Basic

📁 Source: Mathlib/Algebra/Group/Basic.lean

Statistics

Metric	Count
Definitions `toGrindIntModule`, `toGrindNatModule`, `toDivInvOneMonoid`, `toSubNegZeroMonoid`	4
Theorems `to_isAssociative`, `to_isLawfulIdentity`, `toGrindAddRightCancel`, `to_isAssociative`, `to_isLawfulIdentity`, `add_add_add_comm`, `add_add_add_comm'`, `add_add_neg_add_cancel`, `add_add_neg_cancel'_right`, `add_add_sub_cancel`, `add_comm_sub`, `add_eq_left`, `add_eq_of_eq_add_neg`, `add_eq_of_eq_neg_add`, `add_eq_of_eq_sub`, `add_eq_of_eq_sub'`, `add_eq_right`, `add_eq_zero_iff_eq_neg`, `add_eq_zero_iff_eq_neg'`, `add_eq_zero_iff_neg_eq`, `add_eq_zero_iff_neg_eq'`, `add_left_comm`, `add_left_iterate`, `add_left_iterate_apply`, `add_left_iterate_apply_zero`, `add_left_surjective`, `add_ne_left`, `add_ne_right`, `add_neg_add_add_cancel`, `add_neg_eq_add_neg_iff_add_eq_add`, `add_neg_eq_iff_eq_add`, `add_neg_eq_of_eq_add`, `add_neg_eq_zero`, `add_one_zsmul`, `add_right_comm`, `add_right_iterate`, `add_right_iterate_apply`, `add_right_iterate_apply_zero`, `add_right_surjective`, `add_rotate`, `add_rotate'`, `add_self_zsmul`, `add_sub`, `add_sub_add_comm`, `add_sub_add_left_eq_sub`, `add_sub_add_right_eq_sub`, `add_sub_assoc'`, `add_sub_cancel`, `add_sub_cancel_left`, `add_sub_left_comm`, `add_sub_one_nsmul`, `add_sub_right_comm`, `add_sub_sub_cancel`, `add_zero_eq_id`, `add_zero_sub`, `add_zsmul`, `add_zsmul_add`, `add_zsmul_self`, `additive_of_isTotal`, `additive_of_symmetric_of_isTotal`, `additive_of_symmetric_of_total`, `additive_of_total`, `boole_nsmul`, `comp_add_left`, `comp_add_right`, `comp_mul_left`, `comp_mul_right`, `conj_eq_one_iff`, `conj_eq_zero_iff`, `const_div_involutive`, `const_sub_involutive`, `dite_pow`, `dite_smul`, `dite_vadd`, `div_div`, `div_div_cancel`, `div_div_cancel_left`, `div_div_div_cancel_left`, `div_div_div_cancel_right`, `div_div_div_comm`, `div_div_div_eq`, `div_div_eq_mul_div`, `div_div_self'`, `div_eq_div_iff_comm`, `div_eq_div_iff_div_eq_div`, `div_eq_div_iff_mul_eq_mul`, `div_eq_div_mul_div`, `div_eq_iff_comm`, `div_eq_iff_eq_mul`, `div_eq_iff_eq_mul'`, `div_eq_inv_mul`, `div_eq_inv_self`, `div_eq_mul_one_div`, `div_eq_of_eq_mul'`, `div_eq_of_eq_mul''`, `div_eq_one`, `div_eq_one_of_eq`, `div_eq_self`, `div_inv_eq_mul`, `div_left_inj`, `div_left_injective`, `div_mul`, `div_mul_cancel_left`, `div_mul_cancel_right`, `div_mul_comm`, `div_mul_div_cancel`, `div_mul_div_cancel'`, `div_mul_div_comm`, `div_mul_eq_div_div`, `div_mul_eq_div_div_swap`, `div_mul_eq_div_mul_one_div`, `div_mul_eq_mul_div`, `div_mul_mul_cancel`, `div_ne_one`, `div_ne_one_of_ne`, `div_one`, `div_pow`, `div_right_comm`, `div_right_inj`, `div_right_injective`, `div_zpow`, `eq_add_neg_iff_add_eq`, `eq_add_neg_of_add_eq`, `eq_add_of_add_neg_eq`, `eq_add_of_neg_add_eq`, `eq_add_of_sub_eq`, `eq_add_of_sub_eq'`, `eq_div_iff_mul_eq'`, `eq_div_iff_mul_eq''`, `eq_div_of_mul_eq'`, `eq_div_of_mul_eq''`, `eq_iff_eq_of_add_eq_add`, `eq_iff_eq_of_div_eq_div`, `eq_iff_eq_of_mul_eq_mul`, `eq_iff_eq_of_sub_eq_sub`, `eq_inv_iff_mul_eq_one`, `eq_inv_mul_iff_mul_eq`, `eq_inv_mul_of_mul_eq`, `eq_inv_of_mul_eq_one_right`, `eq_mul_inv_iff_mul_eq`, `eq_mul_inv_of_mul_eq`, `eq_mul_of_div_eq`, `eq_mul_of_div_eq'`, `eq_mul_of_inv_mul_eq`, `eq_mul_of_mul_inv_eq`, `eq_neg_add_iff_add_eq`, `eq_neg_add_of_add_eq`, `eq_neg_iff_add_eq_zero`, `eq_neg_of_add_eq_zero_right`, `eq_of_add_neg_eq_zero`, `eq_of_div_eq_one`, `eq_of_inv_mul_eq_one`, `eq_of_mul_inv_eq_one`, `eq_of_neg_add_eq_zero`, `eq_of_one_div_eq_one_div`, `eq_of_sub_eq_zero`, `eq_of_zero_sub_eq_zero_sub`, `eq_one_div_of_mul_eq_one_left`, `eq_one_div_of_mul_eq_one_right`, `eq_one_iff_eq_one_of_mul_eq_one`, `eq_sub_iff_add_eq`, `eq_sub_iff_add_eq'`, `eq_sub_of_add_eq`, `eq_sub_of_add_eq'`, `eq_zero_iff_eq_zero_of_add_eq_zero`, `eq_zero_sub_of_add_eq_zero_left`, `eq_zero_sub_of_add_eq_zero_right`, `hom_coe_nsmul`, `hom_coe_pow`, `inv_comp_inv`, `inv_div`, `inv_div'`, `inv_div_comm`, `inv_div_inv`, `inv_div_left`, `inv_eq_iff_eq_inv`, `inv_eq_iff_mul_eq_one`, `inv_eq_one`, `inv_inj`, `inv_injective`, `inv_inv_div_inv`, `inv_involutive`, `inv_mul'`, `inv_mul_eq_div`, `inv_mul_eq_iff_eq_mul`, `inv_mul_eq_inv_mul_iff_mul_eq_mul`, `inv_mul_eq_of_eq_mul`, `inv_mul_eq_one`, `inv_ne_one`, `inv_pow`, `inv_pow_sub`, `inv_surjective`, `inv_unique`, `inv_zpow`, `inv_zpow'`, `ite_add_zero`, `ite_mul_one`, `ite_one_mul`, `ite_pow`, `ite_smul`, `ite_vadd`, `ite_zero_add`, `leftInverse_add_left_sub`, `leftInverse_add_right_neg_add`, `leftInverse_div_mul_left`, `leftInverse_inv`, `leftInverse_inv_mul_mul_right`, `leftInverse_mul_left_div`, `leftInverse_mul_right_inv_mul`, `leftInverse_neg`, `leftInverse_neg_add_add_right`, `leftInverse_sub_add_left`, `left_eq_add`, `left_eq_mul`, `left_ne_add`, `left_ne_mul`, `mul_comm_div`, `mul_div`, `mul_div_assoc'`, `mul_div_cancel`, `mul_div_cancel_left`, `mul_div_div_cancel`, `mul_div_left_comm`, `mul_div_mul_comm`, `mul_div_mul_left_eq_div`, `mul_div_mul_right_eq_div`, `mul_div_right_comm`, `mul_eq_left`, `mul_eq_of_eq_div`, `mul_eq_of_eq_div'`, `mul_eq_of_eq_inv_mul`, `mul_eq_of_eq_mul_inv`, `mul_eq_one_iff_eq_inv`, `mul_eq_one_iff_eq_inv'`, `mul_eq_one_iff_inv_eq`, `mul_eq_one_iff_inv_eq'`, `mul_eq_right`, `mul_inv`, `mul_inv_eq_iff_eq_mul`, `mul_inv_eq_mul_inv_iff_mul_eq_mul`, `mul_inv_eq_of_eq_mul`, `mul_inv_eq_one`, `mul_inv_mul_mul_cancel`, `mul_left_comm`, `mul_left_iterate`, `mul_left_iterate_apply`, `mul_left_iterate_apply_one`, `mul_left_surjective`, `mul_mul_div_cancel`, `mul_mul_inv_cancel'_right`, `mul_mul_inv_mul_cancel`, `mul_mul_mul_comm`, `mul_mul_mul_comm'`, `mul_ne_left`, `mul_ne_right`, `mul_one_div`, `mul_one_eq_id`, `mul_pow`, `mul_pow_sub_one`, `mul_right_comm`, `mul_right_iterate`, `mul_right_iterate_apply`, `mul_right_iterate_apply_one`, `mul_right_surjective`, `mul_rotate`, `mul_rotate'`, `mul_self_zpow`, `mul_zpow`, `mul_zpow_mul`, `mul_zpow_neg_one`, `mul_zpow_self`, `mul_zsmul`, `mul_zsmul'`, `multiplicative_of_isTotal`, `multiplicative_of_symmetric_of_isTotal`, `multiplicative_of_symmetric_of_total`, `multiplicative_of_total`, `natAbs_nsmul_eq_zero`, `natCast_sub_natCast_zsmul`, `natCast_sub_one_zsmul`, `ne_iff_ne_of_add_eq_add`, `ne_iff_ne_of_mul_eq_mul`, `neg_add`, `neg_add'`, `neg_add_eq_iff_eq_add`, `neg_add_eq_neg_add_iff_add_eq_add`, `neg_add_eq_of_eq_add`, `neg_add_eq_sub`, `neg_add_eq_zero`, `neg_comp_neg`, `neg_eq_iff_add_eq_zero`, `neg_eq_iff_eq_neg`, `neg_eq_zero`, `neg_inj`, `neg_injective`, `neg_involutive`, `neg_ne_zero`, `neg_neg_sub_neg`, `neg_nsmul`, `neg_one_zsmul_add`, `neg_sub`, `neg_sub'`, `neg_sub_comm`, `neg_sub_left`, `neg_sub_neg`, `neg_surjective`, `neg_unique`, `neg_zsmul`, `nsmul_add`, `nsmul_add_nsmul_eq_zero`, `nsmul_add_sub_nsmul`, `nsmul_eq_mod_nsmul`, `nsmul_iterate`, `nsmul_sub`, `nsmul_zero_sub`, `one_add_zsmul`, `one_div_div`, `one_div_mul_eq_div`, `one_div_mul_one_div`, `one_div_mul_one_div_rev`, `one_div_one`, `one_div_one_div`, `one_div_pow`, `one_div_zpow`, `one_eq_inv`, `one_mul_eq_id`, `one_sub_natCast_zsmul`, `one_zpow`, `pow_boole`, `pow_dite`, `pow_eq_pow_mod`, `pow_ite`, `pow_iterate`, `pow_mul_pow_eq_one`, `pow_mul_pow_sub`, `pow_natAbs_eq_one`, `pow_sub`, `pow_sub_mul_pow`, `pow_sub_one_mul`, `rightInverse_inv`, `rightInverse_neg`, `right_eq_add`, `right_eq_mul`, `right_ne_add`, `right_ne_mul`, `smul_dite`, `smul_ite`, `sub_add`, `sub_add_add_cancel`, `sub_add_cancel_left`, `sub_add_cancel_right`, `sub_add_comm`, `sub_add_eq_add_sub`, `sub_add_eq_sub_add_zero_sub`, `sub_add_eq_sub_sub`, `sub_add_eq_sub_sub_swap`, `sub_add_sub_cancel`, `sub_add_sub_cancel'`, `sub_add_sub_comm`, `sub_eq_add_zero_sub`, `sub_eq_iff_comm`, `sub_eq_iff_eq_add`, `sub_eq_iff_eq_add'`, `sub_eq_neg_add`, `sub_eq_neg_self`, `sub_eq_of_eq_add`, `sub_eq_of_eq_add'`, `sub_eq_self`, `sub_eq_sub_add_sub`, `sub_eq_sub_iff_add_eq_add`, `sub_eq_sub_iff_comm`, `sub_eq_sub_iff_sub_eq_sub`, `sub_eq_zero`, `sub_eq_zero_of_eq`, `sub_left_inj`, `sub_left_injective`, `sub_ne_zero`, `sub_ne_zero_of_ne`, `sub_neg_eq_add`, `sub_nsmul`, `sub_nsmul_neg`, `sub_nsmul_nsmul_add`, `sub_one_nsmul_add`, `sub_one_zsmul`, `sub_right_comm`, `sub_right_inj`, `sub_right_injective`, `sub_sub`, `sub_sub_cancel`, `sub_sub_cancel_left`, `sub_sub_eq_add_sub`, `sub_sub_self`, `sub_sub_sub_cancel_left`, `sub_sub_sub_cancel_right`, `sub_sub_sub_comm`, `sub_sub_sub_eq`, `sub_zero`, `sub_zsmul`, `vadd_dite`, `vadd_ite`, `zero_add_eq_id`, `zero_eq_neg`, `zero_sub_add_eq_sub`, `zero_sub_add_zero_sub`, `zero_sub_add_zero_sub_rev`, `zero_sub_sub`, `zero_sub_zero`, `zero_sub_zero_sub`, `zpow_add`, `zpow_add_one`, `zpow_comm`, `zpow_eq_zpow_emod`, `zpow_eq_zpow_emod'`, `zpow_induction_left`, `zpow_induction_right`, `zpow_iterate`, `zpow_mul`, `zpow_mul'`, `zpow_mul_comm`, `zpow_natCast_sub_natCast`, `zpow_natCast_sub_one`, `zpow_neg`, `zpow_one_add`, `zpow_one_sub_natCast`, `zpow_sub`, `zpow_sub_one`, `zsmul_add`, `zsmul_add_comm`, `zsmul_comm`, `zsmul_induction_left`, `zsmul_induction_right`, `zsmul_iterate`, `zsmul_neg`, `zsmul_neg'`, `zsmul_sub`, `zsmul_zero`, `zsmul_zero_sub`	437
Total	441

AddCommGroup

Definitions

Name	Category	Theorems
`toGrindIntModule` 📖	CompOp	—

AddCommMonoid

Definitions

Name	Category	Theorems
`toGrindNatModule` 📖	CompOp	1 math math: `instNoNatZeroDivisorsOfIsAddTorsionFree`

AddSemigroup

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`to_isAssociative` 📖	mathematical	—	`toAdd`	—	`add_assoc`
`to_isLawfulIdentity` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddZero.toZero`	—	`zero_add` `add_zero`

