precompR_apply`, `MonoidAlgebra.isLocalHom_singleOneRingHom`, `LaurentSeries.exists_ratFunc_val_lt`, `sameRay_smul_left_iff`, `RingHom.SurjectiveOnStalks.tensorProductMap`, `ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le`, `Valuation.RankOne.exists_val_lt`, `AddChar.forall_apply_eq_zero`, `NonUnitalAlgHom.toAlgHom_zero`, `integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable`, `LinearMap.minpoly_toMatrix'`, `IsPrimitiveRoot.autToPow_injective`, `LieSubalgebra.coe_ad_pow`, `Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat`, `LinearMap.BilinForm.IsPosSemidef.smul`, `FormalMultilinearSeries.iteratedFDerivSeries_eq_zero`, `Submodule.FG.restrictScalars_iff`, `Seminorm.comp_smul`, `DividedPowers.dpow_mul_right`, `LieRinehartRing.lie_smul_eq_mul'`, `absorbent_nhds_zero`, `ContMDiffAt.const_smul_section`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd'`, `WeierstrassCurve.Projective.add_of_Z_eq_zero_left`, `IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two`, `hasDerivAtFilter_one`, `ContinuousLinearMap.homeomorphOfUnit_apply`, `Real.fourierIntegral_iteratedDeriv`, `MvPolynomial.irreducible_of_forall_totalDegree_le`, `MonoidWithZeroHom.valueGroup_eq_range`, `MultilinearMap.dfinsuppFamily_smul`, `Derivation.leibniz'`, `Matrix.GeneralLinearGroup.IsParabolic.pow`, `Derivation.leibniz_zpow`, `iteratedDerivWithin_smul_const`, `ordinaryHypergeometricSeries_apply_eq'`, `Mathlib.Tactic.Module.NF.sub_eq_eval₃`, `MeasureTheory.hasFDerivAt_convolution_right_with_param`, `InnerProductSpace.exists_of_rankOne_eq_rankOne`, `fderiv_pow'`, `MeasureTheory.Lp.coeFn_smul`, `Submodule.restrictScalars_image_smul_eq`, `smoothSheafCommRing.isUnit_stalk_iff`, `Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd`, `ContMDiffSection.coe_smul`, `ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf`, `Algebra.Generators.Hom.comp_id`, `Finset.addConst_le_subConst_sq`, `AffineEquiv.coe_homothetyUnitsMulHom_apply_symm`, `DirichletCharacter.Even.toUnitHom_eval_neg_one`, `Asymptotics.IsLittleO.isLittleOTVS`, `LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem`, `hasDerivAt_ofNat`, `SchwartzMap.postcompCLM_apply`, `ArithmeticFunction.pow_carmichael`, `exists_isIntegral_leadingCoeff_pow_smul_sub_of_isIntegralElem_of_mul_mem_range`, `Polynomial.rootMultiplicity_eq_nat_find_of_nonzero`, `Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero`, `Asymptotics.IsLittleOTVS.neg_left`, `CommAlgCat.lift_unop_hom`, `EulerSine.sin_pi_mul_eq`, `Ideal.tensorCotangentHom_tmul`, `ContinuousLinearMap.toSpanSingleton_pow`, `iteratedFDerivWithin_eq_equiv_comp`, `AlgebraicGeometry.exists_eq_pow_mul_of_is_compact_of_quasi_separated_space_aux_aux`, `integral_mul_cexp_neg_mul_sq`, `Polynomial.derivative_X_sub_C_pow`, `LinearMap.toMatrix₂_comp`, `DifferentiableAt.isBigOTVS_sub`, `Polynomial.eval₂_reflect_mul_pow`, `Polynomial.cyclotomic_mul_prime_dvd_eq_pow`, `NumberField.mixedEmbedding.span_idealLatticeBasis`, `nhds_basis_balanced`, `LinearMap.restrictScalars_smul`, `Commute.add_pow`, `OreLocalization.subsingleton_iff`, `Module.Quotient.mk_smul_mk`, `IsRelPrime.neg_right`, `AlternatingMap.mkContinuousAlternating_norm_le`, `Equiv.mulRight₀_apply`, `HasCompactSupport.hasFDerivAt_convolution_right`, `prime_pow_succ_dvd_mul`, `Algebra.isNilpotent_trace_of_isNilpotent`, `isometry_cfcₙHom`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime`, `MulChar.pow_apply_coe`, `Valued.hasBasis_nhds_zero`, `Polynomial.IsMonicOfDegree.exists_natDegree_lt`, `SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv`, `ContDiffMapSupportedIn.structureMapCLM_zero_apply`, `PrimeSpectrum.mem_image_comap_basicOpen`, `VonNeumannAlgebra.centralizer_centralizer'`, `CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left`, `FormalMultilinearSeries.mkPiRing_coeff_eq`, `IntermediateField.exists_algHom_adjoin_of_splits_of_aeval`, `Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup`, `ZMod.card_units`, `differentialIdeal_le_iff`, `pow_eq_zero_iff'`, `IsLocalizedModule.exist_integer_multiples_of_finite`, `MvPolynomial.aeval_expand`, `mul_gaussSum_inv_eq_gaussSum`, `SchwartzMap.integral_bilinear_deriv_right_eq_neg_left`, `Associates.factors_subsingleton`, `RightPreLieAlgebra.toSMulCommClass`, `IntermediateField.LinearDisjoint.basisOfBasisRight_apply`, `ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap`, `abs_sq`, `ZMod.card_units_eq_totient`, `Unitization.starMap_id`, `IsLocalization.isUnit_piRingHom_algebraMap_comp_piEvalRingHom`, `Ideal.sup_pow_eq_top'`, `LinearMap.lsmul_flip_apply`, `TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply`, `IsModuleTopology.instProd`, `Filter.tendsto_neg_const_mul_pow_atTop`, `LinearIndependent.smul_left_injective`, `isLocalizedModule_iff`, `HahnEmbedding.Partial.exists_sub_mem_ball`, `AlgebraicIndependent.lift_reprField`, `WithZero.instNontrivialUnits`, `Matrix.SeparatingRight.toLinearMap₂'`, `Algebra.Extension.Hom.sub_one_tmul`, `ModularForm.levelOne_weight_zero_rank_one`, `Representation.asModuleEquiv_symm_map_smul`, `X_pow_sub_C_irreducible_iff_of_prime_pow`, `ContinuousLinearMap.coe_pow'`, `Asymptotics.IsLittleOTVS.pi`, `Field.span_map_pow_expChar_pow_eq_top_of_isSeparable`, `Unitary.spectrum_star_right_conjugate`, `Submodule.mem_span_iff_exists_finset_subset`, `WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero`, `UniqueFactorizationMonoid.factors_pos`, `AlgebraicGeometry.Proj.basicOpenIsoSpec_inv_ι`, `LinearEquiv.transvection.apply`, `DualNumber.lift_smul`, `InnerProductSpace.comp_rankOne`, `OrthonormalBasis.starProjection_eq_sum_rankOne`, `SpecialLinearGroup.det_eq_one`, `IntermediateField.isAlgebraic_adjoin`, `PowerSeries.constantCoeff_invOfUnit`, `Complex.I_pow_eq_pow_mod`, `SameRay.exists_pos_right`, `CongruenceSubgroup.strictWidthInfty_Gamma0`, `associated_zero_iff_eq_zero`, `Coalgebra.sum_counit_smul`, `HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum`, `WeierstrassCurve.Affine.nonsingular_iff_variableChange`, `NNReal.smulCommClass_left`, `sq_pos_of_pos`, `Polynomial.isRoot_of_unity_of_root_cyclotomic`, `iteratedDerivWithin_const_smul_field`, `Submodule.mem_iSup_iff_exists_dfinsupp`, `ENNReal.mulLeftOrderIso_toEquiv`, `Quaternion.imK_fst_dualNumberEquiv`, `pow_lt_pow_iff_right_of_lt_one₀`, `Polynomial.Monic.eq_X_pow_iff_natTrailingDegree_eq_natDegree`, `QuadraticForm.tensorRId_apply`, `LinearMap.exists_eq_smul_id_of_forall_notLinearIndependent`, `MvPolynomial.rTensor_apply_X_tmul`, `Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs`, `IsDiscreteValuationRing.addVal_def'`, `Bundle.Pretrivialization.continuousLinearMap.isLinear`, `wittPolynomial_one`, `Algebra.zariskisMainProperty_iff'`, `Perfection.mk_comp_teichmuller'`, `CFC.posPart_smul`, `TotallyBounded.isVonNBounded`, `UpperHalfPlane.hasStrictDerivAt_smul`, `instIsLiouvilleSubtypeMemIntermediateField`, `WeierstrassCurve.variableChange_b₆`, `smul_min_of_nonpos`, `WeierstrassCurve.Δ_of_isShortNF`, `IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two`, `IsPrimitiveRoot.prod_pow_sub_one_eq_order`, `Algebra.TensorProduct.lmulEquiv_eq_lidOfCompatibleSMul`, `Matrix.pow_apply_pos_iff_nonempty_path`, `Polynomial.sum_C_mul_X_pow_eq`, `LinearMap.pow_eq_aeval_mod_charpoly`, `IsRelPrime.mul_add_left_right`, `LinearMap.prodEquiv_symm_apply`, `AffineIsometryEquiv.ofTop_symm_apply_coe`, `IsNilpotent.isUnit_add_one`, `NonUnitalSubalgebra.inclusion_injective`, `MvPolynomial.eval_eq'`, `absorbs_iInter`, `ZMod.pow_card`, `Seminorm.comp_zero`, `selfAdjoint.continuous_expUnitary`, `LinearMap.tensorProductEnd_apply`, `ContinuousLinearMap.adjoint_inner_left`, `AddChar.sum_apply_eq_zero_iff_ne_zero`, `Bialgebra.TensorProduct.assoc_tmul`, `ContinuousLinearMap.hasStrictDerivAt_of_bilinear`, `lift_rank_lt_rank_dual'`, `Polynomial.not_isUnit_of_degree_pos`, `WeierstrassCurve.Jacobian.addX_of_Z_ne_zero`, `PointwiseConvergenceCLM.isInducing_inducingFn`, `Matrix.toLpLin_pow`, `KaehlerDifferential.tensorKaehlerEquiv_tmul`, `FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le`, `norm_exp_mul_sq_le`, `Module.ext_iff`, `WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero`, `ZMod.inv_coe_unit`, `isQuotientCoveringMap_npow`, `Nonneg.val_unitsHomeomorphPos_symm_apply_coe`, `Module.AEval'.X_pow_smul_of`, `Units.toEquiv_mulLeftLinearEquiv`, `Bornology.IsVonNBounded.image_multilinear`, `StarConvex.sub`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc`, `LieRinehartAlgebra.Hom.map_smul_apply'`, `WeierstrassCurve.Affine.addX_eq_addX_negY_sub`, `Algebra.Generators.H1Cotangent.δAux_toAlgHom`, `ENNReal.rpow_two`, `DirichletCharacter.toUnitHom_eq_char'`, `Polynomial.as_sum_support_C_mul_X_pow`, `WeierstrassCurve.Jacobian.addX_eq'`, `IsCyclic.val_inv_mulAutMulEquiv_apply`, `ContDiffMapSupportedIn.seminorm_monoLM_le`, `pow_four_le_pow_two_of_pow_two_le`, `Finsupp.linearCombination_single_index`, `Polynomial.toFinsupp_X_pow`, `SignType.pow_even`, `Monovary.smul_add_smul_le_smul_add_smul`, `CochainComplex.HomComplex.Cochain.shift_smul`, `ContinuousLinearMap.isBoundedBilinearMap`, `WeakFEPair.Λ₀_eq`, `nnnorm_pow`, `LinearMap.restrictScalars_self`, `ContinuousMultilinearMap.hasBasis_nhds_zero`, `IsSymmetricAlgebra.equiv_symm_comp`, `ball_normSeminorm`, `HasFPowerSeriesWithinOnBall.sum`, `LinearMap.BilinForm.separatingRight_toMatrix'_iff`, `LinearMap.extendTo𝕜_apply`, `Matrix.isUnit_toLin'_iff`, `IsPrimitiveRoot.sum_eq_zero_iff_forall_eq`, `NumberField.Units.fundSystem_mk`, `RingTheory.Sequence.isWeaklyRegular_singleton_iff`, `IsValuativeTopology.mem_nhds_iff'`, `HasDerivAt.sub`, `ENNReal.tendsto_pow_atTop_nhds_zero_of_lt_one`, `WeierstrassCurve.Affine.equation_iff_variableChange`, `Subalgebra.instCovariantClassHSMulLe`, `MeromorphicAt.fun_pow`, `Module.piEquiv_apply_apply`, `DirichletCharacter.changeLevel_toUnitHom`, `Associates.mem_factorSet_some`, `isSimpleModule_self_iff_isUnit`, `Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T`, `LinearMap.BilinForm.smul_left`, `Polynomial.degree_quadratic_le`, `Asymptotics.IsBigOWith.pow'`, `Polynomial.eq_quadratic_of_degree_le_two`, `egauge_pi`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right`, `compContinuousLinearMap_zero`, `Finsupp.lift_apply`, `UpperHalfPlane.denom_cocycle`, `preNormEDS'_odd`, `ConvexOn.convex_epigraph`, `HasLineDerivWithinAt.smul`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply`, `nonunits.isClosed`, `Complex.norm_exp_sub_sum_le_norm_mul_exp`, `RatFunc.Luroth.algEquiv_algebraMap`, `Submodule.dualCoannihilator_map_linearEquiv_flip`, `mdifferentiable_smul_const_section`, `HasStrictDerivAt.sum`, `Polynomial.adjSylvester_comp_sylveserMap`, `Finset.expect_eq_single_of_mem`, `FormalMultilinearSeries.apply_eq_pow_smul_coeff`, `Matrix.GeneralLinearGroup.coe_one`, `fderivWithin_continuousMultilinear_apply_const`, `not_isUnit_zero`, `FormalMultilinearSeries.le_radius_compContinuousLinearMap`, `Polynomial.rootsExpandPowToRoots_apply`, `Ideal.ResidueField.liftₐ_comp_toAlgHom`, `Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds`, `Differentiable.fderiv_two`, `continuousMultilinearCurryFin0_symm_apply`, `Polynomial.reflect_one`, `Polynomial.dvd_term_of_isRoot_of_dvd_terms`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `TensorAlgebra.toClifford_ι`, `RootPairing.GeckConstruction.trace_toEnd_eq_zero`, `instNontrivialUnitsOfDenselyOrdered`, `Asymptotics.isBigOTVS_congr`, `Submonoid.pointwise_smul_le_iff₀`, `MeasureTheory.integrable_withDensity_iff_integrable_smul₀`, `AdicCompletion.AdicCauchySequence.smul_apply`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec`, `Matrix.toLin'_mul`, `Differentiable.fun_pow`, `Seminorm.neg_mem_ball_zero`, `star_ratCast_smul`, `Submodule.mapsTo_smul_closure`, `isPurelyInseparable_iff_pow_mem`, `IsArtinian.range_smul_pow_stabilizes`, `pos_nilpotencyClass_iff`, `LieModule.lie_mem_maxGenEigenspace_toEnd`, `Unitary.conjStarAlgAut_ext_iff'`, `WithVal.strictMono_valueGroupOrderIso₀`, `Submodule.iSup_eq_range_dfinsupp_lsum`, `ModularGroup.lcRow0Extend_apply`, `LinearMap.isScalarTower_of_injective`, `Matrix.isSymmetric_toEuclideanLin_iff`, `Ideal.torsionOf_eq_span_pow_pOrder`, `LinearMap.isNilpotent_toMatrix_iff`, `Units.mulRightLinearEquiv_mul_apply`, `LinearMap.BilinForm.lieInvariant_iff`, `Polynomial.card_support_eq`, `cfcₙHom_predicate`, `ContinuousLinearEquiv.symm_smul_apply`, `Asymptotics.isBigOTVS_neg_right`, `LieModule.Cohomology.twoCochain_skew`, `PeriodPair.weierstrassPExcept_eq_tsum`, `Irreducible.addVal_pow`, `LieModule.IsTriangularizable.maxGenEigenspace_eq_top`, `TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply`, `Polynomial.reflect_monomial`, `VectorField.lieBracketWithin_smul_left`, `LinearMap.BilinForm.dotProduct_toMatrix_mulVec`, `hasDerivAt_update`, `VectorField.mlieBracketWithin_const_smul_left`, `ENNReal.rpow_mul_natCast`, `convex_halfSpace_ge`, `AffineMap.right_vsub_lineMap`, `Quaternion.re_fst_dualNumberEquiv`, `ContinuousAlternatingMap.ofSubsingletonLIE_apply`, `Module.End.rTensorAlgHom_apply_apply`, `zero_pow_eq_one₀`, `ZMod.unitsMap_comp`, `LieSubmodule.trace_eq_trace_restrict_of_le_idealizer`, `MeromorphicOn.fun_pow`, `ConvexOn.translate_left`, `FormalMultilinearSeries.compAlongComposition_bound`, `Polynomial.leadingCoeff_pow_X_add_C`, `NonUnitalSubalgebra.iSupLift_mk`, `continuousMultilinearCurryRightEquiv_symm_apply`, `OrthonormalBasis.equiv_apply`, `TemperedDistribution.fourierMultiplierCLM_apply`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le`, `SchwartzMap.lineDeriv_eq_fourierMultiplierCLM`, `convex_list_sum`, `ZMod.instSubsingletonUnits`, `UpperHalfPlane.coe_smul_of_det_pos`, `Algebra.isReduced_of_isGeometricallyReduced`, `Seminorm.bound_of_continuous`, `WeierstrassCurve.VariableChange.inv_def`, `spectrum.map_pow`, `FractionalIdeal.canonicalEquiv_mk0`, `AddMonoidAlgebra.le_inf_support_pow`, `Associates.factors_mk`, `PowerBasis.equivAdjoinSimple_aeval`, `HasStrictDerivAt.smul`, `Mathlib.Tactic.Ring.neg_mul`, `inner_eq_sum_norm_sq_div_four`, `AntivaryOn.sum_smul_le_sum_comp_perm_smul`, `Matrix.isUnit_submatrix_equiv`, `IsAlgClosed.exists_pow_nat_eq`, `fderiv_pow_ring`, `constFormalMultilinearSeries_apply_zero`, `NumberField.IsCMField.indexRealUnits_mul_eq`, `IntermediateField.isPurelyInseparable_tower_bot`, `ProbabilityTheory.complexMGF_gaussianReal`, `LinearMap.ker_toAddSubmonoid`, `le_separableClosure_iff`, `hasDerivAt_tsum`, `DifferentiableAt.fderiv_restrictScalars`, `starConvex_iff_forall_ne_pos`, `LieModule.isFaithful_iff`, `AnalyticAt.fun_smul`, `hasFTaylorSeriesUpToOn_top_iff'`, `add_pow_le`, `ContinuousLinearMap.lsmul_apply`, `Matrix.Module.smul_def`, `Representation.IntertwiningMap.smul_apply`, `nnnorm_pow_le`, `Commute.pow_dvd_add_pow_of_pow_eq_zero_left`, `AdicCompletion.transitionMap_comp_eval`, `NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion`, `IsMulTorsionFree.mk'`, `Associates.le_singleton_iff`, `IsTopologicallyNilpotent.exists_pow_mem_of_mem_nhds`, `LinearIsometryEquiv.conjStarAlgEquiv_trans`, `FormalMultilinearSeries.radius_smul_eq`, `selfAdjoint.unitarySelfAddISMul_coe`, `RootPairing.smul_coroot_eq_of_root_add_root_eq`, `AffineIsometryEquiv.ofEq_symm`, `Matrix.GeneralLinearGroup.val_mk'`, `Matrix.ofLp_toLpLin`, `traceForm_dualSubmodule_adjoin`, `Polynomial.associated_map_map`, `AlgebraicGeometry.Proj.pullbackAwayιIso_inv_snd`, `ContinuousMap.linearIsometryBoundedOfCompact_symm_apply`, `WittVector.mul_polyOfInterest_aux4`, `AlgebraicGeometry.Proj.pullbackAwayιIso_inv_fst_assoc`, `neg_one_pow_expChar`, `ContinuousLinearMap.bilinearComp_zero_right`, `Matrix.GeneralLinearGroup.map_comp`, `Polynomial.X_pow_sub_X_sub_one_irreducible`, `AddChar.sum_ne_zero_iff_eq_zero`, `DivisibleHull.instIsStrictOrderedModuleNNRat`, `ContinuousLinearMap.toContinuousAddMonoidHom_comp`, `Matrix.toMatrix₂Aux_toLinearMap₂'Aux`, `IsContMDiffRiemannianBundle.exists_contMDiff`, `Filter.tendsto_const_mul_pow_atTop_iff`, `ConcaveOn.comp_affineMap`, `Nat.Partition.summable_genFun_term`, `Matrix.toBilin'_symm`, `Unitization.isStarProjection_inr_iff`, `WithTop.pow_lt_top`, `LinearMap.charpoly_eq_X_pow_iff`, `ModuleCat.smulShortComplex_g`, `StarConvex.zero_smul`, `Function.support_smul`, `MeasureTheory.volume_sum_rpow_le`, `Nonneg.coe_pow`, `DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul`, `Matrix.vandermonde_apply`, `Submodule.restrictScalars_map_smul_eq`, `ENNReal.tendsto_pow_atTop_nhds_top_iff`, `PiTensorProduct.piTensorHomMap_tprod_tprod`, `BaireSpace.instBarrelledSpace`, `RatFunc.algEquivOfTranscendental_symm_gen`, `Unitization.starLift_range`, `Polynomial.leadingCoeff_X_pow_sub_C`, `MvPolynomial.coeff_sum_X_pow_of_fintype`, `ContinuousMap.unitsOfForallIsUnit_apply`, `LaurentPolynomial.mk'_eq`, `hasDerivAtFilter_add_const_iff`, `associatesNonZeroDivisorsEquiv_mk_mk`, `WeierstrassCurve.Projective.negAddY_of_X_eq'`, `MvPowerSeries.coeff_subst`, `WithVal.strictMono_valueGroupOrderIso₀_symm`, `MultilinearMap.map_update_smul_left`, `Matrix.UnitaryGroup.map_star_inv_eq_transpose`, `MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec`, `Matrix.exp_nsmul`, `ENNReal.tsum_geometric_add_one`, `AlgHom.IsArithFrobAt.apply_of_pow_eq_one`, `IsArtinianRing.isUnitSubmonoid_eq_of_mulOpposite`, `IsPrimitiveRoot.primitiveRootsPowEquiv_symm_apply_coe`, `hasDerivAt_jacobiTheta₂_fst`, `MvPolynomial.irreducible_of_disjoint_support`, `HomologicalComplex.units_smul_f_apply`, `uniform_continuous_npow_on_bounded`, `InnerProductSpace.rank_rankOne`, `ContMDiffOn.cle_arrowCongr`, `OrderIso.smulRight_symm_apply`, `HasDerivWithinAt.scomp_of_eq`, `pow_le_pow_iff_left₀`, `Algebra.Generators.localizationAway_σ`, `MDifferentiableAt.const_smul`, `Ideal.mul_sup`, `Complex.sinh_sq`, `MvPowerSeries.constantCoeff_smul`, `Squarefree.gcd_left`, `VertexOperator.ncoeff_apply`, `Valuation.IsUniformizer.val`, `Module.Dual.transpose_comp`, `ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply`, `IsSl2Triple.lie_h_e_smul`, `Unitary.mulLeft_trans_mulLeft`, `Algebra.Extension.CotangentSpace.map_toInfinitesimal_bijective`, `NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq`, `IsAzumaya.mulLeftRight_comp_congr`, `ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq`, `TrivSqZeroExt.inr_mul_inr`, `IsNilpotent.isUnit_one_add`, `AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι`, `LinearMap.BilinForm.isSymm_iff_flip`, `convex_openSegment`, `Convex.taylor_approx_two_segment`, `MDifferentiableOn.clm_prodMap`, `IntermediateField.LinearDisjoint.of_le_right`, `DiffContOnCl.const_smul`, `MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval`, `Polynomial.sup_aeval_range_eq_top_of_isCoprime`, `Complex.cpow_nat_mul`, `LinearMap.flip_bijective_iff₁`, `subset_balancedHull`, `ConvexCone.pointed_positive`, `VectorFourier.fourierIntegral_convergent_iff`, `DilationEquiv.mulRight_symm_apply`, `LinearMap.flip_bijective_iff₂`, `WithConv.matrixToLin'StarAlgEquiv_apply`, `sub_pow_char`, `WittVector.frobeniusPoly_zmod`, `Algebra.Extension.Cotangent.mk_eq_zero_iff`, `IsLocalizedModule.subsingleton_iff`, `ContinuousLinearMap.adjointAux_apply`, `QuadraticAlgebra.mem_unitary`, `RCLike.real_smul_eq_coe_smul`, `eq_separableClosure_iff`, `NumberField.mixedEmbedding.fundamentalCone.unit_smul_mem_iff_mem_torsion`, `Algebra.Generators.Hom.toExtensionHom_id`, `MulChar.exists_mulChar_orderOf_eq_card_units`, `Set.zero_mem_smul_set_iff`, `RingSeminorm.exists_index_pow_le`, `ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self`, `LinearMap.det_toLin'`, `DividedPowers.nilpotent_of_mem_dpIdeal`, `Submodule.linearEquiv_det_reflection`, `IsCompactOperator.hasEigenvalue_or_mem_resolventSet`, `WithZero.unitsWithZeroEquiv_symm_apply`, `fderivWithin_fun_mul'`, `CategoryTheory.Functor.map_smul`, `Polynomial.iterate_derivative_comp_one_sub_X`, `sup_eq_half_smul_add_add_abs_sub'`, `Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt`, `ValuationSubring.coe_unitGroupMulEquiv_apply`, `Finset.associated_lcm_prod`, `ProperCone.innerDual_singleton`, `PeriodPair.weierstrassPExcept_def`, `VonNeumannAlgebra.coe_mk`, `MulActionWithZero.smul_zero`, `TensorAlgebra.lift_comp_ι`, `cfcₙHom_comp`, `RingOfIntegers.norm_algebraMap`, `LieSubmodule.toEnd_comp_subtype_mem`, `Asymptotics.IsLittleO.smul_isBigO`, `MonotoneOn.convex_lt`, `HasFPowerSeriesWithinOnBall.sub`, `TemperedDistribution.fourierMultiplierCLM_const`, `IsDiscreteValuationRing.exists_irreducible`, `NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer`, `MvPowerSeries.HasSubst.const_coeff`, `MvPolynomial.tensorEquivSum_one_tmul_C`, `HasLineDerivAt.tendsto_slope_zero_left`, `Nat.Primes.prodNatEquiv_apply`, `Polynomial.coeff_scaleRoots`, `StrictConvexOn.add`, `Matrix.kroneckerMapBilinear_apply_apply`, `Subgroup.IsArithmetic.isFiniteRelIndexSL`, `Balanced.subset_smul`, `LinearMap.minpoly_dvd_charpoly`, `ConcaveOn.mul'`, `CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt`, `emultiplicity_pow_self`, `ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall`, `NumberField.Units.rank_modTorsion`, `Ideal.mul_mono`, `Ideal.pi_tensorProductMk_quotient_surjective`, `spectrum.pow_image_subset`, `derivWithin_const_smul_field`, `StrictConvexOn.map_sum_eq_iff`, `MvPolynomial.rTensor_apply_tmul`, `Antitone.convex_ge`, `OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply`, `hasFDerivAt_list_prod'`, `Convex.mem_extremePoints_iff_mem_diff_convexHull_diff`, `hasFDerivAt_integral_of_dominated_loc_of_lip'`, `WittVector.pow_dvd_ghostComponent_of_dvd_coeff`, `CliffordAlgebra.invOf_ι_mul_ι_mul_ι`, `Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular`, `Matrix.toLinearMapRight'_mul_apply`, `ConvexCone.coe_strictlyPositive`, `SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf`, `Asymptotics.isLittleO_const_smul_left`, `RKHS.kerFun_dense`, `VectorField.mpullback_const_smul`, `HahnSeries.SummableFamily.support_pow_subset_closure`, `Submodule.annihilator_smul`, `InnerProductSpace.rankOne_def`, `Submodule.jacobson_smul_lt_top`, `HasDerivAt.smul_const`, `ConvexOn.add_strictConvexOn`, `BilinForm.toMatrix_comp`, `Matrix.GeneralLinearGroup.map_inv`, `Polynomial.div_wf_lemma`, `smul_vsub_vadd_mem_affineSpan_pair`, `Matrix.det_kronecker`, `HasDerivAtFilter.sub_const`, `IsUnit.not_isNilpotent`, `arithGeom_same_eq_mul_div'`, `Finset.smul_finset_subset_iff₀`, `smul_nonneg_of_nonpos_of_nonpos`, `Polynomial.generalizedEisenstein`, `LieAlgebra.ad_nilpotent_of_nilpotent`, `OreLocalization.numeratorRingHom_apply`, `PadicInt.continuousAddCharEquiv_of_norm_mul_apply`, `ContinuousLinearMap.coe_flipₗᵢ'`, `MDifferentiableAt.clm_bundle_apply₂`, `AlgHom.mulLeftRight_apply`, `Mathlib.Tactic.CancelDenoms.pow_subst`, `ValuationSubring.unitGroup_injective`, `WeakFEPair.h_feq'`, `exists_pow_lt_of_lt_one`, `star_nnrat_smul`, `ENNReal.rpow_natCast_mul`, `Complex.isCauSeq_norm_exp`, `ContinuousLinearMap.adjointAux_inner_left`, `uniqueDiffWithinAt_iff`, `SchwartzMap.convolution_apply`, `Polynomial.prod_cyclotomic'_eq_X_pow_sub_one`, `Matrix.isParabolic_conj_iff`, `deriv_inv`, `IntermediateField.normal_iff_forall_fieldRange_le`, `Submodule.IsPrincipal.mem_iff_eq_smul_generator`, `MonomialOrder.Monic.pow`, `PointedCone.pointed_toConvexCone`, `fderivWithin_fderivWithin_eq_of_mem_nhds`, `LinearMap.lTensor_smul_action`, `transpose_dualTensorHom`, `Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom`, `Submodule.IsLattice.smul`, `Char.card_pow_card`, `ContinuousLinearMap.norm_smulRight_apply`, `ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv`, `Valuation.pow_Uniformizer_is_pow_generator`, `SModEq.pow_mul_of_le`, `one_add_mul_sub_le_pow`, `Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime`, `TensorProduct.AlgebraTensorModule.assoc_tmul`, `Set.zero_mem_smul_iff`, `WithVal.valueGroupEquiv_apply`, `contDiff_iff_continuous_differentiable`, `Asymptotics.IsLittleOTVS.exists_eventuallyLE_mul_ennreal`, `tendsto_pow_div_pow_atTop_zero`, `Finsupp.instFaithfulSMulOfNonempty`, `Ideal.exists_relNorm_eq_pow_of_isPrime`, `hasDerivAt_const`, `dslope_sub_smul_of_ne`, `TensorAlgebra.ι_range_disjoint_one`, `spectrum.units_conjugate`, `MvPolynomial.degreeOf_pow_eq`, `LieModule.rank_eq_natTrailingDegree`, `iteratedDerivWithin_comp_three`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right`, `Finset.centerMass_smul_left`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx'`, `Matrix.toLin_pow`, `Submodule.coe_tensorSpanEquivSpan_apply_tmul`, `Algebra.TensorProduct.lmul'_comp_map`, `LieSubmodule.mem_baseChange_iff`, `associatesNonZeroDivisorsEquiv_symm_mk_mk`, `Module.End.aeval_apply_of_hasEigenvector`, `Perfection.coeff_mk`, `DilationEquiv.mulLeft_symm_apply`, `AdicCompletion.instIsHausdorff`, `CategoryTheory.Abelian.Ext.smul_comp`, `QuadraticMap.associated_tmul`, `meromorphicOrderAt_pow_id_sub_const`, `PrincipalIdeals.normal`, `LinearMap.smulRight_eq_comp`, `PowerBasis.mem_span_pow'`, `IsAzumaya.bij`, `fderiv_mul'`, `LinearIsometryEquiv.conjStarAlgEquiv_ext_iff`, `IsGalois.normalAutEquivQuotient_apply`, `PowerSeries.coeff_invUnitsSub`, `PowerBasis.repr_gen_pow_isIntegral`, `spectrum.zero_mem_resolventSet_of_unit`, `Filter.EventuallyEq.ftaylorSeriesWithin`, `ProbabilityTheory.Kernel.HasSubgaussianMGF.add`, `UniformSpace.Completion.norm_toComplL`, `Seminorm.uniformContinuous_of_continuousAt_zero`, `Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_comp_inl`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow'`, `WithLp.prod_nnnorm_eq_of_L2`, `Associates.dvd_of_mem_factors'`, `IsRegular.smul_right_injective`, `fderivWithin_const_smul_of_field`, `Bornology.IsVonNBounded.tendsto_smallSets_nhds`, `Matrix.toLin_self`, `Units.continuousOn_zpow₀_spectrum`, `Polynomial.Separable.map_irreducible_of_isPurelyInseparable`, `LipschitzWith.edist_iterate_succ_le_geometric`, `ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply`, `KummerDedekind.emultiplicity_factors_map_eq_emultiplicity`, `ContinuousMap.toLp_def`, `Subgroup.mem_inv_pointwise_smul_iff₀`, `Units.instLieGroupModelWithCornersSelf`, `kroneckerTMulLinearEquiv_one`, `ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker`, `natCast_le_analyticOrderAt`, `isRadical_iff_squarefree_of_ne_zero`, `Complex.hasDerivAt_Gammaℂ_one`, `VectorField.lieBracket_fmul_left`, `Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem`, `Complex.hasSum_sin`, `NonUnitalAlgHom.injective_codRestrict`, `Module.Basis.SmithNormalForm.snf`, `Asymptotics.IsBigOTVS.snd`, `iteratedDerivWithin_fun_const_smul_field`, `LieDerivation.exp_apply`, `sup_eq_half_smul_add_add_abs_sub`, `RootPairing.pairing_neg_one_neg_four_iff`, `Valuation.RankOne.strictMono`, `SchwartzMap.integral_bilin_fourier_eq`, `geom_sum_Ico_mul`, `HasFDerivWithinAt.lim`, `pow_mul_apply_eq_pow_mul`, `KaehlerDifferential.ker_map`, `intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right`, `ConcaveOn.quasiconcaveOn`, `DifferentiableOn.clm_comp`, `ContDiffMapSupportedIn.monoCLM_apply`, `WeierstrassCurve.Jacobian.nonsingularLift_some`, `Algebra.TensorProduct.lift_comp_includeRight`, `ftaylorSeriesWithin_zero`, `WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis`, `ContinuousMultilinearMap.prodL_apply`, `Seminorm.add_comp`, `TensorProduct.AlgebraTensorModule.rightComm_tmul`, `isRelPrime_zero_right`, `segment_eq_image`, `AdicCompletion.coe_eval`, `IsPrimitiveRoot.geom_sum_isUnit'`, `HasStrictDerivAt.mul_const`, `IsCyclotomicExtension.isSplittingField_X_pow_sub_one`, `Matrix.conjTranspose_inv_ofNat_smul`, `Subgroup.HasDetOne.det_eq`, `set_smul_mem_nhds_zero_iff`, `instPosSMulStrictMono`, `LinearMap.separatingLeft_toMatrix₂'_iff`, `NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component`, `hasFTaylorSeriesUpToOn_succ_iff_right`, `StrictConcaveOn.convex_gt`, `ContinuousOn.clm_bundle_apply₂`, `EisensteinSeries.hasSum_e2Summand_symmetricIco`, `PowerSeries.X_pow_mul`, `ContinuousLinearMap.coe_flipMultilinearEquiv`, `Matrix.GeneralLinearGroup.fixpointPolynomial_eq_zero_iff`, `four_mul_le_sq_add`, `WeierstrassCurve.Projective.addX_of_Z_eq_zero_left`, `StrictConvex.add_left`, `LieAlgebra.trace_toEnd_eq_zero`, `Matrix.isUnit_det_J`, `Seminorm.bddAbove_iff`, `ValuativeRel.pow_vle_pow_of_one_vle`, `LaurentSeries.exists_Polynomial_intValuation_lt`, `DirectSum.coe_mul_apply`, `Convex.is_linear_preimage`, `Polynomial.card_support_binomial`, `IntermediateField.LinearDisjoint.finrank_right_eq_finrank`, `NonUnitalAlgHom.coe_Lmul`, `QuadraticForm.equivalent_weightedSumSquares`, `ContinuousLinearMap.toSpanSingleton_comp`, `Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C'`, `HomogeneousLocalization.awayMapₐ_apply`, `ContinuousMultilinearMap.norm_map_init_le`, `MulChar.restrict_ofUnitHom`, `AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_right`, `LinearEquiv.map_smulₛₗ`, `ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite`, `ModuleFilterBasis.smul_left'`, `pow_lt_one_iff_of_nonneg`, `TensorProduct.AlgebraTensorModule.assoc_symm_tmul`, `SchwartzMap.compCLMOfAntilipschitz_apply`, `spectrum.pow_nnnorm_pow_one_div_tendsto_nhds_spectralRadius`, `TensorProduct.algebraMap_gradedMul`, `Subalgebra.centralizer_coe_map_includeRight_eq_center_tensorProduct`, `IsLocalization.lift_mk'`, `FiniteField.algebraMap_norm_eq_pow`, `SchwartzMap.fourierInv_apply_eq`, `SchwartzMap.smulRightCLM_apply_apply`, `HasDerivWithinAt.fun_neg`, `MonomialOrder.leadingCoeff_pow_of_pow_leadingCoeff_ne_zero`, `NormedSpace.expSeries_summable'`, `hasEigenvector_toLin'_diagonal`, `geom_sum_Ico_mul_neg`, `WeierstrassCurve.Projective.dblX_smul`, `Commute.add_pow_dvd_pow_of_pow_eq_zero_left`, `LinearIsometryEquiv.conjStarAlgEquiv_refl`, `Matrix.GeneralLinearGroup.toLin'_apply`, `HasDerivAt.tendsto_slope_zero_left`, `IntermediateField.rank_adjoin_eq_one_iff`, `InnerProductSpace.laplacian_smul`, `HasDerivAt.complexToReal_fderiv'`, `IsBaseChange.lift_comp`, `LinearMap.separatingRight_iff_flip_ker_eq_bot`, `Valued.coe_valuation_eq_rankOne_hom_comp_valuation`, `MvPolynomial.mkDerivationₗ_monomial`, `MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin`, `geom_sum_eq`, `ModuleCat.MonoidalCategory.rightUnitor_hom_apply`, `starConvex_iff_openSegment_subset`, `ValuationSubring.mem_unitGroup_iff`, `mem_segment_iff_sameRay`, `IsStrictlyPositive.rpow`, `LinearMap.toMatrixAlgEquiv'_apply`, `LieAlgebra.ad_pow_lie`, `Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin`, `CongruenceSubgroup.isArithmetic_conj_SL2Z`, `ContinuousAlternatingMap.map_update_smul`, `binomialSeries_apply`, `eventually_singleton_add_smul_subset`, `SlashInvariantForm.slash_action_generators`, `SubMulAction.algebraMap_mem`, `val_cfcUnits`, `IsLocalization.Away.map_surjective_iff`, `Matrix.fin_two_smul_prod`, `LinearMap.IsSymmetric.toSelfAdjoint_apply`, `TensorProduct.finsuppScalarRight_smul`, `InnerProductSpace.volume_ball`, `Module.Ray.units_smul_of_pos`, `Polynomial.Monic.isUnit_iff`, `isCyclotomicExtension_iff_eq_adjoin`, `Antivary.sum_smul_lt_sum_comp_perm_smul_iff`, `isQuasiregular_iff_isUnit`, `isNilpotent_iff_eq_zero`, `mem_extremePoints_iff_forall_segment`, `LieModule.Cohomology.d₁₂_apply_coe_apply_apply`, `circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const`, `Asymptotics.IsBigOTVS.fun_symm`, `Orientation.map_eq_det_inv_smul`, `SchwartzMap.toTemperedDistributionCLM_apply_apply`, `EisensteinSeries.q_expansion_riemannZeta`, `AdicCompletion.factorₐ_evalₐ_one`, `IsCauSeq.geo_series`, `Seminorm.continuousAt_zero'`, `ContinuousLinearMap.coe_restrict_scalarsL'`, `Function.Antiperiodic.nat_mul_sub_eq`, `fderivWithin_fderivWithin_eq_of_eventuallyEq`, `IsRelPrime.mul_add_left_left`, `Unitization.inrNonUnitalStarAlgHom_apply`, `StandardSubspace.IsCyclic`, `IsSMulRegular.submodule`, `AlgebraicGeometry.Scheme.basicOpen_pow`, `Real.fourierIntegral_real_eq_integral_exp_smul`, `Matrix.toLinearMapₛₗ₂'_toMatrix'`, `ConvexCone.mem_map`, `CochainComplex.HomComplex.Cochain.leftUnshift_smul`, `LinearMap.toMatrix'_algebraMap`, `InnerProductSpace.laplacianWithin_smul`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2`, `StrongDual.polarSubmodule_eq_polar`, `HasDerivWithinAt.Ici_of_Ioi`, `TensorProduct.tensorQuotEquivQuotSMul_tmul_mk`, `Polynomial.separable_X_pow_sub_C'`, `StrictConvex.affinity`, `summable_prod_mul_pow`, `AlgCat.hom_hom_rightUnitor`, `Irreducible.isUnit_gcd_iff`, `algebraMap_smul`, `Commute.sq_sub_sq`, `finsuppTensorFinsupp_single`, `Real.deriv_fourierIntegral`, `DirectSum.decompose_mul_add_left`, `IsSelfAdjoint.nnnorm_mul_self`, `PiTensorProduct.liftEquiv_symm_apply`, `PiToModule.fromMatrix_apply_single_one`, `LocalizedModule.coe_map_eq`, `NonUnitalStarSubalgebra.toNonUnitalSubalgebra_subtype`, `NonUnitalSubalgebra.toSubring_subtype`, `Ideal.add_pow_mem_of_pow_mem_of_le`, `Polynomial.fact_irreducible_factor`, `IsCyclotomicExtension.splits_X_pow_sub_one`, `MonoidWithZeroHom.fst_comp_inl`, `Algebra.Extension.CotangentSpace.map_sub_map`, `TestFunction.coe_ofSupportedInLM`, `HasStrictDerivAt.cexp`, `QuadraticMap.associated_toQuadraticMap`, `Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable`, `IsDiscreteValuationRing.irreducible_iff_uniformizer`, `Polynomial.coeff_pow_mul_natDegree`, `extDerivWithin_fun_smul`, `Polynomial.valuation_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X`, `Unitization.starMap_inl`, `SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux`, `DilationEquiv.mulLeft_apply`, `inner_smul_real_right`, `Polynomial.leval_eq_smeval.linearMap`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum`, `quadratic_eq_zero_iff_discrim_eq_sq`, `Asymptotics.isLittleOTVS_fun_neg_right`, `FreeLieAlgebra.liftAux_map_add`, `IsPrimitiveRoot.geom_sum_isUnit`, `ftaylorSeries_fun_zero`, `SchauderBasis.proj_apply`, `IsLocalizedModule.mem_ker_iff`, `IsPrimitiveRoot.associated_sub_one_map_sub_one`, `SModEq.pow_add_one`, `ConvexCone.strictlyPositive_le_positive`, `Finset.smul_finset_symmDiff₀`, `AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec`, `ContDiffWithinAt.smul`, `HasDerivAt.add_const`, `NonUnitalStarSubalgebra.range_val`, `Matrix.IsUnit.kronecker`, `LieModule.isNilpotent_toEnd_of_isNilpotent₂`, `SzemerediRegularity.coe_stepBound`, `CovariantDerivative.affine_combination_toFun`, `Asymptotics.IsLittleOTVS.triangle`, `Seminorm.closedBall_finset_sup`, `Antivary.sum_smul_le_sum_smul_comp_perm`, `MeasureTheory.SignedMeasure.re_toComplexMeasure`, `Matrix.ProjGenLinGroup.mk_surjective`, `TemperedDistribution.smulLeftCLM_sub`, `fromTangentSpace_mfderiv_smul'`, `HasDerivAt.of_isLittleO`, `HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap`, `Module.reflection_mul_reflection_pow`, `ZMod.algebraOfModule.proof`, `Seminorm.uniformSpace_eq_of_hasBasis`, `eq_pos_convex_span_of_mem_convexHull`, `neg_one_pow_eq_pow_mod_two`, `BilinearForm.toMatrixAux_eq`, `ModularGroup.denom_S`, `QuadraticMap.two_nsmul_associated`, `SchwartzMap.postcompCLM_postcompCLM`, `NumberField.mixedEmbedding.covolume_idealLattice`, `TensorProduct.lid_tmul`, `PolynomialModule.isScalarTower'`, `IntermediateField.finrank_eq_fixingSubgroup_index`, `IsBoundedLinearMap.smul`, `Commute.cfcₙHom`, `Submodule.localized₀_smul`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `MvPolynomial.degrees_pow_le`, `DualNumber.exists_mul_left_or_mul_right`, `RootPairing.GeckConstruction.span_range_h'_eq_top`, `Perfection.coeff_quotientMulEquiv`, `iteratedDerivWithin_scomp_eq_sum_orderedFinpartition`, `Submodule.norm_subtypeL`, `SModEq.smul'`, `intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae`, `fourierCoeff.const_smul`, `QuasispectrumRestricts.continuous_nonUnitalStarAlgHom`, `Matrix.SeparatingLeft.toBilin`, `ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear`, `FreeNonUnitalNonAssocAlgebra.lift_symm_apply`, `BddBelow.smul_of_nonpos`, `WeierstrassCurve.Projective.addZ_smul`, `monovary_iff_forall_smul_nonneg`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_range_eq_top`, `Submodule.smul_le_smul`, `closure_openSegment`, `HasDerivAt.sub_const`, `LinearMap.toMatrixOrthonormal_symm_apply`, `biUnion_associatedPrimes_eq_zero_divisors`, `ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear`, `isLocalization_iff`, `SimpleGraph.IsSRGWith.matrix_eq`, `IsLocalizedModule.map_linearCombination`, `hasSum_cauchyPowerSeries_integral`, `Complex.pow_cpow_ofNat_inv`, `Convex.combo_interior_self_subset_interior`, `ContinuousLinearMap.aestronglyMeasurable_comp₂`, `Circle.coe_pow`, `CStarAlgebra.inv_le_inv_iff`, `Module.Flat.eqLocus_lTensor_eq`, `QuadraticForm.tmul_tensorAssoc_apply`, `FiniteField.algebraMap_norm_eq_prod_pow`, `NNReal.rpow_ofNat`, `MeasureTheory.Lp.instFourierSMul`, `WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero`, `SchwartzMap.smulLeftCLM_const`, `NumberField.house_pow_le`, `Polynomial.isUnit_of_coeff_isUnit_isNilpotent`, `smul_top_inf_eq_smul_of_isSMulRegular_on_quot`, `Polynomial.Bivariate.swap_monomial`, `LinearEquiv.piRing_symm_apply`, `Polynomial.not_isUnit_of_natDegree_pos_of_isReduced`, `MDifferentiableAt.smul_section`, `Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det`, `trace_eq_trace_adjoin`, `Ideal.Filtration.Stable.exists_pow_smul_eq_of_ge`, `Absorbs.iInter`, `ConvexCone.disjoint_hull_left_of_convex`, `Set.OrdConnected.convex`, `Polynomial.associated_of_dvd_of_natDegree_le`, `Asymptotics.IsBigOTVS.congr_left`, `Polynomial.eval_homogenize`, `Valued.isClosed_ball`, `OreLocalization.zsmul_eq_zsmul`, `dvd_pow_sub_one_of_dvd`, `NormedSpace.expSeries_div_hasSum_exp_of_mem_ball`, `ENNReal.mulRightOrderIso_apply`, `Matrix.exp_sum_of_commute`, `Mathlib.Tactic.LinearCombination.smul_le_const`, `strictConvexSpace_iff`, `Polynomial.cyclotomic_prime_pow_eq_geom_sum`, `Nat.Partition.powerSeriesMk_card_restricted_eq_tprod`, `Polynomial.smeval_X_pow_mul`, `IsUnit.sub_iff`, `AffineSubspace.toContinuousAffineMap_subtypeₐᵢ`, `QuadraticMap.associated_left_inverse'`, `HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt`, `Asymptotics.IsLittleOTVS.smul_left`, `ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff`, `MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt`, `WeierstrassCurve.c₄_of_isCharTwoJNeZeroNF`, `LieModule.Cohomology.mem_twoCochain_iff`, `Valuation.associated_of_isUniformizer`, `IsIntegral.pow`, `AdicCompletion.ofTensorProductEquivOfFiniteNoetherian_symm_of`, `hasDerivAt_of_tendstoUniformlyOn`, `Asymptotics.isLittleO_const_smul_right`, `NumberField.IsCMField.unitsMulComplexConjInv_apply_torsion`, `AddSubgroup.pointwise_smul_le_iff₀`, `Summable.alternating`, `NumberField.mixedEmbedding.fundamentalCone.exists_unitSMul_mem_integerSet`, `WeierstrassCurve.Jacobian.addY_of_Z_ne_zero`, `smul_right_injective`, `NonUnitalSubalgebra.iSupLift_inclusion`, `Unitization.starMap_inr`, `IsRelPrime.of_mul_add_right_right`, `Asymptotics.IsBigOTVS.proj`, `Set.Icc.coe_pow`, `AffineMap.hasDerivAt`, `Ideal.sup_mul_right_self`, `hasDerivWithinAt_congr_set`, `Mathlib.Tactic.Ring.natCast_mul`, `CFC.rpow_natCast`, `Even.pow_pos`, `StarConvex.linear_image`, `sameRay_smul_left_iff_of_ne`, `TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf`, `Algebra.Extension.Hom.toRingHom_algebraMap`, `WeakDual.CharacterSpace.coe_toNonUnitalAlgHom`, `smul_sphere`, `TensorProduct.lTensorHomToHomLTensor_apply`, `Valuation.restrict_lt_one_iff`, `IsLocalization.algebraMap_isUnit_iff`, `LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap`, `FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq`, `strictConvex_Iio`, `MeasureTheory.Measure.toSignedMeasure_smul`, `Polynomial.toTupleMvPolynomial_one_eq`, `star_inv_intCast_smul`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff_of_mem_mul`, `IsRelPrime.neg_left_iff`, `OnePoint.isBoundedAt_iff`, `HVertexOperator.compHahnSeries_smul`, `Matrix.nondegenerate_toBilin_iff`, `LinearEquiv.det_symm`, `Matrix.vandermonde_transpose_mul_vandermonde`, `HasStrictDerivAt.scomp_of_eq`, `Matrix.SpecialLinearGroup.isInducing_mapGL`, `DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap`, `HasStrictDerivAt.fun_finset_prod`, `ConvexCone.toPointedCone_top`, `fourierIntegral_eq_half_sub_half_period_translate`, `LinearMap.range_toContinuousLinearMap`, `IsAdicComplete.StrictMono.factorPow_comp_eq_of_factorPow_comp_succ_eq`, `Bornology.IsVonNBounded.of_sub_right`, `Submodule.traceDual_le_span_map_traceDual`, `linearDepOn_iff`, `PowerSeries.invOneSubPow_inv_zero_eq_one`, `Ideal.exact_mulQuot_quotOfMul`, `pow_le_pow_of_le_one`, `CharTwo.list_sum_sq`, `Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe`, `gaussSum_aux_of_mulShift`, `AdicCompletion.mk_smul_mk`, `TensorProduct.AlgebraTensorModule.cancelBaseChange_tmul`, `Matrix.inner_toEuclideanCLM`, `RingSeminorm.isBoundedUnder`, `Ideal.Cotangent.smul_eq_zero_of_mem`, `Polynomial.isUnit_C`, `meromorphicOrderAt_eq_int_iff`, `ContinuousLinearMap.norm_precompR_le`, `hasFDerivWithinAt_pow'`, `isUnit_of_mem_nonZeroDivisors`, `Matrix.toLin'_reindex`, `Ideal.mul_le`, `TrivSqZeroExt.isNilpotent_inl_iff`, `hasStrictDerivAt_finCons'`, `Submodule.mem_colon_iff_le`, `LocalizedModule.subsingleton_iff_ker_eq_top`, `LinearMap.transvection.apply`, `InfiniteGalois.proj_adjoin_singleton_val`, `contMDiffOn_baseSet_localFrame_coeff`, `PowerSeries.exp_pow_sum`, `Irreducible.exists_dvd_monic_irreducible_of_isIntegral`, `IsArtinianRing.isUnit_iff_mem_nonZeroDivisors`, `hasDerivWithinAt_taylorWithinEval_at_Icc`, `IntermediateField.lift_inf`, `Module.FinitePresentation.exists_free_localizedModule_powers`, `geom_sum_one`, `IsSemiprimaryRing.isNilpotent`, `WeierstrassCurve.C_Ψ₂Sq`, `ContinuousLinearMap.isBoundedLinearMap_comp_right`, `Ideal.span_singleton_eq_top`, `Complex.sq_nonneg_iff`, `quadraticChar_exists_neg_one'`, `NNReal.iSup_pow_of_ne_zero`, `Matrix.PosSemidef.toLinearMap₂'_zero_iff`, `Polynomial.natDegree_quadratic_le`, `WeierstrassCurve.Jacobian.dblY_of_Z_ne_zero`, `IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank`, `HasFDerivAt.iterate`, `Polynomial.rootSet_C_mul_X_pow`, `Polynomial.eq_quo_mul_pow_add_sum_rem_mul_pow`, `LinearMap.BilinForm.toMatrix'_compLeft`, `Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂`, `Matrix.toLinearMapₛₗ₂_apply`, `IsLocalization.Away.instAlgebraMapSubmonoidPowersOfCoeRingHomAlgebraMap`, `Polynomial.Monic.irreducible_of_irreducible_map`, `ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear`, `HasFPowerSeriesWithinAt.pi`, `IsLocalizedModule.fromLocalizedModule_mk`, `Module.Basis.isUnitSMul_apply`, `MvPolynomial.instIsLocalHomRingHomAlgebraMap`, `NormedSpace.isVonNBounded_iff'`, `LinearMap.mulRight_tmul`, `IsPrimitiveRoot.associated_map_sub_one_map_sub_one`, `VonNeumannAlgebra.mem_carrier`, `IsFractionRing.isUnit_map_of_injective`, `AlgebraicGeometry.RingedSpace.isUnit_of_isUnit_germ`, `TestFunction.lineDerivCLM_add`, `NonUnitalStarSubalgebra.inclusion_mk`, `Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence`, `hasStrictDerivAt_finCons`, `PiTensorProduct.liftEquiv_apply`, `LinearMap.smul_lTensor`, `Polynomial.iterate_derivative_X_pow_eq_natCast_mul`, `Asymptotics.IsLittleOTVS.trans_isBigOTVS`, `WfDvdMonoid.not_unit_iff_exists_factors_eq`, `WeakDual.isBounded_iff_isVonNBounded`, `HasDerivWithinAt.congr_of_eventuallyEq_of_mem`, `selfZPow_of_neg`, `Associates.prod_add`, `has_antideriv_at_fourier_neg`, `ModularForm.discriminant_eq_q_prod`, `Ideal.quotientMulEquivQuotientProd_snd`, `hasFTaylorSeriesUpTo_top_iff'`, `Set.neg_smul`, `AddMonoidAlgebra.cardinalMk_of_fintype`, `NormedSpace.expSeries_apply_eq`, `Associates.factors_le`, `fderivWithin_iteratedFDerivWithin`, `fromTangentSpace_mfderiv_smul_apply'`, `MvPolynomial.coeff_single_X_pow`, `Unitization.algebraMap_eq_inl`, `IsCyclotomicExtension.zeta_pow`, `complEDS'_odd`, `Convex.isLittleO_alternate_sum_square`, `Polynomial.le_rootMultiplicity_iff`, `SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply`, `HahnModule.instIsScalarTowerHahnSeries_1`, `rescale_to_shell`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `WithAbs.toAbs_pow`, `HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero`, `mem_openSegment_add_sub`, `ConvexOn.map_sum_le`, `MultilinearMap.mkContinuousLinear_norm_le`, `WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup`, `LinearIsometry.toSpanSingleton_apply`, `Submodule.mem_span_set`, `emultiplicity_zero`, `ContinuousMultilinearMap.piLinearEquiv_apply`, `AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_apply`, `WeierstrassCurve.Δ_of_isShortNF_of_char_three`, `GradedMonoid.smulCommClass_right`, `Subspace.flip_quotDualCoannihilatorToDual_bijective`, `Matrix.GeneralLinearGroup.continuous_upperRightHom`, `PiTensorProduct.liftAux_tprodCoeff`, `UpperHalfPlane.im_smul`, `Derivation.commutator_coe_linear_map`, `ContinuousLinearMap.deriv_of_bilinear`, `IsRelPrime.mul_add_right_right`, `balanced_neg`, `Orientation.areaForm'_apply`, `HasStrictDerivAt.comp_of_eq`, `mem_perfectClosure_iff`, `Units.mem_posSubgroup`, `segment_inter_eq_endpoint_of_linearIndependent_of_ne`, `pinGroup.conjAct_smul_ι_mem_range_ι`, `PadicInt.valuation_pow`, `openSegment_eq_image`, `IntermediateField.exists_finset_of_mem_supr''`, `Polynomial.isUnit_resultant_iff_isCoprime`, `IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable`, `Complex.sin_three_mul`, `ContinuousLinearMap.nnnorm_holder_apply_apply_le`, `TrivSqZeroExt.mul_inv_cancel`, `NonUnitalSubalgebraClass.subtype_injective`, `Submodule.set_smul_eq_map`, `Associated.of_mul_right`, `eqOn_iteratedDerivWithin_cotTerm_upperHalfPlaneSet`, `Polynomial.coe_smul`, `AffineMap.isCentralScalar`, `IntermediateField.exists_algHom_of_splits`, `IsPurelyInseparable.exponent_def'`, `ZMod.pow_card_sub_one_eq_one`, `Asymptotics.isTheta_const_smul_left`, `LinearMap.BilinForm.apply_sq_lt_iff_linearIndependent_of_symm`, `LieHom.toNonUnitalAlgHom_toFun`, `IsReduced.tensorProduct_of_flat_of_forall_fg`, `MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero`, `TensorProduct.isPushout`, `upperBounds_smul_of_neg`, `Distribution.mapCLM_apply`, `exists_nat_pow_near`, `MvPolynomial.map_expand_pow_char`, `isLocalHom_of_comp`, `FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1`, `OnePoint.IsZeroAt.smul_iff`, `Polynomial.support_C_mul_X_pow'`, `FormalMultilinearSeries.norm_compContinuousLinearMap_le`, `Module.End.isSemisimple_sub_algebraMap_iff`, `ENNReal.continuous_pow`, `CStarAlgebra.isStrictlyPositive_iff_eq_mul_star_self`, `PowerBasis.equivAdjoinSimple_gen`, `Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange`, `xInTermsOfW_aux`, `HasDerivAtFilter.star`, `Polynomial.aeval_apply_smul_mem_of_le_comap`, `isSMulRegular_of_isSMulRegular_on_submodule_on_quotient`, `Matrix.Nondegenerate.toBilin`, `IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_mk'`, `WeakDual.CharacterSpace.toAlgHom_apply`, `Ring.descPochhammer_smeval_add`, `DivisorChain.isPrimePow_of_has_chain`, `WeierstrassCurve.Jacobian.dblY_smul`, `SimpleGraph.adjMatrix_pow_apply_eq_card_walk`, `hasDerivAt_inv`, `TensorProduct.finsuppScalarRight_apply_tmul_apply`, `LinearMap.BilinForm.nondegenerate_toBilin'_iff_det_ne_zero`, `WeierstrassCurve.Jacobian.X_eq_iff`, `Derivation.coe_comp`, `DFinsupp.instPosSMulStrictMono`, `ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule`, `infEdist_smul₀`, `Field.Emb.Cardinal.equivSucc_coherence`, `ContinuousLinearMap.bilinear_hasTemperateGrowth`, `LinearMap.toMatrix'_apply`, `UpperHalfPlane.σ_neg`, `IsBoundedBilinearMap.isBoundedLinearMap_deriv`, `Polynomial.rootMultiplicity_mul_X_sub_C_pow`, `UpperHalfPlane.smulFDeriv_J_mul`, `Unitization.inrRangeEquiv_apply_coe_snd`, `Bornology.isVonNBounded_iff_smul_tendsto_zero`, `NumberField.mixedEmbedding.adjust_f`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin`, `Monotone.convex_lt`, `LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ`, `QuadraticForm.tmul_tensorComm_apply`, `Module.Basis.repr_symm_single`, `Matrix.toLpLin_toLp`, `RingEquiv.moduleEndSelf_apply`, `listProd_apply_eq_zero'`, `IsLocalization.Away.isUnit_of_dvd`, `NumberField.mixedEmbedding.fundamentalCone.quotIntNorm_apply`, `apply_eq_dotProduct_toMatrix₂_mulVec`, `Ideal.fst_comp_quotientMulEquivQuotientProd`, `Polynomial.degreeLT.addLinearEquiv_apply`, `PeriodPair.summable_weierstrassPSummand`, `MeasureTheory.MemLp.integrable_enorm_pow`, `Module.reflection_reflection_iterate`, `instIsFiniteRelIndexGeneralLinearGroupAdjoinNegOne`, `TrivSqZeroExt.inv_mul_cancel`, `OrderMonoidIso.unitsWithZero_apply`, `DividedPowers.RatAlgebra.dpow_apply`, `IsValuativeTopology.isClosed_closedBall`, `Submodule.smul_toAddSubmonoid`, `LinearMap.coe_toContinuousLinearMap`, `Ring.isUnit_iff_mul_inverse_cancel`, `ContinuousLinearMap.prodMapL_apply`, `Convex.smul`, `Ideal.span_mul_span'`, `ContinuousLinearMap.uncurryLeft_apply`, `HilbertBasis.dense_span`, `lp.instSMulCommClassSubtypePreLpMemAddSubgroup`, `Subsemiring.smul_mem_pointwise_smul_iff₀`, `LinearMap.BilinForm.separatingRight_toMatrix_iff`, `HasDerivAtFilter.scomp`, `Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero`, `RootPairing.prod_rootForm_smul_coroot_mem_range_domRestrict`, `AffineMap.lineMap_apply_module'`, `LinearMap.flip_apply`, `NNReal.rpow_two`, `map_equiv_traceDual`, `TensorProduct.finsuppLeft_apply`, `LieAlgebra.Basis.iSupIndep_rootSpace`, `IntermediateField.restrictScalars_adjoin_eq_sup`, `Submodule.orthogonal_orthogonal_eq_closure`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `MvPolynomial.irreducible_sumSMulX`, `LieRinehartRing.leibniz_smul_right'`, `AnalyticOn.const_smul`, `HomogeneousLocalization.awayMap_fromZeroRingHom`, `StrictConvex.linear_preimage`, `LinearMap.BilinForm.SeparatingLeft.toMatrix'`, `isSMulRegular_iff_torsionBy_eq_bot`, `AffineSubspace.convex`, `TensorProduct.mapBilinear_apply`, `Submodule.smul_starProjection_singleton`, `NumberField.Units.mem_torsion`, `PeriodPair.hasSumLocallyUniformly_weierstrassPExcept`, `finsuppTensorFinsuppRid_symm_single_smul`, `FiniteGaloisIntermediateField.isGalois`, `ContinuousLinearMap.map_smulₛₗ`, `contMDiff_smul`, `Polynomial.card_support_eq'`, `MeasureTheory.dist_convolution_le`, `smul_add_one_sub_smul`, `Polynomial.valuation_aeval_eq_valuation_X_pow_natDegree_of_one_lt_valuation_X`, `UpperHalfPlane.coe_smul`, `isUnit_iff_ne_zero`, `PointedCone.convex`, `WithZero.val_inv_expOrderIso_apply`, `ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap`, `UniformFun.continuousSMul_induced_of_range_bounded`, `ConvexOn.neg`, `Matrix.isRepresentation.toEnd_exists_mem_ideal`, `intervalIntegral.integral_hasStrictFDerivAt`, `ENNReal.pow_lt_pow_left_iff`, `with_gaugeSeminormFamily`, `Representation.asAlgebraHom_single_one`, `CStarAlgebra.linear_combination_nonneg`, `AlgebraicGeometry.exists_of_res_zero_of_qcqs_of_top`, `ThreeGPFree.smul_set₀`, `MeasureTheory.FiniteMeasure.instContinuousSMulNNReal`, `LinearMap.isUnit_det`, `fderivWithin_mul_const'`, `Submodule.mem_span_finset'`, `ContinuousAlternatingMap.curryLeft_compContinuousLinearMap`, `summable_powerSeries_of_norm_lt_one`, `NonUnitalStarSubalgebra.unitization_injective`, `intervalIntegral.integral_deriv_smul_eq_sub_of_hasDeriv_right`, `HasDerivWithinAt.fun_smul`, `map_rootsOfUnity_eq_pow_self`, `IsBilinearMap.toContinuousBilinearMap_apply`, `smul_left_injective`, `right_mem_openSegment_iff`, `val_unitsNonZeroDivisorsEquiv_symm_apply_coe`, `inv_natCast_smul_comm`, `NonUnitalSubalgebra.smul_mem'`, `ZMod.invDFT_def'`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_apply`, `TestFunction.lineDerivOp_eq_lineDerivCLM`, `ConvexCone.blunt_strictlyPositive`, `Module.toCentroidHom_apply_toFun`, `contMDiffOn_continuousLinearMapCoordChange`, `fderivWithin_smul`, `WeierstrassCurve.variableChange_def`, `NonUnitalStarSubalgebra.unitization_apply`, `Complex.log_sub_self_isBigO`, `IsAdic.hasBasis_nhds_zero`, `IsUnit.isStrictlyPositive_star_left_conjugate_iff`, `ContinuousMultilinearMap.curryFinFinset_apply_const`, `InnerProductSpace.enorm_rankOne`, `aestronglyMeasurable_smul_const_iff`, `IsPrimitiveRoot.minpoly_dvd_expand`, `WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero`, `absConvexHull_add_subset`, `MvPowerSeries.le_weightedOrder_smul`, `HasStrictDerivAt.fun_div`, `Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoin`, `CliffordAlgebra.foldr'_algebraMap`, `differentiableAt_complex_iff_differentiableAt_real`, `NNRat.instContinuousSMulOfIsScalarTowerOfRat`, `ContinuousMultilinearMap.compContinuousLinearMapLRight_apply`, `IsRegular.isSMulRegular`, `Convex.exists_forall_hasDerivWithinAt`, `Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator`, `cfcHom_real_eq_restrict`, `ConvexCone.IsGenerating.top_le_span`, `SpecialLinearGroup.det_coe`, `TensorProduct.AlgebraTensorModule.dualDistrib_apply`, `hasDerivWithinAt_taylor_coeff_within`, `IntermediateField.LinearDisjoint.finrank_left_eq_finrank`, `IntermediateField.Lifts.lt_iff`, `WeierstrassCurve.Projective.addMap_eq`, `spectrum.inv₀_mem_inv_iff`, `Seminorm.iSup_apply`, `HasFPowerSeriesAt.hasStrictDerivAt`, `Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul`, `SchwartzMap.fourierMultiplierCLM_apply`, `AnalyticOn.smul`, `Matrix.charpoly_one`, `ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self`, `Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable`, `LieSubalgebra.coe_incl'`, `Subfield.roots_X_pow_char_sub_X_bot`, `IntermediateField.extendScalars_le_iff`, `Algebra.TensorProduct.toLinearEquiv_tensorTensorTensorComm`, `Polynomial.aeval_eq_smeval`, `instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure`, `CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary`, `Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff`, `ClosedSubmodule.mem_symplComp_iff`, `LieModule.Cohomology.d₁₂_apply_apply_ofTrivial`, `WithSeminorms.tendsto_nhds`, `Polynomial.natSepDegree_X_pow_char_pow_sub_C`, `LaurentPolynomial.algebraMap_X_pow`, `hasFDerivAt_list_prod_finRange'`, `GradedTensorProduct.auxEquiv_mul`, `Ideal.isRadical_bot_iff`, `Polynomial.homogenize_X_pow`, `ContDiff.smulRight`, `Fintype.linearIndependent_iff'ₛ`, `QuadraticForm.tmul_tensorRId_apply`, `Complex.cosh_sq`, `PeriodPair.derivWeierstrassP_sq`, `not_linearIndependent_iffₒₛ`, `zero_isRadical_iff`, `ContinuousMultilinearMap.flipLinear_apply_apply`, `ZMod.AddAutEquivUnits_apply`, `Asymptotics.IsBigOTVS.trans_isLittleOTVS`, `ConvexOn.translate_right`, `PowerSeries.isWeierstrassFactorizationAt_iff`, `Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe`, `Matrix.inv_adjugate`, `SymmetricAlgebra.algebraMap_eq_zero_iff`, `Cardinal.power_nat_eq`, `MvPowerSeries.eval₂_eq_tsum`, `Algebra.PreSubmersivePresentation.isUnit_jacobian_of_cotangentRestrict_bijective`, `Submodule.lTensorOne'_tmul`, `RingTheory.Sequence.IsWeaklyRegular.regular_mod_prev`, `minpoly.isRadical`, `Representation.instIsScalarTowerMonoidAlgebraAsModule`, `ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall`, `Module.FinitePresentation.linearEquivMap_apply`, `NumberField.Units.regOfFamily_div_regulator`, `ContinuousMap.coe_smul'`, `NumberField.mixedEmbedding.fundamentalCone.exists_unit_smul_mem`, `CochainComplex.HomComplex.δ_smul`, `isReduced_localizationPreserves`, `LinearMap.hasDerivWithinAt`, `WithSeminorms.isOpen_iff_mem_balls`, `summable_choose_mul_geometric_of_norm_lt_one`, `CStarMatrix.toCLM_apply_single`, `hasSum_two_pi_I_cauchyPowerSeries_integral`, `Real.fourier_fderiv`, `convexHull_pair`, `Polynomial.IsPrimitive.Int.irreducible_iff_irreducible_map_cast`, `isCoprime_zero_left`, `Set.Subsingleton.strictConvex`, `pow_mulLeftLinearMap`, `rescale_to_shell_semi_normed`, `IsStrictlyPositive.smul`, `MvPolynomial.rTensorAlgHom_toLinearMap`, `Units.inv_pos`, `FormalMultilinearSeries.comp_id`, `WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero`, `QuadraticAlgebra.norm_natCast`, `range_cfcₙ_eq_range_cfcₙHom`, `fderivWithin_comp_smul_eq_fderivWithin_smul`, `ContinuousMap.nnnorm_smul_const`, `WeierstrassCurve.Jacobian.dblX_smul`, `Matrix.det_one_add_X_smul`, `smul_eq_zero_iff_left`, `IsLocalizedModule.exists_isLocalizedModule_powers_of_finitePresentation`, `wittStructureRat_rec`, `ContinuousMap.adjoin_id_eq_span_one_union`, `CategoryTheory.Linear.comp_units_smul`, `Ring.inverse_pow_mul_eq_iff_eq_mul`, `WeierstrassCurve.Projective.equation_of_Z_eq_zero`, `WittVector.mul_polyOfInterest_vars`, `MeasureTheory.condExp_smul`, `Valuation.cauchy_iff`, `AlgebraicGeometry.StructureSheaf.smul_const`, `TrivSqZeroExt.invOf_eq_inv`, `LinearMap.llcomp_apply'`, `WeierstrassCurve.Jacobian.Y_eq_of_Y_ne`, `Seminorm.const_isBounded`, `Splits.algebraicClosure`, `hasFTaylorSeriesUpTo_succ_nat_iff_right`, `PowerBasis.equivAdjoinSimple_symm_gen`, `LaurentSeries.of_powerSeries_localization`, `LieModule.exists_forall_pow_toEnd_eq_zero`, `Circle.instContinuousSMul`, `IsCovariantDerivativeOn.leibniz`, `Seminorm.preimage_metric_closedBall`, `FiniteField.isSplittingField_of_nat_card_eq`, `WeierstrassCurve.Jacobian.addXYZ_smul`, `tangentConeAt_of_mem_nhds`, `SchwartzMap.compSubConstCLM_zero`, `geom_sum_mul`, `ContDiffMapSupportedIn.seminorm_top_le_iff`, `neg_concaveOn_iff`, `convexOn_of_convex_epigraph`, `eqOn_iteratedDeriv_cotTerm`, `FreeLieAlgebra.liftAux_map_mul`, `ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun`, `NonUnitalSubalgebra.instSMulCommClass`, `Unitization.starMap_surjective`, `Algebra.Extension.CotangentSpace.map_cotangentComplex`, `LocalizedModule.mk_cancel_common_right`, `VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip`, `RCLike.wInner_smul_right`, `IntermediateField.coe_val`, `Complex.restrictScalars_one_smulRight`, `LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem`, `Ideal.pow_le_self`, `QuotSMulTop.equivQuotTensor_naturality`, `LinearMap.smulRightₗ_apply`, `IsPrimitiveRoot.minpoly_dvd_mod_p`, `LinearMap.IsNonneg.smul`, `IsModuleTopology.isoₛₗ`, `Submodule.rTensorOne'_tmul`, `JacobsonNoether.exist_pow_eq_zero_of_le`, `ClosedSubmodule.iInf_orthogonal`, `WeierstrassCurve.Jacobian.negDblY_of_Z_eq_zero`, `WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne`, `IsValuativeTopology.mem_nhds_zero_iff`, `Asymptotics.isLittleOTVS_iff_smallSets`, `normalize_apply`, `IsCyclotomicExtension.Rat.mem_zpowers_galEquivZMod_of_mem_stabilizer`, `Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero`, `hasDerivAt_fourier_neg`, `ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors`, `nhds_hasBasis_absConvex`, `smul_add_smul_lt_smul_add_smul'`, `MeasureTheory.smul_extend`, `Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub`, `LinearMap.toMatrix'_symm`, `Module.End.IsSemisimple.aeval`, `HahnEmbedding.Partial.eval_smul`, `HasDerivAt.clm_comp`, `isReduced_iff_pow_one_lt`, `WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_left`, `PowerSeries.invUnitsSub_mul_sub`, `HasFPowerSeriesOnBall.neg`, `VectorFourier.fderiv_fourierIntegral`, `iteratedDerivWithin_scomp_three`, `ProperCone.dual_singleton`, `Algebra.Extension.cotangentComplexBaseChange_eq_lTensor_cotangentComplex`, `PowerSeries.X_irreducible`, `ContinuousLinearMap.uncurryBilinear_apply`, `exists_root_adjoin_eq_top_of_isCyclic`, `LinearMap.IsSymmetric.isSymmetric_smul_iff`, `CStarAlgebra.isStrictlyPositive_iff_exists_isStrictlyPositive_and_eq_mul_self`, `NonUnitalStarSubalgebraClass.coe_subtype`, `HomogeneousLocalization.Away.span_mk_prod_pow_eq_top`, `Matrix.isStrictlyPositive_iff_posDef`, `AdicCompletion.of_bijective_iff`, `range_cfcₙHom_le`, `groupCohomology.norm_ofAlgebraAutOnUnits_eq`, `StrongDual.extendRCLikeₗ_apply`, `WeierstrassCurve.Affine.addPolynomial_eq`, `LinearMap.mapMatrix_smul`, `Submodule.projective_units`, `HasFDerivWithinAt.smul_const`, `AntivaryOn.card_smul_sum_le_sum_smul_sum`, `LieAlgebra.IsKilling.isSimple_iff_isIrreducible`, `Seminorm.sSup_empty`, `KaehlerDifferential.derivationQuotKerTotal_apply`, `InnerProductGeometry.norm_ofLp_crossProduct`, `AdicCompletion.transitionMap_comp_reduceModIdeal`, `MeasureTheory.integral_posConvolution`, `WittVector.exists_eq_pow_p_mul'`, `Asymptotics.isLittleOTVS_iff_tendsto_div`, `hasStrictDerivAt_abs`, `one_le_sq_iff_one_le_abs`, `TensorProduct.AlgebraTensorModule.uncurry_apply`, `Algebra.Extension.tensorCotangentSpace_tmul`, `MeasureTheory.LocallyIntegrableOn.smul_continuousOn`, `InnerProductSpace.volume_ball_of_dim_odd`, `AddChar.tendsto_eval_one_sub_pow`, `CStarAlgebra.inv_le_one`, `QuadraticAlgebra.norm_coe`, `Matrix.IsHermitian.cfcAux_apply`, `SchwartzMap.fourierInv_lineDerivOp_eq`, `VectorFourier.integral_fourierIntegral_swap`, `IsAbsoluteValue.abv_pow`, `Complex.cos_two_mul'`, `WeierstrassCurve.variableChange_a₂`, `Polynomial.pow_eq_one_of_mahlerMeasure_eq_one`, `AlternatingMap.domCoprod'_apply`, `Associates.factors_prime_pow`, `Matrix.UnitaryGroup.det_isUnit`, `Complex.tendsto_euler_sin_prod`, `Perfection.coeff_iterate_frobenius`, `IsArtinianRing.nonZeroDivisorsLeft_eq_isUnitSubmonoid`, `smoothingFun_le`, `exists_eq_pow_of_mul_eq_pow`, `monovary_iff_smul_rearrangement`, `Module.AEval.X_pow_smul_of`, `IsCyclotomicExtension.Rat.Three.eta_sq`, `Polynomial.degree_X_pow_sub_C`, `LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues`, `ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear`, `odd_sq_dvd_geom_sum₂_sub`, `NormedSpace.isVonNBounded_of_isBounded`, `AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule`, `IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero`, `iteratedFDeriv_eq_equiv_comp`, `sum_Ioo_inv_sq_le`, `NumberField.Units.coe_neg_one`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `Real.smul_iInf_of_nonpos`, `NNReal.rpow_natCast_mul`, `Mathlib.Tactic.Ring.atom_pf'`, `LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap`, `CFC.log_monotoneOn`, `MonoidAlgebra.isLocalHom_singleOneAlgHom`, `Monovary.sum_comp_perm_smul_lt_sum_smul_iff`, `Submodule.baseChange_eq_span`, `not_isRelPrime_zero_zero`, `IsLocalRing.isUnit_or_isUnit_of_isUnit_add`, `tensorKaehlerQuotKerSqEquiv_symm_tmul_D`, `eventually_norm_pow_le`, `WeierstrassCurve.variableChange_a₃`, `CliffordAlgebra.isUnit_ι_iff`, `Matrix.conjTranspose_ratCast_smul`, `Differentiable.continuousMultilinearMapCompContinuousLinearMap`, `Unitization.norm_eq_sup`, `WeierstrassCurve.Projective.addZ_eq`, `MonovaryOn.sum_smul_sum_le_card_smul_sum`, `Algebra.discr_of_matrix_mulVec`, `LinearEquiv.toSpanNonzeroSingleton_apply`, `Matrix.kroneckerTMulAlgEquiv_symm_apply`, `ContinuousMap.toLp_norm_eq_toLp_norm_coe`, `AddChar.sum_eq_zero_of_ne_one`, `continuousWithinAt_const_smul_iff₀`, `PowerSeries.monomial_pow`, `Submodule.mem_span_insert'`, `Matrix.ofLp_toEuclideanCLM`, `Ideal.coe_restrictScalars`, `hasFTaylorSeriesUpToOn_succ_nat_iff_right`, `Fourier.fourierIntegral_const_smul`, `HasDerivWithinAt.comp_hasDerivAt_of_eq`, `Nat.cast_le_pow_sub_div_sub`, `QuadraticAlgebra.isUnit_iff_norm_isUnit`, `MulChar.pow_apply'`, `summable_pow_div_add`, `hasDerivAtFilter_iff_isLittleO`, `WfDvdMonoid.exists_irreducible_factor`, `Absorbent.eventually_nhdsNE_zero`, `MvPolynomial.coeff_prod_X_pow`, `HasDerivAt.fun_const_smul`, `CStarAlgebra.inv_le_iff`, `NormedSpace.expSeries_div_summable`, `Irreducible.natSepDegree_eq_one_iff_of_monic`, `HasDerivAt.fun_sub`, `IsStrictlyPositive.nnrpow`, `NNReal.exists_pow_lt_of_lt_one`, `Polynomial.natDegree_X_pow_add_C`, `CStarMatrix.toCLM_apply_eq_sum`, `TensorProduct.AlgebraTensorModule.coe_lTensor`, `Set.Subsingleton.convex`, `Submodule.span_algebraMap_image_of_tower`, `HasStrictFDerivAt.restrictScalars`, `LinearMap.exact_smul_id_smul_top_mkQ`, `Ideal.mk_mem_cotangentIdeal`, `RingHom.isLocalHom_comp`, `Coalgebra.rTensor_counit_comp_comul`, `FiniteField.two_pow_card`, `MeasureTheory.Measure.ae_smul_measure_iff`, `balancedHull_add_subset`, `Projectivization.mk_eq_mk_iff`, `add_pow_two`, `ProbabilityTheory.gaussianReal_mul_const`, `Valuation.IsRankOneDiscrete.embedding_generator'`, `IntermediateField.finrank_eq_finrank_subalgebra`, `Polynomial.isUnit_iff_coeff_isUnit_isNilpotent`, `summable_descFactorial_mul_geometric_of_norm_lt_one`, `EulerSine.integral_sin_mul_sin_mul_cos_pow_eq`, `Matrix.GeneralLinearGroup.ext_iff`, `differentiableOn_pow`, `StarConvex.preimage_smul`, `Mathlib.Tactic.Ring.inv_mul`, `IsSelfAdjoint.norm_pow_two_pow`, `PowerSeries.eq_X_pow_mul_shift_add_trunc`, `Matrix.kroneckerTMulStarAlgEquiv_apply`, `QuadraticForm.sigNeg_weightedSumSquares`, `LieSubmodule.toEnd_restrict_eq_toEnd`, `tsum_choose_mul_geometric_of_norm_lt_one`, `HasFPowerSeriesWithinAt.sub`, `ClosedSubmodule.sup_orthogonal`, `ENNReal.mulLeftOrderIso_symm_apply`, `ordinaryHypergeometric_eq_tsum`, `ConvexOn.quasiconvexOn`, `strictConvex_Ici`, `hasDerivAt_exp_smul_const`, `IsUnit.det_zpow`, `AddMonoidAlgebra.instIsPushout`, `IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable'`, `Finset.sum_pow_of_commute`, `CStarAlgebra.le_inv_iff`, `HasDerivAtFilter.add_const`, `Meromorphic.fun_smul`, `Dilation.ratio_pow`, `FiniteField.sum_subgroup_pow_eq_zero`, `instFinitePresentationLocalizationLocalizedModule`, `Unitary.linearIsometryEquiv_coe_symm_apply`, `HasSum.smul`, `MvPolynomial.eval_eq`, `Asymptotics.isBigOTVS_neg_left`, `NormedSpace.expSeries_apply_eq_div`, `MDifferentiable.slash`, `TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_eq`, `Balanced.closure`, `AdicCompletion.ofPowSMul_injective`, `AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left`, `ZMod.sq_add_sq`, `MeasureTheory.eLpNormEssSup_smul_measure`, `NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm`, `NumberField.mixedEmbedding.logMap_eq_logEmbedding`, `ContDiffMapSupportedIn.locallyConvexSpace`, `hasFDerivWithinAt_comp_smul_smul_iff`, `WeierstrassCurve.ψ_even`, `MulChar.IsQuadratic.gaussSum_frob_iter`, `fourierCoeff_toLp`, `IsLocalizedModule.mk'_cancel'`, `IntermediateField.restrictRestrictAlgEquivMapHom_injective`, `AdicCompletion.isAdicComplete`, `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`, `Algebra.Generators.H1Cotangent.δAux_ofComp`, `exists_jacobiSum_eq_neg_one_add`, `Algebra.Extension.CotangentSpace.map_tmul_eq_tmul_map`, `Polynomial.coeff_pow_of_natDegree_le`, `Ideal.pow_right_mono`, `ContinuousMultilinearMap.smul_prod_smul`, `IsSepClosed.exists_pow_nat_eq`, `Polynomial.taylor_X_pow`, `IsAdicComplete.of_comp_lift`, `CategoryTheory.Functor.mapExactFunctor_smul`, `Nat.choose_lt_pow_div`, `DifferentiableAt.fun_pow`, `smul_lt_smul_iff_of_neg_left`, `HasStrictDerivAt.congr_deriv`, `ZMod.euler_criterion_units`, `ProbabilityTheory.hasDerivAt_complexMGF`, `TensorProduct.AlgebraTensorModule.homTensorHomMap_apply`, `instIsCyclicUnitsOfFinite`, `AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff`, `Polynomial.reverse_X_pow_mul`, `AlgebraicGeometry.LocallyRingedSpace.Hom.prop`, `RootPairing.reflectionPerm_root`, `DifferentiableWithinAt.isBigOTVS_sub`, `AddChar.card_eq`, `Associates.count_pow`, `ContMDiffWithinAt.smul`, `Matrix.isElliptic_conj_iff`, `LinearMap.isPositive_toContinuousLinearMap_iff`, `Matrix.range_toLin'`, `LinearOrder.concaveOn_of_lt`, `Complex.tsum_exp_neg_quadratic`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn'`, `Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff`, `LinearIsometryEquiv.toSpanUnitSingleton_apply`, `Asymptotics.IsBigOWith.smul`, `Asymptotics.IsLittleOTVS.congr'`, `ContinuousMapZero.nonUnitalStarAlgHom_precomp_apply`, `IsScalarTower.rat`, `LinearMap.prodMapLinear_apply`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd'`, `Convex.translate`, `LieModule.IsFaithful.injective_toEnd`, `PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent`, `AddChar.wInner_cWeight_eq_one_iff_eq`, `StrictConvexOn.map_sum_lt`, `map_inv_natCast_smul`, `iteratedDeriv_comp_const_smul`, `iteratedDerivWithin_one_div`, `norm_inner_eq_norm_tfae`, `Associates.reducible_notMem_factorSet`, `Submodule.map₂_span_singleton_eq_map_flip`, `LinearPMap.mkSpanSingleton'_apply`, `CategoryTheory.ShortComplex.smul_τ₃`, `Submonoid.mem_inv_pointwise_smul_iff₀`, `LinearMap.pi_apply_eq_sum_univ`, `DilationEquiv.smulTorsor_apply`, `FormalMultilinearSeries.changeOrigin_eval_of_finite`, `frobeniusEquiv_symm_pow`, `Module.sum_smul_eq_zero_of_isTrivialRelation`, `Ideal.iSup_mul`, `intervalIntegral.integral_smul`, `complEDS₂_four`, `ZMod.dft_apply`, `Seminorm.map_eq_zero_of_norm_eq_zero`, `PiTensorProduct.piTensorHomMap_tprod_eq_map`, `Algebra.TensorProduct.distribBaseChange_comp_includeLeftSubRight`, `CuspForm.coe_translate`, `Polynomial.IsUnitTrinomial.not_isUnit`, `WeierstrassCurve.Jacobian.negDblY_smul`, `Quaternion.fst_imJ_dualNumberEquiv_symm`, `fderivWithin_fun_pow`, `exists_nonneg_right_iff_sameRay`, `pow_le_pow_right₀`, `Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff`, `IsCyclotomicExtension.discr_prime_pow_ne_two`, `Polynomial.comp_C_mul_X_coeff`, `iteratedFDerivWithin_two_apply'`, `smul_algebraMap`, `HasDerivAt.const_smul`, `LinearMap.mul_toMatrix'`, `Polynomial.cyclotomic_prime_pow_mul_X_pow_sub_one`, `UniqueDiffWithinAt.smul_iff`, `MvPolynomial.isUnit_iff_eq_C_of_isReduced`, `NumberField.IsCMField.closure_realFundSystem_sup_torsion`, `FiniteField.coe_frobeniusAlgEquivOfAlgebraic_iterate`, `MvPowerSeries.HasEval.pow`, `Complex.conj_mul'`, `Convex.add_smul_mem`, `Balanced.interior`, `isRadical_iff_span_singleton`, `MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit`, `deriv.scomp`, `balancedCoreAux_balanced`, `HasStrictDerivAt.add`, `ContinuousLinearEquiv.symm_smul`, `continuousAt_const_smul_iff₀`, `AnalyticAt.analyticOrderAt_eq_natCast`, `Polynomial.resultant_X_sub_C_pow_left`, `TensorProduct.LieModule.coe_liftLie_eq_lift_coe`, `inr_comp_cfcₙHom_eq_cfcₙAux`, `Complex.canonicalFactor_def`, `Submodule.finite_quotient_smul`, `NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe`, `IntermediateField.LinearDisjoint.finrank_sup`, `NumberField.Units.instIsCyclicSubtypeUnitsRingOfIntegersMemSubgroupTorsion`, `MvPolynomial.monomial_add_single`, `IsBaseChange.pi`, `StarConvex.add_left`, `IsUnit.isNilpotent_unit_mul_of_commute_iff`, `AlgebraicGeometry.RingedSpace.isUnit_res_of_isUnit_germ`, `bernsteinPolynomial.variance`, `concaveOn_univ_piecewise_Ici_of_antitoneOn_Ici_monotoneOn_Iic`, `IsLocalizedModule.lift_comp_iso`, `WeierstrassCurve.Jacobian.addMap_of_Z_eq_zero_right`, `hasDerivAt_taylorWithinEval_succ`, `WeierstrassCurve.Projective.addZ_of_Z_eq_zero_right`, `IsMIntegralCurveAt.hasMFDerivAt`, `IsCyclotomicExtension.Rat.inertiaDeg_eq`, `pow_mulRightLinearMap`, `Convex.closure`, `Bornology.IsBounded.smul₀`, `MvPolynomial.le_coeffsIn_pow`, `Algebra.zariskisMainProperty_iff_exists_saturation_eq_top`, `MemHolder.smul`, `HVertexOperator.of_coeff_coeff`, `NNReal.rpow_add_natCast`, `WeierstrassCurve.variableChange_c₆`, `Ideal.Quotient.isUnit_mk_pow_iff_isUnit_mk`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `Module.Basis.mem_submodule_iff'`, `unitary.norm_argSelfAdjoint`, `skewAdjoint.negISMul_apply_coe`, `Submodule.smithNormalFormBotBasis_def`, `insert_endpoints_openSegment`, `Polynomial.toLaurent_X_pow`, `Perfection.coeffMonoidHom_eq_coeff`, `Ideal.Filtration.Stable.exists_pow_smul_eq`, `not_linearIndependent_iffₛ`, `MvPolynomial.IsWeightedHomogeneous.pow`, `DiffContOnCl.circleAverage_smul_div`, `MonomialOrder.degree_pow_le`, `ContinuousLinearMap.range_smulRight_apply`, `IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two`, `Complex.cosh_eq_tsum`, `IsLocalFrameOn.eventually_eq_sum_coeff_smul`, `groupCohomology.exists_div_of_norm_eq_one`, `Matrix.toLpLin_symm_id`, `Polynomial.eval_iterate_derivative_rootMultiplicity`, `lp.infty_coeFn_pow`, `OreLocalization.right_distrib`, `Complex.I_pow_four`, `Set.val_unitEquivUnitsInteger_apply_coe`, `AdicCompletion.smul_mk`, `NonUnitalStarSubalgebra.iSupLift_inclusion`, `Matrix.UnitaryGroup.inv_val`, `AddMonoidAlgebra.instIsPushout'`, `lp.infty_smulCommClass`, `Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub`, `unitary.spectrum_subset_circle`, `AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot`, `geom_sum_of_lt_one`, `IntermediateField.finrank_adjoin_eq_one_iff`, `TensorProduct.lid'_apply_tmul`, `Algebra.Norm.Transitivity.det_det_aux`, `HasSum.exists_hasSum_smul_of_apply_eq_zero`, `Polynomial.bernoulli_eq_sub_sum`, `AdicCompletion.exists_smodEq_pow_add_one_smul`, `KaehlerDifferential.instSMulCommClassTensorProduct_1`, `DirectSum.coe_of_mul_apply_of_not_le`, `Algebra.Extension.Cotangent.val_smul'`, `Finsupp.weight_single_index`, `quasispectrum.mem_of_not_quasiregular`, `DiscreteConvolution.ConvolutionExistsAt.smul_convolution`, `TensorProduct.map_smul_right`, `MvPolynomial.isNilpotent_iff`, `HVertexOperator.coeff_inj_iff`, `HasFPowerSeriesAt.fderiv_eq`, `CategoryTheory.endomorphism_simple_eq_smul_id`, `IntermediateField.normal_iff_forall_map_le'`, `Finset.sum_Ico_by_parts`, `Polynomial.leadingCoeff_pow'`, `spectrum.map_pow_of_nonempty`, `PowerSeries.isUnit_weierstrassUnit`, `Matrix.isPositive_toEuclideanLin_iff`, `HasDerivAtFilter.scomp_of_eq`, `ContinuousLinearMap.coe_restrictScalarsIsometry`, `MeasureTheory.Integrable.bdd_smul`, `Finsupp.linearCombination_apply`, `rank_eq_one_iff`, `Representation.IntertwiningMap.toLinearMap_smul`, `LocalizedModule.exists_subsingleton_away`, `Polynomial.comp_neg_X_leadingCoeff_eq`, `ContinuousLinearMap.memLp_of_bilin`, `TensorAlgebra.ofDirectSum_toDirectSum`, `HasFPowerSeriesOnBall.tendstoUniformlyOn`, `IntermediateField.normal_iff_forall_fieldRange_eq`, `MatrixModCat.mem_toModuleCatObj`, `HasDerivAt.scomp_hasDerivWithinAt_of_eq`, `FreeAlgebra.toTensor_ι`, `Perfection.teichmullerFun_sModEq`, `IsCyclotomicExtension.Rat.galEquivZMod_apply_of_pow_eq`, `GradedAlgHom.restrictScalars_coe_linearMap`, `ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap`, `SchwartzMap.smulLeftCLM_smulLeftCLM_apply`, `arithGeom_eq`, `VectorField.mlieBracketWithin_smul_left`, `PowerSeries.one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_pow`, `Convex.combo_self`, `Unitization.inrRangeEquiv_apply_coe_fst`, `NormedRing.inverse_add`, `CStarMatrix.reindexₐ_apply`, `WeakBilin.instContinuousSMul`, `ContinuousLinearMap.isometry_iff_adjoint_comp_self`, `continuousMultilinearCurryFin0_apply`, `smul_le_smul_iff_of_neg_left`, `Polynomial.degree_C_mul_X_pow_le`, `sub_pow`, `HasFDerivWithinAt.mapsTo_tangent_cone`, `DivisibleHull.coeAddMonoidHom_apply`, `LocalizedModule.smul'_mk`, `Polynomial.le_trailingDegree_C_mul_X_pow`, `PiTensorProduct.dualSeminorms_bounded`, `DivisibleHull.instIsOrderedCancelAddMonoid`, `NonUnitalSubalgebra.inclusion_inclusion`, `FormalMultilinearSeries.radius_neg`, `Module.Flat.isSMulRegular_of_isRegular`, `LinearEquiv.isUnit_det'`, `absorbs_iff_eventually_cobounded_mapsTo`, `MvPolynomial.eval₂_eq'`, `FiniteField.splits_X_pow_nat_card_sub_X`, `HasFDerivWithinAt.mul_const'`, `InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal`, `extDeriv_smul`, `Valuation.ltSubmodule_monotone`, `LinearMap.mul_toMatrix₂`, `TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq`, `Module.algebraMap_end_eq_smul_id`, `HasStrictFDerivAt.iterate`, `Algebra.Extension.Cotangent.map_comp`, `HasDerivAt.comp_const_sub`, `convex_Ioo`, `AddMonoidAlgebra.toDirectSum_pow`, `Submodule.mulRightMap_eq_mulMap_comp`, `HasDerivAt.norm_sq`, `Algebra.TensorProduct.basis_repr_symm_apply'`, `StarConvex.smul`, `LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing`, `ContinuousLinearMap.opNorm_extend_le`, `Submodule.orthogonal_closure`, `HasDerivWithinAt.add`, `IsSelfAdjoint.conj_adjoint`, `Ideal.mul_mem_mul`, `LinearMap.surjective_compr₂_of_equiv`, `ContinuousMultilinearMap.curryMidEquiv_apply`, `TensorProduct.AlgebraTensorModule.rid_eq_rid`, `Units.mul_right_eq_zero`, `StrictConvexSpace.strictConvex_closedBall`, `one_div_pow_lt_one_div_pow_of_lt`, `nonunits.subset_compl_ball`, `Real.fourier_eq`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq`, `IsBaseChange.prodMap`, `Matrix.val_planeConformalMatrix`, `Associates.factors_mono`, `kroneckerTMulLinearEquiv_mul`, `Algebra.trace_comp_trace_of_basis`, `QuadraticMap.discr_comp`, `Subfield.continuousSMul`, `AffineMap.lineMap_vadd_apply`, `Mathlib.Tactic.LinearCombination.smul_lt_const_weak`, `exists_eq_pow_of_mul_eq_pow_of_coprime`, `differentialIdeal_le_fractionalIdeal_iff`, `IsRelPrime.add_mul_right_right`, `HasStrictFDerivAt.continuousMultilinear_apply_const`, `Matrix.discr_of_card_eq_two`, `sq_lt_sq'`, `LinearMap.lsmul_eq_DistribMulAction_toLinearMap`, `Asymptotics.IsLittleOTVS.sup`, `IntermediateField.finrank_bot`, `Perfection.teichmuller_sModEq`, `MvPolynomial.eval_monomial`, `Associates.factors_eq_some_iff_ne_zero`, `ContDiffMapSupportedIn.monoLM_eq_zero`, `WeierstrassCurve.Jacobian.negAddY_smul`, `kroneckerTMulLinearEquiv_symm_kroneckerTMul`, `SMulPosReflectLT.toSMulPosReflectLE`, `sameRay_neg_smul_left_iff_of_ne`, `Valuation.isNontrivial_iff_exists_unit`, `AdicCompletion.map_mk`, `Set.OrdConnected.convex_of_chain`, `ContinuousLinearMap.opNorm_mulLeftRight_apply_le`, `ContinuousLinearMap.analyticOnNhd_bilinear`, `UniqueFactorizationMonoid.radical_associated`, `MultilinearMap.freeFinsuppEquiv_def`, `localizedModuleIsLocalizedModule`, `ConvexOn.convex_lt`, `Prod.openSegment_subset`, `TensorProduct.AlgebraTensorModule.map_eq`, `WeakBilin.instIsScalarTower`, `Units.sq_eq_sq_iff_eq_or_eq_neg`, `associated_abs_left_iff`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`, `LinearMap.lsum_single`, `DoubleCentralizer.algebraMap_snd`, `Finset.expect_dite_eq'`, `Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality`, `SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf`, `UniqueFactorizationMonoid.associated_iff_normalizedFactors_eq_normalizedFactors`, `Convex.add`, `FiniteMultiplicity.or_of_add`, `WeierstrassCurve.Jacobian.addX_of_X_eq`, `ConvexCone.smul_mem_iff`, `LieModule.trace_comp_toEnd_genWeightSpace_eq`, `Associates.map_subtype_coe_factors'`, `pow_lt_pow_iff_right₀`, `lp.instStarModuleSubtypePreLpMemAddSubgroup`, `AnalyticAt.analyticOrderNatAt_eq_iff`, `Complex.isOpenQuotientMap_pow`, `TensorProduct.gradedMul_one`, `Matrix.kronecker_mem_unitary`, `lcm_assoc'`, `QuadraticForm.tensorComm_toLinearEquiv`, `CharTwo.sum_sq`, `MeasureTheory.integrable_smul_const`, `SchauderBasis.RankOneDecomposition.basisCoeff_spec`, `hasFiniteFPowerSeriesOnBall_const`, `InfiniteGalois.restrict_fixedField`, `coe_subset_nonunits`, `Module.End.smulLeft_apply`, `ProbabilityTheory.gaussianReal_map_div_const`, `geom_sum₂_mul_of_le`, `HahnModule.SMulCommClass`, `Ideal.mul_sup_eq_of_coprime_left`, `ZMod.invDFT_apply'`, `iteratedFDerivWithin_succ_apply_left`, `pow_left_monotoneOn`, `PerfectionMap.comp_equiv'`, `PowerSeries.IsWeierstrassFactorizationAt.isUnit`, `Mathlib.Tactic.Ring.one_pow`, `instIsDecompositionFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupStabilizerIdealOfIsGalois`, `SpecialLinearGroup.coe_mul`, `Matrix.linearIndependent_cols_iff_isUnit`, `Submodule.starProjection_unit_singleton`, `Matrix.dualNumberEquiv_symm_apply`, `Finset.weightedVSub_const_smul`, `LinearMap.toMatrix'_mul`, `complEDS_odd`, `Algebra.TensorProduct.productMap_eq_comp_map`, `SchwartzMap.fourier_evalCLM_eq`, `Valuation.embedding_restrict`, `IsBaseChange.end`, `one_add_le_pow_of_two_add_nonneg`, `Perfection.teichmuller₀_sModEq`, `Valuation.Integers.valuation_unit`, `convex_convexHull`, `IsLocalization.localization_localization_map_units`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear`, `DualNumber.exp_eps`, `Submodule.mul_smul_mul_eq_smul_mul_smul`, `IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvd`, `Asymptotics.IsBigOTVS.prodMk`, `wittStructureRat_rec_aux`, `IntermediateField.sepDegree_bot`, `ValuationSubring.unitGroup_strictMono`, `isIdempotentElem_one_sub_one_sub_pow_pow`, `Subgroup.isArithmetic_iff_finiteIndex`, `normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure`, `Polynomial.iterate_derivative_X_pow_eq_smul`, `ENNReal.toReal_pow`, `KaehlerDifferential.tensorKaehlerEquiv_left_inv`, `factorPowSucc.isUnit_of_isUnit_image`, `pow_add_mul_le_add_pow`, `WeierstrassCurve.Projective.eval_polynomialZ`, `DilationEquiv.mulRight_apply`, `UniqueFactorizationMonoid.primeFactors_pow`, `AdicCompletion.pow_smul_top_eq_ker_eval`, `ContinuousLinearEquiv.trans_smul`, `hasDerivWithinAt_natCast`, `Polynomial.resultant_scaleRoots`, `PowerSeries.WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero`, `IsTopologicalSemiring.toOppositeIsModuleTopology`, `Units.divp_sub_divp_same`, `MvPowerSeries.WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero`, `CliffordAlgebra.foldl_algebraMap`, `PowerBasis.mem_span_pow`, `Submodule.rTensorOne_tmul`, `ProjectiveSpectrum.zeroLocus_singleton_pow`, `Polynomial.card_support_eq_three`, `spectrum.mem_resolventSet_iff`, `arithGeom_zero_eq_sum`, `IsLocalizedModule.rTensor`, `PowerSeries.le_order_pow_of_constantCoeff_eq_zero`, `AlgebraicGeometry.SpecToEquivOfLocalRing_apply_fst`, `Matrix.isIrreducible_iff_exists_pow_pos`, `fderiv_pow_ring'`, `LinearMap.toSpanSingleton_apply`, `MeasureTheory.memL1_smul_of_L1_withDensity`, `Squarefree.isRadical`, `ContinuousLinearMap.bilinearComp_apply`, `analyticAt_iff_analytic_fun_smul`, `isCyclic_subgroup_units`, `killingForm_apply_apply`, `derivWithin_pow_field`, `Matrix.isUnit_det_transpose`, `Module.End.restrict_eigenspace`, `imaginaryPart_eq_neg_I_smul_skewAdjointPart`, `Matrix.SpecialLinearGroup.toGL_injective`, `LinearMap.toMatrix_algebraMap`, `AddSubmonoid.mem_inv_pointwise_smul_iff₀`, `midpoint_vsub_left`, `DiscreteConvolution.ConvolutionExistsAt.convolution_smul`, `QuadraticModuleCat.toIsometry_hom_rightUnitor`, `TemperedDistribution.instLineDerivSMulReal`, `LinearMap.spectrum_toMatrix`, `AdicCompletion.ofAlgEquiv_apply`, `Function.HasTemperateGrowth.pow`, `iteratedDeriv_comp_neg`, `Polynomial.Separable.of_pow'`, `PowerBasis.constr_pow_gen`, `NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero`, `RatFunc.minpolyX_aeval_X`, `LinearMap.BilinForm.congr_refl`, `Nonneg.unitsHomeomorphPos_apply_coe`, `NonUnitalSubalgebra.map_toNonUnitalSubsemiring`, `FractionalIdeal.isPrincipal_of_unit_of_comap_mul_span_singleton_eq_top`, `Polynomial.resultant_X_sub_C_pow_right`, `Submodule.range_lsum_smul`, `RatFunc.algEquivOfTranscendental_symm_aeval`, `LieAlgebra.smulCommClass`, `SchwartzMap.evalCLM_apply_apply`, `Matrix.Module.instIsScalarTowerForall`, `LieSubalgebra.mem_engel_iff`, `WittVector.iterate_frobenius_coeff`, `Finset.sum_smul_const_vsub_eq_neg_weightedVSub`, `Polynomial.smeval_C_mul`, `Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule`, `WithTop.coe_pow`, `cfcUnits_pow`, `Algebra.norm_eq_norm_adjoin`, `NormedRing.inverse_one_sub`, `AlgebraicGeometry.Proj.awayι_toSpecZero`, `LieAlgebra.lie_smul`, `LinearMap.SeparatingRight.toMatrix₂`, `Cardinal.isUnit_iff`, `IsRelPrime.of_add_mul_left_right`, `Ideal.add_pow_add_pred_mem_of_pow_mem_of_commute`, `ContinuousLinearMap.coe_pow`, `NormedRing.inverse_add_norm`, `NumberField.Units.closure_fundSystem_sup_torsion_eq_top`, `IsSelfAdjoint.sq_spectrumRestricts`, `MvPolynomial.eval_pow`, `geom_sum₂_with_one`, `Matrix.isUnit_toLin_iff`, `Polynomial.degreeLT.addLinearEquiv_apply'`, `AddChar.expect_eq_zero_iff_ne_zero`, `DiffContOnCl.smul_const`, `Algebra.discr_of_matrix_vecMul`, `spectrum.spectralRadius_pow_le`, `Convex.linear_image`, `ContMDiffWithinAt.clm_bundle_apply₂`, `sq_le_sq₀`, `Matrix.posDef_iff_eq_conjTranspose_mul_self`, `MeasureTheory.condExpIndL1_smul'`, `Submodule.singleton_smul`, `LinearMap.conjugate_apply`, `circleEquivGen_symm_apply`, `Unitization.mem_spectrum_inr_of_not_isUnit`, `IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic`, `PowerSeries.derivative_invOf`, `Polynomial.resultant_succ_left_deg`, `Commute.geom_sum₂_Ico`, `Unitary.conjStarAlgAut_apply`, `TopologicalGroup.IsSES.integrate_apply`, `UpperHalfPlane.volume_eq_lintegral`, `Submodule.unitsToPic_apply`, `tendsto_integral_exp_smul_cocompact_of_inner_product`, `PowerSeries.one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_val`, `HasDerivAt.fun_div`, `Submodule.toConvexCone_le_toConvexCone`, `tsum_const_smul''`, `vadd_segment`, `Projectivization.mk_eq_mk_iff_crossProduct_eq_zero`, `iterateFrobeniusEquiv_one_apply`, `Matrix.Module.scalar_smul`, `Matrix.diagonal_toLin'`, `Matrix.vandermonde_mul_vandermonde_transpose`, `Matrix.adjugate_smul`, `Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy`, `IntermediateField.LinearDisjoint.norm_algebraMap`, `contDiff_smul_const`, `HasFTaylorSeriesUpToOn.fderivWithin`, `NNRat.cast_pow`, `Prod.image_mk_openSegment_right`, `CStarMatrix.toCLM_apply`, `KaehlerDifferential.kerTotal_map`, `IntermediateField.restrictScalars_bot_eq_self`, `Module.End.mem_genEigenspace_top`, `LieModule.lie_smul`, `Polynomial.eval₂_def`, `Valued.closure_coe_completion_v_lt`, `zero_pow_le_one`, `AlgebraicGeometry.Proj.awayToSection_comp_appLE`, `DoubleCentralizer.algebraMap_toProd`, `Ring.isUnit_iff_inverse_mul_cancel`, `continuousMultilinearCurryFin0_symm_apply_apply`, `HasDerivWithinAt.fun_const_smul`, `PowerSeries.IsWeierstrassDivisorAt.isUnit_shift`, `ConcaveOn.le_map_sum`, `Algebra.TensorProduct.mul_one`, `Polynomial.hilbertPoly_X_pow_succ`, `RingTheory.Sequence.isWeaklyRegular_append_iff'`, `ContinuousLinearMap.ker_self_comp_adjoint`, `EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF`, `Matrix.charpoly_toLin'`, `Quaternion.fst_imI_dualNumberEquiv_symm`, `ValueDistribution.characteristic_pow_zero`, `Mathlib.Meta.NormNum.IsNat.nnreal_rpow_eq_nnreal_pow`, `LinearMap.BilinForm.toMatrix_symm`, `Polynomial.isEquivalent_atBot_lead`, `bernoulliFourierCoeff_eq`, `cfc_comp_zpow`, `exists_nontrivial_relation_sum_zero_of_not_affine_ind`, `FormalMultilinearSeries.id_comp`, `circleIntegral.integral_smul`, `ContinuousLinearMap.norm_map_tail_le`, `LieModule.iterate_toEnd_mem_lowerCentralSeries₂`, `LinearMap.BilinMap.toQuadraticMap_smul`, `invOf_two_smul_add_invOf_two_smul`, `Matrix.toLinearMap₂'_toMatrix'`, `isSMulRegular_algebraMap_iff`, `Polynomial.pow_sub_dvd_iterate_derivative_pow`, `HasFPowerSeriesAt.restrictScalars`, `iterateFrobenius_def`, `IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral`, `hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval`, `not_dvd_geom_sum₂`, `ENNReal.tsum_geometric_two`, `ConcaveOn.convex_hypograph`, `rank_dual_eq_card_dual_of_aleph0_le_rank'`, `WithZeroTopology.nhds_coe_units`, `ContinuousLinearMap.instStarModuleId`, `Complex.cosh_two_mul`, `ContDiff.smul_const`, `Submodule.range_unitsToPic`, `RCLike.wInner_smul_left`, `Matrix.toLinearMapₛₗ₂'_apply`, `edist_smul₀`, `AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.isPrime_carrier`, `Matrix.projVandermonde_apply_zero_right`, `Polynomial.associated_of_dvd_of_degree_eq`, `intervalIntegral.integral_smul_deriv_eq_deriv_smul_of_hasDeriv_right`, `Seminorm.convex_ball`, `VectorField.mlieBracketWithin_smul_right`, `Convex.combo_closure_interior_subset_interior`, `CategoryTheory.ShiftedHom.comp_smul`, `PolynomialModule.eval_lsingle`, `WeierstrassCurve.Projective.dblXYZ_of_Z_eq_zero`, `MultilinearMap.map_nonempty`, `Algebra.Extension.H1Cotangent.equivOfFormallySmooth_apply`, `DoubleCentralizer.instIsCentralScalar`, `spectrum.isUnit_one_sub_smul_of_lt_inv_radius`, `Subsemiring.mem_inv_pointwise_smul_iff₀`, `HasDerivWithinAt.const_mul`, `Module.End.genEigenspace_one`, `IsUnit.cfcNNRpow`, `ContinuousLinearMapWOT.instContinuousSMul`, `HasFDerivAt.continuousAlternatingMap_apply_const`, `Algebra.TensorProduct.mk_one_injective_of_isScalarTower`, `CochainComplex.HomComplex.Cochain.smul_comp`, `Nat.tendsto_pow_atTop_atTop_of_one_lt`, `Submodule.smul_le_right`, `Commute.geom_sum₂`, `Submodule.span_eq_closure`, `Finpartition.coe_energy`, `map_pow_le_pow'`, `Matrix.toLin'_pow`, `PiTensorProduct.injectiveSeminorm_apply`, `NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le`, `ContinuousLinearMap.isBoundedLinearMap_comp_left`, `MonoidWithZeroHom.ValueGroup₀.mk_eq_of_ne_zero`, `Polynomial.roots_X_pow_char_sub_C_pow`, `LieAdmissibleAlgebra.toIsScalarTower`, `IsNilpotent.map`, `IsSymmetricAlgebra.equiv_symm_apply`, `LinearIsometryEquiv.toLinearEquiv_smul`, `HomogeneousLocalization.NumDenSameDeg.num_pow`, `LieModule.Cohomology.mem_twoCocycle_iff`, `normalize_coe_units`, `LinearEquiv.symm_smul`, `Units.val_inv_cfcRpow`, `NormedSpace.exp_units_conj'`, `CliffordAlgebra.ofBaseChangeAux_ι`, `Ideal.ker_tensorProductMk_quotient`, `WeierstrassCurve.coe_inv_variableChange_Δ'`, `norm_fderiv_iteratedFDeriv`, `Unitary.toAlgEquiv_conjStarAlgAut`, `Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1`, `Complex.abel_aux`, `Unitization.lift_range`, `CommAlgCat.tensorHom_hom`, `WittVector.irreducible`, `TestFunction.lineDerivCLM_eq_fderivCLM`, `Submodule.exists_isInternal_prime_power_torsion_of_pid`, `DistribMulActionHom.instLinearMapClassId`, `TopologicalAddGroup.IsSES.integrate_mono`, `HasDerivWithinAt.div`, `LinearMap.BilinForm.SeparatingLeft.toMatrix`, `meromorphicOrderAt_smul`, `Asymptotics.isLittleOTVS_map`, `instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient`, `Polynomial.isNilpotent_iterate_newtonMap_sub_of_isNilpotent`, `IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable`, `Bornology.IsVonNBounded.sub`, `WeierstrassCurve.Jacobian.Y_sub_Y_add_Y_sub_negY`, `Associates.mem_factors'_iff_dvd`, `ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply`, `hasFDerivAt_pow`, `Subgroup.instHasDetOneMinGeneralLinearGroup`, `instIsStrictOrderedModuleOfIsCancelAdd`, `Matrix.rectVandermonde_apply_zero_right`, `QuadraticMap.basisRepr_eq_of_iIsOrtho`, `segment_subset_Icc`, `continuousOn_const_smul_iff₀`, `TensorProduct.AlgebraTensorModule.mapBilinear_apply`, `Ideal.span_mul_span`, `LinearMap.BilinMap.toQuadraticMapLinearMap_apply`, `convexOn_univ_piecewise_Ici_of_monotoneOn_Ici_antitoneOn_Iic`, `TemperedDistribution.fourier_lineDerivOp_eq`, `pow_lt_self_of_lt_one₀`, `Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub`, `Matrix.toLinAlgEquiv'_apply`, `groupHomology.inhomogeneousChains.d_single`, `isCusp_SL2Z_iff`, `Perfection.teichmuller₀_spec'`, `PadicInt.isUnit_iff`, `Matrix.l2_opNNNorm_def`, `ContinuousLinearEquiv.strictConvex_image`, `ContinuousMultilinearMap.instIsBoundedSMul`, `IntermediateField.mem_lift`, `IntermediateField.isAlgebraic_adjoin_pair`, `cfcₙHom_isClosedEmbedding`, `LocalizedModule.mk_neg`, `WfDvdMonoid.max_power_factor`, `Nat.factors_eq`, `HahnSeries.isUnit_iff`, `AdjoinRoot.algEquivOfAssociated_toAlgHom`, `hasDerivAtFilter_sub_const_iff`, `LinearEquiv.det_conj`, `alternating_series_error_bound`, `IsRealClosed.exists_eq_pow_of_isSquare`, `spectrum.hasDerivAt_resolvent`, `smul_mem_nhds_smul_iff₀`, `Module.Basis.sum_toMatrix_smul_self`, `IsDiscreteValuationRing.associated_of_irreducible`, `AdicCompletion.val_apply_mem_smul_top_iff`, `ContinuousLinearMap.adjointAux_adjointAux`, `apply_eq_star_dotProduct_toMatrix₂_mulVec`, `mdifferentiableOn_baseSet_localFrame_coeff`, `tensorKaehlerQuotKerSqEquiv_tmul_D`, `MvPolynomial.mkDerivation_monomial`, `Ideal.pow_mem_of_mem`, `PowerBasis.basis_eq_pow`, `LinearMap.aeval_eq_aeval_mod_charpoly`, `Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder`, `smul_nonpos_iff_neg_imp_nonneg`, `Complex.volume_sum_rpow_lt`, `Finsupp.linearCombination_single`, `HasStrictDerivAt.const_add`, `realPart_I_smul`, `fderivWithin_continuousMultilinearMapCompContinuousLinearMap`, `Submodule.exists_smul_notMem_of_rank_lt`, `Convex.add_smul`, `LaurentPolynomial.isUnit_T`, `NNRat.den_pow`, `LinearMap.toMatrix₂_compl₁₂`, `LinearMap.BilinForm.IsSymm.smul`, `Valued.cauchy_iff`, `pinGroup.units_mem_iff`, `linearIndependent_smul`, `Seminorm.exists_apply_eq_finset_sup`, `WeierstrassCurve.inv_variableChange_Δ'`, `LinearMap.hasEigenvalue_zero_tfae`, `ExteriorAlgebra.instGradedMonoidNatSubmoduleExteriorPower`, `Polynomial.iterate_derivative_eq_sum`, `Matrix.minpoly_toLin'`, `Algebra.FormallyUnramified.isReduced_of_field`, `WeierstrassCurve.Projective.Point.fromAffine_some`, `PolynomialModule.smul_apply`, `QuadraticForm.tensorDistrib_tmul`, `Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero`, `CFC.rpow_neg_one_eq_inv`, `ContMDiffAt.clm_precomp`, `selfAdjoint.realPart_unitarySelfAddISMul`, `Matrix.nonsing_inv_apply`, `Subalgebra.centralizer_tensorProduct_eq_center_tensorProduct_left`, `Complex.hasDerivAt_logTaylor`, `pow_two_sub_pow_two`, `TestFunction.lineDerivCLM_apply`, `Multiset.sum_smul`, `RingQuot.pow_quot`, `Nonneg.unitsEquivPos_apply_coe`, `WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded`, `MeasureTheory.FiniteMeasure.smul_testAgainstNN_apply`, `Algebra.PreSubmersivePresentation.isUnit_jacobian_of_linearIndependent_of_span_eq_top`, `MvPolynomial.mul_esymm_eq_sum`, `Mathlib.Tactic.Module.NF.zero_sub_eq_eval`, `iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow`, `deriv_smul`, `Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence`, `geom_sum₂_mul_add`, `Polynomial.resultant_pow_right`, `Prod.image_mk_segment_right`, `GradedTensorProduct.mulHom_apply`, `VectorField.mpullbackWithin_smul_apply`, `PositiveLinearMap.gnsStarAlgHom_apply`, `IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat`, `LieModule.toEnd_eq_iff`, `BilinForm.toMatrix_compRight`, `Real.fourier_iteratedDeriv`, `Units.mulRightLinearEquiv_trans_mulRightLinearEquiv`, `iter_deriv_pow'`, `RingOfIntegers.isUnit_norm`, `extract_gcd`, `MeasureTheory.Integrable.smul_of_top_left`, `LinearMap.BilinForm.nondegenerate_toMatrix'_iff`, `HasFDerivWithinAt.iterate`, `Polynomial.natDegree_C_mul_X_pow`, `Asymptotics.IsBigOTVS.symm`, `ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin`, `Polynomial.wronskianBilin_apply`, `hasDerivAt_iff_tendsto_slope_zero`, `LinearMap.toMatrix₂_toLinearMap₂`, `StrictConvex.affine_preimage`, `IntermediateField.finrank_sup_le`, `ENNReal.mulRightOrderIso_toEquiv`, `Polynomial.evalEval_pow`, `TensorAlgebra.algebraMap_eq_one_iff`, `AlgCat.hom_whiskerLeft`, `NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrank`, `spectrum.inv₀_mem`, `ValuationSubring.valuation_eq_iff`, `IsExposed.convex`, `ordinaryHypergeometricSeries_apply_eq`, `LinearMap.norm_extendTo𝕜'_apply_sq`, `SpecialLinearGroup.coe_pow`, `Asymptotics.isLittleOTVS_iff_isLittleO`, `WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right`, `AddMonoidAlgebra.cardinalMk_eq_lift_of_fintype`, `Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub`, `surjective_cosetToCuspOrbit`, `AffineSubspace.wSameSide_smul_vsub_vadd_left`, `TrivSqZeroExt.inv_inv`, `ZMod.val_coe_unit_coprime`, `SchwartzMap.integral_pow_mul_iteratedFDeriv_le`, `inner_product_apply_eigenvector`, `HasFTaylorSeriesUpToOn.hasFDerivAt`, `WeakFEPair.hf_zero`, `LinearMap.toMatrix'_intrinsicStar`, `Complex.cpow_mul_nat`, `MultilinearMap.domCoprod'_apply`, `Polynomial.of_irreducible_expand_pow`, `hasStrictFDerivAt_inv`, `LinearMap.BilinForm.congr_congr`, `Polynomial.C_mul_X_pow_eq_self`, `scalarSMulCLE_apply`, `Summable.one_sub_mul_tsum_pow`, `ContinuousLinearMap.flip_add`, `WeierstrassCurve.Projective.negMap_of_Z_ne_zero`, `QuadraticMap.polar_smul_left`, `exists_pos_left_iff_sameRay`, `Polynomial.leadingCoeff_X_pow`, `IntermediateField.adjoinRootEquivAdjoin_apply_root`, `hasFiniteFPowerSeriesAt_const`, `MDifferentiable.clm_prodMap`, `Algebra.Extension.Cotangent.map_id`, `MeasureTheory.Integrable.toL1_smul'`, `ModuleCat.ExtendScalars.smul_tmul`, `Seminorm.uniformContinuous`, `IsPrimitiveRoot.isRoot_geom_sum`, `QuadraticForm.tensorComm_apply`, `IsRelPrime.add_mul_right_left_iff`, `Commute.add_pow_eq_zero_of_add_le_succ_of_pow_eq_zero`, `AffineSubspace.isometryEquivMap.coe_apply`, `infDist_smul₀`, `Submodule.smul_mem_iff_of_isUnit`, `Nat.Partition.hasProd_powerSeriesMk_card_restricted`, `ContinuousAlternatingMap.hasBasis_nhds_zero`, `IsFractionRing.associated_num_den_inv`, `MeasureTheory.LocallyIntegrable.integrable_smul_left_of_hasCompactSupport`, `Bornology.isBounded_iff_isVonNBounded`, `Antivary.sum_smul_lt_sum_smul_comp_perm_iff`, `Convex.min_le_combo`, `cross_apply`, `monovaryOn_iff_smul_rearrangement`, `Odd.strictMono_pow`, `cfcₙHom_le_iff`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff_of_mem`, `NNReal.hasSum_geometric`, `LinearEquiv.lieConj_apply`, `Commute.sub_dvd_pow_sub_pow`, `VectorFourier.fourierSMulRight_apply`, `LieModule.isNilpotent_toEnd_of_mem_rootSpace`, `UniqueFactorizationMonoid.irreducible_of_factor`, `HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp`, `Associated.lcm`, `ConcaveOn.translate_right`, `Units.mk0_mul`, `Derivation.leibniz`, `ContinuousLinearMap.isSelfAdjoint_iff'`, `HasFDerivWithinAt.restrictScalars`, `LinearIsometry.map_smulₛₗ`, `DoubleCentralizer.pow_toProd`, `UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp`, `OrthonormalBasis.equiv_apply_euclideanSpace`, `RootPairing.PolarizationIn_apply`, `AlternatingMap.eq_smul_basis_det`, `LinearMap.BilinForm.toMatrixAux_apply`, `MeasureTheory.euclideanHausdorffMeasure_homothety_image`, `IsCyclotomicExtension.iff_singleton`, `PiTensorProduct.mapMultilinear_apply`, `Convex.interior`, `integral_cexp_quadratic`, `CochainComplex.HomComplex.Cochain.rightShift_smul`, `TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq`, `NormedRing.inverse_add_norm_diff_second_order`, `LinearMap.liftQ₂_mk`, `ContinuousLinearMap.toContinuousAddMonoidHom_injective`, `ContractingWith.exists_fixedPoint`, `IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree`, `Polynomial.cyclotomic_irreducible_of_irreducible_pow`, `ProbabilityTheory.evariance_def'`, `MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp`, `Seminorm.coe_sSup_eq'`, `Polynomial.mul_X_pow_comp`, `ContinuousMultilinearMap.uncurryRight_apply`, `CongruenceSubgroup.strictWidthInfty_Gamma1`, `Seminorm.closedBall_smul`, `IntermediateField.rank_bot`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow`, `Polynomial.roots_ofMultiset`, `HasDerivAt.comp_const_add`, `ENNReal.smulCommClass_left`, `RCLike.ofReal_pow`, `Matrix.isUnit_fromBlocks_iff_of_invertible₂₂`, `IsRelPrime.add_mul_left_left_iff`, `Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq`, `ContinuousLinearMap.isVonNBounded_iff`, `SchwartzMap.fourierMultiplierCLM_ofReal`, `InnerProductSpace.Core.inner_smul_ofReal_left`, `AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_stalk_isLocalHom`, `Real.isScalarTower`, `UpperHalfPlane.J_smul`, `fderiv_inv`, `WeierstrassCurve.Projective.nonsingularLift_iff`, `Module.End.isNilpotent_restrict_maxGenEigenspace_sub_algebraMap`, `FiniteField.unit_isSquare_iff`, `Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable`, `differentiableWithinAt_iff_restrictScalars`, `IsModuleTopology.iso`, `AdicCompletion.of_surjective`, `TrivSqZeroExt.exp_def`, `MeasureTheory.euclideanHausdorffMeasure_homothety_preimage`, `SlashInvariantForm.slash_action_eqn''`, `Polynomial.cyclotomic.dvd_X_pow_sub_one`, `derivWithin_comp_mul_left`, `Finset.expect_mul_sq_le_sq_mul_sq`, `Algebra.Generators.Cotangent.exact`, `Holor.slice_unitVec_mul`, `Polynomial.eraseLead_C_mul_X_pow`, `HurwitzZeta.sinZeta_two_mul_nat_add_one'`, `MvPowerSeries.HasSubst.X_pow`, `Seminorm.coe_bot`, `WittVector.coeff_frobenius_charP`, `hasDerivAt_circleMap`, `LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv'`, `Submodule.smul_top_eq_range_lsum`, `mk_mem_nonZeroDivisors_associates`, `LinearMap.toMatrix_smulRight`, `IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem`, `Matrix.adjugate_adjugate'`, `Polynomial.Monic.natSepDegree_eq_one_iff`, `Nat.sum_divisors_filter_squarefree`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq`, `WeierstrassCurve.Projective.polynomialX_eq`, `Subfield.pow_mem`, `contMDiffAt_localFrame_coeff`, `vectorSpan_segment`, `kroneckerTMulLinearEquiv_tmul`, `Module.stabilizer_units_eq_bot_of_ne_zero`, `HahnSeries.binomial_power`, `Associates.instNoZeroDivisors`, `ProperCone.smul_mem`, `derivWithin_fun_smul`, `ContinuousLinearMap.bilinearComp_zero`, `LinearMap.toMatrix₂Aux_eq`, `HasFDerivAt.fun_pow'`, `LocalizedModule.subsingleton_iff`, `Convex.mem_toCone`, `le_restrictScalars_separableClosure`, `HasDerivWithinAt.scomp_hasDerivAt_of_eq`, `uniformity_basis_edist_inv_two_pow`, `AddMonoidAlgebra.coe_liftNCAlgHom`, `imaginaryPart_apply_coe`, `add_one_pow_unbounded_of_pos`, `ContinuousLinearMap.isVonNBounded_image2_apply`, `MonoidWithZeroHom.inr_mono`, `segment_same`, `Module.End.natCast_def`, `X_pow_sub_C_irreducible_of_prime`, `ZMod.isCyclic_units_of_prime_pow`, `IsIntegral.pow_iff`, `Unitary.openPartialHomeomorph_target`, `iteratedDeriv_eq_equiv_comp`, `SchwartzMap.smulLeftCLM_add`, `Complex.cos_bound`, `modularCyclotomicCharacter.unique`, `pinGroup.conjAct_smul_range_ι`, `Units.nnnorm_pos`, `LinearMap.lsmul_apply`, `HasMFDerivWithinAt.mul'`, `EisensteinSeries.eisensteinSeries_SIF_apply`, `X_pow_mul_sub_C_irreducible`, `WfDvdMonoid.wfDvdMonoid_associates`, `TensorProduct.AlgebraTensorModule.restrictScalars_rTensor`, `LieDerivation.toLinearMapLieHom_injective`, `UnitAddTorus.hasSum_mFourier_series_L2`, `FreeLieAlgebra.liftAux_spec`, `MultilinearMap.mkContinuousLinear_norm_le'`, `Complex.cpow_natCast`, `norm_fderivWithin_iteratedFDerivWithin`, `Submodule.smul_closure_subset`, `HasFTaylorSeriesUpToOn.shift_of_succ`, `CentroidHom.instSMulCommClass_1`, `vecMulVecBilin_apply_apply`, `spectrum_subset_unitary_of_mem_unitary`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply`, `QuadraticForm.tmul_comp_tensorMap`, `isAdjointPair_toLinearMap₂'`, `ConvexCone.mem_add`, `Associates.mk_normalize`, `SemimoduleCat.Algebra.instSMulCommClassCarrier`, `summable_powerSeries_of_norm_lt`, `Matrix.toLin'_apply'`, `QuotSMulTop.map_exact`, `WeierstrassCurve.VariableChange.one_def`, `WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF`, `Nat.card_eq_card_units_add_one`, `Mathlib.Tactic.Ring.pow_one_cast`, `FormalMultilinearSeries.ofScalarsSum_eq_tsum`, `NumberField.discr_eq_basisMatrix_det_sq`, `Representation.asModuleEquiv_symm_map_rho`, `Matrix.det_of_mem_unitary`, `MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart`, `IsStrictlyPositive.sqrt`, `LinearMap.toMatrix₂_symm`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff`, `AlgebraicGeometry.Proj.awayι_toSpecZero_assoc`, `IsLocalRing.exists_factor_valuationRing`, `Module.End.commute_exp_left_of_commute`, `IntermediateField.instIsScalarTowerSubtypeMem_1`, `ArithmeticFunction.ppow_apply`, `arithGeom_same_eq_mul_div`, `Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero`, `Filter.not_tendsto_pow_atTop_atBot`, `HasDerivWithinAt.neg`, `integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2`, `isLocalHom_id`, `ContinuousLinearMap.norm_extendTo𝕜'_bound`, `TensorPower.toTensorAlgebra_gMul`, `geom_sum_eq_zero_iff_neg_one`, `IsModuleTopology.continuous_of_distribMulActionHomₑ`, `Matrix.ker_toLin'_eq_bot_iff`, `ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap`, `Polynomial.rootMultiplicity_expand`, `Polynomial.bernoulli_comp_one_add_X`, `IsLocalHom.of_specComap_surjective`, `Polynomial.X_pow_dvd_iff`, `le_egauge_smul_right`, `ContinuousMultilinearMap.integral_apply`, `NonUnitalSubalgebra.unitization_apply`, `isCoprime_self`, `LinearMap.vecCons₂_apply`, `IsAzumaya.coe_tensorEquivEnd`, `unitary.joined`, `cfc_zpow`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `SeminormFamily.basisSets_smul`, `DualNumber.lift_apply_apply`, `HasStrictDerivAt.smul_const`, `LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg`, `LocalizedModule.smul_def`, `Matrix.charpoly_fin_two`, `LinearMap.eval_charpoly`, `LinearMap.SeparatingLeft.toMatrix₂`, `Submodule.span_eq_iUnion_nat`, `HasStrictDerivAt.sub`, `NumberField.mixedEmbedding.det_matrixToStdBasis`, `UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvd`, `Valuation.IsRankOneDiscrete.generator'_zpowers_eq_top`, `WithVal.toVal_pow`, `LinearMap.toMatrix'_toLinearMap₂'`, `SameRay.sameRay_nonneg_smul_right`, `Algebra.mul_sub_algebraMap_pow_commutes`, `TensorPower.toTensorAlgebra_gOne`, `Matrix.det_succ_column`, `Derivation.llcomp_apply`, `HasFiniteFPowerSeriesOnBall.neg`, `ModuleTopology.eq_coinduced_of_surjectiveₛₗ`, `CStarAlgebra.one_le_inv_iff_le_one`, `MulAction.bijective₀`, `Multiset.prod_map_le_pow_card`, `AddChar.starComp_apply`, `CentroidHom.instIsScalarTower_1`, `Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval`, `inv_smul_lt_iff_of_pos`, `Basis.multilinearMap_apply_apply`, `HasDerivWithinAt.Ioo_of_Ioi`, `LinearMap.BilinForm.toLin'Flip_apply`, `TensorProduct.tensorQuotEquivQuotSMul_symm_mk`, `LinearMap.reduceModIdeal_apply`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `WithTop.pow_lt_top_iff`, `Polynomial.resultant_C_left`, `RingTheory.Sequence.isWeaklyRegular_append_iff`, `LocalizedModule.lift_comp`, `PadicInt.continuous_addChar_of_value_at_one`, `Complex.iteratedDeriv_even_cos`, `Asymptotics.IsEquivalent.pow`, `lineDifferentiableWithinAt_smul_iff`, `UpperHalfPlane.denom_neg`, `Fintype.expect_ite_mem`, `UniqueFactorizationMonoid.radical_pow_dvd`, `BilinForm.toMatrix_mul_basis_toMatrix`, `LinearMap.convexOn`, `DifferentiableWithinAt.smul_const`, `IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply`, `MultilinearMap.dfinsuppFamilyₗ_apply`, `Prime.not_unit`, `Submodule.le_span_singleton_iff`, `hasDerivAt_fourier`, `Ideal.IsTwoSided.instHPowNat`, `Unitization.lift_symm_apply`, `Rep.standardComplex.d_of`, `HahnSeries.SummableFamily.coeff_smul`, `nonempty_oreSet_of_strongRankCondition`, `Asymptotics.IsBigOTVS.congr_right`, `NumberField.Units.regOfFamily_div_regOfFamily`, `Complex.sin_sq_add_cos_sq`, `Polynomial.irreducible_of_degree_eq_one_of_isRelPrime_coeff`, `IsNilpotent.pow_succ`, `Subring.le_pointwise_smul_iff₀`, `spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadius`, `Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd`, `QuadraticMap.half_moduleEnd_apply_eq_half_smul`, `smul_lie`, `Finset.pluennecke_ruzsa_inequality_pow_div`, `Seminorm.neg_closedBall`, `emultiplicity_geom_sum₂_eq_one`, `LinearMap.BilinForm.mul_toMatrix'`, `IntermediateField.finrank_bot_mul_relfinrank`, `Perfection.ext_iff`, `LieModule.toEnd_lie`, `Valuation.Integers.isUnit_of_one`, `cfcₙ_map_prod`, `Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree`, `QuadraticForm.tensorAssoc_symm_apply`, `LaurentPolynomial.eval₂_C_mul_T_neg_n`, `AffineMap.lineMap_apply`, `Language.mem_pow`, `Matrix.charpoly_units_conj`, `ContinuousLinearEquiv.toLinearEquiv_smul`, `Finsupp.linearCombination_unique`, `ProbabilityTheory.gaussianReal_map_mul_const`, `zero_mul`, `WeierstrassCurve.Affine.CoordinateRing.mk_Ψ_sq`, `add_pow_char_pow_of_commute`, `TrivSqZeroExt.inr_mul_inl`, `smul_eq_zero_iff_right`, `CFC.sq_eq_sq_iff`, `AntivaryOn.sum_smul_comp_perm_eq_sum_smul_iff`, `StrongDual.extendRCLikeₗᵢ_symm_apply`, `Asymptotics.IsThetaTVS.isBigOTVS`, `LinearMap.map_mul_iff`, `WeierstrassCurve.Projective.polynomialY_eq`, `MultilinearMap.map_update_smul'`, `Real.fourier_bilin_convolution_eq`, `SymmetricAlgebra.algHom_ext_iff`, `FiniteField.Matrix.charpoly_pow_card`, `Asymptotics.superpolynomialDecay_mul_param_pow_iff`, `irreducible_iff_prime_of_exists_prime_factors`, `RatFunc.irreducible_minpolyX`, `isOpenMap_smul₀`, `Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero`, `IsLocalizedModule.mk'_cancel_right`, `AntitoneOn.quasiconcaveOn`, `segment_eq_image'`, `CStarMatrix.mul_entry_mul_eq_inner_toCLM`, `Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd`, `Module.supportDim_quotSMulTop_succ_eq_supportDim`, `ConvexOn.smul_concaveOn`, `Units.mul_inv'`, `Matrix.toLinearMap₂_symm`, `Subring.smul_mem_pointwise_smul_iff₀`, `Matrix.GeneralLinearGroup.isParabolic_conj_iff'`, `ZMod.orderOf_one_add_four_mul`, `Submodule.convex`, `Module.End.isRoot_of_hasEigenvalue`, `ExteriorAlgebra.toTrivSqZeroExt_ι`, `WeierstrassCurve.Projective.negDblY_eq`, `FormalMultilinearSeries.le_comp_radius_of_summable`, `ContinuousLinearMap.le_opNorm₂`, `ContinuousLinearMap.lpPairing_eq_integral`, `TrivSqZeroExt.snd_invOf`, `Polynomial.expand_X`, `Matrix.coe_toEuclideanCLM_eq_toEuclideanLin`, `slope_fun_def`, `Seminorm.continuous_iff`, `HasFDerivAt.smul_const`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `ContinuousLinearMap.norm_uncurryMid`, `Submodule.unitsQuotEquivRelPic_symm_apply`, `QuadraticForm.equivalent_sum_squares`, `Submodule.torsionBy.mk_ideal_smul`, `TopologicalGroup.IsSES.pushforward_apply_apply`, `SymmetricAlgebra.equivMvPolynomial_symm_X`, `CongruenceSubgroup.finiteIndex_conjGL`, `IntermediateField.LinearDisjoint.of_basis_right`, `Matrix.sub_scalar_sq_eq_disc`, `Submodule.mem_span_iff_of_fintype`, `MvPolynomial.coeff_linearCombination_X_pow`, `InnerProductSpace.rankOne_def'`, `Polynomial.resultant_zero_left`, `sq_lt_one_iff_abs_lt_one`, `ContinuousLinearMap.opNorm_mul_le`, `ContinuousLinearMap.uncurryLeft_norm`, `WeierstrassCurve.Φ_ofNat`, `isUnit_iff_not_dvd_char`, `DualNumber.ringHom_ext_iff`, `LeftPreLieAlgebra.ext_iff`, `LinearMap.toMatrixAlgEquiv_symm`, `WeierstrassCurve.Projective.addY_of_Z_eq_zero_right`, `star_inv_natCast_smul`, `TestFunction.instLineDerivLeftSMulRealTopENat`, `LinearMap.toMatrixRight'_id`, `leibniz_cross`, `mem_vectorSpan_pair_rev`, `PiTensorProduct.smul_tprodCoeff_aux`, `hasStrictDerivAt_abs_neg`, `pow_lt_pow_right₀`, `HasFDerivAt.comp_hasDerivWithinAt`, `sq_sum_le_card_mul_sum_sq`, `ContinuousLinearMap.holder_smul_right`, `WithSeminorms.continuous_seminorm`, `Commute.mul_geom_sum₂`, `HasFPowerSeriesOnBall.tendstoUniformlyOn'`, `AdicCompletion.ofPowSMul_val_apply_eq_zero`, `HasFPowerSeriesWithinOnBall.const_smul`, `PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply`, `Matrix.isUnit_iff_isUnit_det`, `geom_sum_succ'`, `Matrix.disc_fin_two`, `HVertexOperator.coeff_inj`, `PolynomialModule.smul_single_apply`, `MvPolynomial.prod_X_pow_eq_monomial`, `FiniteField.trace_pow_card`, `TensorProduct.rid_tmul`, `IsPrimitiveRoot.primitiveRootsPowEquivOfCoprime_apply_coe`, `Submodule.coe_torsionBySet`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul`, `IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite`, `Asymptotics.IsLittleOTVS.comp_tendsto`, `Subalgebra.smul_mem_pointwise_smul`, `add_pow_prime_eq`, `Polynomial.Monic.irreducible_iff_natDegree`, `inv_smul_le_iff_of_pos`, `LinearMap.minpoly_toMatrix`, `ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero`, `Submodule.instFiniteQuotientIdealHSMulTop`, `Ideal.pow_le_pow_right`, `IsUltrametricDist.algNormOfAlgEquiv_apply`, `MulChar.ofUnitHom_eq`, `Mathlib.Tactic.Module.NF.neg_eq_eval`, `Representation.TensorProduct.rid_apply`, `SchwartzMap.fourierMultiplierCLM_const`, `HasFPowerSeriesOnBall.sub`, `SchwartzMap.integral_sesq_fourierIntegral_eq`, `IntermediateField.finiteDimensional_adjoin`, `Associates.is_pow_of_dvd_count`, `Matrix.SpecialLinearGroup.range_toGL`, `Real.fourierIntegral_eq'`, `IsLocalRing.isUnit_or_isUnit_of_add_one`, `Real.circleAverage_fun_smul`, `RootPairing.coroot_root_two`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left`, `TestFunction.monoCLM_eq_of_scalars`, `Polynomial.splits_X_pow_nat_card_sub_X`, `UniformConvergenceCLM.isVonNBounded_image2_apply`, `CategoryTheory.ShortComplex.cyclesMap'_smul`, `QuadraticModuleCat.toIsometry_inv_rightUnitor`, `PiTensorProduct.piTensorHomMapFun₂_smul`, `LieModule.Cohomology.add_apply_apply`, `Matrix.nondegenerate_toLinearMap₂'_iff_nondegenerate_toLinearMap₂`, `EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `Complex.hasSum_taylorSeries_on_emetric_ball`, `LinearEquiv.smulOfNeZero_apply`, `HasStrictDerivAt.of_notMem_tsupport`, `fderiv_continuousMultilinear_apply_const_apply`, `MeasureTheory.integrable_withDensity_iff_integrable_smul`, `IntermediateField.lift_injective`, `Asymptotics.IsLittleOTVS.congr`, `MeasureTheory.Integrable.convolution_integrand`, `ENNReal.log_pow`, `sub_pow_char_pow`, `LieModule.exists_forall_lie_eq_smul`, `FormalMultilinearSeries.radius_compContinuousLinearMap_eq`, `Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe`, `norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul`, `WeierstrassCurve.Jacobian.nonsingularLift_zero`, `Projectivization.exists_smul_eq_mk_rep`, `Module.reflection_mul_reflection_pow_apply_self`, `IsCyclotomicExtension.Rat.galEquivZMod_stabilizer`, `Matrix.SpecialLinearGroup.isEmbedding_toGL`, `Valuation.restrict_pos_iff`, `LinearMap.toMatrixOrthonormal_apply`, `DivisibleHull.qsmul_def`, `hasFPowerSeriesOn_cauchy_integral`, `IsUnit.natCast_of_isNilpotent_of_coprime`, `HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod`, `WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero`, `ContinuousLinearEquiv.unitsEquivAut_symm_apply`, `MvPolynomial.coeff_rTensorAlgHom_tmul`, `PerfectRing.ofFiniteOfIsReduced`, `antitone_smul_left`, `Polynomial.card_roots_X_pow_sub_C`, `IsDiscreteValuationRing.ideal_eq_span_pow_irreducible`, `Representation.asAlgebraHom_of`, `CFC.sqrt_sq`, `LinearEquiv.fixedReduce_eq_smul_iff`, `MonoidWithZeroHom.snd_inr`, `cfcₙHom_eq_cfcₙ_extend`, `concaveOn_of_convex_hypograph`, `MonoidWithZeroHom.snd_inl_apply_of_ne_zero`, `deriv_inv''`, `Valuation.HasExtension.instIsLocalHomValuationInteger`, `NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt`, `StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone`, `contDiffOn_tsum_cexp`, `Cardinal.mk_finsupp_of_fintype`, `LinearMap.IsPositive.smul_of_nonneg`, `NormedSpace.vonNBornology_eq`, `cfcₙAux_injective`, `KaehlerDifferential.isBaseChange`, `Function.Periodic.const_smul₀`, `IsScalarTower.algebraMap_smul`, `IsValuativeTopology.isClopen_ball`, `ConvexBody.smul_le_of_le`, `IsValuativeTopology.hasBasis_nhds`, `WeierstrassCurve.Projective.addZ_eq'`, `ConvexOn.lt_right_of_left_lt'`, `Algebra.IsUnramifiedAt.not_minpoly_sq_dvd`, `SchwartzMap.integral_bilinear_laplacian_right_eq_left`, `LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux`, `LinearMap.lTensor_comp_mk`, `AlgHom.instNonUnitalAlgHomClassOfAlgHomClass`, `isUnit_zero_iff`, `KaehlerDifferential.instSMulCommClassTensorProduct`, `iteratedDeriv_fun_const_smul_field`, `Ideal.Filtration.stable_iff_exists_pow_smul_eq_of_ge`, `HasFDerivAt.lim`, `RatFunc.Luroth.algEquiv_X`, `Associates.dvdNotUnit_iff_lt`, `Seminorm.comp_apply`, `WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv`, `IsPrimitiveRoot.primitiveRootsPowEquiv_apply_coe`, `hasDerivWithinAt_const`, `openSegment_eq_image_lineMap`, `divisor_closure_eq_closure`, `Polynomial.pow_scaleRoots_of_isReduced`, `FormalMultilinearSeries.compAlongComposition_norm`, `ContinuousLinearMap.isometry_mul`, `LieSubalgebra.isNilpotent_ad_of_isNilpotent_ad`, `Polynomial.mul_scaleRoots`, `Complex.circleIntegral_sub_center_inv_smul_eq_of_differentiable_on_annulus_off_countable`, `VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral'`, `QuasispectrumRestricts.nonUnitalStarAlgHom_injective`, `MvPowerSeries.rescale_homogeneous_eq_smul`, `isCoveringMapOn_npow`, `Polynomial.X_pow_sub_X_sub_one_irreducible_aux`, `NonUnitalCommCStarAlgebra.toStarModule`, `Polynomial.X_pow_sub_one_separable_iff`, `tendsto_pow_atTop_atTop_of_one_lt`, `RingEquiv.map_pow`, `multiple_mem_span_of_mem_localization_span`, `OrthonormalBasis.sum_repr_symm`, `Meromorphic.pow`, `IntermediateField.isSeparable_adjoin_simple_iff_isSeparable`, `Int.coe_negOnePow`, `WeierstrassCurve.Jacobian.addY_of_Z_eq_zero_right`, `MultilinearMap.cons_smul`, `Odd.pow_inj`, `Dynamics.coverMincard_le_pow`, `Orientation.kahler_apply_self`, `Pi.single_smul₀`, `DifferentiableWithinAt.restrictScalars_fderivWithin`, `Module.Invertible.rTensorInv_leftInverse`, `Ideal.span_singleton_mul_span_singleton`, `WeierstrassCurve.Projective.add_of_Z_eq_zero_right`, `Polynomial.derivative_sq`, `IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrder`, `AlgebraicGeometry.Proj.pullbackAwayιIso_hom_SpecMap_awayMap_left_assoc`, `Polynomial.leadingCoeff_C_mul_X_pow`, `WittVector.frobeniusPolyAux_eq`, `LinearMap.prodMapAlgHom_apply_apply`, `MonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `Mathlib.Tactic.Ring.pow_bit1`, `Module.End.eigenspace_def`, `IntermediateField.AdjoinSimple.trace_gen_eq_zero`, `HasStrictFDerivAt.continuousAlternatingMap_apply`, `WeierstrassCurve.Φ_three`, `NormedSpace.exp_nsmul`, `Orthonormal.inner_left_sum`, `NonUnitalSubalgebra.instSMulMemClass`, `Matrix.SpecialLinearGroup.coe_GLPos_neg`, `Dynamics.coverMincard_mul_le_pow`, `MeasureTheory.FiniteMeasure.normalize_eq_inv_mass_smul_of_nonzero`, `ZMod.coe_int_isUnit_iff_isCoprime`, `HahnSeries.SummableFamily.isPWO_iUnion_support_powers`, `cfc_inv_id`, `DiscreteConvolution.AddConvolutionExistsAt.convolution_vadd`, `StrongDual.extendRCLikeₗ_symm_apply`, `hasSum_geom_series_inverse`, `HasDerivAtFilter.congr_of_eventuallyEq`, `HasStrictDerivAt.complexToReal_fderiv'`, `spectrum.of_inv₀_mem_inv`, `SymmetricAlgebra.lift_comp_ι`, `nilpotencyClass_eq_one`, `constFormalMultilinearSeries_apply_of_nonzero`, `PadicInt.mem_span_pow_iff_le_valuation`, `fourierIntegral_gaussian_innerProductSpace`, `RootPairing.CoPolarization_apply`, `egauge_ball_one_le_of_one_lt_norm`, `HasFTaylorSeriesUpToOn.add`, `Polynomial.not_isUnit_X_add_C`, `NormedSpace.norm_expSeries_summable'`, `Polynomial.Monic.irreducible_of_irreducible_map_of_isPrime_nilradical`, `MeasureTheory.dist_convolution_le'`, `Matrix.linftyOpNormSMulClass`, `Submodule.span_range_natDegree_eq_adjoin`, `finsuppTensorFinsuppRid_single_tmul_single`, `AddMonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `isQuotientCoveringMap_zpow`, `Polynomial.degree_cubic`, `Real.circleAverage_smul`, `NNRat.addSubmonoid_closure_range_pow`, `LinearMap.isNilpotent_iff_charpoly`, `LieModule.shiftedGenWeightSpace.coe_lie_shiftedGenWeightSpace_apply`, `AlternatingMap.curryLeftLinearMap_apply`, `SymmetricAlgebra.lift_ι`, `Subalgebra.inclusion.isScalarTower_right`, `ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM`, `WithLp.normSMulClassSeminormedAddCommGroupToProd`, `ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff`, `PiTensorProduct.piTensorHomMap₂_tprod_tprod_tprod`, `gcd_neg'`, `DividedPowers.dpow_mul`, `VectorField.lieBracket_const_smul_right`, `Module.preReflection_apply`, `Asymptotics.isBigOTVS_pi`, `WeierstrassCurve.Projective.addX_eq`, `Algebra.toMatrix_lmul'`, `NormedSpace.norm_expSeries_div_summable_of_mem_ball`, `Perfection.mk_comp_teichmuller`, `multiplicity_pow_self`, `DFinsupp.instPosSMulReflectLE`, `IsRelPrime.of_add_mul_right_right`, `LieAlgebra.ad_apply`, `CovariantDerivative.torsion_eq_zero_iff`, `PiLp.smul_apply`, `LieAlgebra.toEnd_pow_apply_mem`, `TrivSqZeroExt.hasSum_expSeries_of_smul_comm`, `DifferentiableWithinAt.clm_comp`, `IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral'`, `ProbabilityTheory.hasDerivAt_neg_exp_mul_exp`, `Matrix.isUnit_fromBlocks_zero₁₂`, `PowerSeries.trunc_trunc_pow`, `hasSum_coe_mul_geometric_of_norm_lt_one`, `MDifferentiableOn.cle_arrowCongr`, `PiLp.normSMulClassSeminormedAddCommGroupToPi`, `CommAlgCat.whiskerLeft_hom`, `cexp_neg_quadratic_isLittleO_abs_rpow_cocompact`, `ExteriorAlgebra.isUnit_algebraMap`, `Unitary.symm_mulRight`, `Valuation.restrict_def`, `LinearIsometryEquiv.strictConvex_image`, `Filter.tendsto_const_mul_pow_atBot_iff`, `ContinuousMultilinearMap.isEmbedding_toUniformOnFun`, `MultilinearMap.mkContinuousMultilinear_norm_le'`, `Matrix.SpecialLinearGroup.coe_pow`, `MvPolynomial.isLocalHom_expand`, `CochainComplex.HomComplex.Cochain.shift_units_smul`, `IsUnit.algebraMap_of_algebraMap`, `AffineMap.homothety_linear`, `isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow`, `RingPreordering.unitsInv_mem`, `MonoidWithZeroHom.inl_injective`, `AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.coequalizer_π_app_isLocalHom`, `Algebra.Extension.contangentEquiv_tmul`, `MulAction.surjective₀`, `Unitization.norm_def`, `convex_uIcc`, `ContMDiff.clm_bundle_apply₂`, `EisensteinSeries.qExpansion_identity_pnat`, `RatFunc.natDegree_minpolyX`, `ENNReal.tsum_condensed_le`, `Unitary.conjStarAlgAut_symm_apply`, `mul_zero`, `Polynomial.cyclotomic_mul_prime_pow_eq`, `DirectSum.coe_mul_of_apply_of_mem_zero`, `ModuleTopology.eq_coinduced_of_surjective`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso`, `LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace`, `Ideal.quotOfMul_surjective`, `Real.iteratedDeriv_fourier`, `Subalgebra.coe_smul`, `Polynomial.Splits.pow`, `WittVector.RecursionBase.solution_spec`, `map_natCast_smul`, `SchwartzMap.eLpNorm_le_seminorm`, `Function.Antiperiodic.add_nat_mul_eq`, `WeierstrassCurve.Projective.addMap_of_Y_eq`, `HahnSeries.pow_add`, `MDifferentiableAt.smul`, `Polynomial.dickson_one_one_charP`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_surjective`, `PerfectionMap.comp_equiv`, `LinearMap.isNilpotent_mulRight_iff`, `Submodule.det_reflection`, `ClassGroup.mk_mk0`, `Affine.Simplex.centroid_eq_smul_vsub_vadd_point`, `ZMod.isUnit_prime_iff_not_dvd`, `NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le`, `HasStrictDerivAt.const_smul`, `Polynomial.degree_X_pow`, `selfAdjoint.star_coe_unitarySelfAddISMul`, `StrictConvex.add`, `RatFunc.irreducible_minpolyX'`, `HasDerivAt.fun_sum`, `AntivaryOn.pow_left₀`, `Quiver.Path.weight_nonneg`, `MvPolynomial.of_irreducible_expand`, `hasFDerivAtFilter_iff_isLittleOTVS`, `IntermediateField.finSepDegree_adjoin_simple_le_finrank`, `FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp`, `TensorProduct.finsuppScalarLeft_apply_tmul_apply`, `Finset.sum_sq_le_sum_mul_sum_of_sq_eq_mul`, `Matrix.ker_diagonal_toLin'`, `NumberField.IsCMField.unitsMulComplexConjInv_ker`, `mul_geom_sum`, `second_derivative_symmetric`, `Prime.finiteMultiplicity_mul`, `ContinuousAlternatingMap.curryLeft_same`, `ContinuousMultilinearMap.curryRight_apply`, `CategoryTheory.Abelian.Ext.comp_smul`, `NormedSpace.expSeries_apply_eq'`, `Distribution.dsupport_smulLeftCLM_subset`, `Matrix.det_adjugate`, `ArithmeticFunction.mul_smul'`, `one_le_pow_iff_of_nonneg`, `WeierstrassCurve.preΨ'_odd`, `Polynomial.leadingCoeff_comp`, `DFinsupp.instPosSMulMono`, `Subsemiring.instSMulCommClassSubtypeMemCenter_1`, `Units.isOpen`, `WeierstrassCurve.twoTorsionPolynomial_discr_isUnit`, `Balanced.absorbs_self`, `CategoryTheory.Linear.comp_smul`, `star_nnqsmul`, `Module.End.mem_iInf_maxGenEigenspace_iff`, `HasFPowerSeriesOnBall.uniform_geometric_approx'`, `image_segment`, `LinearMap.coe_rTensorHom`, `Unitary.toRingEquiv_conjStarAlgAut`, `Ideal.snd_comp_quotientMulEquivQuotientProd`, `ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero`, `hasSum_choose_mul_geometric_of_norm_lt_one'`, `Polynomial.isEisensteinAt_iff`, `Function.support_const_smul_of_ne_zero`, `ContinuousLinearMap.extendTo𝕜_apply`, `QuadraticForm.sigPos_weightedSumSquares`, `Submodule.starConvex`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars`, `Algebra.TensorProduct.assoc_toLinearEquiv`, `Module.Basis.symmetricAlgebra_repr_apply`, `IsRadical.squarefree`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const`, `Algebra.TensorProduct.assoc_symm_tmul`, `Ring.inverse_unit`, `IsPrimitiveRoot.injOn_pow_mul`, `PowerSeries.coeff_smul`, `Module.AEval.of_symm_X_smul`, `IntermediateField.card_algHom_adjoin_integral`, `HasFDerivAt.comp_hasDerivWithinAt_of_eq`, `EuclideanSpace.volume_ball_fin_three`, `Polynomial.aeval_coe_eq_smeval`, `SzemerediRegularity.add_div_le_sum_sq_div_card`, `WeierstrassCurve.Projective.negDblY_smul`, `dvd_geom_sum₂_self`, `convexOn_univ_piecewise_Iic_of_antitoneOn_Iic_monotoneOn_Ici`, `Derivation.leibniz_of_mul_eq_one`, `Polynomial.natDegree_pow_le_of_le`, `FiniteField.isSplittingField_of_card_eq`, `Prime.pow_dvd_of_dvd_mul_right`, `Associates.mem_factorSet_top`, `AffineSubspace.mem_affineSpan_insert_iff`, `Complex.linearEquiv_det_conjAe`, `ConvexCone.pointed_zero`, `one_le_sq_iff₀`, `MeromorphicAt.pow`, `AffineSubspace.subtypeₐᵢ_linear`, `LieModule.traceForm_eq_sum_finrank_nsmul`, `LieAlgebra.Basis.baseSupp_apply_smul_e`, `Matrix.toBilin'_apply`, `sq_lt_sq`, `Seminorm.closedBall_eq_emptyset`, `Commute.isNilpotent_mul_left_iff`, `LipschitzWith.iterate`, `Convex.strictConvex'`, `egauge_le_of_smul_mem`, `IntermediateField.relrank_dvd_rank_bot`, `LinearMap.det_restrictScalars`, `hasStrictFDerivAt_pow'`, `add_sq_le`, `convex_Icc`, `Ideal.finite_mulSupport_coe`, `IsBoundedSMul.of_enorm_smul_le`, `ContinuousLinearMap.applySMulCommClass`, `Polynomial.dickson_one_one_zmod_p`, `MvPolynomial.coe_pow`, `strictConvex_Ioc`, `LieAlgebra.conj_ad_apply`, `IsValuativeTopology.hasBasis_nhds_zero`, `LinearMap.flip_injective_iff₂`, `QuadraticForm.tensorRId_toLinearEquiv`, `Bound.pow_le_pow_right_of_le_one_or_one_le`, `RestrictScalars.ringEquiv_map_smul`, `AddSubmonoid.smul_mem_pointwise_smul_iff₀`, `ContinuousLinearMap.norm_extendTo𝕜'`, `ValuationSubring.unitGroup_le_unitGroup`, `Matrix.isUnit_fromBlocks_iff_of_invertible₁₁`, `Perfection.teichmuller_zero`, `Finset.sum_pow_eq_sum_piAntidiag_of_commute`, `RootPairing.prod_rootFormIn_smul_coroot_mem_range_PolarizationIn`, `IsUnit.natCast_factorial_of_algebra`, `GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I'`, `frobeniusEquiv_def`, `HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope`, `RestrictScalars.lsmul_apply_apply`, `Matrix.ProjGenLinGroup.val_signDet_mk`, `IsIntegralClosure.range_le_span_dualBasis`, `DifferentiableWithinAt.pow`, `Matrix.exists_left_inverse_iff_isUnit`, `ContinuousMapZero.toContinuousMapHom_toNNReal`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply`, `ModularForm.SL_slash_def`, `WeierstrassCurve.variableChange_Δ`, `Associates.prod_mono`, `Valuation.IsEquiv.orderMonoidIso_trans`, `WithVal.strictMono_valueGroupEquiv_symm`, `AddChar.norm_apply`, `IsCyclotomicExtension.Rat.Three.Units.mem`, `Matrix.toLin_apply`, `StandardEtalePresentation.exists_mul_aeval_x_g_pow_eq_aeval_x`, `CFC.log_pow'`, `Polynomial.Splits.C_mul_X_pow`, `IsStarProjection.inr`, `Asymptotics.IsLittleOTVS.fun_symm`, `HasDerivAtFilter.const_add`, `Matrix.toLin'_one`, `Commute.smul_right_iff₀`, `NumberField.Units.complexEmbedding_apply`, `HasDerivWithinAt.of_notMem_tsupport`, `StrictConvex.preimage_smul`, `PeriodPair.hasSum_weierstrassP`, `not_linearIndependent_iff_finsupp`, `ContinuousLinearEquiv.unitsEquivAut_apply_symm`, `AdicCompletion.mk_surjective`, `Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPart`, `MDifferentiableAt.clm_precomp`, `WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne'`, `MvPowerSeries.monomial_pow`, `ContDiffMapSupportedIn.postcompCLM_apply`, `ValuationSubring.principal_units_le_units`, `SchwartzMap.compSubConstCLM_comp`, `NonUnitalStarSubalgebra.iSupLift_of_mem`, `HasDerivWithinAt.mono_of_mem_nhdsWithin`, `TemperedDistribution.smulLeftCLM_add`, `DoubleCentralizer.coeHom_apply`, `summable_norm_pow_mul_geometric_div_one_sub`, `ContinuousAlternatingMap.curryLeft_zero`, `Associates.ufm`, `RootPairing.reflection_dualMap_eq_coreflection`, `Matrix.Module.smul_apply`, `DualNumber.coe_lift_symm_apply`, `Matrix.ProjGenLinGroup.signDet_mk`, `ContinuousMultilinearMap.analyticOn_uncurry_of_linear`, `WeierstrassCurve.Projective.negAddY_of_Z_eq_zero_right`, `ExpGrowth.expGrowthSup_pow`, `OnePoint.smul_infty_eq_ite`, `ContinuousAlternatingMap.restrictScalarsLI_apply`, `Complex.restrictScalars_toSpanSingleton`, `ClassGroup.mk_eq_one_iff`, `Ideal.toCotangent_eq_zero`, `mul_eq_mul_prime_pow`, `Complex.volume_closedBall`, `Module.Basis.constr_apply_fintype`, `NumberField.fractionalIdeal_rank`, `Complex.hasSum_cos'`, `fwdDiff_smul`, `Asymptotics.IsTheta.isThetaTVS`, `Commute.exists_add_pow_prime_eq`, `WeierstrassCurve.coe_inv_map_Δ'`, `LieSubmodule.Quotient.isCentralScalar`, `AddMonoidAlgebra.liftMagma_apply_apply`, `Polynomial.opRingEquiv_symm_C_mul_X_pow`, `TensorProduct.LieModule.lift_apply`, `Ideal.Filtration.pow_smul_le_pow_smul`, `IsArtinianRing.isUnit_iff_isLeftRegular`, `pinGroup.toUnits_injective`, `IsLocalizedModule.fromLocalizedModule'_add`, `ContinuousAlternatingMap.cons_smul`, `NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single`, `gaussSum_pow_eq_prod_jacobiSum_aux`, `HasFPowerSeriesOnBall.tendsto_partialSum`, `Valuation.mem_ltAddSubgroup_iff`, `inhomogeneousCochains.d_hom_apply`, `NNReal.smul_def`, `WeierstrassCurve.variableChange_a₄`, `ZMod.dft_dft`, `Quaternion.imJ_snd_dualNumberEquiv`, `HasDerivWithinAt.Ioi_of_Ioo`, `inv_smul_eq_iff₀`, `val_inv_cfcUnits`, `HasDerivWithinAt.fun_mul`, `DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap`, `AbsConvex.closure`, `cfcₙHom_map_quasispectrum`, `IsDiscreteValuationRing.addVal_pow`, `AddAut.mulRight_apply`, `Filter.Tendsto.zero_smul_isBoundedUnder_le`, `CoalgCat.MonoidalCategoryAux.counit_tensorObj`, `MultilinearMap.piFamilyₗ_apply`, `fderiv_fun_mul'`, `TrivSqZeroExt.liftEquivOfComm_apply`, `Finset.centerMass_segment'`, `TensorProduct.isBaseChange`, `ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft`, `isGroupLikeElem_unitsInv`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroup`, `AdicCompletion.pow_smul_top_le_ker_eval`, `NormedSpace.expSeries_sum_eq_rat`, `Polynomial.monic_geom_sum_X`, `Submodule.top_le_span_range_iff_forall_exists_fun`, `HasFPowerSeriesWithinAt.prod`, `MeasureTheory.iteratedDeriv_charFun`, `HasDerivWithinAt.pow'`, `LinearPMap.map_smul`, `Ideal.pow_mem_of_pow_mem`, `Module.End.finite_spectrum`, `ContMDiffMap.coe_smul`, `unitary.coe_inv`, `Set.neg_smul_set`, `LinearMap.concaveOn`, `Derivation.instIsCentralScalar`, `WeierstrassCurve.Projective.negMap_eq`, `Ideal.mul_assoc`, `IsLocalizedModule.exists_integer_multiple`, `AddChar.coe_doubleDualEquiv`, `Valuation.isClosed_closedBall`, `ContinuousLinearMap.adjoint_comp_self_injective_iff`, `KummerDedekind.Ideal.irreducible_map_of_irreducible_minpoly`, `Convex.is_linear_image`, `NonUnitalStarSubalgebra.prod_inf_prod`, `FormalMultilinearSeries.leftInv_coeff_one`, `WithAbs.ofAbs_pow`, `LinearMap.IsSymmetric.smul`, `Module.Basis.smul_eq_map`, `Matrix.det_succ_column_zero`, `MultilinearMap.smulRight_apply`, `Units.exists0'`, `PosSMulReflectLT.toPosSMulReflectLE`, `FiniteMultiplicity.neg_iff`, `QuasispectrumRestricts.isClosedEmbedding_nonUnitalStarAlgHom`, `WeierstrassCurve.c₆_of_isCharNeTwoNF`, `mdifferentiableOn_continuousLinearMapCoordChange`, `jacobiTheta₂'_functional_equation`, `CommAlgCat.whiskerRight_hom`, `instIsPushoutPolynomial`, `Polynomial.separable_C`, `AdicCompletion.map_ext''_iff`, `hasDerivAtFilter_intCast`, `ContDiffMapSupportedIn.fderivCLM_eq_of_scalars`, `MonoidAlgebra.instIsPushout'`, `Asymptotics.IsThetaTVS.symm`, `Polynomial.instIsLocalHomRingHomC`, `Polynomial.aeval_apply_smul_mem_of_le_comap'`, `CategoryTheory.ShortComplex.RightHomologyMapData.smul_φH`, `Polynomial.IsUnitTrinomial.irreducible_of_coprime'`, `MvPowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero`, `Matrix.IsHermitian.spectral_theorem`, `Submodule.exists_smith_normal_form_of_rank_eq`, `Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd`, `MeasureTheory.L1.setToL1_smul`, `pinGroup.units_mem_lipschitzGroup`, `prime_factors_unique`, `Commute.pow_dvd_sub_pow_of_pow_eq_zero_left`, `hasFPowerSeriesAt_pi_iff`, `NNReal.sum_mul_le_sqrt_mul_sqrt`, `MeasureTheory.eLpNorm'_const_smul`, `IsBaseChange.iff_lift_unique`, `IntermediateField.LinearDisjoint.of_inf_eq_bot`, `Algebra.Extension.Cotangent.map_toInfinitesimal_bijective`, `QuadraticMap.canLift'`, `NNReal.smulCommClass_right`, `toPrincipalIdeal_eq_iff`, `HahnSeries.orderTop_nsmul_le_orderTop_pow`, `Ideal.cotangentEquivIdeal_apply`, `ClassGroup.norm_lt`, `Antitone.convex_gt`, `Antivary.pow_right₀`, `hasDerivWithinAt_univ`, `LinearMap.det_eq_sign_charpoly_coeff`, `AlgebraicGeometry.Proj.opensRange_awayι`, `UniqueFactorizationMonoid.radical_pow`, `Asymptotics.isLittleOTVS_neg_right`, `Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub`, `finrank_eq_one_iff'`, `AnalyticWithinAt.pow`, `TrivSqZeroExt.isUnit_inv_iff`, `Seminorm.ball_zero_absorbs_ball_zero`, `Module.Basis.smulTower'_apply`, `Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_pow`, `ModuleCat.smulShortComplex_f`, `Complex.cos_sq_add_sin_sq`, `Submodule.pointed_toConvexCone`, `TensorProduct.add_smul`, `FiniteDimensional.isUnit`, `Associates.exists_mem_multiset_le_of_prime`, `PadicInt.isUnit_den`, `Submodule.span_range_update_sub_smul`, `Submodule.topologicalClosure_mem_invtSubmodule`, `IsPrimitiveRoot.associated_pow_add_sub_sub_one`, `iterate_frobenius`, `TensorProduct.AlgebraTensorModule.lTensor_comp`, `PowerSeries.map_invUnitsSub`, `emultiplicity_prime_eq_emultiplicity_image_by_factor_orderIso`, `Algebra.smul_units_def`, `Matrix.GeneralLinearGroup.mem_center_iff_val_eq_scalar`, `pow_four_add_four_mul_pow_four`, `UpperHalfPlane.coe_J_smul`, `ContinuousLinearMap.toContinuousAddMonoidHom_inj`, `ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear`, `exists_open_convex_of_notMem`, `Polynomial.finiteMultiplicity_of_degree_pos_of_monic`, `Valuation.Integers.isUnit_of_one'`, `Polynomial.irreducible_of_degree_le_three_of_not_isRoot`, `NumberField.Units.coe_pow`, `homTensorHomEquiv_toLinearMap`, `lp.coeFn_smul`, `IsPurelyInseparable.algebraMap_elemReduct_eq'`, `smul_upperBounds_subset_lowerBounds_smul`, `InnerProductSpace.isStarProjection_rankOne_self`, `Polynomial.degreeLT.addLinearEquiv_symm_apply`, `WithVal.ofVal_pow`, `coord_norm'`, `StrictConvex.smul`, `ProperCone.relative_hyperplane_separation`, `OrderedFinpartition.compAlongOrderedFinpartitionL_apply`, `ContinuousAlternatingMap.piLIE_symm_apply_apply`, `PadicInt.norm_le_pow_iff_mem_span_pow`, `Complex.exp_sub_sum_range_succ_isLittleO_pow`, `ENNReal.top_pow`, `affineSegment_eq_segment`, `IsLocalRing.residue_ne_zero_iff_isUnit`, `ContinuousMap.continuous_isUnit_unit`, `PMF.binomial_apply`, `Ideal.sum_pow_mem_span_pow`, `endVecAlgEquivMatrixEnd_apply_apply`, `Unitary.coe_div`, `Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence`, `Submodule.coe_torsionBy`, `AlgebraicGeometry.Proj.basicOpen_pow`, `NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis`, `Quaternion.snd_imK_dualNumberEquiv_symm`, `strictConvex_Ico`, `Complex.continuousOn_prod_circle_transform_function`, `HasFPowerSeriesAt.hasFDerivAt`, `StrictConvex.linearIsometry_preimage`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply`, `Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub`, `ConcaveOn.openSegment_subset_strict_hypograph`, `ENat.pow_lt_top_iff`, `TensorAlgebra.toDirectSum_comp_ofDirectSum`, `Complex.pow_cpow_nat_inv`, `ConvexCone.coe_positive`, `ENat.epow_def`, `Bornology.IsVonNBounded.extend_scalars`, `KaehlerDifferential.submodule_span_range_eq_ideal`, `WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal'`, `WeierstrassCurve.ψ_odd`, `analyticAt_iff_analytic_smul`, `Complex.natCast_cpow_natCast_mul`, `spec_cfcₙAux`, `Asymptotics.IsBigOTVS.congr`, `iteratedDerivWithin_pow`, `CStarAlgebra.inv_le_inv`, `root_X_pow_sub_C_pow`, `LinearEquiv.smul_apply`, `instInvertibleReprₛ`, `selfAdjoint.val_pow`, `Submodule.range_powSMulQuotInclusion`, `StrongDual.extendRCLikeₗᵢ_apply`, `AlgebraicIndependent.liftAlgHom_comp_reprField`, `WeierstrassCurve.Ψ_even`, `Subalgebra.inclusion.faithfulSMul`, `gcd_mul_left'`, `HasDerivAt.ofReal_comp`, `HasFPowerSeriesWithinOnBall.compContinuousLinearMap`, `Bialgebra.TensorProduct.coalgebra_rid_eq_algebra_rid_apply`, `Algebra.TensorProduct.map_range`, `PerfectionMap.comp_symm_equiv`, `DivisibleHull.qsmul_of_nonneg`, `cfcₙHom_injective`, `Perfection.coeff_surjective`, `Ideal.associatesEquivIsPrincipal_symm_apply`, `IntermediateField.finrank_top'`, `LinearMap.BilinForm.nondegenerate_congr_iff`, `LinearMap.mkContinuous₂_norm_le`, `bernsteinPolynomial.sum_mul_smul`, `CochainComplex.HomComplex.Cochain.units_smul_v`, `LinearMap.aeval_self_charpoly`, `Polynomial.natDegree_X_pow_mul`, `Positive.val_pow`, `Matrix.GeneralLinearGroup.map_swap`, `Matrix.trace_toLin'_eq`, `IsBilinearMap.smul_left`, `MvPowerSeries.le_order_smul`, `NumberField.IsCMField.unitsMulComplexConjInv_apply`, `HomologicalComplex.smul_f_apply`, `FiniteMultiplicity.of_not_isUnit`, `Algebra.TensorProduct.tmul_pow`, `IsLocalizedModule.smul_inj`, `FormalMultilinearSeries.zero_radius`, `smul_unitBall`, `IsLocalization.linearMap_compatibleSMul`, `Algebra.Extension.H1Cotangent.val_smul`, `WeierstrassCurve.Φ_four`, `Quaternion.sq_eq_neg_normSq`, `LinearMap.BilinForm.flip_apply`, `WeierstrassCurve.j_of_isCharTwoJEqZeroNF`, `Subalgebra.isScalarTower_mid`, `Set.unit_valuation_eq_one`, `HasDerivAt.hasFDerivAt_equiv`, `PolynomialModule.instIsScalarTower`, `AlternatingMap.curryLeft_smul`, `WeierstrassCurve.Jacobian.polynomialZ_eq`, `WithSeminorms.congr_equiv`, `IntermediateField.inclusion_self`, `NumberField.Units.abs_det_eq_abs_det`, `ContinuousLinearMap.hasFPowerSeriesAt_bilinear`, `unitsEquivNeZero_apply_coe`, `AdjoinRoot.algEquivOfAssociated_symm`, `TrivSqZeroExt.inv_neg`, `IntermediateField.lift_bot`, `LaurentPolynomial.eval₂_toLaurent`, `IsPurelyInseparable.algebraMap_iterateFrobenius`, `Ideal.add_pow_add_pred_mem_of_pow_mem`, `VertexOperator.ext_iff`, `PowerSeries.le_order_pow`, `StrictConcaveOn.map_sum_eq_iff'`, `Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral`, `analyticOrderAt_pow`, `hasStrictDerivAt_const`, `AlgebraicGeometry.LocallyRingedSpace.isLocalHomStalkMap'`, `Rat.cast_smul_eq_qsmul`, `Set.smul_mem_center`, `PerfectField.toPerfectRing`, `LinearMap.isNilpotent_trace_of_isNilpotent`, `DivisibleHull.coeOrderAddMonoidHom_apply`, `QuadraticAlgebra.norm_intCast`, `PosSMulMono.toSMulPosMono`, `QuadraticAlgebra.mker_norm_eq_unitary`, `Commute.add_sq`, `SymmetricAlgebra.equivMvPolynomial_ι_apply`, `PosSMulStrictMono.nnrat_of_rat`, `intervalIntegral.integral_smul_deriv_eq_deriv_smul`, `emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso`, `CongruenceSubgroup.strictPeriods_Gamma1`, `ContinuousLinearMap.self_comp_adjoint_injective_iff`, `LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank`, `Associates.out_eq_zero_iff`, `Module.algebraMap_end_apply`, `AlgebraicGeometry.structureSheafInType.add_apply`, `hasStrictFDerivAt_list_prod_attach'`, `Polynomial.eval_mul_X_pow`, `WeierstrassCurve.Jacobian.dblU_eq`, `Module.FinitePresentation.linearEquivMapExtendScalars_apply`, `Polynomial.isNilpotent_monomial_iff`, `IsLocalizedModule.iso_symm_apply_aux`, `IsPrimitiveRoot.norm_pow_sub_one_two`, `NumberField.mixedEmbedding.convexBodyLT'_volume`, `MvPowerSeries.isUnit_constantCoeff`, `GroupLike.val_toUnits_apply`, `IntermediateField.normalClosure_of_normal`, `HasStrictDerivAt.scomp`, `HasFPowerSeriesWithinAt.restrictScalars`, `Subsemiring.centralizer_toSubmonoid`, `tangentConeAt_real_subset_isRCLikeNormedField`, `isUnit_iff_mem_nonZeroDivisors_of_finite`, `preNormEDS'_even`, `seminormFromConst_isPowMul`, `Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem`, `Matrix.PosDef.isStrictlyPositive`, `Module.Basis.parallelepiped_eq_map`, `PowerSeries.X_pow_mul_injective`, `pow_right_strictAnti₀`, `LieAlgebra.rootSpace_comap_eq_genWeightSpace`, `Algebra.discr_powerBasis_eq_prod`, `Module.Invertible.rTensorInv_injective`, `TensorProduct.AlgebraTensorModule.lTensor_mul`, `ContDiffMapSupportedIn.norm_apply_le_seminorm`, `Complex.deriv_tan`, `Algebra.TensorProduct.map_comp_includeRight`, `LinearEquiv.toLinearMap_smul`, `Matrix.vandermonde_cons`, `geom_sum_neg_iff`, `associated_norm_prod_smith`, `MvPolynomial.ker_eval₂Hom_universalFactorizationMap`, `IsValuativeTopology.isOpen_closedBall`, `WithCStarModule.instContinuousSMul`, `MeasureTheory.Lp.instIsCentralScalar`, `Polynomial.factorial_mul_shiftedLegendre_eq`, `ContinuousLinearMap.restrictScalars_smul`, `DivisibleHull.nsmul_mk`, `ContinuousAlternatingMap.piLinearEquiv_symm_apply`, `fderiv_continuousAlternatingMap_apply_apply`, `Matrix.scalar_comm_iff`, `Polynomial.isNilpotent_iff`, `DirectSum.coe_mul_of_apply_aux`, `SchwartzMap.hasDerivAt`, `HasDerivWithinAt.fun_sub`, `Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_T_eq_poly_in_T`, `Module.End.mem_eigenspace_iff`, `lp.single_smul`, `Finset.sum_pow_mul_eq_add_pow`, `Algebra.TensorProduct.one_mul`, `Polynomial.natDegree_X_pow_le`, `OnePoint.IsBoundedAt.smul_iff`, `Seminorm.inf_apply`, `Ideal.constr_basisSpanSingleton`, `ClassGroup.mk_eq_mk`, `TrivSqZeroExt.sndHom_comp_map`, `PiTensorProduct.mapLMultilinear_apply_apply`, `iteratedDeriv_comp_two`, `IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f`, `RatFunc.minpolyX_eq_zero_iff`, `HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq`, `Units.neg_smul`, `HasFDerivWithinAt.clm_comp`, `LinearEquiv.isUnit_det`, `ContinuousLinearMap.evalL_apply`, `LinearPMap.supSpanSingleton_apply_smul_self`, `WfDvdMonoid.max_power_factor'`, `RootPairing.range_polarizationIn`, `IsRelPrime.of_add_mul_left_left`, `CategoryTheory.Functor.map_units_smul`, `isBoundedBilinearMap_apply`, `WeierstrassCurve.twoTorsionPolynomial_disc_isUnit`, `geom_sum_zero`, `Submodule.pow_mem_pow`, `InfiniteGalois.isOpen_iff_finite`, `FormalMultilinearSeries.analyticOnNhd`, `Ideal.pow_sup_eq_top'`, `ContinuousLinearEquiv.map_smulₛₗ`, `Submodule.mem_span_range_iff_exists_fun`, `Unitization.nnreal_cfcₙ_eq_cfc_inr`, `exteriorPower.presentation_relation`, `UniqueFactorizationMonoid.factors_prod`, `StarConvex.add_smul_sub_mem`, `LinearMap.polyCharpolyAux_map_aeval`, `hasDerivAtFilter_iff_tendsto`, `Associates.mem_factors_iff_dvd`, `Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero`, `MvPolynomial.monic_monomial_eq`, `NormedSpace.expSeries_div_summable_of_mem_ball`, `Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun`, `isSplittingField_AdjoinRoot_X_pow_sub_C`, `convex_hyperplane`, `HasStrictDerivAt.comp`, `WeierstrassCurve.Jacobian.Y_eq_of_Y_ne'`, `HVertexOperator.ext_iff`, `Complex.cpow_ofNat_mul`, `Finset.weightedVSubOfPoint_apply_const`, `PosSMulMono.toPosSMulStrictMono`, `Polynomial.natSepDegree_pow_of_ne_zero`, `isLocalHom_of_isIso`, `hasStrictFDerivAt_ringInverse`, `KaehlerDifferential.map_compDer`, `Polynomial.isUnit_of_self_mul_dvd_separable`, `PadicInt.ker_toZModPow`, `Matrix.inv_pow'`, `LinearMap.liftBaseChange_tmul`, `ContinuousLinearMap.mul_apply'`, `LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ`, `IntermediateField.isSplittingField_iSup`, `starConvex_singleton`, `AffineSubspace.wOppSide_smul_vsub_vadd_right`, `Algebra.traceMatrix_of_basis`, `fromTangentSpace_mfderiv_smul`, `TrivSqZeroExt.map_comp_map`, `Polynomial.natDegree_pow_le`, `TensorProduct.quotTensorEquivQuotSMul_symm_mk`, `CStarMatrix.reindexₐ_symm`, `ContDiff.smul`, `Unitary.norm_map`, `AdicCompletion.of_ofLinearEquiv_symm`, `tendsto_const_mul_pow_nhds_iff`, `AdicCompletion.kerProj_of`, `ConcaveOn.add`, `Polynomial.coeff_X_pow_self`, `LinearMap.instStarModuleId`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn`, `Polynomial.natDegree_pow`, `NNReal.convex_iff`, `LieDerivation.commutator_coe_linear_map`, `MonoidAlgebra.liftMagma_symm_apply`, `IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen`, `LieModule.Cohomology.smul_apply_apply`, `AddMonoidAlgebra.liftMagma_symm_apply`, `LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply`, `Polynomial.dvd_C_mul_X_sub_one_pow_add_one`, `DifferentiableOn.fun_pow`, `InnerProductSpace.rankOne_comp_rankOne`, `smulAddHom_apply`, `MeasureTheory.convolution_lsmul_swap`, `ProbabilityTheory.gaussianPDFReal_inv_mul`, `zero_pow_eq`, `Matrix.spectrum_toLin`, `AddMonoidAlgebra.gradeBy.gradedMonoid`, `TensorAlgebra.