DivisionMonoid

Definitions

Name	Category	Theorems
`toDivInvOneMonoid` 📖	CompOp	2413 math math: `le_inv_comm₀`, `GroupFilterBasis.one`, `GrpCat.FilteredColimits.colimit_inv_mk_eq`, `Polynomial.natDegree_mul_leadingCoeff_inv`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset`, `unitary.star_eq_inv'`, `Pi.update_eq_div_mul_mulSingle`, `nhds_basis_one_mabs_lt`, `Subgroup.mem_centralizer_iff_commutator_eq_one`, `nnnorm_inv`, `div_le_one_of_le₀`, `NormedSpace.exp_neg_of_mem_ball`, `CategoryTheory.PresheafOfGroups.OneCochain.one_ev`, `Subgroup.mulSingle_mem_pi`, `SemidirectProduct.rightHom_inl`, `GroupFilterBasis.conj`, `Homeomorph.smulOfNeZero_symm_apply`, `pow_inv_comm`, `Rat.cast_inv_of_ne_zero`, `oneLePart_eq_one`, `pow_card_eq_one`, `upperClosure_one`, `mulTSupport_mul_inv`, `div_mul_cancel_left`, `Filter.tendsto_inv_atBot_iff`, `ContMDiffAt.inv`, `ordinaryHypergeometric_sum_eq`, `GroupSeminorm.apply_one`, `hasSum_geometric_of_norm_lt_one`, `Polynomial.coe_normUnit_of_ne_zero`, `Finset.mul_inv_eq_inv_mul_of_doubling_lt_two`, `conj_inv`, `inv_le'`, `infEdist_inv`, `monovaryOn_inv₀`, `OrderMonoidIso.val_inv_unitsWithZero_symm_apply`, `CommGroupWithZero.coe_normUnit`, `Monoid.CoprodI.NeWord.inv_head`, `Antivary.inv_right`, `QuotientGroup.mk_one`, `MulAut.symm_inv`, `Valuation.inversion_estimate'`, `ValuationSubring.valuation_lt_one_iff`, `inv_lt'`, `pow_sub_of_lt`, `mul_inv_le_iff_le_mul`, `Function.mulSupport_inv`, `TendstoLocallyUniformly.inv`, `Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub`, `HasStrictDerivAt.to_localInverse`, `Subgroup.mem_normalizer_iff''`, `mul_inv_cancel_of_invertible`, `tendsto_inv_atTop_zero`, `UpperSet.coe_one`, `RatFunc.num_div`, `QuaternionGroup.a_one_pow_n`, `inv_eq_zero`, `Valuation.isEquiv_iff_val_sub_one_lt_one`, `MulAut.one_apply`, `mul_inv_eq_mul_inv_iff`, `LinearIsometryEquiv.trans_one`, `RingAut.one_eq_refl`, `RestrictedProduct.mulSingle_inv`, `NormedSpace.expSeries_eq_ofScalars`, `UniformCauchySeqOn.inv`, `RCLike.tendsto_inverse_atTop_nhds_zero_nat`, `MeasureTheory.measure_sdiff_inv_smul`, `UniformContinuous.inv`, `MeasureTheory.IsFundamentalDomain.mk''`, `MeasureTheory.Measure.haar_singleton`, `CoxeterSystem.IsReflection.pow_two`, `Finset.inv_smul_mem_iff`, `Filter.tendsto_inv_atTop_iff`, `groupHomology.d₁₀_single_one`, `map_mul_right_nhds_one`, `inv_atBot₀`, `AddAut.inv_symm`, `SemidirectProduct.one_left`, `MeasurableEquiv.symm_mulRight₀`, `inv_le_mabs`, `CauSeq.Completion.ofRat_inv`, `Filter.tendsto_comp_inv_atBot_iff`, `AddAut.apply_inv_self`, `Lagrange.eval_interpolate_not_at_node'`, `Valuation.mem_maximalIdeal_iff`, `Right.one_le_inv_iff`, `MeasureTheory.quasiMeasurePreserving_inv_mul`, `Lagrange.nodalWeight_eq_eval_nodal_erase_inv`, `isConj_iff`, `AdjoinRoot.minpoly_root`, `round_neg_two_inv`, `IsUnit.inv_mul_eq_inv_mul_iff`, `spinGroup.star_eq_inv`, `TendstoLocallyUniformlyOn.inv₀`, `Algebra.normalizedTrace_eq_of_finiteDimensional`, `TendstoUniformly.inv`, `AlgEquiv.one_apply`, `Submonoid.coe_invOrderIso_apply`, `Int.log_inv`, `CategoryTheory.Grp_Class.comp_inv`, `support_comp_inv_smul₀`, `nndist_inv_inv`, `CommRing.Pic.mk_dual`, `Finset.mulETransformRight_one`, `monovary_inv`, `Mathlib.Meta.NormNum.isRat_inv_pos`, `GroupWithZero.conj_pow₀`, `MeasureTheory.integral_domSMul`, `inv_le_one'`, `Finset.preimage_mul_left_one`, `Meromorphic.fun_inv`, `inseparable_one_iff_norm`, `Valued.toNormedField.norm_le_one_iff`, `CauSeq.inv_aux`, `lt_inv_mul_iff_lt`, `GroupExtension.Section.mul_inv_mem_range_inl`, `MulAut.inv_apply`, `SeminormedGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_one`, `groupHomology.d₃₂_single`, `Polynomial.div_def`, `tendsto_inv_nhdsLE`, `zpow_sub_one`, `Filter.inv_nhdsWithin_ne_zero`, `Subgroup.pointwise_smul_subset_iff`, `Asymptotics.SuperpolynomialDecay.param_inv_mul`, `List.prod_map_ite_eq`, `Commute.inv_right_iff₀`, `Submonoid.isUnit_iff_and`, `DifferentiableAt.fun_inv`, `MulAut.conjNormal_symm_apply`, `OrderIso.mulRight₀_symm`, `ValuationSubring.mem_or_inv_mem`, `Set.inv_mem_centralizer₀`, `Right.one_lt_inv_iff`, `OpenPartialHomeomorph.hasDerivAt_symm`, `map_mul_left_nhds_one₀`, `mabs_le`, `Subgroup.normal_subgroupOf_iff`, `spectrum.inv₀_mem_iff`, `CoxeterSystem.inv_simple`, `Representation.Coinvariants.mk_inv_tmul`, `le_mabs'`, `ProfiniteGrp.limit_one_val`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar`, `NormedCommGroup.nhds_one_basis_norm_lt`, `FiniteField.pow_card_sub_one_eq_one`, `Subgroup.subset_pointwise_smul_iff`, `CoxeterSystem.simple_mul_simple_pow`, `one_mem_commutatorSet`, `Function.Antiperiodic.const_mul`, `inv_smul_smul₀`, `inv_lt_one₀`, `one_le_inv₀`, `conj_zpow`, `mul_inv_le_one`, `unitary.inv_mul_mem_iff`, `MeasureTheory.measure_inv_null`, `DilationEquiv.smulTorsor_symm_apply`, `norm_smul_inv_norm'`, `Finset.ruzsa_triangle_inequality_invMul_mul_mul`, `le_inv_mul_iff_mul_le`, `Finset.inv_smul_finset_distrib`, `Lagrange.leadingCoeff_basis`, `oneLePart_one`, `GroupFilterBasis.nhds_one_eq`, `MeasureTheory.mlconvolution_assoc₀`, `Int.ceil_div_ceil_inv_sub_one`, `conj_mul`, `isQuotientCoveringMap_iff`, `Set.smul_inter_ne_empty_iff`, `tendsto_one_iff_mabs_tendsto_one`, `Quaternion.coe_inv`, `Set.mem_smul_set_inv`, `Pell.IsFundamental.mul_inv_x_pos`, `List.alternatingProd_eq_finset_prod`, `Ring.inverse_eq_inv'`, `closure_one_eq`, `CommGrpTypeEquivalenceCommGrp.inverse_obj_one`, `one_eq_inv`, `le_div_self_iff`, `SemiconjBy.inv_inv_symm_iff`, `Representation.ofCoinvariantsTprodLeftRegular_mk_tmul_single`, `group_inseparable_iff`, `MulAction.stabilizerEquivStabilizer_symm_apply`, `div_lt_self_iff`, `Affine.Simplex.centroid_eq_smul_sum_vsub_vadd`, `mabs_one`, `round_two_inv`, `AddSubgroup.mem_inv_pointwise_smul_iff`, `Valuation.val_le_one_or_val_inv_lt_one`, `MonoidAlgebra.antipode_single`, `IsOfFinOrder.inv`, `mem_leftCoset_iff`, `Rep.diagonalHomEquiv_symm_apply`, `Ideal.mem_pointwise_smul_iff_inv_smul_mem`, `SemidirectProduct.inl_aut`, `MeasureTheory.inv_absolutelyContinuous`, `GroupWithZero.isConj_iff₀`, `IsCompact.mul_closedBall_one`, `FDRep.char_conj`, `mul_inv_le_iff_le_mul'`, `GroupExtension.Section.mul_inv_mul_mul_mem_range_inl`, `Pell.Solution₁.eq_one_or_neg_one_iff_y_eq_zero`, `Finset.singleton_zpow`, `minpoly.eq_of_irreducible`, `spinGroup.star_eq_inv'`, `TrivSqZeroExt.inv_inl`, `CategoryTheory.PresheafOfGroups.Cochain₀.inv_apply`, `inv_eq_one`, `commutatorElement_one_left`, `HasStrictDerivAt.of_local_left_inverse`, `groupHomology.mem_cycles₂_iff`, `tendsto_norm_nhdsNE_one`, `AddSubmonoid.le_pointwise_smul_iff`, `pinGroup.val_inv_toUnits_apply`, `inv_mul_lt_of_lt_mul`, `groupHomology.single_isCycle₂_iff_inv`, `tendsto_inv_nhdsGE_inv`, `Ideal.subset_pointwise_smul_iff`, `inv_atTop₀`, `ValuativeRel.inv_srel_one`, `IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply`, `IsStrictOrderedRing.toContinuousInv₀`, `Set.mem_inv_smul_set_iff₀`, `Differentiable.fun_inv`, `RestrictedProduct.mulSingle_zpow`, `GroupExtension.rightHom_inl`, `Set.preimage_smul_inv₀`, `inv_intCast_smul_eq`, `leOnePart_eq_inv_inf_one`, `TrivSqZeroExt.inv_one`, `Set.inv_Ico`, `differentiableWithinAt_inv`, `Mathlib.Meta.NormNum.isNat_inv_zero`, `Polynomial.degree_mul_leadingCoeff_inv`, `mem_ball_one_iff`, `ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl`, `NormedSpace.exp_series_hasSum_exp'`, `Lagrange.eval_interpolate_not_at_node`, `Submonoid.coe_invOrderIso_symm_apply`, `Mathlib.Tactic.FieldSimp.one_zpow'`, `IsTopologicalGroup.mulInvClosureNhd.nhds`, `le_mul_inv_left`, `ValuationSubring.valuation_unit`, `monovary_inv_left`, `Commute.conj`, `Set.inv_Ioc`, `DiffContOnCl.inv`, `isGLB_inv'`, `IsTopologicalGroup.ext_iff`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity`, `eq_mul_inv_of_mul_eq`, `AnalyticOn.fun_inv`, `inv_lt_one'`, `one_lt_mabs`, `AlgEquiv.coe_inv`, `Function.sSup_div_semiconj`, `AddCircle.homeomorphAddCircle_apply_mk`, `Valuation.IsEquiv.valuedCompletion_le_one_iff`, `FiniteGaloisIntermediateField.mem_fixingSubgroup_iff`, `TendstoLocallyUniformlyOn.fun_inv₀_of_disjoint`, `Commute.inv_left_iff`, `ball_div_one`, `lineMap_inv_two`, `MeasureTheory.Measure.IsHaarMeasure.isInvInvariant_of_regular`, `lowerClosure_one`, `Subring.center.coe_inv`, `leOnePart_le_one`, `inv_natCast_smul_eq`, `Finset.subset_smul_finset_iff`, `LinearEquiv.coe_inv`, `Action.rightDual_ρ`, `Submonoid.mem_inv`, `sub_inv_antitoneOn_Ioi`, `two_inv_lt_one`, `SpecialLinearGroup.coe_one`, `AntilipschitzWith.inv`, `ENNReal.orderIsoRpow_symm_apply`, `IsMulTorsionFree.zpow_eq_one_iff_left`, `difference_quotients_converge_uniformly`, `TendstoLocallyUniformly.fun_inv₀`, `IsTopologicalGroup.mulInvClosureNhd.inv`, `nhds_basis_Ioo_one_lt`, `pow_sub`, `WeierstrassCurve.Affine.Point.toClass_zero`, `SemiconjBy.inv_right₀`, `AntivaryOn.inv_left₀`, `le_inv_iff_mul_le_one_left`, `Valuation.isNontrivial_iff_exists_lt_one`, `mulSupport_comp_inv_smul`, `Valuation.Integers.valuation_irreducible_lt_one`, `hasFDerivWithinAt_inv`, `MeasureTheory.eventuallyConst_inv_set_ae`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity`, `Representation.ofMulAction_apply`, `LinearEquiv.dilatransvections_pow_mono`, `Ring.choose_eq_smul`, `norm_smul_inv_norm`, `groupHomology.d₃₂_single_one_thd`, `MonovaryOn.inv_right`, `GroupFilterBasis.one'`, `Pi.mulSingle_div`, `lt_inv_self_iff`, `leOnePart_div_oneLePart`, `Finset.one_mem_div_iff`, `Unitary.inv_mul_mem_iff`, `Set.image_mul_right'`, `max_inv_one`, `Set.op_smul_inter_ne_empty_iff`, `inv_pow_le_inv_pow_of_le`, `CategoryTheory.Groupoid.vertexGroup.inv_eq_inv`, `Subgroup.quotientEquivProdOfLE_apply`, `inv_pow_anti`, `Filter.inv_nhdsNE_zero`, `Filter.inv_atTop`, `Subring.mem_pointwise_smul_iff_inv_smul_mem`, `Polynomial.roots_degree_eq_one`, `inv_mul_le_of_le_mul₀`, `inv_intCast_smul_comm`, `le_mul_inv_iff_mul_le`, `deriv_fun_inv''`, `ValuationSubring.mem_inv_pointwise_smul_iff`, `Finset.preimage_mul_left_singleton`, `Finset.small_alternating_pow_of_small_tripling`, `tsum_geometric_of_norm_lt_one`, `IsArithFrobAt.mul_inv_mem_inertia`, `Asymptotics.isTheta_inv`, `MeasureTheory.measurePreserving_prod_inv_mul_swap`, `nhds_one_symm'`, `IsometryEquiv.inv_apply_self`, `Rep.finsuppToCoinvariantsTensorFree_single`, `HNNExtension.equiv_eq_conj`, `Set.inv_Iio₀`, `Function.mulSupport_mul_inv`, `MulArchimedeanClass.top_eq_mk_iff`, `IsSelfAdjoint.inv`, `Set.inv_Ioo_0_right`, `inv_le_inv_of_neg`, `inv_pow_strictAnti`, `CoxeterSystem.getD_leftInvSeq`, `groupCohomology.smul_map_inv_div_map_inv_of_isMulCocycle₂`, `Set.star_inv'`, `antivary_inv₀`, `groupHomology.isBoundary₁_of_mem_boundaries₁`, `Valuation.Integers.map_le_one`, `Equiv.divLeft_symm_apply`, `UniformCauchySeqOn.fun_inv`, `leOnePart_eq_one'`, `dist_inv_inv₀`, `Subgroup.closure_toSubmonoid`, `tendsto_norm_inv_nhdsNE_zero_atTop`, `Filter.map_inv'`, `HasFPowerSeriesOnBall.hasSum_iteratedFDeriv`, `IsOpen.mul_closure_one_eq`, `ClassGroup.mk0_eq_one_iff`, `Pell.IsFundamental.zpow_eq_one_iff`, `tendsto_inv_nhdsLE_inv`, `inv_le_one_iff₀`, `Representation.Coinvariants.mk_tmul_inv`, `uniformity_eq_comap_mul_inv_nhds_one_swapped`, `Finset.inv_op_smul_finset_distrib`, `rightCoset_eq_iff`, `IsPrimitiveRoot.inv_iff`, `Finset.image_mul_left'`, `Module.reflection_inv`, `NonemptyInterval.snd_inv`, `LinearOrderedCommGroup.Subgroup.genLTOne_lt_one`, `comap_conj_nhds_one`, `Subring.mem_pointwise_smul_iff_inv_smul_mem₀`, `le_mabs`, `Circle.exp_two_pi_mul_int`, `lt_inv_mul_iff₀'`, `MeasureTheory.Measure.div_mem_nhds_one_of_haar_pos_ne_top`, `inv_inv_div_inv`, `one_lt_inv_iff₀`, `MeasureTheory.div_ae_eq_one`, `lt_inv_smul_iff_of_pos`, `MeromorphicAt.inv_iff`, `inv_strictAntiOn`, `tendsto_inv_nhdsGT_inv`, `InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois`, `GroupFilterBasis.mem_nhds_one`, `tendsto_inv_nhdsWithin_Iic_inv`, `inv_lt_zero'`, `div_eq_one_iff_eq`, `IsQuotientCoveringMap.disjoint`, `NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk`, `AddChar.map_neg_eq_inv`, `Matrix.conjTranspose_inv_intCast_smul`, `LinearEquiv.one_mem_transvections`, `max_inv_inv'`, `mul_inv_lt_one_iff`, `Multipliable.finite_mulSupport_of_discreteTopology`, `Mathlib.Meta.NormNum.isNat_inv_one`, `SemiconjBy.inv_inv_symm`, `monovaryOn_inv`, `Mathlib.Tactic.FieldSimp.NF.eval_inv`, `squeeze_one_norm`, `CoxeterSystem.wordProd_reverse`, `MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo`, `HasLineDerivAt.tendsto_slope_zero_right`, `one_div_pow`, `ball_mul_one`, `DilationEquiv.coe_one`, `Subgroup.zpowers_inv`, `MeasureTheory.measurePreserving_mul_prod_inv_right`, `Filter.inv_nhdsGT`, `MeasureTheory.Measure.Regular.inv`, `groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂`, `Finset.mulDysonETransform_snd`, `groupCohomology.map_one_of_isMulCocycle₁`, `AlgEquiv.aut_inv`, `ContDiffAt.inv`, `inv_mul_lt_one₀`, `Hyperreal.infinitesimal_inv_of_infinite`, `CoxeterSystem.prod_leftInvSeq`, `Set.image_inv_Ici`, `CategoryTheory.PresheafOfGroups.Cochain₀.one_apply`, `DualNumber.inv_eps`, `mul_inv_lt_iff_lt_mul`, `MeasureTheory.AEEqFun.inv_mk`, `mabs_eq_mabs`, `Subgroup.leftTransversals.diff_self`, `Submonoid.mem_inv_pointwise_smul_iff`, `GroupSeminormClass.map_one_eq_zero`, `HNNExtension.NormalWord.ReducedWord.empty_head`, `le_inv_of_neg`, `antivaryOn_inv_left₀`, `leftInverse_inv_mul_mul_right`, `inv_mul'`, `Derivation.leibniz_div`, `groupHomology.d₂₁_single_inv_mul_ρ_add_single`, `div_mul_cancel_left₀`, `NormedSpace.exp_eq_tsum`, `TendstoLocallyUniformlyOn.fun_inv`, `Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min`, `mabs_le'`, `Nonneg.inv_mk`, `mul_eq_one_iff_inv_eq₀`, `Ideal.pointwise_smul_subset_iff`, `mul_inv`, `isOfFinOrder_inv_iff`, `IsUnit.smul_sub_iff_sub_inv_smul`, `Valuation.val_lt_one_iff`, `mul_inv_lt_iff₀`, `groupCohomology.cocycles₂_map_one_fst`, `bddAbove_inv`, `HNNExtension.inv_t_mul_of`, `Subgroup.val_list_prod`, `mul_inv_eq_one`, `Valuation.val_le_one_or_val_inv_le_one`, `EulerProduct.eulerProduct_completely_multiplicative`, `Quaternion.inv_def`, `singleton_mul_closedBall_one`, `Set.exists_smul_inter_smul_subset_smul_inv_mul_inter_inv_mul`, `leOnePart_lt`, `Finset.ruzsa_triangle_inequality_mul_mul_invMul`, `smul_inv_smul₀`, `GenContFract.convs'_succ`, `eq_one_or_nnnorm_pos`, `Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField`, `le_inv_iff_mul_le_one_right`, `div_le_inv_mul_iff`, `List.prod_reverse_noncomm`, `Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval`, `antivaryOn_inv_right`, `Finset.smul_inv_mul_eq_inv_mul_opSMul`, `Polynomial.irreducible_mul_leadingCoeff_inv`, `LocallyLipschitz.inv`, `Function.mulSupport_div`, `MulAut.inv_apply_self`, `div_self_mul_self'`, `QuotientGroup.leftRel_eq`, `inv_mul_eq_iff_eq_mul₀`, `one_le_mul_mabs`, `Equiv.Perm.VectorsProdEqOne.vectorEquiv_apply_coe`, `mulInvariantVector_mlieBracket`, `norm_one'`, `Commute.inv_sub_inv`, `Filter.tendsto_inv_atTop_atBot`, `antivary_inv`, `eq_mul_inv_iff_mul_eq₀`, `EMetric.preimage_mul_left_closedBall`, `Subgroup.IsComplement.mul_inv_toRightFun_mem`, `le_mul_inv_iff_le`, `MeasureTheory.inv_ae`, `DistribMulAction.toLinearEquiv_symm_apply`, `CoxeterSystem.length_one`, `spinGroup.val_inv_toUnits_apply`, `one_div_neg`, `inv_mul_le_one`, `LowerSet.Iic_one`, `IsAlgebraic.inv`, `one_div_zpow`, `Hyperreal.inv_omega`, `MeasurableEquiv.symm_mulLeft₀`, `MonoidAlgebra.single_mul_apply`, `CategoryTheory.Functor.map_inv'`, `Valuation.one_lt_val_iff`, `Hyperreal.infinite_iff_infinitesimal_inv`, `IsTopologicalGroup.isOpenMap_iff_nhds_one`, `mul_inv_mul_mul_cancel`, `Subfield.coe_inv`, `abs_inv`, `isSquare_inv`, `MulArchimedeanClass.mk_inv`, `ValuationSubring.valuation_lt_one_or_eq_one`, `lt_mul_inv_iff₀`, `map_eq_zero_iff_eq_one`, `Filter.inv_cobounded₀`, `ContinuousCohomology.I_obj_ρ_apply`, `ValuationRing.iff_isInteger_or_isInteger`, `Metric.preimage_smul_closedEBall`, `Int.clog_of_right_le_one`, `inv_mul_le_one₀`, `MeromorphicOn.divisor_inv`, `Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose`, `mem_closure_one_iff_norm`, `ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem`, `le_inv_mul_right`, `IsTopologicalGroup.exists_antitone_basis_nhds_one`, `inv_sup`, `Multipliable.inv`, `Subgroup.list_prod_mem`, `MeasureTheory.measure_inv_smul_sdiff`, `Valuation.val_eq_one_iff`, `inv_pow_lt_inv_pow_of_lt`, `Monoid.Coprod.con_inv_mul_cancel`, `NormedSpace.expSeries_sum_eq`, `commutatorElement_one_right`, `div_le_one'`, `Finset.mem_inv_smul_finset_iff`, `Finset.preimage_mul_right_one'`, `Subgroup.mem_iSup_prop`, `Multipliable.tendsto_cofinite_one`, `StarAlgEquiv.one_apply`, `mul_inv_le_mul_inv_iff'`, `smul_closedBall_one`, `isOfFinOrder_iff_zpow_eq_one`, `ContMDiff.inv`, `nndist_inv_inv₀`, `IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk`, `nhds_basis_Icc_one_lt`, `Submonoid.mem_nonunits_iff`, `NormedSpace.smul_mem_polar`, `RingAut.one_apply`, `GroupFilterBasis.t2Space_iff_sInter_subset`, `Subgroup.coe_inv`, `CommRing.Pic.mk_eq_one`, `invMonoidHom_apply`, `Subgroup.closure_insert_one`, `pow_inv_comm₀`, `StrictMono.inv`, `leOnePart_le_one'`, `div_helper`, `FractionalIdeal.one_div_spanSingleton`, `MeasureTheory.Measure.IsOpenPosMeasure.inv`, `RootPairing.coreflection_inv`, `Commute.inv_left_iff₀`, `monovary_inv_right₀`, `zpow_eq_one_iff_modEq`, `oneLePart_eq_ite_lt`, `MulAut.coe_inv`, `ValuativeRel.one_rel_inv`, `Group.conj_mem_conjugatesOfSet`, `Set.mulIndicator_div`, `IntermediateField.inv_mem'`, `Set.inv_Ioi`, `MulAut.coe_one`, `TrivSqZeroExt.eq_smul_exp_of_ne_zero`, `CoxeterSystem.getD_leftInvSeq_mul_self`, `Derivation.leibniz_inv`, `List.alternatingProd_append`, `inv_add_inv'`, `CircleDeg1Lift.coe_toOrderIso_inv`, `groupCohomology.map_inv_of_isCocycle₁`, `Con.mem_subgroup_iff`, `NormedSpace.exp_conj`, `Homeomorph.smul_symm_apply`, `MeasureTheory.ProgMeasurable.inv`, `RingPreordering.inv_mem`, `IsCompact.div_closedBall`, `Rat.cast_inv_int`, `inv_mul_lt_iff₀`, `zpow_pow_orderOf`, `MeasureTheory.Measure.InnerRegular.inv`, `IsApproximateSubgroup.one_mem`, `Subgroup.smul_diff_smul'`, `groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂`, `oneLePart_inv`, `LinearIsometryEquiv.reflections_generate_dim_aux`, `Polynomial.natDegree_mul_leadingCoeff_self_inv`, `AddAut.coe_inv`, `isLUB_inv`, `CategoryTheory.GrpObj.inv_comp_assoc`, `Antivary.inv_right₀`, `eventually_cobounded_mapsTo`, `inv_zpow'`, `LinearMap.GeneralLinearGroup.ofLinearEquiv_inv`, `Subgroup.mem_goursatFst`, `Matrix.conjTranspose_inv_natCast_smul`, `mul_eq_one_iff_eq_inv`, `MonoidHom.inv_apply`, `inv_mul_eq_inv_mul_iff`, `Filter.tendsto_inv₀_cobounded`, `mul_eq_one_iff_inv_eq`, `Submodule.mem_smul_iff_inv_mul_mem`, `SpecialLinearGroup.coe_inv`, `powCoprime_inv`, `CommRing.Pic.inv_eq_dual`, `MulAction.smul_inv_mem_fixedBy_iff_mem_fixedBy`, `MeasureTheory.mconv_withDensity_eq_mlconvolution`, `one_zpow`, `zero_zpow_eq`, `CoxeterSystem.leftInvSeq_concat`, `QuotientGroup.nhds_one_hasBasis`, `CoxeterSystem.not_isLeftDescent_one`, `CategoryTheory.SingleObj.inv_as_inv`, `Rep.indToCoindAux_fst_mul_inv`, `div_self_eq_one₀`, `Monoid.PushoutI.NormalWord.Transversal.one_mem`, `IsLUB.inv`, `mul_inv_le_one_iff`, `max_one_div_max_inv_one_eq_self`, `WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul`, `MvPowerSeries.constantCoeff_inv`, `SkewMonoidAlgebra.coeff_mul_right`, `Valuation.mem_unitGroup_iff`, `GroupExtension.Section.inv_mul_mem_range_inl`, `Submonoid.isUnit_iff_of_ne_zero`, `groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv`, `Set.image_inv_Ioo`, `Ring.inverse_eq_inv`, `div_le_self_iff`, `derivWithin_inv`, `EMetric.preimage_mul_left_ball`, `Set.image_inv_Icc`, `ContinuousCohomology.Iobj_ρ_apply`, `norm_commutator_sub_one_le`, `IsUnit.eq_mul_inv_iff_mul_eq`, `pow_natAbs_eq_one`, `smul_inv'`, `CoxeterSystem.IsReflection.inv`, `FractionalIdeal.count_ne_zero`, `inv_zpow`, `RCLike.normSq_inv`, `ValuationSubring.valuation_le_one`, `eq_one_or_norm_pos`, `RootPairing.reflection_sq`, `inv_le_self_iff`, `MonoidHom.fiberEquiv_symm_apply`, `GroupCone.coe_oneLE`, `lt_mul_inv_iff_lt`, `Circle.exp_two_pi`, `mul_notMem_of_exponent_two`, `singleton_div_closedBall_one`, `mulTSupport_fun_inv`, `monovaryOn_inv_right`, `Function.Antiperiodic.const_inv_smul₀`, `AnalyticWithinAt.inv`, `RatFunc.numDenom_div`, `groupCohomology.cocycles₂_map_one_snd`, `Real.Angle.toCircle_zero`, `powCoprime_one`, `fderivWithin_inv'`, `TannakaDuality.FiniteGroup.sumSMulInv_apply`, `Filter.isBoundedUnder_ge_inv`, `conj_pow`, `MvPowerSeries.coeff_inv`, `geom_sum_lt`, `Module.Basis.smul_det`, `sub_inv_antitoneOn_Icc_left`, `NormedSpace.norm_expSeries_summable_of_mem_ball'`, `mul_eq_one_iff_inv_eq'`, `inv_mul_le_iff_le_mul'`, `inv_mabs_le`, `le_mul_inv_iff₀'`, `tendsto_inv_nhdsGT_zero`, `leftCoset_eq_iff`, `geom_sum_inv`, `inv_mul_eq_div`, `MeasureTheory.Measure.div_mem_nhds_one_of_haar_pos`, `MulSemiringAction.toAlgEquiv_symm_apply`, `HasLineDerivAt.tendsto_slope_zero`, `UniformContinuousOn.fun_inv₀`, `HasStrictDerivAt.to_local_left_inverse`, `ball_one_eq`, `Submonoid.le_pointwise_smul_iff₀`, `ordinaryHypergeometricSeries_apply_eq'`, `MulAction.toPerm_symm_apply`, `DifferentiableOn.inv`, `sSup_inv`, `MeasureTheory.lintegral_lintegral_mul_inv`, `mapClusterPt_one_atTop_pow`, `MeasureTheory.innerRegular_inv_iff`, `Filter.tendsto_inv_cobounded`, `StarAlgEquiv.aut_inv`, `Finset.empty_zpow`, `inv_neg`, `one_lt_inv'`, `differentiableAt_inv_iff`, `mul_gaussSum_inv_eq_gaussSum`, `ContMDiffWithinAt.inv`, `GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_range`, `IsometryEquiv.divLeft_symm_apply`, `RegularWreathProduct.left_inl`, `comap_mabs_nhds_one`, `inv_lt_of_mabs_lt`, `MonovaryOn.inv_left₀`, `IsDiscrete.exists_nhds_eq_one_of_image_mulRight_inter_nonempty`, `groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv`, `Subring.mem_inv_pointwise_smul_iff`, `ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier`, `Filter.tendsto_inv_atBot_atTop`, `GroupCone.mem_oneLE`, `Commute.inv_inv_iff`, `CategoryTheory.Aut.Aut_inv_def`, `groupHomology.isCycle₂_of_mem_cycles₂`, `AffineEquiv.inv_def`, `norm_eq_zero'`, `DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem`, `isGLB_inv`, `AffineIsometryEquiv.coe_inv`, `Hyperreal.infinitePos_iff_infinitesimal_inv_pos`, `Finset.card_mul_inv_eq_convolution_inv`, `mul_inv_lt_of_lt_mul₀`, `groupHomology.single_one_fst_sub_single_one_fst_mem_boundaries₂`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem`, `map_inv₀`, `inv_eq_self`, `Submonoid.pointwise_smul_le_iff₀`, `SemiconjBy.inv_right`, `NonemptyInterval.fst_inv`, `Equidecomp.IsDecompOn.of_leftInvOn`, `Circle.exp_neg`, `QuotientGroup.eq`, `CategoryTheory.Grp.Hom.hom_hom_inv`, `AddChar.neg_apply'`, `Finset.one_mem_inv_mul_iff`, `Valuation.isEquiv_iff_val_le_one`, `Set.star_inv`, `traceForm_dualSubmodule_adjoin`, `Antivary.inv_left₀`, `oneLePart_inf_leOnePart_eq_one`, `eq_on_inv`, `Filter.Tendsto.uniformity_inv_iff`, `Polynomial.roots_C_mul_X_add_C`, `ContinuousMonoidHom.inv_toFun`, `AddCircle.equivAddCircle_apply_mk`, `Set.inv_zero`, `div_ball`, `MeasureTheory.Measure.map_mul_right_inv_eq_self`, `Multipliable.tprod_eq_mul_tprod_ite`, `uniformity_eq_comap_inv_mul_nhds_one`, `OrderIso.smulRight_symm_apply`, `sInf_inv`, `one_lt_div'`, `LinearMap.GeneralLinearGroup.toLinearEquiv_inv`, `IsSquare.inv`, `Subgroup.instCanLiftSetCoeAndMemOfNatForallForallForallForallHMulForallForallInv`, `meromorphicNFAt_inv`, `Set.preimage_mul_left_one`, `inv_mul_le_one_iff`, `inv_mul_mul_self`, `Pell.IsFundamental.mul_inv_y_nonneg`, `sup_eq_half_smul_add_add_abs_sub'`, `Valuation.mem_valuationSubring_iff`, `inv_le_leOnePart`, `HasLineDerivAt.tendsto_slope_zero_left`, `nnnorm_inv'`, `mul_inv_le_iff₀`, `Finset.prod_inv_distrib`, `Subgroup.smul_apply_eq_smul_apply_inv_smul`, `ValuationRing.isFractionRing_iff`, `Pi.mulSingle_inv`, `Set.inv_Ici`, `CommRing.Pic.mk_eq_one_iff`, `CommRing.Pic.instFreeAsModuleOfNat`, `Submonoid.isUnit_iff`, `LipschitzWith.inv`, `Finset.smul_finset_subset_iff₀`, `EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers`, `leOnePart_eq_ite_lt`, `Valuation.Integers.isIntegral_iff_v_le_one`, `antivary_inv_right₀`, `deriv_inv`, `nhds_translation_mul_inv₀`, `Subring.pointwise_smul_subset_iff`, `Monovary.inv_right`, `HNNExtension.NormalWord.empty_head`, `comap_norm_nhdsGT_zero'`, `Valuation.isEquiv_iff_val_eq_one`, `IsUnit.eq_inv_mul_iff_mul_eq`, `OpenSubgroup.mem_nhds_one`, `one_div_nonneg`, `Rep.indResAdjunction_counit_app_hom_hom`, `Action.FintypeCat.toEndHom_apply`, `IsGalois.normalBasis_apply`, `mul_mul_div`, `Circle.coe_inv_eq_conj`, `Subgroup.mem_inv_pointwise_smul_iff₀`, `CauSeq.coe_inv`, `Finset.ruzsa_triangle_inequality_invMul_invMul_invMul`, `tendsto_inv_atBot_nhdsLT_zero`, `IsApproximateSubgroup.pow_inter_pow`, `Unitary.inv_mem`, `Matrix.conjTranspose_inv_ofNat_smul`, `inv_pos`, `Algebra.norm_inv`, `inv_nonneg_of_nonneg`, `Equiv.mulLeft_one`, `TannakaDuality.FiniteGroup.leftRegular_apply`, `Metric.preimage_smul_eball`, `NormedSpace.expSeries_summable'`, `Commute.inv_mul_eq_inv_mul_iff`, `Submonoid.mk_mul_mk_inv_eq_one`, `ValuationSubring.valuation_le_one_iff`, `HasDerivAt.tendsto_slope_zero_left`, `ValuationSubring.mem_unitGroup_iff`, `MeasureTheory.Measure.inv.instIsMulLeftInvariant`, `Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero`, `Submonoid.mk_inv_mul_mk_eq_one`, `Pi.mulSingle_zpow`, `arrowAction_smul`, `Filter.inv_nhdsLT`, `Pell.Solution₁.eq_one_of_x_eq_one`, `Set.image_mul_right`, `EulerProduct.eulerProduct_completely_multiplicative_tprod`, `Multipliable.tendsto_atTop_one`, `Finset.mulConst_inv_left`, `IsUnit.mul_inv_cancel_right`, `MeasureTheory.mconv_eq_withDensity_mlconvolution_rnDeriv`, `Set.Nonempty.zpow`, `Set.Nonempty.one_mem_div`, `Representation.linHom_apply`, `nndist_one_left`, `inv_mul_lt_one_iff`, `Quaternion.normSq_inv`, `Set.mul_eq_one_iff`, `Set.mulIndicator_inv'`, `meromorphicOrderAt_inv`, `Algebra.normalizedTrace_eq_of_fininteDimensional`, `inv_nhdsGT_zero`, `Pell.Solution₁.exists_pos_variant`, `Set.inv_Icc`, `Bornology.IsBounded.inv`, `ProbabilityTheory.IndepFun.pdf_mul_eq_mlconvolution_pdf`, `MonoidHom.fiberEquivKer_apply`, `Finset.invMulSubgroup_eq_mul_inv`, `CoxeterSystem.getD_rightInvSeq_mul_self`, `GroupExtension.Section.mul_mul_mul_inv_mem_range_inl`, `AddSubgroup.pointwise_smul_le_iff₀`, `BddAbove.inv`, `star_inv_intCast_smul`, `LinearEquiv.det_symm`, `multipliable_const_iff`, `SeminormedGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_one`, `IsCompact.closedBall_one_mul`, `Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe`, `FractionalIdeal.mul_generator_self_inv`, `zero_zpow_eq_one₀`, `RCLike.inv_im`, `dist_inv_inv`, `MeasureTheory.absolutelyContinuous_inv`, `FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul`, `MonovaryOn.inv_right₀`, `IsApproximateSubgroup.inv_eq_self`, `NormedSpace.expSeries_apply_eq`, `MvPowerSeries.C_inv`, `groupHomology.isBoundary₂_of_mem_boundaries₂`, `GroupFilterBasis.conj'`, `Set.subset_smul_set_iff`, `ContDiffWithinAt.inv`, `MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le`, `FiniteMulArchimedeanClass.liftOrderHom_mk`, `groupCohomology.cocycles₁_map_inv`, `tendsto_inv_atTop_nhdsGT_zero`, `TrivSqZeroExt.mul_inv_cancel`, `Subgroup.closure_singleton_one`, `pinGroup.star_eq_inv'`, `MeasureTheory.Measure.IsFiniteMeasureOnCompacts.inv`, `Finset.inv_zero`, `ball_div`, `hasDerivAt_inv`, `Monovary.inv_left`, `mem_emetric_ball_one_iff`, `Subgroup.closure_singleton_inv`, `div_eq_inv_self`, `enorm_inv'`, `TrivSqZeroExt.inv_mul_cancel`, `one_le_div'`, `Filter.map_inv_atBot`, `le_inv_mul_iff₀'`, `zero_eq_inv`, `Pell.Solution₁.x_one`, `Multipliable.countable_mulSupport`, `WithZero.val_inv_expOrderIso_apply`, `tendsto_inv_atBot_zero`, `edist_one_right`, `Finset.centroidWeights_apply`, `MeasureTheory.measure_symmDiff_inv_smul`, `eq_or_eq_inv_of_mabs_eq`, `PowerSeries.constantCoeff_inv`, `MeasureTheory.Pi.isInvInvariant_volume`, `inv_natCast_smul_comm`, `IsMulTorsionFree.zpow_eq_one_iff_right`, `Rep.ihom_obj_ρ_apply`, `AnalyticWithinAt.fun_inv`, `inv_neg''`, `AddSubmonoid.pointwise_smul_le_iff`, `QuaternionGroup.one_def`, `Function.Antiperiodic.const_inv_mul`, `Monoid.CoprodI.NeWord.inv_last`, `spectrum.inv₀_mem_inv_iff`, `MonoidHom.map_inv₂`, `Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul`, `RootPairing.Equiv.weightEquiv_inv`, `AddAut.conj_inv_apply`, `mem_lowerCentralSeries_succ_iff`, `UniformContinuousOn.inv₀`, `DilationEquiv.ratio_inv`, `mul_mul_inv_mul_cancel`, `SemidirectProduct.one_right`, `Subgroup.toSubmonoid_zpowers`, `ZMod.AddAutEquivUnits_apply`, `Equiv.Perm.VectorsProdEqOne.mem_iff`, `MeromorphicOn.inv_iff`, `Filter.Tendsto.uniformity_inv`, `nnnorm_eq_zero'`, `Hyperreal.inv_epsilon`, `TrivSqZeroExt.invOf_eq_inv`, `MeasurableEquiv.symm_mulRight`, `TannakaDuality.FiniteGroup.equivApp_inv`, `Subgroup.disjoint_def'`, `inv_lt_inv_of_neg`, `Set.mulIndicator_div'`, `smul_mem_nhds_self`, `mul_inv_le_one_of_le₀`, `MulArchimedeanClass.mk_antitoneOn`, `singleton_div_ball_one`, `MulArchimedeanClass.mk_monotoneOn`, `IsSelfAdjoint.inv₀`, `CategoryTheory.PresheafOfGroups.OneCocycle.ev_symm`, `Subsemiring.pointwise_smul_subset_iff`, `PresentedGroup.mk_eq_one_iff`, `Metric.preimage_smul_sphere`, `EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric`, `Finsupp.prod_inv`, `DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem`, `IsUnit.mul_inv_eq_mul_inv_iff`, `leOnePart_eq_one`, `Submodule.reflection_inv`, `sum_Ioo_inv_sq_le`, `Mathlib.Meta.NormNum.isNNRat_inv_pos`, `meromorphicTrailingCoeffAt_inv`, `Equiv.inv_mulRight`, `Pell.Solution₁.y_inv`, `MeasureTheory.measure_inter_inv_smul`, `DifferentiableAt.inv`, `coe_invMonoidHom`, `EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers`, `pow_card_eq_one'`, `inv_mul_eq_one₀`, `DifferentiableWithinAt.inv`, `uniformity_eq_comap_mul_inv_nhds_one`, `Metric.preimage_mul_left_ball`, `CancelDenoms.inv_subst`, `Finset.preimage_mul_right_one`, `ordinaryHypergeometric_eq_tsum`, `Subgroup.one_mem`, `Subgroup.normalizerMonoidHom_apply_apply_coe`, `Polynomial.degree_mul_leadingCoeff_self_inv`, `eq_inv_mul_iff_mul_eq₀`, `Pell.IsFundamental.mul_inv_x_lt_x`, `TendstoUniformlyOn.fun_inv`, `inv_lt_iff_one_lt_mul₀`, `gauge_smul_left_of_nonneg`, `closedBall_one_div_singleton`, `meromorphicNFOn_inv`, `AddChar.inv_apply`, `map_inv_natCast_smul`, `Submonoid.mem_inv_pointwise_smul_iff₀`, `Mathlib.Meta.NormNum.isInt_inv_neg_one`, `Subgroup.IsComplement.inv_mul_toLeftFun_mem`, `Submodule.reflection_mul_reflection`, `HNNExtension.of_mul_inv_t`, `Set.image_inv_Ioi`, `isLUB_inv'`, `eq_inv_mul_of_mul_eq`, `groupHomology.isCycle₁_of_mem_cycles₁`, `BddAbove.range_inv`, `LinearMap.toMatrix_smulBasis_right`, `GenContFract.convs_succ`, `Matrix.UnitaryGroup.inv_val`, `Finset.smul_finset_subset_iff`, `Equiv.mulRight_symm`, `FDRep.char_linHom`, `one_le_inv_iff₀`, `ContinuousInv.induced`, `Set.iUnion_inv_smul`, `LieAlgebra.IsKilling.rootSpace_one_div_two_smul`, `lt_mul_inv_iff_mul_lt`, `Set.op_smul_inter_nonempty_iff`, `inv_pow`, `leOnePart_inv`, `div_eq_self`, `cfc_inv`, `Finset.inv_smul_finset_distrib₀`, `Antivary.inv`, `eq_inv_mul_iff_mul_eq`, `dist_mulIndicator`, `absorbs_iff_eventually_cobounded_mapsTo`, `antivaryOn_inv₀`, `mul_inv_eq_mul_inv_iff_mul_eq_mul`, `InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal`, `Unitary.mul_inv_mem_iff`, `RootPairing.Equiv.coweightEquiv_inv`, `Metric.preimage_smul_closedBall`, `IsUnit.div_mul_left`, `mulAutArrow_apply_symm_apply`, `CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv`, `Subgroup.disjoint_def`, `MeasureTheory.rnDeriv_mconv`, `Field.isSeparable_inv`, `AddCircle.toCircle_zero`, `GroupCone.oneLE.hasMemOrInvMem`, `Set.inv_mem_Ioc_iff`, `groupHomology.isBoundary₀_of_mem_coinvariantsKer`, `div_self_le_one`, `nhds_eq_iInf_mabs_div`, `contDiffAt_inv`, `infEdist_inv_inv`, `Mathlib.Tactic.Ring.inv_zero`, `SemidirectProduct.inl_aut_inv`, `le_mul_inv_right`, `Right.inv_lt_one_iff`, `MeasureTheory.continuous_integral_apply_inv_mul`, `Valuation.Integers.valuation_unit`, `Metric.preimage_mul_left_closedEBall`, `Finset.convolution_inv`, `EulerProduct.eulerProduct_completely_multiplicative_hasProd`, `norm_inv'`, `Hyperreal.IsSt.inv`, `pow_gcd_card_eq_one_iff`, `AddSubmonoid.mem_inv_pointwise_smul_iff₀`, `Monovary.inv_right₀`, `Antivary.inv₀`, `nhds_translation_mul_inv`, `lt_mul_inv_iff₀'`, `NormedSpace.exp_conj'`, `Right.inv_le_one_iff`, `MulAut.conj_apply`, `LieGroup.contMDiff_inv`, `Multiset.prod_map_inv'`, `Multipliable.mulIndicator`, `LinearMap.conjugate_apply`, `Fin.partialProd_left_inv`, `RegularWreathProduct.inv_left`, `edist_one_eq_enorm`, `IsClosed.mul_closure_one_eq`, `Finset.mulETransformLeft_one`, `Action.leftRegularTensorIso_hom_hom`, `CoxeterSystem.getElem_rightInvSeq`, `Set.inv_smul_set_distrib₀`, `zpow_eq_one_iff_right₀`, `nhds_inv₀`, `commutatorElement_inv`, `Height.mulHeight₁_inv`, `Hyperreal.coe_inv`, `Subsemiring.mem_inv_pointwise_smul_iff₀`, `groupHomology.single_isCycle₁_iff`, `NormedField.continuousAt_inv`, `MeasureTheory.Measure.instIsInvInvariantCount`, `ValuativeRel.inv_rel_one`, `IsKleinFour.mul_self`, `mul_inv_lt_iff_le_mul'`, `List.prod_inv_reverse`, `AffineEquiv.coe_one`, `LinearEquiv.transvections_pow_mono`, `Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv`, `lt_inv'`, `Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub`, `groupHomology.inhomogeneousChains.d_single`, `MeasureTheory.rnDeriv_mconv'`, `NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj`, `MeromorphicOn.inv`, `Finset.card_smul_inter`, `Filter.tendsto_inv₀_nhdsWithin_ne_zero`, `conj_injective`, `leOnePart_one`, `HNNExtension.NormalWord.prod_empty`, `inv_lt_one_iff_one_lt`, `eq_mul_inv_iff_mul_eq`, `MeasureTheory.measure_lintegral_div_measure`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem`, `zpow_abs_eq_one`, `mul_one_div_cancel`, `lt_inv_iff_mul_lt_one'`, `MulSemiringAction.toRingEquiv_symm_apply`, `totallyBounded_inv`, `hasDerivAt_iff_tendsto_slope_zero`, `Mathlib.Tactic.FieldSimp.list_prod_zpow'`, `eq_inv_iff_mul_eq_one`, `EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric`, `spectrum.inv₀_mem`, `norm_inv`, `ordinaryHypergeometricSeries_apply_eq`, `ValuativeRel.one_apply_posSubmonoid`, `Pell.Solution₁.x_inv`, `TrivSqZeroExt.inv_inv`, `Left.inv_lt_one_iff`, `Polynomial.dvd_mul_leadingCoeff_inv`, `MulArchimedeanClass.mk_one`, `map_units_inv`, `Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero`, `hasStrictFDerivAt_inv`, `Set.preimage_smul`, `groupHomology.isBoundary₂_iff`, `inv_eq_self₀`, `IsFractionRing.associated_num_den_inv`, `dist_one`, `CoxeterSystem.isRightDescent_inv_iff`, `AddChar.inv_apply'`, `OnePoint.equivProjectivization_symm_apply_mk`, `IsPrimitiveRoot.zpow_eq_one`, `fderiv_inv`, `Submonoid.coe_inv`, `mul_eq_one_iff_eq_inv₀`, `Set.image_inv_Iio`, `GroupSeminorm.inv'`, `ball_one_div_singleton`, `IsLeftUniformGroup.uniformity_eq`, `CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizers`, `Right.inv_nonneg`, `inv_sub_inv`, `Set.preimage_smul_inv`, `Valuation.extendToLocalization_mk'`, `Monovary.inv_left₀`, `Set.nonempty_image_mulLeft_inv_inter_iff`, `Filter.Tendsto.inv_inv`, `Unitary.inv_mem_iff`, `Homeomorph.mulLeft₀_symm_apply`, `GroupFilterBasis.nhds_one_hasBasis`, `OneHom.div_comp`, `inv_pos_of_pos`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `CategoryTheory.Hom.inv_def`, `groupHomology.single_isCycle₂_iff`, `Nonneg.coe_inv`, `mem_sphere_one_iff_norm`, `AddChar.starComp_apply`, `mul_inv_lt_mul_inv_iff'`, `IsKleinFour.inv_eq_self`, `inv_smul_lt_iff_of_pos`, `Set.singleton_zpow`, `MeasurableEquiv.symm_mulLeft`, `Finset.weightedVSubOfPoint_smul`, `TendstoUniformlyOnFilter.fun_inv`, `Set.mem_inv_smul_set_iff`, `AnalyticOn.inv`, `ball_one_mul_singleton`, `Subring.le_pointwise_smul_iff₀`, `MulDistribMulAction.toMulEquiv_symm_apply`, `CoxeterSystem.simple_mul_simple_pow'`, `Finset.pluennecke_ruzsa_inequality_pow_div`, `mul_inv_left_le`, `GenContFract.of_s_head`, `AffineBasis.coord_apply_centroid`, `Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd`, `MonoidHom.mulExact_of_comp_of_mem_range`, `Units.mul_inv'`, `slope_fun_def`, `CategoryTheory.Grp_Class.inv_comp`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `UpperSet.Ici_one`, `IsPGroup.smul_mul_inv_trivial_or_surjective`, `star_inv_natCast_smul`, `Filter.isBoundedUnder_le_inv`, `CategoryTheory.instIsMonHomInvHomOfIsCommMonObj`, `Height.logHeight₁_inv`, `mem_eball_one_iff`, `NormedField.tendsto_norm_inv_nhdsNE_zero_atTop`, `IsRightUniformGroup.uniformity_eq`, `inv_smul_le_iff_of_pos`, `lipschitzWith_inv_iff`, `commutatorElement_self`, `tendsto_conj_nhds_one`, `Units.smul_inv`, `Subgroup.Commensurable.commensurable_inv`, `Commute.inv_mul_cancel`, `oneLePart_le_one`, `MonoidWithZeroHom.snd_inl_apply_of_ne_zero`, `deriv_inv''`, `TendstoLocallyUniformly.fun_inv₀_of_disjoint`, `selfAdjoint.val_inv`, `NormedDivisionRing.to_continuousInv₀`, `Quandle.conj_act_eq_conj`, `Function.Periodic.const_smul₀`, `HasFDerivAt.lim`, `MulAut.conj_inv_apply`, `nndist_mulIndicator`, `Subfield.inv_mem`, `AddConstEquiv.coe_val_inv_equivUnits_apply`, `mul_self_mul_inv`, `OneHom.coe_div