ι_leftInverse`, `IntermediateField.relfinrank_bot_left`, `TestFunction.mkCLM_apply`, `Algebra.IsPushout.tensorProduct_tensorProduct`, `Associates.prime_mk`, `ProbabilityTheory.charFun_inv_sqrt_mul_sum`, `pinGroup.mem_lipschitzGroup`, `isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C`, `PolyEquivTensor.toFunBilinear_apply_apply`, `Commute.add_pow'`, `Unitization.starLift_apply`, `HasDerivAtFilter.comp_of_eq`, `Prime.isRadical`, `LinearMap.toMatrix'_comp`, `Matrix.toLinearEquiv'_apply`, `LinearMap.isUnit_toMatrix'_iff`, `lp.instIsCentralScalarSubtypePreLpMemAddSubgroup`, `IsPrimitiveRoot.eq_pow_of_mem_rootsOfUnity`, `CommAlgCat.associator_inv_hom`, `ModuleCat.ihom_coev_app`, `IsCoprime.isUnit_of_dvd`, `Ideal.span_singleton_mul_left_mono`, `Polynomial.ofMultiset_apply`, `Antitone.tendsto_le_alternating_series`, `Matrix.toBilin_toMatrix`, `hasDerivAtFilter_finCons'`, `Asymptotics.IsBigOTVS.eventually_smallSets`, `Matrix.GeneralLinearGroup.coe_inv`, `fwdDiff_iter_eq_factorial`, `MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul`, `WeierstrassCurve.isUnit_Δ`, `Module.AEval.mem_mapSubmodule_symm_apply`, `Valuation.ltSubmodule_le_leSubmodule`, `IsSumSq.sum_sq`, `PolyEquivTensor.toFunLinear_tmul_apply`, `Submonoid.mem_nonunits_iff_or`, `ContinuousMap.toLp_injective`, `PowerSeries.invOneSubPow_add`, `StrictConcaveOn.map_sum_eq_iff`, `ArithmeticFunction.coe_zeta_smul_apply`, `IsBezout.associated_gcd_gcd`, `TestFunction.fderivCLM_eq_of_scalars`, `midpoint_vsub_right`, `IsCoprime.pow_right_iff`, `ContinuousLinearMap.comp_smulₛₗ`, `NumberField.Units.coe_injective`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iff`, `setIntegral_withDensity_eq_setIntegral_smul`, `IsLocalizedModule.mk'_smul_mk'`, `DoubleCentralizer.pow_fst`, `ConcaveOn.translate_left`, `CStarAlgebra.isUnit_of_le`, `Valuation.toTopologicalSpace_eq`, `geom_sum_alternating_of_lt_neg_one`, `Matrix.nondegenerate_toLinearMap₂_iff`, `CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left`, `SlashInvariantForm.coe_trace`, `Function.Antiperiodic.const_smul₀`, `gcd_isUnit_iff`, `WeierstrassCurve.Δ_of_isCharNeTwoNF`, `nnnorm_pow_le'`, `isConformalMap_complex_linear_conj`, `MeromorphicAt.meromorphicTrailingCoeffAt_smul`, `fderiv_smul_const`, `Finset.smul_univ₀'`, `EisensteinSeries.E_qExpansion_coeff`, `WittVector.mul_polyOfInterest_aux1`, `StrictConvexOn.convex_lt`, `LinearMap.BilinForm.comp_congr`, `hasDerivWithinAt_finCons'`, `AffineMap.coe_lineMap`, `Matrix.toBilin'_comp`, `PMF.binomial_apply_self`, `Matrix.isHermitian_iff_isSymmetric`, `TrivSqZeroExt.instL1IsBoundedSMul`, `LieModule.Cohomology.instLinearMapClassSubtypeLinearMapIdMemSubmoduleTwoCochain`, `cfcₙHomSuperset_id`, `VectorField.mpullbackWithin_const_smul_apply`, `LieModule.toEnd_pow_lie`, `WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq'`, `Polynomial.Chebyshev.T_neg_two`, `Asymptotics.Filter.Tendsto.isBigOTVS_one`, `StarConvex.preimage_add_left`, `Quaternion.sq_eq_normSq`, `Associates.count_mul_of_coprime'`, `AdicCompletion.evalOneₐ_of`, `PowerSeries.order_pow`, `antivaryOn_iff_smul_rearrangement`, `TestFunction.lineDerivCLM_eq_of_scalars`, `Polynomial.rootMultiplicity_eq_multiplicity`, `NumberField.mixedEmbedding.logMap_unit_smul`, `convex_RCLike_iff_convex_real`, `NumberField.Units.coe_one`, `PointedCone.mem_span_set`, `sq_eq_sq_iff_abs_eq_abs`, `Cardinal.mk_finset_of_fintype`, `WeierstrassCurve.Jacobian.addMap_of_Z_eq_zero_left`, `Module.End.HasUnifEigenvector.apply_eq_smul`, `Algebra.TensorProduct.tensorTensorTensorComm_toLinearEquiv`, `WithZero.logEquiv_apply`, `Valued.integer.norm_unit`, `powers_le_nonZeroDivisors_of_noZeroDivisors`, `Complex.exp_sub_sum_range_isBigO_pow`, `IntermediateField.LinearDisjoint.rank_sup`, `IntermediateField.le_extendScalars_iff`, `Matrix.det_neg`, `TannakaDuality.FiniteGroup.sumSMulInv_single_id`, `Module.AEval.X_smul_of`, `Associates.factors_eq_top_iff_zero`, `Algebra.FormallySmooth.iff_split_surjection`, `algebraMap.coe_smul'`, `DirichletCharacter.norm_LFunction_product_ge_one`, `Convex.combo_closure_interior_mem_interior`, `irreducible_iff_prime_of_existsUnique_irreducible_factors`, `InnerProductSpace.rankOne_comp`, `Matrix.discr_conj'`, `spectrum.map_inv`, `Unitary.joined`, `Perfection.pthRootMonoidHom_eq_pthRoot`, `frobenius_def`, `CochainComplex.HomComplex.Cochain.rightShift_units_smul`, `CharTwo.sq_injective`, `ValueDistribution.characteristic_pow_top`, `WeierstrassCurve.Jacobian.negDblY_of_Y_eq`, `derivWithin_inv'`, `Asymptotics.isLittleOTVS_fun_comm`, `Polynomial.Chebyshev.S_two`, `FormalMultilinearSeries.apply_eq_prod_smul_coeff`, `Complex.I_pow_three`, `Unitization.starMap_comp`, `pow_le_one_iff_of_nonneg`, `neg_one_pow_char_pow`, `ClassGroup.equivPic_symm_apply`, `LocalizedModule.lift_mk`, `Cardinal.not_irreducible_of_aleph0_le`, `CStarAlgebra.le_one_of_one_le_inv`, `Finset.sum_range_by_parts`, `Asymptotics.IsTheta.const_smul_left`, `CliffordAlgebra.invOf_ι`, `Matrix.PosSemidef.pow`, `Subring.pointwise_smul_le_iff₀`, `DifferentiableWithinAt.fun_smul`, `sq_nonpos_iff`, `Asymptotics.isLittleOTVS_comm`, `intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le`, `Rep.leftRegularHom_hom_single`, `Matrix.isUnit_comp_iff`, `HasDerivWithinAt.scomp`, `Algebra.TensorProduct.ext_iff`, `lp.instIsScalarTowerPreLp`, `ContinuousLinearMap.hasBasis_nhds_zero_of_basis`, `IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable'`, `Asymptotics.IsLittleOTVS.snd`, `hasFPowerSeriesWithinAt_pi_iff`, `Ideal.IsTwoSided.mul_one`, `IsLocalizedModule.exists_of_eq`, `MeasureTheory.eLpNorm_const_smul`, `Unitary.mulLeft_mul_apply`, `Valuation.ltAddSubgroup_le_leAddSubgroup`, `IsAdicComplete.StrictMono.of_comp_lift`, `MulChar.exists_apply_ne_one_iff_exists_monoidHom`, `IntermediateField.rank_sup_le_of_isAlgebraic`, `TensorAlgebra.GradedAlgebra.ι_apply`, `Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod`, `neg_one_geom_sum`, `LieSubmodule.coe_toEnd`, `hasDerivWithinAt_comp_mul_left_smul_iff`, `Ideal.restrictScalars_mul`, `Algebra.pow_smul_mem_adjoin_smul`, `NumberField.IsCMField.mem_realUnits_iff`, `IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace`, `hasDerivAt_iff_isLittleO_nhds_zero`, `inner_smul_right`, `Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds`, `QuadraticMap.toFun_smul`, `SchwartzMap.tsupport_smulLeftCLM_subset`, `DFinsupp.instSMulPosReflectLT`, `DistribMulActionHom.coe_toLinearMap`, `Real.fourierIntegral_fderiv`, `Ideal.sup_mul_eq_of_coprime_right`, `InnerProductSpace.toMatrix_rankOne`, `PowerSeries.Unit_of_divided_by_X_pow_order_nonzero`, `HasFDerivWithinAt.continuousMultilinear_apply_const`, `Bornology.IsVonNBounded.vadd`, `LinearMap.equivariantProjection_apply`, `LinearOrderedCommGroupWithZero.fst_comp_inl`, `Polynomial.Monic.irreducible_iff_degree_lt`, `OrderIso.mulLeft₀_symm_apply`, `cfcₙHom_real_eq_restrict`, `Quiver.Path.weightOfEPs_pos`, `Subgroup.pointwise_smul_le_iff₀`, `MvPolynomial.support_X_pow`, `UniqueFactorizationMonoid.finprod_pow_count_eq_of_subsingleton_units`, `MvPolynomial.rTensor_symm_apply_single`, `Units.val_add`, `Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule`, `LinearMap.polar_AbsConvex`, `abs_pow_sub_pow_le`, `Polynomial.natDegree_X_pow`, `Polynomial.divX_C_mul_X_pow`, `Submodule.mker_spanSingleton`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₁`, `LieModule.toEnd_apply_apply`, `vadd_openSegment`, `MeasureTheory.ComplexMeasure.im_apply`, `PerfectClosure.mk_succ_pow`, `LinearMap.IsPerfPair.bijective_right`, `PiTensorProduct.liftIsometry_comp_mapL`, `Polynomial.X_pow_mul_monomial`, `mul_geom_sum₂_Ico`, `geom_series_mul_one_add`, `iteratedFDeriv_smul_const_apply`, `FractionalIdeal.den_mul_self_eq_num`, `HasStrictDerivAt.fun_const_smul`, `WeierstrassCurve.Jacobian.equation_iff`, `add_smul`, `HasDerivWithinAt.congr_deriv`, `Ideal.pow_sup_pow_eq_top'`, `CochainComplex.HomComplex.Cochain.rightUnshift_smul`, `Seminorm.continuous_iSup`, `LinearMap.mul_toMatrix₂_mul`, `Submodule.map_smul'`, `RootPairing.pairingIn_one_four_iff`, `AnalyticAt.fun_pow`, `MeasureTheory.Lp.instIsBoundedSMul`, `RootPairing.Equiv.instSMulCommClassAut`, `InnerProductSpace.isSymmetric_rankOne_self`, `IsUnit.val_subInvSMul`, `Polynomial.map_expand_pow_char`, `ContinuousLinearMap.toSpanSingleton_comp_toSpanSingleton`, `Matrix.isUnit_conjTranspose`, `Seminorm.ball_smul_ball`, `IsSMulRegular.of_flat_of_isBaseChange`, `TensorAlgebra.hom_ext_iff`, `ContinuousMap.coe_toLp`, `CommRingCat.equalizer_ι_isLocalHom'`, `WeierstrassCurve.Projective.addMap_of_Z_eq_zero_right`, `Real.fourierIntegral_convergent_iff`, `IsLocalRing.surjective_units_map_of_local_ringHom`, `MvPolynomial.isRegular_X_pow`, `Padic.valuation_pow`, `AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo'`, `PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept`, `skewAdjointPart_apply_coe`, `Associates.count_factors_eq_find_of_dvd_pow`, `mem_skewAdjointMatricesLieSubalgebra_unit_smul`, `continuousMultilinearCurryLeftEquiv_apply`, `OreLocalization.nontrivial_of_nonZeroDivisorsRight`, `one_lt_sq_iff_one_lt_abs`, `Associates.out_zero`, `PeriodPair.weierstrassPSeries_hasSum`, `SlashInvariantForm.slash_action_eqn_SL''`, `LinearMap.BilinForm.tensorDistribEquiv_tmul`, `Filter.tendsto_pow_atTop_iff`, `Prime.dvd_pow_iff_dvd`, `differentiable_pow`, `ZMod.orderOf_one_add_prime`, `AddChar.starComp_eq_inv`, `EuclideanDomain.gcd_isUnit_iff`, `IsIntegralCurveAt.hasDerivAt`, `coe_powMonoidWithZeroHom`, `Complex.ofReal_comp_pow`, `linearIndependent_add_smul_iff`, `LocalizedModule.eq_zero_of_smul_eq_zero`, `IsStrictlyPositive.commute_iff`, `MonoidAlgebra.GroupSMul.linearMap_apply`, `ProbabilityTheory.HasSubgaussianMGF.add`, `Matrix.toEuclideanLin_conjTranspose_eq_adjoint`, `isUnit_gcd_of_eq_mul_gcd`, `Commute.pow_add_mul_le_add_pow`, `MvPowerSeries.map_iterateFrobenius_expand`, `MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iff`, `Seminorm.coe_sSup_eq`, `Polynomial.cyclotomic_mul_prime_eq_pow_of_not_dvd`, `dvd_dvd_iff_associated`, `AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier`, `CongruenceSubgroup.strictWidthInfty_Gamma`, `LieModule.commute_toEnd_of_mem_center_right`, `ContMDiffAt.clm_prodMap`, `unitary.norm_map`, `Asymptotics.IsBigOTVS.rfl`, `NumberField.mixedEmbedding.unitSMul_smul`, `fourierCoeff_eq_intervalIntegral`, `IntermediateField.inclusion_injective`, `Ideal.mul_le_left`, `ProbabilityTheory.Fernique.measure_le_mul_measure_gt_normThreshold_le_of_map_rotation_eq_self`, `Differential.instDifferentialAlgebraSubtypeMemIntermediateField`, `Seminorm.bddBelow_range_add`, `Ring.KrullDimLE.isNilpotent_iff_mem_maximalIdeal`, `NonUnitalSubalgebra.instSMulCommClass'`, `Polynomial.derivative_pow`, `Submodule.nat_power_gradedMonoid`, `IsDedekindDomain.HeightOneSpectrum.intValuation_def`, `iterate_frobeniusEquiv_symm_pow_p_pow`, `Asymptotics.IsLittleOTVS.bot`, `IsSemisimpleModule.exists_end_algEquiv`, `SchwartzMap.tsupport_fderivCLM_subset`, `ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv`, `ContinuousLinearMap.isBigOTVS_comp`, `ContDiffAt.smul_const`, `Nat.prime_iff_card_units`, `CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply`, `Finpartition.IsEquipartition.sum_nonUniforms_lt`, `WeierstrassCurve.Jacobian.add_of_X_ne`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec`, `Polynomial.reverse_add_C`, `Set.smul_set_sdiff₀`, `Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq`, `IntermediateField.LinearDisjoint.bot_right`, `TensorAlgebra.range_lift`, `RootPairing.GeckConstruction.isNilpotent_f`, `MeasurableSet.const_smul_of_ne_zero`, `IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective`, `WeierstrassCurve.Projective.negDblY_eq'`, `Irreducible.normalizedFactors_pow`, `Commute.pow_eq_pow_iff_of_coprime`, `Module.supportDim_le_supportDim_quotSMulTop_succ`, `AnalyticAt.exists_eq_sum_add_pow_mul`, `QuotSMulTop.equivQuotTensor_naturality_mk`, `Ideal.ResidueField.algHom_ext_iff`, `Complex.exp_bound`, `ContinuousLinearMap.restrictScalarsIsometry_toLinearMap`, `SymmetricAlgebra.algebraMap_eq_one_iff`, `WithLp.smul_fst`, `iteratedDerivWithin_comp_const_smul`, `pow_right_injective₀`, `ContinuousMap.canLift`, `WeierstrassCurve.Projective.addZ_of_Z_eq_zero_left`, `ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf`, `Matrix.pow_col_eq_zero_of_le`, `Matrix.toLpLinAlgEquiv_apply_apply_ofLp`, `preNormEDS_mul_complEDS₂`, `IsPrimitiveRoot.squarefree_minpoly_mod`, `pow_right_mono₀`, `Complex.taylorSeries_eq_on_eball`, `LinearMap.toMatrix'_id`, `InnerProductSpace.gramSchmidt_def''`, `Real.hasDerivAt_fourierChar`, `Algebra.TensorProduct.algEquivIncludeRange_toAlgHom`, `ContinuousLinearMap.intervalIntegral_apply`, `Polynomial.eval_eq_sum_range'`, `ZMod.unitsMap_val`, `LinearMap.range_smul'`, `MvPolynomial.esymmAlgHomMonomial_single_one`, `Function.noZeroSMulDivisors`, `MonoidAlgebra.cardinalMk_lift_of_fintype`, `span_fourierLp_closure_eq_top`, `not_irreducible_expand`, `LieModule.toEnd_baseChange`, `selfAdjointPartL_apply_coe`, `HasFDerivWithinAt.comp_hasDerivWithinAt`, `Cardinal.mk_finsupp_lift_of_fintype`, `WeierstrassCurve.Jacobian.Y_eq_iff'`, `LocalizedModule.mul_by_divBy`, `hasDerivAt_intCast`, `Associates.sup_mul_inf`, `Seminorm.absorbent_ball_zero`, `IsRegular.smul_eq_zero_iff_right`, `FiniteMultiplicity.neg`, `HasDerivWithinAt.inv`, `ENNReal.pow_le_pow_left_iff`, `WeierstrassCurve.Jacobian.isUnit_dblZ_of_Y_ne'`, `Ideal.associatesEquivIsPrincipal_apply`, `PiTensorProduct.liftIsometry_symm_apply`, `Derivation.tensorProductTo_mul`, `nnnorm_cfcₙHom`, `ModularFormClass.hasSum_qExpansion_of_abs_lt`, `IsCompactOperator.smul_iff₀`, `fderivWithin_continuousAlternatingMap_apply_apply`, `Matrix.toLinearMapₛₗ₂_symm`, `DvdNotUnit.isUnit_of_irreducible_right`, `ZMod.isCyclic_units_four`, `SchwartzMap.smulLeftCLM_neg`, `adjoinRootXPowSubCEquiv_root`, `ContinuousLinearMap.opNNNorm_mul`, `ContinuousMultilinearMap.iteratedFDerivComponent_apply`, `Polynomial.valuation_monomial_eq_valuation_X_pow`, `differentiableOn_inverse`, `LSeries.iteratedDeriv_alternating`, `arithGeom_same_eq_sum`, `RootPairing.pairingIn_neg_one_neg_four_iff`, `IntermediateField.normal_iff_forall_map_le`, `LinearMap.BilinMap.tensorDistrib_tmul`, `Polynomial.smeval_at_zero`, `Projectivization.cross_mk`, `RestrictScalars.addEquiv_symm_map_smul_smul`, `ContinuousLinearMap.toContinuousAddMonoidHom_neg`, `IsBilinearMap.smul_right`, `AdicCompletion.mk_smul_top_ofAlgEquiv_symm`, `LinearMap.BilinForm.mul_toMatrix_mul`, `ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear`, `associatesEquivOfUniqueUnits_apply`, `CharP.sq_add_sq`, `PowerSeries.constantCoeff_smul`, `FormalMultilinearSeries.leftInv_comp`, `Quiver.Path.weight_pos`, `Asymptotics.IsTheta.pow`, `LieModule.smul_lie`, `IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap`, `Submodule.span_range_update_add_smul`, `ValuationSubring.ofPrime_scalar_tower`, `Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map`, `IsLocalization.smul_mem_iff`, `mem_pNilradical`, `Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson`, `HasFPowerSeriesAt.const_smul`, `iteratedFDeriv_succ_eq_comp_right`, `IsPrimitiveRoot.isPrimitiveRoot_iff`, `IsScalarTower.of_compHom`, `ContinuousMultilinearMap.changeOriginSeries_support`, `WeakFEPair.functional_equation₀`, `PrincipalIdealRing.factors_spec`, `separableClosure.isAlgebraic`, `DiscreteConvolution.AddConvolutionExistsAt.vadd_convolution`, `Finsupp.linearCombination_comp_addSingleEquiv`, `convex_multiset_sum`, `Associates.le_of_mul_le_mul_left`, `AbsoluteValue.tendsto_div_one_add_pow_nhds_one`, `Real.tendsto_integral_cexp_sq_smul`, `UpperHalfPlane.meromorphicOrderAt_comp_smul`, `QuadraticForm.comp_tensorRId_eq`, `Asymptotics.isBigOTVS_fun_comm`, `TrivSqZeroExt.algebraMap_eq_inl`, `ContDiffMapSupportedIn.seminorm_apply`, `LinearMap.BilinForm.toMatrix_mul_basis_toMatrix`, `IsDiscreteValuationRing.addVal_eq_zero_iff`, `AffineSubspace.sSameSide_smul_vsub_vadd_right`, `AntivaryOn.pow_right₀`, `LinearAlgebra.FreeProduct.rel_id`, `Matrix.toLinAlgEquiv_apply`, `WithSeminorms.tendsto_nhds_atTop`, `Submodule.mem_smul_top_iff`, `FiniteField.X_pow_card_sub_X_natDegree_eq`, `Ideal.span_range_pow_eq_top`, `NumberField.IsCMField.unitsComplexConj_eq_self_iff`, `Matrix.exp_units_conj'`, `HasFDerivAt.isThetaTVS_sub`, `ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom`, `DifferentiableAt.clm_comp`, `Polynomial.IsMonicOfDegree.pow`, `SubmodulesRingBasis.leftMul`, `Fintype.not_linearIndependent_iff`, `Matrix.IsPrimitive.exists_pos_pow`, `LinearMap.nondegenerate_toMatrix₂'_iff`, `Monovary.sum_smul_comp_perm_lt_sum_smul_iff`, `MonovaryOn.sum_comp_perm_smul_lt_sum_smul_iff`, `HomogeneousLocalization.Away.isLocalization_mul`, `CochainComplex.HomComplex.Cochain.smul_v`, `ODE.hasDerivWithinAt_picard_Icc`, `Module.support_quotSMulTop`, `LinearMap.BilinForm.toMatrix'_comp`, `Module.equiv_free_prod_directSum`, `FiniteField.pow_card`, `Submodule.map_map₂`, `MeasureTheory.lpNorm_const_smul`, `Polynomial.isRegular_X_pow`, `VectorField.lieBracket_smul_left`, `DualNumber.range_inlAlgHom_sup_adjoin_eps`, `Polynomial.prod_cyclotomic_eq_geom_sum`, `Submodule.smul_one_eq_span`, `Real.iteratedFDeriv_fourier`, `list_sum_pow_char_pow`, `Seminorm.smul_closedBall_subset`, `Submodule.span_singleton_smul_eq`, `circleAverage_sub_sub_inv_smul_of_differentiable_on`, `Algebra.Generators.CotangentSpace.exact`, `Algebra.Generators.H1Cotangent.δAux_X`, `TopologicalAddGroup.IsSES.pushforward_def`, `DoubleCentralizer.algebraMap_fst`, `hasDerivWithinAt_diff_singleton`, `ValuationSubring.surjective_unitGroupToResidueFieldUnits`, `WeierstrassCurve.Projective.add_smul_of_not_equiv`, `fderiv_continuousLinearEquiv_comp`, `Submodule.mem_span_image_finset_iff_exists_fun`, `FiniteField.pow_dichotomy`, `MvPowerSeries.coeff_rescale`, `spectrum.mem_iff`, `ContinuousLinearMap.intrinsicStar_smulRight`, `EisensteinSeries.q_expansion_bernoulli`, `Submodule.exists_injOn_mkQ_image_span_eq_of_span_eq_map_mkQ_of_le_jacobson_bot`, `deriv_clm_comp`, `SchwartzMap.convolution_continuous_left`, `ContinuousLinearMap.adjoint_toSpanSingleton`, `HomogeneousLocalization.isUnit_iff_isUnit_val`, `quasispectrumRestricts_iff_spectrumRestricts_inr`, `Submodule.mem_annihilator_span`, `Bornology.IsVonNBounded.of_topologicalSpace_le`, `IsArtinianRing.isNilpotent_jacobson_bot`, `mulLinearMap_apply_apply`, `MonoidWithZeroHom.snd_mono`, `DifferentiableAt.fun_smul`, `rootOfSplitsXPowSubC_pow`, `circleIntegral.integral_smul_const`, `ContDiffMapSupportedIn.structureMapCLM_top_apply`, `inner_smul_real_left`, `Polynomial.not_isUnit_X_sub_C`, `NonUnitalSubalgebra.map_topologicalClosure_le`, `Balanced.zero_insert_interior`, `Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zero`, `Submodule.map_pointwise_smul`, `Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card`, `MvPolynomial.degreeOf_pow_le`, `Matrix.pow_sub'`, `MvPolynomial.dvd_X_iff_exists`, `IsLocalization.surj_of_gcd_domain`, `IsLocalization.map_eq_toLinearMap_mapₐ`, `IsRingFiltration.toGradedMonoid`, `tsum_prod_pow_eq_tsum_sigma`, `isRelPrime_of_no_nonunits_factors`, `FiniteField.splits_X_pow_card_sub_X`, `HomogeneousLocalization.Away.val_mk`, `IntermediateField.rank_eq_one_iff`, `WeierstrassCurve.leadingCoeff_ΨSq`, `Polynomial.card_support_eq_two`, `HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow`, `triple_product_eq_det`, `Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero`, `ContDiffMapSupportedIn.seminorm_eq_bot_of_gt`, `Subgroup.relindex_adjoinNegOne_eq_two`, `TensorAlgebra.algebraMap_inj`, `IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime`, `AdicCompletion.factor_eval_liftRingHom`, `QuadraticMap.coe_associatedHom`, `LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplitting`, `Real.hasDerivAt_Gamma_one_half`, `Polynomial.Monic.geom_sum`, `IsClosed.balancedCore`, `ENat.pow_eq_top_iff`, `IsRelPrime.neg_right_iff`, `toSpanSingleton_derivWithin`, `WeierstrassCurve.Affine.Point.toClass_some`, `Asymptotics.IsBigOTVS.triangle`, `Odd.pow_pos_iff`, `pow_right_anti₀`, `LocalizedModule.map_exact`, `LinearMap.mulLeft_tmul`, `NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral`, `IsOrderedModule.of_smul_nonneg`, `ZMod.cast_descFactorial`, `ContinuousLinearMap.isEmbedding_restrictScalars`, `lowerBounds_smul_of_neg`, `Matrix.det_smul_adjugate_adjugate`, `MulRingNorm.isPowMul`, `spectrum.hasFDerivAt_resolvent`, `Valuation.isClopen_ball`, `KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination`, `IntermediateField.adjoin_rank_le_of_isAlgebraic_right`, `WeierstrassCurve.coe_Δ'`, `QuadraticAlgebra.coe_pow`, `CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt`, `HasFiniteFPowerSeriesOnBall.eq_partialSum'`, `Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem`, `Module.End.HasUnifEigenvalue.pow`, `VectorField.mlieBracket_const_smul_left`, `EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd`, `IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left`, `CategoryTheory.ShortComplex.homologyMap'_smul`, `IsLocalization.map_units_map_submonoid`, `polynomial_expand_eq`, `ValuationSubring.principalUnitGroupEquiv_apply`, `Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_ite`, `Module.End.eigenspace_div`, `IsScalarTower.to_smulCommClass`, `LieHom.toNonUnitalAlgHom_apply`, `HasDerivAt.comp_hasDerivWithinAt`, `Algebra.SubmersivePresentation.aeval_invJacobianOfHasCoeffs`, `Complex.wedgeIntegral_add_wedgeIntegral_eq`, `Algebra.Extension.Hom.subToKer_apply_coe`, `IsBoundedBilinearMap.toContinuousLinearMap_apply`, `Equiv.smulRight_symm_apply`, `Matrix.toLinearMapRight'_apply`, `Module.annihilator_eq_bot`, `Unitary.toLinearEquiv_mulRight`, `isSMulRegular_of_ker_lsmul_eq_bot`, `Bornology.isVonNBounded_sub`, `ModuleFilterBasis.smul'`, `LinearMap.BilinForm.toMatrix_mul`, `MatrixModCat.isScalarTower_toModuleCat`, `ModuleCat.restrictScalars.smul_def`, `LinearIndependent.sum_smul_of_nondegenerate`, `HasFPowerSeriesOnBall.pi`, `spectralNorm.eq_of_normalClosure`, `CauSeq.coe_pow`, `Submodule.toSubMulAction_strictMono`, `HasFPowerSeriesWithinOnBall.fderivWithin_eq`, `jacobson_density`, `nhds_basis_closed_balanced`, `Module.FaithfullyFlat.tensorProduct_mk_injective`, `Polynomial.span_minpoly_eq_annihilator`, `Ideal.isUnit_of_sub_one_mem_jacobson_bot`, `ProbabilityTheory.Fernique.measure_gt_normThreshold_le_rpow`, `ContinuousMultilinearMap.piₗᵢ_symm_apply`, `orderOf_neg_one`, `HurwitzZeta.sinZeta_two_mul_nat_add_one`, `IsCyclotomicExtension.union_left`, `IntermediateField.LinearDisjoint.linearIndependent_right`, `ray_pos_smul`, `Unitization.fstHom_apply`, `Matrix.instIsScalarTowerForall`, `HasDerivAt.scomp`, `IsIntegral.mem_span_pow`, `HomogeneousLocalization.val_awayMap_eq_aux`, `LinearMap.nonUnitalAlgHom_comp_convMul_distrib`, `Polynomial.reflect_C_mul_X_pow`, `Polynomial.card_support_eq_one`, `Subgroup.HasDetPlusMinusOne.det_eq`, `Module.End.genEigenrange_nat`, `PiTensorProduct.tprod_noncommProd`, `ContDiffMapSupportedIn.structureMapLM_top_apply`, `PowerSeries.coeff_mul_X_pow'`, `ContinuousLinearMap.ker_adjoint_comp_self`, `AnalyticAt.analyticOrderAt_ne_top`, `Matrix.GeneralLinearGroup.map_mul_map_inv`, `ENNReal.le_tsum_condensed`, `Commute.mul_neg_geom_sum₂`, `Quaternion.normSq_def'`, `HasFDerivWithinAt.pow'`, `SchwartzMap.pairing_continuous_left`, `Associates.instIsCancelMulZero`, `PolyEquivTensor.invFun_monomial`, `LieAlgebra.SpecialLinear.val_single`, `CochainComplex.HomComplex.Cochain.comp_units_smul`, `IsDedekindDomain.selmerGroup.fromUnit_ker`, `ENNReal.pow_lt_pow_left`, `LocalizedModule.subsingleton_iff_support_subset`, `Matrix.ofLp_toEuclideanLin_apply`, `Polynomial.coe_expand`, `ContinuousLinearMap.smulRight_comp_smulRight`, `balancedCoreAux_subset`, `spectralNorm.eq_of_normalClosure'`, `Submodule.mem_span_pair`, `Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable`, `Matrix.toLinearMap₂_apply`, `IsRelPrime.mul_add_left_left_iff`, `Filter.Tendsto.isVonNBounded_range`, `AdicCompletion.of_inj`, `NNReal.instContinuousSMulOfReal`, `continuous_cfcₙHom_of_cfcHom`, `Module.Basis.det_inv`, `Units.symm_mulLeftLinearEquiv_apply`, `HasDerivAt.const_mul`, `Real.hasFDerivAt_fourierIntegral`, `intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left`, `HasDerivWithinAt.congr`, `SchwartzMap.integralCLM_apply`, `EulerSine.tendsto_integral_cos_pow_mul_div`, `NonUnitalStarSubalgebra.inclusion_right`, `linearEquiv_det_rotation`, `LieModule.isNilpotent_iff_forall`, `IsCovariantDerivativeOn.add_one_form`, `Matrix.transpose_pow`, `Polynomial.irreducible_factor`, `Polynomial.aroots_C_mul_X_pow`, `Matrix.GeneralLinearGroup.val_inv_det_apply`, `InnerProductSpace.rankOne_one_right_eq_toSpanSingleton`, `PolynormableSpace.withSeminorms'`, `Ideal.quotientMulEquivQuotientProd_fst`, `hasDerivAt_one`, `HasDerivAtFilter.fun_neg`, `SameRay.exists_nonneg_left`, `CliffordAlgebra.forall_mul_self_eq_iff`, `LinearMap.IsSymmetric.apply_eigenvectorBasis`, `add_pow_expChar_of_commute`, `IsOpen.strictConvex_iff`, `RootPairing.coroot_root_eq_pairing`, `EuclideanSpace.volume_ball_fin_two`, `Matrix.Module.single_smul`, `hasFDerivAt_iff_isLittleOTVS`, `Representation.smul_tprod_one_asModule`, `LieModule.isNilpotent_toEnd_sub_algebraMap`, `rTensorHomEquivHomRTensor_toLinearMap`, `NonUnitalStarSubalgebraClass.subtype_injective`, `IsBaseChange.ofEquiv`, `CFC.nnrpow_eq_nnrpow_pi`, `IsBoundedSMul.of_nnnorm_smul_le`, `AdicCompletion.ofTensorProduct_tmul`, `mulLeftLinearMap_eq_mulLeft`, `isClosedEmbedding_cfcₙHom_of_cfcHom`, `Polynomial.degreeLT.addLinearEquiv_symm_apply'`, `RootPairing.GeckConstruction.isNilpotent_e`, `LinearEquiv.toSpanNonzeroSingleton_symm_apply_smul`, `Polynomial.resultant_add_right_deg`, `HasFTaylorSeriesUpToOn.hasStrictFDerivAt`, `AnalyticAt.const_smul`, `Matrix.GeneralLinearGroup.center_eq_range_units`, `smul_nonneg_iff`, `DividedPowers.OfInvertibleFactorial.dpow_eq_of_mem`, `KaehlerDifferential.kerTotal_mkQ_single_smul`, `LinearMap.nondegenerate_toLinearMap₂'_iff_det_ne_zero`, `MvPolynomial.rTensor_apply_monomial_tmul`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective`, `ContinuousAt.clm_bundle_apply₂`, `FormalMultilinearSeries.div_le_radius_compContinuousLinearMap`, `Polynomial.isUnit_primPart_C`, `Perfection.coe_teichmuller_eq_teichmuller₀`, `NonUnitalStarSubalgebra.coe_smul`, `Submodule.instInvertibleSubtypeMemVal`, `IsReduced.pow_eq_zero_iff`, `Polynomial.iterate_derivative_mul_X_pow`, `HahnSeries.SummableFamily.binomialFamily_apply`, `PiTensorProduct.piTensorHomMapFun₂_add`, `ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis`, `Matrix.mulVecBilin_apply`, `nat_smul_eq_nsmul`, `sign_pow`, `ZMod.map_smul`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow'`, `IsLocalRing.isLocalHom_iff_comap_closedPoint`, `Algebra.Generators.repr_CotangentSpaceMap`, `ContinuousLinearMap.toContinuousAddMonoidHom_restrictScalars`, `ContinuousMultilinearMap.isVonNBounded_image2_apply`, `DividedPowerAlgebra.dp_sum_smul`, `hasLineDerivAt_iff_tendsto_slope_zero`, `IsAdjoinRootMonic.modByMonicHom_root_pow`, `MultilinearMap.piFamily_smul`, `DividedPowers.dpow_linearCombination`, `AlternatingMap.uncurryFin_smul`, `Ideal.mem_iInf_smul_pow_eq_bot_iff`, `lieEquivMatrix'_symm_apply`, `HasFDerivAt.list_prod'`, `HomogeneousLocalization.val_awayMap_mk`, `separableClosure.isSepClosure`, `Fin.sum_pow_mul_eq_add_pow`, `WeierstrassCurve.b_relation_of_char_three`, `MeasureTheory.SignedMeasure.singularPart_smul_nnreal`, `Polynomial.coeff_inv_units`, `LieSubalgebra.instIsNoetherianSubtypeMem`, `InfiniteGalois.toAlgEquivAux_eq_liftNormal`, `Matrix.proj_diagonal`, `Polynomial.eval₂_pow`, `separatingDual_iff_injective`, `fderivWithin_const_smul_field`, `Pi.openSegment_subset`, `Polynomial.smeval_pow`, `fderiv_continuousMultilinearMapCompContinuousLinearMap`, `Ideal.Filtration.pow_smul_le`, `IsUnit.isNilpotent_mul_unit_of_commute_iff`, `AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap_assoc`, `lcm_units_coe_left`, `ModularGroup.im_smul_eq_div_normSq`, `AnalyticWithinAt.fun_pow`, `Matrix.rectVandermonde_apply`, `isNilpotent_tensor_residueField_iff`, `LinearEquiv.isSMulRegular_congr'`, `Differential.logDeriv_pow`, `IsCoprime.pow`, `MvPolynomial.pderiv_pow`, `MeasureTheory.taylorWithinEval_charFun_two_zero`, `Module.Basis.smulTower_apply`, `LinearMap.map_smul₂`, `IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable'`, `IsSelfAdjoint.commute_cfcₙHom`, `IsLocalizedModule.isScalarTower_module`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle`, `AffineMap.homothety_apply`, `HasDerivWithinAt.smul_const`, `BialgHomClass.map_comp_comulAlgHom`, `Polynomial.sup_ker_aeval_le_ker_aeval_mul`, `LinearMap.intrinsicStarModule`, `IntermediateField.normalClosure_def''`, `inner_eq_ofReal_norm_sq_left_iff`, `DifferentiableOn.smul`, `contDiff_nat_iff_continuous_differentiable`, `QuasispectrumRestricts.nonUnitalStarAlgHom_apply`, `hasFDerivAt_pow'`, `Mathlib.Tactic.Ring.pow_add`, `ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis`, `sameRay_smul_right_iff_of_ne`, `Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint`, `absorbent_ball`, `Matrix.SpecialLinearGroup.coe_GL_coe_matrix`, `MeasureTheory.Lp.simpleFunc.coe_smul`, `Unitization.starMap_apply`, `Seminorm.zero_or_exists_apply_eq_finset_sup`, `Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto`, `CStarAlgebra.pow_antitone`, `SchwartzMap.lineDerivOp_fourierInv_eq`, `LinearIsometryEquiv.symm_conjStarAlgEquiv`, `zero_pow_eq_zero`, `WeierstrassCurve.Affine.equation_iff`, `Submodule.topologicalClosure_eq_top_iff`, `StarConvex.affinity`, `MonomialOrder.coeff_pow_nsmul_degree`, `hasDerivAt_abs`, `Valued.isOpen_closedBall`, `LinearMap.IsContPerfPair.bijective_right`, `HasFiniteFPowerSeriesOnBall.add`, `ContractingWith.exists_fixedPoint'`, `geom_sum_mul_of_one_le`, `ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le`, `IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots`, `WeierstrassCurve.Projective.addU_smul`, `iteratedDeriv_comp_const_sub`, `Valuation.instNontrivialSubtypeUnitsMemSubgroupValueGroupOfIsNontrivial`, `LinearMap.isUnit_toMatrix_iff`, `LinearMap.det_smul`, `Ideal.irreducible_of_irreducible_absNorm`, `ValuativeRel.pow_rel_pow_of_one_rel`, `Subfield.relrank_eq_rank_of_le`, `Submodule.coe_smul`, `NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt'`, `MonoidWithZeroHom.fst_apply_coe`, `IsCyclotomicExtension.Rat.inertiaDegIn_eq`, `Ideal.rootsOfUnityMapQuot_apply`, `ContinuousLinearMap.opNorm_lsmul_le`, `LieAlgebra.Basis.cartanMatrix_base_eq`, `LinearMapClass.map_smul`, `EuclideanSpace.volume_ball`, `pow_le_descPochhammer_eval`, `MonoidWithZeroHom.fst_inl`, `IsAlgebraic.pow`, `MonoidWithZeroHom.fst_surjective`, `LocalizedModule.map_id`, `NonUnitalAlgHom.comp_mul'`, `Seminorm.ball_comp`, `Valuation.hasBasis_nhds`, `Mathlib.Tactic.Ring.add_overlap_pf`, `intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae`, `TensorProduct.AlgebraTensorModule.rTensor_mul`, `MultilinearMap.mkContinuousMultilinear_norm_le`, `LinearMap.BilinForm.toMatrix_compLeft`, `Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeff`, `WithLp.instProdNormSMulClass`, `RootPairing.polarizationEquiv_symm_apply_coroot`, `BilinForm.toMatrix_apply`, `ContDiffMapSupportedIn.monoCLM_eq_zero`, `StrictConvex.sum_mem_interior`, `DualNumber.commute_eps_left`, `LinearIndependent.map_pow_expChar_pow_of_isSeparable`, `IntermediateField.isSeparable_tower_bot`, `KaehlerDifferential.isLocalizedModule`, `Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius`, `FiniteField.isSquare_iff`, `Matrix.linfty_opNorm_toMatrix`, `IntermediateField.minpoly_eq`, `Commute.expUnitary_add`, `hasDerivAt_natCast`, `IsMprojection.Mnorm`, `smul_vsub_rev_mem_vectorSpan_pair`, `isSimplyConnected_smul_set₀_iff`, `HasDerivAtFilter.fun_sub`, `nonZeroDivisors.associated_coe`, `TrivSqZeroExt.kerIdeal_sq`, `Summable.tsum_pow_mul_one_sub`, `AddMonoidAlgebra.Monic.supDegree_pow`, `Polynomial.Monic.C_dvd_iff_isUnit`, `Polynomial.coeff_X_add_one_pow`, `ContinuousMap.coeFn_toLp`, `Seminorm.rescale_to_shell`, `AffineSubspace.direction_affineSpan_pair_le_iff_exists_smul`, `Matrix.toBilin'_apply'`, `HasDerivWithinAt.union`, `ValuativeRel.isNontrivial_iff_nontrivial_units`, `UniqueFactorizationMonoid.prod_normalizedFactors`, `ContinuousLinearMap.homeomorphOfUnit_symm_apply`, `IsUnit.mk0`, `Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le`, `Real.hasDerivAt_Gamma_one`, `Convex.toCone_isLeast`, `segment_translate_image`, `ArithmeticFunction.smul_map`, `Real.fourier_bilin_convolution_eq_integral`, `Derivation.map_aeval`, `Matrix.toLinearMap₂'_single`, `closedBall_normSeminorm`, `Ideal.smul_restrictScalars`, `Complex.coe_smul`, `SchauderBasis.RankOneDecomposition.exists_coeff`, `ContinuousWithinAt.clm_bundle_apply₂`, `Matrix.smul_eq_mulVec`, `Matrix.det_eq_sum_row_mul_submatrix_succAbove_succAbove_det`, `WittVector.iterate_verschiebung_mul_coeff`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate`, `ContinuousLinearMap.coe_restrictScalarsL`, `LinearMap.separatingRight_toLinearMap₂'_of_det_ne_zero'`, `Algebra.TensorProduct.mul_assoc`, `ModuleFilterBasis.smul_left`, `MonoidWithZeroHom.valueGroup_def`, `MemHolder.nnHolderNorm_smul`, `CongruenceSubgroup.mem_conjGL`, `isUnit_iff_not_dvd_char_of_ringChar_ne_zero`, `Convex.combo_interior_self_mem_interior`, `Complex.val_inv_UnitI`, `Subring.continuousSMul`, `Unitary.isPathConnected_ball`, `HasDerivWithinAt.add_const`, `legendreSym.eq_pow`, `sq_add_sq_mul_sq_add_sq`, `ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric`, `Polynomial.card_support_C_mul_X_pow_le_one`, `instFiniteZModUnits`, `IntermediateField.isSplittingField_iff`, `iter_deriv_inv`, `Module.IsTorsionBySet.isScalarTower`, `MeasureTheory.Integrable.integral_smul`, `Polynomial.eval_eq_sum_degreeLTEquiv`, `Polynomial.monomial_mul_X_pow`, `lp.mem_lp_const_smul`, `WeierstrassCurve.Jacobian.dblY_of_Y_eq`, `Matrix.star_dotProduct_gram_mulVec`, `Bornology.IsVonNBounded.of_add_left`, `LocalizedModule.instIsScalarTower`, `LinearMap.BilinForm.mul_toMatrix`, `ContinuousLinearMap.norm_compL_le`, `Seminorm.continuousAt_zero_of_forall`, `ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap`, `SeminormFamily.withSeminorms_iff_nhds_eq_iInf`, `Module.Basis.tensorAlgebra_repr_apply`, `GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I`, `Ideal.count_associates_eq`, `Ideal.cotangentToQuotientSquare_injective`, `Matrix.vecMul_injective_iff_isUnit`, `MonomialOrder.leadingCoeff_pow`, `Polynomial.support_C_mul_X_pow`, `Valued.mem_nhds_zero`, `EulerSine.antideriv_cos_comp_const_mul`, `MvPolynomial.prod_C_add_X_eq_sum_esymm`, `ZMod.orderOf_dvd_card_sub_one`, `CauSeq.pow_apply`, `Valuation.RankLeOne.exists_val_lt`, `IsArtinianRing.isUnit_iff_mem_nonZeroDivisors_of_mulOpposite`, `squarefree_mul_iff`, `CFC.rpow_intCast`, `Module.isTorsionBySet_quotient_iff`, `denomsClearable_C_mul_X_pow`, `not_irreducible_zero`, `fderivWithin_clm_comp`, `TrivSqZeroExt.isUnit_inr_iff`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars`, `Algebra.EssFiniteType.aux`, `Polynomial.binomial_eq_binomial`, `sameRay_neg_smul_right_iff_of_ne`, `associated_abs_right_iff`, `meromorphicOrderAt_smul_of_ne_zero`, `HasDerivWithinAt.congr_set`, `Submodule.mem_smul_span`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀`, `IsRelPrime.mul_add_right_left_iff`, `Matrix.normSMulClass`, `Polynomial.iterate_derivative_X_pow_eq_C_mul`, `Bornology.isVonNBounded_add`, `AlgebraicGeometry.exists_of_res_eq_of_qcqs_of_top`, `IsPurelyInseparable.pow_mem`, `Matrix.GeneralLinearGroup.coe_map_mul_map_inv`, `WeierstrassCurve.b_relation`, `Matrix.charpoly_vecMulVec`, `DualNumber.algHom_ext_iff`, `MonomialOrder.degree_pow`, `Valued.isOpen_ball`, `WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF_of_char_two`, `IntermediateField.topEquiv_symm_apply_coe`, `HasFPowerSeriesAt.sub`, `MvPolynomial.support_smul_eq`, `QuadraticMap.associated_linMulLin`, `MeasureTheory.JordanDecomposition.toSignedMeasure_smul`, `PadicInt.not_isUnit_iff`, `Polynomial.derivative_X_pow`, `MeasureTheory.Lp.instSMulCommClass`, `FiniteGaloisIntermediateField.adjoin_val`, `OrderDual.instIsOrderedModule`, `complEDS₂_mul_b`, `LieAlgebra.rank_le_finrank_engel`, `Finset.centerMass_segment`, `emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity`, `Finsupp.sum_option_index_smul`, `OrthogonalFamily.range_linearIsometry`, `QuadraticForm.associated_isSymm`, `IsBaseChange.dual`, `Matrix.SpecialLinearGroup.coe_to_GLPos_to_GL_det`, `TensorProduct.finsuppScalarLeft_apply_tmul`, `Real.tendsto_integral_exp_smul_cocompact`, `Polynomial.rootsExpandToRoots_apply`, `NNRat.cast_smul_eq_nnqsmul`, `Units.val_set_image_rootsOfUnity_two`, `mellin_convergent_iff_norm`, `RestrictScalars.isScalarTower`, `ValuationSubring.mem_principalUnitGroup_iff`, `TensorAlgebra.tprod_apply`, `fderivWithin_inv`, `Polynomial.eval_eq_sum`, `HomogeneousLocalization.awayMapAux_mk`, `fderiv_continuousMultilinear_apply_const`, `Orientation.kahler_mul`, `tendsto_const_smul_iff₀`, `quadraticCharFun_eq_pow_of_char_ne_two`, `HasDerivWithinAt.smul`, `GaussianFourier.integral_cexp_neg_mul_sum_add`, `RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq`, `Units.add_eq_mul_one_add_div`, `WeierstrassCurve.Jacobian.Y_sub_Y_mul_Y_sub_negY`, `Associates.irreducible_of_mem_factorSet`, `Subalgebra.pow_mem`, `Matrix.of_mem_specialOrthogonalGroup_fin_two_iff`, `Mathlib.Tactic.LinearCombination.smul_const_lt`, `StandardEtalePair.HasMap.isUnit_derivative_f`, `Matrix.SpecialLinearGroup.toLin'_to_linearMap`, `ModularFormClass.qExpansion_coeff_eq_circleIntegral`, `IsGroupLikeElem.isUnit`, `Valued.mem_nhds`, `SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left`, `MvPolynomial.tensorEquivSum_X_tmul_X`, `PowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero`, `MeasureTheory.L1.SimpleFunc.integral_smul`, `DifferentiableOn.pow`, `iteratedDerivWithin_smul`, `NonUnitalStarSubalgebra.instSMulCommClass'`, `ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv`, `ContinuousLinearMap.opNNNorm_mul_flip_apply`, `HasDerivWithinAt.fun_pow`, `Mathlib.Tactic.Ring.pow_bit0`, `HasDerivWithinAt.finset_prod`, `LinearMap.mul_toMatrix₂'_mul`, `smul_le_smul_of_nonpos_left`, `IsNilpotent.exp_eq_sum`, `Polynomial.isUnit_aeval_of_isUnit_aeval_of_isNilpotent_sub`, `Rep.coinvariantsTensor_hom_ext_iff`, `Algebra.discr_isUnit_of_basis`, `LinearMap.toMatrix₂'_mul`, `ConvexOn.sub_strictConcaveOn`, `HasFPowerSeriesOnBall.hasFDerivAt`, `Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotent`, `NonUnitalStarSubalgebra.iSupLift_comp_inclusion`, `IntermediateField.rank_top'`, `add_pow_prime_pow_eq'`, `IsRelPrime.of_add_mul_right_left`, `IntermediateField.isAlgebraic_adjoin_simple`, `Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero`, `egauge_eq_zero_iff`, `ZMod.orderOf_one_add_mul_prime_pow`, `Complex.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq`, `AdicCompletion.transitionMap_map_pow`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_left`, `cfcHom_isStrictlyPositive_iff`, `HasDerivWithinAt.mono`, `Polynomial.Monic.pow`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₂`, `inv_pow_sub₀`, `Matrix.isUnit_charpolyRev_of_isNilpotent`, `CategoryTheory.Mat.instIsEquivalenceMat_SingleObjMulOppositeEquivalenceSingleObjInverse`, `Algebra.Extension.Cotangent.val_smul`, `fourierIntegral_gaussian`, `MeromorphicNFAt.smul_analytic`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff`, `zero_mem_absConvexHull`, `WeierstrassCurve.Projective.negAddY_eq`, `WeierstrassCurve.Φ_two`, `pow_lt_one₀`, `LinearMap.BilinForm.flip_flip`, `Submodule.powSMulQuotInclusion_mk`, `ContinuousMultilinearMap.curryMid_apply`, `AntitoneOn.quasilinearOn`, `Even.add_pow_le`, `OnePoint.smul_infty_def`, `WeierstrassCurve.Jacobian.equation_of_Z_eq_zero`, `Matrix.conjTranspose_pow`, `IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f`, `inv_smul_lt_iff_of_neg`, `IntermediateField.AdjoinSimple.normal_algebraicClosure`, `Algebra.toMatrix_lsmul`, `HasFDerivWithinAt.comp_hasDerivAt`, `SchwartzMap.compCLM_apply`, `AddSubgroup.smul_mem_pointwise_smul_iff₀`, `convex_Ici`, `EisensteinSeries.tendsto_double_sum_S_act`, `Subsemiring.instSMulCommClassSubtypeMemCenter`, `iter_deriv_inv'`, `sq_pos_iff`, `Finset.weightedVSub_eq_linear_combination`, `TemperedDistribution.fourierMultiplierCLM_apply_apply`, `LinearMap.intrinsicStar_single`, `CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right`, `DirectSum.of_zero_pow`, `Module.Basis.map_orientation_eq_det_inv_smul`, `ClosedSubmodule.sInf_orthogonal`, `intervalIntegral.fderivWithin_integral_of_tendsto_ae`, `MvPolynomial.coeff_rTensorAlgHom_monomial_tmul`, `concaveOn_iff_pairwise_pos`, `HasDerivAt.mul`, `ContinuousMap.toLp_comp_toContinuousMap`, `Function.HasTemperateGrowth.smul`, `KaehlerDifferential.polynomial_D_apply`, `NNReal.coe_pow`, `IsRelPrime.of_mul_add_left_left`, `PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm`, `StarAlgHom.coe_toNonUnitalStarAlgHom`, `WithTop.pow_eq_top_iff`, `FloorSemiring.eventually_mul_pow_lt_factorial_sub`, `IntermediateField.normal_iff_forall_map_eq'`, `Matrix.ProjGenLinGroup.lift_comp_mk`, `HasStrictFDerivAt.isBigOTVS_sub`, `Matrix.separatingLeft_toLinearMap₂'_iff`, `AnalyticOnNhd.fun_pow`, `TensorProduct.AlgebraTensorModule.map_smul_right`, `rescale_to_shell_zpow`, `Polynomial.newtonMap_apply_of_isUnit`, `ConvexCone.mem_zero`, `ContMDiff.clm_postcomp`, `Asymptotics.IsLittleOTVS.tendsto_inv_smul`, `PolynomialModule.eval_apply`, `IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq`, `Complex.sinh_eq_tsum`, `LieAlgebra.isScalarTower`, `triple_product_permutation`, `LinearMap.separatingLeft_toLinearMap₂'_of_det_ne_zero'`, `MvPowerSeries.map.isLocalHom`, `WeierstrassCurve.Jacobian.addX_eq`, `balanced_closedBall_zero`, `TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent`, `IntermediateField.intermediateFieldMap_apply_coe`, `Polynomial.X_pow_mem_lifts`, `Polynomial.dvd_term_of_dvd_eval_of_dvd_terms`, `IntermediateField.topEquiv_apply`, `Associates.count_mul`, `multiplicity_mul`, `LinearMap.intrinsicStar_smulRight`, `Finset.neg_smul_finset`, `IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f`, `DivisibleHull.mk_add_mk`, `MeasureTheory.Lp.smul_comm`, `Metric.unitSphere.coe_pow`, `Submodule.smul_mem_iff`, `Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two`, `Module.End.baseChangeHom_apply_apply`, `isBoundedBilinearMap_smul`, `fderivWithin_continuousAlternatingMap_apply_const`, `Polynomial.taylor_monomial`, `sq_nonneg`, `LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace`, `ConcaveOn.map_add_sum_le`, `convexOn_pow`, `Matrix.isRepresentation.toEnd_surjective`, `MonoidWithZeroHom.snd_comp_inr`, `IntermediateField.LinearDisjoint.symm`, `BilinForm.toMatrix_mul`, `IntermediateField.exists_algHom_adjoin_of_splits'`, `EulerSine.antideriv_sin_comp_const_mul`, `LinearMap.map_smul`, `mapsTo_tangentConeAt_pi`, `Finset.sum_smul_sum_eq_sum_perm`, `PowerSeries.coeff_subst_X_pow`, `IsPurelyInseparable.minpoly_eq_X_pow_sub_C`, `Polynomial.integralNormalization_coeff_mul_leadingCoeff_pow`, `strictConvex_singleton`, `Algebra.Generators.CotangentSpace.compEquiv_symm_inr`, `CongruenceSubgroup.strictPeriods_Gamma`, `ContinuousLinearMap.norm_restrictScalars`, `ZMod.isUnit_prime_of_not_dvd`, `MvPolynomial.isHomogeneous_C_mul_X_pow`, `Asymptotics.IsLittleOTVS.isBigOTVS`, `coe_normSeminorm`, `Polynomial.valuation_aeval_monomial_eq_valuation_pow`, `MvPolynomial.tensorEquivSum_C_tmul_one`, `Submodule.restrictScalars.isScalarTower`, `LinearMap.charpoly_one`, `Module.reflection_mul_reflection_zpow_apply_self`, `Algebra.normalizedTrace_def`, `MvPolynomial.map_iterateFrobenius_expand`, `MvPolynomial.vars_pow`, `Module.associatedPrimes.mem_associatedPrimes_atPrime_of_mem_associatedPrimes`, `ConvexCone.coe_add`, `Valuation.isOpen_ball`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_component`, `ENNReal.rpow_ofNat`, `MDifferentiableWithinAt.clm_postcomp`, `cosetToCuspOrbit_apply_mk`, `CochainComplex.HomComplex.Cochain.leftUnshift_units_smul`, `convex_Iio`, `Matrix.toLinAlgEquiv_self`, `RootPairing.coreflection_apply`, `IsGroupLikeElem.of_unitsInv`, `geom_sum_pos`, `convex_halfSpace_gt`, `ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear`, `NumberField.Units.coe_zpow`, `UniqueFactorizationMonoid.iff_exists_prime_factors`, `UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors`, `NumberField.mem_span_basisOfFractionalIdeal`, `HasDerivWithinAt.const_sub`, `MonoidWithZeroHom.valueMonoid_eq_closure`, `Algebra.Extension.tensorCotangentInvFun_smul_mk`, `ContDiffBump.convolution_eq_right`, `Units.continuousOn_inv₀_spectrum`, `Matrix.kroneckerMapBilinear_mul_mul`, `ContinuousMultilinearMap.map_update_smul`, `Ideal.radical_pow`, `Matrix.unitOfDetInvertible_eq_nonsingInvUnit`, `TemperedDistribution.instFourierInvSMul`, `sameRay_neg_smul_right_iff`, `MeasureTheory.AEEqFun.Integrable.smul`, `Submodule.mul_smul`, `ContinuousLinearMap.toContinuousAddMonoidHom_id`, `pow_eq_one_iff_of_ne_zero`, `HasDerivWithinAt.const_smul`, `Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer`, `FiniteField.minpoly_frobeniusAlgHom`, `AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι_assoc`, `Matrix.separatingLeft_toBilin'_iff`, `ContMDiff.clm_prodMap`, `ContDiffOn.smul`, `sub_pow_two`, `mem_vectorSpan_pair`, `MulChar.IsQuadratic.gaussSum_frob`, `Subalgebra.isUnit_of_isUnit_val_of_eventually`, `WeakFEPair.hf_modif_FE`, `integral_gaussian_sq_complex`, `not_irreducible_of_not_unit_dvdNotUnit`, `Units.zero_notMem_spectrum`, `Homeomorph.compStarAlgEquiv'_apply`, `Module.AEval'_def`, `HasDerivWithinAt.hasDerivAt`, `FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card`, `mem_convexHull_iff_exists_fintype`, `DirectSum.decompose_symm_mul`, `ContinuousLinearMap.opNorm_mul_apply_le`, `deriv_smul_const`, `Coalgebra.TensorProduct.assoc_tmul`, `NNReal.rpow_sub_natCast'`, `Algebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one`, `DirectSum.coe_mul_of_apply_add`, `intervalIntegral.integral_hasFDerivWithinAt`, `IntermediateField.AdjoinSimple.isIntegral_gen`, `HasFPowerSeriesAt.tendsto_partialSum`, `deriv_pow_field`, `WeierstrassCurve.b₈_of_char_three`, `TopologicalGroup.IsSES.pushforward_mono`, `ContinuousLinearMap.smul_def`, `LinearMap.toMatrix₂_mul_basis_toMatrix`, `ContinuousLinearMap.orthogonal_range`, `Units.exists_iff_ne_zero`, `Unitary.conjStarAlgAut_mul_apply`, `Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T`, `Antitone.quasilinearOn`, `HasFiniteFPowerSeriesAt.add`, `Matrix.conjTranspose_intCast_smul`, `Matrix.GeneralLinearGroup.val_inv_scalar_apply`, `spectrum.units_conjugate'`, `HasFPowerSeriesAt.hasDerivAt`, `TensorProduct.AlgebraTensorModule.lift_apply`, `ContinuousLinearMap.toContinuousAddMonoidHom_sub`, `RatFunc.natDegree_num_le_natDegree_minpolyX`, `hasDerivWithinAt_congr_set'`, `Module.End.IsSemisimple_smul`, `Finsupp.mem_span_range_iff_exists_finsupp`, `LieAlgebra.IsKilling.rootSystem_pairing_apply`, `Module.Basis.toMatrix_eq_toMatrix_constr`, `geom_sum₂_mul`, `Module.Finite.toModuleEnd_moduleEnd_surjective`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply`, `TensorProduct.comul_tmul`, `NormedSpace.norm_smul_le`, `ContinuousLinearMap.isThetaTVS_comp`, `Real.volume_pi_le_diam_pow`, `Matrix.isUnit_nonsing_inv_iff`, `Polynomial.trinomial_def`, `DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul`, `meromorphicOrderAt_pow`, `DirectLimit.Module.hom_ext_iff`, `IsNilpotent.map_iff`, `StrictConcaveOn.neg`, `fourierIntegral_half_period_translate`, `pow_sum_le_card_mul_sum_pow`, `ediam_smul₀`, `selfZPow_natCast`, `CategoryTheory.ShiftedHom.map_smul`, `HasFDerivAt.linear_multilinear_comp`, `Ideal.pi_mkQ_rTensor`, `HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap`, `AddCommMonoid.nat_isScalarTower`, `spectrum.pow_norm_pow_one_div_tendsto_nhds_spectralRadius`, `AddMonoidAlgebra.sup_support_pow_le`, `tendsto_smul_congr_of_tendsto_left_cobounded_of_isBoundedUnder`, `TestFunction.fderivCLM_apply_of_gt`, `MeasureTheory.withDensitySMulLI_apply`, `frobeniusEquiv_symm_pow_p`, `ContinuousMapZero.toContinuousMapHom_apply`, `IntermediateField.exists_lt_finrank_of_infinite_dimensional`, `Asymptotics.isLittleOTVS_congr`, `HasStrictFDerivAt.isThetaTVS_sub`, `IntermediateField.adjoin_rank_le_of_isAlgebraic`, `hasDerivWithinAt_const_add_iff`, `OnePoint.exists_mem_SL2`, `convexHull_toCone_isLeast`, `WittVector.nth_mul_coeff`, `ConvexCone.IsGenerating.span_eq_top`, `MeasureTheory.Measure.addHaar_nnreal_smul`, `PerfectField.separable_iff_squarefree`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `Polynomial.irreducible_iff_degree_lt`, `IsDedekindDomain.selmerGroup.fromUnitLift_injective`, `ContinuousLinearMap.spectralRadius_eq_nnnorm`, `Complex.taylorSeries_eq_on_emetric_ball`, `Polynomial.aeval_eq_sum_range`, `finsuppTensorFinsuppLid_apply_apply`, `spectrum.spectralRadius_pow_le'`, `Unitary.mulRight_apply`, `MeasureTheory.convolutionExistsAt_iff_integrable_swap`, `finiteMultiplicity_mul_aux`, `isCyclotomicExtension_iff`, `Module.toModuleEnd_apply`, `Polynomial.resultant_C_zero_left`, `AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk`, `MonoidAlgebra.mapDomainNonUnitalAlgHom_apply`, `CFC.isUnit_rpow_iff`, `TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_symm_tmul`, `Asymptotics.IsBigOWith.const_mul_right'`, `AdicCompletion.of_injective`, `AlgebraicGeometry.Proj.awayι_preimage_basicOpen`, `mem_segment_iff_wbtw`, `deriv_div`, `torusIntegral_smul`, `PolyEquivTensor.toFunBilinear_apply_eq_smul`, `WithConv.symm_matrixToLin'StarAlgEquiv_apply`, `LinearEquiv.smulOfNeZero_symm_apply`, `WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero`, `AffineEquiv.coe_homothetyUnitsMulHom_apply`, `NonUnitalStarSubalgebra.toSubring_subtype`, `IntermediateField.normal_iInf`, `WeierstrassCurve.Jacobian.addX_smul`, `ConcaveOn.neg`, `VectorField.mpullback_smul`, `hasDerivAt_ofReal_cpow_const`, `NumberField.Units.logEmbeddingQuot_injective`, `Monovary.sum_comp_perm_smul_eq_sum_smul_iff`, `Monovary.sum_comp_perm_smul_le_sum_smul`, `IsRelPrime.add_mul_left_right_iff`, `Submodule.factorPow_comp_powSMulQuotInclusion`, `CliffordAlgebraDualNumber.equiv_ι`, `WeierstrassCurve.Projective.Point.zero_def`, `Derivation.leibniz_pow`, `Polynomial.X_pow_sub_X_sub_one_irreducible_rat`, `convex_iff_div`, `AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType`, `Polynomial.sum_taylor_eq`, `hasDerivAt_norm_rpow`, `DirectSum.coe_of_mul_apply_of_le`, `Associates.eq_pow_of_mul_eq_pow`, `Algebra.IsAlgebraic.isNormalClosure_normalClosure`, `ContinuousLinearMap.spectrum_eq`, `HomogeneousLocalization.NumDenSameDeg.den_pow`, `MvPolynomial.coeffsIn_pow`, `CanonicallyOrderedAdd.pow_pos`, `TensorProduct.lcurry_apply`, `cfc_unitary_iff`, `IsLocalizedModule.smul_injective`, `DirectSum.coe_mul_of_apply_of_le`, `TrivSqZeroExt.snd_map`, `le_isUnit_iff_zero_notMem`, `gcd_one_right'`, `DivisorChain.second_of_chain_is_irreducible`, `NonUnitalAlgebra.map_top`, `IntermediateField.isPurelyInseparable_bot`, `Ideal.mem_torsionOf_iff`, `Associates.exists_non_zero_rep`, `smul_algebra_smul_comm`, `AlgebraicGeometry.exists_eq_pow_mul_of_isAffineOpen`, `NumberField.mixedEmbedding.unit_smul_eq_zero`, `Polynomial.mem_normalizedFactors_iff`, `concaveOn_univ_piecewise_Iic_of_monotoneOn_Iic_antitoneOn_Ici`, `IsLocalRing.isLocalHom_residue`, `ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply`, `IsHausdorff.eq_iff_smodEq`, `Submodule.mem_span_triple`, `QuadraticMap.radical_eq_ker_associated`, `PadicInt.valuation_p_pow_mul`, `FiniteField.sum_pow_units`, `NNReal.tendsto_pow_atTop_nhds_zero_of_lt_one`, `cyclotomicCharacter.toZModPow_toFun`, `DirectSum.coe_of_mul_apply_of_mem_zero`, `Matrix.instSMulCommClassForall`, `pow_div_pow_eventuallyEq_atTop`, `AlgebraicGeometry.Proj.awayMap_awayToSection`, `geom_sum_mul_add`, `HasStrictDerivAt.fun_sub`, `MvPolynomial.monomial_eq`, `DivisibleHull.archimedeanClassOrderIso_apply`, `LinearEquiv.trans_smul`, `DividedPowers.dpow_smul_right`, `HasDerivWithinAt.star`, `Module.End.hasEigenvalue_iff_isRoot`, `Submodule.mem_torsionBy_iff`, `Polynomial.isNilpotent_C_iff`, `AdicCompletion.restrictScalars_range_ofPowSMul_eq_ker_eval`, `Matrix.pow_row_eq_zero_of_le`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `Unitary.mulRight_mul_apply`, `TensorProduct.smul_tmul_smul`, `Module.Invertible.instFaithfulSMul`, `Seminorm.smul_closedBall_preimage`, `Module.Invertible.rTensorEquiv_symm_apply_apply`, `HasFDerivWithinAt.unique_on`, `LinearMap.surjective_compr₂_of_exists_rightInverse`, `ValuationSubring.coe_unitGroupMulEquiv_symm_apply`, `TensorProduct.comul_def`, `MeromorphicOn.extract_zeros_poles`, `MonoidWithZeroHom.inr_apply_unit`, `Quiver.Path.weightOfEPs_nonneg`, `CategoryTheory.Free.lift_map_single`, `HasDerivAtFilter.prodMk`, `cfcₙAux_mem_range_inr`, `Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero`, `LinearMap.eqLocus_toAddSubmonoid`, `ContinuousLinearMap.norm_bilinearRestrictScalars`, `MonoidWithZeroHom.valueMonoid_eq_valueGroup'`, `ContinuousLinearMap.nhds_zero_eq`, `WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero`, `PiTensorProduct.liftIsometry_apply_apply`, `ContinuousMultilinearMap.prodL_symm_apply`, `ContinuousMap.adjoin_id_eq_span_one_add`, `Ring.KrullDimLE.isNilpotent_iff_mem_nonunits`, `Matrix.mem_glpos`, `Ideal.range_finsuppTotal`, `Complex.sin_eq_tsum`, `IsValuativeTopology.isClosed_ball`, `AlgebraicIndependent.aevalEquivField_apply_coe`, `Multiset.esymm_neg`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear`, `CliffordAlgebra.foldr'Aux_apply_apply`, `HasDerivAt.sum`, `ProbabilityTheory.covarianceBilin_map`, `IsLocalRing.isUnit_of_mem_nonunits_one_sub_self`, `AlgebraicGeometry.Proj.SpecMap_awayMap_awayι`, `zero_mem_tangentConeAt`, `MvPolynomial.irreducible_toPolynomialAdjoinImageCompl`, `SchwartzMap.instFourierSMul`, `AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE_assoc`, `CategoryTheory.Abelian.Ext.smul_eq_comp_mk₀`, `NonUnitalAlgHom.toAlgHom_apply`, `LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent`, `HasFPowerSeriesOnBall.prod`, `Unitization.nnnorm_eq_sup`, `Valuation.Integer.not_isUnit_iff_valuation_lt_one`, `Finsupp.sum_smul_index_semilinearMap'`, `MvPowerSeries.instIsScalarTower`, `MvPowerSeries.map_frobenius_expand`, `SchwartzMap.fourierTransformCLM_apply`, `IsStarProjection.two_mul_sub_one_mem_unitary`, `LinearEquiv.isSMulRegular_congr`, `HasFPowerSeriesWithinOnBall.neg`, `zero_mem_lowerBounds_smoothingSeminormSeq_range`, `IsLocalization.submonoid_map_le_is_unit`, `PowerSeries.invOneSubPow_val_eq_mk_sub_one_add_choose_of_pos`, `selfAdjointPart_apply_coe`, `QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last`, `IntermediateField.LinearDisjoint.exists_field_of_isDomain`, `multiplicity_zero_eq_zero_of_ne_zero`, `Seminorm.bound_of_shell_sup`, `Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `Finset.expect_univ`, `Complex.cpow_nat_mul'`, `WeakSpace.instContinuousSMul`, `Subgroup.le_adjoinNegOne`, `AlgEquiv.moduleEndSelfOp_symm_apply`, `TensorProduct.directSumRight'_restrict`, `Ideal.torsionMapQuot_injective`, `ConcaveOn.mul`, `skewAdjointPartL_apply_coe`, `WeierstrassCurve.Projective.dblY_smul`, `Perfection.teichmuller_eq_teichmuller₀_toMonoidHom`, `PowerSeries.exp_pow_eq_rescale_exp`, `Module.End.isNilpotent_restrict_sub_algebraMap`, `minpoly_algEquiv_toLinearMap`, `Finset.weightedVSub_apply`, `Ideal.primaryComponent_mem`, `ContinuousLinearMap.bilinearComp_zero_left`, `HasStrictDerivAt.finCons`, `inv_pow_sub_of_lt`, `ContinuousLinearMap.nnnorm_smulRight_apply`, `WeierstrassCurve.Jacobian.eval_polynomial`, `Matrix.blockDiagonal_pow`, `NoZeroSMulDivisors.isReduced`, `PowerSeries.X_pow_eq`, `RootPairing.pairing_neg_one_neg_four_iff'`, `hasFPowerSeriesWithinOnBall_pi_iff`, `HasDerivAt.fun_smul`, `RingTheory.Sequence.IsRegular.quot_ofList_smul_nontrivial`, `pinGroup.mem_iff`, `hasDerivAt_zero`, `LinearIsometryEquiv.smul_trans`, `RingHom.Finite.tensorProductMap`, `Convex.add_smul_sub_mem_interior'`, `Matrix.toBilin'Aux_eq`, `SchwartzMap.fderivCLM_fourier_eq`, `minpoly.natSepDegree_eq_one_iff_pow_mem`, `TensorProduct.lift.equiv_symm_apply`, `MvPowerSeries.coeff_invOfUnit`, `ContinuousMultilinearMap.instContinuousSMul`, `IsLocalizedModule.mk'_smul`, `HasFDerivWithinAt.isLittleOTVS`, `ConvexOn.sup`, `addMonoidHomLequivNat_apply`, `MvPolynomial.aeval_comp_expand`, `one_sub_dvd_one_sub_pow`, `mellin_const_smul`, `LieAlgebra.IsKilling.cartanEquivDual_apply_apply`, `LinearRecurrence.geom_sol_iff_root_charPoly`, `Ideal.Quotient.isUnit_mk_pow_iff_notMem`, `Subalgebra.centralizer_coe_range_includeLeft_eq_center_tensorProduct`, `ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt`, `UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors`, `arithGeom_zero_eq_mul_div`, `ContMDiffOn.const_smul_section`, `LinearOrderedCommGroupWithZero.fst_apply`, `LinearIndependent.units_smul`, `FormalMultilinearSeries.ofScalars_smul`, `SchwartzMap.derivCLM_apply`, `LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix'`, `Matrix.toLin_finTwoProd_toContinuousLinearMap`, `IsBaseChange.linearMapLeftRight`, `HomogeneousLocalization.Away.eventually_smul_mem`, `IntermediateField.isSeparable_adjoin_pair_of_isSeparable`, `Module.End.IsSemisimple_smul_iff`, `Odd.pow`, `IsPrimitiveRoot.isPrimitiveRoot_iff'`, `PowerSeries.monomial_eq_C_mul_X_pow`, `PowerSeries.mul_X_pow_injective`, `Valuation.exists_pow_Uniformizer`, `StandardEtalePair.cond`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `WeierstrassCurve.Projective.addX_eq'`, `Fintype.sum_smul_sum`, `Ideal.top_mul`, `Matrix.disc_conj`, `Nat.Partition.summable_genFun_term'`, `MvPolynomial.HomogeneousSubmodule.gradedMonoid`, `hasDerivWithinAt_inter'`, `MulAction.injective₀`, `Seminorm.coe_comp`, `exists_squarefree_dvd_pow_of_ne_zero`, `Absorbs.biInter`, `IntermediateField.finiteDimensional_left`, `LinearMap.map_smulₛₗ`, `DirectSum.GAlgebra.smul_def`, `op_geom_sum`, `HasDerivWithinAt.scomp_hasDerivAt`, `AffineSubspace.subtypeₐᵢ_linearIsometry`, `Nat.Partition.multipliable_powerSeriesMk_card_restricted`, `Unitary.inner_map_map`, `legendreSym.card_sqrts`, `Matrix.isSymm_iff_intrinsicStar_toLin'`, `LinearMap.toMatrixAlgEquiv'_symm`, `IntermediateField.finiteDimensional_iSup_of_finite`, `PrimeSpectrum.zeroLocus_singleton_pow`, `Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T`, `MvPowerSeries.expand_X`, `ContDiffBump.dist_normed_convolution_le`, `instIsPushout_1`, `MeasureTheory.FiniteMeasure.map_smul`, `WeierstrassCurve.Jacobian.dblXYZ_of_Z_eq_zero`, `MDifferentiableOn.clm_precomp`, `IsPrecomplete.prec`, `VectorField.lieBracketWithin_smul_right`, `Algebra.Extension.Hom.sub_aux`, `WeierstrassCurve.Jacobian.dblX_of_Z_eq_zero`, `DualNumber.commute_eps_right`, `ConvexOn.mul_concaveOn`, `StrictConvexOn.sup`, `hasDerivAt_exp_smul_const_of_mem_ball'`, `PadicInt.pow_p_dvd_int_iff`, `IsRelPrime.add_mul_right_left`, `IsNilpotent.isUnit_one_sub`, `extremePoints_convexHull_subset`, `PolynomialModule.eval_smul`, `Finset.weightedVSubOfPoint_const_smul`, `LinearEquiv.isScalarTower`, `ZMod.gauss_lemma_aux`, `instIsPushoutFractionRingPolynomial`, `ContinuousMap.linearIsometryBoundedOfCompact_apply_apply`, `StarConvex.is_linear_preimage`, `PowerSeries.divXPowOrder_pow`, `IsPrimitiveRoot.geom_sum_eq_zero`, `WithTop.pow_lt_pow_left`, `deriv_comp_mul_left`, `Submodule.mem_span_image_finset_iff_exists_fun'`, `hasDerivAtFilter_finCons`, `ContinuousLinearMap.adjoint_comp`, `iteratedFDeriv_zero_eq_comp`, `HasStrictDerivAt.prodMk`, `Module.End.mem_genEigenspace_one`, `LieModule.toEnd_eq_zero_iff`, `intervalIntegral.integral_hasDerivAt_right`, `UniqueFactorizationMonoid.instIsMulTorsionFree`, `hasFTaylorSeriesUpToOn_succ_iff_left`, `HasDerivWithinAt.mul_const`, `UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrime`, `mem_segment_iff_div`, `WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded`, `MonotoneOn.quasiconcaveOn`, `HasCompactSupport.hasDerivAt_convolution_left`, `Polynomial.geom_sum_X_comp_X_add_one_eq_sum`, `PadicInt.continuous_multichoose`, `Ideal.isUnit_iff`, `Complex.hasSum_taylorSeries_neg_log`, `AlgebraicClosure.instIsScalarTower`, `HasDerivWithinAt.cexp`, `le_perfectClosure_iff`, `perfectClosure.isAlgebraic`, `MvPolynomial.aevalTower_comp_toAlgHom`, `Polynomial.isUnit_or_eq_zero_of_separable_expand`, `Submodule.smul_comap_le_comap_smul`, `DualNumber.instIsLocalRing`, `Matrix.GeneralLinearGroup.val_map_apply`, `VectorFourier.integral_bilin_fourierIntegral_eq_flip`, `LinearMap.charpoly_sub_smul`, `LaurentPolynomial.eval₂_T_neg_n`, `smul_inv_le_iff_of_neg`, `Unitary.norm_sub_eq`, `LinearEquiv.congrRight₂_trans`, `deriv_clm_apply`, `unitary_iff_isStarNormal_and_spectrum_subset_unitary`, `algebraMap.smul'`, `SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left`, `Associates.irreducible_iff_prime_iff`, `PowerSeries.X_pow_order_dvd`, `HasFPowerSeriesWithinOnBall.add`, `exposedPoints_subset_extremePoints`, `WeierstrassCurve.Jacobian.isUnit_Y_of_Z_eq_zero`, `Module.isTorsionBy_quotient_iff`, `CategoryTheory.ShortComplex.LeftHomologyMapData.smul_φK`, `IntermediateField.isSeparable_sup`, `Units.divp_add_divp_same`, `Finset.centerMass_pair`, `Algebra.TensorProduct.lTensor_ker`, `contDiff_smul`, `exists_maximal_linearIndepOn`, `MvPolynomial.eval₂_X_pow`, `Submodule.span_singleton_eq_one_iff`, `FiniteGaloisIntermediateField.finiteDimensional`, `PairReduction.exists_radius_le`, `derivWithin_fun_pow`, `Algebra.norm_one_add_smul`, `TensorProduct.AlgebraTensorModule.rTensor_id`, `minpoly.neg`, `IsOpen.smul₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `AffineMap.hasStrictDerivAt`, `two_mul_le_add_pow_two`, `Matrix.kroneckerTMulBilinear_apply`, `Submonoid.mem_nonunits_iff_of_ne_zero`, `cexp_neg_quadratic_isLittleO_rpow_atTop`, `InnerProductSpace.toLinearMap_rankOne`, `Ideal.associatesEquivIsPrincipal_mul`, `openSegment_translate_preimage`, `DvdNotUnit.not_unit`, `ContinuousLinearMap.comp_hasFPowerSeriesOnBall`, `meromorphicNFAt_smul_iff_right_of_analyticAt`, `HasDerivWithinAt.Ioi_of_Ici`, `Module.reflection_mul_reflection_zpow_apply`, `Polynomial.cyclotomic.irreducible_rat`, `Polynomial.coe_normUnit`, `ContinuousLinearMap.adjointAux_inner_right`, `DividedPowers.RatAlgebra.dpow_eq_of_mem`, `HasDerivWithinAt.Ioi_iff_Ioo`, `smoothingSeminormSeq_bddBelow`, `VectorField.mpullback_mfderivWithin_apply_smul`, `VectorField.mpullbackWithin_const_smul`, `MeromorphicOn.smul`, `WeierstrassCurve.c₄_of_isCharNeTwoNF`, `Seminorm.finset_sup_smul`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `Complex.integral_boundary_rect_of_continuousOn_of_hasFDerivAt_real`, `Complex.taylorSeries_eq_on_ball`, `TemperedDistribution.instLineDerivSMulComplex`, `ProbabilityTheory.integrable_pow_abs_mul_cexp_of_re_mem_interior_integrableExpSet`, `MulChar.ofRootOfUnity_spec`, `StrictConcaveOn.translate_left`, `Commute.add_pow_dvd_pow_of_pow_eq_zero_right`, `LinearMap.restrict_smul_one`, `prod_indicator_const`, `InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj`, `Complex.iteratedDeriv_odd_cos`, `Perfection.lift_apply_apply_coe`, `HasStrictFDerivAt.clm_apply`, `Algebra.norm_apply`, `Complex.exp_bound'`, `AffineBasis.isUnit_toMatrix_iff`, `WeierstrassCurve.Jacobian.dblU_smul`, `le_self_pow₀`, `RingHom.smulOneHom_apply`, `WittVector.polyOfInterest_vars_eq`, `IntermediateField.coe_smul`, `ContMDiffAt.clm_bundle_apply₂`, `Nat.cast_smul_eq_nsmul`, `ContDiffMapSupportedIn.fderivLM_apply`, `finsuppTensorFinsupp_symm_single`, `RegularExpression.matches'_pow`, `smul_lowerBounds_subset_upperBounds_smul`, `associated_of_factorization_eq`, `Polynomial.det_taylorLinearEquiv`, `addMonoidHomLequivInt_symm_apply`, `summable_geometric_iff_norm_lt_one`, `Seminorm.isBounded_sup`, `Polynomial.aroots_X_pow`, `ProbabilityTheory.integrable_pow_mul_cexp_of_re_mem_interior_integrableExpSet`, `LinearMap.prodMap_smul`, `IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end`, `LinearMap.trace_tensorProduct`, `continuousMultilinearCurryRightEquiv_symm_apply'`, `AntitoneOn.convex_ge`, `comp_dualTensorHom`, `Polynomial.resultant_deriv`, `MeasureTheory.condExpInd_smul'`, `NormedSpace.expSeries_sum_eq_div`, `LocalizedModule.lift_mk_one`, `WithBot.coe_pow`, `Summable.tsum_smul_const`, `Homotopy.smul_hom`, `Module.Invertible.instLocalizationLocalizedModule`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply`, `Convex.add_smul_mem_interior'`, `UpperHalfPlane.det_J`, `LinearEquiv.mem_stabilizer_fixedSubmodule`, `ENNReal.coe_pow`, `gcd_pow_left_dvd_pow_gcd`, `HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos`, `measurable_smul_const`, `AffineSubspace.wSameSide_smul_vsub_vadd_right`, `WeakFEPair.functional_equation`, `ModularGroup.coe_one`, `add_pow`, `list_sum_pow_char`, `hasEigenvalue_toLin'_diagonal_iff`, `SchwartzMap.smul_apply`, `ContDiffMapSupportedIn.continuousSMul`, `ContinuousLinearMap.prodL_apply`, `LinearEquiv.map_smul`, `ProjectiveSpectrum.basicOpen_pow`, `summable_pow_mul_geometric_of_norm_lt_one`, `LieAlgebra.isNilpotent_ad_of_mem_rootSpace`, `UniqueFactorizationMonoid.multiplicative_prime_power`, `ContDiffMapSupportedIn.structureMapLM_zero_injective`, `gcd_isUnit_iff_isRelPrime`, `toSpanSingleton_deriv`, `exists_leadingCoeff_pow_smul_mem_conductor`, `Complex.I_sq`, `GaussianFourier.integrable_cexp_neg_mul_sq_norm_add`, `IsLocalizedModule.mk_eq_mk'`, `IsLocalizedModule.map_injective_iff_localizedModuleMap_injective`, `Coalgebra.TensorProduct.assoc_symm_tmul`, `Polynomial.support_X_pow`, `convex_Ioc`, `Valuation.hasBasis_uniformity`, `Matrix.IsHermitian.pow`, `LinearEquiv.smul_id_of_finrank_eq_one_apply`, `MvPolynomial.pderiv_inr_universalFactorizationMap_X`, `LinearMap.toMatrix'_toLinearMapₛₗ₂'`, `Polynomial.integralNormalization_coeff_degree_ne`, `Submodule.smul_torsionBy`, `FractionalIdeal.mul_inv_cancel_iff_isUnit`, `CStarAlgebra.isStrictlyPositive_iff_eq_star_mul_self`, `TrivSqZeroExt.fst_map`, `HasDerivWithinAt.fun_add`, `AdicCompletion.transitionMap_ideal_mk`, `IsPrimitiveRoot.zpowers_eq`, `LinearMap.BilinForm.smul_right`, `Associated.of_mul_left`, `LinearMap.isStarProjection_toContinuousLinearMap_iff`, `AbsoluteValue.map_pow`, `CategoryTheory.Limits.IsColimit.ι_smul`, `MeromorphicOn.divisor_smul`, `Algebra.TensorProduct.tensorTensorTensorComm_tmul`, `WeierstrassCurve.j_eq_zero_iff_of_char_two'`, `IsLinearMap.isLinearMap_smul`, `IsLocalization.map_units`, `LocalizedModule.mk'_smul_mk`, `Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone`, `PowerSeries.coeff_X_pow_self`, `HasFDerivAtFilter.isLittleOTVS`, `CommRingCat.equalizer_ι_isLocalHom`, `Representation.ofModule_asAlgebraHom_apply_apply`, `Ideal.mul_le_inf`, `IsCyclic.mulAutMulEquiv_symm_apply_symm_apply`, `Submodule.smul_le`, `Matrix.toLpLin_mul`, `isUnit_gcd_one_left`, `iteratedDerivWithin_eq_equiv_comp`, `pow_abs`, `IsNilpotent.pow_iff_pos`, `Valued.toNormedField.norm_def`, `TensorProduct.map_convMul_map`, `TensorAlgebra.equivDirectSum_symm_apply`, `RatFunc.single_one_eq_pow`, `PadicInt.p_nonunit`, `MvPowerSeries.coeff_smul`, `InfiniteGalois.restrictNormalHom_continuous`, `HasDerivAt.const_add`, `exists_pow_btwn`, `ModularForm.coe_norm`, `associated_gcd_right_iff`, `Matrix.toLin'_submatrix`, `TensorProduct.gradedMul_algebraMap`, `IntermediateField.isAlgebraic_iSup`, `slope_sub_smul`, `IsPrimitiveRoot.pow_sub_one_eq`, `WeierstrassCurve.Jacobian.X_eq_of_equiv`, `AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE`, `Polynomial.monomial_one_right_eq_X_pow`, `iteratedFDerivWithin_two_apply`, `Matrix.conjTranspose_ofNat_smul`, `Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub`, `extDerivWithin_smul`, `Units.isEmbedding_val₀`, `AddAction.automorphize_smul_left`, `Complex.sq_nonpos_iff`, `NormedSpace.expSeries_div_hasSum_exp`, `Module.End.isIntegral`, `Derivation.compAEval_eq`, `preNormEDS_even`, `Complex.cpow_nat_inv_pow`, `ContDiffMapSupportedIn.seminorm_postcompLM_le`, `AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen`, `Subgroup.strictPeriods_SL2Z`, `ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap`, `pow_sub₀`, `Matrix.separatingLeft_toLinearMap₂_iff`, `CategoryTheory.MonoidalLinear.smul_whiskerRight`, `sq_eq_sq_iff_eq_or_eq_neg`, `HahnSeries.SummableFamily.powers_toFun`, `Derivation.tensorProductTo_tmul`, `Module.End.mem_maxGenEigenspace`, `IsExtreme.convex_diff`, `Ideal.finite_quotient_pow`, `DoubleCentralizer.coe_fst`, `spectrum.setOf_isUnit_inter_mul_comm`, `WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero`, `HasDerivAt.prodMk`, `Subring.pointwise_smul_le_pointwise_smul_iff₀`, `HasStrictFDerivAt.fun_smul`, `Valuation.toUniformSpace_eq`, `Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero`, `AdicCompletion.transitionMap_map_mul`, `ProbabilityTheory.charFun_stdGaussian`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap`, `associated_normalize_iff`, `AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul`, `AdjoinRoot.coe_mapAlgEquiv`, `Polynomial.aeval_endomorphism`, `IsUnit.ringInverse`, `MvPolynomial.instIsPushout_1`, `Module.End.genEigenspace_div`, `DivisibleHull.zsmul_mk`, `smul_inv_lt_iff_of_neg`, `punctured_nhds_smul₀`, `CompactlySupportedContinuousMap.toReal_smul`, `Perfection.pthRoot_eq_symm_frobeniusEquiv`, `tendsto_pow_atTop_nhds_zero_of_lt_one`, `IsGalois.of_separable_splitting_field_aux`, `PreTilt.untilt_iterate_frobeniusEquiv_symm_pow`, `WeierstrassCurve.Projective.negMap_of_Z_eq_zero`, `IntermediateField.coe_equivMap_apply`, `Derivation.map_smul`, `WeierstrassCurve.Affine.CoordinateRing.mk_ψ₂_sq`, `IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt`, `pow_one_sub_dvd_pow_mul_sub_one`, `not_squarefree_zero`, `IsLocalRing.nonunits_add`, `Seminorm.closedBall_bot`, `LocallyConvexSpace.convex_open_basis_zero`, `Submodule.adjoint_orthogonalProjection`, `Transcendental.pow`, `CategoryTheory.MonoidalLinear.whiskerLeft_smul`, `TensorProduct.homTensorHomMap_apply`, `Polynomial.Splits.coeff_zero_eq_leadingCoeff_mul_prod_roots`, `Filter.HasBasis.isBigOTVS_iff`, `Real.sInf_smul_of_nonpos`, `LinearMap.tensorEqLocus_tmul`, `Matrix.isRepresentation.eq_toEnd_of_represents`, `wbtw_smul_vadd_smul_vadd_of_nonneg_of_le`, `HasFDerivAt.pow'`, `Polynomial.rootMultiplicity_le_iff`, `LieModule.traceForm_apply_apply`, `Function.Odd.smul_even`, `Units.val_oneSub`, `HasStrictFDerivAt.pow'`, `cross_dot_cross`, `LinearMap.toMatrix₂_apply`, `ContDiffWithinAt.smul_const`, `Complex.IsConservativeOn.hasDerivAt_wedgeIntegral`, `Convex.smul_mem_of_zero_mem`, `PowerSeries.heval_unit`, `Real.fourierIntegral_continuousLinearMap_apply'`, `CurveIntegrable.smul`, `Units.inv_neg`, `IsLocalRing.exists_maximalIdeal_pow_le_of_isArtinianRing_quotient`, `AffineIsometryEquiv.ofEq_rfl`, `IntermediateField.finInsepDegree_bot`, `DivisorChain.eq_pow_second_of_chain_of_has_chain`, `LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra`, `RootPairing.rootFormIn_self_smul_coroot`, `MvPolynomial.C_mem_pow_idealOfVars_iff`, `PowerSeries.invOneSubPow_eq_inv_one_sub_pow`, `Finset.centroid_pair`, `TopModuleCat.hom_smul`, `ProbabilityTheory.complexMGF_id_gaussianReal`, `Polynomial.isUnit_iff_degree_eq_zero`, `ContinuousLinearMap.hasFDerivAt_of_bilinear`, `cfcₙHom_continuous`, `starConvex_iff_forall_pos`, `Submodule.tensorToSpan_apply_tmul`, `one_add_mul_le_pow_of_sq_nonneg`, `CancelMonoidWithZero.toIsCancelMulZero`, `IsCyclotomicExtension.iff_adjoin_eq_top`, `lp.infty_isScalarTower`, `FormalMultilinearSeries.min_radius_le_radius_add`, `IsPurelyInseparable.exponent_min`, `krullTopology_mem_nhds_one_iff`, `CFC.abs_sq`, `Valuation.norm_def`, `hasStrictDerivAt_one`, `IsPrecomplete.prec'`, `FormalMultilinearSeries.ofScalars_comp_neg_id`, `Affine.Simplex.point_vsub_centroid_eq_smul_vsub`, `IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two`, `RootPairing.corootForm_self_smul_root`, `FiniteField.unitsMap_norm_surjective`, `nilpotent_iff_mem_prime`, `gaussSum_pow_eq_prod_jacobiSum`, `Nat.choose_le_pow_div`, `HasDerivWithinAt.of_isLittleO`, `SymmetricAlgebra.algHom_surjective`, `quadraticChar_sq_one'`, `exists_pow_lt₀`, `contMDiffAt_iff_localFrame_coeff`, `Algebra.baseChange_lmul`, `TensorProduct.AlgebraTensorModule.tensorQuotientEquiv_apply_tmul`, `QuadraticForm.tensorAssoc_apply`, `StrongDual.extendRCLike_apply`, `ZMod.orderOf_lt`, `zero_mem_nonunits`, `ContinuousLinearMap.closed_range_of_antilipschitz`, `Complex.norm_eq_one_of_mem_rootsOfUnity`, `IsPurelyInseparable.minpoly_eq_X_sub_C_pow`, `NormalizationMonoid.normUnit_mul`, `Matrix.frobeniusNormSMulClass`, `Complex.exp_rat_mul_pi_mul_I_pow_two_mul_den`, `ArithmeticFunction.carmichael_eq_exponent'`, `LieModule.trace_toEnd_genWeightSpaceChain_eq_zero`, `IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot`, `HasDerivAt.div_const`, `strictConvex_iff_div`, `HasDerivAt.scomp_of_eq`, `VonNeumannAlgebra.coe_toStarSubalgebra`, `nilradical_eq_bot_iff`, `Matrix.toEuclideanLin_apply_piLp_toLp`, `LieAlgebra.SemiDirectSum.smul_eq_mk`, `AlgebraicGeometry.RingedSpace.isUnit_res_basicOpen`, `BddAbove.smul_of_nonpos`, `lie_eq_smul`, `SeminormFamily.basisSets_singleton_mem`, `Units.sub_divp`, `ZMod.not_isCyclic_units_eight`, `Ideal.ofList_cons_smul`, `Module.AEval.of_aeval_smul`, `WeierstrassCurve.Jacobian.negY_smul`, `Finset.centerMass_eq_of_sum_1`, `Asymptotics.isLittleOTVS_iff_tendsto_inv_smul`, `Commute.isNilpotent_finsum`, `IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin`, `Ring.not_isUnit_iff_inverse_eq_zero`, `pow_div_pow_eventuallyEq_atBot`, `LieModule.Cohomology.twoCochain_val_apply`, `ContDiffMapSupportedIn.continuous_iff_comp_order_le`, `LieAlgebra.ext_iff`, `add_pow_prime_eq'`, `WeierstrassCurve.Projective.addMap_of_Z_ne_zero`, `Mathlib.Tactic.Module.NF.sub_eq_eval₂`, `pow_lt_pow_right_of_lt_one₀`, `X_pow_sub_C_irreducible_of_prime_pow`, `TensorialAt.mkHom₂_apply`, `minpoly.not_isUnit`, `Odd.pow_lt_pow`, `ConvexCone.disjoint_hull_right_of_convex`, `ContinuousAlternatingMap.curryLeft_add`, `ValueDistribution.proximity_pow_top`, `Ideal.sup_mul_eq_of_coprime_left`, `hasFDerivAt_integral_of_dominated_of_fderiv_le`, `Ideal.finprod_count`, `TopologicalAddGroup.IsSES.integral_inducedMeasure`, `HasFPowerSeriesAt.pi`, `nonZeroDivisorsEquivUnits_apply`, `TensorAlgebra.ι_inj`, `WeierstrassCurve.Jacobian.addY_of_X_eq'`, `StrictConcaveOn.add_concaveOn`, `divp_mk0`, `smul_ball`, `ZMod.expand_card`, `Subalgebra.instIsScalarTowerSubtypeMem`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn'`, `Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd`, `map_intCast_smul`, `AddAut.mulLeft_apply_apply`, `IntervalIntegrable.continuousOn_smul`, `Seminorm.smul_ball_preimage`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply`, `hasStrictDerivAt_pi`, `Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero'`, `ContDiff.hasStrictDerivAt`, `PowerSeries.IsWeierstrassDivision.isWeierstrassFactorization`, `LinearIsometry.strictConvexSpace_range_iff`, `SameRay.exists_pos`, `VectorFourier.fourierPowSMulRight_apply`, `cfcₙHomSuperset_continuous`, `HasFDerivWithinAt.smul`, `skewAdjointPart_eq_I_smul_imaginaryPart`, `AlgEquiv.smul_units_def`, `MultilinearMap.piLinearMap_apply_apply_apply`, `finsuppTensorFinsuppRid_apply_apply`, `Module.Basis.repr_sum_self`, `WfDvdMonoid.iff_wellFounded_associates`, `WeierstrassCurve.Jacobian.polynomialX_eq`, `TensorProduct.toLinearMap_symm_lid`, `normEDS_ofNat`, `Matrix.isUnit_det_of_left_inverse`, `HasDerivAt.cexp`, `dvd_prime_pow`, `WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero`, `TensorAlgebra.ι_eq_zero_iff`, `NonUnitalSubalgebra.coe_smul`, `OreLocalization.mul_inv_cancel`, `CoalgCat.MonoidalCategoryAux.comul_tensorObj`, `ContinuousAlternatingMap.prodLIE_apply`, `MvPolynomial.C_mul_X_pow_eq_monomial`, `Finsupp.linearCombination_option`, `ValueDistribution.logCounting_pow_zero`, `lipschitzGroup.coe_mem_iff_mem`, `StarSubalgebra.coe_isUnit`, `Ideal.mul_iSup`, `PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal`, `discrim_eq_sq_of_quadratic_eq_zero`, `Polynomial.iterate_derivative_X_sub_pow_self`, `Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson`, `Associates.le_one_iff`, `QuadraticMap.associated_sq`, `LinearMap.dualMap_def`, `hasDerivAt_pow`, `DirectSum.coe_mul_of_apply`, `iSupIndep_iff_dfinsupp_lsum_injective`, `image_extremePoints`, `UniqueFactorizationMonoid.primeFactors_eq_empty_iff`, `TrivSqZeroExt.liftEquivOfComm_symm_apply_coe`, `Polynomial.degreeLT_eq_span_X_pow`, `Summable.smul_const`, `ZMod.pow_card_pow`, `NormedRing.inverse_add_norm_diff_first_order`, `AlgebraicGeometry.Proj.valuativeCriterion_existence_aux`, `pow_two_pos_of_ne_zero`, `WithTop.top_pow`, `Associates.out_mul`, `QuadraticMap.associated_comp`, `FormalMultilinearSeries.summable_nnnorm_mul_pow`, `Ideal.add_pow_mem_of_pow_mem_of_le_of_commute`, `MeasureTheory.Lp.simpleFunc.toLp_smul`, `LieAlgebra.IsKilling.chainLength_smul`, `normUnit_one`, `isNilpotent_sum`, `segment_eq_image_lineMap`, `Odd.pow_nonpos`, `ENat.toENNReal_pow`, `KaehlerDifferential.ker_map_of_surjective`, `Polynomial.isNilpotent_mul_X_iff`, `TensorProduct.tmul_of_gradedMul_of_tmul`, `sub_smul_slope`, `IsDiscreteValuationRing.addVal_eq_zero_of_unit`, `ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le`, `IsPowMul.restriction`, `MonoidWithZeroHom.fst_inr_apply_of_ne_zero`, `dist_smul₀`, `cyclotomicCharacter.spec`, `convexCombination_eq_sum`, `Module.zero_smul`, `concaveOn_iff_forall_pos`, `ftaylorSeries_zero`, `Polynomial.discr_of_degree_eq_two`, `associated_gcd_left_iff`, `PadicInt.mahlerEquiv_apply`, `Submodule.span_singleton_eq_range`, `Ring.exists_not_isUnit_of_not_isField`, `CStarAlgebra.pow_monotone`, `PerfectRing.ofSurjective`, `SchwartzMap.convolution_flip`, `Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul`, `QuadraticMap.associated_isOrtho`, `HasDerivWithinAt.isLittleO`, `norm_pow_le'`, `Perfection.mk_teichmuller₀`, `ContinuousLinearMap.opNorm_flip`, `LieRinehartAlgebra.Hom.map_smul_apply`, `Module.Basis.parallelepiped_map`, `Subgroup.mem_strictPeriods_iff`, `isNilpotent_neg_iff`, `Algebra.H1Cotangent.isLocalizedModule`, `Algebra.TensorProduct.lift_comp_includeRight'`, `cfcₙ_apply_pi`, `MvPolynomial.psum_eq_mul_esymm_sub_sum`, `Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible`, `Polynomial.reflect_C`, `Seminorm.bound_of_shell_smul`, `Finset.squarefree_prod_of_pairwise_isCoprime`, `Odd.pow_neg`, `mem_unitary_of_spectrum_subset_unitary`, `HasDerivWithinAt.prodMk`, `continuousOn_integral_bilinear_of_locally_integrable_of_compact_support`, `exists_associated_pow_of_mul_eq_pow`, `LinearOrderedCommMonoidWithZero.toIsMulTorsionFree`, `IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization.unique_irreducible`, `DirectSum.coe_mul_apply_eq_dfinsuppSum`, `FormalMultilinearSeries.radius_compContinuousLinearMap_le`, `hasDerivWithinAt_derivWithin_iff`, `hasDerivAt_sub_const_iff`, `midpoint_mem_segment`, `Valuation.exists_div_eq_of_unit`, `ZMod.exists_one_add_mul_pow_prime_eq`, `HasStrictFDerivAt.mul_const'`, `ContinuousLinearMap.IsPositive.adjoint_conj`, `IntermediateField.isSeparable_iSup`, `EisensteinSeries.G2_eq_tsum_cexp`, `GroupWithZero.zpow_succ'`, `IsCoprime.isRelPrime`, `LinearMap.smulRightₗ_apply_apply`, `Valuation.restrict_le_one_iff`, `krullTopology_mem_nhds_one_iff_of_normal`, `HasDerivAt.div`, `geom₂_sum_of_lt`, `GroupLike.val_inv_toUnits_apply`, `RingHom.map_geom_sum₂`, `Bialgebra.comul_pow`, `IsConformalMap.smul`, `DvdNotUnit.not_associated`, `IsArtinianRing.isUnit_of_mem_nonZeroDivisors_of_mulOpposite`, `isCoveringMap_npow`, `Valuation.isClosed_ball`, `NonUnitalStarAlgHom.subtype_comp_codRestrict`, `Associates.mk_eq_zero`, `HasDerivWithinAt.pow`, `Submodule.IsPrincipal.associated_generator_span_self`, `ContinuousLinearEquiv.smul_trans`, `TensorProduct.AlgebraTensorModule.lTensor_one`, `MeasureTheory.withDensityᵥ_smul_eq_withDensityᵥ_withDensity`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `AlgebraicGeometry.Scheme.mem_basicOpen_top`, `DivisibleHull.neg_mk`, `Matrix.dualNumberEquiv_apply`, `IsCyclotomicExtension.Rat.Three.eq_one_or_neg_one_of_unit_of_congruent`, `add_pow_eq_mul_pow_add_pow_div_expChar_of_commute`, `ConvexCone.isGenerating_top`, `pow_dvd_of_mul_eq_pow`, `MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub`, `CategoryTheory.Pretriangulated.Triangle.smul_hom₃`, `Matrix.separatingRight_toBilin'_iff`, `Matrix.GeneralLinearGroup.val_swap`, `Complex.hasDerivAt_Gamma_one`, `LieModule.maxGenEigenSpace_toEnd_eq_top`, `TemperedDistribution.fourierMultiplierCLM_sum`, `LinearMap.restrictScalars_extendScalarsOfIsLocalization`, `Submodule.smul_le_of_le_smul_of_le_jacobson_bot`, `LinearMap.vecEmpty₂_apply`, `MvPowerSeries.substAlgHom_monomial`, `Matrix.isNilpotent_iff`, `geom_sum_Ico'`, `CFC.log_pow`, `orderOf_eq_zero_iff_eq_zero`, `PeriodPair.hasSum_weierstrassPExcept`, `IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_or_add_one_of_lambda_not_dvd`, `Matrix.charpoly_inv`, `intervalIntegral.integral_smul_const`, `IsRightCancelMulZero.faithfulSMul`, `ENNReal.iSup_pow`, `FormalMultilinearSeries.derivSeries_eq_zero`, `InnerProductSpace.laplacianWithin_smul_nhds`, `AntitoneOn.quasiconvexOn`, `selfZPow_sub_natCast`, `QuotientGroup.automorphize_smul_left`, `Complex.GammaSeq_mul`, `TestFunction.lineDerivCLM_smul`, `Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq`, `spectrum.unit_mem_mul_comm`, `Polynomial.eval₂_pow'`, `exists_add_pow_prime_eq`, `Unitization.instStarModule`, `Algebra.Generators.H1Cotangent.δ_eq_δAux`, `ContDiffWithinAt.smulRight`, `ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF`, `HasDerivWithinAt.congr_of_eventuallyEq`, `UniqueFactorizationMonoid.normalizedFactors_pow`, `Irreducible.coprime_pow_of_not_dvd`, `Equiv.mulRight₀_symm_apply`, `HasDerivAtFilter.isEquivalent_sub`, `pow_right_inj₀`, `Matrix.toLinAlgEquiv'_toMatrixAlgEquiv'`, `LinearEquiv.lieConj_symm`, `FractionalIdeal.spanSingleton_eq_spanSingleton`, `ContinuousLinearMap.star_eq_adjoint`, `SchwartzMap.integral_fourier_smul_eq`, `EReal.exp_nmul`, `pow_le_pow_iff_right₀`, `ProbabilityTheory.meas_ge_le_evariance_div_sq`, `LieAlgebra.rank_eq_natTrailingDegree`, `FormalMultilinearSeries.comp_rightInv`, `Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point`, `Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable`, `WithZeroTopology.tendsto_units`, `IsBaseChange.equiv_tmul`, `ContinuousMultilinearMap.curryLeft_apply`, `Module.End.ker_aeval_ring_hom'_unit_polynomial`, `differentiableAt_pow`, `Finset.centerMass_smul`, `Algebra.lmul_isUnit_iff`, `ContDiffWithinAt.pow`, `LinearMap.tensorProduct_apply`, `OrderIso.withZeroUnits_apply`, `Monotone.quasiconvexOn`, `Submodule.mem_toConvexCone`, `iteratedDeriv_comp_three`, `AffineSpace.asymptoticNhds_eq_smul`, `smul_max_of_nonpos`, `EisensteinSeries.qExpansion_identity`, `HasStrictDerivAt.fun_neg`, `AffineSubspace.direction_smul`, `AlternatingMap.uncurryFin_uncurryFinLM_comp_of_symmetric`, `IsDiscreteValuationRing.associated_pow_irreducible`, `Associates.FactorSet.coe_add`, `NumberField.isUnit_iff_norm`, `Complex.iteratedDeriv_even_sin`, `ContDiffAt.fun_smul`, `HasFPowerSeriesWithinAt.neg`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one`, `RootPairing.pairing_smul_coroot_eq`, `CStarAlgebra.isStrictlyPositive_TFAE`, `Bornology.IsVonNBounded.closure`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec`, `WeierstrassCurve.c₆_of_char_two`, `IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot`, `ModularForm.prod_fintype_slash`, `GaussianFourier.integral_cexp_neg_sum_mul_add`, `isLocalHom_of_le_jacobson_bot`, `QuotSMulTop.map_comp`, `finsuppTensorFinsuppLid_single_tmul_single`, `Prime.squarefree`, `ProbabilityTheory.tendsto_charFun_inv_sqrt_mul_pow`, `AlgebraicGeometry.Scheme.isNilpotent_of_isNilpotent_cover`, `CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos`, `NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply`, `Polynomial.as_sum_range_C_mul_X_pow`, `Asymptotics.isThetaTVS_comm`, `hasStrictDerivAt_inv`, `Projectivization.cross_mk_of_ne`, `fderivWithin_list_prod'`, `Algebra.tensorH1CotangentOfIsLocalization_toLinearMap`, `AlternatingMap.mkContinuousLinear_norm_le`, `Matrix.kroneckerTMulAlgEquiv_apply`, `Matrix.SpecialLinearGroup.coe_GLPos_coe_GL_coe_matrix`, `ProperCone.hyperplane_separation_of_notMem`, `NonUnitalStarAlgebra.range_id`, `IsCoprime.pow_right`, `ConvexOn.mul'`, `Polynomial.isNilpotent_reflect_iff`, `isPrimePow_def`, `LieAlgebra.Basis.borelUpper_le_biSup`, `sub_sq'`, `Module.End.genEigenspace_nat`, `WeierstrassCurve.Jacobian.smul_fin3_ext`, `Unitization.complex_cfcₙ_eq_cfc_inr`, `Module.ker_algebraMap_end`, `RCLike.re_ofReal_pow`, `IsFormallyReal.instIsReduced`, `fderiv_clm_apply`, `separableClosure.isSeparable`, `LieAdmissibleAlgebra.ext_iff`, `listProd_apply_eq_zero`, `DualNumber.eps_pow_two`, `ContinuousAlternatingMap.curryLeftLI_apply`, `Complex.tendsto_one_add_pow_exp_of_tendsto`, `smul_pos_iff_of_neg_left`, `endVecAlgEquivMatrixEnd_symm_apply_apply`, `HasDerivAt.iterate`, `pow_le_kstar`, `ContMDiffWithinAt.const_smul_section`, `tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow`, `ContinuousLinearEquiv.smul_apply`, `Polynomial.derivative_C_mul_X_pow`, `AdicCompletion.of_bijective`, `Bialgebra.TensorProduct.assoc_toCoalgEquiv`, `iteratedFDerivWithin_zero_eq_comp`, `HasFiniteFPowerSeriesAt.sub`, `Polynomial.support_binomial`, `Ideal.span_singleton_mul_left_inj`, `Matrix.mem_specialOrthogonalGroup_fin_two_iff`, `HasFDerivWithinAt.fun_mul'`, `ContinuousLinearMap.norm_compSL_le`, `IsLocalization.tensorProduct_compatibleSMul`, `WittVector.isUnit_of_coeff_zero_ne_zero`, `TestFunction.monoCLM_apply`, `QuadraticMap.Ring.associated_pi`, `Polynomial.roots_X_pow_char_sub_C`, `isRelPrime_iff_isCoprime`, `ContinuousAlternatingMap.instIsCentralScalar`, `fderivWithin_smul_const`, `Unitization.inrNonUnitalAlgHom_apply`, `VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral`, `Balanced.neg`, `nnnorm_commutator_units_sub_one_le`, `NonUnitalAlgebra.comap_top`, `LinearMap.nondegenerate_toMatrix₂_iff`, `WeierstrassCurve.Jacobian.addY_of_X_eq`, `Matrix.trace_kroneckerMapBilinear`, `WeierstrassCurve.Affine.evalEval_polynomial`, `AddMonoidAlgebra.single_pow`, `ContDiffMapSupportedIn.withSeminorms`, `Valuation.IsEquiv.orderMonoidIso_eq_refl`, `LinearMap.frobenius_def`, `ConvexCone.mem_strictlyPositive`, `AlgHom.ker_kerSquareLift`, `AnalyticOn.fun_const_smul`, `MeasureTheory.withDensityᵥ_smul`, `wbtw_or_wbtw_smul_vadd_of_nonneg`, `ContDiffAt.exists_eventually_eq_hasDerivAt`, `MvPolynomial.instIsPushout`, `IsUnit.val_inv_subInvSMul`, `IsAdicComplete.StrictMono.factorPow_comp_extend`, `ContinuousLinearEquiv.continuousSMul`, `DivisibleHull.qsmul_of_nonpos`, `ModuleCat.extendScalarsComp_hom_app_one_tmul`, `Matrix.GeneralLinearGroup.map_apply`, `TopologicalAddGroup.IsSES.pushforward_mono`, `Bornology.isVonNBounded_vadd`, `Algebra.norm_eq_prod_roots`, `star_mul_self_sub_self_mul_star`, `derivWithin_fun_const_smul'`, `IsModuleTopology.continuous_of_distribMulActionHom`, `convex_halfSpace_le`, `Convex.openSegment_closure_interior_subset_interior`, `LieAlgebra.mem_corootSpace'`, `CategoryTheory.ShortComplex.RightHomologyMapData.smul_φQ`, `Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower`, `ConvexOn.convex_strict_epigraph`, `HasFDerivWithinAt.isBigOTVS_sub`, `AbsoluteValue.tendsto_div_one_add_pow_nhds_zero`, `Complex.log_sub_logTaylor_isBigO`, `Matrix.toLinAlgEquiv'_one`, `Polynomial.Monic.isUnit_leadingCoeff_of_dvd`, `DirectSum.support_smul`, `convexHull_isClosed`, `Valued.integer.isUnit_iff_norm_eq_one`, `Mathlib.Tactic.Ring.pow_prod_atom`, `Polynomial.natTrailingDegree_X_pow`, `WeierstrassCurve.coe_variableChange_Δ'`, `SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left`, `Polynomial.Separable.squarefree`, `iteratedDeriv_const_smul_field`, `Polynomial.integralNormalization_eval₂_leadingCoeff_mul_of_commute`, `IntermediateField.adjoin.finiteDimensional`, `PowerSeries.catalanSeries_sq_mul_X_add_one`, `PowerSeries.coeff_subst_finite`, `SlashInvariantForm.vAdd_width_periodic`, `Units.mulLeftLinearEquiv_mul_apply`, `IntermediateField.botEquiv_def`, `UpperHalfPlane.denom_one`, `Matrix.isUnit_of_left_inverse`, `Seminorm.absorbent_closedBall`, `SemilinearEquivClass.map_smulₛₗ`, `Valuation.IsUniformizer.not_isUnit`, `CategoryTheory.NatTrans.app_smul`, `Submodule.FG.jacobson_smul_lt`, `inf_eq_half_smul_add_sub_abs_sub`, `InnerProductSpace.isIdempotentElem_rankOne_self_iff`, `HasDerivAt.tendsto_slope_zero`, `le_algebraicClosure_iff`, `IsCauSeq.geo_series_const`, `Matrix.isUnit_exp`, `fderivWithin_continuousLinearEquiv_comp`, `ContinuousMultilinearMap.toUniformOnFun_toFun`, `Quaternion.re_snd_dualNumberEquiv`, `AddChar.doubleDualEquiv_symm_doubleDualEmb_apply`, `PowerSeries.coeff_X_pow`, `Matrix.toLin_transpose`, `IntermediateField.adjoin_adjoin_comm`, `Valuation.map_pow`, `geom_sum_succ`, `sq_le_one_iff_abs_le_one`, `sub_mem_posTangentConeAt_of_openSegment_subset`, `Submodule.span_singleton_mul`, `Valuation.RankOne.zero_of_hom_zero`, `iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum`, `spectrum.isUnit_of_zero_notMem`, `Fintype.card_eq_card_units_add_one`, `div_le_egauge_ball`, `TrivSqZeroExt.algebraMap_eq_inlHom`, `hasDerivAtFilter_pi`, `Polynomial.ascPochhammer_smeval_eq_eval`, `Ideal.mem_mul_span_singleton`, `HahnSeries.order_pow`, `Asymptotics.IsThetaTVS.trans`, `unitary.expUnitary_eq_mul_inv`, `ContinuousLinearMap.map_smul₂`, `ContinuousLinearMap.coe_flipₗᵢ`, `ContinuousSMul.of_basis_zero`, `PadicInt.mkUnits_eq`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty`, `Representation.leftRegular_norm_apply`, `segment_subset_uIcc`, `BilinForm.mul_toMatrix`, `TensorProduct.liftAux.smul`, `inner_map_polarization`, `Ideal.IsTwoSided.pow_add`, `HasFDerivAtFilter.iterate`, `ModularFormClass.hasSum_qExpansion_of_norm_lt`, `nonZeroDivisorsEquivUnits_symm_apply_coe`, `ENNReal.tsum_geometric_two_encode_le_two`, `not_linearIndepOn_finset_iff`, `Complex.volume_ball`, `ENat.top_pow`, `nilpotencyClass_zero`, `Module.End.IsSemisimple.minpoly_squarefree`, `AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun_asIdeal`, `IntermediateField.val_mk`, `NonUnitalAlgHom.range_comp`, `OrthonormalBasis.sum_repr`, `hasDerivAtFilter_const_add_iff`, `MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀`, `TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq`, `ZMod.orderOf_five`, `Real.iteratedFDeriv_fourierIntegral`, `Set.center_units_eq`, `SMulPosMono.toSMulPosStrictMono`, `Valuation.IsEquiv.valueGroup₀Fun_zero`, `Mathlib.Tactic.Module.NF.eval_smul`, `IsFractionRing.num_den_unique`, `StieltjesFunction.measure_smul`, `MeasureTheory.Lp.coe_LpSubmodule`, `WithZero.withZeroUnitsEquiv_symm_apply`, `IsPurelyInseparable.hasExponent_iff'`, `Submodule.exists_of_finrank_lt`, `Matrix.isNilpotent_trace_of_isNilpotent`, `Bornology.isVonNBounded_insert`, `Algebra.Generators.CotangentSpace.map_toComp_injective`, `hasDerivWithinAt_abs_neg`, `Polynomial.coeff_eq_esymm_roots_of_card`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `TestFunction.instLocallyConvexSpaceReal`, `TensorProduct.mk_surjective`, `ArithmeticFunction.carmichael_eq_exponent`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff'`, `AdicCompletion.evalₐ_of`, `Module.End.lTensorAlgHom_apply_apply`, `StieltjesFunction.ae_hasDerivAt`, `InnerProductSpaceable.innerProp`, `Continuous.clm_bundle_apply₂`, `IntermediateField.rank_sup_le`, `NumberField.Units.instFGUnitsRingOfIntegers`, `Matrix.toLpLin_symm_comp`, `IntermediateField.LinearDisjoint.self_right`, `Polynomial.aeval_monomial`, `jacobiTheta_eq_tsum_nat`, `LinearIsometry.strictConvexSpace_range`, `Algebra.Extension.H1Cotangent.equivOfFormallySmooth_toLinearMap`, `MvPowerSeries.aeval_eq_sum`, `LieAlgebra.IsKilling.lieIdealOrderIso_right_inv`, `Algebra.IsPushout.cancelBaseChange_symm_comp_lTensor`, `Matrix.toLinearMapₛₗ₂_apply_basis`, `WittVector.RecursionBase.solution_pow`, `MonoidAlgebra.single_pow`, `FormalMultilinearSeries.ofScalars_series_eq_zero`, `CochainComplex.HomComplex.Cochain.leftShift_units_smul`, `Antivary.sum_smul_comp_perm_eq_sum_smul_iff`, `Asymptotics.IsLittleOTVS.mono`, `LieAlgebra.ad_lie`, `fderivWithin_pow_ring'`, `ContinuousLinearMap.analyticOn_uncurry_of_multilinear`, `isPrecomplete_iff`, `Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub`, `LocalizedModule.mk_smul_mk`, `TensorProduct.finsuppLeft_apply_tmul`, `ConvexCone.mem_hull_of_convex`, `LinearEquiv.coord_apply_smul`, `FormalMultilinearSeries.changeOrigin_eval`, `Unitization.lift_range_le`, `VertexOperator.ncoeff_of_coeff`, `Polynomial.eval_eq_sum_range`, `IsLocalRing.notMem_maximalIdeal`, `NormedRing.inverse_continuousAt`, `LinearMap.toSeminorm_ball_zero`, `AffineMap.homothety_def`, `WeierstrassCurve.map_Δ'`, `prod_indicator_const_apply`, `ContinuousAlternatingMap.norm_alternatizeUncurryFin_le`, `NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply`, `ExteriorAlgebra.liftAlternating_algebraMap`, `Set.preimage_smul₀`, `StrictConvex.add_smul_sub_mem`, `UpperHalfPlane.val_J`, `ValuativeRel.pow_srel_pow`, `inner_smul_left_eq_smul`, `Finset.expect_dite_eq`, `iter_deriv_inv_linear_sub`, `Convex.sum_mem`, `MeromorphicOn.pow`, `pow_left_strictMonoOn₀`, `CategoryTheory.Free.lift_map`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap`, `WeierstrassCurve.Jacobian.Point.zero_point`, `AlgebraicGeometry.exists_of_res_zero_of_qcqs`, `midpoint_sub_left`, `Submodule.mem_span_set'`, `ContinuousLinearMap.reApplyInnerSelf_smul`, `ConcaveOn.smul'`, `Polynomial.isIntegrallyClosed_iff'`, `PowerSeries.coeff_subst'`, `NonUnitalCStarAlgebra.toIsScalarTower`, `Asymptotics.IsThetaTVS.trans_isLittleOTVS`, `MonoidWithZeroHom.inr_strictMono`, `IntermediateField.coe_pow`, `Valuation.IsUniformizer.iff`, `ConcaveOn.smul`, `LinearIsometryEquiv.symm_units_smul`, `LinearEquiv.coe_inv_det`, `VertexOperator.ncoeff_eq_zero_of_lt_order`, `IsSelfAdjoint.adjoint_conj`, `Asymptotics.IsBigOTVS.trans_isThetaTVS`, `Bornology.IsVonNBounded.image`, `DirectLimit.Module.lift_apply`, `not_linearIndependent_iff`, `Complex.taylorSeries_eq_on_eball'`, `OreLocalization.zero_oreDiv'`, `AlgebraicGeometry.Proj.basicOpenIsoSpec_hom`, `closedAbsConvexHull_eq_closure_absConvexHull`, `FiniteMultiplicity.of_prime_left`, `EReal.coe_pow`, `LinearMap.toMatrix₂_symm'`, `MonovaryOn.sum_comp_perm_smul_eq_sum_smul_iff`, `lucas_primality_iff`, `NonUnitalSubalgebra.toNonUnitalSubsemiring_subtype`, `DivisibleHull.archimedeanClassOrderIso_symm_apply`, `RootPairing.pairing_smul_root_eq`, `Polynomial.aeval_eq_sum_range'`, `FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField`, `VectorFourier.fourierIntegral_continuousMultilinearMap_apply`, `Units.submodule_isFractional`, `Unitary.symm_mulLeft`, `HasDerivAt.inner`, `HasFPowerSeriesAt.prod`, `AlgebraicGeometry.exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isAffineOpen`, `TensorProduct.lidOfCompatibleSMul_tmul`, `midpoint_vsub`, `LinearMap.toSeminorm_apply`, `AlgEquiv.restrictNormalHom_apply`, `LieModule.isNilpotent_iff_forall'`, `InfiniteGalois.mk_toAlgEquivAux`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germ`, `LinearIndependent.units_smul_iff`, `linearDepOn_iffₛ`, `hasDerivAt_ofReal_cpow_const'`, `hasStrictDerivAt_natCast`, `Polynomial.expand_char`, `Complex.hasDerivAt_Gamma_one_half`, `IsLocalizedModule.fromLocalizedModule'_mk`, `convex_sum`, `Valued.hasBasis_uniformity`, `Associates.eq_pow_find_of_dvd_irreducible_pow`, `ModularForm.slash_def`, `pow_eq_one_iff_cases`, `LinearMap.mulRight_toAddMonoidHom`, `MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff`, `Mathlib.Tactic.Ring.pow_nat`, `instIsAbelianGaloisSubtypeMemIntermediateField`, `HasFPowerSeriesAt.isBigO_sub_partialSum_pow`, `ZMod.invDFT_def`, `lineDeriv_smul`, `ContinuousMap.smul_apply'`, `AlternatingMap.mkContinuousAlternating_norm_le_max`, `LinearMap.map_smul'`, `PiTensorProduct.mapL_pow`, `Valuation.mem_ltSubmodule_iff`, `Units.val_ofNearby`, `IntermediateField.adjoin_simple_comm`, `isCoprime_zero_right`, `algebraicClosure.isAlgClosure`, `FormalMultilinearSeries.ofScalars_sum_eq`, `IsLocalization.AtPrime.isUnit_mk'_iff`, `Polynomial.leadingCoeff_X_pow_sub_one`, `Polynomial.natDegree_of_mem_normalizedFactors_cyclotomic`, `pinGroup.involute_act_ι_mem_range_ι`, `OrthonormalBasis.sum_rankOne_eq_id`, `Subsemiring.pow_mem`, `Module.End.mem_genEigenspace_nat`, `MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot`, `Odd.add_dvd_pow_add_pow`, `hasDerivAt_finCons'`, `HasStrictDerivAt.hasDerivAt`, `pow_add_mul_le_add_pow_of_sq_nonneg`, `Matrix.mulVec_surjective_iff_isUnit`, `segment.lift`, `MeasureTheory.Lp.toTemperedDistribution_toLp_eq`, `SymmetricAlgebra.algebraMap_leftInverse`, `Asymptotics.IsLittleOTVS.trans`, `HahnSeries.isUnit_of_orderTop_pos`, `absorbs_iff_eventually_nhds_zero`, `LinearMap.Nondegenerate.toMatrix₂'`, `RingHom.isUnit_map`, `Finsupp.support_smul_eq`, `StrictConvex.add_smul_mem`, `Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero`, `UpperHalfPlane.instContinuousGLSMul`, `WeierstrassCurve.Projective.add_smul_of_equiv`, `TensorProduct.equivFinsuppOfBasisRight_symm`, `LinearMap.BilinForm.apply_sq_le_of_symm`, `TensorProduct.AlgebraTensorModule.ker_mapOfCompatibleSMul`, `GradedMonoid.isScalarTower_right`, `LocalSubring.le_def`, `HasFPowerSeriesWithinAt.add`, `Antivary.card_smul_sum_le_sum_smul_sum`, `IntermediateField.inclusion_inclusion`, `MvPolynomial.eval₂_eq`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `NumberField.IsCMField.indexRealUnits_eq_two_iff`, `ContDiffMapSupportedIn.fderivCLM_apply_of_le`, `inf_eq_half_smul_add_sub_abs_sub'`, `IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_add_one_of_dvd_add_one`, `one_add_mul_le_pow'`, `ContinuousLinearMap.adjoint_inner_right`, `exists_extension_norm_eq`, `MeasureTheory.taylorWithinEval_charFun_two_zero'`, `SignType.pow_odd`, `Real.tendsto_integral_gaussian_smul`, `map_nnratCast_smul`, `HVertexOperator.compHahnSeries_coeff`, `LinearMap.liftBaseChange_comp`, `HahnSeries.map_smul`, `emultiplicity_pow_prime_sub_pow_prime`, `IsCoprime.pow_iff`, `IsSMulRegular.subsingleton_linearMap_iff`, `FiniteField.X_pow_card_pow_sub_X_natDegree_eq`, `UniqueFactorizationMonoid.normalizedFactors_eq_zero_iff`, `HasFDerivWithinAt.fun_pow'`, `IsPrimitiveRoot.self_sub_one_pow_dvd_order`, `isReduced_zmod`, `StarAlgEquiv.ofInjective'_apply`, `LieSubmodule.coe_toEnd_pow`, `Module.Basis.orientation_unitsSMul`, `Commute.isNilpotent_mul_right_iff`, `ConvexOn.comp_affineMap`, `AlgebraicGeometry.SpecToEquivOfLocalRing_symm_apply`, `Submodule.lTensorOne_tmul`, `sum_Ioc_inv_sq_le_sub`, `IntervalIntegrable.integral_smul`, `gcd_comm'`, `SkewMonoidAlgebra.distribMulActionHom_ext'_iff`, `Matrix.Nondegenerate.toBilin'`, `HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt`, `Finset.inv_smul_mem_iff₀`, `WeierstrassCurve.φ_four`, `spectrum.preimage_units_mul_comm`, `CliffordAlgebra.isUnit_ι_of_isUnit`, `QuadraticForm.radical_weightedSumSquares`, `WeierstrassCurve.Jacobian.negDblY_of_Z_ne_zero`, `UniqueFactorizationMonoid.irreducible_of_normalized_factor`, `StrictConvex.convex`, `IntermediateField.extendScalars_restrictScalars`, `FractionalIdeal.map_canonicalEquiv_mk0`, `HasStrictFDerivAt.continuousAlternatingMap_apply_const`, `VectorFourier.fourierIntegral_comp_add_right`, `MeasureTheory.condExp_bilin_of_stronglyMeasurable_right`, `LinearMap.isIntegral`, `Ideal.mul_mono_left`, `CategoryTheory.Mat.instFullMat_SingleObjMulOppositeEquivalenceSingleObjInverse`, `ContDiffMapSupportedIn.postcompLM_apply`, `LinearMap.BilinForm.congr_trans`, `DFinsupp.instSMulPosReflectLE`, `LinearMap.BilinForm.toMatrix'_mul`, `Submodule.mem_colon_singleton`, `UnitAddTorus.span_mFourier_closure_eq_top`, `analyticOrderAt_smul`, `ContinuousLinearMap.norm_smulRightL_le`, `Real.smul_iSup_of_nonpos`, `MvPolynomial.monomial_pow`, `Convex.combo_le_max`, `MeasureTheory.withDensityᵥ_smul'`, `Algebra.discr_powerBasis_eq_prod''`, `Perfection.coeff_zero_symm_quotientMulEquiv`, `ModularForm.is_invariant_one'`, `TensorAlgebra.algebraMap_leftInverse`, `NonUnitalAlgebra.map_bot`, `differentiableAt_iff_restrictScalars`, `TemperedDistribution.smulLeftCLM_smulLeftCLM_apply`, `hasDerivAtFilter_const`, `smul_mem_asymptoticCone_iff`, `Mathlib.Tactic.Module.NF.add_eq_eval`, `minpoly.IsIntegrallyClosed.isIntegral_iff_isUnit_leadingCoeff`, `LinearIsometryEquiv.symm_smul_apply`, `EisensteinSeries.eisensteinSeriesSIF_apply`, `SchwartzMap.tsupport_derivCLM_subset`, `MvPowerSeries.IsNilpotent_subst`, `Matrix.disc_of_card_eq_two`, `DirectSum.smul_apply`, `Polynomial.orderOf_root_cyclotomic_dvd`, `MvPowerSeries.monomial_one_eq`, `Algebra.Extension.Hom.sub_tmul`, `StrictConvex.preimage_add_right`, `LinearEquiv.reduce_mk`, `hasDerivAt_single`, `deriv_fun_const_smul_field`, `Convex.combo_self_interior_mem_interior`, `LieAlgebra.isNilpotent_range_ad_iff`, `PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent`, `SubMulAction.val_neg`, `tendsto_integral_exp_inner_smul_cocompact`, `Nat.pow_le_choose`, `MvPolynomial.eval₂_monomial`, `QuadraticMap.polar_smul_right_of_tower`, `CategoryTheory.Linear.instEpiHSMulHomOfInvertible`, `Polynomial.integralNormalization_coeff`, `StrictConvex.linear_image`, `SimpleGraph.binomialRandom_singleton`, `Finset.centroid_pair_fin`, `preNormEDS_odd`, `ContinuousLinearMap.coe_symm_flipMultilinearEquiv`, `inner_smul_right_eq_smul`, `IsAdicComplete.mk_lift`, `LieModule.mem_genWeightSpaceOf`, `DistribMulActionHom.ext_ring_iff`, `ProperCone.pointed_toConvexCone`, `ConvexCone.Pointed.of_nonempty_of_isClosed`, `emultiplicity_eq_zero_of_irreducible_ne`, `Rep.ihom_coev_app_hom`, `LieAlgebra.IsKilling.coe_invtSubmoduleToLieIdeal_eq_iSup`, `StarConvex.is_linear_image`, `isReduced_ofLocalizationMaximal`, `Commute.mul_geom_sum₂_Ico`, `Polynomial.exists_irreducible_of_natDegree_ne_zero`, `QuadraticMap.apply_linearCombination`, `Submodule.top_smul`, `Polynomial.natDegree_cubic`, `LinearMap.toMatrix₂'_compl₂`, `IsSMulRegular.isSMulRegular_on_quot_iff_smul_top_inf_eq_smul`, `MulAction.automorphize_smul_left`, `Polynomial.irreducible_X`, `DualNumber.exp_smul_eps`, `SchwartzMap.integral_smul_laplacian_right_eq_left`, `StrictConvexOn.convexOn`, `AdicCompletion.factor_evalₐ_eq_eval`, `Function.Surjective.isLocalHom`, `ContinuousMultilinearMap.smulRight_apply`, `IsLocalization.Away.surj`, `UpperHalfPlane.mul_smul'`, `Basis.multilinearMap_apply`, `Algebra.TensorProduct.comm_comp_map`, `FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin`, `StrictConcaveOn.add_const`, `tsum_smul_tsum`, `WeierstrassCurve.isElliptic_iff`, `Polynomial.coeff_eq_esymm_roots_of_splits`, `Set.OrdConnected.strictConvex`, `TrivSqZeroExt.map_inl`, `FormalMultilinearSeries.radius_prod_eq_min`, `ExpGrowth.expGrowthInf_pow`, `Matrix.toLinAlgEquiv'_symm`, `imaginaryPart_smul`, `CliffordAlgebra.foldr_algebraMap`, `IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one`, `Quaternion.snd_imI_dualNumberEquiv_symm`, `emultiplicity_pow`, `IsPrimitiveRoot.autToPow_spec`, `OrthonormalBasis.coe_equiv_euclideanSpace`, `StrongDual.im_extendRCLike_apply`, `VectorFourier.fourierIntegral_probChar`, `Polynomial.not_isUnit_X_pow_sub_one`, `ZMod.isCyclic_units_two`, `SlashInvariantFormClass.norm_petersson_smul`, `Valuation.Integers.isUnit_iff_valuation_eq_one`, `Unitary.symm_mulRight_apply`, `ModuleCat.restrictScalars.smul_def'`, `ZMod.isUnit_cast_of_dvd`, `Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass`, `not_prime_pow`, `Polynomial.toFinsupp_C_mul_X_pow`, `continuous_cfcₙAux`, `Polynomial.expand_eval`, `Mathlib.Tactic.Module.NF.eq_const_cons`, `openSegment_same`, `MvPolynomial.prod_X_pow`, `Seminorm.preimage_metric_ball`, `IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary`, `summable_norm_geometric_of_norm_lt_one`, `derivWithin_div`, `NonUnitalCommCStarAlgebra.toSMulCommClass`, `Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeff`, `LocallyConvexSpace.convex_basis`, `Submodule.smul_mem_span_smul'`, `HasFDerivAt.mul_const'`, `Polynomial.Monic.irreducible_iff_natDegree'`, `WeierstrassCurve.Jacobian.dblXYZ_smul`, `Finset.pluennecke_ruzsa_inequality_pow_div_pow_div`, `MvPolynomial.derivation_C_mul`, `essSup_smul_measure`, `MulChar.coe_toUnitHom`, `RatFunc.C_minpolyX`, `LieAlgebra.IsKilling.traceForm_coroot`, `PeriodPair.weierstrassPExceptSeries_hasSum`, `ZMod.val_pow`, `Polynomial.dickson_two`, `mem_segment_add_sub`, `IsCyclic.mulAutMulEquiv_symm_apply_apply`, `WeierstrassCurve.Jacobian.addU_smul`, `Module.toAddMonoidEnd_apply_apply`, `InfiniteGalois.proj_of_le`, `ClassGroup.mk_eq_one_of_coe_ideal`, `ContinuousLinearMap.le_of_opNorm₂_le_of_le`, `Polynomial.derivative_X_add_C_sq`, `Submodule.span_smul_eq`, `Commute.add_pow_prime_eq`, `WittVector.RecursionBase.solution_spec'`, `Complex.arg_pow_coe_angle`, `LieAlgebra.Basis.borelLower_eq`, `AddSubgroup.mem_inv_pointwise_smul_iff₀`, `ZMod.coe_unitOfCoprime`, `Polynomial.cyclotomic_three`, `norm_commutator_units_sub_one_le`, `Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective`, `Fourier.fourierIntegral_def`, `NonUnitalStarSubalgebra.instIsScalarTower`, `Complex.isOpenQuotientMap_pow_compl_zero`, `geom_sum_of_one_lt`, `Complex.IsExactOn.with_val_at`, `LinearMap.rid_comp_lTensor`, `ContinuousMultilinearMap.currySum_apply`, `exists_convex_convex_compl_subset`, `Matrix.det_sum_smul_le`, `Ideal.cotangentEquivIdeal_symm_apply`, `Submodule.mem_colon`, `FiniteField.expand_card`, `NormSMulClass.toIsBoundedSMul`, `DirichletCharacter.factorsThrough_iff_ker_unitsMap`, `NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis`, `Ideal.finprod_heightOneSpectrum_factorization_coe`, `Matrix.Module.diagonal_const_smul`, `MeasureTheory.ComplexMeasure.re_apply`, `FormalMultilinearSeries.ofScalars_comp_neg`, `IsArtinianRing.isUnit_submonoid_eq_of_isIntegral`, `absorbent_iff_inv_smul`, `MvPolynomial.tensorEquivSum_one_tmul_X`, `SeminormedSpace.Core.norm_smul`, `Polynomial.comp_eq_sum_left`, `continuous_const_smul_iff₀`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `Matrix.nondegenerate_toLinearMap₂'_iff`, `contDiffAt_ringInverse`, `Unitary.coe_neg`, `Seminorm.comp_mono`, `HasDerivAt.pow'`, `Unitization.norm_splitMul_snd_sq`, `LinearMap.separatingRight_toMatrix₂_iff`, `SameRay.sameRay_pos_smul_right`, `geom_series_mul_neg`, `Matrix.IsHermitian.star_mul_self_mul_eq_diagonal`, `AdjoinRoot.coe_algEquivOfEq`, `pow_pos_iff`, `Matrix.det_kroneckerTMul`, `WeierstrassCurve.Projective.dblY_of_Z_eq_zero`, `DirectSum.coe_mul_apply_eq_sum_antidiagonal`, `HasStrictFDerivAt.fun_pow'`, `CFC.nnrpow_eq_nnrpow_prod`, `Antitone.alternating_series_le_tendsto`, `Complex.exp_nat_mul`, `ContinuousLinearMap.smulRight_id`, `Associates.prime_pow_le_iff_le_bcount`, `continuousMultilinearCurryRightEquiv_apply'`, `ContinuousLinearMap.flipₗᵢ'_symm`, `WeierstrassCurve.Jacobian.Point.zero_def`, `DirectSum.decompose_mul`, `le_egauge_ball_one`, `NumberField.Units.logEmbeddingEquiv_apply`, `Ideal.instNoZeroDivisors`, `ConcaveOn.left_lt_of_lt_right'`, `Coalgebra.lTensor_counit_comp_comul`, `TestFunction.instLineDerivSMulTopENat`, `WeierstrassCurve.Affine.evalEval_polynomialX`, `Matrix.charpoly_mul_comm'`, `rank_eq_zero_iff`, `PowerSeries.eval₂_trunc_eq_sum_range`, `toPrincipalIdeal_def`, `Unitary.norm_argSelfAdjoint`, `KaehlerDifferential.isBaseChange_of_formallyEtale`, `Ideal.mem_radical_iff`, `IsLocalizedModule.map_units`, `NonUnitalSubalgebra.instIsScalarTowerSubtypeMem`, `TemperedDistribution.lineDerivOp_fourierInv_eq`, `Complex.cos_sq`, `LieAlgebra.nilpotent_ad_of_nilpotent_algebra`, `QuotientAddGroup.automorphize_smul_left`, `quadraticChar_eq_pow_of_char_ne_two`, `Complex.hasSum_taylorSeries_log`, `fourierCoeffOn_eq_integral`, `DivisibleHull.instIsStrictOrderedModuleRat`, `CliffordAlgebra.changeForm.associated_neg_proof`, `factor_orderIso_map_one_eq_bot`, `Algebra.SubmersivePresentation.jacobian_isUnit`, `Polynomial.leval_coe_eq_smeval`, `CompactConvergenceCLM.continuousSMul`, `mfderiv_smul`, `HasFiniteFPowerSeriesOnBall.hasFDerivAt`, `geom_sum_mul_neg`, `NumberField.Units.isMaxRank_iff_closure_finiteIndex`, `IsNilpotent.isUnit_add_left_of_commute`, `NumberField.Units.exist_unique_eq_mul_prod`, `LinearMap.BilinForm.IsNonneg.smul`, `IntermediateField.lift_adjoin`, `WeierstrassCurve.Jacobian.dblU_of_Z_eq_zero`, `hasStrictDerivAt_zero`, `NumberField.basisOfFractionalIdeal_apply`, `Asymptotics.SuperpolynomialDecay.mul_param_pow`, `sq_le_sq'`, `PeriodPair.hasSum_sumInvPow`, `ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real`, `Ideal.IsDedekindDomain.emultiplicity_map_eq_zero_of_ne`, `ContinuousAlternatingMap.alternatizeUncurryFin_add`, `Units.contMDiff_val`, `add_pow_eq_mul_pow_add_pow_div_expChar`, `CStarRing.norm_coe_unitary_mul`, `Complex.hasDerivAt_tan`, `ContinuousLinearMap.isBigOTVS_fun_comp`, `MvPowerSeries.monomial_eq`, `Coalgebra.TensorProduct.rid_tmul`, `Pi.image_update_segment`, `Matrix.GeneralLinearGroup.map_one`, `HasDerivAtFilter.finCons`, `instIsReducedOfIsSemisimpleRing`, `IsPrimitiveRoot.pow_isRoot_minpoly`, `Algebra.Generators.Hom.toAlgHom_monomial`, `Finset.sum_smul_vsub_const_eq_weightedVSub`, `le_egauge_of_forall_ne_zero`, `IsBoundedSMul.of_norm_smul_le`, `NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image`, `List.prod_map_le_pow_length₀`, `Finset.sum_smul_vsub_const_eq_affineCombination_vsub`, `Submodule.mulExact_unitsMap_spanSingleton_unitsToPic`, `Polynomial.eval_eq_smeval`, `convex_of_nonneg_surjective_algebraMap`, `FormalMultilinearSeries.coeff_iterate_fslope`, `Ideal.associatesEquivIsPrincipal_map_zero`, `QuotSMulTop.map_apply_mk`, `EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn`, `LieModule.instIsFaithfulEnd`, `HasFPowerSeriesAt.eq_zero`, `AbsolutelyContinuousOnInterval.fun_smul`, `Matrix.cramer_smul`, `ZMod.cast_pow`, `MultilinearMap.mkPiAlgebraFin_apply_const`, `Matrix.represents_iff'`, `ContinuousLinearMap.flip_zero`, `IsCoprime.isUnit_of_associated`, `FormalMultilinearSeries.leftInv_removeZero`, `Commute.isNilpotent_add`, `PowerSeries.X_pow_order_mul_divXPowOrder`, `Valuation.restrict_lt_iff`, `MvPolynomial.irreducible_of_totalDegree_eq_one`, `ContMDiffWithinAt.clm_prodMap`, `deriv_const_smul'`, `ContDiffMapSupportedIn.fderivCLM_apply`, `Filter.zero_pow_eventuallyEq`, `DualNumber.lift_apply_inl`, `tendsto_pow_div_pow_atTop_atTop`, `NumberField.mixedEmbedding.logMap_torsion_smul`, `PadicInt.continuousAddCharEquiv_symm_apply`, `smul_pi₀`, `Matrix.GeneralLinearGroup.map_mul`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `hasStrictDerivAt_exp_smul_const_of_mem_ball'`, `Polynomial.pow_mul_divByMonic_rootMultiplicity_eq`, `Localization.awayMap_injective_iff`, `modularCyclotomicCharacter'.spec'`, `MvPolynomial.coe_expand`, `ProbabilityTheory.measure_le_mul_measure_gt_le_of_map_rotation_eq_self`, `MonovaryOn.pow_left₀`, `tangentConeAt_subset_zero`, `ContinuousLinearMap.extendTo𝕜'_apply`, `LocalizedModule.smul_eq_iff_of_mem`, `Finset.mem_inv_smul_finset_iff₀`, `LieAlgebra.IsKilling.mem_rootSet_invtSubmoduleToLieIdeal`, `TestFunction.fderivCLM_apply`, `NumberField.Units.rootsOfUnity_eq_one`, `Units.symm_mulRightLinearEquiv_apply`, `NonUnitalStarSubalgebra.inclusion_injective`, `CharTwo.CommRing.sq_inj`, `ContinuousLinearMap.isAdjointPair_inner`, `IsPurelyInseparable.exponent_min'`, `LinearMap.coe_smulRight`, `WeierstrassCurve.inv_map_Δ'`, `min_le_emultiplicity_add`, `NormedSpace.norm_expSeries_div_summable`, `PolynomialModule.monomial_smul_apply`, `Polynomial.map_frobenius_expand`, `analyticOrderNatAt_pow`, `Algebra.TensorProduct.map_restrictScalars_comp_includeRight`, `posSMulMono_iff_posSMulStrictMono`, `integral_gaussian_complex`, `AddChar.linearIndependent`, `WeierstrassCurve.c₆_of_char_three`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `AdicCompletion.eval_of`, `FractionalIdeal.finite_factors'`, `WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF`, `MonoidWithZeroHom.one_mem_valueMonoid`, `SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply`, `circleMap_zero_pow`, `DivisibleHull.coe_add`, `isSelfAdjoint_smul_of_mem_skewAdjoint`, `CommAlgCat.associator_hom_hom`, `Submodule.setSemiring_smul_def`, `FormalMultilinearSeries.changeOriginSeries_finite_of_finite`, `Module.End.isNilpotent_restrict_genEigenspace_top`, `Complex.tan_sq_div_one_add_tan_sq`, `complexOfReal_hasDerivAt`, `LieSubmodule.exists_smul_add_of_span_sup_eq_top`, `not_linearIndepOn_finset_iffₛ`, `Convex.starConvex_iff`, `openSegment_subset_Ioo`, `Polynomial.natDegree_coe_units`, `Convex.add_smul_sub_mem`, `HVertexOperator.coeff_comp`, `AlgebraicGeometry.StructureSheaf.comap_basicOpen`, `DifferentiableAt.smul_const`, `StrictConvexOn.add_const`, `convexHull_smul`, `KaehlerDifferential.mvPolynomialBasis_repr_symm_single`, `Finset.sum_Ioc_by_parts`, `ZMod.eq_one_or_isUnit_sub_one`, `Subring.instSMulCommClassSubtypeMemCenter_1`, `summable_bernoulli_fourier`, `Real.fourier_continuousMultilinearMap_apply`, `Polynomial.eval₂_eq_sum_range`, `NonUnitalSubalgebra.coe_inclusion`, `IsSl2Triple.HasPrimitiveVectorWith.lie_h`, `Unitization.splitMul_injective`, `AlgebraicGeometry.Scheme.mem_basicOpen''`, `Matrix.SpecialLinearGroup.mapGL_coe_matrix`, `Polynomial.degree_cubic_le`, `Cardinal.mk_quaternion`, `WeakFEPair.f_modif_aux1`, `IsLocalization.AtPrime.isUnit_to_map_iff`, `MDifferentiableAt.smul_const_section`, `Unitary.mulLeft_apply`, `IntermediateField.rank_eq_rank_subalgebra`, `NonUnitalSubalgebraClass.subtype_apply`, `Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1`, `FormalMultilinearSeries.ofScalars_series_injective`, `ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id`, `collinear_iff_exists_forall_eq_smul_vadd`, `MeasureTheory.Lp.smul_assoc`, `ContDiffMapSupportedIn.continuous_iff_comp`, `quadraticChar_eq_pow_of_char_ne_two'`, `Asymptotics.IsTheta.const_smul_right`, `Valued.isClosed_closedBall`, `ContinuousLinearMap.smulRight_comp`, `LieAlgebra.Basis.root_mem_or_mem_neg`, `Algebra.normalizedTrace_trans`, `spectrum.inv₀_mem_inv`, `squarefree_iff_no_irreducibles`, `DualNumber.lift_op_smul`, `Submodule.map_range_rTensor_subtype_lid`, `QuadraticMap.Isometry.tmul_apply`, `ContMDiffOn.smul_section_of_tsupport`, `WeierstrassCurve.Jacobian.Y_eq_iff`, `Polynomial.leadingCoeff_X_pow_add_one`, `ArithmeticFunction.isUnit_iff_isUnit_apply_one`, `Seminorm.uniformContinuous'`, `Metric.unitClosedBall.coe_pow`, `HasStrictDerivAt.div_const`, `HasStrictDerivAt.fun_mul`, `CharP.isUnit_natCast_iff`, `ContMDiffWithinAt.smul_section`, `IsLocalization.Away.associated_sec_fst`, `FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite`, `IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap`, `InnerProductSpace.volume_closedBall`, `ContinuousLinearEquiv.coord_norm'`, `HahnSeries.coeff_toOrderTopSubOnePos_pow`, `DirectSum.decompose_one`, `deriv_fun_pow`, `sq_abs`, `TrivSqZeroExt.mul_right_eq_one`, `Subalgebra.continuousSMul`, `Valuation.isOpen_closedBall`, `exists_bijective_map_powers`, `fderivWithin_continuousAlternatingMap_apply`, `LinearMap.mul'_tensor`, `GaussianFourier.integrable_cexp_neg_sum_mul_add`, `Valuation.coe_ltAddSubgroup`, `ContinuousMultilinearMap.instIsCentralScalar`, `HasDerivAt.fun_inv`, `OrderIso.smulRightDual_symm_apply`, `PowerSeries.invOneSubPow_val_one_eq_invUnitSub_one`, `IsBaseChange.comp`, `smul_mem_asymptoticCone`, `IsLocalizedModule.iso_localizedModule_eq_refl`, `Matrix.GeneralLinearGroup.coe_mul`, `absConvexHull_eq_convexHull_balancedHull`, `IsLocalization.map_linearMap_eq_toLinearMap_mapₐ`, `jacobi_cross`, `tendsto_add_one_pow_atTop_atTop_of_pos`, `IntermediateField.LinearDisjoint.of_finrank_sup`, `ProbabilityTheory.hasDerivAt_mgf`, `AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe`, `HasFPowerSeriesAt.eq_zero_of_eventually`, `LinearMap.separatingLeft_toMatrix₂_iff`, `Complex.hasSum_sinh`, `Set.OrdConnected.starConvex`, `Matrix.pow_inv_comm'`, `Derivation.apply_aeval_eq'`, `smul_add_smul_le_smul_add_smul'`, `NonUnitalAlgebra.range_eq_top`, `HVertexOperator.coeff_apply_apply`, `div_le_egauge_closedBall`, `StrictConcaveOn.add`, `SymmetricAlgebra.algebraMap_inj`, `hasStrictFDerivAt_inv'`, `MeasureTheory.Integrable.smul_prod`, `IntermediateField.lift_sup`, `AdicCompletion.evalₐ_mk`, `LinearMap.mem_span_iff_bound`, `cfcₙL_apply`, `Representation.asModuleEquiv_map_smul`, `Set.Finite.convexHull_eq_image`, `pow_lt_pow_left₀`, `MvPolynomial.coeff_linearCombination_X_pow_of_fintype`, `sq_dvd_add_pow_sub_sub`, `MonoidWithZeroHom.inl_mono`, `Finset.subset_smul_finset_iff₀`, `Complex.norm_exp_sub_sum_le_exp_norm_sub_sum`, `Subalgebra.centralizer_coe_image_includeLeft_eq_center_tensorProduct`, `WithSeminorms.partial_sups`, `Convex.lift`, `Nat.cast_pow`, `Submodule.coe_set_smul`, `ConcaveOn.sub`, `SameRay.exists_pos_left`, `HasDerivAt.scomp_hasDerivWithinAt`, `MeasureTheory.Lp.toTemperedDistribution_apply`, `SchwartzMap.smulLeftCLM_sub`, `PerfectionMap.comp_symm_equiv'`, `TemperedDistribution.smulLeftCLM_const`, `UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow`, `SchwartzMap.smulLeftCLM_apply_apply`, `deriv_inv'`, `Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicity`, `HasStrictDerivAt.add_const`, `IsNilpotent.pow_of_pos`, `Matrix.projVandermonde_apply`, `wbtw_or_wbtw_smul_vadd_of_nonpos`, `iteratedDeriv_cexp_const_mul`, `ConvexCone.salient_positive`, `normalClosure.normal`, `zpow_natCast_sub_one₀`, `Bornology.IsVonNBounded.smul_tendsto_zero`, `WeierstrassCurve.Jacobian.Point.toAffineLift_eq`, `intervalIntegral.integral_hasStrictDerivAt_right`, `CategoryTheory.Mat.equivalenceSingleObjInverse_map`, `Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid`, `fwdDiff_addChar_eq`, `NonUnitalStarSubalgebra.topologicalClosure_map`, `RatFunc.valuation_eq_valuation_uniformizingPolynomial_pow_of_valuation_X_le_one`, `fromModuleCatToModuleCatLinearEquiv_apply`, `ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero`, `count_associates_factors_eq`, `Polynomial.not_isUnit_X`, `iteratedDeriv_fun_pow_zero`, `GradedAlgHom.coe_addMonoidHom_injective`, `SchwartzMap.fourier_fderivCLM_eq`, `Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv`, `Asymptotics.isBigO_const_smul_left`, `Matrix.det_units_conj`, `LinearMap.BilinForm.toMatrix'_toBilin'`, `FiniteField.isSplittingField_sub`, `Fintype.linearCombination_apply_single`, `LinearEquiv.symm_smul_apply`, `HVertexOperator.of_coeff_apply`, `Units.norm_pos`, `MDifferentiableOn.smul_section`, `Polynomial.leadingCoeff_pow`, `AlgHom.toRingHom_toAddMonoidHom`, `MonoidAlgebra.cardinalMk_of_fintype`, `Subsemiring.pointwise_smul_le_pointwise_smul_iff₀`, `MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv`, `geom_sum_mul_of_le_one`, `QuadraticMap.PosDef.smul`, `SchwartzMap.fourier_convolution_apply`, `IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat`, `Seminorm.smul_ball_zero`, `Polynomial.exists_irreducible_of_natDegree_pos`, `Multiset.prod_X_add_C_eq_sum_esymm`, `Fintype.linearCombination_apply`, `mem_openSegment_iff_div`, `MvPolynomial.totalDegree_smul_le`, `Real.iteratedDeriv_fourierIntegral`, `Asymptotics.isBigOTVS_map`, `neg_cross`, `Projectivization.generalLinearGroup_smul_def`, `iteratedFDeriv_two_apply`, `starConvex_compl_Iic`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap`, `fromModuleCatToModuleCatLinearEquiv_symm_apply_coe`, `pow_eq_neg_one_iff`, `PointedCone.mem_toConvexCone`, `Polynomial.eval₂_reverse_mul_pow`, `IsLocalization.Away.exists_of_eq`, `LocalizedModule.map_mk`, `PowerBasis.liftEquiv'_symm_apply_apply`, `CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux`, `AffineSubspace.isometryEquivMap.apply_symm_apply`, `PiTensorProduct.map_update_smul`, `Quaternion.normSq_intCast`, `IsAdicComplete.StrictMono.of_lift`, `DirectSum.decompose_mul_add_right`, `InnerProductSpace.volume_closedBall_of_dim_odd`, `Polynomial.Monic.nextCoeff_pow`, `isUnit_ringInverse`, `IsRelPrime.mul_add_left_right_iff`, `LieModule.coe_lcs_range_toEnd_eq`, `ContDiffAt.smul`, `ModuleCat.ofHom₂_compr₂`, `isLocalHom_of_iso`, `LieModule.toEnd_module_end`, `IntermediateField.adjoin_adjoin_left`, `Associates.mem_factors_of_dvd`, `LieAlgebra.mem_zeroRootSubalgebra`, `TemperedDistribution.smulLeftCLM_sum`, `Associates.instCanonicallyOrderedMul`, `mahler_apply`, `PowerBasis.constr_pow_mul`, `aestronglyMeasurable_const_smul_iff₀`, `AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen`, `sub_pow_char_of_commute`, `intervalIntegral.integral_hasStrictDerivAt_left`, `StrictConvex.sub`, `iter_deriv_inv_linear`, `EuclideanDomain.divRadical_isUnit`, `RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul`, `TensorProduct.map_smul_left`, `LaurentPolynomial.eval₂_T_n`, `Asymptotics.IsBigOTVS.neg_left`, `SubMulAction.mem_one'`, `WeierstrassCurve.Jacobian.negAddY_eq'`, `IsCyclotomicExtension.adjoin_roots`, `LieAlgebra.IsKilling.restr_invtSubmoduleToLieIdeal_eq_iSup`, `Complex.hasSum_sin'`, `AddAut.mulLeft_apply_symm_apply`, `normEDS_odd`, `ModuleCat.Algebra.instSMulCommClassCarrier`, `IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C'`, `LinearMap.det_toMatrix'`, `LieAlgebra.isRegular_iff_finrank_engel_eq_rank`, `IntermediateField.normalClosure_mono`, `antivaryOn_iff_forall_smul_nonpos`, `Matrix.separatingLeft_toBilin_iff`, `IntermediateField.AdjoinSimple.coe_aeval_gen_apply`, `gauge_smul`, `ConvexCone.isGenerating_bot_iff`, `MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero`, `MDifferentiable.clm_precomp`, `PadicInt.ideal_eq_span_pow_p`, `InnerProductSpace.laplacian_smul_nhds`, `NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndex`, `IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base`, `FiniteMultiplicity.pow`, `Unitization.starLift_range_le`, `Polynomial.scaleRoots_zero`, `FormalMultilinearSeries.enorm_compContinuousLinearMap_le`, `Polynomial.derivative_X_add_C_pow`, `Polynomial.homogenize_C`, `ContDiffMapSupportedIn.fderivLM_apply_of_le`, `Polynomial.cyclotomic_prime`, `sameRay_smul_right_iff`, `IsUltrametricDist.isPowMul_algNormOfAlgEquiv`, `LinearMap.Nondegenerate.toMatrix₂`, `Matrix.map_pow`, `Pi.segment_subset`, `Nat.Partition.hasProd_genFun`, `MultilinearMap.mkPiRing_apply`, `WeierstrassCurve.Jacobian.smul_eq`, `Subgroup.IsArithmetic.finiteIndex_comap`, `LinearMap.toMatrixAlgEquiv_apply'`, `IsLocalizedModule.eq_iff_exists`, `MulChar.ofUnitHom_coe`, `Fintype.expect_ite_eq'`, `CFC.sqrt_map_pi`, `Convex.strictConvex_of_isOpen`, `WeierstrassCurve.Jacobian.addX_of_X_eq'`, `FormalMultilinearSeries.le_radius_pi`, `UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors`, `NormedSpace.exp_eq_tsum_rat`, `AffineSpace.asymptoticNhds_eq_smul_vadd`, `MvPowerSeries.coeff_subst_finite`, `BoxIntegral.unitPartition.volume_box`, `Ideal.count_associates_eq'`, `continuousMultilinearCurryLeftEquiv_symm_apply`, `isSemiprimaryRing_iff`, `Finset.pluennecke_ruzsa_inequality_pow_mul`, `Matrix.SpecialLinearGroup.det_mapGL`, `Ideal.pow_mem_pow`, `MultilinearMap.map_smul_univ`, `WithLp.unitization_mul`, `UnitAddTorus.mFourierCoeff_eq_integral`, `hasDerivAt_exp_smul_const'`, `CategoryTheory.ShortComplex.smul_τ₁`, `SubMulAction.smul_mem_iff`, `TrivSqZeroExt.exp_def_of_smul_comm`, `isNilpotent_finsum`, `DoubleCentralizer.instStarModule`, `sq_pos_of_ne_zero`, `Polynomial.Chebyshev.leadingCoeff_T`, `ZMod.isCyclic_units_two_pow_iff`, `ZMod.coe_unitOfIsCoprime`, `Associated.abs_right`, `Subring.pow_mem`, `HasStrictDerivAt.finset_prod`, `WeierstrassCurve.Jacobian.isUnit_dblZ_of_Y_ne`, `TensorProduct.tensorQuotEquivQuotSMul_comp_mk`, `LinearMap.existsUnique_eq_smul_id_of_finrank_eq_one`, `Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero`, `one_div_pow_le_one_div_pow_of_le`, `ContinuousMultilinearMap.smulRightL_apply`, `op_geom_sum₂`, `WittVector.mul_polyOfInterest_aux5`, `NNReal.instIsStrictOrderedModule`, `StrictConcaveOn.concaveOn`, `hasSum_one_div_pow_mul_fourier_mul_bernoulliFun`, `IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply`, `GroupLike.val_pow`, `Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow`, `IntermediateField.restrictNormalHom_ker`, `FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin`, `ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eq`, `Absorbs.univ`, `MvPolynomial.expand_zmod`, `Subgroup.HasDetPlusMinusOne.abs_det`, `Representation.smul_one_tprod_asModule`, `EuclideanSpace.nnnorm_eq`, `selfZPow_neg_natCast`, `smul_nonneg_iff_pos_imp_nonneg`, `Convex.second_derivative_within_at_symmetric_of_mem_interior`, `ContinuousLinearMap.isUniformEmbedding_toUniformOnFun`, `iteratedDerivWithin_scomp_two`, `exists_pos_left_iff_sameRay_and_ne_zero`, `Unitary.symm_mulLeft_apply`, `IsRelPrime.mul_add_right_right_iff`, `CochainComplex.HomComplex.Cochain.comp_smul`, `Finset.smul_finset_inter₀`, `Complex.sin_eq_tsum'`, `eq_inv_smul_iff₀`, `sameRay_neg_smul_left_iff`, `LieSubalgebra.instIsScalarTowerSubtypeMem`, `Algebra.algebraMapSubmonoid_powers`, `ClassGroup.equiv_mk0`, `lp.norm_const_smul_le`, `TestFunction.instContinuousSMulReal`, `Asymptotics.IsLittleOTVS.congr_right`, `IntermediateField.adjoin_rank_le_of_isAlgebraic_left`, `Memℓp.infty_pow`, `UpperHalfPlane.denom_J_mul`, `MvPowerSeries.HasSubst.pow`, `ModularForm.SL_slash_apply`, `Matrix.disc_conj'`, `IsCyclotomicExtension.Rat.inertiaDeg_of_not_dvd`, `ContinuousMap.norm_smul_const`, `iteratedFDeriv_succ_eq_comp_left`, `DirectSum.toAddMonoidAlgebra_pow`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen`, `ContinuousMapZero.toNNReal_neg_smul`, `WeierstrassCurve.Jacobian.neg_of_Z_ne_zero`, `LinearMap.BilinForm.Nondegenerate.toMatrix'`, `Submodule.smul_mem_smul`, `antivary_iff_forall_smul_nonpos`, `Polynomial.resultant_self`, `ContinuousLinearMap.smul_compLpL`, `AddChar.wInner_cWeight_eq_boole`, `Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U`, `VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral`, `summable_geometric_of_norm_lt_one`, `unitary.isPathConnected_ball`, `infinite_range_add_smul_iff`, `IntermediateField.insepDegree_bot`, `Subalgebra.pointwise_smul_toSubsemiring`, `Cardinal.sum_pow_eq_max_aleph0`, `DivisibleHull.mk_zero`, `Commute.pow_dvd_sub_pow_of_pow_eq_zero_right`, `one_div_pow_anti`, `Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl`, `ContDiffMapSupportedIn.fderivLM_apply_of_gt`, `IsLocalizedModule.smul_mem_finsetIntegerMultiple_span`, `Ideal.top_pow`, `HasDerivAt.hasDerivAtFilter`, `ContinuousMapZero.nonUnitalStarAlgHom_postcomp_apply`, `Convex.sub`, `cfcₙ_const_mul`, `IntermediateField.equivOfEq_apply`, `MonoidWithZeroHom.mem_valueMonoid_iff`, `Homeomorph.compStarAlgEquiv'_symm_apply`, `AffineMap.homothety_add`, `Commute.isNilpotent_mul_right`, `NormedSpace.ext_iff`, `SkewPolynomial.instSMulCommClass`, `CategoryTheory.ShortComplex.smul_τ₂`, `NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr`, `DivisibleHull.zero_qsmul`, `Polynomial.splits_X_pow`, `Polynomial.degree_linear_lt_degree_C_mul_X_sq`, `LinearMap.charpoly_zero`, `HasDerivAt.comp_hasDerivWithinAt_of_eq`, `ContinuousLinearMap.opNorm_mulLeftRight_le`, `Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange`, `ConvexOn.mul`, `IsArtinianRing.isUnitSubmonoid_eq`, `MvPolynomial.irreducible_sumSMulXSMulY`, `NNReal.rpow_mul_natCast`, `Mathlib.Tactic.Ring.atom_pf`, `gauge_smul_left`, `Finset.sum_smul_vsub_eq_affineCombination_vsub`, `Algebra.norm_algebraMap`, `Submodule.map_toAddSubgroup`, `IsPurelyInseparable.algebraMap_elemReduct_eq`, `ClosedSubmodule.orthogonal_closure`, `DualNumber.lift_comp_inlHom`, `ModuleFilterBasis.smul`, `AntivaryOn.sum_smul_le_sum_smul_comp_perm`, `EisensteinSeries.eisSummand_SL2_apply`, `AlgHom.linearMapMk_toAddHom`, `CommRingCat.isLocalHom_comp`, `LinearMap.toSeminormFamily_apply`, `MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure`, `Polynomial.rootSet_X_pow`, `PowerSeries.X_pow_dvd_iff`, `sub_pow_eq_mul_pow_sub_pow_div_char`, `AddChar.map_neg_eq_conj`, `NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne`, `ProbabilityTheory.variance_smul'`, `Subsemiring.continuousSMul`, `Module.End.mem_spectrum_iff_isRoot_charpoly`, `IsLocalizedModule.fromLocalizedModule.surj`, `ContDiffMapSupportedIn.structureMapCLM_zero_injective`, `Seminorm.ball_finset_sup_eq_iInter`, `Associates.dvd_out_iff`, `ZMod.isCyclic_units_zero`, `LinearMap.piApply_apply_apply`, `Finset.pluennecke_ruzsa_inequality_nsmul_sub`, `SModEq.pow`, `Matrix.SeparatingRight.toBilin'`, `IsGroupLikeElem.unitsInv`, `ENNReal.isUnit_iff`, `LinearMap.lflip_symm`, `LieAlgebra.commute_ad_of_commute`, `LinearMap.compQuadraticMap_polarBilin`, `ContinuousMultilinearMap.piₗᵢ_apply`, `meromorphicAt_smul_iff_of_ne_zero`, `Polynomial.isNilpotent_pow_X_mul_C_of_isNilpotent`, `Module.Basis.opNNNorm_le`, `Derivation.leibniz_div_const`, `Polynomial.resultant_one_left`, `Module.End.smulLeft_eq`, `enorm_pow`, `Associates.out_injective`, `BilinForm.apply_eq_dotProduct_toMatrix_mulVec`, `ContMDiffWithinAt.clm_precomp`, `Polynomial.not_irreducible_C`, `iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod`, `Convex.exists_mem_add_smul_eq`, `NormedRing.inverse_one_sub_nth_order'`, `AdicCompletion.ofLinearEquiv_apply`, `Commute.smul_left_iff₀`, `Polynomial.degree_quadratic_lt_degree_C_mul_X_cb`, `TensorProduct.lift_compr₂`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_surjective`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply`, `Ideal.sup_pow_eq_top`, `KaehlerDifferential.range_kerCotangentToTensor`, `Ideal.mul_top`, `WeierstrassCurve.Jacobian.addMap_eq`, `Polynomial.coeff_C_mul_X_pow`, `IntermediateField.fieldRange_val`, `ValuativeRel.restrict_lt_orderMonoidIso`, `HasDerivAtFilter.comp`, `cfc_pow_id`, `IntermediateField.liftAlgEquiv_apply`, `DualNumber.algHom_ext'_iff`, `Ideal.pow_eq_top_iff`, `MeasureTheory.Integrable.fourier_smul`, `LinearMap.coe_toContinuousLinearMap_symm`, `Matrix.range_diagonal`, `Unitization.lift_apply_apply`, `IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable`, `Mathlib.Tactic.FieldSimp.zpow'_ofNat`, `IntermediateField.LinearDisjoint.of_basis_mul`, `AdicCompletion.mk_apply_coe`, `hasStrictFDerivAt_list_prod'`, `finsum_smul'`, `sq_add_sq_mul`, `WittVector.teichmuller_mul_pow_coeff`, `right_sub_midpoint`, `balancedHull.balanced`, `Submodule.torsionBySet.mk_smul`, `continuousMultilinearCurryFin1_symm_apply`, `HasStrictDerivAt.fun_add`, `Convex.toCone_eq_sInf`, `AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff`, `MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound`, `balancedCore_zero_mem`, `PowerSeries.X_pow_mul_inj`, `HasSum.smul_const`, `separableClosure_le_separableClosure_iff`, `LieModule.Cohomology.mem_twoCocycle_iff_of_trivial`, `Set.smul_mem_centralizer`, `FormalMultilinearSeries.radius_pi_le`, `NumberField.Units.instFiniteIntAdditiveQuotientUnitsRingOfIntegersSubgroupTorsion`, `EisensteinSeries.eisensteinSeries_SIF_MDifferentiable`, `DualNumber.ideal_trichotomy`, `HasDerivAt.comp_of_eq`, `VectorFourier.integral_fourierIntegral_smul_eq_flip`, `WeierstrassCurve.φ_two`, `Nat.Prime.dvd_add_pow_sub_pow_of_dvd`, `UniqueFactorizationMonoid.radical_pow_of_prime`, `IsSymmetricAlgebra.comp_equiv`, `AffineSubspace.sOppSide_smul_vsub_vadd_left`, `LieModule.iterate_toEnd_mem_lowerCentralSeries`, `Complex.integral_boundary_rect_of_differentiableOn_real`, `PadicInt.mahlerEquiv_symm_apply`, `ContinuousLinearMap.lsmul_flip_apply`, `smul_vsub_mem_vectorSpan_pair`, `RootPairing.Base.cartanMatrixIn_mul_diagonal_eq`, `Submodule.mem_annihilator_span_singleton`, `cfc_isStrictlyPositive_iff`, `Module.reflection_apply`, `CategoryTheory.Functor.linear_iff`, `hasDerivAt_iff_tendsto`, `IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one`, `Polynomial.homogenize_X`, `ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe`, `Mathlib.Meta.Positivity.pow_zero_pos`, `ConvexCone.coe_hull_of_convex`, `Submodule.mem_span_set_iff_exists_finsupp_le_finrank`, `HasStrictFDerivAt.smul_const`, `Complex.sin_sq`, `SchwartzMap.coe_apply`, `Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint`, `sq_eq_sq₀`, `four_mul_le_pow_two_add`, `integral_mul_cpow_one_add_sq`, `Complex.IsExpCmpFilter.isLittleO_pow_mul_exp`, `sub_smul_dslope`, `ConvexOn.smul'`, `PointedCone.dual_eq_comap_dual_eval`, `UniformOnFun.continuousSMul_submodule_of_image_bounded`, `ValuationSubring.valuation_eq_one_iff`, `IsLocalRing.map_mkQ_eq_top`, `IsFractionRing.num_den_reduced`, `ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply`, `isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule`, `LinearMap.trace_comp_comm`, `instIsLocalHomZModRingHomOfIsLocalRingOfNontrivial`, `WeakSpace.instIsScalarTower`, `Subbimodule.smul_mem`, `SchwartzMap.smulLeftCLM_ofReal`, `LinearMap.pow_mulLeft`, `StarConvex.sub'`, `LinearMap.range_smulRight_apply`, `norm_iteratedFDeriv_smul_le`, `KaehlerDifferential.instIsScalarTowerTensorProduct_1`, `realPart_smul`, `exists_eq_smul_of_parallel`, `ContDiffAt.differentiableAt_iteratedFDeriv`, `pow_eq_one_iff_of_nonneg`, `BilinForm.toMatrix_compLeft`, `WeierstrassCurve.Projective.dblX_eq`, `TrivSqZeroExt.inv_zero`, `SMulCommClass.nnrat`, `Asymptotics.IsBigO.pow`, `PowerSeries.expand_X`, `spectralValue_eq_zero_iff`, `Fintype.sum_pow_mul_eq_add_pow`, `MeasureTheory.Integrable.smul_const`, `Finset.smul_finset_sdiff₀`, `Ideal.iInf_pow_smul_eq_bot_of_isTorsionFree`, `Algebra.coe_lmul_eq_mul`, `Matrix.isUnit_transpose`, `Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn`, `ContinuousLinearMap.prodₗ_apply`, `mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop`, `Monotone.convex_le`, `ContinuousLinearEquiv.coord_norm`, `Matrix.trace_units_conj'`, `map_prime_of_factor_orderIso`, `ContinuousMultilinearMap.nnnorm_smulRight`, `SlashInvariantForm.slash_action_eqn'`, `AddChar.doubleDualEmb_doubleDualEquiv_symm_apply`, `AlgebraicGeometry.Proj.instIsOpenImmersionAwayι`, `HasDerivAt.finset_prod`, `Ring.uniformContinuousConstSMul_op`, `intervalIntegral.integral_hasDerivAt_left`, `spectrum.inv_mem_resolventSet`, `ContinuousLinearMap.norm_map_iff_adjoint_comp_self`, `AddChar.coe_complexBasis`, `zero_mem_tangentConeAt_iff`, `Units.divp_sub_divp`, `NonUnitalSubalgebra.map_map`, `DirichletCharacter.Odd.toUnitHom_eval_neg_one`, `ContDiffOn.smulRight`, `QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar`, `Convex.subset_toCone`, `NormedSpace.isUnit_exp`, `IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1`, `LinearIsometryEquiv.map_smul`, `Algebra.TensorProduct.lmul''_eq_lid_comp_mapOfCompatibleSMul`, `DualNumber.eps_mul_eps`, `MeasureTheory.lpMeasToLpTrim_smul`, `RootPairing.pairing_one_four_iff`, `LinearMap.toMatrix₂'_comp`, `MvPolynomial.rTensor_apply`, `NNReal.instSMulPosStrictMono`, `PadicInt.continuousAddCharEquiv_apply`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap`, `Matrix.toLinearMap₂_apply_basis`, `MDifferentiableOn.smul_section_of_tsupport`, `WeierstrassCurve.ΨSq_three`, `Subalgebra.mem_perfectClosure_iff`, `MonoidWithZeroHom.inv_mem_valueGroup`, `ConcaveOn.mul_convexOn`, `LinearEquiv.conjAlgEquiv_surjective`, `ContinuousLinearMap.norm_adjoint_comp_self`, `Antivary.pow_left₀`, `LinearMap.commute_transvections_iff_of_basis`, `LinearEquiv.smul_trans`, `multiplicity_add_eq_min`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith`, `Pi.evalStarAlgHom_apply`, `Polynomial.coeff_mul_X_pow'`, `spectrum.hasDerivAt_resolvent_const_right`, `summable_norm_pow_mul_geometric_of_norm_lt_one`, `Polynomial.coeff_mul_mirror`, `hasDerivWithinAt_intCast`, `Polynomial.degree_pow'`, `MeasureTheory.integral_bilinear_hasDerivAt_eq_sub`, `Convex.add_smul_sub_mem_interior`, `Rep.MonoidalClosed.linearHomEquivComm_symm_hom`, `Asymptotics.IsBigO.const_smul_self`, `NNReal.summable_condensed_iff`, `CircleIntegrable.out`, `IsFractionRing.associated_den_num_inv`, `NonUnitalStarSubalgebra.prod_top`, `Module.End.hasEigenvalue_iff_mem_spectrum`, `PolynomialModule.monomial_smul_lsingle`, `ContMDiff.clm_precomp`, `birkhoffAverage_apply_sub_birkhoffAverage`, `NNReal.rpow_inv_natCast_pow`, `IsLinearTopology.tendsto_smul_zero`, `pow_dvd_pow_iff`, `locallyConvexSpace_iff_zero`, `PadicInt.mem_nonunits`, `TensorPower.toTensorAlgebra_galgebra_toFun`, `Nat.divisors_filter_squarefree`, `Finset.sum_pow`, `NormedSpace.expSeries_hasSum_exp_of_mem_ball'`, `TensorProduct.Algebra.moduleAux_apply`, `fderivWithin_pow`, `ContinuousLinearMap.continuousConstSMul_apply`, `Lagrange.nodal_subgroup_eq_X_pow_card_sub_one`, `HasFPowerSeriesWithinAt.compContinuousLinearMap`, `pow_eq_pow_iff_of_ne_zero`, `WittVector.peval_polyOfInterest'`, `RingTheory.Sequence.map_first_exact_on_four_term_right_exact_of_isSMulRegular_last`, `LinearMap.not_hasEigenvalue_zero_tfae`, `ContinuousLinearMap.isCentralScalar`, `ContinuousMultilinearMap.norm_smulRight`, `LinearMap.toMatrix_pow`, `TensorAlgebra.algebraMap_eq_zero_iff`, `MvPolynomial.aeval_monomial`, `LSeries_hasDerivAt`, `LinearPMap.closure_inverse_graph`, `ConcaveOn.lt_right_of_left_lt'`, `ModularGroup.det_coe`, `RingTheory.Sequence.isWeaklyRegular_iff`, `Polynomial.resultant_C_mul_left`, `FiniteField.sum_subgroup_units`, `Polynomial.resultant_pow_left`, `IntermediateField.rank_bot_mul_relrank`, `Ideal.exists_disjoint_powers_of_span_eq_top`, `Real.hasDerivAt_fourierIntegral`, `Perfection.lift_symm_apply`, `Antivary.sum_smul_le_sum_comp_perm_smul`, `SameRay.sameRay_pos_smul_left`, `Antitone.quasiconcaveOn`, `ContinuousMapZero.elemental_eq_top`, `isLocalHom_of_exists_map_ne_one`, `LieDerivation.coe_ad_apply_eq_ad_apply`, `ContMDiffOn.clm_prodMap`, `PowerSeries.invUnitsSub_mul_X`, `ContinuousMapZero.adjoin_id_dense`, `ContinuousLinearEquiv.strictConvex_preimage`, `HasStrictDerivAt.iterate`, `pow_eq_pow_iff_of_coprime`, `Module.Basis.orientation_neg_single`, `DividedPowerAlgebra.dp_smul`, `Nat.cast_le_pow_div_sub`, `Polynomial.eval₂_eq_sum`, `CategoryTheory.ShortComplex.rightHomologyMap'_smul`, `LinearMap.BilinMap.polarBilin_toQuadraticMap`, `Polynomial.mem_nthRoots`, `Mathlib.Tactic.LinearCombination.smul_const_le`, `IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C`, `Algebra.trace_apply`, `ContinuousLinearMap.hasDerivWithinAt`, `Submodule.Convex.semilinear_range`, `UpperHalfPlane.IsZeroAtImInfty.slash`, `Antivary.sub_smul_sub_nonpos`, `hasStrictFDerivAt_pow`, `Mathlib.Tactic.Module.NF.sub_eq_eval`, `IsPrimitiveRoot.eq_pow_of_pow_eq_one`, `TensorAlgebra.toDirectSum_ι`, `HasDerivWithinAt.comp_of_eq`, `FormalMultilinearSeries.derivSeries_apply_diag`, `CFC.negPart_smul`, `MultilinearMap.currySum_smul`, `Submodule.norm_orthogonalProjection`, `Seminorm.coe_iSup_eq`, `Monotone.alternating_series_le_tendsto`, `LinearMap.BilinForm.toMatrix_comp`, `StrictConvex.preimage_add_left`, `SameRay.exists_nonneg_right`, `StarOrderedRing.isStrictlyPositive_iff_spectrum_pos`, `lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup`, `EisensteinSeries.E_qExpansion_coeff_zero`, `UniqueFactorizationMonoid.factors_mul`, `Matrix.SpecialLinearGroup.toLin'_symm_apply`, `ClosedSubmodule.symplComp_sup`, `spectrum.unit_smul_eq_smul`, `ContinuousMapZero.toNNReal_smul`, `MvPolynomial.C_pow`, `Unitary.toLinearEquiv_mulLeft`, `fderiv_comp_smul`, `LinearMap.map_smul_inv`, `integrable_cexp_quadratic`, `AlgebraicGeometry.Scheme.isLocalHom_stalkClosedPointTo`, `Asymptotics.IsLittleOTVS.add`, `ProbabilityTheory.gaussianReal_div_const`, `Units.val_mk0`, `convex_vadd`, `ContinuousLinearMap.opNorm_lsmul`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one`, `Polynomial.eval₂_eq_sum_range'`, `IsLocalizedModule.map_integerMultiple`, `Submodule.comap_smul'`, `Polynomial.roots_X_pow`, `Seminorm.zero_comp`, `ValuationSubring.ker_unitGroupToResidueFieldUnits`, `Polynomial.opRingEquiv_op_C_mul_X_pow`, `irreducible_iff_prime`, `Algebra.Generators.CotangentSpace.fst_compEquiv_apply`, `Submodule.mem_set_smul`, `FormalMultilinearSeries.norm_changeOriginSeriesTerm`, `TemperedDistribution.smulLeftCLM_smul`, `ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply`, `WithZero.withZeroUnitsEquiv_apply`, `Seminorm.continuous_of_continuousAt_zero`, `pow_succ_pos`, `left_mem_openSegment_iff`, `IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn`, `LeftPreLieAlgebra.toIsScalarTower`, `instIsInertiaFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupInertiaOfIsGalois`, `NormedRing.inverse_add_nth_order`, `TrivSqZeroExt.isUnit_inl_iff`, `finsum_smul`, `TrivSqZeroExt.instIsScalarTower`, `Module.Basis.det_unitsSMul_self`, `Matrix.GeneralLinearGroup.val_inv_swap`, `VectorField.lieBracketWithin_const_smul_right`, `Polynomial.dickson_one_one_eval_add_inv`, `HasGradientAt.hasDerivAt`, `UpperHalfPlane.denom_cocycle'`, `ContinuousLinearEquiv.symm_conjContinuousAlgEquiv`, `IsFractionRing.self_iff_nonZeroDivisors_le_isUnit`, `Units.mk0_prod`, `StrictConvexOn.add_convexOn`, `Algebra.FormallyUnramified.comp_sec`, `Units.zero_lt`, `GenContFract.sub_convs_eq`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe`, `IsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprime`, `HasFTaylorSeriesUpTo.zero_eq'`, `AffineSubspace.setOf_sOppSide_eq_image2`, `ENNReal.tsum_geometric`, `AlgCat.hom_tensorHom`, `TrivSqZeroExt.isUnit_iff_isUnit_fst`, `ArithmeticFunction.iteratedDeriv_LSeries_alternating`, `PrimeSpectrum.mem_image_comap_zeroLocus_sdiff`, `integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable`, `Submonoid.LocalizationMap.lift₀_apply`, `Valuation.ltIdeal_mono`, `DifferentiableAt.pow`, `LinearMap.toMatrix'_one`, `Representation.dual_apply`, `LieAlgebra.SpecialLinear.val_singleSubSingle`, `normalize_eq_one`, `WeierstrassCurve.Jacobian.addX_neg`, `Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable`, `ProbabilityTheory.gaussianPDFReal_mul`, `Subsemiring.pointwise_smul_le_iff₀`, `Associates.quot_out_zero`, `lipschitzGroup.involute_act_ι_mem_range_ι`, `ContinuousAlternatingMap.map_smul_univ`, `Circle.toUnits_apply`, `Polynomial.contentIdeal_mul_le_mul_contentIdeal`, `AdicCompletion.transitionMap_comp_eval_apply`, `Finsupp.linearCombination_comapDomain`, `MonoidAlgebra.cardinalMk_eq_lift_of_fintype`, `IsIntegrallyClosed.pow_dvd_pow_iff`, `IsNilpotent.isUnit_add_right_of_commute`, `Even.convexOn_pow`, `Associates.dvd_of_mem_factors`, `AdicCompletion.of_injective_iff`, `Submodule.comap_smul''`, `fourierCoeffOn.const_smul`, `Matrix.cstar_norm_def`, `ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id`, `spectralAlgNorm_isPowMul`, `PointwiseConvergenceCLM.withSeminorms`, `Submodule.baseChange_span`, `NNRat.coe_pow`, `Function.Odd.smul_odd`, `ModuleCat.smulShortComplex_X₃_isModule`, `WeierstrassCurve.b₈_of_isShortNF`, `WeierstrassCurve.b₆_of_char_two`, `inv_smul_le_iff_of_neg`, `WeierstrassCurve.ΨSq_four`, `MeasureTheory.convolution_eq_swap`, `KaehlerDifferential.tensorKaehlerEquiv_tmul_D`, `Real.fourierInv_eq`, `CFC.isUnit_nnrpow_iff`, `Module.Basis.opNorm_le`, `WittVector.mul_polyOfInterest_aux3`, `Complex.inv_one_add_tan_sq`, `UniformCauchySeqOnFilter.one_smulRight`, `isConformalMap_complex_linear`, `mulInvariantVectorField_smul`, `Commute.add_pow_prime_eq'`, `ModularForm.coe_translate`, `hasDerivAt_const_add_iff`, `Unitization.starLift_symm_apply`, `PowerSeries.coeff_C_mul_X_pow`, `SpecialLinearGroup.coe_mk`, `ContinuousMultilinearMap.curryFinFinset_symm_apply`, `HasFPowerSeriesWithinOnBall.pi`, `Polynomial.hilbertPoly_mul_one_sub_pow_add`, `HasFPowerSeriesWithinOnBall.tendsto_partialSum`, `LieAlgebra.isNilpotent_iff_forall`, `ENNReal.pow_pos`, `SchwartzMap.smulLeftCLM_apply`, `ContDiffMapSupportedIn.withSeminorms'`, `TensorAlgebra.lift_unique`, `Convex.translate_preimage_left`, `AlgebraicGeometry.SpecToEquivOfLocalRing_eq_iff`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply`, `IntermediateField.finiteDimensional_map`, `RingHom.map_geom_sum`, `TensorProduct.quotTensorEquivQuotSMul_comp_mk`, `Submodule.map_toAddSubmonoid'`, `WittVector.nthRemainder_spec`, `LieAlgebra.ad_ker_eq_bot_of_hasTrivialRadical`, `Mathlib.Tactic.Ring.toProd_pf`, `Projectivization.mk_eq_mk_iff'`, `Complex.cpow_mul_ofNat`, `InnerProductSpace.Core.re_inner_smul_ofReal_smul_self`, `Polynomial.shiftedLegendre_eval_symm`, `isPRadical_iff`, `MeasureTheory.Measure.euclideanHausdorffMeasure_smul₀`, `algebraMap.coe_pow`, `WithSeminorms.continuous_iff_continuous_comp`, `IsQuasiregular.isUnit_one_add`, `HahnSeries.SummableFamily.powers_of_orderTop_pos`, `Coalgebra.TensorProduct.assoc_toLinearEquiv`, `WeakDual.seminormFamily_apply`, `Set.smul_set_subset_iff₀`, `selfZPow_of_nonneg`, `IsCyclotomicExtension.union_right`, `NumberField.Units.finrank_mul_regulator_eq_det`, `Matrix.adjugate_pow`, `RatFunc.algEquivOfTranscendental_algebraMap`, `one_lt_pow₀`, `HasFTaylorSeriesUpTo.fderiv`, `ENNReal.rpow_inv_natCast_pow`, `linearIndependent_pow`, `concaveOn_iff_convex_hypograph`, `UpperHalfPlane.neg_smul`, `cross_cross_eq_smul_sub_smul'`, `Seminorm.ball_finset_sup`, `WfDvdMonoid.wellFoundedLT_associates`, `DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul`, `ConvexOn.add`, `IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_roots`, `mem_tangentConeAt_of_add_smul_mem`, `geom_sum₂_mul_of_ge`, `ClassGroup.mk_canonicalEquiv`, `QuadraticForm.tmul_comp_tensorAssoc`, `TensorProduct.rTensorHomToHomRTensor_apply`, `WittVector.coe_mkUnit`, `neg_strictConcaveOn_iff`, `WeierstrassCurve.Jacobian.addY_of_Z_eq_zero_left`, `IsPrimitiveRoot.minpoly_eq_pow`, `LinearMap.tensorKerEquiv_apply`, `StarAlgEquiv.ofLeftInverse'_symm_apply`, `IsRegular.smul_right_inj`, `IsModuleTopology.instPi`, `WeierstrassCurve.Projective.equation_iff`, `Equiv.smulRight_apply`, `Submodule.span_smul_span`, `AlternatingMap.alternatizeUncurryFin_smul`, `Complex.hasSum_arctan`, `LinearMap.toMatrixₛₗ₂'_apply`, `ContinuousLinearMap.norm_holderL_le`, `Module.mem_freeLocus`, `AdicCompletion.eval_lift_apply`, `hasFDerivWithinAt_pow`, `IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right`, `gaugeSeminorm_lt_one_of_isOpen`, `WeierstrassCurve.j_eq_zero_iff_of_char_three'`, `IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul`, `Ideal.mul_mono_right`, `isLittleO_pow_const_const_pow_of_one_lt`, `Asymptotics.IsLittleOTVS.fun_add`, `PolynormableSpace.withSeminorms`, `Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvd`, `Nonneg.val_inv_unitsEquivPos_symm_apply_coe`, `SchwartzMap.smulLeftCLM_compL_smulLeftCLM`, `Submodule.mem_biSup_iff_exists_dfinsupp`, `CharTwo.add_sq`, `Algebra.IsIntegral.isLocalHom`, `hasFDerivWithinAt_iff_isLittleOTVS`, `Matrix.GeneralLinearGroup.val_scalar_apply`, `TensorProduct.AlgebraTensorModule.range_lTensor_idealMap`, `hasDerivWithinAt_inv`, `sub_pow_eq_mul_pow_sub_pow_div_expChar_of_commute`, `geom_sum_Ico`, `ContinuousAffineMap.toConstProdContinuousLinearMap_fst`, `Asymptotics.isBigOTVS_prodMk_left`, `Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C`, `segment_subset_closure_openSegment`, `gaugeSeminormFamily_ball`, `IsStrictlyPositive.add_nonneg`, `Matrix.toLinearMapRight'_one`, `Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map`, `Mathlib.Tactic.Module.NF.add_eq_eval₂`, `ConvexOn.add_const`, `WeierstrassCurve.Jacobian.isUnit_X_of_Z_eq_zero`, `HahnModule.instIsTorsionFree`, `mdifferentiable_smul_section`, `Derivative.normalizedDerivOfComplex_pow`, `isSMulRegular_iff_ker_lsmul_eq_bot`, `SubMulAction.neg_mem_iff`, `Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace`, `RatFunc.associated_num_inv`, `WeierstrassCurve.Jacobian.addX_of_Z_eq_zero_right`, `HasFDerivWithinAt.mul'`, `Units.mul_left_eq_zero`, `LieAlgebra.LoopAlgebra.twoCocycleOfBilinear_coe`, `WfDvdMonoid.exists_factors`, `PresheafOfModules.germ_ringCat_smul`, `IsArtinianRing.isUnit_iff_isRightRegular`, `IntermediateField.normalClosure_le_iff_of_normal`, `rank_le_one_iff`, `QuadraticForm.associated_tmul`, `UpperHalfPlane.σ_eventuallyEq`, `QuadraticMap.polarSym2_map_smul`, `Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip`, `SchwartzMap.instFourierInvSMul`, `AnalyticAt.pow`, `Seminorm.comp_smul_apply`, `differentiableWithinAt_complex_iff_differentiableWithinAt_real`, `OreLocalization.inv_zero`, `MonoidWithZeroHom.snd_apply_coe`, `Associates.coprime_iff_inf_one`, `instIsPushout`, `TemperedDistribution.derivCLM_apply_apply`, `Algebra.essFiniteType_iff`, `PerfectClosure.instReduced`, `AffineBasis.linear_combination_coord_eq_self`, `TorusIntegrable.function_integrable`, `Set.Finite.absorbs_biInter`, `NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral`, `Algebra.EssFiniteType.cond`, `RootPairing.smul_coroot_eq_of_root_eq_smul`, `AffineSubspace.setOf_wSameSide_eq_image2`, `Submodule.coe_toSubMulAction`, `PowerSeries.order_eq_emultiplicity_X`, `AlgHom.fieldRange_of_normal`, `NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype`, `LinearMap.toMatrixAlgEquiv_reindexRange`, `Matrix.GeneralLinearGroup.map_id`, `Units.exists0`, `Polynomial.finiteMultiplicity_X_sub_C`, `Complex.hasSum_cosh`, `IntermediateField.Lifts.eq_iff`, `PowerSeries.coeff_X_pow_mul'`, `riemannZeta_neg_nat_eq_bernoulli`, `Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub`, `ClassGroup.equivPic_apply`, `Complex.taylorSeries_eq_of_entire'`, `geom_sum₂_Ico`, `SlashInvariantFormClass.petersson_smul`, `hasDerivWithinAt_Ici_of_tendsto_deriv`, `associates_irreducible_iff_prime`, `spectrum.hasDerivAt_resolvent_const_left`, `WeierstrassCurve.Affine.CoordinateRing.XYIdeal'_eq`, `PowerSeries.binomialSeries_nat`, `Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson`, `NumberField.Units.sum_mult_mul_log`, `Valuation.restrict_exists_div_eq`, `LinearMap.hasDerivAt`, `Submodule.smulMemClass`, `CategoryTheory.ShortComplex.rightHomologyMap_smul`, `TensorProduct.one_gradedMul`, `Monotone.tendsto_le_alternating_series`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq`, `MDifferentiableWithinAt.smul`, `IsLocalizedModule.map_iso_commute`, `Module.Basis.sum_equivFun`, `IsCovariantDerivativeOn.affine_combination`, `Module.End.mem_genEigenspace`, `TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor`, `Submodule.index_smul_le`, `Associates.count_mul_of_coprime`, `egauge_smul_right`, `Polynomial.degree_sum_fin_lt`, `neg_one_pow_mul_eq_zero_iff`, `VectorField.lieBracket_smul_right`, `midpoint_vsub_midpoint_same_left`, `TensorProduct.piScalarRightHom_tmul`, `AlgebraicGeometry.Scheme.Modules.Hom.app_smul`, `HasFDerivAtFilter.restrictScalars`, `Balanced.smul_eq`, `TensorAlgebra.ofDirectSum_comp_toDirectSum`, `LinearMap.hasDerivAtFilter`, `Submodule.topologicalClosure_iSup_map_single`, `iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod`, `QuadraticForm.tensorComm_symm`, `convex_halfSpace_lt`, `intervalIntegral.integral_hasFDerivAt`, `AffineBasis.isUnit_toMatrix`, `minpoly.irreducible`, `LinearMap.flip_surjective_iff₂`, `IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable'`, `PeriodPair.summable_weierstrassPExceptSummand`, `Polynomial.IsEisensteinAt.irreducible`, `Units.mulArchimedean_iff`, `Polynomial.expand_aeval`, `PowerSeries.coe_pow`, `deriv_pow'`, `Valuation.IsEquiv.orderMonoidIso_spec`, `Subalgebra.pointwise_smul_toSubmodule`, `HasFiniteFPowerSeriesOnBall.fderiv_eq`, `Bialgebra.counit_pow`, `IsPrimitiveRoot.card_nthRoots`, `Polynomial.irreducible_X_sub_C`, `WeierstrassCurve.Projective.addX_of_Z_eq_zero_right`, `NormedSpace.exp_sum_of_commute`, `ConvexOn.pow`, `Bialgebra.mul_compr₂_comul`, `smul_closedBall`, `PointedCone.to_isOrderedModule`, `ContMDiffOn.smul`, `ModularForm.coe_trace`, `WithZeroTopology.singleton_mem_nhds_of_units`, `integrable_mul_cexp_neg_mul_sq`, `MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound`, `AnalyticOnNhd.pow`, `IsLocalFrameOn.coeff_sum_eq`, `IsBaseChange.linearMapRight`, `PadicInt.unitCoeff_spec`, `Valued.integer.norm_coe_unit`, `IntermediateField.normalClosure_map_eq`, `Complex.hasDerivAt_log_sub_logTaylor`, `PointedCone.mem_hull_set`, `Polynomial.Monic.as_sum`, `IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd`, `TestFunction.lineDerivCLM_apply_of_gt`, `WeierstrassCurve.j_of_isShortNF`, `WithSeminorms.isVonNBounded_iff_seminorm_bounded`, `Polynomial.degreeLE_eq_span_X_pow`, `DualNumber.snd_mul`, `WeierstrassCurve.Jacobian.negMap_eq`, `ContinuousLinearMap.smulRight_apply`, `Module.Basis.repr_unitsSMul`, `HasFPowerSeriesAt.locally_zero_iff`, `Valuation.RankOne.hom_eq_zero_iff`, `Matrix.isUnit_diagonal`, `LocalizedModule.zero_mk`, `hasDerivAt_iff_tendsto_slope`, `TrivSqZeroExt.isUnit_or_isNilpotent`, `intervalIntegral.fderiv_integral`, `right_vsub_midpoint`, `UniqueFactorizationMonoid.isRelPrime_iff_no_prime_factors`, `MeasureTheory.IntegrableOn.continuousOn_smul_of_subset`, `intervalIntegral.integral_unitInterval_deriv_eq_sub`, `RootPairing.reflection_apply`, `ContinuousLinearMap.analyticAt_bilinear`, `Matrix.toLpLin_apply`, `Matrix.det_succ_row_zero`, `integral_withDensity_eq_integral_smul₀`, `lcm_units_coe_right`, `Odd.pow_add_pow_eq_zero`, `CharTwo.sq_inj`, `IntermediateField.relrank_bot_left`, `IsModuleFiltration.toGradedSMul`, `Subring.coe_pow`, `HasFDerivWithinAt.comp_hasDerivAt_of_eq`, `AlgHom.kerSquareLift_mk`, `HasFPowerSeriesAt.hasStrictFDerivAt`, `Polynomial.aevalTower_comp_toAlgHom`, `sum_four_sq_mul_sum_four_sq`, `IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension`, `Mathlib.Tactic.Ring.intCast_mul`, `PowerSeries.coeff_pow`, `Quaternion.im_sq`, `gcd_greatest_associated`, `WeierstrassCurve.Projective.dblX_eq'`, `HasDerivWithinAt.comp_hasDerivAt`, `AnalyticOnNhd.fun_const_smul`, `tendsto_pow_cobounded_cobounded`, `MvPolynomial.eval_expand`, `reverse_lucas_primality`, `Matrix.toLin'_apply`, `Matrix.zpow_neg_natCast`, `MeasureTheory.integral_prod_smul`, `Set.add_smul_subset`, `QuotSMulTop.map_id`, `Subalgebra.coe_pow`, `convex_closed_sInter`, `MulChar.coe_equivToUnitHom`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right`, `Submodule.exists_mem_and_smul_eq_self_of_fg_of_le_smul`, `Polynomial.IsPrimitive.isUnit_iff_isUnit_map`, `Unitization.algebraMap_eq_inlRingHom`, `AddChar.complexBasis_apply`, `LinearEquiv.det_refl`, `Matrix.GLPos.coe_neg_GL`, `GroupWithZero.eq_zero_or_unit`, `isBoundedLinearMap_continuousMultilinearMap_comp_linear`, `spectrum.units_smul_resolvent`, `ZMod.isCyclic_units_prime`, `Ideal.map_toCotangent_ker`, `WeierstrassCurve.coeff_ΨSq`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm`, `LieAlgebra.isNilpotent_ad_of_isNilpotent`, `Submodule.map_dualCoannihilator_linearEquiv_flip`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp`, `Module.Basis.constr_apply`, `fderivWithin_mul'`, `AffineSubspace.sSameSide_smul_vsub_vadd_left`, `sub_dvd_pow_sub_pow`, `Derivation.leibniz_invOf`, `hasStrictDerivAt_exp_smul_const_of_mem_ball`, `Polynomial.ofMultiset_injective`, `NumberField.mixedEmbedding.convexBodySum_volume`, `Module.Baer.ExtensionOfMaxAdjoin.eqn`, `KaehlerDifferential.mulActionBaseChange_smul_zero`, `smul_neg_iff_of_neg_left`, `gcd_pow_right_dvd_pow_gcd`, `ContMDiff.const_smul_section`, `AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen`, `IsGroupLikeElem.pow`, `Polynomial.X_pow_comp`, `HasDerivWithinAt.fun_sum`, `riemannZeta_two_mul_nat`, `Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eq_poly_in_U`, `HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap`, `PowerSeries.coeff_one_pow`, `mdifferentiableAt_localFrame_coeff`, `pow_sum_div_card_le_sum_pow`, `Unitary.openPartialHomeomorph_apply`, `Valued.isClopen_closedBall`, `Ideal.map_pointwise_smul`, `lp.instSMulCommClassPreLp`, `WeierstrassCurve.Jacobian.addX_of_Z_eq_zero_left`, `RatFunc.algebraMap_monomial`, `Real.hasDerivAt_Gamma_nat`, `LinearMap.rTensor_smul`, `TensorProduct.isPushout'`, `Matrix.det_updateCol_smul_left`, `MvPowerSeries.monomial_smul_const`, `Convex.affinity`, `PowerSeries.coeff_mul_X_pow`, `MeasureTheory.FiniteMeasure.map_snd_prod`, `Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary`, `IsNilpotent.isUnit_quotient_mk_iff`, `TopologicalGroup.IsSES.integrate_mono`, `NumberField.Units.regulator_eq_det'`, `WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero`, `Unitary.argSelfAdjoint_coe`, `Complex.ofReal_pow`, `FreeNonUnitalNonAssocAlgebra.lift_of_apply`, `LinearMap.BilinForm.SeparatingRight.toMatrix'`, `LinearPMap.supSpanSingleton_apply_mk`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt`, `Polynomial.bernoulli_comp_one_sub_X`, `IsLocalizedModule.instIsTorsionFreeLocalizationLocalizedModuleOfIsDomain`, `NormedAddGroupHom.coe_smul`, `TensorProduct.toLinearMap_symm_rid`, `hasDerivAt_pi`, `Matrix.GeneralLinearGroup.coe_map_inv_mul_map`, `Submodule.smul_top_le_comap_smul_top`, `HasStrictDerivAt.hasStrictFDerivAt_equiv`, `strictConvex_uIoc`, `MeasureTheory.ContinuousMap.inner_toLp`, `convexOn_const`, `Valuation.RankOne.restrict_RankOne_hom_eq`, `Submodule.set_smul_top_eq_span`, `HasDerivAt.of_notMem_tsupport`, `ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars`, `RestrictScalars.isCentralScalar`, `derivWithin_fun_inv'`, `IsSymmetricAlgebra.equiv_toAlgHom`, `integral_bilinear_fderiv_right_eq_neg_left_of_integrable`, `Ideal.sup_mul`, `Cardinal.mk_univ_quaternion`, `CategoryTheory.Linear.toCatCenter_apply_app`, `Polynomial.taylor_pow`, `skewAdjoint.I_smul_neg_I`, `Meromorphic.fun_pow`, `Odd.pow_injective`, `Derivation.linearEquiv_coe_comp`, `FiniteField.coe_frobeniusAlgHom`, `hasFDerivAt_inv'`, `ModuleCat.sMulCommClass_mk`, `PowerSeries.smul_eq_C_mul`, `Nonneg.mk_pow`, `SeminormFamily.basisSets_mem`, `AffineIndependent.units_lineMap`, `LinearMap.flip_flip`, `Polynomial.irreducible_C_mul_X_add_C`, `geom_sum₂_succ_eq`, `MvPolynomial.tensorEquivSum_X_tmul_one`, `Polynomial.smul_X_eq_monomial`, `Submodule.powSMulQuotInclusion_injective`, `HasDerivAt.fun_mul`, `Finset.zero_mem_smul_iff`, `HasStrictDerivAt.const_sub`, `Matrix.exp_units_conj`, `hasDerivWithinAt_finCons`, `Polynomial.commute_X_pow`, `TensorProduct.AlgebraTensorModule.coe_rTensor`, `ProbabilityTheory.charFun_gaussianReal`, `Ideal.quotTorsionOfEquivSpanSingleton_apply_mk`, `NonUnitalStarSubalgebra.map_topologicalClosure_le`, `PresheafOfModules.germ_smul`, `Submodule.smul_le_span`, `Polynomial.Chebyshev.C_two`, `LinearOrderedCommGroupWithZero.inl_apply`, `SpecialLinearGroup.baseChange_apply_coe`, `OreLocalization.nontrivial_of_nonZeroDivisorsLeft`, `Polynomial.resultant_X_pow_left`, `IntermediateField.le_normalClosure`, `CFC.abs_smul`, `Projectivization.map_mk`, `exists_continuousLinearEquiv_fderiv_symm_eq`, `IsArtinianRing.isUnit_of_isIntegral_of_nonZeroDivisor`, `CongruenceSubgroup.IsCongruenceSubgroup.conjGL`, `HasDerivAt.smul`, `Units.isOpenEmbedding_val`, `QuadraticMap.tensorDistrib_tmul`, `FormalMultilinearSeries.rightInv_coeff`, `Seminorm.absorbent_ball`, `emultiplicity_pow_self_of_prime`, `Meromorphic.smul`, `OpenPartialHomeomorph.unitBallBall_symm_apply`, `Convex.mem_toCone'`, `AddSubgroup.le_pointwise_smul_iff₀`, `LieAlgebra.Extension.twoCocycleOf_coe_coe`, `LinearOrderedCommGroupWithZero.inr_apply`, `NormedSpace.exp_units_conj`, `LinearMap.separatingLeft_toLinearMap₂'_iff_det_ne_zero`, `TensorialAt.mkHom₂_apply_eq_extend`, `TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand'`, `Absorbs.sInter`, `Module.Basis.dvd_coord_smul`, `Complex.hasSum_cos`, `Matrix.Module.smul_def'`, `Complex.logTaylor_succ`, `IsLinearMap.map_smul`, `cfcₙHom_of_cfcHom_map_quasispectrum`, `LinearMap.map_smulₛₗ₂`, `SModEq.smul`, `IntermediateField.equivOfEq_trans`, `ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot`, `MvPowerSeries.hasSum_eval₂`, `WeierstrassCurve.c₄_of_isCharThreeJNeZeroNF_of_char_three`, `geom_sum₂_comm`, `LinearMap.BilinForm.Nondegenerate.toMatrix`, `Ideal.IsTwoSided.instHMul`, `Convex.affine_preimage`, `WeierstrassCurve.Jacobian.equation_of_Z_ne_zero`, `not_linearIndepOn_finset_iffₒₛ`, `Polynomial.integralNormalization_coeff_ne_natDegree`, `isClosedMap_smul_left`, `Asymptotics.IsBigOTVS.mono`, `emultiplicity_eq_emultiplicity_span`, `Asymptotics.IsLittleOTVS.proj`, `ContinuousLinearMap.isPositive_adjoint_comp_self`, `SchwartzMap.integral_clm_comp_laplacian_right_eq_left`, `Polynomial.le_trailingDegree_X_pow`, `Polynomial.reverse_C_add`, `UpperHalfPlane.contMDiff_smul`, `IntermediateField.normalClosure_def'`, `LinearMap.dualCoannihilator_range_eq_ker_flip`, `Polynomial.normUnit_X`, `ContDiffOn.differentiableOn_iteratedFDerivWithin`, `PowerSeries.IsWeierstrassDivisorAt.seq_one`, `NormedSpace.expSeries_summable_of_mem_ball'`, `AlgCat.hom_whiskerRight`, `eqOn_iteratedDerivWithin_cotTerm_integerComplement`, `QuadraticMap.associated_flip`, `PosSMulStrictMono.toSMulPosStrictMono`, `IsPrimitiveRoot.associated_pow_sub_one_pow_of_coprime`, `ConcaveOn.add_strictConcaveOn`, `LinearMap.BilinForm.congr_symm`, `Associates.factors_self`, `Algebra.TensorProduct.map_bijective`, `Subgroup.instHasDetOneMapSpecialLinearGroupGeneralLinearGroupMapGL`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn'`, `ClosedSubmodule.orthogonal_closure'`, `autAdjoinRootXPowSubC_root`, `zeta_nat_eq_tsum_of_gt_one`, `AlgebraicGeometry.LocallyRingedSpace.isLocalHom_stalkMap_congr`, `PerfectionMap.of`, `WeierstrassCurve.Projective.negAddY_of_Z_eq_zero_left`, `IsPrimePow.pow`, `Matrix.l2_opNorm_def`, `Nat.Partition.multipliable_powerSeriesMk_card_countRestricted`, `SignType.coe_pow`, `Polynomial.toLaurent_C_mul_X_pow`, `Rat.cast_pow`, `DivisorChain.element_of_chain_eq_pow_second_of_chain`, `ZMod.instIsScalarTower`, `Matrix.rank_unit`, `Real.fourierInv_eq'`, `AnalyticOn.fun_pow`, `Ideal.hasFiniteMulSupport_inv`, `RestrictScalars.addEquiv_symm_map_algebraMap_smul`, `Asymptotics.IsBigOTVS.trans`, `Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div'`, `LinearMap.toMatrixAlgEquiv_mul`, `Asymptotics.isLittleO_pow_pow_cobounded_of_lt`, `WithVal.strictMono_valueGroupEquiv`, `Ideal.span_pair_mul_span_pair`, `MvPowerSeries.le_order_pow`, `AddSubmonoid.le_pointwise_smul_iff₀`, `PowerSeries.WithPiTopology.multipliable_one_sub_X_pow`, `HasFiniteFPowerSeriesOnBall.sub`, `IsPurelyInseparable.exponent_def`, `ContinuousMultilinearMap.norm_compContinuousLinearMapL_le`, `Bornology.isVonNBounded_singleton`, `Matrix.toEuclideanLin_toLp`, `ConvexCone.mem_toPointedCone`, `ModuleCat.isScalarTower_of_algebra_moduleCat`, `FiniteMultiplicity.multiplicity_add_of_gt`, `mem_segment_translate`, `PowerSeries.order_X_pow`, `ZMod.euler_criterion`, `ENNReal.inv_pow`, `TensorProduct.lift_mk_compr₂`, `Associates.prod_le`, `Polynomial.pow_scaleRoots'`, `Complex.canonicalFactor_apply`, `Convex.convexJoin`, `Algebra.Extension.Cotangent.map_mk`, `RootPairing.CoPolarizationIn_apply`, `HasStrictDerivAt.neg`, `ZMod.eq_unit_mul_divisor`, `MellinConvergent.cpow_smul`, `ContDiffOn.fun_smul`, `IsValuativeTopology.mem_nhds_iff`, `Real.fourierIntegral_deriv`, `Seminorm.closedBall_comp`, `ContinuousLinearMap.holderL_apply_apply`, `FormalMultilinearSeries.comp_rightInv_aux2`, `DivisorChain.first_of_chain_isUnit`, `IsStrictlyPositive.of_le`, `CauSeq.const_pow`, `TrivSqZeroExt.mul_inv_rev`, `AddChar.expect_apply_eq_ite`, `Algebra.Extension.CotangentSpace.map_comp`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_ker`, `isRoot_of_unity_iff`, `Module.Basis.units_smul_span_eq_top`, `OreLocalization.nontrivial_iff`, `normalize_associated`, `sub_one_dvd_pow_sub_one`, `AdicCompletion.eval_surjective`, `LaurentPolynomial.eval₂_C_mul_T_n`, `Perfection.coeff_pow_p`, `CliffordAlgebra.GradedAlgebra.ι_sq_scalar`, `Matrix.GeneralLinearGroup.injective_upperRightHom`, `Polynomial.degree_mul_X_pow`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt`, `Unitization.quasispectrum_eq_spectrum_inr`, `LocalizedModule.lift'_add`, `fwdDiff_smul_const`, `Asymptotics.isLittleOTVS_insert`, `IsScalarTower.restrictScalars`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction`, `AdicCompletion.ofPowSMul_val_apply`, `Polynomial.sylveserMap_comp_adjSylvester`, `isClosedEmbedding_smul_left`, `ModuleCat.Algebra.instIsScalarTowerCarrier`, `MeasureTheory.condExpL1CLM_smul`, `Matrix.entryLinearMap_toAddMonoidHom`, `isConformalMap_const_smul`, `tendsto_pow_atTop_nhds_zero_of_norm_lt_one`, `Submodule.smul_mem_iff''`, `hasDerivWithinAt_iff_tendsto_slope'`, `IsScalarTower.of_algebraMap_smul`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand`, `Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1`, `ConvexOn.comp_linearMap`, `MeromorphicAt.smul`, `SeminormFamily.basisSets_iff`, `Complex.isCauSeq_exp`, `PowerBasis.constr_pow_aeval`, `Submodule.FG.smul`, `AffineSubspace.subtypeₐᵢ_toAffineMap`, `NonUnitalAlgHom.coe_codRestrict`, `Perfection.coeff_iterate_frobenius'`, `VectorFourier.hasFDerivAt_fourierChar_smul`, `Polynomial.coeff_comp_degree_mul_degree`, `IntermediateField.mem_restrict`, `Ideal.iInf_pow_smul_eq_bot_of_noZeroSMulDivisors`, `MeasureTheory.LocallyIntegrableOn.continuousOn_smul`, `integrable_cexp_quadratic'`, `Finset.neg_smul`, `ConvexCone.IsReproducing.sub_eq_univ`, `LinearMap.IsAdjointPair.smul`, `Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero`, `stronglyMeasurable_const_smul_iff₀`, `Real.fourierIntegral_real_eq`, `IsBaseChange.finitePow`, `ContMDiffWithinAt.cle_arrowCongr`, `Matrix.scalar_commute_iff`, `fderiv_const_smul_of_field`, `PowerSeries.rescale_neg_one_invOneSubPow`, `IsFractionRing.self_iff_nonZeroDivisors_eq_isUnit`, `perfectClosure.perfectRing`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `cfcₙHomSuperset_apply`, `PowerSeries.coeff_mul_mem_ideal_mul_ideal_of_coeff_mem_ideal'`, `FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm`, `Polynomial.isLocalHom_expand`, `CStarAlgebra.exists_sum_four_unitary`, `PowerSeries.coeff_subst_finite'`, `spectrum.map_pow_of_pos`, `Localization.awayLift_mk`, `HasLineDerivAt.smul`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.num_mem_carrier_iff`, `OrthonormalBasis.sum_repr'`, `Finset.expect_ite_eq`, `isRelPrime_zero_left`, `continuousMultilinearCurryRightEquiv_apply`, `Seminorm.convex_closedBall`, `cfcₙ_apply`, `neg_gcd'`, `WeierstrassCurve.Projective.dblY_of_Y_eq'`, `Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_right`, `HasDerivAt.comp_add_const`, `NumberField.Units.dirichletUnitTheorem.exists_unit`, `Polynomial.natDegree_pow_X_add_C`, `Algebra.traceForm_toMatrix_powerBasis`, `Matrix.minpoly_toLin`, `PadicInt.unitCoeff_coe`, `Bornology.isVonNBounded_of_smul_tendsto_zero`, `Module.Presentation.tautologicalRelations_relation`, `ENNReal.smulCommClass_right`, `Module.End.HasEigenvector.pow_apply`, `ContDiffMapSupportedIn.structureMapLM_zero_apply`, `Units.chartAt_source`, `HasCompactSupport.comp_smul`, `CoalgHom.coe_toAddMonoidHom`, `Module.p_pow_smul_lift`, `Matrix.toLin'_toMatrix'`, `Ideal.sup_mul_left_self`, `ContinuousAlternatingMap.prodLIE_symm_apply`, `analyticOrderAt_smul_eq_top_of_right`, `circleAverage_sub_sub_inv_smul_of_differentiable_on_off_countable`, `convex_zero`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen`, `fwdDiff_iter_sum_mul_pow_eq_zero`, `ENNReal.ofReal_pow`, `isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt`, `Polynomial.Monic.irreducible_of_degree_eq_one`, `concaveOn_const`, `AlternatingMap.alternatizeUncurryFinLM_apply`, `Mathlib.Tactic.ComputeDegree.coeff_pow_of_natDegree_le_of_eq_ite'`, `AnalyticOnNhd.const_smul`, `DifferentiableOn.hasDerivAt`, `Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zero`, `Seminorm.continuous_of_forall`, `Polynomial.isNilpotent_reverse_iff`, `Bornology.sUnion_isVonNBounded_eq_univ`, `StarConvex.add_right`, `NumberField.IsCMField.map_unitsMulComplexConjInv_torsion`, `LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmodule`, `finrank_eq_one_iff_of_nonzero'`, `EisensteinSeries.eisensteinSeriesSIF_mdifferentiable`, `SchwartzMap.integral_smul_deriv_right_eq_neg_left`, `Polynomial.scaleRoots_eval_mul`, `QuadraticMap.polar_smul_right`, `Odd.geom_sum_pos`, `ContinuousLinearMap.apply_apply'`, `mem_rootsOfUnity_iff_isRoot`, `HasFPowerSeriesWithinAt.hasFDerivWithinAt`, `ZMod.injective_stdAddChar`, `Valued.exists_pow_lt_of_le_exp_neg_one`, `Finset.expect_pow`, `qExpansion_of_pow`, `IntermediateField.LinearDisjoint.isDomain`, `Language.kstar_eq_iSup_pow`, `AlgebraicGeometry.exists_of_res_eq_of_qcqs`, `WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_eq_zero`, `PosSMulMono.toPosSMulReflectLE`, `Ideal.finprod_not_dvd`, `tendsto_pow_atTop_nhds_zero_iff`, `Polynomial.IsUnitTrinomial.irreducible_aux1`, `Polynomial.roots_C_mul_X_add_C_of_IsUnit`, `LaurentSeries.X_order_mul_powerSeriesPart`, `Submodule.localized'_smul`, `ContMDiffAt.smul_section`, `AlgebraicGeometry.isReduced_stalk_of_isReduced`, `instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation`, `fderiv_list_prod'`, `SchwartzMap.fourier_convolution`, `OnePoint.isZeroAt_iff`, `Module.Basis.unitsSMul_apply`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app`, `UnitAddTorus.span_mFourierLp_closure_eq_top`, `fderivWithin_comp_smul`, `AlgebraicGeometry.Scheme.Hom.instIsLocalHomCarrierStalkCommRingCatPresheafCoeContinuousMapCarrierCarrierHomTopCatBaseRingHomHomStalkMap`, `Complex.cpow_ofNat_inv_pow`, `nnratCast_smul_eq`, `HahnSeries.val_toOrderTopSubOnePos_coe`, `IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int`, `strictConvex_Ioi`, `WeierstrassCurve.variableChange_c₄`, `Perfection.teichmuller₀_mapMonoidHom_idealQuotientMk`, `MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp`, `Valuation.RankLeOne.strictMono'`, `PadicInt.coe_dpow_eq`, `HomogeneousLocalization.Away.finiteType`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear`, `IntermediateField.finrank_dvd_of_le_right`, `LinearMap.BilinForm.nondegenerate_toBilin'_of_det_ne_zero'`, `Orthonormal.inner_right_fintype`, `MultilinearMap.snoc_smul`, `NonUnitalStarSubalgebra.instSMulCommClass`, `LinearEquiv.smul_refl`, `HasMFDerivAt.mul'`, `Module.Basis.coord_unitsSMul`, `multiplicity_self`, `ContinuousLinearMap.flipₗᵢ_symm`, `HasFPowerSeriesAt.compContinuousLinearMap`, `Commute.isNilpotent_sub`, `PowerSeries.mul_X_pow_inj`, `MvPolynomial.scalarRTensor_apply_tmul_apply`, `AddMonoidAlgebra.grade.gradedMonoid`, `Polynomial.bernoulli_comp_neg_X`, `Asymptotics.IsBigOTVS.refl`, `PerfectionMap.lift_apply`, `two_mul_le_add_mul_sq`, `Polynomial.mul_prod_pow_inverse_eq_quo_add_sum_rem_mul_pow_inverse`, `Matrix.Represents.algebraMap`, `LieSubalgebra.instSMulMemClass`, `isUnit_of_associated_mul`, `WeierstrassCurve.Jacobian.add_of_Z_eq_zero`, `IsLocalRing.finite_quotient_iff`, `convex_closedConvexHull`, `WeakFEPair.f_modif_aux2`, `cfcₙ_comp_const_mul`, `SkewMonoidAlgebra.DistribMulActionHom.single_toFun`, `Asymptotics.isTheta_const_smul_right`, `mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactors`, `DivisorChain.exists_chain_of_prime_pow`, `HahnSeries.mem_orderTopSubOnePos_iff`, `C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum`, `matPolyEquiv_eq_X_pow_sub_C`, `Polynomial.cyclotomic_eq_X_pow_sub_one_div`, `fderivWithin_clm_apply`, `IsLocalizedModule.mk'_cancel`, `Algebra.trace_comp_trace`, `AddChar.zmodAddEquiv_apply`, `gaussSum_mul_gaussSum_eq_card`, `QuadraticMap.associated_isSymm`, `nilpotencyClass_eq_succ_iff`, `IsRelPrime.neg_neg_iff`, `PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero`, `exists_continuousLinearEquiv_fderivWithin_symm_eq`, `spectralValue_X_pow`, `spectrum.spectralRadius_le_pow_nnnorm_pow_one_div`, `ZMod.orderOf_units_dvd_card_sub_one`, `ENNReal.mulLeftOrderIso_apply`, `eHolderNorm_smul`, `SemimoduleCat.MonoidalCategory.leftUnitor_hom_apply`, `denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units`, `ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz`, `Polynomial.coeff_divByMonic_X_sub_C`, `hasDerivAt_of_tendsto_locally_uniformly_on'`, `Set.smul_set_pi₀'`, `BoundedContinuousFunction.coe_npowRec`, `NormedSpace.exp_mem_unitary_of_mem_skewAdjoint`, `AdicCompletion.transitionMap_map_one`, `mellin_cpow_smul`, `AlternatingMap.mkContinuousLinear_norm_le_max`, `ModularGroup.coeHom_apply`, `FormalMultilinearSeries.rightInv_coeff_one`, `LinearMap.SeparatingLeft.toMatrix₂'`, `EuclideanSpace.edist_eq`, `MDifferentiableWithinAt.pow`, `ZMod.isCyclic_units_four_mul_iff`, `IsDiscreteValuationRing.eq_unit_mul_pow_irreducible`, `IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar`, `QuotSMulTop.mem_annihilator`, `TensorProduct.toMatrix_comm`, `Polynomial.degree_C_mul_X_pow`, `Subgroup.le_pointwise_smul_iff₀`, `Module.Basis.sum_repr`, `Bialgebra.mul_compr₂_counit`, `ContinuousMapZero.coe_toContinuousMapHom`, `Polynomial.C_pow`, `IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq`, `fderiv_continuousAlternatingMap_apply_const_apply`, `Differentiable.smul_const`, `WithLp.instProdIsBoundedSMul`, `RootPairing.coreflection_apply_coroot`, `WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF_of_char_three`, `Complex.cos_sq'`, `Matrix.charpoly_ofNat`, `SpecialLinearGroup.coe_div`, `TensorAlgebra.ι_eq_algebraMap_iff`, `NumberField.Units.complexEmbedding_inj`, `HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap`, `IntermediateField.finrank_le_of_le_right`, `Valuation.exists_setOf_restrict_le_iff`, `LinearMap.toMatrix₂'_apply`, `Ideal.mul_right_self_sup`, `LieDerivation.ofGrading_apply_apply`, `RightPreLieAlgebra.ext_iff`, `Rep.standardComplex.d_single`, `Submodule.toSubMulAction_one`, `Submodule.image_smul_top_eq_range_lsum`, `ContinuousLinearMap.isBigOTVS_id`, `PointedCone.instCanLiftConvexConeToConvexConePointed`, `Subgroup.strictWidthInfty_SL2Z`, `Unitary.conjStarAlgAut_star_apply`, `Module.End.genEigenspace_le_smul`, `isLocalHom_toRingHom`, `pow_le_of_le_one`, `MonoidWithZeroHom.inr_injective`, `HahnSeries.val_inv_toOrderTopSubOnePos_coe`, `CFC.continuousOn_rpow`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono`, `MeasureTheory.condExpIndL1Fin_smul'`, `Units.mk0_val`, `RatFunc.natDegree_denom_le_natDegree_minpolyX`, `ContinuousLinearMap.norm_holder_apply_apply_le`, `IsLocalRing.local_hom_TFAE`, `LieModule.Cohomology.d₂₃_comp_d₁₂`, `add_sq'`, `ClosedSubmodule.symplComp_inf`, `Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff`, `AdjoinRoot.algEquivOfEq_toAlgHom`, `neg_one_pow_expChar_pow`, `LinearMap.ker_tensorProductMk`, `pow_add_pow_le'`, `ringKrullDim_le_ringKrullDim_quotSMulTop_succ`, `Unitization.lift_apply`, `Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes`, `UniformConvergenceCLM.isVonNBounded_iff`, `Associates.factors_one`, `DualNumber.instIsPrincipalIdealRing`, `Algebra.Generators.CotangentSpace.map_ofComp_surjective`, `MvPowerSeries.monomial_smul_eq`, `Matrix.sub_scalar_sq_eq_discr`, `AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparated`, `WittVector.mul_pow_charP_coeff_succ`, `absorbent_ball_zero`, `Asymptotics.IsBigOTVS.fst`, `SMulCommClass.nnrat'`, `Nat.cast_pow_eq_one`, `Matrix.kroneckerStarAlgEquiv_apply`, `SlashInvariantFormClass.slash_action_eq`, `LieModule.commute_toEnd_of_mem_center_left`, `LinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent_of_basis`, `Real.exists_lt_of_strictMono`, `Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂`, `Submodule.norm_subtypeL_le`, `RootPairing.Equiv.instSMulCommClassMulOppositeAut`, `ContinuousLinearMap.hasStrictDerivAt`, `ContinuousLinearMap.analyticAt_uncurry_of_multilinear`, `IsUltrametricDist.isPowMul_invariantExtension`, `Ideal.cotangentIdeal_square`, `fderivWithin_pow_ring`, `MonoidWithZeroHom.commute_inl_inr`, `IsDedekindDomain.HeightOneSpectrum.associates_irreducible`, `isGalois_bot`, `hasDerivWithinAt_iff_tendsto_slope`, `LinearMap.BilinForm.separatingLeft_toMatrix_iff`, `MvPolynomial.tensorEquivSum_C_tmul_C`, `constFormalMultilinearSeries_apply_succ`, `Submodule.sup_smul_eq_sup_smul_of_le_smul_of_le_jacobson`, `TensorProduct.sum_tmul_basis_left_injective`, `StrictConvex.vadd`, `LieAlgebra.Basis.coe_baseSupportEquiv_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero`, `StrictConvexOn.sub`, `OreLocalization.add_smul`, `FormalMultilinearSeries.continuousOn`, `Polynomial.irreducible_iff_lt_natDegree_lt`, `Polynomial.natSepDegree_X_pow`, `hasFDerivAt_inv`, `IntermediateField.intermediateFieldMap_symm_apply_coe`, `Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero`, `ZMod.smul_mem`, `Mathlib.Tactic.Module.NF.smul_eq_eval`, `NonUnitalStarAlgHom.subsingleton`, `HasStrictFDerivAt.clm_comp`, `MonoidWithZeroHom.fst_comp_inr`, `Matrix.SpecialLinearGroup.isInducing_toGL`, `ZMod.dft_smul_const`, `ProbabilityTheory.Kernel.integral_withDensity`, `Module.torsion_by_prime_power_decomposition`, `ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap`, `Module.AEval.mem_mapSubmodule_apply`, `pow_eq_pow_iff_cases`, `Ring.inverse_of_isUnit`, `AlgebraicGeometry.structureSheafInType.smul_apply`, `ContinuousMap.isUnit_iff_forall_ne_zero`, `UniqueFactorizationMonoid.radical_eq_one_iff`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀`, `PerfectClosure.mk_pow`, `SlashInvariantForm.slash_action_eqn`, `LieAlgebra.of_symm_smul`, `ContinuousMultilinearMap.isUniformInducing_toUniformOnFun`, `LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff`, `Submodule.basis_of_pid_aux`, `Submodule.span_singleton_eq_span_singleton`, `NumberField.mixedEmbedding.norm_unit`, `TensorProduct.coe_directSumRight`, `WeierstrassCurve.variableChange_a₆`, `Algebra.prod_embeddings_eq_finrank_pow`, `QuadraticForm.associated_baseChange`, `Module.Basis.toMatrix_unitsSMul`, `Representation.IntertwiningMap.coe_smul`, `Real.volume_preserving_transvectionStruct`, `seminormFromConst_seq_def`, `Matrix.UnitaryGroup.transpose_inv_eq_map_star`, `VectorFourier.fourierIntegral_fderiv`, `ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv`, `ContinuousLinearMap.fpowerSeries_apply_one`, `TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM`, `summable_pow_mul_cexp`, `Convex.finsum_mem`, `Valuation.IsRankOneDiscrete.exists_generator_lt_one`, `fderiv_continuousLinearEquiv_comp'`, `mulSupport_comp_inv_smul₀`, `ContinuousLinearMap.smulRightL_apply_apply`, `Representation.asAlgebraHom_mem_of_forall_mem`, `NNReal.iSup_pow`, `AddMonoidAlgebra.isLocalHom_singleZeroAlgHom`, `KaehlerDifferential.map_liftBaseChange_smul`, `ContinuousAlternatingMap.piLinearEquiv_apply`, `logDeriv_pow`, `Complex.cpow_ofNat`, `LieAlgebra.Basis.linearIndependent_baseSupp`, `ContractingWith.apriori_edist_iterate_efixedPoint_le`, `WeakFEPair.Λ_residue_zero`, `LinearMap.range_smul`, `ModularFormClass.hasSum_qExpansion`, `ContinuousLinearMap.toSpanSingletonCLE_apply_apply`, `derivWithin_pow`, `Matrix.toLpLinAlgEquiv_symm_apply`, `sub_pow_expChar_pow`, `MDifferentiableWithinAt.clm_prodMap`, `HasFDerivAt.fun_mul'`, `Polynomial.isMonicOfDegree_X_pow`, `Commute.geom_sum₂_Ico_mul`, `Matrix.toBilin'_toMatrix'`, `LieSubalgebra.instIsCentralScalarSubtypeMem`, `Seminorm.continuous_iff_continuous_comp`, `unitary.coe_neg`, `LieAlgebra.ad_ker_eq_self_module_ker`, `IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int`, `one_add_mul_le_pow`, `Algebra.Generators.Hom.id_comp`, `ModularFormClass.qExpansion_coeff_eq_intervalIntegral`, `NonUnitalStarSubalgebraClass.subtype_apply`, `Algebra.Generators.H1Cotangent.map_comp_cotangentComplex_baseChange`, `AdicCompletion.eval_apply`, `constFormalMultilinearSeries_zero`, `StarConvex.add`, `Polynomial.cyclotomic_prime_mul_X_sub_one`, `UniqueFactorizationMonoid.factors_eq_zero`, `Asymptotics.IsBigOTVS.of_egauge_le_mul`, `Ideal.mul_eq_bot`, `Asymptotics.IsLittleOTVS.symm`, `OpenPartialHomeomorph.unitBallBall_apply`, `threeGPFree_smul_set₀`, `Real.fourierIntegralInv_eq`, `HasStrictFDerivAt.continuousMultilinearMap_apply`, `Submodule.instSMulCommClassSubtypeMemTorsion'`, `cfcₙ_const_mul_id`, `Asymptotics.IsBigO.isBigOTVS`, `IsRelPrime.add_mul_right_right_iff`, `Int.cast_smul_eq_zsmul`, `IsScalarTower.nnrat`, `CliffordAlgebra.contractLeftAux_apply_apply`, `Polynomial.Chebyshev.C_neg_two`, `Associates.FactorSet.sup_add_inf_eq_add`, `WeierstrassCurve.Jacobian.add_smul_of_equiv`, `Polynomial.smeval_commute_left`, `AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap`, `Asymptotics.isLittleOTVS_neg_left`, `IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure`, `NumberField.Units.regOfFamily_eq_det'`, `ContDiffBump.convolution_tendsto_right_of_continuous`, `Matrix.toLinearMapₛₗ₂_toMatrix₂`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top`, `LinearIsometryEquiv.toContinuousLinearEquiv_smul`, `WeierstrassCurve.Projective.eval_polynomialY`, `Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSet`, `LinearMap.BilinForm.IsAlt.smul`, `Complex.cpow_two`, `ContinuousLinearMap.opNNNorm_mul_apply`, `UniqueFactorizationMonoid.multiplicity_eq_count_normalizedFactors`, `PowerSeries.constantCoeff_subst_X_pow`, `OreLocalization.nontrivial_of_nonZeroDivisors`, `le_comap_range_rTensor`, `LaurentPolynomial.instIsScalarTowerPolynomial`, `ContinuousMultilinearMap.curryFinFinset_apply`, `gcd_zero_left'`, `MultilinearMap.domCoprodDep'_apply`, `Polynomial.natDegree_cubic_le`, `LieRinehartAlgebra.LieRinehartRing.lie_smul_eq_mul`, `ContDiffAt.smulRight`, `LinearMap.toMatrix'_mulVec`, `NormedField.nhdsWithin_isUnit_neBot`, `TensorProduct.AlgebraTensorModule.rightComm_symm`, `Unitization.inrRangeEquiv_symm_apply`, `Convex.add_smul_mem_interior`, `NumberField.Embeddings.pow_eq_one_of_norm_eq_one`, `TestFunction.injective_toBoundedContinuousFunctionCLM`, `Submodule.le_traceDual_iff_map_le_one`, `Commute.pow_dvd_add_pow_of_pow_eq_zero_right`, `unitary.mem_pathComponentOne_iff`, `pow_two_pow_sub_pow_two_pow`, `VertexOperator.coeff_eq_ncoeff`, `derivWithin_smul_const`, `FormalMultilinearSeries.changeOriginSeriesTerm_bound`, `CommRingCat.instIsLocalHomCarrierPtWalkingParallelPairEqualizerForkRingHomHomι`, `ConjRootClass.irreducible_minpoly`, `FiniteField.algebraMap_norm_eq_pow_sum`, `WeierstrassCurve.Jacobian.addMap_of_Y_eq`, `IsLocalizedModule.map_LocalizedModules`, `Matrix.SeparatingLeft.toLinearMap₂`, `MultilinearMap.uncurrySum_smul`, `HasDerivWithinAt.sum`, `IntermediateField.finiteDimensional_adjoin_pair`, `Set.mem_smul_set_iff_inv_smul_mem₀`, `Perfection.coeff_pow_p'`, `Units.toEquiv_mulRightLinearEquiv`, `mem_unitary_iff_isStarNormal_and_realPart_sq_add_imaginaryPart_sq_eq_one`, `summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp`, `pow_inj_of_not_isUnit`, `Ideal.finite_mulSupport_inv`, `Fintype.not_linearIndependent_iffₒₛ`, `KaehlerDifferential.kerTotal_map'`, `convex_Ioi`, `ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply`, `Submodule.mulExact_unitsToPic_mapAlgebra`, `UpperHalfPlane.c_mul_im_sq_le_normSq_denom`, `Units.mulLeftLinearEquiv_apply`, `IntermediateField.normal_sup`, `IsAlgClosed.associated_iff_roots_eq_roots`, `Asymptotics.IsLittleOTVS.of_tendsto_div`, `WithZero.val_logOrderIso_symm_apply`, `SchwartzMap.toZeroAtInftyCLM_apply`, `sum_pow_char`, `FormalMultilinearSeries.constFormalMultilinearSeries_radius`, `Odd.pow_nonpos_iff`, `NonUnitalStarSubalgebra.iSupLift_mk`, `Asymptotics.isLittleOTVS_sup`, `MvPolynomial.instIsLocalHomRingHomC`, `wbtw_smul_vadd_smul_vadd_of_nonpos_of_le`, `IntermediateField.coe_algebraMap_apply`, `LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zero`, `ENNReal.pow_eq_top_iff`, `cfcₙHom_nonneg_iff`, `Bialgebra.TensorProduct.assoc_symm_tmul`, `ContinuousLinearMap.toSpanSingletonCLE_symm_apply`, `isUnit_two_iff_forall_even`, `Units.mulRightLinearEquiv_apply`, `MvPolynomial.coeff_add_pow`, `VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le`, `AdjoinRoot.coe_mapRingEquiv`, `AlgebraicGeometry.RingedSpace.mem_basicOpen`, `smul_pos_of_neg_of_neg`, `Finset.sum_pow'`, `Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval`, `TensorProduct.quotTensorEquivQuotSMul_symm_comp_mkQ`, `ContinuousLinearMap.norm_precompL_le`, `NumberField.IsCMField.complexConj_torsion`, `HasFTaylorSeriesUpToOn.restrictScalars`, `Differentiable.smul`, `isConformalMap_iff_is_complex_or_conj_linear`, `IsPrimePow.not_unit`, `ZMod.dft_def`, `succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul`, `starConvex_iff_div`, `HasDerivAtFilter.neg`, `Units.isOpenMap_val`, `CStarMatrix.mapₙₐ_apply`, `ContinuousLinearMap.apply_apply`, `ConcaveOn.sub_strictConvexOn`, `Rep.barComplex.d_single`, `AbsolutelyContinuousOnInterval.smul`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `egauge_zero_right`, `MulChar.apply_mem_rootsOfUnity`, `dotProduct_toMatrix₂_mulVec`, `Module.Presentation.tautological_relation`, `Asymptotics.isThetaTVS_iff_isTheta`, `WeierstrassCurve.Ψ_odd`, `Algebra.Extension.CotangentSpace.map_comp_apply`, `IsUnit.natCast_factorial_of_isNilpotent`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk`, `ContinuousLinearMap.norm_map_removeNth_le`, `Module.End.exists_isNilpotent_isSemisimple`, `Polynomial.natDegree_quadratic`, `Nat.Partition.multipliable_genFun`, `LinearMap.associated_det_comp_equiv`, `ContinuousMultilinearMap.hasStrictFDerivAt_uncurry`, `IsRelPrime.of_mul_add_left_right`, `IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul`, `separableClosure.isGalois`, `Polynomial.natDegree_C_mul_X_pow_le`, `Real.fourierIntegral_continuousMultilinearMap_apply'`, `ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply`, `DirichletCharacter.changeLevel_eq_cast_of_dvd`, `HomogeneousLocalization.instIsLocalHomAtPrimeRingHomLocalRingHom`, `HasGradientAtFilter.hasDerivAtFilter`, `GroupWithZero.toNoZeroSMulDivisors`, `HVertexOperator.comp_apply`, `TensorProduct.gradedComm_gradedMul`, `AlternatingMap.mkContinuousAlternating_apply`, `IsSymmSndFDerivWithinAt.eq`, `ContinuousLinearMap.map_smulₛₗ₂`, `Asymptotics.superpolynomialDecay_param_pow_mul_iff`, `geom₂_sum_of_gt`, `Module.End.HasUnifEigenvalue.mem_spectrum`, `PiTensorProduct.mapLMultilinear_opNorm`, `Polynomial.instIsLocalHomRingHomAlgebraMap`, `hasDerivWithinAt_inter`, `IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one`, `fderivWithin_restrictScalars_comp`, `pow_unbounded_of_one_lt`, `isSMulRegular_of_range_eq_ker`, `Seminorm.uniformContinuous_of_forall'`, `Bialgebra.TensorProduct.assoc_toAlgEquiv`, `PiLp.instIsBoundedSMul`, `AdicCompletion.exists_smodEq_pow_smul_top_and_mkQ_eq`, `hasFPowerSeriesAt_iff'`, `Quaternion.normSq_ratCast`, `StarConvex.neg`, `Matrix.diagonal_comp_single`, `CategoryTheory.ShiftedHom.smul_comp`, `Polynomial.coe_pow`, `WeierstrassCurve.Jacobian.isUnit_addZ_of_X_ne`, `StrictConvex.smul_mem_of_zero_mem`, `Real.fourier_eq'`, `Odd.pow_le_pow`, `CompactlySupportedContinuousMap.instIsScalarTower`, `AlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinLM_comp_of_symmetric`, `IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀`, `UpperHalfPlane.hasStrictFDerivAt_smul`, `FreeNonUnitalNonAssocAlgebra.hom_ext_iff`, `hasDerivAt_exp_smul_const_of_mem_ball`, `analyticAt_inverse`, `Module.IsTorsionBy.mk_smul`, `LinearIsometryEquiv.conjStarAlgEquiv_apply_apply`, `TensorPower.toTensorAlgebra_tprod`, `SymplecticGroup.symplectic_det`, `measurable_const_smul_iff₀`, `MvPolynomial.monomial_single_add`, `RingTheory.Sequence.isRegular_cons_iff'`, `Real.fourierIntegral_iteratedFDeriv`, `hasMellin_const_smul`, `Subgroup.IsArithmetic.discreteTopology`, `IntermediateField.restrictScalars_adjoin`, `Algebra.Extension.CotangentSpace.map_comp_cotangentComplex`, `LinearMap.toMatrixAlgEquiv_transpose_apply`, `pow_mem_range_pow_of_coprime`, `deriv_const_smul_field`, `Finset.smul_univ₀`, `Units.inv_mul'`, `UpperHalfPlane.smulAux'_im`, `NonUnitalCStarAlgebra.toSMulCommClass`, `UpperHalfPlane.det_smulFDeriv`, `mem_convexJoin`, `wittPolynomial_eq_sum_C_mul_X_pow`, `IntermediateField.finiteDimensional_iSup_of_finset'`, `Submodule.orthogonalProjection_norm_le`, `DividedPowers.dpow_smul`, `Matrix.coe_units_zpow`, `OreLocalization.universalHom_commutes`, `HasFDerivAt.mul'`, `Ring.map_choose`, `WeierstrassCurve.Jacobian.isUnit_dblU_of_Y_eq`, `DirectSum.instIsScalarTower`, `WeakFEPair.Λ_residue_k`, `Matrix.det_eq_sign_charpoly_coeff`, `convex_iff_forall_pos`, `IntermediateField.finrank_adjoin_simple_eq_one_iff`, `InnerProductSpace.volume_ball_of_dim_even`, `integrable_cexp_neg_mul_sq`, `WithSeminorms.hasBasis_ball`, `Polynomial.homogenize_one`, `Polynomial.dvd_pow_natDegree_of_aeval_eq_zero`, `Complex.sq_cpow_two_inv`, `ContDiff.fun_smul`, `Convex.openSegment_interior_closure_subset_interior`, `Monovary.sum_smul_sum_le_card_smul_sum`, `EuclideanSpace.volume_closedBall`, `exteriorPower.presentation.relations_relation`, `Even.pow_abs`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply`, `Fourier.fourierIntegral_comp_add_right`, `derivWithin_clm_apply`, `Finset.sum_smul_sum`, `FractionalIdeal.coe_mk0`, `ClassGroup.mk_def`, `NonUnitalSubalgebra.map_id`, `Polynomial.discr_of_degree_eq_three`, `smul_finsum`, `CStarRing.norm_coe_unitary`, `Associates.mem_factors'_of_dvd`, `Quaternion.fst_re_dualNumberEquiv_symm`, `IntermediateField.LinearDisjoint.map`, `PowerSeries.derivative_inv`, `Module.Basis.is_basis_iff_det`, `gaussSum_sq`, `PowerSeries.isUnit_constantCoeff`, `IsLocalizedModule.lift_iso`, `TrivSqZeroExt.mem_kerIdeal_iff_inr`, `SchwartzMap.fourierMultiplierCLM_smul`, `SpecialLinearGroup.coe_dualMap`, `Commute.add_pow_prime_pow_eq'`, `WittVector.ghostComponent_teichmuller`, `MeasureTheory.MemLp.toLp_const_smul`, `AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective`, `QuadraticMap.basisRepr_apply`, `ValuationSubring.coe_unitGroupToResidueFieldUnits_apply`, `Set.smul_univ₀'`, `Set.Finite.isVonNBounded`, `LinearMap.isNilpotent_mulLeft_iff`, `slope_def_module`, `openSegment_subset_union`, `Ideal.associatesEquivIsPrincipal_map_one`, `smul_right_inj`, `IsBaseChange.endHom_comp`, `Module.End.eigenspace_aeval_polynomial_degree_1`, `HasStrictDerivAt.congr_of_eventuallyEq`, `Height.logHeight_pow`, `le_egauge_closedBall_one`, `hasFDerivAt_list_prod_attach'`, `Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_div`, `IsSMulRegular.of_isLocalizedModule`, `Quaternion.imI_snd_dualNumberEquiv`, `Polynomial.resultant_C_mul_right`, `RatFunc.algEquivOfTranscendental_apply`, `zero_pow`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd`, `NonUnitalStarSubalgebra.inclusion_self`, `MeasureTheory.IntegrableOn.smul_continuousOn_of_subset`, `MonoidWithZeroHom.ValueGroup₀.embedding_strictMono`, `DirectSum.coe_of_mul_apply`, `geom_series_eq_inverse`, `MeasureTheory.norm_condExpL2_le_one`, `HasCompactSupport.convolution_integrand_bound_right`, `Polynomial.irreducible_of_degree_eq_one`, `IsNilpotent.of_pow`, `CStarAlgebra.inv_le_one_iff_one_le`, `MeromorphicAt.meromorphicTrailingCoeffAt_pow`, `bddAbove_smul_iff_of_neg`, `ZMod.exists_one_add_mul_pow_prime_pow_eq`, `HasFPowerSeriesWithinOnBall.hasFDerivWithinAt`, `MonovaryOn.smul_add_smul_le_smul_add_smul`, `CategoryTheory.ShiftedHom.mk₀_smul`, `tsum_geometric_nnreal`, `SkewPolynomial.smul_monomial`, `Submodule.mem_span_insert`, `DirectSum.decompose_smul`, `Polynomial.resultant_zero_left_deg`, `Algebra.leftMulMatrix_apply`, `AddChar.inv_apply_eq_conj`, `Asymptotics.isBigOTVS_comm`, `Submodule.toConvexCone_bot`, `Seminorm.finset_sup_le_sum`, `Polynomial.Chebyshev.derivative_T_eval_one`, `Subalgebra.pointwise_smul_toSubring`, `normalClosure.is_finiteDimensional`, `HasDerivAt.comp_semilinear`, `Set.smul_set_symmDiff₀`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply`, `WeierstrassCurve.Affine.CoordinateRing.basis_apply`, `IsLocalizedModule.isInteger_smul`, `convexJoin_singleton_right`, `LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv`, `IsSMulRegular.of_ne_zero`, `AdicCompletion.ofLinearEquiv_symm_of`, `InnerProductSpace.symm_toEuclideanLin_rankOne`, `LinearMap.BilinForm.toMatrix'_compRight`, `isBoundedBilinearMap_smulRight`, `HasDerivAt.clog_real`, `HasDerivAt.comp_sub_const`, `ModuleFilterBasis.smul_right'`, `ENNReal.iSup₂_pow_of_ne_zero`, `LocalizedModule.mkLinearMap_apply`, `Polynomial.derivative_apply`, `convexHull_eq_self`, `IntermediateField.finiteDimensional_sup`, `PeriodPair.derivWeierstrassPExcept_def`, `NonUnitalStarSubalgebra.map_id`, `Algebra.Extension.Cotangent.ker_mk`, `ContMDiffAt.cle_arrowCongr`, `VertexOperator.coeff_eq_zero_of_lt_order`, `modularCyclotomicCharacter'.unique'`, `IntermediateField.Lifts.le_iff`, `Matrix.det_pow`, `LinearMap.toAddMonoidHom_mulRight`, `IsLocalizedModule.mk'_cancel_left`, `spectrum.isUnit_resolvent`, `Submodule.map_toAddSubmonoid`, `Associates.prod_coe`, `Matrix.op_smul_eq_vecMul`, `Associates.out_top`, `WeierstrassCurve.Affine.Point.toClass_apply`, `Polynomial.normalizedFactors_cyclotomic_card`, `HomogeneousLocalization.Away.map_mk`, `WeierstrassCurve.Jacobian.eval_polynomialZ`, `convexOn_iff_convex_epigraph`, `IsNilpotent.zero`, `HasFDerivAt.clm_comp`, `PMF.binomial_apply_last`, `CFC.inv_nonneg_of_nonneg`, `ContinuousLinearMap.adjoint_innerSL_apply`, `EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act`, `SameRay.pos_smul_right`, `StrictConvexOn.map_sum_eq_iff'`, `Function.support_pow'`, `LSeries.hasDerivAt_term`, `gaugeSeminorm_toFun`, `Polynomial.resultant_zero_right_deg`, `LieAlgebra.Basis.baseSupp_apply_h'`, `Finset.expect_ite_eq'`, `IsBoundedBilinearMap.smul_right`, `Int.cast_negOnePow_natCast`, `Units.mk0_one`, `LinearPMap.IsClosable.graph_closure_eq_closure_graph`, `Asymptotics.isLittleOTVS_pi`, `Algebra.Extension.Hom.toAlgHom_id`, `Module.finrank_eq_zero_iff`, `pow_right_strictMono₀`, `geom_sum_Ico_le_of_lt_one`, `Bundle.Pretrivialization.continuousLinearMapCoordChange_apply`, `WeierstrassCurve.Projective.nonsingularLift_zero`, `DifferentiableWithinAt.smul`, `Asymptotics.isLittleO_pow_pow_atTop_of_lt`, `MDifferentiableOn.pow`, `ContDiffMapSupportedIn.structureMapLM_apply`, `CStarAlgebra.span_unitary`, `Matrix.ProjGenLinGroup.mk_smul`, `ContinuousLinearMap.mem_invtSubmodule_adjoint_iff`, `TensorProduct.AlgebraTensorModule.lcurry_apply`, `HasDerivWithinAt.iterate`, `Finset.mulConst_le_divConst_sq`, `IsCompactOperator.hasEigenvalue_iff_mem_spectrum`, `LieDerivation.instSMulBase`, `trace_adjoinSimpleGen`, `DivisorChain.card_subset_divisors_le_length_of_chain`, `Polynomial.self_sub_C_mul_X_pow`, `derivWithin_const_smul'`, `Convex.mem_smul_of_zero_mem`, `Polynomial.monomial_comp`, `isBoundedLinearMap_prod_multilinear`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle'`, `Matrix.SeparatingRight.toBilin`, `Ideal.span_singleton_pow`, `Polynomial.IsEisensteinAt.notMem`, `Module.reflection_mul_reflection_mul_reflection_pow_apply_self`, `Subgroup.IsArithmetic.conj`, `LinearEquiv.reduce_mkQ`, `AlgEquiv.eq_linearEquivConjAlgEquiv`, `Orthonormal.inner_sum`, `Module.End.algebraMap_isUnit_inv_apply_eq_iff`, `IntermediateField.normal_iff_normalClosure_eq`, `WeierstrassCurve.VariableChange.map_u`, `HasCompactSupport.convolution_integrand_bound_right_of_subset`, `PreTilt.coeff_def`, `Prime.pow_dvd_of_dvd_mul_left`, `IntermediateField.rank_adjoin_simple_eq_one_iff`, `hasStrictDerivAt_of_hasDerivAt_of_continuousAt`, `Finsupp.weight_apply`, `HasStrictDerivAt_ofNat`, `Function.Periodic.const_inv_smul₀`, `geom_sum_pos_and_lt_one`, `IsFractionRing.isUnit_den_zero`, `SlashInvariantForm.coe_norm`, `fourier_gaussian_pi`, `Real.fourier_smul_convolution_eq`, `Module.reflection_mul_reflection_mul_reflection_zpow_apply_self`, `PointedCone.smul_mem`, `IsPrimitiveRoot.nthRoots_eq`, `CliffordAlgebra.contractLeftAux_contractLeftAux`, `PowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero`, `Module.reflection_mul_reflection_zpow`, `lipschitzGroup.conjAct_smul_range_ι`, `balancedCore_eq_iInter`, `ConcaveOn.convex_gt`, `Filter.tendsto_pow_atTop`, `AntitoneOn.convex_lt`, `AlgebraicGeometry.Proj.awayToSection_comp_appLE_assoc`, `MvPowerSeries.monomial_eq'`, `HasFiniteFPowerSeriesAt.comp`, `PerfectionMap.equiv_apply`, `Submodule.exists_smith_normal_form_of_le`, `AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective`, `Subring.mem_inv_pointwise_smul_iff₀`, `PowerSeries.map.isLocalHom`, `second_derivative_symmetric_of_eventually_of_real`, `hasDerivWithinAt_iff_tendsto`, `Associates.gcd_mk_mk`, `WithZero.logEquiv_unitsMk0`, `Valuation.IsRankOneDiscrete.generator_mem_range`, `Matrix.isUnit_nonsing_inv_det`, `AlgHom.coe_toAddMonoidHom`, `IsLocalHom.of_comap_surjective`, `irreducible_X_pow_sub_C_of_root_adjoin_eq_top`, `lp.instIsScalarTowerSubtypePreLpMemAddSubgroup`, `Convex.convexIndependent_extremePoints`, `ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero`, `WithZero.val_inv_logOrderIso_symm_apply`, `balancedHull_convexHull_subseteq_absConvexHull`, `Unitary.path_apply`, `IsAdicComplete.StrictMono.mkQ_comp_lift`, `ContDiffAt.hasStrictDerivAt'`, `Matrix.vecMul_surjective_iff_isUnit`, `cyclotomicCharacter.continuous`, `StrictConvex.mem_smul_of_zero_mem`, `ascPochhammer_eval_neg_eq_descPochhammer`, `TensorProduct.toMatrix_map`, `emultiplicity_mul`, `Unitary.conjStarAlgAut_ext_iff`, `Matrix.toLinAlgEquiv_toMatrixAlgEquiv`, `finrank_le_one_iff`, `Matrix.rank_vecMulVec`, `Matrix.isUnit_det_of_right_inverse`, `TemperedDistribution.laplacianCLM_apply`, `Perfection.teichmuller_spec`, `LieAlgebra.IsKilling.rootSystem_root_apply`, `unitary.two_mul_one_sub_cos_norm_argSelfAdjoint`, `Seminorm.finset_sup_apply_le`, `ConvexBody.coe_smul'`, `AdicCompletion.map_of`, `PowerSeries.invOneSubPow_val_succ_eq_mk_add_choose`, `NumberField.IsCMField.Units.complexConj_eq_self_iff`, `IsLocalRing.isUnit_one_sub_self_of_mem_nonunits`, `Unitary.spectrum_subset_circle`, `DilationEquiv.ratio_pow`, `IsLocalization.mem_span_iff`, `IntermediateField.isIntegral_iff`, `Monovary.sub_smul_sub_nonneg`, `PresheafOfModules.Sheafify.SMulCandidate.h`, `HasDerivAt.star_conj`, `MeasureTheory.SignedMeasure.toJordanDecomposition_smul`, `Wbtw.mem_segment`, `Polynomial.neg_one_pow_mul_shiftedLegendre_comp_one_sub_X_eq`, `Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single`, `PowerSeries.coeff_X_pow_mul`, `continuousAt_gaussian_integral`, `Matrix.permanent_smul`, `Bornology.IsVonNBounded.insert`, `FiniteField.prod_univ_units_id_eq_neg_one`, `NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne`, `le_inv_smul_iff_of_pos`, `IntermediateField.LinearDisjoint.isField_of_isAlgebraic`, `segment_inter_eq_endpoint_of_linearIndependent_sub`, `Polynomial.resultant_integralNormalization`, `IsLocalizedModule.mk'_eq_iff`, `IsValuativeTopology.isClopen_closedBall`, `NonUnitalStarSubalgebra.instIsScalarTower'`, `Seminorm.continuousAt_zero`, `ftaylorSeriesWithin_fun_zero`, `ContinuousLinearMap.norm_smulRightL_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_apply`, `Submodule.torsionBy.mk_smul`, `hasDerivAt_finCons`, `Asymptotics.IsThetaTVS.rfl`, `Algebra.Extension.Hom.toAlgHom_apply`, `inner_eq_ofReal_norm_sq_right_iff`, `Polynomial.content_X_pow`, `AddChar.exists_apply_ne_zero`, `spinGroup.toUnits_injective`, `Valuation.exists_div_eq_of_surjective`, `HasFDerivAt.smul`, `Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow`, `RatFunc.associated_denom_inv`, `Real.deriv_fourier`, `CStarAlgebra.exists_sum_four_nonneg`, `RootPairing.EmbeddedG2.threeShortAddLongRoot_eq`, `Complex.taylorSeries_eq_on_emetric_ball'`, `PairReduction.logSizeRadius_le_card_smallBall`, `CategoryTheory.Linear.smul_comp`, `Mathlib.Tactic.LinearCombination.smul_const_lt_weak`, `Submodule.toSubMulAction_injective`, `CategoryTheory.Pretriangulated.Triangle.smul_hom₁`, `orderOf_abs_ne_one`, `Matrix.toLinAlgEquiv_symm`, `SchwartzMap.smulLeftCLM_smul`, `Algebra.Norm.Transitivity.det_mul_corner_pow`, `LinearIndependent.pair_add_smul_add_smul_iff`, `Polynomial.Monic.irreducible_iff_roots_eq_zero_of_degree_le_three`, `AlgebraicGeometry.StructureSheaf.instIsLocalizedModuleObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInTypeOpBasicOpenPowersToOpenₗ`, `Module.FinitePresentation.exists_basis_localizedModule_powers`, `KaehlerDifferential.instIsScalarTowerTensorProduct_2`, `DoubleCentralizer.coe_snd`, `Valuation.mem_nhds_iff`, `MemHolder.smul_iff`, `ContinuousLinearMap.opNorm_le_bound₂`, `hasFPowerSeriesAt_iff`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_one`, `WeierstrassCurve.Projective.isUnit_addZ_of_X_ne`, `isUnit_one_sub_of_norm_lt_one`, `MeasureTheory.integral_convolution`, `ValuationSubring.principalUnitGroup_injective`, `Seminorm.closedBall_finset_sup_eq_iInter`, `instPerfectRingProd`, `PosSMulMono.of_smul_nonneg`, `CategoryTheory.ShortComplex.leftHomologyMap_smul`, `IsLocalRing.spanFinrank_eq_finrank_quotient`, `Seminorm.comp_add_le`, `MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero`, `DivisibleHull.nnqsmul_mk`, `ZMod.stdAddChar_apply`, `separableClosure.normalClosure_eq_self`, `PiLp.nndist_eq_of_L2`, `LinearMap.toMatrixAlgEquiv_transpose_apply'`, `Polynomial.trailingDegree_X_pow`, `Affine.Simplex.centroid_vsub_point_eq_smul_vsub`, `Polynomial.mkDerivation_apply`, `CFC.nnrpow_map_prod`, `sq_sub_sq`, `pow_lt_pow_iff_left₀`, `LinearMap.baseChangeHom_apply`, `hasStrictDerivAt_pow`, `mulLinearMap_eq_mul`, `FractionalIdeal.count_coe`, `Representation.TensorProduct.lid_apply`, `LinearMap.toMatrixRight'_comp`, `Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero`, `Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul`, `sub_div_sub_smul_slope_add_sub_div_sub_smul_slope`, `SemimoduleCat.forget₂_map`, `LieSubalgebra.instIsArtinianSubtypeMem`, `Associates.FactorSet.prod_eq_zero_iff`, `TrivSqZeroExt.snd_expSeries_of_smul_comm`, `PositiveLinearMap.preGNS_norm_sq`, `ContinuousMultilinearMap.norm_curryMid`, `normEDS_even`, `EulerSine.integral_cos_mul_cos_pow_even`, `Submodule.smul_mem`, `Matrix.kroneckerStarAlgEquiv_symm_apply`, `zero_mem_tangentCone`, `AddChar.expect_eq_ite`, `Algebra.Generators.H1Cotangent.δ_map`, `IsLocalization.Away.algebraMap_isUnit`, `ContinuousAffineMap.instIsCentralScalar`, `modularCyclotomicCharacter.toFun_spec''`, `CategoryTheory.ShortComplex.opcyclesMap'_smul`, `Perfection.frobenius_pthRoot`, `TopologicalAddGroup.IsSES.integrate_apply`, `Associates.le_zero`, `NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvd`, `WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three`, `Matrix.isPrimitive_iff`, `IntermediateField.adjoin.powerBasis_dim`, `hasDerivAt_of_tendstoUniformlyOnFilter`, `AdicCompletion.of_apply`, `Submodule.starProjection_tendsto_closure_iSup`, `instDiscreteTopologySubtypeGeneralLinearGroupMemSubgroupAdjoinNegOneOfIsTopologicalRingOfT2Space`, `Submodule.ker_unitsMap_spanSingleton`, `LieSubalgebra.smul_mem`, `LaurentSeries.valuation_X_pow`, `TensorProduct.AlgebraTensorModule.assoc_eq`, `Commute.geom_sum₂_comm`, `IsArtinianRing.isUnit_iff_isRegular`, `SimpContFract.determinant_aux`, `IsCyclotomicExtension.autEquivPow_symm_apply`, `TrivSqZeroExt.inv_inr`, `MeasureTheory.Lp.toTemperedDistribution_smul_eq`, `Associated.gcd`, `MvPolynomial.isHomogeneous_X_pow`, `UpperHalfPlane.IsBoundedAtImInfty.slash`, `IsPrimitiveRoot.pow_add_pow_eq_prod_add_mul`, `SchwartzMap.laplacian_eq_fourierMultiplierCLM`, `Nat.Partition.genFun_eq_tprod`, `QuadraticMap.toMatrix'_smul`, `abs_pow`, `Asymptotics.IsBigOTVS.pi`, `egauge_le_of_smul_mem_of_ne`, `HasFDerivAt.isLittleOTVS`, `normalize_eq_normalize_iff_associated`, `HasDerivAt.inv`, `Finset.sum_mul_sq_le_sq_mul_sq`, `IsGalois.of_fixedField_normal_subgroup`, `Algebra.TensorProduct.lift_includeLeft_includeRight`, `SpecialLinearGroup.toLinearEquiv_to_linearMap`, `Commute.expUnitary`, `HVertexOperator.coeff_of_coeff`, `IsAddUnit.smul_right`, `AlgebraicGeometry.Proj.awayι_comp_map`, `MeasureTheory.Lp_toLp_restrict_smul`, `sub_pow_expChar`, `const_smul_mfderiv`, `Filter.EventuallyEq.hasDerivAtFilter_iff`, `Seminorm.smul_le_smul`, `LinearMap.lTensor_eqLocus_subtype_tensoreqLocusEquiv_symm`, `WithZero.unitsWithZeroEquiv_apply`, `IntermediateField.essFiniteType_iff`, `pow_le_one₀`, `Field.Emb.cardinal_separableClosure`, `HasMFDerivAt.const_smul`, `HasDerivAtFilter.fun_sum`, `IsCovariantDerivativeOn.finite_affine_combination`, `MvPolynomial.bind₁_monomial`, `Complex.ofReal_choose`, `Matrix.toBilin_comp`, `WeierstrassCurve.Projective.Point.toAffineLift_eq`, `IntermediateField.isPurelyInseparable_sup`, `Prime.dvd_prime_iff_associated`, `NonUnitalCommCStarAlgebra.toIsScalarTower`, `NNReal.instIsScalarTowerOfReal`, `CharP.isUnit_intCast_iff`, `IsCusp.smul`, `Polynomial.emultiplicity_le_one_of_separable`, `Set.smul_set_pi₀`, `map_inv_intCast_smul`, `IsOpenUnits.of_isAdic`, `cyclotomicCharacter.toFun_spec`, `NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart`, `FormalMultilinearSeries.hasFPowerSeriesOnBall`, `KaehlerDifferential.mulActionBaseChange_smul_tmul`, `SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj`, `ModuleFilterBasis.continuousSMul`, `ContinuousLinearMap.coe_mulₗᵢ`, `deriv_fun_const_smul'`, `sq_tsub_sq`, `IntermediateField.splits_of_splits`, `Units.map_neg_one`, `LinearMap.BilinForm.apply_smul_sub_smul_sub_eq`, `SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent`, `galois_poly_separable`, `add_pow_char_of_commute`, `lsum_comp_mapRange_toSpanSingleton`, `ContinuousLinearMap.isUnit_iff_bijective`, `TensorProduct.instIsCentralScalar`, `Matrix.SpecialLinearGroup.toGL_inj`, `balancedCoreAux_empty`, `Complex.one_div_sub_hasFPowerSeriesOnBall_zero`, `Polynomial.coeff_X_add_C_pow`, `MDifferentiableOn.clm_bundle_apply₂`, `ClassGroup.equiv_mk`, `ValuativeRel.pow_vlt_pow`, `cfc_comp_inv`, `Even.pow_pos_iff`, `IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two`, `IsAdicComplete.StrictMono.mk_lift`, `WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y`, `Polynomial.resultant_zero_zero`, `Seminorm.sSup_apply`, `NonUnitalSubalgebra.range_val`, `Quaternion.normSq_coe`, `Module.isTorsionBy_quotient_element_smul`, `Seminorm.ball_bot`, `MonoidWithZeroHom.inl_apply_unit`, `LocalizedModule.oreEqv_eq_r`, `Valuation.is_topological_valuation`, `egauge_pi'`, `ModularGroup.smul_eq_lcRow0_add`, `Asymptotics.IsBigO.smul_isLittleO`, `left_sub_midpoint`, `HasFDerivWithinAt.continuousAlternatingMap_apply_const`, `Algebra.TensorProduct.mul_apply`, `UniversalEnvelopingAlgebra.lift_ι_apply'`, `ContinuousLinearMap.innerSL_apply_comp`, `WeierstrassCurve.preΨ_even`, `normalize_associated_iff`, `Matrix.SpecialLinearGroup.toLin'_apply`, `PerfectRing.lift_aux`, `Module.Finite.of_isComplemented_codomain`, `fourierIntegral_gaussian_pi'`, `Balanced.smul_mono`, `DualNumber.isNilpotent_eps`, `Ring.isUnit_iff_inverse_ne_zero`, `Complex.tendsto_tsum_powerSeries_nhdsWithin_lt`, `CategoryTheory.ShortComplex.leftHomologyMap'_smul`, `Matrix.GeneralLinearGroup.toLin_apply`, `Polynomial.Chebyshev.add_one_mul_T_eq_poly_in_U`, `ContinuousLinearMap.toSesqForm_apply_norm_le`, `MonoidWithZeroHom.snd_surjective`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd`, `Squarefree.dvd_pow_iff_dvd`, `Matrix.mulVec_injective_iff_isUnit`, `hasDerivAt_abs_pos`, `mem_convexAddSubmonoid`, `Matrix.isNilpotent_iff_forall_col`, `Valuation.inversion_estimate`, `PiLp.edist_eq_of_L2`, `midpoint_vsub_midpoint_same_right`, `ContinuousLinearMap.coeFn_holder`, `Perfection.teichmuller_spec'`, `Ideal.isRadical_iff_quotient_reduced`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow`, `ContDiffMapSupportedIn.structureMapLM_eq`, `QuadraticMap.nondegenerate_associated_iff`, `Algebra.lsmul_coe`, `Affine.Simplex.centroid_vsub_eq`, `NonUnitalStarSubalgebra.inclusion_inclusion`, `Mathlib.Meta.NormNum.IsInt.nnreal_rpow_eq_inv_nnreal_pow`, `openSegment.lift`, `UniqueFactorizationMonoid.exists_reduced_factors'`, `HilbertBasis.hasSum_repr_symm`, `ContinuousLinearMap.map_smul`, `CStarMatrix.norm_def`, `ContinuousAlternatingMap.smulRight_apply`, `Polynomial.degree_coe_units`, `AlgHom.IsArithFrobAt.restrict_apply`, `Function.Antiperiodic.sub_nat_mul_eq`, `AlternatingMap.instIsCentralScalar`, `ContMDiff.cle_arrowCongr`, `ContinuousLinearMap.coe_deriv₂`, `IsDedekindDomain.selmerGroup.valuation_ker_eq`, `IsMIntegralCurveAt.eventually_hasDerivAt`, `ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply`, `openSegment_subset_iff_segment_subset`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le`, `RestrictScalars.smul_def`, `ModuleCat.ihom_ev_app`, `ContMDiffOn.clm_bundle_apply₂`, `Cardinal.power_natCast`, `inner_smul_left`, `Unitary.coe_inv`, `Mathlib.Tactic.Ring.pow_congr`, `Associated.of_pow_associated_of_prime'`, `natCard_units_lt`, `Valuation.IsEquiv.orderMonoidIso_symm`, `Polynomial.natDegree_pow'`, `TrivSqZeroExt.eq_smul_exp_of_invertible`, `Submodule.restrictScalars_self`, `Complex.tan_two_mul`, `Polynomial.derivative_C_mul_X_sq`, `derivWithin_fun_pow'`, `LieModule.Weight.hasEigenvalueAt`, `WeierstrassCurve.Δ_of_char_two`, `integral_gaussian_complex_Ioi`, `fun_meromorphicOrderAt_pow`, `DividedPowers.OfInvertibleFactorial.dpow_mul`, `LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton`, `Matrix.linearIndependent_rows_iff_isUnit`, `TensorProduct.finsuppLeft'_apply`, `ValuationSubring.principalUnitGroup_symm_apply`, `DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap`, `ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply`, `Seminorm.continuous_of_le`, `mem_segment_sub_add`, `ContinuousLinearMap.adjoint_adjoint`, `Ideal.exists_pow_inf_eq_pow_smul`, `StrictConvexOn.sub_concaveOn`, `HasCompactSupport.hasFDerivAt_convolution_left`, `PadicInt.coe_pow`, `NumberField.Units.instFreeIntAdditiveQuotientUnitsRingOfIntegersSubgroupTorsion`, `ProbabilityTheory.charFunDual_stdGaussian`, `TrivSqZeroExt.map_id`, `Submodule.flip_quotDualCoannihilatorToDual_injective`, `Algebra.Extension.H1Cotangent.map_comp`, `Matrix.fromBlocks_diagonal_pow`, `LinearMap.lflip_apply`, `HolderWith.smul_iff`, `Subgroup.hasDetPlusMinusOne_iff_abs_det`, `selfAdjoint.expUnitary_coe`, `WithZero.withZeroUnitsEquiv_strictMono`, `spectrum.not_isUnit_of_zero_mem`, `HasDerivWithinAt.fun_inv`, `MeasureTheory.Integrable.smul_of_top_right`, `Polynomial.card_support_trinomial`, `WeierstrassCurve.c_relation_of_char_three`, `TensorProduct.lift.equiv_apply`, `MonovaryOn.sub_smul_sub_nonneg`, `IsBaseChange.linearMapLeftRightHom_comp`, `Polynomial.mem_nthRootsFinset`, `HasDerivWithinAt.finCons`, `HasStrictDerivAt.clm_apply`, `IsLocalizedModule.fromLocalizedModule'_smul`, `MvPolynomial.WeightedHomogeneousSubmodule.gradedMonoid`, `TemperedDistribution.smulLeftCLM_apply_apply`, `X_pow_sub_C_irreducible_iff_of_prime`, `HasDerivAt.congr_deriv`, `Subalgebra.centralizer_range_includeRight_eq_center_tensorProduct`, `IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ`, `Matrix.SpecialLinearGroup.mem_center_iff`, `Polynomial.irreducible_of_dvd_cyclotomic_of_natDegree`, `HasDerivAt.tendsto_slope_zero_right`, `WittVector.nth_mul_coeff'`, `Submodule.toSubMulAction_mono`, `TensorProduct.Algebra.mul'_comp_tensorTensorTensorComm`, `add_pow_expChar`, `Matrix.SpecialLinearGroup.isEmbedding_mapGL`, `ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc`, `NonUnitalAlgHom.subtype_comp_codRestrict`, `Matrix.Nondegenerate.toLinearMap₂'`, `geom_sum_pos'`, `Polynomial.map_iterateFrobenius_expand`, `AlgHom.mulLeftRightMatrix.comp_inv`, `WithSeminorms.hasBasis_zero_ball`, `PrimeSpectrum.basicOpen_eq_bot_iff`, `AdicCompletion.eval_comp_of`, `Finset.sum_smul_vsub_eq_weightedVSub_sub`, `wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos`, `NNReal.sq_sqrt`, `Polynomial.roots_X_pow_char_pow_sub_C`, `Ideal.to_quotient_square_comp_toCotangent`, `NNReal.tendsto_pow_atTop_nhds_zero_iff`, `DFinsupp.instSMulPosStrictMono`, `IsPrimitiveRoot.toInteger_cube_eq_one`, `ContinuousLinearMap.hasDerivAt_of_bilinear`, `Circle.norm_smul`, `tendsto_pow_atTop_nhdsWithin_zero_of_lt_one`, `ConvexOn.map_add_sum_le`, `instIsPushoutFractionRingMvPolynomial_1`, `Matrix.isUnit_comp_symm_iff`, `IsFractionRing.isUnit_den_iff`, `Submodule.fg_unit`, `locallyConvexSpace_iff_exists_convex_subset_zero`, `AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen`, `second_derivative_symmetric_of_eventually`, `Set.subset_smul_set_iff₀`, `AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact`, `Convex.mem_extremePoints_iff_convex_diff`, `HasFDerivAt.comp_hasDerivAt_of_eq`, `mem_rootsOfUnity_prime_pow_mul_iff`, `IsLocalizedModule.map_lTensor`, `LinearEquiv.coe_det`, `Submodule.restrictScalars_localized'_smul`, `Matrix.separatingRight_toLinearMap₂'_iff_separatingRight_toLinearMap₂`, `LinearMap.mulLeft_toAddMonoidHom`, `VectorField.lieBracketWithin_const_smul_left`, `mellin_comp_mul_left`, `HahnSeries.cardSupp_pow_le`, `DifferentiableOn.fun_smul`, `Submodule.map_smul`, `convexOn_iff_pairwise_pos`, `Convex.combo_affine_apply`, `FiniteField.Extension.frob_iterate_apply`, `IsCyclotomicExtension.autEquivPow_apply`, `convex_segment`, `IsPurelyInseparable.elemExponent_def`, `vadd_left_mem_affineSpan_pair`, `Polynomial.exists_irreducible_of_degree_pos`, `Finsupp.linearCombination_onFinset`, `derivWithin_pow'`, `IsCyclotomicExtension.discr_prime_pow`, `AlgebraicGeometry.affine_isReduced_iff`, `IsAdjoinRootMonic.coeff_root_pow`, `zero_geom_sum`, `MeasureTheory.SignedMeasure.im_toComplexMeasure`, `HasDerivAtFilter.const_sub`, `Ideal.mem_jacobson_bot`, `int_smul_eq_zsmul`, `MvPolynomial.eval₂Hom_comp_expand`, `HasStrictFDerivAt.smul`, `ContinuousLinearMap.orthogonal_ker`, `LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul`, `left_vsub_midpoint`, `Associated.abs_left`, `isReduced_of_noZeroDivisors`, `LinearMap.IsRefl.ker_flip`, `dvd_geom_sum₂_iff_of_dvd_sub'`, `AnalyticAt.hasStrictDerivAt`, `multiplicity_pow_self_of_prime`, `LinearMap.toMatrixAlgEquiv'_comp`, `LinearMap.ker_smul`, `WittVector.peval_polyOfInterest`, `IsSelfAdjoint.nnnorm_pow_two_pow`, `iter_deriv_pow`, `Asymptotics.IsThetaTVS.refl`, `PowerSeries.hasSum_eval₂`, `Asymptotics.IsLittleO.const_smul_left`, `differentiableAt_iteratedDerivWithin_cexp`, `ContDiffMapSupportedIn.norm_toBoundedContinuousFunction`, `AffineMap.coe_homothety`, `ContMDiff.smul_section`, `spectrum.notMem_iff`, `IsArtinianRing.isUnitSubmonoid_eq_nonZeroDivisorsRight`, `TensorProduct.AlgebraTensorModule.tensorTensorTensorComm_tmul`, `pi_mul_cot_pi_q_exp`, `LinearPMap.IsClosable.existsUnique`, `Filter.EventuallyEq.hasDerivWithinAt_iff`, `Matrix.UnitaryGroup.inv_apply`, `Matrix.charpoly_of_card_eq_two`, `aemeasurable_const_smul_iff₀`, `WeierstrassCurve.Jacobian.isUnit_addU_of_Y_ne`, `emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_emultiplicity`, `Seminorm.neg_mem_closedBall_zero`, `LinearMap.toMatrix₂Aux_apply`, `PeriodPair.weierstrassPExcept_add`, `Units.eq_or_eq_neg_of_sq_eq_sq`, `AlgebraicGeometry.Scheme.Modules.map_smul`, `SeminormFamily.basisSets_smul_left`, `AlgebraicGeometry.RingedSpace.mem_basicOpen'`, `LieModule.rank_le_natTrailingDegree_charpoly_ad`, `InnerProductSpace.norm_rankOne`, `MeasureTheory.Measure.ae_smul_measure_eq`, `mem_nilradical`, `IsStrictlyPositive.nonneg_add`, `TensorProduct.quotTensorEquivQuotSMul_mk_tmul`, `Complex.hasDerivAt_Gamma_nat`, `Pi.noZeroSMulDivisors`, `Submodule.unitsQuotEquivRelPic_apply_coe`, `RestrictScalars.addEquiv_map_smul`, `derivationQuotKerSq_mk`, `hasFDerivAt_integral_of_dominated_loc_of_lip`, `LieSubalgebra.coe_ad`, `WithZeroTopology.hasBasis_nhds_units`, `Mathlib.Tactic.Ring.pow_zero`, `IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two`, `smul_eq_zero`, `tendsto_smul_comp_nat_floor_of_tendsto_nsmul`, `Units.add_divp`, `ArchimedeanClass.mk_smul`, `DistribMulActionHom.instSemilinearMapClass`, `IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem`, `TensorProduct.uncurry_apply`, `Polynomial.smeval_mul_X_pow`, `Submodule.map_le_smul_top`, `Antivary.sum_comp_perm_smul_eq_sum_smul_iff`, `Units.chartAt_apply`, `Polynomial.X_sub_C_pow_dvd_iff`, `PiTensorProduct.mapLMultilinear_toFun_apply`, `IsLocalizedModule.eq_zero_iff`, `VectorField.mlieBracket_smul_right`, `MDifferentiable.pow`, `TensorProduct.tensorQuotEquivQuotSMul_symm_comp_mkQ`, `CStarMatrix.inner_toCLM_conjTranspose_right`, `SlashInvariantForm.T_zpow_width_invariant`, `MeasureTheory.taylorWithinEval_charFun_zero`, `HasDerivAtFilter.fun_const_smul`, `Complex.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq`, `instDenselyOrderedUnits`, `AddSubmonoid.pointwise_smul_le_iff₀`, `CFC.isUnit_sqrt_iff`, `instSMulMemClassHomogeneousSubmodule`, `MonomialOrder.degree_pow_of_pow_leadingCoeff_ne_zero`, `LinearIsometryEquiv.map_smulₛₗ`, `EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF`, `AlgebraicGeometry.Scheme.mem_basicOpen`, `LieModule.toEnd_matrix`, `real_inner_I_smul_self`, `AnalyticWithinAt.smul`, `spinGroup.val_toUnits_apply`, `Seminorm.closedBall_smul_closedBall`, `ContinuousAffineMap.toConstProdContinuousLinearMap_snd`, `balancedCore_subset_balancedCoreAux`, `FiniteMultiplicity.mul_iff`, `Orthonormal.inner_right_sum`, `circleEquivGen_apply`, `mellin_comp_mul_right`, `Polynomial.aroots_pow`, `IsLocalizedModule.surj`, `cfcUnits_zpow`, `IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq`, `MvPolynomial.universalFactorizationMapPresentation_jacobian`, `Polynomial.coeff_zero_eq_prod_roots_of_monic_of_splits`, `PointedCone.dual_singleton`, `RingFilterBasis.SubmodulesBasis.smul`, `isCyclic_tfae`, `ContinuousMultilinearMap.curryMidEquiv_symm_apply`, `FormalMultilinearSeries.comp_summable_nnreal`, `Polynomial.integralNormalization_eval₂_leadingCoeff_mul`, `WeierstrassCurve.c₄_of_char_two`, `MvPowerSeries.prod_smul_X_eq_smul_monomial_one`, `LinearMap.sum_repr_mul_repr_mul`, `Polynomial.add_scaleRoots_of_natDegree_eq`, `fderiv_eq_smul_deriv`, `unitary.inner_map_map`, `StrictConvex.add_right`, `CStarMatrix.toCLM_apply_single_apply`, `bernsteinPolynomial.iterate_derivative_at_1`, `ContinuousMultilinearMap.uncurryRight_norm`, `ContinuousLinearMap.flipAlternating_apply_apply`, `LinearMap.ker_toContinuousLinearMap`, `TensorProduct.AlgebraTensorModule.lTensor_tmul`, `Ring.inverse_pow`, `PointedCone.salient_iff_inter_neg_eq_singleton`, `IntermediateField.adjoin_rootSet_isSplittingField`, `LinearOrderedRing.orderOf_le_two`, `IsLocalizedModule.iso_mk_one`, `IntermediateField.nonempty_algHom_adjoin_of_splits`, `Submodule.span_smul_of_span_eq_top`, `IntermediateField.isScalarTower_mid`, `IntermediateField.finSepDegree_bot`, `QuadraticModuleCat.hom_hom_associator`, `Polynomial.C_smul_derivation_apply`, `exists_pos_right_iff_sameRay_and_ne_zero`, `closedConvexHull_isClosed`, `LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple`, `LinearMap.toLinearMap₂'Aux_toMatrix₂Aux`, `LieModule.toEnd_pow_comp_lieHom`, `ZMod.unitsMap_def`, `Polynomial.X_pow_mul_C`, `ContinuousSMul.induced`, `LieHom.toNonUnitalAlgHom_injective`, `Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx_mul`, `UpperHalfPlane.mdifferentiable_smul`, `PointedCone.toConvexCone_injective`, `Subring.centralizer_toSubmonoid`, `HasDerivAt.mul_const`, `LinearMap.isSymm_iff_isHermitian_toMatrix`, `HasStrictDerivAt.fun_smul`, `QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `Monotone.convex_gt`, `ModularForm.slash_apply`, `selfAdjoint.joined_one_expUnitary`, `Multiset.prod_X_sub_C_coeff`, `IsPrimitiveRoot.minpoly_dvd_x_pow_sub_one`, `ContinuousLinearMap.algebraMap_apply`, `sq_eq_zero_iff`, `Subsemiring.le_pointwise_smul_iff₀`, `Matrix.blockDiagonal'_pow`, `MvPowerSeries.truncFinset_truncFinset_pow`, `IsCyclotomicExtension.discr_prime_pow_ne_two'`, `Representation.leftRegularMapEquiv_symm_apply_toFun`, `Seminorm.uniformity_eq_of_hasBasis`, `WeierstrassCurve.Projective.negDblY_of_Y_eq'`, `LinearMap.lsmul_eq_distribSMultoLinearMap`, `IsAzumaya.AlgHom.mulLeftRight_bij`, `MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable`, `Finpartition.IsEquipartition.card_interedges_sparsePairs_le'`, `Polynomial.eval_geom_sum`, `IsPRadical.pow_mem'`, `MDifferentiableWithinAt.smul_section`, `Matrix.toBilin'_single`, `IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed`, `ContMDiffOn.smul_section`, `StarConvex.linear_preimage`, `PadicInt.addChar_of_value_at_one_def`, `IntermediateField.LinearDisjoint.linearIndependent_left`, `Polynomial.isMonicOfDegree_sub_add_two`, `perfectClosure.isPurelyInseparable`, `TensorProduct.liftAux.smulₛₗ`, `Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup`, `contMDiffOn_iff_localFrame_coeff`, `Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply`, `iteratedFDeriv_succ_apply_left`, `Valued.extensionValuation_toFun`, `IsSymmSndFDerivAt.eq`, `WithSeminorms.finset_sups`, `IsMulTorsionFree.pow_right_injective₀`, `le_iff_norm_sqrt_mul_sqrt_inv`, `LinearEquiv.conjAlgEquiv_ext_iff`, `Polynomial.cyclotomic'_eq_X_pow_sub_one_div`, `Polynomial.X_pow_mul`, `WeierstrassCurve.c_relation_of_char_two`, `Submodule.restrictScalars_map`, `IntermediateField.isSeparable_adjoin_iff_isSeparable`, `hasDerivWithinAt_sub_const_iff`, `Convex.linear_preimage`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux`, `IsPrimitiveRoot.pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum`, `TensorProduct.restrictScalar_directSumRight`, `Perfection.coeff_frobenius`, `TensorProduct.includeRight_lid`, `Polynomial.eval_monomial`, `FreeNonUnitalNonAssocAlgebra.lift_comp_of`, `Polynomial.Monic.neg_one_pow_natDegree_mul_comp_neg_X`, `Complex.restrictScalars_toSpanSingleton'`, `AffineSubspace.sOppSide_smul_vsub_vadd_right`, `Matrix.GLPos.coe_neg`, `HasFDerivWithinAt.list_prod'`, `HasFDerivAt.continuousMultilinearMap_apply`, `Complex.hasSum_taylorSeries_on_eball`, `ofMul_uzpow`, `WittVector.mul_charP_coeff_succ`, `exists_smul_eq_of_finrank_eq_one`, `Quaternion.imK_snd_dualNumberEquiv`, `prod_galRestrict_eq_norm`, `Module.Flat.isSMulRegular_of_nonZeroDivisors`, `fderiv_inv'`, `TensorProduct.finsuppLeft_apply_tmul_apply`, `ContinuousLinearMapWOT.ext_inner_iff`, `AdicCompletion.eval_lift`, `PowerSeries.derivative_pow`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le`, `unitary.continuousOn_argSelfAdjoint`, `UniqueFactorizationMonoid.exists_mem_factors_of_dvd`, `NormedSpace.exp_eq_expSeries_sum`, `TwoSidedIdeal.coe_mop_smul`, `ZMod.pow_div_two_eq_neg_one_or_one`, `Perfection.teichmullerFun_eq_teichmuller₀`, `Convex.asymptoticCone`, `Monovary.sum_smul_comp_perm_eq_sum_smul_iff`, `Polynomial.of_irreducible_expand`, `Holor.sum_unitVec_mul_slice`, `GaloisField.splits_zmod_X_pow_sub_X`, `instIsPushoutFractionRingMvPolynomial`, `PolynomialModule.eval_single`, `VectorField.mlieBracket_const_smul_right`, `norm_inner_div_norm_mul_norm_eq_one_iff`, `Valuation.HasExtension.instIsScalarTowerInteger`, `Submodule.disjoint_span_singleton''`, `HasStrictDerivAt.star`, `tendsto_zero_geometric_tsum_pnat`, `Polynomial.eval₂_smulOneHom_eq_smeval`, `Unitary.mulRight_one`, `FormalMultilinearSeries.comp_assoc`, `IsNonarchimedean.add_pow_le`, `egauge_smul_left`, `HasFPowerSeriesWithinAt.comp`, `Matrix.discr_fin_two`, `Polynomial.monic_X_pow_sub`, `IsLocalizedModule.mk'_sub_mk'`, `ContinuousSMul.of_nhds_zero`, `IsAdjoinRootMonic.basis_apply`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul`, `gaussSum_mulShift`, `MvPolynomial.pderiv_inl_universalFactorizationMap_X`, `Algebra.Extension.H1Cotangent.map_toInfinitesimal_bijective`, `Polynomial.isIntegral_isLocalization_polynomial_quotient`, `fderivWithin_pow'`, `Algebra.Extension.Cotangent.val_smul''`, `QuadraticModuleCat.hom_inv_associator`, `ModuleCat.forget₂_map`, `balanced_zero`, `continuousMultilinearCurryFin1_apply`, `Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits`, `NonUnitalStarAlgHom.range_comp`, `locallyConvexSpace_iff_exists_convex_subset`, `IsAlgClosed.perfectRing`, `Matrix.GeneralLinearGroup.val_det_apply`, `RootPairing.reflection_apply_root`, `LineDifferentiableAt.smul`, `Cardinal.mk_quaternionAlgebra`, `StarConvex.mem_smul`, `UpperHalfPlane.petersson_slash`, `IsLocalizedModule.injective_iff_isRegular`, `Matrix.spectrum_toLin'`, `star_intCast_smul`, `associated_normalize`, `RootPairing.reflectionPerm_eq_iff_smul_coroot`, `LinearMap.dualAnnihilator_ker_eq_range_flip`, `OreLocalization.inv_def`, `AdjoinRoot.coe_algEquivOfAssociated`, `unitary.linearIsometryEquiv_coe_apply`, `TensorialAt.smul`, `AdicCompletion.ofAlgEquiv_symm_of`, `HilbertBasis.finite_spans_dense`, `Derivation.apply_aeval_eq`, `Module.notMem_support_iff'`, `LieSubalgebra.ad_comp_incl_eq`, `Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint`, `HasStrictDerivAt.fun_pow`, `RingHom.map_pow`, `WeierstrassCurve.variableChange_b₄`, `Matrix.GeneralLinearGroup.fin_two_smul_prod`, `Ideal.mulQuot_injective`, `LinearIsometry.adjoint_comp_self`, `add_pow_eq_mul_pow_add_pow_div_char`, `Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun`, `ConvexCone.mem_comap`, `emultiplicity_neg`, `WeierstrassCurve.Projective.dblZ_smul`, `Mathlib.Tactic.Ring.pow_atom`, `Matrix.isNilpotent_charpoly_sub_pow_of_isNilpotent`, `MvPolynomial.rTensorAlgHom_apply_eq`
`toMulZeroOneClass` 📖	CompOp	1631 math math: `Finset.sup'_mul_le_mul_sup'_of_nonneg`, `Set.center_units_subset`, `normalize_one`, `nonZeroDivisors_le_comap_nonZeroDivisors_of_injective`, `Valuation.mem_nhds_zero_iff`, `Ordinal.opow_mul`, `GCDMonoid.lcm_zero_right`, `Polynomial.degree_normalize`, `UniqueFactorizationMonoid.factors_one`, `IsGaloisGroup.smul_mem_of_normal`, `Ordinal.lt_omega0_opow_succ`, `unitsEquivNeZero_symm_apply`, `MeasureTheory.eLpNormEssSup_const_smul_le`, `Valued.isOpen_closedball`, `RatFunc.mk_def_of_ne`, `gcd_one_left'`, `HasStrictFDerivAt.fun_mul'`, `sq_lt_one_iff₀`, `RatFunc.liftMonoidWithZeroHom_apply`, `Valuation.IsTrivialOn.valuation_algebraMap_le_one`, `AlgEquiv.moduleEndSelfOp_apply_apply`, `ofDual_toAdd_zero`, `GrpWithZero.forget_map`, `Set.preimage_const_mul_Ioi₀`, `RatFunc.mk_coe_def`, `le_mul_div_mul_left`, `Valuation.inversion_estimate'`, `Homeomorph.coe_mulRight₀`, `Polynomial.roots_normalize`, `Set.image_mul_left_Iio`, `pow_sub_of_lt`, `nonZeroDivisorsLeft_eq_nonZeroSMulDivisors`, `Valuation.FiniteField.algebraMap_le_one`, `Valuation.FiniteField.algebraMap_eq_one`, `mul_inv_cancel_of_invertible`, `neg_of_div_neg_right`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal`, `Ideal.finite_setOf_absNorm_le₀`, `NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet_mixedEmbedding`, `inv_eq_zero`, `isSMulRegular_iff_mem_nonZeroSMulDivisors`, `mul_inf₀`, `MeasureTheory.eLpNorm_smul_le_mul_eLpNorm`, `lcm_dvd_lcm_mul_right`, `mul_inv_eq_mul_inv_iff`, `lcm_eq_zero_iff`, `ClassGroup.mk0_integralRep`, `Valuation.one_apply_lt_one_iff`, `Quaternion.snd_imJ_dualNumberEquiv_symm`, `zero_zpow`, `Valuation.isClopen_closedBall`, `hasStrictFDerivAt_list_prod_finRange'`, `normalize_dvd_iff`, `Ordinal.isNormal_mul_right`, `mul_div_mul_right`, `IsRelPrime.moebius_mul`, `Set.preimage_mul_const_Icc₀`, `ClassGroup.mk0_eq_mk0_iff`, `Valuation.val_mrange_zero`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `Ordinal.exists_lt_mul`, `HasProd.congr_cofinite₀`, `StrictMono.mul`, `div_le_iff₀`, `Valuation.map_one_add_of_lt`, `Multiset.lcm_eq_zero_iff`, `UniqueFactorizationMonoid.moebius_one`, `Valuation.mem_supp_iff`, `Matrix.toLinearMapRight'_mul`, `mem_nonZeroDivisors_iff_left`, `isReduced_of_injective`, `MonoidWithZeroHom.snd_comp_inl`, `MeasureTheory.MemLp.smul`, `Valuation.isEquiv_map_self_of_strictMono`, `gcd_dvd_gcd_mul_right`, `GroupWithZero.conj_pow₀`, `gcd_mul_lcm`, `UniqueFactorizationMonoid.exists_reduced_factors`, `Ordinal.instIsLeftCancelMulZero`, `RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk`, `WithZero.withZeroUnitsEquiv_symm_apply_coe`, `div_sq_cancel`, `Valued.extension_extends`, `Ring.mul_inverse_cancel_right`, `StrictMono.const_mul`, `MulChar.map_one`, `mul_div_mul_right_le`, `Ordinal.principal_mul_of_le_two`, `mul_inv_cancel_left₀`, `mul_eq_of_eq_inv_mul₀`, `Set.natCard_smul_set₀`, `ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors`, `Commute.inv_right_iff₀`, `mul_right_mem_nonZeroDivisors_eq_zero_iff`, `NumberField.RingOfIntegers.instSMulDistribClass`, `OrderIso.mulRight₀_symm`, `pow_pos`, `Set.inv_mem_centralizer₀`, `map_mul_left_nhds_one₀`, `ONote.nf_repr_split'`, `Ordinal.noZeroDivisors`, `Decidable.mul_lt_mul''`, `div_mul_cancel₀`, `MulChar.toMonoidWithZeroHom_apply`, `fderivWithin_fun_pow'`, `IsClosed.smul₀`, `signHom_apply`, `mul_div_cancel_of_invertible`, `Associates.prod_top`, `mul_inv_le_one`, `le_div_iff₀'`, `isClosedEmbedding_cfcₙAux`, `Ring.ordFrac_eq_div`, `gcd_mul_left`, `NNReal.exists_lt_of_strictMono`, `GroupWithZero.isOpen_singleton_zero`, `Ordinal.deriv_add_eq_mul_omega0_add`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst`, `ArithmeticFunction.isMultiplicative_one`, `unitsNonZeroDivisorsEquiv_apply`, `Set.preimage_const_mul_Iio₀`, `Valuation.IsTrivialOn.eq_one`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `Finset.gcd_empty`, `Ordinal.mulRightMono`, `gcd_greatest`, `gauge_smul_of_nonneg`, `Filter.NeBot.zero_div_nonneg`, `WithZeroTopology.nhds_zero`, `UniqueFactorizationMonoid.primeFactors_zero`, `DualNumber.range_lift`, `measurableEmbedding_mulRight₀`, `Valuation.toFun_eq_coe`, `CliffordAlgebraDualNumber.equiv_symm_eps`, `Ordinal.CNF.eval_single_add'`, `associatesEquivOfUniqueUnits_symm_apply`, `WithVal.valueGroupOrderIso₀_restrict`, `GroupWithZero.isConj_iff₀`, `Set.image_mul_left_Ioi`, `MulChar.map_ringChar`, `smulMonoidWithZeroHom_apply`, `zpow_add_one₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `Commute.div_right`, `RatFunc.map_apply_ofFractionRing_mk`, `Ring.inverse_mul_eq_iff_eq_mul`, `Ring.inverse_mul_cancel`, `MonoidWithZeroHom.ValueGroup₀.monoidWithZeroHom_strictMono`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal`, `Ordinal.CNF.coeff_opow_mul_add`, `LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex`, `Multiset.prod_eq_zero`, `Set.image_mul_right_Icc'`, `Pi.single_apply_smul`, `isRightRegular_iff_mem_nonZeroDivisorsRight`, `Normal.minpoly_eq_iff_mem_orbit`, `zpow_left_injOn₀`, `Set.preimage_const_mul_Ioo₀`, `Valued.toUniformSpace_eq`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply`, `lowerBounds_smul_of_pos`, `Quaternion.snd_re_dualNumberEquiv_symm`, `GCDMonoid.toIsCancelMulZero`, `SemiconjBy.div_right`, `HasStrictFDerivAt.mul'`, `le_mul_inv_left`, `emultiplicity_zero_eq_zero_of_ne_zero`, `DFinsupp.prod_eq_zero_iff`, `le_zero_iff`, `Localization.liftOn_zero`, `Ordinal.lt_mul_div_add`, `FractionalIdeal.absNorm_eq'`, `pow_mul_eq_zero_of_le`, `pow_nonneg`, `prime_mul_iff`, `Ordinal.mul_div_gc`, `Valuation.restrict_eq_one_iff`, `GCDMonoid.gcd_mul_lcm`, `Quaternion.imJ_fst_dualNumberEquiv`, `IsFractionRing.mk'_eq_one_iff_eq`, `normUnit_mul_normUnit`, `ENNReal.orderIsoRpow_symm_apply`, `Rat.isFractionRingDen`, `MvPowerSeries.monomial_mem_nonzeroDivisors`, `SemiconjBy.inv_right₀`, `left_mem_segment`, `OreLocalization.nontrivial`, `pow_eq_zero_iff`, `Finsupp.single_smul`, `mul_inv_cancel₀`, `MonoidWithZeroHom.map_eq_zero_iff`, `WithZeroTopology.nhds_zero_of_units`, `mul_left_bijective_of_finite₀`, `ValuationClass.toMonoidWithZeroHomClass`, `Ordinal.add_log_le_log_mul`, `Ideal.absNorm_pos_iff_mem_nonZeroDivisors`, `fderiv_fun_pow'`, `normalize_eq_normalize`, `IsFractionRing.mk'_eq_div`, `Submodule.mem_torsion_iff`, `ArithmeticFunction.isMultiplicative_finsetProd`, `ValuationSubring.mapOfLE_valuation_apply`, `NormalizedGCDMonoid.normalize_lcm`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le`, `pow_eq_zero_of_le`, `RatFunc.liftOn_ofFractionRing_mk`, `mul_eq_of_eq_mul_inv₀`, `Monotone.mul_const`, `inv_mul_le_of_le_mul₀`, `Submonoid.LocalizationMap.mk'_zero`, `Finset.div_zero_subset`, `ValuationSubring.mem_inv_pointwise_smul_iff`, `div_mul_cancel_of_imp`, `Function.support_pow`, `Ordinal.div_le`, `OrderDual.instIsStrictOrderedModule`, `Set.star_inv'`, `Ordinal.isPrincipal_mul_omega0_opow_opow`, `div_self_mul_self`, `Associates.out_one`, `MulChar.one_apply_coe`, `lt_div_iff₀'`, `Filter.tendsto_mul_iff_of_ne_zero`, `Ordinal.lt_mul_iff_div_lt`, `mem_nonZeroDivisors_iff`, `ClassGroup.mk0_eq_one_iff`, `one_le_finprod`, `inv_le_one_iff₀`, `MonoidWithZeroHom.valueGroup.mk_mul`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefree`, `MonoidWithZeroHom.fst_mono`, `Valuation.IsEquiv.restrict`, `lt_inv_mul_iff₀'`, `Int.normalize_of_nonneg`, `RatFunc.liftMonoidWithZeroHom_apply_div'`, `one_lt_inv_iff₀`, `Quaternion.imI_fst_dualNumberEquiv`, `Ordinal.div_lt`, `gcd_dvd_gcd_mul_left_right`, `MvPowerSeries.monomial_mem_nonzeroDivisorsLeft`, `IsReduced.pow_eq_zero_iff'`, `num_isRoot_scaleRoots_of_aeval_eq_zero`, `Ring.inverse_invertible`, `gcd_zero_right'`, `Real.sInf_smul_of_nonneg`, `UniqueFactorizationMonoid.normalizedFactors_zero`, `lt_div_iff₀`, `IsFractionRing.exists_reduced_fraction`, `ConjAct.toConjAct_zero`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion`, `Ordinal.opow_add`, `Ordinal.lt_mul_succ_div`, `ONote.repr_mul`, `Ordinal.div_add_mod`, `List.one_le_prod`, `Ordinal.mul_add_div`, `one_lt_sq_iff₀`, `Valued.isClopen_ball`, `Ordinal.principal_mul_omega0`, `Ordinal.nfp_mul_opow_omega0_add`, `ValuativeRel.ValueGroupWithZero.embed_strictMono`, `Valuation.IsEquiv.pos_iff`, `DualNumber.lift_apply_eps`, `MulActionWithZero.zero_smul`, `Set.image_mul_left_Icc'`, `MeasureTheory.SignedMeasure.singularPart_smul`, `inv_mul_lt_one₀`, `gcd_mul_right'`, `Prime.dvd_mul`, `Multiset.lcm_singleton`, `GrpWithZero.hom_comp`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval`, `HasStrictFDerivAt.list_prod'`, `Valuation.unit_map_eq`, `Real.sSup_smul_of_nonneg`, `NeZero.pow`, `GrpWithZero.coe_id`, `Valuation.hasBasis_nhds_zero`, `inf_mul₀`, `div_mul_cancel_left₀`, `ValuativeExtension.mapValueGroupWithZero_mk`, `mul_div_mul_left_le`, `NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply`, `Nonneg.inv_mk`, `mul_eq_one_iff_inv_eq₀`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff`, `Finset.gcd_eq_zero_iff`, `Ordinal.IsInitial.principal_mul`, `mem_nonZeroSMulDivisors_iff`, `Finset.extract_gcd`, `Ordinal.opow_mul_add_pos`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁`, `Mathlib.Tactic.FieldSimp.NF.cons_pos`, `mul_inv_lt_iff₀`, `MonoidWithZeroHom.valueGroup.mk_inj`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `Commute.zpow_right₀`, `NormedAddGroupHom.isCentralScalar`, `StrictAnti.const_mul`, `closure_smul₀`, `Valuation.restrict_le_iff`, `inv_zero`, `le_mul_div_mul_right`, `Submonoid.LocalizationMap.subsingleton_iff`, `Finset.lcm_singleton`, `Polynomial.Monic.normalize_eq_self`, `CompactlySupportedContinuousMap.toRealLinearMap_apply_apply`, `gcd_eq_normalize`, `Set.image_mul_right_Icc`, `not_prime_zero`, `div_self_mul_self'`, `Valued.is_topological_valuation`, `inv_mul_eq_iff_eq_mul₀`, `Ordinal.mul_lt_of_lt_div`, `Finset.prod_ite_zero`, `Ordinal.mul_lt_omega0_opow`, `IsValuativeTopology.isOpen_ball`, `Ideal.absNorm_ne_zero_iff_mem_nonZeroDivisors`, `coe_inverse`, `MulPosMono.toMulPosStrictMono`, `HasStrictDerivAt.real_of_complex`, `eq_mul_inv_iff_mul_eq₀`, `orderOf_zero`, `range_cfcₙHom`, `Rat.associated_num_den`, `Set.image_const_mul_Ioi_zero`, `MonoidWithZeroHom.one_apply_val_unit`, `one_div_neg`, `RatFunc.mk_eq_localization_mk`, `Ring.mul_inverse_rev'`, `inv_mul_le_one`, `Ordinal.div_mul_cancel`, `Valuation.restrict_eq_zero_iff`, `mul_dvd_mul_iff_right`, `inv_mul_cancel_left₀`, `Ordinal.natCast_mul_omega0`, `factorization_mul`, `MvPowerSeries.mem_nonZeroDivisors_of_constantCoeff`, `Valuation.restrict_eq_mk`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `lt_mul_inv_iff₀`, `Equiv.divRight₀_symm_apply`, `Valuation.one_apply_of_ne_zero`, `Valued.continuous_valuation`, `mul_lt_one_of_nonneg_of_lt_one_left`, `rank_lt_rank_dual'`, `RatFunc.mk_eq_mk'`, `GrpWithZero.coe_comp`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst`, `inv_mul_le_one₀`, `ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem`, `le_inv_mul_right`, `ArithmeticFunction.IsMultiplicative.multiplicative_factorization`, `Multiset.prod_nonneg`, `OrderMonoidWithZeroHom.mul_comp`, `Monotone.mul_strictMono`, `PosMulReflectLT.toPosMulReflectLE`, `Valuation.restrict_lt_iff_lt_embedding`, `Set.preimage_const_mul_Ico₀`, `NormalizationMonoid.normUnit_zero`, `OrderIso.divRight₀_symm_apply`, `UniqueFactorizationMonoid.normalize_normalized_factor`, `Associates.out_mk`, `CompactlySupportedContinuousMap.coe_toRealLinearMap`, `ValuationSubring.smul_mem_pointwise_smul_iff`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `pow_inv_comm₀`, `div_helper`, `Quaternion.fst_imK_dualNumberEquiv_symm`, `Commute.inv_left_iff₀`, `normalize_eq_normalize_iff`, `Ordinal.isPrincipal_mul_omega0`, `ValuativeExtension.mapValueGroupWithZero_strictMono`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `fderiv_mul_const'`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `DualNumber.fst_eq_zero_iff_eps_dvd`, `IsValuativeTopology.isClopen_sphere`, `nonZeroDivisors_dvd_iff_dvd_coe`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero`, `TrivSqZeroExt.inl_mul_inr`, `IsNilpotent.smul`, `inv_mul_lt_iff₀`, `IsSelfAdjoint.zpow₀`, `zero_div`, `OrderMonoidIso.withZeroUnits_symm_apply`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_of_ne_zero`, `MonoidWithZeroHom.inl_strictMono`, `mul_left_mem_nonZeroDivisors_eq_zero_iff`, `Polynomial.leadingCoeff_normalize`, `mul_lt_one_of_nonneg_of_lt_one_right`, `inv_mul_eq_inv_mul_iff`, `MvPowerSeries.monomial_mem_nonzeroDivisorsRight`, `Valuation.coe_coe`, `Valuation.subgroups_basis`, `IsGaloisGroup.mulEquivCongr_apply_smul`, `OrderMonoidIso.withZeroUnits_apply`, `Ordinal.mul_mod`, `UniqueFactorizationMonoid.normalizedFactors_mul`, `zero_zpow_eq`, `ofAdd_bot`, `Valuation.IsEquiv.one_lt_iff_one_lt`, `Ordinal.principal_mul_ord`, `Set.div_mem_centralizer₀`, `Ordinal.log_opow_mul`, `powMonoidWithZeroHom_apply`, `Ordinal.opow_one_add`, `Valued.isOpen_sphere`, `DualNumber.lift_inlAlgHom_eps`, `Valuation.restrict_le_iff_le_embedding`, `Finset.sup'_mul₀`, `Associates.factors_zero`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `IsDedekindDomain.HeightOneSpectrum.valuation_def`, `val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe`, `UniqueFactorizationMonoid.normalizedFactors_one`, `List.prod_map_lt_prod_map`, `Ordinal.opow_mul_add_lt_opow`, `Prime.not_dvd_mul`, `Ordinal.smul_eq_mul`, `Finset.le_prod_max_one`, `mem_nonZeroDivisors_iff_right`, `Multiset.prod_eq_zero_iff`, `Commute.div_left`, `Fintype.prod_ite_zero`, `mul_mem_nonZeroDivisorsLeft_of_mem_nonZeroDivisorsLeft`, `lcm_mul_left`, `pow_succ_nonneg`, `isUnit_gcd_one_right`, `OrderIso.withZeroUnits_symm_apply`, `Valuation.isEquiv_restrict`, `isRadical_iff_squarefree_or_zero`, `UniqueFactorizationMonoid.primeFactors_one`, `mulLeft_bijective₀`, `not_isNilpotent_one`, `Prime.not_dvd_one`, `monotone_mul_right_of_nonneg`, `sq_le_one_iff₀`, `cfcₙAux_id`, `lt_mul_right`, `DualNumber.isNilpotent_iff_eps_dvd`, `one_le_pow₀`, `le_mul_inv_iff₀'`, `one_lt_pow_iff_of_nonneg`, `DualNumber.isMaximal_span_singleton_eps`, `Finset.prod_le_one`, `mul_le_of_le_div₀`, `ConjAct.ofConjAct_zero`, `IsUnit.mul_left_eq_zero`, `zpow_left_strictMonoOn₀`, `ArithmeticFunction.IsMultiplicative.map_prod_of_prime`, `Valuation.RankOne.exists_val_lt`, `exists_right_inv_of_exists_left_inv`, `MonoidWithZeroHom.valueGroup_eq_range`, `fderiv_pow'`, `Ordinal.CNF.eval_single`, `Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes`, `Submonoid.LocalizationMap.nonZeroDivisors_le_comap`, `CompactlySupportedContinuousMap.toRealLinearMap_apply`, `OreLocalization.subsingleton_iff`, `Valued.hasBasis_nhds_zero`, `Ordinal.iSup_mul_nat`, `pow_eq_zero_iff'`, `MulChar.coe_mk`, `DualNumber.lift_smul`, `Finset.gcd_mul_left`, `Ordinal.lt_mul_add_one_iff`, `associated_zero_iff_eq_zero`, `sq_pos_of_pos`, `GrpWithZero.Iso.mk_hom`, `Quaternion.imK_fst_dualNumberEquiv`, `Submonoid.LocalizationMap.noZeroDivisors`, `Finset.normalize_lcm`, `lift_rank_lt_rank_dual'`, `NonUnitalRingHom.one_def`, `Ordinal.instPosMulStrictMono`, `mul_inv_lt_of_lt_mul₀`, `RatFunc.liftMonoidWithZeroHom_apply_div`, `not_isUnit_zero`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `pos_nilpotencyClass_iff`, `Quaternion.re_fst_dualNumberEquiv`, `zero_pow_eq_one₀`, `MulPosReflectLE.of_posMulReflectLT_of_mulPosMono`, `FractionalIdeal.canonicalEquiv_mk0`, `Valuation.toMonoidWithZeroHom_one`, `gcd_eq_zero_iff`, `QuadraticAlgebra.star_mem_nonZeroDivisors_iff`, `SignType.castHom_apply`, `Set.inv_zero`, `Nonneg.coe_pow`, `MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm'`, `associatesNonZeroDivisorsEquiv_mk_mk`, `mulMonoidWithZeroHom_apply`, `Multiset.extract_gcd'`, `zpow_add'`, `Valuation.HasExtension.val_map_le_one_iff`, `IsUnit.mul_right_eq_zero`, `Ordinal.nfp_mul_eq_opow_omega0`, `inv_mul_mul_self`, `fderivWithin_fun_mul'`, `coe_nonZeroDivisorsRight_eq`, `SemiconjBy.zpow_right₀`, `mul_div_cancel_left₀`, `mul_inv_le_iff₀`, `hasFDerivAt_list_prod'`, `MulChar.eq_one_iff`, `Polynomial.notMem_nonZeroDivisors_iff`, `Matrix.toLinearMapRight'_mul_apply`, `Finset.mul_inf_le_inf_mul_of_nonneg`, `div_eq_iff_mul_eq`, `Finset.gcd_eq_gcd_filter_ne_zero`, `IsFractionRing.mk'_num_den'`, `nhds_translation_mul_inv₀`, `ONote.repr_scale`, `ValuativeExtension.mapValueGroupWithZero_valuation`, `Set.preimage_const_mul_Ici₀`, `one_div_nonneg`, `Prime.not_isSquare`, `associatesNonZeroDivisorsEquiv_symm_mk_mk`, `fderiv_mul'`, `finprod_zero_le_one`, `Multiset.extract_gcd`, `mul_mul_div`, `dvd_mul_gcd_of_dvd_mul`, `instSMulDistribClassAlgEquiv`, `UniqueFactorizationMonoid.normalizedFactorsEquiv_symm_apply`, `Polynomial.smeval_C`, `pow_mul_apply_eq_pow_mul`, `isRelPrime_zero_right`, `IsFractionRing.div_surjective`, `inv_pos`, `inv_nonneg_of_nonneg`, `ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀`, `pow_lt_one_iff_of_nonneg`, `MonoidWithZeroHom.one_comp`, `Multiset.gcd_singleton`, `Ordinal.nfp_mul_zero`, `MulChar.val_neg_one_eq_one_of_odd_order`, `Commute.inv_mul_eq_inv_mul_iff`, `MeasureTheory.MemLp.const_smul`, `Valued.coe_valuation_eq_rankOne_hom_comp_valuation`, `Multiset.prod_map_nonneg`, `isPrimal_zero`, `isNilpotent_iff_eq_zero`, `IsNilpotent.eq_zero_of_isIdempotentElem`, `mul_left_coe_nonZeroDivisors_eq_zero_iff`, `Associates.normalize_out`, `MonoidWithZeroHom.fst_comp_inl`, `mul_le_of_le_inv_mul₀`, `div_nonpos_of_nonpos_of_nonneg`, `Ordinal.isSuccPrelimit_mul_right`, `MulChar.coe_toMonoidHom`, `UniqueFactorizationMonoid.radical_of_prime`, `Valuation.map_add_le_max'`, `IsIdempotentElem.iff_eq_zero_or_one`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_range_eq_top`, `Polynomial.content_C_mul`, `Ring.mul_inverse_cancel`, `Multiset.lcm_zero`, `eq_zero_of_zpow_eq_zero`, `Valued.isClosed_ball`, `Valuation.zero_iff`, `dvd_cancel_right_coe_nonZeroDivisors`, `mul_right_coe_nonZeroDivisors_eq_zero_iff`, `Valuation.restrict_lt_one_iff`, `MonoidWithZeroHom.one_apply_apply_eq`, `lcm_dvd_mul`, `strictMono_mul_right_of_pos`, `HahnSeries.map_one`, `one_lt_mul`, `Ideal.span_singleton_nonZeroDivisors`, `hasFDerivWithinAt_pow'`, `IsArtinianRing.isUnit_iff_mem_nonZeroDivisors`, `LinearMap.ker_toSpanSingleton_eq_bot_iff`, `Set.univ_smul_nhds_zero`, `ArithmeticFunction.IsMultiplicative.prod_primeFactors`, `gcd_one_left`, `zero_zpow_eq_one₀`, `PNat.equivNonZeroDivisorsNat_symm_apply_coe`, `IsFractionRing.isUnit_map_of_injective`, `MulCharClass.toMonoidHomClass`, `map_mem_nonZeroDivisors`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `ContinuousInv₀.of_nhds_one`, `continuousOn_div`, `emultiplicity_zero`, `Valued.isClopen_sphere`, `UniqueFactorizationMonoid.multiplicative_of_coprime`, `Int.normalize_coe_nat`, `normalize_eq_zero`, `lcm_mul_right`, `div_mul_div_cancel₀'`, `Finset.inv_zero`, `MulPosReflectLT.toMulPosStrictMono`, `map_eq_zero`, `LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ`, `Valued.isClosed_sphere`, `IsValuativeTopology.isClosed_closedBall`, `Ring.isUnit_iff_mul_inverse_cancel`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `factorization_zero`, `Polynomial.normalize_content`, `le_inv_mul_iff₀'`, `zero_eq_inv`, `FiniteField.valuation_algebraMap_eq_one`, `div_eq_div_iff`, `ThreeGPFree.smul_set₀`, `fderivWithin_mul_const'`, `val_unitsNonZeroDivisorsEquiv_symm_apply_coe`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_apply`, `inv_neg''`, `Valuation.one_apply_eq_zero_iff`, `NormalizedGCDMonoid.normalize_gcd`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_mk'`, `Finsupp.prod_eq_zero_iff`, `hasFDerivAt_list_prod_finRange'`, `zero_isRadical_iff`, `Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe`, `normalize_gcd`, `strictMonoOn_mul_self`, `Finsupp.support_sym2Mul_subset`, `Commute.zpow_zpow_self₀`, `Ring.inverse_pow_mul_eq_iff_eq_mul`, `Valuation.cauchy_iff`, `normalize_apply`, `isReduced_iff_pow_one_lt`, `mul_inv_le_one_of_le₀`, `Ordinal.principal_mul_omega`, `range_cfcₙHom_le`, `IsSelfAdjoint.inv₀`, `Valuation.apply_posSubmonoid_pos`, `Valuation.one_srel_iff`, `Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg`, `MulDivCancelClass.mul_div_cancel`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `not_isRelPrime_zero_zero`, `Commute.ringInverse_ringInverse`, `Set.image_mul_left_Ioc`, `notMem_nonZeroDivisors_iff`, `dvd_mul_gcd_iff_dvd_mul`, `UniqueFactorizationMonoid.primeFactors_mul_eq_union`, `inv_mul_eq_one₀`, `Valuation.IsRankOneDiscrete.embedding_generator'`, `UniqueFactorizationMonoid.primeFactors_mul_eq_disjUnion`, `WithZeroTopology.isClosed_iff`, `zpow_eq_zero_iff`, `List.prod_pos`, `eq_inv_mul_iff_mul_eq₀`, `Ordinal.mul_eq_right_iff_opow_omega0_dvd`, `Ordinal.mul_succ`, `Mathlib.Meta.NormNum.isNat_ordinalMul`, `inv_lt_iff_one_lt_mul₀`, `gauge_smul_left_of_nonneg`, `WithZeroTopology.hasBasis_nhds_zero`, `zpow_nonneg`, `Finset.lcm_empty`, `MonomialOrder.mem_nonZeroDivisors_of_leadingCoeff_mem_nonZeroDivisors`, `hasProd_zero_of_exists_eq_zero`, `Quaternion.fst_imJ_dualNumberEquiv_symm`, `map_le_nonZeroDivisors_of_injective`, `Finset.Nonempty.zero_div`, `NumberField.Ideal.tendsto_norm_le_div_atTop₀`, `MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit`, `IsLeftRegular.mem_nonZeroDivisorsLeft`, `IsUnit.isNilpotent_unit_mul_of_commute_iff`, `Ordinal.opow_mul_add_lt_opow_mul`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `div_lt_iff₀`, `ValuationSubring.monotone_mapOfLE`, `Prime.dvd_prod_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight`, `one_le_inv_iff₀`, `Set.preimage_mul_const_Ioo₀`, `Finset.inv_smul_finset_distrib₀`, `div_nonpos_of_nonneg_of_nonpos`, `Valuation.restrict_inj`, `HasFDerivWithinAt.mul_const'`, `Units.mul_right_eq_zero`, `Filter.top_smul_nhds_zero`, `ValuativeRel.RankLeOneStruct.strictMono`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `mul_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `Valued.integer.mulArchimedean_mrange_of_isCompact_integer`, `Associated.eq_zero_iff`, `Padic.valuation_p_lt_one`, `pow_left_monotoneOn`, `Matrix.dualNumberEquiv_symm_apply`, `le_mul_inv_right`, `Valuation.embedding_restrict`, `Ordinal.principal_add_mul_of_principal_add`, `DualNumber.exp_eps`, `Commute.zpow_self₀`, `Valuation.map_mul`, `not_isPrimePow_zero`, `Submodule.annihilator_top_inter_nonZeroDivisors`, `fderiv_pow_ring'`, `lt_mul_inv_iff₀'`, `sup_mul₀`, `mul_div_cancel_of_imp'`, `DirichletCharacter.modOne_eq_one`, `zero_pow_le_one`, `Ring.isUnit_iff_inverse_mul_cancel`, `Set.inv_smul_set_distrib₀`, `IsSMulRegular.zero`, `Polynomial.Monic.mem_nonZeroDivisors`, `ArithmeticFunction.IsMultiplicative.map_one`, `Quaternion.fst_imI_dualNumberEquiv_symm`, `Valued.valuation_isClosedMap`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval`, `IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral`, `rank_dual_eq_card_dual_of_aleph0_le_rank'`, `mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff`, `mul_inv_cancel_right₀`, `Set.image_mul_right_Ioo`, `mul_right_mem_nonZeroDivisorsRight_eq_zero_iff`, `IsNilpotent.map`, `Valued.closure_coe_completion_v_mul_v_lt`, `normalize_coe_units`, `Ordinal.lt_div`, `Polynomial.mem_nonZeroDivisors_iff`, `Polynomial.mem_nonZeroDivisors_of_trailingCoeff`, `Submonoid.IsLocalizationMap.map_zero`, `WfDvdMonoid.max_power_factor`, `ONote.repr_opow_aux₁`, `Ordinal.iSup_mul_natCast`, `Valued.cauchy_iff`, `Valuation.one_apply_le_one`, `mul_one_div_cancel`, `extract_gcd`, `Mathlib.Tactic.FieldSimp.list_prod_zpow'`, `gcd_one_right`, `gcd_mul_dvd_mul_gcd`, `den_dvd_of_is_root`, `mul_div_cancel₀`, `Ordinal.IsInitial.isPrincipal_mul`, `IsRightRegular.mem_nonZeroDivisorsRight`, `IsFractionRing.associated_num_den_inv`, `Units.mk0_mul`, `Set.image_mul_left_Icc`, `Valuation.map_one_sub_of_lt`, `eq_zero_of_nilpotencyClass_eq_one`, `Ordinal.log_opow_mul_add`, `mul_eq_one_iff_eq_inv₀`, `mk_mem_nonZeroDivisors_associates`, `noZeroDivisors_iff_forall_mem_nonZeroDivisors`, `Associates.instNoZeroDivisors`, `HasFDerivAt.fun_pow'`, `Right.inv_nonneg`, `Prime.dvd_finsuppProd_iff`, `lcm_dvd_lcm_mul_right_right`, `MonoidWithZeroHom.inr_mono`, `Valuation.extendToLocalization_mk'`, `IsIdempotentElem.eq_zero_of_isNilpotent`, `HasMFDerivWithinAt.mul'`, `Ideal.card_norm_le_eq_card_norm_le_add_one`, `Homeomorph.mulLeft₀_symm_apply`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply`, `Associates.mk_normalize`, `eq_zero_of_ne_zero_of_mul_right_eq_zero`, `zpow_pos`, `Prime.not_dvd_prod`, `inv_pos_of_pos`, `Ordinal.natCast_mul`, `Submonoid.LocalizationMap.map_nonZeroDivisors_le`, `DualNumber.lift_apply_apply`, `Set.preimage_mul_const_Iic₀`, `Ordinal.mul_mod_mul`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `UniqueFactorizationMonoid.radical_one`, `mulPosReflectLE_iff_mulPosReflectLT`, `MulChar.mul_apply`, `IsNilpotent.pow_succ`, `Valuation.map_one`, `mul_inv_left_le`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_right`, `Ring.inverse_non_unit`, `TrivSqZeroExt.inr_mul_inl`, `IsLocalization.nonZeroDivisors_le_comap`, `Finset.zero_div_subset`, `Polynomial.mem_nonZeroDivisors_of_leadingCoeff`, `strictMono_mul_left_of_pos`, `MulEquivClass.map_nonZeroDivisors`, `Units.mul_inv'`, `gcd_same`, `Cardinal.mk_smul_set₀`, `DualNumber.ringHom_ext_iff`, `LinearMap.toMatrixRight'_id`, `eq_zero_or_one_of_sq_eq_self`, `Ordinal.le_mul_right`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul`, `Ordinal.add_eq_right_iff_mul_omega0_le`, `Finset.extract_gcd'`, `Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe`, `Valuation.restrict_pos_iff`, `Commute.zpow_left₀`, `gcd_zero_right`, `MonoidWithZeroHom.snd_inr`, `MonoidWithZeroHom.snd_inl_apply_of_ne_zero`, `Ordinal.mul_add_div_mul`, `Valuation.one_vlt_iff`, `cfcₙAux_injective`, `Ordinal.nsmul_eq_mul`, `IsValuativeTopology.isClopen_ball`, `isUnit_zero_iff`, `WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv`, `divisor_closure_eq_closure`, `mem_nonZeroDivisors_iff'`, `mul_self_mul_inv`, `mul_le_of_le_mul_inv₀`, `Pi.single_smul₀`, `nilpotencyClass_eq_one`, `mul_div_cancel_right₀`, `MulChar.restrict_eq_one_iff`, `lcm_one_left`, `gcd_neg'`, `Set.indicator_pi_one_apply`, `IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral'`, `Valuation.one_vle_iff`, `Mathlib.Tactic.FieldSimp.zpow'_eq_zero_iff`, `Valuation.restrict_def`, `MonoidWithZeroHom.inl_injective`, `ArithmeticFunction.prodPrimeFactors_apply`, `lcm_dvd_lcm_mul_left`, `one_lt_mul_of_le_of_lt`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_surjective`, `ClassGroup.mk_mk0`, `Set.image_mul_left_Ico`, `lt_inv_mul_iff₀`, `Prime.finiteMultiplicity_mul`, `mul_inv_right_le`, `Ordinal.nfp_add_eq_mul_omega0`, `MeasureTheory.eLpNorm_const_smul_le`, `one_le_pow_iff_of_nonneg`, `isLeftRegular_iff_mem_nonZeroDivisorsLeft`, `Set.inv_Ioi₀`, `Ordinal.mul_add_mod_self`, `IsPrimitiveRoot.injOn_pow_mul`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons`, `ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring`, `one_le_sq_iff₀`, `IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt`, `hasStrictFDerivAt_pow'`, `Ordinal.mul_eq_opow_log_succ`, `Valuation.IsEquiv.eq_zero`, `Bound.one_lt_mul`, `Ideal.absNorm_pos_of_nonZeroDivisors`, `IsLeftCancelMulZero.toFaithfulSMul_opposite`, `DualNumber.coe_lift_symm_apply`, `Matrix.ProjGenLinGroup.signDet_mk`, `mul_eq_mul_prime_pow`, `Quaternion.imJ_snd_dualNumberEquiv`, `Set.preimage_const_mul_Icc₀`, `fderiv_fun_mul'`, `Valuation.isClosed_closedBall`, `UniqueFactorizationMonoid.radical_zero`, `Units.exists0'`, `Ordinal.leftDistribClass`, `NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet`, `smul_zpow₀'`, `MeasureTheory.Lp.coeFn_lpSMul`, `Int.normalize_of_nonpos`, `GroupWithZero.dvd_iff`, `zpow_add₀`, `Multiset.one_le_prod`, `Ordinal.lt_omega0_opow`, `Function.support_inv`, `le_inv_mul_iff₀`, `NonUnitalRingHom.coe_one`, `Quaternion.snd_imK_dualNumberEquiv_symm`, `antitoneOn_inv_pos`, `spec_cfcₙAux`, `gcd_mul_left'`, `MulChar.one_apply`, `mul_dvd_mul_iff_left`, `MeasurableSet.const_smul₀`, `RatFunc.liftMonoidWithZeroHom_injective`, `unitsEquivNeZero_apply_coe`, `finprod_eq_zero`, `Finset.prod_eq_zero_iff`, `RatFunc.liftAlgHom_apply_ofFractionRing_mk`, `Finset.inv_op_smul_finset_distrib₀`, `List.prod_eq_zero`, `Associates.out_eq_zero_iff`, `hasStrictFDerivAt_list_prod_attach'`, `isUnit_iff_mem_nonZeroDivisors_of_finite`, `Prime.not_dvd_finsuppProd`, `IsValuativeTopology.isOpen_closedBall`, `MvPowerSeries.mem_nonZeroDivisorsLeft_of_constantCoeff`, `Finset.gcd_singleton`, `div_eq_iff`, `WfDvdMonoid.max_power_factor'`, `normalize_lcm`, `inv_nonneg`, `LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ`, `zero_pow_eq`, `Valuation.integer.v_irreducible_pos`, `lcm_same`, `Ordinal.isSuccLimit_mul`, `Submonoid.mem_nonunits_iff_or`, `Ordinal.CNF.foldr`, `Set.image_mul_right_Ioc`, `Valuation.toTopologicalSpace_eq`, `SemiconjBy.inv_symm_left₀`, `Associates.factors_eq_top_iff_zero`, `Valuation.leIdeal_zero`, `inv_mul_left_le`, `pow_le_one_iff_of_nonneg`, `Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos`, `Valuation.map_apply`, `Function.support_div'`, `IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq`, `Polynomial.normalize_eq_self_iff_monic`, `LinearOrderedCommGroupWithZero.fst_comp_inl`, `smul_floorDiv`, `Set.preimage_mul_const_Ici₀`, `inv_mul_lt_of_lt_mul₀`, `mul_right_surjective₀`, `OreLocalization.nontrivial_of_nonZeroDivisorsRight`, `Finsupp.coe_sym2Mul`, `Associates.out_zero`, `coe_powMonoidWithZeroHom`, `GroupWithZero.mul_right_injective`, `not_lt_zero'`, `Irreducible.normalizedFactors_pow`, `Submonoid.LocalizationMap.map_zero`, `CompactlySupportedContinuousMap.toNNRealLinear_apply`, `Ordinal.isPrincipal_mul_of_le_two`, `Submonoid.instMonoidWithZeroHomClassLocalizationMap`, `WithZeroTopology.isOpen_iff`, `associatesEquivOfUniqueUnits_apply`, `List.prod_eq_zero_iff`, `mul_cancel_right_coe_nonZeroDivisors`, `inv_mul_le_iff₀`, `Valuation.toMonoidWithZeroHom_coe_eq_coe`, `WithZeroTopology.instContinuousMul`, `div_mul_cancel_of_invertible`, `Valuation.srel_one_iff`, `DualNumber.range_inlAlgHom_sup_adjoin_eps`, `QuadraticAlgebra.star_mem_nonZeroDivisors`, `GCDMonoid.lcm_zero_left`, `floorDiv_one`, `MonoidWithZeroHom.snd_mono`, `Finset.sup_mul_le_mul_sup_of_nonneg`, `posMulReflectLE_iff_posMulReflectLT`, `UniqueFactorizationMonoid.normalizedFactors_irreducible`, `Int.abs_eq_normalize`, `Valuation.IsUniformizer.val_pos`, `tprod_of_exists_eq_zero`, `Valuation.isClopen_ball`, `smul_ceilDiv`, `div_le_div_iff₀`, `MeasureTheory.Integrable.smul_essSup`, `Matrix.toLinearMapRight'_apply`, `div_lt_iff₀'`, `Ordinal.mulLeftMono`, `Set.preimage_const_mul_Ioc₀`, `UniqueFactorizationMonoid.moebius_zero`, `HasFDerivWithinAt.pow'`, `Associates.instIsCancelMulZero`, `NumberField.exists_ideal_in_class_of_norm_le`, `ArithmeticFunction.IsMultiplicative.eq_iff_eq_on_prime_powers`, `Valuation.vle_one_iff`, `eq_zero_of_ne_zero_of_mul_left_eq_zero`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective`, `IsReduced.pow_eq_zero_iff`, `HasFDerivAt.list_prod'`, `IsUnit.isNilpotent_mul_unit_of_commute_iff`, `lcm_units_coe_left`, `RatFunc.liftRingHom_apply_ofFractionRing_mk`, `hasFDerivAt_pow'`, `Ordinal.principal_mul_two`, `mul_le_one₀`, `coe_nonZeroDivisorsLeft_eq`, `Valuation.Integers.valuation_pos_iff_ne_zero`, `zero_pow_eq_zero`, `Valued.isOpen_closedBall`, `Ordinal.deriv_mul_eq_opow_omega0_mul`, `ceilDiv_one`, `MeasureTheory.Lp.smul_def`, `Ordinal.isPrincipal_mul_omega`, `MonoidWithZeroHom.fst_apply_coe`, `MonoidWithZeroHom.fst_inl`, `MonoidWithZeroHom.fst_surjective`, `gcd_dvd_gcd_mul_right_right`, `Valuation.hasBasis_nhds`, `mem_nonZeroDivisorsLeft_iff`, `Ordinal.principal_mul_iff_mul_left_eq`, `nonZeroDivisors.associated_coe`, `Valuation.IsEquiv.one_le_iff_one_le`, `Finset.prod_pos`, `IsGaloisGroup.coe_quotient_smul`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `Finset.gcd_div_id_eq_one`, `gcd_zero_left`, `Valued.mem_nhds_zero`, `Valuation.RankLeOne.exists_val_lt`, `IsArtinianRing.isUnit_iff_mem_nonZeroDivisors_of_mulOpposite`, `squarefree_mul_iff`, `not_irreducible_zero`, `Valuation.HasExtension.val_map_eq_one_iff`, `mul_eq_mul_of_div_eq_div`, `Ring.inverse_one`, `PNat.equivNonZeroDivisorsNat_apply_coe`, `DualNumber.algHom_ext_iff`, `Valued.isOpen_ball`, `OrderDual.instIsOrderedModule`, `one_le_inv_mul₀`, `HasDerivAt.real_of_complex`, `mulRight_bijective₀`, `Valued.mem_nhds`, `OrderMonoidWithZeroHom.coe_mul`, `eq_div_iff_mul_eq`, `Set.preimage_mul_const_Ico₀`, `inv_pow_sub₀`, `zpow_sub_one₀`, `Ordinal.forall_lt_mul`, `pow_lt_one₀`, `AlgEquiv.moduleEndSelf_apply_apply`, `Ordinal.mul_div_cancel`, `NNReal.orderIsoRpow_symm_eq`, `ofDual_toAdd_eq_top_iff`, `UniqueFactorizationMonoid.normalizedFactors_prod_eq`, `multiplicity_mul`, `MonoidWithZeroHom.snd_comp_inr`, `smul_inv₀`, `NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply`, `Valuation.isOpen_ball`, `boole_smul`, `UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors`, `ArithmeticFunction.pdiv_apply`, `Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer`, `ValuationSubring.coe_pointwise_smul`, `ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity`, `Ordinal.add_mul_of_isSuccLimit`, `count_span_normalizedFactors_eq`, `NormedDivisionRing.toNormSMulClass`, `Finset.prod_boole`, `Ordinal.card_mul`, `Set.image_mul_left_Iic`, `mul_inv_eq_one₀`, `smul_div₀'`, `mul_div_cancel_left_of_imp`, `IsNilpotent.map_iff`, `Matrix.isAdjMatrix_iff_hadamard`, `one_lt_mul_of_lt_of_le`, `instIsCancelMulZero`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `finiteMultiplicity_mul_aux`, `Valuation.rel_one_iff`, `NonUnitalRingHom.mul_def`, `Finset.support_prod_subset`, `CliffordAlgebraDualNumber.equiv_ι`, `IsPrimal.mul`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero`, `gcd_one_right'`, `Ordinal.mul_le_right_iff_opow_omega0_dvd`, `Valuation.IsEquiv.eq_one_iff_eq_one`, `Ordinal.mul_sub`, `isRegular_iff_mem_nonZeroDivisors`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `Finset.prod_eq_zero`, `IsUnit.mem_nonZeroDivisors`, `MonoidWithZeroHom.inr_apply_unit`, `cfcₙAux_mem_range_inr`, `Polynomial.X_mem_nonzeroDivisors`, `IsValuativeTopology.isClosed_ball`, `Ring.inverse_mul_cancel_right`, `ArithmeticFunction.IsMultiplicative.map_prod`, `one_div_pos`, `Set.Nonempty.div_zero`, `multiplicity_zero_eq_zero_of_ne_zero`, `AlgEquiv.moduleEndSelfOp_symm_apply`, `biUnion_associatedPrimes_eq_compl_nonZeroDivisors`, `Right.inv_pos`, `inv_le_iff_one_le_mul₀`, `Polynomial.smeval_monomial`, `inv_pow_sub_of_lt`, `NoZeroSMulDivisors.isReduced`, `inv_lt_zero`, `gcd_mul_right`, `inv_mul_right_le`, `le_nonZeroDivisors_of_noZeroDivisors`, `le_mul_inv_iff₀`, `UniqueFactorizationMonoid.radical_of_isUnit`, `UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors`, `LinearOrderedCommGroupWithZero.fst_apply`, `map_mul_right_nhds₀`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `GrpWithZero.hom_id`, `right_mem_segment`, `Valuation.vlt_one_iff`, `inv_le_iff_one_le_mul₀'`, `IsSMulRegular.not_zero`, `not_isPrimePow_one`, `DualNumber.instIsLocalRing`, `Ordinal.opow_add_one`, `IsFractionRing.num_mul_den_eq_num_iff_eq`, `mul_self_lt_mul_self`, `IsGaloisGroup.smul_eq_self`, `VectorField.mpullback_mfderivWithin_apply_smul`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `Ordinal.principal_mul_omega0_opow_opow`, `mul_div_mul_left`, `UniqueFactorizationMonoid.multiplicative_prime_power`, `HahnModule.one_smul'`, `mem_nonZeroDivisors_of_ne_zero`, `Valuation.hasBasis_uniformity`, `inv_mul_cancel_of_invertible`, `dvd_normalize_iff`, `zpow_neg_mul_zpow_self`, `isUnit_gcd_one_left`, `IsNilpotent.pow_iff_pos`, `Valued.toNormedField.norm_def`, `inv_mul_lt_iff₀'`, `IsSelfAdjoint.inv₀_iff`, `Ordinal.omega0_opow_mul_nat_lt`, `ClassGroup.exists_mk0_eq_mk0`, `pow_sub₀`, `Finset.one_le_prod`, `MeasureTheory.integrable_smul_iff`, `Valuation.toUniformSpace_eq`, `MulChar.map_nonunit`, `associated_normalize_iff`, `DirichletCharacter.apply_eq_toArithmeticFunction_apply`, `IsPrimitiveRoot.zero`, `Valuation.isOpen_sphere`, `not_squarefree_zero`, `Valuation.IsEquiv.le_one_iff_le_one`, `HasFDerivAt.pow'`, `HasStrictFDerivAt.pow'`, `Multiset.normalize_lcm`, `Valuation.norm_def`, `Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange`, `zero_mem_nonunits`, `NormalizationMonoid.normUnit_mul`, `NonUnitalRingHom.coe_mul`, `ArithmeticFunction.pmul_comm`, `Ring.not_isUnit_iff_inverse_eq_zero`, `inv_lt_iff_one_lt_mul₀'`, `nonZeroDivisorsEquivUnits_apply`, `Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMul`, `ClassGroup.mk0_surjective`, `zero_le'`, `MulChar.restrict_apply`, `OreLocalization.mul_inv_cancel`, `mem_nonZeroDivisors_iff_ne_zero`, `Associates.out_mul`, `normUnit_one`, `MonoidWithZeroHom.fst_inr_apply_of_ne_zero`, `Ordinal.lt_mul_iff_of_isSuccLimit`, `Valuation.exists_div_eq_of_unit`, `HasStrictFDerivAt.mul_const'`, `map_mul_right_nhds_one₀`, `Valuation.restrict_le_one_iff`, `Valuation.isClosed_ball`, `Associates.mk_eq_zero`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `Matrix.dualNumberEquiv_apply`, `MeasureTheory.eLpNorm'_const_smul_le`, `eq_zero_of_one_div_eq_zero`, `orderOf_eq_zero_iff_eq_zero`, `CommGroupWithZero.normalize_eq_one`, `ValuationSubring.mem_smul_pointwise_iff_exists`, `ArithmeticFunction.IsMultiplicative.iff_ne_zero`, `OrderIso.withZeroUnits_apply`, `neg_gcd`, `Valuation.leAddSubgroup_zero`, `WithZeroTopology.Iio_mem_nhds_zero`, `Fintype.prod_boole`, `fderivWithin_list_prod'`, `Submonoid.LocalizationMap.isCancelMulZero`, `Ring.mul_inverse_rev`, `mul_inv_eq_iff_eq_mul₀`, `DualNumber.eps_pow_two`, `Homeomorph.mulRight₀_symm_apply`, `HasFDerivWithinAt.fun_mul'`, `Commute.div_eq_div_iff`, `ModuleCat.extendScalarsComp_hom_app_one_tmul`, `Ordinal.add_mul_succ`, `Valuation.HasExtension.mk_smul_mk`, `divMonoidWithZeroHom_apply`, `Finset.gcd_mul_right`, `Quaternion.re_snd_dualNumberEquiv`, `Ordinal.CNF.opow_mul_add`, `nonZeroDivisorsEquivUnits_symm_apply_coe`, `nilpotencyClass_zero`, `MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀`, `Set.center_units_eq`, `IsFractionRing.num_den_unique`, `WithZero.withZeroUnitsEquiv_symm_apply`, `ClassGroup.exists_min`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff'`, `fderivWithin_pow_ring'`, `Ordinal.mul_add_mod_mul`, `IsSMulRegular.mem_nonZeroSMulDivisors`, `Commute.self_zpow₀`, `Valuation.Integers.valuation_irreducible_pos`, `Ring.inverse_mul_cancel_left`, `Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow`, `pow_left_strictMonoOn₀`, `NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMap`, `MonoidWithZeroHom.inr_strictMono`, `Ordinal.isSuccLimit_mul_right`, `OreLocalization.zero_oreDiv'`, `zpow_one_add₀`, `Valued.hasBasis_uniformity`, `Real.smul_iSup_of_nonneg`, `MulChar.trivial_apply`, `Ordinal.CNF.eval_single_add`, `inv_mul_le_one_of_le₀`, `Ordinal.opow_mul_lt_opow`, `Ring.mul_inverse_cancel_left`, `Multiset.one_le_prod_map`, `FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm`, `QuadraticAlgebra.coe_mem_nonZeroDivisors_iff`, `Multiset.gcd_zero`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `Set.image_mul_left_Ioo`, `zero_lt_iff`, `HasFDerivWithinAt.fun_pow'`, `Ordinal.isSuccPrelimit_mul_left`, `not_prime_one`, `FractionalIdeal.map_canonicalEquiv_mk0`, `invOf_eq_inv`, `LinearOrderedCommMonoidWithZero.toMulPosStrictMono`, `Homeomorph.coe_mulLeft₀`, `invOf_div`, `div_mul_cancel_right₀`, `one_div_mul_cancel`, `div_pos`, `div_nonneg`, `DualNumber.exp_smul_eps`, `IsRegular.mem_nonZeroDivisors`, `Set.preimage_mul_const_Ioc₀`, `Quaternion.snd_imI_dualNumberEquiv_symm`, `Antitone.mul_const`, `continuous_cfcₙAux`, `FiniteField.valuation_algebraMap_le_one`, `ONote.repr_opow_aux₂`, `Finset.mul₀_sup'`, `HasFDerivAt.mul_const'`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `mul_cancel_left_coe_nonZeroDivisors`, `StrictMono.mul_monotone`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `pow_pos_iff`, `HasStrictFDerivAt.fun_pow'`, `MeasurableEquiv.coe_mulLeft₀`, `OrderIso.mulLeft₀_symm`, `List.prod_map_le_pow_length₀`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg`, `Valuation.restrict_lt_iff`, `Filter.zero_pow_eventuallyEq`, `DualNumber.lift_apply_inl`, `IsSMulRegular.not_zero_iff`, `Set.Nonempty.zero_div`, `Ordinal.mul_le_iff_le_div`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `bddBelow_smul_iff_of_pos`, `UniqueFactorizationMonoid.radical_mul_dvd`, `Real.hasFDerivAt_fourierChar_neg_bilinear_right`, `WithZeroTopology.tendsto_zero`, `IsLocalRing.ResidueField.residue_smul`, `prod_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `zero_notMem_nonZeroDivisorsRight`, `Valued.isClosed_closedBall`, `squarefree_iff_no_irreducibles`, `DualNumber.lift_op_smul`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_left`, `Valuation.isOpen_closedBall`, `Ordinal.isPrincipal_mul_one`, `RatFunc.taylor_mem_nonZeroDivisors`, `inv_nonpos`, `Metric.unitClosedBall.instIsCancelMulZero`, `MonoidWithZeroHom.inl_mono`, `mul_inv_lt_iff₀'`, `UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow`, `IsNilpotent.pow_of_pos`, `GroupWithZero.mul_left_injective`, `Ordinal.isPrincipal_add_mul_of_isPrincipal_add`, `Commute.mul_inv_eq_mul_inv_iff`, `dvd_gcd_mul_of_dvd_mul`, `one_div_nonpos`, `MulCharClass.map_nonunit`, `Set.image_mul_right_Ico`, `Ordinal.mul_omega0_opow_opow`, `bddAbove_smul_iff_of_pos`, `Commute.zpow_zpow₀`, `DirichletCharacter.isMultiplicative_toArithmeticFunction`, `instIsCancelMulZero_1`, `Polynomial.content_C`, `IsUnit.integrable_smul_iff`, `div_lt_div_iff₀`, `Valuation.RankOne.isNontrivial_restrict`, `ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eq`, `MvPowerSeries.X_mem_nonzeroDivisors`, `ClassGroup.equiv_mk0`, `Ordinal.nfp_mul_one`, `IsSMulRegular.zero_iff_subsingleton`, `Ordinal.opow_succ`, `bot_eq_zero''`, `UniqueFactorizationMonoid.prod_normalizedFactors_eq`, `dvd_cancel_left_coe_nonZeroDivisors`, `gauge_smul_left`, `NumberField.mixedEmbedding.fundamentalCone.mem_idealSet`, `DualNumber.lift_comp_inlHom`, `NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop`, `MvPowerSeries.mem_nonZeroDivisorsRight_of_constantCoeff`, `UniqueFactorizationMonoid.factors_zero`, `Valuation.HasExtension.val_map_lt_one_iff`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_surjective`, `ValuativeRel.restrict_lt_orderMonoidIso`, `strictAntiOn_inv_pos`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂`, `Ordinal.isPrincipal_mul_two`, `DualNumber.algHom_ext'_iff`, `hasStrictFDerivAt_list_prod'`, `DualNumber.ideal_trichotomy`, `NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply`, `UniqueFactorizationMonoid.radical_pow_of_prime`, `Set.zero_div_subset`, `notMem_nonZeroDivisors_iff_left`, `mem_nonZeroDivisors_of_injective`, `Ordinal.le_mul_left`, `IsFractionRing.num_den_reduced`, `QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff`, `pow_eq_one_iff_of_nonneg`, `Valuation.norm_pos_iff_valuation_pos`, `isClosedMap_smul₀`, `Ordinal.nfp_add_zero`, `MonoidWithZeroHomClass.ext_rat_iff`, `Commute.inv_right₀`, `IsFractionRing.associated_den_num_inv`, `Set.div_zero_subset`, `Ordinal.mul_two`, `ContinuousMapZero.elemental_eq_top`, `mul_right_bijective_of_finite₀`, `lcm_dvd_lcm_mul_left_right`, `UniqueFactorizationMonoid.factors_mul`, `ClassGroup.mk0_eq_mk0_inv_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft`, `Valuation.coe_mk`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one`, `inv_lt_one_iff₀`, `Multiset.gcd_eq_zero_iff`, `DirichletCharacter.map_zero'`, `WithZero.withZeroUnitsEquiv_apply`, `pow_succ_pos`, `Finsupp.sym2Mul_apply_mk`, `continuousOn_zpow₀`, `IsFractionRing.self_iff_nonZeroDivisors_le_isUnit`, `Units.zero_lt`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe`, `OrderMonoidWithZeroHom.comp_mul`, `Mathlib.Tactic.FieldSimp.zpow'_add`, `Submonoid.LocalizationMap.lift₀_apply`, `normalize_eq_one`, `Valuation.IsEquiv.lt_one_iff_lt_one`, `ProbabilityTheory.gaussianPDFReal_mul`, `Associates.quot_out_zero`, `le_div_iff₀`, `comap_nonZeroDivisors_le_of_injective`, `star_div₀`, `ValuationSubring.smul_mem_pointwise_smul`, `one_lt_pow₀`, `ONote.scale_opowAux`, `star_zpow₀`, `PosMulReflectLT.toPosMulStrictMono`, `Matrix.toLinearMapRight'_one`, `mul_mem_nonZeroDivisorsRight_of_mem_nonZeroDivisorsRight`, `HasFDerivWithinAt.mul'`, `Units.mul_left_eq_zero`, `mul_inv_le_of_le_mul₀`, `OreLocalization.inv_zero`, `MonoidWithZeroHom.snd_apply_coe`, `Set.inv_Ioo_0_left`, `LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono`, `inverse_apply`, `Units.exists0`, `MulChar.map_nonunit'`, `Ordinal.mul_div_mul_cancel`, `Valuation.restrict_exists_div_eq`, `Valuation.leSubmodule_zero`, `Ordinal.add_le_right_iff_mul_omega0_le`, `eq_div_iff`, `Valuation.one_apply_def`, `posMulMono_iff_posMulStrictMono`, `Valuation.IsEquiv.orderMonoidIso_spec`, `Ordinal.isPrincipal_mul_iff_mul_left_eq`, `Ordinal.isSuccLimit_mul_left`, `Finset.lcm_eq_zero_iff`, `lcm_units_coe_right`, `Polynomial.mem_nonzeroDivisors_of_coeff_mem`, `GroupWithZero.eq_zero_or_unit`, `LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered`, `Multipliable.tsum_congr_cofinite₀`, `fderivWithin_mul'`, `zpow_left_monoOn₀`, `Multiset.lcm_ne_zero_iff`, `Function.support_inv'`, `Multiset.normalize_gcd`, `StrictAnti.mul_const`, `Valued.isClopen_closedBall`, `Valuation.RankOne.restrict_RankOne_hom_eq`, `PosMulMono.toPosMulStrictMono`, `div_le_iff₀'`, `Finset.Nonempty.div_zero`, `Nonneg.mk_pow`, `mul_left_surjective₀`, `LinearOrderedCommGroupWithZero.inl_apply`, `OreLocalization.nontrivial_of_nonZeroDivisorsLeft`, `map_mul_left_nhds₀`, `List.prod_map_le_prod_map₀`, `LinearOrderedCommGroupWithZero.inr_apply`, `Ordinal.lift_mul`, `Monotone.const_mul`, `mul_sup₀`, `dvd_gcd_mul_iff_dvd_mul`, `SignType.coe_pow`, `IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers`, `mul_inv_mul_cancel`, `monotone_mul_left_of_nonneg`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `div_eq_zero_iff`, `QuadraticAlgebra.norm_mem_nonZeroDivisors_iff`, `SignType.coe_zpow`, `StrictMono.mul_const`, `OreLocalization.nontrivial_iff`, `normalize_associated`, `MeasureTheory.hasFiniteIntegral_smul_iff`, `MulChar.map_zero`, `Valuation.pos_iff`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction`, `MeasureTheory.integrable_fun_smul_iff`, `zero_notMem_nonZeroDivisorsLeft`, `VectorFourier.hasFDerivAt_fourierChar_smul`, `IsFractionRing.num_mul_den_eq_num_iff_eq'`, `Irreducible.gcd_eq_one_iff`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `isRelPrime_zero_left`, `neg_gcd'`, `MulChar.coeToFun_mul`, `inv_mul_cancel₀`, `Commute.inv_left₀`, `Polynomial.monic_normalize`, `lt_mul_left`, `Ordinal.lt_omega0_omega0_opow`, `fderiv_list_prod'`, `Finset.inf'_mul_le_mul_inf'_of_nonneg`, `zero_notMem_nonZeroDivisors`, `Valuation.map_zero`, `HasMFDerivAt.mul'`, `Mathlib.Tactic.FieldSimp.NF.eval_cons`, `ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply`, `ArithmeticFunction.IsMultiplicative.map_div_of_coprime`, `Multiset.gcd_map_mul`, `nilpotencyClass_eq_succ_iff`, `div_zero`, `Antitone.const_mul`, `ofAdd_toDual_eq_zero_iff`, `Valuation.exists_setOf_restrict_le_iff`, `mul_self_div_self`, `ClassGroup.integralRep_mem_nonZeroDivisors`, `MonoidWithZeroHom.inr_injective`, `mul_div_cancel_of_imp`, `notMem_nonZeroDivisorsLeft_iff`, `DualNumber.instIsPrincipalIdealRing`, `WithZeroTopology.nhds_eq_update`, `Real.exists_lt_of_strictMono`, `eq_mul_of_mul_inv_eq₀`, `MonoidWithZeroHom.commute_inl_inr`, `notMem_nonZeroDivisors_iff_right`, `Ordinal.mul_omega0`, `MonoidWithZeroHom.fst_comp_inr`, `Finsupp.mem_sym2_support_of_mul_ne_zero`, `normalize_zero`, `Ordinal.principal_mul_one`, `UniqueFactorizationMonoid.radical_eq_one_iff`, `mul_mem_nonZeroDivisors`, `Mathlib.Tactic.FieldSimp.zero_zpow'`, `VectorFourier.fourierIntegral_fderiv`, `UniqueFactorizationMonoid.radical_mul`, `Multiset.prod_pos`, `Localization.mk_zero`, `gcd_neg`, `HasFDerivAt.fun_mul'`, `threeGPFree_smul_set₀`, `UniqueFactorizationMonoid.toIsCancelMulZero`, `Ordinal.le_div`, `UniqueFactorizationMonoid.multiplicity_eq_count_normalizedFactors`, `OreLocalization.nontrivial_of_nonZeroDivisors`, `IsValuativeTopology.isOpen_sphere`, `gcd_zero_left'`, `div_mul_div_cancel₀`, `UniqueFactorizationMonoid.zero_notMem_normalizedFactors`, `lt_mul_self`, `lcm_eq_one_iff`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃`, `ValuationSubring.mapOfLE_comp_valuation`, `MonoidWithZeroHom.ext_int_iff`, `RatFunc.laurentAux_ofFractionRing_mk`, `NONote.repr_mul`, `normalize_idem`, `GroupWithZero.toNoZeroSMulDivisors`, `Units.inv_mul'`, `HasFDerivAt.mul'`, `GroupWithZero.noZeroDivisors`, `Finset.normalize_gcd`, `SemiconjBy.inv_symm_left_iff₀`, `lcm_eq_normalize`, `FractionalIdeal.coe_mk0`, `Quaternion.fst_re_dualNumberEquiv_symm`, `hasFDerivAt_list_prod_attach'`, `Quaternion.imI_snd_dualNumberEquiv`, `zero_pow`, `MonoidWithZeroHomClass.ext_nnrat_iff`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero`, `MonoidWithZeroHom.ValueGroup₀.embedding_strictMono`, `IsNilpotent.of_pow`, `ArithmeticFunction.IsMultiplicative.map_mul_of_coprime`, `Ring.inverse_zero`, `Associates.out_top`, `IsNilpotent.zero`, `Function.support_pow'`, `gcd_dvd_gcd_mul_left`, `eq_mul_of_inv_mul_eq₀`, `Ring.eq_mul_inverse_iff_mul_eq`, `Finset.prod_nonneg`, `div_mul_eq_mul_div₀`, `Set.image_mul_left_Ici`, `one_le_mul_of_one_le_of_one_le`, `IsFractionRing.isUnit_den_zero`, `Set.preimage_const_mul_Iic₀`, `Submonoid.LocalizationMap.lift₀_def`, `notMem_nonZeroDivisorsRight_iff`, `emultiplicity_mul`, `neg_of_div_neg_left`, `Finset.support_prod`, `Set.preimage_mul_const_Iio₀`, `IsValuativeTopology.isClopen_closedBall`, `Valuation.exists_div_eq_of_surjective`, `upperBounds_smul_of_pos`, `smul_inv₀'`, `Valuation.mem_nhds_iff`, `NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal`, `Int.nonneg_iff_normalize_eq_self`, `Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange`, `LinearMap.toMatrixRight'_comp`, `IsFractionRing.lift_mk'`, `Associates.FactorSet.prod_eq_zero_iff`, `ArithmeticFunction.IsMultiplicative.eq_zero_of_squarefree_of_dvd_eq_zero`, `Associates.le_zero`, `Submonoid.LocalizationMap.sec_zero_fst`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm`, `normalize_eq_normalize_iff_associated`, `mulPosMono_iff_mulPosStrictMono`, `pow_le_one₀`, `factorization_one`, `Set.preimage_mul_const_Ioi₀`, `OrderMonoidWithZeroHom.mul_apply`, `Ordinal.mod_def`, `PowerSeries.X_eq_normalizeX`, `Filter.EventuallyEq.div_mul_cancel`, `Real.smul_iInf_of_nonneg`, `MonoidWithZeroHom.inl_apply_unit`, `Valuation.is_topological_valuation`, `mul_eq_mul_prime_prod`, `normalize_associated_iff`, `Valuation.one_rel_iff`, `Valuation.le_one_of_subsingleton`, `Polynomial.X_eq_normalize`, `MonoidWithZeroHom.snd_surjective`, `ite_zero_smul`, `Valuation.isClopen_sphere`, `UniqueFactorizationMonoid.exists_reduced_factors'`, `PosSMulStrictMono.toPosSMulReflectLT`, `MeasurableEquiv.coe_mulRight₀`, `star_inv₀`, `Polynomial.content_monomial`, `Set.inv_op_smul_set_distrib₀`, `inv_mul_cancel_right₀`, `Ordinal.isPrincipal_mul_ord`, `WithZero.withZeroUnitsEquiv_strictMono`, `le_inv_mul_left`, `one_lt_inv_mul₀`, `LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered`, `Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow`, `Function.support_div`, `Polynomial.map_normalize`, `normalize_eq`, `IsFractionRing.isUnit_den_iff`, `Valuation.isClosed_sphere`, `SemiconjBy.inv_right_iff₀`, `IsTopologicallyNilpotent.zero`, `inv_mul_le_iff₀'`, `isReduced_of_noZeroDivisors`, `MulPosReflectLT.toMulPosReflectLE`, `Valuation.one_apply_eq_one_iff`, `Ordinal.mul_div_le`, `FiniteMultiplicity.mul_iff`, `cfcUnits_zpow`, `WithZeroTopology.instContinuousInv₀`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top`, `lcm_one_right`, `Ordinal.mul_le_iff_of_isSuccLimit`, `LinearOrderedCommMonoidWithZero.toZeroLeOneClass`, `sq_eq_zero_iff`, `Filter.NeBot.div_zero_nonneg`, `Ordinal.mul_omega0_dvd`, `GrpWithZero.Iso.mk_inv`, `NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply`, `Valued.extensionValuation_toFun`, `Mathlib.Tactic.FieldSimp.mul_zpow'`, `mul_inv_le_iff₀'`, `HasFDerivWithinAt.list_prod'`, `List.prod_nonneg`, `Quaternion.imK_snd_dualNumberEquiv`, `IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk'`, `measurableEmbedding_mulLeft₀`, `fderivWithin_pow'`, `Finsupp.sym2_support_eq_preimage_support_mul`, `IsLocalization.map_nonZeroDivisors_le`, `mem_nonZeroDivisorsRight_iff`, `associated_normalize`, `Finset.gcd_div_eq_one`, `OreLocalization.inv_def`, `Ordinal.lt_mul_iff`
`toSemigroupWithZero` 📖	CompOp	170 math math: `UniqueFactorizationMonoid.dvd_radical_iff`, `lcm_dvd_lcm_mul_right`, `normalize_dvd_iff`, `Ordinal.dvd_add_iff`, `Prime.isPrimal`, `gcd_dvd_gcd_mul_right`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff`, `Ordinal.antisymm`, `Finset.gcd_dvd`, `IsRadical.of_dvd`, `Prime.dvd_or_dvd`, `UniqueFactorizationMonoid.isRadical_radical`, `Prime.exists_mem_multiset_map_dvd`, `gcd_dvd_gcd_mul_left_right`, `Finset.dvd_gcd`, `Prime.exists_mem_finset_dvd`, `Dvd.dvd.lcm_left`, `Prime.dvd_mul`, `emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactors`, `UniqueFactorizationMonoid.dvd_of_mem_normalizedFactors`, `Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd`, `dvd_lcm_right`, `lcm_dvd`, `Prime.exists_mem_multiset_dvd`, `Prime.left_dvd_or_dvd_right_of_dvd_mul`, `mul_dvd_mul_iff_right`, `ONote.split_dvd`, `Associates.out_dvd_iff`, `Multiset.lcm_mono`, `Prime.not_dvd_finset_prod`, `ONote.NF.of_dvd_omega0`, `Ordinal.dvd_of_mod_eq_zero`, `Finset.lcm_dvd_prod`, `normalize_eq_normalize_iff`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `nonZeroDivisors_dvd_iff_dvd_coe`, `lcm_eq_left_iff`, `Ordinal.opow_dvd_opow`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `dvd_and_not_dvd_iff`, `Prime.not_dvd_mul`, `isRadical_iff_squarefree_or_zero`, `Prime.not_dvd_one`, `dvd_of_lcm_left_dvd`, `dvd_lcm_of_dvd_left`, `prime_pow_succ_dvd_mul`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right`, `Associates.dvd_of_mem_factors'`, `dvd_mul_gcd_of_dvd_mul`, `isRadical_iff_squarefree_of_ne_zero`, `isPrimal_zero`, `Irreducible.isUnit_gcd_iff`, `lcm_dvd_mul`, `GCDMonoid.dvd_gcd`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `zero_isRadical_iff`, `Finset.gcd_mono`, `dvd_mul_gcd_iff_dvd_mul`, `WfDvdMonoid.exists_irreducible_factor`, `Ordinal.mul_eq_right_iff_opow_omega0_dvd`, `Prime.dvd_prod_iff`, `Ordinal.dvd_iff_mod_eq_zero`, `Squarefree.isRadical`, `UniqueFactorizationMonoid.radical_dvd_radical_iff_primeFactors_subset_primeFactors`, `Associates.mem_factors'_iff_dvd`, `WfDvdMonoid.max_power_factor`, `gcd_mul_dvd_mul_gcd`, `UniqueFactorizationMonoid.dvd_of_dvd_mul_right_of_no_prime_factors`, `dvd_lcm_left`, `lcm_dvd_iff`, `lcm_dvd_lcm_mul_right_right`, `Prime.not_dvd_prod`, `Finset.dvd_gcd_iff`, `UniqueFactorizationMonoid.radical_pow_dvd`, `Finset.lcm_dvd`, `Ordinal.opow_dvd_opow_iff`, `UniqueFactorizationMonoid.dvd_radical_iff_of_irreducible`, `lcm_eq_right_iff`, `lcm_dvd_lcm_mul_left`, `Multiset.gcd_mono`, `Prime.pow_dvd_of_dvd_mul_right`, `Squarefree.dvd_of_squarefree_of_mul_dvd_mul_left`, `UniqueFactorizationMonoid.radical_prod_dvd`, `Prime.dvd_or_dvd_of_dvd_lcm`, `GroupWithZero.dvd_iff`, `mul_dvd_mul_iff_left`, `WfDvdMonoid.max_power_factor'`, `Associates.mem_factors_iff_dvd`, `Prime.isRadical`, `Associates.count_factors_eq_find_of_dvd_pow`, `Prime.dvd_pow_iff_dvd`, `dvd_dvd_iff_associated`, `Squarefree.dvd_of_squarefree_of_mul_dvd_mul_right`, `Dvd.dvd.lcm_right`, `Ordinal.isSuccPrelimit_iff_omega0_dvd`, `Multiset.dvd_gcd`, `dvd_of_lcm_right_dvd`, `gcd_dvd_gcd_mul_right_right`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `ONote.NF.of_dvd_omega0_opow`, `UniqueFactorizationMonoid.radical_dvd_self`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_left`, `UniqueFactorizationMonoid.dvd_of_dvd_mul_left_of_no_prime_factors`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `finiteMultiplicity_mul_aux`, `IsPrimal.mul`, `Ordinal.mul_le_right_iff_opow_omega0_dvd`, `dvd_lcm_of_dvd_right`, `Associates.exists_prime_dvd_of_not_inf_one`, `exists_squarefree_dvd_pow_of_ne_zero`, `gcd_pow_left_dvd_pow_gcd`, `dvd_normalize_iff`, `associated_gcd_right_iff`, `dvd_prime_pow`, `Prime.not_dvd_lcm`, `IsRadical.dvd_radical`, `associated_gcd_left_iff`, `lcm_dvd_lcm`, `Associates.count_ne_zero_iff_dvd`, `pow_dvd_of_mul_eq_pow`, `mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors`, `Finset.lcm_mono_fun`, `UniqueFactorizationMonoid.radical_dvd_iff_primeFactors_subset`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff'`, `UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactors`, `Associates.eq_pow_find_of_dvd_irreducible_pow`, `GCDMonoid.gcd_dvd_left`, `smul_pi₀`, `UniqueFactorizationMonoid.radical_mul_dvd`, `squarefree_iff_no_irreducibles`, `instDecompositionMonoidOfNonemptyGCDMonoid`, `dvd_gcd_mul_of_dvd_mul`, `Prime.dvd_of_dvd_pow`, `prime_dvd_prime_iff_eq`, `Multiset.gcd_dvd`, `Multiset.dvd_lcm`, `Associates.dvd_out_iff`, `UniqueFactorizationMonoid.dvd_of_mem_factors`, `gcd_eq_left_iff`, `pow_dvd_pow_iff`, `lcm_dvd_lcm_mul_left_right`, `Associates.dvd_of_mem_factors`, `GCDMonoid.gcd_dvd_right`, `Multiset.lcm_dvd`, `Finset.lcm_dvd_iff`, `Finset.lcm_mono`, `gcd_pow_right_dvd_pow_gcd`, `UniqueFactorizationMonoid.instDecompositionMonoid`, `UniqueFactorizationMonoid.radical_dvd_radical`, `dvd_gcd_mul_iff_dvd_mul`, `Multiset.prod_primes_dvd`, `Irreducible.gcd_eq_one_iff`, `Finset.dvd_lcm`, `Set.smul_set_pi₀'`, `lcm_eq_one_iff`, `succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul`, `UniqueFactorizationMonoid.radical_dvd_radical_iff_normalizedFactors_subset_normalizedFactors`, `Prime.dvd_finset_prod_iff`, `gcd_dvd_gcd_mul_left`, `Prime.pow_dvd_of_dvd_mul_left`, `Finset.prod_primes_dvd`, `Prime.dvd_prime_iff_associated`, `Set.smul_set_pi₀`, `gcd_eq_right_iff`, `Ordinal.isSuccLimit_iff_omega0_dvd`, `Squarefree.dvd_pow_iff_dvd`, `Finset.gcd_mono_fun`, `gcd_dvd_gcd`, `Prime.dvd_lcm`, `dvd_gcd_iff`
`toZero` 📖	CompOp	4 math math: `GroupWithZero.inv_zero`, `zero_mul`, `mul_zero`, `CancelMonoidWithZero.toIsCancelMulZero`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_zero` 📖	mathematical	—	`Semigroup.toMul` `Monoid.toSemigroup` `toMonoid` `toZero`	—	—
`zero_mul` 📖	mathematical	—	`Semigroup.toMul` `Monoid.toSemigroup` `toMonoid` `toZero`	—	—