`, `antivary_inv_left`, `Subgroup.exists_inv_mem_iff_exists_mem`, `csSup_inv`, `CategoryTheory.SingleObj.differenceFunctor_map`, `IsUniformGroup.cauchy_map_iff_tendsto`, `ProbabilityTheory.IndepFun.pdf_mul_eq_mlconvolution_pdf'`, `CoxeterSystem.simple_sq`, `cfc_inv_id`, `Rep.diagonalSuccIsoTensorTrivial_hom_hom_single`, `NormedSpace.norm_expSeries_summable'`, `DifferentiableOn.fun_inv`, `antivaryOn_inv`, `mul_notMem_of_orderOf_eq_two`, `ValuationSubring.pointwise_smul_subset_iff`, `div_mabs_eq_inv_leOnePart_sq`, `MulAction.stabilizer_quotient`, `inv_le_inv_iff`, `Submonoid.pointwise_smul_subset_iff`, `Homeomorph.shearMulRight_symm_coe`, `Set.preimage_mul_right_singleton`, `Metric.unitSphere.coe_inv`, `Filter.map_inv_atTop`, `ValuativeRel.one_vlt_inv`, `neg_one_zpow_eq_ite`, `SimpleGraph.FarFromTriangleFree.lt_half`, `mem_upperCentralSeriesStep`, `lt_inv_mul_iff₀`, `mul_mul_inv_cancel'_right`, `List.prod_set'`, `Equiv.mulLeft_symm_apply`, `Commute.mul_inv_eq_mul_inv_iff_of_isUnit`, `mul_inv_right_le`, `NormedSpace.expSeries_apply_eq'`, `bddBelow_inv`, `Finset.ruzsa_triangle_inequality_mulInv_mul_mul`, `Set.inv_Ioi₀`, `contDiffOn_inv`, `Monotone.inv`, `Valued.toNormedField.one_lt_norm_iff`, `IsTopologicalGroup.t2Space_iff_one_closed`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem`, `Finset.zpow_eq_empty`, `Equiv.Perm.VectorsProdEqOne.one_eq`, `exists_zpow_eq_one`, `AddAut.coe_one`, `Valuation.IsNontrivial_iff_exists_one_lt`, `Subgroup.mem_goursatSnd`, `InvMemClass.coe_inv`, `IsCompact.mul_closure_one_eq_closure`, `ClassGroup.mk_eq_one_iff`, `tendsto_norm_one`, `RatFunc.denom_div`, `groupHomology.d₃₂_single_one_fst`, `inv_smul_eq_iff₀`, `val_inv_cfcUnits`, `TendstoLocallyUniformlyOn.inv₀_of_disjoint`, `Finsupp.comapSMul_apply`, `unitary.coe_inv`, `Set.inv_smul_set_distrib`, `pow_intGCD_eq_one`, `max_one_mul_max_inv_one_eq_mabs_self`, `Finset.mulETransformRight_inv`, `UniformContinuous.inv₀`, `antivaryOn_inv_left`, `groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self`, `TopologicalGroup.isOpenMap_iff_nhds_one`, `TrivSqZeroExt.isUnit_inv_iff`, `AntitoneOn.inv`, `commutatorElement_eq_one_iff_commute`, `Function.support_inv`, `Function.MulExact.iff_monoidHom_rangeRestrict`, `groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁`, `Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap`, `le_inv_mul_iff₀`, `Monovary.inv₀`, `GroupNorm.eq_one_of_map_eq_zero'`, `inv_lt_comm₀`, `Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub`, `Finset.card_inv_mul_of_doubling_lt_three_halves`, `Valuation.map_inv`, `Action.ρ_self_inv_apply`, `lt_inv_comm₀`, `inv_antitoneOn_Icc_right`, `CategoryTheory.GrpObj.inv_eq_inv`, `SkewMonoidAlgebra.coeff_mul_single`, `Commute.inv_left`, `GroupSeminormClass.map_inv_eq_map`, `IsPrimitiveRoot.inv`, `dist_one_left`, `TrivSqZeroExt.inv_neg`, `inv_lt_inv'`, `Finset.inv_op_smul_finset_distrib₀`, `IsTopologicalGroup.toContinuousInv`, `stdSimplex.barycenter_apply`, `LinearIsometryEquiv.coe_inv`, `CoxeterSystem.IsReflection.conj`, `lowerCentralSeries_succ`, `Rat.cast_inv`, `LinearEquiv.one_mem_dilatransvections`, `Set.mulIndicator_inv`, `ContinuousLinearEquiv.det_coe_symm`, `Filter.not_one_le_div_iff`, `hasFPowerSeriesOnBall_inv_one_sub`, `Commute.inv_right_iff`, `CategoryTheory.ActionCategory.curry_apply_left`, `Polynomial.div_C`, `comap_norm_nhds_one`, `Unitary.val_inv_toUnits_apply`, `HasProd.inv`, `MeromorphicOn.divisor_fun_inv`, `Set.preimage_mul_right_one`, `inv_nhdsLT_zero`, `inv_nonneg`, `IsUpperSet.inv`, `RegularWreathProduct.one_right`, `Polynomial.leadingCoeff_preHilbertPoly`, `contMDiff_inv`, `Hyperreal.infinitesimal_iff_infinite_inv`, `AlgEquiv.one_toLinearMap`, `IsometryEquiv.apply_inv_self`, `CoxeterSystem.IsReflection.mul_self`, `IsUnit.eq_on_inv`, `IsUnit.mul_one_div_cancel`, `Submonoid.mem_nonunits_iff_or`, `Circle.exp_zero`, `ValuationSubring.mem_or_inv_mem'`, `Function.Antiperiodic.const_smul₀`, `GroupNorm.apply_one`, `AddAction.toPermHom_apply_symm_apply`, `IsUnit.div_eq_one_iff_eq`, `Set.mulIndicator_compl'`, `tendsto_inv_iff₀`, `SemiconjBy.inv_symm_left₀`, `instContMDiffInv₀ModelWithCornersSelf`, `mabs_div_pos`, `GroupFilterBasis.inv`, `TannakaDuality.FiniteGroup.sumSMulInv_single_id`, `tendsto_algebraMap_inverse_atTop_nhds_zero_nat`, `Subgroup.inv_mem`, `spectrum.map_inv`, `MonotoneOn.inv`, `inv_lt_iff_one_lt_mul`, `derivWithin_inv'`, `MulChar.inv_apply_eq_inv'`, `inv_mul_left_le`, `neg_inv`, `MeasureTheory.Measure.modularCharacterFun_map_one`, `inv_lt_iff_one_lt_mul'`, `Subring.pointwise_smul_le_iff₀`, `groupCohomology.cocycles₁_map_one`, `MeasureTheory.measure_inv_smul_symmDiff`, `Subgroup.pointwise_smul_le_iff₀`, `Set.inv_Ioo`, `mem_closedBall_one_iff`, `StrictMonoOn.inv`, `inv_le_div_iff_le_mul'`, `inv_mul_lt_of_lt_mul₀`, `CoxeterSystem.prod_alternatingWord_eq_mul_pow`, `CoxeterSystem.wordProd_mul_getD_rightInvSeq`, `UniformFun.hasBasis_nhds_one`, `Set.zpow_eq_empty`, `inv_mabs_le_inv`, `Positive.coe_inv`, `Subgroup.mem_normalizer_iff`, `AddChar.starComp_eq_inv`, `Even.neg_one_zpow`, `Function.mulSupport_fun_inv`, `IsCompact.closedBall_one_div`, `Asymptotics.IsBigO.inv_rev`, `Valuation.IsNontrivial.exists_one_lt`, `RootPairing.coreflection_sq`, `QuotientGroup.mk_inv`, `Finset.ruzsa_triangle_inequality_mulInv_mulInv_mulInv`, `CommGrpTypeEquivalenceCommGrp.inverse_obj_inv`, `uniformity_eq_comap_nhds_one_swapped`, `Subgroup.eq_bot_iff_forall`, `CommRing.Pic.mk_eq_one_iff_free`, `SemiconjBy.inv_symm_left`, `IsUnit.div_mul_right`, `LinearEquiv.baseChange_inv`, `mem_upperCentralSeries_succ_iff`, `HasDerivWithinAt.inv`, `StrictAnti.inv`, `Left.inv_le_one_iff`, `TendstoUniformlyOnFilter.inv`, `support_comp_inv_smul`, `Set.image_mul_left'`, `QuotientGroup.rightRel_apply`, `inv_mul_le_iff₀`, `RCLike.inv_pos_of_pos`, `Function.Periodic.const_inv_mul`, `RingAut.inv_apply`, `ValuationSubring.inv_mem_nonunits_iff`, `inv_mul_lt_iff_lt_mul`, `logDeriv_inv`, `MulAction.period_inv`, `inv_inf`, `Pell.Solution₁.y_one`, `HomotopyGroup.one_def`, `Set.one_notMem_inv_mul_iff`, `inv_eq_self_of_orderOf_eq_two`, `FiniteMulArchimedeanClass.lift_mk`, `IsCyclic.card_pow_eq_one_le`, `MonovaryOn.inv₀`, `CauchySeq.inv`, `FreeGroup.prod_mk`, `LinearIsometryEquiv.coe_one`, `Set.inv_uIcc`, `Asymptotics.IsTheta.inv`, `PresentedGroup.one_of_mem`, `Subgroup.coe_one`, `GroupExtension.inl_conjAct_comm`, `DirectLimit.inv₀_def`, `CategoryTheory.GrpObj.inv_comp`, `CoxeterSystem.wordProd_nil`, `MulAction.smul_fixedBy`, `Subgroup.inv_mem'`, `Equiv.smulRight_symm_apply`, `MeasureTheory.Measure.haar.nonempty_iInter_clPrehaar`, `Subgroup.coe_topologicalClosure_bot`, `mabs_eq_one`, `CoxeterSystem.isLeftInversion_inv_iff`, `one_lt_oneLePart_iff`, `RootPairing.Equiv.reflection_inv`, `Function.Antiperiodic.mul_const`, `MulAut.conj_symm_apply`, `Fin.insertNth_div_same`, `NumberField.linearDisjoint_of_isGalois_isCoprime_discr`, `MeasureTheory.measure_inv_smul_union`, `mabs_mul_eq_mul_mabs_iff`, `one_le_inv'`, `Filter.comap_inv_atBot`, `List.alternatingProd_cons'`, `Asymptotics.IsLittleO.inv_rev`, `MeasureTheory.IsFundamentalDomain.mk'`, `MeasureTheory.quasiMeasurePreserving_inv_of_right_invariant`, `OrderIso.mulLeft_symm`, `coe_set_eq_one`, `Set.inv_mem_Ioo_iff`, `inv_pow_sub`, `one_le_leOnePart`, `Valuation.IsEquiv.val_sub_one_lt_one_iff`, `GenContFract.of_s_tail`, `IsStrictOrderedRing.toHasContinuousInv₀`, `inv_le_comm₀`, `hasLineDerivAt_iff_tendsto_slope_zero`, `Algebra.normalizedTrace_minpoly`, `Circle.coe_eq_one`, `ValuationSubring.mem_nonunits_iff_or`, `Polynomial.coeff_inv_units`, `inv_div'`, `unitary.inv_mem`, `Function.Antiperiodic.const_smul`, `groupHomology.d₂₁_single_one_fst`, `GroupFilterBasis.N_one`, `Algebra.IsIntegral.inv_mem`, `CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc`, `injective_iff_map_eq_one'`, `inv_le_iff_one_le_mul'`, `Metric.preimage_mul_left_eball`, `leOnePart_eq_inv`, `tendsto_div_comap_self`, `Representation.self_inv_apply`, `MonoidHom.eq_iff`, `IsUniformGroup.cauchy_iff_tendsto_swapped`, `Subgroup.zpowers_eq_bot`, `List.Vector.prod_set'`, `GroupSeminorm.map_one'`, `AffineIsometryEquiv.coe_one`, `Metric.preimage_mul_left_closedBall`, `Subgroup.IsComplement.inv_toLeftFun_mul_mem`, `Polynomial.monic_mul_leadingCoeff_inv`, `monovaryOn_inv_left₀`, `iter_deriv_inv`, `Circle.exp_int_mul_two_pi`, `TendstoUniformly.fun_inv`, `PowerSeries.coeff_inv`, `inv_sub_inv'`, `ContDiff.inv`, `Function.Periodic.mul_const_inv`, `Mathlib.Tactic.FieldSimp.NF.one_eq_eval`, `RCLike.inv_def`, `AddAut.inv_apply`, `Algebra.normalizedTrace_eq_of_finiteDimensional_apply`, `Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply`, `Set.image_inv_Ico`, `one_le_inv_mul₀`, `ValuationSubring.mem_principalUnitGroup_iff`, `fderivWithin_inv`, `Commute.inv_mul_eq_inv_mul_iff_of_isUnit`, `FractionalIdeal.div_spanSingleton`, `MeasureTheory.eventually_nhds_one_measure_smul_diff_lt`, `IsUnit.inv_mul_eq_one`, `Finset.smul_convolution_eq_convolution_inv_mul`, `inv_pow_sub₀`, `RatFunc.num_div_dvd'`, `zpow_neg`, `zpow_sub_one₀`, `inv_smul_lt_iff_of_neg`, `iter_deriv_inv'`, `analyticOn_inv`, `NNReal.orderIsoRpow_symm_eq`, `CategoryTheory.PreGaloisCategory.IsFundamentalGroup.non_trivial`, `HomotopyGroup.inv_spec`, `div_mul_cancel_right`, `LinearEquiv.inv_mem_dilatransvections_iff`, `Asymptotics.IsLittleOTVS.tendsto_inv_smul`, `lipschitzOnWith_inv_iff`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset`, `inv_mul_lt_iff_lt_mul'`, `mabs_inv`, `groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂`, `MulArchimedeanClass.out_top`, `Equiv.mulLeft_symm`, `inv_mul_lt_one_iff_lt`, `smul_inv₀`, `Fin.inv_partialProd_mul_eq_contractNth`, `Filter.one_le_div_iff`, `Set.image_inv_Ioc`, `Algebra.normalizedTrace_def`, `Subgroup.inv_subset_closure`, `nnnorm_one'`, `Units.continuousOn_inv₀_spectrum`, `Monovary.inv`, `IsAbsoluteValue.abv_inv`, `Filter.comap_inv_atTop`, `BddBelow.inv`, `IntermediateField.coe_inv`, `Monoid.Coprod.inv_def`, `div_ball_one`, `Polynomial.degree_add_degree_leadingCoeff_inv`, `MeasurableSet.mul_closure_one_eq`, `inv_div_comm`, `mul_inv_eq_one₀`, `tendsto_inv_nhdsGE`, `MeasureTheory.AEEqFun.coeFn_inv`, `hasProd_ite_div_hasProd`, `oneLePart_def`, `CauSeq.inv_apply`, `self_eq_inv₀`, `TendstoLocallyUniformlyOn.fun_inv₀`, `Disjoint.one_notMem_div_set`, `LinearEquiv.smulOfNeZero_symm_apply`, `Subgroup.isComplement_iff_existsUnique_inv_mul_mem`, `Submonoid.subset_pointwise_smul_iff`, `RingAut.coe_one`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem`, `Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg`, `DistribMulAction.toAddEquiv_symm_apply`, `IsUnit.inv_mul_eq_iff_eq_mul`, `tendsto_inv_nhdsLT_zero`, `Finset.card_inter_smul`, `div_eq_one`, `NormedSpace.exp_neg`, `Seminorm.smul_closedBall_preimage`, `Set.one_notMem_div_iff`, `Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero`, `RCLike.inv_pos`, `IsLocalMin.inv`, `TensorProduct.AlgebraTensorModule.congr_one`, `AddAut.inv_def`, `Rep.indResAdjunction_unit_app_hom_hom`, `HahnSeries.inv_def`, `Valuation.Integer.not_isUnit_iff_valuation_lt_one`, `one_div_pos`, `SeminormedGroup.disjoint_nhds_one`, `IsometryEquiv.constSMul_symm`, `Right.inv_pos`, `EMetric.preimage_smul_closedBall`, `inv_le_iff_one_le_mul₀`, `inv_pow_sub_of_lt`, `inv_lt_zero`, `inv_mul_right_le`, `le_mul_inv_iff₀`, `Circle.coe_inv`, `Set.smul_inter_nonempty_iff`, `mul_ball_one`, `Real.Angle.toCircle_neg`, `commutatorElement_eq_one_iff_mul_comm`, `SemiconjBy.inv_symm_left_iff`, `AddSubmonoid.mem_inv_pointwise_smul_iff`, `Subgroup.inv_mem_iff`, `inv_le_iff_one_le_mul₀'`, `Valuation.map_eq_one_of_forall_lt`, `NNReal.tendsto_inverse_atTop_nhds_zero_nat`, `Set.image_mul_left`, `MeasureTheory.measure_inv_smul_inter`, `NNRat.cast_inv`, `TendstoLocallyUniformly.inv₀_of_disjoint`, `singleton_mul_ball_one`, `smul_inv_le_iff_of_neg`, `leOnePart_eq_ite`, `pinGroup.star_eq_inv`, `MulChar.inv_apply'`, `Submonoid.mem_nonunits_iff_of_ne_zero`, `MeasurableEquiv.symm_smul₀`, `List.prod_range_div'`, `Asymptotics.SuperpolynomialDecay.inv_param_mul`, `Submonoid.leftInvEquiv_symm_eq_inv`, `IsometryEquiv.mulRight_symm`, `Filter.Tendsto.inv_tendsto_nhdsLT_zero`, `nnnorm_commutator_sub_one_le`, `IsUnit.mul_eq_one_iff_inv_eq`, `Group.card_pow_eq_card_pow_card_univ`, `TendstoLocallyUniformlyOn.inv`, `Set.inv_op_smul_set_distrib`, `IsIntegral.inv_mem`, `TendstoLocallyUniformly.inv₀`, `Finset.divConst_inv_right`, `AnalyticAt.fun_inv`, `leOnePart_def`, `Finset.mulConst_inv_right`, `inv_mul_cancel_of_invertible`, `EulerProduct.one_sub_inv_eq_geometric_of_summable_norm`, `Finset.preimage_mul_left_one'`, `zpow_neg_mul_zpow_self`, `IsCyclic.mulAutMulEquiv_symm_apply_symm_apply`, `Finset.card_pow_quotient_mul_pow_inter_subgroup_le`, `inv_mul_lt_iff₀'`, `Polynomial.roots_C_mul_X_sub_C`, `ValuativeRel.one_vle_inv`, `Commute.conj_iff`, `SemiconjBy.inv_right_iff`, `pow_sub₀`, `smul_inv_lt_iff_of_neg`, `Homeomorph.divLeft_symm_apply`, `GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero`, `Asymptotics.IsEquivalent.inv`, `Subgroup.leftTransversals.diff_inv`, `MulAction.fixedBy_inv`, `Finset.centroid_pair`, `CoxeterSystem.prod_rightInvSeq`, `orderOf_dvd_iff_zpow_eq_one`, `unitary.mul_inv_mem_iff`, `krullTopology_mem_nhds_one_iff`, `Subsemiring.subset_pointwise_smul_iff`, `oneLePart_lt`, `Finset.ruzsa_triangle_inequality_mul_mulInv_mul`, `CategoryTheory.GrpObj.comp_inv_assoc`, `AddAut.symm_inv`, `div_div_cancel_left`, `Asymptotics.isLittleOTVS_iff_tendsto_inv_smul`, `inv_lt_iff_one_lt_mul₀'`, `Finset.Nonempty.zpow`, `inv_strictAnti₀`, `List.prod_range_div`, `Seminorm.smul_ball_preimage`, `edist_inv_inv`, `SeparationQuotient.mk_eq_one_iff`, `Finset.image_inv`, `Subgroup.closure_inv`, `mabs_eq_inv_self`, `Finset.one_notMem_inv_mul_iff`, `MonoidWithZeroHom.fst_inr_apply_of_ne_zero`, `nhds_one_symm`, `tendsto_inv_nhdsLT_inv`, `Module.Basis.toMatrix_smul_left`, `tendsto_one_iff_norm_tendsto_zero`, `MeasurableEquiv.symm_smul`, `LinearIsometryEquiv.reflections_generate_dim`, `map_mul_right_nhds_one₀`, `krullTopology_mem_nhds_one_iff_of_normal`, `CoxeterSystem.simple_mul_simple_self`, `Set.mulIndicator_diff`, `HasContinuousInv₀.measurableInv`, `Set.inv_mem_center`, `CommGroupWithZero.normalize_eq_one`, `Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point`, `TendstoUniformlyOn.inv`, `Finset.invMulSubgroup_eq_inv_mul`, `CoxeterSystem.getD_leftInvSeq_mul_wordProd`, `mul_inv_le_one_iff_le`, `lt_inv_of_neg`, `lt_mabs`, `hasStrictDerivAt_inv`, `Mathlib.Meta.NormNum.isRat_inv_neg`, `GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv`, `Set.mabs_mulIndicator_symmDiff`, `RootPairing.reflection_inv`, `tendsto_div_nhds_one_iff`, `FractionalIdeal.exists_eq_spanSingleton_mul`, `QuotientGroup.norm_eq_infDist`, `mul_inv_eq_iff_eq_mul₀`, `Homeomorph.mulRight₀_symm_apply`, `GroupTopology.continuous_inv'`, `CategoryTheory.Grp_Class.inv_eq_inv`, `AdjoinRoot.minpoly_powerBasis_gen`, `AntivaryOn.inv`, `Finset.one_notMem_div_iff`, `MulAut.inv_symm`, `ValuationSubring.mem_nonunits_iff`, `one_lt_leOnePart_iff`, `DilationEquiv.one_def`, `HasDerivAt.tendsto_slope_zero`, `sub_one_div_inv_le_two`, `Set.one_mem_div_iff`, `groupCohomology.map_inv_of_isMulCocycle₁`, `inverse_mfderiv_mul_left`, `Representation.leftRegular_norm_apply`, `div_self_of_invertible`, `FDRep.char_orthonormal`, `uniformContinuousOn_inv₀`, `CategoryTheory.GrpObj.comp_inv`, `Finset.card_smul_inter_smul`, `Subgroup.isComplement_iff_existsUnique_mul_inv_mem`, `Set.preimage_mul_left_singleton`, `MulArchimedeanClass.mk_eq_top_iff`, `NumberField.InfinitePlace.mem_stabilizer_mk_iff`, `Representation.ind_mk`, `mabs_choice`, `Rat.cast_inv_nat`, `Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub`, `Filter.Tendsto.inv_tendsto_nhdsGT_zero`, `Set.preimage_smul₀`, `squeeze_one_norm'`, `iter_deriv_inv_linear_sub`, `HNNExtension.ReducedWord.map_fst_eq_and_of_prod_eq`, `groupHomology.d₂₁_single_one_snd`, `RCLike.conj_inv`, `LinearIsometryEquiv.symm_units_smul`, `inv_mul_le_of_le_mul`, `inv_mul_le_one_of_le₀`, `Filter.mul_eq_one_iff`, `IsAlgebraic.inv_iff`, `Finset.mulETransformLeft_inv`, `Submonoid.inv_mem_of_isUnit`, `CategoryTheory.PresheafOfGroups.OneCocycle.ev_refl`, `CommGrpCat.one_apply`, `Subgroup.quotientEquivProdOfLE'_apply`, `groupHomology.d₃₂_single_one_snd`, `MeasureTheory.Measure.inv.instIsMulRightInvariant`, `inf_eq_half_smul_add_sub_abs_sub'`, `monovary_inv₀`, `Set.preimage_mul_right_one'`, `div_lt_one'`, `AntivaryOn.inv_right₀`, `Valuation.integer.v_irreducible_lt_one`, `Set.image_inv_Iic`, `sum_Ioc_inv_sq_le_sub`, `SemidirectProduct.inv_left`, `div_inv_eq_mul`, `Finset.inv_smul_mem_iff₀`, `groupHomology.isBoundary₀_iff`, `PowerSeries.C_inv`, `Subgroup.mem_inv_pointwise_smul_iff`, `one_div_mul_eq_div`, `CategoryTheory.ActionCategory.homOfPair.val`, `AddSubgroup.pointwise_smul_le_iff`, `mabs_eq_max_inv`, `LinearEquiv.transvection.inv_eq'`, `IsUnit.mul_eq_one_iff_eq_inv`, `Submonoid.mem_closure_inv`, `LinearIsometryEquiv.symm_smul_apply`, `invOf_eq_inv`, `Mathlib.Tactic.FieldSimp.zpow'_neg`, `sub_inv_antitoneOn_Icc_right`, `invOf_div`, `Interval.mul_eq_one_iff`, `Finset.mulETransformRight_snd`, `div_mul_cancel_right₀`, `IsUniformGroup.ext_iff`, `Finset.centroid_pair_fin`, `AddAut.one_def`, `Hyperreal.st_inv`, `edist_inv`, `Valuation.IsNontrivial.exists_lt_one`, `one_div_mul_cancel`, `Polynomial.degree_leadingCoeff_inv`, `MulAut.inv_def`, `RegularWreathProduct.one_left`, `Finset.coe_zpow`, `Asymptotics.IsBigOWith.inv_rev`, `IsMulFreimanHom.inv`, `Valuation.Integers.isUnit_iff_valuation_eq_one`, `SkewMonoidAlgebra.coeff_mul_left`, `CategoryTheory.Grp.Hom.hom_inv`, `ContDiffOn.inv`, `Finset.pluennecke_ruzsa_inequality_pow_div_pow_div`, `LieAlgebra.IsKilling.traceForm_coroot`, `Finset.centroidWeights_eq_const`, `FiniteMulArchimedeanClass.mk_inv`, `Commute.inv_mul_cancel_assoc`, `ClassGroup.mk_eq_one_of_coe_ideal`, `ValuativeRel.inv_vle_one`, `AddSubgroup.mem_inv_pointwise_smul_iff₀`, `DihedralGroup.r_one_pow_n`, `analyticAt_inv`, `FDRep.char_dual`, `IsometryEquiv.coe_one`, `absorbent_iff_inv_smul`, `AddAut.one_apply`, `MeasureTheory.quasiMeasurePreserving_inv`, `GrpCat.one_apply`, `Metric.preimage_smul_ball`, `Function.Antiperiodic.mul_const_inv`, `MeasureTheory.regular_inv_iff`, `Unitary.star_eq_inv`, `orderOf_inv`, `toPrincipalIdeal_def`, `inv_lt_div_iff_lt_mul`, `le_inv_self_iff`, `BddBelow.range_inv`, `IsUnit.mul_mul_div`, `inv_antitoneOn_Ioi`, `mul_eq_one_iff_eq_inv'`, `Action.diagonalSuccIsoTensorTrivial_hom_hom_apply`, `OrderIso.mulLeft₀_symm`, `IsometryEquiv.mulLeft_symm`, `IsIntegral.inv`, `IsUnit.mul_inv_eq_one`, `RegularWreathProduct.inv_right`, `MulAut.conjNormal_inv_apply`, `Subring.subset_pointwise_smul_iff`, `Submodule.mulExact_unitsMap_spanSingleton_unitsToPic`, `SemidirectProduct.inv_right`, `DihedralGroup.one_def`, `IsLowerSet.inv`, `UniformOnFun.hasBasis_nhds_one`, `instContinuousInvSubtypeMemSubmonoidUnitaryOfContinuousStar`, `mabs_lt`, `rotation_symm`, `div_mul_eq_div_mul_one_div`, `Finset.mem_inv_smul_finset_iff₀`, `CoxeterSystem.not_isRightDescent_one`, `Set.inv_mem_Icc_iff`, `MeromorphicAt.inv`, `Set.pairwise_disjoint_smul_iff`, `LinearEquiv.coe_one`, `DilationEquiv.inv_def`, `Subgroup.zpowers_eq_zpowers_iff`, `MeromorphicOn.fun_inv`, `one_le_div₀`, `tprod_inv`, `spectrum.inv₀_mem_inv`, `Finset.Nonempty.one_mem_div`, `Meromorphic.inv`, `Set.mem_smul_set_iff_inv_smul_mem`, `MeasureTheory.mlconvolution_assoc`, `inv_le_inv'`, `inv_closedBall`, `HasDerivAt.fun_inv`, `DilationEquiv.coe_inv`, `OrderIso.smulRightDual_symm_apply`, `inv_nonpos`, `groupCohomology.smul_map_inv_sub_map_inv_of_isCocycle₂`, `Filter.tendsto_comp_inv_atTop_iff`, `ValuativeRel.inv_vlt_one`, `hasStrictFDerivAt_inv'`, `PowerSeries.inv_eq_inv_aux`, `RegularWreathProduct.mul_def`, `Finset.subset_smul_finset_iff₀`, `mul_inv_lt_iff₀'`, `MonoidAlgebra.mul_apply_right`, `IsUnit.div_div_cancel_left`, `deriv_inv'`, `LinearEquiv.det_coe_symm`, `analyticAt_inv_one_sub`, `groupHomology.d₁₀_single_inv`, `IsTopologicalGroup.exist_mul_closure_nhds`, `inv_div_inv`, `Rep.indToCoindAux_snd_mul_inv`, `Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid`, `QuotientGroup.preimage_mk_one`, `Commute.mul_inv_eq_mul_inv_iff`, `CategoryTheory.PreGaloisCategory.IsFundamentalGroup.non_trivial'`, `one_div_nonpos`, `Filter.Tendsto.inv_tendsto_atTop`, `MeasureTheory.tendsto_measure_smul_diff_isCompact_isClosed`, `RCLike.inv_eq_conj`, `iter_deriv_inv_linear`, `MonovaryOn.inv`, `AddAut.mulLeft_apply_symm_apply`, `CategoryTheory.PresheafOfGroups.OneCochain.inv_ev`, `tendsto_inverse_atTop_nhds_zero_nat`, `QuotientGroup.rightRel_eq`, `MeasureTheory.measurePreserving_prod_inv_mul`, `WeierstrassCurve.Affine.Point.toClass_eq_zero`, `ContinuousInv₀.measurableInv`, `inv_lt_div_iff_lt_mul'`, `OrderIso.mulRight_symm`, `inv_cthickening`, `Polynomial.smul_eval`, `Finset.pluennecke_ruzsa_inequality_pow_mul`, `MeasureTheory.measure_mul_lintegral_eq`, `le_inv'`, `smul_eq_iff_eq_inv_smul`, `inv_mul_eq_of_eq_mul`, `CoxeterSystem.IsReflection.isReflection_inv`, `antilipschitzWith_inv_iff`, `ValuationRing.isInteger_or_isInteger`, `CommRing.Pic.mk_self`, `cmp_div_one'`, `eq_on_inv₀`, `LocallyLipschitzOn.inv`, `CoxeterSystem.isReflection_conj_iff`, `CoxeterSystem.isLeftDescent_inv_iff`, `oneLePart_eq_self`, `MeasureTheory.measurePreserving_mul_prod_inv`, `eq_inv_smul_iff₀`, `mulTSupport_inv`, `monovary_inv_left₀`, `groupHomology.single_one_mem_boundaries₁`, `Action.leftDual_ρ`, `Set.nonempty_image_mulRight_inv_inter_iff`, `inv_le_one₀`, `IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq`, `Nat.inv_pos_of_nat`, `exists_inv_mem_iff_exists_mem`, `LinearIsometryEquiv.one_def`, `GenContFract.IntFractPair.exists_succ_nth_stream_of_fr_zero`, `gauge_smul_left`, `AddSubgroup.le_pointwise_smul_iff`, `ContMDiffOn.inv`, `GroupCone.oneLE.isMaxMulCone`, `Subgroup.IsComplement.toRightFun_mul_inv_mem`, `Derivation.leibniz_div_const`, `MulAut.apply_inv_self`, `NumberField.ComplexEmbedding.IsConj.comp`, `mul_inv_eq_of_eq_mul`, `OrderIso.divLeft_symm_apply`, `one_le_mabs`, `IntermediateField.inv_mem`, `MeasureTheory.inv_smul_ae_eq_self`, `Valuation.one_le_val_iff`, `groupHomology.d₂₁_single`, `DFinsupp.prod_inv`, `Equiv.divRight_eq_mulRight_inv`, `ValuationSubring.valuation_eq_one_iff`, `leOnePart_eq_inv'`, `Set.mulIndicator_compl`, `Circle.exp_eq_one`, `Function.Periodic.const_smul`, `TrivSqZeroExt.inv_zero`, `QuotientGroup.image_coe`, `Finset.divConst_inv_left`, `inv_le_of_neg`, `IsUnit.mul_inv_eq_iff_eq_mul`, `Subgroup.equivSMul_symm_apply_coe`, `IsTopologicalGroup.one_eq_hSpace_e`, `Commute.inv_right₀`, `inv_lt_self_iff`, `Set.inv_Iic`, `CauSeq.const_inv`, `MeasureTheory.Integrable.comp_inv`, `IsFractionRing.associated_den_num_inv`, `birkhoffAverage_apply_sub_birkhoffAverage`, `Algebra.normalizedTrace_eq_of_fininteDimensional_apply`, `QuaternionGroup.a_zero`, `NormedSpace.expSeries_hasSum_exp_of_mem_ball'`, `div_eq_inv_mul`, `MeasureTheory.Measure.IsHaarMeasure.isInvInvariant_of_innerRegular`, `compl_mul_closure_one_eq_iff`, `coe_powCardSubgroup`, `Polynomial.div_C_mul`, `IsUniformGroup.cauchy_iff_tendsto`, `Hyperreal.infinitesimal_pos_iff_infinitePos_inv`, `oneLePart_eq_ite`, `Int.log_of_right_le_one`, `IsCompact.div_closedBall_one`, `Fin.partialProd_right_inv`, `div_div_cancel_left'`, `ClassGroup.mk0_eq_mk0_inv_iff`, `AntivaryOn.inv₀`, `MeasureTheory.Measure.measurePreserving_mul_right_inv`, `MonoidAlgebra.mul_single_apply`, `inv_lt_one_iff₀`, `SemidirectProduct.right_inl`, `HNNExtension.equiv_symm_eq_conj`, `analyticOnNhd_inv`, `GenContFract.sub_convs_eq`, `Set.disjoint_smul_set_left`, `Subgroup.IsComplement.equiv_fst_eq_mul_inv`, `Mathlib.Tactic.FieldSimp.zpow'_zero_of_ne_zero`, `groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁`, `inv_le_of_mabs_le`, `FreeGroup.lift_mk`, `div_eq_one_of_eq`, `monovary_inv_right`, `Representation.dual_apply`, `ProbabilityTheory.gaussianPDFReal_mul`, `Subsemiring.pointwise_smul_le_iff₀`, `Submonoid.closure_inv`, `NormedDivisionRing.to_hasContinuousInv₀`, `EMetric.preimage_smul_ball`, `inv_smul_le_iff_of_neg`, `one_div_neg_one_eq_neg_one`, `conj_eq_one_iff`, `Submonoid.fromLeftInv_eq_inv`, `mulInvariantVectorField_smul`, `Left.one_le_inv_iff`, `CoxeterSystem.getElem_leftInvSeq`, `homothety_inv_two`, `IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk`, `List.prod_drop_succ`, `inv_ball`, `Set.smul_set_subset_iff₀`, `smul_ball_one`, `Rep.indResHomEquiv_apply_hom`, `tendsto_inv_nhdsLT`, `inv_mul_eq_inv_mul_iff_mul_eq_mul`, `ValuativeRel.one_srel_inv`, `Set.disjoint_smul_set_right`, `IsUniformGroup.cauchy_map_iff_tendsto_swapped`, `Filter.tendsto_inv₀_nhdsNE_zero`, `Valuation.isEquiv_iff_val_lt_one`, `DifferentiableWithinAt.fun_inv`