MulDivCancelClass

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_div_cancel` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass`	—	—

MulZeroClass

Definitions

Name	Category	Theorems
`toMul` 📖	CompOp	1057 math math: `Finset.sup'_mul_le_mul_sup'_of_nonneg`, `Set.center_units_subset`, `Ordinal.opow_mul`, `WithZero.unzero_mul`, `WithBot.mul_bot'`, `Ordinal.lt_omega0_opow_succ`, `WithZero.exp_add`, `ProbabilityTheory.cdf_measure_stieltjesFunction`, `HasStrictFDerivAt.fun_mul'`, `isRegular_iff_subsingleton`, `AlgEquiv.moduleEndSelfOp_apply_apply`, `Set.preimage_const_mul_Ioi₀`, `WithBot.instPosMulStrictMono`, `le_mul_div_mul_left`, `Valuation.inversion_estimate'`, `Homeomorph.coe_mulRight₀`, `Set.image_mul_left_Iio`, `pow_sub_of_lt`, `mul_inv_cancel_of_invertible`, `WithVal.valueGroupOrderIso₀_symm_apply`, `mul_inf₀`, `lcm_dvd_lcm_mul_right`, `mul_inv_eq_mul_inv_iff`, `Quaternion.snd_imJ_dualNumberEquiv_symm`, `instPosMulMonoWithZeroOfMulLeftMono`, `hasStrictFDerivAt_list_prod_finRange'`, `mul_neg_of_neg_of_pos`, `Matrix.single_hadamard_single_eq`, `Ordinal.isNormal_mul_right`, `mul_div_mul_right`, `IsRelPrime.moebius_mul`, `Set.preimage_mul_const_Icc₀`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `Ordinal.exists_lt_mul`, `HasProd.congr_cofinite₀`, `mul_nonneg`, `StrictMono.mul`, `div_le_iff₀`, `Function.support_mul_subset_right`, `Matrix.toLinearMapRight'_mul`, `IsLeftRegular.mul_left_eq_zero_iff`, `mul_self_eq_zero`, `gcd_dvd_gcd_mul_right`, `GroupWithZero.conj_pow₀`, `gcd_mul_lcm`, `UniqueFactorizationMonoid.exists_reduced_factors`, `Ordinal.instIsLeftCancelMulZero`, `WithZero.withZeroUnitsEquiv_symm_apply_coe`, `div_sq_cancel`, `Ring.mul_inverse_cancel_right`, `StrictMono.const_mul`, `mul_div_mul_right_le`, `Ordinal.principal_mul_of_le_two`, `mul_inv_cancel_left₀`, `mul_eq_of_eq_inv_mul₀`, `Commute.inv_right_iff₀`, `Matrix.one_kronecker`, `mul_right_mem_nonZeroDivisors_eq_zero_iff`, `Set.inv_mem_centralizer₀`, `map_mul_left_nhds_one₀`, `ONote.nf_repr_split'`, `Ordinal.noZeroDivisors`, `Decidable.mul_lt_mul''`, `div_mul_cancel₀`, `WithTop.mul_def`, `WithBot.instMulPosMono`, `fderivWithin_fun_pow'`, `mul_div_cancel_of_invertible`, `mul_inv_le_one`, `WithTop.top_mul'`, `Matrix.hadamard_one_eq_zero_iff`, `le_div_iff₀'`, `isClosedEmbedding_cfcₙAux`, `OrderMonoidIso.withZero_symm_apply_symm_apply`, `gcd_mul_left`, `OrderMonoidIso.withZero_symm_apply_apply`, `Ordinal.deriv_add_eq_mul_omega0_add`, `Set.preimage_const_mul_Iio₀`, `Ordinal.mulRightMono`, `Nonneg.mk_div_mk`, `CompactlySupportedContinuousMap.coe_mul`, `ite_zero_mul_ite_zero`, `DualNumber.range_lift`, `measurableEmbedding_mulRight₀`, `CliffordAlgebraDualNumber.equiv_symm_eps`, `Ordinal.CNF.eval_single_add'`, `associatesEquivOfUniqueUnits_symm_apply`, `WithVal.valueGroupOrderIso₀_restrict`, `GroupWithZero.isConj_iff₀`, `Set.image_mul_left_Ioi`, `Right.mul_pos`, `zpow_add_one₀`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `Commute.div_right`, `WithTop.untop₀_mul`, `IsRegular.of_ne_zero`, `Ring.inverse_mul_eq_iff_eq_mul`, `Ring.inverse_mul_cancel`, `WithVal.valueGroupOrderIso₀_apply`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply`, `Ordinal.CNF.coeff_opow_mul_add`, `LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex`, `mul_nonpos_of_nonpos_of_nonneg`, `mul_self_le_mul_self`, `Set.image_mul_right_Icc'`, `MulEquiv.isRightCancelMulZero_iff`, `IsIdempotentElem.zero`, `Set.preimage_const_mul_Ioo₀`, `Set.mul_zero_subset`, `Quaternion.snd_re_dualNumberEquiv_symm`, `GCDMonoid.toIsCancelMulZero`, `SemiconjBy.div_right`, `HasStrictFDerivAt.mul'`, `Unitization.inl_mul_inr`, `le_mul_inv_left`, `posMulMono_iff_covariant_pos`, `ContinuousMapZero.coe_mul`, `Ordinal.lt_mul_div_add`, `pow_mul_eq_zero_of_le`, `Function.support_mul_of_ne_zero_right`, `prime_mul_iff`, `Ordinal.mul_div_gc`, `GCDMonoid.gcd_mul_lcm`, `Quaternion.imJ_fst_dualNumberEquiv`, `normUnit_mul_normUnit`, `ENNReal.orderIsoRpow_symm_apply`, `RestrictedProduct.single_mul`, `SemiconjBy.inv_right₀`, `mul_inv_cancel₀`, `mul_left_bijective_of_finite₀`, `Ordinal.add_log_le_log_mul`, `fderiv_fun_pow'`, `ArithmeticFunction.pmul_apply`, `Unitization.isIdempotentElem_inr_iff`, `Real.volume_val`, `WithTop.top_mul`, `mul_eq_of_eq_mul_inv₀`, `Monotone.mul_const`, `inv_mul_le_of_le_mul₀`, `div_mul_cancel_of_imp`, `isLeftRegular_zero_iff_subsingleton`, `Ordinal.div_le`, `Set.star_inv'`, `Ordinal.isPrincipal_mul_omega0_opow_opow`, `div_self_mul_self`, `lt_div_iff₀'`, `Nonneg.mk_zpow`, `Filter.tendsto_mul_iff_of_ne_zero`, `Matrix.zero_kronecker`, `Ordinal.lt_mul_iff_div_lt`, `MonoidWithZeroHom.valueGroup.mk_mul`, `lt_inv_mul_iff₀'`, `Quaternion.imI_fst_dualNumberEquiv`, `Ordinal.div_lt`, `gcd_dvd_gcd_mul_left_right`, `SimpleGraph.adjMatrix_hadamard_ofNat`, `Ring.inverse_invertible`, `lt_div_iff₀`, `ite_zero_mul`, `Ordinal.opow_add`, `Ordinal.lt_mul_succ_div`, `tendsto_mul_cofinite_nhds_zero`, `ONote.repr_mul`, `Ordinal.div_add_mod`, `List.one_le_prod`, `Ordinal.mul_add_div`, `Pi.single_mul_left_apply`, `Ordinal.principal_mul_omega0`, `Ordinal.nfp_mul_opow_omega0_add`, `Commute.zero_left`, `mulPosMono_iff_covariant_pos`, `DualNumber.lift_apply_eps`, `IsRightRegular.mul_right_eq_zero_iff`, `Set.image_mul_left_Icc'`, `Matrix.hadamard_diagonal_eq_diagonal_iff`, `MeasureTheory.SignedMeasure.singularPart_smul`, `inv_mul_lt_one₀`, `gcd_mul_right'`, `Prime.dvd_mul`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval`, `HasStrictFDerivAt.list_prod'`, `not_isRightRegular_zero`, `SemiconjBy.zero_right`, `inf_mul₀`, `div_mul_cancel_left₀`, `mul_div_mul_left_le`, `Nonneg.inv_mk`, `mul_eq_one_iff_inv_eq₀`, `Ordinal.IsInitial.principal_mul`, `Finset.extract_gcd`, `Ordinal.opow_mul_add_pos`, `Finsupp.sum_smul_index`, `Matrix.single_eq_single_vecMulVec_single`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁`, `Filter.EventuallyLE.mul_le_mul`, `mul_inv_lt_iff₀`, `MonoidWithZeroHom.valueGroup.mk_inj`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `Commute.zpow_right₀`, `Holor.zero_mul`, `StrictAnti.const_mul`, `mul_eq_left₀`, `ValuativeRel.nonempty_orderIso_withZeroMul_int_iff`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_strictMono`, `left_eq_mul₀`, `le_mul_div_mul_right`, `Function.support_mul'`, `CompactlySupportedContinuousMap.toRealLinearMap_apply_apply`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj`, `WithTop.mul_top`, `Set.image_mul_right_Icc`, `div_self_mul_self'`, `inv_mul_eq_iff_eq_mul₀`, `Ordinal.mul_lt_of_lt_div`, `Ordinal.mul_lt_omega0_opow`, `zero_mul`, `MulPosMono.toMulPosStrictMono`, `HasStrictDerivAt.real_of_complex`, `eq_mul_inv_iff_mul_eq₀`, `mul_right_cancel_iff_of_pos`, `range_cfcₙHom`, `Set.image_const_mul_Ioi_zero`, `Ring.mul_inverse_rev'`, `inv_mul_le_one`, `Ordinal.div_mul_cancel`, `fun_meromorphicOrderAt_zpow`, `mul_dvd_mul_iff_right`, `inv_mul_cancel_left₀`, `Ordinal.natCast_mul_omega0`, `factorization_mul`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `lt_mul_inv_iff₀`, `ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction`, `Equiv.divRight₀_symm_apply`, `CompactlySupportedContinuousMap.mul_apply`, `mul_lt_one_of_nonneg_of_lt_one_left`, `rank_lt_rank_dual'`, `WithBot.mul_coe_eq_bind`, `WithTop.mul_coe_eq_bind`, `Matrix.hadamard_one`, `inv_mul_le_one₀`, `Tendsto.tendsto_mul_zero_of_disjoint_cocompact_left`, `RestrictedProduct.mul_single`, `SimpleGraph.adjMatrix_hadamard_intCast`, `le_inv_mul_right`, `Monotone.mul_strictMono`, `PosMulReflectLT.toPosMulReflectLE`, `Real.volume_eq_stieltjes_id`, `mul_eq_mul_left_iff`, `Set.preimage_const_mul_Ico₀`, `WithBot.bot_lt_mul`, `OrderIso.divRight₀_symm_apply`, `SimpleGraph.adjMatrix_hadamard_diagonal`, `CompactlySupportedContinuousMap.coe_toRealLinearMap`, `Complex.UnitDisc.conj_mul`, `pow_inv_comm₀`, `WithBot.instPosMulReflectLE`, `div_helper`, `Quaternion.fst_imK_dualNumberEquiv_symm`, `Commute.inv_left_iff₀`, `Ordinal.isPrincipal_mul_omega0`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `MulEquiv.withZero_apply_symm_apply`, `fderiv_mul_const'`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `DualNumber.fst_eq_zero_iff_eps_dvd`, `WithZero.lt_mul_exp_iff_le`, `posMulReflectLT_iff_contravariant_pos`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero`, `TrivSqZeroExt.inl_mul_inr`, `inv_mul_lt_iff₀`, `IsSelfAdjoint.zpow₀`, `OrderMonoidIso.withZeroUnits_symm_apply`, `isRegular_iff_ne_zero`, `mul_left_mem_nonZeroDivisors_eq_zero_iff`, `mul_lt_one_of_nonneg_of_lt_one_right`, `inv_mul_eq_inv_mul_iff`, `zero_eq_mul`, `OrderMonoidIso.withZeroUnits_apply`, `Ordinal.mul_mod`, `UniqueFactorizationMonoid.normalizedFactors_mul`, `SimpleGraph.intCast_hadamard_adjMatrix`, `Ordinal.principal_mul_ord`, `Set.div_mem_centralizer₀`, `CompactlySupportedContinuousMap.instSMulCommClass`, `ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ`, `Ordinal.log_opow_mul`, `Ordinal.opow_one_add`, `DualNumber.lift_inlAlgHom_eps`, `Finset.sup'_mul₀`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `WithTop.untopD_zero_mul`, `List.prod_map_lt_prod_map`, `Ordinal.opow_mul_add_lt_opow`, `Prime.not_dvd_mul`, `Ordinal.smul_eq_mul`, `IsSquare.zero`, `MulEquiv.toMonoidWithZeroHom_apply`, `Commute.div_left`, `mul_mem_nonZeroDivisorsLeft_of_mem_nonZeroDivisorsLeft`, `lcm_mul_left`, `Pi.single_mul_right`, `mul_zero_eq_const`, `mul_boole`, `Monotone.ae_hasDerivAt`, `mulLeft_bijective₀`, `WithBot.instMulPosStrictMono`, `monotone_mul_right_of_nonneg`, `cfcₙAux_id`, `lt_mul_right`, `DualNumber.isNilpotent_iff_eps_dvd`, `isRegular_of_ne_zero`, `le_mul_inv_iff₀'`, `DualNumber.isMaximal_span_singleton_eps`, `mul_le_of_le_div₀`, `IsUnit.mul_left_eq_zero`, `MulPosReflectLE.toMulPosReflectLT`, `exists_right_inv_of_exists_left_inv`, `fderiv_pow'`, `Ordinal.CNF.eval_single`, `StieltjesFunction.measurable_measure`, `SimpleGraph.diagonal_hadamard_adjMatrix`, `tendsto_mul_coprod_nhds_zero_inf_of_disjoint_cocompact`, `CompactlySupportedContinuousMap.toRealLinearMap_apply`, `MulEquiv.withZero_apply_apply`, `Ordinal.iSup_mul_nat`, `mul_eq_zero_of_right`, `Unitization.inr_mul`, `DualNumber.lift_smul`, `Finset.gcd_mul_left`, `Ordinal.lt_mul_add_one_iff`, `GrpWithZero.Iso.mk_hom`, `Quaternion.imK_fst_dualNumberEquiv`, `Submonoid.LocalizationMap.noZeroDivisors`, `lift_rank_lt_rank_dual'`, `Ordinal.instPosMulStrictMono`, `WithZero.instNoZeroDivisors`, `mul_inv_lt_of_lt_mul₀`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `WithVal.strictMono_valueGroupOrderIso₀`, `Quaternion.re_fst_dualNumberEquiv`, `not_isLeftRegular_zero`, `MulPosReflectLE.of_posMulReflectLT_of_mulPosMono`, `HasDerivWithinAt.complexToReal_fderiv`, `OrderMonoidIso.withZero_apply_symm_apply`, `mul_eq_zero_of_left`, `WithVal.strictMono_valueGroupOrderIso₀_symm`, `zpow_add'`, `IsUnit.mul_right_eq_zero`, `Ordinal.nfp_mul_eq_opow_omega0`, `inv_mul_mul_self`, `fderivWithin_fun_mul'`, `SemiconjBy.zpow_right₀`, `mul_div_cancel_left₀`, `MulPosStrictMono.toMulPosMono`, `mul_inv_le_iff₀`, `WithTop.coe_mul_eq_bind`, `hasFDerivAt_list_prod'`, `Matrix.toLinearMapRight'_mul_apply`, `Finset.mul_inf_le_inf_mul_of_nonneg`, `div_eq_iff_mul_eq`, `Commute.zero_right`, `nhds_translation_mul_inv₀`, `ONote.repr_scale`, `Set.preimage_const_mul_Ici₀`, `Prime.not_isSquare`, `fderiv_mul'`, `Multiset.extract_gcd`, `mul_mul_div`, `Function.support_mul_of_ne_zero_left`, `dvd_mul_gcd_of_dvd_mul`, `UniqueFactorizationMonoid.normalizedFactorsEquiv_symm_apply`, `pow_mul_apply_eq_pow_mul`, `ENat.map_natCast_mul`, `Ordinal.nfp_mul_zero`, `Commute.inv_mul_eq_inv_mul_iff`, `Matrix.one_hadamard_eq_diagonal_iff`, `HasDerivAt.complexToReal_fderiv`, `WithZero.toMulBot_lt`, `mul_left_coe_nonZeroDivisors_eq_zero_iff`, `MeasureTheory.FinStronglyMeasurable.mul`, `mul_le_of_le_inv_mul₀`, `Ordinal.isSuccPrelimit_mul_right`, `IsIdempotentElem.iff_eq_zero_or_one`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `Ring.mul_inverse_cancel`, `SimpleGraph.one_hadamard_adjMatrix`, `mul_right_coe_nonZeroDivisors_eq_zero_iff`, `lcm_dvd_mul`, `strictMono_mul_right_of_pos`, `one_lt_mul`, `hasFDerivWithinAt_pow'`, `Filter.NeBot.zero_mul_nonneg`, `mul_eq_mul_right_iff`, `mul_eq_mul_iff_eq_and_eq_of_pos'`, `Matrix.single_kronecker_single`, `WithZero.instLeftDistribClass`, `UniqueFactorizationMonoid.multiplicative_of_coprime`, `lcm_mul_right`, `div_mul_div_cancel₀'`, `MeasureTheory.SimpleFunc.FinMeasSupp.mul`, `MulPosReflectLT.toMulPosStrictMono`, `Function.support_mul_subset_left`, `Ring.isUnit_iff_mul_inverse_cancel`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `le_inv_mul_iff₀'`, `div_eq_div_iff`, `tsupport_mul_subset_left`, `fderivWithin_mul_const'`, `hasFDerivAt_list_prod_finRange'`, `WithBot.instPosMulMono`, `mul_pos_iff_of_pos_right`, `strictMonoOn_mul_self`, `Commute.zpow_zpow_self₀`, `Ring.inverse_pow_mul_eq_iff_eq_mul`, `WithBot.unbotD_zero_mul`, `Finsupp.single_mul`, `normalize_apply`, `mul_inv_le_one_of_le₀`, `Ordinal.principal_mul_omega`, `range_cfcₙHom_le`, `IsSelfAdjoint.inv₀`, `MulDivCancelClass.mul_div_cancel`, `Set.zero_mem_centralizer`, `WithZero.log_mul`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `Commute.ringInverse_ringInverse`, `Set.image_mul_left_Ioc`, `notMem_nonZeroDivisors_iff`, `dvd_mul_gcd_iff_dvd_mul`, `UniqueFactorizationMonoid.primeFactors_mul_eq_union`, `inv_mul_eq_one₀`, `UniqueFactorizationMonoid.primeFactors_mul_eq_disjUnion`, `List.prod_pos`, `eq_inv_mul_iff_mul_eq₀`, `Ordinal.mul_eq_right_iff_opow_omega0_dvd`, `Ordinal.mul_succ`, `Mathlib.Meta.NormNum.isNat_ordinalMul`, `inv_lt_iff_one_lt_mul₀`, `Quaternion.fst_imJ_dualNumberEquiv_symm`, `MonoidWithZeroHom.inl_mul_inr_eq_mk_of_unit`, `OrderMonoidIso.withZero_apply_apply`, `noZeroDivisors_iff_left_eq_zero_of_mul`, `IsUnit.isNilpotent_unit_mul_of_commute_iff`, `Ordinal.opow_mul_add_lt_opow_mul`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `div_lt_iff₀`, `WithBot.bot_mul_bot`, `WithZero.toMulBot_coe_ofAdd`, `Prime.dvd_prod_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight`, `mul_eq_right₀`, `Set.preimage_mul_const_Ioo₀`, `HasFDerivWithinAt.mul_const'`, `FunctionField.InftyValuation.map_mul'`, `Units.mul_right_eq_zero`, `Matrix.hadamard_one_eq_one_iff`, `WithZero.instMulLeftMono`, `mul_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat`, `Matrix.dualNumberEquiv_symm_apply`, `le_mul_inv_right`, `mul_left_eq_self₀`, `Ordinal.principal_add_mul_of_principal_add`, `DualNumber.exp_eps`, `Commute.zpow_self₀`, `Matrix.one_hadamard_eq_one_iff`, `Valuation.map_mul`, `mul_eq_zero`, `mul_eq_zero_iff_left`, `fderiv_pow_ring'`, `SimpleGraph.ofNat_hadamard_adjMatrix`, `lt_mul_inv_iff₀'`, `sup_mul₀`, `Left.mul_nonneg`, `Finsupp.mul_apply`, `Metric.unitBall.instIsLeftCancelMulZero`, `mul_div_cancel_of_imp'`, `Ring.isUnit_iff_inverse_mul_cancel`, `Quaternion.fst_imI_dualNumberEquiv_symm`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval`, `rank_dual_eq_card_dual_of_aleph0_le_rank'`, `mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff`, `mul_inv_cancel_right₀`, `Set.image_mul_right_Ioo`, `Matrix.single_hadamard_single_of_ne`, `mul_right_mem_nonZeroDivisorsRight_eq_zero_iff`, `Valued.closure_coe_completion_v_mul_v_lt`, `Ordinal.lt_div`, `WfDvdMonoid.max_power_factor`, `ONote.repr_opow_aux₁`, `Ordinal.iSup_mul_natCast`, `ZeroAtInftyContinuousMap.coe_mul`, `mul_one_div_cancel`, `extract_gcd`, `Mathlib.Tactic.FieldSimp.list_prod_zpow'`, `gcd_mul_dvd_mul_gcd`, `WithBot.mul_def`, `mul_div_cancel₀`, `mul_zero`, `Matrix.one_hadamard`, `Ordinal.IsInitial.isPrincipal_mul`, `not_isRightRegular_zero_iff`, `WithZero.instRightDistribClass`, `Units.mk0_mul`, `Set.image_mul_left_Icc`, `Matrix.zero_hadamard`, `Ordinal.log_opow_mul_add`, `mul_eq_one_iff_eq_inv₀`, `noZeroDivisors_iff_forall_mem_nonZeroDivisors`, `Finset.Nonempty.mul_zero`, `HasFDerivAt.fun_pow'`, `lcm_dvd_lcm_mul_right_right`, `Valuation.extendToLocalization_mk'`, `HasMFDerivWithinAt.mul'`, `Homeomorph.mulLeft₀_symm_apply`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply`, `Prime.not_dvd_prod`, `Ordinal.natCast_mul`, `DualNumber.lift_apply_apply`, `Set.preimage_mul_const_Iic₀`, `Ordinal.mul_mod_mul`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `WithZero.instMulLeftReflectLT`, `mulPosReflectLE_iff_mulPosReflectLT`, `MulChar.mul_apply`, `ProbabilityTheory.instIsProbabilityMeasureCondCDF`, `WithBot.bot_mul'`, `mul_inv_left_le`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_right`, `TrivSqZeroExt.inr_mul_inl`, `strictMono_mul_left_of_pos`, `Units.mul_inv'`, `DualNumber.ringHom_ext_iff`, `LinearMap.toMatrixRight'_id`, `Ordinal.le_mul_right`, `Ordinal.add_eq_right_iff_mul_omega0_le`, `Commute.zpow_left₀`, `mul_lt_mul_of_nonneg`, `Ordinal.mul_add_div_mul`, `cfcₙAux_injective`, `Ordinal.nsmul_eq_mul`, `WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv`, `mul_self_mul_inv`, `mul_le_of_le_mul_inv₀`, `Matrix.hadamard_zero`, `WithZero.toMulBot_zero`, `mul_div_cancel_right₀`, `lcm_dvd_lcm_mul_left`, `one_lt_mul_of_le_of_lt`, `Set.indicator_mul`, `Set.image_mul_left_Ico`, `lt_inv_mul_iff₀`, `WithTop.mul_top'`, `Prime.finiteMultiplicity_mul`, `mul_inv_right_le`, `Ordinal.nfp_add_eq_mul_omega0`, `PosMulStrictMono.toPosMulMono`, `Ordinal.mul_add_mod_self`, `IsPrimitiveRoot.injOn_pow_mul`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons`, `Complex.UnitDisc.instIsCancelMulZero`, `Matrix.kronecker_one`, `hasStrictFDerivAt_pow'`, `Ordinal.mul_eq_opow_log_succ`, `Valuation.IsEquiv.orderMonoidIso_trans`, `mul_pos`, `Bound.one_lt_mul`, `DualNumber.coe_lift_symm_apply`, `ProbabilityTheory.measure_cdf`, `mul_eq_mul_prime_pow`, `Quaternion.imJ_snd_dualNumberEquiv`, `Set.preimage_const_mul_Icc₀`, `fderiv_fun_mul'`, `Ordinal.leftDistribClass`, `Unitization.inr_mul_inl`, `zpow_add₀`, `instMulPosMonoWithZeroOfMulRightMono`, `Ordinal.lt_omega0_opow`, `le_inv_mul_iff₀`, `coord_norm'`, `Quaternion.snd_imK_dualNumberEquiv_symm`, `spec_cfcₙAux`, `Matrix.one_hadamard_eq_zero_iff`, `gcd_mul_left'`, `mul_dvd_mul_iff_left`, `Nonneg.mk_mul_mk`, `Matrix.one_kronecker_one`, `tendsto_mul_cocompact_nhds_zero`, `MulEquiv.noZeroDivisors_iff`, `WithBot.instNoZeroDivisors`, `List.prod_eq_zero`, `Matrix.diagonal_hadamard`, `hasStrictFDerivAt_list_prod_attach'`, `HasCompactSupport.mul_right`, `Complex.UnitDisc.coe_mul`, `ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic`, `div_eq_iff`, `WfDvdMonoid.max_power_factor'`, `ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ`, `MulEquiv.isLeftCancelMulZero_iff`, `Unitization.IsIdempotentElem.inr`, `Ordinal.isSuccLimit_mul`, `Ordinal.CNF.foldr`, `Set.image_mul_right_Ioc`, `SemiconjBy.inv_symm_left₀`, `Set.Nonempty.zero_mul`, `inv_mul_left_le`, `Filter.NeBot.mul_zero_nonneg`, `Set.preimage_mul_const_Ici₀`, `inv_mul_lt_of_lt_mul₀`, `Set.zero_mul_subset`, `mul_right_surjective₀`, `Matrix.vecMulVec_zero`, `GroupWithZero.mul_right_injective`, `mul_pos_iff_of_pos_left`, `CompactlySupportedContinuousMap.toNNRealLinear_apply`, `Ordinal.isPrincipal_mul_of_le_two`, `Matrix.diagonal_kronecker`, `associatesEquivOfUniqueUnits_apply`, `List.prod_eq_zero_iff`, `inv_mul_le_iff₀`, `Holor.mul_zero`, `WithZeroTopology.instContinuousMul`, `div_mul_cancel_of_invertible`, `DualNumber.range_inlAlgHom_sup_adjoin_eps`, `Finset.sup_mul_le_mul_sup_of_nonneg`, `posMulReflectLE_iff_posMulReflectLT`, `Left.mul_pos`, `div_le_div_iff₀`, `Matrix.toLinearMapRight'_apply`, `div_lt_iff₀'`, `Ordinal.mulLeftMono`, `Set.preimage_const_mul_Ioc₀`, `tendsto_mul_nhds_zero_of_disjoint_cocompact`, `HasFDerivWithinAt.pow'`, `tendsto_mul_prod_nhds_zero_of_disjoint_cocompact`, `Set.indicator_mul_const`, `mul_lt_mul''`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective`, `HasFDerivAt.list_prod'`, `IsIdempotentElem.coe_zero`, `IsUnit.isNilpotent_mul_unit_of_commute_iff`, `SimpleGraph.adjMatrix_hadamard_self`, `hasFDerivAt_pow'`, `Ordinal.principal_mul_two`, `mul_le_one₀`, `Ordinal.deriv_mul_eq_opow_omega0_mul`, `Ordinal.isPrincipal_mul_omega`, `gcd_dvd_gcd_mul_right_right`, `Ordinal.principal_mul_iff_mul_left_eq`, `WithBot.mul_eq_bot_iff`, `Set.indicator_const_mul`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `mul_eq_mul_iff_eq_and_eq_of_pos`, `squarefree_mul_iff`, `mul_eq_mul_of_div_eq_div`, `DualNumber.algHom_ext_iff`, `one_le_inv_mul₀`, `HasDerivAt.real_of_complex`, `mulRight_bijective₀`, `Nonneg.coe_mul`, `OrderMonoidWithZeroHom.coe_mul`, `eq_div_iff_mul_eq`, `Set.preimage_mul_const_Ico₀`, `inv_pow_sub₀`, `zpow_sub_one₀`, `Ordinal.forall_lt_mul`, `AlgEquiv.moduleEndSelf_apply_apply`, `Ordinal.mul_div_cancel`, `NNReal.orderIsoRpow_symm_eq`, `not_isLeftRegular_zero_iff`, `multiplicity_mul`, `WithTop.top_mul_top`, `WithZero.toMulBot_coe`, `Ordinal.add_mul_of_isSuccLimit`, `Ordinal.card_mul`, `Set.image_mul_left_Iic`, `WithTop.mul_lt_top`, `mul_inv_eq_one₀`, `mul_div_cancel_left_of_imp`, `meromorphicOrderAt_pow`, `ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic`, `Matrix.isAdjMatrix_iff_hadamard`, `one_lt_mul_of_lt_of_le`, `instIsCancelMulZero`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `HasCompactSupport.mul_left`, `finiteMultiplicity_mul_aux`, `NonUnitalRingHom.mul_def`, `CliffordAlgebraDualNumber.equiv_ι`, `IsPrimal.mul`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero`, `Ordinal.mul_le_right_iff_opow_omega0_dvd`, `Ordinal.mul_sub`, `cfcₙAux_mem_range_inr`, `Ring.inverse_mul_cancel_right`, `WithBot.instMulPosReflectLT`, `AlgEquiv.moduleEndSelfOp_symm_apply`, `inv_le_iff_one_le_mul₀`, `inv_pow_sub_of_lt`, `gcd_mul_right`, `inv_mul_right_le`, `le_mul_inv_iff₀`, `Metric.unitBall.instIsRightCancelMulZero`, `zero_mul_eq_const`, `map_mul_right_nhds₀`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `inv_le_iff_one_le_mul₀'`, `Matrix.diagonal_kronecker_diagonal`, `DualNumber.instIsLocalRing`, `Ordinal.opow_add_one`, `mul_self_lt_mul_self`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `HasMFDerivWithinAt.mul`, `mul_eq_zero_comm`, `Ordinal.principal_mul_omega0_opow_opow`, `mul_div_mul_left`, `Matrix.diagonal_hadamard_diagonal`, `UniqueFactorizationMonoid.multiplicative_prime_power`, `inv_mul_cancel_of_invertible`, `zpow_neg_mul_zpow_self`, `inv_mul_lt_iff₀'`, `IsSelfAdjoint.inv₀_iff`, `Ordinal.omega0_opow_mul_nat_lt`, `pow_sub₀`, `MulEquiv.isCancelMulZero_iff`, `HasFDerivAt.pow'`, `HasStrictFDerivAt.pow'`, `Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange`, `Matrix.vecMulVec_eq_zero`, `WithBot.mul_bot`, `NormalizationMonoid.normUnit_mul`, `NonUnitalRingHom.coe_mul`, `Matrix.diagonal_hadamard_eq_diagonal_iff`, `inv_lt_iff_one_lt_mul₀'`, `SemiconjBy.zero_left`, `Associates.out_mul`, `Ordinal.lt_mul_iff_of_isSuccLimit`, `HasStrictFDerivAt.mul_const'`, `map_mul_right_nhds_one₀`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `Matrix.dualNumberEquiv_apply`, `mul_eq_zero_iff_right`, `ArithmeticFunction.IsMultiplicative.iff_ne_zero`, `zero_eq_mul_self`, `fderivWithin_list_prod'`, `Submonoid.LocalizationMap.isCancelMulZero`, `Ring.mul_inverse_rev`, `mul_inv_eq_iff_eq_mul₀`, `DualNumber.eps_pow_two`, `Homeomorph.mulRight₀_symm_apply`, `HasFDerivWithinAt.fun_mul'`, `mul_nonpos_of_nonneg_of_nonpos`, `Commute.div_eq_div_iff`, `Valuation.IsEquiv.orderMonoidIso_eq_refl`, `Ordinal.add_mul_succ`, `Finset.gcd_mul_right`, `Quaternion.re_snd_dualNumberEquiv`, `Ordinal.CNF.opow_mul_add`, `WithBot.instMulPosReflectLE`, `Set.center_units_eq`, `WithZero.withZeroUnitsEquiv_symm_apply`, `mul_ite_zero`, `StieltjesFunction.ae_hasDerivAt`, `fderivWithin_pow_ring'`, `Ordinal.mul_add_mod_mul`, `ProbabilityTheory.measure_condCDF_Iic`, `Commute.self_zpow₀`, `Ring.inverse_mul_cancel_left`, `Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow`, `Pi.single_mul_left`, `Ordinal.isSuccLimit_mul_right`, `not_isRegular_zero`, `zpow_one_add₀`, `ProbabilityTheory.measurable_measure_condCDF`, `Ordinal.CNF.eval_single_add`, `inv_mul_le_one_of_le₀`, `Ordinal.opow_mul_lt_opow`, `Ring.mul_inverse_cancel_left`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `meromorphicOrderAt_zpow`, `Set.image_mul_left_Ioo`, `HasFDerivWithinAt.fun_pow'`, `Ordinal.isSuccPrelimit_mul_left`, `ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat`, `invOf_eq_inv`, `LinearOrderedCommMonoidWithZero.toMulPosStrictMono`, `Homeomorph.coe_mulLeft₀`, `Matrix.zero_vecMulVec`, `invOf_div`, `div_mul_cancel_right₀`, `one_div_mul_cancel`, `DualNumber.exp_smul_eps`, `Set.preimage_mul_const_Ioc₀`, `Quaternion.snd_imI_dualNumberEquiv_symm`, `Antitone.mul_const`, `continuous_cfcₙAux`, `ONote.repr_opow_aux₂`, `Finset.mul₀_sup'`, `HasFDerivAt.mul_const'`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `StrictMono.mul_monotone`, `HasStrictFDerivAt.fun_pow'`, `MulEquiv.withZero_symm_apply_apply`, `MeasurableEquiv.coe_mulLeft₀`, `IsLeftCancelMulZero.to_noZeroDivisors`, `List.prod_map_le_pow_length₀`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg`, `DualNumber.lift_apply_inl`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `Ordinal.mul_le_iff_le_div`, `UniqueFactorizationMonoid.radical_mul_dvd`, `Real.hasFDerivAt_fourierChar_neg_bilinear_right`, `IsDedekindDomain.HeightOneSpectrum.intValuation.map_mul'`, `ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction`, `ProbabilityTheory.measure_condCDF_univ`, `MulHom.single_apply`, `squarefree_iff_no_irreducibles`, `DualNumber.lift_op_smul`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_left`, `ContinuousLinearEquiv.coord_norm'`, `Ordinal.isPrincipal_mul_one`, `WithTop.mul_left_strictMono`, `Function.support_mul`, `Finset.Nonempty.zero_mul`, `Metric.unitClosedBall.instIsCancelMulZero`, `mul_inv_lt_iff₀'`, `GroupWithZero.mul_left_injective`, `Ordinal.isPrincipal_add_mul_of_isPrincipal_add`, `Set.Nonempty.mul_zero`, `Commute.mul_inv_eq_mul_inv_iff`, `dvd_gcd_mul_of_dvd_mul`, `Set.image_mul_right_Ico`, `Ordinal.mul_omega0_opow_opow`, `WithBot.bot_mul`, `Commute.zpow_zpow₀`, `instIsCancelMulZero_1`, `div_lt_div_iff₀`, `instMulPosStrictMonoWithZeroOfMulRightStrictMono`, `WithTop.coe_mul`, `Ordinal.nfp_mul_one`, `ContinuousMapZero.toNNReal_neg_smul`, `Ordinal.opow_succ`, `WithZero.toMulBot_le`, `DualNumber.lift_comp_inlHom`, `MonoidWithZeroHom.map_mul`, `ValuativeRel.restrict_lt_orderMonoidIso`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂`, `Ordinal.isPrincipal_mul_two`, `DualNumber.algHom_ext'_iff`, `hasStrictFDerivAt_list_prod'`, `DualNumber.ideal_trichotomy`, `notMem_nonZeroDivisors_iff_left`, `boole_mul`, `Ordinal.le_mul_left`, `tsupport_mul_subset_right`, `Complex.UnitDisc.instPNatPowAssoc`, `isRightRegular_zero_iff_subsingleton`, `Matrix.hadamard_diagonal`, `Ordinal.nfp_add_zero`, `Metric.unitBall.instIsCancelMulZero`, `Commute.inv_right₀`, `Finsupp.coe_mul`, `Ordinal.mul_two`, `ContinuousMapZero.elemental_eq_top`, `mul_right_bijective_of_finite₀`, `lcm_dvd_lcm_mul_left_right`, `UniqueFactorizationMonoid.factors_mul`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft`, `WithZero.withZeroUnitsEquiv_apply`, `Finsupp.sym2Mul_apply_mk`, `Mathlib.Tactic.FieldSimp.zpow'_add`, `MeasureTheory.charFun_map_eq_charFunDual_smul`, `Submonoid.LocalizationMap.lift₀_apply`, `ProbabilityTheory.gaussianPDFReal_mul`, `mul_eq_zero_of_ne_zero_imp_eq_zero`, `le_div_iff₀`, `star_div₀`, `Set.inter_indicator_one`, `Matrix.IsAdjMatrix.hadamard_self`, `ONote.scale_opowAux`, `star_zpow₀`, `PosMulReflectLT.toPosMulStrictMono`, `Matrix.toLinearMapRight'_one`, `mul_mem_nonZeroDivisorsRight_of_mem_nonZeroDivisorsRight`, `HasFDerivWithinAt.mul'`, `Units.mul_left_eq_zero`, `mulPosReflectLT_iff_contravariant_pos`, `mul_inv_le_of_le_mul₀`, `mul_right_eq_self₀`, `Ordinal.mul_div_mul_cancel`, `Set.inter_indicator_mul`, `Set.indicator_mul_right`, `Ordinal.add_le_right_iff_mul_omega0_le`, `eq_div_iff`, `posMulMono_iff_posMulStrictMono`, `Valuation.IsEquiv.orderMonoidIso_spec`, `Ordinal.isPrincipal_mul_iff_mul_left_eq`, `WithBot.coe_mul_eq_bind`, `Set.indicator_mul_left`, `Ordinal.isSuccLimit_mul_left`, `SimpleGraph.adjMatrix_hadamard_natCast`, `HasStrictDerivAt.complexToReal_fderiv`, `LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered`, `Multipliable.tsum_congr_cofinite₀`, `fderivWithin_mul'`, `StrictAnti.mul_const`, `PosMulMono.toPosMulStrictMono`, `div_le_iff₀'`, `WithTop.instNoZeroDivisors`, `mul_left_surjective₀`, `Finset.zero_mul_subset`, `Right.mul_lt_mul_of_nonneg`, `map_mul_left_nhds₀`, `List.prod_map_le_prod_map₀`, `Ordinal.lift_mul`, `Monotone.const_mul`, `mul_sup₀`, `WithBot.instPosMulReflectLT`, `dvd_gcd_mul_iff_dvd_mul`, `mul_inv_mul_cancel`, `monotone_mul_left_of_nonneg`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `StrictMono.mul_const`, `MeasureTheory.AEFinStronglyMeasurable.mul`, `VectorFourier.hasFDerivAt_fourierChar_smul`, `WithZero.coe_mul`, `Finset.mul_zero_subset`, `instPosMulStrictMonoWithZeroOfMulLeftStrictMono`, `MulChar.coeToFun_mul`, `inv_mul_cancel₀`, `Commute.inv_left₀`, `lt_mul_left`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zero`, `Ordinal.lt_omega0_omega0_opow`, `fderiv_list_prod'`, `HasMFDerivWithinAt.prod`, `Finset.inf'_mul_le_mul_inf'_of_nonneg`, `ZeroAtInftyContinuousMap.mul_apply`, `HasMFDerivAt.mul'`, `Mathlib.Tactic.FieldSimp.NF.eval_cons`, `ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply`, `Multiset.gcd_map_mul`, `MulEquiv.noZeroDivisors`, `Antitone.const_mul`, `mul_self_div_self`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono`, `mul_div_cancel_of_imp`, `notMem_nonZeroDivisorsLeft_iff`, `DualNumber.instIsPrincipalIdealRing`, `eq_mul_of_mul_inv_eq₀`, `MonoidWithZeroHom.commute_inl_inr`, `notMem_nonZeroDivisors_iff_right`, `Ordinal.mul_omega0`, `Ordinal.principal_mul_one`, `mul_mem_nonZeroDivisors`, `WithTop.mul_right_strictMono`, `VectorFourier.fourierIntegral_fderiv`, `UniqueFactorizationMonoid.radical_mul`, `Left.mul_lt_mul_of_nonneg`, `HasFDerivAt.fun_mul'`, `UniqueFactorizationMonoid.toIsCancelMulZero`, `Ordinal.le_div`, `SimpleGraph.natCast_hadamard_adjMatrix`, `div_mul_div_cancel₀`, `Right.mul_nonneg`, `lt_mul_self`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `SignType.coe_mul`, `mul_neg_of_pos_of_neg`, `WithZero.toMulBot_symm_bot`, `NONote.repr_mul`, `right_eq_mul₀`, `Set.zero_mem_center`, `Set.indicator_prod_one`, `CompactlySupportedContinuousMap.instIsScalarTower`, `Units.inv_mul'`, `HasFDerivAt.mul'`, `GroupWithZero.noZeroDivisors`, `mul_left_cancel_iff_of_pos`, `SemiconjBy.inv_symm_left_iff₀`, `Quaternion.fst_re_dualNumberEquiv_symm`, `hasFDerivAt_list_prod_attach'`, `Quaternion.imI_snd_dualNumberEquiv`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero`, `ArithmeticFunction.IsMultiplicative.map_mul_of_coprime`, `Pi.single_mul_right_apply`, `gcd_dvd_gcd_mul_left`, `eq_mul_of_inv_mul_eq₀`, `Ring.eq_mul_inverse_iff_mul_eq`, `div_mul_eq_mul_div₀`, `Matrix.kronecker_diagonal`, `Set.image_mul_left_Ici`, `one_le_mul_of_one_le_of_one_le`, `Matrix.IsDiag.kronecker`, `WithZero.toMulBot_strictMono`, `Set.preimage_const_mul_Iic₀`, `Matrix.hadamard_one_eq_diagonal_iff`, `notMem_nonZeroDivisorsRight_iff`, `emultiplicity_mul`, `noZeroDivisors_iff_eq_zero_of_mul`, `Tendsto.tendsto_mul_zero_of_disjoint_cocompact_right`, `Set.preimage_mul_const_Iio₀`, `NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal`, `SimpleGraph.adjMatrix_hadamard_one`, `LinearMap.toMatrixRight'_comp`, `mulPosMono_iff_mulPosStrictMono`, `Set.preimage_mul_const_Ioi₀`, `OrderMonoidWithZeroHom.mul_apply`, `Ordinal.mod_def`, `Filter.EventuallyEq.div_mul_cancel`, `mul_eq_mul_prime_prod`, `UniqueFactorizationMonoid.exists_reduced_factors'`, `MeasurableEquiv.coe_mulRight₀`, `Valuation.IsEquiv.orderMonoidIso_symm`, `star_inv₀`, `fun_meromorphicOrderAt_pow`, `MeromorphicAt.meromorphicOrderAt_comp`, `inv_mul_cancel_right₀`, `Ordinal.isPrincipal_mul_ord`, `WithZero.withZeroUnitsEquiv_strictMono`, `le_inv_mul_left`, `one_lt_inv_mul₀`, `LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered`, `Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow`, `SemiconjBy.inv_right_iff₀`, `inv_mul_le_iff₀'`, `ProbabilityTheory.IsCondKernelCDF.toKernel_apply`, `MulPosReflectLT.toMulPosReflectLE`, `ProbabilityTheory.instIsProbabilityMeasurecdf`, `Ordinal.mul_div_le`, `PosMulReflectLE.toPosMulReflectLT`, `noZeroDivisors_iff_right_eq_zero_of_mul`, `IsRightCancelMulZero.to_noZeroDivisors`, `FiniteMultiplicity.mul_iff`, `MulEquiv.withZero_symm_apply_symm_apply`, `Ordinal.mul_le_iff_of_isSuccLimit`, `Matrix.kronecker_zero`, `Ordinal.mul_omega0_dvd`, `GrpWithZero.Iso.mk_inv`, `tendsto_mul_nhds_zero_prod_of_disjoint_cocompact`, `Mathlib.Tactic.FieldSimp.mul_zpow'`, `mul_inv_le_iff₀'`, `exists_mem_nhds_zero_mul_subset`, `Pi.single_mul`, `HasFDerivWithinAt.list_prod'`, `List.prod_nonneg`, `Quaternion.imK_snd_dualNumberEquiv`, `WithTop.mul_eq_top_iff`, `measurableEmbedding_mulLeft₀`, `fderivWithin_pow'`, `WithBot.coe_mul`, `Ordinal.lt_mul_iff`
`toZero` 📖	CompOp	10338 math math: `Finset.map_nsmul_piAntidiag_univ`, `MvPolynomial.is_id`, `QuaternionAlgebra.coe_sub`, `range_cfcₙ_nnreal`, `AddMonoidAlgebra.sup_support_list_prod_le`, `Matrix.l2_opNorm_toEuclideanCLM`, `ContinuousMapZero.coe_star`, `IsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one`, `ascPochhammer_ne_zero_eval_zero`, `Finsupp.image_prodMap_embDomain_antidiagonal`, `AddMonoidAlgebra.instIsLeftCancelAddZeroOfIsCancelAddOfUniqueSums`, `MvPolynomial.pUnitAlgEquiv_symm_monomial`, `MvPowerSeries.coeff_zero_eq_constantCoeff_apply`, `RatFunc.instFaithfulSMulPolynomialLaurentSeries`, `HasDerivAt.fun_neg`, `Ideal.mem_bot`, `Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff`, `Subsemiring.mem_sumSq`, `MvPolynomial.funext_iff`, `ValueDistribution.logCounting_zero`, `MvPolynomial.eval_indicator_apply_eq_one`, `TestFunction.lineDerivCLM_apply_of_le`, `Quaternion.normSq_eq_zero`, `absorbent_iff_eventually_nhdsNE_zero`, `Height.logHeight_eval_ge`, `AddMonoidAlgebra.modOf_apply_add_self`, `MvPolynomial.join₁_rename`, `MvPolynomial.vanishingIdeal_anti_mono`, `MvPowerSeries.hasSubst_def`, `one_le_div_iff`, `LinearMap.IsSymmetric.clm_adjoint_eq`, `RingCone.mem_nonneg`, `Num.cast_to_int`, `Valuation.mem_nhds_zero_iff`, `GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one`, `GCDMonoid.lcm_zero_right`, `MvPolynomial.eval₂_mul_eq_zero_of_left`, `AlgebraicGeometry.AffineSpace.map_Spec_map`, `ContinuousMap.toLp_inj`, `CStarAlgebra.preimage_inr_Icc_zero_one`, `Nat.pos_of_floor_pos`, `ArithmeticFunction.dirichletInverseFun_apply_zero`, `Matrix.isTotallyUnimodular_iff`, `Quaternion.star_mul_self`, `MvPolynomial.aeval_sum`, `Matrix.det_updateCol_eq_zero`, `Finsupp.sum_toMultiset`, `continuousSMul_sphere_ball`, `instContMDiffAddOfNatWithTopENatOfContinuousAdd`, `MvPolynomial.dvd_monomial_one_iff_exists`, `instPosSMulStrictMonoIntOfIsOrderedAddMonoid`, `Quaternion.coe_normSq_add`, `WittVector.bind₁_frobeniusPoly_wittPolynomial`, `AddMonoidAlgebra.instIsCancelAddZeroOfIsCancelAddOfUniqueSums`, `MonomialOrder.le_degree_of_mem_support`, `Num.minFac_to_nat`, `LaurentPolynomial.smeval_eq_sum`, `LSeries.convolution_one_eq_convolution_zeta`, `fderiv_iteratedFDeriv`, `mul_self_nonneg`, `Finsupp.finite_of_degree_le`, `WithBot.mul_bot'`, `HasStrictDerivAt.fun_pow'`, `sign_intCast`, `IsGaloisGroup.smul_mem_of_normal`, `FormalMultilinearSeries.comp_rightInv_aux1`, `tendsto_zero_iff_meromorphicOrderAt_pos`, `Affine.Simplex.affineCombination_mem_closedInterior_iff`, `AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq`, `MonoidAlgebra.ofCoeff_injective`, `mul_nonpos_iff_neg_imp_nonneg`, `IsAlgClosed.roots_eq_zero_iff_degree_nonpos`, `Unitization.isometry_inr`, `unitsEquivNeZero_symm_apply`, `Matrix.natCast_kronecker`, `Nonneg.instIsScalarTower`, `cfcₙ_def`, `LinearMap.mkContinuous₂_norm_le'`, `IsCyclotomicExtension.neZero_of_mem`, `AddCircle.coe_equivIco_mk_apply`, `KaehlerDifferential.mvPolynomialBasis_apply`, `IsSelfAdjoint.sq_nonneg`, `MeasureTheory.eLpNormEssSup_const_smul_le`, `ContinuousMultilinearMap.norm_mkPiRing`, `AddMonoidAlgebra.supportedEquivFinsupp_apply_apply`, `MvPowerSeries.WithPiTopology.tendsto_trunc_atTop`, `Matrix.toLinAlgEquiv_one`, `Finsupp.linearCombination_apply_of_mem_supported`, `ContinuousLinearMap.derivWithin_of_bilinear`, `HahnModule.support_smul_subset_vadd_support'`, `PEquiv.vecMul_toMatrix_toPEquiv`, `AddMonoidAlgebra.mul_single_apply`, `Polynomial.isLeftCancelMulZero_iff`, `affineHomeomorph_image_Ioc`, `Matrix.PosDef.diag_pos`, `ProperCone.dual_insert`, `HasDerivWithinAt.clm_comp`, `LaurentPolynomial.degree_C_mul_T_ite`, `AlgebraicGeometry.Scheme.height_of_isClosed`, `MvPolynomial.coeff_neg`, `RatFunc.mk_def_of_ne`, `Module.Basis.equivFun_self`, `Polynomial.mem_aroots'`, `NonUnitalStarSubalgebra.coe_zero`, `SkewMonoidAlgebra.domCongr_support`, `MvPolynomial.support_sum`, `Module.Presentation.cokernelRelations_relation`, `FirstOrder.Language.presburger.mul_not_definable`, `HasDerivWithinAt.congr_of_mem`, `Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff`, `RootPairing.GeckConstruction.h_def`, `MonomialOrder.sPolynomial_leadingTerm_mul'`, `MvPolynomial.degrees_neg`, `ProbabilityTheory.cdf_measure_stieltjesFunction`, `continuous_cfcₙHomSuperset_left`, `hasDerivWithinAt_Iio_iff_Iic`, `cfcₙL_integral`, `Nat.ofDigits_eq_sum_mapIdx_aux`, `MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top`, `TrivSqZeroExt.exp_inr`, `MvPolynomial.coe_C`, `Matrix.list_prod_inv_reverse`, `Algebra.PreSubmersivePresentation.jacobiMatrix_naive`, `Function.locallyFinsuppWithin.logCounting_single_eq_log_sub_const`, `RingHom.ker_evalRingHom`, `LinearMap.mkContinuous₂_apply`, `IsDiscreteValuationRing.addVal_zero`, `Matrix.swap_mul_self`, `isRegular_iff_subsingleton`, `exists_quadratic_eq_zero`, `RCLike.pos_iff_exists_ofReal`, `MvPolynomial.isJacobsonRing`, `Complex.UnitDisc.coe_eq_zero`, `AffineMap.hasStrictDerivAt_lineMap`, `ContinuousLinearMap.isPositive_iff_eq_sum_rankOne`, `MvPowerSeries.coeff_zero_eq_constantCoeff`, `LinearMap.BilinForm.zero_right`, `dot_self_cross`, `MvPolynomial.support_mul`, `CliffordAlgebra.contractRight_algebraMap`, `AddMonoidAlgebra.lift_apply'`, `InnerProductSpace.isPositive_rankOne_self`, `MvPolynomial.algHom_ext_iff`, `MonomialOrder.span_leadingTerm_sdiff_singleton_zero`, `Quaternion.re_star`, `ENat.floor_pos`, `AddMonoidAlgebra.mapDomainRingEquiv_apply`, `MvPolynomial.map_bind₁`, `HahnSeries.instNoZeroDivisorsFinsuppNat`, `MonoidAlgebra.liftMagma_apply_apply`, `ValuativeRel.zero_veq_iff`, `DFinsupp.toMultiset_sup`, `MvPolynomial.vars_sum_of_disjoint`, `QuaternionAlgebra.coe_mul_eq_smul`, `MvPowerSeries.zero_inv`, `PrimeSpectrum.isClopen_iff_mul_add`, `Orthonormal.inner_left_finsupp`, `collapse_eq`, `MvPolynomial.totalDegree_monomial`, `Matrix.invOf_fromBlocks₂₂_eq`, `WeierstrassCurve.Jacobian.addXYZ_self`, `Algebra.Generators.aeval_val_surjective`, `AlgebraicGeometry.AffineSpace.map_toSpecMvPoly_assoc`, `ofDual_toAdd_zero`, `IncidenceAlgebra.prod_mk`, `Function.locallyFinsuppWithin.logCounting_strictMono`, `ContinuousLinearMap.mulLeftRight_isBoundedBilinear`, `RootPairing.coxeterWeight_nonneg`, `norm_cfcₙHom`, `logDeriv_const`, `Module.Basis.mem_submodule_iff`, `discrim_le_zero_of_nonpos`, `HasFDerivWithinAt.continuousMultilinearMap_apply`, `Matrix.transposeInvertibleEquivInvertible_symm_apply`, `IntermediateField.aeval_gen_minpoly`, `FractionalIdeal.eq_zero_iff`, `MvPolynomial.mul_X_divMonomial`, `MDifferentiableOn.clm_postcomp`, `ArithmeticFunction.sigma_pos`, `CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_snd`, `cfcₙHom_mono`, `WithBot.instPosMulStrictMono`, `hasDerivWithinAt_ofNat`, `IsIsotypic.linearEquiv_fun`, `ContinuousLinearMap.analyticWithinAt_bilinear`, `ENat.top_pos`, `MvPolynomial.radical_le_vanishingIdeal_zeroLocus`, `Matrix.frobeniusIsBoundedSMul`, `Quaternion.instSMulCommClass`, `HasCompactSupport.convolution_integrand_bound_left`, `NonUnitalSubsemiring.mem_bot`, `Module.Relations.Solution.ofπ'_var`, `ContinuousLinearMap.compSL_apply`, `QuaternionAlgebra.self_add_star`, `ContinuousLinearMap.continuous₂`, `Module.Basis.end_repr_apply`, `QuaternionAlgebra.coe_pow`, `AddMonoidAlgebra.mul_apply`, `NonUnitalSubalgebra.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallForallHSMul`, `Polynomial.ofFn_zero`, `Algebra.Presentation.differentials.comm₁₂_single`, `Polynomial.toLaurent_eq_zero`, `wittPolynomial_zmod_self`, `PointedCone.ofSubmodule_lineal`, `Nat.coe_properDivisors_eq_prod_pow_lt_factorization`, `HasDerivAt.const_sub`, `MvPolynomial.aeval_X_left`, `hasDerivWithinAt_add_const_iff`, `Nat.Prime.exists_orderOf_eq_pow_factorization_exponent`, `MvPowerSeries.coeff_zero`, `MvPolynomial.map_mapRange_eq_iff`, `Matroid.eRk_loops`, `FormalMultilinearSeries.comp_partialSum`, `MvPowerSeries.weightedOrder_monomial`, `MvPolynomial.map_comp_C`, `MvPolynomial.DirectSum.coeLinearMap_eq_dfinsuppSum`, `MvPolynomial.coeffs_add`, `nonZeroDivisorsLeft_eq_nonZeroSMulDivisors`, `HasDerivAtFilter.sum`, `EisensteinSeries.gammaSet_div_gcd_to_gammaSet10_bijection`, `MvPowerSeries.eq_iff_frequently_trunc'_eq`, `PowerSeries.coeff_mul_of_lt_order`, `MvPolynomial.pUnitAlgEquiv_apply`, `LucasLehmer.mersenne_coe_X`, `LinearIndependent.pair_iff`, `Filter.Tendsto.div_atTop`, `Nat.Primes.prodNatEquiv_symm_apply`, `Nat.multiplicity_eq_factorization`, `Finset.affineCombinationSingleWeights_apply_of_ne`, `ZMod.pow_card_sub_one`, `Fintype.linearIndependent_iffₒₛ`, `tendsto_inv_atTop_zero`, `Bornology.isVonNBounded_iff_tendsto_smallSets_nhds`, `AnalyticOnNhd.eq_zero_or_eq_zero_of_smul_eq_zero`, `neg_of_div_neg_right`, `MvPolynomial.eval₂Hom_X`, `Polynomial.monomial_eq_monomial_iff`, `Polynomial.ofFinsupp_zero`, `tendsto_const_mul_pow_nhds_iff'`, `dotProduct_zero'`, `Nat.factorization_eq_zero_of_not_dvd`, `ConjRootClass.mk_zero`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `MvPolynomial.toMvPowerSeries_uniformContinuous`, `HasDerivWithinAt.Iio_of_Iic`, `affineHomeomorph_image_Ico`, `hasStrictDerivAt_intCast`, `MvPolynomial.exists_finset_rename`, `MonomialOrder.monic_X_sub_C`, `MvPolynomial.hom_C`, `Polynomial.Chebyshev.U_eval_zero`, `cfcₙ_norm_nonneg`, `IsPrimePow.exists_ordCompl_eq_one`, `AlgebraicIndependent.of_aeval`, `NormedRing.inverse_one_sub_norm`, `MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_same`, `inv_eq_zero`, `Polynomial.coeff_X_pow_mul'`, `MeasureTheory.convolution_eq_right'`, `EisensteinSeries.hasSum_e2Summand_symmetricIcc`, `MeasureTheory.eLpNorm_smul_le_mul_eLpNorm`, `NonUnitalIsometricContinuousFunctionalCalculus.isometric`, `PowerSeries.coeff_of_lt_order_toNat`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn`, `Quaternion.im_add`, `ExteriorAlgebra.ι_eq_algebraMap_iff`, `AddMonoidAlgebra.coeffEquiv_symm_apply`, `Polynomial.coeff_natTrailingDegree_eq_zero`, `MvPowerSeries.truncFinset_one`, `lcm_eq_zero_iff`, `cfcₙHom_apply_mem_elemental`, `NormedSpace.hasFPowerSeriesAt_exp_zero_of_radius_pos`, `HahnSeries.mem_cardSuppLTSubfield`, `Polynomial.homogenize_map`, `MvPowerSeries.trunc'_trunc'`, `SimpleGraph.lapMatrix_toLinearMap₂'`, `nonneg_of_mem_doublyStochastic`, `curveIntegral_smul`, `Valuation.one_apply_lt_one_iff`, `CStarAlgebra.mem_Icc_algebraMap_iff_norm_le`, `Quaternion.snd_imJ_dualNumberEquiv_symm`, `sign_mul_self`, `Metric.externalCoveringNumber_eq_zero`, `Num.cast_lt`, `inner_vsub_right_eq_zero_symm`, `Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col`, `CFC.monotoneOn_one_sub_one_add_inv`, `Subring.center.smulCommClass_right`, `Quaternion.imI_zero`, `RCLike.tendsto_inverse_atTop_nhds_zero_nat`, `MvPolynomial.support_finSuccEquiv`, `zero_zpow`, `Set.encard_eq_zero`, `Matrix.add_mul_mul_invOf_mul_eq_one`, `Algebra.PreSubmersivePresentation.cotangentComplexAux_apply`, `MvPolynomial.rTensor_apply_tmul_apply`, `InnerProductSpace.rankOne_one_left_eq_innerSL`, `MvPolynomial.degrees_monomial`, `Submonoid.exists_finsupp_of_mem_closure_range`, `mul_neg_of_neg_of_pos`, `Nat.Prime.factorization_pos_of_dvd`, `StandardEtalePair.inv_aeval_X_g`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv`, `Matrix.single_hadamard_single_eq`, `MvPolynomial.zero_divMonomial`, `Ideal.mem_span_iff_exists_isHomogeneous`, `emultiplicity_of_isUnit_right`, `Function.FactorizedRational.divisor`, `cfcₙ_zero`, `CliffordAlgebraQuaternion.j_quaternionBasis`, `MvPolynomial.coeff_divMonomial`, `Left.neg_of_mul_neg_left`, `WittVector.aeval_verschiebung_poly'`, `NonUnitalStarAlgHom.inl_apply`, `StrongDual.norm_extendRCLike`, `bernsteinPolynomial.eval_at_1`, `Quaternion.imJ_im`, `Quaternion.coe_natCast`, `Matrix.Nondegenerate.eq_zero_of_ortho`, `Quaternion.instNoZeroDivisors`, `MvPolynomial.eval_zero'`, `Polynomial.natDegree_le_iff_coeff_eq_zero`, `PowerSeries.heval_C`, `QuadraticAlgebra.coe_mul_eq_smul`, `HasFiniteFPowerSeriesAt.neg`, `inv_atBot₀`, `MonomialOrder.degree_add_of_ne`, `Submodule.mem_ideal_smul_span_iff_exists_sum`, `nnnorm_cfcₙ_nnreal_le_iff`, `MvPolynomial.sum_def`, `FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero`, `RootPairing.Base.not_nonneg_iff_neg_of_sum_mem_range_root`, `MvPolynomial.rTensorAlgEquiv_apply`, `MvPolynomial.one_def`, `ClassGroup.mk0_eq_mk0_iff`, `IsAbsoluteValue.abv_nonneg'`, `Algebra.Generators.H1Cotangent.δAux_mul`, `MvPowerSeries.coeff_mul_monomial`, `ContinuousLinearMap.map_add_add`, `Algebra.Presentation.naive_toGenerators`, `Complex.UnitDisc.instIsScalarTower_circle`, `SeminormFamily.basisSets_smul_right`, `Multiset.toFinsupp_add`, `Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall`, `QuadraticMap.sum_polar_sub_repr_sq`, `Matrix.kronecker_natCast`, `Metric.packingNumber_eq_zero`, `AddSubgroup.zero_smul`, `RootPairing.RootPositiveForm.zero_lt_posForm_apply_root`, `MeromorphicOn.divisor_fun_smul`, `Valuation.val_mrange_zero`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `MonoidAlgebra.support_one_subset`, `FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite`, `HasDerivWithinAt.div_const`, `Unitization.inrNonUnitalAlgHom_toFun`, `MvPolynomial.mem_image_support_coeff_finSuccEquiv`, `mul_nonneg`, `Finset.sum_boole_mul`, `Commute.lie_eq`, `MvPolynomial.mapEquiv_symm`, `meromorphicOrderAt_const_ofNat`, `ContDiffMapSupportedIn.seminorm_monoLM_eq`, `fderivWithin_fun_smul`, `ContinuousMultilinearMap.norm_iteratedFDerivComponent_le`, `Metric.unitSphere.coe_one`, `Finsupp.toMultiset_strictMono`, `HasDerivWithinAt.congr_mono`, `ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff`, `MvPolynomial.scalarRTensor_apply_monomial_tmul`, `AffineMap.hasDerivAtFilter`, `Polynomial.update_zero_eq_erase`, `ArithmeticFunction.cardFactors_pow`, `Subring.zero_mem`, `MvPolynomial.comapEquiv_symm_coe`, `Multiset.lcm_eq_zero_iff`, `MvPolynomial.homogeneousComponent_eq_zero'`, `dvd_zero`, `Module.basisUnique_repr_eq_zero_iff`, `Matrix.single_vecMul`, `WeierstrassCurve.Projective.eval_polynomial`, `Function.support_mul_subset_right`, `Valuation.mem_supp_iff`, `Polynomial.rootMultiplicity_eq_rootMultiplicity`, `Nat.factorization_prod_pow_eq_self_of_le_factorization`, `fderivWithin_fderivWithin_eq_of_mem_nhdsWithin`, `Matrix.charpoly.univ_map_map`, `SkewMonoidAlgebra.coeff_single_one_mul`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm`, `tendsto_const_div_atTop_nhds_zero_nat`, `Nat.ordCompl_le`, `LinearMap.IsPositive.ne_zero_iff`, `EuclideanDomain.mod_zero`, `MvPolynomial.eval₂_expand`, `Quaternion.star_smul`, `hasDerivAt_integral_of_dominated_loc_of_lip`, `PadicInt.coe_zero`, `Ideal.single_mem_pi`, `MvPolynomial.isOpenMap_comap_C`, `MvPolynomial.weightedDegree_eq_zero_iff`, `ZMod.LFunction_modOne_eq`, `Mathlib.Meta.Positivity.pos_of_isNNRat`, `ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds`, `Matrix.one_div_pow`, `Matrix.det_add_replicateCol_mul_replicateRow`, `NonUnitalStarAlgebra.mem_bot`, `IsLeftRegular.mul_left_eq_zero_iff`, `MvPolynomial.universalFactorizationMap_comp_map`, `MvPolynomial.aeval_algebraMap_eq_zero_iff`, `Representation.ofMulActionSelfAsModuleEquiv_symm_apply`, `CFC.inv_nonneg`, `MDifferentiableAt.cle_arrowCongr`, `IsUnit.isStrictlyPositive_star_right_conjugate_iff`, `discrim_eq_zero_iff`, `Absorbs.eventually_nhds_zero`, `Polynomial.aeval_primPart_eq_zero`, `Matroid.eRk_empty`, `MvPowerSeries.support_expand`, `Algebra.norm_eq_zero_iff_of_basis`, `spectrum.subset_closedBall_norm_mul`, `cfcₙ_const_zero`, `continuousSMul_sphere_sphere`, `Polynomial.resultant_eq_zero_of_lt_lt`, `CStarAlgebra.nonneg_iff_exists_isSelfAdjoint_and_eq_mul_self`, `ProperCone.dual_sUnion`, `PEquiv.single_mul_single_of_ne`, `cfcₙHom_of_cfcHom_injective`, `SimpleGraph.adjMatrix_mulVec_apply`, `Mathlib.Tactic.Ring.single_pow`, `Nat.multiplicative_factorization'`, `mem_nonZeroDivisors_iff_left`, `HahnSeries.C_injective`, `hasFTaylorSeriesUpToOn_top_iff_right`, `isReduced_of_injective`, `NNRat.not_cast_lt_zero`, `MonomialOrder.degree_monomial`, `Polynomial.coeff_one`, `sign_eq_of_affineCombination_mem_affineSpan_pair`, `MeasureTheory.Lp.const_smul_mem_Lp`, `MvPolynomial.coeff_X_mul'`, `Subsemiring.closure_insert_zero`, `IsPrimePow.minFac_pow_factorization_eq`, `Matrix.cramer_transpose_row_self`, `IncidenceAlgebra.zeta_mul_kappa`, `MeasureTheory.MemLp.smul`, `PointedCone.ofSubmodule_sSup`, `AffineSubspace.setOf_sSameSide_eq_image2`, `NumberField.Units.fun_eq_repr`, `ContinuousMultilinearMap.analyticAt_uncurry_of_linear`, `Nat.factorization_prod_pow_eq_self`, `tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_map`, `Matrix.trace_mul_conjTranspose_self_eq_zero_iff`, `mul_self_eq_zero`, `eval₂_minpolyDiv_self`, `Matrix.iSup_eigenspace_toLin'_diagonal_eq_top`, `FormalMultilinearSeries.radius_pi_eq_iInf`, `MvPolynomial.expand_X`, `WittVector.teichmuller_mul_pow_coeff_of_ne`, `Multiset.equivDFinsupp_symm_apply`, `SchwartzMap.pairing_apply_apply`, `InnerProductSpace.isIdempotentElem_rankOne_self`, `algebraicIndependent_iff_ker_eq_bot`, `factorization_pow`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply`, `Matrix.cstar_nnnorm_def`, `IsBaseChange.basis_repr_comp_apply`, `PrimeSpectrum.isClopen_iff_mul_add_zeroLocus`, `WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_X`, `Differentiable.clm_comp`, `Padic.withValUniformEquiv_norm_le_one_iff`, `Module.DualBases.basis_repr_symm_apply`, `Module.Basis.toDual_linearCombination_left`, `mul_nonneg_iff_of_pos_right`, `MvPolynomial.IsSymmetric.map`, `Commute.cfcₙ_nnreal`, `Ideal.rank_prime_pow_ramificationIdx`, `Polynomial.aeval_algebraMap_eq_zero_iff`, `SkewMonoidAlgebra.algHom_ext'_iff`, `tendsto_cobounded_iff_meromorphicOrderAt_neg`, `RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra`, `AddMonoidAlgebra.supDegree_single`, `FreeAbelianGroup.toFinsupp_toFreeAbelianGroup`, `Nat.sub_one_mul_sum_log_div_pow_eq_sub_sum_digits`, `ConjRootClass.aeval_minpoly_iff`, `PowerSeries.coeff_trunc`, `ArithmeticFunction.carmichael_pow_of_prime_ne_two`, `cfc_const_zero`, `ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars`, `hasDerivWithinAt_Ioi_iff_Ici`, `ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto`, `HasStrictDerivAt.pow`, `MvPolynomial.derivation_eq_of_forall_mem_vars`, `LieModule.trace_toEnd_eq_zero_of_mem_lcs`, `Algebra.Generators.cotangentSpaceBasis_apply`, `Matroid.eRank_loopyOn`, `IsAdjoinRootMonic.coeff_apply`, `Module.Relations.Solution.surjective_π_iff_span_eq_top`, `Quaternion.imI_sub`, `SkewMonoidAlgebra.lift_apply'`, `FormalMultilinearSeries.changeOriginSeriesTerm_apply`, `Subring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg`, `Asymptotics.isLittleOTVS_one`, `Multiset.toDFinsupp_support`, `NNRat.cast_eq_zero`, `Quaternion.rank_eq_four`, `Filter.inv_nhdsWithin_ne_zero`, `meromorphicOrderAt_const`, `MvPolynomial.IsWeightedHomogeneous.pderiv`, `Cubic.of_a_eq_zero'`, `SkewMonoidAlgebra.support_single_mul`, `PointedCone.coe_ofSubmodule`, `HasDerivAt.hasDerivWithinAt`, `Rep.coindToInd_of_support_subset_orbit`, `ContinuousLinearMap.hasDerivAtFilter`, `AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply`, `ValuativeRel.valuation_eq_zero_iff`, `LucasLehmer.X.ofNat_snd`, `PowerSeries.zero_weierstrassDiv`, `OrderMonoidWithZeroHom.toFun_eq_coe`, `WithIdealFilter.mem_nhds_zero_iff`, `root_X_pow_sub_C_eq_zero_iff`, `Quaternion.star_eq_neg`, `Matrix.zero_mulVec`, `MvPolynomial.instIsReduced`, `toIcoMod_eq_fract_mul`, `MvPolynomial.X_pow_eq_monomial`, `MvPolynomial.isEmptyRingEquiv_apply`, `LinearMap.toMatrix_apply'`, `WittVector.ghostComponent_apply`, `Set.natCard_smul_set₀`, `MvPolynomial.ker_map`, `HahnModule.coeff_single_smul_vadd`, `ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors`, `ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall`, `HasDerivWithinAt.fun_div`, `Finset.weightedVSubVSubWeights_apply_of_ne`, `TrivSqZeroExt.isNilpotent_iff_isNilpotent_fst`, `Nonneg.isStrictOrderedRing`, `isRegular_iff_eq_zero_of_mul`, `ProperCone.innerDual_univ`, `Matrix.one_kronecker`, `MvPolynomial.map_leftInverse`, `aeval_wittPolynomial`, `HasFPowerSeriesOnBall.add`, `HahnSeries.leadingCoeff_mul`, `Quaternion.finrank_eq_four`, `CStarAlgebra.inr_mem_Icc_iff_norm_le`, `mul_right_mem_nonZeroDivisors_eq_zero_iff`, `Polynomial.rootMultiplicity_eq_natTrailingDegree'`, `tendsto_zpow_nhdsNE_zero_cobounded`, `NumberField.RingOfIntegers.instSMulDistribClass`, `OrderIso.mulRight₀_symm`, `AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop`, `pow_pos`, `ArithmeticFunction.cardFactors_multiset_prod`, `EuclideanDomain.lt_one`, `MonoidAlgebra.supportedEquivFinsupp_symm_apply_coe_apply`, `noZeroDivisors_iff_isDomain_or_subsingleton`, `IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff_mem_primeCompl`, `ContinuousMap.toLp_denseRange`, `AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero`, `Nat.ceil_pos`, `Matrix.repr_toLin`, `Seminorm.ball_smul_closedBall`, `ContinuousLinearMap.integral_apply`, `MvPolynomial.aeval_range`, `Matrix.mul_single_apply_same`, `SkewMonoidAlgebra.coeff_single_mul_of_not_exists_mul`, `PowerSeries.IsWeierstrassDivisorAt.div_coe_eq_zero`, `HasDerivAt.fun_finset_prod`, `QuadraticAlgebra.C_pow`, `Set.Icc.coe_zero`, `GradedTensorProduct.tmul_zero_coe_mul_coe_tmul`, `Filter.nonneg_of_eventually_pow_nonneg`, `MvPowerSeries.coeff_pow`, `Module.forall_dual_apply_eq_zero_iff`, `SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left`, `IsLocalization.to_map_eq_zero_iff`, `KaehlerDifferential.mvPolynomialBasis_repr_D_X`, `PowerSeries.zero_weierstrassMod`, `Matrix.empty_vecMul`, `Int.fract_div_mul_self_mem_Ico`, `PowerBasis.repr_pow_isIntegral`, `MvPolynomial.optionEquivLeft_C`, `hensels_lemma`, `Padic.AddValuation.map_one`, `MvPolynomial.rename_rename`, `Finsupp.linearCombination_id_surjective`, `WithTop.mul_def`, `quasispectrumRestricts_iff_spectrumRestricts_inr'`, `QuaternionAlgebra.star_eq_two_re_sub`, `Matrix.isParabolic_iff_exists`, `WithBot.instMulPosMono`, `IsLocalization.noZeroDivisors`, `stdSimplexHomeomorphUnitInterval_symm_apply_coe`, `MonomialOrder.degree_X`, `noZeroDivisors_tfae`, `MvPolynomial.iterToSum_sumToIter`, `constantCoeff_wittStructureRat`, `IsClosed.smul₀`, `Subalgebra.comap_map_eq`, `HasFDerivWithinAt.clm_apply`, `Algebra.Generators.toAlgHom_ofComp_localizationAway`, `CliffordAlgebraQuaternion.toQuaternion_star`, `hasFPowerSeriesOnBall_pi_iff`, `signHom_apply`, `WithVal.toVal_zero`, `eval_det_add_X_smul`, `Continuous.convolution_integrand_fst`, `Associates.prod_top`, `ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries`, `SimpleGraph.sum_incMatrix_apply`, `pos_of_mul_neg_left`, `MvPolynomial.leibniz_iff_X`, `ContDiffMapSupportedIn.structureMapCLM_apply`, `iteratedFDerivWithin_succ_eq_comp_right`, `Polynomial.mem_rootSet_of_injective`, `HahnSeries.instIsStrictOrderedRingLexOfIsDomain`, `Hyperreal.not_infinite_zero`, `Representation.freeLift_single_single`, `WithTop.top_mul'`, `Finsupp.sum_zsmul`, `WeierstrassCurve.HasAdditiveReduction.badReduction`, `HasFPowerSeriesWithinAt.const_smul`, `Matrix.Pivot.listTransvecCol_mul_last_col`, `Matrix.hadamard_one_eq_zero_iff`, `LaurentSeries.LaurentSeriesRingEquiv_def`, `isDomain_iff_cancelMulZero_and_nontrivial`, `SchwartzMap.lineDerivOp_fourier_eq`, `FirstOrder.Field.realize_genericMonicPolyHasRoot`, `PowerSeries.coeff_of_lt_order`, `SimpleGraph.chromaticNumber_pos`, `ValueDistribution.logCounting_zero_mul_le`, `MvPowerSeries.constantCoeff_subst`, `RCLike.pos_iff`, `PadicInt.valuation_zero`, `geom_sum_alternating_of_le_neg_one`, `isClosedEmbedding_cfcₙAux`, `TensorAlgebra.toTrivSqZeroExt_ι`, `Polynomial.homogenize_smul`, `AddMonoidAlgebra.ofCoeff_update`, `linearIndepOn_finset_iff`, `eval₂_minpolyDiv_of_eval₂_eq_zero`, `MvPolynomial.divMonomial_add_modMonomial`, `Commute.mul_nonneg`, `HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq`, `Order.krullDim_nonneg_iff`, `Dynamics.coverMincard_eq_zero_iff`, `Quaternion.coe_inv`, `HasFPowerSeriesWithinOnBall.restrictScalars`, `ArithmeticFunction.zeta_apply`, `MvPowerSeries.trunc'_expand_trunc'`, `ArithmeticFunction.intCoe_one`, `Submonoid.mem_pos`, `GradedAlgHom.default_apply`, `TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars`, `HasFTaylorSeriesUpTo.hasFDerivAt`, `NonUnitalAlgebra.coe_bot`, `ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap`, `AddCommMonCat.free_obj_coe`, `GroupWithZero.isOpen_singleton_zero`, `Submodule.orthogonalProjectionFn_inner_eq_zero`, `MvPolynomial.optionEquivLeft_X_some`, `Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv`, `Representation.LinearizeMonoidal.ε_η`, `Unitization.splitMul_apply`, `ArithmeticFunction.isMultiplicative_one`, `ContMDiffOn.clm_postcomp`, `MonomialOrder.leadingCoeff_eq_zero_iff`, `IsDomain.to_noZeroDivisors`, `MvPolynomial.eval₂Hom_monomial`, `SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `LinearMap.adjoint_eq_toCLM_adjoint`, `LinearMap.BilinForm.IsNonneg.nonneg`, `Finset.gcd_empty`, `Quaternion.normSq_natCast`, `minpoly.eq_iff_aeval_eq_zero`, `AddValuation.top_iff`, `LucasLehmer.X.zero_fst`, `fwdDiff_iter_pow_eq_zero_of_lt`, `MvPolynomial.homogeneousComponent_of_mem`, `Mathlib.Tactic.Linarith.mul_nonpos`, `Polynomial.zero_le_degree_iff`, `AddMonoidAlgebra.zero_divOf`, `LinearIndependent.linearCombination_repr`, `HahnSeries.SummableFamily.powers_zero`, `Matrix.mul_invOf_eq_iff_eq_mul_right`, `ContinuousMap.range_toLp`, `SkewMonoidAlgebra.mapDomain_one`, `exteriorPower.basis_repr_ne`, `Quaternion.im_intCast`, `Quaternion.imJ_smul`, `TensorProduct.gradedComm_tmul_one`, `HahnSeries.embDomain_smul`, `MvPolynomial.aeval_X_left_apply`, `Nat.factorization_le_factorization_mul_left`, `Polynomial.toPowerSeries_toMvPowerSeries`, `Nonneg.mk_div_mk`, `ContinuousLinearMap.IsPositive.inner_nonneg_right`, `MvPolynomial.le_vanishingIdeal_zeroLocus`, `gauge_smul_of_nonneg`, `Quaternion.imK_natCast`, `HahnSeries.coeff_single_mul_add`, `RootPairing.Base.cartanMatrix_map_abs`, `AddMonoidAlgebra.coeff_comapDomain`, `Filter.NeBot.zero_div_nonneg`, `NonUnitalStarAlgebra.coe_bot`, `Algebra.Presentation.differentials.comm₂₃`, `rank_finsupp_self`, `NormedRing.inverse_add_norm_diff_nth_order`, `MvPolynomial.homogeneousComponent_mem`, `WithZeroTopology.nhds_zero`, `Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single`, `UniqueFactorizationMonoid.primeFactors_zero`, `MvPolynomial.pUnitAlgEquiv_symm_apply`, `EuclideanDomain.zero_div`, `sbtw_iff_mem_image_Ioo_and_ne`, `MvPowerSeries.coeff_monomial_mul`, `LinearMap.det_zero`, `CompactlySupportedContinuousMap.coe_mul`, `derivWithin_fderivWithin`, `ENat.iSup_zero`, `LinearMap.toMatrix_one`, `WithLp.isBoundedSMulSeminormedAddCommGroupToProd`, `SkewMonoidAlgebra.smul_of`, `Finsupp.weight_single_one_apply`, `MvPolynomial.expand_eq_zero`, `ite_zero_mul_ite_zero`, `Matrix.isNilpotent_transpose_iff`, `DualNumber.range_lift`, `ContinuousMapZero.instCanLift`, `MvPowerSeries.exists_finsupp_eq_lexOrder_of_ne_zero`, `Module.Basis.mk_repr`, `Polynomial.roots_monomial`, `QuadraticAlgebra.coe_mul`, `SimpleGraph.dotProduct_mulVec_adjMatrix`, `Module.Flat.finsupp`, `ProperCone.coe_positive`, `MultilinearMap.mkContinuousMultilinear_apply`, `MvPowerSeries.coeff_X_pow`, `ArithmeticFunction.cardDistinctFactors_apply`, `CauSeq.abv_pos_of_not_limZero`, `Multiset.Nat.antidiagonalTuple_zero_right`, `WeierstrassCurve.Jacobian.baseChange_polynomialZ`, `AddSubgroup.exists_finsupp_of_mem_closure_range`, `Valuation.toFun_eq_coe`, `MvPolynomial.support_monomial`, `RingEquiv.map_list_sum`, `PosSMulReflectLE_iff_posSMulReflectLT`, `CliffordAlgebraDualNumber.equiv_symm_eps`, `Polynomial.cyclotomic_pos'`, `Algebra.Presentation.localizationAway_relation`, `StrongDual.norm_extendRCLike_bound`, `Nonneg.nontrivial`, `MvPolynomial.monomial_finsupp_sum_index`, `Fin.sum_neg_one_pow`, `CFC.negPart_eq_zero_of_not_isSelfAdjoint`, `LinearMap.isSelfAdjoint_toContinuousLinearMap_iff`, `PadicInt.nthHom_zero`, `ArithmeticFunction.sum_Ioc_mul_zeta_eq_sum`, `MvPolynomial.weightedHomogeneousSubmodule_mul`, `Nat.cast_pos`, `ENat.card_pos`, `Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span`, `NeZero.one`, `DividedPowers.OfInvertibleFactorial.dpow_apply`, `Ideal.span_pow_eq_map_homogeneousSubmodule`, `Submodule.Quotient.instIsBoundedSMul`, `MvPolynomial.coeffs_mul_X`, `Polynomial.isCoveringMapOn_eval`, `AddChar.sum_mulShift`, `PowerSeries.HasSubst.zero`, `MvPolynomial.mul_def`, `Complex.UnitDisc.instSMulCommClass_closedBall_left`, `Matrix.conjTranspose_mul_self_mulVec_eq_zero`, `ExteriorAlgebra.ι_eq_zero_iff`, `segment_eq_image₂`, `Matrix.IsAdjMatrix.apply_ne_one_iff`, `Polynomial.nextCoeffUp_C_eq_zero`, `MulChar.map_ringChar`, `uzpow_zero`, `ContinuousLinearMap.opNorm_lsmul_apply_le`, `ContDiffMapSupportedIn.fderivLM_eq_of_scalars`, `Polynomial.coeff_pow_eq_ite_of_natDegree_le_of_le`, `Module.Basis.repr_isUnitSMul`, `MvPolynomial.natDegree_finSuccEquiv`, `Mathlib.Tactic.Ring.cast_neg`, `OrthonormalBasis.orthogonalProjection_eq_sum_rankOne`, `ZeroAtInftyContinuousMap.instIsScalarTower`, `Finsupp.prod_toMultiset`, `Submodule.mem_orthogonal_singleton_iff_inner_right`, `stdSimplex_fin_two`, `IsUnit.star_right_conjugate_nonneg_iff`, `StandardEtalePresentation.toPresentation_algebra_smul`, `Nat.coe_divisors_eq_prod_pow_le_factorization`, `Representation.linearize_single`, `fderiv_clm_comp`, `IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers`, `PointedCone.dual_sup`, `Right.mul_pos`, `IsOrderedRing.toPosMulMono`, `smulMonoidWithZeroHom_apply`, `MvPolynomial.totalDegree_X_pow`, `cfc_comp_smul`, `Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero`, `SchwartzMap.bilinLeftCLM_apply`, `Matrix.inv_fromBlocks_zero₁₂_of_isUnit_iff`, `Ideal.span_eq_map_homogeneousSubmodule`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_zero`, `fderiv_continuousAlternatingMap_apply_const`, `Filter.tendsto_const_mul_atBot_iff_neg`, `Filter.tendsto_const_mul_atTop_iff_pos`, `RootPairing.GeckConstruction.trace_h_eq_zero`, `AnalyticOnNhd.circleAverage_log_norm`, `NonUnitalStarSubalgebra.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallForallHSMulForallForallStar`, `FirstOrder.Language.presburger.isSemilinearSet_boundedFormula_realize`, `LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian`, `DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap`, `Finsupp.toMultiset_zero`, `PowerSeries.Unit_of_divided_by_X_pow_order_zero`, `MvPolynomial.bind₂_comp_C`, `Matrix.cramer_row_self`, `Span.repr_def`, `Int.padicValuation_lt_one_iff`, `ArchimedeanClass.stdPart_zero`, `AffineMap.hasDerivWithinAt`, `HahnSeries.single_zero_ofScientific`, `QuaternionAlgebra.mul_star_eq_coe`, `MeromorphicOn.divisor_const`, `HasDerivAt.clm_apply`, `Matrix.detp_neg_one_one`, `exists_ne_zero_dotProduct_eq_zero`, `CentroidHom.zero_apply`, `MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt`, `ContDiffMapSupportedIn.seminorm_fderivLM_le`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C`, `toMatrix_distrib_mul_action_toLinearMap`, `instSMulCommClass_sphere_sphere_sphere`, `MvPolynomial.eval₂_zero'_apply`, `FixedPoints.minpoly.eval₂'`, `Polynomial.nextCoeffUp_zero`, `invOf_pos`, `mul_apply_eq_zero`, `ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le`, `Nonneg.isOrderedRing`, `IsNilpotent.isNilpotent_exp_sub_one`, `ContDiffMapSupportedIn.seminorm_fderivLM_top`, `ArithmeticFunction.moebius_eq_or`, `WithTop.untop₀_mul`, `MvPolynomial.image_comap_C_basicOpen`, `NormedSpace.toIsBoundedSMul`, `IsLocalization.coeffIntegerNormalization_of_coeff_zero`, `MvPowerSeries.X_pow_eq`, `cfc_apply_of_not_and`, `QuasispectrumRestricts.nonUnitalStarAlgHom_id`, `Left.neg_of_mul_neg_right`, `HasFPowerSeriesAt.neg`, `Submodule.isOrtho_iff_inner_eq`, `AbsoluteValue.eq_zero`, `Polynomial.roots_C_mul_X_pow`, `MvPolynomial.degreeOf_C`, `curveIntegralFun_smul`, `WeierstrassCurve.Projective.polynomial_relation`, `finprod_nonneg`, `hasDerivAt_exp_zero_of_radius_pos`, `ClosedSubmodule.mem_orthogonal'`, `Module.Basis.smul_eq_zero`, `BoundedContinuousFunction.instSMulCommClass_1`, `Matrix.toMvPolynomial_add`, `Rep.coindToInd_indToCoind`, `Mathlib.Tactic.Linarith.mul_zero_eq`, `Finsupp.le_weight_of_ne_zero'`, `LieAlgebra.Basis.borelLower_le_biSup`, `MvPolynomial.mem_support_iff`, `MonoidAlgebra.mul_def`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply`, `mem_doublyStochastic_iff_sum`, `Polynomial.dickson_two_zero`, `MvPolynomial.mvPolynomialEquivMvPolynomial_symm_apply`, `inv_atTop₀`, `MvPolynomial.algHom_ext'_iff`, `hasDerivWithinAt_iff_isLittleO`, `LaurentSeries.valuation_le_iff_coeff_lt_eq_zero`, `mul_nonpos_of_nonpos_of_nonneg`, `Matrix.PosSemidef.intCast`, `IntermediateField.mem_adjoin_iff`, `Module.FaithfullyFlat.finsupp`, `Polynomial.coeff_zero_eq_eval_zero`, `AlgebraicIndependent.repr_ker`, `HahnSeries.ofPowerSeries_X_pow`, `IsStrictOrderedRing.toContinuousInv₀`, `ArithmeticFunction.cardFactors_apply`, `LinearMap.BilinForm.toMatrix'_apply`, `Multiset.prod_eq_zero`, `instLieGroupOfNatWithTopENatOfIsTopologicalGroup`, `Subring.mk_eq_zero`, `MonomialOrder.leadingCoeff_mul_of_isRegular_right`, `chevalley_mvPolynomial_mvPolynomial`, `MvPolynomial.mem_range_map_iff_coeffs_subset`, `PEquiv.toMatrix_toPEquiv_mulVec`, `Module.length_eq_zero`, `NonUnitalStarRingHom.coe_zero`, `linearIndependent_iff_injective_finsuppLinearCombination`, `ContinuousAlternatingMap.piLIE_apply_apply`, `MvPolynomial.notMem_support_iff`, `AddMonoidAlgebra.exists`, `convexComboPair_one`, `Matrix.map_swap`, `LaurentSeries.valuation_single_zpow`, `MvPolynomial.aeval_X`, `MvPolynomial.comapEquiv_coe`, `MvPolynomial.vars_sub_of_disjoint`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_left`, `hasDerivWithinAt_zero`, `HahnSeries.single_pow`, `Matrix.mulVec_single_one`, `HasStrictDerivAt.pow'`, `TestFunction.monoCLM_eq_zero`, `Pi.single_apply_smul`, `MvPolynomial.exists_dvd_map_of_isAlgebraic`, `NumberField.Units.dirichletUnitTheorem.seq_decreasing`, `CStarAlgebra.mem_Icc_iff_norm_le_one`, `AddMonoidAlgebra.mapDomainAddEquiv_apply`, `hasDerivAt_star_conj_iff`, `Num.gcd_to_nat_aux`, `Nat.ofDigits_one`, `Polynomial.pUnitAlgEquiv_symm_toPowerSeries`, `ContDiffAt.hasStrictDerivAt`, `MvPolynomial.scalarRTensor_apply_X_tmul_apply`, `NoZeroDivisors.toIsCancelMulZero`, `Nat.factorization_eq_of_coprime_right`, `Order.krullDim_pos_iff`, `Normal.minpoly_eq_iff_mem_orbit`, `Num.of_to_nat'`, `Num.div_to_nat`, `MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent`, `MulEquiv.isRightCancelMulZero_iff`, `NonUnitalSubsemiringClass.noZeroDivisors`, `Nat.factorization_mul_apply_of_coprime`, `Num.sub_to_nat`, `MonoidAlgebra.exists`, `zpow_left_injOn₀`, `Num.succ'_to_nat`, `FormalMultilinearSeries.hasSum_of_finite`, `IsIdempotentElem.zero`, `div_nonneg_of_nonpos`, `LieModule.Weight.coe_zero`, `cross_self`, `eval_minpolyDiv_of_aeval_eq_zero`, `Quaternion.imI_mul`, `sub_one_mul_padicValNat_factorial`, `PadicInt.coe_eq_zero`, `hasDerivAtFilter_ofNat`, `SkewMonoidAlgebra.support_mul_single`, `MvPowerSeries.ext_trunc'`, `PointedCone.DualFG.dual_dual_flip`, `Matrix.blockDiagonal'RingHom_apply`, `Algebra.FormallyUnramified.finite_of_free_aux`, `MvPolynomial.smul_monomial`, `ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one`, `MonoidWithZeroHom.one_apply_zero`, `Ideal.pow_eq_zero_of_mem`, `MvPolynomial.eval₂_pow`, `LieAlgebra.coe_zeroRootSubalgebra`, `IsDedekindDomain.HeightOneSpectrum.intValuation_le_one`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₃`, `curveIntegrable_smul_iff`, `tendsto_bdd_div_atTop_nhds_zero`, `WeierstrassCurve.isCharTwoJNeZeroNF_iff`, `CharZero.neg_eq_self_iff`, `Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff`, `Set.mul_zero_subset`, `Matrix.swap_mulVec_apply`, `MvPolynomial.irreducible_mul_X_add`, `HasFPowerSeriesOnBall.restrictScalars`, `ValuativeRel.zero_srel_coe_posSubmonoid`, `smul_nonneg_iff_neg_imp_nonpos`, `Module.Basis.prod_repr_inl`, `Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff`, `AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin`, `lowerBounds_smul_of_pos`, `Int.instIsCancelMulZero`, `WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral`, `Matrix.permMatrix_mem_rowStochastic`, `ContinuousLinearMap.isometry_mul_flip`, `MvPowerSeries.LinearTopology.basis_le_iff`, `Quaternion.snd_re_dualNumberEquiv_symm`, `MonomialOrder.leadingCoeff_mul`, `MonomialOrder.degree_sub_le`, `GCDMonoid.toIsCancelMulZero`, `Nat.prod_pow_pos_of_zero_notMem_support`, `Algebra.PreSubmersivePresentation.cotangentComplexAux_zero_iff`, `AnalyticOnNhd.eval_linearMap'`, `WeierstrassCurve.Jacobian.Z_eq_zero_of_equiv`, `Nat.ordCompl_dvd_ordCompl_iff_dvd`, `Quaternion.coe_ratCast`, `Unitization.inl_mul_inr`, `MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_same`, `Ideal.span_singleton_eq_bot`, `LieModule.isNilpotent_toEnd_genWeightSpace_zero`, `HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt`, `Quaternion.imJ_one`, `Polynomial.isFixedPt_newtonMap_of_isUnit_iff`, `Sym.coe_equivNatSum_apply_apply`, `CFC.negPart_mul_posPart`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective`, `HasStrictFDerivAt.comp_hasStrictDerivAt`, `ContinuousLinearMap.adjoint_id`, `isLinearTopology_iff_hasBasis_open_twoSidedIdeal`, `ClosedSubmodule.inf_orthogonal`, `Num.toNat_injective`, `HasFDerivWithinAt.linear_multilinear_comp`, `MvPolynomial.optionEquivLeft_apply`, `emultiplicity_zero_eq_zero_of_ne_zero`, `iteratedFDerivWithin_succ_eq_comp_left`, `ContFract.convs_eq_convs'`, `posMulMono_iff_covariant_pos`, `Commute.isNilpotent_mul_left`, `MvPolynomial.instIsScalarTower`, `MvPolynomial.bind₂_C_left`, `DFinsupp.prod_eq_zero_iff`, `contDiffOn_iff_continuousOn_differentiableOn`, `ArchimedeanClass.FiniteResidueField.mk_eq_zero`, `le_zero_iff`, `isQuasiregular_iff`, `MvPolynomial.totalDegree_coeff_finSuccEquiv_add_le`, `ContinuousMapZero.coe_mul`, `IsNilpotent.neg`, `ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint`, `Ideal.coe_connectedComponentOfZero`, `Ideal.Factors.fact_ramificationIdx_neZero`, `Multiset.Icc_eq`, `Height.fun_mulHeight_zero`, `MvPolynomial.map_comp_rename`, `Localization.liftOn_zero`, `PowerSeries.coeff_ne_zero_C`, `SchwartzMap.laplacianCLM_eq`, `fderiv_fun_smul`, `CStarModule.innerSL_apply`, `Monoid.neZero_exponent_of_finite`, `ContinuousLinearMap.hasDerivWithinAt_of_bilinear`, `ArithmeticFunction.moebius_ne_zero_iff_eq_or`, `LinearIsometryEquiv.conjStarAlgEquiv_apply`, `Module.Relations.Solution.surjective_fromQuotient_iff_surjective_π`, `MvPolynomial.ACounit_X`, `WittVector.mul_polyOfInterest_aux2`, `MvPolynomial.prime_rename_iff`, `HasDerivWithinAt.sub`, `Nat.ordProj_of_not_prime`, `exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent_aux`, `AddMonoidAlgebra.ofCoeff_eq_zero`, `instContMDiffInv₀OfNatWithTopENatOfContinuousInv₀`, `Polynomial.eval_eq_div_eval_toTupleMvPolynomial`, `bind₁_xInTermsOfW_wittPolynomial`, `dotProduct_star_self_eq_zero`, `Matrix.posDef_iff_dotProduct_mulVec`, `MeasureTheory.ConvolutionExistsAt.integrable`, `NNRat.mk_zero`, `Set.Ioo.lt_one`, `HahnSeries.embDomainLinearMap_apply`, `ArithmeticFunction.cardDistinctFactors_apply_prime_pow`, `Function.locallyFinsuppWithin.zero_iff_logCounting_bounded`, `WeierstrassCurve.Jacobian.eval_polynomialY`, `AddMonoidAlgebra.supportedEquivFinsupp_apply_support_val`, `QuaternionAlgebra.Basis.lift_zero`, `exists_pos_right_iff_sameRay`, `Finsupp.linearCombination_zero_apply`, `pow_mul_eq_zero_of_le`, `Nat.WithBot.add_eq_two_iff`, `HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap`, `pow_nonneg`, `CStarAlgebra.pow_nonneg`, `Filter.tendsto_div_const_atTop_iff_pos`, `BoundedContinuousFunction.toContinuousMapLinearMap_apply`, `Polynomial.resultant_zero_right`, `Function.support_mul_of_ne_zero_right`, `MvPowerSeries.min_lexOrder_le`, `AddMonoidAlgebra.instNoZeroDivisorsOfUniqueSums`, `AlgebraicGeometry.exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isCompact`, `OnePoint.smul_infty_eq_self_iff`, `nonneg_and_nonneg_or_nonpos_and_nonpos_of_smul_nonneg`, `MvPolynomial.constantCoeff_rename`, `Polynomial.aroots_X`, `Polynomial.content_eq_zero_iff`, `mulRightLinearMap_one`, `CStarAlgebra.span_nonneg_inter_unitBall`, `hasLineDerivAt_iff_isLittleO_nhds_zero`, `MonoidAlgebra.single_one_mul_apply`, `MvPolynomial.eval₂_prod`, `Module.Basis.repr_self_apply`, `Algebra.PreSubmersivePresentation.jacobiMatrix_reindex`, `TestFunction.continuous_iff_continuous_comp`, `MvPolynomial.map_bind₂`, `Num.castNum_eq_bitwise`, `PointedCone.dual_hull`, `HasFiniteFPowerSeriesOnBall.sum`, `Quaternion.coe_pow`, `FractionalIdeal.divMod_zero_left`, `Matrix.exists_right_inverse_iff_isUnit`, `WeierstrassCurve.IsCharTwoJNeZeroNF.a₃`, `ContinuousLinearMap.opNorm_mul_flip_apply`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars`, `mul_nonpos_iff_pos_imp_nonpos`, `FractionalIdeal.count_finsuppProd`, `Quaternion.imJ_fst_dualNumberEquiv`, `Finsupp.add_sub_single_one`, `Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff`, `InnerProductSpace.inner_left_rankOne_apply`, `Finsupp.mem_span_iff_linearCombination`, `Commute.add_pow_add_eq_zero_of_pow_eq_zero`, `cfcₙHom_nnreal_eq_restrict`, `contDiff_zero`, `MvPolynomial.iterToSum_C_X`, `AlgebraicClosure.maxIdeal.isMaximal`, `TestFunction.toBoundedContinuousFunctionCLM_apply`, `Metric.unitBall.instContinuousMul`, `CliffordAlgebraQuaternion.toQuaternion_ofQuaternion`, `MvPolynomial.map_eval₂`, `Nat.pow_succ_factorization_not_dvd`, `MvPolynomial.eval_map`, `IsLocalFrameOn.coeff_apply_of_mem`, `Nat.sum_le_ofDigits`, `CommRingCat.free_map_coe`, `ENNReal.orderIsoRpow_symm_apply`, `Algebra.FinitePresentation.mvPolynomial_of_finitePresentation`, `Algebra.SubmersivePresentation.ofSubsingleton_algebra_algebraMap`, `RestrictedProduct.single_mul`, `MonoidAlgebra.coeff_smul`, `ContinuousLinearMap.smul_compLp`, `Finset.weightedVSubOfPoint_indicator_subset`, `TwoSidedIdeal.mem_mk`, `setBasisOfLinearIndependentOfCardEqFinrank_repr_apply`, `neg_of_mul_neg_right`, `Algebra.Presentation.differentials.hom₁_single`, `Set.Icc.nonneg`, `Nat.modEq_digits_sum`, `HasDerivWithinAt.sub_const`, `ContinuousLinearMap.norm_extendTo𝕜`, `discrim_le_zero`, `MvPolynomial.killCompl_comp_rename`, `AlgebraicIndependent.matroid_isFlat_of_subsingleton`, `HasSum.hasSum_at_zero`, `MonoidAlgebra.single_eq_zero`, `cfcₙHom_mem_elemental`, `ConditionallyCompleteLinearOrderedField.toZeroLEOneClass`, `MvPolynomial.map_eval₂Hom`, `HasFPowerSeriesAt.add`, `left_mem_segment`, `OreLocalization.nontrivial`, `Matrix.PosSemidef.natCast`, `MvPolynomial.supportedEquivMvPolynomial_symm_X`, `SkewMonoidAlgebra.domCongrAlg_apply`, `ContinuousAlternatingMap.curryLeft_smul`, `Finsupp.Lex.single_strictAnti`, `pow_eq_zero_iff`, `Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe`, `LinearMap.sum_repr_mul_repr_mulₛₗ`, `cfcₙ_map_pi`, `Finsupp.single_smul`, `Matrix.diagonal_pow`, `MonoidWithZeroHom.map_eq_zero_iff`, `MonoidWithZeroHom.one_apply_eq_zero_iff`, `WithZeroTopology.nhds_zero_of_units`, `MvPolynomial.pderiv_one`, `ProperCone.mem_map`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn`, `MvPolynomial.mkDerivation_X`, `Matrix.toMvPolynomial_one`, `ContMDiffAt.clm_postcomp`, `MvPolynomial.pderiv_mul`, `TensorProduct.zero_smul`, `Matrix.smul_one_eq_diagonal`, `Polynomial.content_zero`, `Num.cast_le`, `Representation.ofMulAction_apply`, `ContMDiffWithinAt.clm_postcomp`, `WeierstrassCurve.Jacobian.addXYZ_of_X_eq`, `invOf_nonneg`, `quasispectrum.coe_zero`, `hasDerivWithinAt_pi`, `Algebra.Generators.compLocalizationAwayAlgHom_toAlgHom_toComp`, `Nat.Prime.factorization_pow`, `Real.integrable_prod_sub`, `Nonneg.mk_nnratCast`, `ArithmeticFunction.pmul_apply`, `ContinuousLinearMap.eq_adjoint_iff`, `SimpleGraph.radius_eq_zero_iff`, `char_dvd_card_solutions_of_add_lt`, `LinearMap.mulLeft_zero_eq_zero`, `zpow_two_nonneg`, `MvPolynomial.comp_eval₂Hom`, `FractionalIdeal.spanFinset_eq_zero`, `Polynomial.eval₂_zero`, `ArithmeticFunction.LSeries_zeta_mul_Lseries_moebius`, `MvPolynomial.ACounit_surjective`, `Matrix.blockTriangular_transvection'`, `AffineBasis.coord_apply_ne`, `PiTensorProduct.toDualContinuousMultilinearMap_apply_apply`, `Unitization.isIdempotentElem_inr_iff`, `RCLike.nonpos_iff`, `PointedCone.maxTensorProduct_mono`, `RCLike.nonpos_iff_exists_ofReal`, `TopModuleCat.coe_freeObj`, `NNRat.coe_zero`, `MvPolynomial.supported_eq_adjoin_X`, `Polynomial.div_tendsto_zero_iff_degree_lt`, `RCLike.wInner_of_isEmpty`, `MonomialOrder.degree_lt_iff`, `Real.volume_val`, `MvPolynomial.eval₂_zero`, `cfcHom_nonneg_iff`, `Polynomial.degree_list_prod`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le`, `Int.padicValuation_eq_one_iff`, `smul_nonpos_iff`, `HasFPowerSeriesAt.comp`, `HasFDerivAt.continuousMultilinear_apply_const`, `HasFDerivWithinAt.continuousAlternatingMap_apply`, `ContinuousLinearMap.IsPositive.smul_of_nonneg`, `MvPolynomial.degreeOf_mul_le`, `InnerProductSpace.rankOne_apply`, `ArithmeticFunction.isMultiplicative_finsetProd`, `Module.End.HasUnifEigenvalue.isNilpotent_of_isNilpotent`, `Polynomial.Chebyshev.T_eval_zero`, `MvPolynomial.degreeOf_sum_le`, `FormalMultilinearSeries.sum_of_finite`, `CFC.quasispectrum_zero_eq`, `MeromorphicOn.divisor_pow`, `WeierstrassCurve.Projective.add_of_Z_eq_zero`, `PowerSeries.coe_add`, `SkewMonoidAlgebra.mapDomain_mul`, `LinearOrderedField.smul_Iio`, `IsOrderedRing.toZeroLEOneClass`, `HasFTaylorSeriesUpToOn.zero_eq'`, `KaehlerDifferential.quotKerTotalEquiv_symm_comp_D`, `pow_eq_zero_of_le`, `emultiplicity_of_one_right`, `strongRankCondition_iff_forall_not_injective`, `IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply`, `RootPairing.RootPositiveForm.zero_lt_posForm_iff`, `MvPolynomial.aeval_eq_eval`, `MvPolynomial.supDegree_esymmAlgHomMonomial`, `Finsupp.support_mul`, `Matrix.rank_one`, `SchwartzMap.compCLMOfContinuousLinearEquiv_apply`, `AddSubmonoid.mem_closure_range_iff`, `AddMonoidAlgebra.instIsRightCancelAddZeroOfIsCancelAddOfUniqueSums`, `Filter.inv_nhdsNE_zero`, `dot_cross_self`, `Order.height_pos`, `MonoidAlgebra.mem_adjoin_support`, `MvPolynomial.schwartz_zippel_totalDegree`, `cfc_apply_mkD`, `MonoidAlgebra.ofCoeff_mapRange`, `Convex.mapsTo_lineMap`, `Matrix.fromBlocks_eq_of_invertible₁₁`, `HasStrictDerivAt.clm_comp`, `Submonoid.LocalizationMap.mk'_zero`, `Rep.ε_def`, `IsStrictOrderedRing.toMulPosStrictMono`, `ArithmeticFunction.sigma_apply`, `LieAlgebra.instNontrivialSubtypeMemLieSubmoduleLieSubalgebraGenWeightSpaceOfNatForall`, `PowerSeries.coeff_heval`, `PiLp.isBoundedSMulSeminormedAddCommGroupToPi`, `WeierstrassCurve.Projective.Point.zero_point`, `WeierstrassCurve.Jacobian.addU_of_Z_eq_zero_right`, `Cardinal.toENat_eq_zero`, `PointedCone.coe_map`, `MvPolynomial.aeval_ite_mem_eq_self`, `MvPolynomial.support_sdiff_support_subset_support_add`, `Finset.div_zero_subset`, `Quaternion.coe_commutes`, `DividedPowers.dpow_null`, `Polynomial.coeff_natTrailingDegree_pred_eq_zero`, `cfcₙ_eq_cfcₙL_mkD`, `Algebra.SubmersivePresentation.map_jacobianOfHasCoeffs`, `MvPolynomial.le_weightedTotalDegree`, `Matrix.isTotallyUnimodular_iff_fintype`, `MeasureTheory.convolution_integrand_bound_right_of_le_of_subset`, `AddSubmonoid.exists_finsupp_of_mem_closure_range`, `ContinuousMap.toLp_norm_le`, `ValuationSubring.mem_inv_pointwise_smul_iff`, `FormalMultilinearSeries.id_apply_one'`, `LieModule.chainTop_zero`, `MvPolynomial.IsWeightedHomogeneous.mul`, `ContDiffMapSupportedIn.monoLM_apply`, `HasDerivWithinAt.Iic_of_Iio`, `stdSimplexHomeomorphUnitInterval_zero`, `ContinuousMultilinearMap.norm_smulRightL_le`, `IsManifold.instLEInftyOfNatWithTopENat_2`, `bdd_le_mul_tendsto_zero'`, `Function.locallyFinsuppWithin.logCounting_nonneg`, `MvPolynomial.eval₂Hom_C_id_eq_join₁`, `Nonneg.canonicallyOrderedAdd`, `derivWithin_clm_comp`, `finsuppTensorFinsupp'_symm_single_eq_tmul_single_one`, `Function.support_pow`, `ContinuousLinearMap.precompL_apply`, `Seminorm.closedBall_smul_ball`, `ArithmeticFunction.abscissaOfAbsConv_zeta`, `Mathlib.Tactic.Ring.mul_zero`, `IsSelfAdjoint.adjoint_eq`, `Rep.finsuppToCoinvariantsTensorFree_single`, `Module.Relations.Solution.IsPresentation.linearEquiv_symm_var`, `Submodule.mem_dualAnnihilator`, `Set.inv_Iio₀`, `isLeftRegular_zero_iff_subsingleton`, `QuaternionAlgebra.smul_coe`, `Set.inv_Ioo_0_right`, `Submodule.mem_ideal_smul_span_iff_exists_sum'`, `Finsupp.toMultiset_toFinsupp`, `CStarAlgebra.mem_Icc_iff_nnnorm_le_one`, `MvPolynomial.eval_mem`, `PolynomialLaw.exists_lift'`, `HahnSeries.SummableFamily.lsum_apply`, `ax_grothendieck_of_definable`, `Matrix.charpoly_natCast`, `Hyperreal.InfiniteNeg.lt_zero`, `Order.krullDim_eq_zero_of_unique`, `Algebra.Generators.algebraMap_surjective`, `FirstOrder.Field.realize_eqZero`, `HasDerivWithinAt.clm_apply`, `DifferentiableAt.hasDerivAt`, `Set.Ioc.coe_pow`, `CStarAlgebra.nonneg_iff_eq_sqrt_mul_sqrt`, `OrderDual.instIsStrictOrderedModule`, `Nat.Partition.toFinsuppAntidiag_mem_finsuppAntidiag`, `IntermediateField.adjoin_zero`, `MeasureTheory.upcrossingsBefore_zero'`, `Module.Presentation.cokernel_relation`, `MvPolynomial.totalDegree_add_eq_right_of_totalDegree_lt`, `MvPolynomial.pow_idealOfVars`, `instIsReducedZModOfFactSquarefreeNat`, `RKHS.kernel_apply`, `HasDerivAt.finCons`, `spectrum_diagonal`, `MvPolynomial.join₂_comp_map`, `WittVector.teichmuller_zero`, `MvPolynomial.idealOfVars_eq_restrictSupportIdeal`, `PolynomialLaw.toFun_eq_rTensor_φ_toFun'`, `HahnSeries.coeff_mul`, `Unitization.isQuasiregular_inr_iff`, `MvPolynomial.comap_id`, `QuadraticAlgebra.norm_zero`, `Height.logHeight_eval_ge'`, `Polynomial.coeff_mul_X_zero`, `HasDerivAtFilter.add`, `AddChar.IsPrimitive.zmod_char_eq_one_iff`, `WeierstrassCurve.a₃_of_isCharThreeJNeZeroNF`, `exists_nonneg_left_iff_sameRay`, `LinearMap.leftInverse_splittingOfFinsuppSurjective`, `IncidenceAlgebra.zeta_mul_zeta`, `Representation.ofMulActionSubsingletonEquivTrivial_symm_apply`, `MvPolynomial.eval_rename_prod_mk`, `FormalMultilinearSeries.radius_le_smul`, `ArithmeticFunction.cardDistinctFactors_apply_prime`, `instIsSemirealOfIsStrictOrderedRingOfExistsAddOfLE`, `linearIndependent_iff_ker`, `Nonneg.mk_zpow`, `Set.Ioo.one_minus_pos`, `MDifferentiable.clm_postcomp`, `Orientation.map_eq_neg_iff_det_neg`, `TrivSqZeroExt.map_inr`, `Unitization.starLift_symm_apply_apply`, `AddMonoidAlgebra.ofCoeff_neg`, `ZMod.natCast_self`, `MvPolynomial.optionEquivRight_C`, `Module.presentationFinsupp_G`, `Finset.prod_indicator_biUnion_finset_sub_indicator`, `sub_one_mul_padicValNat_choose_eq_sub_sum_digits`, `Matrix.zero_kronecker`, `CStarMatrix.toCLM_injective`, `ContinuousMap.mem_idealOfSet`, `minpoly.coeff_zero_eq_zero`, `ContinuousLinearMap.isPositive_self_comp_adjoint`, `MvPolynomial.monomial_zero`, `tendsto_norm_inv_nhdsNE_zero_atTop`, `half_pos`, `MvPolynomial.map_mvPolynomial_eq_eval₂`, `Quaternion.imJ_zero`, `LinearMap.adjoint_toContinuousLinearMap`, `ZNum.gcd_to_nat`, `Mathlib.Tactic.Linarith.sub_nonpos_of_le`, `Polynomial.coe_eq_zero_iff`, `Polynomial.Bivariate.Polynomial.Bivariate.pderiv_one_equivMvPolynomial`, `Height.mulHeight_cons_cons_cons_zero`, `MonomialOrder.degree_reduce_lt`, `hasDerivAt_iff_isLittleO`, `MvPolynomial.eval_eval₂`, `mem_nonZeroDivisors_iff`, `MvPolynomial.aevalTower_comp_C`, `Absorbs.eventually_nhdsNE_zero`, `IsIdempotentElem.one_sub_mul_self`, `Finsupp.llift_apply`, `MonoidAlgebra.coeff_update`, `MvPolynomial.totalDegree_eq`, `inv_le_one_iff₀`, `ArithmeticFunction.sigma_one_apply_prime_pow`, `LaurentSeries.ofPowerSeries_powerSeriesPart`, `MvPolynomial.rename_msymm`, `MvPolynomial.comap_comp_apply`, `AddChar.sum_eq_ite`, `cfc_nonneg_iff`, `wbtw_lineMap_iff`, `MvPolynomial.eval₂_id`, `Quaternion.instFree`, `BoundedContinuousFunction.instSMulCommClass_2`, `Continuous.cfc_nnreal'`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq`, `hasFPowerSeriesAt_const`, `AddMonoidAlgebra.single_apply`, `Matrix.fromRows_zero`, `HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap`, `emultiplicity_pos_of_dvd`, `AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.zero_mem`, `Submodule.starProjection_inner_eq_zero`, `CFC.eq_zero_of_quasispectrum_eq_zero`, `LaurentSeries.single_order_mul_powerSeriesPart`, `HasFPowerSeriesOnBall.const_smul`, `ContinuousLinearMap.toSesqForm_apply_coe`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefree`, `Finsupp.linearCombination_smul`, `Nat.factorization_factorial`, `MvPolynomial.eval₂Hom_C_eq_bind₁`, `mem_vectorSpan_iff_eq_weightedVSub`, `Polynomial.coeff_eq_zero_of_lt_natTrailingDegree`, `MeromorphicOn.extract_zeros_poles_log`, `ValuativeRel.ValueGroupWithZero.mk_pos`, `Fintype.bilinearCombination_apply_single`, `Representation.leftRegularTensorTrivialIsoFree_symm_apply_single_single`, `minpolyDiv_eval_eq_zero_of_ne_of_aeval_eq_zero`, `ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear`, `Matrix.derivative_det_one_add_X_smul`, `FormalMultilinearSeries.radius_compNeg`, `isCancelMulZero_iff_isDomain_or_subsingleton`, `Odd.pow_nonneg_iff`, `CharTwo.two_nsmul`, `ENat.card_eq_zero_iff_empty`, `MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zero`, `Dynamics.coverMincard_empty`, `Bundle.Trivialization.localFrame_coeff_eq_coeff`, `IsLocalRing.residue_eq_zero_iff`, `linearIndepOn_finset_iffₒₛ`, `MvPolynomial.X_mul_cancel_right_iff`, `Num.cast_bit0`, `PointedCone.subset_dual_dual`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_relation`, `AddCommMonCat.free_map`, `MvPolynomial.degreeOf_coeff_finSuccEquiv`, `PreQuasiregular.add_inv_add_mul_eq_zero`, `LinearMap.rank_diagonal`, `Multiset.toFinsupp_sum_eq`, `NormedRing.inverse_one_sub_nth_order`, `HasStrictDerivAt.fun_sum`, `Matrix.isNilpotent_iff_forall_row`, `EuclideanDomain.lcm_zero_left`, `LinearIsometryEquiv.adjoint_eq_symm`, `MvPolynomial.mem_pow_idealOfVars_iff`, `extDeriv_fun_smul`, `Nat.ceil_eq_zero`, `Quaternion.im_smul`, `Even.pow_nonneg`, `one_lt_inv_iff₀`, `zpow_neg_two_nonneg`, `ContinuousAlternatingMap.toAlternatingMap_curryLeft`, `HahnSeries.embDomainRingHom_apply`, `Multiset.toDFinsupp_apply`, `Height.logHeight_cons_cons_cons_zero`, `Int.floor_eq_zero_iff`, `inv_strictAntiOn`, `AlternatingMap.map_basis_eq_zero_iff`, `MvPolynomial.X_prime`, `minpoly.degree_pos`, `Polynomial.natTrailingDegree_ne_zero`, `algebraMap_pos`, `Quaternion.imI_fst_dualNumberEquiv`, `HasDerivAt.congr_of_eventuallyEq`, `CFC.rpow_def`, `LinearMap.IsPositive.isPositive_smul_iff`, `LieModule.iSup_ucs_le_genWeightSpace_zero`, `MvPolynomial.rename_id_apply`, `IsIsotypic.submodule_linearEquiv_fun`, `VectorFourier.fourierPowSMulRight_eq_comp`, `inv_lt_zero'`, `Matrix.permMatrixHom_apply`, `Cubic.mem_roots_iff`, `Quaternion.im_zero`, `HasFPowerSeriesOnBall.tendsto_partialSum_prod`, `ContinuousLinearMap.hasFDerivWithinAt_of_bilinear`, `RootPairing.pairing_eq_zero_iff`, `LinearMap.toMatrixAlgEquiv'_id`, `WeierstrassCurve.Projective.negAddY_self`, `Matrix.dotProduct_star_self_pos_iff`, `MvPolynomial.constantCoeff_C`, `IsCyclotomicExtension.aeval_zeta`, `ContinuousLinearMap.opNorm_mul`, `LinearMap.BilinForm.nondegenerate_iff`, `Representation.LinearizeMonoidal.μ_apply_single_single`, `descPochhammer_ne_zero_eval_zero`, `SimpleGraph.adjMatrix_hadamard_ofNat`, `Ring.DirectLimit.of.zero_exact`, `ContDiffMapSupportedIn.fderivCLM_apply_of_gt`, `TestFunction.fderivCLM_apply_of_le`, `IsReduced.pow_eq_zero_iff'`, `CompletelyPositiveMapClass.map_cstarMatrix_nonneg'`, `mul_neg_one_pow_eq_zero_iff`, `Quaternion.algebraMap_def`, `TensorProduct.equivFinsuppOfBasisLeft_apply_tmul_apply`, `ContinuousAlternatingMap.constOfIsEmptyLIE_apply`, `Mathlib.Tactic.Linarith.zero_lt_one`, `Finsupp.lmapDomain_linearCombination`, `MvPowerSeries.trunc_C`, `gcd_zero_right'`, `SimpleGraph.isHermitian_adjMatrix`, `Matrix.mulVecᵣ_eq`, `ArithmeticFunction.moebius_sq`, `MulRingSeminorm.apply_one`, `MvPolynomial.map_map`, `Real.sInf_smul_of_nonneg`, `PointedCone.subset_hull`, `UniqueFactorizationMonoid.normalizedFactors_zero`, `MvPolynomial.support_eq_empty`, `MonomialOrder.degree_mem_support_iff`, `Quaternion.imJ_coe`, `Module.Basis.repr_algebraMap`, `Polynomial.eval₂_reflect_eq_zero_iff`, `List.sum_take_map_length_splitWrtComposition`, `Finset.map_nsmul_piAntidiag`, `PEquiv.map_toMatrix`, `Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg`, `Rep.μ_def`, `ConjAct.toConjAct_zero`, `MvPolynomial.eval₂Hom_comp_bind₂`, `Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map`, `TestFunction.lineDerivOpCLM_eq_lineDerivCLM`, `MDifferentiable.cle_arrowCongr`, `pos_of_mul_pos_left`, `ite_zero_mul`, `Nat.ordCompl_div_of_dvd`, `MvPolynomial.degrees_def`, `MvPolynomial.coe_one`, `Mathlib.Tactic.ComputeDegree.coeff_mul_add_of_le_natDegree_of_eq_ite`, `HasFTaylorSeriesUpTo.fderiv_eq`, `MvPolynomial.nonempty_support_finSuccEquiv`, `HasDerivAt.fun_pow'`, `Unitization.nnnorm_def`, `Unitization.dist_inr`, `Matrix.conjTranspose_natCast`, `tendsto_mul_cofinite_nhds_zero`, `Polynomial.degree_list_prod_le`, `Int.fract_floor`, `RatFunc.coe_X`, `HahnSeries.single_mul_single`, `isScalarTower_closedBall_closedBall_closedBall`, `ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear`, `Positive.val_one`, `Set.Icc.one_sub_mem`, `TestFunction.fderivCLM_ofSupportedIn`, `Function.locallyFinsuppWithin.logCounting_eval_zero`, `Nat.cast_nonneg`, `Algebra.Generators.cotangentSpaceBasis_repr_one_tmul`, `CStarMatrix.zero_mul`, `MvPolynomial.mvPolynomialEquivMvPolynomial_apply`, `HasFDerivAt.fun_smul`, `NormedSpace.exp_hasFPowerSeriesOnBall`, `ContinuousLinearMap.flipMultilinear_apply_apply`, `ContinuousMultilinearMap.uncurrySum_apply`, `MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotent`, `Pi.single_mul_left_apply`, `MvPolynomial.pderiv_rename`, `PowerSeries.coeff_coe`, `HasLineDerivAt.tendsto_slope_zero_right`, `HasDerivAt.nonneg_of_monotone`, `isScalarTower_sphere_closedBall_closedBall`, `Algebra.Presentation.comp_relation_inr`, `fderiv_continuousAlternatingMapCompContinuousLinearMap`, `AffineBasis.coord_apply`, `Commute.zero_left`, `Quaternion.normSq_smul`, `HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope`, `ConditionallyCompleteLinearOrderedField.toPosMulStrictMono`, `Matrix.op_smul_one_eq_diagonal`, `MeromorphicOn.divisor_natCast`, `IncidenceAlgebra.instIsScalarTower`, `Finsupp.basis_repr`, `Matrix.toBilin_apply`, `IsLocalRing.basisQuotient_repr`, `mulPosMono_iff_covariant_pos`, `QuadraticAlgebra.omega_mul_coe_mul_mk`, `WeierstrassCurve.Affine.equation_iff'`, `Nat.ofDigits_eq_sum_mapIdx`, `ZMod.add_self_eq_zero_iff_eq_zero`, `ENat.sSup_eq_zero`, `IsAlgClosed.exists_eval₂_eq_zero_of_injective`, `Polynomial.map_rootOfSplits`, `Valuation.IsEquiv.pos_iff`, `PiTensorProduct.mapL_smul`, `Module.End.maxGenEigenspace_eq_maxGenEigenspace_zero`, `PowerSeries.constantCoeff_X`, `Module.Relations.surjective_toQuotient`, `MvPolynomial.monomial_eq_monomial_iff`, `IsAbsoluteValue.abv_nonneg`, `MonoidAlgebra.support_gen_of_gen'`, `RCLike.I_mul_I`, `DualNumber.lift_apply_eps`, `IsRightRegular.mul_right_eq_zero_iff`, `RootPairing.Base.pos_or_neg_of_sum_smul_root_mem`, `ContinuousLinearMap.adjointAux_norm`, `RCLike.toIsStrictOrderedModule`, `MvPolynomial.mem_vars`, `CStarMatrix.norm_def'`, `ContinuousOn.cfc_nnreal'`, `exists_lt_mul_self`, `MulActionWithZero.zero_smul`, `IsGreatest.nnnorm_cfc_nnreal`, `NNRat.coe_indicator`, `MonomialOrder.toSyn_strictMono`, `MvPowerSeries.coeff_X`, `Right.neg_of_mul_neg_right`, `ArithmeticFunction.moebius_apply_one`, `Polynomial.exists_root_of_splits'`, `Representation.ofMulAction_single`, `ValueDistribution.logCounting_mul_zero_eventuallyLE`, `LinearMap.nilRankAux_basis_indep`, `FiniteField.cast_card_eq_zero`, `ValueDistribution.logCounting_top`, `Polynomial.Chebyshev.T_eval_two_mul_zero`, `MonomialOrder.leadingTerm_zero`, `PreQuasiregular.inv_add_add_mul_eq_zero`, `ProperCone.coe_bot`, `spectrum.zero_notMem_iff`, `MvPolynomial.eval₂_mul_monomial`, `hasDerivAtFilter_natCast`, `Matrix.hadamard_diagonal_eq_diagonal_iff`, `MvPolynomial.weightedHomogeneousComponent_zero`, `Finsupp.linearCombination_one_tmul`, `Polynomial.coeff_ofFinsupp`, `Matrix.updateRow_eq_transvection`, `FormalMultilinearSeries.ofScalars_eq_zero`, `AddMonoidAlgebra.coeff_add`, `meromorphicOrderAt_ne_top_iff`, `Polynomial.le_trailingDegree_C`, `MvPolynomial.support_killCompl`, `WeierstrassCurve.Affine.polynomial_eq`, `intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip`, `ArithmeticFunction.not_LSeriesSummable_moebius_at_one`, `PowerSeries.gaussNorm_zero`, `Matrix.mul_inv_of_invertible`, `AffineBasis.toMatrix_mul_toMatrix`, `AlgebraicIndependent.aeval_comp_repr`, `algebraMap.coe_eq_zero_iff`, `FormalMultilinearSeries.ofScalars_apply_zero`, `HahnSeries.SummableFamily.hsum_smul_module`, `PointedCone.dual_ker`, `LinearMap.ker_smul'`, `DualNumber.inv_eps`, `IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite`, `Polynomial.integralNormalization_aeval_eq_zero`, `WeierstrassCurve.Jacobian.add_of_Y_eq`, `ContinuousLinearMap.hasStrictFDerivAt_of_bilinear`, `MonomialOrder.div_single`, `MvPolynomial.esymmAlgHomMonomial_single`, `MvPolynomial.homogeneousComponent_C_mul`, `Module.Basis.map_repr`, `Right.neg_of_mul_neg_left`, `SameRay.exists_eq_smul_add`, `LaurentSeries.coe_algebraMap`, `PrimeSpectrum.zeroLocus_diff_singleton_zero`, `HomogeneousLocalization.val_zero`, `LieAlgebra.Basis.cartan_eq`, `Nonneg.segment_eq_uIcc`, `Matrix.toLinearMapₛₗ₂'_single`, `QuadraticAlgebra.mul_coe_eq_smul`, `Unitization.inl_mul`, `LDL.lowerInv_orthogonal`, `AnalyticAt.exists_eventuallyEq_sum_add_pow_mul`, `MvPolynomial.IsHomogeneous.map`, `Polynomial.trailingDegree_eq_zero`, `PowerSeries.support_expand_subset`, `MvPolynomial.map_expand`, `AddMonoidAlgebra.coeff_sub`, `neg_of_mul_neg_left`, `MonomialOrder.image_leadingTerm_sdiff_singleton_zero`, `Matrix.vecMul_diagonal`, `Finsupp.card_toMultiset`, `RCLike.re_nonneg_of_nonneg`, `RootPairing.Base.exists_root_eq_sum_nat_or_neg`, `HahnSeries.single_zero_mul_eq_smul`, `pow_two_nonneg`, `WeierstrassCurve.Projective.dblU_of_Z_eq_zero`, `FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop`, `Matrix.SpecialLinearGroup.coe_one`, `LinearMap.toMatrixAlgEquiv_apply`, `MvPolynomial.map_aeval`, `Finset.mem_convexHull'`, `PointedCone.DualFG.exists_fg_dual`, `cfcₙ_apply_mkD`, `RatFunc.coe_coe`, `Asymptotics.IsLittleO.tendsto_div_nhds_zero`, `LaurentPolynomial.invOf_T`, `Polynomial.leadingCoeff_zero`, `FiniteField.sum_pow_lt_card_sub_one`, `SchwartzMap.fourier_lineDerivOp_eq`, `MvPolynomial.instFree`, `Algebra.TensorProduct.basis_repr_tmul`, `cfcₙHom_id`, `Real.sSup_smul_of_nonneg`, `AlgebraicGeometry.IsReduced.component_reduced`, `LinearMap.BilinForm.apply_dualBasis_left`, `ENat.map_natCast_eq_zero`, `AddChar.wInner_cWeight_eq_zero_iff_ne`, `Sym.coe_equivNatSum_symm_apply`, `div_neg_iff`, `segment_single_subset_stdSimplex`, `Mathlib.Tactic.Ring.cast_rat`, `MvPolynomial.map_frobenius_expand`, `not_isRightRegular_zero`, `WeierstrassCurve.a₁_of_isShortNF`, `Matrix.det_add_mul`, `CStarMatrix.inner_toCLM_conjTranspose_left`, `Polynomial.root_left_of_root_gcd`, `geom_sum_pos_iff`, `MvPolynomial.coeffs_one`, `ENat.toNat_zero`, `SemiconjBy.zero_right`, `hasStrictDerivAt_exp_smul_const`, `div_le_one_iff`, `RCLike.ofReal_nonneg`, `NeZero.pow`, `QuaternionAlgebra.star_mul_eq_coe`, `NNRat.num_pos`, `Polynomial.C_eq_zero`, `MvPolynomial.renameEquiv_trans`, `QuadraticAlgebra.C_eq_algebraMap`, `MvPolynomial.weightedDecomposition.decompose'_apply`, `Valuation.hasBasis_nhds_zero`, `Filter.EventuallyEq.ftaylorSeries`, `isBoundedBilinearMap_comp`, `LieAlgebra.Orthogonal.jb_transform`, `Height.logHeight_eval_le'`, `LaurentSeries.Cauchy.coeff_tendsto`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx`, `CFC.abs_nonneg`, `Polynomial.isRightCancelMulZero_iff`, `SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv`, `Matrix.PosSemidef.one`, `Matrix.det_zero_of_column_eq`, `TensorProduct.toMatrix_assoc`, `AlgebraicGeometry.RingedSpace.exists_res_eq_zero_of_germ_eq_zero`, `Nonneg.inv_mk`, `MonoidWithZeroHom.coe_mk`, `one_div_strictAntiOn`, `NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd`, `CFC.continuousOn_sqrt`, `FirstOrder.Ring.lift_genericPolyMap`, `hasStrictDerivAt_add_const_iff`, `inrNonUnitalStarAlgHom_comp_cfcₙHom_eq_cfcₙAux`, `Nat.ordCompl_dvd_ordCompl_of_dvd`, `CanonicallyOrderedAdd.multiset_prod_pos`, `Finset.gcd_eq_zero_iff`, `CFC.abs_zero`, `MvPolynomial.coeffs_one_of_nontrivial`, `RootPairing.exists_ge_zero_eq_rootForm`, `Module.DualBases.eval_of_ne`, `MvPolynomial.expand_monomial`, `Matrix.Pivot.mul_listTransvecRow_last_col`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord`, `Polynomial.eval₂_list_sum`, `Finsupp.sum_smul_index`, `Matrix.single_eq_single_vecMulVec_single`, `FormalMultilinearSeries.rightInv_removeZero`, `HahnSeries.order_mul`, `arithGeom_zero_eq_mul_div'`, `tendsto_zpow_atTop_zero`, `WeierstrassCurve.hasGoodReduction_iff`, `MvPolynomial.expand_char`, `Asymptotics.isLittleO_pow_pow`, `Mathlib.Tactic.FieldSimp.NF.cons_pos`, `Polynomial.coeff_C_ne_zero`, `StarOrderedRing.pos_iff`, `ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply`, `ClosedSubmodule.orthogonal_closure''`, `RootPairing.pairing_eq_zero_iff'`, `Quaternion.normSq_le_zero`, `HasDerivWithinAt.comp`, `hasStrictDerivAt_exp_smul_const'`, `Module.Basis.mk_coord_apply_ne`, `ArithmeticFunction.moebius_mul_coe_zeta`, `Odd.zpow_nonpos_iff`, `ExteriorAlgebra.algebraMap_eq_zero_iff`, `Int.fract_pos`, `MvPolynomial.monomial_mul_mem_coeffsIn`, `Matrix.det_one_add_smul`, `Polynomial.coeff_list_sum_map`, `QuaternionAlgebra.star_im`, `LinearMap.toMatrix_id`, `MvPolynomial.eval₂Hom_congr`, `Polynomial.smul_monomial`, `HasDerivAt.add`, `complEDS'_zero`, `SchwartzMap.smulLeftCLM_real_smul`, `Polynomial.degree_pos_of_root`, `CompletelyPositiveMap.map_cstarMatrix_nonneg`, `WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero`, `NonUnitalSubring.zero_mem`, `MvPolynomial.map_rename`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc`, `LinearMap.BilinForm.apply_eq_dotProduct_toMatrix_mulVec`, `ArithmeticFunction.moebius_apply_prime_pow`, `KaehlerDifferential.kerTotal_eq`, `HahnSeries.coeff_mul_left'`, `HasStrictDerivAt.div`, `LinearMap.BilinForm.isNonneg_def`, `Finsupp.span_image_eq_map_linearCombination`, `MvPowerSeries.hasSum_aeval`, `Matrix.mul_reindexLinearEquiv_one`, `AbsoluteValue.map_sub_eq_zero_iff`, `star_pos_iff`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_σ'`, `MvPolynomial.killCompl_C`, `Algebra.Presentation.quotientEquiv_symm`, `MvPolynomial.eval₂_const_pUnitAlgEquiv_symm`, `Holor.zero_mul`, `RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff`, `OreLocalization.zero_smul`, `Quaternion.inv_def`, `ProperCone.mem_dual`, `MvPowerSeries.coeff_truncFinset_of_mem`, `hasDerivAtFilter_zero`, `MvPowerSeries.weightedOrder_monomial_of_ne_zero`, `ProperCone.innerDual_sUnion`, `MvPolynomial.eval_comp_toMvPolynomial`, `Polynomial.coeff_erase`, `Algebra.Generators.H1Cotangent.δAux_C`, `NormedAddGroupHom.isCentralScalar`, `Algebra.Generators.map_toComp_ker`, `MvPolynomial.support_finSuccEquiv_nonempty`, `SimpleGraph.mul_adjMatrix_apply`, `Algebra.Generators.Hom.toExtensionHom_toAlgHom_apply`, `mul_sub_mul_div_mul_nonpos_iff`, `spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul`, `WeierstrassCurve.Projective.addX_of_X_eq`, `Mathlib.Tactic.Ring.neg_zero`, `AddMonoidAlgebra.divOf_apply`, `seminormFromBounded_zero`, `closure_smul₀`, `MvPolynomial.eval₂_sum`, `LinearIndependent.repr_eq_single`, `PowerSeries.support_expand`, `prod_indicator_apply`, `MvPolynomial.bind₁_X_left`, `PowerSeries.HasEval.zero`, `discrim_eq_zero_of_existsUnique`, `Order.krullDim_nonpos_iff_forall_isMax`, `PowerSeries.coeff_inv_aux`, `HahnSeries.toMvPowerSeries_symm_apply_coeff`, `MvPowerSeries.X_pow_dvd_iff`, `Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem`, `inv_zero`, `Polynomial.C_0`, `LaurentSeries.inducing_coe`, `Matrix.eq_zero_of_forall_index_sum_pow_mul_eq_zero`, `CategoryTheory.HomOrthogonal.matrixDecomposition_id`, `UnitAddTorus.mFourierCoeff_toLp`, `MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero`, `instLieAddGroupOfNatWithTopENatOfIsTopologicalAddGroup`, `FirstOrder.Ring.realize_termOfFreeCommRing`, `Nat.three_dvd_iff`, `IsAdjoinRootMonic.basis_repr`, `Representation.leftRegular_norm_eq_zero_iff`, `LieAlgebra.Orthogonal.indefiniteDiagonal_assoc`, `ofBoolAlg_bot`, `Metric.unitSphere.coe_mul`, `Matrix.conjTranspose_permMatrix`, `MvPolynomial.sumAlgEquiv_comp_rename_inr`, `AntitoneOn.derivWithin_nonpos`, `MvPowerSeries.HasEval.zero`, `Matrix.inv_zero`, `SubmodulesBasis.smul`, `ContinuousLinearMap.mulLeftRight_apply`, `PowerSeries.coe_smul`, `Nat.factorization_mul`, `WeierstrassCurve.Projective.dblZ_of_Z_eq_zero`, `MvPolynomial.aevalTower_toAlgHom`, `LieIdeal.mem_killingCompl`, `OrderMonoidWithZeroHom.monotone'`, `Algebra.Generators.ofComp_val`, `curveIntegral_fun_smul`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum`, `AddChar.sum_eq_zero_iff_ne_zero`, `Nat.instIsCancelMulZero`, `MvPolynomial.coe_eq_one_iff`, `Submonoid.LocalizationMap.subsingleton_iff`, `Algebra.Presentation.map_relationOfHasCoeffs`, `AddMonoidAlgebra.ofCoeff_injective`, `FormalMultilinearSeries.ofScalarsSum_of_subsingleton`, `HahnSeries.SummableFamily.powerSeriesFamily_of_not_orderTop_pos`, `LaurentSeries.continuous_coe`, `LinearMap.polyCharpoly_coeff_isHomogeneous`, `Algebra.TensorProduct.basisAux_map_smul`, `Function.support_mul'`, `Subalgebra.zero_mem`, `Pi.basis_repr_single`, `Fin.instNeZeroHAddNatOfNat_mathlib_1`, `SameRay.exists_eq_smul`, `isPrimePow_iff_factorization_eq_single`, `ContinuousMultilinearMap.curryRight_norm`, `QuaternionAlgebra.star_coe`, `Module.Relations.Solution.fromQuotient_toQuotient`, `ContinuousLinearMap.analyticOn_bilinear`, `Matrix.IsHermitian.eigenvectorUnitary_mulVec`, `dotProduct_eq_zero`, `IsLprojection.coe_zero`, `LaurentSeries.algebraMap_C_mem_adicCompletionIntegers`, `iteratedFDeriv_comp_const_smul`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj`, `WeierstrassCurve.Affine.nonsingular_zero`, `Function.locallyFinsuppWithin.logCounting_eventually_le`, `Cubic.degree_of_a_eq_zero'`, `MvPolynomial.eval₂_map`, `HasStrictDerivAt.mul`, `TensorProduct.equivFinsuppOfBasisRight_apply_tmul`, `MvPolynomial.X_mul_pderiv_monomial`, `OrthogonalIdempotents.iff_mul_eq`, `MvPowerSeries.lexOrder_def_of_ne_zero`, `MonomialOrder.degree_add_le`, `Module.Basis.ofEquivFun_repr_apply`, `not_prime_zero`, `Valued.is_topological_valuation`, `MDifferentiableAt.clm_postcomp`, `MvPolynomial.degree_optionEquivLeft`, `NonUnitalAlgHom.zero_apply`, `fderiv_continuousAlternatingMap_apply`, `MvPolynomial.mapAlgHom_id`, `ValuativeRel.zero_srel_mul`, `Algebra.Generators.naive_val`, `MvPowerSeries.coeff_index_single_X`, `Submodule.mem_span_finset`, `Num.castNum_shiftRight`, `ContDiffMapSupportedIn.monoLM_eq_of_scalars`, `IsIdempotentElem.spectrum_subset`, `Finset.prod_ite_zero`, `Module.Basis.sumQuot_repr_left`, `MonomialOrder.leadingCoeff_prod_of_regular`, `Matrix.toLinearMap₂'Aux_single`, `ArithmeticFunction.moebius_eq_zero_of_not_squarefree`, `Polynomial.aeval_eq_zero_of_mem_rootSet`, `MvPowerSeries.LinearTopology.mem_basis_iff`, `ZNum.cmp_to_int`, `MvPowerSeries.subst_monomial`, `inner_eq_zero_of_right`, `Representation.ofMulAction_self_smul_eq_mul`, `NeZero.of_faithfulSMul`, `LinearMap.IsSymmetric.inner_map_self_eq_zero`, `Module.Basis.reindexRange_repr'`, `Unitization.lift_symm_apply_apply`, `HasDerivAt.pow`, `deriv_fderiv`, `MvPolynomial.totalDegree_list_prod`, `RegularNormedAlgebra.isometry_mul'`, `IsSelfAdjoint.conjugate_nonneg`, `Multiset.equivDFinsupp_apply`, `PointedCone.dual_union`, `MvPolynomial.coeff_expand_smul`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on_of_nonzero`, `Module.length_eq_zero_of_subsingleton_ring`, `Algebra.Generators.algebraMap_apply`, `IsLocalization.map_eq_zero_iff`, `NonUnitalContinuousFunctionalCalculus.predicate_zero`, `zero_mul`, `MulPosMono.toMulPosStrictMono`, `Module.Basis.reindexRange_repr`, `Matrix.GeneralLinearGroup.upperRightHom_apply`, `SimpleGraph.natCast_card_dart_eq_dotProduct`, `Lagrange.eval_nodal_at_node`, `two_nsmul_lie_lmul_lmul_add_add_eq_zero`, `mul_nonneg_iff`, `ringKrullDim_nonneg_of_nontrivial`, `Matrix.adjugate_fin_one`, `orderOf_zero`, `CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM`, `WittVector.coeff_p`, `quadraticCharFun_eq_zero_iff`, `MvPolynomial.map_esymm`, `AddMonoidAlgebra.coeff_sum`, `range_cfcₙHom`, `TestFunction.limitCLM_apply`, `PowerSeries.binomialSeries_zero`, `Set.image_const_mul_Ioi_zero`, `one_div_neg`, `TensorProduct.equivFinsuppOfBasisLeft_apply_tmul`, `RatFunc.mk_eq_localization_mk`, `RCLike.toPosMulReflectLT`, `hasFPowerSeriesOnBall_const`, `NNRat.coe_pos`, `MvPolynomial.weightedHomogeneousComponent_eq_zero'`, `ringKrullDimZero_iff_ringKrullDim_eq_zero`, `PiTensorProduct.ofFinsuppEquiv'_tprod_single`, `HasFDerivAt.clm_apply`, `openSegment_eq_image'`, `HasStrictDerivAt.const_mul`, `ContDiffMapSupportedIn.seminorm_le_iff`, `QuasispectrumRestricts.map_zero`, `Nat.factorization_eq_card_pow_dvd_of_lt`, `Valuation.restrict_eq_zero_iff`, `MvPolynomial.IsHomogeneous.add`, `MvPowerSeries.coeff_of_lt_order`, `MonoidAlgebra.single_mul_apply`, `ContinuousLinearMap.hasDerivAt`, `hasDerivAt_of_tendstoUniformly`, `MvPolynomial.coe_eq_zero_iff`, `Polynomial.coeff_C_mul_X`, `Complex.UnitDisc.instSMulCommClass_circle_left`, `ArithmeticFunction.sigma_zero_apply`, `Orientation.map_eq_iff_det_pos`, `smul_nonpos_iff_pos_imp_nonpos`, `commutative_ring_iff_abelian_lie_ring`, `DFinsupp.toMultiset_single`, `MvPolynomial.expand_C`, `Polynomial.isCancelMulZero_iff`, `PadicInt.fwdDiff_tendsto_zero`, `MvPowerSeries.trunc'_trunc'_pow`, `factorization_mul`, `HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq`, `Quaternion.normSq_nonneg`, `WeierstrassCurve.hasMultiplicativeReduction_iff`, `MonomialOrder.eq_C_of_degree_eq_zero`, `MvPowerSeries.coeff_embDomain_rename`, `List.sum_smul`, `StarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar`, `Quaternion.instNontrivial`, `Polynomial.finsuppSum_homogenize_eq`, `hasFDerivAt_ringInverse`, `LinearMap.IsPositive.inner_nonneg_left`, `MonoidAlgebra.mapRingHom_apply`, `PointedCone.tmul_mem_maxTensorProduct`, `ContinuousMultilinearMap.opNorm_smul_le`, `HahnSeries.instIsCancelMulZeroOfIsCancelAdd`, `HasFDerivAt.continuousAlternatingMap_apply`, `instIsIntegralMvPolynomial`, `conjneg_pos`, `AddMonoidAlgebra.ofCoeff_erase`, `MeasureTheory.convolution_precompR_apply`, `MvPolynomial.derivation_eq_zero_of_forall_mem_vars`, `ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction`, `ValuativeRel.zero_rel`, `hasFTaylorSeriesUpTo_zero_iff`, `matPolyEquiv_coeff_apply_aux_1`, `WeierstrassCurve.Projective.addXYZ_of_X_eq`, `NormedSpace.eq_zero_iff_forall_dual_eq_zero`, `Affine.Simplex.affineCombination_mem_interior_face_iff_mem_Ioo`, `SchwartzMap.compSubConstCLM_apply`, `Filter.inv_cobounded₀`, `Cubic.coeff_eq_zero`, `MvPolynomial.coeffs_C`, `Polynomial.zero_isRoot_of_coeff_zero_eq_zero`, `AddMonoidAlgebra.neg_apply`, `CompactlySupportedContinuousMap.mul_apply`, `TensorProduct.finsuppScalarRight_apply`, `VectorFourier.fourierIntegral_iteratedFDeriv`, `Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero`, `HomogeneousIdeal.coe_bot`, `LieAlgebra.Basis.borelUpper_eq`, `Order.krullDim_nonpos_iff_forall_isMin`, `HahnSeries.orderTop_mul_of_nonzero`, `isConjRoot_iff_aeval_eq_zero`, `Matrix.mem_unitaryGroup_iff`, `Polynomial.coeff_X_pow`, `Algebra.adjoin_singleton_zero`, `InnerProductSpace.nnnorm_rankOne`, `Polynomial.resultant_self_eq_zero`, `RatFunc.mk_eq_mk'`, `Algebra.Generators.compLocalizationAwayAlgHom_X_inl`, `AlgEquiv.default_apply`, `MvPolynomial.optionEquivRight_X_none`, `spectrum.zero_mem_iff`, `MvPolynomial.homogeneousComponent_isHomogeneous`, `nonneg_and_nonneg_or_nonpos_and_nonpos_of_mul_nonneg`, `MvPolynomial.rename_psum`, `DirichletCharacter.sum_characters_eq`, `Module.Relations.Solution.ofQuotient_var`, `fderiv_smul`, `BoundedContinuousFunction.mem_charPoly`, `ArithmeticFunction.one_smul'`, `Matrix.separatingLeft_def`, `Polynomial.coeff_isUnit_isNilpotent_of_isUnit`, `Num.size_to_nat`, `Module.Presentation.directSum_relation`, `Module.length_pos_iff`, `Algebra.Generators.map_ofComp_ker`, `Finsupp.toMultiset_apply`, `PointedCone.DualFG.top`, `spectrum.zero_mem`, `MvPowerSeries.lexOrder_mul`, `Matrix.hadamard_one`, `Hyperreal.infinitePos_iff`, `spectrum.zero_notMem`, `BoundedContinuousFunction.charAlgHom_apply`, `instIsOrderedModule`, `HasDerivAt.fun_pow`, `ArithmeticFunction.cardDistinctFactors_eq_zero`, `SkewMonoidAlgebra.lift_of`, `hasDerivAt_of_tendstoLocallyUniformlyOn`, `hasDerivAtFilter_iff_tendsto_slope`, `RootPairing.zero_lt_pairingIn_iff'`, `star_right_conjugate_pos`, `ContinuousLinearMap.norm_toSpanSingleton`, `Finset.univ_of_card_le_three`, `WeierstrassCurve.b₆_of_isCharTwoJNeZeroNF_of_char_two`, `FormalMultilinearSeries.continuousOn_of_finite`, `TensorProduct.finsuppScalarRight_apply_tmul`, `Tendsto.tendsto_mul_zero_of_disjoint_cocompact_left`, `Matrix.PosSemidef.trace_eq_zero_iff`, `RestrictedProduct.mul_single`, `SkewMonoidAlgebra.lift_single`, `LinearOrderedField.smul_Ico`, `WeierstrassCurve.Jacobian.polynomialY_eq`, `Quaternion.coe_zpow`, `Polygon.edgeSet_eq_image_edgePath`, `MvPolynomial.sum_homogeneousComponent`, `AffineIndependent.indicator_eq_of_affineCombination_eq`, `ZNum.mod_to_int`, `Matrix.gram_zero`, `ContinuousAlternatingMap.curryLeft_apply_apply`, `Mathlib.Meta.Positivity.nonneg_of_isNNRat`, `ContinuousLinearMap.flip_smul`, `single_mem_stdSimplex`, `MvPolynomial.expand_zero`, `MeromorphicOn.divisor_inv`, `Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos`, `HasDerivAtFilter.mono`, `HahnSeries.SummableFamily.coe_powers`, `Quaternion.im_one`, `Submodule.norm_eq_iInf_iff_inner_eq_zero`, `MvPolynomial.support_add`, `SimpleGraph.adjMatrix_hadamard_intCast`, `HasDerivWithinAt.fun_pow'`, `Unitization.quasispectrum_inr_eq`, `ZMod.natCast_self'`, `WeierstrassCurve.Jacobian.equiv_zero_of_Z_eq_zero`, `MonomialOrder.sPolynomial_self`, `ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem`, `FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed`, `Polynomial.eraseLead_coeff`, `HasCompactSupport.hasDerivAt_convolution_right`, `Finsupp.coe_pointwise_smul`, `InnerProductSpace.isSymmetricProjection_rankOne_self`, `Matrix.isNilpotent_toLin'_iff`, `HasFTaylorSeriesUpToOn.eventually_hasFDerivAt`, `HasDerivWithinAt.const_add`, `Quaternion.imJ_nnratCast`, `SimpleGraph.edist_self`, `HahnSeries.SummableFamily.co_support_zero`, `MvPolynomial.degreesLE_nsmul`, `MvPolynomial.coe_monomial`, `cfcₙ_apply_zero`, `zero_dvd_iff`, `SkewMonoidAlgebra.lift_apply`, `MeromorphicOn.divisor_fun_pow`, `ArithmeticFunction.IsMultiplicative.multiplicative_factorization`, `Subfield.coe_zero`, `Mathlib.Meta.Positivity.nonneg_of_isNat`, `Commute.isNilpotent_sum`, `ascPochhammer_eval_zero`, `Multiset.prod_nonneg`, `WeierstrassCurve.Jacobian.eval_polynomialX`, `MvPowerSeries.X_def`, `Polynomial.mem_span_C_X_sub_C_X_sub_C_iff_eval_eval_eq_zero`, `MvPolynomial.totalDegree_rename_le`, `ExteriorAlgebra.GradedAlgebra.ι_sq_zero`, `ModuleFilterBasis.smul_right`, `MeasureTheory.ConvolutionExistsAt.integrable_swap`, `MvPolynomial.C_apply`, `Quaternion.re_zero`, `MonomialOrder.leadingCoeff_mul_of_right_mem_nonZeroDivisors`, `PosMulReflectLT.toPosMulReflectLE`, `MvPolynomial.coe_mapEquivMonic_comp'`, `Real.volume_eq_stieltjes_id`, `Matrix.one_fromCols_isTotallyUnimodular_iff`, `HasFiniteFPowerSeriesOnBall.eq_partialSum`, `RingCon.ofMatrix_rel`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left`, `HahnSeries.map_C`, `Algebra.Presentation.naive_relation`, `hasDerivAt_tsum_of_isPreconnected`, `HahnSeries.one_minus_single_neg_mul`, `cfcₙ_predicate_zero`, `mul_eq_mul_left_iff`, `Finset.centerMass_filter_ne_zero`, `CStarAlgebra.span_nonneg`, `FloorSemiring.tendsto_pow_div_factorial_atTop`, `Finsupp.DegLex.single_lt_iff`, `MonomialOrder.coeff_eq_zero_of_lt`, `Matrix.toLinearEquiv'_symm_apply`, `tendsto_one_div_add_atTop_nhds_zero_nat`, `sub_one_mul_padicValNat_choose_eq_sub_sum_digits'`, `LaurentSeries.val_le_one_iff_eq_coe`, `WeierstrassCurve.Projective.eval_polynomialX`, `nnnorm_cfcₙ_nnreal_lt`, `Polynomial.scaleRoots_eval₂_eq_zero`, `Polynomial.nthRoots_zero_right`, `Submodule.topologicalClosure_eq_self`, `LinearMap.hasStrictDerivAt`, `WeierstrassCurve.Projective.baseChange_polynomial`, `Module.Basis.repr_smul`, `OnePoint.smul_some_eq_ite`, `NormalizationMonoid.normUnit_zero`, `RingHom.ker_isRadical_iff_reduced_of_surjective`, `AffineMap.hasDerivAt_lineMap`, `PrimeSpectrum.isIdempotentElemEquivClopens_symm_bot`, `LinearMap.toMatrixAlgEquiv_id`, `EisensteinSeries.gammaSetDivGcdSigmaEquiv_symm_eq`, `fderivWithin_continuousAlternatingMap_apply_const_apply`, `Matrix.PosDef.natCast`, `Nat.ordProj_dvd_ordProj_iff_dvd`, `Matrix.toMvPolynomial_map`, `MvPolynomial.single_eq_monomial`, `HasDerivWithinAt.nonpos_of_antitoneOn`, `Polynomial.toMvPolynomial_eq_rename_comp`, `MvPowerSeries.trunc_one`, `finsuppTensorFinsupp'_single_tmul_single`, `SimpleGraph.adjMatrix_hadamard_diagonal`, `PEquiv.mul_toMatrix_apply`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_const`, `DividedPowerAlgebra.dp_mul`, `MonomialOrder.le_degree`, `isStrictlyPositive_add`, `HasDerivWithinAt.fun_finset_prod`, `Matrix.permanent_one`, `Polynomial.aeval_homogenize_X_one`, `Module.Basis.orientation_eq_iff_det_pos`, `CliffordAlgebraQuaternion.k_quaternionBasis`, `Quaternion.re_add_im`, `MvPolynomial.adjoin_range_X`, `FreeRing.coe_zero`, `ENat.zero_epow`, `Valued.extension_eq_zero_iff`, `LDL.lowerInv_triangular`, `ArithmeticFunction.coe_mul`, `MvPolynomial.mul_X_mem_coeffsIn`, `mul_nonneg_iff_pos_imp_nonneg`, `NumberField.canonicalEmbedding.integralBasis_repr_apply`, `ChevalleyThm.chevalley_mvPolynomialC`, `ValuationSubring.smul_mem_pointwise_smul_iff`, `MvPolynomial.coeff_C`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `MeromorphicOn.divisor_fun_prod`, `WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero`, `MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure`, `AddMonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure`, `cfcₙ_apply_of_not_map_zero`, `DividedPowers.OfInvertibleFactorial.dpow_null`, `invOf_lt_zero`, `MvPolynomial.bind₂_map`, `AddMonoidAlgebra.smul_single`, `Finset.Nat.antidiagonalTuple_zero_right`, `MvPolynomial.totalDegree_mul_of_isDomain`, `Num.castNum_xor`, `HasFPowerSeriesOnBall.fderiv_eq`, `Finsupp.weight_single`, `Metric.coveringNumber_empty`, `WithBot.instPosMulReflectLE`, `Nat.exists_factorization_lt_of_lt`, `Rep.coindVEquiv_symm_apply_coe`, `isConjRoot_zero_iff_eq_zero_of_injective`, `CharTwo.intCast_cases`, `ArithmeticFunction.moebius_apply_of_squarefree`, `UpperHalfPlane.zero_form_isBoundedAtImInfty`, `Quaternion.fst_imK_dualNumberEquiv_symm`, `Finsupp.antidiagonal_single`, `ArithmeticFunction.IsMultiplicative.eulerProduct_hasProd`, `MvPolynomial.X_dvd_X`, `MvPolynomial.transcendental_polynomial_aeval_X_iff`, `CFC.posPart_zero`, `MvPolynomial.aeval_algebraMap_eq_zero_iff_of_injective`, `MvPolynomial.eval₂_neg`, `MvPolynomial.coeff_X`, `collapse_nonneg`, `QuadraticMap.map_finsuppSum`, `HasDerivAtFilter.fun_add`, `Matrix.nonneg_vecMul_of_mem_rowStochastic`, `Algebra.Generators.algebraMap_eq`, `NonUnitalClosedEmbeddingContinuousFunctionalCalculus.isClosedEmbedding`, `ContinuousMapZero.instStarOrderedRing`, `PowerSeries.coeff_invOfUnit`, `SchwartzMap.smulLeftCLM_sum`, `constantCoeff_wittStructureInt`, `Affine.Simplex.affineCombination_mem_closedInterior_face_iff_nonneg`, `LieModule.Weight.IsZero.eq`, `QuaternionAlgebra.imK_swapEquiv_symm_apply`, `Polynomial.coeff_zero_eq_zero_of_zero_isRoot`, `CStarAlgebra.nonneg_iff_isSelfAdjoint_and_negPart_eq_zero`, `Metric.externalCoveringNumber_empty`, `Quaternion.coe_zero`, `AffineMap.hasDerivWithinAt_lineMap`, `WeierstrassCurve.Projective.Y_sub_Y_mul_Y_sub_negY`, `CFC.posPart_eq_zero_iff`, `PowerBasis.leftMulMatrix`, `cfc_real_eq_nnreal`, `Algebra.SubmersivePresentation.ofSubsingleton_relation`, `ContinuousLinearMap.fderiv_of_bilinear`, `Finsupp.sub_add_single_one_cancel`, `toBoolAlg_zero`, `basisOfLinearIndependentOfCardEqFinrank_repr_apply`, `SkewMonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `Int.ModEq.listSum_map_zero`, `StandardEtalePair.equivMvPolynomialQuotient_symm_apply`, `MonomialOrder.leadingTerm_monomial`, `HahnSeries.mem_cardSuppLTSubring`, `MvPolynomial.X_mul_mem_coeffsIn`, `Nat.ordCompl_pow_mul_eq_self_iff`, `MvPolynomial.support_rename_of_injective`, `PowerSeries.coe_mul`, `cfcₙHom_integral`, `Commute.list_sum_left`, `Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomial`, `MvPolynomial.comap_comp`, `Set.Icc.mk_zero`, `MvPowerSeries.monomial_def`, `MvPolynomial.eval_ofNat`, `ContinuousLinearMap.nnnorm_toSpanSingleton`, `MonomialOrder.degree_mul_leadingTerm`, `Matroid.eRank_emptyOn`, `HahnSeries.order_single_mul_of_isRegular`, `Polynomial.abs_tendsto_atTop_iff`, `ContinuousAlternatingMap.alternatizeUncurryFin_smul`, `RingSubgroupsBasis.hasBasis_nhds_zero`, `mul_star_self_nonneg`, `AddMonoidAlgebra.ofCoeff_sub`, `Finsupp.toFreeAbelianGroup_comp_singleAddHom`, `xInTermsOfW_eq`, `Matrix.linftyOpIsBoundedSMul`, `LinearMap.nilRank_eq_polyCharpoly_natTrailingDegree`, `Ideal.span_single_eq_top`, `Module.Relations.range_map`, `Module.Basis.forall_coord_eq_zero_iff`, `Polynomial.taylor_zero'`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `ContDiffMapSupportedIn.monoCLM_eq_of_scalars`, `Set.Icc.one_sub_le_one`, `ValuativeRel.zero_srel_one`, `star_left_conjugate_pos`, `CStarAlgebra.isStrictlyPositive_iff_exists_isUnit_and_isSelfAdjoint_and_eq_mul_self`, `TestFunction.postcompCLM_apply`, `MvPolynomial.eval_eq_eval_mv_eval'`, `Nat.factorization_eq_one_of_squarefree`, `MvPolynomial.IsHomogeneous.degree_eq_sum_deg_support`, `hasDerivAt_iff_tendsto_slope_left_right`, `BoundedContinuousFunction.instStarModule`, `MvPolynomial.degrees_map_of_injective`, `DualNumber.fst_eq_zero_iff_eps_dvd`, `Filter.IsIncreasingApproximateUnit.eventually_nonneg`, `Polynomial.eval₂_eq_zero_of_dvd_of_eval₂_eq_zero`, `Polynomial.isUnit_iff'`, `MvPolynomial.ACounit_C`, `HasFTaylorSeriesUpToOn.hasFDerivWithinAt`, `TrivSqZeroExt.eq_smul_exp_of_ne_zero`, `CStarAlgebra.nonneg_iff_exists_nonneg_and_eq_mul_self`, `WeierstrassCurve.j_eq_zero_iff'`, `LinearMap.polyCharpoly_baseChange`, `Representation.LinearizeMonoidal.μ_comp_assoc`, `Submodule.adjoint_subtypeL`, `MvPolynomial.eq_zero_of_eval_eq_zero`, `LieModule.Weight.zero_apply`, `posMulReflectLT_iff_contravariant_pos`, `Matrix.charmatrix_blockTriangular_iff`, `MvPolynomial.transcendental_supported_X_iff`, `convexHull_basis_eq_stdSimplex`, `Module.Basis.trace_traceDual_mul`, `SimpleGraph.lapMatrix_mulVec_const_eq_zero`, `HasDerivAtFilter.sub`, `Polynomial.monomial_eq_zero_iff`, `Filter.tendsto_const_mul_atBot_iff`, `Polynomial.homogenize_add`, `CliffordAlgebraQuaternion.i_quaternionBasis`, `Nat.factorization_choose_prime_pow_add_factorization`, `MvPolynomial.vanishingIdeal_pointToPoint`, `HahnSeries.coeff_single_zero_mul`, `Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smul`, `ContinuousLinearMap.opNorm_mul_apply`, `HahnSeries.isUnit_of_isUnit_leadingCoeff_AddUnitOrder`, `ContinuousLinearMap.norm_smulRightL`, `TrivSqZeroExt.inl_mul_inr`, `Pi.mem_spanSubset_iff`, `MvPolynomial.optionEquivLeft_X_none`, `IsNilpotent.smul`, `PowerSeries.rescale_zero_apply`, `Quaternion.star_eq_two_re_sub`, `Matrix.permMatrix_mul`, `MvPowerSeries.coeff_trunc'_mul_trunc'_eq_coeff_mul`, `MvPolynomial.algebraicIndependent_polynomial_aeval_X`, `HahnSeries.instNontrivialSubalgebra`, `IsLinearTopology.hasBasis_twoSidedIdeal`, `unitSphereToUnits_apply_coe`, `MvPowerSeries.le_lexOrder_iff`, `Function.FactorizedRational.mulSupport`, `LinearMap.toBilin'Aux_toMatrixAux`, `Height.mulHeight_cons_cons_zero`, `SkewMonoidAlgebra.coeff_mul_single_of_not_exists_mul`, `PosSMulMono.nnrat_of_rat`, `MvPowerSeries.expand_one_apply`, `Valued.tendsto_zero_pow_of_le_exp_neg_one`, `zero_div`, `Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec`, `HasFDerivWithinAt.fun_smul`, `OrderMonoidIso.withZeroUnits_symm_apply`, `MvPolynomial.IsHomogeneous.HomogeneousSubmodule.gcommSemiring`, `ContinuousMapZero.integral_apply`, `AddMonoidAlgebra.support_mul_single_subset`, `Representation.coinvariantsTprodLeftRegularLEquiv_apply`, `MvPolynomial.degreeOf_rename_of_injective`, `MeasureTheory.convolution_def`, `QuaternionAlgebra.star_smul'`, `quasispectrum.zero_mem`, `MvPolynomial.degreesLE_add`, `Subring.comap_map_eq`, `ContinuousMultilinearMap.curryLeft_norm`, `SimpleGraph.edist_top`, `finsuppTensorFinsuppLid_symm_single_smul`, `Ideal.span_pair_zero`, `MonoidAlgebra.ofCoeff_sub`, `mul_self_add_mul_self_eq_zero`, `MvPolynomial.exists_rename_eq_of_vars_subset_range`, `Matrix.one_fromRows_isTotallyUnimodular_iff`, `InnerProductSpace.trace_rankOne`, `MonomialOrder.span_leadingTerm_eq_span_monomial`, `MvPolynomial.optionEquivRight_symm_apply`, `Nat.factorization_prod_apply`, `PowerSeries.heval_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp`, `TensorPower.algebraMap₀_one`, `MDifferentiableWithinAt.cle_arrowCongr`, `sq_pos_of_neg`, `mul_left_mem_nonZeroDivisors_eq_zero_iff`, `MvPowerSeries.LinearTopology.isTopologicallyNilpotent_iff_constantCoeff`, `HasFPowerSeriesWithinOnBall.prod`, `units_smul_eq_self_iff`, `MDifferentiableWithinAt.clm_precomp`, `Mathlib.Tactic.Ring.zero_mul`, `MvPolynomial.instIsPrimeVanishingIdealSingletonForallSet`, `MvPowerSeries.one_le_order_iff_constCoeff_eq_zero`, `HasDerivAt.fun_add`, `Nonneg.coe_nnratCast`, `MvPolynomial.eval₂Hom_zero_apply`, `Multiset.toFinsupp_union`, `HasDerivAt.neg`, `MonomialOrder.span_leadingTerm_eq_span_monomial₀`, `sign_mul_abs`, `HahnSeries.addVal_le_of_coeff_ne_zero`, `Polynomial.degree_C`, `Matrix.nonneg_vecMul_of_mem_colStochastic`, `Module.End.HasEigenvalue.isNilpotent_of_isNilpotent`, `Quaternion.im_natCast`, `sign_eq_of_affineCombination_mem_affineSpan_single_lineMap`, `Matrix.isBoundedSMul`, `PowerSeries.coe_sub`, `HasDerivAt.star`, `MvPolynomial.scalarRTensor_apply_tmul`, `pos_and_pos_or_neg_and_neg_of_mul_pos`, `MvPolynomial.degrees_C`, `ZMod.natCast_pow_eq_zero_of_le`, `NeZero.nat_of_injective`, `ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply`, `MonomialOrder.degree_neg`, `Matrix.det_zero_of_row_eq`, `WithZeroMulInt.toNNReal_lt_one_iff`, `Quaternion.star_add_self`, `Finsupp.prod_zpow`, `hasStrictDerivAt_const_add_iff`, `isBoundedBilinearMap_compMultilinear`, `zero_eq_mul`, `SimpleGraph.chromaticNumber_eq_zero_of_isEmpty`, `Nat.properDivisors_eq_image_Iio_factorization_prod_pow`, `Real.log_nat_eq_sum_factorization`, `WeierstrassCurve.Jacobian.polynomial_relation`, `Quaternion.sub_re_self`, `Matrix.TransvectionStruct.det_toMatrix_prod`, `SimpleGraph.isUniform_singleton`, `Filter.tendsto_inv₀_cobounded`, `KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one`, `PowerSeries.expand_one_apply`, `HahnSeries.embDomain_one`, `List.sum_map_mul_right`, `finsuppTensorFinsupp'_symm_single_mul`, `ENNReal.smul_top`, `IsGaloisGroup.mulEquivCongr_apply_smul`, `ContinuousLinearMap.compL_apply`, `OrderMonoidIso.withZeroUnits_apply`, `RingPreordering.eq_zero_of_mem_of_neg_mem`, `ContinuousLinearMap.lsmul_flip_inj`, `LinearMap.polyCharpolyAux_map_eval`, `ZSpan.repr_ceil_apply`, `units_smul_eq_neg_iff`, `MvPolynomial.eval_prod`, `iteratedDeriv_fun_id_zero`, `zero_dotProduct`, `LinearMap.polyCharpoly_coeff_eq_zero_of_basis`, `HasFPowerSeriesOnBall.uniform_geometric_approx`, `TrivSqZeroExt.isNilpotent_inr`, `ProperCone.innerDual_zero`, `Matrix.isUnit_fromBlocks_zero₂₁`, `MvPolynomial.C_mul_X_eq_monomial`, `Algebra.Generators.Hom.aeval_val`, `LaurentPolynomial.T_zero`, `ContDiffMapSupportedIn.structureMapLM_eq_of_scalars`, `RingHom.mem_ker`, `QuadraticAlgebra.C_mul`, `ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM`, `Matrix.charpoly_zero`, `MonoidAlgebra.coeff_neg`, `zero_zpow_eq`, `LinearMap.mulLeft_eq_zero_iff`, `MeromorphicOn.divisor_sub_const_self`, `Polynomial.mem_roots_map_of_injective`, `ArithmeticFunction.two_mul_carmichael_two_pow_of_three_le_eq_totient`, `Matrix.pow_apply_nonneg`, `Polynomial.MonicDegreeEq.freeMonic_coe`, `contDiffWithinAt_zero`, `SimpleGraph.intCast_hadamard_adjMatrix`, `HasDerivAtFilter.const_smul`, `LaurentSeries.algebraMap_apply`, `DualNumber.maximalIdeal_eq_span_singleton_eps`, `NumberField.Units.instNeZeroNatTorsionOrder`, `Int.floor_nonneg`, `ofAdd_bot`, `Valued.tendsto_zero_pow_of_v_lt_one`, `LinearIndependent.eq_zero_of_smul_mem_span`, `Matrix.PosSemidef.diagonal`, `Polynomial.div_tendsto_atBot_zero_of_degree_lt`, `Matrix.ker_mulVecLin_eq_bot_iff`, `MvPowerSeries.coeff_index_single_self_X`, `DividedPowerAlgebra.natFactorial_mul_dp_eq`, `HasFPowerSeriesWithinAt.fderivWithin_eq`, `lp.zeroBasis_repr_apply`, `MvPolynomial.degreeOf_mul_eq`, `Algebra.Presentation.comp_aeval_relation_inl`, `isCoveringMap_zpow`, `Mathlib.Tactic.Ring.zero_pow`, `MvPowerSeries.WithPiTopology.as_tsum`, `RatFunc.laurent_at_zero`, `Ideal.single_mem_jacobson_matrix`, `LinearIndepOn.eq_zero_of_smul_mem_span`, `CompactlySupportedContinuousMap.instSMulCommClass`, `MvPolynomial.degreeOf_le_iff`, `MvPolynomial.C_0`, `WittVector.mulN_coeff`, `SkewMonoidAlgebra.coeff_mul_right`, `FormalMultilinearSeries.id_comp'`, `OrderedSemiring.toPosSMulMonoNat`, `ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ`, `LaurentPolynomial.smeval_C`, `IsConjRoot.eq_zero_of_injective`, `NeZero.nat_of_neZero`, `WeierstrassCurve.IsShortNF.a₂`, `FormalMultilinearSeries.hasSum`, `ContinuousLinearMap.IsPositive.conj_adjoint`, `ContinuousLinearMap.flip_apply`, `MvPolynomial.bind₂_monomial`, `MonovaryOn.sub_mul_sub_nonneg`, `Matrix.toEuclideanCLM_toLp`, `Module.Basis.addSubgroupOfClosure_repr_apply`, `MvPolynomial.isUnit_iff_totalDegree_of_isReduced`, `HasDerivAt.comp`, `MvPolynomial.totalDegree_finset_prod`, `LinearMap.trace_eq_zero_of_mapsTo_ne`, `AddMonoidAlgebra.smul_apply`, `DualNumber.lift_inlAlgHom_eps`, `DifferentiableWithinAt.hasDerivWithinAt`, `CFC.posPart_mul_negPart`, `Module.Basis.span_repr_eq_single`, `MvPolynomial.monomialOneHom_apply`, `PowerSeries.rescale_zero`, `Associates.factors_zero`, `Module.Basis.repr_range`, `Unitization.zero_mem_spectrum_inr`, `AlgebraicIndependent.matroid_spanning_iff_of_subsingleton`, `Representation.ofMulActionSubsingletonEquivTrivial_apply`, `RootPairing.zero_lt_pairingIn_iff`, `HasFPowerSeriesOnBall.sum`, `Convex.mem_Ioo`, `HasFDerivAt.comp_hasDerivAt`, `Matrix.nonneg_mulVec_of_mem_colStochastic`, `contMDiff_zero_iff`, `basis_toMatrix_basisFun_mul`, `cross_anticomm'`, `Int.fract_intCast`, `HasDerivWithinAt.mul`, `absorbs_iff_eventually_nhdsNE_zero`, `IsCompactOperator.antilipschitz_of_not_hasEigenvalue`, `WithTop.untopD_zero_mul`, `MvPolynomial.leadingCoeff_esymmAlgHomMonomial`, `MvPolynomial.zero_notMem_coeffs`, `ValuativeRel.supp_def`, `fderiv_inverse`, `Nat.factorization_one_right`, `MonoidAlgebra.mem_span_support`, `instFinitePresentationFinsupp`, `AddMonoidAlgebra.le_inf_support_add`, `SchwartzMap.smulLeftCLM_fun_neg`, `FractionalIdeal.count_ne_zero`, `Algebra.SubmersivePresentation.jacobianRelations_spec`, `tendsto_fract_right'`, `SkewMonoidAlgebra.of_apply`, `toBilin'Aux_toMatrixAux`, `ContMDiffOn.clm_precomp`, `MvPolynomial.pderiv_sumToIter`, `Matrix.detp_one_one`, `Matrix.IsIrreducible.nonneg`, `MvPolynomial.coeff_homogeneousComponent`, `AddMonoidAlgebra.sup_support_multiset_prod_le`, `DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap`, `contDiffOn_nat_iff_continuousOn_differentiableOn`, `MvPolynomial.support_expand_subset`, `Module.Basis.isScalarTower_finsupp`, `Rep.coindFunctorIso_inv_app_hom_toFun_coe`, `Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff`, `ContinuousLinearMap.bilinearRestrictScalars_apply_apply`, `LieModule.coe_genWeightSpaceOf_zero`, `LucasLehmer.residue_eq_zero_iff_sMod_eq_zero`, `Nat.ModEq.listSum_map`, `linearIndepOn_iff''`, `InnerProductSpace.adjoint_rankOne`, `FormalMultilinearSeries.compAlongComposition_nnnorm`, `DihedralGroup.oddCommuteEquiv_symm_apply`, `MonomialOrder.coeff_prod_sum_degree`, `Quaternion.imK_coe`, `DirectSum.coe_mul_of_apply_of_not_le`, `MvPolynomial.totalDegree_C`, `HahnSeries.map_mul`, `EisensteinSeries.gammaSet_one_mem_iff`, `TrivSqZeroExt.mul_left_eq_one`, `SimpleGraph.eccent_eq_zero_iff`, `Int.ceil_eq_zero_iff`, `LinearMap.toMvPolynomial_add`, `Filter.EventuallyEq.hasDerivAt_iff`, `InnerProductSpace.rankOne_eq_zero`, `IsSquare.zero`, `WeierstrassCurve.Projective.polynomialZ_eq`, `fderivWithin_continuousMultilinear_apply_const_apply`, `orthogonalIdempotents_iff`, `CharTwo.add_self_eq_zero`, `bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt`, `MonomialOrder.lex_lt_iff_of_unique`, `LinearMap.BilinForm.nondegenerate_iff'`, `hasDerivAt_deriv_iff`, `Unitization.splitMul_injective_of_clm_mul_injective`, `Matrix.num_zero`, `Matrix.toLpLin_one`, `mem_nonZeroDivisors_iff_right`, `WeierstrassCurve.a₁_of_isCharNeTwoNF`, `Module.Basis.trace_mul_traceDual`, `Multiset.prod_eq_zero_iff`, `ContinuousAlternatingMap.norm_curryLeft`, `finsuppTensorFinsupp'_apply_apply`, `ite_eq_mem_stdSimplex`, `WeierstrassCurve.toCharNeTwoNF_r`, `MvPolynomial.IsSymmetric.one`, `LieModule.chainBot_zero`, `Set.encard_empty`, `Num.to_of_nat`, `tsum_pow_div_one_sub_eq_tsum_sigma`, `Matrix.charpoly.univ_monic`, `MvPolynomial.totalDegree_pow`, `MvPolynomial.coeff_rename_embDomain`, `CFC.nnrpow_map_pi`, `CStarMatrix.algebraMap_apply`, `MvPolynomial.isUnit_iff`, `Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_isIntegral`, `LieModule.exists_forall_mem_corootSpace_smul_add_eq_zero`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `IsIdempotentElem.mul_one_sub_self`, `Polynomial.fwdDiff_iter_degree_add_one_eq_zero`, `Fintype.prod_ite_zero`, `InnerProductSpace.inner_right_rankOne_apply`, `CFC.negPart_eq_neg`, `FreeAbelianGroup.equivFinsupp_symm_apply`, `Rep.coinvariantsTensorFreeLEquiv_apply`, `ContDiff.differentiable_iteratedFDeriv`, `IsLocalization.Away.map_injective_iff`, `SchwartzMap.pairing_apply`, `MvPolynomial.monomial_left_inj`, `EuclideanDomain.mod_one`, `Module.Basis.reindexRange_repr_self`, `AddMonoidAlgebra.support_single_mul_subset`, `Num.castNum_shiftLeft`, `Polynomial.coeffList_eraseLead`, `DirectSum.coe_decompose_mul_of_left_mem`, `MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt`, `AddCommGroup.equiv_free_prod_directSum_zmod`, `Matrix.invOf_eq_nonsing_inv`, `MvPolynomial.X_dvd_monomial`, `Pi.single_mul_right`, `RootPairing.zero_le_rootForm`, `MvPolynomial.coe_zero`, `Int.ModEq.listSum_zero`, `MonomialOrder.degLex_le_iff`, `meromorphicOrderAt_const_natCast`, `NumberField.RingOfIntegers.coe_eq_zero_iff`, `ArithmeticFunction.sigma_apply_prime_pow`, `fderivWithin_continuousAlternatingMapCompContinuousLinearMap`, `Int.nneg_mul_add_sq_of_abs_le_one`, `pow_succ_nonneg`, `LaurentPolynomial.degree_C`, `TensorProduct.toIntegralClosure_mvPolynomial_bijective`, `fderivWithin_inv'`, `MvPolynomial.finSuccEquiv_coeff_coeff`, `Mathlib.Tactic.Linarith.mul_neg`, `hasDerivAt_add_const_iff`, `MvPolynomial.rename_comp_expand`, `Asymptotics.isLittleO_pow_id`, `CharTwo.list_sum_mul_self`, `Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix`, `Algebra.PreSubmersivePresentation.jacobiMatrix_apply`, `IsDedekindDomain.HeightOneSpectrum.intValuation.map_zero'`, `HahnSeries.cardSuppLTSubfield_carrier`, `mul_zero_eq_const`, `OrderIso.withZeroUnits_symm_apply`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_C'`, `MvPowerSeries.monomial_zero_eq_C`, `Finsupp.multinomial_of_support_subset`, `MvPowerSeries.coeff_inv`, `isRadical_iff_squarefree_or_zero`, `MvPolynomial.coeff_C_mul`, `mul_boole`, `SkewMonoidAlgebra.lift_unique`, `Monotone.ae_hasDerivAt`, `MvPolynomial.rename_esymm`, `Rep.δ_def`, `MvPolynomial.IsHomogeneous.sub`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply`, `ContinuousLinearMap.fderivWithin_of_bilinear`, `Cubic.leadingCoeff_of_b_ne_zero'`, `CFC.posPart_eq_zero_of_not_isSelfAdjoint`, `Finsupp.support_mul_subset_right`, `MvPolynomial.quotient_map_C_eq_zero`, `HasFPowerSeriesOnBall.compContinuousLinearMap`, `Finsupp.linearCombination_linear_comp`, `MvPolynomial.iterToSum_X`, `MeromorphicOn.divisor_prod`, `preNormEDS_zero`, `Module.Basis.repr_eq_iff`, `Quaternion.smul_coe`, `MeromorphicOn.divisor_intCast`, `Fintype.sum_single_smul`, `unitSphereToUnits_injective`, `FiniteField.sum_subgroup_units_eq_zero`, `Ring.multichoose_zero_succ`, `MvPolynomial.coeff_X_pow`, `not_isNilpotent_one`, `MvPolynomial.C_mul_monomial`, `WithBot.instMulPosStrictMono`, `Nat.nine_dvd_iff`, `AnalyticAt.meromorphicOrderAt_nonneg`, `AddMonoidAlgebra.lift_apply`, `ContDiffMapSupportedIn.uniformSpace_eq_iInf`, `LinearEquiv.mem_transvections_iff`, `Function.locallyFinsuppWithin.logCounting_eventuallyLE`, `iteratedFDerivWithin_smul_const_apply`, `tendsto_pow_atTop_nhds_zero_iff_norm_lt_one`, `cfc_nonpos_iff`, `cfcₙAux_id`, `Nonneg.val_unitsEquivPos_symm_apply_coe`, `Algebra.Generators.H1Cotangent.δAux_monomial`, `Module.Basis.sumQuot_repr_inl`, `eq_zero_of_mul_eq_self_right`, `SkewMonoidAlgebra.domCongrAlg_toAlgHom`, `MvPolynomial.vars_monomial`, `minpoly.dvd_iff`, `PiTensorProduct.liftIsometry_tprodL`, `Algebra.trace_isNilpotent_of_isNilpotent`, `quadraticChar_eq_zero_iff`, `RingEquiv.map_eq_zero_iff`, `MvPolynomial.pow_idealOfVars_eq_span`, `DualNumber.isNilpotent_iff_eps_dvd`, `LieAlgebra.killingForm_apply_eq_zero_of_mem_rootSpace_of_add_ne_zero`, `IsStarNormal.zero`, `Quaternion.instIsDomain`, `LieSubmodule.traceForm_eq_zero_of_isTrivial`, `Matrix.equiv_compl_fromCols_mul_fromRows_eq_one_comm`, `Nat.ordProj_mul_ordCompl_eq_self`, `AnalyticOnNhd.eval_linearMap`, `isStrictlyPositive_algebraMap`, `hasDerivWithinAt_one`, `WeierstrassCurve.IsMinimal.val_Δ_maximal`, `MvPolynomial.IsHomogeneous.pow`, `Nat.pairwise_coprime_pow_primeFactors_factorization`, `ValuativeRel.not_vlt_zero`, `LaurentPolynomial.C_apply`, `tendsto_inv_nhdsGT_zero`, `MvPolynomial.IsWeightedHomogeneous.sum`, `Int.fract_natCast`, `DualNumber.isMaximal_span_singleton_eps`, `Polynomial.toFinsupp_eq_zero`, `RCLike.instMulPosReflectLE`, `AffineSubspace.setOf_wOppSide_eq_image2`, `quadraticChar_zero`, `Algebra.Generators.toAlgHom_ofComp_surjective`, `Ideal.span_sdiff_singleton_zero`, `Num.of_to_nat`, `TestFunction.coe_ofSupportedInCLM`, `Matrix.mulVecLin_zero`, `NNRat.coe_eq_zero`, `WittVector.mem_span_p_pow_iff_le_coeff_eq_zero`, `KaehlerDifferential.kerTotal_mkQ_single_add`, `IsBaseChange.of_basis`, `MvPolynomial.bind₁_comp_bind₁`, `IsSelfAdjoint.inr`, `MvPolynomial.commAlgEquiv_C`, `MvPolynomial.coeff_zero_C`, `topologicalKrullDim_zero_of_discreteTopology`, `continuousSMul_closedBall_ball`, `Odd.pow_neg_iff`, `MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported`, `Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero`, `ConjAct.ofConjAct_zero`, `InnerProductSpace.rankOne_eq_rankOne_iff_comm`, `ArithmeticFunction.LSeries_zeta_eq`, `Algebra.Generators.Hom.algebraMap_toAlgHom'`, `Hyperreal.infinitePos_iff_infinite_and_pos`, `add_self_eq_zero`, `HasLineDerivAt.tendsto_slope_zero`, `HasDerivWithinAt.inner`, `Algebra.FinitePresentation.ker_fg_of_mvPolynomial`, `Algebra.Generators.cotangentSpaceBasis_repr_tmul`, `MonomialOrder.monic_X_add_C`, `HahnSeries.SummableFamily.embDomain_succ_smul_powers`, `ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear`, `Matrix.TransvectionStruct.inv_mul`, `ContinuousLinearMap.precompR_apply`, `IsUnit.mul_left_eq_zero`, `Ideal.span_singleton_zero`, `LaurentSeries.exists_ratFunc_val_lt`, `sameRay_smul_left_iff`, `zpow_left_strictMonoOn₀`, `Quaternion.coe_smul`, `Set.smul_indicator_one_apply`, `ArithmeticFunction.IsMultiplicative.map_prod_of_prime`, `ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le`, `MvPolynomial.aevalTower_X`, `ZMod.valMinAbs_zero`, `MulPosReflectLE.toMulPosReflectLT`, `MvPolynomial.vars_sub_subset`, `FormalMultilinearSeries.iteratedFDerivSeries_eq_zero`, `RingEquiv.map_zero`, `IsGreatest.nnnorm_cfcₙ_nnreal`, `UnitAddTorus.mFourier_zero`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd'`, `MvPolynomial.bind₂_monomial_one`, `WeierstrassCurve.Jacobian.addZ_neg`, `hasDerivAtFilter_one`, `MvPolynomial.irreducible_of_forall_totalDegree_le`, `MonoidWithZeroHom.valueGroup_eq_range`, `RootPairing.GeckConstruction.apply_sum_inl_eq_zero_of_mem_span_h`, `isScalarTower_sphere_sphere_sphere`, `MvPolynomial.mem_support_notMem_vars_zero`, `Polynomial.IsRoot.def`, `MeasureTheory.hasFDerivAt_convolution_right_with_param`, `MvPolynomial.commAlgEquiv_X`, `CStarAlgebra.span_nonneg_inter_unitClosedBall`, `InnerProductSpace.exists_of_rankOne_eq_rankOne`, `Filter.Tendsto.zero_mul_isBoundedUnder_le`, `ContinuousFunctionalCalculus.predicate_zero`, `Quaternion.imI_neg`, `IsSumSq.natCast`, `StieltjesFunction.measurable_measure`, `hasDerivAt_ofNat`, `SchwartzMap.postcompCLM_apply`, `AddMonoidAlgebra.modOf_apply_of_not_exists_add`, `ArithmeticFunction.pow_carmichael`, `SimpleGraph.diagonal_hadamard_adjMatrix`, `ValuativeRel.rel_zero_iff`, `finprod_cond_nonneg`, `Matrix.exp_diagonal`, `MonoidWithZeroHom.toZeroHom_coe`, `MvPolynomial.mapEquiv_apply`, `tendsto_mul_coprod_nhds_zero_inf_of_disjoint_cocompact`, `iteratedFDerivWithin_eq_equiv_comp`, `AddMonoidAlgebra.leadingCoeff_eq_zero`, `MvPolynomial.eval₂Hom_congr'`, `Polynomial.coeff_monomial_of_ne`, `Algebra.TensorProduct.equivFinsuppOfBasis_apply`, `conjugate_nonneg_of_nonneg`, `linearIndependent_iff'`, `Matrix.charpoly.univ_coeff_eval₂Hom`, `ArithmeticFunction.cardFactors_pos_iff_one_lt`, `OreLocalization.subsingleton_iff`, `PointedCone.minTensorProduct_mono`, `Polynomial.ofFinsupp_eq_one`, `AlternatingMap.mkContinuousAlternating_norm_le`, `Multiset.toFinsupp_inter`, `MvPolynomial.optionEquivRight_X_some`, `HasCompactSupport.hasFDerivAt_convolution_right`, `Algebra.isNilpotent_trace_of_isNilpotent`, `isometry_cfcₙHom`, `Valued.hasBasis_nhds_zero`, `meromorphicOrderAt_id`, `SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv`, `Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod`, `WeierstrassCurve.Projective.addX_neg`, `ContDiffMapSupportedIn.structureMapCLM_zero_apply`, `FormalMultilinearSeries.mkPiRing_coeff_eq`, `MonomialOrder.degree_le_iff`, `Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff`, `pow_eq_zero_iff'`, `PowerSeries.derivativeFun_C`, `MvPolynomial.aeval_expand`, `ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap`, `Quaternion.coeComplex_zero`, `Odd.zpow_nonpos`, `Matrix.invOf_mul_eq_iff_eq_mul_left`, `mul_eq_zero_of_right`, `Quaternion.imI_nnratCast`, `MonoidAlgebra.support_mul_single_eq_image`, `Matrix.charpoly_fromBlocks_zero₂₁`, `HahnEmbedding.Partial.exists_sub_mem_ball`, `AlgebraicIndependent.lift_reprField`, `Hyperreal.coe_nonneg`, `Unitization.inr_mul`, `Set.Ico.coe_zero`, `killingForm_eq_zero_of_mem_zeroRoot_mem_posFitting`, `GenContFract.zero_le_of_den`, `ZNum.cast_lt`, `MvPolynomial.instCharZero`, `IsLinearTopology.hasBasis_open_ideal`, `CompositionAsSet.blocks_partial_sum`, `LeftInvariantDerivation.map_zero`, `Submodule.mem_span_iff_exists_finset_subset`, `PointedCone.ofSubmodule_sInf`, `DualNumber.lift_smul`, `Module.Basis.repr_linearCombination`, `Module.Basis.dualBasis_apply_self`, `InnerProductSpace.comp_rankOne`, `OrthonormalBasis.starProjection_eq_sum_rankOne`, `MvPolynomial.aeval_algebraMap_apply`, `Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux`, `PowerSeries.order_monomial`, `SameRay.exists_pos_right`, `ArithmeticFunction.zeta_mul_pow_eq_sigma`, `Matrix.one_zpow`, `associated_zero_iff_eq_zero`, `HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum`, `ENat.sInf_eq_zero`, `CFC.negPart_nonneg`, `NonUnitalSubsemiring.mem_sumSq`, `LaurentPolynomial.T_apply`, `RCLike.I_eq_zero_or_im_I_eq_one`, `IsDiscreteValuationRing.toWithBotNat_zero`, `WeierstrassCurve.Affine.nonsingular_iff_variableChange`, `sq_pos_of_pos`, `LinearMap.BilinForm.apply_apply_same_eq_zero_iff`, `Unitization.LE.le.of_inr`, `MvPolynomial.C_1`, `Real.logb_nat_eq_sum_factorization`, `PointedCone.mem_dual`, `MvPolynomial.eval₂Hom_X'`, `EuclideanDomain.xgcdAux_val`, `Quaternion.imK_fst_dualNumberEquiv`, `Field.gcd_zero_eq`, `IsNonarchimedean.eval_mvPolynomial_le`, `Quaternion.imK_nnratCast`, `Algebra.TensorProduct.equivFinsuppOfBasis_symm_apply`, `MvPolynomial.eval₂_one`, `MvPolynomial.rTensor_apply_X_tmul`, `Algebra.SubmersivePresentation.map_invJacobianOfHasCoeffs`, `Algebra.SubmersivePresentation.linearIndependent_aeval_val_pderiv_relation`, `Bundle.Pretrivialization.continuousLinearMap.isLinear`, `dotProduct_star_self_nonneg`, `HahnSeries.of_symm_smul_of_eq_mul`, `wittPolynomial_one`, `emultiplicity_eq_zero_iff_multiplicity_eq_zero`, `MvPolynomial.pderiv_X`, `Algebra.FiniteType.baseChangeAux_surj`, `MvPowerSeries.coeff_homogeneousComponent`, `Nat.one_div_cast_pos`, `MvPolynomial.eval₂_mul_eq_zero_of_right`, `Submonoid.LocalizationMap.noZeroDivisors`, `Nat.isSumSq`, `Mathlib.Tactic.Ring.cast_zero`, `Matrix.pow_apply_pos_iff_nonempty_path`, `continuousOn_cfc_nnreal`, `Matrix.J_squared`, `InnerProductSpace.gramSchmidt_orthogonal`, `Height.logHeight_zero`, `MonoidAlgebra.mapRangeAlgHom_apply`, `MvPolynomial.eval_eq'`, `NonUnitalSubsemiring.coe_bot`, `PiLp.basisFun_repr`, `Dynamics.netMaxcard_empty`, `MvPolynomial.uniqueFactorizationMonoid`, `ContinuousLinearMap.adjoint_inner_left`, `MvPolynomial.restrictSupport_univ`, `PointedCone.DualFG.dual_flip_dual`, `instPosSMulMonoNatOfIsOrderedAddMonoid`, `ContinuousLinearMap.hasStrictDerivAt_of_bilinear`, `PointwiseConvergenceCLM.isInducing_inducingFn`, `PowerBasis.liftEquiv_symm_apply`, `FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le`, `PrimeSpectrum.basicOpen_zero`, `zpow_two_pos_of_ne_zero`, `IsStrictOrderedRing.toIsStrictOrderedModule`, `WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero`, `SimpleGraph.FarFromTriangleFree.nonpos`, `Nonneg.val_unitsHomeomorphPos_symm_apply_coe`, `RatFunc.eval_eq_zero_of_eval₂_denom_eq_zero`, `LaurentSeries.Cauchy.exists_lb_coeff_ne`, `Stream'.Seq.length'_nil`, `InnerProductSpace.gramSchmidt_pairwise_orthogonal`, `IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff`, `Matrix.nonsing_inv_mul`, `Finsupp.exists_le_degree_eq`, `Algebra.Generators.H1Cotangent.δAux_toAlgHom`, `PointedCone.dual_empty`, `PointedCone.lineal_eq_sSup`, `Representation.LinearizeMonoidal.ε_one`, `ContDiffMapSupportedIn.seminorm_monoLM_le`, `NormedSpace.hasFPowerSeriesOnBall_exp_of_radius_pos`, `Finsupp.linearCombination_single_index`, `ContinuousLinearMap.isBoundedBilinearMap`, `Filter.tendsto_mul_const_atTop_iff_neg`, `FreeAbelianGroup.toFinsupp_comp_toFreeAbelianGroup`, `HasFPowerSeriesWithinOnBall.sum`, `instModuleFinite`, `Matrix.l2_opNorm_diagonal`, `IsPrimitiveRoot.sum_eq_zero_iff_forall_eq`, `Hyperreal.infinitePos_iff_infinitesimal_inv_pos`, `Matrix.den_zero`, `HasDerivAt.sub`, `MvPolynomial.eval₂_C`, `SkewMonoidAlgebra.support_mul_single_eq_image`, `WeierstrassCurve.Affine.equation_iff_variableChange`, `Matrix.eRank_one`, `Order.coheight_pos_of_lt_top`, `WeierstrassCurve.HasGoodReduction.goodReduction`, `IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd`, `PosNum.pred'_to_nat`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right`, `NNRat.cast_nonneg`, `Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero`, `compContinuousLinearMap_zero`, `Finsupp.lift_apply`, `MeromorphicOn.divisor_sub_const_of_ne`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply`, `LinearIndependent.linearCombinationEquiv_apply_coe`, `Subalgebra.mvPolynomial_aeval_coe`, `Matrix.det_zero`, `Sum.elimZeroLeft_apply`, `Nat.factorization_choose_le_one`, `HasStrictDerivAt.sum`, `Matrix.GeneralLinearGroup.coe_one`, `Matrix.conjTranspose_swap`, `AlgebraicGeometry.RingedSpace.res_zero`, `fderivWithin_continuousMultilinear_apply_const`, `not_isUnit_zero`, `FormalMultilinearSeries.le_radius_compContinuousLinearMap`, `Differentiable.fderiv_two`, `continuousMultilinearCurryFin0_symm_apply`, `Module.Relations.Solution.range_π`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `RootPairing.GeckConstruction.trace_toEnd_eq_zero`, `IsLocalization.Away.mvPolynomialQuotientEquiv_apply`, `AdjoinRoot.mk_eq_zero`, `RingHom.ENatMap_apply`, `AddMonoidAlgebra.mul_def`, `pos_nilpotencyClass_iff`, `Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff`, `Nat.Prime.factorization`, `Representation.LinearizeMonoidal.μ_comp_rTensor`, `TensorProduct.gradedComm_tmul_of_zero`, `LinearMap.isNilpotent_toMatrix_iff`, `cfcₙHom_predicate`, `WeierstrassCurve.isCharThreeJNeZeroNF_iff`, `TensorProduct.equivFinsuppOfBasisRight_apply_tmul_apply`, `hasDerivAt_update`, `cfc_nnreal_eq_real`, `CliffordAlgebraQuaternion.equiv_apply`, `Quaternion.re_fst_dualNumberEquiv`, `ContinuousAlternatingMap.ofSubsingletonLIE_apply`, `SubsemiringClass.noZeroDivisors`, `zero_pow_eq_one₀`, `ArithmeticFunction.zeta_pos`, `Algebra.Presentation.naive_relation_apply`, `Orthonormal.isHilbertSum`, `FormalMultilinearSeries.compAlongComposition_bound`, `iteratedDeriv_fun_id`, `Quaternion.eq_re_of_eq_coe`, `continuousMultilinearCurryRightEquiv_symm_apply`, `not_isLeftRegular_zero`, `Matrix.IsTotallyUnimodular.fromCols_one`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le`, `MulPosReflectLE.of_posMulReflectLT_of_mulPosMono`, `MvPolynomial.C_add`, `Algebra.isReduced_of_isGeometricallyReduced`, `AddMonoidAlgebra.le_inf_support_pow`, `HahnSeries.embDomainRingHom_C`, `PolynomialLaw.exists_lift`, `HasStrictDerivAt.smul`, `LinearMap.toMvPolynomial_zero`, `Multiset.toFinsupp_apply`, `Quaternion.imK_zero`, `gcd_eq_zero_iff`, `constFormalMultilinearSeries_apply_zero`, `hasDerivAt_tsum`, `MonoidAlgebra.single_mul_apply_aux`, `hasFTaylorSeriesUpToOn_top_iff'`, `ContinuousLinearMap.lsmul_apply`, `Finsupp.toFreeAbelianGroup_single`, `Module.rankAtStalk_eq_zero_iff_subsingleton`, `MvPolynomial.vars_eq_support_biUnion_support`, `PrimeSpectrum.zeroLocus_insert_zero`, `not_isCoprime_zero_zero`, `LinearIsometryEquiv.conjStarAlgEquiv_trans`, `FormalMultilinearSeries.radius_smul_eq`, `Set.Icc.coe_mul`, `MvPolynomial.isHomogeneous_C_mul_X`, `Nat.support_factorization`, `hasFTaylorSeriesUpToOn_zero_iff`, `Metric.unitClosedBall.coe_mul`, `ContinuousMap.linearIsometryBoundedOfCompact_symm_apply`, `WittVector.mul_polyOfInterest_aux4`, `Matrix.det_permutation`, `neg_of_mul_pos_right`, `Polynomial.abs_tendsto_atBot_iff`, `ContinuousLinearMap.bilinearComp_zero_right`, `Order.height_pos_of_bot_lt`, `CStarRing.star_mul_self_eq_zero_iff`, `IsSumSq.isSumNonzeroSq_of_ne_zero`, `DivisibleHull.instIsStrictOrderedModuleNNRat`, `LinearIndependent.linearCombination_comp_repr`, `Order.IsMax.coheight_eq_zero`, `affineHomeomorph_image_I`, `Matrix.toMatrix₂Aux_toLinearMap₂'Aux`, `Filter.tendsto_const_mul_pow_atTop_iff`, `MvPowerSeries.weightedHomogeneousComponent_of_lt_weightedOrder_eq_zero`, `CliffordAlgebra.one_le_evenOdd_zero`, `SignType.castHom_apply`, `Unitization.isStarProjection_inr_iff`, `MvPolynomial.rename_eval₂`, `Set.inv_zero`, `MonomialOrder.support_leadingTerm'`, `Function.support_smul`, `Nonneg.coe_pow`, `single_dotProduct`, `DirichletCharacter.LSeries.mul_mu_eq_one`, `MvPolynomial.eq_divMonomial_single`, `mul_eq_zero_of_left`, `MvPolynomial.coeff_sum_X_pow_of_fintype`, `MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm'`, `hasDerivAtFilter_add_const_iff`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_some`, `Height.fun_logHeight_zero`, `MvPowerSeries.coeff_subst`, `ZNum.le_to_int`, `MvPolynomial.coeff_smul`, `MvPowerSeries.expand_eq_expand`, `MvPolynomial.irreducible_of_disjoint_support`, `Monovary.sub_mul_sub_nonneg`, `uniform_continuous_npow_on_bounded`, `InnerProductSpace.rank_rankOne`, `CauSeq.zero_apply`, `Matrix.PosDef.one`, `ContMDiffOn.cle_arrowCongr`, `HasDerivWithinAt.scomp_of_eq`, `Algebra.Generators.localizationAway_σ`, `MvPolynomial.isWeightedHomogeneous_one`, `SkewMonoidAlgebra.support_single_mul_eq_image`, `Quaternion.norm_coe`, `Height.mulHeight_eq_mulHeight_restrict_support`, `Representation.LinearizeMonoidal.μ_δ`, `IsFractionRing.num_eq_zero`, `CFC.nnrpow_def`, `PointedCone.FG.dual_dualfg`, `Ideal.finrank_prime_pow_ramificationIdx`, `ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply`, `cfcₙ_apply_of_not_predicate`, `PointedCone.maxTensorProduct_map_le`, `Matrix.UnitaryGroup.one_apply`, `Subsemiring.noZeroDivisors`, `TrivSqZeroExt.inr_mul_inr`, `ArithmeticFunction.zeta_mul_comm`, `Polynomial.noZeroDivisors_iff`, `MvPolynomial.mapAlgEquiv_apply`, `Polynomial.Bivariate.equivMvPolynomial_symm_X_0`, `MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval`, `Nat.dvd_ordCompl_of_dvd_not_dvd`, `MvPolynomial.finitePresentation_universalFactorizationMap`, `ArithmeticFunction.sigma_eq_zero`, `IsUnit.mul_right_eq_zero`, `Algebra.SubmersivePresentation.sectionCotangent_eq_iff`, `Matrix.mulVecLin_one`, `MvPolynomial.mapAlgEquiv_refl`, `WittVector.frobeniusPoly_zmod`, `Hyperreal.coe_pos`, `CFC.negPart_eq_zero_iff`, `Positive.val_mul`, `RootPairing.Base.cartanMatrix_apply_eq_zero_iff_pairing`, `Rat.valuation_le_one_iff_den`, `CauSeq.const_limZero`, `Height.mulHeight_cons_zero`, `ContinuousLinearMap.adjointAux_apply`, `MvPolynomial.totalDegree_multiset_prod`, `Finsupp.finite_of_nat_weight_le`, `PreTilt.valAux_zero`, `DirichletCharacter.sum_char_inv_mul_char_eq`, `MvPolynomial.eval_neg`, `Algebra.FiniteType.iff_quotient_mvPolynomial'`, `SimpleGraph.edist_pos_of_ne`, `nonneg_of_mul_nonneg_right`, `ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self`, `BoundedContinuousFunction.instIsScalarTower_1`, `ArithmeticFunction.coe_mk`, `DividedPowers.nilpotent_of_mem_dpIdeal`, `IsCompactOperator.hasEigenvalue_or_mem_resolventSet`, `MvPolynomial.map_restrict_dom_evalₗ`, `coe_nonZeroDivisorsRight_eq`, `Algebra.Presentation.differentials.surjective_hom₁`, `MvPowerSeries.killCompl_monomial_embDomain`, `ProperCone.innerDual_singleton`, `Polynomial.sum_eq_natDegree_of_mem_support_homogenize`, `frobenius_zero`, `Nat.Prime.dvd_iff_one_le_factorization`, `mem_Icc_of_mem_stdSimplex`, `cfcₙHom_comp`, `ProperCone.dual_univ`, `MulPosStrictMono.toMulPosMono`, `Matrix.Represents.zero`, `HasFPowerSeriesWithinOnBall.sub`, `MvPowerSeries.HasSubst.const_coeff`, `MvPolynomial.tensorEquivSum_one_tmul_C`, `HasLineDerivAt.tendsto_slope_zero_left`, `Filter.isBoundedUnder_le_mul_tendsto_zero`, `tendsto_nhds_iff_meromorphicOrderAt_nonneg`, `MvPolynomial.eq_modMonomial_single_iff`, `LaurentSeries.powerSeriesPart_coeff`, `ConjRootClass.carrier_zero`, `ArithmeticFunction.carmichael_two_pow_of_le_two`, `CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt`, `Nat.eq_factorization_iff`, `ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall`, `Cubic.degree_of_d_ne_zero`, `MvPolynomial.rTensor_apply_tmul`, `OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply`, `MonoidWithZeroHom.one_apply_def`, `hasFDerivAt_integral_of_dominated_loc_of_lip'`, `Matrix.cRank_diagonal`, `RKHS.kerFun_dense`, `Polynomial.support_ofFinsupp`, `ArithmeticFunction.IsMultiplicative.eulerProduct_tprod`, `IsLinearTopology.tendsto_mul_zero_of_left`, `PointedCone.dual_insert`, `HahnSeries.SummableFamily.support_pow_subset_closure`, `InnerProductSpace.rankOne_def`, `CliffordAlgebraQuaternion.equiv_symm_apply`, `HasDerivAt.smul_const`, `EuclideanDomain.gcdB_zero_left`, `InnerProductSpace.Core.inner_self_eq_zero`, `MvPolynomial.IsWeightedHomogeneous.weightedHomogeneousComponent_ne`, `HasDerivAtFilter.sub_const`, `IsUnit.not_isNilpotent`, `NNRat.nonpos_iff_eq_zero`, `QuaternionAlgebra.star_eq_self`, `ContinuousLinearMap.coe_flipₗᵢ'`, `Finset.gcd_eq_gcd_filter_ne_zero`, `MvPolynomial.IsSymmetric.mul`, `Module.Basis.linearCombination_dualBasis`, `Finsupp.isLowerSet_range_embDomain`, `ContinuousLinearMap.adjointAux_inner_left`, `FiniteDimensional.basisSingleton_repr_apply`, `Commute.zero_right`, `MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right`, `Matrix.fromCols_replicateCol0_isTotallyUnimodular_iff`, `WeierstrassCurve.Jacobian.baseChange_polynomialY`, `MonomialOrder.Monic.pow`, `MonomialOrder.degree_mul_of_isRegular_right`, `fderivWithin_fderivWithin_eq_of_mem_nhds`, `PointedCone.dual_antitone`, `MvPolynomial.map_ofNat`, `Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom`, `ContinuousLinearMap.norm_smulRight_apply`, `ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv`, `MvPolynomial.coeff_monomial_mul`, `Set.zero_mem_smul_iff`, `contDiff_iff_continuous_differentiable`, `Polynomial.degree_freeMonic`, `one_div_nonneg`, `tendsto_pow_div_pow_atTop_zero`, `MvPolynomial.IsWeightedHomogeneous.add`, `NonUnitalAlgHom.map_zero`, `hasDerivAt_const`, `MvPolynomial.eval₂Hom_rename`, `MvPolynomial.degreeOf_pow_eq`, `LieModule.rank_eq_natTrailingDegree`, `IsAlgebraic.exists_nonzero_coeff_and_aeval_eq_zero`, `MvPolynomial.bind₂_id`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx'`, `Module.Basis.equivFunL_symm_apply_repr`, `lineMap_le_left_iff_nonpos`, `PowerBasis.repr_gen_pow_isIntegral`, `spectrum.zero_mem_resolventSet_of_unit`, `MvPolynomial.X_mul_cancel_left_iff`, `Filter.EventuallyEq.ftaylorSeriesWithin`, `UniformSpace.Completion.norm_toComplL`, `NonUnitalSubalgebra.noZeroDivisors`, `finprod_zero_le_one`, `Bornology.IsVonNBounded.tendsto_smallSets_nhds`, `Rep.coindToInd_apply`, `WeierstrassCurve.j_of_isCharTwoJEqZeroNF_of_char_two`, `ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply`, `instSMulCommClass_sphere_closedBall_closedBall`, `Function.support_mul_of_ne_zero_left`, `ContinuousMap.toLp_def`, `ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker`, `instSMulDistribClassAlgEquiv`, `Set.Icc.coe_nonneg`, `pi_eq_sum_univ'`, `mul_nonneg_iff_left_nonneg_of_pos`, `Matrix.transvection_zero`, `Nat.WithBot.add_eq_one_iff`, `ArithmeticFunction.sigma_le_pow_succ`, `NonUnitalAlgHom.coe_inr`, `MvPolynomial.sumAlgEquiv_comp_rename_inl`, `vieta_formula_quadratic`, `Subalgebra.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply`, `Polynomial.smeval_C`, `Cardinal.ofENat_eq_zero`, `KaehlerDifferential.ker_map`, `MvPolynomial.dvd_monomial_iff_exists`, `tendsto_inv_atBot_nhdsLT_zero`, `DifferentiableOn.clm_comp`, `WeierstrassCurve.Projective.baseChange_polynomialY`, `ContDiffMapSupportedIn.monoCLM_apply`, `AlgebraicIndependent.aeval_of_algebraicIndependent`, `TensorAlgebra.instNoZeroDivisors`, `ftaylorSeriesWithin_zero`, `Finset.eq_zero_iff_eq_zero_of_mem_box`, `mulRightLinearMap_zero_eq_zero`, `SimpleGraph.IsUniform.pos`, `ArithmeticFunction.sigma_one_apply`, `ContinuousMultilinearMap.prodL_apply`, `LinearMap.BilinForm.sum_repr_mul_repr_mul`, `Module.Basis.mulOpposite_repr_op`, `MvPolynomial.aeval_bind₁`, `isRelPrime_zero_right`, `Matrix.IsTotallyUnimodular.apply`, `IsFractionRing.to_map_eq_zero_iff`, `segment_eq_image`, `ENat.ceil_pos`, `HasStrictDerivAt.mul_const`, `neg_iff_pos_of_mul_neg`, `instPosSMulStrictMono`, `inv_pos`, `Module.Basis.smulTower'_repr_mk`, `hasFTaylorSeriesUpToOn_succ_iff_right`, `EisensteinSeries.hasSum_e2Summand_symmetricIco`, `ContinuousLinearMap.coe_flipMultilinearEquiv`, `CliffordAlgebraQuaternion.ofQuaternion_star`, `emultiplicity_eq_zero`, `MonoidAlgebra.lift_unique`, `LieAlgebra.trace_toEnd_eq_zero`, `inv_nonneg_of_nonneg`, `NonUnitalAlgHom.coe_Lmul`, `PowerSeries.coeff_succ_C`, `ContinuousMultilinearMap.norm_map_init_le`, `Hyperreal.infiniteNeg_iff_infinite_and_neg`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite`, `MonomialOrder.degree_sum_le`, `ordinaryHypergeometricSeries_apply_zero`, `CliffordAlgebra.contractLeft_contractLeft`, `MvPolynomial.coeff_modMonomial_of_le`, `MonomialOrder.degree_mul_of_mul_leadingCoeff_ne_zero`, `SchwartzMap.compCLMOfAntilipschitz_apply`, `MvPolynomial.X_dvd_mul_iff`, `TensorProduct.algebraMap_gradedMul`, `Order.krullDim_nonpos_of_subsingleton`, `NumberField.house.exists_ne_zero_int_vec_house_le`, `SchwartzMap.fourierInv_apply_eq`, `Function.Periodic.nat_mul_eq`, `Matrix.mul_single_apply_of_ne`, `Order.height_eq_zero`, `NonUnitalStarAlgHom.inr_apply`, `SchwartzMap.smulRightCLM_apply_apply`, `HasDerivWithinAt.fun_neg`, `Matrix.cramer_zero`, `MonomialOrder.leadingCoeff_pow_of_pow_leadingCoeff_ne_zero`, `Polynomial.MonicDegreeEq.coeff_of_ge`, `hasEigenvector_toLin'_diagonal`, `MvPolynomial.DirectSum.coeAddMonoidHom_eq_support_sum`, `EuclideanDomain.div_zero`, `LinearIsometryEquiv.conjStarAlgEquiv_refl`, `Matrix.GeneralLinearGroup.toLin'_apply`, `HasDerivAt.tendsto_slope_zero_left`, `Num.cast_bit1`, `Representation.linearizeTrivialIso_apply`, `MvPolynomial.algebraMap_apply`, `WeierstrassCurve.a₄_of_isCharThreeJNeZeroNF`, `MeasureTheory.MemLp.const_smul`, `Matrix.one_hadamard_eq_diagonal_iff`, `MvPolynomial.mkDerivationₗ_monomial`, `IsStrictlyPositive.rpow`, `Finsupp.le_weight`, `NNRat.instContinuousInv₀`, `LinearMap.toMatrixAlgEquiv'_apply`, `MvPolynomial.killCompl_monomial_eq_zero_of_not_subset`, `PowerSeries.IsWeierstrassDivision.eq_zero`, `Matrix.PosSemidef.nonneg`, `Int.fract_int`, `eventually_singleton_add_smul_subset`, `Odd.pos`, `MvPolynomial.exists_fin_rename`, `TensorProduct.finsuppScalarRight_smul`, `Matrix.IsTotallyUnimodular.one_fromRows`, `Multiset.prod_map_nonneg`, `isPrimal_zero`, `Ring.choose_zero_ite`, `LinearMap.toMvPolynomial_baseChange`, `IncidenceAlgebra.prod_apply`, `LinearMap.BilinForm.IsAlt.self_eq_zero`, `isNilpotent_iff_eq_zero`, `AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero`, `PowerSeries.weierstrassDiv_zero`, `affineIndependent_iff_indicator_eq_of_affineCombination_eq`, `EisensteinSeries.q_expansion_riemannZeta`, `Polynomial.ofFinsupp_one`, `CategoryTheory.Free.single_comp_single`, `fderivWithin_fderivWithin_eq_of_eventuallyEq`, `cfc_def`, `Unitization.inrNonUnitalStarAlgHom_apply`, `MvPolynomial.optionEquivLeft_coeff_coeff`, `ValuativeRel.zero_vlt_one`, `HahnSeries.algebraMap_apply`, `seminormFromBounded_is_norm_iff`, `MonomialOrder.degree_subsingleton`, `HasDerivAt.nonpos_of_antitone`, `Affine.Simplex.affineCombination_mem_setInterior_face_iff_mem`, `ArithmeticFunction.moebius_apply_prime`, `IsNilpotent.eq_zero_of_isIdempotentElem`, `Odd.zpow_neg`, `QuadraticForm.finrank_radical_of_equiv_weightedSumSquares`, `MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv`, `HasDerivWithinAt.Ici_of_Ioi`, `Matrix.charpoly.optionEquivLeft_symm_univ_isHomogeneous`, `Matrix.op_smul_eq_mul_diagonal`, `PiTensorProduct.liftEquiv_symm_apply`, `PiToModule.fromMatrix_apply_single_one`, `Matrix.nonneg_iff_posSemidef`, `mul_left_coe_nonZeroDivisors_eq_zero_iff`, `Nat.factorization_zero`, `MeasureTheory.FinStronglyMeasurable.mul`, `ArithmeticFunction.cardFactors_eq_sum_factorization`, `Cardinal.mk_finsupp_nat`, `MvPolynomial.sum_weightedHomogeneousComponent`, `MvPolynomial.exists_degree_lt`, `ArithmeticFunction.intCoe_mul`, `Quaternion.normSq_inv`, `NonUnitalSubalgebra.coe_zero`, `TestFunction.coe_ofSupportedInLM`, `HasStrictDerivAt.cexp`, `MvPowerSeries.truncFinset_C`, `QuaternionAlgebra.star_add_self`, `extDerivWithin_fun_smul`, `MonoidAlgebra.coeffLinearEquiv_symm_apply`, `toIcoDiv_zero_one`, `RCLike.wInner_zero_right`, `MvPolynomial.C_surjective`, `Unitization.starMap_inl`, `MvPowerSeries.HasSubst.coeff_zero`, `ZMod.neg_val`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum`, `quadratic_eq_zero_iff_discrim_eq_sq`, `ftaylorSeries_fun_zero`, `MvPolynomial.pderiv_def`, `ConvexCone.strictlyPositive_le_positive`, `HasDerivAt.add_const`, `div_nonpos_of_nonpos_of_nonneg`, `MvPolynomial.isEmptyRingEquiv_symm_apply`, `eisSummand_of_gammaSet_eq_divIntMap`, `MonoidAlgebra.lift_apply'`, `MvPolynomial.finsupp_support_eq_support`, `Quaternion.imI_im`, `ArithmeticFunction.convolution_vonMangoldt_zeta`, `AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord`, `RingHom.functions_ext_iff`, `SkewPolynomial.monomial_zero_right`, `Finset.mulConst_empty_left`, `DFinsupp.toMultiset_le_toMultiset`, `Matrix.single_mul_apply_same`, `MonomialOrder.degree_leadingTerm_mul`, `RootPairing.pairing_eq_zero_of_add_notMem_of_sub_notMem`, `fromTangentSpace_mfderiv_smul'`, `HasDerivAt.of_isLittleO`, `MvPolynomial.hom_eq_hom`, `HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap`, `LieModule.Weight.coe_eq_zero_iff`, `Subfield.zero_mem`, `Nat.ceilRoot_def`, `eq_pos_convex_span_of_mem_convexHull`, `Matrix.mem_range_scalar_iff_commute_single`, `Matrix.UnitaryGroup.one_val`, `MvPolynomial.mem_pow_idealOfVars_iff'`, `Module.Basis.repr_reindex`, `Valuation.map_add_le_max'`, `MvPolynomial.mem_supported`, `SchwartzMap.postcompCLM_postcompCLM`, `CFC.negPart_zero`, `Matrix.TransvectionStruct.prod_mul_reverse_inv_prod`, `stdSimplex.vertex_coe`, `inv_nhdsGT_zero`, `List.Nat.antidiagonalTuple_zero_right`, `Commute.cfcₙHom`, `CliffordAlgebraQuaternion.toQuaternion_comp_ofQuaternion`, `WeierstrassCurve.Projective.addXYZ_neg`, `Matrix.toMvPolynomial_zero`, `PointedCone.basis_coord_mem_dual`, `IsIdempotentElem.iff_eq_zero_or_one`, `MvPolynomial.renameEquiv_apply`, `MvPowerSeries.expand_one`, `MvPolynomial.degrees_pow_le`, `Finsupp.DegLex.single_antitone`, `Finsupp.Lex.single_lt_iff`, `MvPolynomial.rename_esymmAlgHom`, `RootPairing.posRootForm_posForm_pos_of_ne_zero`, `Num.castNum_or`, `QuasispectrumRestricts.continuous_nonUnitalStarAlgHom`, `Submodule.mem_orthogonal'`, `eq_zero_of_localization`, `ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear`, `Module.subsingletonEquiv_symm_apply`, `Nat.dvd_iff_div_factorization_eq_tsub`, `List.IsZeckendorfRep.sum_fib_lt`, `Unitization.inl_mul_inl`, `HasDerivAt.sub_const`, `MvPolynomial.ne_zero_iff`, `ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear`, `SimpleGraph.IsSRGWith.matrix_eq`, `IsLocalizedModule.map_linearCombination`, `Int.fract_one`, `LocallyConstant.charFn_eq_zero`, `MvPolynomial.coeff_single_X`, `ContinuousLinearMap.aestronglyMeasurable_comp₂`, `continuousSMul_sphere_closedBall`, `rank_finsupp_self'`, `Module.Basis.algebraMapCoeffs_repr_apply_toFun`, `Rat.instPosMulMono`, `RingNorm.apply_one`, `MvPolynomial.aeval_eq_zero`, `SchwartzMap.smulLeftCLM_const`, `WeierstrassCurve.isCharNeTwoNF_iff`, `SimpleGraph.one_hadamard_adjMatrix`, `MvPolynomial.eval₂_cast_comp`, `eq_zero_of_zpow_eq_zero`, `exists_abs_lt`, `Algebra.PreSubmersivePresentation.naive_toPresentation`, `PEquiv.toMatrix_toPEquiv_mul`, `MvPowerSeries.constantCoeff_zero`, `Lagrange.eval_basisDivisor_right`, `MonoidAlgebra.coeffEquiv_symm_apply`, `Polynomial.eval_homogenize`, `LinearMap.toMatrix_mulVec_repr`, `LinearMap.BilinForm.zero_left`, `AlgebraicGeometry.Scheme.evaluation_eq_zero_iff_notMem_basicOpen`, `ContinuousMapZero.toContinuousMapCLM_apply`, `Cubic.of_c_eq_zero'`, `Valuation.zero_iff`, `HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt`, `Matrix.permMatrix_l2_opNorm_le`, `ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff`, `AddMonoidAlgebra.apply_add_of_supDegree_le`, `mul_right_coe_nonZeroDivisors_eq_zero_iff`, `Function.locallyFinsuppWithin.toClosedBall_divisor`, `TrivSqZeroExt.lift_apply_inr`, `evalRingHom_mapMatrix_comp_polyToMatrix`, `hasDerivAt_of_tendstoUniformlyOn`, `Matrix.mul_zero`, `QuadraticAlgebra.smul_C`, `Balanced.smul_mem_mono`, `PowerSeries.X_inv`, `Set.Ico.nonneg`, `Unitization.starMap_inr`, `Set.Icc.coe_pow`, `finsuppTensorFinsupp'_symm_single_eq_single_one_tmul`, `AffineMap.hasDerivAt`, `Matrix.toLin_apply_eq_zero_iff`, `hasDerivWithinAt_congr_set`, `MvPolynomial.modMonomial_add_divMonomial`, `Finset.weightedVSubVSubWeights_self`, `Even.pow_pos`, `HasDerivWithinAt.nonneg_of_monotoneOn`, `sameRay_smul_left_iff_of_ne`, `AddMonoidAlgebra.modOf_apply_of_exists_add`, `Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus`, `MonomialOrder.span_leadingTerm_eq_span_monomial'`, `Finsupp.mem_toMultiset`, `ArithmeticFunction.sigma_pos_iff`, `FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq`, `MvPolynomial.bind₁_C_right`, `HahnSeries.order_mul_of_nonzero`, `WeierstrassCurve.twoTorsionPolynomial_disc_of_char_two`, `MvPolynomial.coe_coeffs_map`, `Polynomial.toTupleMvPolynomial_one_eq`, `inner_zero_left`, `HahnSeries.map_one`, `IsAbsoluteValue.abv_zero`, `HasStrictDerivAt.scomp_of_eq`, `DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap`, `HasStrictDerivAt.fun_finset_prod`, `ConvexCone.toPointedCone_top`, `IncidenceAlgebra.sum_Icc_mu_left`, `linearDepOn_iff`, `AddMonoidAlgebra.coe_add`, `MvPolynomial.decompose'_apply`, `CharTwo.list_sum_sq`, `Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe`, `Quaternion.im_coe`, `Matrix.inner_toEuclideanCLM`, `Quaternion.re_exp`, `ContinuousLinearMap.norm_precompR_le`, `RootPairing.coxeterWeight_zero_iff_isOrthogonal`, `TrivSqZeroExt.isNilpotent_inl_iff`, `Quaternion.algebraMap_injective`, `hasStrictDerivAt_finCons'`, `abs_mul_sign`, `RCLike.neg_iff`, `isScalarTower_closedBall_ball_ball`, `MvPolynomial.rename_zero`, `Filter.NeBot.zero_mul_nonneg`, `Continuous.cfc_nnreal_of_mem_nhdsSet`, `mul_eq_mul_right_iff`, `Set.univ_smul_nhds_zero`, `WithVal.ofVal_zero`, `MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left`, `meromorphicNFAt_iff_analyticAt_or`, `ContinuousLinearMap.isBoundedLinearMap_comp_right`, `ArithmeticFunction.sigma_one`, `TruncatedWittVector.coeff_zero`, `MonoidWithZeroHom.map_zero`, `Module.Basis.algebraMapCoeffs_repr_apply_apply`, `ArithmeticFunction.IsMultiplicative.prod_primeFactors`, `Matrix.PosSemidef.toLinearMap₂'_zero_iff`, `quadratic_eq_zero_iff_of_discrim_eq_zero`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing`, `Polynomial.rootSet_C_mul_X_pow`, `Matrix.toLinearMapₛₗ₂_apply`, `zero_zpow_eq_one₀`, `ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear`, `cfc_apply_zero`, `HasFPowerSeriesWithinAt.pi`, `Nat.WithBot.add_eq_three_iff`, `Cubic.natDegree_of_b_eq_zero'`, `MultilinearMap.freeDFinsuppEquiv_single`, `MvPolynomial.instIsLocalHomRingHomAlgebraMap`, `Matrix.eRank_diagonal`, `CategoryTheory.Free.embedding_map`, `WittVector.bind₁_wittMulN_wittPolynomial`, `PowerSeries.order_zero`, `LinearMap.BilinForm.dualBasis_repr_apply`, `TestFunction.lineDerivCLM_add`, `Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence`, `hasStrictDerivAt_finCons`, `PiTensorProduct.liftEquiv_apply`, `MvPowerSeries.coeff_one`, `PolynomialLaw.exists_range_φ_eq_of_fg`, `PowerSeries.one_le_order_iff_constCoeff_eq_zero`, `extDerivFun_zero`, `Polynomial.nextCoeff_eq_zero`, `Algebra.FinitePresentation.mvPolynomial`, `HasDerivWithinAt.congr_of_eventuallyEq_of_mem`, `Matrix.single_kronecker_single`, `MvPowerSeries.truncFinset_map`, `hasFTaylorSeriesUpTo_top_iff'`, `div_pos_iff_of_pos_right`, `PiLp.basisFun_apply`, `fderivWithin_iteratedFDerivWithin`, `MvPolynomial.coeff_single_X_pow`, `Unitization.algebraMap_eq_inl`, `Localization.instNoZeroDivisors`, `Polynomial.fwdDiff_iter_eq_zero_of_degree_lt`, `WittVector.mem_ker_truncate`, `HahnModule.instIsScalarTowerHahnSeries_1`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `ContinuousInv₀.of_nhds_one`, `HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero`, `WithAbs.toAbs_eq_zero`, `MultilinearMap.mkContinuousLinear_norm_le`, `continuousOn_div`, `Submodule.mem_span_set`, `emultiplicity_zero`, `AddMonoidAlgebra.leadingCoeff_zero`, `Height.mulHeight_zero`, `MvPolynomial.dvd_X_mul_iff`, `AddMonoidAlgebra.mul_of'_modOf`, `Asymptotics.superpolynomialDecay_zero`, `SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet`, `Matrix.eval_charpolyRev`, `MonomialOrder.degree_X_sub_C`, `ContinuousLinearMap.deriv_of_bilinear`, `MvPolynomial.monomial_one_mul_cancel_left_iff`, `HasStrictDerivAt.comp_of_eq`, `Matrix.conjTranspose_eq_natCast`, `MvPolynomial.eq_zero_iff`, `Units.mem_posSubgroup`, `PowerSeries.weierstrassDiv_zero_right`, `normalize_eq_zero`, `openSegment_eq_image`, `Module.Basis.sumQuot_repr_inl_of_mem`, `MvPolynomial.aevalTower_C`, `single_one_dotProduct`, `Continuous.cfcₙ_nnreal`, `tendsto_inv_atTop_nhdsGT_zero`, `TensorPower.algebraMap₀_eq_smul_one`, `ContinuousLinearMap.nnnorm_holder_apply_apply_le`, `RCLike.ofReal_mul_pos_iff`, `MvPolynomial.expand_one_apply`, `NNRat.tendsto_inv_atTop_nhds_zero_nat`, `Matrix.adjugate_eq_one_of_card_eq_one`, `MeasureTheory.SimpleFunc.FinMeasSupp.mul`, `MvPowerSeries.coeff_truncFinset_mul_truncFinset_eq_coeff_mul`, `cfcₙ_nonpos`, `IsLocalization.away_snd`, `MvPolynomial.coe_basisMonomials`, `Nat.exponent_eq_exponent_mul_factorization_of_prime_pow_eq_base_pow`, `affineIndependent_iff`, `Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe`, `Finset.inv_zero`, `MulPosReflectLT.toMulPosStrictMono`, `Cubic.of_b_eq_zero'`, `Matrix.mul_single_eq_updateCol_zero`, `wbtw_zero_one_iff`, `IncidenceAlgebra.zeta_prod_apply`, `MvPolynomial.map_expand_pow_char`, `one_lt_div_iff`, `FormalMultilinearSeries.norm_compContinuousLinearMap_le`, `CStarAlgebra.isStrictlyPositive_iff_eq_mul_star_self`, `Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange`, `xInTermsOfW_aux`, `Quaternion.normSq_eq_norm_mul_self`, `HasDerivAtFilter.star`, `SimpleGraph.adjMatrix_pow_apply_eq_card_walk`, `Polynomial.degree_pos_of_ne_zero_of_nonunit`, `withBotSucc_zero`, `TensorProduct.finsuppScalarRight_apply_tmul_apply`, `Algebra.Presentation.span_range_relation_eq_ker`, `map_eq_zero`, `Matrix.adjugate_apply`, `SimpleGraph.dotProduct_adjMatrix`, `Matrix.eq_zero_of_mulVec_eq_zero`, `MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero`, `starConvex_zero_iff`, `DFinsupp.instPosSMulStrictMono`, `MvPolynomial.mapRange_eq_map`, `ContinuousLinearMap.bilinear_hasTemperateGrowth`, `LinearMap.toMatrix'_apply`, `ascPochhammer_eval_eq_zero_iff`, `IsBoundedBilinearMap.isBoundedLinearMap_deriv`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin`, `MvPolynomial.monomial_mem_pow_idealOfVars_iff`, `AddMonoidAlgebra.mul_single_zero_apply`, `Module.Basis.repr_symm_single`, `Set.Ico.coe_eq_zero`, `listProd_apply_eq_zero'`, `Function.support_mul_subset_left`, `SimpleGraph.toGraph_adjMatrix_eq`, `apply_eq_dotProduct_toMatrix₂_mulVec`, `MonoidAlgebra.ofCoeff_finsuppSum`, `Polynomial.ite_le_natDegree_coeff`, `ZMod.cast_zmod_eq_zero_iff_of_le`, `DividedPowers.RatAlgebra.dpow_apply`, `MonomialOrder.degree_smul_le`, `ContinuousLinearMap.prodMapL_apply`, `ContinuousLinearMap.uncurryLeft_apply`, `HilbertBasis.dense_span`, `HasDerivAtFilter.scomp`, `MultilinearMap.freeDFinsuppEquiv_def`, `LieAlgebra.Basis.iSupIndep_rootSpace`, `Submodule.orthogonal_orthogonal_eq_closure`, `MvPolynomial.irreducible_sumSMulX`, `factorization_zero`, `AnalyticOnNhd.aeval_mvPolynomial`, `Subgroup.mem_closure_range_iff`, `Polynomial.cyclotomic_pos_and_nonneg`, `MvPolynomial.totalDegree_eq_zero_iff_eq_C`, `WithZeroMulInt.toNNReal_le_one_iff`, `zero_eq_inv`, `Polynomial.mem_annIdeal_iff_aeval_eq_zero`, `EuclideanDomain.lcm_zero_right`, `finsuppTensorFinsuppRid_symm_single_smul`, `ENat.toENNReal_zero`, `WeierstrassCurve.j_eq_zero`, `ArithmeticFunction.carmichael_two_pow_of_le_two_eq_totient`, `Matrix.eq_zero_of_forall_index_sum_mul_pow_eq_zero`, `NonUnitalSubring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg`, `MvPowerSeries.coeff_expand_smul`, `Unitization.isSelfAdjoint_inr`, `MeromorphicOn.divisor_ofNat`, `finsetBasisOfTopLeSpanOfCardEqFinrank_repr_apply`, `NonUnitalSubring.val_zero`, `RCLike.toZeroLEOneClass`, `tsupport_mul_subset_left`, `PointedCone.convex`, `comap_mulLeft_nhdsGT_zero`, `MonoidAlgebra.ofCoeff_eq_zero`, `HomogeneousIdeal.mem_irrelevant_iff`, `MonoidAlgebra.coeff_comapDomain`, `Num.cast_to_nat`, `Real.contDiffAt_arcsin_iff`, `tendsto_inv_atBot_zero`, `Representation.LinearizeMonoidal.η_toLinearMap`, `Algebra.Generators.Hom.toAlgHom_X`, `MvPolynomial.weightedTotalDegree_eq_zero_iff`, `AlgebraicGeometry.exists_of_res_zero_of_qcqs_of_top`, `ThreeGPFree.smul_set₀`, `MvPolynomial.bind₁_rename`, `WittVector.verschiebungFun_coeff`, `Filter.tendsto_mul_const_atTop_iff_pos`, `Polynomial.scaleRoots_aeval_eq_zero`, `Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe`, `ContinuousAlternatingMap.curryLeft_compContinuousLinearMap`, `MvPolynomial.degreeOf_sub_le`, `Irreducible.degree_pos`, `HasDerivWithinAt.fun_smul`, `SkewMonoidAlgebra.domCongr_refl`, `slope_pos_iff`, `CFC.zero_rpow`, `TestFunction.lineDerivOp_eq_lineDerivCLM`, `AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly_assoc`, `contMDiffOn_continuousLinearMapCoordChange`, `fderivWithin_smul`, `MvPolynomial.degreeOf_mul_X_eq_degreeOf_add_one_iff`, `algebraMap.lift_map_eq_zero_iff`, `IsAdic.hasBasis_nhds_zero`, `IsUnit.isStrictlyPositive_star_left_conjugate_iff`, `wittStructureRat_prop`, `ContinuousMultilinearMap.curryFinFinset_apply_const`, `InnerProductSpace.enorm_rankOne`, `Nat.Partition.toFinsuppAntidiag_injective`, `Module.Basis.restrictScalars_repr_apply`, `WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero`, `Orthonormal.inner_finsupp_eq_sum_right`, `HasStrictDerivAt.fun_div`, `inv_neg''`, `contDiffOn_zero`, `QuaternionGroup.one_def`, `ProperCone.dual_iUnion`, `ContinuousMultilinearMap.compContinuousLinearMapLRight_apply`, `MvPolynomial.degrees_rename`, `Convex.exists_forall_hasDerivWithinAt`, `AddMonoidAlgebra.mapAddEquiv_apply`, `MvPolynomial.vars_neg`, `Algebra.Presentation.comp_relation`, `MvPolynomial.eval₂Hom_zero'`, `Polynomial.Bivariate.equivMvPolynomial_symm_C`, `Valuation.one_apply_eq_zero_iff`, `HasFPowerSeriesAt.hasStrictDerivAt`, `SchwartzMap.fourierMultiplierCLM_apply`, `Algebra.Generators.instIsScalarTowerRing`, `FunctionField.InftyValuation.map_one'`, `Matrix.charpoly_one`, `ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self`, `HahnSeries.C_eq_algebraMap`, `MvPowerSeries.aeval_coe`, `HahnSeries.instNoZeroDivisors`, `Finsupp.span_eq_range_linearCombination`, `Module.Basis.equivFunL_apply`, `ContinuousAt.cfcₙ_nnreal`, `AddMonoidAlgebra.le_inf_support_list_prod`, `Nat.factorization_centralBinom_eq_zero_of_two_mul_lt`, `Finsupp.prod_eq_zero_iff`, `Polynomial.support_update_zero`, `SimpleGraph.vertexCoverNum_eq_zero`, `NNRat.num_zero`, `MvPowerSeries.truncFinset_monomial_eq_zero`, `MonoidAlgebra.smul_single`, `HahnSeries.leadingCoeff_mul_of_ne_zero`, `MonomialOrder.toSyn_degree_mul_le`, `Ideal.isRadical_bot_iff`, `WithBot.instPosMulMono`, `Polynomial.homogenize_X_pow`, `ContDiff.smulRight`, `mul_pos_iff_of_pos_right`, `not_linearIndependent_iffₒₛ`, `zero_isRadical_iff`, `ArithmeticFunction.zeta_apply_ne`, `ContinuousMultilinearMap.flipLinear_apply_apply`, `CharTwo.two_zsmul`, `WittVector.IsPoly.poly`, `MvPolynomial.map_hsymm`, `AddValuation.map_zero`, `Asymptotics.isLittleO_iff_tendsto'`, `Squarefree.natFactorization_le_one`, `MvPolynomial.monomial_le_degreeOf`, `SymmetricAlgebra.algebraMap_eq_zero_iff`, `HahnSeries.ofPowerSeries_apply_coeff`, `strictMonoOn_mul_self`, `Polynomial.Monic.degree_pos`, `MvPowerSeries.eval₂_eq_tsum`, `Finsupp.support_sym2Mul_subset`, `ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall`, `Multiset.toDFinsupp_replicate`, `Derivation.map_zero`, `isReduced_localizationPreserves`, `LinearMap.hasDerivWithinAt`, `MvPowerSeries.homogeneousComponent_of_lt_order_eq_zero`, `Algebra.Generators.cotangentRestrict_bijective_of_isCompl`, `MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination`, `MvPolynomial.finite_universalFactorizationMap`, `LaurentSeries.Cauchy.coeff_support_bddBelow`, `CStarMatrix.toCLM_apply_single`, `div_nonpos_iff`, `Module.Relations.map_single`, `FractionalIdeal.divMod_zero_of_not_le`, `Module.presentationFinsupp_R`, `isCoprime_zero_left`, `nonpos_of_mul_nonneg_right`, `CStarModule.inner_self`, `IsStrictlyPositive.smul`, `MvPolynomial.rTensorAlgHom_toLinearMap`, `Units.inv_pos`, `RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra'`, `FormalMultilinearSeries.comp_id`, `QuaternionAlgebra.Basis.lift_one`, `range_cfcₙ_eq_range_cfcₙHom`, `ContinuousMap.nnnorm_smul_const`, `smul_eq_zero_iff_left`, `ArithmeticFunction.natCoe_one`, `wittStructureRat_rec`, `Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod`, `WeierstrassCurve.Projective.equation_of_Z_eq_zero`, `WittVector.mul_polyOfInterest_vars`, `Nat.divisors_eq_map_attach_Iic_factorization_prod_pow`, `Finset.expect_boole_mul'`, `hasFTaylorSeriesUpTo_succ_nat_iff_right`, `LaurentSeries.of_powerSeries_localization`, `WithBot.unbotD_zero_mul`, `ContinuousOn.cfc_nnreal_of_mem_nhdsSet`, `SpectrumRestricts.eq_zero_of_neg`, `SchwartzMap.compSubConstCLM_zero`, `ContDiffMapSupportedIn.seminorm_top_le_iff`, `HahnSeries.embDomainAlgHom_apply_coeff`, `LinearMap.BilinForm.zero_apply`, `MvPolynomial.isRegular_prod_X`, `MonoidAlgebra.mapRangeAddEquiv_apply`, `MvPolynomial.homogeneousSubmodule_zero`, `MvPolynomial.coeff_sumSMulX`, `Finsupp.single_mul`, `MvPolynomial.expand_eq_C`, `Finsupp.multinomial_eq_of_support_subset`, `OrthogonalIdempotents.mul_sum_of_notMem`, `OrderedFinpartition.neZero_length`, `JacobsonNoether.exist_pow_eq_zero_of_le`, `ClosedSubmodule.iInf_orthogonal`, `IsValuativeTopology.mem_nhds_zero_iff`, `diagonal_dotProduct`, `ofBoolRing_zero`, `Polynomial.comp_eq_zero_iff`, `ArithmeticFunction.carmichael_dvd`, `MvPowerSeries.le_weightedOrder_subst`, `ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors`, `Matrix.eRank_zero`, `NonUnitalStarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar`, `algebraicIndependent_iff`, `Polynomial.isNilpotent_aeval_sub_of_isNilpotent_sub`, `Finsupp.mapDomainEmbedding_apply`, `Polynomial.coeff_monomial`, `HahnSeries.coeff_mul_order_add_order`, `Multiset.uIcc_eq`, `HasDerivAt.clm_comp`, `MvPowerSeries.trunc'_expand`, `isReduced_iff_pow_one_lt`, `MvPolynomial.universalFactorizationMapPresentation_map`, `Matrix.col_eq_zero_of_commute_single`, `HasFPowerSeriesOnBall.neg`, `IsIntegralClosure.mk'_zero`, `AffineBasis.coord_apply_combination_of_notMem`, `ProperCone.dual_singleton`, `MvPolynomial.coeff_rename_mapDomain`, `ContinuousLinearMap.uncurryBilinear_apply`, `Nat.factorization_choose_of_lt_three_mul`, `Num.castNum_ldiff`, `CStarAlgebra.isStrictlyPositive_iff_exists_isStrictlyPositive_and_eq_mul_self`, `Matrix.isStrictlyPositive_iff_posDef`, `Matrix.det_one_sub_mul_comm`, `Algebra.TensorProduct.basisAux_tmul`, `range_cfcₙHom_le`, `ZMod.natCast_eq_zero_iff`, `StrongDual.extendRCLikeₗ_apply`, `Finsupp.multinomial_update`, `EuclideanDomain.zero_mod`, `iccHomeoI_apply_coe`, `MvPowerSeries.monomial_zero_eq_C_apply`, `MonomialOrder.degree_mul_le`, `AddSubgroup.mem_closure_range_iff`, `HasFDerivWithinAt.smul_const`, `Module.Basis.singleton_repr`, `MvPolynomial.restrictSupport_mono`, `KaehlerDifferential.derivationQuotKerTotal_apply`, `Valuation.apply_posSubmonoid_pos`, `Finsupp.count_toMultiset`, `QuaternionAlgebra.Basis.k_self`, `Orthonormal.linearIsometryEquiv_symm_apply_single_one`, `MonoidAlgebra.coe_add`, `MvPolynomial.algebraTensorAlgEquiv_symm_X`, `Matrix.add_mul_mul_invOf_mul_eq_one'`, `AddChar.tendsto_eval_one_sub_pow`, `mulRightLinearMap_eq_zero_iff`, `Matrix.IsHermitian.cfcAux_apply`, `DividedPowers.OfInvertibleFactorial.dpow_eq_of_not_mem`, `SchwartzMap.fourierInv_lineDerivOp_eq`, `RatFunc.valuation_eq_LaurentSeries_valuation`, `MvPolynomial.expand_injective`, `Polynomial.coeff_X_of_ne_one`, `Polynomial.integralNormalization_eval₂_eq_zero`, `Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg`, `CStarModule.inner_zero_left`, `MvPolynomial.mem_restrictDegree`, `Set.zero_mem_centralizer`, `MvPolynomial.support_coeff_finSuccEquiv`, `ExteriorAlgebra.ι_sq_zero`, `minpoly.aeval`, `ENat.mul_top'`, `Nat.ofDigits_eq_foldr`, `SkewMonoidAlgebra.coe_algebraMap`, `ZMod.completedLFunction_eq`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `MonomialOrder.monic_monomial`, `Algebra.Presentation.aeval_val_relation`, `Quaternion.imJ_neg`, `ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear`, `iteratedFDeriv_eq_equiv_comp`, `LinearMap.polyCharpolyAux_map_eq_charpoly`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `MvPolynomial.totalDegree_neg`, `Mathlib.Tactic.Ring.atom_pf'`, `MvPolynomial.expand_one`, `CFC.log_monotoneOn`, `pos_of_right_mul_lt_le`, `not_isRelPrime_zero_zero`, `PointedCone.coe_lineal`, `Differentiable.continuousMultilinearMapCompContinuousLinearMap`, `HahnSeries.orderTop_mul_of_ne_zero`, `Unitization.norm_eq_sup`, `RCLike.nonneg_iff`, `notMem_nonZeroDivisors_iff`, `Nat.ofNat_pos`, `associator_eq_zero_iff_associative`, `FreeAbelianGroup.toFinsupp_of`, `AbsoluteValue.IsEquiv.equivWithAbs_image_mem_nhds_zero`, `ContinuousMap.toLp_norm_eq_toLp_norm_coe`, `AddChar.sum_eq_zero_of_ne_one`, `Nat.ModEq.listSum_map_zero`, `MvPolynomial.degrees_map_le`, `RCLike.ofReal_zero`, `Matrix.ofLp_toEuclideanCLM`, `Num.cast_ofZNum`, `hasFTaylorSeriesUpToOn_succ_nat_iff_right`, `HasDerivWithinAt.comp_hasDerivAt_of_eq`, `PowerSeries.HasSubst.zero'`, `MvPolynomial.esymmAlgHom_fin_surjective`, `Polynomial.roots_X`, `IsLprojection.coe_bot`, `conjneg_zero`, `MvPolynomial.expand_inj`, `Polynomial.toFinsupp_one`, `hasDerivAtFilter_iff_isLittleO`, `LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff`, `Absorbent.eventually_nhdsNE_zero`, `MvPolynomial.coeff_prod_X_pow`, `MvPolynomial.support_neg`, `HasDerivAt.fun_const_smul`, `ArithmeticFunction.cardDistinctFactors_prod`, `CommRingCat.HomTopology.mvPolynomialHomeomorph_symm_apply_hom`, `HasDerivAt.fun_sub`, `MvPolynomial.supDegree_esymm`, `IsStrictlyPositive.nnrpow`, `CStarMatrix.toCLM_apply_eq_sum`, `GradedRingHom.map_zero`, `ENat.lift_zero`, `Nat.factorization_lt`, `LinearMap.toMatrix_transpose_apply`, `MvPolynomial.indicator_mem_restrictDegree`, `DirectSum.coe_decompose_mul_of_right_mem_of_not_le`, `dotProduct_self_eq_zero`, `MvPolynomial.coeffsIn_mul`, `Polynomial.isUnit_iff_coeff_isUnit_isNilpotent`, `DirectSum.coe_decompose_mul_of_left_mem_of_not_le`, `Pi.basis_repr`, `CompleteOrthogonalIdempotents.single`, `QuadraticForm.sigNeg_weightedSumSquares`, `PowerSeries.constantCoeff_subst_eq_zero`, `HasFPowerSeriesWithinAt.sub`, `ClosedSubmodule.sup_orthogonal`, `Nat.ordCompl_pow_mul_of_not_dvd`, `WithZeroTopology.isClosed_iff`, `hasDerivAt_exp_smul_const`, `AlgebraicGeometry.AffineSpace.map_toSpecMvPoly`, `Finset.dens_empty`, `zpow_eq_zero_iff`, `HasDerivAtFilter.add_const`, `SkewMonoidAlgebra.instFree`, `FiniteField.sum_subgroup_pow_eq_zero`, `toMatrix_dualTensorHom`, `MvPolynomial.eval_eq`, `List.prod_pos`, `MvPowerSeries.rename_coe`, `MonoidAlgebra.mul_apply_mul_eq_mul_of_uniqueMul`, `MonomialOrder.sPolynomial_def`, `mul_pos_iff`, `hasFDerivWithinAt_comp_smul_smul_iff`, `HahnSeries.unit_aux`, `fourierCoeff_toLp`, `Nat.not_dvd_ordCompl`, `MvPolynomial.mk_eq_eval₂`, `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`, `MonomialOrder.sPolynomial_antisymm`, `Algebra.Generators.H1Cotangent.δAux_ofComp`, `MvPolynomial.restrictSupport_zero`, `SimpleGraph.incMatrix_mul_transpose`, `AlgebraicGeometry.exists_appTop_map_eq_zero_of_isAffine_of_isLimit`, `EuclideanDomain.gcd_zero_left`, `HasStrictDerivAt.congr_deriv`, `gauge_smul_left_of_nonneg`, `Module.Relations.Quotient.linearMap_ext_iff`, `WithZeroTopology.hasBasis_nhds_zero`, `MeromorphicOn.divisor_fun_zpow`, `zpow_nonneg`, `Finset.affineCombination_indicator_subset`, `LinearMap.isPositive_toContinuousLinearMap_iff`, `Module.Presentation.ofExact_relation`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn'`, `Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff`, `NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat`, `ContinuousMapZero.nonUnitalStarAlgHom_precomp_apply`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd'`, `Nat.factorization_lcm`, `PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent`, `LinearIndependent.span_repr_eq`, `PowerSeries.map_eq_zero`, `MvPolynomial.killCompl_monomial_mapDomain`, `IntermediateField.list_sum_mem`, `MonomialOrder.mem_nonZeroDivisors_of_leadingCoeff_mem_nonZeroDivisors`, `LinearMap.pi_apply_eq_sum_univ`, `RootPairing.rootForm_self_eq_zero_iff`, `QuaternionAlgebra.re_swapEquiv_symm_apply`, `FormalMultilinearSeries.changeOrigin_eval_of_finite`, `hasProd_zero_of_exists_eq_zero`, `Matrix.conjTranspose_eq_ofNat`, `SeparatingDual.eq_zero_iff_forall_dual_eq_zero`, `Quaternion.fst_imJ_dualNumberEquiv_symm`, `exists_nonneg_right_iff_sameRay`, `MonomialOrder.le_add_right`, `IsFormallyReal.eq_zero_of_isSumSq_of_neg_isSumSq`, `MvPolynomial.as_sum`, `descPochhammer_nonneg`, `iteratedFDerivWithin_two_apply'`, `MonomialOrder.degree_mul_of_left_mem_nonZeroDivisors`, `Matrix.fromRows_one_isTotallyUnimodular_iff`, `EuclideanDomain.gcd_zero_right`, `Matrix.det_fromBlocks₁₁`, `HasDerivAt.const_smul`, `Finset.Nonempty.zero_div`, `Polynomial.coeff_X_zero`, `MvPolynomial.isUnit_iff_eq_C_of_isReduced`, `Polynomial.Chebyshev.U_eval_zero_of_odd`, `LinearMap.det_eq_zero_iff_ker_ne_bot`, `RCLike.zero_re`, `MonomialOrder.leadingCoeff_monomial`, `IsSemisimpleRing.exists_ringEquiv_pi_matrix_divisionRing`, `AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero`, `Algebra.Presentation.differentials.comm₂₃'`, `cfcₙ_tsub`, `evalRingHom_mapMatrix_comp_compRingEquiv`, `HasStrictDerivAt.add`, `MvPolynomial.psum_zero`, `Matrix.isDiag_conjTranspose_iff`, `inr_comp_cfcₙHom_eq_cfcₙAux`, `SimpleGraph.incMatrix_apply_eq_one_iff`, `noZeroDivisors_iff_left_eq_zero_of_mul`, `CFC.rpow_neg_one_eq_cfc_inv`, `InnerProductSpace.gramSchmidt_triangular`, `MvPolynomial.monomial_add_single`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_X_none`, `IsUnit.isNilpotent_unit_mul_of_commute_iff`, `QuadraticAlgebra.basis_repr_apply`, `Mathlib.Tactic.Bound.Nat.cast_pos_of_pos`, `CFC.monotoneOn_one_sub_one_add_inv_real`, `HahnSeries.ofPowerSeries_X`, `WeierstrassCurve.b₂_of_isShortNF`, `MvPolynomial.le_coeffsIn_pow`, `MvPolynomial.supported_strictMono`, `IsUnit.star_left_conjugate_nonneg_iff`, `ZMod.valMinAbs_eq_zero`, `Polynomial.toFn_zero`, `CStarModule.inner_zero_right`, `PowerBasis.repr_mul_isIntegral`, `Matrix.vecMul_permMatrix`, `TrivSqZeroExt.inrCLM_apply`, `MvPolynomial.IsWeightedHomogeneous.pow`, `Matrix.mul_adjugate_apply`, `MonomialOrder.degree_pow_le`, `MeasureTheory.Filtration.filtrationOfSet_eq_natural`, `QuadraticAlgebra.C_mul_eq_smul`, `MvPolynomial.eval_add`, `WeierstrassCurve.Projective.map_polynomialX`, `MvPolynomial.pointToPoint_zeroLocus_le`, `Matrix.toLpLin_symm_id`, `Matrix.vecMul_ofNat`, `LieAlgebra.zero_rootSpace_eq_top_of_nilpotent`, `mul_self_pos`, `Module.Basis.toDual_eq_repr`, `Num.succ_to_nat`, `Matroid.eRk_loopyOn`, `IsCyclotomicExtension.neZero_of_mem'`, `Algebra.SubmersivePresentation.map_jacobianRelationsOfHasCoeffs`, `Unitization.inrHom_apply`, `unitary.spectrum_subset_circle`, `AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot`, `Mathlib.Tactic.Ring.natCast_zero`, `iteratedDerivWithin_fun_id`, `Algebra.Norm.Transitivity.det_det_aux`, `Finsupp.smul_single'`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight`, `exists_integral_inj_algHom_of_quotient`, `QuaternionAlgebra.comm`, `one_le_inv_iff₀`, `DirectSum.coe_of_mul_apply_of_not_le`, `MvPowerSeries.trunc_map`, `Finsupp.weight_single_index`, `MvPolynomial.isNilpotent_iff`, `HasFPowerSeriesAt.fderiv_eq`, `Module.Basis.sum_repr_mul_repr`, `NumberField.Units.dirichletUnitTheorem.seq_norm_le`, `LinearMap.BilinForm.dualBasis_eq_iff`, `MeromorphicOn.divisor_apply`, `Topology.RelCWComplex.skeletonLT_zero_eq_base`, `HasDerivAtFilter.scomp_of_eq`, `ContinuousWithinAt.cfcₙ_nnreal`, `AbsoluteValue.pos`, `mul_sub_mul_div_mul_neg`, `Finsupp.linearCombination_apply`, `PointedCone.mem_map`, `ContinuousLinearMap.memLp_of_bilin`, `WittVector.iterate_verschiebung_coeff_eq_zero`, `Cubic.leadingCoeff_of_c_eq_zero'`, `HasFPowerSeriesOnBall.tendstoUniformlyOn`, `MatrixModCat.mem_toModuleCatObj`, `Matrix.add_mul_mul_mul_invOf_eq_one`, `HasDerivAt.scomp_hasDerivWithinAt_of_eq`, `Polynomial.nextCoeff_C_eq_zero`, `Nat.factorization_ceilRoot`, `Differential.logDeriv_one`, `QuaternionAlgebra.star_add_self'`, `SchwartzMap.smulLeftCLM_smulLeftCLM_apply`, `Unitization.inrRangeEquiv_apply_coe_fst`, `NormedRing.inverse_add`, `ContinuousLinearMap.isometry_iff_adjoint_comp_self`, `MvPolynomial.instNoZeroDivisors`, `NumberField.integralBasis_repr_apply`, `Finset.inv_smul_finset_distrib₀`, `Matrix.toBilin'Aux_single`, `continuousMultilinearCurryFin0_apply`, `exists_finite_inj_algHom_of_fg`, `AlgHom.default_apply`, `Polynomial.coeff_natTrailingDegree_eq_zero_of_trailingDegree_lt`, `ZMod.val_zero`, `IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem`, `Mathlib.Meta.Positivity.nonneg_of_isRat`, `div_nonpos_of_nonneg_of_nonpos`, `LieAlgebra.rootSpace_zero_eq`, `Matrix.det_diagonal`, `PiTensorProduct.dualSeminorms_bounded`, `MonoidAlgebra.support_mul_single_subset`, `FormalMultilinearSeries.radius_neg`, `MvPolynomial.eval₂_eq'`, `Quaternion.imK_mul`, `extDeriv_smul`, `Matrix.det_fromBlocks_one₁₁`, `HasDerivAt.comp_const_sub`, `MonomialOrder.monic_monomial_one`, `Submodule.mulRightMap_eq_mulMap_comp`, `LaurentSeries.coe_X_compare`, `eq_zero_of_mul_eq_self_left`, `Matrix.blockDiagonal'_mul`, `ContinuousLinearMap.opNorm_extend_le`, `Submodule.orthogonal_closure`, `MvPolynomial.zeroLocus_bot`, `HasDerivWithinAt.add`, `IsSelfAdjoint.conj_adjoint`, `AddMonoidAlgebra.ofCoeff_mapRange`, `WeierstrassCurve.Jacobian.baseChange_polynomial`, `ContinuousMultilinearMap.curryMidEquiv_apply`, `Units.mul_right_eq_zero`, `ZMod.eq_zero_iff_gcd_ne_one`, `MvPolynomial.aeval_def`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq`, `RingHom.codomain_trivial_iff_map_one_eq_zero`, `Module.Basis.linearMap_repr_apply`, `Affine.Simplex.affineCombination_mem_interior_iff`, `MvPolynomial.monomial_eq_zero`, `AddMonoidAlgebra.coeffLinearEquiv_apply`, `HasStrictFDerivAt.continuousMultilinear_apply_const`, `Set.Icc.instIsCancelMulZero`, `Set.Icc.mul_le_left`, `Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos`, `PointedCone.coe_closure`, `MvPolynomial.eval_monomial`, `ContDiffMapSupportedIn.monoLM_eq_zero`, `Matrix.hadamard_one_eq_one_iff`, `Quaternion.coe_div`, `MvPolynomial.eq_modMonomial_single`, `sameRay_neg_smul_left_iff_of_ne`, `isLinearTopology_iff_hasBasis_ideal`, `CFC.continuousOn_nnrpow`, `ContinuousLinearMap.opNorm_mulLeftRight_apply_le`, `ContinuousLinearMap.analyticOnNhd_bilinear`, `Polynomial.coeff_natDegree_succ_eq_zero`, `Relation.cutExpand_le_invImage_lex`, `HahnSeries.cardSupp_div_le`, `MultilinearMap.freeFinsuppEquiv_def`, `Filter.top_smul_nhds_zero`, `MonomialOrder.degree_C`, `AbsoluteValue.nonneg`, `IsSimpleRing.exists_algEquiv_matrix_divisionRing_finite`, `conjneg_nonpos`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `DoubleCentralizer.algebraMap_snd`, `MvPolynomial.coeff_monomial_mul'`, `RootPairing.Base.not_nonpos_iff_pos_of_sum_mem_range_root`, `NormedSpace.expSeries_apply_zero`, `MvPolynomial.monomial_mem_coeffsIn`, `MonomialOrder.toSyn_monotone`, `MvPolynomial.degrees_sub_le`, `ArithmeticFunction.sigma_eq_prod_primeFactors_sum_range_factorization_pow_mul`, `AbsoluteValue.pos_iff`, `LieIdeal.rootSet_apply_coroot_eq_zero_of_notMem_rootSet`, `MonoidAlgebra.instIsCancelMulZeroOfIsCancelAddOfUniqueProds`, `Associated.eq_zero_iff`, `MvPolynomial.coe_eval₂Hom`, `MonotoneOn.derivWithin_nonneg`, `MvPowerSeries.coeff_trunc'`, `IsAdjoinRoot.repr_zero_mem_span`, `ProperCone.innerDual_union`, `hasFiniteFPowerSeriesOnBall_const`, `SkewMonoidAlgebra.coeff_mul`, `CauSeq.coe_zero`, `MvPolynomial.vars_C_mul`, `Polynomial.coeff_C`, `exists_le_mul_self`, `FormalMultilinearSeries.ofScalarsSum_zero`, `HahnModule.SMulCommClass`, `Mathlib.Tactic.Ring.inv_zero`, `iteratedFDerivWithin_succ_apply_left`, `EuclideanSpace.toLp_single`, `LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero`, `ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat`, `pow_left_monotoneOn`, `MvPolynomial.coeff_zero_X`, `bdd_le_mul_tendsto_zero`, `Polynomial.eval_zero`, `Matroid.IsLoop.eRk_eq`, `MonomialOrder.sPolynomial_left_zero`, `Polynomial.rootOfSplits'_eq_rootOfSplits`, `AbsoluteValue.eval_mvPolynomial_le`, `Matrix.mulVec_zero`, `NonUnitalSubring.mem_bot`, `MvPowerSeries.coeff_zero_mul_X`, `mul_left_eq_self₀`, `Polynomial.degree_intCast_le`, `NonUnitalAlgHom.inl_apply`, `Behrend.sphere_zero_subset`, `PointedCone.tmul_subset_maxTensorProduct`, `Algebra.Generators.toAlgHom_ofComp_rename`, `RingCon.ofMatrix_rel'`, `ZNum.cast_inj`, `Mathlib.Tactic.Ring.add_pf_zero_add`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear`, `IsStrictlyPositive.spectrum_pos`, `DualNumber.exp_eps`, `MonomialOrder.support_leadingTerm`, `Finsupp.linearCombination_embDomain`, `Algebra.FinitePresentation.iff`, `Matrix.one_hadamard_eq_one_iff`, `MonoidWithZeroHom.map_one'`, `DividedPowerAlgebra.dp_zero`, `wittStructureRat_rec_aux`, `Polynomial.Bivariate.equivMvPolynomial_symm_X_1`, `PosNum.to_int_eq_succ_pred`, `MvPolynomial.eval₂_add`, `not_isPrimePow_zero`, `Function.locallyFinsuppWithin.exists_single_le_pos`, `MonomialOrder.image_leadingTerm_insert_zero`, `WeierstrassCurve.Projective.eval_polynomialZ`, `LinearMap.splittingOfFinsuppSurjective_injective`, `MvPowerSeries.coeff_inv_aux`, `Nat.prod_pow_dvd_of_le_factorization`, `PadicInt.mk_zero`, `WittVector.verschiebung_coeff_zero`, `MvPolynomial.supported_mono`, `mem_quasispectrum_iff`, `RootPairing.zero_le_posForm`, `hasDerivWithinAt_natCast`, `mul_eq_zero`, `MeromorphicOn.divisor_fun_mul`, `NonUnitalSubring.coe_bot`, `DFinsupp.toMultiset_toDFinsupp`, `Module.length_bot`, `Matrix.invOf_fromBlocks_zero₁₂_eq`, `HahnSeries.cardSupp_mul_single_le`, `ENat.ceil_zero`, `MeromorphicOn.divisor_zpow`, `CliffordAlgebra.ι_mul_ι_mem_evenOdd_zero`, `WeierstrassCurve.Jacobian.addXYZ_neg`, `Algebra.Generators.ker_localizationAway`, `Polynomial.card_support_eq_three`, `RatFunc.algebraMap_apply_div`, `Mathlib.Tactic.Linarith.mul_eq`, `MonoidAlgebra.supportedEquivFinsupp_symm_apply_coe_support_val`, `Set.Nonempty.encard_pos`, `Finsupp.DegLex.lt_iff`, `mul_eq_zero_iff_left`, `Matrix.single_mul_single_same`, `arithGeom_zero_eq_sum`, `Matrix.isIrreducible_iff_exists_pow_pos`, `ProperCone.dual_zero`, `EuclideanDomain.mod_self`, `MonomialOrder.sPolynomial_decomposition`, `star_mul_self_nonneg`, `MonomialOrder.degLex_single_le_iff`, `MvPolynomial.constantCoeff_smul`, `HahnSeries.C_zero`, `ContinuousLinearMap.bilinearComp_apply`, `MvPolynomial.totalDegree_expand`, `HahnSeries.addVal_apply_of_ne`, `MvPolynomial.algHom_C`, `SimpleGraph.ofNat_hadamard_adjMatrix`, `PerfectClosure.mk_zero_right`, `MvPolynomial.leadingCoeff_toLex_C`, `WeierstrassCurve.Affine.evalEval_polynomial_zero`, `Nat.WithBot.lt_zero_iff`, `Ideal.hasBasis_nhds_zero_adic`, `Nonneg.unitsHomeomorphPos_apply_coe`, `MvPolynomial.support_mul_X`, `Filter.tendsto_mul_const_atTop_iff`, `range_cfcₙ_nnreal_eq_image_cfcₙ_real`, `Matrix.adjugate_diagonal`, `cfcUnits_pow`, `Matrix.transpose_invOf`, `IsAlgClosed.exists_aeval_eq_zero_of_injective`, `Representation.LinearizeMonoidal.assoc_comp_δ`, `PosNum.div'_to_nat`, `LinearOrderedField.smul_Ioo`, `Left.mul_nonneg`, `WeierstrassCurve.Projective.addU_of_Z_eq_zero_left`, `wittStructureInt_prop`, `Subring.coe_eq_zero_iff`, `Matrix.one_submatrix_mul`, `MvPowerSeries.coeff_weightedHomogeneousComponent`, `ClosedSubmodule.mem_orthogonal`, `Matrix.diagonal_mul`, `NormedRing.inverse_add_norm`, `Matrix.smul_eq_mul_diagonal`, `MvPolynomial.eval_pow`, `AddChar.expect_eq_zero_iff_ne_zero`, `QuadraticAlgebra.algebraMap_eq`, `Finsupp.mul_apply`, `Representation.ofMulActionSelfAsModuleEquiv_apply`, `Metric.unitBall.instIsLeftCancelMulZero`, `Unitization.mem_spectrum_inr_of_not_isUnit`, `Filter.Tendsto.cfcₙ_nnreal`, `rat_mul_continuous_lemma`, `IsFractionRing.inv_def`, `HasDerivAt.fun_div`, `lipschitzOnWith_cfcₙ_fun`, `Matrix.charmatrix_natCast`, `Quaternion.mul_star_eq_coe`, `Projectivization.mk_eq_mk_iff_crossProduct_eq_zero`, `Matrix.diagonal_toLin'`, `Cubic.natDegree_of_a_eq_zero'`, `TensorPower.mul_one`, `spectrum.exists_mem_of_not_isUnit_aeval_prod`, `HasFTaylorSeriesUpToOn.fderivWithin`, `MvPolynomial.eval₂Hom_zero'_apply`, `SimpleGraph.adjMatrix_mulVec_const_apply`, `Finsupp.NonTorsionWeight.eq_zero_of_smul_eq_zero`, `CStarMatrix.toCLM_apply`, `KaehlerDifferential.kerTotal_map`, `MvPowerSeries.lexOrder_zero`, `Subring.closure_insert_zero`, `CFC.nnrpow_zero`, `PowerSeries.coe_zero`, `MvPolynomial.psumPart_zero`, `QuadraticMap.map_finsuppSum'`, `zero_pow_le_one`, `BooleanRing.add_self`, `DoubleCentralizer.algebraMap_toProd`, `ValuationSubring.zero_mem`, `Set.inv_smul_set_distrib₀`, `continuousMultilinearCurryFin0_symm_apply_apply`, `HasDerivWithinAt.fun_const_smul`, `NonUnitalStarAlgHom.coe_zero`, `IsSMulRegular.zero`, `Subsemiring.coe_sumSq`, `mul_nonneg_of_nonpos_of_nonpos`, `sign_mul`, `ContinuousLinearMap.ker_self_comp_adjoint`, `LieModule.eq_zero_of_mem_genWeightSpace_mem_posFitting`, `ArithmeticFunction.IsMultiplicative.map_one`, `Quaternion.fst_imI_dualNumberEquiv_symm`, `Finsupp.degLex_def`, `tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero`, `NonUnitalRingHom.zero_apply`, `exists_nontrivial_relation_sum_zero_of_not_affine_ind`, `FormalMultilinearSeries.id_comp`, `Finset.mem_convexHull`, `AlgebraicIndependent.mvPolynomialOptionEquivPolynomialAdjoin_apply`, `ContinuousLinearMap.norm_map_tail_le`, `ZNum.cast_le`, `deriv_update`, `HasFPowerSeriesAt.restrictScalars`, `Polynomial.sylvester_zero_left_deg`, `hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `ArithmeticFunction.sum_Ioc_zeta`, `Nat.sum_digits_ofDigits_eq_sum`, `orthonormal_subtype_iff_ite`, `AddMonoidAlgebra.support_mul_single_eq_image`, `Nonneg.coe_nnqsmul`, `mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff`, `neg_iff_neg_of_mul_pos`, `MvPolynomial.le_zeroLocus_iff_le_vanishingIdeal`, `ContinuousLinearMap.instStarModuleId`, `MvPolynomial.support_esymm'`, `Subalgebra.noZeroDivisors`, `Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg`, `Matrix.projVandermonde_apply_zero_right`, `mul_neg_iff`, `TensorProduct.finsuppScalarRight_symm_apply_single`, `ArithmeticFunction.sum_Ioc_mul_eq_sum_prod_filter`, `Finsupp.sum_id_lt_of_lt`, `Matrix.single_hadamard_single_of_ne`, `mul_right_mem_nonZeroDivisorsRight_eq_zero_iff`, `WeierstrassCurve.Projective.dblXYZ_of_Z_eq_zero`, `spectrum.subset_singleton_zero_compl`, `HasDerivWithinAt.const_mul`, `HasFDerivAt.continuousAlternatingMap_apply_const`, `PiTensorProduct.injectiveSeminorm_apply`, `ContinuousLinearMap.isBoundedLinearMap_comp_left`, `IsNilpotent.map`, `Module.Basis.mem_span_image`, `Representation.linearizeOfMulActionIso_apply`, `PowerSeries.zero_inv`, `Matrix.conjTranspose_eq_intCast`, `ValuativeRel.zero_vlt_coe_posSubmonoid`, `AnalyticOnNhd.codiscreteWithin_setOf_analyticOrderAt_eq_zero_or_top`, `Polynomial.mem_nonZeroDivisors_iff`, `NumberField.RingOfIntegers.mk_zero`, `norm_fderiv_iteratedFDeriv`, `Int.floor_zero`, `WeierstrassCurve.IsShortNF.a₃`, `Nat.dvd_iff_dvd_digits_sum`, `exists_pos_lt_mul`, `RootPairing.RootPositiveForm.rootLength_pos`, `TestFunction.lineDerivCLM_eq_fderivCLM`, `MonomialOrder.leadingCoeff_mul_of_left_mem_nonZeroDivisors`, `HasDerivWithinAt.div`, `MvPolynomial.mkₐ_eq_aeval`, `Polynomial.isNilpotent_iterate_newtonMap_sub_of_isNilpotent`, `MvPolynomial.derivation_C`, `NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst`, `MvPolynomial.mem_support_coeff_optionEquivLeft`, `ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply`, `PointedCone.dual_zero`, `Matrix.rank_zero`, `HahnSeries.toPowerSeriesAlg_apply`, `Algebra.Presentation.fg_ker`, `Height.mulHeight_eval_ge`, `Matrix.empty_mul_empty`, `Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv`, `Module.Basis.localizationLocalization_repr_algebraMap`, `instIsStrictOrderedModuleOfIsCancelAdd`, `instIsAlgebraicMvPolynomialOfNoZeroDivisors`, `Matrix.rectVandermonde_apply_zero_right`, `MvPolynomial.eval_zero`, `Submonoid.IsLocalizationMap.map_zero`, `contDiffGroupoid_zero_eq`, `Polynomial.eval_X_toTupleMvPolynomial_zero_eq`, `PowerSeries.monomial_eq_mk`, `Matrix.l2_opNNNorm_def`, `ContinuousMultilinearMap.instIsBoundedSMul`, `cfcₙHom_isClosedEmbedding`, `MonoidAlgebra.coeff_injective`, `Matrix.permanent_diagonal`, `HahnSeries.isUnit_iff`, `MvPolynomial.dvd_smul_X_iff_exists`, `PowerSeries.inv_eq_zero`, `hasDerivAtFilter_sub_const_iff`, `Module.Basis.dualBasis_apply`, `Algebra.Generators.σ_smul`, `IsDedekindDomain.HeightOneSpectrum.intValuation.map_one'`, `Filter.tendsto_inv₀_nhdsWithin_ne_zero`, `spectrum.hasDerivAt_resolvent`, `SimpleGraph.edist_bot`, `MvPowerSeries.coeff_trunc`, `MvPolynomial.mem_supported_vars`, `ContinuousLinearMap.adjointAux_adjointAux`, `HahnSeries.toPowerSeriesAlg_symm_apply_coeff`, `ContinuousMap.notMem_setOfIdeal`, `Num.castNum_and`, `apply_eq_star_dotProduct_toMatrix₂_mulVec`, `MvPolynomial.mkDerivation_monomial`, `MvPolynomial.degrees_sum_le`, `isIdempotentElem_iff_quasispectrum_subset`, `smul_nonpos_iff_neg_imp_nonneg`, `Complex.coe_basisOneI_repr`, `Finsupp.linearCombination_single`, `HasStrictDerivAt.const_add`, `fderivWithin_continuousMultilinearMapCompContinuousLinearMap`, `Module.Presentation.CokernelData.π_lift`, `Quaternion.normSq_add`, `WittVector.zero_coeff`, `PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen`, `HahnSeries.cardSupp_single_mul_le`, `IsSumSq.mul`, `LinearMap.hasEigenvalue_zero_tfae`, `Algebra.Presentation.relation_mem_ker`, `Algebra.Generators.Hom.toExtensionHom_toRingHom`, `Algebra.FormallyUnramified.isReduced_of_field`, `Finsupp.ofSupportFinite_fin_two_eq`, `MvPolynomial.schwartz_zippel_sup_sum`, `Module.Basis.reindexFinsetRange_repr_self`, `AddMonoidAlgebra.mul_apply_left`, `mem_compactlySupported`, `ContMDiffAt.clm_precomp`, `Set.Icc.le_one`, `Algebra.Generators.comp_localizationAway_ker`, `Matrix.vecMul_conjTranspose_mul_self_eq_zero`, `MvPolynomial.mem_map_C_iff`, `ExteriorAlgebra.