, `HahnSeries.inv_single`, `Nonneg.val_inv_unitsEquivPos_symm_apply_coe`, `Valuation.IsUniformizer.val_lt_one`, `orbit_subgroup_one_eq_self`, `LinearEquiv.one_eq_refl`, `hasDerivWithinAt_inv`, `locallyLipschitz_inv_iff`, `Equiv.mulRight_symm_apply`, `GroupLieAlgebra.bracket_def`, `Commute.inv_inv`, `IsIntegral.inv_mem_adjoin`, `mul_inv_le_of_le_mul₀`, `Set.inv_Ioo_0_left`, `MonoidHom.mulExact_iff`, `OpenPartialHomeomorph.hasStrictDerivAt_symm`, `multipliable_inv_iff`, `LinearEquiv.inv_mem_transvections_iff`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem`, `LinearIsometryEquiv.inv_def`, `Valuation.mem_integer_iff`, `NumberField.ComplexEmbedding.IsReal.isConjGal_one`, `norm_le_zero_iff'`, `MonoidHom.fiberEquiv_apply`, `NormedCommGroup.tendsto_nhds_one`, `differentiableAt_inv`, `Equiv.Perm.mem_conj_support`, `AnalyticAt.inv`, `Set.inv_Iio`, `Subgroup.zpowers_one_eq_bot`, `MeromorphicNFAt.inv`, `inv_le_div_iff_le_mul`, `Representation.ind_apply`, `LinearEquiv.baseChange_one`, `LinearOrderedCommGroup.Subgroup.exists_generator_lt_one`, `NNRat.cast_inv_of_ne_zero`, `Submonoid.IsUnit.Submonoid.coe_inv`, `Subgroup.normalizerMonoidHom_apply_symm_apply_coe`, `CoxeterSystem.isRightInversion_inv_iff`, `algebraMap.coe_inv`, `ValuationSubring.top_coe_inv`, `lt_inv_iff_mul_lt_one`, `Function.support_inv'`, `tendsto_algebraMap_inv_atTop_nhds_zero_nat`, `edist_one_left`, `ValuationSubring.subset_pointwise_smul_iff`, `Function.Periodic.mul_const`, `RegularWreathProduct.mul_left`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply`, `min_inv_inv'`, `MeasureTheory.mconv_withDensity_eq_mlconvolution₀`, `lt_inv_mul_iff_mul_lt`, `Rep.diagonalSuccIsoFree_hom_hom_single`, `Subgroup.disjoint_iff_mul_eq_one`, `ContMDiffMap.coe_inv`, `derivWithin_fun_inv'`, `hasFDerivAt_inv'`, `mulInvariantVectorField_eq_mpullback`, `Set.image_inv`, `inv_thickening`, `NonarchimedeanGroup.multipliable_iff_tendsto_cofinite_one`, `Subalgebra.inv_mem_of_algebraic`, `uniformContinuous_inv`, `OpenPartialHomeomorph.unitBallBall_symm_apply`, `AddSubgroup.le_pointwise_smul_iff₀`, `QuotientGroup.eq_one_iff`, `FDRep.scalar_product_char_eq_finrank_equivariant`, `CategoryTheory.PresheafOfGroups.OneCohomologyRelation.refl`, `spectrum.resolvent_isBigO_inv`, `GrpCat.FilteredColimits.colimit_one_eq`, `le_inv_mul_of_mul_le`, `isometry_inv`, `Finset.mul_eq_one_iff`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset`, `NormedSpace.expSeries_summable_of_mem_ball'`, `mul_inv_le_inv_mul_iff`, `Subgroup.closure_eq_bot_iff`, `SemiconjBy.eq_one_iff`, `Int.neg_log_inv_eq_clog`, `mem_rightCoset_iff`, `infEDist_inv_inv`, `Representation.inv_self_apply`, `Antitone.inv`, `AddSubmonoid.le_pointwise_smul_iff₀`, `AntivaryOn.inv_right`, `AddCircle.equivAddCircle_symm_apply_mk`, `Filter.NeBot.one_le_div`, `IsUnit.one_div_mul_cancel`, `Monoid.PushoutI.NormalWord.empty_head`, `MonovaryOn.inv_left`, `mul_inv_lt_inv_mul_iff`, `Finset.preimage_mul_right_singleton`, `mul_inv_mul_cancel`, `TendstoLocallyUniformly.fun_inv`, `RatFunc.single_inv`, `SignType.coe_zpow`, `closedBall_one_mul_singleton`, `TrivSqZeroExt.mul_inv_rev`, `nhds_basis_mabs_div_lt`, `AntivaryOn.inv_left`, `AddAut.neg_conj_apply`, `MeasureTheory.measure_union_inv_smul`, `groupHomology.single_isCycle₁_of_mem_fixedPoints`, `RCLike.ofReal_inv`, `Rep.coinvariantsTensorIndInv_mk_tmul_indMk`, `PerfectClosure.mk_inv`, `Commute.inv_left₀`, `List.prod_zpow`, `Set.smul_set_subset_iff_subset_inv_smul_set`, `antivaryOn_inv_right₀`, `OneHom.zpow_apply`, `Equiv.mulRight_one`, `inv_lt_of_neg`, `SemidirectProduct.left_inr`, `NumberField.ComplexEmbedding.isConj_one_iff`, `PowerSeries.smul_inv`, `smul_inv''`, `mul_inv_eq_iff_eq_mul`, `Finset.image_mul_right'`, `inv_mul_le_iff_le_mul`, `enorm_inv`, `IsTopologicalDivisionRing.toContinuousInv₀`, `div_lt_one₀`, `Valued.toNormedField.norm_lt_one_iff`, `two_mul_le_add_mul_sq`, `Subgroup.IsComplement.equiv_snd_eq_inv_mul`, `gaussSum_mul_gaussSum_eq_card`, `Subgroup.le_pointwise_smul_iff₀`, `inv_eq_self_of_exponent_two`, `nhds_translation_inv_mul`, `Polynomial.mod_def`, `nhds_translation_div`, `Commute.inv_add_inv`, `CoxeterSystem.length_eq_zero_iff`, `DirectLimit.inv_def`, `Homeomorph.mulLeft_symm`, `mulTSupport_div`, `Subgroup.isLeast_of_closure_iff_eq_mabs`, `Valuation.Integers.one_of_isUnit`, `Action.ρAut_apply_inv`, `groupHomology.d₂₁_single_ρ_add_single_inv_mul`, `Circle.coe_one`, `conjugate_commutatorElement`, `Equiv.inv_mulLeft`, `Int.neg_clog_inv_eq_log`, `hasFDerivAt_inv`, `map_mul_left_nhds_one`, `inv_lt_inv_iff`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀`, `Differentiable.inv`, `inv_nonpos'`, `tendsto_tprod_compl_atTop_one`, `Action.ρ_inv_self_apply`, `mulSupport_comp_inv_smul₀`, `HahnSeries.cardSupp_inv_le`, `mabs_div_le_one`, `Set.injOn_iff_map_eq_one`, `ValueDistribution.logCounting_inv`, `Function.Antiperiodic.const_inv_smul`, `NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff`, `exists_one_lt'`, `unitary.star_eq_inv`, `MulAut.one_def`, `MeromorphicAt.fun_inv`, `GrpCat.SurjectiveOfEpiAuxs.one_smul`, `Set.mem_smul_set_iff_inv_smul_mem₀`, `MvPowerSeries.smul_inv`, `Submodule.mulExact_unitsToPic_mapAlgebra`, `Subgroup.closure_diff_one`, `one_div_neg_eq_neg_one_div`, `DihedralGroup.inv_r`, `discreteTopology_iff_isOpen_singleton_one`, `one_div_mul_one_div`, `CategoryTheory.PresheafOfGroups.OneCohomologyRelation.symm`, `MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot`, `UniformSpace.Completion.hatInv_extends`, `NumberField.IsCMField.complexConj_torsion`, `AnalyticOnNhd.fun_inv`, `MeasureTheory.integral_inv_eq_self`, `IsArithFrobAt.conj`, `lt_inv_mul_of_mul_lt`, `Function.Periodic.const_mul`, `Rep.barComplex.d_single`, `csInf_inv`, `IsPrimitiveRoot.zpow_eq_one_iff_dvd`, `Monoid.Coprod.mk_of_inv_mul`, `RestrictedProduct.mulSingle_div`, `Subgroup.closure_union_one`, `sub_inv_antitoneOn_Iio`, `le_inv_mul_iff_le`, `AddCircle.toCircle_neg`, `MeasurableDiv.toMeasurableInv`, `Set.mulIndicator_diff'`, `Set.inv_mem_centralizer`, `dist_inv`, `Valuation.val_le_one_iff`, `IsMulTorsionFree.zpow_eq_one_iff`, `uniformity_eq_comap_nhds_one'`, `Polynomial.eval_smul'`, `Transcendental.linearIndependent_sub_inv`, `mulInvariantVectorField_add`, `Units.inv_mul'`, `CauSeq.lim_inv`, `Valued.toNormedField.one_le_norm_iff`, `ArchimedeanClass.stdPart_inv`, `SemiconjBy.inv_symm_left_iff₀`, `rat_inv_continuous_lemma`, `mapClusterPt_inv_atTop_pow`, `Finset.mulETransformLeft_snd`, `one_lt_ltOnePart_iff`, `slope_def_module`, `inv_antitoneOn_Icc_left`, `Unitary.star_eq_inv'`, `Nat.cast_inv_le_one`, `LinearEquiv.transvection.inv_eq`, `inv_eq_of_aeval_divX_ne_zero`, `List.alternatingProd_cons`, `Subfield.inv_mem'`, `inv_mul_eq_iff_eq_mul`, `MulAction.toPerm_one`, `SubfieldClass.toInvMemClass`, `div_self`, `uniformity_eq_comap_nhds_one`, `MeasureTheory.mlconvolution_comm`, `AddChar.inv_apply_eq_conj`, `zpow_sub`, `leftInverse_mul_right_inv_mul`, `tendsto_inv_atTop_nhds_zero_nat`, `Subgroup.mem_bot`, `groupHomology.isBoundary₁_iff`, `WeierstrassCurve.Affine.Point.toClass_apply`, `Antivary.inv_left`, `inv_neg_one`, `antivary_inv_left₀`, `HasDerivAt.of_local_left_inverse`, `Affine.Simplex.faceOppositeCentroid_eq_affineCombination`, `Polynomial.coeff_preHilbertPoly_self`, `Function.Periodic.const_inv_smul₀`, `Filter.IsBoundedUnder.isLittleO_sub_self_inv`, `MeasureTheory.aemeasurable_mlconvolution`, `locallyLipschitzOn_inv_iff`, `dist_one_right`, `LinearEquiv.coe_toLinearMap_one`, `Group.exponent_dvd_iff_forall_zpow_eq_one`, `monovaryOn_inv_right₀`, `Subring.mem_inv_pointwise_smul_iff₀`, `Set.inv_mem_Ico_iff`, `finprod_inv_distrib`, `Commute.commutator_eq`, `infEDist_inv`, `WithZero.val_inv_logOrderIso_symm_apply`, `LipschitzOnWith.inv`, `Int.clog_inv`, `Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single`, `Subsemiring.mem_inv_pointwise_smul_iff`, `NonemptyInterval.inv_pure`, `le_inv_smul_iff_of_pos`, `MonoidHom.mulExact_of_comp_eq_one_of_ker_le_range`, `one_lt_div₀`, `List.alternatingProd_reverse`, `uniformity_eq_comap_inv_mul_nhds_one_swapped`, `GenContFract.of_s_succ`, `smul_inv₀'`, `AddChar.inv_mulShift`, `star_inv`, `ArchimedeanClass.mk_inv`, `inv_lt_inv₀`, `Ideal.mem_inv_pointwise_smul_iff`, `GroupNormClass.eq_one_of_map_eq_zero`, `Set.preimage_mul_left_one'`, `DihedralGroup.sr_mul_self`, `RootPairing.Equiv.indexEquiv_inv`, `differentiableOn_inv`, `GroupFilterBasis.inv'`, `mabs_le_one`, `Subgroup.coe_bot`, `RCLike.inv_I`, `div_le_one₀`, `GenContFract.IntFractPair.succ_nth_stream_eq_some_iff`, `TrivSqZeroExt.inv_inr`, `tendsto_mabs_nhdsNE_one`, `HasDerivAt.inv`, `UniformContinuous.fun_inv₀`, `groupHomology.mem_cycles₁_iff`, `Multiset.prod_map_inv`, `inv_antitoneOn_Iio`, `map_inv_intCast_smul`, `inv_anti₀`, `IsUnit.inv_mul_cancel_right`, `HNNExtension.ReducedWord.exists_normalWord_prod_eq`, `Mathlib.Tactic.FieldSimp.NF.inv_eq_eval`, `Filter.tendsto_inv₀_cobounded'`, `Homeomorph.mulRight_symm`, `Finset.smul_inv_mul_opSMul_eq_mul_of_doubling_lt_three_halves`, `Subgroup.pow_exponent_eq_one`, `Function.Periodic.const_inv_smul`, `MeasureTheory.AEEqFun.inv_toGerm`, `isCancelSMul_iff_eq_one_of_smul_eq`, `inv_le_iff_one_le_mul`, `antivary_inv_right`, `SkewMonoidAlgebra.coeff_single_mul`, `groupHomology.single_mem_cycles₂_iff_inv`, `groupHomology.d₁₀_single`, `Set.empty_zpow`, `CoxeterSystem.length_inv`, `tendsto_inv_nhdsGT`, `IsDiscrete.exists_nhds_eq_one_of_image_mulLeft_inter_nonempty`, `Finset.prod_Ico_eq_mul_inv`, `mabs_cases`, `Valuation.inversion_estimate`, `Finset.image_mul_left`, `Affine.Simplex.centroid_vsub_eq`, `IsGLB.inv`, `Subgroup.Normal.conj_mem'`, `MeasureTheory.IntegrableOn.comp_inv`, `Unitary.coe_inv`, `LinearIsometryEquiv.one_trans`, `IsKleinFour.eq_finset_univ`, `star_inv₀`, `Set.inv_op_smul_set_distrib₀`, `norm_eq_of_mem_sphere'`, `HasDerivWithinAt.fun_inv`, `le_inv_mul_left`, `Filter.Tendsto.inv_tendsto_atBot`, `FDRep.simple_iff_char_is_norm_one`, `one_lt_inv_mul₀`, `GenContFract.IntFractPair.stream_succ_of_some`, `Rep.indResHomEquiv_symm_apply_hom`, `inv_eq_of_root_of_coeff_zero_ne_zero`, `HasDerivAt.tendsto_slope_zero_right`, `Monoid.PushoutI.NormalWord.eq_one_of_smul_normalized`, `self_eq_inv`, `Subgroup.Normal.conj_mem`, `Set.subset_smul_set_iff₀`, `FractionalIdeal.spanSingleton_inv`, `nndist_one_right`, `AddCircle.homeomorphAddCircle_symm_apply_mk`, `SemiconjBy.inv_right_iff₀`, `inv_mul_le_iff₀'`, `Finset.image_mul_right`, `DihedralGroup.r_zero`, `AddAut.inv_apply_self`, `inv_add_inv`, `Matrix.UnitaryGroup.inv_apply`, `CategoryTheory.PreGaloisCategory.instContinuousInvAutFunctorFintypeCat`, `Left.one_lt_inv_iff`, `StrictAntiOn.inv`, `uniformity_eq_comap_nhds_one_left`, `Set.one_mem_inv_mul_iff`, `inv_mul_eq_one`, `RCLike.inv_re`, `MeasureTheory.one_le_div_ae`, `AddSubmonoid.pointwise_smul_le_iff₀`, `CompletableTopField.nice`, `AnalyticOnNhd.inv`, `finprod_mem_inv_distrib`, `NonemptyInterval.mul_eq_one_iff`, `WithZeroTopology.instContinuousInv₀`, `OneHom.div_apply`, `GroupFilterBasis.t2Space_iff`, `NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat`, `List.prod_inv`, `injective_iff_map_eq_one`, `MeasureTheory.QuotientMeasureEqMeasurePreimage.covolume_ne_top`, `AddValuation.map_inv`, `Lagrange.nodalWeight_eq_eval_derivative_nodal`, `QuotientGroup.out_conj_pow_minimalPeriod_mem`, `edist_mulIndicator`, `one_lt_inv₀`, `Padic.valuation_inv`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `QuaternionGroup.xa_pow_four`, `Subsemiring.le_pointwise_smul_iff₀`, `one_le_oneLePart`, `GenContFract.IntFractPair.stream_succ`, `inv_le_inv₀`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply`, `UniformSpace.Completion.coe_inv`, `QuotientGroup.leftRel_apply`, `Lagrange.eval_basis_not_at_node`, `mul_inv_le_iff₀'`, `NonemptyInterval.inv_mem_inv`, `Commute.inv_right`, `inv_eq_iff_mul_eq_one`, `fderiv_inv'`, `tendsto_prod_nat_add`, `IsTopologicalGroup.isInducing_iff_nhds_one`, `Subgroup.mk_eq_one`, `AffineEquiv.one_def`, `monovaryOn_inv_left`, `Finset.convolution_op_smul_eq_convolution_mul_inv`, `Filter.inv_cobounded`, `MeasureTheory.quasiMeasurePreserving_inv_mul_swap`, `MulEquiv.inv_apply`, `mabs_eq_self`, `CoxeterSystem.getD_rightInvSeq`, `MeasureTheory.measure_mul_closure_one`, `MulAut.conjNormal_apply`, `DihedralGroup.inv_sr`, `SeminormedGroup.tendstoUniformlyOn_one`, `NormedSpace.exp_eq_ofScalarsSum`, `MonoidAlgebra.mul_apply_left`