ι_add_mul_swap`, `AffineMap.lineMap_apply_zero`, `TestFunction.lineDerivCLM_apply`, `MvPolynomial.rename_monomial`, `inner_zero_right`, `LieAlgebra.Orthogonal.s_as_blocks`, `Nonneg.unitsEquivPos_apply_coe`, `Representation.coind'_apply_apply`, `MvPolynomial.aeval_toMvPolynomial`, `ZeroAtInftyContinuousMap.coe_mul`, `ContinuousOn.cfc_nnreal`, `MvPolynomial.mul_esymm_eq_sum`, `Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence`, `nnnorm_cfcₙ_nnreal_lt_iff`, `MvPolynomial.prime_C_iff`, `inner_self_eq_zero`, `mul_star_self_pos`, `LaurentSeries.exists_powerSeries_of_memIntegers`, `FractionalIdeal.mem_zero_iff`, `ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin`, `Matrix.trace_conjTranspose_mul_self_eq_zero_iff`, `MvPolynomial.eval_mul`, `PointedCone.minTensorProduct_le_maxTensorProduct`, `hasDerivAt_iff_tendsto_slope_zero`, `LaurentSeries.continuous_coe'`, `MvPolynomial.restrictScalars_restrictSupportIdeal`, `MvPolynomial.instFiniteSubtypeMemSubmoduleRestrictDegreeOfFinite`, `AddMonoidAlgebra.exists_supDegree_mem_support`, `Orthonormal.inner_right_finsupp`, `LinearMap.toMatrix_transpose_apply'`, `MvPowerSeries.eq_zero_iff_forall_coeff_eq_zero_and`, `WithBot.mul_def`, `WeierstrassCurve.ofJ0_c₄`, `isConjRoot_zero_iff_eq_zero`, `RingHom.ker_eq_bot_iff_eq_zero`, `ValueDistribution.characteristic_sub_characteristic_inv`, `MvPolynomial.IsHomogeneous.coeff_eq_zero`, `MvPolynomial.mem_restrictSupport_iff`, `Module.Basis.repr_symm_single_one`, `mul_zero`, `IsLocalization.integerNormalization_aeval_eq_zero`, `SchwartzMap.integral_pow_mul_iteratedFDeriv_le`, `ConjRootClass.mk_eq_zero_iff`, `HasFTaylorSeriesUpToOn.hasFDerivAt`, `Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero`, `Matrix.one_hadamard`, `MvPolynomial.degreesLE_zero`, `Rat.toNNRat_of_nonpos`, `IsFormallyReal.eq_zero_of_add_left`, `AddMonoidAlgebra.GradesBy.decompose_single`, `ContinuousLinearMap.flip_add`, `MvPolynomial.universalFactorizationMapPresentation_relation`, `exists_pos_left_iff_sameRay`, `hasFiniteFPowerSeriesAt_const`, `TrivSqZeroExt.inrHom_apply`, `GenContFract.IntFractPair.succ_nth_stream_eq_none_iff`, `MonoidAlgebra.mapAlgHom_apply`, `inv_eq_self₀`, `SimpleGraph.ediam_eq_zero_of_subsingleton`, `MvPolynomial.aevalTower_comp_algebraMap`, `Commute.add_pow_eq_zero_of_add_le_succ_of_pow_eq_zero`, `MvPolynomial.monic_esymm`, `MonoidAlgebra.ofCoeff_neg`, `ArithmeticFunction.IsMultiplicative.eulerProduct`, `QuadraticAlgebra.lift_symm_apply_coe`, `Matrix.mem_range_scalar_iff_commute_single'`, `Polynomial.Monic.mem_rootSet`, `ValuativeRel.trivialRel_eq_ofValuation_one`, `MvPolynomial.eval₂_zero_apply`, `LaurentSeries.Cauchy.exists_lb_eventual_support`, `not_isRightRegular_zero_iff`, `Matrix.exists_mulVec_eq_zero_iff`, `Algebra.PreSubmersivePresentation.aevalDifferential_single`, `Num.ofZNum_toNat`, `MvPolynomial.isWeightedHomogeneous_monomial`, `AlgebraicIndependent.algebraMap_aevalEquiv`, `cfcₙHom_le_iff`, `MvPolynomial.isWeightedHomogeneous_zero`, `HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp`, `MonomialOrder.coeff_degree_eq_zero_iff`, `Units.mk0_mul`, `ContinuousLinearMap.isSelfAdjoint_iff'`, `ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq`, `MvPolynomial.aeval_id_rename`, `MvPowerSeries.hasEval_def`, `WeierstrassCurve.Affine.equation_zero`, `CStarAlgebra.mem_Icc_algebraMap_iff_nnnorm_le`, `OnePoint.equivProjectivization_symm_apply_mk`, `NormedSpace.exp_zero`, `eq_zero_of_zero_eq_one`, `NormedRing.inverse_add_norm_diff_second_order`, `IsStrictOrderedRing.noZeroDivisors`, `Matrix.zero_hadamard`, `Finset.divConst_empty_left`, `ContinuousMultilinearMap.uncurryRight_apply`, `Finsupp.sum_nsmul`, `Finsupp.toMultiset_add`, `Nat.primeFactorsList_count_eq`, `Set.Ioc.mk_one`, `WithLp.unitization_nnnorm_inr`, `HasDerivAt.comp_const_add`, `Quaternion.imI_star`, `RootPairing.pairingIn_le_zero_iff`, `Multiset.toFinsupp_singleton`, `Representation.LinearizeMonoidal.rTensor_comp_δ`, `Matrix.isUnit_fromBlocks_iff_of_invertible₂₂`, `ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq_on`, `eq_zero_of_nilpotencyClass_eq_one`, `PowerSeries.weierstrassMod_zero_left`, `nnnorm_cfc_nnreal_lt`, `Cubic.natDegree_of_c_eq_zero'`, `MvPolynomial.degreeOf_mul_X_self`, `MonomialOrder.monic_C_one`, `MvPolynomial.eq_C_of_isEmpty`, `Matrix.single_mul_mul_single`, `TrivSqZeroExt.exp_def`, `CharZero.eq_neg_self_iff`, `Finset.prod_nonneg_of_card_nonpos_even`, `Matrix.BlockTriangular.of_charmatrix`, `MvPolynomial.coeff_one`, `CliffordAlgebraQuaternion.ofQuaternion_mk`, `Holor.slice_unitVec_mul`, `MonomialOrder.sPolynomial_right_zero`, `self_mul_sign`, `Quaternion.imI_smul`, `AddMonoidAlgebra.mapAlgHom_apply`, `LinearMap.toMatrix_smulRight`, `Metric.coveringNumber_pos_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisors`, `Finset.Nonempty.mul_zero`, `linearIndependent_iff_eq_zero_of_smul_mem_span`, `Module.Relations.solutionFinsupp_var`, `Polynomial.trailingDegree_C`, `Matrix.BlockTriangular.toBlock_inverse_mul_toBlock_eq_one`, `WeierstrassCurve.Projective.polynomialX_eq`, `RingSeminormClass.toNonnegHomClass`, `Algebra.adjoin_range_eq_range_aeval`, `HahnSeries.binomial_power`, `Associates.instNoZeroDivisors`, `ContinuousLinearMap.bilinearComp_zero`, `SkewMonoidAlgebra.coeff_mul_antidiagonal_finsum`, `RootPairing.pairingIn_lt_zero_iff`, `Convex.mem_toCone`, `Right.inv_nonneg`, `ArithmeticFunction.mul_apply_one`, `HasDerivWithinAt.scomp_hasDerivAt_of_eq`, `isScalarTower_sphere_sphere_closedBall`, `Prime.dvd_finsuppProd_iff`, `Multiset.toFinsupp_symm_apply`, `Complex.UnitDisc.instSMulCommClass_closedBall_right`, `IntermediateField.coe_zero`, `IsValuativeTopology.hasBasis_nhds_zero'`, `MvPolynomial.monomial_zero'`, `PointedCone.gc_ofSubmodule_lineal`, `Nat.setOf_pow_dvd_eq_Icc_factorization`, `PowerSeries.coe_C`, `iteratedDeriv_eq_equiv_comp`, `SchwartzMap.smulLeftCLM_add`, `Polynomial.homogenize_finsetSum`, `FreeAbelianGroup.equivFinsupp_apply`, `IsIdempotentElem.eq_zero_of_isNilpotent`, `MvPolynomial.eval₂_sub`, `MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero`, `Matrix.mul_invOf_cancel_right`, `OrthonormalBasis.inner_eq_zero`, `MultilinearMap.mkContinuousLinear_norm_le'`, `MvPolynomial.weightedHomogeneousComponent_directSum`, `norm_fderivWithin_iteratedFDerivWithin`, `HasFTaylorSeriesUpToOn.shift_of_succ`, `Quaternion.imK_star`, `CStarMatrix.mul_zero`, `NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul`, `Algebra.Generators.aeval_val_σ`, `MvPolynomial.msymm_zero`, `WeierstrassCurve.hasAdditiveReduction_iff`, `WeierstrassCurve.VariableChange.one_def`, `MvPolynomial.totalDegree_add`, `RootPairing.Base.toCoweightBasis_repr_coroot`, `Submodule.isOrtho_span`, `eq_zero_of_ne_zero_of_mul_right_eq_zero`, `IsStrictlyPositive.sqrt`, `Polynomial.homogenize_C_mul`, `WeierstrassCurve.c₆_of_isCharTwoJEqZeroNF_of_char_two`, `AdjoinRoot.powerBasisAux'_repr_symm_apply`, `MvPowerSeries.coeff_prod`, `Matrix.swap_mul_apply_right`, `zpow_pos`, `ArithmeticFunction.ppow_apply`, `ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq`, `Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero`, `MvPowerSeries.exists_coeff_ne_zero_and_order`, `Int.ceil_zero`, `HasDerivWithinAt.neg`, `MvPowerSeries.map_eq_zero`, `ContinuousLinearMap.norm_extendTo𝕜'_bound`, `QuadraticForm.sigPos_of_equiv_weightedSumSquares`, `Polynomial.leadingCoeff_smul_of_smul_regular`, `WeierstrassCurve.a₃_of_isCharNeTwoNF`, `MvPolynomial.mem_zeroLocus_iff`, `IsConjRoot.eq_zero`, `geom_sum_eq_zero_iff_neg_one`, `Matrix.ker_toLin'_eq_bot_iff`, `ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap`, `inv_pos_of_pos`, `Representation.freeLift_toLinearMap`, `Matrix.algebraMap_eq_diagonal`, `Quaternion.normSq_exp`, `Polynomial.X_pow_dvd_iff`, `Nat.factorization_choose'`, `MvPowerSeries.truncFinset_monomial`, `ContinuousMultilinearMap.integral_apply`, `AddMonoidAlgebra.coeff_smul`, `SeminormFamily.basisSets_smul`, `DualNumber.lift_apply_apply`, `HasStrictDerivAt.smul_const`, `HasStrictDerivAt.sub`, `IsSelfAdjoint.exp_nonneg`, `MvPolynomial.coe_add`, `PointedCone.tmul_subset_minTensorProduct`, `IsCyclotomicExtension.neZero`, `Nonneg.coe_inv`, `TensorPower.toTensorAlgebra_gOne`, `Matrix.cRank_one`, `HasFiniteFPowerSeriesOnBall.neg`, `LinearMap.trace_comp_eq_zero_of_commute_of_trace_restrict_eq_zero`, `DividedPowers.dpow_eval_zero`, `Matrix.PosSemidef.zero`, `Basis.multilinearMap_apply_apply`, `MulSemiringActionHom.map_zero`, `HasDerivWithinAt.Ioo_of_Ioi`, `DFinsupp.toMultiset_inf`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed`, `MvPolynomial.totalDegree_coeff_optionEquivLeft_add_le`, `Nat.factorization_choose_le_log`, `LinearMap.charpoly_constantCoeff_eq_zero_iff`, `WithAbs.ofAbs_zero`, `cfc_eq_cfcL_mkD`, `MvPolynomial.modMonomial_X`, `WeierstrassCurve.HasAdditiveReduction.additiveReduction`, `MvPolynomial.homogeneousComponent_apply`, `Submonoid.coe_unitSphere`, `mulPosReflectLE_iff_mulPosReflectLT`, `Nat.factorization_eq_zero_of_not_prime`, `cfcₙ_real_eq_nnreal`, `Set.Icc.mem_iff_one_sub_mem`, `Rep.standardComplex.d_of`, `PowerSeries.coe_neg`, `Quaternion.star_add_self'`, `ProbabilityTheory.instIsProbabilityMeasureCondCDF`, `MvPolynomial.vars_prod`, `IsNilpotent.pow_succ`, `MonomialOrder.leadingCoeff_add_of_lt`, `Matrix.zero_vecMul`, `WithBot.bot_mul'`, `stdSimplexHomeomorphUnitInterval_apply_coe`, `MvPolynomial.eval_indicator_apply_eq_zero`, `Module.Basis.coe_finTwoProd_repr`, `MvPolynomial.sumToIter_iterToSum`, `Representation.LinearizeMonoidal.μ_comp_lTensor`, `Complex.UnitDisc.instIsScalarTower_closedBall`, `ArithmeticFunction.carmichael_finset_lcm`, `QuaternionAlgebra.coe_commute`, `MvPolynomial.divMonomial_mul_monomial`, `MvPolynomial.map_surjective_iff`, `AlgebraicIndependent.eq_zero_of_aeval_eq_zero`, `LieModule.chainBotCoeff_zero`, `Ring.inverse_non_unit`, `ArithmeticFunction.cardDistinctFactors_zero`, `Matrix.fromBlocks_eq_of_invertible₂₂`, `constantCoeff_wittPolynomial`, `Finsupp.linearCombination_unique`, `TrivSqZeroExt.inr_mul_inl`, `StrongDual.extendRCLikeₗᵢ_symm_apply`, `RingHom.withTopMap_apply`, `Metric.sphere.instContinuousMul`, `WeierstrassCurve.Projective.polynomialY_eq`, `MvPolynomial.aeval_eq_constantCoeff_of_vars`, `nnnorm_cfc_nnreal_le`, `Algebra.Presentation.tensorModelOfHasCoeffsEquiv_tmul`, `Finset.zero_div_subset`, `BooleanRing.add_eq_zero'`, `AddMonoidAlgebra.support_mul`, `MonoidAlgebra.instNoZeroDivisorsOfUniqueProds`, `PowerSeries.order_exp`, `segment_eq_image'`, `CStarMatrix.mul_entry_mul_eq_inner_toCLM`, `MvPolynomial.weightedHomogeneousComponent_finsupp`, `ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet`, `half_lt_self_iff`, `ExteriorAlgebra.toTrivSqZeroExt_ι`, `WeierstrassCurve.Projective.negDblY_eq`, `FormalMultilinearSeries.le_comp_radius_of_summable`, `ContinuousLinearMap.le_opNorm₂`, `AlgebraicGeometry.Proj.zero_apply`, `associator_cocycle`, `ContinuousLinearMap.lpPairing_eq_integral`, `Matrix.coe_toEuclideanCLM_eq_toEuclideanLin`, `ArithmeticFunction.sigma_zero_apply_prime_pow`, `InnerProductSpace.Core.inner_zero_right`, `HasFDerivAt.smul_const`, `Finsupp.linearCombination_mapDomain`, `Nat.WithBot.one_le_iff_zero_lt`, `ContinuousLinearMap.norm_uncurryMid`, `PowerSeries.instNoZeroDivisors`, `sbtw_mul_sub_add_iff`, `QuaternionAlgebra.imI_swapEquiv_symm_apply`, `Cardinal.mk_smul_set₀`, `Span.finsupp_linearCombination_repr`, `cfc_nnreal_le_iff`, `SymmetricAlgebra.equivMvPolynomial_symm_X`, `AffineIndependent.exists_affineCombination_eq_smul_eq_of_fintype`, `quadratic_eq_zero_iff`, `Polynomial.notMem_support_iff`, `Positive.isOrderedMonoid`, `CauSeq.lim_eq_zero_iff`, `zero_dotProduct'`, `MvPolynomial.coeff_linearCombination_X_pow`, `InnerProductSpace.rankOne_def'`, `Polynomial.resultant_zero_left`, `ContinuousLinearMap.opNorm_mul_le`, `List.dvd_sum`, `ContinuousLinearMap.uncurryLeft_norm`, `MeromorphicOn.divisor_restrict`, `Order.coheight_eq_zero`, `DualNumber.ringHom_ext_iff`, `MvPolynomial.expand_bind₁`, `MvPolynomial.map_injective_iff`, `LinearMap.toMatrixRight'_id`, `Continuous.cfc_nnreal`, `eq_zero_or_one_of_sq_eq_self`, `minpoly.isIntegrallyClosed_dvd_iff`, `HasFDerivAt.comp_hasDerivWithinAt`, `MvPolynomial.linearIndependent_X`, `SkewMonoidAlgebra.lift_unique'`, `NormedSpace.exp_hasFPowerSeriesAt_zero`, `HasFPowerSeriesOnBall.tendstoUniformlyOn'`, `MvPolynomial.coeff_mul_X'`, `DividedPowers.OfSquareZero.dpow_of_two_le`, `HasFPowerSeriesWithinOnBall.const_smul`, `PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply`, `Matrix.mem_rowStochastic_iff_sum`, `List.sum_map_mul_left`, `MvPolynomial.prod_X_pow_eq_monomial`, `IsFractionRing.eq_zero_of_num_eq_zero`, `NormedField.tendsto_norm_inv_nhdsNE_zero_atTop`, `Submodule.mem_dualCoannihilator`, `IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite`, `ZMod.intCast_zmod_eq_zero_iff_dvd`, `Matrix.num_ofNat`, `isScalarTower_sphere_sphere_ball`, `PointedCone.subset_span`, `ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero`, `PiToModule.fromEnd_apply_single_one`, `nnnorm_cfc_nnreal_le_iff`, `Nat.twoPowSum_bitIndices`, `MvPolynomial.map_injective`, `MonoidAlgebra.mapRingEquiv_apply`, `matrixEquivTensor_apply_single`, `HasFPowerSeriesOnBall.sub`, `ContinuousLinearMap.IsPositive.inner_nonneg_left`, `MvPolynomial.constantCoeff_monomial`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left`, `TestFunction.monoCLM_eq_of_scalars`, `DirectSum.coe_decompose_mul_of_right_mem`, `MvPolynomial.coeff_mul_X`, `Representation.LinearizeMonoidal.rightUnitor_δ`, `MonoidAlgebra.sum_single`, `Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction`, `MvPolynomial.smul_eval`, `ringChar.Nat.cast_ringChar`, `Finsupp.multinomial_eq`, `Polynomial.trailingCoeff_zero`, `MvPolynomial.eval₂Hom_zero`, `Polynomial.degree_one_le`, `MvPowerSeries.substAlgHom_coe`, `finsetProd_apply_eq_zero`, `HasStrictDerivAt.of_notMem_tsupport`, `fderiv_continuousMultilinear_apply_const_apply`, `ENat.epow_eq_one_iff`, `commute_iff_mul_nonneg`, `TwoSidedIdeal.coe_bot`, `MeasureTheory.Integrable.convolution_integrand`, `FormalMultilinearSeries.radius_compContinuousLinearMap_eq`, `ExteriorAlgebra.ιMulti_family_mul_of_not_disjoint`, `WeierstrassCurve.Jacobian.nonsingularLift_zero`, `Valuation.restrict_pos_iff`, `MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap`, `Quaternion.im_exp`, `LucasLehmer.X.ω_pow_trace`, `MvPolynomial.degrees_one`, `MvPolynomial.C_eq_zero`, `DivisibleHull.qsmul_def`, `MonoidAlgebra.mapRangeRingEquiv_apply`, `gcd_zero_right`, `AbsoluteValue.nonnegHomClass`, `MvPolynomial.supDegree_toLex_C`, `HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod`, `WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero`, `MvPolynomial.coeff_rTensorAlgHom_tmul`, `MvPolynomial.aeval_zero`, `MulSemiringAction.eval_charpoly`, `Quaternion.re_one`, `cfcₙHom_eq_cfcₙ_extend`, `ProjectiveSpectrum.zeroLocus_singleton_zero`, `NormedDivisionRing.to_continuousInv₀`, `sign_one`, `Matrix.trace_single_mul`, `NormedSpace.vonNBornology_eq`, `Subring.exists_list_of_mem_closure`, `cfcₙAux_injective`, `Module.Presentation.finsupp_relation`, `MvPolynomial.killCompl_rename_app`, `Algebra.Norm.Transitivity.eval_zero_comp_det`, `WeierstrassCurve.c₄_of_isShortNF_of_char_three`, `ZeroAtInftyContinuousMap.instCStarRing`, `isUnit_zero_iff`, `IsAdjoinRootMonic.coeff_apply_lt`, `Nat.Icc_factorization_eq_pow_dvd`, `LieModule.traceForm_eq_zero_if_mem_lcs_of_mem_ucs`, `IsPrimitiveRoot.neZero'`, `hasDerivWithinAt_const`, `openSegment_eq_image_lineMap`, `Nat.factorization_le_iff_dvd`, `FormalMultilinearSeries.compAlongComposition_norm`, `Polynomial.tendsto_nhds_iff`, `ContinuousLinearMap.isometry_mul`, `Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff`, `dvd_iff_emultiplicity_pos`, `ArithmeticFunction.self_mul_dirichletInverse`, `Nonneg.instContinuousFunctionalCalculus`, `CFC.sqrt_zero`, `Filter.EventuallyLE.mul_nonneg`, `QuasispectrumRestricts.nonUnitalStarAlgHom_injective`, `MvPolynomial.mem_weightedHomogeneousSubmodule`, `Representation.apply_eq_of_leftRegular_eq_of_generator`, `Matrix.invOf_add_mul_mul`, `MvPolynomial.hom_congr_vars`, `isCoveringMapOn_npow`, `Nat.ordCompl_pos`, `logDeriv_eq_zero_of_not_differentiableAt`, `MvPolynomial.comp_aeval`, `RingEquiv.prodZeroRing_apply`, `Cubic.monic_of_b_eq_one'`, `Set.Ioo.mem_iff_one_sub_mem`, `Matrix.IsIrreducible.exists_pos`, `DirectSum.IsInternal.collectedBasis_repr_of_mem_ne`, `MvPolynomial.support_map_of_injective`, `MvPolynomial.constantCoeff_X`, `MvPolynomial.divMonomial_monomial`, `Matrix.Pivot.mul_listTransvecRow_last_row`, `MvPolynomial.frobenius_zmod`, `Module.Basis.toMatrix_apply`, `IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd`, `QuaternionAlgebra.self_add_star'`, `Pi.single_smul₀`, `Matrix.hadamard_zero`, `KaehlerDifferential.mvPolynomialBasis_repr_apply`, `WittVector.frobeniusPolyAux_eq`, `IntermediateField.AdjoinSimple.trace_gen_eq_zero`, `pos_of_slope_pos`, `HasStrictFDerivAt.continuousAlternatingMap_apply`, `Rat.cast_list_sum`, `PadicInt.fwdDiff_iter_le_of_forall_le`, `spectrum_nonneg_of_nonneg`, `MvPolynomial.optionEquivLeft_coeff_some_coeff_none`, `Matrix.conjTranspose_one`, `MvPowerSeries.coeff_zero_one`, `IsStarProjection.mem_Icc`, `Valued.integer.coe_span_singleton_eq_closedBall`, `HahnSeries.SummableFamily.isPWO_iUnion_support_powers`, `MatrixEquivTensor.invFun_smul`, `IntermediateField.mem_adjoin_range_iff`, `ArchimedeanClass.FiniteElement.val_zero`, `Order.coheight_top`, `Nat.ordCompl_mul`, `isIdempotentElem_iff_spectrum_subset`, `StrongDual.extendRCLikeₗ_symm_apply`, `Polynomial.Chebyshev.U_eval_two_mul_zero`, `HasDerivAtFilter.congr_of_eventuallyEq`, `Rat.toNNRat_pos`, `tendsto_pow_neg_atTop`, `LinearMap.IsNonneg.nonneg`, `nilpotencyClass_eq_one`, `constFormalMultilinearSeries_apply_of_nonzero`, `DividedPowerAlgebra.mkAlgHom_surjective`, `cfcₙ_comp_smul`, `HasFTaylorSeriesUpToOn.add`, `MeasureTheory.dist_convolution_le'`, `Cubic.monic_of_c_eq_one'`, `finsuppTensorFinsuppRid_single_tmul_single`, `WittVector.coeff_frobeniusFun`, `Matrix.IsAdjMatrix.toGraph_compl_eq`, `Composition.blocks_sum`, `LinearIndependent.linearCombinationEquiv_symm_apply`, `Set.chainHeight_empty`, `ENat.epow_eq_zero_iff`, `Nat.ordProj_le`, `IsNilpotent.exp_zero`, `MvPolynomial.renameEquiv_refl`, `Localization.mk_list_sum`, `ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM`, `Module.DualBases.basis_repr_apply`, `ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff`, `MvPolynomial.totalDegree_renameEquiv`, `Num.lt_to_nat`, `Set.indicator_pi_one_apply`, `SignType.intCast_cast`, `SkewMonoidAlgebra.sum_smul_index`, `Algebra.toMatrix_lmul'`, `Nat.dvd_iff_exists_le_factorization`, `MvPowerSeries.rescale_zero`, `AddMonoidAlgebra.ofCoeff_zero`, `DFinsupp.instPosSMulReflectLE`, `MvPolynomial.expand_mul`, `MvPolynomial.mem_coeffsIn`, `sum_hom_units_eq_zero`, `PowerSeries.derivativeFun_one`, `Matrix.det_fromBlocks_one₂₂`, `TrivSqZeroExt.hasSum_expSeries_of_smul_comm`, `Algebra.Presentation.tensorModelOfHasCoeffsHom_tmul`, `DifferentiableWithinAt.clm_comp`, `AddMonoidAlgebra.single_mul_apply`, `ValuativeRel.vle_zero_iff`, `Matrix.isUnit_fromBlocks_zero₁₂`, `ArithmeticFunction.id_apply`, `Metric.unitSphere.coe_inv`, `Representation.LinearizeMonoidal.η_single`, `MDifferentiableOn.cle_arrowCongr`, `AlgebraicGeometry.AffineSpace.map_SpecMap`, `hasFDerivAt_exp_zero`, `WeierstrassCurve.Projective.baseChange_polynomialX`, `Mathlib.Tactic.FieldSimp.zpow'_eq_zero_iff`, `Module.Relations.Solution.isPresentation_iff`, `Nat.factorization_le_factorization_choose_add`, `Set.Ioc.coe_pos`, `Affine.Simplex.affineCombination_mem_interior_face_iff_pos`, `Filter.tendsto_const_mul_pow_atBot_iff`, `Module.DualBases.dual_lc`, `Matroid.eRank_eq_zero_iff`, `MultilinearMap.mkContinuousMultilinear_norm_le'`, `MvPolynomial.isLocalHom_expand`, `tendsto_one_div_atTop_nhds_zero_nat`, `Stream'.Seq.length'_eq_zero_iff_nil`, `Unitization.norm_def`, `MvPolynomial.exists_mem_support_not_dvd_of_forall_totalDegree_le`, `ContinuousMapZero.instTrivialStar`, `ZMod.cast_zero`, `Polynomial.Bivariate.pderiv_zero_equivMvPolynomial`, `WeierstrassCurve.Jacobian.addZ_of_X_eq`, `ArithmeticFunction.prodPrimeFactors_apply`, `NoZeroDivisors.of_faithfulSMul`, `Matrix.blockDiagonal_mul`, `ArithmeticFunction.sigma_eq_one_iff`, `MvPolynomial.weightedHomogeneousComponent_of_isWeightedHomogeneous_ne`, `cfc_nonneg`, `MvPolynomial.C_mul'`, `Num.ppred_to_nat`, `AlgebraicClosure.le_maxIdeal`, `tendsto_nhdsLT_zero_of_comp_inv_tendsto_atBot`, `WeierstrassCurve.Projective.addMap_of_Y_eq`, `HahnSeries.pow_add`, `Polynomial.mem_roots_iff_aeval_eq_zero`, `LaurentSeries.Cauchy.eventually_mem_nhds`, `MvPolynomial.isEmptyAlgEquiv_apply`, `LieAlgebra.lieCharacter_apply_of_mem_derived`, `LinearMap.isNilpotent_mulRight_iff`, `Set.indicator_mul`, `MvPolynomial.bind₂_X_right`, `HasStrictDerivAt.const_smul`, `Finsupp.llift_symm_apply`, `HasDerivAt.fun_sum`, `Quiver.Path.weight_nonneg`, `MvPolynomial.of_irreducible_expand`, `Subsemiring.zero_mem`, `FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp`, `TensorProduct.finsuppScalarLeft_apply_tmul_apply`, `Quaternion.self_add_star'`, `nonpos_of_mul_nonpos_left`, `WithTop.mul_top'`, `Matrix.ker_diagonal_toLin'`, `AddMonoidAlgebra.modOf_apply_self_add`, `second_derivative_symmetric`, `Algebra.Generators.cMulXSubOneCotangent_eq`, `ContinuousAlternatingMap.curryLeft_same`, `DividedPowerAlgebra.submodule_span_prod_dp_eq_top`, `MvPolynomial.map_C`, `ContinuousMultilinearMap.curryRight_apply`, `Profinite.NobelingProof.GoodProducts.finsuppSum_mem_span_eval`, `MvPolynomial.isHomogeneous_monomial`, `Subfield.list_sum_mem`, `MeasureTheory.eLpNorm_const_smul_le`, `ArithmeticFunction.mul_smul'`, `DFinsupp.instPosSMulMono`, `LinearMap.polyCharpolyAux_baseChange`, `Set.inv_Ioi₀`, `MonoidAlgebra.smul_apply`, `Finsupp.prod_pow`, `Polynomial.coeff_ofNat_succ`, `Polynomial.Bivariate.equivMvPolynomial_X`, `Finsupp.sum_antidiagonal_swap`, `HasFPowerSeriesOnBall.uniform_geometric_approx'`, `HahnSeries.orderTop_mul`, `PosMulStrictMono.toPosMulMono`, `AddMonoidAlgebra.supported_eq_map`, `MvPolynomial.C_dvd_iff_dvd_coeff`, `AddMonoidAlgebra.support_one_subset`, `Quaternion.coe_mul_eq_smul`, `contDiffOn_inv`, `ZeroAtInftyContinuousMap.instSMulCommClass`, `Set.Icc.coe_eq_zero`, `HahnSeries.coeff_toPowerSeries`, `ZMod.intCast_eq_zero_iff_even`, `Hyperreal.coe_eq_zero`, `MvPolynomial.pderiv_C_mul`, `QuadraticForm.sigPos_weightedSumSquares`, `Polynomial.homogenize_finsetProd`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars`, `dotProduct_single_one`, `Nat.card_divisors`, `Module.Basis.symmetricAlgebra_repr_apply`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const`, `Matrix.num_natCast`, `LucasLehmer.X.snd_intCast`, `Quaternion.instIsStarNormal`, `AddMonoidAlgebra.mapRingEquiv_apply`, `HasFDerivAt.comp_hasDerivWithinAt_of_eq`, `MonomialOrder.degree_smul_of_isRegular`, `Complex.UnitDisc.instIsCancelMulZero`, `Mathlib.Tactic.Ring.inv_single`, `ascPochhammer_eval_neg_coe_nat_of_lt`, `ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring`, `Matrix.nonneg_of_mem_colStochastic`, `Matrix.kronecker_one`, `MvPowerSeries.mul_zero`, `PointedCone.ext_iff`, `RootPairing.pairingIn_eq_zero_iff`, `AlgebraicClosure.toSplittingField_coeff`, `ZLattice.exists_forall_abs_repr_le_norm`, `SimpleGraph.eccent_pos_iff`, `MvPolynomial.eval₂_mul`, `Commute.isNilpotent_mul_left_iff`, `Matrix.toMvPolynomial_eval_eq_apply`, `SymplecticGroup.inv_left_mul_aux`, `Ring.multichoose_succ_neg_natCast`, `Nat.Prime.factorization_self`, `isScalarTower_sphere_closedBall_ball`, `IsBoundedSMul.of_enorm_smul_le`, `MvPolynomial.coe_pow`, `IsValuativeTopology.hasBasis_nhds_zero`, `Valuation.IsEquiv.eq_zero`, `MvPowerSeries.coeff_add_mul_monomial`, `AddMonoidAlgebra.single_mul_apply_of_not_exists_add`, `LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring`, `Matrix.adjugate_def`, `ContinuousLinearMap.norm_extendTo𝕜'`, `Matrix.isUnit_fromBlocks_iff_of_invertible₁₁`, `Perfection.teichmuller_zero`, `MonomialOrder.degree_one`, `MvPolynomial.natDegree_optionEquivLeft`, `HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope`, `Matrix.charpoly.univ_coeff_isHomogeneous`, `MvPolynomial.isHomogeneous_one`, `Matrix.ProjGenLinGroup.val_signDet_mk`, `ExteriorAlgebra.ιMulti_eq_zero_of_not_inj`, `Polynomial.aeval_algebraMap_eq_zero_iff_of_injective`, `SimpleGraph.vertexCoverNum_of_subsingleton`, `Matrix.exists_left_inverse_iff_isUnit`, `ContinuousMapZero.toContinuousMapHom_toNNReal`, `LinearMap.toMatrix_prodMap`, `HahnModule.coeff_single_zero_smul`, `ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial`, `Matrix.toLin_apply`, `Submodule.inner_left_of_mem_orthogonal`, `instZeroLEOneClass`, `dotProduct_single`, `IsStarProjection.inr`, `mul_pos`, `WittVector.constantCoeff_wittMul`, `bernsteinPolynomial.iterate_derivative_succ_at_0_eq_zero`, `HasDerivAtFilter.const_add`, `Matrix.toLin'_one`, `Lagrange.eval_basis_of_ne`, `HasDerivWithinAt.of_notMem_tsupport`, `Complex.UnitDisc.pow_eq_zero`, `not_linearIndependent_iff_finsupp`, `ArithmeticFunction.sigma_mono`, `MvPolynomial.totalDegree_eq_zero_iff`, `MDifferentiableAt.clm_precomp`, `MvPowerSeries.monomial_pow`, `Quaternion.summable_coe`, `ContDiffMapSupportedIn.postcompCLM_apply`, `AlgebraicGeometry.AffineSpace.SpecIso_inv_over_assoc`, `SchwartzMap.compSubConstCLM_comp`, `HasDerivWithinAt.mono_of_mem_nhdsWithin`, `QuadraticAlgebra.smul_coe`, `DoubleCentralizer.coeHom_apply`, `ContinuousAlternatingMap.curryLeft_zero`, `IsLeftCancelMulZero.toFaithfulSMul_opposite`, `DualNumber.coe_lift_symm_apply`, `FractionalIdeal.spanSingleton_zero`, `Algebra.Generators.self_algebra_smul`, `ContinuousMultilinearMap.analyticOn_uncurry_of_linear`, `NonUnitalSubsemiring.coe_sumSq`, `OnePoint.smul_infty_eq_ite`, `ContinuousAlternatingMap.restrictScalarsLI_apply`, `MultilinearMap.freeFinsuppEquiv_apply`, `ProbabilityTheory.measure_cdf`, `AddMonoidAlgebra.apply_eq_zero_of_not_le_supDegree`, `Nat.ofNat_nonneg`, `Finsupp.linearCombination_range`, `Odd.zpow_nonneg_iff`, `Matrix.vecMul_surjective_iff_exists_left_inverse`, `CFC.log_zero`, `NormedDivisionRing.unitClosedBall_eq_univ_of_discrete`, `StrictOrderedSemiring.toSMulPosStrictMonoNat`, `AddMonoidAlgebra.liftMagma_apply_apply`, `Nat.ordProj_dvd_ordProj_of_dvd`, `MvPolynomial.decomposition.decompose'_apply`, `CentroidHom.toEnd_zero`, `MvPolynomial.restrictSupport_nsmul`, `CliffordAlgebra.ι_mul_ι_add_swap_of_isOrtho`, `HasFPowerSeriesOnBall.tendsto_partialSum`, `isIdempotentElem_iff_one_sub_mul_self`, `MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd`, `Algebra.Generators.toKaehler_tmul_D`, `MvPolynomial.mem_support_finSuccEquiv`, `Quaternion.imJ_snd_dualNumberEquiv`, `HasDerivWithinAt.Ioi_of_Ioo`, `AddMonoidAlgebra.coeffAddEquiv_symm_apply`, `locallyFinsuppWithin.logCounting_divisor`, `AbsoluteValue.nonpos_iff`, `Algebra.smulTower_leftMulMatrix_algebraMap_ne`, `HasDerivWithinAt.fun_mul`, `DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap`, `Nat.ModEq.listSum_zero`, `minpoly.aeval_algHom`, `Quaternion.star_im`, `cfcₙHom_map_quasispectrum`, `Polynomial.coeff_smul`, `HahnSeries.SummableFamily.finite_co_support_prod_mul`, `MvPolynomial.psum_one`, `conjneg_eq_zero`, `MvPolynomial.mem_degreesLE`, `Order.krullDim_eq_zero_iff_of_orderTop`, `ValuativeRel.not_vle_one_zero`, `Matrix.diagonal_mul_diagonal'`, `ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft`, `Rep.coind'_ext_iff`, `inner_eq_zero_of_left`, `doublyStochastic_eq_convexHull_permMatrix`, `CFC.rpow_nonneg`, `MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous`, `HasFPowerSeriesWithinAt.prod`, `HasDerivWithinAt.pow'`, `LaurentSeries.valuation_LaurentSeries_equal_extension`, `Quaternion.re_natCast`, `MvPolynomial.isNoetherianRing_fin`, `ZMod.neg_eq_self_iff`, `ContinuousLinearMap.adjoint_comp_self_injective_iff`, `Polynomial.degree_one`, `Module.length_pos`, `FormalMultilinearSeries.leftInv_coeff_one`, `Polynomial.coeff_C_succ`, `MvPolynomial.X_dvd_iff_modMonomial_eq_zero`, `Finsupp.coe_orderIsoMultiset_symm`, `MvPolynomial.funext_set_iff`, `RootPairing.rootForm_self_sum_of_squares`, `UniqueFactorizationMonoid.radical_zero`, `MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing`, `Units.exists0'`, `PosSMulReflectLT.toPosSMulReflectLE`, `IsAlgClosed.exists_eval₂_eq_zero`, `QuasispectrumRestricts.isClosedEmbedding_nonUnitalStarAlgHom`, `SkewMonoidAlgebra.support_mul_single_subset`, `mdifferentiableOn_continuousLinearMapCoordChange`, `Ideal.zero_mem`, `hasDerivAtFilter_intCast`, `ContDiffMapSupportedIn.fderivCLM_eq_of_scalars`, `Orthonormal.inner_finsupp_eq_sum_left`, `Sylow.card_eq_multiplicity`, `cfcHom_nnreal_eq_restrict`, `MvPolynomial.X_mul_divMonomial`, `MvPolynomial.map_monomial`, `Matrix.IsHermitian.spectral_theorem`, `MvPolynomial.monomial_mem_restrictSupport`, `algebraicIndependent_iff_injective_aeval`, `LinearOrderedField.inducedMap_zero`, `Num.bit_to_nat`, `RootPairing.GeckConstruction.diagonal_elim_mem_span_h_iff`, `MvPolynomial.vars_map_of_injective`, `hasFPowerSeriesAt_pi_iff`, `MvPolynomial.aeval_map_algebraMap`, `Algebra.Generators.Hom.toAlgHom_C`, `Ring.choose_zero_pos`, `smul_zpow₀'`, `MeasureTheory.Lp.coeFn_lpSMul`, `Unitization.inr_mul_inl`, `HahnSeries.orderTop_nsmul_le_orderTop_pow`, `LinearIndependent.finsuppLinearCombination_injective`, `hasDerivWithinAt_univ`, `GroupWithZero.dvd_iff`, `QuadraticAlgebra.omega_mul_omega_eq_mk`, `WeierstrassCurve.isMinimal_iff`, `WeierstrassCurve.b₄_of_isCharThreeJNeZeroNF`, `ValueDistribution.logCounting_zero_mul_eventually_le`, `Matrix.diagonalAlgHom_apply`, `Representation.ker_leftRegular_norm_eq`, `Matrix.diagonal_mulVec_single`, `PosNum.mod'_to_nat`, `MvPowerSeries.coeff_zero_X_mul`, `IsSelfAdjoint.mul_self_nonneg`, `Function.support_inv`, `MvPolynomial.rename_comp_toMvPolynomial`, `Height.mulHeightBound_eq`, `Matrix.kronecker_ofNat`, `Nat.one_sub_one_div_cast_nonneg`, `MvPolynomial.comap_C_surjective`, `ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear`, `MvPolynomial.finSuccEquiv_comp_C_eq_C`, `AlgebraicGeometry.eq_zero_of_basicOpen_eq_bot`, `InnerProductSpace.isStarProjection_rankOne_self`, `LieModule.isCompl_genWeightSpace_zero_posFittingComp`, `Matrix.PosDef.trace_pos`, `MvPolynomial.esymmAlgHom_zero`, `OrderedFinpartition.compAlongOrderedFinpartitionL_apply`, `ContinuousAlternatingMap.piLIE_symm_apply_apply`, `ContinuousMapZero.instContinuousNeg`, `Quaternion.snd_imK_dualNumberEquiv_symm`, `LaurentSeries.LaurentSeries_coe`, `MvPolynomial.homogeneousComponent_eq_zero`, `Mathlib.Tactic.Linarith.sub_neg_of_lt`, `MonoidAlgebra.instIsLeftCancelMulZeroOfIsCancelAddOfUniqueProds`, `HasFPowerSeriesAt.hasFDerivAt`, `Nat.Iio_factorization_prod_pow_injective`, `Matrix.single_mul_single_of_ne`, `Nat.factorization_centralBinom_of_two_mul_self_lt_three_mul`, `MvPolynomial.eval₂_eta`, `MvPolynomial.coeToMvPowerSeries.algHom_apply`, `ENat.epow_def`, `antitoneOn_inv_pos`, `Finsupp.DegLex.single_le_iff`, `Hyperreal.coe_zero`, `Polynomial.degree_zero_le`, `Polynomial.Monic.degree_pos_of_not_isUnit`, `spec_cfcₙAux`, `Mathlib.Tactic.Linarith.add_neg`, `IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff`, `exists_signed_sum'`, `Int.cast_list_sum`, `Matrix.mulVec_eq_sum`, `Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero`, `MonoidAlgebra.coeffLinearEquiv_apply`, `MvPolynomial.degreeOf_eq_sup`, `WeierstrassCurve.a₁_of_isCharTwoJEqZeroNF`, `StrongDual.extendRCLikeₗᵢ_apply`, `Matrix.one_hadamard_eq_zero_iff`, `AlgebraicIndependent.liftAlgHom_comp_reprField`, `MvPowerSeries.constantCoeff_subst_eq_zero`, `Finset.expect_boole_mul`, `AddMonoidAlgebra.supportedEquivFinsupp_symm_apply_coe_support_val`, `DividedPowerAlgebra.algHom_ext_iff`, `legendreSym.eq_zero_iff`, `HasFPowerSeriesWithinOnBall.compContinuousLinearMap`, `MvPolynomial.rename_rightInverse`, `ContinuousOn.cfcₙ_nnreal'`, `Submodule.inner_right_of_mem_orthogonal`, `LinearMap.IsPositive.trace_nonneg`, `NonUnitalStarSubalgebra.coe_eq_zero`, `cfcₙHom_injective`, `LinearMap.mkContinuous₂_norm_le`, `MeasurableSet.const_smul₀`, `Nonneg.mk_mul_mk`, `Rat.cast_nonneg`, `Fintype.linearIndependent_iff`, `char_dvd_card_solutions`, `Algebra.SubmersivePresentation.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs`, `MonoidAlgebra.support_mul_single`, `Filter.tendsto_const_mul_atTop_iff_neg`, `Positive.val_pow`, `wbtw_one_zero_iff`, `TensorProduct.gradedComm_of_zero_tmul`, `ValuativeRel.zero_vle`, `DirichletCharacter.sum_characters_eq_zero`, `SkewMonoidAlgebra.coeff_mul_single`, `Matrix.one_kronecker_one`, `PEquiv.single_mul_single_right`, `Mathlib.Tactic.ENatToNat.coe_zero`, `FormalMultilinearSeries.zero_radius`, `tendsto_mul_cocompact_nhds_zero`, `LaurentSeries.powerSeries_ext_subring`, `MulEquiv.noZeroDivisors_iff`, `Quaternion.sq_eq_neg_normSq`, `Algebra.Presentation.differentials.comm₁₂`, `Set.unit_valuation_eq_one`, `MvPowerSeries.order_eq_top_iff`, `ringKrullDim_eq_zero_of_isField`, `WeierstrassCurve.Jacobian.polynomialZ_eq`, `Matrix.mul_submatrix_one`, `WeierstrassCurve.Jacobian.dblZ_of_Z_eq_zero`, `Module.Basis.sumQuot_repr_inr_of_mem`, `MonomialOrder.sPolynomial_monomial_mul`, `ContinuousLinearMap.hasFPowerSeriesAt_bilinear`, `unitsEquivNeZero_apply_coe`, `Mathlib.Tactic.Ring.add_pf_add_zero`, `MvPolynomial.hsymmPart_zero`, `Module.IsLocalRing.linearCombination_bijective_of_flat`, `finprod_eq_zero`, `MvPolynomial.eval₂Hom_map_hom`, `Quaternion.imK_neg`, `Finsupp.coe_basisSingleOne`, `WithBot.instNoZeroDivisors`, `MvPolynomial.isRegular_X`, `ascPochhammer_pos`, `Order.height_bot`, `MvPolynomial.mem_homogeneousSubmodule`, `Polynomial.isBoundedUnder_abs_atBot_iff`, `hasStrictDerivAt_const`, `WeierstrassCurve.Affine.equation_add_iff`, `Finset.prod_eq_zero_iff`, `SkewMonoidAlgebra.support_mul`, `Mathlib.Tactic.Linarith.zero_mul_eq`, `LinearMap.isNilpotent_trace_of_isNilpotent`, `RCLike.ofReal_eq_zero`, `MvPolynomial.finSuccEquiv_eq`, `char_dvd_card_solutions_of_sum_lt`, `Polynomial.eval_listSum`, `Quaternion.coe_one`, `Metric.unitSphere.coe_zpow`, `SymmetricAlgebra.equivMvPolynomial_ι_apply`, `PosSMulStrictMono.nnrat_of_rat`, `Nat.ordCompl_self_pow_mul`, `Finset.inv_op_smul_finset_distrib₀`, `List.prod_eq_zero`, `ContinuousLinearMap.self_comp_adjoint_injective_iff`, `Associates.out_eq_zero_iff`, `Matrix.diagonal_hadamard`, `SkewMonoidAlgebra.mapDomainAlgHom_apply`, `Module.Basis.repr_injective`, `mul_nonpos_iff`, `Polynomial.isNilpotent_monomial_iff`, `Int.one_le_ceil_iff`, `AddMonoidAlgebra.ofCoeff_add`, `HasCompactSupport.mul_right`, `RingHom.IsStandardSmooth.exists_etale_mvPolynomial`, `MonoidAlgebra.mul_single_apply_of_not_exists_mul`, `deriv_single`, `ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic`, `stdSimplex.zero_le`, `Quaternion.imK_ratCast`, `LinearMap.mulRight_zero_eq_zero`, `HasStrictDerivAt.scomp`, `PowerSeries.constantCoeff_divXPowOrder_eq_zero_iff`, `MvPolynomial.homogeneousComponent_zero`, `LinearIndependent.repr_range`, `HasFPowerSeriesWithinAt.restrictScalars`, `LinearMap.polyCharpoly_eq_of_basis`, `ProperCone.innerDual_insert`, `PowerSeries.coeff_monomial`, `ENat.iSup_eq_zero`, `AbsoluteValue.hasBasis_uniformity`, `Matrix.PosDef.isStrictlyPositive`, `Polynomial.natDegree_monomial`, `Prime.not_dvd_finsuppProd`, `range_cfc_nnreal`, `InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular`, `ContDiffMapSupportedIn.norm_apply_le_seminorm`, `TensorProduct.piScalarRight_symm_single`, `geom_sum_neg_iff`, `associated_norm_prod_smith`, `MvPolynomial.ker_eval₂Hom_universalFactorizationMap`, `Complex.UnitDisc.im_zero`, `Module.Basis.repr_apply_eq`, `fderiv_continuousAlternatingMap_apply_apply`, `Polynomial.isNilpotent_iff`, `MvPolynomial.monomial_left_injective`, `IsSemisimpleModule.exists_end_ringEquiv`, `HasDerivWithinAt.fun_sub`, `MvPolynomial.bind₁_comp_rename`, `Matrix.Pivot.listTransvecCol_mul_last_row_drop`, `MvPolynomial.coeff_map`, `hasFPowerSeriesOnBall_inv_one_sub`, `PiTensorProduct.mapLMultilinear_apply_apply`, `NonUnitalStarRingHom.zero_apply`, `MonomialOrder.degree_le_degree_of_support_subset`, `HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq`, `HasFDerivWithinAt.clm_comp`, `MvPolynomial.monomial_sum_index`, `Matrix.add_mul_mul_mul_invOf_eq_one'`, `Finsupp.linearCombination_comp`, `MonomialOrder.degree_eq_zero_iff_totalDegree_eq_zero`, `MvPolynomial.degrees_prod_le`, `isBoundedBilinearMap_apply`, `geom_sum_zero`, `FormalMultilinearSeries.analyticOnNhd`, `WeierstrassCurve.isCharTwoJEqZeroNF_iff`, `Matroid.eRk_eq_zero_iff'`, `instIsReducedLocalization`, `Unitization.nnreal_cfcₙ_eq_cfc_inr`, `exteriorPower.presentation_relation`, `NonUnitalSeminormedRing.isBoundedSMul`, `LinearMap.polyCharpolyAux_map_aeval`, `hasFPowerSeriesOnBall_inverse_one_sub`, `Matrix.mvPolynomialX_mapMatrix_eval`, `hasDerivAtFilter_iff_tendsto`, `MvPolynomial.monic_monomial_eq`, `MeromorphicOn.divisor_fun_inv`, `MvPowerSeries.coeff_zero_iff`, `Matrix.single_mul_eq_updateRow_zero`, `SkewMonoidAlgebra.liftNC_mul`, `ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ`, `inv_nhdsLT_zero`, `PadicInt.zmodRepr_zero`, `MvPolynomial.image_support_finSuccEquiv`, `inv_nonneg`, `IsLocalization.eq_zero_of_fst_eq_zero`, `HasStrictDerivAt.comp`, `PosSMulMono.toPosSMulStrictMono`, `Invertible.toNeZero`, `hasStrictFDerivAt_ringInverse`, `MvPolynomial.support_nonempty`, `PowerSeries.coeff_X`, `AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply`, `MvPolynomial.pderiv_monomial_single`, `Matrix.nonsing_inv_cancel_or_zero`, `MulEquiv.isLeftCancelMulZero_iff`, `AddMonoidAlgebra.mul_single_apply_aux`, `IsConjRoot.aeval_eq_zero`, `ContinuousLinearMap.mul_apply'`, `Mathlib.Tactic.Linarith.add_nonpos`, `NonUnitalSeminormedRing.isBoundedSMulOpposite`, `MvPolynomial.degreeOf_prod_eq`, `fromTangentSpace_mfderiv_smul`, `ordinaryHypergeometric_zero`, `MvPolynomial.eval₂_rename`, `AlgebraicIndependent.aeval_repr`, `Polynomial.degree_pos_of_not_isUnit_of_dvd_monic`, `RingHom.map_zero`, `MvPolynomial.support_expand`, `MeromorphicNFOn.zero_set_eq_divisor_support`, `Unitization.IsIdempotentElem.inr`, `AddMonoidAlgebra.sup_support_mul_le`, `NumberField.inverse_basisMatrix_mulVec_eq_repr`, `Finsupp.range_linearCombination`, `HahnSeries.coeff_toPowerSeries_symm`, `LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply`, `Finsupp.toFreeAbelianGroup_toFinsupp`, `InnerProductSpace.rankOne_comp_rankOne`, `MonomialOrder.degree_eq_zero_iff`, `MeromorphicOn.circleAverage_log_norm`, `zero_pow_eq`, `Valuation.integer.v_irreducible_pos`, `Polynomial.eval₂_at_zero`, `MonomialOrder.degree_mem_support`, `MvPolynomial.add_divMonomial`, `PowerSeries.constantCoeff_zero`, `TestFunction.mkCLM_apply`, `Matrix.PosSemidef.det_nonneg`, `MvPolynomial.instFiniteSubtypeMemSubmoduleRestrictTotalDegreeOfFinite`, `Polynomial.Bivariate.equivMvPolynomial_C_X`, `AddChar.mulShift_zero`, `LieModule.LinearWeights.map_lie`, `Quaternion.tsum_coe`, `Nat.factorization_one`, `HasDerivAtFilter.comp_of_eq`, `lp.instIsCentralScalarSubtypePreLpMemAddSubgroup`, `Differential.logDeriv_zero`, `MvPolynomial.IsSymmetric.rename`, `PointedCone.dual_iUnion`, `MvPolynomial.IsHomogeneous.aeval`, `Submodule.orthogonal_closure'`, `Module.Relations.ker_toQuotient`, `hasDerivAtFilter_finCons'`, `MvPolynomial.isEmptyRingEquiv_symm_toRingHom`, `CompleteOrthogonalIdempotents.iff_ortho_complete`, `IsSumSq.sum_sq`, `Submonoid.mem_nonunits_iff_or`, `ConjRootClass.exists_mem_carrier_add_eq_zero`, `dotProduct_self_star_nonneg`, `ContinuousMap.toLp_injective`, `Finsupp.bilinearCombination_apply`, `TestFunction.fderivCLM_eq_of_scalars`, `CFC.negPart_one`, `NNRat.divNat_zero`, `MonomialOrder.leadingTerm_C`, `MvPolynomial.DirectSum.coeLinearMap_eq_finsum`, `RingQuot.zero_quot`, `Finsupp.antidiagonal_zero`, `geom_sum_alternating_of_lt_neg_one`, `TensorPower.list_prod_gradedMonoid_mk_single`, `Num.cast_inj`, `Finsupp.apply_linearCombination`, `fderiv_smul_const`, `MonoidAlgebra.support_gen_of_gen`, `Matrix.nonsing_inv_apply_not_isUnit`, `EisensteinSeries.E_qExpansion_coeff`, `WittVector.mul_polyOfInterest_aux1`, `Module.Relations.Solution.IsPresentation.surjective_π`, `analyticOrderAt_id`, `hasDerivWithinAt_finCons'`, `Finset.centroidWeightsIndicator_def`, `Matrix.IsAdjMatrix.apply_ne_zero_iff`, `MonoidAlgebra.mul_single_one_apply`, `TrivSqZeroExt.instL1IsBoundedSMul`, `MvPolynomial.support_monomial_subset`, `cfcₙHomSuperset_id`, `MvPolynomial.monomial_mul`, `MonomialOrder.toSyn_eq_zero_iff`, `MvPolynomial.quotientEquivQuotientMvPolynomial_leftInverse`, `Quaternion.continuous_im`, `PNat.mk_ofNat`, `BoundedContinuousFunction.instIsBoundedSMul_1`, `KaehlerDifferential.kerTotal_mkQ_single_mul`, `WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq'`, `PointedCone.coe_ofConeComb`, `AddMonoidAlgebra.coeff_eq_zero`, `LaurentPolynomial.ext_iff`, `Polynomial.coeff_eq_zero_of_lt_trailingDegree`, `Asymptotics.Filter.Tendsto.isBigOTVS_one`, `LinearMap.toMatrix_directSum_collectedBasis_eq_blockDiagonal'`, `Quaternion.sq_eq_normSq`, `Set.Ioo.one_sub_mem`, `TwoSidedIdeal.coe_mk`, `Set.Nonempty.zero_mul`, `TestFunction.lineDerivCLM_eq_of_scalars`, `PointedCone.mem_span_set`, `instContMDiffInv₀ModelWithCornersSelf`, `Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row`, `MultilinearMap.freeFinsuppEquiv_single`, `ContinuousMapZero.evalCLM_apply`, `AdjoinRoot.eval₂_root`, `TannakaDuality.FiniteGroup.sumSMulInv_single_id`, `Quaternion.re_coe`, `Associates.factors_eq_top_iff_zero`, `Mathlib.Meta.Positivity.pos_of_isNat`, `tendsto_algebraMap_inverse_atTop_nhds_zero_nat`, `InnerProductSpace.rankOne_comp`, `LaurentSeries.powerSeriesRingEquiv_coe_apply`, `Polynomial.aeval_root_of_mapAlg_eq_multiset_prod_X_sub_C`, `Valuation.leIdeal_zero`, `MvPowerSeries.weightedOrder_eq_nat`, `ENat.recTopCoe_zero`, `IsRealClosed.toIsSemireal`, `ArithmeticFunction.carmichael_dvd_totient`, `Height.mulHeight_eval_le`, `Submodule.mem_orthogonal`, `Matrix.detp_one_diagonal`, `StrongDual.mem_polarSubmodule`, `Matrix.den_intCast`, `MonoidAlgebra.coeff_finsuppSum`, `MvPowerSeries.totalDegree_trunc'`, `Matrix.mul_swap_of_ne`, `Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos`, `sq_nonpos_iff`, `intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le`, `Rep.leftRegularHom_hom_single`, `HasDerivWithinAt.scomp`, `ZMod.natCast_eq_zero_iff_even`, `hasFPowerSeriesWithinAt_pi_iff`, `Function.support_div'`, `HahnSeries.orderTop_add_le_mul`, `Module.Basis.end_repr_symm_apply`, `MvPowerSeries.expand_monomial`, `neg_one_geom_sum`, `ArithmeticFunction.cardDistinctFactors_eq_one_iff`, `hasDerivWithinAt_comp_mul_left_smul_iff`, `FirstOrder.Ring.MvPolynomialSupportLEEquiv_symm_apply_coeff`, `MvPolynomial.aeval_bind₂`, `Matrix.vecMul_diagonal_const`, `hasDerivAt_iff_isLittleO_nhds_zero`, `SchwartzMap.tsupport_smulLeftCLM_subset`, `PadicInt.hasSum_mahler`, `MvPolynomial.rename_bind₁`, `Function.Periodic.int_mul_eq`, `CliffordAlgebra.contractRight_contractRight`, `InnerProductSpace.toMatrix_rankOne`, `HasFDerivWithinAt.continuousMultilinear_apply_const`, `Filter.NeBot.mul_zero_nonneg`, `pi_eq_sum_univ`, `RingCon.matrix_apply_single`, `Affine.Simplex.affineCombination_mem_affineSpan_faceOpposite_iff`, `Matrix.exp_blockDiagonal`, `LieAlgebra.InvariantForm.mem_orthogonal`, `Quiver.Path.weightOfEPs_pos`, `Int.sub_floor_div_mul_nonneg`, `MvPolynomial.support_X_pow`, `MvPolynomial.rTensor_symm_apply_single`, `Complex.UnitDisc.instSMulCommClass_circle_right`, `EuclideanSpace.ofLp_single`, `WittVector.ghostComponent_zero_verschiebung`, `smul_floorDiv`, `Complex.UnitDisc.mk_zero`, `Quaternion.imJ_mul`, `MvPolynomial.pderiv_X_of_ne`, `CFC.zero_nnrpow`, `Module.Basis.toMatrix_mul_toMatrix_flip`, `MvPolynomial.prod_X_add_C_coeff`, `MvPolynomial.renameSymmetricSubalgebra_symm_apply_coe`, `MvPolynomial.IsSymmetric.zero`, `Algebra.Generators.Hom.toAlgHom_comp_apply`, `PiTensorProduct.liftIsometry_comp_mapL`, `MvPolynomial.degree_finSuccEquiv`, `Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const`, `MvPowerSeries.inv_eq_zero`, `Complex.UnitDisc.mk_eq_zero`, `Polynomial.Bivariate.Polynomial.Bivariate.pderiv_zero_equivMvPolynomial`, `iteratedFDeriv_smul_const_apply`, `HasStrictDerivAt.fun_const_smul`, `Set.Icc.mk_one`, `Int.image_fract`, `AddMonoidAlgebra.mul_apply_add_eq_mul_of_uniqueAdd`, `MvPolynomial.isNoetherianRing_fin_0`, `WeierstrassCurve.Affine.evalEval_polynomialY_zero`, `WeierstrassCurve.Jacobian.equation_iff`, `RCLike.nonneg_iff_exists_ofReal`, `HasDerivWithinAt.congr_deriv`, `LaurentPolynomial.toLaurent_support`, `slope_pos_iff_gt`, `Matrix.det_blockDiagonal`, `Representation.free_single_single`, `Quaternion.im_nnratCast`, `Asymptotics.isLittleO_iff_exists_eq_mul`, `Submodule.map_smul'`, `Set.zero_mul_subset`, `MvPolynomial.nonempty_support_optionEquivLeft`, `MeasureTheory.Lp.instIsBoundedSMul`, `InnerProductSpace.isSymmetric_rankOne_self`, `linearIndependent_iff''`, `Matrix.PosSemidef.dotProduct_mulVec_nonneg`, `MvPolynomial.pderiv_monomial`, `Matrix.det_eq_zero_of_not_linearIndependent_cols`, `WeierstrassCurve.Projective.dblZ_of_Y_eq`, `Seminorm.ball_smul_ball`, `Polynomial.toFinsupp_eq_one`, `ContinuousMap.coe_toLp`, `Positive.coe_inv`, `Rat.cast_nonpos`, `MvPolynomial.isRegular_X_pow`, `Module.Basis.apply_eq_iff`, `Module.Flat.iff_forall_exists_factorization`, `continuousMultilinearCurryLeftEquiv_apply`, `OreLocalization.nontrivial_of_nonZeroDivisorsRight`, `Matrix.toBlock_inverse_eq_zero`, `Matrix.mul_right_eq_iff_eq_mul_invOf`, `Finsupp.coe_sym2Mul`, `Module.Basis.mk_coord_apply`, `Matrix.rank_diagonal`, `SkewMonoidAlgebra.coeff_mul_single_one`, `Associates.out_zero`, `Polynomial.mem_closure_X_union_C`, `Nat.prod_pow_primeFactors_factorization`, `bind₁_rename_expand_wittPolynomial`, `Ideal.primeHeight_eq_zero_iff`, `MonoidAlgebra.support_single_mul_eq_image`, `HahnSeries.ofPowerSeriesAlg_apply_coeff`, `Matrix.vecMulVec_zero`, `Algebra.adjoin_eq_range`, `ringChar.spec`, `MvPolynomial.degrees_add_le`, `MvPolynomial.mapAlgEquiv_symm`, `LaurentSeries.powerSeriesEquivSubring_apply`, `Algebra.Generators.toComp_toAlgHom_monomial`, `IsStrictlyPositive.commute_iff`, `Module.Relations.Solution.π_comp_map`, `Polynomial.exists_root_of_splits`, `LinearMap.polar_eq_biInter_preimage`, `MvPolynomial.counit_surjective`, `ProperCone.toPointedCone_bot`, `ContinuousMapZero.instSMulCommClass'`, `Polynomial.eval_zero_map`, `DFinsupp.toMultiset_injective`, `MvPolynomial.rename_injective`, `Multiset.toFinsupp_zero`, `MvPolynomial.isHomogeneous_zero`, `Ring.KrullDimLE.isNilpotent_iff_mem_maximalIdeal`, `ENat.floor_zero`, `QuadraticAlgebra.omega_mul_algebraMap_mul_mk`, `RCLike.ofReal_nonpos`, `AffineMap.homothety_zero`, `IsDedekindDomain.HeightOneSpectrum.intValuation_def`, `mul_pos_iff_of_pos_left`, `IsSemisimpleModule.exists_end_algEquiv`, `ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv`, `ArithmeticFunction.dirichletInverse_mul_self`, `Matrix.stdBasis_eq_single`, `Quaternion.coe_sub`, `one_half_pos`, `MvPolynomial.degrees_mul_le`, `not_lt_zero'`, `RootPairing.GeckConstruction.isNilpotent_f`, `WeierstrassCurve.Projective.negDblY_eq'`, `MvPolynomial.quotient_mk_comp_C_injective`, `AnalyticAt.exists_eq_sum_add_pow_mul`, `Submonoid.LocalizationMap.map_zero`, `MvPolynomial.monomial_mem_homogeneousSubmodule_pow_degree`, `MonomialOrder.leadingCoeff_neg`, `Algebra.SubmersivePresentation.aeval_jacobianOfHasCoeffs`, `ArithmeticFunction.moebius_sq_eq_one_of_squarefree`, `Matrix.pow_col_eq_zero_of_le`, `Rat.instIsScalarTowerRight`, `Affine.Simplex.faceOpposite_point_eq_point_succAbove`, `OrthogonalIdempotents.ortho`, `LinearMap.toMatrix'_id`, `CliffordAlgebra.even_toSubmodule`, `Multiset.toFinsupp_toMultiset`, `setBasisOfTopLeSpanOfCardEqFinrank_repr_apply`, `ContinuousLinearMap.intervalIntegral_apply`, `LinearMap.polyCharpolyAux_coeff_eval`, `LinearMap.range_smul'`, `MvPolynomial.esymmAlgHomMonomial_single_one`, `Function.noZeroSMulDivisors`, `AddMonoidAlgebra.le_inf_support_mul`, `AlgebraicClosure.Monics.map_eq_prod`, `MvPolynomial.coe_smul`, `HasFDerivWithinAt.comp_hasDerivWithinAt`, `CentroidHom.coe_zero`, `hasDerivAt_intCast`, `MonomialOrder.degree_prod_le`, `LinearOrderedSemifield.toPosSMulStrictMono_rat`, `Module.End.genEigenspace_zero_nat`, `MvPolynomial.totalDegree_add_eq_left_of_totalDegree_lt`, `NonUnitalSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul`, `emultiplicity_of_unit_right`, `MonoidAlgebra.supportedEquivFinsupp_apply_support_val`, `IncidenceAlgebra.one_prod_one`, `PiTensorProduct.liftIsometry_symm_apply`, `nnnorm_cfcₙHom`, `FractionalIdeal.zero_mem`, `fderivWithin_continuousAlternatingMap_apply_apply`, `SchwartzMap.smulLeftCLM_neg`, `ContinuousLinearMap.opNNNorm_mul`, `ContinuousMultilinearMap.iteratedFDerivComponent_apply`, `Matrix.diagonal_kronecker`, `Projectivization.orthogonal_mk`, `LSeries_one_mul_Lseries_moebius`, `Quaternion.self_mul_star`, `Polynomial.smeval_at_zero`, `Projectivization.cross_mk`, `MvPolynomial.map_rightInverse`, `WithZeroTopology.isOpen_iff`, `ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin`, `NormedField.completeSpace_iff_isComplete_closedBall`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear`, `isLinearTopology_iff_hasBasis_open_ideal`, `MvPolynomial.finrank_eq_zero`, `FractionalIdeal.divMod_zero_right`, `FormalMultilinearSeries.leftInv_comp`, `MvPolynomial.dvd_monomial_mul_iff_exists`, `List.prod_eq_zero_iff`, `MvPolynomial.killCompl_map`, `Quiver.Path.weight_pos`, `spectrum.differentiableOn_inverse_one_sub_smul`, `Polynomial.coeff_X_mul_zero`, `mem_pNilradical`, `Matrix.conjTranspose_eq_one`, `Continuous.cfcₙ_nnreal_of_mem_nhdsSet`, `MonomialOrder.span_leadingTerm_insert_zero`, `HasFPowerSeriesAt.const_smul`, `Matrix.mul_swap_apply_left`, `iteratedFDeriv_succ_eq_comp_right`, `PowerSeries.heval_X`, `RCLike.inv_pos_of_pos`, `Quaternion.imJ_ratCast`, `ContinuousMultilinearMap.changeOriginSeries_support`, `Algebra.FiniteType.iff_quotient_mvPolynomial`, `MeasureTheory.upcrossingsBefore_eq_sum`, `Finsupp.linearCombination_comp_addSingleEquiv`, `Holor.mul_zero`, `ValuationSubring.inv_mem_nonunits_iff`, `AddMonoidAlgebra.mem_grade_iff`, `Finsupp.DegLex.isStrictOrder`, `WittVector.mul_pow_charP_coeff_zero`, `Matrix.posSemidef_intCast_iff`, `Matrix.det_updateRow_eq_zero`, `ContDiffMapSupportedIn.seminorm_apply`, `RootPairing.GeckConstruction.ω_mul_ω`, `SimpleGraph.ediam_eq_zero_iff_subsingleton`, `IsDiscreteValuationRing.addVal_eq_zero_iff`, `WithVal.toVal_eq_zero`, `OrthogonalFamily.eq_ite`, `Matrix.toLinAlgEquiv_apply`, `IsFractionRing.mk'_eq_zero_iff_eq_zero`, `Module.Basis.coe_ofRepr`, `ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom`, `DifferentiableAt.clm_comp`, `Matrix.IsPrimitive.exists_pos_pow`, `GeneralSchauderBasis.ortho`, `WeierstrassCurve.ofJ0_j`, `LieAlgebra.matrix_trace_commutator_zero`, `MeasureTheory.Lp.simpleFunc.isBoundedSMul`, `Module.equiv_free_prod_directSum`, `DualNumber.range_inlAlgHom_sup_adjoin_eps`, `list_sum_pow_char_pow`, `GCDMonoid.lcm_zero_left`, `Algebra.Norm.Transitivity.mul_auxMat_blockTriangular`, `Polynomial.coeff_zero_eq_aeval_zero`, `Algebra.Generators.H1Cotangent.δAux_X`, `DoubleCentralizer.algebraMap_fst`, `MonomialOrder.div_set`, `AddMonoidAlgebra.grade.decompose_single`, `MvPowerSeries.zero_mul`, `MvPolynomial.aeval_eq_bind₁`, `hasDerivWithinAt_diff_singleton`, `fderiv_continuousLinearEquiv_comp`, `MvPolynomial.support_optionEquivLeft`, `MvPowerSeries.coeff_rescale`, `floorDiv_one`, `ZNum.abs_to_nat`, `EisensteinSeries.q_expansion_bernoulli`, `deriv_clm_comp`, `MonoidAlgebra.ofCoeff_zero`, `ContinuousLinearMap.adjoint_toSpanSingleton`, `hasStrictFDerivAt_exp_zero_of_radius_pos`, `quasispectrumRestricts_iff_spectrumRestricts_inr`, `LSeries.one_convolution_eq_zeta_convolution`, `Quaternion.im_neg`, `ContDiffMapSupportedIn.structureMapCLM_top_apply`, `posMulReflectLE_iff_posMulReflectLT`, `Polynomial.trailingDegree_ne_zero`, `Submodule.mulLeftMap_eq_mulMap_comp`, `MvPolynomial.X_mul_modMonomial`, `Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zero`, `Matroid.eRk_eq_zero_iff`, `Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card`, `Finset.sum_single_ite`, `MvPolynomial.degreeOf_pow_le`, `MvPolynomial.dvd_X_iff_exists`, `mul_nonneg_iff_of_pos_left`, `Int.fract_eq_zero_iff`, `tsum_prod_pow_eq_tsum_sigma`, `Matrix.exists_vecMul_eq_zero_iff`, `MvPowerSeries.WithPiTopology.hasSum_of_monomials_self`, `MvPolynomial.finSuccEquiv_X_succ`, `ArithmeticFunction.abs_moebius_eq_one_of_squarefree`, `Polynomial.card_support_eq_two`, `HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow`, `Valuation.IsUniformizer.val_pos`, `MvPolynomial.aeval_ofNat`, `AddMonoidAlgebra.mem_adjoin_support`, `Left.mul_pos`, `ContDiffMapSupportedIn.seminorm_eq_bot_of_gt`, `MonomialOrder.degree_zero`, `Algebra.smulTower_leftMulMatrix_algebraMap`, `Quaternion.imK_intCast`, `Mathlib.Tactic.Linarith.le_of_le_of_eq`, `CStarAlgebra.span_nonneg_inter_closedBall`, `toSpanSingleton_derivWithin`, `CStarAlgebra.isClosed_nonneg`, `Odd.pow_pos_iff`, `tprod_of_exists_eq_zero`, `IsOrderedModule.of_smul_nonneg`, `spectrum.hasFDerivAt_resolvent`, `PadicComplex.coe_zero`, `Algebra.Presentation.aeval_val_relationOfHasCoeffs`, `NNRat.cast_pos`, `KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination`, `QuadraticAlgebra.coe_pow`, `NonUnitalSubring.coe_eq_zero_iff`, `CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt`, `smul_ceilDiv`, `MvPolynomial.eval₂Hom_eq_zero`, `Nat.sum_zeckendorf_fib`, `HasFiniteFPowerSeriesOnBall.eq_partialSum'`, `HahnSeries.SummableFamily.one_sub_self_mul_hsum_powers`, `MvPolynomial.instCharP`, `PowerSeries.coeff_one`, `Nat.ordProj_self_pow`, `Filter.tendsto_mul_const_atBot_iff_pos`, `AddMonoidAlgebra.single_eq_zero`, `MvPolynomial.expand_comp_bind₁`, `MvPolynomial.mapAlgEquiv_trans`, `MonomialOrder.leadingCoeff_C`, `IsAddTorsionFree.to_noZeroSMulDivisors_nat`, `apply_le_nnnorm_cfc_nnreal`, `AbsoluteValue.nonneg'`, `MeromorphicOn.AnalyticOnNhd.divisor_nonneg`, `HasDerivAt.comp_hasDerivWithinAt`, `Algebra.SubmersivePresentation.aeval_invJacobianOfHasCoeffs`, `exists_ordCompl_eq_one_iff_isPrimePow`, `SimpleGraph.adjMatrix_mul_apply`, `IsDedekindDomain.HeightOneSpectrum.intValuationDef_zero`, `MeasureTheory.Integrable.smul_essSup`, `IsBoundedBilinearMap.toContinuousLinearMap_apply`, `MvPolynomial.ker_mapAlgHom`, `Matrix.charpoly_fromBlocks_zero₁₂`, `ArchimedeanClass.mk_le_mk_iff_denselyOrdered`, `Finsupp.degree_preimage_nsmul`, `cfc_nonneg_of_predicate`, `Matrix.row_eq_zero_of_commute_single`, `Subalgebra.coe_zero`, `ModuleFilterBasis.smul'`, `PosNum.cast_pos`, `Nat.factorization_le_factorization_mul_right`, `MvPolynomial.aeval_injective_iff_of_isEmpty`, `HasFPowerSeriesOnBall.pi`, `MvPolynomial.support_one`, `mul_sub_mul_div_mul_nonpos`, `WittVector.constantCoeff_wittAdd`, `HasFPowerSeriesWithinOnBall.fderivWithin_eq`, `Finsupp.instIsScalarTowerForall`, `ContinuousMultilinearMap.piₗᵢ_symm_apply`, `FiniteField.exists_root_sum_quadratic`, `Algebra.Generators.ofComp_kerCompPreimage`, `MonoidAlgebra.coeffAddEquiv_symm_apply`, `MvPolynomial.X_mem_supported`, `Rep.indCoindIso_hom_hom_toLinearMap`, `Nat.multinomial_single`, `Matrix.diagonalRingHom_apply`, `MvPolynomial.coeff_zero`, `dividedPowersBot_dpow_eq`, `Module.Flat.exists_factorization_of_apply_eq_zero_of_free`, `Cardinal.toENatAux_zero`, `Polynomial.root_right_of_root_gcd`, `HasDerivAt.scomp`, `MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder`, `Nat.prod_factorization_eq_prod_primeFactors`, `MvPolynomial.eval_sub`, `Polynomial.card_support_eq_one`, `Nat.factorization_eq_zero_iff_remainder`, `LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul`, `MvPolynomial.mem_restrictDegree_iff_sup`, `WittVector.one_coeff_eq_of_pos`, `ContDiffMapSupportedIn.structureMapLM_top_apply`, `tendsto_mul_nhds_zero_of_disjoint_cocompact`, `PowerSeries.coeff_mul_X_pow'`, `ContinuousLinearMap.ker_adjoint_comp_self`, `MvPolynomial.esymmAlgHom_fin_injective`, `UniqueFactorizationMonoid.moebius_zero`, `ProjectiveSpectrum.basicOpen_zero`, `Quaternion.normSq_def'`, `SchwartzMap.pairing_continuous_left`, `Associates.instIsCancelMulZero`, `LieAlgebra.SpecialLinear.val_single`, `tendsto_mul_prod_nhds_zero_of_disjoint_cocompact`, `Set.indicator_mul_const`, `lipschitzOnWith_cfcₙ_fun_of_subset`, `range_cfc_nnreal_eq_image_cfc_real`, `SimpContFract.of_isContFract`, `Matrix.toLinearMap₂_apply`, `Matrix.invOf_diagonal_eq`, `continuous_cfcₙHom_of_cfcHom`, `HasDerivAt.const_mul`, `AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top`, `MvPolynomial.aeval_comp_bind₁`, `tendsto_const_mul_zpow_atTop_zero`, `Matrix.mem_orthogonalGroup_iff`, `Quaternion.imI_add`, `MvPolynomial.hsymm_one`, `GenContFract.zeroth_contAux_eq_one_zero`, `HasDerivWithinAt.congr`, `SchwartzMap.integralCLM_apply`, `Nat.Prime.pow_dvd_iff_dvd_ordProj`, `MvPolynomial.weightedHomogeneousComponent_eq_zero_of_notMem`, `ZLattice.abs_repr_lt_of_norm_lt`, `Matrix.swap_mulVec`, `Polynomial.aroots_C_mul_X_pow`, `InnerProductSpace.rankOne_one_right_eq_toSpanSingleton`, `Matrix.inv_mul_of_invertible`, `Height.logHeight_eval_le`, `hasDerivAt_one`, `HasDerivAtFilter.fun_neg`, `SameRay.exists_nonneg_left`, `MultilinearMap.freeDFinsuppEquiv_apply`, `QuaternionAlgebra.Basis.i_self`, `QuaternionAlgebra.coe_commutes`, `descPochhammer_eval_coe_nat_of_lt`, `ArithmeticFunction.LSeries_zeta_eq_riemannZeta`, `MonoidAlgebra.supportedEquivFinsupp_apply_apply`, `Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow`, `Nat.prod_pow_factorization_eq_self`, `Matrix.Module.single_smul`, `LieModule.genWeightSpace_zero_normalizer_eq_self`, `SimpleGraph.incMatrix_mul_transpose_diag`, `Matrix.isHermitian_natCast`, `ArithmeticFunction.IsMultiplicative.eq_iff_eq_on_prime_powers`, `CFC.nnrpow_eq_nnrpow_pi`, `IsBoundedSMul.of_nnnorm_smul_le`, `isClosedEmbedding_cfcₙHom_of_cfcHom`, `QuadraticAlgebra.algHom_ext_iff`, `CongruenceSubgroup.Gamma1_mem`, `MvPolynomial.totalDegree_sub`, `eq_zero_of_ne_zero_of_mul_left_eq_zero`, `RootPairing.GeckConstruction.isNilpotent_e`, `HasFTaylorSeriesUpToOn.hasStrictFDerivAt`, `Polynomial.degree_eq_zero_of_isUnit`, `smul_nonneg_iff`, `Matrix.adjugate_zero`, `AddMonoidAlgebra.domCongr_support`, `Matrix.swap_mul_of_ne`, `KaehlerDifferential.kerTotal_mkQ_single_smul`, `Polynomial.monic_freeMonic`, `scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero`, `MvPolynomial.rTensor_apply_monomial_tmul`, `WeierstrassCurve.ofJ_0_of_three_eq_zero`, `FormalMultilinearSeries.div_le_radius_compContinuousLinearMap`, `Nat.one_div_cast_nonneg`, `MvPolynomial.IsWeightedHomogeneous.prod`, `Nat.ordCompl_div_pow_of_dvd`, `IsReduced.pow_eq_zero_iff`, `HahnSeries.SummableFamily.binomialFamily_apply`, `MvPolynomial.eval₂_const_pUnitAlgEquiv`, `sign_pow`, `Algebra.Generators.repr_CotangentSpaceMap`, `MonoidAlgebra.lift_apply`, `Module.Basis.dualBasis_repr`, `QuaternionAlgebra.im_star`, `nonneg_of_mul_nonneg_left`, `DividedPowerAlgebra.dp_sum_smul`, `hasLineDerivAt_iff_tendsto_slope_zero`, `Algebra.intNorm_zero`, `IsIdempotentElem.add_iff`, `DividedPowers.dpow_linearCombination`, `TwoSidedIdeal.mem_iff`, `IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_divisionRing`, `Matrix.dotProduct_vecMul_hadamard`, `conjugate_pos'`, `MvPowerSeries.eq_zero_iff_forall_coeff_zero`, `Polynomial.annIdealGenerator_aeval_eq_zero`, `ValuationSubring.mem_nonunits_iff_or`, `MonomialOrder.degLex_lt_iff`, `Matrix.proj_diagonal`, `MvPolynomial.coeff_X'`, `Polynomial.aeval_eq_zero_of_dvd_aeval_eq_zero`, `fderiv_continuousMultilinearMapCompContinuousLinearMap`, `Matrix.permMatrix_mulVec`, `IsIdempotentElem.coe_zero`, `Polynomial.root_gcd_iff_root_left_right`, `IsUnit.isNilpotent_mul_unit_of_commute_iff`, `Set.Ioc.coe_eq_one`, `Matrix.self_mul_conjTranspose_mulVec_eq_zero`, `MvPolynomial.pderiv_pow`, `constantCoeff_wittStructureRat_zero`, `HahnSeries.support_mul_subset_add_support`, `IsSelfAdjoint.commute_cfcₙHom`, `SimpleGraph.adjMatrix_hadamard_self`, `PowerSeries.forall_coeff_eq_zero`, `HasDerivWithinAt.smul_const`, `Polynomial.algebraMap_hahnSeries_apply`, `HahnModule.orderTop_vAdd_le_orderTop_smul`, `WeierstrassCurve.Jacobian.map_polynomialZ`, `Polynomial.support_update`, `Field.instNeZeroFinSepDegree`, `WittVector.verschiebungFun_coeff_zero`, `AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq_of_fintype`, `inner_eq_ofReal_norm_sq_left_iff`, `contDiff_nat_iff_continuous_differentiable`, `QuasispectrumRestricts.nonUnitalStarAlgHom_apply`, `MonoidAlgebra.coeff_zero`, `WeierstrassCurve.Projective.addZ_self`, `MvPolynomial.aeval_esymm_eq_multiset_esymm`, `sameRay_smul_right_iff_of_ne`, `MvPolynomial.supported_le_supported_iff`, `MvPolynomial.totalDegree_zero`, `Set.Ioc.coe_le_one`, `AddMonoidAlgebra.coeffLinearEquiv_symm_apply`, `extremePoints_doublyStochastic`, `coe_nonZeroDivisorsLeft_eq`, `Unitization.starMap_apply`, `Matrix.det_fromBlocks₂₂`, `Valuation.Integers.valuation_pos_iff_ne_zero`, `SchwartzMap.lineDerivOp_fourierInv_eq`, `LinearIsometryEquiv.symm_conjStarAlgEquiv`, `zero_pow_eq_zero`, `IsFractionRing.num_zero`, `Submodule.topologicalClosure_eq_top_iff`, `MonomialOrder.coeff_pow_nsmul_degree`, `Num.dvd_to_nat`, `Nat.WithBot.lt_one_iff_le_zero`, `MvPolynomial.bind₂_C_right`, `NumberField.mixedEmbedding.stdBasis_apply_isReal`, `normEDS_zero`, `MvPowerSeries.algebraMap_apply'`, `PowerSeries.coeff_C`, `MvPolynomial.constantCoeff_eq`, `HasFiniteFPowerSeriesOnBall.add`, `LinearMap.toMvPolynomial_constantCoeff`, `Int.floor_le_neg_one_iff`, `ZNum.to_of_int`, `invOf_nonpos`, `ceilDiv_one`, `Quaternion.imK_smul`, `MeasureTheory.Lp.smul_def`, `ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le`, `HahnSeries.coeff_toMvPowerSeries_symm`, `WeierstrassCurve.Projective.map_polynomialZ`, `MvPolynomial.eval_rename`, `LaurentPolynomial.smeval_single`, `ContinuousLinearMap.opNorm_lsmul_le`, `Module.Basis.linearCombination_repr`, `MvPolynomial.mkDerivationₗ_C`, `Subsemiring.mem_closure_iff_exists_list`, `Matrix.fromRows_replicateRow0_isTotallyUnimodular_iff`, `union_support_maximal_linearIndependent_eq_range_basis`, `Matrix.mul_left_eq_iff_eq_invOf_mul`, `Representation.LinearizeMonoidal.leftUnitor_δ`, `MvPolynomial.vars_one`, `StandardEtalePresentation.toPresentation_σ'`, `MultilinearMap.mkContinuousMultilinear_norm_le`, `Polynomial.monomial_zero_right`, `MvPolynomial.totalDegree_finsetSum_le`, `mem_nonZeroDivisorsLeft_iff`, `PowerSeries.order_zero_of_unit`, `Module.FinitePresentation.out`, `CauSeq.one_not_equiv_zero`, `MvPolynomial.weightedTotalDegree_piSingle`, `Nat.factorization_eq_primeFactorsList_multiset`, `RootPairing.Base.exists_root_eq_sum_int`, `ContDiffMapSupportedIn.monoCLM_eq_zero`, `DualNumber.commute_eps_left`, `Matrix.vecMul_natCast`, `Nonneg.mk_smul`, `Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius`, `ArithmeticFunction.instCompleteSpace`, `MvPolynomial.isIntegral_iff_isIntegral_coeff`, `hasDerivAt_natCast`, `witt_structure_prop`, `HasDerivAtFilter.fun_sub`, `ContinuousMap.coeFn_toLp`, `MvPowerSeries.weightedOrder_le`, `HasDerivWithinAt.union`, `Quaternion.im_star`, `Set.Icc.coe_one`, `Nat.factorization_floorRoot`, `Module.Basis.linearCombination_coord`, `Finset.sum_weightedVSubVSubWeights`, `Finset.prod_pos`, `MvPolynomial.map_surjective`, `MvPowerSeries.order_ne_zero_iff_constCoeff_eq_zero`, `Matrix.fromCols_mul_fromRows_eq_one_comm`, `Quaternion.coe_mul`, `Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_ker`, `Real.fourier_bilin_convolution_eq_integral`, `LieModule.zero_genWeightSpace_eq_top_of_nilpotent`, `IsGaloisGroup.coe_quotient_smul`, `Matrix.toLinearMap₂'_single`, `Set.indicator_const_mul`, `Matrix.Pivot.mul_listTransvecRow_last_col_take`, `isConjRoot_zero_iff_eq_zero'`, `range_cfcₙ_nnreal_subset`, `Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero`, `NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate`, `MvPolynomial.degreeOf_one`, `MvPolynomial.coe_eval₂AlgHom`, `HasDerivWithinAt.add_const`, `WittVector.constantCoeff_wittNSMul`, `ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric`, `CauSeq.Completion.ofRat_zero`, `Matrix.det_fromBlocks_zero₁₂`, `mulLeftLinearMap_one`, `ArchimedeanClass.FiniteElement.mk_zero`, `MonoidAlgebra.mapAddEquiv_apply`, `Positive.isOrderedCancelMonoid`, `OrderedSemiring.toSMulPosMonoNat`, `LinearMap.toMvPolynomial_comp`, `Module.Basis.toDual_apply`, `PowerSeries.coeff_inv`, `ProperCone.innerDual_empty`, `IsSepClosed.exists_eval₂_eq_zero_of_injective`, `stdSimplexHomeomorphUnitInterval_one`, `hasStrictFDerivAt_exp_zero`, `ContinuousLinearMap.norm_compL_le`, `MvPowerSeries.coeff_expand_of_not_dvd`, `gcd_zero_left`, `MvPolynomial.eval₂Hom_eq_bind₂`, `ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap`, `Module.Basis.tensorAlgebra_repr_apply`, `Nat.floorRoot_def`, `MvPolynomial.IsHomogeneous.rename_isHomogeneous_iff`, `QuaternionAlgebra.coe_ofNat`, `MvPolynomial.vars_bind₁`, `MonomialOrder.leadingCoeff_pow`, `WittVector.bind₁_verschiebungPoly_wittPolynomial`, `Valued.mem_nhds_zero`, `AbsoluteValue.zeroHomClass`, `MvPolynomial.prod_C_add_X_eq_sum_esymm`, `Unitization.instIsStarNormal`, `Odd.zpow_pos_iff`, `Module.projective_def'`, `not_irreducible_zero`, `fderivWithin_clm_comp`, `TrivSqZeroExt.isUnit_inr_iff`, `Algebra.Presentation.instFinitePresentationModelOfHasCoeffsOfFinite`, `RootPairing.eq_zero_iff_forall_coroot'_eq_zero`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars`, `AddMonoidAlgebra.single_zero`, `Polynomial.binomial_eq_binomial`, `HahnSeries.SummableFamily.pow_finite_co_support`, `IsIdempotentElem.mul_eq_zero_of_anticommute`, `Polynomial.Chebyshev.T_eval_zero_of_even`, `WeierstrassCurve.isShortNF_iff`, `sameRay_neg_smul_right_iff_of_ne`, `HasDerivWithinAt.congr_set`, `MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero_of_le_card`, `Subring.coe_zero`, `IsAdjoinRootMonic.coeff_algebraMap`, `MvPolynomial.eval₂_map_comp_C`, `Matrix.GeneralLinearGroup.coe_map_mul_map_inv`, `Nonneg.instIsOrderedModule`, `DualNumber.algHom_ext_iff`, `MonomialOrder.degree_pow`, `MvPowerSeries.coeff_zero_C`, `HasFPowerSeriesAt.sub`, `ENat.add_one_pos`, `MvPolynomial.support_smul_eq`, `Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply`, `Cubic.zero`, `OrderDual.instIsOrderedModule`, `Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map`, `MvPolynomial.optionEquivRight_apply`, `Module.Basis.equivFun_apply`, `Polynomial.coeff_expand`, `MvPolynomial.finSuccEquiv_apply`, `Finsupp.sum_option_index_smul`, `OrthogonalFamily.range_linearIsometry`, `Nonneg.mk_nnqsmul`, `TensorProduct.finsuppScalarLeft_apply_tmul`, `MvPowerSeries.coeff_monomial`, `MvPowerSeries.X_dvd_iff`, `Monotone.deriv_nonneg`, `Polynomial.X_dvd_iff`, `MvPolynomial.vanishingIdeal_empty`, `ArithmeticFunction.LSeriesSummable_moebius_iff`, `fderiv_continuousMultilinear_apply_const`, `monovary_iff_forall_mul_nonneg`, `MvPowerSeries.coeff_C`, `ContinuousMapZero.coe_sum`, `HasDerivWithinAt.smul`, `MvPolynomial.C_eq_coe_nat`, `WeierstrassCurve.Projective.add_of_Y_eq`, `WeierstrassCurve.Jacobian.Y_sub_Y_mul_Y_sub_negY`, `AffineMap.lineMap_eq_left_iff`, `PowerSeries.order_one`, `Module.Relations.directSum_relation`, `ArithmeticFunction.sum_moebius_mul_log_eq`, `Module.Basis.mulOpposite_repr_eq`, `MvPolynomial.tensorEquivSum_X_tmul_X`, `Nonneg.coe_mul`, `Quaternion.normSq_zpow`, `Module.Basis.coe_repr_symm`, `Quaternion.coe_nnratCast`, `ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv`, `ContinuousLinearMap.opNNNorm_mul_flip_apply`, `Module.Basis.smulTower'_repr`, `IsLocalization.mk'_zero`, `TwoSidedIdeal.listSum_mem`, `WeierstrassCurve.Affine.slope_of_Y_eq`, `HasDerivWithinAt.fun_pow`, `Finset.centerMass_ite_eq`, `Nat.one_div_pos_of_nat`, `HasDerivWithinAt.finset_prod`, `QuaternionAlgebra.Basis.j_self`, `Polynomial.degree_le_iff_coeff_zero`, `cfc_smul`, `Module.Relations.toQuotient_map_apply`, `Nonneg.instNonUnitalContinuousFunctionalCalculus`, `Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype`, `isSumNonzeroSq_iff_isSumSq`, `MvPolynomial.comp_aeval_apply`, `MvPolynomial.vars_mul`, `WithZeroMulInt.toNNReal_eq_one_iff`, `HasFPowerSeriesOnBall.hasFDerivAt`, `Nat.prod_factorization_pow_eq_self`, `MonoidAlgebra.support_single_mul`, `Algebra.Presentation.relation_comp_localizationAway_inl`, `WittVector.coeff_p_zero`, `MvPolynomial.bind₂_comp_bind₂`, `QuadraticAlgebra.mul_C_eq_smul`, `egauge_eq_zero_iff`, `WittVector.coeff_select`, `cfc_apply_of_not_predicate`, `PowerSeries.coeff_expand_of_not_dvd`, `cfcHom_isStrictlyPositive_iff`, `Finsupp.toFinset_toMultiset`, `HasDerivWithinAt.mono`, `Matrix.mem_colStochastic`, `Submodule.IsOrtho.inner_eq`, `Matrix.det_mul_add_one_comm`, `CategoryTheory.CatCenter.localization_zero`, `FirstOrder.Field.instModelField`, `MvPolynomial.aeval_unique`, `WeierstrassCurve.Jacobian.baseChange_polynomialX`, `LaurentSeries.coeff_zero_of_lt_valuation`, `MonoidAlgebra.mul_apply`, `Module.Presentation.tensor_relation`, `Nat.dvd_prod_pow_of_factorization_le`, `cfc_zero`, `ArithmeticFunction.carmichael_finset_prod`, `ContinuousMultilinearMap.curryMid_apply`, `linearIndependent_iff`, `Algebra.toMatrix_lsmul`, `HasFDerivWithinAt.comp_hasDerivAt`, `SchwartzMap.compCLM_apply`, `Quaternion.coe_starAe`, `sq_pos_iff`, `TemperedDistribution.fourierMultiplierCLM_apply_apply`, `DividedPowerAlgebra.dp_def`, `SchwartzMap.schwartzSeminormFamily_apply_zero`, `ClosedSubmodule.sInf_orthogonal`, `analyticOn_inv`, `HahnSeries.embDomain_mul`, `NNReal.orderIsoRpow_symm_eq`, `MvPolynomial.coeff_rTensorAlgHom_monomial_tmul`, `Finsupp.linearCombination_fin_zero`, `HasDerivAt.mul`, `ContinuousMap.toLp_comp_toContinuousMap`, `ZMod.erdos_ginzburg_ziv_multiset`, `PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm`, `ContinuousSqrt.sqrt_nonneg`, `MvPolynomial.bind₁_bind₁`, `LaurentSeries.powerSeriesEquivSubring_coe_apply`, `WeierstrassCurve.IsCharThreeJNeZeroNF.a₄`, `ArithmeticFunction.coe_mul_zeta_apply`, `MvPolynomial.support_sum_monomial_coeff`, `ofDual_toAdd_eq_top_iff`, `MvPolynomial.degreeOf_mul_C_le`, `LinearMap.mulRight_eq_zero_iff`, `MvPolynomial.mem_coeffsIn_iff_coeffs_subset`, `Module.Relations.Solution.π_relation`, `not_isLeftRegular_zero_iff`, `neg_of_slope_pos`, `NonUnitalAlgHom.coe_inl`, `MvPolynomial.esymmAlgHomMonomial_add`, `LieModule.Weight.apply_lie`, `ContMDiff.clm_postcomp`, `exteriorPower.basis_repr_apply`, `Matrix.linfty_opNormOneClass`, `Polynomial.isBoundedUnder_abs_atTop_iff`, `Int.fract_neg_eq_zero`, `MvPolynomial.algebraTensorAlgEquiv_symm_map`, `Matrix.nonneg_mulVec_of_mem_rowStochastic`, `MonoidWithZeroHom.map_ite_one_zero`, `LinearIndependent.repr_eq`, `instContinuousSMulSubtypeLeOfNat`, `Matrix.mem_colStochastic_iff_sum`, `TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent`, `instSMulCommClass_sphere_ball_ball`, `Module.Basis.toMatrix_update`, `pos_iff_neg_of_mul_neg`, `PiLp.basis_toMatrix_basisFun_mul`, `Quaternion.sub_im_self`, `Nat.neZero_totient`, `Metric.unitSphere.coe_pow`, `MvPolynomial.coeff_sub`, `MvPolynomial.rename_polynomial_aeval_X`, `Quaternion.inner_self`, `fderivWithin_continuousAlternatingMap_apply_const`, `MvPolynomial.weightedDecomposition.decompose'_eq`, `sq_nonneg`, `MvPolynomial.degrees_mul_eq`, `convexOn_pow`, `MvPolynomial.coeff_expand_of_not_dvd`, `iccHomeoI_symm_apply_coe`, `Matrix.det_mul_aux`, `Polynomial.toFinsupp_apply`, `WittVector.map_eq_zero_iff`, `Finsupp.linearCombination_equivMapDomain`, `smul_inv₀`, `SkewMonoidAlgebra.of_injective`, `Matrix.isDiag_smul_one`, `descPochhammer_pos`, `Pi.basisFun_apply`, `Rep.linearization_map`, `MvPowerSeries.lexOrder_eq_top_iff_eq_zero`, `Matrix.IsDiag.conjTranspose`, `Rep.leftRegularHomEquiv_symm_single`, `QuaternionAlgebra.imJ_swapEquiv_symm_apply`, `PowerSeries.coeff_subst_X_pow`, `DividedPowerAlgebra.dp_sum`, `Algebra.Generators.Hom.equivAlgHom_symm_apply_val`, `MvPolynomial.isHomogeneous_C_mul_X_pow`, `MvPolynomial.tensorEquivSum_C_tmul_one`, `Module.length_eq_zero_iff`, `Finsupp.le_weight_of_ne_zero`, `MvPolynomial.map_iterateFrobenius_expand`, `MvPolynomial.vars_pow`, `AntivaryOn.sub_mul_sub_nonpos`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn`, `sub_mul_sub_pos_iff`, `Matrix.submatrixEquivInvertibleEquivInvertible_apply`, `MDifferentiableWithinAt.clm_postcomp`, `boole_smul`, `geom_sum_pos`, `Valuation.norm_eq_zero`, `RatFunc.eval_zero`, `ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear`, `Finsupp.Lex.single_antitone`, `Polynomial.toMvPolynomial_X`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop`, `AddMonoidAlgebra.coeff_finsuppSum`, `HasDerivWithinAt.const_sub`, `ValuativeRel.veq_zero_iff`, `Int.fract_ofNat`, `sameRay_neg_smul_right_iff`, `MeasureTheory.AEEqFun.Integrable.smul`, `RootPairing.RootPositiveForm.exists_pos_eq`, `ArithmeticFunction.pdiv_apply`, `PowerSeries.coe_X`, `HasDerivWithinAt.const_smul`, `ValuationSubring.coe_pointwise_smul`, `Module.Basis.baseChange_repr_tmul`, `WeierstrassCurve.Jacobian.addU_of_Z_eq_zero_left`, `MvPolynomial.hsymm_zero`, `RCLike.ofReal_pos`, `ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity`, `Matrix.charmatrix_one`, `Units.zero_notMem_spectrum`, `Polynomial.zero_isRoot_iff_coeff_zero_eq_zero`, `PointedCone.ofSubmodule_iSup`, `HasDerivWithinAt.hasDerivAt`, `FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card`, `mem_convexHull_iff_exists_fintype`, `MvPolynomial.sumAlgEquiv_apply`, `ContinuousLinearMap.opNorm_mul_apply_le`, `Algebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one`, `HasFPowerSeriesAt.tendsto_partialSum`, `circleAverage_log_norm_factorizedRational`, `RCLike.wInner_zero_left`, `Matrix.posSemidef_iff_dotProduct_mulVec`, `ZSpan.repr_fract_apply`, `ContinuousLinearMap.orthogonal_range`, `NormedDivisionRing.toNormSMulClass`, `IsLocalization.isInteger_zero`, `Basis.mem_ideal_iff`, `Matrix.Pivot.listTransvecCol_mul_last_row`, `HasFiniteFPowerSeriesAt.add`, `Matrix.GeneralLinearGroup.val_inv_scalar_apply`, `Multiset.toFinsupp_eq_iff`, `HasFPowerSeriesAt.hasDerivAt`, `Finset.prod_boole`, `CStarAlgebra.nonneg_iff_eq_star_mul_self`, `hasDerivWithinAt_congr_set'`, `ArithmeticFunction.LSeriesSummable_zeta_iff`, `Finsupp.mem_span_range_iff_exists_finsupp`, `MeromorphicOn.min_divisor_le_divisor_add`, `Algebra.Generators.ker_comp_eq_sup`, `MvPolynomial.degreeOf_C_mul_le`, `AnalyticOnNhd.eq_zero_or_eq_zero_of_mul_eq_zero`, `GradedTensorProduct.tmul_coe_mul_zero_coe_tmul`, `smul_div₀'`, `PointedCone.minTensorProduct_map_le`, `instContMDiffVectorBundleOfNatWithTopENat_1`, `Polynomial.mem_roots_map`, `Algebra.TensorProduct.basis_repr_symm_apply`, `Rep.indCoindIso_inv_hom_toLinearMap`, `PolynomialLaw.zero_smul`, `instSymmEqInnerOfNat`, `IsNilpotent.map_iff`, `algebraicIndependent_subtype`, `ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic`, `FreeCommRing.isSupported_zero`, `LaurentSeries.instLaurentSeriesComplete`, `LinearMap.polyCharpoly_map_eq_charpoly`, `MonomialOrder.degree_add_eq_right_of_lt`, `Matrix.isAdjMatrix_iff_hadamard`, `HasFDerivAt.linear_multilinear_comp`, `MvPolynomial.coeffsIn_eq_span_monomial`, `HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap`, `AddMonoidAlgebra.sup_support_pow_le`, `Matrix.num_one`, `Odd.zpow_neg_iff`, `MvPolynomial.sumToIter_Xr`, `instIsCancelMulZero`, `MvPowerSeries.killCompl_X_eq_zero`, `TestFunction.fderivCLM_apply_of_gt`, `ContinuousMapZero.toContinuousMapHom_apply`, `SimpleGraph.incMatrix_transpose_mul_diag`, `LinearMap.polyCharpoly_monic`, `Orthonormal.inner_finsupp_eq_zero`, `Polynomial.natDegree_freeMonic`, `Quaternion.self_add_star`, `Algebra.Generators.ofComp_toAlgHom_monomial_sumElim`, `Quaternion.normSq_def`, `hasDerivWithinAt_const_add_iff`, `Quaternion.continuous_coe`, `Finsupp.single_mem_span_single`, `KaehlerDifferential.quotKerTotalEquiv_symm_apply`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `LaurentSeries.coeff_zero_of_lt_intValuation`, `Quaternion.imK_one`, `NNRat.cast_nonpos`, `ContinuousLinearMap.spectralRadius_eq_nnnorm`, `finsuppTensorFinsuppLid_apply_apply`, `IsLocalization.integerNormalization_eval₂_eq_zero`, `HasCompactSupport.mul_left`, `MeasureTheory.convolutionExistsAt_iff_integrable_swap`, `MvPolynomial.exists_finset_rename₂`, `Metric.unitBall.coe_mul`, `Hyperreal.omega_pos`, `LaurentPolynomial.invert_apply`, `self_eq_inv₀`, `NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop`, `Representation.LinearizeMonoidal.η_ε`, `LinearIndependent.repr_ker`, `CliffordAlgebra.contractRight_one`, `ArithmeticFunction.cardDistinctFactors_mul`, `Matrix.charpoly.univ_natDegree`, `Representation.LinearizeMonoidal.lTensor_comp_δ`, `WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero`, `MvPolynomial.algebraMap_eq`, `Rat.cast_lt_zero`, `Matrix.Pivot.reindex_exists_list_transvec_mul_mul_list_transvec_eq_diagonal`, `Quaternion.coe_commute`, `MvPolynomial.algebraicIndependent_X`, `Representation.leftRegularTensorTrivialIsoFree_apply_single_tmul_single`, `MvPolynomial.eval_toMvPolynomial`, `Int.fract_eq_self`, `Finset.support_prod_subset`, `Quaternion.coe_injective`, `StarOrderedRing.nonneg_iff`, `CliffordAlgebraDualNumber.equiv_ι`, `Algebra.Presentation.algebraTensorAlgEquiv_symm_relation`, `WeierstrassCurve.Projective.Point.zero_def`, `HahnSeries.single_div_single`, `Cardinal.toENatAux_eq_zero`, `Algebra.Generators.aeval_val_eq_zero`, `ContinuousLinearMap.spectrum_eq`, `Matrix.blockTriangular_inv_of_blockTriangular`, `MvPolynomial.coeffsIn_pow`, `MvPolynomial.sum_C`, `EuclideanDomain.xgcd_zero_left`, `CanonicallyOrderedAdd.pow_pos`, `Polynomial.trailingDegree_one`, `le_isUnit_iff_zero_notMem`, `Polynomial.algebraMap_hahnSeries_injective`, `Subring.center.smulCommClass_left`, `MvPolynomial.totalDegree_one`, `Matrix.diagonalInvertibleEquivInvertible_symm_apply`, `Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg`, `MvPowerSeries.constantCoeff_X`, `AddMonoidAlgebra.support_divOf`, `FiniteField.sum_pow_units`, `Ideal.span_eq_bot`, `tendsto_inv_nhdsLT_zero`, `LaurentSeries.valuation_surjective`, `Matrix.PosSemidef.dotProduct_mulVec_zero_iff`, `HasStrictDerivAt.fun_sub`, `MvPolynomial.esymmAlgHom_apply`, `ContinuousLinearMap.isPositive_iff`, `LaurentSeries.valuation_coe_ratFunc`, `MvPolynomial.monomial_eq`, `HasDerivWithinAt.star`, `Matrix.trace_mul_single`, `Polynomial.isNilpotent_C_iff`, `WeierstrassCurve.Jacobian.dblZ_of_Y_eq`, `Matrix.pow_row_eq_zero_of_le`, `Polynomial.cyclotomic_nonneg`, `ZMod.lift_injective`, `Module.isTorsionFree_iff_smul_eq_zero`, `Order.krullDim_pos_iff_of_orderTop`, `prod_indicator`, `QuaternionAlgebra.coe_basisOneIJK_repr`, `Representation.LinearizeMonoidal.δ_apply_single`, `Finset.prod_eq_zero`, `MvPolynomial.homogeneousSubmodule_eq_finsupp_supported`, `Function.locallyFinsuppWithin.restrict_posPart`, `MeromorphicOn.extract_zeros_poles`, `MvPolynomial.aeval_eq_eval₂Hom`, `Nat.factorizationEquiv_symm_apply_coe`, `Quiver.Path.weightOfEPs_nonneg`, `preNormEDS'_zero`, `CategoryTheory.Free.lift_map_single`, `HasDerivAtFilter.prodMk`, `cfcₙAux_mem_range_inr`, `ContinuousLinearMap.norm_bilinearRestrictScalars`, `RCLike.inv_pos`, `MonoidAlgebra.supported_eq_map`, `Nat.totient_eq_prod_factorization`, `PiTensorProduct.liftIsometry_apply_apply`, `ContinuousMultilinearMap.prodL_symm_apply`, `MvPolynomial.vars_C`, `IsFormallyReal.eq_zero_of_add_right`, `LinearIndependent.eq_zero_of_pair'`, `FractionalIdeal.spanSingleton_eq_zero_iff`, `MvPolynomial.rename_prod_mk_eval₂`, `Ring.KrullDimLE.isNilpotent_iff_mem_nonunits`, `Matrix.posDef_natCast_iff`, `Matrix.mem_glpos`, `nonneg_of_mul_nonpos_right`, `Complex.UnitDisc.re_zero`, `Nat.factorization_div`, `AlgebraicIndependent.aevalEquivField_apply_coe`, `MvPolynomial.IsSymmetric.smul`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear`, `HasDerivAt.sum`, `WeierstrassCurve.Projective.neg_of_Z_eq_zero`, `MvPolynomial.aeval_C`, `ProbabilityTheory.covarianceBilin_map`, `MvPolynomial.support_map_subset`, `MonoidAlgebra.ofCoeff_sum`, `ArithmeticFunction.IsMultiplicative.map_prod`, `IsTranscendenceBasis.mvPolynomial`, `Set.Ico.coe_mul`, `Ideal.span_zero`, `Nat.factorization_choose_eq_zero_of_lt`, `cfcₙ_norm_sq_nonneg`, `HahnSeries.inv_def`, `Cardinal.ofENat_pos`, `AnalyticOnNhd.sum_divisor_le`, `HasFPowerSeriesOnBall.prod`, `Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top`, `Unitization.nnnorm_eq_sup`, `WithBot.instMulPosReflectLT`, `one_div_pos`, `Matrix.IsPrimitive.nonneg`, `Set.Nonempty.div_zero`, `HasFPowerSeriesWithinOnBall.neg`, `IsDiscreteValuationRing.addVal_eq_top_iff`, `centralBinom_factorization_small`, `PointedCone.ofSubmodule_inf`, `multiplicity_zero_eq_zero_of_ne_zero`, `Matrix.Represents.one`, `WeierstrassCurve.b₄_of_isCharTwoJNeZeroNF`, `MvPolynomial.toMvPowerSeries_pUnitAlgEquiv`, `Cubic.degree_of_d_eq_zero'`, `Module.End.eigenspace_zero`, `MvPolynomial.transcendental_polynomial_aeval_X`, `MvPolynomial.pderiv_map`, `PadicInt.fwdDiff_mahlerSeries`, `Polynomial.coeff_list_sum`, `IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite`, `ENat.sub_top`, `Right.inv_pos`, `Nat.prod_pow_factorization_choose`, `Int.Ioc_filter_dvd_eq`, `Polynomial.smeval_monomial`, `ContinuousLinearMap.bilinearComp_zero_left`, `PowerSeries.IsWeierstrassDivisorAt.mod_zero`, `HasStrictDerivAt.finCons`, `CategoryTheory.Mat.id_apply_of_ne`, `ContinuousLinearMap.nnnorm_smulRight_apply`, `WeierstrassCurve.Jacobian.eval_polynomial`, `Matrix.blockDiagonal_pow`, `NoZeroSMulDivisors.isReduced`, `hasFPowerSeriesWithinOnBall_pi_iff`, `Quaternion.re_neg`, `inv_lt_zero`, `Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff`, `Polynomial.degree_lt_iff_coeff_zero`, `HasDerivAt.fun_smul`, `hasDerivAt_zero`, `div_pos_iff`, `SchwartzMap.fderivCLM_fourier_eq`, `MvPowerSeries.coeff_invOfUnit`, `IsLocalization.mk'_eq_zero_iff`, `IsDiscreteValuationRing.toWithBotNat_eq_bot_iff`, `Representation.linearizeOfMulActionIso_symm_apply`, `MonoidWithZeroHom.val_mrange_zero`, `Quaternion.re_im`, `Quaternion.imI_intCast`, `exists_pos_mul_lt`, `MvPolynomial.aeval_comp_expand`, `Polynomial.toLaurent_one`, `Metric.unitBall.instIsRightCancelMulZero`, `Algebra.Generators.naive_σ`, `Rat.cast_pos_of_pos`, `arithGeom_zero_eq_mul_div`, `PointedCone.dual_le_dual`, `AlgebraicIndependent.aevalEquiv_apply_coe`, `Quaternion.star_mul_eq_coe`, `MvPolynomial.esymm_eq_sum_monomial`, `Polynomial.homogenize_monomial_of_lt`, `SchwartzMap.derivCLM_apply`, `Finsupp.logHeight_eq_log_mulHeight`, `Ring.choose_zero_succ`, `RCLike.map_nonneg_iff`, `zero_mul_eq_const`, `WeierstrassCurve.IsCharThreeJNeZeroNF.a₁`, `WittVector.wittMul_zero`, `MeromorphicOn.negPart_divisor_add_le_max`, `Ideal.eq_zero_of_constant_mem_of_maximal`, `IncidenceAlgebra.zeta_mul_mu`, `MvPolynomial.rename_C`, `Polynomial.div_tendsto_atBot_zero_iff_degree_lt`, `Finsupp.toMultiset_sum`, `minpoly.zero`, `MvPolynomial.HomogeneousSubmodule.gradedMonoid`, `right_mem_segment`, `hasDerivWithinAt_inter'`, `QuaternionAlgebra.coe_mul`, `openSegment_eq_image₂`, `PowerSeries.gaussNorm_eq_zero_iff`, `ArithmeticFunction.mul_zeta_apply`, `WeierstrassCurve.j_eq_zero_of_char_three`, `FirstOrder.realize_genericPolyMapSurjOnOfInjOn`, `HasDerivWithinAt.scomp_hasDerivAt`, `TensorPower.gOne_def`, `MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc'`, `WeierstrassCurve.Jacobian.dblXYZ_of_Z_eq_zero`, `MDifferentiableOn.clm_precomp`, `TensorPower.one_mul`, `Multiset.toDFinsupp_injective`, `Nat.factorization_prime_le_iff_dvd`, `CompositionAsSet.blocks_sum`, `Matrix.invOf_mul_cancel_right`, `MvPolynomial.eval₂_mul_C`, `DualNumber.commute_eps_right`, `MonomialOrder.degree_lt_of_left_ne_zero_of_degree_mul_lt`, `StandardEtalePresentation.aeval_val_equivMvPolynomial`, `hasDerivAt_exp_smul_const_of_mem_ball'`, `LaurentPolynomial.degree_C_ite`, `ContinuousMap.linearIsometryBoundedOfCompact_apply_apply`, `AddAction.minimalPeriod_pos`, `IsPrimitiveRoot.geom_sum_eq_zero`, `Complex.UnitDisc.coe_zero`, `Polynomial.smul_C`, `NNReal.tendsto_inverse_atTop_nhds_zero_nat`, `Polynomial.mem_rootSet'`, `Matrix.diagonal_kronecker_diagonal`, `hasDerivAtFilter_finCons`, `Nat.sum_divisors`, `ContinuousLinearMap.adjoint_comp`, `PointedCone.mem_closure`, `affineHomeomorph_image_Ioo`, `iteratedFDeriv_zero_eq_comp`, `HasStrictDerivAt.prodMk`, `hasFTaylorSeriesUpToOn_succ_iff_left`, `conjugate_nonneg'`, `LaurentSeries.valuation_compare`, `HasDerivWithinAt.mul_const`, `LinearOrderedField.smul_Ici`, `mem_segment_iff_div`, `HasCompactSupport.hasDerivAt_convolution_left`, `SkewMonoidAlgebra.isScalarTower_self`, `HahnSeries.coeff_mul_right'`, `OrthogonalIdempotents.mul_eq`, `IsSMulRegular.not_zero`, `MvPolynomial.instFiniteOfIsEmpty`, `Hyperreal.tendsto_atBot_iff`, `Nat.prod_primeFactors_prod_factorization`, `MvPolynomial.C_neg`, `WeierstrassCurve.Projective.Z_eq_zero_of_equiv`, `HasDerivWithinAt.cexp`, `PointedCone.subset_dual_flip_iff_subset_dual`, `MvPolynomial.weightedHomogeneousComponent_eq_zero`, `MvPolynomial.aevalTower_comp_toAlgHom`, `MvPowerSeries.HasSubst.zero`, `MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection`, `Nat.one_le_ceil_iff`, `Function.locallyFinsuppWithin.logCounting_mono`, `deriv_clm_apply`, `Matrix.inv_fromBlocks_zero₂₁_of_isUnit_iff`, `MvPowerSeries.X_inv`, `Height.logHeight₁_zero`, `MvPowerSeries.killCompl_monomial_eq_zero`, `ArithmeticFunction.cardFactors_zero`, `Matrix.matrixOfPolynomials_blockTriangular`, `HahnSeries.leadingCoeff_one`, `CStarAlgebra.nonneg_iff_eq_mul_star_self`, `Even.zpow_pos_iff`, `SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left`, `WeierstrassCurve.IsCharTwoJNeZeroNF.a₄`, `MvPolynomial.coeToMvPowerSeries.ringHom_apply`, `Metric.unitClosedBall.coe_one`, `HasFPowerSeriesWithinOnBall.add`, `MvPolynomial.restrictSupport_add`, `Rep.linearization_obj_V`, `MvPolynomial.eval₂_X_pow`, `Matrix.mul_invOf_cancel_left`, `isAlgebraic_zero`, `NoZeroDivisors.to_isCancelMulZero`, `AffineMap.hasStrictDerivAt`, `MvPolynomial.zeroLocus_span`, `MvPolynomial.instIsCancelMulZeroOfIsCancelAdd`, `QuadraticMap.apply_linearCombination'`, `IsGaloisGroup.smul_eq_self`, `InnerProductSpace.toLinearMap_rankOne`, `ContinuousLinearMap.comp_hasFPowerSeriesOnBall`, `HasDerivWithinAt.Ioi_of_Ici`, `mem_doublyStochastic`, `MvPolynomial.coeffs_map`, `LaurentPolynomial.smeval_one`, `ContinuousLinearMap.adjointAux_inner_right`, `Int.ceil_pos`, `HasDerivWithinAt.Ioi_iff_Ioo`, `VectorField.mpullback_mfderivWithin_apply_smul`, `MvPolynomial.totalDegree_monomial_le`, `Convex.mem_Icc`, `Finset.subConst_empty_right`, `Quaternion.normSq_neg`, `Cubic.natDegree_of_zero`, `Nat.factorization_pow_self`, `Order.krullDim_eq_zero`, `MvPowerSeries.totalDegree_truncFinset`, `MvPolynomial.IsHomogeneous.rename_isHomogeneous`, `prod_indicator_const`, `HasStrictFDerivAt.clm_apply`, `mul_eq_zero_comm`, `Representation.linearizeMap_single`, `Polynomial.aroots_monomial`, `Algebra.norm_eq_zero_iff'`, `WittVector.polyOfInterest_vars_eq`, `ContDiffMapSupportedIn.fderivLM_apply`, `InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular'`, `Module.Basis.toMatrix_isUnitSMul`, `Polynomial.aroots_X_pow`, `Even.intCast_zmod_two`, `CFC.sqrt_eq_cfc`, `IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end`, `continuousMultilinearCurryRightEquiv_symm_apply'`, `NormedAlgebra.Real.exists_isMonicOfDegree_two_and_aeval_eq_zero`, `ProperCone.mem_bot`, `Filter.tendsto_div_const_atTop_iff_neg`, `InnerProductSpace.Core.inner_self_of_eq_zero`, `Polynomial.degree_le_zero_iff`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply`, `WeierstrassCurve.Jacobian.map_polynomial`, `HahnSeries.C_mul_eq_smul`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom`, `RingEquiv.zeroRingProd_apply`, `Finsupp.linearCombination_linearCombination`, `MvPolynomial.mapEquiv_trans`, `LaurentPolynomial.single_zero_one_eq_one`, `HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos`, `MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop`, `Module.Relations.Solution.IsPresentation.desc_comp_π`, `Matrix.diagonal_hadamard_diagonal`, `list_sum_pow_char`, `hasEigenvalue_toLin'_diagonal_iff`, `ContDiffMapSupportedIn.continuousSMul`, `Matrix.circulant_single`, `Matrix.cRank_zero`, `ContDiffMapSupportedIn.structureMapLM_zero_injective`, `toSpanSingleton_deriv`, `HahnModule.one_smul'`, `MvPolynomial.isNoetherianRing`, `Polynomial.coeff_eq_zero_of_natDegree_lt`, `MvPolynomial.constantCoeff_comp_C`, `Even.natCast_zmod_two`, `MvPolynomial.pderiv_inr_universalFactorizationMap_X`, `MvPolynomial.degrees_zero`, `Subalgebra.list_sum_mem`, `CStarAlgebra.isStrictlyPositive_iff_eq_star_mul_self`, `HasDerivWithinAt.fun_add`, `LinearOrderedField.inducedMap_nonneg`, `MvPolynomial.IsHomogeneous.mul`, `LinearMap.isStarProjection_toContinuousLinearMap_iff`, `ZNum.of_to_int`, `MeromorphicOn.divisor_smul`, `MvPolynomial.sumAlgEquiv_symm_apply`, `WeierstrassCurve.j_eq_zero_iff_of_char_two'`, `Matrix.natCast_mulVec`, `Matrix.mem_unitaryGroup_iff'`, `Complex.UnitDisc.tendsto_pow_atTop_nhds_zero`, `LucasLehmer.X.one_snd`, `Set.encard_pos`, `Order.krullDim_pos_iff_of_orderBot`, `iteratedDerivWithin_eq_equiv_comp`, `NonUnitalStarSubalgebra.instNoZeroDivisors`, `AddMonoidAlgebra.coeffAddEquiv_apply`, `IsNilpotent.pow_iff_pos`, `MvPolynomial.eval₂_comp`, `RatFunc.single_one_eq_pow`, `Matrix.vecMulᵣ_eq`, `HasDerivAt.const_add`, `MvPolynomial.weightedHomogeneousComponent_C_mul`, `exists_pow_btwn`, `MonomialOrder.leadingCoeff_zero`, `Nat.digit_sum_le`, `MvPolynomial.eval₂_pUnitAlgEquiv_symm`, `WeierstrassCurve.Jacobian.negAddY_self`, `TensorProduct.gradedMul_algebraMap`, `Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul`, `IsAdjoinRootMonic.coeff_one`, `NonnegSpectrumClass.nonneg_of_mem_quasispectrum`, `iteratedFDerivWithin_two_apply`, `extDerivWithin_smul`, `QuaternionAlgebra.re_swapEquiv_apply`, `Nat.factorizationEquiv_apply`, `CongruenceSubgroup.Gamma1_to_Gamma0_mem`, `ContDiffMapSupportedIn.seminorm_postcompLM_le`, `Polynomial.eval₂_mul_eq_zero_of_right`, `MeasureTheory.integrable_smul_iff`, `Submonoid.mem_closure_range_iff`, `HahnSeries.SummableFamily.powers_toFun`, `DoubleCentralizer.coe_fst`, `Filter.Tendsto.cfc_nnreal`, `WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero`, `HasDerivAt.prodMk`, `HasStrictFDerivAt.fun_smul`, `MvPolynomial.dvd_C_iff_exists`, `Finsupp.lift_symm_apply`, `Algebra.Generators.ker_eq_ker_aeval_val`, `MulChar.map_nonunit`, `MvPolynomial.instIsPushout_1`, `DirichletCharacter.apply_eq_toArithmeticFunction_apply`, `IsPrimitiveRoot.zero`, `MulEquiv.isCancelMulZero_iff`, `Differential.logDeriv_eq_zero`, `tendsto_pow_atTop_nhds_zero_of_lt_one`, `MvPowerSeries.coeff_zero_X`, `ascPochhammer_zero_eval_zero`, `WeierstrassCurve.Projective.negMap_of_Z_eq_zero`, `AddMonoidAlgebra.coeff_injective`, `Mathlib.Tactic.Linarith.eq_of_eq_of_eq`, `Matrix.diagonalInvertibleEquivInvertible_apply`, `Subring.closure_singleton_zero`, `WittVector.wittNeg_zero`, `norm_cfcₙ_one_sub_one_add_inv_lt_one`, `not_squarefree_zero`, `NumberField.mixedEmbedding.latticeBasis_repr_apply`, `Submodule.adjoint_orthogonalProjection`, `ZMod.LFunction_apply_zero_of_even`, `Rat.cast_zero`, `Algebra.Generators.ker_ofAlgHom`, `continuousOn_cfcₙ_nnreal`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_add_of_squarefree`, `FreeCommRing.restriction_of`, `MvPolynomial.mul_monomial_mem_coeffsIn`, `ContinuousMapZero.instCStarRing`, `MvPolynomial.IsHomogeneous.sum`, `MonoidAlgebra.single_zero`, `QuaternionAlgebra.eq_re_iff_mem_range_coe`, `PowerSeries.heval_unit`, `CurveIntegrable.smul`, `Multiset.toDFinsupp_le_toDFinsupp`, `Units.inv_neg`, `IsDomain.toIsCancelMulZero`, `Subalgebra.coe_eq_zero`, `Finset.mulConst_empty_right`, `MvPolynomial.supported_empty`, `MvPolynomial.C_mem_pow_idealOfVars_iff`, `Multiset.toDFinsupp_toMultiset`, `Module.Basis.ext_elem_iff`, `CompleteOrthogonalIdempotents.pair_iff'ₛ`, `Polynomial.isUnit_iff_degree_eq_zero`, `ContinuousLinearMap.hasFDerivAt_of_bilinear`, `cfcₙHom_continuous`, `pos_invOf_of_invertible_cast`, `EuclideanDomain.gcd_eq_zero_iff`, `Polynomial.degree_pos_of_aeval_root`, `FormalMultilinearSeries.min_radius_le_radius_add`, `hasStrictDerivAt_one`, `multisetProd_apply_eq_zero'`, `instIsAlgebraicMvPolynomialOfNoZeroDivisors_1`, `Unitization.instNormOneClass`, `instIsContMDiffRiemannianBundleOfNatWithTopENat`, `Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply`, `LinearOrderedField.smul_Ioi`, `nilpotent_iff_mem_prime`, `ArithmeticFunction.cardDistinctFactors_one`, `HasDerivWithinAt.of_isLittleO`, `isLeftRegular_iff_right_eq_zero_of_mul`, `MvPolynomial.esymmPart_zero`, `Algebra.Generators.toExtension_algebra₁`, `KaehlerDifferential.mvPolynomialBasis_repr_D`, `Polynomial.modByMonic_X`, `Matrix.vecMulVec_eq_zero`, `LieModule.instIsNilpotentSubtypeMemLieSubmoduleGenWeightSpaceOfNatForallOfIsNoetherian`, `zero_mem_nonunits`, `ContinuousLinearMap.closed_range_of_antilipschitz`, `Rep.η_def`, `ArithmeticFunction.carmichael_eq_exponent'`, `MonomialOrder.sPolynomial_monomial_mul'`, `LieModule.trace_toEnd_genWeightSpaceChain_eq_zero`, `LinearMap.IsPositive.inner_nonneg_right`, `HasDerivAt.div_const`, `HasDerivAt.scomp_of_eq`, `nilradical_eq_bot_iff`, `Matrix.diagonal_hadamard_eq_diagonal_iff`, `HahnSeries.coeff_toMvPowerSeries`, `AddMonoidAlgebra.supportedEquivFinsupp_symm_apply_coe_apply`, `Asymptotics.isLittleOTVS_iff_tendsto_inv_smul`, `Commute.isNilpotent_finsum`, `Representation.LinearizeMonoidal.μ_toLinearMap`, `Polynomial.map_rootOfSplits'`, `Ring.not_isUnit_iff_inverse_eq_zero`, `FirstOrder.Field.model_hasChar_of_charP`, `ContDiffMapSupportedIn.continuous_iff_comp_order_le`, `LaurentSeries.coe_range_dense`, `InnerProductSpace.inner_gramSchmidtOrthonormalBasis_eq_zero`, `MonoidAlgebra.mapDomainRingEquiv_apply`, `WeierstrassCurve.Projective.equiv_zero_of_Z_eq_zero`, `IsCancelMulZero.of_faithfulSMul`, `ContinuousAlternatingMap.curryLeft_add`, `hasFDerivAt_integral_of_dominated_of_fderiv_le`, `Polynomial.mem_aroots`, `HasFPowerSeriesAt.pi`, `MvPolynomial.pderiv_eq_zero_of_notMem_vars`, `Multiset.toDFinsupp_singleton`, `WittVector.map_frobeniusPoly`, `AddMonoidAlgebra.sup_support_add_le`, `Representation.LinearizeMonoidal.μ_leftUnitor`, `Unitization.quasispectrum_eq_spectrum_inr'`, `Nonneg.noZeroDivisors`, `Set.Ioo.pos`, `Polynomial.eraseLead_coeff_natDegree`, `Nat.factorization_eq_card_pow_dvd`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn'`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply`, `hasStrictDerivAt_pi`, `MvPolynomial.sum_eval_eq_zero`, `MvPolynomial.support_divMonomial`, `ZNum.cast_mul`, `ContDiff.hasStrictDerivAt`, `zero_le'`, `SameRay.exists_pos`, `cfcₙHomSuperset_continuous`, `CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq`, `HasFDerivWithinAt.smul`, `MvPolynomial.le_degrees_add_right`, `MvPolynomial.weightedTotalDegree'_zero`, `Polynomial.coeff_zero`, `finsuppTensorFinsuppRid_apply_apply`, `Module.Basis.repr_sum_self`, `WittVector.constantCoeff_wittZSMul`, `MulChar.restrict_apply`, `CauSeq.const_zero`, `WeierstrassCurve.Jacobian.polynomialX_eq`, `linearIndepOn_iff'`, `HasDerivAt.cexp`, `TensorAlgebra.ι_eq_zero_iff`, `OreLocalization.mul_inv_cancel`, `MvPolynomial.aeval_C_comp_left`, `HahnSeries.orderTop_self_sub_one_pos_iff`, `MvPolynomial.transcendental_X`, `RootPairing.Base.toWeightBasis_repr_root`, `ZNum.div_to_int`, `ContinuousAlternatingMap.prodLIE_apply`, `Matrix.invertibleEquivDetInvertible_apply`, `MvPolynomial.msymm_one`, `Submodule.mem_orthogonal_singleton_iff_inner_left`, `MvPolynomial.C_mul_X_pow_eq_monomial`, `MonoidAlgebra.instIsRightCancelMulZeroOfIsCancelAddOfUniqueProds`, `MvPolynomial.totalDegree_mul`, `Finsupp.linearCombination_option`, `ValueDistribution.logCounting_pow_zero`, `SemiconjBy.zero_left`, `HahnSeries.coeff_mul_single`, `SkewMonoidAlgebra.support_single_mul_subset`, `Finset.addConst_empty_left`, `MonoidAlgebra.coeffAddEquiv_apply`, `IsAdjoinRoot.map_self`, `Algebra.leftMulMatrix_mulVec_repr`, `DirectSum.coe_mul_of_apply`, `SimpleGraph.adjMatrix_mulVec_const_apply_of_regular`, `Matrix.adjugate_subsingleton`, `MvPowerSeries.order_monomial`, `IsSumSq.nonneg`, `Submodule.mem_adjoint_iff`, `NormedRing.inverse_add_norm_diff_first_order`, `Polynomial.eval_mul_X_sub_C`, `pow_two_pos_of_ne_zero`, `Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal`, `Rep.standardComplex.d_apply`, `factorization_eq_count`, `isNilpotent_sum`, `Finsupp.linearCombination_eq_fintype_linearCombination`, `Nat.factorization_factorial_mul_succ`, `MvPolynomial.weightedHomogeneousComponent_mem`, `segment_eq_image_lineMap`, `Odd.pow_nonpos`, `KaehlerDifferential.ker_map_of_surjective`, `inner_eq_zero_symm`, `PosNum.divMod_to_nat_aux`, `HahnSeries.SummableFamily.hsum_smul`, `Matrix.invOf_add_mul_mul'`, `IsDiscreteValuationRing.addVal_eq_zero_of_unit`, `Algebra.Norm.Transitivity.mul_auxMat_toSquareBlock_eq`, `PreQuasiregular.val_one`, `Finsupp.basisSingleOne_repr`, `LieModule.zero_genWeightSpace_eq_top_of_nilpotent'`, `MvPolynomial.degrees_rename_of_injective`, `Module.zero_smul`, `ftaylorSeries_zero`, `Finset.dens_eq_zero`, `ValuativeRel.ValueGroupWithZero.mk_eq_zero`, `legendreSym.eq_zero_mod_of_eq_neg_one`, `Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digits`, `PolynomialLaw.range_φ`, `PadicInt.mahlerEquiv_apply`, `MvPolynomial.coeff_add`, `Ring.exists_not_isUnit_of_not_isField`, `ZMod.one_eq_zero_iff`, `ProperCone.dual_empty`, `Polynomial.div_tendsto_atTop_zero_of_degree_lt`, `Orthonormal.orthogonalFamily`, `toIcoMod_zero_one`, `Mathlib.Tactic.Linarith.le_of_eq_of_le`, `Matrix.diagonal_const_mulVec`, `continuousSMul_closedBall_closedBall`, `ContinuousLinearMap.opNorm_flip`, `OrderedFinpartition.neZero_partSize`, `isNilpotent_neg_iff`, `Matrix.Nondegenerate.eq_zero_of_ortho'`, `cfcₙ_apply_pi`, `MvPolynomial.psum_eq_mul_esymm_sub_sum`, `Matrix.cramer_one`, `Hyperreal.infinitesimal_zero`, `LieModule.iSup_ucs_eq_genWeightSpace_zero`, `Matrix.posDef_intCast_iff`, `Odd.pow_neg`, `HasDerivWithinAt.prodMk`, `continuousOn_integral_bilinear_of_locally_integrable_of_compact_support`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight`, `MvPolynomial.eval_C`, `DirectSum.coe_mul_apply_eq_dfinsuppSum`, `MvPolynomial.IsWeightedHomogeneous.C_mul`, `AlgebraicGeometry.Proj.basicOpen_zero`, `FormalMultilinearSeries.radius_compContinuousLinearMap_le`, `Module.Basis.smulTower_repr_mk`, `hasDerivWithinAt_derivWithin_iff`, `Module.Basis.repr_support_subset_of_mem_span`, `MvPolynomial.mapAlgHom_apply`, `Polynomial.taylor_zero`, `hasDerivAt_sub_const_iff`, `MvPolynomial.support_zero`, `Algebra.Generators.cotangentRestrict_mk`, `limit_zero_of_norm_tendsto_zero`, `Valuation.exists_div_eq_of_unit`, `Nat.factorization_ordCompl`, `ENat.toNat_eq_zero`, `ContinuousLinearMap.IsPositive.adjoint_conj`, `Polynomial.comp_zero`, `EisensteinSeries.G2_eq_tsum_cexp`, `WeierstrassCurve.c₄_of_isCharTwoJEqZeroNF_of_char_two`, `Cubic.of_d_eq_zero'`, `Module.DualBases.finite`, `HasDerivAt.div`, `MvPolynomial.optionEquivLeft_monomial`, `Nat.multiplicative_factorization`, `Matrix.det_fromBlocks_zero₂₁`, `IsConformalMap.smul`, `AddMonoidAlgebra.ofCoeff_sum`, `isCoveringMap_npow`, `ArithmeticFunction.IsMultiplicative.mul`, `Associates.mk_eq_zero`, `Irreducible.maximalIdeal_eq_closedBall`, `HasDerivWithinAt.pow`, `CStarAlgebra.directedOn_nonneg_ball`, `Algebra.Generators.cotangentRestrict_bijective_of_basis_kaehlerDifferential`, `PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map`, `Matrix.det_one`, `MeasureTheory.eLpNorm'_const_smul_le`, `mul_eq_zero_iff_right`, `ValuativeRel.posSubmonoid_def`, `eq_zero_of_one_div_eq_zero`, `InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular`, `TensorProduct.gradedComm_one_tmul`, `Matrix.GeneralLinearGroup.val_swap`, `LieModule.maxGenEigenSpace_toEnd_eq_top`, `AddMonoidAlgebra.support_single_mul`, `MvPolynomial.rename_eq_zero_iff_of_injective`, `MvPowerSeries.substAlgHom_monomial`, `Matrix.isNilpotent_iff`, `RootPairing.InvariantForm.apply_root_root_zero_iff`, `Matrix.zero_mul`, `orderOf_eq_zero_iff_eq_zero`, `Polynomial.coeff_homogenize`, `stdSimplex.barycenter_eq_centerMass`, `NNRat.Nonneg.coe_ofScientific`, `Representation.diagonalOneEquivLeftRegular_symm_apply_single`, `FormalMultilinearSeries.derivSeries_eq_zero`, `tendsto_const_mul_zpow_atTop_nhds_iff`, `QuadraticAlgebra.norm_one`, `Matrix.adjugate_one`, `TestFunction.lineDerivCLM_smul`, `Polynomial.div_tendsto_zero_of_degree_lt`, `contDiffAt_zero`, `Matrix.posSemidef_diagonal_iff`, `ContinuousLinearMap.isPositive_iff'`, `Algebra.Generators.H1Cotangent.δ_eq_δAux`, `ContDiffWithinAt.smulRight`, `HasDerivWithinAt.congr_of_eventuallyEq`, `Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat`, `IsSimpleRing.exists_ringEquiv_matrix_divisionRing`, `Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul`, `Mathlib.Meta.Positivity.pos_of_isRat`, `Module.Basis.linearMap_repr_symm_apply`, `MonomialOrder.leadingCoeff_mul_of_isRegular_left`, `Matrix.permMatrix_mem_colStochastic`, `Nat.Prime.emultiplicity_one`, `ContinuousLinearMap.star_eq_adjoint`, `CFC.sqrt_eq_zero_iff`, `KaehlerDifferential.mvPolynomialBasis_repr_comp_D`, `HahnSeries.C_one`, `LieAlgebra.rank_eq_natTrailingDegree`, `MonoidAlgebra.coeff_eq_zero`, `FormalMultilinearSeries.comp_rightInv`, `WittVector.bind₁_onePoly_wittPolynomial`, `RootPairing.rootForm_pos_of_ne_zero`, `ContinuousMultilinearMap.curryLeft_apply`, `ValuationSubring.mem_smul_pointwise_iff_exists`, `Dynamics.netMaxcard_eq_zero_iff`, `map_wittPolynomial`, `ArithmeticFunction.IsMultiplicative.iff_ne_zero`, `MvPowerSeries.coeff_truncFinset_eq_zero`, `OrderIso.withZeroUnits_apply`, `StandardEtalePresentation.toPresentation_algebra_algebraMap_apply`, `MvPolynomial.optionEquivLeft_symm_apply`, `exteriorPower.pairingDual_apply_apply_eq_one_zero`, `HasStrictDerivAt.fun_neg`, `MvPolynomial.exists_coeff_ne_zero`, `IsRealClosed.nonneg_iff_isSquare`, `Valuation.leAddSubgroup_zero`, `DividedPowers.IsSubDPIdeal.dpow_eq`, `HasFPowerSeriesWithinAt.neg`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one`, `ZNum.lt_to_int`, `zero_eq_mul_self`, `ENat.le_one_iff_eq_zero_or_eq_one`, `sub_mul_sub_nonpos_iff`, `CStarAlgebra.isStrictlyPositive_TFAE`, `WithZeroTopology.Iio_mem_nhds_zero`, `continuousOn_cfcₙ_setProd`, `SkewMonoidAlgebra.coeff_mul_antidiagonal_of_finset`, `PointedCone.DualFG.inf`, `jacobiSum_eq_sum_sdiff`, `Nat.factorizationEquiv_inv_apply`, `finsuppTensorFinsuppLid_single_tmul_single`, `ArithmeticFunction.tendsTo_eulerProduct_of_tendsTo`, `AlgebraicGeometry.Scheme.isNilpotent_of_isNilpotent_cover`, `Fintype.prod_boole`, `CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos`, `Projectivization.cross_mk_of_ne`, `AlternatingMap.mkContinuousLinear_norm_le`, `Representation.LinearizeMonoidal.μ_rightUnitor`, `Finsupp.mul_sum`, `Subsemiring.coe_zero`, `ProperCone.hyperplane_separation_of_notMem`, `ArithmeticFunction.LSeriesHasSum_zeta`, `Submonoid.LocalizationMap.isCancelMulZero`, `LieAlgebra.Basis.borelUpper_le_biSup`, `RCLike.ofReal_mul_neg_iff`, `Subring.instNoZeroDivisorsSubtypeMem`, `MvPolynomial.isLocalization_C_mk'`, `AddMonoidAlgebra.support_single_mul_eq_image`, `IsFormallyReal.instIsReduced`, `LieModule.chainTopCoeff_zero`, `Module.Basis.finTwoProd_zero`, `PosNum.divMod_to_nat`, `fderiv_clm_apply`, `MvPolynomial.algebraTensorAlgEquiv_tmul`, `PEquiv.toMatrix_injective`, `listProd_apply_eq_zero`, `DualNumber.eps_pow_two`, `ContinuousAlternatingMap.curryLeftLI_apply`, `antivaryOn_iff_forall_mul_nonpos`, `LinearMap.det_zero''`, `MvPolynomial.vars_map`, `iteratedDerivWithin_id`, `IsSquare.nonneg`, `tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow`, `Set.Icc.one_sub_nonneg`, `algebraMap_nonneg`, `iteratedFDerivWithin_zero_eq_comp`, `HasFiniteFPowerSeriesAt.sub`, `SimpleGraph.vertexCoverNum_bot`, `MvPolynomial.mem_support_coeff_finSuccEquiv`, `QuadraticAlgebra.mk_eq_add_smul_omega`, `Unitization.LE.le.inr`, `Nat.factorization_eq_zero_iff'`, `Ideal.span_insert_zero`, `ContinuousLinearMap.norm_compSL_le`, `MvPolynomial.homogeneousSubmodule_one_eq_span_X`, `HahnSeries.support_mul_subset`, `TestFunction.monoCLM_apply`, `Matrix.commute_diagonal`, `Algebra.Generators.aeval_val_σ'`, `MvPolynomial.support_sub`, `fderivWithin_smul_const`, `Polynomial.mem_rootSet`, `Unitization.inrNonUnitalAlgHom_apply`, `mul_nonpos_of_nonneg_of_nonpos`, `WittVector.wittOne_zero_eq_one`, `AdjoinRoot.aeval_algHom_eq_zero`, `MvPolynomial.eval₂Hom_id_X_eq_join₂`, `HahnSeries.leadingCoeff_mul_of_nonzero`, `Algebra.Generators.Hom.toAlgHom_id`, `Algebra.Generators.Hom.comp_val`, `MvPolynomial.degreeOf_C_mul`, `Matrix.conjTranspose_list_prod`, `AddMonoidAlgebra.ext_iff`, `ContDiffMapSupportedIn.withSeminorms`, `cfc_smul_id`, `Matrix.updateRow_zero_mul_updateCol_zero`, `span_range_eq_top_iff_surjective_finsuppLinearCombination`, `instContMDiffMulOfNatWithTopENatOfContinuousMul`, `Matrix.nondegenerate_def`, `MeasureTheory.withDensityᵥ_smul`, `PointedCone.support_eq`, `MvPolynomial.instIsPushout`, `Matrix.num_intCast`, `ModuleCat.extendScalarsComp_hom_app_one_tmul`, `MvPolynomial.C_injective`, `Affine.Simplex.affineCombination_mem_closedInterior_face_iff_mem_Icc`, `ArithmeticFunction.cardDistinctFactors_pos`, `Pi.linearIndependent_single_one`, `NormMulClass.toNoZeroDivisors`, `Module.Relations.Solution.ofπ_var`, `cfcₙ_nnreal_eq_real`, `MonoidAlgebra.mem_supported`, `NormedSpace.continuousOn_exp`, `AbsoluteValue.tendsto_div_one_add_pow_nhds_zero`, `Matrix.toLinAlgEquiv'_one`, `LinearOrderedField.smul_Ioc`, `MvPolynomial.C_mul`, `CommRingCat.HomTopology.mvPolynomialHomeomorph_apply_fst`, `Mathlib.Tactic.Ring.pow_prod_atom`, `Matrix.toLin_one`, `Metric.unitSphere.coe_div`, `PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1`, `CategoryTheory.Mat.id_apply`, `PowerSeries.coeff_subst_finite`, `Matrix.self_mul_conjTranspose_mul_eq_zero`, `Representation.LinearizeMonoidal.δ_μ`, `spectrum.resolvent_tendsto_cobounded`, `MvPolynomial.esymm_eq_multiset_esymm`, `Algebra.norm_zero`, `ArithmeticFunction.pow_apply`, `MvPolynomial.comap_apply`, `LaurentPolynomial.support_C_mul_T_of_ne_zero`, `ContinuousAlgEquiv.map_eq_zero_iff`, `InnerProductSpace.isIdempotentElem_rankOne_self_iff`, `HasDerivAt.tendsto_slope_zero`, `fderivWithin_continuousLinearEquiv_comp`, `Quaternion.re_snd_dualNumberEquiv`, `PowerSeries.coeff_X_pow`, `Matrix.invOf_fromBlocks_zero₂₁_eq`, `IsAdjoinRoot.map_eq_zero_iff`, `PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top`, `CompleteOrthogonalIdempotents.prod_one_sub`, `Matrix.IsTotallyUnimodular.one_fromCols`, `bernsteinPolynomial.eval_at_0`, `AlgebraicGeometry.AffineSpace.over_over`, `Polynomial.abs_isBoundedUnder_iff`, `Quaternion.re_add`, `MvPolynomial.vars_rename`, `Mathlib.Tactic.Linarith.natCast_nonneg`, `hasDerivAtFilter_pi`, `MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars`, `HahnSeries.order_pow`, `multisetProd_apply_eq_zero`, `AlgebraicGeometry.germ_eq_zero_of_pow_mul_eq_zero`, `ContinuousLinearMap.coe_flipₗᵢ`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty`, `WittVector.bind₁_zero_wittPolynomial`, `Representation.leftRegular_norm_apply`, `nonpos_of_mul_nonneg_left`, `Function.locallyFinsuppWithin.logCounting_le`, `MonoidWithZeroHom.map_ite_zero_one`, `Subsemiring.list_sum_mem`, `Finset.addConst_empty_right`, `FDRep.char_orthonormal`, `ValuativeRel.ValueGroupWithZero.mk_zero`, `Finsupp.weight_sub_single_add`, `cfc_tsub`, `WithBot.instMulPosReflectLE`, `IsTranscendenceBasis.mvPolynomial'`, `MvPowerSeries.coeff_killCompl`, `nilpotencyClass_zero`, `Matrix.invOf_submatrix_equiv_eq`, `MvPolynomial.totalDegree_finset_sum`, `hasDerivAtFilter_const_add_iff`, `TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq`, `SimpleGraph.incMatrix_of_notMem_incidenceSet`, `MeasureTheory.Lp.coe_LpSubmodule`, `Module.Relations.Solution.fromQuotient_comp_toQuotient`, `WithZero.withZeroUnitsEquiv_symm_apply`, `ClassGroup.exists_min`, `Matrix.eq_zero_of_vecMul_eq_zero`, `Matrix.isNilpotent_trace_of_isNilpotent`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `cfcₙ_apply_of_not_and_and`, `WeierstrassCurve.ofJ_0_of_two_eq_zero`, `ArithmeticFunction.carmichael_eq_exponent`, `subsingleton_iff_zero_eq_one`, `mul_ite_zero`, `StieltjesFunction.ae_hasDerivAt`, `CharTwo.add_eq_zero`, `MonomialOrder.lex_lt_iff`, `finsetProd_apply_eq_zero'`, `Filter.Tendsto.const_div_atTop`, `Polynomial.Splits.exists_eval_eq_zero`, `Module.Basis.SmithNormalForm.repr_comp_embedding_eq_smul`, `SimpleGraph.adjMatrix_vecMul_apply`, `Nat.sub_one_mul_factorization_factorial`, `instSMulCommClass_closedBall_closedBall_ball`, `Matrix.det_one_add_replicateCol_mul_replicateRow`, `LeftInvariantDerivation.coe_zero`, `MvPowerSeries.aeval_eq_sum`, `Polynomial.natDegree_eq_zero_iff_degree_le_zero`, `Representation.ind_mk`, `Module.Basis.toDual_linearCombination_right`, `AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp`, `Algebra.Norm.Transitivity.eval_zero_det_det`, `Matrix.zero_zpow_eq`, `MvPolynomial.support_esymm''`, `CanonicallyOrderedAdd.prod_pos`, `ZMod.inv_zero`, `FormalMultilinearSeries.ofScalars_series_eq_zero`, `Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec`, `MvPolynomial.isLocalization`, `stdSimplexEquivIcc_apply_coe`, `ContinuousLinearMap.analyticOn_uncurry_of_multilinear`, `ProbabilityTheory.measure_condCDF_Iic`, `ConvexCone.mem_hull_of_convex`, `FormalMultilinearSeries.changeOrigin_eval`, `HahnSeries.order_C`, `Unitization.nndist_inr`, `MvPolynomial.instExpChar`, `PiTensorProduct.ofFinsuppEquiv'_apply_apply`, `Filter.tendsto_div_const_atBot_iff`, `AddMonoidAlgebra.single_zero_mul_apply`, `SkewMonoidAlgebra.single_eq_algebraMap_mul_of`, `Valuation.Integers.valuation_irreducible_pos`, `prod_indicator_const_apply`, `ContinuousAlternatingMap.norm_alternatizeUncurryFin_le`, `LinearMap.finrank_maxGenEigenspace_zero_eq`, `MvPolynomial.divMonomial_monomial_mul`, `sbtw_lineMap_iff`, `StandardEtalePresentation.toPresentation_val`, `Pi.single_mul_left`, `Matrix.mulVec_surjective_iff_exists_right_inverse`, `LaurentSeries.comparePkg_eq_extension`, `AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen`, `pow_left_strictMonoOn₀`, `CategoryTheory.Free.lift_map`, `Module.Basis.norm_zero`, `LinearMap.det_zero'`, `WeierstrassCurve.Jacobian.Point.zero_point`, `WeierstrassCurve.j_eq_zero_iff_of_char_three`, `AlgebraicGeometry.exists_of_res_zero_of_qcqs`, `Int.log_zero_right`, `AlgebraicGeometry.AffineSpace.homOfVector_toSpecMvPoly`, `MonomialOrder.notMem_support_of_degree_lt`, `Polynomial.mem_rootSet_of_ne`, `Quaternion.mul_coe_eq_smul`, `MvPolynomial.instIsCancelAddOfIsLeftCancelAdd`, `isQuasiregular_iff_isUnit'`, `Nat.ordProj_dvd`, `Num.cmp_to_nat`, `LinearMap.toMatrix_toSpanSingleton`, `LieAlgebra.eq_rootSpace_zero_iff_isCartan`, `IsSelfAdjoint.adjoint_conj`, `not_isRegular_zero`, `OreLocalization.zero_oreDiv'`, `MvPolynomial.divMonomial_zero`, `IsAdjoinRoot.aeval_root_self`, `MonoidWithZeroHom.mk_coe`, `MonoidAlgebra.ext_iff`, `MvPolynomial.sum_monomial_eq`, `Set.Icc.coe_eq_one`, `MvPolynomial.rename_comp_bind₁`, `ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zero`, `CStarModule.inner_self_nonneg`, `HasDerivAt.inner`, `HasFPowerSeriesAt.prod`, `AlgebraicGeometry.exists_pow_mul_eq_zero_of_res_basicOpen_eq_zero_of_isAffineOpen`, `Nonneg.coe_div`, `nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts`, `linearDepOn_iffₛ`, `hasStrictDerivAt_natCast`, `analyticOrderAt_of_not_analyticAt`, `Nonneg.nat_ceil_coe`, `ProbabilityTheory.measurable_measure_condCDF`, `MvPolynomial.degrees_monomial_eq`, `Nat.WithBot.add_eq_zero_iff`, `Real.smul_iSup_of_nonneg`, `MvPolynomial.zeroLocus_top`, `WeierstrassCurve.Jacobian.Point.toAffine_zero`, `FirstOrder.Language.presburger.definable₁_iff_ultimately_periodic`, `MvPolynomial.aeval_id_eq_join₁`, `Polynomial.aeval_zero`, `HasFPowerSeriesAt.isBigO_sub_partialSum_pow`, `SimpleGraph.not_isUniform_zero`, `PowerSeries.IsWeierstrassDivisorAt.eq_zero_of_mul_eq`, `mulLeftLinearMap_zero_eq_zero`, `HahnSeries.SummableFamily.isPWO_iUnion_support_prod_mul`, `MulChar.trivial_apply`, `AlternatingMap.mkContinuousAlternating_norm_le_max`, `Int.fract_eq_zero_or_add_one_sub_ceil`, `cfcₙ_nonneg_iff`, `isCoprime_zero_right`, `Matrix.isHermitian_one`, `MvPolynomial.rename_X`, `Polynomial.eval_smul`, `Height.logHeight_eq_logHeight_restrict_support`, `OrthonormalBasis.sum_rankOne_eq_id`, `QuaternionAlgebra.eq_re_of_eq_coe`, `hasDerivAt_finCons'`, `Quaternion.im_ratCast`, `HasStrictDerivAt.hasDerivAt`, `Num.to_nat_to_int`, `Module.finrank_finsupp_self`, `HahnSeries.isUnit_of_orderTop_pos`, `Matrix.mulVec_empty`, `absorbs_iff_eventually_nhds_zero`, `MvPolynomial.IsSymmetric.C`, `MvPolynomial.pUnitAlgEquiv_monomial`, `Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero`, `HahnModule.support_smul_subset_vadd_support`, `RatFunc.single_zpow`, `DividedPowers.CharP.dpow_of_prime_le`, `MvPolynomial.le_totalDegree`, `MvPolynomial.coeff_monomial`, `isScalarTower_sphere_ball_ball`, `ConditionallyCompleteLinearOrderedField.inducedMap_zero`, `MvPolynomial.coeff_mul_monomial`, `Polynomial.homogenize_sub`, `CliffordAlgebraDualNumber.ι_mul_ι`, `BooleanRing.mul_add_mul`, `iteratedDeriv_id`, `HasFPowerSeriesWithinAt.add`, `Quaternion.imJ_add`, `Multiset.gcd_zero`, `MvPolynomial.eval₂_eq`, `MvPolynomial.degreeOf_zero`, `ContDiffMapSupportedIn.fderivCLM_apply_of_le`, `div_nonneg_iff`, `exteriorPower.basis_repr`, `ContinuousLinearMap.adjoint_inner_right`, `mul_nonneg_iff_neg_imp_nonpos`, `Associates.count_reducible`, `LaurentSeries.valuation_def`, `MvPolynomial.ringHom_ext'_iff`, `MvPolynomial.mem_ideal_span_monomial_image_iff_dvd`, `MvPolynomial.IsHomogeneous.eq_zero_of_forall_eval_eq_zero`, `Algebra.mvPolynomial`, `zero_lt_iff`, `Num.ofZNum'_toNat`, `MatrixEquivTensor.invFun_zero`, `IsRegular.monomial`, `Quaternion.im_sub`, `Matrix.charpoly.univ_map_eval₂Hom`, `isReduced_zmod`, `Profinite.NobelingProof.CC_comp_zero`, `Polynomial.erase_same`, `Commute.isNilpotent_mul_right_iff`, `ClassGroup.finsetApprox.zero_notMem`, `HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt`, `Matrix.PosDef.diagonal`, `hasStrictDerivAt_exp_zero_of_radius_pos`, `MonomialOrder.leadingCoeff_prod_of_mem_nonZeroDivisors`, `Nat.ceil_zero`, `LinearMap.isPositive_iff`, `QuadraticForm.radical_weightedSumSquares`, `ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat`, `Module.Relations.Solution.span_relation_le_ker_π`, `MulEquivClass.toZeroHomClass`, `HasStrictFDerivAt.continuousAlternatingMap_apply_const`, `MvPolynomial.comap_id_apply`, `ContDiffMapSupportedIn.postcompLM_apply`, `LinearMap.isNonneg_def`, `MvPolynomial.aeval_one_tmul`, `HahnSeries.order_one`, `minpoly.eq_iff_aeval_minpoly_eq_zero`, `Algebra.SubmersivePresentation.ofSubsingleton_σ'`, `ContinuousLinearMap.norm_smulRightL_le`, `Nat.factorization_def`, `MvPolynomial.monomial_pow`, `Finsupp.prod_antidiagonal_swap`, `AddMonoidAlgebra.domCongr_apply`, `CliffordAlgebraQuaternion.ofQuaternion_comp_toQuaternion`, `hasFiniteSupport_of_finsum_eq_one`, `MvPolynomial.divMonomial_add_modMonomial_single`, `AffineMap.lineMap_symm`, `MeasureTheory.withDensityᵥ_smul'`, `MvPolynomial.eval_sum`, `Quaternion.imI_natCast`, `Sum.elimZeroRight_apply`, `MonomialOrder.degree_prod`, `star_right_conjugate_nonneg`, `RingHom.isIntegralElem_zero`, `hasDerivAtFilter_const`, `analyticOrderAt_eq_zero`, `SchwartzMap.tsupport_derivCLM_subset`, `MvPowerSeries.IsNilpotent_subst`, `IsBaseChange.basis_repr_comp`, `AddChar.zmod_zero`, `MvPowerSeries.monomial_zero_one`, `IntermediateField.zero_mem`, `LinearOrderedCommMonoidWithZero.toMulPosStrictMono`, `MvPowerSeries.monomial_one_eq`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_on`, `RCLike.normSq_zero`, `hasDerivAt_single`, `Rat.cast_pos`, `Matrix.ofNat_kronecker`, `Polynomial.evalEval_zero`, `PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_isNilpotent`, `MvPolynomial.degreeOf_sub_lt`, `WeierstrassCurve.Projective.addY_self`, `ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomial`, `NNRat.instIsScalarTowerRight`, `ArithmeticFunction.cardFactors_eq_zero_iff_eq_zero_or_one`, `OrthonormalBasis.coe_toBasis_repr_apply`, `Matrix.zero_vecMulVec`, `MvPolynomial.smul_eq_C_mul`, `FunctionField.inftyValuation.C`, `MvPolynomial.eval₂_monomial`, `PowerSeries.coeff_expand`, `Nat.coprime_ordCompl`, `PerfectClosure.zero_def`, `MvPolynomial.counitNat_C`, `Matrix.vecMulVec_mulVec`, `ArithmeticFunction.inv_zetaUnit`, `ContinuousLinearMap.coe_symm_flipMultilinearEquiv`, `Matrix.mul_one`, `Rep.coinvariantsTensorIndHom_mk_tmul_indVMk`, `Cubic.degree_of_b_ne_zero'`, `exists_add_lt_and_pos_of_lt`, `emultiplicity_eq_zero_of_irreducible_ne`, `ZLattice.normBound_spec`, `ProperCone.dual_union`, `isReduced_ofLocalizationMaximal`, `QuadraticMap.apply_linearCombination`, `nnnorm_cfc_nnreal_lt_iff`, `Finsupp.support_mul_subset_left`, `orthonormal_iff_ite`, `HahnSeries.instIsOrderedRingLexOfNoZeroDivisors`, `eq_zero_of_zero_dvd`, `div_pos`, `Polynomial.coe_zero`, `Polynomial.degree_leadingCoeff_inv`, `Polynomial.support_toFinsupp`, `div_nonneg`, `DualNumber.exp_smul_eps`, `Even.zpow_nonneg`, `WeierstrassCurve.twoTorsionPolynomial_discr_of_char_two`, `ArithmeticFunction.coe_zeta_mul_comm`, `WeierstrassCurve.Jacobian.equation_zero`, `MvPolynomial.finSuccEquiv_rename_finSuccEquiv`, `Nat.Prime.pow_dvd_iff_le_factorization`, `Algebra.Presentation.HasCoeffs.relation_mem_range_map`, `FormalMultilinearSeries.radius_prod_eq_min`, `MvPolynomial.rename_expand`, `IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one`, `Quaternion.snd_imI_dualNumberEquiv_symm`, `LaurentPolynomial.smeval_C_mul_T_n`, `AffineIndependent.exists_affineCombination_eq_smul_eq`, `Rep.indToCoind_coindToInd`, `MvPolynomial.homogeneousSubmodule_one_pow`, `neg_one_lt_zero`, `isDomain_iff_noZeroDivisors_and_nontrivial`, `MvPolynomial.coeff_mapRange`, `SkewMonoidAlgebra.coeff_mul_left`, `Algebra.Generators.fg_ker_of_finitePresentation`, `Finsupp.Colex.single_le_iff`, `continuous_cfcₙAux`, `RCLike.neg_iff_exists_ofReal`, `cfcₙ_nonpos_iff`, `MvPolynomial.prod_X_pow`, `WeierstrassCurve.Projective.dblX_of_Z_eq_zero`, `MonoidAlgebra.ofCoeff_smul`, `conjneg_nonneg`, `MvPolynomial.universalFactorizationMapPresentation_algebra_smul`, `MonomialOrder.degree_smul`, `Asymptotics.isLittleO_iff_tendsto`, `Set.indicator_eq_zero_iff_notMem`, `Algebra.FiniteType.instMvPolynomialOfFinite`, `MvPolynomial.IsHomogeneous.sum_X_mul_pderiv`, `MvPolynomial.derivation_C_mul`, `AdjoinRoot.powerBasisAux'_repr_apply_to_fun`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `RCLike.to_complex_nonneg_iff`, `IsAdjoinRootMonic.coeff_apply_coe`, `AlgebraicGeometry.Scheme.basicOpen_zero`, `RCLike.sqrt_zero`, `ContinuousLinearMap.le_of_opNorm₂_le_of_le`, `CFC.eq_zero_of_spectrum_subset_zero`, `Module.Basis.mapCoeffs_repr`, `PointedCone.mem_comap`, `LieAlgebra.Basis.borelLower_eq`, `Filter.tendsto_div_const_atTop_iff`, `Matrix.diagonal_mul_diagonal`, `ContinuousMultilinearMap.currySum_apply`, `Matrix.blockTriangular_transvection`, `MvPolynomial.aeval_sumElim_pderiv_inl`, `IsSumSq.prod`, `WeierstrassCurve.Jacobian.addX_self`, `MvPolynomial.monomial_one_dvd_monomial_one`, `NormSMulClass.toIsBoundedSMul`, `Module.Basis.traceDual_repr_apply`, `TwoSidedIdeal.mem_ker`, `Nat.modEq_eleven_digits_sum`, `AnalyticAt.aeval_mvPolynomial`, `StarOrderedRing.nonneg_iff_spectrum_nonneg`, `Matrix.Module.diagonal_const_smul`, `MvPolynomial.mul_monomial_modMonomial`, `MvPolynomial.eval₂_natCast`, `MvPolynomial.tensorEquivSum_one_tmul_X`, `dotProduct_eq_zero_iff`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `Nat.factorization_factorial_le_div_pred`, `LinearMap.polyCharpoly_coeff_eq_zero_iff_of_basis`, `Matrix.fromCols_one_isTotallyUnimodular_iff`, `HasDerivAt.pow'`, `Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul`, `WeierstrassCurve.Projective.nonsingular_zero`, `Unitization.norm_splitMul_snd_sq`, `EuclideanDomain.gcdA_zero_left`, `NNRat.den_zero`, `Matrix.IsHermitian.star_mul_self_mul_eq_diagonal`, `MvPolynomial.iterToSum_C_C`, `MvPolynomial.mapEquiv_refl`, `pow_pos_iff`, `MvPolynomial.totalDegree_sub_C_le`, `WithAbs.toAbs_zero`, `IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing`, `MvPolynomial.coeffAddMonoidHom_apply`, `discrim_lt_zero`, `Cardinal.zero_eq_ofENat`, `CanonicallyOrderedAdd.mul_pos`, `HahnSeries.ofPowerSeries_apply`, `LieAlgebra.toLieSubmodule_le_rootSpace_zero`, `Valued.toNormedField.setOf_mem_integer_eq_closedBall`, `continuousMultilinearCurryRightEquiv_apply'`, `ValuativeRel.zero_vlt_mul`, `ContinuousLinearMap.flipₗᵢ'_symm`, `WeierstrassCurve.Jacobian.Point.zero_def`, `Nat.sum_sum_digits_eq`, `TestFunction.instLineDerivSMulTopENat`, `MvPolynomial.IsWeightedHomogeneous.coeff_eq_zero`, `MvPolynomial.coeff_X_mul`, `Polynomial.coeff_zero_eq_aeval_zero'`, `PowerSeries.expand_one`, `AddMonoidAlgebra.support_gen_of_gen`, `Matrix.conjTranspose_mul_self_eq_zero`, `Matrix.PosSemidef.trace_nonneg`, `AddMonoidAlgebra.single_mul_apply_aux`, `Polynomial.eval₂_gcd_eq_zero`, `IsLeftCancelMulZero.to_noZeroDivisors`, `antivary_iff_forall_mul_nonpos`, `DivisibleHull.instIsStrictOrderedModuleRat`, `GroupAlgebra.mul_average_left`, `LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero`, `Commute.cfc_nnreal`, `Matrix.l2_opNNNorm_diagonal`, `MvPolynomial.supported_univ`, `WeierstrassCurve.Jacobian.addZ_self`, `Module.Relations.toQuotient_relation`, `MeromorphicOn.negPart_divisor_add_le_add`, `MvPolynomial.isSymmetric_rename`, `Matrix.vecMul_swap_apply`, `inv_antitoneOn_Ioi`, `Polynomial.degree_pos_of_irreducible`, `HasFiniteFPowerSeriesOnBall.hasFDerivAt`, `RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff`, `Module.Flat.exists_factorization_of_comp_eq_zero_of_free`, `MvPolynomial.one_coeffsIn`, `MvPolynomial.mkDerivationₗ_X`, `NNRat.cast_zero`, `MvPolynomial.eval₂_C_mk_eq_zero`, `hasStrictDerivAt_zero`, `Ideal.IsDedekindDomain.emultiplicity_map_eq_zero_of_ne`, `ContinuousAlternatingMap.alternatizeUncurryFin_add`, `OrderIso.mulLeft₀_symm`, `Cubic.degree_of_b_eq_zero'`, `MvPolynomial.mem_degrees`, `AddMonoidAlgebra.mem_supported'`, `ZNum.cast_to_int`, `TrivSqZeroExt.nnnorm_inr`, `Module.Basis.ofZLatticeComap_repr_apply`, `RCLike.normSq_eq_zero`, `cfc_predicate_zero`, `MvPowerSeries.monomial_eq`, `MvPolynomial.universalFactorizationMap_freeMonic`, `ArithmeticFunction.cardFactors_eq_one_iff_prime`, `HasDerivAtFilter.finCons`, `Matrix.permanent_zero`, `WeierstrassCurve.Projective.addZ_neg`, `instIsReducedOfIsSemisimpleRing`, `LaurentSeries.uniformContinuous_coeff`, `Algebra.Generators.Hom.toAlgHom_monomial`, `Mathlib.Meta.Positivity.zpow_zero_pos`, `CanonicallyOrderedAdd.list_prod_pos`, `IsBoundedSMul.of_norm_smul_le`, `ArithmeticFunction.mul_apply`, `Polynomial.homogenize_zero`, `FormalMultilinearSeries.coeff_iterate_fslope`, `Ideal.associatesEquivIsPrincipal_map_zero`, `GenContFract.zero_le_of_contsAux_b`, `HasFPowerSeriesAt.eq_zero`, `MvPolynomial.le_degrees_add_left`, `Finsupp.DegLex.wellFoundedLT`, `WeierstrassCurve.IsCharTwoJEqZeroNF.a₁`, `MonomialOrder.sPolynomial_mem_ideal`, `ContinuousLinearMap.flip_zero`, `FormalMultilinearSeries.leftInv_removeZero`, `Commute.isNilpotent_add`, `MvPolynomial.mem_ideal_of_coeff_mem_ideal`, `DihedralGroup.one_def`, `MvPolynomial.irreducible_of_totalDegree_eq_one`, `ValuativeRel.not_rel_one_zero`, `QuaternionAlgebra.algebraMap_eq`, `MvPolynomial.universalFactorizationMapPresentation_val`, `round_zero`, `Module.projective_def`, `ContDiffMapSupportedIn.fderivCLM_apply`, `Filter.zero_pow_eventuallyEq`, `MvPolynomial.rename_comp_rename`, `DualNumber.lift_apply_inl`, `PadicInt.continuousAddCharEquiv_symm_apply`, `AffineIndependent.eq_zero_of_sum_eq_zero_subtype`, `Finsupp.mem_ideal_span_range_iff_exists_finsupp`, `hasStrictDerivAt_exp_smul_const_of_mem_ball'`, `MonomialOrder.leadingCoeff_sub_of_lt`, `Localization.awayMap_injective_iff`, `HahnSeries.toMvPowerSeries_apply`, `MvPolynomial.coe_expand`, `PEquiv.toMatrix_mul_apply`, `Rep.indResHomEquiv_symm_apply`, `IsSMulRegular.not_zero_iff`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero`, `IsDiscreteValuationRing.addVal_one`, `dotProduct_self_star_eq_zero`, `AddMonoidAlgebra.mem_span_support'`, `Nat.modEq_three_digits_sum`, `TestFunction.fderivCLM_apply`, `CompletelyPositiveMap.map_cstarMatrix_nonneg'`, `PowerSeries.coe_one`, `MvPowerSeries.weightedOrder_zero`, `ContinuousLinearMap.isAdjointPair_inner`, `NonUnitalAlgHom.inr_apply`, `Polynomial.signVariations_eq_eraseLead_add_ite`, `Set.Ico.mk_zero`, `MvPolynomial.aeval_sumElim`, `MvPolynomial.universalFactorizationMapPresentation_σ'`, `Set.Nonempty.zero_div`, `Representation.linearizeMap_toLinearMap`, `posSMulMono_iff_posSMulStrictMono`, `SimpleGraph.adjMatrix_mul_self_apply_self`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `Multiset.toDFinsupp_inter`, `RCLike.instPosMulReflectLE`, `Cubic.natDegree_of_b_ne_zero'`, `Set.Icc.coe_le_one`, `MvPolynomial.aeval_comp_rename`, `SimpleGraph.incMatrix_of_mem_incidenceSet`, `IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing_finite`, `FormalMultilinearSeries.changeOriginSeries_finite_of_finite`, `LinearMap.toMvPolynomial_eval_eq_apply`, `bddBelow_smul_iff_of_pos`, `Quaternion.coe_intCast`, `UnitAddTorus.mFourier_single`, `WithZeroTopology.tendsto_zero`, `IsLocalRing.ResidueField.residue_smul`, `KaehlerDifferential.mvPolynomialBasis_repr_symm_single`, `Ring.ord_one`, `AlgebraicGeometry.exists_appTop_map_eq_zero_of_isLimit`, `Height.mulHeight_sumElim_zero_eq`, `MvPowerSeries.coeff_monomial_ne`, `Rat.toNNRat_zero`, `ArithmeticFunction.coe_zeta_mul_moebius`, `ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction`, `Padic.norm_rat_le_one_iff_padicValuation_le_one`, `emultiplicity_pos_iff`, `zero_notMem_nonZeroDivisorsRight`, `Unitization.splitMul_injective`, `LieAlgebra.IsKilling.traceForm_eq_zero_of_mem_ker_of_mem_span_coroot`, `Function.ExtendByZero.linearMap_apply`, `discrim_lt_zero_of_neg`, `ProbabilityTheory.measure_condCDF_univ`, `Antitone.deriv_nonpos`, `MulHom.single_apply`, `Module.Basis.toMatrix_transpose_apply`, `Num.natSize_to_nat`, `Num.le_to_nat`, `CStarAlgebra.inr_mem_Icc_iff_nnnorm_le`, `MvPolynomial.mem_symmetricSubalgebra`, `ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id`, `Nonneg.Icc_subset_segment`, `MonoidAlgebra.domCongr_support`, `ContDiffMapSupportedIn.continuous_iff_comp`, `Module.finite_finsupp_self_iff`, `WeierstrassCurve.Projective.dblX_of_Y_eq`, `AddMonoidAlgebra.decomposeAux_single`, `Ideal.span_range_eq_span_range_support`, `cfcₙ_eq_cfcₙL`, `QuaternionAlgebra.im_smul`, `DualNumber.lift_op_smul`, `MonomialOrder.degree_mul_of_isRegular_left`, `IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed`, `PowerSeries.order_eq_top`, `MonotoneOn.nnnorm_cfc`, `LaurentPolynomial.degree_eq_bot_iff`, `MvPowerSeries.instNoZeroDivisors`, `analyticAt_inverse_one_sub`, `Cubic.degree_of_c_ne_zero'`, `ArithmeticFunction.isUnit_iff_isUnit_apply_one`, `Metric.unitClosedBall.coe_pow`, `HasStrictDerivAt.div_const`, `HasStrictDerivAt.fun_mul`, `FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite`, `conjugate_pos`, `Algebra.Norm.Transitivity.auxMat_toSquareBlock_ne`, `IsLinearTopology.hasBasis_ideal`, `Polynomial.rootSet_monomial`, `MvPolynomial.support_rename_killCompl_subset`, `Set.integer_valuation_le_one`, `HahnSeries.coeff_toOrderTopSubOnePos_pow`, `CFC.posPart_nonneg`, `Nat.dvd_ordProj_of_dvd`, `TrivSqZeroExt.mul_right_eq_one`, `Mathlib.Tactic.Ring.cast_pos`, `fderivWithin_continuousAlternatingMap_apply`, `Nat.factorization_pow`, `zero_ne_one_or_forall_eq_0`, `PreTilt.map_eq_zero`, `Cubic.degree_of_d_ne_zero'`, `MvPolynomial.eval₂_rename_prod_mk`, `Nat.properDivisors_eq_map_attach_Iio_factorization_prod_pow`, `inv_nonpos`, `AddMonoidAlgebra.ofCoeff_finsuppSum`, `jacobi_cross`, `Quaternion.re_smul`, `Function.support_mul`, `AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe`, `affineHomeomorph_image_Icc`, `OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose`, `Finset.Nonempty.zero_mul`, `HasFPowerSeriesAt.eq_zero_of_eventually`, `SkewMonoidAlgebra.coeff_mul_single_aux`, `Metric.unitClosedBall.instIsCancelMulZero`, `Finsupp.DegLex.le_iff`, `Algebra.IsAlgebraic.rank_fractionRing_mvPolynomial`, `Topology.CWComplex.skeletonLT_zero_eq_empty`, `GenContFract.zeroth_conv'Aux_eq_zero`, `hasStrictFDerivAt_inv'`, `PointedCone.tmul_mem_minTensorProduct`, `Finset.prod_indicator_biUnion_sub_indicator`, `Quaternion.eq_re_iff_mem_range_coe`, `spectrum.nonzero_mul_comm`, `Order.IsMin.height_eq_zero`, `cfcₙL_apply`, `Nat.ordProj_pos`, `MvPolynomial.coeff_linearCombination_X_pow_of_fintype`, `QuaternionAlgebra.coe_algebraMap`, `MvPolynomial.mapAlgHom_coe_ringHom`, `ContinuousOn.cfcₙ_nnreal`, `StarOrderedRing.nonneg_iff_quasispectrum_nonneg`, `MvPolynomial.monomial_sum_one`, `Fin.instNeZeroNatHSubVal_mathlib`, `MvPowerSeries.truncFinset_truncFinset`, `bind₁_wittPolynomial_xInTermsOfW`, `Metric.externalCoveringNumber_pos_iff`, `MonoidAlgebra.mul_apply_right`, `Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff`, `SameRay.exists_pos_left`, `HasDerivAt.scomp_hasDerivWithinAt`, `AlgebraicGeometry.exists_app_map_eq_zero_of_isLimit`, `SchwartzMap.smulLeftCLM_sub`, `Nat.ordCompl_eq_self_iff_zero_or_not_dvd`, `Polynomial.IsRoot.eq_zero`, `SimpleGraph.adjMatrix_dotProduct`, `AbsoluteValue.eq_zero'`, `SchwartzMap.smulLeftCLM_apply_apply`, `Matrix.det_eq_zero_of_column_eq_zero`, `HasStrictDerivAt.add_const`, `IsNilpotent.pow_of_pos`, `Module.Basis.ofZLatticeBasis_repr_apply`, `analyticAt_inv_one_sub`, `Num.cast_mul`, `WeierstrassCurve.j_of_isShortNF_of_char_three`, `Representation.char_orthonormal`, `Matrix.IsHermitian.eigenvalues_eq_zero_iff`, `IsStarProjection.one_sub_mul_self`, `Subgroup.transferTransversal_apply''`, `Matrix.isIrreducible_iff`, `MvPolynomial.schwartz_zippel_sum_degreeOf`, `quasispectrum_eq_spectrum_union_zero`, `NonUnitalStarAlgHom.coe_inr`, `MvPolynomial.isHomogeneous_C`, `Matrix.det_vecMulVec`, `iteratedDeriv_fun_pow_zero`, `SchwartzMap.fourier_fderivCLM_eq`, `NonUnitalAlgHom.coe_zero`, `Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv`, `convexComboPair_zero`, `PointedCone.DualFG.dual_of_fg`, `Nat.prod_primeFactors_invOn_squarefree`, `Set.Nonempty.mul_zero`, `Fintype.linearCombination_apply_single`, `Quaternion.coe_add`, `MulAction.minimalPeriod_pos`, `Algebra.FinitePresentation.out`, `Matrix.aeval_self_charpoly`, `Nat.ordProj_mul`, `ZMod.cast_sub_one`, `Nat.factorization_eq_zero_of_remainder`, `one_div_nonpos`, `Matrix.single_mulVec`, `Matrix.mem_orthogonalGroup_iff'`, `Filter.Tendsto.inv_tendsto_atTop`, `MvPolynomial.rename_leftInverse`, `mem_openSegment_iff_div`, `MvPolynomial.totalDegree_smul_le`, `MulCharClass.map_nonunit`, `Finsupp.sum_mul`, `MvPowerSeries.support_truncFinset_subset`, `ArithmeticFunction.sum_Ioc_sigma0_eq_sum_div`, `iteratedFDeriv_two_apply`, `PointedCone.mem_toConvexCone`, `MonomialOrder.Monic.mul`, `NonUnitalSubring.list_sum_mem`, `ax_grothendieck_of_locally_finite`, `Quaternion.normSq_intCast`, `ValuativeRel.ValueGroupWithZero.lift_zero`, `MvPowerSeries.coeff_truncFinset`, `LieAlgebra.Orthogonal.pso_inv`, `CFC.posPart_eq_self`, `Nat.ofDigits_neg_one`, `Algebra.FiniteType.iff_quotient_mvPolynomial''`, `Metric.unitClosedBall.instContinuousMul`, `Mathlib.Tactic.Ring.intCast_zero`, `Matrix.blockDiagonalRingHom_apply`, `Irreducible.maximalIdeal_pow_eq_closedBall_pow`, `bddAbove_smul_iff_of_pos`, `Algebra.Presentation.quotientEquiv_mk`, `Finsupp.toMultiset_single`, `MvPolynomial.esymmAlgHom_fin_bijective`, `IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C'`, `lp.zeroBasis_repr_symm_apply_coe`, `DirichletCharacter.isMultiplicative_toArithmeticFunction`, `MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero`, `tendsto_inverse_atTop_nhds_zero_nat`, `PresheafOfModules.Sheafify.zero_smul`, `LinearIndependent.eq_zero_of_pair`, `MDifferentiable.clm_precomp`, `MvPolynomial.esymmAlgEquiv_apply`, `convexHull_rangle_single_eq_stdSimplex`, `Set.Icc.mul_le_right`, `MonoidWithZeroHom.map_mul'`, `instIsCancelMulZero_1`, `Metric.unitClosedBall.coe_eq_one`, `Hyperreal.InfinitePos.pos`, `Polynomial.scaleRoots_zero`, `FormalMultilinearSeries.enorm_compContinuousLinearMap_le`, `DirichletCharacter.convolution_mul_moebius`, `AddMonoid.neZero_exponent_of_finite`, `WeierstrassCurve.IsCharNeTwoNF.a₃`, `Polynomial.homogenize_C`, `ContDiffMapSupportedIn.fderivLM_apply_of_le`, `MvPolynomial.eval₂AlgHom_X`, `sameRay_smul_right_iff`, `LaurentSeries.ratfuncAdicComplRingEquiv_apply`, `LinearMap.toMatrixAlgEquiv_apply'`, `AddMonoidAlgebra.sup_support_finset_prod_le`, `MvPolynomial.mem_vanishingIdeal_iff`, `MonomialOrder.degree_add_of_lt`, `CFC.sqrt_map_pi`, `MvPolynomial.mem_vanishingIdeal_singleton_iff`, `FormalMultilinearSeries.le_radius_pi`, `Polynomial.eval₂_primPart_eq_zero`, `MvPowerSeries.coeff_subst_finite`, `MonomialOrder.div`, `Basis.equivFun_symm_single`, `CFC.sqrt_nonneg`, `continuousMultilinearCurryLeftEquiv_symm_apply`, `TwoSidedIdeal.instSMulMemClassMulOpposite`, `IsUnit.integrable_smul_iff`, `hasDerivAt_exp_smul_const'`, `MvPolynomial.weightedTotalDegree'_eq_bot_iff`, `TrivSqZeroExt.exp_def_of_smul_comm`, `isNilpotent_finsum`, `IsIdempotentElem.quasispectrum_subset`, `PowerSeries.IsWeierstrassDivisorAt.div_zero`, `mulLeftLinearMap_eq_zero_iff`, `DoubleCentralizer.instStarModule`, `sq_pos_of_ne_zero`, `AlgebraicGeometry.AffineSpace.SpecIso_inv_over`, `HasStrictDerivAt.finset_prod`, `Finsupp.linearCombination_surjective`, `affineIndependent_def`, `star_nonpos_iff`, `ZMod.toAddCircle_eq_zero`, `LinearMap.BilinForm.isOrtho_def`, `ContinuousMultilinearMap.smulRightL_apply`, `WittVector.mul_polyOfInterest_aux5`, `Multiset.toDFinsupp_lt_toDFinsupp`, `IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply`, `MvPolynomial.scalarRTensor_symm_apply_single`, `IsLocalization.away_fst`, `Matrix.num_eq_zero_iff`, `ENat.floor_eq_zero`, `MvPolynomial.expand_zmod`, `PowerSeries.coeff_heval_zero`, `ArithmeticFunction.natCoe_apply`, `WeierstrassCurve.Projective.X_eq_zero_of_Z_eq_zero`, `PowerSeries.order_ne_zero_iff_constCoeff_eq_zero`, `Order.krullDim_nonneg`, `Polynomial.nextCoeff_eq_zero_of_eraseLead_eq_zero`, `smul_nonneg_iff_pos_imp_nonneg`, `MonomialOrder.lex_le_iff`, `Complex.UnitDisc.star_eq_zero`, `NonUnitalSubsemiring.coe_zero`, `exists_pos_left_iff_sameRay_and_ne_zero`, `NonUnitalRingHom.coe_zero`, `HahnSeries.instIsDomainOfIsCancelAdd`, `LaurentSeries.Cauchy.coeff_eventually_equal`, `sameRay_neg_smul_left_iff`, `AlgebraicIndependent.matroid_closure_of_subsingleton`, `HahnSeries.ofPowerSeries_injective`, `MvPolynomial.aeval_zero'`, `Nat.floor_zero`, `MonoidWithZeroHomClass.toZeroHomClass`, `ContinuousMap.mem_idealOfSet_compl_singleton`, `Module.Basis.prod_repr_inr`, `Filter.Tendsto.div_atBot`, `Multiset.toDFinsupp_union`, `MvPolynomial.weightedTotalDegree_rename_of_injective`, `Quaternion.re_sub`, `isIntegral_zero`, `WeierstrassCurve.Projective.Point.toAffine_zero`, `stdSimplexEquivIcc_symm_apply_coe`, `meromorphicOrderAt_of_not_meromorphicAt`, `ContinuousMap.norm_smul_const`, `Polynomial.aeval_iterate_derivative_of_lt`, `iteratedFDeriv_succ_eq_comp_left`, `MvPolynomial.range_mapAlgHom`, `IsSMulRegular.zero_iff_subsingleton`, `MvPolynomial.counit_C`, `IncidenceAlgebra.prod_mul_prod'`, `Polynomial.resultant_self`, `Matrix.det_eq_zero_of_row_eq_zero`, `ContinuousLinearMap.smul_compLpL`, `AddChar.wInner_cWeight_eq_boole`, `Nonneg.nat_floor_coe`, `VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral`, `LinearOrderedField.smul_Iic`, `MeromorphicOn.AnalyticOnNhd.divisor_apply`, `continuousOn_cfc_nnreal_setProd`, `MvPolynomial.weightedHomogeneousComponent_of_mem`, `QuaternionAlgebra.mul_coe_eq_smul`, `bot_eq_zero''`, `Matrix.TransvectionStruct.reverse_inv_prod_mul_prod`, `ArithmeticFunction.carmichael_mul`, `Finsupp.linearCombination_comp_lmapDomain`, `ContDiffMapSupportedIn.fderivLM_apply_of_gt`, `LinearMap.toMatrix_basis_equiv`, `HasDerivAt.hasDerivAtFilter`, `ContinuousMapZero.nonUnitalStarAlgHom_postcomp_apply`, `EuclideanDomain.lcm_eq_zero_iff`, `WeierstrassCurve.Projective.baseChange_polynomialZ`, `Finsupp.mem_span_image_iff_linearCombination`, `Commute.isNilpotent_mul_right`, `Nat.inv_pos_of_nat`, `MvPowerSeries.WithPiTopology.variables_tendsto_zero`, `HahnSeries.coeff_mul_single_add`, `MvPolynomial.IsHomogeneous.prod`, `algebraMap.coe_zero`, `SimpleGraph.sum_incMatrix_apply_of_notMem_edgeSet`, `Complex.UnitDisc.star_zero`, `OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self`, `MvPowerSeries.order_eq_nat`, `ExteriorAlgebra.basis_mul_of_not_disjoint`, `Nat.factorization_choose_prime_pow`, `HasDerivAt.comp_hasDerivWithinAt_of_eq`, `ContinuousLinearMap.opNorm_mulLeftRight_le`, `Polynomial.degree_cyclotomic_pos`, `Metric.coveringNumber_eq_zero`, `ENat.card_pos_iff_nonempty`, `MvPolynomial.irreducible_sumSMulXSMulY`, `AffineBasis.toMatrix_self`, `Order.coheight_pos`, `Matrix.den_one`, `ZNum.dvd_to_int`, `Cubic.toPoly_eq_zero_iff`, `Mathlib.Tactic.Ring.atom_pf`, `gauge_smul_left`, `LieModule.traceForm_apply_eq_zero_of_mem_lcs_of_mem_center`, `RingInvo.map_eq_zero_iff`, `ClosedSubmodule.orthogonal_closure`, `DualNumber.lift_comp_inlHom`, `ModuleFilterBasis.smul`, `SimpleGraph.edist_eq_zero_iff`, `sign_cases_of_C_mul_pow_nonneg`, `meromorphicOrderAt_const_intCast`, `MvPowerSeries.IsWeightedHomogeneous.coeff_eq_zero`, `MvPolynomial.counitNat_X`, `MonomialOrder.degree_sPolynomial_le`, `Polynomial.degree_pos_of_eval₂_root`, `Polynomial.rootSet_X_pow`, `WeierstrassCurve.a₃_of_isShortNF`, `MonomialOrder.degree_X_add_C`, `PowerSeries.X_pow_dvd_iff`, `exteriorPower.ιMultiDual_apply_nondiag`, `MvPolynomial.eval₂Hom_bind₂`, `Set.Ioc.coe_one`, `MvPolynomial.mem_ideal_span_monomial_image`, `MvPowerSeries.coeff_rename_eq_zero`, `ringKrullDim_eq_zero_of_field`, `CFC.nnrpow_nonneg`, `ContDiffMapSupportedIn.structureMapCLM_zero_injective`, `ArithmeticFunction.carmichael_factorization`, `Matrix.vecMul_self_mul_conjTranspose_eq_zero`, `Finset.box_zero`, `SkewMonoidAlgebra.ringHom_ext'_iff`, `WithVal.ofVal_eq_zero`, `ENat.iInf_eq_zero`, `MvPolynomial.rename_toMvPolynomial`, `Matrix.adjugate_fin_zero`, `Matrix.scalar_apply`, `Polynomial.ofFinsupp_eq_zero`, `MvPolynomial.aeval_rename`, `IsAdjoinRootMonic.coeff_apply_le`, `CStarAlgebra.nonneg_TFAE`, `MonomialOrder.Monic.add_of_lt`, `ContinuousMultilinearMap.piₗᵢ_apply`, `Module.Basis.opNNNorm_le`, `CFC.log_one`, `WittVector.bind₁_frobeniusPolyRat_wittPolynomial`, `MvPolynomial.optionEquivLeft_symm_C_X`, `MvPolynomial.mul_X_modMonomial`, `BilinForm.apply_eq_dotProduct_toMatrix_mulVec`, `ContMDiffWithinAt.clm_precomp`, `Height.logHeight_cons_cons_zero`, `Num.mod_to_nat`, `UniqueFactorizationMonoid.factors_zero`, `Nat.moebius_eq`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply`, `Nat.factorization_choose`, `Polynomial.coeff_C_mul_X_pow`, `strictAntiOn_inv_pos`, `Metric.packingNumber_pos_iff`, `HasDerivAtFilter.comp`, `Num.to_nat_inj`, `Matrix.single_one_vecMul`, `DualNumber.algHom_ext'_iff`, `Matrix.range_diagonal`, `Matrix.mulVec_single`, `MvPolynomial.bind₂_bind₂`, `IsCyclotomicExtension.neZero'`, `HahnSeries.coeff_mul_single_zero`, `dotProduct_diagonal'`, `BooleanRing.mul_one_add_self`, `Module.Relations.toQuotient_map`, `continuousMultilinearCurryFin1_symm_apply`, `PowerSeries.derivative_C`, `HasStrictDerivAt.fun_add`, `Representation.leftRegularMapEquiv_symm_single`, `Cubic.degree_of_c_eq_zero`, `Rat.toNNRat_eq_zero`, `MvPolynomial.IsSymmetric.antitone_supDegree`, `WittVector.aeval_verschiebungPoly`, `complEDS_zero`, `LaurentPolynomial.support_C_mul_T`, `FormalMultilinearSeries.radius_pi_le`, `DualNumber.ideal_trichotomy`, `HasDerivAt.comp_of_eq`, `MvPolynomial.eval₂Hom_bind₁`, `Nat.cast_list_sum`, `Set.zero_div_subset`, `PadicInt.mahlerEquiv_symm_apply`, `Polynomial.eval₂_mul_eq_zero_of_left`, `ContinuousLinearMap.lsmul_flip_apply`, `RootPairing.Base.cartanMatrixIn_mul_diagonal_eq`, `div_neg_of_neg_of_pos`, `PointedCone.isClosed_dual`, `Quaternion.re_ratCast`, `cfc_isStrictlyPositive_iff`, `Module.rankAtStalk_eq_zero_of_subsingleton`, `hasDerivAt_iff_tendsto`, `IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one`, `pos_of_left_mul_lt_le`, `Polynomial.homogenize_X`, `Mathlib.Meta.Positivity.pow_zero_pos`, `notMem_nonZeroDivisors_iff_left`, `ConvexCone.coe_hull_of_convex`, `boole_mul`, `Submodule.mem_span_set_iff_exists_finsupp_le_finrank`, `HasStrictFDerivAt.smul_const`, `Module.Basis.constr_def`, `ArithmeticFunction.abs_moebius_le_one`, `MvPolynomial.finSuccEquiv_X_zero`, `LieModule.Weight.apply_eq_zero_of_isNilpotent`, `MvPolynomial.isJacobsonRing_MvPolynomial_fin`, `Num.gcd_to_nat`, `MvPolynomial.degreeOf_prod_le`, `MonomialOrder.monic_one`, `MvPolynomial.degreeOf_eq_natDegree`, `Matrix.eq_zero_of_forall_pow_sum_mul_pow_eq_zero`, `Matrix.PosDef.intCast`, `MvPowerSeries.support_expand_subset`, `Filter.Tendsto.const_div_atBot`, `NonUnitalStarAlgHom.coe_inl`, `Function.locallyFinsuppWithin.one_isLittleO_logCounting_single`, `SchwartzMap.smulLeftCLM_ofReal`, `MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_degree`, `Matrix.single_mul_apply_of_ne`, `DualNumber.inr_eq_smul_eps`, `tsupport_mul_subset_right`, `MvPolynomial.coeff_weightedHomogeneousComponent`, `PowerSeries.weierstrassMod_zero_right`, `AlgebraicGeometry.basicOpen_eq_bot_iff`, `ContDiffAt.differentiableAt_iteratedFDeriv`, `WeierstrassCurve.Projective.dblX_eq`, `MeromorphicNFAt.meromorphicOrderAt_eq_zero_iff`, `TrivSqZeroExt.inv_zero`, `MonomialOrder.coeff_mul_of_degree_add`, `Num.castNum_testBit`, `PowerSeries.order_eq`, `Matrix.maxGenEigenspace_toLin_diagonal_eq_eigenspace`, `Algebra.Presentation.baseChange_relation`, `Int.fract_nonneg`, `MonomialOrder.degree_sub_leadingTerm_lt_degree`, `Module.Basis.toDual_apply_left`, `ArithmeticFunction.cardFactors_mul`, `Matrix.separatingRight_def`, `ContinuousMultilinearMap.nnnorm_smulRight`, `Height.mulHeight₁_zero`, `isRightRegular_zero_iff_subsingleton`, `Valuation.norm_pos_iff_valuation_pos`, `MonomialOrder.coeff_sPolynomial_sup_eq_zero`, `HasDerivAt.finset_prod`, `ExteriorAlgebra.comp_ι_sq_zero`, `MonomialOrder.sPolynomial_mem_sup_ideal`, `isClosedMap_smul₀`, `ContinuousLinearMap.norm_map_iff_adjoint_comp_self`, `Matrix.hadamard_diagonal`, `LieAlgebra.lieCharacter_apply_lie`, `ContDiffOn.smulRight`, `QuadraticMap.sum_repr_sq_add_sum_repr_mul_polar`, `Module.End.IsSemisimple.eq_zero_iff_forall_eigenvalue`, `instFactMemSetQuasispectrumOfNat`, `MvPolynomial.esymm_zero`, `Matrix.mem_rowStochastic`, `DualNumber.eps_mul_eps`, `AdjoinRoot.mk_self`, `WeierstrassCurve.twoTorsionPolynomial_of_char_two`, `MvPolynomial.rTensor_apply`, `ax_grothendieck_univ`, `PadicInt.continuousAddCharEquiv_apply`, `Positive.coe_zpow`, `List.sum_zipWith_distrib_left`, `PointedCone.mem_ofSubmodule_iff`, `Metric.unitBall.instIsCancelMulZero`, `IsAdjoinRootMonic.coeff_root`, `MvPolynomial.C_mem_coeffsIn`, `ContinuousLinearMap.norm_adjoint_comp_self`, `HomogeneousLocalization.NumDenSameDeg.num_zero`, `Polynomial.map_monic_eq_zero_iff`, `MvPolynomial.bind₁_X_right`, `MvPolynomial.coeff_rename_eq_zero`, `MvPolynomial.disjoint_support_monomial`, `Polynomial.coeff_mul_X_pow'`, `spectralNorm_zero`, `MvPowerSeries.monomial_mul_monomial`, `Int.preimage_fract`, `Module.DualBases.lc_def`, `MonomialOrder.coeff_mul_of_add_of_degree_le`, `hasDerivWithinAt_intCast`, `ConditionallyCompleteLinearOrderedField.inducedMap_nonneg`, `WeierstrassCurve.Jacobian.nonsingular_zero`, `MonoidAlgebra.coeffEquiv_apply`, `ContMDiff.clm_precomp`, `Set.div_zero_subset`, `Num.size_eq_natSize`, `MonoidAlgebra.mapDomainAddEquiv_apply`, `Matrix.exp_blockDiagonal'`, `MvPolynomial.join₂_map`, `QuaternionGroup.a_zero`, `AddMonoidAlgebra.lift_unique`, `ArithmeticFunction.natCoe_mul`, `HasFPowerSeriesWithinAt.compContinuousLinearMap`, `MvPolynomial.eval₂Hom_C_left`, `Quaternion.instIsScalarTower`, `PowerSeries.coeff_zero_X_mul`, `LinearMap.not_hasEigenvalue_zero_tfae`, `ContinuousMultilinearMap.norm_smulRight`, `MvPolynomial.transcendental_supported_polynomial_aeval_X_iff`, `TensorAlgebra.algebraMap_eq_zero_iff`, `MvPolynomial.aeval_monomial`, `hasFDerivAt_exp_zero_of_radius_pos`, `MonoidAlgebra.ofCoeff_erase`, `PowerSeries.X_dvd_iff`, `CStarAlgebra.span_nonneg_inter_ball`, `instSMulCommClass_sphere_closedBall_ball`, `Hyperreal.infinitesimal_pos_iff_infinitePos_inv`, `FiniteField.sum_subgroup_units`, `SkewMonoidAlgebra.domCongr_single`, `Finsupp.coe_mul`, `PowerSeries.weierstrassMod_zero`, `Polynomial.homogenize_eq_zero_iff`, `CStarAlgebra.isBasis_nonneg_sections`, `ContinuousMapZero.elemental_eq_top`, `AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over`, `Module.Relations.Solution.IsPresentation.exact`, `StandardEtalePresentation.toPresentation_relation`, `ContinuousMapZero.adjoin_id_dense`, `WithAbs.ofAbs_eq_zero`, `AlgEquiv.prodUnique_symm_apply`, `IsAbsoluteValue.abv_eq_zero'`, `DividedPowerAlgebra.dp_smul`, `ExteriorAlgebra.ι_mul_prod_list`, `eq_zero_of_mul_self_add_mul_self_eq_zero`, `Cubic.natDegree_of_c_ne_zero'`, `MvPolynomial.leadingCoeff_toLex`, `IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C`, `ContinuousLinearMap.hasDerivWithinAt`, `IsAddTorsionFree.to_noZeroSMulDivisors_int`, `Polynomial.toMvPolynomial_injective`, `Nat.modEq_nine_digits_sum`, `Algebra.PreSubmersivePresentation.localizationAway_jacobiMatrix`, `AddMonoidAlgebra.ofCoeff_smul`, `HasDerivWithinAt.comp_of_eq`, `FormalMultilinearSeries.derivSeries_apply_diag`, `Nat.factorization_eq_zero_iff`, `ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_on'`, `MvPolynomial.coeff_eval_eq_eval_coeff`, `SameRay.exists_nonneg_right`, `StarOrderedRing.isStrictlyPositive_iff_spectrum_pos`, `lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup`, `Subring.list_sum_mem`, `AddMonoidAlgebra.coeff_zero`, `RingSeminorm.apply_one`, `Matrix.swap_mul_apply_left`, `NumberField.canonicalEmbedding_eq_basisMatrix_mulVec`, `MvPolynomial.C_pow`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft`, `MonoidAlgebra.ofCoeff_update`, `QuadraticAlgebra.coe_algebraMap`, `fderiv_comp_smul`, `AffineIndependent.eq_zero_of_sum_eq_zero`, `Module.Relations.solutionFinsupp_isPresentation`, `MonoidAlgebra.mul_single_apply`, `NonUnitalAlgebra.mem_bot`, `LinearMap.polyCharpoly_natDegree`, `isRightRegular_iff_left_eq_zero_of_mul`, `ContinuousLinearMap.opNorm_lsmul`, `QuaternionAlgebra.imJ_swapEquiv_apply`, `descPochhammer_zero_eval_zero`, `inv_lt_one_iff₀`, `MvPolynomial.coeffs_C_subset`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_val`, `Multiset.gcd_eq_zero_iff`, `Submodule.comap_smul'`, `Polynomial.roots_X_pow`, `Module.Basis.reindexFinsetRange_repr`, `Matrix.natCast_kronecker_natCast`, `DirichletCharacter.map_zero'`, `LinearOrderedField.smul_Icc`, `Matrix.mulVec_diagonal`, `isCoveringMapOn_zpow`, `LieAlgebra.lieCharacter_apply_lie'`, `MvPolynomial.IsSymmetric.add`, `FormalMultilinearSeries.norm_changeOriginSeriesTerm`, `ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply`, `WithZero.withZeroUnitsEquiv_apply`, `ValuativeRel.zero_srel_iff`, `Nonneg.coe_zpow`, `pow_succ_pos`, `LieAlgebra.Orthogonal.indefiniteDiagonal_transform`, `WeierstrassCurve.j_eq_zero_iff_of_char_two`, `Module.Basis.continuous_coe_repr`, `MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRing`, `MonomialOrder.degree_mul`, `NormedRing.inverse_add_nth_order`, `Finsupp.sym2Mul_apply_mk`, `TensorProduct.finsuppScalarLeft_apply`, `MonomialOrder.degree_monomial_le`, `MvPolynomial.C_sub`, `isScalarTower_closedBall_closedBall_ball`, `Matrix.GeneralLinearGroup.val_inv_swap`, `continuousOn_zpow₀`, `Algebra.Generators.self_algebra_algebraMap`, `ContinuousMapZero.instIsScalarTower'`, `Matrix.intCast_mulVec`, `HahnSeries.order_mul_of_ne_zero`, `analyticOnNhd_inv`, `hasDerivAt_exp_zero`, `Units.zero_lt`, `GenContFract.sub_convs_eq`, `MvPolynomial.esymm_eq_sum_subtype`, `Module.Basis.smulTower_repr`, `descPochhammer_eval_zero`, `HasFTaylorSeriesUpTo.zero_eq'`, `PointedCone.mem_positive`, `Module.Basis.toDual_apply_right`, `AffineSubspace.setOf_sOppSide_eq_image2`, `WeierstrassCurve.a₁_of_isCharThreeJNeZeroNF`, `WeierstrassCurve.IsCharThreeJNeZeroNF.a₃`, `Finsupp.toMultiset_sup`, `Module.End.mem_genEigenspace_zero`, `Polynomial.natDegree_pos_iff_degree_pos`, `ArithmeticFunction.zeta_eq_zero`, `MvPolynomial.coeff_mul_monomial'`, `LinearMap.toMatrix'_one`, `LieAlgebra.SpecialLinear.val_singleSubSingle`, `MonomialOrder.Monic.prod`, `MvPolynomial.ringKrullDim_of_isNoetherianRing`, `MvPowerSeries.lexOrder_le_of_coeff_ne_zero`, `ProbabilityTheory.gaussianPDFReal_mul`, `Associates.quot_out_zero`, `CompactlySupportedContinuousMap.instMulRightMono`, `mul_eq_zero_of_ne_zero_imp_eq_zero`, `Finsupp.linearCombination_comapDomain`, `Subsemiring.closure_singleton_zero`, `Module.DualBases.coeffs_apply`, `DFinsupp.toMultiset_inj`, `Matrix.cstar_norm_def`, `ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id`, `PointwiseConvergenceCLM.withSeminorms`, `ArithmeticFunction.sum_Ioc_mul_eq_sum_sum`, `MvPolynomial.pderiv_X_self`, `MvPolynomial.quotientEquivQuotientMvPolynomial_rightInverse`, `LieAlgebra.Orthogonal.pb_inv`, `Quaternion.imJ_star`, `MeasureTheory.convolution_eq_swap`, `Set.Ioc.coe_mul`, `MulRingNorm.apply_one`, `QuaternionAlgebra.imI_swapEquiv_apply`, `Module.Basis.opNorm_le`, `AddMonoidAlgebra.le_inf_support_finset_prod`, `IsLprojection.mul_compl_self`, `WittVector.mul_polyOfInterest_aux3`, `Nat.Prime.exists_addOrderOf_eq_pow_padic_val_nat_add_exponent`, `Matrix.invOf_eq`, `UniformCauchySeqOnFilter.one_smulRight`, `Nat.card_pair_lcm_eq`, `WittVector.verschiebungPoly_zero`, `hasDerivAt_const_add_iff`, `MvPolynomial.pderiv_C`, `PowerSeries.coeff_C_mul_X_pow`, `Nat.factorization_eq_zero_of_non_prime`, `MonomialOrder.degLex_single_lt_iff`, `ProperCone.innerDual_iUnion`, `Matrix.detp_neg_one_diagonal`, `MvPowerSeries.trunc'_one`, `ContinuousMultilinearMap.curryFinFinset_symm_apply`, `AddMonoidAlgebra.of'_mul_modOf`, `HasFPowerSeriesWithinOnBall.pi`, `HasFPowerSeriesWithinOnBall.tendsto_partialSum`, `SchwartzMap.smulLeftCLM_apply`, `Set.inter_indicator_one`, `dotProduct_zero`, `sbtw_zero_one_iff`, `MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix`, `ContDiffMapSupportedIn.withSeminorms'`, `MvPolynomial.modMonomial_add_divMonomial_single`, `AlgEquiv.uniqueProd_symm_apply`, `pos_of_mul_neg_right`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply`, `ValuationSubring.smul_mem_pointwise_smul`, `Polynomial.eval_rootOfSplits`, `RootPairing.GeckConstruction.lie_h_h`, `constantCoeff_xInTermsOfW`, `WittVector.coeff_p_pow_eq_zero`, `Algebra.norm_eq_zero_iff`, `Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_smul`, `MvPolynomial.C_dvd_iff_zmod`, `Set.Ico.coe_lt_one`, `Matrix.TransvectionStruct.toMatrix_sumInl`, `ContinuousAlgHom.map_zero`, `ZSpan.repr_floor_apply`, `MeromorphicOn.divisor_def`, `Num.mul_to_nat`, `PointedCone.mem_maxTensorProduct`, `PadicInt.limNthHom_zero`, `Matroid.eq_loopyOn_iff_eRank`, `MvRatFunc.rank_eq_max_lift`, `Matrix.vec_mul_eq_vecMul`, `Matrix.iSup_eigenspace_toLin_diagonal_eq_top`, `HahnSeries.SummableFamily.powers_of_orderTop_pos`, `gaussSum_eq_zero_of_isPrimitive_of_not_isPrimitive`, `MvPolynomial.aeval_prod`, `Matrix.IsTotallyUnimodular.fromRows_one`, `ZMod.erdos_ginzburg_ziv`, `MvPolynomial.homogeneousSubmodule_mul`, `MonomialOrder.leadingCoeff_one`, `PiTensorProduct.zero_tprodCoeff`, `HasFTaylorSeriesUpTo.fderiv`, `CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁`, `Module.Basis.repr_symm_apply`, `Int.padicValuation_le_one`, `Finsupp.apply_linearCombination_id`, `Matrix.toMvPolynomial_mul`, `Polynomial.Bivariate.pderiv_one_equivMvPolynomial`, `MonoidAlgebra.single_apply`, `WittVector.wittOne_pos_eq_zero`, `SimpleGraph.adjMatrix_top`, `affineIndependent_iff_of_fintype`, `Filter.tendsto_inv₀_nhdsNE_zero`, `Height.mulHeight_eval_le'`, `AbsoluteValue.listSum_le`, `WittVector.mem_span_p_iff_coeff_zero_eq_zero`, `WeierstrassCurve.Projective.equation_iff`, `PointedCone.dual_singleton_zero`, `minpoly.aeval_of_isScalarTower`, `PosMulReflectLT.toPosMulStrictMono`, `LinearMap.toMatrixₛₗ₂'_apply`, `ContinuousLinearMap.norm_holderL_le`, `HahnSeries.inv_single`, `MvPolynomial.IsHomogeneous.neg`, `MvPowerSeries.trunc_C_mul`, `MvPolynomial.exists_restrict_to_vars`, `LucasLehmer.X.zero_snd`, `WithZero.lift'_zero`, `WeierstrassCurve.j_eq_zero_iff_of_char_three'`, `MvPolynomial.lcoeff_apply`, `wittStructureInt_rename`, `Nonneg.val_inv_unitsEquivPos_symm_apply_coe`, `WittVector.constantCoeff_wittNeg`, `SchwartzMap.smulLeftCLM_compL_smulLeftCLM`, `algebraicIndependent_comp_subtype`, `map_wittStructureInt`, `WeierstrassCurve.ofJ_0_of_three_ne_zero`, `HahnSeries.C_apply`, `Module.Basis.tensorProduct_repr_tmul_apply`, `LinearMap.BilinForm.IsRefl.eq_zero`, `Matrix.GeneralLinearGroup.val_scalar_apply`, `MvPolynomial.algebraTensorAlgEquiv_symm_monomial`, `Finsupp.smul_single_one`, `ENat.coe_zero`, `Mathlib.Tactic.Ring.cast_nnrat`, `ContinuousAffineMap.toConstProdContinuousLinearMap_fst`, `Finsupp.Colex.single_lt_iff`, `PointedCone.dual_neg`, `Module.Basis.coe_ofEquivFun`, `Representation.freeLiftLEquiv_symm_apply`, `exists_signed_sum`, `IsStrictlyPositive.add_nonneg`, `Nonneg.instMulArchimedean`, `Matrix.toLinearMapRight'_one`, `MvPolynomial.restrictSupport_eq_span`, `Nat.prod_pow_factorization_centralBinom`, `CharTwo.intCast_eq_ite`, `ENat.sSup_eq_zero'`, `RingHom.ker_eq`, `quadraticCharFun_zero`, `MonomialOrder.degree_sub_LTerm_lt`, `cfcₙL_integrable`, `not_linearIndependent_iff_linearCombination`, `ENat.map_zero`, `HahnModule.instIsTorsionFree`, `NonnegSpectrumClass.quasispectrum_nonneg_of_nonneg`, `MvPolynomial.constantCoeff_comp_map`, `Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace`, `Units.mul_left_eq_zero`, `Matrix.conjTranspose_mul_self_mul_eq_zero`, `bernsteinPolynomial.iterate_derivative_at_0_eq_zero_of_lt`, `Matrix.det_vandermonde_eq_zero_iff`, `mulPosReflectLT_iff_contravariant_pos`, `PointedCone.dual_flip_dual_dual_flip`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip`, `mul_right_eq_self₀`, `OreLocalization.inv_zero`, `Finsupp.sub_single_one_add`, `Metric.packingNumber_empty`, `eq_zero_of_map_spectralNorm_eq_zero`, `TemperedDistribution.derivCLM_apply_apply`, `Set.inv_Ioo_0_left`, `WeierstrassCurve.a₂_of_isShortNF`, `Representation.free_asModule_free`, `star_mul_self_pos`, `Affine.Simplex.interior_eq_image_Ioo`, `AddMonoidAlgebra.le_inf_support_multiset_prod`, `FirstOrder.Ring.mvPolynomial_zeroLocus_definable`, `AffineSubspace.setOf_wSameSide_eq_image2`, `Algebra.discr_zero_of_not_linearIndependent`, `WittVector.mul_charP_coeff_zero`, `Matrix.invertibleEquivDetInvertible_symm_apply`, `bernsteinPolynomial.iterate_derivative_at_0`, `Units.exists0`, `MvPolynomial.rank_eq`, `MvPolynomial.vars_add_subset`, `MonoidAlgebra.mapDomain_sum`, `PowerSeries.coeff_X_pow_mul'`, `mul_nonneg_of_three`, `Basis.piTensorProduct_repr_tprod_apply`, `MulChar.map_nonunit'`, `ProperCone.mem_toPointedCone`, `MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq`, `Filter.tendsto_mul_const_atBot_iff_neg`, `Finset.weightedVSub_indicator_subset`, `spectrum.hasDerivAt_resolvent_const_left`, `MvPolynomial.aevalTower_algebraMap`, `Module.Relations.Solution.π_comp_map_apply`, `Set.chainHeight_of_isEmpty`, `mul_sub_mul_div_mul_neg_iff`, `Set.inter_indicator_mul`, `cfc_apply_of_not_continuousOn`, `ArithmeticFunction.cardFactors_one`, `Set.indicator_mul_right`, `WeierstrassCurve.Projective.add_of_Y_ne`, `Valuation.restrict_exists_div_eq`, `permMatrix_mem_doublyStochastic`, `LinearMap.hasDerivAt`, `MvPolynomial.optionEquivLeft_elim_eval`, `Valuation.leSubmodule_zero`, `MvPolynomial.esymm_one`, `kstar_zero`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq`, `MvPolynomial.optionEquivLeft_symm_X`, `SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial`, `WeierstrassCurve.HasMultiplicativeReduction.badReduction`, `Matrix.submatrixEquivInvertibleEquivInvertible_symm_apply`, `TensorProduct.finsuppScalarLeft_symm_apply_single`, `MvPolynomial.renameEquiv_symm`, `neg_one_pow_mul_eq_zero_iff`, `PointedCone.dual_sUnion`, `QuadraticAlgebra.omega_mul_mk`, `LinearMap.hasDerivAtFilter`, `HahnSeries.ofPowerSeries_C`, `Finset.subConst_empty_left`, `ProperCone.innerDual_toSubmodule`, `Ideal.algebraMap_residueField_eq_zero`, `MvPolynomial.eval₂Hom_C`, `Valuation.one_apply_def`, `DFinsupp.toMultiset_lt_toMultiset`, `Module.Basis.repr_smul'`, `PowerSeries.coe_pow`, `posMulMono_iff_posMulStrictMono`, `Representation.LinearizeMonoidal.μ_apply_apply`, `MvPolynomial.counitNat_surjective`, `HasFiniteFPowerSeriesOnBall.fderiv_eq`, `Set.indicator_mul_left`, `PointedCone.to_isOrderedModule`, `Finsupp.DegLex.monotone_degree`, `PEquiv.mul_toMatrix_toPEquiv`, `Module.Projective.out`, `SimpleGraph.adjMatrix_hadamard_natCast`, `PointedCone.mem_hull_set`, `Matrix.conjTranspose_intCast`, `Finset.lcm_eq_zero_iff`, `TestFunction.lineDerivCLM_apply_of_gt`, `neg_of_mul_pos_left`, `mul_pos_of_neg_of_neg`, `Module.Basis.repr_unitsSMul`, `HasFPowerSeriesAt.locally_zero_iff`, `Matrix.isUnit_diagonal`, `MvPolynomial.support_symmDiff_support_subset_support_add`, `hasDerivAt_iff_tendsto_slope`, `Function.locallyFinsuppWithin.restrict_negPart`, `TrivSqZeroExt.isUnit_or_isNilpotent`, `ArithmeticFunction.zeta_mul_apply`, `SkewMonoidAlgebra.coeff_single_mul_aux`, `LaurentPolynomial.smeval_zero`, `matPolyEquiv_coeff_apply_aux_2`, `ContinuousLinearMap.analyticAt_bilinear`, `cfcₙ_smul`, `Representation.ind_apply`, `MvPolynomial.isEmptyRingEquiv_eq_coeff_zero`, `Odd.pow_add_pow_eq_zero`, `WeierstrassCurve.Projective.equation_zero`, `PadicInt.norm_natCast_zmodRepr_eq_iff`, `HasFDerivWithinAt.comp_hasDerivAt_of_eq`, `HahnSeries.addVal_apply`, `HasFPowerSeriesAt.hasStrictFDerivAt`, `MvPolynomial.sumToIter_C`, `tendsto_fract_right`, `Matrix.vec_mul_eq_mulVec`, `MvPolynomial.mem_coeffs_iff`, `MvPowerSeries.order_zero`, `MvPolynomial.X_divMonomial`, `Quaternion.im_sq`, `Height.mulHeight_eval_ge'`, `WeierstrassCurve.Projective.dblX_eq'`, `HasDerivWithinAt.comp_hasDerivAt`, `MvPolynomial.eval_expand`, `AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero`, `AddMonoidAlgebra.of'_modOf`, `LaurentSeries.mem_integers_of_powerSeries`, `div_lt_one_iff`, `PointedCone.ofSubmodule_sup`, `support_conjneg`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right`, `FirstOrder.Field.model_fieldOfChar_of_charP`, `ZMod.val_eq_zero`, `RingHom.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial`, `AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen`, `StrictOrderedSemiring.toPosSMulStrictMonoNat`, `GroupWithZero.eq_zero_or_unit`, `isBoundedLinearMap_continuousMultilinearMap_comp_linear`, `ContinuousAt.cfc_nnreal`, `LaurentSeries.Cauchy.exists_lb_support`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm`, `MonoidAlgebra.coeff_sum`, `WittVector.teichmuller_coeff_pos`, `WeierstrassCurve.j_eq_zero_of_char_two`, `MvPolynomial.aeval_comp_toMvPolynomial`, `MvPowerSeries.weightedOrder_eq_top_iff`, `Nat.ordCompl_dvd`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp`, `Module.Basis.constr_apply`, `AbsoluteValue.map_zero`, `Quaternion.imJ_natCast`, `MonoidAlgebra.support_single_mul_subset`, `MvPolynomial.divMonomial_add`, `LaurentSeries.instIsFractionRingPowerSeries`, `MvPolynomial.finrank_eq_one`, `hasStrictDerivAt_exp_smul_const_of_mem_ball`, `zpow_left_monoOn₀`, `WeierstrassCurve.IsCharNeTwoNF.a₁`, `Multiset.lcm_ne_zero_iff`, `Pi.mem_span_range_single_inl_iff`, `CompactlySupportedContinuousMap.instMulLeftMono`, `MvPolynomial.supportedEquivMvPolynomial_symm_C`, `Function.support_inv'`, `Set.Ioc.le_one`, `tendsto_algebraMap_inv_atTop_nhds_zero_nat`, `PowerBasis.aeval_minpolyGen`, `HasDerivWithinAt.fun_sum`, `Commute.list_sum_right`, `HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap`, `AddMonoidAlgebra.sum_single`, `Polynomial.roots_countP_pos_le_signVariations`, `MonoidAlgebra.mul_apply_antidiagonal`, `HahnSeries.toPowerSeries_apply`, `MvPowerSeries.monomial_smul_const`, `AdjoinRoot.coe_algHomOfDvd`, `Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary`, `Polynomial.coeff_X`, `Matrix.toMvPolynomial_constantCoeff`, `Matrix.IsAdjMatrix.adjMatrix_toGraph_eq`, `Matrix.zero_zpow`, `HahnSeries.cardSupp_hsum_powers_le`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply`, `hasDerivAt_pi`, `Matrix.GeneralLinearGroup.coe_map_inv_mul_map`, `MvPowerSeries.trunc'_map`, `Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero`, `Cubic.degree_of_c_eq_zero'`, `WittVector.ghostComponent_zero_verschiebungFun`, `Polynomial.natDegree_lt_coeff_mul`, `MeasureTheory.ContinuousMap.inner_toLp`, `Matrix.mul_nonsing_inv`, `MvPolynomial.derivation_eqOn_supported`, `Matrix.isHermitian_intCast`, `IsStrictOrderedRing.toZeroLEOneClass`, `HasDerivAt.of_notMem_tsupport`, `ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars`, `MvPolynomial.killCompl_monomial_eq_monomial_comapDomain_of_subset`, `PosMulMono.toPosMulStrictMono`, `Finsupp.linearCombination_eq_fintype_linearCombination_apply`, `hasFDerivAt_inv'`, `AddMonoidAlgebra.mapRingHom_apply`, `MvPolynomial.eval₂AlgHom_apply`, `Finset.Nonempty.div_zero`, `Nonneg.mk_pow`, `WithTop.instNoZeroDivisors`, `MvPolynomial.tensorEquivSum_X_tmul_one`, `MvPolynomial.instIsMaximalVanishingIdealSingletonForallSet`, `HasDerivAt.fun_mul`, `Finset.zero_mem_smul_iff`, `HasStrictDerivAt.const_sub`, `hasDerivWithinAt_finCons`, `Quaternion.coe_neg`, `Nat.factorization_eq_zero_of_lt`, `Representation.leftRegularMapEquiv_apply`, `LinearOrderedCommGroupWithZero.inl_apply`, `IsLinearTopology.tendsto_mul_zero_of_right`, `LinearMap.diag_toMatrix_directSum_collectedBasis_eq_zero_of_mapsTo_ne`, `OreLocalization.nontrivial_of_nonZeroDivisorsLeft`, `exists_continuousLinearEquiv_fderiv_symm_eq`, `MvPolynomial.C_inj`, `LaurentSeries.eq_coeff_of_valuation_sub_lt`, `HasDerivAt.smul`, `Finset.zero_mul_subset`, `CStarAlgebra.hasBasis_approximateUnit`, `FormalMultilinearSeries.rightInv_coeff`, `MvPolynomial.expand_mul_eq_comp`, `Matrix.vecMul_intCast`, `isIdempotentElem_iff_mul_one_sub_self`, `WeierstrassCurve.Jacobian.map_polynomialY`, `ValueDistribution.logCounting_coe`, `Matrix.nonneg_of_mem_rowStochastic`, `Convex.mem_toCone'`, `MvPowerSeries.rescale_zero_apply`, `sbtw_one_zero_iff`, `LinearOrderedCommGroupWithZero.inr_apply`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand'`, `Finsupp.Lex.single_le_iff`, `Polynomial.coeff_monomial_succ`, `MvPolynomial.IsHomogeneous.eval₂`, `Subalgebra.LinearDisjoint.basisOfBasisLeft_repr_apply`, `cfcₙHom_of_cfcHom_map_quasispectrum`, `CharP.charP_iff_prime_eq_zero`, `cfcₙ_nonneg`, `MvPolynomial.eval₂_pUnitAlgEquiv`, `DividedPowers.IsNilpotent.dpow_of_prime_le`, `Cubic.leadingCoeff_of_c_ne_zero'`, `MvPolynomial.eval_X`, `convexOn_zpow`, `Mathlib.Tactic.Linarith.lt_of_eq_of_lt`, `MvPowerSeries.hasSum_eval₂`, `Matrix.zpow_neg_mul_zpow_self`, `Ideal.mem_span_pow_iff_exists_isHomogeneous`, `WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq`, `Module.End.genEigenspace_zero`, `not_linearIndepOn_finset_iffₒₛ`, `MvPolynomial.killCompl_monomial`, `ContinuousLinearMap.isPositive_adjoint_comp_self`, `SchwartzMap.integral_clm_comp_laplacian_right_eq_left`, `instSMulCommClass_sphere_sphere_closedBall`, `PointedCone.ofSubmodule_iInf`, `ContDiffOn.differentiableOn_iteratedFDerivWithin`, `EuclideanSpace.single_eq_zero_iff`, `RootPairing.GeckConstruction.h_eq_diagonal`, `ValueDistribution.log_counting_zero_sub_logCounting_top`, `WithBot.instPosMulReflectLT`, `Polynomial.map_map_freeMonic`, `MonomialOrder.degree_prod_of_regular`, `ContinuousMapZero.instStarModule`, `Nat.Partition.coeff_genFun`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn'`, `ClosedSubmodule.orthogonal_closure'`, `Matrix.l2_opNorm_def`, `SignType.coe_pow`, `ConditionallyCompleteLinearOrderedField.toMulPosStrictMono`, `mem_finsuppAffineCoords_iff_linearCombination`, `MvPolynomial.supported_eq_range_rename`, `Polynomial.trailingCoeff_eq_zero`, `Quaternion.hasSum_coe`, `PEquiv.toMatrix_trans`, `RingHom.codomain_trivial_iff_range_trivial`, `Subsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul`, `Nat.factorization_gcd`, `LinearMap.splittingOfFinsuppSurjective_splits`, `HasFiniteFPowerSeriesOnBall.sub`, `matrixEquivTensor_apply`, `RCLike.wInner_nonneg`, `ContinuousMultilinearMap.norm_compContinuousLinearMapL_le`, `MvPolynomial.trdeg_of_isDomain`, `ConvexCone.mem_toPointedCone`, `Function.locallyFinsuppWithin.coe_finsum`, `LinearMap.IsSymmetric.toMatrix_eigenvectorBasis`, `HasStrictDerivAt.neg`, `Ideal.height_bot`, `ArithmeticFunction.carmichael_lcm`, `ContinuousLinearMap.holderL_apply_apply`, `Module.Basis.repr_eq_iff'`, `linearDepOn_iff'`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `div_eq_zero_iff`, `FormalMultilinearSeries.comp_rightInv_aux2`, `IsStrictlyPositive.of_le`, `RatFunc.single_inv`, `SignType.coe_zpow`, `stdSimplexEquivIcc_one`, `Set.Ico.coe_nonneg`, `Matrix.charpoly_diagonal`, `PowerSeries.heval_mul`, `OreLocalization.nontrivial_iff`, `nonneg_of_mul_nonpos_left`, `MeasureTheory.hasFiniteIntegral_smul_iff`, `LocallyConstant.coe_charFn`, `Quaternion.imI_coe`, `Hyperreal.infiniteNeg_iff`, `Unitization.quasispectrum_eq_spectrum_inr`, `MulChar.map_zero`, `Valuation.pos_iff`, `MeasureTheory.integrable_fun_smul_iff`, `isConformalMap_const_smul`, `tendsto_pow_atTop_nhds_zero_of_norm_lt_one`, `ArithmeticFunction.intCoe_apply`, `ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero`, `hasDerivWithinAt_iff_tendsto_slope'`, `zero_notMem_nonZeroDivisorsLeft`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand`, `SkewMonoidAlgebra.mem_span_support`, `RootPairing.isFixedPt_reflectionPerm_iff`, `MeasureTheory.AEFinStronglyMeasurable.mul`, `Matrix.mul_diagonal`, `AlgebraicGeometry.Scheme.zero_of_zero_cover`, `Module.Basis.toMatrix_self`, `ContMDiffWithinAt.cle_arrowCongr`, `Algebra.Norm.Transitivity.auxMat_toSquareBlock_eq`, `Quaternion.hom_ext_iff`, `HahnSeries.algebraMap_apply'`, `ContinuousWithinAt.cfc_nnreal`, `star_nonneg_iff`, `Submonoid.coe_pos`, `cfcₙHomSuperset_apply`, `FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm`, `PowerSeries.coeff_subst_finite'`, `Finset.mul_zero_subset`, `isRelPrime_zero_left`, `continuousMultilinearCurryRightEquiv_apply`, `cfcₙ_apply`, `WeierstrassCurve.Projective.dblY_of_Y_eq'`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_right`, `HasDerivAt.comp_add_const`, `Polynomial.leadingCoeff_eq_zero`, `MvPolynomial.support_esymm`, `MvPolynomial.IsHomogeneous.C_mul`, `MvPolynomial.rename_hsymm`, `Module.Presentation.tautologicalRelations_relation`, `Set.chainHeight_eq_zero_iff`, `MonomialOrder.sPolynomial_decomposition'`, `ContDiffMapSupportedIn.structureMapLM_zero_apply`, `nnnorm_cfcₙ_nnreal_le`, `finite_support_of_finsum_eq_one`, `Rep.coinvariantsTensorIndInv_mk_tmul_indMk`, `SkewMonoidAlgebra.lift_def`, `PosNum.to_nat_eq_succ_pred`, `orthonormal_vecCons_iff`, `MvPolynomial.constantCoeff_map`, `ContinuousAlternatingMap.prodLIE_symm_apply`, `fwdDiff_iter_sum_mul_pow_eq_zero`, `Matrix.inv_subsingleton`, `Mathlib.Tactic.ComputeDegree.coeff_pow_of_natDegree_le_of_eq_ite'`, `DifferentiableOn.hasDerivAt`, `CongruenceSubgroup.Gamma_mem`, `MvPolynomial.transcendental_supported_X`, `MvPolynomial.degrees_add_of_disjoint`, `IsLinearSet.definable`, `Odd.geom_sum_pos`, `ContinuousLinearMap.apply_apply'`, `DividedPowerAlgebra.dp_add`, `HasFPowerSeriesWithinAt.hasFDerivWithinAt`, `apply_le_nnnorm_cfcₙ_nnreal`, `Finset.divConst_empty_right`, `IsDedekindDomain.HeightOneSpectrum.valuation_le_one`, `Matrix.smul_eq_diagonal_mul`, `Cardinal.ofENat_zero`, `PosSMulMono.toPosSMulReflectLE`, `tendsto_pow_atTop_nhds_zero_iff`, `Polynomial.IsUnitTrinomial.irreducible_aux1`, `LaurentSeries.X_order_mul_powerSeriesPart`, `ModularGroup.S_mul_S_eq`, `AlgebraicGeometry.isReduced_stalk_of_isReduced`, `IsStrictOrderedRing.toPosMulStrictMono`, `MvPolynomial.aeval_natDegree_le`, `SchwartzMap.fourier_convolution`, `Field.gcd_eq`, `IsTopologicalDivisionRing.toContinuousInv₀`, `AnalyticOnNhd.eval_continuousLinearMap'`, `Quaternion.re_intCast`, `MonoidAlgebra.single_mul_apply_of_not_exists_mul`, `zero_notMem_nonZeroDivisors`, `fderivWithin_comp_smul`, `Valuation.map_zero`, `WeierstrassCurve.a₄_of_isCharTwoJNeZeroNF`, `PrimeSpectrum.zeroLocus_singleton_zero`, `HahnSeries.val_toOrderTopSubOnePos_coe`, `IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int`, `Module.Basis.norm_repr_le_norm`, `Function.locallyFinsuppWithin.single_pos_int_one`, `MvPolynomial.degreeOf_neg`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear`, `QuadraticAlgebra.omega_mul_omega_eq_add`, `Polynomial.div_tendsto_atTop_zero_iff_degree_lt`, `instSMulCommClass_closedBall_closedBall_closedBall`, `ZeroAtInftyContinuousMap.mul_apply`, `AddMonoidAlgebra.coeff_neg`, `Finset.sum_mul_boole`, `Algebra.Norm.Transitivity.auxMat_blockTriangular`, `sub_mul_sub_nonneg_iff`, `ContinuousLinearMap.flipₗᵢ_symm`, `Representation.freeLiftLEquiv_apply`, `HasFPowerSeriesAt.compContinuousLinearMap`, `contMDiffOn_zero_iff`, `Commute.isNilpotent_sub`, `MvPolynomial.scalarRTensor_apply_tmul_apply`, `ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply`, `ArithmeticFunction.IsMultiplicative.map_div_of_coprime`, `MvPolynomial.optionEquivLeft_symm_C_C`, `MvPowerSeries.le_lexOrder_mul`, `Module.Basis.mem_span_repr_support`, `Nonneg.coe_smul`, `Pi.basisFun_repr`, `WeierstrassCurve.Jacobian.add_of_Z_eq_zero`, `dotProduct_diagonal`, `Matrix.adjugate_mul`, `Nat.WithBot.coe_nonneg`, `continuousOn_cfcₙ_nnreal_setProd`, `AddMonoidAlgebra.support_gen_of_gen'`, `HahnSeries.mem_orderTopSubOnePos_iff`, `C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum`, `isLinearTopology_iff_hasBasis_twoSidedIdeal`, `fderivWithin_clm_apply`, `Algebra.leftMulMatrix_eq_repr_mul`, `Algebra.Generators.Hom.algebraMap_toAlgHom`, `nilpotencyClass_eq_succ_iff`, `PowerSeries.WithPiTopology.isTopologicallyNilpotent_of_constantCoeff_zero`, `exists_continuousLinearEquiv_fderivWithin_symm_eq`, `ENat.zero_epow_top`, `Quaternion.re_mul`, `ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz`, `hasDerivAt_of_tendsto_locally_uniformly_on'`, `Quaternion.normSq_div`, `Polynomial.ofFn_coeff_eq_zero_of_ge`, `Matrix.UnitaryGroup.star_mul_self`, `MonoidAlgebra.coeff_add`, `Polynomial.resultant_eq_zero_iff`, `MulEquiv.noZeroDivisors`, `AlternatingMap.mkContinuousLinear_norm_le_max`, `Matrix.self_mul_conjTranspose_eq_zero`, `FormalMultilinearSeries.rightInv_coeff_one`, `MvPolynomial.IsSymmetric.sub`, `Matrix.derivative_det_one_add_X_smul_aux`, `MvPolynomial.coeffsIn_le`, `EuclideanSpace.single_apply`, `TensorProduct.toMatrix_comm`, `Module.Basis.sum_repr`, `ContinuousMapZero.coe_toContinuousMapHom`, `fderiv_continuousAlternatingMap_apply_const_apply`, `WithLp.instProdIsBoundedSMul`, `div_zero`, `MonomialOrder.C_mul_leadingCoeff_monomial_degree`, `WittVector.coeff_frobenius`, `Matrix.PosDef.det_pos`, `ZNum.to_int_inj`, `TensorAlgebra.ι_eq_algebraMap_iff`, `ZSpan.mem_fundamentalDomain`, `MvPolynomial.degreeOf_mul_X_of_ne`, `HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap`, `ofAdd_toDual_eq_zero_iff`, `LinearMap.toMatrix₂'_apply`, `ArithmeticFunction.cardFactors_apply_prime`, `Finsupp.nsmul_single_one_image`, `Rep.standardComplex.d_single`, `MonoidAlgebra.support_mul`, `mul_nonneg_iff_right_nonneg_of_pos`, `Function.locallyFinsuppWithin.single_pos_nat_one`, `CliffordAlgebra.evenOdd_isCompl`, `Finsupp.DegLex.lt_def`, `PointedCone.lineal_le`, `MeromorphicOn.divisor_mul`, `HahnSeries.val_inv_toOrderTopSubOnePos_coe`, `CFC.continuousOn_rpow`, `WeierstrassCurve.c₆_of_isShortNF_of_char_three`, `HahnSeries.toPowerSeries_symm_apply_coeff`, `ContinuousLinearMap.norm_holder_apply_apply_le`, `Module.Basis.toMatrix_mulVec_repr`, `Nonneg.orderedSub`, `WeierstrassCurve.Projective.addX_self`, `AddMonoidAlgebra.sum_single_index`, `Algebra.Generators.comp_σ`, `Finset.Nonempty.dens_pos`, `CliffordAlgebraQuaternion.toQuaternion_ι`, `notMem_nonZeroDivisorsLeft_iff`, `conjugate_nonneg`, `WithLp.unitization_norm_inr`, `AnalyticOnNhd.eval_mvPolynomial`, `ZNum.mul_to_int`, `MvPolynomial.support_smul`, `MvPowerSeries.monomial_smul_eq`, `LaurentSeries.coeff_coe_powerSeries`, `NNReal.tendsto_const_div_atTop_nhds_zero_nat`, `MvPowerSeries.truncFinset_apply`, `Asymptotics.IsLittleO.exists_eq_mul`, `IncidenceAlgebra.prod_mul_prod`, `WithZeroTopology.nhds_eq_update`, `Finsupp.sum_eq_one_iff`, `Algebra.adjoin_insert_zero`, `Matrix.mul_adjp_add_detp`, `DividedPowerAlgebra.dp_null_of_ne_zero`, `RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u`, `ContinuousLinearMap.hasStrictDerivAt`, `WeierstrassCurve.a₂_of_isCharTwoJEqZeroNF`, `ContinuousLinearMap.analyticAt_uncurry_of_multilinear`, `WeierstrassCurve.Projective.map_polynomialY`, `hasDerivWithinAt_iff_tendsto_slope`, `MvPolynomial.tensorEquivSum_C_tmul_C`, `CharP.quotient_iff`, `notMem_nonZeroDivisors_iff_right`, `Quaternion.instFinite`, `constFormalMultilinearSeries_apply_succ`, `MvPolynomial.IsHomogeneous.finSuccEquiv_coeff_isHomogeneous`, `MvPolynomial.finsum_weightedHomogeneousComponent`, `ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero`, `FormalMultilinearSeries.continuousOn`, `isCancelMulZero_iff_noZeroDivisors`, `HasStrictFDerivAt.clm_comp`, `Finsupp.mem_sym2_support_of_mul_ne_zero`, `finsetBasisOfLinearIndependentOfCardEqFinrank_repr_apply`, `EisensteinSeries.gammaSetDivGcdEquiv_eq`, `Algebra.Presentation.instFinitePresentationQuotientOfFinite`, `WeierstrassCurve.Projective.map_polynomial`, `WittVector.wittSub_zero`, `normalize_zero`, `UniqueFactorizationMonoid.radical_eq_one_iff`, `ArithmeticFunction.sigma_eq_sum_div`, `Mathlib.Tactic.FieldSimp.zero_zpow'`, `Submodule.basis_of_pid_aux`, `DividedPowerAlgebra.mkRingHom_C`, `instContinuousConstSMulSubtypeLeOfNat`, `inv_nonpos'`, `Mathlib.Tactic.RingNF.nat_rawCast_0`, `MvPolynomial.eval₂_assoc`, `Module.Basis.toMatrix_unitsSMul`, `MonotoneOn.nnnorm_cfcₙ`, `IsOrderedRing.toMulPosMono`, `VectorFourier.fourierIntegral_fderiv`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree`, `ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv`, `ContinuousLinearMap.fpowerSeries_apply_one`, `Matrix.mul_swap_apply_right`, `range_cfc_nnreal_subset`, `Multiset.prod_pos`, `Localization.mk_zero`, `fderiv_continuousLinearEquiv_comp'`, `ContDiffPointwiseHolderAt.zero_order_iff`, `seminormFromConst_seq_zero`, `MvPolynomial.instIsDomainOfIsCancelAdd`, `ContinuousLinearMap.smulRightL_apply_apply`, `MvPowerSeries.subst_coe`, `PowerSeries.weierstrassDiv_zero_left`, `HahnSeries.cardSupp_inv_le`, `MvPowerSeries.IsHomogeneous.coeff_eq_zero`, `MvPolynomial.coeff_zero_one`, `MvPolynomial.mapEquivMonic_symm_map_algebraMap`, `Sbtw.mem_image_Ioo`, `Module.Basis.algebraMapCoeffs_repr`, `MvPolynomial.support_X`, `WeierstrassCurve.Affine.evalEval_polynomialX_zero`, `constFormalMultilinearSeries_zero`, `WittVector.wittZero_eq_zero`, `MvPolynomial.coe_aeval_eq_eval`, `threeGPFree_smul_set₀`, `UniqueFactorizationMonoid.toIsCancelMulZero`, `HasStrictFDerivAt.continuousMultilinearMap_apply`, `ValueDistribution.logCounting_inv`, `half_le_self_iff`, `Nat.factorization_inj`, `Finsupp.toMultiset_sum_single`, `Polynomial.eval_gcd_eq_zero`, `Matrix.charmatrix_diagonal`, `Bundle.Trivialization.localFrame_coeff_apply_of_mem_baseSet`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top`, `SimpleGraph.natCast_hadamard_adjMatrix`, `LinearIsometryEquiv.toContinuousLinearEquiv_smul`, `WeierstrassCurve.Projective.eval_polynomialY`, `Matrix.one_mulVec`, `AddMonoidAlgebra.coeffEquiv_apply`, `Nat.factorization_prod`, `ContinuousLinearMap.opNNNorm_mul_apply`, `Module.Basis.coord_apply`, `CliffordAlgebra.contractLeft_one`, `OreLocalization.nontrivial_of_nonZeroDivisors`, `spectrum.zero_eq`, `Int.fract_zero`, `commute_iff_lie_eq`, `Multiset.toFinsupp_support`, `ContinuousMultilinearMap.curryFinFinset_apply`, `gcd_zero_left'`, `Quaternion.normSq_star`, `ContDiffAt.smulRight`, `NormedField.nhdsWithin_isUnit_neBot`, `MvPowerSeries.coeff_eq_zero_of_lt_lexOrder`, `DividedPowerAlgebra.prod_dp`, `Quaternion.imK_sub`, `div_pos_of_neg_of_neg`, `prodXSubSMul.eval`, `TestFunction.injective_toBoundedContinuousFunctionCLM`, `Right.mul_nonneg`, `exists_integral_inj_algHom_of_fg`, `Matrix.invOf_fromBlocks₁₁_eq`, `MvPolynomial.coeff_rename_ne_zero`, `Module.Basis.mem_span_iff_repr_mem`, `Module.Basis.SmithNormalForm.repr_eq_zero_of_notMem_range`, `FormalMultilinearSeries.changeOriginSeriesTerm_bound`, `WeierstrassCurve.Jacobian.addMap_of_Y_eq`, `TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr`, `Module.Relations.Solution.IsPresentation.ker_π`, `KaehlerDifferential.quotKerTotalEquiv_apply`, `HasDerivWithinAt.sum`, `Real.contDiffAt_arccos_iff`, `AddMonoidAlgebra.mul_apply_right`, `NonUnitalSubalgebra.coe_eq_zero`, `MvPowerSeries.coeff_mul_of_add_lexOrder`, `spectrum.subset_circle_of_unitary`, `Polynomial.leadingCoeff_eq_zero_iff_deg_eq_bot`, `UniqueFactorizationMonoid.zero_notMem_normalizedFactors`, `Fintype.not_linearIndependent_iffₒₛ`, `spectrum.subset_closedBall_norm`, `KaehlerDifferential.kerTotal_map'`, `AlgebraicIndependent.matroid_isBasis_iff_of_subsingleton`, `SchwartzMap.toZeroAtInftyCLM_apply`, `Num.pred_to_nat`, `FormalMultilinearSeries.constFormalMultilinearSeries_radius`, `Odd.pow_nonpos_iff`, `Polynomial.cyclotomic_pos`, `MvPolynomial.instIsLocalHomRingHomC`, `hasEigenvector_toLin_diagonal`, `Cubic.degree_of_zero`, `cfcₙHom_nonneg_iff`, `MvPolynomial.eval₂_eq_eval_map`, `CStarRing.mul_star_self_eq_zero_iff`, `MvPolynomial.coeff_add_pow`, `AffineIndependent.eq_zero_of_affineCombination_mem_affineSpan`, `QuaternionAlgebra.star_eq_neg`, `VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le`, `Polynomial.toFinsupp_zero`, `Finsupp.weight_eq_zero_iff_eq_zero`, `ContinuousLinearMap.norm_precompL_le`, `Function.locallyFinsuppWithin.logCounting_even`, `HasFTaylorSeriesUpToOn.restrictScalars`, `Finsupp.toMultiset_map`, `Int.Ico_filter_dvd_eq`, `MvPolynomial.weightedTotalDegree_zero`, `Matrix.charpoly.univ_coeff_card`, `Finset.univ_of_card_le_two`, `HasDerivAtFilter.neg`, `MvPowerSeries.HasEval.tendsto_zero`, `Polynomial.Bivariate.equivMvPolynomial_C_C`, `Order.krullDim_eq_zero_iff_of_orderBot`, `ContinuousLinearMap.apply_apply`, `MonomialOrder.degree_sub_of_lt`, `IsStarProjection.mul_one_sub_self`, `Rep.barComplex.d_single`, `DividedPowerAlgebra.mkAlgHom_C`, `SignType.coe_mul`, `FreeAlgebra.algebraMap_eq_zero_iff`, `Module.Presentation.tautological_relation`, `MvPolynomial.isWeightedHomogeneous_C`, `ContinuousLinearMap.norm_map_removeNth_le`, `WeierstrassCurve.Jacobian.addY_self`, `MvPolynomial.linearMap_ext_iff`, `Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff`, `Matrix.one_mul`, `ContinuousMultilinearMap.hasStrictFDerivAt_uncurry`, `mul_neg_of_pos_of_neg`, `FirstOrder.Language.presburger.term_realize_eq_add_dotProduct`, `MvPolynomial.map_X`, `instWellFoundedGTWithZeroMultiplicativeIntLeOne`, `ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply`, `GroupWithZero.toNoZeroSMulDivisors`, `instSMulCommClass_sphere_sphere_ball`, `LaurentSeries.powerSeriesPart_zero`, `AlternatingMap.mkContinuousAlternating_apply`, `IsSymmSndFDerivWithinAt.eq`, `PiTensorProduct.mapLMultilinear_opNorm`, `hasDerivWithinAt_inter`, `fderivWithin_restrictScalars_comp`, `PiLp.instIsBoundedSMul`, `Quaternion.normSq_ratCast`, `Matrix.diagonal_comp_single`, `AddMonoidAlgebra.coeff_erase`, `Filter.tendsto_mul_const_atBot_iff`, `Set.zero_mem_center`, `Subsemiring.mem_nonneg`, `IsStarProjection.zero`, `IncidenceAlgebra.zeta_prod_mk`, `MulChar.sum_eq_zero_of_ne_one`, `Quaternion.imK_im`, `Set.indicator_prod_one`, `CompactlySupportedContinuousMap.instIsScalarTower`, `PerfectClosure.mk_zero`, `Matrix.vecMul_zero`, `hasDerivAt_exp_smul_const_of_mem_ball`, `MvPolynomial.eval_assoc`, `LieAlgebra.IsKilling.corootSpace_zero_eq_bot`, `LinearIsometryEquiv.conjStarAlgEquiv_apply_apply`, `MvPolynomial.monomial_single_add`, `LaurentSeries.exists_ratFunc_eq_v`, `HahnSeries.SummableFamily.powerSeriesFamily_smul`, `ax_grothendieck_zeroLocus`, `LinearMap.toMatrixAlgEquiv_transpose_apply`, `hasStrictDerivAt_exp_zero`, `Polynomial.trailingDegree_one_le`, `Quaternion.imK_add`, `wittPolynomial_eq_sum_C_mul_X_pow`, `FixedPoints.minpoly.eval₂`, `Matrix.fromCols_zero`, `associator_eq_zero`, `ENat.ceil_eq_zero`, `GroupWithZero.noZeroDivisors`, `Module.Basis.repr_self`, `star_left_conjugate_nonneg`, `Polynomial.homogenize_one`, `MvPolynomial.support_X_mul`, `PiLp.linearIndependent_single_one`, `MvPolynomial.coeffs_zero`, `exteriorPower.presentation.relations_relation`, `derivWithin_clm_apply`, `dotProduct_nonneg_of_nonneg`, `MvPolynomial.monomial_one_mul_cancel_right_iff`, `rat_inv_continuous_lemma`, `WeierstrassCurve.Projective.dblXYZ_of_Y_eq`, `Algebra.intNorm_eq_zero`, `MonoidAlgebra.domCongr_apply`, `Matrix.den_natCast`, `Quaternion.fst_re_dualNumberEquiv_symm`, `MonomialOrder.degree_mul'`, `IsSepClosed.exists_aeval_eq_zero`, `MvPowerSeries.coeff_eq_zero_of_lt_weightedOrder`, `TrivSqZeroExt.mem_kerIdeal_iff_inr`, `PowerSeries.IsWeierstrassDivisorAt.seq_zero`, `constantCoeff_wittStructureInt_zero`, `Polynomial.homogenizeLM_apply`, `LinearMap.isNilpotent_mulLeft_iff`, `Quaternion.continuous_normSq`, `Antivary.sub_mul_sub_nonpos`, `Filter.tendsto_div_const_atBot_iff_neg`, `Algebra.Generators.ker_naive`, `MvPolynomial.degreeOf_monomial_eq`, `Finsupp.linearCombination_zero`, `WithLp.unitization_isometry_inr`, `HasStrictDerivAt.congr_of_eventuallyEq`, `MvPolynomial.vanishingIdeal_zeroLocus_eq_radical`, `exists_eq_sum_perm_of_mem_doublyStochastic`, `Polynomial.exists_monic_aeval_eq_zero_forall_mem_of_mem_map`, `Nat.bitIndices_twoPowsum`, `conjneg_neg'`, `Quaternion.imI_snd_dualNumberEquiv`, `zero_pow`, `cfcₙ_smul_id`, `linearIndependent_iffₒₛ`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd`, `Nat.factorization_mul_of_coprime`, `Multiset.toFinsupp_strictMono`, `DirectSum.coe_of_mul_apply`, `Finsupp.lcomapDomain_eq_linearProjOfIsCompl`, `HasCompactSupport.convolution_integrand_bound_right`, `Polynomial.homogenize_mul`, `LinearIndepOn.pair_iff`, `IsNilpotent.of_pow`, `ArithmeticFunction.coe_zetaUnit`, `HasFPowerSeriesWithinOnBall.hasFDerivWithinAt`, `WeierstrassCurve.Affine.Point.xRep_zero`, `ArithmeticFunction.IsMultiplicative.map_mul_of_coprime`, `MonomialOrder.degree_sPolynomial_lt_sup_degree`, `MonomialOrder.leadingTerm_eq_zero_iff`, `QuadraticAlgebra.norm_eq_zero_iff_eq_zero`, `MvPolynomial.coeff_eq_zero_of_totalDegree_lt`, `left_lt_lineMap_iff_pos`, `instFreeMvPolynomialKaehlerDifferential`, `isPrimePow_iff_minFac_pow_factorization_eq`, `Mathlib.Meta.Positivity.natCeil_pos`, `ArithmeticFunction.cardFactors_apply_prime_pow`, `HasDerivAt.comp_semilinear`, `Matrix.IsHermitian.star_eigenvectorUnitary_mulVec`, `MvPolynomial.hom_bind₁`, `InnerProductSpace.symm_toEuclideanLin_rankOne`, `WeierstrassCurve.Jacobian.map_polynomialX`, `MvPolynomial.coeff_expand_zero`, `isBoundedBilinearMap_smulRight`, `MvPolynomial.C_dvd_iff_map_hom_eq_zero`, `Matrix.single_vecMul_diagonal`, `MvPolynomial.IsSymmetric.neg`, `HasDerivAt.comp_sub_const`, `ModuleFilterBasis.smul_right'`, `Matrix.inv_diagonal`, `QuaternionAlgebra.imK_swapEquiv_apply`, `Finsupp.toMultiset_inf`, `LieIdeal.root_apply_eq_zero_of_notMem_rootSet`, `SkewMonoidAlgebra.domCongr_symm`, `balanced_iff_closedBall_smul`, `Ring.inverse_zero`, `IsSimpleRing.exists_algEquiv_matrix_divisionRing`, `Module.subsingletonEquiv_apply`, `ContMDiffAt.cle_arrowCongr`, `tendsto_inv_atTop_nhds_zero_nat`, `support_factorization`, `rank_mvPolynomial_mvPolynomial`, `AnalyticOnNhd.eval_continuousLinearMap`, `Pi.single_mul_right_apply`, `MvPowerSeries.LinearTopology.hasBasis_nhds_zero`, `IncidenceAlgebra.zeta_prod_zeta`, `Associates.out_top`, `Polynomial.Monic.degree_le_zero_iff_eq_one`, `WeierstrassCurve.Jacobian.eval_polynomialZ`, `MvPowerSeries.weightedOrder_one`, `IsNilpotent.zero`, `PointedCone.closure_eq`, `HasFDerivAt.clm_comp`, `CFC.inv_nonneg_of_nonneg`, `FirstOrder.Language.presburger.isSemilinearSet_formula_realize_semilinear`, `ContinuousLinearMap.adjoint_innerSL_apply`, `Polynomial.degreeLT.basis_repr`, `IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_end`, `Function.support_pow'`, `MvPolynomial.vars_sum_subset`, `WittVector.le_coeff_eq_iff_le_sub_coeff_eq_zero`, `stdSimplex_subset_Icc`, `Ring.eq_self_iff_eq_zero_of_char_ne_two`, `Finset.affineCombinationLineMapWeights_apply_of_ne`, `MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton`, `Finset.prod_nonneg`, `Bundle.Pretrivialization.continuousLinearMapCoordChange_apply`, `WeierstrassCurve.Projective.nonsingularLift_zero`, `IsOrderedRing.toIsOrderedModule`, `ContDiffMapSupportedIn.structureMapLM_apply`, `Matrix.conjTranspose_ofNat`, `MonoidAlgebra.support_one`, `ContinuousLinearMap.mem_invtSubmodule_adjoint_iff`, `PowerSeries.isWeierstrassDivisionAt_zero`, `Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial`, `IsCompactOperator.hasEigenvalue_iff_mem_spectrum`, `AddMonoidAlgebra.mem_gradeBy_iff`, `Nat.ordCompl_self_pow`, `Matrix.det_eq_zero_of_not_linearIndependent_rows`, `toBoolRing_bot`, `MvPolynomial.degreeOf_add_le`, `AddMonoidAlgebra.mul_single_apply_of_not_exists_add`, `Matrix.kronecker_diagonal`, `Matrix.mvPolynomialX_mapMatrix_aeval`, `isBoundedLinearMap_prod_multilinear`, `Module.Basis.repr_reindex_apply`, `MvPolynomial.algebraMap_def`, `Set.Ioo.one_minus_lt_one`, `WeierstrassCurve.j_eq_zero_iff`, `HasCompactSupport.convolution_integrand_bound_right_of_subset`, `IsSemilinearSet.definable`, `Matrix.IsDiag.kronecker`, `hasStrictDerivAt_of_hasDerivAt_of_continuousAt`, `MonomialOrder.leadingCoeff_mul_of_mul_leadingCoeff_ne_zero`, `Finsupp.weight_apply`, `HasStrictDerivAt_ofNat`, `geom_sum_pos_and_lt_one`, `IsFractionRing.isUnit_den_zero`, `Quaternion.imJ_intCast`, `PointedCone.dual_anti`, `IsSepClosed.exists_eval₂_eq_zero`, `PointedCone.smul_mem`, `wbtw_mul_sub_add_iff`, `Matrix.algebraMap_matrix_apply`, `CauSeq.const_pos`, `Finset.sum_mul_self_eq_zero_iff`, `MvPolynomial.support_C`, `MvPolynomial.supported_eq_vars_subset`, `Matrix.transposeInvertibleEquivInvertible_apply`, `LaurentPolynomial.degree_zero`, `MvPolynomial.coeffs_X_mul`, `MvPowerSeries.monomial_eq'`, `HasFiniteFPowerSeriesAt.comp`, `DividedPowerAlgebra.embed_def`, `LinearMap.toMatrix_apply`, `linearDepOn_iff'ₛ`, `Matrix.BlockTriangular.mul`, `ArithmeticFunction.coe_zeta_mul_apply`, `MonomialOrder.degree_sub_leadingTerm_lt_iff`, `MvPolynomial.IsHomogeneous.coeff_isHomogeneous_of_optionEquivLeft_symm`, `hasDerivWithinAt_iff_tendsto`, `RootPairing.GeckConstruction.apply_inr_eq_zero_of_mem_span_range_u`, `AddMonoidAlgebra.mapDomain_sum`, `MvPolynomial.eval₂_comp_right`, `Representation.linearize_apply`, `TwoSidedIdeal.zero_mem`, `Matrix.transpose_list_prod`, `CategoryTheory.Mat.id_def`, `Nat.factorization_zero_right`, `pos_of_mul_pos_right`, `NumberField.house.basis_repr_norm_le_const_mul_house`, `ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero`, `MonoidAlgebra.neg_apply`, `ContDiffAt.hasStrictDerivAt'`, `MvPolynomial.weightedHomogeneousComponent_apply`, `Matrix.posDef_diagonal_iff`, `Matrix.hadamard_one_eq_diagonal_iff`, `FractionalIdeal.zero_divMod`, `notMem_nonZeroDivisorsRight_iff`, `Unitization.inlRingHom_apply`, `neg_of_div_neg_left`, `noZeroDivisors_iff_eq_zero_of_mul`, `Polynomial.aeval_homogenize_of_eq_one`, `RootPairing.isOrthogonal_iff_pairing_eq_zero`, `InnerProductSpace.Core.inner_zero_left`, `Nat.pow_factorization_choose_le`, `Finsupp.coe_orderIsoMultiset`, `Tendsto.tendsto_mul_zero_of_disjoint_cocompact_right`, `Unitary.spectrum_subset_circle`, `MonomialOrder.degree_mul_of_right_mem_nonZeroDivisors`, `Nat.factorization_le_of_le_pow`, `HasDerivAt.star_conj`, `ContinuousMapZero.coeFnAddMonoidHom_apply`, `Finset.support_prod`, `Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single`, `MvPolynomial.map_eval`, `ArithmeticFunction.sum_eq_iff_sum_smul_moebius_eq_on`, `WeierstrassCurve.IsShortNF.a₁`, `MonomialOrder.degree_sub_leadingTerm_le`, `Field.instNeZeroFinInsepDegree`, `IsManifold.instOfNatWithTopENat`, `Representation.diagonalOneEquivLeftRegular_apply_single`, `Matrix.vecMul_swap`, `ftaylorSeriesWithin_fun_zero`, `ContinuousLinearMap.norm_smulRightL_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_apply`, `AddMonoidAlgebra.mem_span_support`, `hasDerivAt_finCons`, `PowerSeries.coeff_zero_mul_X`, `inner_eq_ofReal_norm_sq_right_iff`, `Valuation.exists_div_eq_of_surjective`, `upperBounds_smul_of_pos`, `HasFDerivAt.smul`, `Polynomial.homogenize_dvd`, `MvPolynomial.rename_eq`, `AddMonoidAlgebra.support_mul_single`, `CStarAlgebra.exists_sum_four_nonneg`, `ZMod.eq_zero_of_gcd_ne_one`, `MvPolynomial.rank_eq_lift`, `IsLinearTopology.hasBasis_open_twoSidedIdeal`, `SchwartzMap.smulLeftCLM_smul`, `Finsupp.linearIndependent_single_one`, `smul_inv₀'`, `RingCone.coe_nonneg`, `LinearMap.map_finsupp_linearCombination`, `Nat.Prime.sub_one_mul_multiplicity_factorial`, `Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det`, `MvPolynomial.totalDegree_coeff_optionEquivLeft_le`, `PointedCone.DualFG.iff_exists_fg_dual`, `Finsupp.lt_wf`, `DoubleCentralizer.coe_snd`, `WeierstrassCurve.Jacobian.neg_of_Z_eq_zero`, `ContinuousLinearMap.opNorm_le_bound₂`, `Quaternion.exp_coe`, `hasFPowerSeriesAt_iff`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_one`, `MvPolynomial.derivation_ext_iff`, `MvPolynomial.coeff_mul`, `tendsto_nhdsGT_zero_of_comp_inv_tendsto_atTop`, `MonoidAlgebra.mem_supported'`, `LSeries.convolution_map_zero`, `MeasureTheory.integral_convolution`, `Int.clog_zero_right`, `Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination`, `PosSMulMono.of_smul_nonneg`, `SimpleGraph.adjMatrix_hadamard_one`, `LinearMap.toMatrixAlgEquiv_transpose_apply'`, `Module.Relations.Solution.π_single`, `Module.Basis.finTwoProd_one`, `Subgroup.exists_finsupp_of_mem_closure_range`, `HahnSeries.support_one`, `MvPolynomial.eval₂Hom_smul`, `Quaternion.star_coe`, `Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero`, `WittVector.wittAdd_zero`, `Associates.FactorSet.prod_eq_zero_iff`, `Finsupp.DegLex.single_strictAnti`, `ContinuousMultilinearMap.norm_curryMid`, `ArithmeticFunction.IsMultiplicative.eq_zero_of_squarefree_of_dvd_eq_zero`, `Filter.tendsto_const_mul_atBot_iff_pos`, `AddChar.expect_eq_ite`, `MvPolynomial.mapEquivMonic_symm_map`, `differentiableOn_inv`, `Associates.le_zero`, `Mathlib.Tactic.Linarith.lt_of_lt_of_eq`, `ringKrullDim_mvPolynomial_of_isEmpty`, `MvPolynomial.IsHomogeneous.pderiv`, `Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg`, `MvPolynomial.mem_ideal_span_X_image`, `Matrix.isPrimitive_iff`, `Quaternion.imI_one`, `hasDerivAt_of_tendstoUniformlyOnFilter`, `Submonoid.LocalizationMap.sec_zero_fst`, `Submodule.starProjection_tendsto_closure_iSup`, `Matrix.det_one_add_mul_comm`, `FirstOrder.Language.presburger.definable_iff_isSemilinearSet`, `LaurentSeries.valuation_X_pow`, `stdSimplex_eq_inter`, `LaurentPolynomial.degree_C_le`, `char_dvd_card_solutions_of_fintype_sum_lt`, `MvPolynomial.mem_restrictTotalDegree`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm`, `Module.presentationFinsupp_var`, `MvPolynomial.vars_0`, `IsLocalization.subsingleton_iff`, `TrivSqZeroExt.inv_inr`, `Quaternion.exp_eq`, `Polynomial.homogenize_neg`, `MvPolynomial.isHomogeneous_X_pow`, `IsLinearTopology.hasBasis_right_ideal`, `PointedCone.dual_univ`, `mulPosMono_iff_mulPosStrictMono`, `ZNum.of_to_int'`, `MvPolynomial.vars_add_of_disjoint`, `Matrix.invOf_mul_cancel_left`, `IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem`, `MvPolynomial.restrictTotalDegree_le_restrictDegree`, `Filter.EventuallyEq.hasDerivAtFilter_iff`, `exists_mem_doublyStochastic_eq_smul_iff`, `Nat.factorization_eq_of_coprime_left`, `factorization_one`, `HasMFDerivAt.const_smul`, `HasDerivAtFilter.fun_sum`, `EisensteinSeries.mem_gammaSet_one`, `nonpos_of_mul_nonpos_right`, `Algebra.SubmersivePresentation.basisDeriv_apply`, `MvPolynomial.bind₁_monomial`, `MonoidAlgebra.sum_single_index`, `Polynomial.integralNormalization_eval₂_eq_zero_of_commute`, `Int.Matrix.exists_ne_zero_int_vec_norm_le`, `inv_antitoneOn_Iio`, `IsAbsoluteValue.abv_eq_zero`, `Finset.zero_mem_box`, `TensorProduct.coe_finsuppScalarRight'`, `TwoSidedIdeal.mem_bot`, `LinearMap.polyCharpoly_coeff_eval`, `FormalMultilinearSeries.hasFPowerSeriesOnBall`, `SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj`, `ContinuousLinearMap.coe_mulₗᵢ`, `CompleteOrthogonalIdempotents.pair_iffₛ`, `Filter.tendsto_inv₀_cobounded'`, `MvPolynomial.induction_on_monomial`, `Matrix.det_invOf`, `MvPolynomial.degreeOf_lt_iff`, `Quaternion.imJ_sub`, `SimpleGraph.eccent_eq_zero_of_subsingleton`, `Even.pow_pos_iff`, `MonomialOrder.degree_smul_of_mem_nonZeroDivisors`, `Module.Basis.repr_unop_eq_mulOpposite_repr`, `Multiset.toDFinsupp_inj`, `Polynomial.resultant_zero_zero`, `GenContFract.convs'Aux_succ_none`, `Real.smul_iInf_of_nonneg`, `MvPolynomial.coe_coeffsIn`, `Unitization.norm_inr`, `Quaternion.normSq_coe`, `nnqsmul_nonneg`, `MvPolynomial.coe_mul`, `SkewMonoidAlgebra.coeff_single_mul`, `Valuation.is_topological_valuation`, `Module.Relations.tensor_relation`, `HasFDerivWithinAt.continuousAlternatingMap_apply_const`, `ContinuousLinearMap.innerSL_apply_comp`, `MvPolynomial.mem_image_comap_C_basicOpen`, `NonUnitalStarAlgHom.zero_apply`, `Polynomial.coeff_natDegree_eq_zero_of_degree_lt`, `inner_vsub_left_eq_zero_symm`, `Balanced.smul_mono`, `DualNumber.isNilpotent_eps`, `MvPolynomial.continuous_eval`, `NonnegSpectrumClass.iff_spectrum_nonneg`, `ContinuousLinearMap.toSesqForm_apply_norm_le`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd`, `Unitization.inr_nonneg_iff`, `ite_zero_smul`, `sub_mul_sub_neg_iff`, `Algebra.Presentation.mem_ker_naive`, `MvPolynomial.C_eq_smul_one`, `Matrix.isNilpotent_iff_forall_col`, `Representation.linearizeTrivial_def`, `Polynomial.coeffList_monomial`, `ContinuousLinearMap.coeFn_holder`, `PointedCone.dual_eq_iInter_dual_singleton`, `AddMonoidAlgebra.supDegree_mem_support`, `pos_iff_pos_of_mul_pos`, `MvPowerSeries.coeff_mul`, `MvPolynomial.coeff_killCompl`, `ContDiffMapSupportedIn.structureMapLM_eq`, `MvPolynomial.vars_monomial_single`, `MvPolynomial.evalₗ_apply`, `div_neg_of_pos_of_neg`, `Polynomial.degree_natCast_le`, `PosSMulStrictMono.toPosSMulReflectLT`, `CStarMatrix.norm_def`, `Polynomial.degree_coe_units`, `FirstOrder.Field.charP_iff_model_fieldOfChar`, `ContMDiff.cle_arrowCongr`, `WeierstrassCurve.HasMultiplicativeReduction.multiplicativeReduction`, `ContinuousLinearMap.coe_deriv₂`, `MonoidAlgebra.coeff_sub`, `IsAlgClosed.exists_aeval_eq_zero`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le`, `exists_isIdempotentElem_mul_eq_zero_of_ker_isNilpotent`, `Finsupp.Colex.single_strictMono`, `Representation.IndV.hom_ext_iff`, `Polynomial.natDegree_list_prod_le`, `Matrix.dotProduct_self_star_pos_iff`, `cfcₙ_apply_of_not_continuousOn`, `ValuativeRel.zero_vlt_iff`, `TrivSqZeroExt.eq_smul_exp_of_invertible`, `Module.Relations.Solution.IsPresentation.π_desc_apply`, `Polynomial.coeff_eq_zero_of_degree_lt`, `Unitization.continuous_inr`, `MvPolynomial.esymmAlgHom_surjective`, `eventually_nhdsGT_zero_mul_left`, `Nat.Iic_factorization_prod_pow_injective`, `AddMonoidAlgebra.coeff_update`, `WeierstrassCurve.IsCharTwoJEqZeroNF.a₂`, `Finsupp.toFreeAbelianGroup_comp_toFinsupp`, `Set.inv_op_smul_set_distrib₀`, `MvPolynomial.aevalTower_ofNat`, `exteriorPower.basis_repr_self`, `PointedCone.dual_dual_flip_dual`, `DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap`, `ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply`, `ContinuousLinearMap.adjoint_adjoint`, `MonoidWithZeroHom.toZeroHom_injective`, `RootPairing.GeckConstruction.lie_e_f_ne`, `HasCompactSupport.hasFDerivAt_convolution_left`, `MvPolynomial.killCompl_monomial_eq_zero_of_notMem_range`, `spectrum.spectralRadius_zero`, `Matrix.fromBlocks_diagonal_pow`, `PointedCone.coe_comap`, `WithZero.withZeroUnitsEquiv_strictMono`, `HahnSeries.coeff_single_mul`, `SkewMonoidAlgebra.liftNC_smul`, `Convex.mem_Ioc`, `Quaternion.re_nnratCast`, `CFC.abs_eq_zero_iff`, `Unitization.isStarNormal_inr`, `Filter.Tendsto.inv_tendsto_atBot`, `MvPolynomial.monomial_modMonomial`, `HasDerivWithinAt.finCons`, `ENat.lt_one_iff_eq_zero`, `HasStrictDerivAt.clm_apply`, `MvPolynomial.WeightedHomogeneousSubmodule.gradedMonoid`, `TemperedDistribution.smulLeftCLM_apply_apply`, `HasDerivAt.congr_deriv`, `star_neg_iff`, `Nonneg.existsAddOfLE`, `instPosSMulStrictMonoNatOfIsOrderedAddMonoid`, `GenContFract.IntFractPair.nth_stream_fr_nonneg`, `MonoidAlgebra.coeff_erase`, `PointedCone.dual_eq_dual_id_map`, `HasDerivAt.tendsto_slope_zero_right`, `RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict`, `MvPolynomial.esymmAlgEquiv_symm_apply`, `Function.support_div`, `geom_sum_pos'`, `MvPowerSeries.lexOrder_mul_ge`, `PrimeSpectrum.basicOpen_eq_bot_iff`, `Matrix.mul_self_mul_conjTranspose_eq_zero`, `WeierstrassCurve.Projective.addU_of_Z_eq_zero_right`, `ContinuousLinearMap.hasDerivAt_of_bilinear`, `Module.Flat.exists_factorization_of_isFinitelyPresented`, `ArithmeticFunction.carmichael_two_pow_of_ne_two`, `WeierstrassCurve.Projective.addXYZ_self`, `Int.ModEq.listSum_map`, `tendsto_pow_atTop_nhdsWithin_zero_of_lt_one`, `instIsPushoutFractionRingMvPolynomial_1`, `rat_add_continuous_lemma`, `MvPolynomial.rename_surjective`, `Finsupp.toMultiset_eq_iff`, `second_derivative_symmetric_of_eventually`, `KaehlerDifferential.linearCombination_surjective`, `AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact`, `HasFDerivAt.comp_hasDerivAt_of_eq`, `GroupAlgebra.mul_average_right`, `ArithmeticFunction.toFun_eq`, `HahnSeries.cardSupp_pow_le`, `LieAlgebra.Orthogonal.pd_inv`, `Module.Basis.sumQuot_repr_inr`, `MvPolynomial.map_id`, `Filter.tendsto_const_mul_atTop_iff`, `IsTopologicallyNilpotent.zero`, `ValueDistribution.logCounting_mul_zero_le`, `Finsupp.linearCombination_onFinset`, `QuadraticAlgebra.algebraMap_im`, `MvPowerSeries.coeff_add_monomial_mul`, `WeierstrassCurve.Jacobian.add_of_Y_ne`, `AlgebraicGeometry.affine_isReduced_iff`, `IsAdjoinRootMonic.coeff_root_pow`, `PowerSeries.divXPowOrder_zero`, `OrthonormalBasis.inner_eq_ite`, `zero_geom_sum`, `HasDerivAtFilter.const_sub`, `MvPolynomial.eval₂Hom_comp_expand`, `HasStrictFDerivAt.smul`, `AddMonoidAlgebra.mul_apply_antidiagonal`, `ContinuousLinearMap.orthogonal_ker`, `CharTwo.range_intCast`, `AddMonoidAlgebra.support_one`, `Module.Basis.coord_repr_symm`, `isReduced_of_noZeroDivisors`, `DihedralGroup.r_zero`, `Module.Relations.Solution.linearCombination_var_relation`, `Matrix.PosDef.dotProduct_mulVec_pos`, `Set.Ioo.coe_mul`, `ZMod.dft_apply_zero`, `Polynomial.toMvPolynomial_C`, `AnalyticAt.hasStrictDerivAt`, `ProbabilityTheory.IsCondKernelCDF.toKernel_apply`, `ENat.epow_zero`, `Matrix.TransvectionStruct.mul_inv`, `ENat.not_lt_zero`, `MonomialOrder.degree_sub_LTerm_le`, `PointedCone.mem_lineal`, `Nonneg.segment_eq_Icc`, `Polynomial.Chebyshev.U_eval_zero_of_even`, `MulPosReflectLT.toMulPosReflectLE`, `Rat.padicValuation_le_one_iff`, `ContDiffMapSupportedIn.norm_toBoundedContinuousFunction`, `Matrix.one_div_zpow`, `Set.indicator_eq_one_iff_mem`, `Nat.factorization_le_factorization_of_dvd_right`, `Continuous.cfcₙ_nnreal'`, `Filter.EventuallyEq.hasDerivWithinAt_iff`, `left_le_lineMap_iff_nonneg`, `ProbabilityTheory.instIsProbabilityMeasurecdf`, `Nat.ordCompl_of_not_prime`, `PEquiv.single_mul_single`, `MonomialOrder.lex_le_iff_of_unique`, `Quaternion.nnnorm_coe`, `MonomialOrder.sPolynomial_mul_monomial`, `lineMap_lt_left_iff_neg`, `TrivSqZeroExt.norm_inr`, `HahnModule.single_zero_smul_eq_smul`, `MonomialOrder.degree_prod_of_mem_nonZeroDivisors`, `PowerSeries.IsRestricted.zero`, `Algebra.Generators.toExtension_commRing`, `Matrix.conjTranspose_invOf`, `Nat.factorization_factorial_mul`, `SimpleGraph.incMatrix_apply_eq_zero_iff`, `Unitization.algebraMap_eq_inl_comp`, `InnerProductSpace.norm_rankOne`, `HahnSeries.cardSupp_mul_le`, `mem_nilradical`, `IsStrictlyPositive.nonneg_add`, `Nonneg.instIsometricContinuousFunctionalCalculus`, `Pi.noZeroSMulDivisors`, `PosMulReflectLE.toPosMulReflectLT`, `ArithmeticFunction.cardDistinctFactors_eq_cardFactors_iff_squarefree`, `IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers`, `hasFDerivAt_integral_of_dominated_loc_of_lip`, `LinearMap.BilinForm.iIsOrtho_def`, `Mathlib.Tactic.Ring.pow_zero`, `smul_eq_zero`, `MvPowerSeries.trunc'_C`, `MvPowerSeries.prod_monomial`, `OnePoint.equivProjectivization_apply_infinity`, `Convex.mem_Ico`, `Hyperreal.epsilon_pos`, `MonoidAlgebra.mul_single_apply_aux`, `LucasLehmer.X.snd_natCast`, `noZeroDivisors_iff_right_eq_zero_of_mul`, `LinearMap.BilinForm.apply_dualBasis_right`, `PiTensorProduct.mapLMultilinear_toFun_apply`, `ZLattice.abs_repr_le`, `CStarMatrix.inner_toCLM_conjTranspose_right`, `HasDerivAtFilter.fun_const_smul`, `IsRightCancelMulZero.to_noZeroDivisors`, `MonomialOrder.degree_pow_of_pow_leadingCoeff_ne_zero`, `ArithmeticFunction.moebius_apply_isPrimePow_not_prime`, `DirectSum.IsInternal.collectedBasis_repr_of_mem`, `Module.Basis.coe_sumCoords`, `Algebra.Generators.Hom.equivAlgHom_apply_coe`, `Seminorm.closedBall_smul_closedBall`, `Finset.dens_pos`, `ContinuousAffineMap.toConstProdContinuousLinearMap_snd`, `MvPolynomial.decomposition.decompose'_eq`, `ENat.top_mul'`, `Matrix.charmatrix_zero`, `cfcUnits_zpow`, `WithZeroTopology.instContinuousInv₀`, `IsAbsoluteValue.abv_pos`, `Algebra.Generators.C_mul_X_sub_one_mem_ker`, `cfcₙ_nonneg_of_predicate`, `MvPolynomial.universalFactorizationMapPresentation_jacobian`, `Rat.cast_eq_zero`, `MonoidAlgebra.ofCoeff_add`, `PointedCone.dual_singleton`, `ContinuousMultilinearMap.curryMidEquiv_symm_apply`, `FormalMultilinearSeries.comp_summable_nnreal`, `Representation.LinearizeMonoidal.ε_toLinearMap`, `Unitization.nnnorm_inr`, `WeierstrassCurve.b₂_of_isCharTwoJEqZeroNF`, `Matrix.mul_adjugate`, `NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat`, `Polynomial.eval₂_reverse_eq_zero_iff`, `MvPowerSeries.prod_smul_X_eq_smul_monomial_one`, `LinearMap.sum_repr_mul_repr_mul`, `DividedPowerAlgebra.dp_eq_mkRingHom`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top`, `MonomialOrder.sPolynomial_leadingTerm_mul`, `Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap`, `CStarMatrix.toCLM_apply_single_apply`, `NNRat.cast_lt_zero`, `ContinuousMultilinearMap.uncurryRight_norm`, `ContinuousLinearMap.flipAlternating_apply_apply`, `Nat.squarefree_iff_factorization_le_one`, `MonoidAlgebra.mapRangeRingHom_apply`, `PointedCone.salient_iff_inter_neg_eq_singleton`, `Metric.sphere.instIsTopologicalGroup`, `Int.Matrix.exists_ne_zero_int_vec_norm_le'`, `MvPolynomial.esymmAlgHom_injective`, `Representation.linearizeTrivialIso_symm_apply`, `exists_pos_right_iff_sameRay_and_ne_zero`, `Hyperreal.tendsto_atTop_iff`, `MvPolynomial.coeff_sum`, `MvPowerSeries.trunc'_C_mul`, `MvPolynomial.commAlgEquiv_C_X`, `MvPolynomial.expand_zero_apply`, `LinearMap.toLinearMap₂'Aux_toMatrix₂Aux`, `Polynomial.homogenize_monomial`, `cfc_nonpos`, `LinearOrderedCommMonoidWithZero.toZeroLeOneClass`, `Matrix.gram_single`, `Quaternion.star_eq_self`, `HasDerivAt.mul_const`, `HasStrictDerivAt.fun_smul`, `List.sum_fixedLengthDigits_sum`, `Function.locallyFinsuppWithin.toClosedBall_eval_within`, `WeierstrassCurve.b₄_of_isCharTwoJEqZeroNF_of_char_two`, `Filter.tendsto_div_const_atBot_iff_pos`, `Finsupp.DegLex.wellFounded`, `LinearMap.trace_lie`, `PowerBasis.liftEquiv_apply_coe`, `Module.Basis.ofIsLocalizedModule_repr_apply`, `LaurentSeries.powerSeriesPart_eq_zero`, `Nonneg.instIsStrictOrderedModule`, `LinearOrderedField.toPosSMulStrictMono_rat`, `sq_eq_zero_iff`, `Matrix.blockDiagonal'_pow`, `MvPowerSeries.truncFinset_truncFinset_pow`, `SkewMonoidAlgebra.mul_def`, `Representation.leftRegularMapEquiv_symm_apply_toFun`, `Matrix.kronecker_zero`, `WeierstrassCurve.Projective.negDblY_of_Y_eq'`, `Filter.NeBot.div_zero_nonneg`, `AddMonoidAlgebra.mem_supported`, `Polynomial.coeff_freeMonic`, `MonomialOrder.degree_sPolynomial`, `Num.add_to_nat`, `Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap'`, `Matrix.toBilin'_single`, `div_pos_iff_of_pos_left`, `Nat.preimage_ceil_zero`, `AddMonoidAlgebra.apply_supDegree_add_supDegree`, `tendsto_mul_nhds_zero_prod_of_disjoint_cocompact`, `polynomialFunctions.comap_compRightAlgHom_iccHomeoI`, `ArithmeticFunction.abscissaOfAbsConv_moebius`, `Module.Relations.Solution.ofQuotient_π`, `FaithfulSMul.algebraMap_eq_zero_iff`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply`, `iteratedFDeriv_succ_apply_left`, `IsSymmSndFDerivAt.eq`, `Height.logHeight_sumElim_zero_eq`, `WeierstrassCurve.Projective.addZ_of_X_eq`, `QuadraticForm.sigNeg_of_equiv_weightedSumSquares`, `Orthonormal.inner_eq_zero`, `MvPolynomial.renameSymmetricSubalgebra_apply_coe`, `hasDerivWithinAt_sub_const_iff`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux`, `Height.logHeight_cons_zero`, `Polynomial.degree_C_le`, `WeierstrassCurve.a₃_of_isCharTwoJNeZeroNF`, `exists_mem_nhds_zero_mul_subset`, `Algebra.FinitePresentation.iff_quotient_mvPolynomial'`, `Pi.single_mul`, `LieAlgebra.SpecialLinear.sl_non_abelian`, `List.prod_nonneg`, `CFC.spectrum_zero_eq`, `HasFDerivAt.continuousMultilinearMap_apply`, `RCLike.zero_im`, `Quaternion.imK_snd_dualNumberEquiv`, `CongruenceSubgroup.Gamma0_mem`, `fderiv_inv'`, `Module.Basis.traceDual_eq_iff`, `Matrix.mul_conjTranspose_mul_self_eq_zero`, `MvPolynomial.monomial_dvd_monomial`, `ContinuousLinearMapWOT.ext_inner_iff`, `Polynomial.Chebyshev.T_eval_zero_of_odd`, `MonomialOrder.degree_X_le_single`, `MvPolynomial.coe_mapEquivMonic_comp`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le`, `MvPolynomial.eq_zero_of_eval_zero_at_prod_finset`, `IsStarProjection.nonneg`, `MvPolynomial.transcendental_supported_polynomial_aeval_X`, `PointedCone.dual_span`, `Quaternion.imI_ratCast`, `Nat.card_finMulAntidiag_of_squarefree`, `stdSimplexEquivIcc_zero`, `PowerSeries.order_eq_nat`, `Matrix.permMatrix_l2_opNorm_eq`, `instIsPushoutFractionRingMvPolynomial`, `Height.max_mulHeightBound_zero_one_eq_one`, `EuclideanDomain.mod_eq_zero`, `HasStrictDerivAt.star`, `tendsto_zero_geometric_tsum_pnat`, `SimpleGraph.incMatrix_mul_transpose_apply_of_adj`, `Matrix.PosSemidef.diag_nonneg`, `FormalMultilinearSeries.comp_assoc`, `LieModule.isCompl_genWeightSpaceOf_zero_posFittingCompOf`, `Set.Icc.instZeroLEOneClass`, `MvPolynomial.monomial_mul_modMonomial`, `MvPolynomial.eval_polynomial_eval_finSuccEquiv`, `MvPolynomial.constantCoeff_comp_algebraMap`, `HasFPowerSeriesWithinAt.comp`, `MvPolynomial.sumToIter_Xl`, `LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly`, `Quaternion.ext_iff`, `NNRat.cast_listSum`, `Finsupp.image_pow_eq_finsuppProd_image`, `Int.fract_eq_iff`, `Representation.ofMulAction_def`, `DividedPowerAlgebra.dp_null`, `CliffordAlgebraQuaternion.ofQuaternion_toQuaternion`, `DividedPowers.dpow_finsupp_sum`, `MvPolynomial.pderiv_inl_universalFactorizationMap_X`, `Nat.eleven_dvd_iff`, `LinearEquiv.piRing_apply`, `Finsupp.sym2_support_eq_preimage_support_mul`, `ArithmeticFunction.abs_moebius`, `WittVector.constantCoeff_wittSub`, `Nat.divisors_eq_image_Iic_factorization_prod_pow`, `SkewMonoidAlgebra.lift_symm_apply`, `hasEigenvalue_toLin_diagonal_iff`, `Mathlib.Tactic.ComputeDegree.coeff_smul`, `Nat.zeckendorf_sum_fib`, `MvPolynomial.counit_X`, `mem_nonZeroDivisorsRight_iff`, `continuousMultilinearCurryFin1_apply`, `Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff`, `Matrix.vecMul_one`, `MvPolynomial.instFaithfulSMul`, `InnerProductSpace.gramSchmidt_inv_triangular`, `MvPolynomial.rename_id`, `AnalyticAt.analyticOrderAt_eq_zero`, `PowerSeries.coeff_zero_X`, `WeierstrassCurve.Jacobian.neg_of_Z_eq_zero'`, `CliffordAlgebra.contractLeft_algebraMap`, `IsStarProjection.one_sub_nonneg`, `OreLocalization.inv_def`, `MvPolynomial.eval₂Hom_comp_C`, `Even.zpow_pos`, `Nat.factorization_factorial_eq_zero_of_lt`, `HilbertBasis.finite_spans_dense`, `RCLike.ofReal_lt_zero`, `HasStrictDerivAt.fun_pow`, `Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val`, `KaehlerDifferential.kerTotal_mkQ_single_algebraMap`, `LinearIsometry.adjoint_comp_self`, `MonoidAlgebra.mul_apply_left`, `Mathlib.Tactic.Ring.pow_atom`, `MvPolynomial.idealOfVars_fg`, `MvPolynomial.rTensorAlgHom_apply_eq`, `List.getElem_splitWrtCompositionAux`, `monovaryOn_iff_forall_mul_nonneg`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_zero` 📖	mathematical	—	`toMul` `toZero`	—	—
`zero_mul` 📖	mathematical	—	`toMul` `toZero`	—	—

MulZeroOneClass

Definitions

Name	Category	Theorems
`toMulOneClass` 📖	CompOp	1759 math math: `ValuativeRel.ValueGroupWithZero.mk_one_one`, `normalize_one`, `LinearMap.det_toContinuousLinearMap`, `IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal`, `IsLocalization.localization_localization_isLocalization_of_has_all_units`, `Matrix.UnitaryGroup.toLin'_one`, `nonZeroDivisors_le_comap_nonZeroDivisors_of_injective`, `AddMonoidAlgebra.singleHom_apply`, `UniqueFactorizationMonoid.factors_one`, `IsLocalization.mul_add_inv_left`, `Matrix.IsAdjMatrix.toGraph_adj`, `Module.Basis.det_comp_basis`, `RatFunc.mk_def_of_ne`, `gcd_one_left'`, `sq_lt_one_iff₀`, `SymplecticGroup.transpose_mem_iff`, `reindex_mem_doublyStochastic`, `AddMonoidAlgebra.lift_apply'`, `MonoidAlgebra.liftMagma_apply_apply`, `groupHomology.mapCycles₂_comp_assoc`, `Valuation.IsTrivialOn.valuation_algebraMap_le_one`, `Rep.trivial_ρ`, `LinearMap.detAux_def''`, `Subring.copy_toSubsemiring`, `RatFunc.mk_coe_def`, `Algebra.norm_algebraMap_of_basis`, `Submonoid.subsemiringClosure_toAddSubmonoid`, `RingHom.map_add'`, `ValuativeRel.ValueGroupWithZero.mk_eq_one`, `AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply`, `MeasureTheory.Measure.addHaar_image_continuousLinearMap`, `Valuation.FiniteField.algebraMap_le_one`, `Valuation.FiniteField.algebraMap_eq_one`, `AddMonoidAlgebra.algHom_ext'_iff`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `Ideal.finite_setOf_absNorm_le₀`, `NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet_mixedEmbedding`, `isSMulRegular_iff_mem_nonZeroSMulDivisors`, `groupCohomology.mem_cocycles₂_def`, `ClassGroup.mk0_integralRep`, `TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular`, `Valuation.one_apply_lt_one_iff`, `RingPreordering.ext_iff`, `RatFunc.coe_mapAlgHom_eq_coe_map`, `groupCohomology.d₂₃_hom_apply`, `reindex_mem_doublyStochastic_iff`, `LocalizedModule.r.isEquiv`, `ClassGroup.mk0_eq_mk0_iff`, `PiTensorProduct.mapLMonoidHom_apply`, `NNReal.rpowMonoidHom_apply`, `Valuation.val_mrange_zero`, `PrimeSpectrum.localization_specComap_range`, `Unitization.inrNonUnitalAlgHom_toFun`, `NonUnitalSubalgebraClass.coe_subtype`, `Ideal.absNorm_span_insert`, `Subsemiring.mem_carrier`, `OrderMonoidWithZeroHom.coe_orderMonoidHom`, `Matrix.UnitaryGroup.toGL_mul`, `Valuation.map_one_add_of_lt`, `UniqueFactorizationMonoid.moebius_one`, `spinGroup.star_eq_inv`, `Circle.exp_arg`, `Algebra.norm_eq_zero_iff_of_basis`, `Circle.injective_arg`, `mem_nonZeroDivisors_iff_left`, `IsLocalization.mk'_spec_mk`, `Submodule.mem_localized'`, `IsLocalization.smul_mem_finsetIntegerMultiple_span`, `WittVector.teichmuller_mul_pow_coeff_of_ne`, `AddMonoidAlgebra.liftNCRingHom_single`, `IsDedekindFiniteMonoid.iff_eq_of_mul_right_eq_one`, `RatFunc.liftMonoidWithZeroHom_apply_ofFractionRing_mk`, `groupHomology.chainsMap_f_3_comp_chainsIso₃_apply`, `NumberField.norm_norm_le_norm_mul_house_pow`, `SkewMonoidAlgebra.algHom_ext'_iff`, `Rep.resCoindToHom_hom_apply_coe`, `spinGroup.coe_star_mul_self`, `SkewMonoidAlgebra.lift_apply'`, `groupHomology.d₃₂_single`, `MulChar.map_one`, `SymplecticGroup.coe_inv`, `Rep.coindToInd_of_support_subset_orbit`, `finrank_quotient_span_eq_natDegree_norm`, `Representation.finsupp_apply`, `Matrix.one_kronecker`, `AffineEquiv.coe_homothetyUnitsMulHom_eq_homothetyHom_coe`, `groupHomology.mapCycles₁_comp_apply`, `IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff_mem_primeCompl`, `pinGroup.coe_star_mul_self`, `IsLocalization.map_surjective_of_surjective`, `FDRep.endRingEquiv_symm_comp_ρ`, `Representation.Coinvariants.mk_inv_tmul`, `MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar`, `LinearEquiv.algEquivOfRing_apply`, `Subring.addEquivOp_apply_coe`, `Real.fderiv_fourierChar_neg_bilinear_right_apply`, `LinearMap.det_mulLeft`, `MulChar.toMonoidWithZeroHom_apply`, `SymplecticGroup.coe_J`, `Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly`, `Algebra.norm_eq_matrix_det`, `WithZero.lift'_symm_apply_apply`, `Representation.asAlgebraHom_single`, `SymplecticGroup.transpose_mem`, `Representation.freeLift_single_single`, `Matrix.reindex_mem_colStochastic_iff`, `Matrix.hadamard_one_eq_zero_iff`, `Representation.asGroupHom_apply`, `MonoidAlgebra.algHom_ext'_iff`, `Ring.ordFrac_eq_div`, `LinearMap.det_pi`, `IsLocalization.map_mk'`, `NonUnitalAlgHom.range_comp_le_range`, `Ideal.intNorm_mem_spanNorm`, `Submonoid.mem_pos`, `Matrix.specialUnitaryGroup_le_unitaryGroup`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst`, `ArithmeticFunction.isMultiplicative_one`, `unitsNonZeroDivisorsEquiv_apply`, `sum_hom_units`, `SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of`, `LocallyConstant.charFn_eq_one`, `Valuation.IsTrivialOn.eq_one`, `AddMonoidAlgebra.mapDomainNonUnitalAlgHom_apply`, `OrderMonoidWithZeroHom.coe_comp_orderMonoidHom`, `MonoidWithZeroHom.mrange_nontrivial`, `Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single`, `LinearMap.det_zero`, `SkewMonoidAlgebra.smul_of`, `NumberField.mixedEmbedding.norm_eq_norm`, `Unitization.algHom_ext'_iff`, `IsLocalization.surj`, `Submodule.toSubalgebra_toSubsemiring`, `NeZero.one`, `Matrix.IsAdjMatrix.apply_ne_one_iff`, `Circle.ofConjDivSelf_coe`, `IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow`, `Representation.linearize_single`, `smulMonoidWithZeroHom_apply`, `OreLocalization.universalHom_apply`, `spinGroup.star_eq_inv'`, `IsLocalization.mk'_pow`, `NonUnitalAlgHom.coe_lmul_eq_mul`, `RatFunc.map_apply_ofFractionRing_mk`, `groupHomology.mem_cycles₂_iff`, `pinGroup.val_inv_toUnits_apply`, `Ring.inverse_mul_cancel`, `Circle.starRingEnd_addChar`, `QuadraticAlgebra.norm_algebraMap`, `IsLocalization.mk'_tmul`, `Rep.coindToInd_indToCoind`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply`, `mem_doublyStochastic_iff_sum`, `NumberField.FinitePlace.prod_eq_inv_abs_norm`, `Localization.localRingHom_mk'`, `groupCohomology.d₁₂_hom_apply`, `IntermediateField.mem_carrier`, `Pi.single_apply_smul`, `isRightRegular_iff_mem_nonZeroDivisorsRight`, `WittVector.map_teichmuller`, `Rep.to_Module_monoidAlgebra_map_aux`, `IsLocalization.lift_mk'_spec`, `groupHomology.mapCycles₁_comp_assoc`, `Representation.directSum_apply`, `ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_apply`, `Submonoid.subsemiringClosure_eq_closure`, `IsLocalization.lift_mem_adjoin_finsetIntegerMultiple`, `ValuativeRel.zero_srel_coe_posSubmonoid`, `Matrix.permMatrix_mem_rowStochastic`, `LocalizedModule.mk_add_mk`, `IsLocalizedModule.liftOfLE_mk'`, `IsLocalization.mem_span_map`, `MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv`, `Localization.liftOn_zero`, `IsLocalizedModule.iso_symm_apply`, `IsLocalization.isUnit_comp`, `Ideal.norm_dvd_iff`, `FractionalIdeal.absNorm_eq'`, `LocalizedModule.liftOn_mk`, `NonUnitalSubalgebra.inclusion_mk`, `pinGroup.star_mul_self`, `Ideal.map_spanIntNorm`, `AddCircle.homeomorphCircle'_symm_apply`, `IsLocalizedModule.iso_apply_mk`, `NonUnitalSubalgebra.topologicalClosure_map_le`, `IsFractionRing.mk'_eq_one_iff_eq`, `isStablyFiniteRing_iff_injective_of_surjective`, `RingHom.coe_monoidHom_id`, `instIsStablyFiniteRingSubtypeMem`, `Rat.isFractionRingDen`, `MvPowerSeries.monomial_mem_nonzeroDivisors`, `LocalizedModule.divBy_apply`, `mul_inv_cancel₀`, `groupCohomology.d₀₁_hom_apply`, `Ideal.absNorm_pos_iff_mem_nonZeroDivisors`, `Representation.ofMulAction_apply`, `IsLocalizedModule.mk'_eq_zero'`, `groupHomology.d₃₂_single_one_thd`, `GradedAlgHom.coe_mks`, `NonUnitalSubalgebra.inclusion_right`, `IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal`, `rotation_apply`, `toMatrix_rotation`, `AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap`, `IsFractionRing.mk'_eq_div`, `FreeNonUnitalNonAssocAlgebra.of_comp_lift`, `Submodule.mem_torsion_iff`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le`, `RatFunc.liftOn_ofFractionRing_mk`, `MulSemiringActionSemiHomClass.toMonoidHomClass`, `MonoidAlgebra.mem_adjoin_support`, `IsLocalization.smul_mk'_self`, `NonUnitalSubalgebra.topologicalClosure_map`, `groupCohomology.map_H0Iso_hom_f_apply`, `StarSubalgebra.toNonUnitalStarSubalgebra_toStarSubalgebra`, `Algebra.dvd_algebraMap_intNorm_self`, `Representation.apply_sub_id_partialSum_eq`, `Submonoid.adjoin_eq_span_of_eq_span`, `Representation.asAlgebraHom_def`, `WittVector.teichmuller_zero`, `Associates.out_one`, `QuadraticAlgebra.norm_zero`, `Submonoid.subsemiringClosure_coe`, `MulChar.one_apply_coe`, `AddMonoidAlgebra.divOfHom_apply_apply`, `IsIdempotentElem.one_compl`, `FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal`, `Orientation.map_eq_neg_iff_det_neg`, `PrincipalIdealRing.mem_submonoid_of_factors_subset_of_units_subset`, `mem_nonZeroDivisors_iff`, `IsLocalization.mk'_mul_cancel_left`, `ClassGroup.mk0_eq_one_iff`, `one_le_finprod`, `Algebra.algebraMap_intNorm`, `OreLocalization.nonempty_oreSet_iff_of_noZeroDivisors`, `Representation.Coinvariants.mk_tmul_inv`, `Matrix.IsHermitian.eigenvectorUnitary_col_eq`, `SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_quotMk`, `MonoidAlgebra.of_mem_span_of_iff`, `IsLocalizedModule.exist_integer_multiples`, `IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe`, `groupCohomology.mem_cocycles₁_def`, `RootPairing.Equiv.weightHom_toLinearMap`, `Matrix.permMatrixHom_apply`, `spinGroup.mem_iff`, `MvPowerSeries.monomial_mem_nonzeroDivisorsLeft`, `SimpleGraph.adjMatrix_hadamard_ofNat`, `Representation.Coinvariants.le_comap_ker`, `NumberField.Units.dirichletUnitTheorem.seq_next`, `num_isRoot_scaleRoots_of_aeval_eq_zero`, `Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_iInf`, `Ring.inverse_invertible`, `IsFractionRing.exists_reduced_fraction`, `LinearMap.det_baseChange`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion`, `RatFunc.map_injective`, `unitInterval.mem_unitIntervalSubmonoid`, `FractionalIdeal.isFractional_span_iff`, `groupCohomology.mapShortComplexH2_comp_assoc`, `MonoidAlgebra.lift_symm_apply`, `IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two`, `List.one_le_prod`, `IsLocalization.isLocalization_iff_of_base_ringEquiv`, `LinearMap.isUnit_iff_isUnit_det`, `one_lt_sq_iff₀`, `NumberField.FinitePlace.prod_eq_inv_abs_norm_int`, `MonoidHom.map_frobeniusEquiv_symm`, `MonoidHom.map_iterate_frobenius`, `LocalizedModule.divBy_mul_by`, `groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply`, `groupCohomology.mapCocycles₂_comp_i_apply`, `MonoidAlgebra.coe_liftNCAlgHom`, `LocalizedModule.mk_mul_mk`, `MonoidAlgebra.support_gen_of_gen'`, `CStarMatrix.norm_def'`, `Representation.ofMulAction_single`, `AlgHom.commutes'`, `groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂`, `groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply`, `RatFunc.coe_mapRingHom_eq_coe_map`, `Subsemiring.addEquivOp_apply_coe`, `Complex.UnitDisc.coe_smul_circle`, `Subring.toSubmonoid_mono`, `Representation.ofDistribMulAction_apply_apply`, `LocalizedModule.mk_eq`, `ValuativeRel.ValueGroupWithZero.mk_eq_div`, `ValuativeRel.ValueGroupWithZero.exact`, `LocalizedModule.lift'_mk`, `groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply`, `FreeNonUnitalNonAssocAlgebra.lift_unique`, `Valuation.unit_map_eq`, `RingHom.rangeS_toSubmonoid`, `linearIndependent_monoidHom`, `MonoidWithZeroHom.coe_copy`, `groupHomology.d₂₁_single_inv_mul_ρ_add_single`, `NonUnitalSubalgebra.iSupLift_of_mem`, `ValuativeExtension.mapValueGroupWithZero_mk`, `NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply`, `SymplecticGroup.mem_iff`, `Subring.mopRingEquivOp_apply_coe`, `Perfection.mk_teichmuller`, `Representation.instIsTrivialSubtypeMemSubgroupSubmoduleInvariantsCompLinearMapIdSubtypeToInvariants`, `mem_nonZeroSMulDivisors_iff`, `Finset.extract_gcd`, `IsLocalizedModule.mk'_add_mk'`, `Matrix.single_eq_single_vecMulVec_single`, `instIsDedekindFiniteMonoidOfIsStablyFiniteRing`, `PreTilt.mk_comp_untilt_eq_coeff_zero`, `IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_pow_ne_two`, `spinGroup.coe_mul_star_self`, `CongruenceSubgroup.Gamma1_mem'`, `MonoidWithZeroHom.map_one`, `LocalizedModule.mk_cancel`, `mul_eq_left₀`, `left_eq_mul₀`, `FreeAbelianGroup.liftMonoid_coe_addMonoidHom`, `Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField`, `Submonoid.LocalizationMap.subsingleton_iff`, `pinGroup.val_toUnits_apply`, `Matrix.IsHermitian.eigenvectorUnitary_mulVec`, `QuadraticAlgebra.norm_eq_one_iff_mem_unitary`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj`, `LocalizedModule.mem_ker_mkLinearMap_iff`, `Rep.ActionToRep_obj_ρ`, `MulRingSeminorm.map_mul'`, `IsIntegral.exists_multiple_integral_of_isLocalization`, `IsLocalization.of_surjective`, `LinearMap.det_mulRight`, `Zsqrtd.mker_norm_eq_unitary`, `Orientation.det_rotation`, `IsLocalization.surj''`, `Ideal.absNorm_ne_zero_iff_mem_nonZeroDivisors`, `RatFunc.map_apply`, `Unitization.lift_symm_apply_apply`, `RingHom.toMonoidHom_eq_coe`, `LocalizedModule.equivTensorProduct_symm_apply_tmul_one`, `IsLocalization.map_eq_zero_iff`, `IsLocalization.integerNormalization_map_to_map`, `Representation.Coinvariants.sub_mem_ker`, `Orientation.rotation_map_complex`, `CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM`, `Rat.associated_num_den`, `Algebra.discr_powerBasis_eq_norm`, `LinearMap.associated_det_of_eq_comp`, `MonoidWithZeroHom.one_apply_val_unit`, `spinGroup.val_inv_toUnits_apply`, `RatFunc.mk_eq_localization_mk`, `Orientation.map_eq_iff_det_pos`, `IsPrimitiveRoot.norm_eq_neg_one_pow`, `MvPowerSeries.mem_nonZeroDivisors_of_constantCoeff`, `Algebra.directSumGAlgebra_toFun_apply`, `IsLocalizedModule.exist_integer_multiples_of_finset`, `IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two`, `Polynomial.leadingCoeffHom_apply`, `Valuation.one_apply_of_ne_zero`, `mul_lt_one_of_nonneg_of_lt_one_left`, `Matrix.mem_unitaryGroup_iff`, `IsLocalizedModule.mk'_eq_mk'_iff`, `LinearMap.det_def`, `RatFunc.mk_eq_mk'`, `FreeLieAlgebra.liftAux_map_smul`, `BoundedContinuousFunction.mem_charPoly`, `MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar`, `Matrix.hadamard_one`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst`, `BoundedContinuousFunction.charAlgHom_apply`, `SkewMonoidAlgebra.lift_of`, `Ideal.relNorm_singleton`, `Representation.single_smul`, `SkewMonoidAlgebra.lift_single`, `Circle.arg_eq_arg`, `SimpleGraph.adjMatrix_hadamard_intCast`, `IsDedekindDomain.HeightOneSpectrum.exists_primeCompl_mul_eq_or_mul_eq`, `Localization.map_isUnit_of_le`, `Ideal.map_relNorm`, `SkewMonoidAlgebra.lift_apply`, `NonUnitalSubalgebra.iSupLift_comp_inclusion`, `LinearMap.detAux_def`, `IsLocalizedModule.finsetIntegerMultiple_image`, `IsLocalization.mk'_sub`, `Subring.neg_mem'`, `Algebra.algebraMap_intNorm_fractionRing`, `AddMonoidAlgebra.of_apply`, `IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk`, `LinearMap.det_eq_one_of_not_module_finite`, `SimpleGraph.adjMatrix_hadamard_diagonal`, `Algebra.norm_eq_prod_embeddings`, `NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le`, `Representation.prod_apply_apply`, `Matrix.coe_detMonoidHom`, `Representation.tprod_apply`, `Localization.mk_intCast`, `fourier_one`, `MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure`, `MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar`, `RingQuot.preLift_def`, `LinearMap.det_toLpLin`, `Module.FinitePresentation.exists_lift_of_isLocalizedModule`, `Matrix.mem_specialOrthogonalGroup_iff`, `StarAlgHom.coe_mk`, `Units.map_neg`, `RingOfIntegers.isUnit_norm_of_isGalois`, `IsLocalization.Away.instMapRingHomPowersOfCoe`, `SkewMonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `Real.Angle.coe_toCircle`, `IsLocalization.mk'_self`, `Representation.IntertwiningMap.isIntertwiningMap_of_mem_center`, `IntermediateField.inv_mem'`, `NonUnitalAlgHom.subsingleton`, `nonZeroDivisors_dvd_iff_dvd_coe`, `Matrix.reindex_mem_rowStochastic_iff`, `doublyStochastic_eq_rowStochastic_inf_colStochastic`, `le_nonZeroDivisors_iff_isRegular`, `MonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of`, `groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂`, `RingQuot.mkRingHom_def`, `groupCohomology.infNatTrans_app`, `NumberField.RingOfIntegers.mk_mul_mk`, `fourier_neg'`, `mul_lt_one_of_nonneg_of_lt_one_right`, `Algebra.map_intNormAux`, `Algebra.norm_localization`, `MonoidAlgebra.liftNCRingHom_single`, `MvPowerSeries.monomial_mem_nonzeroDivisorsRight`, `IsBaseChange.det_endHom`, `MeasureTheory.Measure.addHaar_preimage_continuousLinearMap`, `Algebra.coe_norm_int`, `LinearEquiv.det_symm_mul_det`, `groupHomology.cyclesMap_comp_assoc`, `Representation.Coinvariants.mk_self_apply`, `SimpleGraph.intCast_hadamard_adjMatrix`, `Valuation.IsEquiv.one_lt_iff_one_lt`, `groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply`, `Rep.applyAsHom_comm_apply`, `multiple_mem_adjoin_of_mem_localization_adjoin`, `IsPrimitiveRoot.sub_one_norm_isPrimePow`, `Circle.smul_def`, `MeasureTheory.distribHaarChar_apply`, `groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv`, `IsLocalization.mk'_spec'`, `MvPolynomial.monomialOneHom_apply`, `IsDedekindDomain.HeightOneSpectrum.valuation_def`, `val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coe`, `UniqueFactorizationMonoid.normalizedFactors_one`, `WithZero.lift'_coe`, `MonoidAlgebra.mem_span_support`, `SkewMonoidAlgebra.of_apply`, `Rep.coindFunctorIso_inv_app_hom_toFun_coe`, `IntermediateField.AdjoinSimple.norm_gen_eq_one`, `List.prod_map_lt_prod_map`, `Ideal.exists_le_prime_disjoint`, `Finset.le_prod_max_one`, `AddMonoidAlgebra.ringHom_ext'_iff`, `Algebra.norm_eq_of_equiv_equiv`, `mem_nonZeroDivisors_iff_right`, `QuadraticAlgebra.norm_eq_one`, `groupCohomology.cocycles₂_map_one_snd`, `Ideal.disjoint_map_primeCompl_iff_comap_le`, `IsLocalization.instForallPiUniv`, `mul_mem_nonZeroDivisorsLeft_of_mem_nonZeroDivisorsLeft`, `AbsoluteValue.coe_toMonoidHom`, `LinearMap.det_prodMap`, `TannakaDuality.FiniteGroup.sumSMulInv_apply`, `Representation.mem_invariants_iff_of_forall_mem_zpowers`, `Dilation.ratioHom_apply`, `isUnit_gcd_one_right`, `Algebra.essFiniteType_cond_iff`, `mul_boole`, `UniqueFactorizationMonoid.primeFactors_one`, `not_isNilpotent_one`, `Prime.not_dvd_one`, `AddMonoidAlgebra.lift_apply`, `Representation.ofQuotient_coe_apply`, `sq_le_one_iff₀`, `RootPairing.Hom.coweightHom_injective`, `isIntegral_localization'`, `Perfection.coeff_mapMonoidHom`, `QuadraticAlgebra.norm_neg`, `one_le_pow₀`, `one_lt_pow_iff_of_nonneg`, `Finset.prod_le_one`, `NumberField.Units.norm`, `IsPrimitiveRoot.norm_eq_one`, `Representation.mem_invariants`, `Subsemiring.coe_toSubmonoid`, `IsLocalizedModule.isRegular_of_smul_left_injective`, `IsLocalization.finsetIntegerMultiple_image`, `LocalizedModule.mk_cancel_common_left`, `Algebra.norm_eq_iff`, `Set.smul_indicator_one_apply`, `NonUnitalAlgHom.toAlgHom_zero`, `groupHomology.map_comp_assoc`, `exists_right_inv_of_exists_left_inv`, `IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two`, `AlgebraicGeometry.StructureSheaf.isLocalizedModule_toPushforwardStalkAlgHom_aux`, `MonoidHom.iterate_map_frobenius`, `AlgHom.coe_toMonoidHom`, `Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes`, `SimpleGraph.diagonal_hadamard_adjMatrix`, `Submonoid.LocalizationMap.nonZeroDivisors_le_comap`, `IsLocalization.mk'_eq_algebraMap_mk'_of_submonoid_le`, `OreLocalization.subsingleton_iff`, `VonNeumannAlgebra.centralizer_centralizer'`, `IsLocalizedModule.exist_integer_multiples_of_finite`, `IsLocalization.isUnit_piRingHom_algebraMap_comp_piEvalRingHom`, `MulChar.coe_mk`, `isLocalizedModule_iff`, `SpecialLinearGroup.det_eq_one`, `PrincipalIdealRing.ringHom_mem_submonoid_of_factors_subset_of_units_subset`, `IsIdempotentElem.zero_compl`, `Perfection.mk_comp_teichmuller'`, `IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two`, `groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv`, `Matrix.map_star_mem_unitaryGroup_iff`, `NonUnitalSubalgebra.inclusion_injective`, `pinGroup.star_mem`, `NonUnitalRingHom.one_def`, `Subsemiring.toSubmonoid_mono`, `IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two'`, `IsLocalization.algebraMap_mem_map_algebraMap_iff`, `GroupLike.valMonoidHom_apply`, `zero_pow_eq_one₀`, `LinearMap.det_eq_det_toMatrix_of_finset`, `FiniteField.norm_surjective`, `NonUnitalSubalgebra.iSupLift_mk`, `Algebra.norm_self`, `PiTensorProduct.tprodMonoidHom_apply`, `FractionalIdeal.canonicalEquiv_mk0`, `QuadraticAlgebra.star_mem_nonZeroDivisors_iff`, `Circle.ext_iff`, `ValuativeRel.ValueGroupWithZero.inv_mk`, `SignType.castHom_apply`, `associatesNonZeroDivisorsEquiv_mk_mk`, `Matrix.UnitaryGroup.map_star_inv_eq_transpose`, `Rep.ofMulDistribMulAction_ρ_apply_apply`, `Multiset.extract_gcd'`, `StarSubsemiring.mem_carrier`, `Matrix.UnitaryGroup.one_apply`, `ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq`, `Valuation.HasExtension.val_map_le_one_iff`, `Rep.RepToAction_map_hom`, `IsLocalizedModule.subsingleton_iff`, `LinearMap.det_toLin'`, `coe_nonZeroDivisorsRight_eq`, `RingOfIntegers.norm_algebraMap`, `MonoidWithZeroHom.one_apply_def`, `MulChar.eq_one_iff`, `Polynomial.notMem_nonZeroDivisors_iff`, `EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers`, `groupCohomology.cochainsMap_comp_assoc`, `IsFractionRing.mk'_num_den'`, `Subalgebra.linearEquivOp_apply_coe`, `IsLocalization.isPrime_iff_isPrime_disjoint`, `Subring.mem_closure_iff`, `FDRep.hom_hom_action_ρ`, `associatesNonZeroDivisorsEquiv_symm_mk_mk`, `finprod_zero_le_one`, `Multiset.extract_gcd`, `Representation.FiniteCyclicGroup.coinvariantsKer_eq_range`, `instIsStablyFiniteRingOfOrzechProperty`, `Rep.coindToInd_apply`, `Circle.coe_inv_eq_conj`, `groupHomology.mapCycles₁_comp_i_apply`, `NonUnitalAlgHom.injective_codRestrict`, `Subalgebra.mem_carrier`, `Complex.det_conjAe`, `WithZero.monoidWithZeroHom_ext_iff`, `WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis`, `ValuativeRel.ValueGroupWithZero.mk_eq_mk`, `IsFractionRing.div_surjective`, `MulRingSeminormClass.toMonoidHomClass`, `Algebra.norm_inv`, `NonUnitalAlgHom.coe_Lmul`, `TannakaDuality.FiniteGroup.leftRegular_apply`, `IsLocalization.mk'_algebraMap_eq_mk'`, `groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply`, `pow_lt_one_iff_of_nonneg`, `IsLocalization.lift_mk'`, `FiniteField.algebraMap_norm_eq_pow`, `Circle.coe_mul`, `MulChar.val_neg_one_eq_one_of_odd_order`, `Representation.apply_bijective`, `Matrix.one_hadamard_eq_diagonal_iff`, `Subalgebra.mem_saturation_iff`, `WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis`, `unitInterval.coe_unitIntervalSubmonoid`, `mul_left_coe_nonZeroDivisors_eq_zero_iff`, `Subalgebra.copy_toSubsemiring`, `Representation.linHom_apply`, `NonUnitalSubalgebra.toSubring_subtype`, `IsLocalization.localization_localization_surj`, `MonoidWithZeroHom.one_apply_of_ne_zero`, `FreeLieAlgebra.liftAux_map_add`, `IsLocalizedModule.mem_ker_iff`, `MonoidAlgebra.lift_apply'`, `Real.Angle.arg_toCircle`, `MulChar.coe_toMonoidHom`, `Matrix.UnitaryGroup.one_val`, `IsIdempotentElem.iff_eq_zero_or_one`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `FreeNonUnitalNonAssocAlgebra.lift_symm_apply`, `card_nthRoots_subgroup_units`, `ValuationSubring.mem_carrier`, `isLocalization_iff`, `Circle.coe_pow`, `Ring.mul_inverse_cancel`, `FiniteField.algebraMap_norm_eq_prod_pow`, `SimpleGraph.one_hadamard_adjMatrix`, `Multiset.lcm_zero`, `DistribMulAction.toModuleEnd_apply`, `IsLocalization.iff_map_piEvalRingHom`, `dvd_cancel_right_coe_nonZeroDivisors`, `mul_right_coe_nonZeroDivisors_eq_zero_iff`, `Localization.mapPiEvalRingHom_bijective`, `NonUnitalSubalgebra.iSupLift_inclusion`, `Rep.trivial_ρ_apply`, `WeakDual.CharacterSpace.coe_toNonUnitalAlgHom`, `IsLocalization.algebraMap_isUnit_iff`, `Algebra.PreSubmersivePresentation.jacobian_eq_det_aevalDifferential`, `Polynomial.det_taylorLinearEquiv_toLinearMap`, `HahnSeries.map_one`, `IsLocalization.mk'_self''`, `one_lt_mul`, `Ideal.span_singleton_nonZeroDivisors`, `IsArtinianRing.isUnit_iff_mem_nonZeroDivisors`, `LinearMap.ker_toSpanSingleton_eq_bot_iff`, `Module.FinitePresentation.exists_free_localizedModule_powers`, `IsLocalization.ringEquivOfRingEquiv_eq_map`, `gcd_one_left`, `IsLocalizedModule.fromLocalizedModule_mk`, `PNat.equivNonZeroDivisorsNat_symm_apply_coe`, `IsFractionRing.isUnit_map_of_injective`, `MulCharClass.toMonoidHomClass`, `Matrix.convex_colStochastic`, `map_mem_nonZeroDivisors`, `Subsemiring.addEquivOp_symm_apply_coe`, `groupCohomology.cocycles₁_map_inv`, `NonUnitalSubalgebraClass.subtype_injective`, `ValuativeRel.ValueGroupWithZero.mk_lt_mk`, `pinGroup.star_eq_inv'`, `LieHom.toNonUnitalAlgHom_toFun`, `MonoidAlgebra.freeAlgebra_lift_of_surjective_of_closure`, `Subsemiring.coe_carrier_toSubmonoid`, `WeakDual.CharacterSpace.toAlgHom_apply`, `SimpleGraph.toGraph_adjMatrix_eq`, `Ring.isUnit_iff_mul_inverse_cancel`, `Rep.indToCoindAux_mul_fst`, `FiniteField.valuation_algebraMap_eq_one`, `Circle.invOn_arg_exp`, `Subsemiring.center_toSubmonoid`, `Representation.asAlgebraHom_single_one`, `LinearMap.isUnit_det`, `val_unitsNonZeroDivisorsEquiv_symm_apply_coe`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_apply`, `Localization.r_iff_of_le_nonZeroDivisors`, `IsLocalization.smul_bijective`, `Rep.ihom_obj_ρ_apply`, `IsLocalization.sec_spec'`, `Representation.finsupp_single`, `MeasureTheory.distribHaarChar_eq_of_measure_smul_eq_mul`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_mk'`, `IsLocalization.exists_isIntegral_smul_of_isIntegral_map`, `Subgroup.val_centerUnitsEquivUnitsCenter_symm_apply_coe`, `IsLocalization.mk'_add_eq_iff_add_mul_eq_mul`, `QuadraticAlgebra.norm_natCast`, `IsLocalizedModule.exists_isLocalizedModule_powers_of_finitePresentation`, `Subsemiring.add_mem'`, `FreeLieAlgebra.liftAux_map_mul`, `TannakaDuality.FiniteGroup.equivApp_inv`, `LocalizedModule.mk_cancel_common_right`, `HomogeneousLocalization.den_mem`, `Submodule.toSubalgebra_mk`, `groupCohomology.norm_ofAlgebraAutOnUnits_eq`, `Valuation.apply_posSubmonoid_pos`, `Valuation.one_srel_iff`, `QuadraticAlgebra.norm_coe`, `Matrix.UnitaryGroup.det_isUnit`, `EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `AlgHom.equalizer_toSubsemiring`, `IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero`, `groupCohomology.mem_cocycles₂_iff`, `notMem_nonZeroDivisors_iff`, `IsLocalization.mk'_mem_map_algebraMap_iff`, `QuadraticAlgebra.isUnit_iff_norm_isUnit`, `EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers`, `RatFunc.map_apply_div`, `Circle.star_addChar`, `StarSubalgebra.star_mem'`, `List.prod_pos`, `IsLocalization.algEquivOfAlgEquiv_mk'`, `IsLocalizedModule.mk'_cancel'`, `MvPolynomial.mk_eq_eval₂`, `IsLocalization.algEquivOfAlgEquiv_eq_map`, `RingOfIntegers.norm_norm`, `groupHomology.mapCycles₂_comp_apply`, `Algebra.adjoin_toSubmodule_le`, `TopCat.Presheaf.SubmonoidPresheaf.map`, `Finset.lcm_empty`, `IsLocalization.map_integerMultiple`, `MonoidHom.map_neg`, `MonoidWithZeroHom.one_apply_eq_one_iff`, `MonomialOrder.mem_nonZeroDivisors_of_leadingCoeff_mem_nonZeroDivisors`, `Rep.ofDistribMulAction_ρ_apply_apply`, `PiTensorProduct.singleAlgHom_apply`, `map_le_nonZeroDivisors_of_injective`, `NumberField.Ideal.tendsto_norm_le_div_atTop₀`, `LinearMap.det_eq_zero_iff_ker_ne_bot`, `IsLeftRegular.mem_nonZeroDivisorsLeft`, `SimpleGraph.incMatrix_apply_eq_one_iff`, `Subalgebra.algebraMap_mem'`, `Submodule.natAbs_det_equiv`, `IsLocalizedModule.mk'_one`, `MeasureTheory.Filtration.filtrationOfSet_eq_natural`, `IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two`, `Rep.resCoindHomEquiv_symm_apply`, `Matrix.UnitaryGroup.inv_val`, `MonoidAlgebra.exists_finset_adjoin_eq_top`, `Prime.dvd_prod_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight`, `TannakaDuality.FiniteGroup.equivApp_hom`, `mul_eq_right₀`, `StarAlgHom.mk_coe`, `NumberField.Units.dirichletUnitTheorem.seq_norm_le`, `MonoidAlgebra.smul_of`, `IsLocalization.mk'_mul_mk'_eq_one'`, `ValuativeRel.ValueGroupWithZero.mk_mul_mk`, `NonUnitalSubalgebra.inclusion_inclusion`, `LinearEquiv.isUnit_det'`, `WittVector.dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeff`, `Matrix.UnitaryGroup.transpose_coe`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq`, `AlgEquiv.toLinearMapHom_apply_apply`, `Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos`, `Perfection.teichmuller_sModEq`, `Matrix.hadamard_one_eq_one_iff`, `groupCohomology.mem_cocycles₁_iff`, `WithZero.lift'_unique`, `mul_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `Valued.integer.mulArchimedean_mrange_of_isCompact_integer`, `AddMonoidAlgebra.lift_single`, `MonoidWithZeroHomClass.toMonoidHomClass`, `Algebra.algebraMapSubmonoid_le_comap`, `Padic.valuation_p_lt_one`, `RingEquiv.isStablyFiniteRing_iff`, `QuadraticAlgebra.coe_norm_eq_mul_star`, `mul_left_eq_self₀`, `PowerSeries.coe_divXPowOrderHom`, `Algebra.intNorm_eq_of_isLocalization`, `Subsemiring.toSubmonoid_strictMono`, `IsLocalization.localization_localization_map_units`, `Matrix.one_hadamard_eq_one_iff`, `MonoidWithZeroHom.map_one'`, `Algebra.algebraMapSubmonoid_map_eq`, `WittVector.fontaineThetaModPPow_teichmuller`, `Submodule.annihilator_top_inter_nonZeroDivisors`, `Rep.coinvariantsShortComplex_f`, `SimpleGraph.ofNat_hadamard_adjMatrix`, `AddMonoidAlgebra.lift_symm_apply`, `Module.Finite.exists_smul_of_comp_eq_of_isLocalizedModule`, `Algebra.norm_eq_norm_adjoin`, `OrderRingHom.toFun_eq_coe`, `IsPrimitiveRoot.norm_toInteger_sub_one_eq_one`, `Subsemiring.comap_toSubmonoid`, `IsFractionRing.inv_def`, `IntermediateField.LinearDisjoint.norm_algebraMap`, `DirichletCharacter.modOne_eq_one`, `FractionalIdeal.absNorm_eq`, `zero_pow_le_one`, `Ring.isUnit_iff_inverse_mul_cancel`, `HomogeneousLocalization.map_id`, `Polynomial.Monic.mem_nonZeroDivisors`, `ArithmeticFunction.IsMultiplicative.map_one`, `Representation.norm_comp_self`, `IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral`, `IsPrimitiveRoot.norm_sub_one_of_prime_ne_two'`, `IsLocalization.mk'_self'`, `Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg`, `groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply`, `ValuativeRel.zero_vlt_coe_posSubmonoid`, `normalize_coe_units`, `Rep.coindVEquiv_apply`, `Polynomial.mem_nonZeroDivisors_iff`, `Unitization.lift_range`, `Polynomial.mem_nonZeroDivisors_of_trailingCoeff`, `DistribMulActionHom.instLinearMapClassId`, `le_nonZeroDivisorsLeft_iff_isLeftRegular`, `Matrix.submonoidCenter_eq_scalar_map`, `IsLocalization.isLocalization_of_submonoid_le`, `groupHomology.inhomogeneousChains.d_single`, `Rep.ActionToRep_map`, `Subrepresentation.apply_mem_toSubmodule`, `LinearMap.det_map`, `pinGroup.units_mem_iff`, `LinearMap.hasEigenvalue_zero_tfae`, `Representation.coind'_apply_apply`, `Valuation.one_apply_le_one`, `WittVector.ghostComponentModPPow_teichmuller_coeff`, `RingOfIntegers.isUnit_norm`, `LinearMap.instIsStablyFiniteRingEnd`, `LinearMap.detAux_def'`, `gcd_one_right`, `EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric`, `den_dvd_of_is_root`, `ValuativeRel.one_apply_posSubmonoid`, `Matrix.one_hadamard`, `Circle.leftInverse_exp_arg`, `IsRightRegular.mem_nonZeroDivisorsRight`, `IsFractionRing.associated_num_den_inv`, `RingHom.toFun_eq_coe`, `IsLocalization.mk'_eq_iff_eq`, `Matrix.transpose_mem_rowStochastic_iff_mem_colStochastic`, `Valuation.map_one_sub_of_lt`, `MeasureTheory.Measure.addHaar_image_linearMap`, `jacobiSym.value_at`, `mk_mem_nonZeroDivisors_associates`, `noZeroDivisors_iff_forall_mem_nonZeroDivisors`, `Matrix.mem_specialUnitaryGroup_iff`, `LocalizedModule.subsingleton_iff`, `AddMonoidAlgebra.coe_liftNCAlgHom`, `groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply`, `MulSemiringActionHom.map_one'`, `Valuation.extendToLocalization_mk'`, `IsLocalization.mem_invSubmonoid_iff_exists_mk'`, `RingPreordering.neg_one_notMem'`, `Ideal.card_norm_le_eq_card_norm_le_add_one`, `FreeLieAlgebra.liftAux_spec`, `Representation.asModuleEquiv_symm_map_rho`, `Prime.not_dvd_prod`, `spinGroup.mul_star_self`, `Representation.freeLift_toLinearMap`, `Representation.ofModule_asModule_act`, `Submonoid.LocalizationMap.map_nonZeroDivisors_le`, `LocalizedModule.smul_def`, `LinearMap.eval_charpoly`, `UniqueFactorizationMonoid.radical_one`, `Submonoid.coe_unitSphere`, `Unitization.lift_symm_apply`, `FractionalIdeal.absNorm_span_singleton`, `Circle.norm_coe`, `Valuation.map_one`, `IsLocalization.nonZeroDivisors_le_comap`, `Polynomial.mem_nonZeroDivisors_of_leadingCoeff`, `IsLocalizedModule.mk'_cancel_right`, `MonoidWithZeroHom.toMonoidHom_coe`, `Matrix.UnitaryGroup.mul_val`, `IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two`, `MulEquivClass.map_nonZeroDivisors`, `AddMonoidAlgebra.lift_of`, `fourier_apply`, `Algebra.norm_eq_prod_automorphisms`, `eq_zero_or_one_of_sq_eq_self`, `IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic`, `SkewMonoidAlgebra.lift_unique'`, `Matrix.IsHermitian.eigenvectorUnitary_apply`, `Matrix.mem_rowStochastic_iff_sum`, `Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_mul`, `LinearMap.det_dualMap`, `IsLocalization.mk'_sec`, `Rep.indToCoindAux_mul_snd`, `Subfield.coe_inf`, `Finset.extract_gcd'`, `Subgroup.val_centerUnitsEquivUnitsCenter_apply_coe`, `Representation.asAlgebraHom_of`, `GradedAlgHom.mk_coe`, `Valuation.one_vlt_iff`, `PresheafOfModules.map_comp`, `IsLocalization.mk'_eq_iff_eq_mul`, `isUnit_zero_iff`, `WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv`, `divisor_closure_eq_closure`, `LinearMap.detAux_comp`, `mem_nonZeroDivisors_iff'`, `IsFractionRing.mk'_mk_eq_div`, `multiple_mem_span_of_mem_localization_span`, `Localization.mk_natCast`, `MonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `Module.End.det_eq_prod_roots_charpoly_of_splits`, `Matrix.UnitaryGroup.mul_apply`, `LinearMap.det_id`, `AddMonoidAlgebra.nonUnitalAlgHom_ext'_iff`, `Matrix.IsAdjMatrix.toGraph_compl_eq`, `MulChar.restrict_eq_one_iff`, `lcm_one_left`, `Set.indicator_pi_one_apply`, `Perfection.mk_comp_teichmuller`, `mem_doublyStochastic_iff_mem_rowStochastic_and_mem_colStochastic`, `sum_hom_units_eq_zero`, `IsArtinianRing.isUnit_iff_nonZeroDivisor_of_isIntegral'`, `Subsemiring.mopRingEquivOp_apply_coe`, `Valuation.one_vle_iff`, `IsLocalization.toInvSubmonoid_mul`, `IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow`, `one_lt_mul_of_le_of_lt`, `Submodule.det_reflection`, `ClassGroup.mk_mk0`, `NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le`, `IsLocalization.scaleRoots_commonDenom_mem_lifts`, `Orientation.kahler_rotation_left'`, `ValuativeRel.left_cancel_posSubmonoid`, `one_le_pow_iff_of_nonneg`, `isLeftRegular_iff_mem_nonZeroDivisorsLeft`, `MonoidAlgebra.singleHom_apply`, `Matrix.subsemigroupCenter_eq_scalar_map`, `Module.Basis.det_comp`, `SymplecticGroup.mem_iff'`, `IsPrimitiveRoot.norm_sub_one_of_prime_ne_two`, `ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring`, `Matrix.kronecker_one`, `one_le_sq_iff₀`, `IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt`, `LinearMap.det_restrictScalars`, `MeasureTheory.Measure.addHaar_image_continuousLinearEquiv`, `StarSubalgebra.mem_carrier`, `MonoidHom.map_sub_swap`, `Perfection.teichmuller_zero`, `Matrix.UnitaryGroup.ext_iff`, `Rep.coe_res_obj_ρ'`, `Bound.one_lt_mul`, `AlgHom.coe_mks`, `Ideal.absNorm_pos_of_nonZeroDivisors`, `Ideal.quotientEquiv_apply`, `AddMonoidAlgebra.liftMagma_apply_apply`, `pinGroup.toUnits_injective`, `Matrix.IsAdjMatrix.apply_diag_ne`, `groupCohomology.cochainsMap_f`, `inhomogeneousCochains.d_hom_apply`, `pinGroup.mul_star_self`, `RingEquiv.toMonoidHom_commutes`, `Rep.ρ_mul`, `doublyStochastic_eq_convexHull_permMatrix`, `MulSemiringActionHom.map_mul'`, `Subalgebra.saturation_saturation`, `IsLocalizedModule.exists_integer_multiple`, `IsPrimitiveRoot.norm_eq_one_of_linearly_ordered`, `UniqueFactorizationMonoid.radical_zero`, `NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet`, `Ideal.mem_primeCompl_iff`, `AddMonoidAlgebra.liftNC_smul`, `SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq`, `groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self`, `ClassGroup.norm_lt`, `Complex.expMonoidHom_apply`, `LinearMap.det_eq_sign_charpoly_coeff`, `RingOfIntegers.coe_norm`, `Multiset.one_le_prod`, `groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁`, `PowerSeries.map_invUnitsSub`, `Algebra.smul_units_def`, `NonUnitalRingHom.coe_one`, `Matrix.one_hadamard_eq_zero_iff`, `MulChar.one_apply`, `Matrix.one_kronecker_one`, `IsLocalizedModule.smul_inj`, `pinGroup.star_mem_iff`, `Representation.isTrivial_def`, `IsLocalization.toInvSubmonoid_surjective`, `IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two`, `QuadraticAlgebra.norm_intCast`, `QuadraticAlgebra.mker_norm_eq_unitary`, `RatFunc.liftAlgHom_apply_ofFractionRing_mk`, `List.prod_eq_zero`, `rotationOf_coe`, `Ideal.norm_mem_spanNorm`, `AddMonoidAlgebra.lift_unique'`, `IsLocalizedModule.iso_symm_apply_aux`, `IsPrimitiveRoot.norm_pow_sub_one_two`, `Algebra.norm_complex_apply`, `isUnit_iff_mem_nonZeroDivisors_of_finite`, `RingEquiv.prodProdProdComm_toMulEquiv`, `IsLocalization.isLocalization_of_base_ringEquiv`, `associated_norm_prod_smith`, `IsLocalizedModule.mk'_surjective`, `MvPowerSeries.mem_nonZeroDivisorsLeft_of_constantCoeff`, `LocalizedModule.mk_mul_mk'`, `IsLocalization.map_injective_of_injective`, `RootPairing.range_polarizationIn`, `Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun`, `IsLocalization.mem_localizationLocalizationSubmodule`, `Matrix.IsHermitian.eigenvectorUnitary_coe`, `HomogeneousLocalization.NumDenSameDeg.den_mem`, `zero_mul`, `WittVector.fontaineTheta_teichmuller`, `MonoidAlgebra.liftMagma_symm_apply`, `AddMonoidAlgebra.liftMagma_symm_apply`, `zero_pow_eq`, `pinGroup.mem_lipschitzGroup`, `Subsemiring.mem_toSubmonoid`, `AlgebraicGeometry.Proj.germ_map_sectionInBasicOpen`, `Real.map_linearMap_volume_pi_eq_smul_volume_pi`, `ValuationSubring.mem_or_inv_mem'`, `IsLocalizedModule.mk'_smul_mk'`, `OrderRingHom.monotone'`, `MonoidAlgebra.support_gen_of_gen`, `Matrix.IsAdjMatrix.apply_ne_zero_iff`, `TannakaDuality.FiniteGroup.sumSMulInv_single_id`, `spinGroup.star_mem`, `ValuativeRel.exists_valuation_div_valuation_eq`, `pow_le_one_iff_of_nonneg`, `LocalizedModule.lift_mk`, `Rep.leftRegularHom_hom_single`, `IsLocalizedModule.exists_of_eq`, `IsFractionRing.num_mul_den_eq_num_mul_den_iff_eq`, `MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar`, `Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule`, `Submodule.mker_spanSingleton`, `FractionalIdeal.den_mul_self_eq_num`, `Representation.free_single_single`, `IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two`, `spinGroup.mem_pin`, `Representation.IntertwiningMap.isIntertwining'`, `IsLocalization.localization_localization_exists_of_eq`, `IsLocalization.exists_smul_mem_of_mem_adjoin`, `GradedAlgHom.coe_monoidHom_injective`, `OrderMonoidWithZeroHom.toOrderMonoidHom_injective`, `Algebra.adjoin_eq_span`, `HomogeneousLocalization.map_map`, `LinearMap.det_eq_one_of_finrank_eq_zero`, `Real.hasDerivAt_fourierChar`, `StarSubsemiring.star_mem'`, `Matrix.star_eq_inv`, `AddMonoidAlgebra.lift_of'`, `IsLocalization.mk'_cancel`, `LocalizedModule.mul_by_divBy`, `Orientation.kahler_rotation_left`, `Representation.le_comap_invariants`, `Polynomial.isLocalization`, `List.prod_eq_zero_iff`, `IsLocalization.exist_integer_multiples_of_finset`, `IsLocalization.smul_mem_iff`, `IsLocalization.orderIsoOfPrime_symm_apply_coe`, `mul_cancel_right_coe_nonZeroDivisors`, `OrderMonoidWithZeroHom.toOrderMonoidHom_comp`, `IsScalarTower.of_compHom`, `Representation.invariants_eq_inter`, `IsLocalization.sec_spec`, `AffineMap.linearHom_apply`, `Algebra.norm_eq_one_of_not_exists_basis`, `Valuation.srel_one_iff`, `QuadraticAlgebra.star_mem_nonZeroDivisors`, `Subring.mem_carrier`, `Algebra.norm_eq_of_algEquiv`, `NonUnitalSubalgebra.map_topologicalClosure_le`, `Representation.subrepresentation_apply`, `groupCohomology.cocyclesMap_comp_assoc`, `Algebra.essFiniteType_iff_exists_subalgebra`, `Module.Basis.det_basis`, `Representation.norm_self_apply`, `IsLocalization.map_units_map_submonoid`, `IsLocalization.exist_integer_multiples_of_finite`, `Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_ite`, `LieHom.toNonUnitalAlgHom_apply`, `Rep.indCoindIso_hom_hom_toLinearMap`, `Subalgebra.pi_toSubsemiring`, `LinearMap.nonUnitalAlgHom_comp_convMul_distrib`, `IsLocalization.disjoint_comap_iff`, `MonoidAlgebra.of_commute`, `MonoidHom.map_iterateFrobenius`, `Matrix.mem_orthogonalGroup_iff`, `NumberField.exists_ideal_in_class_of_norm_le`, `Representation.smul_tprod_one_asModule`, `Valuation.vle_one_iff`, `IsLocalization.toInvSubmonoid_eq_mk'`, `MonoidAlgebra.mem_ideal_span_of_image`, `scaleRoots_aeval_eq_zero_of_aeval_mk'_eq_zero`, `Perfection.coe_teichmuller_eq_teichmuller₀`, `MonoidAlgebra.lift_apply`, `Subring.toSubmonoid_strictMono`, `Algebra.intNorm_zero`, `Circle.coe_eq_one`, `IsPrimitiveRoot.card_quotient_toInteger_sub_one`, `Projectivization.smul_def`, `MonoidAlgebra.lift_mapRangeRingHom_algebraMap`, `SimpleGraph.adjMatrix_hadamard_self`, `RatFunc.liftRingHom_apply_ofFractionRing_mk`, `Matrix.instIsStablyFiniteRingOfFinite`, `mul_le_one₀`, `extremePoints_doublyStochastic`, `coe_nonZeroDivisorsLeft_eq`, `Subring.ringEquivOpMop_symm_apply_coe`, `IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots`, `LinearMap.det_smul`, `MonoidAlgebra.of_injective`, `NonUnitalAlgHom.comp_mul'`, `Real.fourierChar_apply`, `IsLocalization.tmul_mk'`, `mem_nonZeroDivisorsLeft_iff`, `Rep.RepToAction_obj_ρ`, `FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal`, `Representation.self_inv_apply`, `nonZeroDivisors.associated_coe`, `RingHom.toSemilinearMap_apply`, `Subsemiring.map_toSubmonoid`, `BialgHom.map_mul'`, `Valuation.IsEquiv.one_le_iff_one_le`, `Subring.coe_toSubmonoid`, `LinearEquiv.isIntertwining_symm_isIntertwining`, `Finset.gcd_div_id_eq_one`, `MeasureTheory.Measure.addHaar_preimage_linearMap`, `IsArtinianRing.isUnit_iff_mem_nonZeroDivisors_of_mulOpposite`, `AddMonoidAlgebra.lift_mapRingHom_algebraMap`, `Valuation.HasExtension.val_map_eq_one_iff`, `AffineMap.coe_homothetyHom`, `Ring.inverse_one`, `PNat.equivNonZeroDivisorsNat_apply_coe`, `Representation.isTrivial_apply`, `Ideal.natAbs_det_equiv`, `Matrix.of_mem_specialOrthogonalGroup_fin_two_iff`, `Complex.uniformContinuous_ringHom_eq_id_or_conj`, `Representation.IsIntertwiningMap.isIntertwining`, `ValuativeRel.right_cancel_posSubmonoid`, `Rep.indResHomEquiv_apply`, `IsLocalization.mk'_one`, `Matrix.mem_colStochastic`, `Subsemiring.ringEquivOpMop_symm_apply_coe`, `pow_lt_one₀`, `MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv`, `Localization.coe_algEquiv`, `MonoidWithZeroHom.map_ite_one_zero`, `Matrix.mem_colStochastic_iff_sum`, `groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂`, `Rep.unit_iso_comm`, `NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_symm_apply`, `SkewMonoidAlgebra.of_injective`, `Matrix.isDiag_smul_one`, `Rep.leftRegularHomEquiv_symm_single`, `OrderMonoidWithZeroHom.copy_eq`, `Ideal.spanNorm_singleton`, `AlgEquiv.ofLinearEquiv_symm`, `BialgHomClass.toMonoidHomClass`, `boole_smul`, `Subsemiring.coe_closure_eq`, `WithZero.lift'_surjective`, `Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer`, `NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr`, `RatFunc.mk_def_of_mem`, `Finset.prod_boole`, `IsLocalization.ker_map`, `Rep.indCoindIso_inv_hom_toLinearMap`, `Matrix.isAdjMatrix_iff_hadamard`, `one_lt_mul_of_lt_of_le`, `AlgebraicGeometry.StructureSheaf.Localizations.comapFun_mk`, `MonoidAlgebra.mapDomainNonUnitalAlgHom_apply`, `Valuation.rel_one_iff`, `LinearMap.det_comp`, `groupHomology.chainsMap_f_hom`, `IsLocalizedModule.smul_injective`, `le_isUnit_iff_zero_notMem`, `gcd_one_right'`, `NonUnitalAlgebra.map_top`, `IsLocalization.mk'_mul_mk'_eq_one`, `Ideal.span_singleton_mem_isPrincipalSubmonoid`, `Valuation.IsEquiv.eq_one_iff_eq_one`, `isRegular_iff_mem_nonZeroDivisors`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `LinearMap.transvection.det`, `IsUnit.mem_nonZeroDivisors`, `Polynomial.X_mem_nonzeroDivisors`, `FreeAbelianGroup.liftMonoid_coe`, `NonUnitalAlgHom.toAlgHom_apply`, `RingPreordering.mem_of_isSquare'`, `IsLocalization.submonoid_map_le_is_unit`, `MonoidAlgebra.lift_mapRingHom_algebraMap`, `RingHom.coe_mk`, `biUnion_associatedPrimes_eq_compl_nonZeroDivisors`, `pinGroup.mem_iff`, `IsLocalization.mk'_eq_zero_iff`, `MonoidWithZeroHom.val_mrange_zero`, `LinearEquiv.det_mul_det_symm`, `le_nonZeroDivisors_of_noZeroDivisors`, `UniqueFactorizationMonoid.radical_of_isUnit`, `Circle.coe_inv`, `Localization.add_mk`, `Summable.norm_lt_one`, `Valuation.vlt_one_iff`, `Matrix.specialUnitaryGroup.coe_star`, `LinearMap.IsSymmetric.det_eq_prod_eigenvalues`, `OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary`, `PrimeSpectrum.isIdempotentElemEquivClopens_symm_top`, `Representation.IntertwiningMap.isIntertwining_assoc`, `not_isPrimePow_one`, `Matrix.reindex_mem_rowStochastic`, `HahnSeries.leadingCoeff_one`, `IsFractionRing.num_mul_den_eq_num_iff_eq`, `pinGroup.star_eq_inv`, `Algebra.norm_one_add_smul`, `groupCohomology.mapCocycles₁_comp_i_apply`, `mem_doublyStochastic`, `RingEquiv.toMonoidHom_refl`, `Algebra.norm_apply`, `RingHom.smulOneHom_apply`, `Algebra.norm_eq_zero_iff'`, `MonoidWithZeroHom.copy_eq`, `WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis`, `LocalizedModule.lift_mk_one`, `MvPowerSeries.renameEquiv_apply`, `HahnModule.one_smul'`, `mem_nonZeroDivisors_of_ne_zero`, `Matrix.mem_unitaryGroup_iff'`, `IsLocalization.map_units`, `LocalizedModule.mk'_smul_mk`, `Subfield.mem_toSubmonoid`, `QuadraticAlgebra.norm_def`, `isUnit_gcd_one_left`, `Matrix.convex_rowStochastic`, `Submodule.mem_localized₀`, `ClassGroup.exists_mk0_eq_mk0`, `RingHom.map_zero'`, `RingHom.IsStableUnderBaseChange.isLocalization_map`, `LinearMap.det_conj`, `Finset.one_le_prod`, `Rep.hom_comm_apply`, `RingHom.isIntegralElem_localization_at_leadingCoeff`, `Matrix.reindex_mem_colStochastic`, `PreTilt.untilt_iterate_frobeniusEquiv_symm_pow`, `Valuation.IsEquiv.le_one_iff_le_one`, `Matrix.transpose_mem_unitaryGroup_iff`, `IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two`, `Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange`, `RingHom.coe_monoidHom_injective`, `MonoidAlgebra.liftNC_smul`, `Real.differentiable_fourierChar`, `Algebra.algebraMap_intNorm_of_isGalois`, `AddMonoidAlgebra.of_injective`, `nonZeroDivisorsEquivUnits_apply`, `Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMul`, `ClassGroup.mk0_surjective`, `groupCohomology.cochainsMap_f_hom`, `IsLocalization.injective_iff_isRegular`, `OreLocalization.mul_inv_cancel`, `mem_nonZeroDivisors_iff_ne_zero`, `lipschitzGroup.coe_mem_iff_mem`, `Subsemiring.mem_mk`, `normUnit_one`, `Ideal.disjoint_primeCompl_of_liesOver`, `MeasureTheory.distribHaarChar_eq_div`, `Representation.toCoinvariants_mk`, `PresheafOfModules.map_id`, `Circle.normSq_coe`, `ValuativeRel.posSubmonoid_def`, `Rep.quotientToCoinvariantsFunctor_map_hom_toLinearMap`, `Representation.IsTrivial.out`, `QuadraticAlgebra.norm_one`, `MonoidAlgebra.mapAlgEquiv_apply`, `Matrix.permMatrix_mem_colStochastic`, `ArithmeticFunction.IsMultiplicative.iff_ne_zero`, `groupCohomology.mapShortComplexH1_comp_assoc`, `NumberField.isUnit_iff_norm`, `SymplecticGroup.neg_mem`, `Fintype.prod_boole`, `isStablyFiniteRing_iff_isDedekindFiniteMonoid_moduleEnd`, `PowerSeries.coe_orderHom`, `MonoidAlgebra.ringHom_ext'_iff`, `MvPolynomial.isLocalization_C_mk'`, `Subsemiring.op_toSubmonoid`, `PEquiv.toMatrix_injective`, `Representation.mem_coindV`, `MonoidAlgebra.single_eq_algebraMap_mul_of`, `LinearMap.det_zero''`, `Representation.coind_apply`, `Matrix.mem_specialOrthogonalGroup_fin_two_iff`, `Unitization.inrNonUnitalAlgHom_apply`, `NonUnitalAlgebra.comap_top`, `Algebra.norm_eq_prod_roots`, `MeasureTheory.distribHaarChar_mul`, `IsModuleTopology.continuous_of_distribMulActionHom`, `MeasureTheory.Measure.addHaar_preimage_linearEquiv`, `Valuation.HasExtension.mk_smul_mk`, `Ideal.mem_isPrincipalSubmonoid_iff`, `Real.expMonoidHom_apply`, `fourier_zero'`, `Algebra.norm_zero`, `ZMod.toCircle_intCast`, `IsLocalization.exists_integer_multiple`, `ZMod.toCircle_natCast`, `MonoidWithZeroHom.map_ite_zero_one`, `nonZeroDivisorsEquivUnits_symm_apply_coe`, `Representation.quotient_apply`, `Ideal.primeCompl_le_nonZeroDivisors`, `Real.deriv_fourierChar`, `NonUnitalAlgHom.range_comp`, `IsLocalization.mk'_spec'_mk`, `SimpleGraph.incMatrix_of_notMem_incidenceSet`, `IsFractionRing.num_den_unique`, `Subsemiring.zero_mem'`, `ClassGroup.exists_min`, `subsingleton_iff_zero_eq_one`, `Subsemiring.coe_set_mk`, `WittVector.teichmuller_coeff_zero`, `Representation.ind_mk`, `MvPolynomial.isLocalization`, `IsSMulRegular.mem_nonZeroSMulDivisors`, `LocalizedModule.mk_smul_mk`, `Unitization.lift_range_le`, `SkewMonoidAlgebra.single_eq_algebraMap_mul_of`, `convex_doublyStochastic`, `NumberField.InfiniteAdeleRing.coe_norm_eq_abs_norm`, `LinearMap.det_zero'`, `NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMap`, `groupHomology.d₂₁_single_one_snd`, `Module.End.mem_submonoidCenter_iff`, `LinearEquiv.coe_inv_det`, `Algebra.norm_eq_one_of_not_module_finite`, `NonUnitalSubalgebra.toNonUnitalSubsemiring_subtype`, `IsLocalizedModule.fromLocalizedModule'_mk`, `Algebra.norm_norm`, `MulChar.trivial_apply`, `IsLocalization.AtPrime.isUnit_mk'_iff`, `Real.differentiable_fourierChar_neg_bilinear_right`, `Multiset.one_le_prod_map`, `FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm`, `Subalgebra.linearEquivOp_symm_apply_coe`, `QuadraticAlgebra.coe_mem_nonZeroDivisors_iff`, `groupHomology.d₃₂_single_one_snd`, `Circle.coeHom_apply`, `rootsOfUnityCircleEquiv_apply`, `SkewMonoidAlgebra.distribMulActionHom_ext'_iff`, `FDRep.Iso.conj_ρ`, `not_prime_one`, `FractionalIdeal.map_canonicalEquiv_mk0`, `Subring.sInf_toSubmonoid`, `FDRep.of_ρ`, `HahnSeries.order_one`, `NonUnitalAlgebra.map_bot`, `IsCyclotomicExtension.norm_zeta_eq_one`, `det_rotation`, `Rep.coinvariantsTensorIndHom_mk_tmul_indVMk`, `Circle.coe_inj`, `instIsStablyFiniteRingEndForallOfFinite`, `AlgHom.mk_coe`, `IsLocalization.mk'_mul_cancel_right`, `IsLocalization.exists_integer_multiple'`, `IsRegular.mem_nonZeroDivisors`, `HomogeneousLocalization.map_comp`, `Rep.indToCoind_coindToInd`, `IsLocalizedModule.mk'_mul_mk'`, `Matrix.UnitaryGroup.map_star_coe`, `FiniteField.valuation_algebraMap_le_one`, `Set.indicator_eq_zero_iff_notMem`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `StarAlgebra.adjoin_eq_span`, `Orientation.kahler_rotation_right`, `mul_cancel_left_coe_nonZeroDivisors`, `QuadraticAlgebra.norm_star`, `IsLocalization.isLocalization_algebraMapSubmonoid_map_algHom`, `RingQuot.preLiftAlgHom_def`, `FreeAbelianGroup.ofMulHom_coe`, `SymplecticGroup.coe_inv'`, `OrderMonoidWithZeroHom.toOrderMonoidHom_eq_coe`, `ValuativeExtension.mapPosSubmonoid_apply_coe`, `fourier_coe_apply'`, `Subsemiring.closure_submonoid_closure`, `IsLocalizedModule.map_units`, `IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one`, `LinearMap.det_ring`, `LinearMap.coe_det`, `Matrix.IsHermitian.eigenvectorUnitary_transpose_apply`, `List.prod_map_le_pow_length₀`, `LinearIsometryEquiv.toMatrix_mem_unitaryGroup`, `IsCyclotomicExtension.norm_zeta_pow_sub_one_two`, `Localization.le_comap_primeCompl_iff`, `MonoidWithZeroHom.toMonoidHom_injective`, `Representation.linHom.mem_invariants_iff_comm`, `Matrix.UnitaryGroup.toLin'_mul`, `Rep.indResHomEquiv_symm_apply`, `Representation.IntertwiningMap.isIntertwining`, `groupHomology.mapCycles₂_comp_i_apply`, `PiTensorProduct.mapMonoidHom_apply`, `SimpleGraph.incMatrix_of_mem_incidenceSet`, `Real.hasFDerivAt_fourierChar_neg_bilinear_right`, `AlgebraicGeometry.StructureSheaf.comap_basicOpen`, `prod_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `NonUnitalSubalgebra.coe_inclusion`, `zero_notMem_nonZeroDivisorsRight`, `QuadraticAlgebra.algebraMap_norm_eq_mul_star`, `IsLocalization.AtPrime.isUnit_to_map_iff`, `NonUnitalSubalgebraClass.subtype_apply`, `RingOfIntegers.algebraMap_norm_algebraMap`, `ValuativeRel.ValueGroupWithZero.mk_le_mk`, `LinearMap.det_eq_det_mul_det`, `ZMod.toCircle_apply`, `IsLocalization.mul_toInvSubmonoid`, `IsLocalization.algebraMap_mk'`, `exists_bijective_map_powers`, `AlgHom.toEnd_apply`, `RatFunc.taylor_mem_nonZeroDivisors`, `NonUnitalAlgebra.range_eq_top`, `Circle.arg_exp`, `LinearEquiv.det_coe_symm`, `IsLocalization.mk'_eq_iff_eq'`, `RingHom.coe_monoidHom_mk`, `groupHomology.d₁₀_single_inv`, `IsLocalization.span_invSubmonoid`, `Representation.ofMulDistribMulAction_apply_apply`, `pinGroup.coe_star`, `Matrix.mem_orthogonalGroup_iff'`, `Rep.res_obj_ρ`, `ValuativeRel.ValueGroupWithZero.lift_zero`, `LinearMap.det_toMatrix'`, `Subsemiring.copy_toSubmonoid`, `Algebra.PowerBasis.norm_gen_eq_prod_roots`, `MonoidWithZeroHom.map_mul'`, `Real.differentiable_fourierChar_neg_bilinear_left`, `OrderMonoidWithZeroHom.coe_copy`, `IsLocalizedModule.eq_iff_exists`, `Rep.RepToAction_obj`, `MonoidAlgebra.lift_def`, `transpose_mem_doublyStochastic_iff`, `FractionalIdeal.equivNum_apply`, `LinearMap.det_cases`, `RingHom.coe_addMonoidHom_mk`, `Representation.smul_one_tprod_asModule`, `MvPowerSeries.X_mem_nonzeroDivisors`, `IsLocalization.invertible_mk'_one_invOf`, `ClassGroup.equiv_mk0`, `Subalgebra.LinearDisjoint.norm_algebraMap`, `Ideal.relNorm_apply`, `ValuativeRel.ValueGroupWithZero.mk_self`, `Submonoid.subsemiringClosure_mem`, `IsLocalizedModule.smul_mem_finsetIntegerMultiple_span`, `Matrix.UnitaryGroup.toGL_one`, `dvd_cancel_left_coe_nonZeroDivisors`, `Rep.applyAsHom_apply`, `NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr`, `Circle.coe_exp`, `Algebra.norm_algebraMap`, `NumberField.mixedEmbedding.fundamentalCone.mem_idealSet`, `NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop`, `IsLocalization.integerNormalization_spec`, `OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal`, `SkewMonoidAlgebra.ringHom_ext'_iff`, `MvPowerSeries.mem_nonZeroDivisorsRight_of_constantCoeff`, `IsLocalization.eq_mk'_iff_mul_eq`, `Valuation.HasExtension.val_map_lt_one_iff`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_surjective`, `fourier_add'`, `Unitization.lift_apply_apply`, `WittVector.teichmuller_mul_pow_coeff`, `Representation.leftRegularMapEquiv_symm_single`, `Subsemiring.sInf_toSubmonoid`, `groupHomology.d₂₁_single`, `NumberField.mixedEmbedding.fundamentalCone.idealSetEquiv_apply`, `BoundedContinuousFunction.charMonoidHom_apply`, `notMem_nonZeroDivisors_iff_left`, `boole_mul`, `mem_nonZeroDivisors_of_injective`, `FractionalIdeal.den_mul_self_eq_num'`, `IsFractionRing.num_den_reduced`, `NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply`, `DualNumber.inr_eq_smul_eps`, `QuadraticAlgebra.algebraMap_mem_nonZeroDivisors_iff`, `pow_eq_one_iff_of_nonneg`, `pinGroup.coe_mul_star_self`, `NonUnitalSubalgebra.map_map`, `Matrix.instIsStablyFiniteRingOfCommSemiring`, `Matrix.mem_rowStochastic`, `IsFractionRing.associated_den_num_inv`, `ValuativeRel.ValueGroupWithZero.lift_valuation`, `ContinuousAlgHom.cont`, `LinearMap.not_hasEigenvalue_zero_tfae`, `Algebra.intNorm_map_algEquiv`, `AddMonoidAlgebra.lift_def`, `Ideal.norm_mem_relNorm`, `Algebra.intNorm_intNorm`, `IsLocalization.mk'_add`, `MonoidHom.map_neg_one`, `RingEquiv.coe_monoidHom_trans`, `Subring.mem_toSubmonoid`, `ClassGroup.mk0_eq_mk0_inv_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft`, `groupHomology.chainsMap_f_0_comp_chainsIso₀_apply`, `QuadraticAlgebra.det_toLinearMap_eq_norm`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_map_one`, `IsLocalizedModule.map_integerMultiple`, `AlgHom.toRingHom_toMonoidHom`, `IsFractionRing.self_iff_nonZeroDivisors_le_isUnit`, `Ideal.associatesNonZeroDivisorsEquivIsPrincipal_coe`, `groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁`, `Submonoid.LocalizationMap.lift₀_apply`, `Representation.dual_apply`, `normalize_eq_one`, `Valuation.IsEquiv.lt_one_iff_lt_one`, `Circle.toUnits_apply`, `Matrix.transpose_mem_colStochastic_iff_mem_rowStochastic`, `comap_nonZeroDivisors_le_of_injective`, `IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk`, `Set.inter_indicator_one`, `Algebra.norm_eq_zero_iff`, `Profinite.NobelingProof.list_prod_apply`, `one_lt_pow₀`, `LinearEquiv.automorphismGroup.toLinearMapMonoidHom_apply`, `DividedPowers.DPMorphism.ext_iff`, `NumberField.InfinitePlace.prod_eq_abs_norm`, `Representation.dualTensorHom_comm`, `WithZero.lift'_zero`, `IsLocalization.mem_map_algebraMap_iff`, `Finsupp.smul_single_one`, `PrimeSpectrum.localization_comap_range`, `Submodule.span.ringHom_apply`, `mul_mem_nonZeroDivisorsRight_of_mem_nonZeroDivisorsRight`, `IsLocalization.orderIsoOfPrime_apply_coe`, `mul_right_eq_self₀`, `ValuativeRel.ValueGroupWithZero.lift_one`, `Algebra.EssFiniteType.cond`, `groupHomology.lsingle_comp_chainsMap_f_assoc`, `MulChar.map_nonunit'`, `permMatrix_mem_doublyStochastic`, `IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq`, `IsLocalization.exist_integer_multiples`, `groupHomology.single_mem_cycles₂_iff`, `Valuation.one_apply_def`, `Algebra.norm_eq_of_ringEquiv`, `Ideal.absNorm_span_singleton`, `PreTilt.mk_untilt_eq_coeff_zero`, `SimpleGraph.adjMatrix_hadamard_natCast`, `ClassGroup.norm_le`, `Representation.ind_apply`, `StarAlgHom.map_star'`, `Polynomial.mem_nonzeroDivisors_of_coeff_mem`, `Representation.isIntertwiningMap_iff`, `RingOfIntegers.coe_algebraMap_norm`, `WittVector.teichmuller_coeff_pos`, `Real.probChar_apply`, `Representation.self_comp_norm`, `Matrix.IsAdjMatrix.adjMatrix_toGraph_eq`, `FreeNonUnitalNonAssocAlgebra.lift_of_apply`, `Subsemiring.toSubmonoid_injective`, `IsPrimitiveRoot.norm_of_cyclotomic_irreducible`, `IsLocalization.lift_eq_iff`, `List.prod_map_le_prod_map₀`, `Circle.coe_injective`, `spinGroup.coe_star`, `RingEquiv.coe_monoidHom_refl`, `RingConeClass.toSubmonoidClass`, `MonoidHom.map_frobenius`, `SignType.coe_pow`, `FreeAbelianGroup.liftMonoid_symm_coe`, `Representation.inv_self_apply`, `MonoidHom.map_iterate_frobeniusEquiv_symm`, `Circle.coe_zpow`, `LinearMap.detAux_id`, `IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers`, `Algebra.isIntegral_norm`, `QuadraticAlgebra.norm_mem_nonZeroDivisors_iff`, `OreLocalization.nontrivial_iff`, `LocallyConstant.coe_charFn`, `FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction`, `zero_notMem_nonZeroDivisorsLeft`, `SkewMonoidAlgebra.mem_span_support`, `Representation.apply_eq_of_coe_eq`, `NonUnitalAlgHom.coe_codRestrict`, `IsFractionRing.num_mul_den_eq_num_iff_eq'`, `MeasureTheory.distribHaarChar_pos`, `Irreducible.gcd_eq_one_iff`, `Submonoid.coe_pos`, `Algebra.norm_eq_prod_embeddings_gen`, `LinearMap.det_toMatrix`, `Rep.coinvariantsTensorIndInv_mk_tmul_indMk`, `Subalgebra.mopAlgEquivOp_apply_coe`, `SkewMonoidAlgebra.lift_def`, `inv_mul_cancel₀`, `AlgebraicGeometry.StructureSheaf.const_apply`, `LinearMap.det_toLin`, `LinearMap.det_eq_one_of_subsingleton`, `Representation.Equiv.conj_apply_self`, `IsLocalization.eq`, `zero_notMem_nonZeroDivisors`, `groupCohomology.H1InfRes_f`, `TopCat.Presheaf.submonoidPresheafOfStalk_obj`, `IsLocalization.lift_surjective_iff`, `Submonoid.subsemiringClosure_toNonUnitalSubsemiring`, `SkewMonoidAlgebra.DistribMulActionHom.single_toFun`, `IsLocalizedModule.mk'_cancel`, `Matrix.UnitaryGroup.star_mul_self`, `Subalgebra.algEquivOpMop_symm_apply_coe`, `IsLocalization.map_algebraMap_ne_top_iff_disjoint`, `LocalizedModule.liftOn₂_mk`, `RootPairing.Equiv.coweightHom_toLinearMap`, `AddMonoidAlgebra.of'_eq_of`, `ClassGroup.integralRep_mem_nonZeroDivisors`, `RingHomClass.toMonoidHomClass`, `Circle.coe_div`, `groupHomology.single_mem_cycles₁_iff`, `notMem_nonZeroDivisorsLeft_iff`, `Unitization.lift_apply`, `groupHomology.d₂₁_single_ρ_add_single_inv_mul`, `WithZero.map'_id`, `Circle.coe_one`, `notMem_nonZeroDivisors_iff_right`, `UniqueFactorizationMonoid.radical_eq_one_iff`, `mul_mem_nonZeroDivisors`, `IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two'`, `Matrix.UnitaryGroup.transpose_inv_eq_map_star`, `le_nonZeroDivisorsRight_iff_isRightRegular`, `GradedRingHom.mk_coe`, `RingHom.toKerIsLocalization_isLocalizedModule`, `SimpleGraph.natCast_hadamard_adjMatrix`, `FractionalIdeal.den_mem_inv`, `Representation.mem_linHom_invariants_iff_isIntertwining`, `Subsemiring.unop_toSubmonoid`, `FiniteField.algebraMap_norm_eq_pow_sum`, `AlgHom.toFun_eq_coe`, `Representation.mem_invtSubmodule`, `SubsemiringClass.toSubmonoidClass`, `lcm_eq_one_iff`, `IsPrimitiveRoot.norm_sub_one_two`, `instIsDedekindFiniteMonoidOfIsArtinianRing`, `Real.fderiv_fourierChar_neg_bilinear_left_apply`, `SignType.coe_mul`, `LinearMap.associated_det_comp_equiv`, `RatFunc.laurentAux_ofFractionRing_mk`, `FDRep.hom_action_ρ`, `MulRingSeminorm.map_one'`, `right_eq_mul₀`, `Set.indicator_prod_one`, `Subfield.mem_carrier`, `FreeNonUnitalNonAssocAlgebra.hom_ext_iff`, `FractionalIdeal.coe_mk0`, `Algebra.intNorm_eq_zero`, `WittVector.ghostComponent_teichmuller`, `Algebra.mem_algebraMapSubmonoid_of_mem`, `Subfield.inv_mem'`, `QuadraticAlgebra.norm_eq_zero_iff_eq_zero`, `Subsemiring.mem_closure_iff`, `IsLocalization.map_id_mk'`, `groupHomology.chainsMap_f_1_comp_chainsIso₁_apply`, `IsLocalization.surj₂`, `Matrix.IsHermitian.star_eigenvectorUnitary_mulVec`, `LocalizedModule.mkLinearMap_apply`, `Localization.sub_mk`, `IsLocalizedModule.mk'_cancel_left`, `algebraMapSubmonoid_le_nonZeroDivisors_of_faithfulSMul`, `Circle.argEquiv_apply_coe`, `ValuativeRel.ValueGroupWithZero.mk_eq_valuation`, `RingOfIntegers.dvd_norm`, `IsLocalization.exists_of_eq`, `IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal`, `SymplecticGroup.J_mem`, `IsStablyFiniteRing.of_injective`, `RatFunc.map_apply_div_ne_zero`, `one_le_mul_of_one_le_of_one_le`, `IsFractionRing.isUnit_den_zero`, `RootPairing.Hom.weightHom_injective`, `groupHomology.H0π_comp_map_apply`, `Complex.det_conjLIE`, `IsLocalization.eq_iff_exists`, `PresheafOfModules.map_comp_assoc`, `Representation.linearize_apply`, `Matrix.hadamard_one_eq_diagonal_iff`, `notMem_nonZeroDivisorsRight_iff`, `Perfection.teichmuller_spec`, `MonoidAlgebra.lift_single`, `IsLocalization.mem_span_iff`, `Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single`, `IsLocalizedModule.mk'_eq_iff`, `TannakaDuality.FiniteGroup.rightRegular_apply`, `spinGroup.toUnits_injective`, `WithZero.coeMonoidHom_apply`, `Subfield.coe_toSubmonoid`, `Module.FinitePresentation.exists_basis_localizedModule_powers`, `Complex.UnitDisc.coe_circle_smul`, `SimpleGraph.adjMatrix_hadamard_one`, `ZMod.stdAddChar_apply`, `AddMonoidAlgebra.mapAlgEquiv_apply`, `HahnSeries.support_one`, `Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange`, `IsFractionRing.lift_mk'`, `BialgHom.map_one'`, `IsLocalization.smul_toInvSubmonoid`, `IsLocalization.subsingleton_iff`, `FDRep.endRingEquiv_comp_ρ`, `Algebra.TensorProduct.lift_includeLeft_includeRight`, `groupHomology.mem_cycles₁_iff`, `exists_mem_doublyStochastic_eq_smul_iff`, `pow_le_one₀`, `factorization_one`, `AlgEquiv.algHomUnitsEquiv_apply_apply`, `IsLocalization.mk'_spec`, `Circle.argPartialEquiv_apply`, `MeasureTheory.charFun_eq_integral_probChar`, `Units.map_neg_one`, `RingHom.mk_coe`, `IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two`, `NonUnitalSubalgebra.range_val`, `Representation.trivial_apply`, `MonoidAlgebra.of_apply`, `groupHomology.single_mem_cycles₂_iff_inv`, `groupHomology.d₁₀_single`, `Valuation.one_rel_iff`, `Valuation.le_one_of_subsingleton`, `MonoidHom.ext_int_iff`, `Representation.linearizeTrivial_def`, `Perfection.teichmuller_spec'`, `Representation.self_norm_apply`, `Representation.IndV.hom_ext_iff`, `Subring.addEquivOp_symm_apply_coe`, `SkewMonoidAlgebra.liftNC_smul`, `ClassGroup.exists_mem_finset_approx'`, `NonUnitalAlgHom.subtype_comp_codRestrict`, `IsFractionRing.isUnit_den_iff`, `LinearEquiv.coe_det`, `Localization.mem_range_mapToFractionRing_iff`, `Subring.toSubmonoid_injective`, `Complex.rotation`, `ClassGroup.exists_mem_finsetApprox`, `Set.indicator_eq_one_iff_mem`, `IsLocalization.exists_mk'_eq`, `Matrix.UnitaryGroup.inv_apply`, `Valuation.one_apply_eq_one_iff`, `SimpleGraph.incMatrix_apply_eq_zero_iff`, `LinearMap.instIsStablyFiniteRing`, `IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two`, `AlgHom.coe_monoidHom_injective`, `IsLocalizedModule.eq_zero_iff`, `spinGroup.star_mul_self`, `spinGroup.val_toUnits_apply`, `spinGroup.star_mem_iff`, `IsLocalizedModule.mk'_mul_mk'_of_map_mul`, `IsLocalizedModule.surj`, `MonoidAlgebra.lift_of`, `Rep.instIsTrivialVOfCompLinearMapIdρ`, `BoundedContinuousFunction.char_apply`, `lcm_one_right`, `IsLocalizedModule.iso_mk_one`, `LieHom.toNonUnitalAlgHom_injective`, `LinearOrderedCommMonoidWithZero.toZeroLeOneClass`, `mul_zero`, `Representation.leftRegularMapEquiv_symm_apply_toFun`, `NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply`, `Localization.coe_algEquiv_symm`, `FreeNonUnitalNonAssocAlgebra.lift_comp_of`, `List.prod_nonneg`, `IsLocalization.mk'_mul`, `prod_galRestrict_eq_norm`, `IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk'`, `IsLocalization.ringEquivOfRingEquiv_mk'`, `groupHomology.chainsMap_f`, `Rep.quotientToCoinvariantsFunctor_obj_V`, `Ideal.absNorm_dvd_norm_of_mem`, `IsDedekindDomain.HeightOneSpectrum.exists_primeCompl_mul_eq_of_integer`, `groupHomology.chainsMap_f_2_comp_chainsIso₂_apply`, `groupCohomology.map_comp_assoc`, `IsLocalizedModule.mk'_sub_mk'`, `Representation.ofMulAction_def`, `Polynomial.isIntegral_isLocalization_polynomial_quotient`, `IsLocalization.map_nonZeroDivisors_le`, `SkewMonoidAlgebra.lift_symm_apply`, `mem_nonZeroDivisorsRight_iff`, `MonoidAlgebra.lift_unique'`, `IsLocalizedModule.injective_iff_isRegular`, `Finset.gcd_div_eq_one`, `OreLocalization.inv_def`, `Localization.localRingHom_mk`, `Rep.coindFunctorIso_hom_app_hom_toFun_hom_toFun`, `IsDedekindFiniteMonoid.iff_eq_of_mul_left_eq_one`
`toMulZeroClass` 📖	CompOp	1234 math math: `Finset.sup'_mul_le_mul_sup'_of_nonneg`, `Set.center_units_subset`, `Ordinal.opow_mul`, `GCDMonoid.lcm_zero_right`, `IsGaloisGroup.smul_mem_of_normal`, `Ordinal.lt_omega0_opow_succ`, `unitsEquivNeZero_symm_apply`, `MeasureTheory.eLpNormEssSup_const_smul_le`, `RatFunc.mk_def_of_ne`, `HasStrictFDerivAt.fun_mul'`, `AlgEquiv.moduleEndSelfOp_apply_apply`, `ofDual_toAdd_zero`, `Set.preimage_const_mul_Ioi₀`, `le_mul_div_mul_left`, `Valuation.inversion_estimate'`, `Homeomorph.coe_mulRight₀`, `Set.image_mul_left_Iio`, `pow_sub_of_lt`, `nonZeroDivisorsLeft_eq_nonZeroSMulDivisors`, `mul_inv_cancel_of_invertible`, `neg_of_div_neg_right`, `inv_eq_zero`, `mul_inf₀`, `MeasureTheory.eLpNorm_smul_le_mul_eLpNorm`, `lcm_dvd_lcm_mul_right`, `mul_inv_eq_mul_inv_iff`, `lcm_eq_zero_iff`, `Quaternion.snd_imJ_dualNumberEquiv_symm`, `zero_zpow`, `hasStrictFDerivAt_list_prod_finRange'`, `Ordinal.isNormal_mul_right`, `mul_div_mul_right`, `IsRelPrime.moebius_mul`, `Set.preimage_mul_const_Icc₀`, `Valuation.val_mrange_zero`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `Ordinal.exists_lt_mul`, `HasProd.congr_cofinite₀`, `StrictMono.mul`, `div_le_iff₀`, `Multiset.lcm_eq_zero_iff`, `Valuation.mem_supp_iff`, `Matrix.toLinearMapRight'_mul`, `mem_nonZeroDivisors_iff_left`, `isReduced_of_injective`, `MeasureTheory.MemLp.smul`, `gcd_dvd_gcd_mul_right`, `GroupWithZero.conj_pow₀`, `gcd_mul_lcm`, `UniqueFactorizationMonoid.exists_reduced_factors`, `Ordinal.instIsLeftCancelMulZero`, `WithZero.withZeroUnitsEquiv_symm_apply_coe`, `div_sq_cancel`, `Ring.mul_inverse_cancel_right`, `StrictMono.const_mul`, `mul_div_mul_right_le`, `Ordinal.principal_mul_of_le_two`, `mul_inv_cancel_left₀`, `OrderMonoidWithZeroHom.toFun_eq_coe`, `mul_eq_of_eq_inv_mul₀`, `Set.natCard_smul_set₀`, `ArithmeticFunction.IsMultiplicative.map_prod_of_subset_primeFactors`, `Commute.inv_right_iff₀`, `Matrix.one_kronecker`, `mul_right_mem_nonZeroDivisors_eq_zero_iff`, `NumberField.RingOfIntegers.instSMulDistribClass`, `OrderIso.mulRight₀_symm`, `pow_pos`, `Set.inv_mem_centralizer₀`, `map_mul_left_nhds_one₀`, `ONote.nf_repr_split'`, `Ordinal.noZeroDivisors`, `Decidable.mul_lt_mul''`, `div_mul_cancel₀`, `fderivWithin_fun_pow'`, `IsClosed.smul₀`, `signHom_apply`, `mul_div_cancel_of_invertible`, `Associates.prod_top`, `mul_inv_le_one`, `Matrix.hadamard_one_eq_zero_iff`, `le_div_iff₀'`, `isClosedEmbedding_cfcₙAux`, `Submonoid.mem_pos`, `gcd_mul_left`, `GroupWithZero.isOpen_singleton_zero`, `Ordinal.deriv_add_eq_mul_omega0_add`, `ArithmeticFunction.isMultiplicative_one`, `Set.preimage_const_mul_Iio₀`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `Finset.gcd_empty`, `Ordinal.mulRightMono`, `gauge_smul_of_nonneg`, `Filter.NeBot.zero_div_nonneg`, `WithZeroTopology.nhds_zero`, `UniqueFactorizationMonoid.primeFactors_zero`, `DualNumber.range_lift`, `measurableEmbedding_mulRight₀`, `Valuation.toFun_eq_coe`, `CliffordAlgebraDualNumber.equiv_symm_eps`, `Ordinal.CNF.eval_single_add'`, `NeZero.one`, `associatesEquivOfUniqueUnits_symm_apply`, `Matrix.IsAdjMatrix.apply_ne_one_iff`, `GroupWithZero.isConj_iff₀`, `Set.image_mul_left_Ioi`, `MulChar.map_ringChar`, `smulMonoidWithZeroHom_apply`, `zpow_add_one₀`, `Commute.div_right`, `Ring.inverse_mul_eq_iff_eq_mul`, `Ring.inverse_mul_cancel`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply`, `Ordinal.CNF.coeff_opow_mul_add`, `Multiset.prod_eq_zero`, `Set.image_mul_right_Icc'`, `Pi.single_apply_smul`, `Normal.minpoly_eq_iff_mem_orbit`, `zpow_left_injOn₀`, `MonoidWithZeroHom.one_apply_zero`, `Set.preimage_const_mul_Ioo₀`, `lowerBounds_smul_of_pos`, `Quaternion.snd_re_dualNumberEquiv_symm`, `GCDMonoid.toIsCancelMulZero`, `SemiconjBy.div_right`, `HasStrictFDerivAt.mul'`, `le_mul_inv_left`, `emultiplicity_zero_eq_zero_of_ne_zero`, `DFinsupp.prod_eq_zero_iff`, `le_zero_iff`, `Localization.liftOn_zero`, `Ordinal.lt_mul_div_add`, `pow_mul_eq_zero_of_le`, `pow_nonneg`, `prime_mul_iff`, `Ordinal.mul_div_gc`, `GCDMonoid.gcd_mul_lcm`, `Quaternion.imJ_fst_dualNumberEquiv`, `normUnit_mul_normUnit`, `ENNReal.orderIsoRpow_symm_apply`, `SemiconjBy.inv_right₀`, `left_mem_segment`, `OreLocalization.nontrivial`, `pow_eq_zero_iff`, `Finsupp.single_smul`, `mul_inv_cancel₀`, `MonoidWithZeroHom.map_eq_zero_iff`, `MonoidWithZeroHom.one_apply_eq_zero_iff`, `WithZeroTopology.nhds_zero_of_units`, `mul_left_bijective_of_finite₀`, `Ordinal.add_log_le_log_mul`, `fderiv_fun_pow'`, `ArithmeticFunction.isMultiplicative_finsetProd`, `pow_eq_zero_of_le`, `mul_eq_of_eq_mul_inv₀`, `Monotone.mul_const`, `inv_mul_le_of_le_mul₀`, `Submonoid.LocalizationMap.mk'_zero`, `Finset.div_zero_subset`, `ValuationSubring.mem_inv_pointwise_smul_iff`, `div_mul_cancel_of_imp`, `Function.support_pow`, `Ordinal.div_le`, `OrderDual.instIsStrictOrderedModule`, `Set.star_inv'`, `Ordinal.isPrincipal_mul_omega0_opow_opow`, `div_self_mul_self`, `lt_div_iff₀'`, `Filter.tendsto_mul_iff_of_ne_zero`, `Ordinal.lt_mul_iff_div_lt`, `mem_nonZeroDivisors_iff`, `inv_le_one_iff₀`, `MonoidWithZeroHom.valueGroup.mk_mul`, `ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefree`, `lt_inv_mul_iff₀'`, `one_lt_inv_iff₀`, `Quaternion.imI_fst_dualNumberEquiv`, `Ordinal.div_lt`, `gcd_dvd_gcd_mul_left_right`, `SimpleGraph.adjMatrix_hadamard_ofNat`, `IsReduced.pow_eq_zero_iff'`, `Ring.inverse_invertible`, `gcd_zero_right'`, `Real.sInf_smul_of_nonneg`, `UniqueFactorizationMonoid.normalizedFactors_zero`, `lt_div_iff₀`, `ConjAct.toConjAct_zero`, `Ordinal.opow_add`, `Ordinal.lt_mul_succ_div`, `ONote.repr_mul`, `Ordinal.div_add_mod`, `List.one_le_prod`, `Ordinal.mul_add_div`, `Ordinal.principal_mul_omega0`, `Ordinal.nfp_mul_opow_omega0_add`, `Valuation.IsEquiv.pos_iff`, `DualNumber.lift_apply_eps`, `MulActionWithZero.zero_smul`, `Set.image_mul_left_Icc'`, `MeasureTheory.SignedMeasure.singularPart_smul`, `inv_mul_lt_one₀`, `gcd_mul_right'`, `Prime.dvd_mul`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval`, `HasStrictFDerivAt.list_prod'`, `Real.sSup_smul_of_nonneg`, `NeZero.pow`, `inf_mul₀`, `div_mul_cancel_left₀`, `mul_div_mul_left_le`, `Nonneg.inv_mk`, `MonoidWithZeroHom.coe_mk`, `mul_eq_one_iff_inv_eq₀`, `Finset.gcd_eq_zero_iff`, `Ordinal.IsInitial.principal_mul`, `Finset.extract_gcd`, `Ordinal.opow_mul_add_pos`, `Matrix.single_eq_single_vecMulVec_single`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁`, `Mathlib.Tactic.FieldSimp.NF.cons_pos`, `mul_inv_lt_iff₀`, `MonoidWithZeroHom.valueGroup.mk_inj`, `Commute.zpow_right₀`, `NormedAddGroupHom.isCentralScalar`, `StrictAnti.const_mul`, `closure_smul₀`, `mul_eq_left₀`, `inv_zero`, `left_eq_mul₀`, `OrderMonoidWithZeroHom.monotone'`, `le_mul_div_mul_right`, `Submonoid.LocalizationMap.subsingleton_iff`, `CompactlySupportedContinuousMap.toRealLinearMap_apply_apply`, `SimpleGraph.incMatrix_apply_mul_incMatrix_apply_of_not_adj`, `Set.image_mul_right_Icc`, `not_prime_zero`, `div_self_mul_self'`, `inv_mul_eq_iff_eq_mul₀`, `Ordinal.mul_lt_of_lt_div`, `Finset.prod_ite_zero`, `Ordinal.mul_lt_omega0_opow`, `MulPosMono.toMulPosStrictMono`, `HasStrictDerivAt.real_of_complex`, `eq_mul_inv_iff_mul_eq₀`, `orderOf_zero`, `range_cfcₙHom`, `Set.image_const_mul_Ioi_zero`, `one_div_neg`, `RatFunc.mk_eq_localization_mk`, `Ring.mul_inverse_rev'`, `inv_mul_le_one`, `Ordinal.div_mul_cancel`, `Valuation.restrict_eq_zero_iff`, `mul_dvd_mul_iff_right`, `inv_mul_cancel_left₀`, `Ordinal.natCast_mul_omega0`, `factorization_mul`, `lt_mul_inv_iff₀`, `Equiv.divRight₀_symm_apply`, `mul_lt_one_of_nonneg_of_lt_one_left`, `rank_lt_rank_dual'`, `RatFunc.mk_eq_mk'`, `Matrix.hadamard_one`, `inv_mul_le_one₀`, `SimpleGraph.adjMatrix_hadamard_intCast`, `ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem`, `le_inv_mul_right`, `ArithmeticFunction.IsMultiplicative.multiplicative_factorization`, `Multiset.prod_nonneg`, `Monotone.mul_strictMono`, `PosMulReflectLT.toPosMulReflectLE`, `Set.preimage_const_mul_Ico₀`, `NormalizationMonoid.normUnit_zero`, `OrderIso.divRight₀_symm_apply`, `SimpleGraph.adjMatrix_hadamard_diagonal`, `CompactlySupportedContinuousMap.coe_toRealLinearMap`, `ValuationSubring.smul_mem_pointwise_smul_iff`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `pow_inv_comm₀`, `div_helper`, `Quaternion.fst_imK_dualNumberEquiv_symm`, `Commute.inv_left_iff₀`, `Ordinal.isPrincipal_mul_omega0`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `fderiv_mul_const'`, `ArithmeticFunction.IsMultiplicative.map_gcd`, `DualNumber.fst_eq_zero_iff_eps_dvd`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons_zero`, `TrivSqZeroExt.inl_mul_inr`, `IsNilpotent.smul`, `inv_mul_lt_iff₀`, `IsSelfAdjoint.zpow₀`, `zero_div`, `OrderMonoidIso.withZeroUnits_symm_apply`, `mul_left_mem_nonZeroDivisors_eq_zero_iff`, `mul_lt_one_of_nonneg_of_lt_one_right`, `inv_mul_eq_inv_mul_iff`, `IsGaloisGroup.mulEquivCongr_apply_smul`, `OrderMonoidIso.withZeroUnits_apply`, `Ordinal.mul_mod`, `UniqueFactorizationMonoid.normalizedFactors_mul`, `zero_zpow_eq`, `SimpleGraph.intCast_hadamard_adjMatrix`, `ofAdd_bot`, `Ordinal.principal_mul_ord`, `Set.div_mem_centralizer₀`, `Ordinal.log_opow_mul`, `Ordinal.opow_one_add`, `DualNumber.lift_inlAlgHom_eps`, `Finset.sup'_mul₀`, `Associates.factors_zero`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `List.prod_map_lt_prod_map`, `Ordinal.opow_mul_add_lt_opow`, `Prime.not_dvd_mul`, `Ordinal.smul_eq_mul`, `mem_nonZeroDivisors_iff_right`, `Multiset.prod_eq_zero_iff`, `MulEquiv.toMonoidWithZeroHom_apply`, `Commute.div_left`, `Fintype.prod_ite_zero`, `mul_mem_nonZeroDivisorsLeft_of_mem_nonZeroDivisorsLeft`, `lcm_mul_left`, `pow_succ_nonneg`, `OrderIso.withZeroUnits_symm_apply`, `isRadical_iff_squarefree_or_zero`, `mul_boole`, `mulLeft_bijective₀`, `not_isNilpotent_one`, `monotone_mul_right_of_nonneg`, `cfcₙAux_id`, `lt_mul_right`, `eq_zero_of_mul_eq_self_right`, `DualNumber.isNilpotent_iff_eps_dvd`, `le_mul_inv_iff₀'`, `DualNumber.isMaximal_span_singleton_eps`, `mul_le_of_le_div₀`, `ConjAct.ofConjAct_zero`, `IsUnit.mul_left_eq_zero`, `zpow_left_strictMonoOn₀`, `Set.smul_indicator_one_apply`, `ArithmeticFunction.IsMultiplicative.map_prod_of_prime`, `exists_right_inv_of_exists_left_inv`, `MonoidWithZeroHom.valueGroup_eq_range`, `fderiv_pow'`, `Ordinal.CNF.eval_single`, `SimpleGraph.diagonal_hadamard_adjMatrix`, `MonoidWithZeroHom.toZeroHom_coe`, `CompactlySupportedContinuousMap.toRealLinearMap_apply`, `OreLocalization.subsingleton_iff`, `Ordinal.iSup_mul_nat`, `pow_eq_zero_iff'`, `DualNumber.lift_smul`, `Finset.gcd_mul_left`, `Ordinal.lt_mul_add_one_iff`, `associated_zero_iff_eq_zero`, `sq_pos_of_pos`, `GrpWithZero.Iso.mk_hom`, `Quaternion.imK_fst_dualNumberEquiv`, `Submonoid.LocalizationMap.noZeroDivisors`, `lift_rank_lt_rank_dual'`, `Ordinal.instPosMulStrictMono`, `mul_inv_lt_of_lt_mul₀`, `not_isUnit_zero`, `WithZero.withZeroUnitsEquiv_symm_strictMono`, `RingHom.ENatMap_apply`, `pos_nilpotencyClass_iff`, `Quaternion.re_fst_dualNumberEquiv`, `zero_pow_eq_one₀`, `MulPosReflectLE.of_posMulReflectLT_of_mulPosMono`, `gcd_eq_zero_iff`, `SignType.castHom_apply`, `Set.inv_zero`, `Nonneg.coe_pow`, `MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm'`, `zpow_add'`, `IsUnit.mul_right_eq_zero`, `Ordinal.nfp_mul_eq_opow_omega0`, `inv_mul_mul_self`, `fderivWithin_fun_mul'`, `coe_nonZeroDivisorsRight_eq`, `SemiconjBy.zpow_right₀`, `mul_div_cancel_left₀`, `mul_inv_le_iff₀`, `hasFDerivAt_list_prod'`, `MonoidWithZeroHom.one_apply_def`, `Matrix.toLinearMapRight'_mul_apply`, `Finset.mul_inf_le_inf_mul_of_nonneg`, `div_eq_iff_mul_eq`, `Finset.gcd_eq_gcd_filter_ne_zero`, `nhds_translation_mul_inv₀`, `ONote.repr_scale`, `Set.preimage_const_mul_Ici₀`, `one_div_nonneg`, `Prime.not_isSquare`, `fderiv_mul'`, `finprod_zero_le_one`, `Multiset.extract_gcd`, `mul_mul_div`, `dvd_mul_gcd_of_dvd_mul`, `instSMulDistribClassAlgEquiv`, `UniqueFactorizationMonoid.normalizedFactorsEquiv_symm_apply`, `Polynomial.smeval_C`, `pow_mul_apply_eq_pow_mul`, `isRelPrime_zero_right`, `inv_pos`, `inv_nonneg_of_nonneg`, `Ordinal.nfp_mul_zero`, `Commute.inv_mul_eq_inv_mul_iff`, `MeasureTheory.MemLp.const_smul`, `Matrix.one_hadamard_eq_diagonal_iff`, `Multiset.prod_map_nonneg`, `isPrimal_zero`, `isNilpotent_iff_eq_zero`, `IsNilpotent.eq_zero_of_isIdempotentElem`, `mul_left_coe_nonZeroDivisors_eq_zero_iff`, `mul_le_of_le_inv_mul₀`, `div_nonpos_of_nonpos_of_nonneg`, `Ordinal.isSuccPrelimit_mul_right`, `Valuation.map_add_le_max'`, `IsIdempotentElem.iff_eq_zero_or_one`, `LocallyConstant.charFn_eq_zero`, `Ring.mul_inverse_cancel`, `SimpleGraph.one_hadamard_adjMatrix`, `eq_zero_of_zpow_eq_zero`, `Valuation.zero_iff`, `mul_right_coe_nonZeroDivisors_eq_zero_iff`, `lcm_dvd_mul`, `strictMono_mul_right_of_pos`, `HahnSeries.map_one`, `one_lt_mul`, `hasFDerivWithinAt_pow'`, `Set.univ_smul_nhds_zero`, `MonoidWithZeroHom.map_zero`, `ArithmeticFunction.IsMultiplicative.prod_primeFactors`, `zero_zpow_eq_one₀`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `ContinuousInv₀.of_nhds_one`, `continuousOn_div`, `emultiplicity_zero`, `UniqueFactorizationMonoid.multiplicative_of_coprime`, `normalize_eq_zero`, `lcm_mul_right`, `div_mul_div_cancel₀'`, `Finset.inv_zero`, `MulPosReflectLT.toMulPosStrictMono`, `map_eq_zero`, `SimpleGraph.toGraph_adjMatrix_eq`, `Ring.isUnit_iff_mul_inverse_cancel`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `factorization_zero`, `le_inv_mul_iff₀'`, `zero_eq_inv`, `div_eq_div_iff`, `ThreeGPFree.smul_set₀`, `fderivWithin_mul_const'`, `inv_neg''`, `Valuation.one_apply_eq_zero_iff`, `Finsupp.prod_eq_zero_iff`, `hasFDerivAt_list_prod_finRange'`, `zero_isRadical_iff`, `strictMonoOn_mul_self`, `Finsupp.support_sym2Mul_subset`, `Commute.zpow_zpow_self₀`, `Ring.inverse_pow_mul_eq_iff_eq_mul`, `normalize_apply`, `isReduced_iff_pow_one_lt`, `mul_inv_le_one_of_le₀`, `Ordinal.principal_mul_omega`, `range_cfcₙHom_le`, `IsSelfAdjoint.inv₀`, `Valuation.apply_posSubmonoid_pos`, `Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg`, `MulDivCancelClass.mul_div_cancel`, `Submonoid.LocalizationMap.map_eq_zero_iff`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `not_isRelPrime_zero_zero`, `Commute.ringInverse_ringInverse`, `Set.image_mul_left_Ioc`, `notMem_nonZeroDivisors_iff`, `dvd_mul_gcd_iff_dvd_mul`, `UniqueFactorizationMonoid.primeFactors_mul_eq_union`, `inv_mul_eq_one₀`, `UniqueFactorizationMonoid.primeFactors_mul_eq_disjUnion`, `WithZeroTopology.isClosed_iff`, `zpow_eq_zero_iff`, `List.prod_pos`, `eq_inv_mul_iff_mul_eq₀`, `Ordinal.mul_eq_right_iff_opow_omega0_dvd`, `Ordinal.mul_succ`, `Mathlib.Meta.NormNum.isNat_ordinalMul`, `inv_lt_iff_one_lt_mul₀`, `gauge_smul_left_of_nonneg`, `WithZeroTopology.hasBasis_nhds_zero`, `zpow_nonneg`, `hasProd_zero_of_exists_eq_zero`, `Quaternion.fst_imJ_dualNumberEquiv_symm`, `Finset.Nonempty.zero_div`, `SimpleGraph.incMatrix_apply_eq_one_iff`, `IsUnit.isNilpotent_unit_mul_of_commute_iff`, `Ordinal.opow_mul_add_lt_opow_mul`, `div_lt_iff₀`, `MeasureTheory.Filtration.filtrationOfSet_eq_natural`, `Prime.dvd_prod_iff`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsRight`, `one_le_inv_iff₀`, `mul_eq_right₀`, `Set.preimage_mul_const_Ioo₀`, `Finset.inv_smul_finset_distrib₀`, `div_nonpos_of_nonneg_of_nonpos`, `HasFDerivWithinAt.mul_const'`, `eq_zero_of_mul_eq_self_left`, `Units.mul_right_eq_zero`, `Matrix.hadamard_one_eq_one_iff`, `Filter.top_smul_nhds_zero`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `mul_mem_nonZeroDivisors_of_mem_nonZeroDivisors`, `Associated.eq_zero_iff`, `pow_left_monotoneOn`, `Matrix.dualNumberEquiv_symm_apply`, `le_mul_inv_right`, `mul_left_eq_self₀`, `Ordinal.principal_add_mul_of_principal_add`, `DualNumber.exp_eps`, `Commute.zpow_self₀`, `Matrix.one_hadamard_eq_one_iff`, `MonoidWithZeroHom.map_one'`, `Valuation.map_mul`, `not_isPrimePow_zero`, `fderiv_pow_ring'`, `SimpleGraph.ofNat_hadamard_adjMatrix`, `lt_mul_inv_iff₀'`, `sup_mul₀`, `mul_div_cancel_of_imp'`, `zero_pow_le_one`, `Ring.isUnit_iff_inverse_mul_cancel`, `Set.inv_smul_set_distrib₀`, `IsSMulRegular.zero`, `ArithmeticFunction.IsMultiplicative.map_one`, `Quaternion.fst_imI_dualNumberEquiv_symm`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval`, `rank_dual_eq_card_dual_of_aleph0_le_rank'`, `mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff`, `mul_inv_cancel_right₀`, `Set.image_mul_right_Ioo`, `mul_right_mem_nonZeroDivisorsRight_eq_zero_iff`, `IsNilpotent.map`, `Valued.closure_coe_completion_v_mul_v_lt`, `Ordinal.lt_div`, `Submonoid.IsLocalizationMap.map_zero`, `WfDvdMonoid.max_power_factor`, `ONote.repr_opow_aux₁`, `Ordinal.iSup_mul_natCast`, `mul_one_div_cancel`, `extract_gcd`, `Mathlib.Tactic.FieldSimp.list_prod_zpow'`, `gcd_mul_dvd_mul_gcd`, `mul_div_cancel₀`, `Matrix.one_hadamard`, `Ordinal.IsInitial.isPrincipal_mul`, `Units.mk0_mul`, `Set.image_mul_left_Icc`, `eq_zero_of_zero_eq_one`, `eq_zero_of_nilpotencyClass_eq_one`, `Ordinal.log_opow_mul_add`, `mul_eq_one_iff_eq_inv₀`, `noZeroDivisors_iff_forall_mem_nonZeroDivisors`, `Associates.instNoZeroDivisors`, `HasFDerivAt.fun_pow'`, `Right.inv_nonneg`, `Prime.dvd_finsuppProd_iff`, `lcm_dvd_lcm_mul_right_right`, `Valuation.extendToLocalization_mk'`, `IsIdempotentElem.eq_zero_of_isNilpotent`, `HasMFDerivWithinAt.mul'`, `Homeomorph.mulLeft₀_symm_apply`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply`, `eq_zero_of_ne_zero_of_mul_right_eq_zero`, `zpow_pos`, `Prime.not_dvd_prod`, `inv_pos_of_pos`, `Ordinal.natCast_mul`, `DualNumber.lift_apply_apply`, `Set.preimage_mul_const_Iic₀`, `Ordinal.mul_mod_mul`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `mulPosReflectLE_iff_mulPosReflectLT`, `MulChar.mul_apply`, `IsNilpotent.pow_succ`, `mul_inv_left_le`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_right`, `Ring.inverse_non_unit`, `TrivSqZeroExt.inr_mul_inl`, `RingHom.withTopMap_apply`, `Finset.zero_div_subset`, `strictMono_mul_left_of_pos`, `Units.mul_inv'`, `Cardinal.mk_smul_set₀`, `DualNumber.ringHom_ext_iff`, `LinearMap.toMatrixRight'_id`, `eq_zero_or_one_of_sq_eq_self`, `Ordinal.le_mul_right`, `Ordinal.add_eq_right_iff_mul_omega0_le`, `Valuation.restrict_pos_iff`, `Commute.zpow_left₀`, `gcd_zero_right`, `Ordinal.mul_add_div_mul`, `cfcₙAux_injective`, `Ordinal.nsmul_eq_mul`, `isUnit_zero_iff`, `WithZero.toMonoidWithZeroHom_withZeroUnitsEquiv`, `mul_self_mul_inv`, `mul_le_of_le_mul_inv₀`, `Pi.single_smul₀`, `nilpotencyClass_eq_one`, `mul_div_cancel_right₀`, `Matrix.IsAdjMatrix.toGraph_compl_eq`, `gcd_neg'`, `Set.indicator_pi_one_apply`, `Mathlib.Tactic.FieldSimp.zpow'_eq_zero_iff`, `ArithmeticFunction.prodPrimeFactors_apply`, `lcm_dvd_lcm_mul_left`, `one_lt_mul_of_le_of_lt`, `Set.image_mul_left_Ico`, `lt_inv_mul_iff₀`, `Prime.finiteMultiplicity_mul`, `mul_inv_right_le`, `Ordinal.nfp_add_eq_mul_omega0`, `MeasureTheory.eLpNorm_const_smul_le`, `Set.inv_Ioi₀`, `Ordinal.mul_add_mod_self`, `IsPrimitiveRoot.injOn_pow_mul`, `Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons`, `Matrix.kronecker_one`, `hasStrictFDerivAt_pow'`, `Ordinal.mul_eq_opow_log_succ`, `Valuation.IsEquiv.eq_zero`, `Bound.one_lt_mul`, `IsLeftCancelMulZero.toFaithfulSMul_opposite`, `DualNumber.coe_lift_symm_apply`, `mul_eq_mul_prime_pow`, `Quaternion.imJ_snd_dualNumberEquiv`, `Set.preimage_const_mul_Icc₀`, `fderiv_fun_mul'`, `UniqueFactorizationMonoid.radical_zero`, `Units.exists0'`, `Ordinal.leftDistribClass`, `smul_zpow₀'`, `MeasureTheory.Lp.coeFn_lpSMul`, `GroupWithZero.dvd_iff`, `zpow_add₀`, `Ordinal.lt_omega0_opow`, `Function.support_inv`, `le_inv_mul_iff₀`, `Quaternion.snd_imK_dualNumberEquiv_symm`, `antitoneOn_inv_pos`, `spec_cfcₙAux`, `Matrix.one_hadamard_eq_zero_iff`, `gcd_mul_left'`, `mul_dvd_mul_iff_left`, `MeasurableSet.const_smul₀`, `Matrix.one_kronecker_one`, `unitsEquivNeZero_apply_coe`, `finprod_eq_zero`, `Finset.prod_eq_zero_iff`, `Finset.inv_op_smul_finset_distrib₀`, `List.prod_eq_zero`, `Associates.out_eq_zero_iff`, `hasStrictFDerivAt_list_prod_attach'`, `Prime.not_dvd_finsuppProd`, `div_eq_iff`, `WfDvdMonoid.max_power_factor'`, `inv_nonneg`, `Invertible.toNeZero`, `zero_pow_eq`, `Valuation.integer.v_irreducible_pos`, `Ordinal.isSuccLimit_mul`, `Submonoid.mem_nonunits_iff_or`, `Ordinal.CNF.foldr`, `Set.image_mul_right_Ioc`, `Matrix.IsAdjMatrix.apply_ne_zero_iff`, `SemiconjBy.inv_symm_left₀`, `Associates.factors_eq_top_iff_zero`, `Valuation.leIdeal_zero`, `inv_mul_left_le`, `Mathlib.Meta.Positivity.div_nonneg_of_nonneg_of_pos`, `Function.support_div'`, `smul_floorDiv`, `Set.preimage_mul_const_Ici₀`, `inv_mul_lt_of_lt_mul₀`, `mul_right_surjective₀`, `OreLocalization.nontrivial_of_nonZeroDivisorsRight`, `Finsupp.coe_sym2Mul`, `Associates.out_zero`, `GroupWithZero.mul_right_injective`, `not_lt_zero'`, `Submonoid.LocalizationMap.map_zero`, `CompactlySupportedContinuousMap.toNNRealLinear_apply`, `Ordinal.isPrincipal_mul_of_le_two`, `WithZeroTopology.isOpen_iff`, `associatesEquivOfUniqueUnits_apply`, `List.prod_eq_zero_iff`, `inv_mul_le_iff₀`, `WithZeroTopology.instContinuousMul`, `div_mul_cancel_of_invertible`, `DualNumber.range_inlAlgHom_sup_adjoin_eps`, `GCDMonoid.lcm_zero_left`, `floorDiv_one`, `Finset.sup_mul_le_mul_sup_of_nonneg`, `posMulReflectLE_iff_posMulReflectLT`, `Valuation.IsUniformizer.val_pos`, `tprod_of_exists_eq_zero`, `smul_ceilDiv`, `div_le_div_iff₀`, `MeasureTheory.Integrable.smul_essSup`, `Matrix.toLinearMapRight'_apply`, `div_lt_iff₀'`, `Ordinal.mulLeftMono`, `Set.preimage_const_mul_Ioc₀`, `UniqueFactorizationMonoid.moebius_zero`, `HasFDerivWithinAt.pow'`, `Associates.instIsCancelMulZero`, `ArithmeticFunction.IsMultiplicative.eq_iff_eq_on_prime_powers`, `eq_zero_of_ne_zero_of_mul_left_eq_zero`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective`, `IsReduced.pow_eq_zero_iff`, `HasFDerivAt.list_prod'`, `IsUnit.isNilpotent_mul_unit_of_commute_iff`, `SimpleGraph.adjMatrix_hadamard_self`, `hasFDerivAt_pow'`, `Ordinal.principal_mul_two`, `mul_le_one₀`, `coe_nonZeroDivisorsLeft_eq`, `Valuation.Integers.valuation_pos_iff_ne_zero`, `zero_pow_eq_zero`, `Ordinal.deriv_mul_eq_opow_omega0_mul`, `ceilDiv_one`, `MeasureTheory.Lp.smul_def`, `Ordinal.isPrincipal_mul_omega`, `gcd_dvd_gcd_mul_right_right`, `mem_nonZeroDivisorsLeft_iff`, `Ordinal.principal_mul_iff_mul_left_eq`, `Finset.prod_pos`, `IsGaloisGroup.coe_quotient_smul`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `gcd_zero_left`, `squarefree_mul_iff`, `not_irreducible_zero`, `mul_eq_mul_of_div_eq_div`, `DualNumber.algHom_ext_iff`, `OrderDual.instIsOrderedModule`, `one_le_inv_mul₀`, `HasDerivAt.real_of_complex`, `mulRight_bijective₀`, `OrderMonoidWithZeroHom.coe_mul`, `eq_div_iff_mul_eq`, `Set.preimage_mul_const_Ico₀`, `inv_pow_sub₀`, `zpow_sub_one₀`, `Ordinal.forall_lt_mul`, `AlgEquiv.moduleEndSelf_apply_apply`, `Ordinal.mul_div_cancel`, `NNReal.orderIsoRpow_symm_eq`, `ofDual_toAdd_eq_top_iff`, `MonoidWithZeroHom.map_ite_one_zero`, `multiplicity_mul`, `smul_inv₀`, `Matrix.isDiag_smul_one`, `boole_smul`, `ArithmeticFunction.pdiv_apply`, `ValuationSubring.coe_pointwise_smul`, `ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity`, `Ordinal.add_mul_of_isSuccLimit`, `NormedDivisionRing.toNormSMulClass`, `Finset.prod_boole`, `Ordinal.card_mul`, `Set.image_mul_left_Iic`, `mul_inv_eq_one₀`, `smul_div₀'`, `mul_div_cancel_left_of_imp`, `IsNilpotent.map_iff`, `Matrix.isAdjMatrix_iff_hadamard`, `one_lt_mul_of_lt_of_le`, `instIsCancelMulZero`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `finiteMultiplicity_mul_aux`, `NonUnitalRingHom.mul_def`, `Finset.support_prod_subset`, `CliffordAlgebraDualNumber.equiv_ι`, `IsPrimal.mul`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero`, `Ordinal.mul_le_right_iff_opow_omega0_dvd`, `Ordinal.mul_sub`, `Finset.prod_eq_zero`, `cfcₙAux_mem_range_inr`, `Ring.inverse_mul_cancel_right`, `ArithmeticFunction.IsMultiplicative.map_prod`, `one_div_pos`, `Set.Nonempty.div_zero`, `multiplicity_zero_eq_zero_of_ne_zero`, `AlgEquiv.moduleEndSelfOp_symm_apply`, `Right.inv_pos`, `inv_le_iff_one_le_mul₀`, `Polynomial.smeval_monomial`, `inv_pow_sub_of_lt`, `NoZeroSMulDivisors.isReduced`, `inv_lt_zero`, `gcd_mul_right`, `inv_mul_right_le`, `MonoidWithZeroHom.val_mrange_zero`, `le_mul_inv_iff₀`, `map_mul_right_nhds₀`, `right_mem_segment`, `inv_le_iff_one_le_mul₀'`, `IsSMulRegular.not_zero`, `DualNumber.instIsLocalRing`, `Ordinal.opow_add_one`, `HahnSeries.leadingCoeff_one`, `mul_self_lt_mul_self`, `IsGaloisGroup.smul_eq_self`, `VectorField.mpullback_mfderivWithin_apply_smul`, `Ordinal.principal_mul_omega0_opow_opow`, `mul_div_mul_left`, `UniqueFactorizationMonoid.multiplicative_prime_power`, `HahnModule.one_smul'`, `inv_mul_cancel_of_invertible`, `zpow_neg_mul_zpow_self`, `IsNilpotent.pow_iff_pos`, `inv_mul_lt_iff₀'`, `IsSelfAdjoint.inv₀_iff`, `Ordinal.omega0_opow_mul_nat_lt`, `pow_sub₀`, `MeasureTheory.integrable_smul_iff`, `MulChar.map_nonunit`, `DirichletCharacter.apply_eq_toArithmeticFunction_apply`, `IsPrimitiveRoot.zero`, `not_squarefree_zero`, `HasFDerivAt.pow'`, `HasStrictFDerivAt.pow'`, `zero_mem_nonunits`, `NormalizationMonoid.normUnit_mul`, `NonUnitalRingHom.coe_mul`, `ArithmeticFunction.pmul_comm`, `Ring.not_isUnit_iff_inverse_eq_zero`, `inv_lt_iff_one_lt_mul₀'`, `zero_le'`, `MulChar.restrict_apply`, `OreLocalization.mul_inv_cancel`, `Associates.out_mul`, `Ordinal.lt_mul_iff_of_isSuccLimit`, `Valuation.exists_div_eq_of_unit`, `HasStrictFDerivAt.mul_const'`, `map_mul_right_nhds_one₀`, `Associates.mk_eq_zero`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `Matrix.dualNumberEquiv_apply`, `MeasureTheory.eLpNorm'_const_smul_le`, `eq_zero_of_one_div_eq_zero`, `orderOf_eq_zero_iff_eq_zero`, `ValuationSubring.mem_smul_pointwise_iff_exists`, `ArithmeticFunction.IsMultiplicative.iff_ne_zero`, `OrderIso.withZeroUnits_apply`, `neg_gcd`, `Valuation.leAddSubgroup_zero`, `WithZeroTopology.Iio_mem_nhds_zero`, `Fintype.prod_boole`, `fderivWithin_list_prod'`, `Submonoid.LocalizationMap.isCancelMulZero`, `Ring.mul_inverse_rev`, `PEquiv.toMatrix_injective`, `mul_inv_eq_iff_eq_mul₀`, `DualNumber.eps_pow_two`, `Homeomorph.mulRight₀_symm_apply`, `HasFDerivWithinAt.fun_mul'`, `Commute.div_eq_div_iff`, `ModuleCat.extendScalarsComp_hom_app_one_tmul`, `Ordinal.add_mul_succ`, `Finset.gcd_mul_right`, `Quaternion.re_snd_dualNumberEquiv`, `Ordinal.CNF.opow_mul_add`, `MonoidWithZeroHom.map_ite_zero_one`, `nilpotencyClass_zero`, `Set.center_units_eq`, `SimpleGraph.incMatrix_of_notMem_incidenceSet`, `WithZero.withZeroUnitsEquiv_symm_apply`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `subsingleton_iff_zero_eq_one`, `fderivWithin_pow_ring'`, `Ordinal.mul_add_mod_mul`, `Commute.self_zpow₀`, `Valuation.Integers.valuation_irreducible_pos`, `Ring.inverse_mul_cancel_left`, `Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow`, `pow_left_strictMonoOn₀`, `Ordinal.isSuccLimit_mul_right`, `OreLocalization.zero_oreDiv'`, `MonoidWithZeroHom.mk_coe`, `zpow_one_add₀`, `Real.smul_iSup_of_nonneg`, `MulChar.trivial_apply`, `Ordinal.CNF.eval_single_add`, `inv_mul_le_one_of_le₀`, `Ordinal.opow_mul_lt_opow`, `Ring.mul_inverse_cancel_left`, `Multiset.gcd_zero`, `Set.image_mul_left_Ioo`, `zero_lt_iff`, `HasFDerivWithinAt.fun_pow'`, `Ordinal.isSuccPrelimit_mul_left`, `HahnSeries.order_one`, `invOf_eq_inv`, `LinearOrderedCommMonoidWithZero.toMulPosStrictMono`, `Homeomorph.coe_mulLeft₀`, `invOf_div`, `div_mul_cancel_right₀`, `one_div_mul_cancel`, `div_pos`, `div_nonneg`, `DualNumber.exp_smul_eps`, `Set.preimage_mul_const_Ioc₀`, `Quaternion.snd_imI_dualNumberEquiv_symm`, `Antitone.mul_const`, `continuous_cfcₙAux`, `ONote.repr_opow_aux₂`, `Finset.mul₀_sup'`, `Set.indicator_eq_zero_iff_notMem`, `HasFDerivAt.mul_const'`, `Submonoid.LocalizationMap.mk'_eq_zero_iff`, `StrictMono.mul_monotone`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `pow_pos_iff`, `HasStrictFDerivAt.fun_pow'`, `MeasurableEquiv.coe_mulLeft₀`, `OrderIso.mulLeft₀_symm`, `List.prod_map_le_pow_length₀`, `Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg`, `Filter.zero_pow_eventuallyEq`, `DualNumber.lift_apply_inl`, `IsSMulRegular.not_zero_iff`, `Set.Nonempty.zero_div`, `Ordinal.mul_le_iff_le_div`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `SimpleGraph.incMatrix_of_mem_incidenceSet`, `bddBelow_smul_iff_of_pos`, `UniqueFactorizationMonoid.radical_mul_dvd`, `Real.hasFDerivAt_fourierChar_neg_bilinear_right`, `WithZeroTopology.tendsto_zero`, `IsLocalRing.ResidueField.residue_smul`, `zero_notMem_nonZeroDivisorsRight`, `squarefree_iff_no_irreducibles`, `DualNumber.lift_op_smul`, `UniqueFactorizationMonoid.radical_mul_of_isUnit_left`, `Ordinal.isPrincipal_mul_one`, `zero_ne_one_or_forall_eq_0`, `inv_nonpos`, `Metric.unitClosedBall.instIsCancelMulZero`, `mul_inv_lt_iff₀'`, `IsNilpotent.pow_of_pos`, `GroupWithZero.mul_left_injective`, `Ordinal.isPrincipal_add_mul_of_isPrincipal_add`, `Commute.mul_inv_eq_mul_inv_iff`, `dvd_gcd_mul_of_dvd_mul`, `one_div_nonpos`, `MulCharClass.map_nonunit`, `Set.image_mul_right_Ico`, `Ordinal.mul_omega0_opow_opow`, `bddAbove_smul_iff_of_pos`, `Commute.zpow_zpow₀`, `DirichletCharacter.isMultiplicative_toArithmeticFunction`, `MonoidWithZeroHom.map_mul'`, `instIsCancelMulZero_1`, `IsUnit.integrable_smul_iff`, `div_lt_div_iff₀`, `MonoidWithZeroHomClass.toZeroHomClass`, `Ordinal.nfp_mul_one`, `IsSMulRegular.zero_iff_subsingleton`, `Ordinal.opow_succ`, `bot_eq_zero''`, `gauge_smul_left`, `DualNumber.lift_comp_inlHom`, `UniqueFactorizationMonoid.factors_zero`, `MonoidWithZeroHom.map_mul`, `strictAntiOn_inv_pos`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₂`, `Ordinal.isPrincipal_mul_two`, `DualNumber.algHom_ext'_iff`, `hasStrictFDerivAt_list_prod'`, `DualNumber.ideal_trichotomy`, `Set.zero_div_subset`, `notMem_nonZeroDivisors_iff_left`, `boole_mul`, `Ordinal.le_mul_left`, `DualNumber.inr_eq_smul_eps`, `Valuation.norm_pos_iff_valuation_pos`, `isClosedMap_smul₀`, `Ordinal.nfp_add_zero`, `Commute.inv_right₀`, `Set.div_zero_subset`, `Ordinal.mul_two`, `ContinuousMapZero.elemental_eq_top`, `mul_right_bijective_of_finite₀`, `lcm_dvd_lcm_mul_left_right`, `UniqueFactorizationMonoid.factors_mul`, `noZeroDivisors_iff_forall_mem_nonZeroDivisorsLeft`, `inv_lt_one_iff₀`, `Multiset.gcd_eq_zero_iff`, `DirichletCharacter.map_zero'`, `WithZero.withZeroUnitsEquiv_apply`, `pow_succ_pos`, `Finsupp.sym2Mul_apply_mk`, `continuousOn_zpow₀`, `Units.zero_lt`, `Mathlib.Tactic.FieldSimp.zpow'_add`, `Submonoid.LocalizationMap.lift₀_apply`, `ProbabilityTheory.gaussianPDFReal_mul`, `Associates.quot_out_zero`, `le_div_iff₀`, `star_div₀`, `Set.inter_indicator_one`, `ValuationSubring.smul_mem_pointwise_smul`, `Matrix.IsAdjMatrix.hadamard_self`, `ONote.scale_opowAux`, `star_zpow₀`, `PosMulReflectLT.toPosMulStrictMono`, `WithZero.lift'_zero`, `Finsupp.smul_single_one`, `Matrix.toLinearMapRight'_one`, `mul_mem_nonZeroDivisorsRight_of_mem_nonZeroDivisorsRight`, `HasFDerivWithinAt.mul'`, `Units.mul_left_eq_zero`, `mul_inv_le_of_le_mul₀`, `mul_right_eq_self₀`, `OreLocalization.inv_zero`, `Set.inv_Ioo_0_left`, `Units.exists0`, `MulChar.map_nonunit'`, `Ordinal.mul_div_mul_cancel`, `Valuation.restrict_exists_div_eq`, `Valuation.leSubmodule_zero`, `Ordinal.add_le_right_iff_mul_omega0_le`, `eq_div_iff`, `Valuation.one_apply_def`, `posMulMono_iff_posMulStrictMono`, `Ordinal.isPrincipal_mul_iff_mul_left_eq`, `Ordinal.isSuccLimit_mul_left`, `SimpleGraph.adjMatrix_hadamard_natCast`, `Finset.lcm_eq_zero_iff`, `GroupWithZero.eq_zero_or_unit`, `LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered`, `Multipliable.tsum_congr_cofinite₀`, `fderivWithin_mul'`, `zpow_left_monoOn₀`, `Multiset.lcm_ne_zero_iff`, `Function.support_inv'`, `StrictAnti.mul_const`, `Matrix.IsAdjMatrix.adjMatrix_toGraph_eq`, `PosMulMono.toPosMulStrictMono`, `div_le_iff₀'`, `Finset.Nonempty.div_zero`, `Nonneg.mk_pow`, `mul_left_surjective₀`, `LinearOrderedCommGroupWithZero.inl_apply`, `OreLocalization.nontrivial_of_nonZeroDivisorsLeft`, `map_mul_left_nhds₀`, `List.prod_map_le_prod_map₀`, `LinearOrderedCommGroupWithZero.inr_apply`, `Ordinal.lift_mul`, `Monotone.const_mul`, `mul_sup₀`, `dvd_gcd_mul_iff_dvd_mul`, `SignType.coe_pow`, `mul_inv_mul_cancel`, `monotone_mul_left_of_nonneg`, `ArithmeticFunction.IsMultiplicative.map_lcm`, `div_eq_zero_iff`, `SignType.coe_zpow`, `StrictMono.mul_const`, `OreLocalization.nontrivial_iff`, `MeasureTheory.hasFiniteIntegral_smul_iff`, `LocallyConstant.coe_charFn`, `MulChar.map_zero`, `Valuation.pos_iff`, `MeasureTheory.integrable_fun_smul_iff`, `zero_notMem_nonZeroDivisorsLeft`, `VectorFourier.hasFDerivAt_fourierChar_smul`, `Submonoid.coe_pos`, `isRelPrime_zero_left`, `neg_gcd'`, `MulChar.coeToFun_mul`, `inv_mul_cancel₀`, `Commute.inv_left₀`, `lt_mul_left`, `Ordinal.lt_omega0_omega0_opow`, `fderiv_list_prod'`, `Finset.inf'_mul_le_mul_inf'_of_nonneg`, `zero_notMem_nonZeroDivisors`, `Valuation.map_zero`, `HasMFDerivAt.mul'`, `Mathlib.Tactic.FieldSimp.NF.eval_cons`, `ArithmeticFunction.IsMultiplicative.lcm_apply_mul_gcd_apply`, `ArithmeticFunction.IsMultiplicative.map_div_of_coprime`, `Multiset.gcd_map_mul`, `nilpotencyClass_eq_succ_iff`, `div_zero`, `Antitone.const_mul`, `ofAdd_toDual_eq_zero_iff`, `mul_self_div_self`, `mul_div_cancel_of_imp`, `notMem_nonZeroDivisorsLeft_iff`, `DualNumber.instIsPrincipalIdealRing`, `WithZeroTopology.nhds_eq_update`, `eq_mul_of_mul_inv_eq₀`, `notMem_nonZeroDivisors_iff_right`, `Ordinal.mul_omega0`, `Finsupp.mem_sym2_support_of_mul_ne_zero`, `normalize_zero`, `Ordinal.principal_mul_one`, `UniqueFactorizationMonoid.radical_eq_one_iff`, `mul_mem_nonZeroDivisors`, `Mathlib.Tactic.FieldSimp.zero_zpow'`, `VectorFourier.fourierIntegral_fderiv`, `UniqueFactorizationMonoid.radical_mul`, `Multiset.prod_pos`, `Localization.mk_zero`, `gcd_neg`, `HasFDerivAt.fun_mul'`, `threeGPFree_smul_set₀`, `UniqueFactorizationMonoid.toIsCancelMulZero`, `Ordinal.le_div`, `SimpleGraph.natCast_hadamard_adjMatrix`, `OreLocalization.nontrivial_of_nonZeroDivisors`, `gcd_zero_left'`, `div_mul_div_cancel₀`, `UniqueFactorizationMonoid.zero_notMem_normalizedFactors`, `lt_mul_self`, `Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃`, `SignType.coe_mul`, `NONote.repr_mul`, `GroupWithZero.toNoZeroSMulDivisors`, `right_eq_mul₀`, `Set.indicator_prod_one`, `Units.inv_mul'`, `HasFDerivAt.mul'`, `GroupWithZero.noZeroDivisors`, `SemiconjBy.inv_symm_left_iff₀`, `Quaternion.fst_re_dualNumberEquiv_symm`, `hasFDerivAt_list_prod_attach'`, `Quaternion.imI_snd_dualNumberEquiv`, `zero_pow`, `LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero`, `IsNilpotent.of_pow`, `ArithmeticFunction.IsMultiplicative.map_mul_of_coprime`, `Ring.inverse_zero`, `Associates.out_top`, `IsNilpotent.zero`, `Function.support_pow'`, `gcd_dvd_gcd_mul_left`, `eq_mul_of_inv_mul_eq₀`, `Ring.eq_mul_inverse_iff_mul_eq`, `Finset.prod_nonneg`, `div_mul_eq_mul_div₀`, `Set.image_mul_left_Ici`, `one_le_mul_of_one_le_of_one_le`, `Set.preimage_const_mul_Iic₀`, `Matrix.hadamard_one_eq_diagonal_iff`, `notMem_nonZeroDivisorsRight_iff`, `emultiplicity_mul`, `neg_of_div_neg_left`, `Finset.support_prod`, `Set.preimage_mul_const_Iio₀`, `Valuation.exists_div_eq_of_surjective`, `upperBounds_smul_of_pos`, `smul_inv₀'`, `NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal`, `SimpleGraph.adjMatrix_hadamard_one`, `HahnSeries.support_one`, `LinearMap.toMatrixRight'_comp`, `Associates.FactorSet.prod_eq_zero_iff`, `ArithmeticFunction.IsMultiplicative.eq_zero_of_squarefree_of_dvd_eq_zero`, `Associates.le_zero`, `Submonoid.LocalizationMap.sec_zero_fst`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm`, `mulPosMono_iff_mulPosStrictMono`, `Set.preimage_mul_const_Ioi₀`, `OrderMonoidWithZeroHom.mul_apply`, `Ordinal.mod_def`, `Filter.EventuallyEq.div_mul_cancel`, `Real.smul_iInf_of_nonneg`, `mul_eq_mul_prime_prod`, `ite_zero_smul`, `UniqueFactorizationMonoid.exists_reduced_factors'`, `PosSMulStrictMono.toPosSMulReflectLT`, `MeasurableEquiv.coe_mulRight₀`, `star_inv₀`, `Set.inv_op_smul_set_distrib₀`, `inv_mul_cancel_right₀`, `MonoidWithZeroHom.toZeroHom_injective`, `Ordinal.isPrincipal_mul_ord`, `WithZero.withZeroUnitsEquiv_strictMono`, `le_inv_mul_left`, `one_lt_inv_mul₀`, `LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered`, `Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow`, `Function.support_div`, `SemiconjBy.inv_right_iff₀`, `IsTopologicallyNilpotent.zero`, `inv_mul_le_iff₀'`, `isReduced_of_noZeroDivisors`, `MulPosReflectLT.toMulPosReflectLE`, `Set.indicator_eq_one_iff_mem`, `SimpleGraph.incMatrix_apply_eq_zero_iff`, `Ordinal.mul_div_le`, `FiniteMultiplicity.mul_iff`, `cfcUnits_zpow`, `WithZeroTopology.instContinuousInv₀`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top`, `Ordinal.mul_le_iff_of_isSuccLimit`, `LinearOrderedCommMonoidWithZero.toZeroLeOneClass`, `sq_eq_zero_iff`, `Filter.NeBot.div_zero_nonneg`, `Ordinal.mul_omega0_dvd`, `GrpWithZero.Iso.mk_inv`, `Mathlib.Tactic.FieldSimp.mul_zpow'`, `mul_inv_le_iff₀'`, `HasFDerivWithinAt.list_prod'`, `List.prod_nonneg`, `Quaternion.imK_snd_dualNumberEquiv`, `measurableEmbedding_mulLeft₀`, `fderivWithin_pow'`, `Finsupp.sym2_support_eq_preimage_support_mul`, `mem_nonZeroDivisorsRight_iff`, `OreLocalization.inv_def`, `Ordinal.lt_mul_iff`
`toZero` 📖	CompOp	2 math math: `zero_mul`, `mul_zero`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_zero` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `toMulOneClass` `toZero`	—	—
`zero_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `toMulOneClass` `toZero`	—	—

NoZeroDivisors

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`eq_zero_or_eq_zero_of_mul_eq_zero` 📖	—	—	—	—	—

SemigroupWithZero

Definitions

Name	Category	Theorems
`toMulZeroClass` 📖	CompOp	36 math math: `Complex.UnitDisc.coe_eq_zero`, `Complex.UnitDisc.instIsScalarTower_circle`, `dvd_zero`, `Complex.UnitDisc.instSMulCommClass_closedBall_left`, `Complex.UnitDisc.conj_neg`, `Complex.UnitDisc.coe_neg`, `Complex.UnitDisc.im_neg`, `Complex.UnitDisc.instSMulCommClass_circle_left`, `zero_dvd_iff`, `Complex.UnitDisc.conj_mul`, `isScalarTower_closedBall_ball_ball`, `Complex.UnitDisc.re_neg`, `Metric.unitBall.instIsLeftCancelMulZero`, `Complex.UnitDisc.instSMulCommClass_closedBall_right`, `Complex.UnitDisc.instIsScalarTower_closedBall`, `Complex.UnitDisc.instIsCancelMulZero`, `Complex.UnitDisc.pow_eq_zero`, `Complex.UnitDisc.mk_neg`, `Complex.UnitDisc.coe_mul`, `Complex.UnitDisc.im_zero`, `Complex.UnitDisc.instSMulCommClass_circle_right`, `Complex.UnitDisc.mk_zero`, `Complex.UnitDisc.mk_eq_zero`, `instSMulCommClass_sphere_ball_ball`, `Complex.UnitDisc.re_zero`, `Metric.unitBall.instIsRightCancelMulZero`, `Complex.UnitDisc.coe_zero`, `Complex.UnitDisc.tendsto_pow_atTop_nhds_zero`, `isScalarTower_sphere_ball_ball`, `eq_zero_of_zero_dvd`, `Complex.UnitDisc.star_neg`, `ArithmeticFunction.pmul_assoc`, `Complex.UnitDisc.star_eq_zero`, `Complex.UnitDisc.star_zero`, `Complex.UnitDisc.instPNatPowAssoc`, `Metric.unitBall.instIsCancelMulZero`
`toSemigroup` 📖	CompOp	539 math math: `IsAlgebraic.exists_nonzero_dvd`, `EuclideanDomain.gcd_eq_left`, `UniqueFactorizationMonoid.dvd_radical_iff`, `MvPolynomial.dvd_monomial_one_iff_exists`, `dvd_add_self_left`, `IsDedekindDomain.differentIdeal_dvd_map_differentIdeal`, `IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two'`, `AlgebraicGeometry.Proj.awayMap_awayToSection_assoc`, `EuclideanDomain.lcm_dvd`, `Ideal.dvd_iff_le`, `IsDedekindDomain.HeightOneSpectrum.equivPrimesOver_apply`, `dvd_nsmul_of_dvd`, `Ideal.span_pair_eq_span_right_iff_dvd`, `lcm_dvd_lcm_mul_right`, `normalize_dvd_iff`, `IsLocalization.Away.algebraMap_isUnit_iff`, `Polynomial.pow_rootMultiplicity_dvd`, `dvd_sub_pow_of_dvd_sub`, `dvd_zero`, `Ordinal.dvd_add_iff`, `Prime.isPrimal`, `IsAdjoinRoot.mem_ker_map`, `gcd_dvd_gcd_mul_right`, `RatFunc.num_div_dvd`, `span_singleton_dvd_span_singleton_iff_dvd`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff`, `Polynomial.leadingCoeff_dvd_leadingCoeff`, `IsPrimitiveRoot.minpoly_dvd_pow_mod`, `abs_dvd`, `Polynomial.cyclotomic_dvd_geom_sum_of_dvd`, `Ordinal.antisymm`, `idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors`, `Polynomial.dvd_iff_content_dvd_content_and_primPart_dvd_primPart`, `Subfield.relrank_dvd_of_le_left`, `RatFunc.denom_mul_dvd`, `Finset.gcd_dvd`, `MvPolynomial.exists_dvd_map_of_isAlgebraic`, `Prime.coprime_iff_not_dvd`, `ValuationRing.TFAE`, `IsCoprime.mul_dvd`, `Polynomial.dvd_iterate_derivative_pow`, `HomogeneousLocalization.range_awayMapAux_subset`, `Ideal.norm_dvd_iff`, `IsRadical.of_dvd`, `Prime.dvd_or_dvd`, `UniqueFactorizationMonoid.isRadical_radical`, `abs_dvd_abs`, `Polynomial.not_dvd_of_degree_lt`, `dvd_sub_self_left`, `Polynomial.map_dvd`, `Prime.exists_mem_multiset_map_dvd`, `Ideal.liesOver_iff_dvd_map`, `NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le`, `Polynomial.exists_monic_irreducible_factor`, `dvd_sub_left`, `Algebra.dvd_algebraMap_intNorm_self`, `Polynomial.scaleRoots_dvd'`, `dvd_geom_sum₂_iff_of_dvd_sub`, `idealFactorsFunOfQuotHom_comp`, `pow_sub_one_dvd_differentIdeal`, `EuclideanDomain.divRadical_dvd_self`, `Polynomial.aeval_pow_two_pow_dvd_aeval_iterate_newtonMap`, `gcd_dvd_gcd_mul_left_right`, `Finset.dvd_gcd`, `zero_mul`, `Prime.exists_mem_finset_dvd`, `EuclideanDomain.dvd_lcm_right`, `PadicInt.norm_lt_one_iff_dvd`, `Polynomial.pow_rootMultiplicity_not_dvd`, `QuadraticAlgebra.algebraMap_dvd_iff`, `Dvd.dvd.lcm_left`, `Prime.dvd_mul`, `IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two`, `emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactors`, `Matrix.minpoly_dvd_charpoly`, `Polynomial.dvd_comp_X_add_C_iff`, `Polynomial.dvd_comp_C_mul_X_add_C_iff`, `IsDiscreteValuationRing.dvd_of_toWithBotNat_le_toWithBotNat`, `UniqueFactorizationMonoid.dvd_of_mem_normalizedFactors`, `dvd_or_isCoprime`, `Polynomial.Gal.restrictDvd_def`, `generator_maximal_submoduleImage_dvd`, `Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvd`, `Polynomial.evalEval_dvd`, `dvd_lcm_right`, `MvPowerSeries.X_pow_dvd_iff`, `MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero`, `Submodule.IsPrincipal.contentIdeal_le_span_iff_dvd`, `lcm_dvd`, `Polynomial.Monic.not_dvd_of_natDegree_lt`, `Submodule.IsPrincipal.contentIdeal_generator_dvd_coeff`, `Prime.exists_mem_multiset_dvd`, `Prime.left_dvd_or_dvd_right_of_dvd_mul`, `Polynomial.eval₂_dvd`, `mul_dvd_mul_iff_right`, `ONote.split_dvd`, `Polynomial.factor_dvd_of_natDegree_ne_zero`, `Associates.out_dvd_iff`, `dvd_add_self_right`, `AdjoinRoot.mk_eq_mk`, `Commute.pow_dvd_pow_of_add_pow_eq_zero`, `Multiset.lcm_mono`, `Prime.not_dvd_finset_prod`, `dvd_add_right`, `min_pow_dvd_add`, `Multiset.prod_X_sub_C_dvd_iff_le_roots`, `divRadical_dvd_derivative`, `zero_dvd_iff`, `ONote.NF.of_dvd_omega0`, `Ordinal.dvd_of_mod_eq_zero`, `Commute.pow_dvd_pow_of_sub_pow_eq_zero`, `Polynomial.X_pow_sub_one_dvd_prod_cyclotomic`, `Polynomial.dvd_C_mul`, `Polynomial.Monic.irreducible_iff_lt_natDegree_lt`, `Int.cast_dvd_cast`, `IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_of_dvd_sub_one`, `dvd_pow_pow_sub_self_of_dvd`, `Finset.lcm_dvd_prod`, `MvPolynomial.X_dvd_X`, `normalize_eq_normalize_iff`, `squarefree_iff_irreducible_sq_not_dvd_of_exists_irreducible`, `DualNumber.fst_eq_zero_iff_eps_dvd`, `nonZeroDivisors_dvd_iff_dvd_coe`, `HomogeneousLocalization.val_awayMap`, `Polynomial.prod_multiset_X_sub_C_dvd`, `AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap`, `dvd_cancel_right_mem_nonZeroDivisors`, `lcm_eq_left_iff`, `Ideal.span_singleton_le_span_singleton`, `IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd`, `minpoly.IsIntegrallyClosed.isIntegral_iff_leadingCoeff_dvd`, `Ordinal.opow_dvd_opow`, `squarefree_iff_irreducible_sq_not_dvd_of_ne_zero`, `dvd_and_not_dvd_iff`, `Prime.not_dvd_mul`, `IsUnit.scaleRoots_dvd_iff`, `Valuation.Integers.dvd_of_le`, `MvPolynomial.X_dvd_monomial`, `isRadical_iff_squarefree_or_zero`, `Nat.cast_dvd_cast`, `dvd_mul_sub_mul_mul_gcd_of_dvd`, `Prime.not_dvd_one`, `minpoly.dvd_iff`, `DualNumber.isNilpotent_iff_eps_dvd`, `dvd_of_lcm_left_dvd`, `Cardinal.nat_coe_dvd_iff`, `Polynomial.resultant_dvd_leadingCoeff_pow`, `Polynomial.modByMonic_eq_zero_iff_dvd`, `Ideal.Quotient.eq_zero_iff_dvd`, `Polynomial.scaleRoots_dvd`, `Polynomial.pow_sub_one_dvd_derivative_of_pow_dvd`, `dvd_sub_right`, `dvd_lcm_of_dvd_left`, `prime_pow_succ_dvd_mul`, `Polynomial.factor_dvd_of_degree_ne_zero`, `EuclideanDomain.dvd_mod_iff`, `IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd`, `RatFunc.num_dvd`, `Polynomial.dvd_term_of_isRoot_of_dvd_terms`, `AdjoinRoot.mk_eq_zero`, `EuclideanDomain.gcd_dvd`, `dvd_mul_sub_mul`, `Polynomial.exists_dvd_map_of_isAlgebraic`, `Commute.pow_dvd_add_pow_of_pow_eq_zero_left`, `LinearMap.minpoly_dvd_charpoly`, `Polynomial.Monic.not_dvd_of_degree_lt`, `WittVector.pow_dvd_ghostComponent_of_dvd_coeff`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_right`, `IsDedekindDomain.map_differentIdeal_dvd_differentIdeal`, `Associates.dvd_of_mem_factors'`, `Polynomial.eval_dvd`, `dvd_mul_gcd_of_dvd_mul`, `isRadical_iff_squarefree_of_ne_zero`, `MvPolynomial.dvd_monomial_iff_exists`, `Valuation.Integers.le_iff_dvd`, `self_dvd_abs`, `MvPolynomial.X_dvd_mul_iff`, `Commute.add_pow_dvd_pow_of_pow_eq_zero_left`, `IsCoprime.dvd_of_dvd_mul_right`, `isPrimal_zero`, `AddMonoidAlgebra.of'_dvd_iff_modOf_eq_zero`, `Irreducible.isUnit_gcd_iff`, `QuadraticAlgebra.coe_dvd_iff_dvd`, `Submodule.IsPrincipal.generator_submoduleImage_dvd_of_mem`, `RatFunc.num_inv_dvd`, `dvd_pow_sub_one_of_dvd`, `dvd_cancel_right_coe_nonZeroDivisors`, `Lagrange.X_sub_C_dvd_nodal`, `IsLocalization.algebraMap_isUnit_iff`, `lcm_dvd_mul`, `Irreducible.exists_dvd_monic_irreducible_of_isIntegral`, `GCDMonoid.dvd_gcd`, `Polynomial.le_rootMultiplicity_iff`, `MvPolynomial.dvd_X_mul_iff`, `Ideal.dvd_bot`, `dvd_sub_comm`, `IntermediateField.relrank_dvd_of_le_left`, `mkFactorOrderIsoOfFactorDvdEquiv_apply_coe`, `IsPrimitiveRoot.minpoly_dvd_expand`, `MvPolynomial.eval₂_dvd`, `zero_isRadical_iff`, `IsBezout.gcd_dvd_left`, `minpoly.isRadical`, `IsPrimitiveRoot.minpoly_dvd_mod_p`, `Finset.gcd_mono`, `odd_sq_dvd_geom_sum₂_sub`, `dvd_mul_sub_mul_mul_left_of_dvd`, `dvd_mul_gcd_iff_dvd_mul`, `WfDvdMonoid.exists_irreducible_factor`, `Ordinal.mul_eq_right_iff_opow_omega0_dvd`, `dvd_generator_iff`, `isRadical_iff_span_singleton`, `dvd_cancel_left_mem_nonZeroDivisors`, `Prime.dvd_prod_iff`, `Ordinal.dvd_iff_mod_eq_zero`, `WittVector.dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeff`, `Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd`, `EuclideanDomain.lcm_dvd_iff`, `Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd`, `Squarefree.isRadical`, `UniqueFactorizationMonoid.radical_dvd_radical_iff_primeFactors_subset_primeFactors`, `Polynomial.X_sub_C_dvd_sub_C_eval`, `Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic`, `AdjoinRoot.mapAlgHom_comp_mapAlghom`, `Polynomial.pow_sub_dvd_iterate_derivative_pow`, `not_dvd_geom_sum₂`, `Associates.mem_factors'_iff_dvd`, `AdjoinRoot.map_comp_map`, `WfDvdMonoid.max_power_factor`, `MvPolynomial.dvd_smul_X_iff_exists`, `Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero`, `dvd_iff_dvd_of_dvd_sub`, `Submodule.IsPrincipal.generator_map_dvd_of_mem`, `gcd_mul_dvd_mul_gcd`, `den_dvd_of_is_root`, `UniqueFactorizationMonoid.dvd_of_dvd_mul_right_of_no_prime_factors`, `Polynomial.dvd_mul_leadingCoeff_inv`, `Polynomial.Chebyshev.derivative_U_eval_one_dvd`, `dvd_lcm_left`, `Commute.sub_dvd_pow_sub_pow`, `not_dvd_differentIdeal_of_isCoprime_of_isSeparable`, `Polynomial.dvd_derivative_iff`, `lcm_dvd_iff`, `Polynomial.cyclotomic.dvd_X_pow_sub_one`, `Polynomial.cyclotomic_dvd_of_mahlerMeasure_eq_one`, `lcm_dvd_lcm_mul_right_right`, `Polynomial.primPart_dvd`, `Prime.not_dvd_prod`, `Polynomial.X_pow_dvd_iff`, `Finset.dvd_gcd_iff`, `Polynomial.IsRoot.dvd_coeff_zero`, `dvd_differentIdeal_iff`, `UniqueFactorizationMonoid.radical_pow_dvd`, `Finset.lcm_dvd`, `Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvd`, `Ordinal.opow_dvd_opow_iff`, `minpoly.dvd_map_of_isScalarTower`, `Polynomial.Splits.dvd_iff_roots_le_roots`, `List.dvd_sum`, `IsCoprime.dvd_of_dvd_mul_left`, `minpoly.isIntegrallyClosed_dvd_iff`, `Polynomial.sub_dvd_eval_sub`, `Algebra.IsUnramifiedAt.not_minpoly_sq_dvd`, `IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd`, `UniqueFactorizationMonoid.dvd_radical_iff_of_irreducible`, `IsArtinianRing.instDecompositionMonoid`, `idealFactorsEquivOfQuotEquiv_symm`, `lcm_eq_right_iff`, `IntermediateField.relrank_dvd_rank_top_of_le`, `lcm_dvd_lcm_mul_left`, `Multiset.gcd_mono`, `MvPolynomial.C_dvd_iff_dvd_coeff`, `dvd_geom_sum₂_self`, `Prime.pow_dvd_of_dvd_mul_right`, `Polynomial.C_dvd_iff_dvd_coeff`, `IntermediateField.relrank_dvd_rank_bot`, `Squarefree.dvd_of_squarefree_of_mul_dvd_mul_left`, `UniqueFactorizationMonoid.radical_prod_dvd`, `Prime.dvd_or_dvd_of_dvd_lcm`, `num_dvd_of_is_root`, `Ideal.span_pair_eq_span_left_iff_dvd`, `Polynomial.dvd_content_iff_C_dvd`, `MvPolynomial.X_dvd_iff_modMonomial_eq_zero`, `IsArtinianRing.instDecompositionMonoidPolynomial`, `Commute.pow_dvd_sub_pow_of_pow_eq_zero_left`, `GroupWithZero.dvd_iff`, `Subfield.relrank_dvd_rank_top_of_le`, `divRadical_dvd_wronskian_right`, `dvd_sub`, `IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one`, `Polynomial.IsPrimitive.Int.dvd_iff_map_cast_dvd_map_cast`, `mul_dvd_mul_iff_left`, `IsBezout.dvd_gcd`, `Polynomial.C_mul_dvd`, `Polynomial.mem_iff_annIdealGenerator_dvd`, `EuclideanDomain.gcd_dvd_right`, `WfDvdMonoid.max_power_factor'`, `Associates.mem_factors_iff_dvd`, `dvd_differentIdeal_of_not_isSeparable`, `IsPrimitiveRoot.toInteger_sub_one_dvd_prime`, `Polynomial.dvd_C_mul_X_sub_one_pow_add_one`, `RatFunc.denom_div_dvd`, `Prime.isRadical`, `Irreducible.dvd_iff_not_isCoprime`, `Finset.dvd_sum`, `LinearMap.IsReflective.dvd_two_mul`, `Polynomial.IsPrimitive.dvd_primPart_iff_dvd`, `Associates.count_factors_eq_find_of_dvd_pow`, `Prime.dvd_pow_iff_dvd`, `dvd_dvd_iff_associated`, `Even.two_dvd`, `minpoly.dvd_map_of_isScalarTower'`, `Polynomial.scaleRoots_dvd_iff`, `MvPolynomial.dvd_monomial_mul_iff_exists`, `Polynomial.factor_dvd_of_not_isUnit`, `Num.dvd_iff_mod_eq_zero`, `Squarefree.dvd_of_squarefree_of_mul_dvd_mul_right`, `Dvd.dvd.linear_comb`, `RatFunc.denom_inv_dvd`, `IsPrimitiveRoot.toInteger_sub_one_dvd_prime'`, `Dvd.dvd.natCast`, `MvPolynomial.dvd_X_iff_exists`, `Submodule.IsPrincipal.dvd_generator_span_iff`, `Dvd.dvd.lcm_right`, `Ordinal.isSuccPrelimit_iff_omega0_dvd`, `HomogeneousLocalization.val_awayMap_eq_aux`, `Ideal.finite_factors`, `not_dvd_differentIdeal_of_isCoprime`, `Multiset.dvd_gcd`, `dvd_of_lcm_right_dvd`, `EuclideanDomain.dvd_gcd`, `EuclideanDomain.dvd_div_of_mul_dvd`, `AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap_assoc`, `Num.dvd_to_nat`, `RatFunc.num_mul_dvd`, `Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_map`, `gcd_dvd_gcd_mul_right_right`, `not_dvd_differentIdeal_iff`, `Polynomial.Monic.C_dvd_iff_isUnit`, `mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coe`, `Polynomial.Monic.dvd_of_fraction_map_dvd_fraction_map`, `MvPowerSeries.X_dvd_iff`, `Polynomial.X_dvd_iff`, `HomogeneousLocalization.awayMapAux_mk`, `ONote.NF.of_dvd_omega0_opow`, `UniqueFactorizationMonoid.radical_dvd_self`, `Squarefree.pow_dvd_of_squarefree_of_pow_succ_dvd_mul_left`, `RatFunc.num_div_dvd'`, `idealFactorsEquivOfQuotEquiv_is_dvd_iso`, `dvd_mul_sub_mul_mul_right_of_dvd`, `dvd_coeff_zero_of_aeval_eq_prime_smul_of_minpoly_isEisensteinAt`, `Polynomial.content_dvd_coeff`, `Polynomial.dvd_term_of_dvd_eval_of_dvd_terms`, `dvd_add_left`, `UniqueFactorizationMonoid.dvd_of_dvd_mul_left_of_no_prime_factors`, `IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_two`, `Dvd.dvd.sub`, `minpoly.isIntegrallyClosed_dvd`, `Polynomial.mem_ker_modByMonic`, `irreducible_sq_not_dvd_iff_eq_zero_and_no_irreducibles_or_squarefree`, `finiteMultiplicity_mul_aux`, `dvd_zsmul_of_dvd`, `IsPrimal.mul`, `Ordinal.mul_le_right_iff_opow_omega0_dvd`, `Polynomial.mem_normalizedFactors_iff`, `AlgebraicGeometry.Proj.awayMap_awayToSection`, `dvd_lcm_of_dvd_right`, `Associates.exists_prime_dvd_of_not_inf_one`, `one_sub_dvd_one_sub_pow`, `dvd_sub_self_right`, `exists_squarefree_dvd_pow_of_ne_zero`, `PadicInt.pow_p_dvd_int_iff`, `PowerBasis.exists_gen_dvd_sub`, `PowerSeries.X_pow_order_dvd`, `ZNum.dvd_iff_mod_eq_zero`, `Cardinal.dvd_of_le_of_aleph0_le`, `Commute.add_pow_dvd_pow_of_pow_eq_zero_right`, `EuclideanDomain.dvd_lcm_left`, `gcd_pow_left_dvd_pow_gcd`, `dvd_normalize_iff`, `idealFactorsFunOfQuotHom_id`, `associated_gcd_right_iff`, `MvPolynomial.dvd_C_iff_exists`, `pow_one_sub_dvd_pow_mul_sub_one`, `Polynomial.rootMultiplicity_le_iff`, `dvd_abs`, `Polynomial.pow_sub_dvd_iterate_derivative_of_pow_dvd`, `dvd_prime_pow`, `Prime.not_dvd_lcm`, `Polynomial.Splits.dvd_of_roots_le_roots`, `Polynomial.X_dvd_sub_C`, `Polynomial.dvd_cancelLeads_of_dvd_of_dvd`, `even_iff_two_dvd`, `IsRadical.dvd_radical`, `associated_gcd_left_iff`, `lcm_dvd_lcm`, `Irreducible.isCoprime_or_dvd`, `Associates.count_ne_zero_iff_dvd`, `pow_dvd_of_mul_eq_pow`, `IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_sub_one_or_add_one_of_lambda_not_dvd`, `Polynomial.dvd_comp_neg_X_iff`, `mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactors`, `NonUnitalSubsemiring.centralizer_toSubsemigroup`, `EuclideanDomain.div_dvd_of_dvd`, `Finset.lcm_mono_fun`, `QuadraticAlgebra.algebraMap_dvd_iff_dvd`, `Submodule.IsPrincipal.contentIdeal_generator_dvd`, `exists_integer_of_is_root_of_monic`, `IsAdjoinRoot.map_eq_zero_iff`, `UniqueFactorizationMonoid.radical_dvd_iff_primeFactors_subset`, `UniqueFactorizationMonoid.mem_normalizedFactors_iff'`, `normEDS_dvd_normEDS_two_mul`, `UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactors`, `Associates.eq_pow_find_of_dvd_irreducible_pow`, `minpoly.dvd`, `Odd.add_dvd_pow_add_pow`, `abs_dvd_self`, `IsCyclotomicExtension.Rat.Three.lambda_pow_four_dvd_cube_add_one_of_dvd_add_one`, `MvPolynomial.mem_ideal_span_monomial_image_iff_dvd`, `Polynomial.exists_irreducible_of_natDegree_ne_zero`, `GCDMonoid.gcd_dvd_left`, `MvPolynomial.monomial_one_dvd_monomial_one`, `Polynomial.map_dvd_map`, `Polynomial.dvd_comp_X_sub_C_iff`, `smul_pi₀`, `Polynomial.dvd_of_infinite_eval_dvd_eval`, `UniqueFactorizationMonoid.radical_mul_dvd`, `idealFactorsFunOfQuotHom_coe_coe`, `squarefree_iff_no_irreducibles`, `EuclideanDomain.gcd_dvd_left`, `sq_dvd_add_pow_sub_sub`, `not_dvd_differentIdeal_of_intTrace_not_mem`, `instDecompositionMonoidOfNonemptyGCDMonoid`, `dvd_gcd_mul_of_dvd_mul`, `Polynomial.exists_irreducible_of_natDegree_pos`, `divRadical_dvd_wronskian_left`, `Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map`, `Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero`, `Prime.dvd_of_dvd_pow`, `Polynomial.dvd_iff_isRoot`, `prime_dvd_prime_iff_eq`, `Multiset.gcd_dvd`, `Commute.pow_dvd_sub_pow_of_pow_eq_zero_right`, `dvd_cancel_left_coe_nonZeroDivisors`, `Multiset.dvd_lcm`, `ZNum.dvd_to_int`, `PowerSeries.X_pow_dvd_iff`, `RatFunc.denom_add_dvd`, `Associates.dvd_out_iff`, `UniqueFactorizationMonoid.dvd_of_mem_factors`, `IsDiscreteValuationRing.addVal_le_iff_dvd`, `Finset.prod_dvd_of_coprime`, `Nat.Prime.dvd_add_pow_sub_pow_of_dvd`, `Multiset.dvd_sum`, `gcd_eq_left_iff`, `Ideal.mem_span_singleton`, `pow_dvd_pow_iff`, `PowerSeries.X_dvd_iff`, `lcm_dvd_lcm_mul_left_right`, `Fintype.prod_dvd_of_coprime`, `ValuationRing.iff_dvd_total`, `IsIntegrallyClosed.pow_dvd_pow_iff`, `Associates.dvd_of_mem_factors`, `GCDMonoid.gcd_dvd_right`, `IsDiscreteValuationRing.toWithBotNat_le_toWithBotNat_iff`, `MvPolynomial.C_dvd_iff_zmod`, `Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero`, `Ideal.exists_notMem_dvd_algebraMap_of_primesOver_eq_singleton`, `Polynomial.X_pow_sub_one_mul_cyclotomic_dvd_X_pow_sub_one_of_dvd`, `Multiset.lcm_dvd`, `exists_reduced_fraction'`, `Finset.lcm_dvd_iff`, `Submodule.IsPrincipal.mem_iff_generator_dvd`, `Polynomial.not_dvd_of_natDegree_lt`, `Finset.lcm_mono`, `Ideal.dvd_span_singleton`, `IsPrimitiveRoot.minpoly_dvd_cyclotomic`, `sub_dvd_pow_sub_pow`, `gcd_pow_right_dvd_pow_gcd`, `Polynomial.exists_primitive_lcm_of_isPrimitive`, `UniqueFactorizationMonoid.instDecompositionMonoid`, `RatFunc.denom_dvd`, `Module.Basis.dvd_coord_smul`, `UniqueFactorizationMonoid.radical_dvd_radical`, `dvd_gcd_mul_iff_dvd_mul`, `Multiset.prod_primes_dvd`, `sub_one_dvd_pow_sub_one`, `IsBezout.gcd_dvd_right`, `Irreducible.gcd_eq_one_iff`, `Finset.dvd_lcm`, `Polynomial.map_dvd_map'`, `Ideal.finprod_not_dvd`, `C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum`, `Set.smul_set_pi₀'`, `pow_sub_one_dvd_differentIdeal_aux`, `Polynomial.irreducible_iff_lt_natDegree_lt`, `EuclideanDomain.dvd_or_coprime`, `Commute.pow_dvd_add_pow_of_pow_eq_zero_right`, `lcm_eq_one_iff`, `succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul`, `UniqueFactorizationMonoid.radical_dvd_radical_iff_normalizedFactors_subset_normalizedFactors`, `Polynomial.dvd_pow_natDegree_of_aeval_eq_zero`, `Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul`, `MvPolynomial.C_dvd_iff_map_hom_eq_zero`, `Prime.dvd_finset_prod_iff`, `gcd_dvd_gcd_mul_left`, `RingOfIntegers.dvd_norm`, `Prime.pow_dvd_of_dvd_mul_left`, `Irreducible.coprime_iff_not_dvd`, `Finset.prod_primes_dvd`, `Dvd.dvd.scaleRoots`, `Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map`, `Polynomial.homogenize_dvd`, `gcd_dvd_iff_exists`, `Nat.dvd_ofDigits_sub_ofDigits`, `IsAlgClosed.dvd_iff_roots_le_roots`, `Valuation.Integers.dvd_iff_le`, `Polynomial.C_content_dvd`, `Prime.dvd_prime_iff_associated`, `Set.smul_set_pi₀`, `PadicInt.zmodRepr_eq_zero_iff_dvd`, `gcd_eq_right_iff`, `Ordinal.isSuccLimit_iff_omega0_dvd`, `Squarefree.dvd_pow_iff_dvd`, `QuadraticAlgebra.coe_dvd_iff`, `Finset.gcd_mono_fun`, `Polynomial.exists_irreducible_of_degree_pos`, `gcd_dvd_gcd`, `dvd_geom_sum₂_iff_of_dvd_sub'`, `FixedPoints.minpoly.of_eval₂`, `Prime.dvd_lcm`, `Polynomial.X_sub_C_pow_dvd_iff`, `mul_zero`, `IsPrimitiveRoot.minpoly_dvd_x_pow_sub_one`, `IsPrimitiveRoot.toInteger_sub_one_not_dvd_two`, `IsCyclotomicExtension.Rat.Three.lambda_dvd_mul_sub_one_mul_sub_eta_add_one`, `MvPolynomial.monomial_dvd_monomial`, `EuclideanDomain.mod_eq_zero`, `dvd_gcd_iff`
`toZero` 📖	CompOp	2 math math: `zero_mul`, `mul_zero`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mul_zero` 📖	mathematical	—	`Semigroup.toMul` `toSemigroup` `toZero`	—	—
`zero_mul` 📖	mathematical	—	`Semigroup.toMul` `toSemigroup` `toZero`	—	—

(root)

Definitions

Name	Category	Theorems
`CancelCommMonoidWithZero` 📖	CompData	—
`CancelMonoidWithZero` 📖	CompData	—
`CommGroupWithZero` 📖	CompData	—
`CommMonoidWithZero` 📖	CompData	—
`IsCancelMulZero` 📖	CompData	41 math math: `AddMonoidAlgebra.instIsCancelAddZeroOfIsCancelAddOfUniqueSums`, `IsRightCancelMulZero.to_isCancelMulZero`, `Function.Injective.isCancelMulZero`, `noZeroDivisors_tfae`, `isDomain_iff_cancelMulZero_and_nontrivial`, `IsLeftCancelMulZero.to_isCancelMulZero`, `isCancelMulZero_iff`, `NoZeroDivisors.toIsCancelMulZero`, `Int.instIsCancelMulZero`, `GCDMonoid.toIsCancelMulZero`, `isCancelMulZero_iff_isDomain_or_subsingleton`, `MulOpposite.instIsCancelMulZero`, `Nat.instIsCancelMulZero`, `MulOpposite.isCancelMulZero_iff`, `Polynomial.isCancelMulZero_iff`, `HahnSeries.instIsCancelMulZeroOfIsCancelAdd`, `PUnit.instIsCancelMulZero`, `instIsCancelMulZeroLex`, `Set.Icc.instIsCancelMulZero`, `MonoidAlgebra.instIsCancelMulZeroOfIsCancelAddOfUniqueProds`, `Ideal.isCancelMulZero`, `Polynomial.instIsCancelMulZeroOfIsCancelAdd`, `Complex.UnitDisc.instIsCancelMulZero`, `Associates.instIsCancelMulZero`, `Subsingleton.to_isCancelMulZero`, `instIsCancelMulZero`, `NoZeroDivisors.to_isCancelMulZero`, `MvPolynomial.instIsCancelMulZeroOfIsCancelAdd`, `OrderDual.instIsCancelMulZero`, `MulEquiv.isCancelMulZero_iff`, `IsDomain.toIsCancelMulZero`, `CancelMonoidWithZero.toIsCancelMulZero`, `IsCancelMulZero.of_faithfulSMul`, `MulZeroMemClass.isCancelMulZero`, `Submonoid.LocalizationMap.isCancelMulZero`, `Metric.unitClosedBall.instIsCancelMulZero`, `instIsCancelMulZero_1`, `Metric.unitBall.instIsCancelMulZero`, `isCancelMulZero_iff_noZeroDivisors`, `UniqueFactorizationMonoid.toIsCancelMulZero`, `isCancelMulZero_iff_forall_isRegular`
`IsLeftCancelMulZero` 📖	CompData	20 math math: `AddMonoidAlgebra.instIsLeftCancelAddZeroOfIsCancelAddOfUniqueSums`, `Polynomial.isLeftCancelMulZero_iff`, `IsRightCancelMulZero.to_isLeftCancelMulZero`, `Ordinal.instIsLeftCancelMulZero`, `noZeroDivisors_tfae`, `isCancelMulZero_iff`, `CancelCommMonoidWithZero.toIsLeftCancelMulZero`, `MulOpposite.isRightCancelMulZero_iff`, `IsCancelMulZero.toIsLeftCancelMulZero`, `Metric.unitBall.instIsLeftCancelMulZero`, `MulZeroMemClass.isLeftCancelMulZero`, `MonoidAlgebra.instIsLeftCancelMulZeroOfIsCancelAddOfUniqueProds`, `MulEquiv.isLeftCancelMulZero_iff`, `instIsLeftCancelMulZeroLex`, `Polynomial.instIsLeftCancelMulZeroOfIsCancelAdd`, `MulOpposite.instIsLeftCancelMulZeroOfIsRightCancelMulZero`, `Function.Injective.isLeftCancelMulZero`, `isLeftCancelMulZero_iff`, `OrderDual.instIsLeftCancelMulZero`, `MulOpposite.isLeftCancelMulZero_iff`
`IsRightCancelMulZero` 📖	CompData	18 math math: `OrderDual.instIsRightCancelMulZero`, `noZeroDivisors_tfae`, `isCancelMulZero_iff`, `MulEquiv.isRightCancelMulZero_iff`, `MulOpposite.instIsRightCancelMulZeroOfIsLeftCancelMulZero`, `AddMonoidAlgebra.instIsRightCancelAddZeroOfIsCancelAddOfUniqueSums`, `Polynomial.instIsRightCancelMulZeroOfIsCancelAdd`, `Polynomial.isRightCancelMulZero_iff`, `MulOpposite.isRightCancelMulZero_iff`, `IsCancelMulZero.toIsRightCancelMulZero`, `isRightCancelMulZero_iff`, `instIsRightCancelMulZeroLex`, `Metric.unitBall.instIsRightCancelMulZero`, `MulZeroMemClass.isRightCancelMulZero`, `MonoidAlgebra.instIsRightCancelMulZeroOfIsCancelAddOfUniqueProds`, `Function.Injective.isRightCancelMulZero`, `IsLeftCancelMulZero.to_isRightCancelMulZero`, `MulOpposite.isLeftCancelMulZero_iff`
`MulDivCancelClass` 📖	CompData	4 math math: `Int.instMulDivCancelClass`, `GroupWithZero.toMulDivCancelClass`, `Nat.instMulDivCancelClass`, `EuclideanDomain.toMulDivCancelClass`
`MulZeroClass` 📖	CompData	—
`MulZeroOneClass` 📖	CompData	—
`SemigroupWithZero` 📖	CompData	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`eq_zero_or_one_of_sq_eq_self` 📖	mathematical	`Monoid.toPow` `MonoidWithZero.toMonoid`	`MulZeroClass.toZero` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `MulOne.toOne` `MulOneClass.toMulOne` `MulZeroOneClass.toMulOneClass`	—	`mul_left_injective₀` `one_mul` `sq`
`inv_zero` 📖	mathematical	—	`DivInvMonoid.toInv` `GroupWithZero.toDivInvMonoid` `MulZeroClass.toZero` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `GroupWithZero.toMonoidWithZero`	—	`GroupWithZero.inv_zero`
`isCancelMulZero_iff` 📖	mathematical	—	`IsCancelMulZero` `IsLeftCancelMulZero` `IsRightCancelMulZero`	—	—
`isCancelMulZero_iff_forall_isRegular` 📖	mathematical	—	`IsCancelMulZero` `IsRegular`	—	`isRegular_iff`
`isLeftCancelMulZero_iff` 📖	mathematical	—	`IsLeftCancelMulZero` `IsLeftRegular`	—	—
`isRightCancelMulZero_iff` 📖	mathematical	—	`IsRightCancelMulZero` `IsRightRegular`	—	—
`mul_div_cancel_left₀` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `CommMonoidWithZero.toMonoidWithZero`	—	`mul_comm` `mul_div_cancel_right₀`
`mul_div_cancel_right₀` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass`	—	`MulDivCancelClass.mul_div_cancel`
`mul_eq_mul_left_iff` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	`MulZeroClass.zero_mul`
`mul_eq_mul_right_iff` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	`MulZeroClass.mul_zero`
`mul_eq_zero` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	`NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zero` `mul_eq_zero_of_left` `mul_eq_zero_of_right`
`mul_eq_zero_comm` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	`mul_eq_zero`
`mul_eq_zero_iff_left` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	—
`mul_eq_zero_iff_right` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	—
`mul_eq_zero_of_left` 📖	mathematical	`MulZeroClass.toZero`	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	`MulZeroClass.zero_mul`
`mul_eq_zero_of_right` 📖	mathematical	`MulZeroClass.toZero`	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	`MulZeroClass.mul_zero`
`mul_inv_cancel_left₀` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `GroupWithZero.toMonoidWithZero` `DivInvMonoid.toInv` `GroupWithZero.toDivInvMonoid`	—	`mul_assoc` `mul_inv_cancel₀` `one_mul`
`mul_inv_cancel_right₀` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `GroupWithZero.toMonoidWithZero` `DivInvMonoid.toInv` `GroupWithZero.toDivInvMonoid`	—	`mul_assoc` `mul_inv_cancel₀` `mul_one`
`mul_inv_cancel₀` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `GroupWithZero.toMonoidWithZero` `DivInvMonoid.toInv` `GroupWithZero.toDivInvMonoid` `MulOne.toOne` `MulOneClass.toMulOne` `MulZeroOneClass.toMulOneClass`	—	`GroupWithZero.mul_inv_cancel`
`mul_left_cancel₀` 📖	—	—	—	—	`IsLeftCancelMulZero.mul_left_cancel_of_ne_zero`
`mul_left_inj'` 📖	—	—	—	—	`mul_left_injective₀`
`mul_left_injective₀` 📖	—	—	—	—	`mul_right_cancel₀`
`mul_ne_zero_comm` 📖	—	—	—	—	`Iff.not` `mul_eq_zero_comm`
`mul_ne_zero_iff` 📖	—	—	—	—	`Iff.not` `mul_eq_zero`
`mul_ne_zero_iff_left` 📖	—	—	—	—	—
`mul_ne_zero_iff_right` 📖	—	—	—	—	—
`mul_right_cancel₀` 📖	—	—	—	—	`IsRightCancelMulZero.mul_right_cancel_of_ne_zero`
`mul_right_inj'` 📖	—	—	—	—	`mul_right_injective₀`
`mul_right_injective₀` 📖	—	—	—	—	`mul_left_cancel₀`
`mul_self_eq_zero` 📖	mathematical	—	`MulZeroClass.toMul` `MulZeroClass.toZero`	—	—
`mul_self_ne_zero` 📖	—	—	—	—	`Iff.not` `mul_self_eq_zero`
`noZeroDivisors_iff` 📖	mathematical	—	`NoZeroDivisors`	—	—
`noZeroDivisors_iff_eq_zero_of_mul` 📖	mathematical	—	`NoZeroDivisors` `MulZeroClass.toMul` `MulZeroClass.toZero`	—	—
`noZeroDivisors_iff_left_eq_zero_of_mul` 📖	mathematical	—	`NoZeroDivisors` `MulZeroClass.toMul` `MulZeroClass.toZero`	—	—
`noZeroDivisors_iff_right_eq_zero_of_mul` 📖	mathematical	—	`NoZeroDivisors` `MulZeroClass.toMul` `MulZeroClass.toZero`	—	—
`pow_mul_apply_eq_pow_mul` 📖	mathematical	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	`MulZeroClass.toMul` `MulZeroOneClass.toMulZeroClass` `MonoidWithZero.toMulZeroOneClass` `Monoid.toPow` `MonoidWithZero.toMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`pow_zero` `one_mul` `pow_succ'` `mul_assoc`
`zero_eq_mul` 📖	mathematical	—	`MulZeroClass.toZero` `MulZeroClass.toMul`	—	`mul_eq_zero`
`zero_eq_mul_self` 📖	mathematical	—	`MulZeroClass.toZero` `MulZeroClass.toMul`	—	—
`zero_ne_mul_self` 📖	—	—	—	—	`Iff.not` `zero_eq_mul_self`

---

← Back to Index