IsRightCancelAdd

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`toGrindAddRightCancel` 📖	mathematical	—	`AddSemigroup.toAdd`	—	`add_right_cancel`

Semigroup

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`to_isAssociative` 📖	mathematical	—	`toMul`	—	`mul_assoc`
`to_isLawfulIdentity` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	`one_mul` `mul_one`

SubtractionMonoid

Definitions

Name	Category	Theorems
`toSubNegZeroMonoid` 📖	CompOp	6041 math, 1 bridge math: `singleton_sub_closedBall_zero`, `SlashAction.slash_eq_zero_iff`, `QuadraticMap.polar_zero_left`, `withSeminorms_iff_mem_nhds_isVonNBounded`, `Hyperreal.InfiniteNeg.neg`, `IsAddUnit.neg_add_cancel_right`, `Matrix.l2_opNorm_toEuclideanCLM`, `Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁`, `MeasureTheory.MemLp.eLpNorm_indicator_le_of_meas`, `ValueDistribution.logCounting_zero`, `Quaternion.normSq_eq_zero`, `norm_eq_zero`, `norm_eq_of_mem_sphere`, `RingCone.nonneg.isMaxCone`, `TangentBundle.tangentMap_tangentBundle_pure`, `Set.preimage_add_right_zero`, `Real.Angle.abs_toReal_neg_coe_eq_self_iff`, `sub_neg`, `LinearMap.IsSymmetric.clm_adjoint_eq`, `Num.cast_to_int`, `Asymptotics.isBigO_const_const_iff`, `negPart_nonpos`, `ContinuousMap.toLp_inj`, `LieHom.coe_zero`, `Real.hasDerivAt_fourier`, `HurwitzZeta.isBigO_atTop_evenKernel_sub`, `Matrix.isTotallyUnimodular_iff`, `Odd.neg`, `Quaternion.star_mul_self`, `HurwitzZeta.expZeta_zero`, `TemperedDistribution.lineDerivOpCLM_eq`, `continuousSMul_sphere_ball`, `Quaternion.coe_normSq_add`, `AbsoluteValue.map_neg`, `ball_sub`, `LieModule.trivial_iff_lower_central_eq_bot`, `MeasureTheory.Lp.toTemperedDistributionCLM_apply`, `Unitization.inr_neg`, `nhds_hasBasis_absConvex_open`, `fderiv_iteratedFDeriv`, `WithLp.ofLp_listSum`, `EuclideanGeometry.Sphere.secondInter_neg`, `groupHomology.π_comp_H2Iso_hom_assoc`, `FormalMultilinearSeries.comp_rightInv_aux1`, `MeasureTheory.Measure.haar.nonempty_iInter_clAddPrehaar`, `Set.neg_Ioo`, `tendsto_zero_iff_meromorphicOrderAt_pos`, `NormedSpace.exp_neg_of_mem_ball`, `Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul`, `norm_smul_le`, `LinearMap.mkContinuous₂_norm_le'`, `zsmul_neg`, `FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_changeOrigin`, `upperClosure_zero`, `ZeroHom.zsmul_apply`, `MeasureTheory.eLpNormEssSup_const_smul_le`, `Finset.Nonempty.zero_mem_sub`, `ContinuousMultilinearMap.norm_mkPiRing`, `Real.fourierInv_eq_fourier_neg`, `RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm`, `ContinuousLinearMap.derivWithin_of_bilinear`, `AddMonoidAlgebra.mul_single_apply`, `HasStrictFDerivAt.isLittleOTVS`, `Bundle.ContMDiffRiemannianMetric.isVonNBounded`, `SummationFilter.instLeAtTopSymmetricIoo`, `Quaternion.star_imJ`, `MvPolynomial.coeff_neg`, `Asymptotics.isBigO_neg_left`, `LieAlgebra.IsKilling.iInf_ker_weight_eq_bot`, `pow_eq_neg_pow_iff`, `Convex.neg`, `differentiableAt_comp_neg`, `MvPolynomial.degrees_neg`, `HahnEmbedding.IsPartial.baseEmbedding_le`, `SkewMonoidAlgebra.single_neg`, `hasDerivWithinAt_Iio_iff_Iic`, `RingPreordering.hasIdealSupport_iff`, `TrivSqZeroExt.exp_inr`, `LinearMap.mkContinuous₂_apply`, `Set.neg_Ioi`, `AffineMap.hasStrictDerivAt_lineMap`, `ContinuousLinearMap.isPositive_iff_eq_sum_rankOne`, `InnerProductSpace.isPositive_rankOne_self`, `Quaternion.re_star`, `Seminorm.absorbent_closedBall_zero`, `negAddMonoidHom_apply`, `CliffordAlgebra.involute_eq_of_mem_odd`, `groupHomology.mapCycles₂_comp_assoc`, `Matrix.invOf_fromBlocks₂₂_eq`, `WeierstrassCurve.Projective.addY_neg`, `Real.Angle.neg_coe_abs_toReal_of_sign_nonpos`, `Function.Periodic.nsmul_sub_eq`, `IsDiscrete.exists_nhds_eq_zero_of_image_addLeft_inter_nonempty`, `Polynomial.ascPochhammer_smeval_neg_eq_descPochhammer`, `CochainComplex.HomComplex.Cochain.fromSingleMk_neg`, `IsTopologicalAddGroup.isInducing_iff_nhds_zero`, `sub_pos`, `Quaternion.add_imJ`, `Seminorm.mem_ball_zero`, `MDifferentiableOn.clm_postcomp`, `locallyLipschitz_neg_iff`, `CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg`, `hasDerivWithinAt_ofNat`, `ContinuousLinearMap.analyticWithinAt_bilinear`, `Complex.restrictScalars_one_smulRight'`, `Matrix.GLPos.coe_neg_apply`, `QuotientAddGroup.leftRel_apply`, `Matrix.frobeniusIsBoundedSMul`, `Quaternion.instSMulCommClass`, `Set.preimage_add_right_zero'`, `lt_neg`, `ContinuousLinearMap.compSL_apply`, `ContinuousLinearMap.continuous₂`, `Quaternion.add_imK`, `Finset.zero_mem_sub_iff`, `Matrix.linfty_opNorm_diagonal`, `SchwartzMap.neg_apply`, `NonemptyInterval.length_zero`, `hasDerivWithinAt_add_const_iff`, `Hyperreal.infinite_neg`, `AddGroupFilterBasis.t2Space_iff`, `FormalMultilinearSeries.comp_partialSum`, `tendsto_birkhoffAverage_apply_sub_birkhoffAverage'`, `Asymptotics.isBigO_zero_right_iff`, `FreeAbelianGroup.neg_bind`, `WithCStarModule.neg_fst`, `binomialSeries_eq_ordinaryHypergeometricSeries`, `LucasLehmer.X.two_mul_ω_pow`, `zpow_eq_zpow_iff_of_ne_zero₀`, `LinearOrderedAddCommGroupWithTop.sub_pos`, `derivWithin_zero_of_frequently_mem`, `Finsupp.neLocus_neg`, `SchwartzMap.integral_sesq_fourier_fourier`, `Bornology.isVonNBounded_iff_tendsto_smallSets_nhds`, `Int.cast_neg`, `sub_lt_zero`, `neg_le_self_iff`, `WithSeminorms.image_isVonNBounded_iff_seminorm_bounded`, `Function.Surjective.isLieAbelian`, `AddMonoidHom.exact_of_comp_of_mem_range`, `Matrix.norm_diagonal`, `CompactlySupportedContinuousMap.coe_sub`, `Real.hasFDerivAt_fourierChar_neg_bilinear_left`, `instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere`, `hasStrictDerivAt_intCast`, `CategoryTheory.ShiftedHom.neg_comp`, `Action.neg_hom`, `EuclideanGeometry.reflection_orthogonal_vadd`, `isSMulRegular_iff_mem_nonZeroSMulDivisors`, `List.alternatingSum_append`, `MeasureTheory.eLpNorm_smul_le_mul_eLpNorm`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn`, `groupCohomology.mem_cocycles₂_def`, `Quaternion.im_add`, `sq_eq_one_iff`, `ExteriorAlgebra.ι_eq_algebraMap_iff`, `MeasureTheory.LocallyIntegrableOn.neg`, `fwdDiff_const`, `SchwartzMap.coe_zero`, `eq_zero_or_nnnorm_pos`, `LieAlgebra.abelian_radical_of_hasTrivialRadical`, `ValueDistribution.proximity_zero`, `curveIntegral_smul`, `Quaternion.snd_imJ_dualNumberEquiv_symm`, `Finset.sum_Ico_eq_add_neg`, `zero_sub_add_zero_sub`, `LieHom.zero_apply`, `sign_mul_self`, `Module.FaithfullyFlat.iff_exact_iff_lTensor_exact`, `CategoryTheory.Abelian.Ext.zero_comp`, `leftInverse_neg_add_add_right`, `Quaternion.imI_zero`, `toIcoDiv_mul_sub_self`, `Set.neg_Icc`, `LieDerivation.zero_apply`, `ExistsContDiffBumpBase.u_support`, `ContinuousLinearMapWOT.neg_apply`, `MeasureTheory.SimpleFunc.integral_piecewise_zero`, `InnerProductSpace.rankOne_one_left_eq_innerSL`, `EuclideanGeometry.oangle_eq_neg_of_angle_eq_of_sign_eq_neg`, `WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF_of_char_three`, `Finset.preimage_add_left_singleton`, `AddCircle.coe_eq_zero_iff`, `Mathlib.Tactic.Abel.term_atomg`, `Quaternion.imJ_im`, `Quaternion.coe_natCast`, `Quaternion.instNoZeroDivisors`, `MeasureTheory.unifTight_iff_real`, `groupHomology.d₁₀_single_one`, `IsUniformAddGroup.cauchy_map_iff_tendsto`, `Algebra.Norm.Transitivity.polyToMatrix_cornerAddX`, `iteratedDerivWithin_fun_const_zero`, `MeasureTheory.aefinStronglyMeasurable_iff_aemeasurable`, `UpperSet.Ici_zero`, `HasFiniteFPowerSeriesAt.neg`, `IsometryEquiv.toRealLinearIsometryEquiv_symm_apply`, `Quaternion.neg_re`, `LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_iff_ne_top`, `FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero`, `MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left`, `CliffordAlgebra.mul_ι_mul_ι_of_isOrtho`, `ContinuousLinearMap.map_add_add`, `Set.smul_set_neg`, `LieAlgebra.IsKilling.restrict_killingForm_eq_sum`, `quadraticChar_card_card`, `BddBelow.neg`, `groupHomology.boundaries₂_le_cycles₂`, `ContinuousLinearMap.sSup_unit_ball_eq_norm`, `Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall`, `FreeGroup.sum_mk`, `rank_le_card_isVisible`, `intervalIntegral.derivWithin_integral_of_tendsto_ae_left`, `QuadraticAlgebra.im_intCast`, `FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite`, `Polynomial.resultant_X_add_C_right`, `taylorWithinEval_hasDerivAt_Ioo`, `Manifold.IsImmersionAtOfComplement.target_subset_preimage_target`, `fderivWithin_fun_smul`, `ContinuousMultilinearMap.norm_iteratedFDerivComponent_le`, `abs_add_eq_add_abs_iff`, `round_neg_two_inv`, `complexOfReal_hasDerivWithinAt`, `ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff`, `AffineMap.hasDerivAtFilter`, `IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic`, `InnerProductGeometry.angle_neg_self_of_nonzero`, `fderivWithin_fderivWithin_eq_of_mem_nhdsWithin`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm`, `VectorField.lieBracketWithin_zero_left`, `Set.indicator_neg`, `Quaternion.star_smul`, `LieSubalgebra.isLieAbelian_lieSpan_iff`, `ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds`, `EuclideanSpace.closedBall_zero_eq`, `Asymptotics.isLittleO_const_left`, `curveIntegrable_segment`, `MeasureTheory.integral_indicator₂`, `Orientation.oangle_eq_zero_iff_oangle_rev_eq_zero`, `MeasureTheory.SimpleFunc.measure_support_lt_top_of_integrable`, `Sbtw.neg`, `MDifferentiableAt.cle_arrowCongr`, `Manifold.IsImmersionAt.map_target_subset_target`, `LinearMap.BilinForm.IsAlt.neg_eq`, `ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm`, `continuousSMul_sphere_sphere`, `MeasureTheory.IntegrableOn.comp_neg`, `WeierstrassCurve.toCharNeTwoNF_t`, `DirichletCharacter.Odd.eval_neg`, `Complex.integral_boundary_rect_eq_zero_of_differentiableOn`, `lt_add_neg_iff_add_lt`, `hasFTaylorSeriesUpToOn_top_iff_right`, `MeasureTheory.Lp.const_smul_mem_Lp`, `RootPairing.reflectionPerm_eq_iff_smul_root`, `NonemptyInterval.snd_neg`, `MeasureTheory.Lp.simpleFunc.toSimpleFunc_indicatorConst`, `sub_le_neg_add_iff`, `CategoryTheory.Pretriangulated.Triangle.invRotate_mor₃`, `MeasureTheory.measurePreserving_prod_neg_add`, `MeasureTheory.MemLp.smul`, `CharacterModule.int.divByNat_self`, `Commute.mul_self_eq_mul_self_iff`, `abs_neg`, `WithLp.nnnorm_toLp_inr`, `ContinuousMultilinearMap.analyticAt_uncurry_of_linear`, `intervalIntegral.integral_hasDerivWithinAt_right`, `LieSubmodule.Quotient.mk_eq_zero`, `Prime.neg`, `deriv_mem_iff`, `CategoryTheory.Idempotents.neg_def`, `Bornology.isVonNBounded_add_of_nonempty`, `FormalMultilinearSeries.radius_pi_eq_iInf`, `hasGradientAtFilter_const`, `SchwartzMap.pairing_apply_apply`, `InnerProductSpace.isIdempotentElem_rankOne_self`, `ProbabilityTheory.Kernel.setIntegral_deterministic'`, `ContDiffMapSupportedIn.iteratedFDerivLM_apply`, `Matrix.cstar_nnnorm_def`, `CategoryTheory.ShortComplex.RightHomologyMapData.neg_φH`, `HahnSeries.order_neg`, `lineDerivWithin_zero_of_not_lineDifferentiableWithinAt`, `Finset.image_neg`, `AddSubgroup.closure_singleton_zero`, `LieAlgebra.Orthogonal.mem_so`, `groupHomology.chainsMap_f_3_comp_chainsIso₃_apply`, `intervalIntegral.integral_hasFDerivAt_of_tendsto_ae`, `QuaternionAlgebra.intCast_imJ`, `TestFunction.coe_neg`, `HahnSeries.SummableFamily.coe_neg`, `Homeomorph.vadd_symm_apply`, `dist_smul_le`, `Filter.neg_atTop`, `Orientation.eq_iff_norm_eq_and_oangle_eq_zero`, `ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars`, `hasDerivWithinAt_Ioi_iff_Ici`, `ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto`, `MeasureTheory.integral_indicator`, `LineDeriv.lineDerivOp_left_zero`, `Finset.tendsto_Ico_neg_atTop_atTop`, `CliffordAlgebra.involute_prod_map_ι`, `hasDerivWithinAt_taylorWithinEval`, `Quaternion.imI_sub`, `NormedSpace.invOf_exp_of_mem_ball`, `Matrix.adjugate_fin_two`, `groupHomology.d₃₂_single`, `FormalMultilinearSeries.changeOriginSeriesTerm_apply`, `Quaternion.one_imI`, `Asymptotics.isLittleOTVS_one`, `Quaternion.rank_eq_four`, `TopModuleCat.hom_zero_apply`, `SymplecticGroup.coe_inv`, `meromorphicOrderAt_const`, `Summable.finite_support_of_discreteTopology`, `ContinuousLinearMap.hasDerivAtFilter`, `neg_lt_neg_iff`, `Asymptotics.isLittleO_const_iff`, `HasFPowerSeriesAt.locally_ne_zero`, `AddCircle.card_torsion_le_of_isSMulRegular`, `Quaternion.star_eq_neg`, `WeierstrassCurve.Projective.negY_eq`, `ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall`, `Real.Angle.cos_zero`, `intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right`, `Polynomial.prod_X_sub_C_nextCoeff`, `ContinuousLinearMap.iSup_rayleigh_eq_iSup_rayleigh_sphere`, `AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds`, `MeasureTheory.lpNorm_neg`, `ordinaryHypergeometric_radius_top_of_neg_nat₃`, `HasFPowerSeriesOnBall.add`, `AddGroupLieAlgebra.bracket_def`, `Quaternion.finrank_eq_four`, `groupHomology.mapCycles₁_comp_apply`, `groupHomology.cyclesIso₀_inv_comp_iCycles_apply`, `AddSubgroup.closure_diff_zero`, `ZMod.LFunction_one_sub`, `SchwartzMap.coeFn_zero`, `Orientation.rotation_eq_self_iff`, `Real.Angle.sign_neg_coe_nonpos_of_nonneg_of_le_pi`, `WeierstrassCurve.Projective.negY_of_Z_eq_zero`, `ContinuousMap.toLp_denseRange`, `FiniteField.isSquare_neg_one_iff`, `IsCoprime.neg_right`, `Bornology.isVonNBounded_add_self`, `derivWithin_const`, `Asymptotics.isBigOWith_neg_right`, `Seminorm.ball_smul_closedBall`, `ArithmeticFunction.coe_moebius_mul_coe_zeta`, `ContinuousLinearMap.integral_apply`, `differentiableWithinAt_neg_iff`, `Submodule.reflection_orthogonal_apply`, `IsUniformAddGroup.ext_iff`, `PolynomialModule.add_apply`, `Polynomial.resultant_add_left_deg`, `hasFDerivAt_stereoInvFunAux`, `SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left`, `IsAddUnit.neg_add_eq_iff_eq_add`, `WithLp.ofLp_neg`, `Quaternion.intCast_imK`, `NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded`, `Asymptotics.isTheta_const_const_iff`, `ZMod.intCast_cast_neg`, `LinearMap.IsSymmetric.diagonalization_apply_self_apply`, `BoundedContinuousFunction.char_neg`, `MeasureTheory.Lp.eq_zero_iff_ae_eq_zero`, `comap_conj_nhds_zero`, `ZMod.dft_even_iff`, `Finset.neg_op_vadd_finset_distrib`, `spectralNorm_neg`, `LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot`, `neg_smul`, `Finset.affineCombination_sdiff_sub`, `AntilipschitzWith.neg`, `Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly`, `intervalIntegral.fderiv_integral_of_tendsto_ae`, `HahnSeries.support_sub_subset`, `SMulPosReflectLE_iff_smulPosReflectLT`, `AlternatingMap.map_linearDependent`, `NormedSpace.isBounded_iff_subset_smul_ball`, `addOrderOf_neg`, `hasFPowerSeriesOnBall_pi_iff`, `ContinuousAffineMap.neg_apply`, `Set.nonempty_image_addRight_neg_inter_iff`, `Continuous.convolution_integrand_fst`, `BoxIntegral.Integrable.neg`, `ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries`, `ContDiffMapSupportedIn.structureMapCLM_apply`, `iteratedFDerivWithin_succ_eq_comp_right`, `HasFPowerSeriesWithinAt.const_smul`, `Finsupp.neLocus_neg_neg`, `IsometryEquiv.subLeft_symm_apply`, `uniformity_eq_comap_add_neg_nhds_zero`, `BoundedContinuousFunction.char_zero_eq_one`, `CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_hom_app`, `SchwartzMap.lineDerivOp_fourier_eq`, `FirstOrder.Field.realize_genericMonicPolyHasRoot`, `Equiv.constVAdd_zero`, `Quaternion.star_imI`, `MeasureTheory.setIntegral_measure_zero`, `QuotientAddGroup.eq`, `LieModule.traceForm_eq_sum_finrank_nsmul'`, `deriv_comp_const_sub`, `Function.support_sub`, `Set.image_neg_Ico`, `Quaternion.coe_inv`, `Filter.tendsto_neg_atBot_atTop`, `SchwartzMap.iteratedPDeriv_zero`, `HasFPowerSeriesWithinOnBall.restrictScalars`, `NormedSpace.isVonNBounded_iff`, `RingHom.map_neg`, `groupHomology.eq_d₃₂_comp_inv`, `Real.Angle.sin_eq_zero_iff`, `ArithmeticFunction.intCoe_one`, `Set.indicator_sub'`, `HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk`, `SchwartzMap.integral_bilin_fourierInv_eq`, `TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars`, `MeasureTheory.Integrable.tendsto_setIntegral_nhds_zero`, `toIocMod_sub_self_eq_mul`, `HasFTaylorSeriesUpTo.hasFDerivAt`, `Real.Angle.sign_neg`, `ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap`, `UniformContinuous.neg`, `hasDerivAt_neg'`, `MeasureTheory.Measure.toSphere_apply_aux`, `Orientation.neg_rotation`, `Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv`, `Antitone.neg`, `ContMDiffOn.clm_postcomp`, `MeasureTheory.SimpleFunc.measure_support_lt_top_of_memLp`, `differentiable_fun_neg_iff`, `smulPosMono_iff_smulPosStrictMono`, `IsLocalExtrOn.neg`, `LinearMap.adjoint_eq_toCLM_adjoint`, `Quaternion.normSq_natCast`, `LinearEquiv.skewSwap_symm_apply`, `LucasLehmer.X.zero_fst`, `IsCyclotomicExtension.discr_odd_prime`, `Finset.expect_neg_distrib`, `AntivaryOn.sub_smul_sub_nonpos`, `zero_memℓp`, `Hyperreal.neg_lt_of_tendsto_zero_of_pos`, `NormedSpace.image_isVonNBounded_iff`, `VectorField.mpullbackWithin_smul`, `ContinuousMap.range_toLp`, `NormedSpace.sphere_nonempty_rclike`, `MeasureTheory.average_zero_measure`, `ModuleCat.linearIndependent_shortExact`, `Quaternion.im_intCast`, `Quaternion.imJ_smul`, `Unitization.inr_sub`, `gauge_smul_of_nonneg`, `Quaternion.imK_natCast`, `NormedRing.inverse_add_norm_diff_nth_order`, `Orientation.eq_rotation_self_iff_angle_eq_zero`, `Function.Periodic.zsmul_sub_eq`, `derivWithin_fderivWithin`, `groupCohomology.map_one_of_isCocycle₁`, `Fintype.balance_zero`, `WithLp.isBoundedSMulSeminormedAddCommGroupToProd`, `derivWithin_natCast`, `Orientation.two_zsmul_oangle_neg_left`, `zero_mem_ℓp'`, `Set.instTietzeExtensionUnitBall`, `AddCircle.equivIccQuot_comp_mk_eq_toIcoMod`, `IsometryEquiv.toRealLinearIsometryEquiv_apply`, `StrictConvexOn.neg`, `Int.ceil_neg`, `MultilinearMap.mkContinuousMultilinear_apply`, `CharTwo.neg_eq'`, `MeasureTheory.integral_non_aestronglyMeasurable`, `LinearPMap.neg_apply`, `TemperedDistribution.lineDerivOp_fourier_eq`, `Asymptotics.isBigO_zero`, `Function.Antiperiodic.neg`, `MeasureTheory.charFun_neg`, `Finset.box_succ_disjUnion`, `WeierstrassCurve.Jacobian.addY_neg`, `Fin.sum_neg_one_pow`, `LinearMap.isSelfAdjoint_toContinuousLinearMap_iff`, `WeierstrassCurve.Projective.addY_of_X_eq'`, `negPart_eq_zero'`, `ContinuousLinearMap.image_rayleigh_eq_image_rayleigh_sphere`, `max_neg_neg`, `Orientation.oangle_zero_left`, `HahnSeries.orderTop_sub_pos`, `MonotoneOn.slope_nonneg`, `Polynomial.Splits.nextCoeff_eq_neg_sum_roots_mul_leadingCoeff`, `contMDiff_neg_sphere`, `Mathlib.Tactic.RingNF.mul_neg`, `ExteriorAlgebra.ι_eq_zero_iff`, `Filter.add_eq_zero_iff`, `tangentConeAt_nonempty_of_properSpace`, `WithCStarModule.neg_snd`, `not_differentiableAt_norm_zero`, `VectorField.pullbackWithin_eq_of_not_isInvertible`, `AddEquiv.neg_apply`, `ContinuousLinearMap.opNorm_lsmul_apply_le`, `CategoryTheory.ShortComplex.RightHomologyMapData.neg_φQ`, `RingEquiv.map_neg`, `RootPairing.zero_notMem_range_root`, `Pi.nnnorm_single`, `MeasurableEquiv.symm_addLeft`, `Matrix.transpose_circulant`, `MeasureTheory.AEEqFun.neg_toGerm`, `Continuous.integral_hasStrictDerivAt`, `OrthonormalBasis.orthogonalProjection_eq_sum_rankOne`, `Filter.eventually_sub_nonneg`, `StrictMono.neg`, `SchwartzMap.bilinLeftCLM_apply`, `Matrix.inv_fromBlocks_zero₁₂_of_isUnit_iff`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_zero`, `Int.cast_le_neg_one_of_neg`, `Bornology.isVonNBounded_pi_iff`, `tangentConeAt_eq_biInter_closure`, `Matrix.transpose_eq_intCast`, `neg_add_lt_iff_lt_add`, `EuclideanGeometry.oangle_eq_angle_or_eq_neg_angle`, `derivWithin_comp_const_sub`, `add_neg_eq_zero`, `posPart_eq_self`, `AffineMap.hasDerivWithinAt`, `HahnSeries.single_zero_ofScientific`, `TrivSqZeroExt.inv_inl`, `HasFPowerSeriesAt.eventually_hasSum`, `neg_le`, `IncidenceAlgebra.moebius_inversion_top`, `Set.iUnion_neg_vadd`, `Quaternion.add_re`, `instSMulCommClass_sphere_sphere_sphere`, `AddCircle.coe_neg`, `DFinsupp.neLocus_neg_neg`, `Bundle.RiemannianMetric.isVonNBounded`, `ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le`, `edist_zero_left`, `Filter.Tendsto.uniformity_neg`, `groupHomology.mem_cycles₂_iff`, `NormedSpace.toIsBoundedSMul`, `IsAlgClosure.of_exists_root`, `HasFPowerSeriesAt.neg`, `Real.Angle.cos_eq_real_cos_iff_eq_or_eq_neg`, `QuadraticMap.neg_apply`, `nhds_basis_Icc_pos`, `rank_zero_iff_forall_zero`, `Function.mulSupport_one_sub'`, `LucasLehmer.X.neg_snd`, `ZNum.cast_zneg`, `curveIntegralFun_smul`, `CochainComplex.HomComplex.δ_neg`, `addInvariantVectorField_smul`, `CategoryTheory.ShortComplex.leftHomologyMap'_neg`, `WeierstrassCurve.Jacobian.addZ_of_Z_eq_zero_right`, `neg_strictConvexOn_iff`, `groupHomology.single_isCycle₂_iff_inv`, `ZNum.of_natCast`, `nhds_basis_abs_sub_lt`, `IsAddUnit.add_zero_sub_cancel`, `egauge_ball_le_of_one_lt_norm`, `QuaternionAlgebra.Basis.k_mul_i`, `LieSubmodule.lie_abelian_iff_lie_self_eq_bot`, `ZMod.exists_sq_eq_neg_one_iff`, `CategoryTheory.ShortComplex.ext_mk₀_f_comp_ext_mk₀_g`, `hasDerivWithinAt_iff_isLittleO`, `lp.eq_zero_iff_coeFn_eq_zero`, `hasStrictFDerivAt_iff_isLittleOTVS`, `groupHomology.cyclesMap_comp_isoCycles₂_hom`, `ZMod.natCast_natAbs_valMinAbs`, `AntivaryOn.neg_left`, `neg_neg_iff_pos`, `differentiableWithinAt_fun_neg_iff`, `MeasureTheory.charFun_eq_fourierIntegral`, `MeasureTheory.lintegral_enorm_neg`, `MeasureTheory.SimpleFunc.tendsto_approxOn_range_L1_enorm`, `ContinuousAlternatingMap.piLIE_apply_apply`, `MeasureTheory.Measure.InnerRegular.neg`, `AntitoneOn.neg`, `BoundedContinuousFunction.coe_neg`, `CategoryTheory.Endofunctor.algebraPreadditive_homGroup_neg_f`, `Module.FaithfullyFlat.lTensor_exact_iff_exact`, `Behrend.sphere_subset_preimage_metric_sphere`, `lintegral_fderiv_lineMap_eq_edist`, `RCLike.normSq_neg`, `IncidenceAlgebra.coe_sub`, `TemperedDistribution.smulLeftCLM_compL_smulLeftCLM`, `Homeomorph.shearAddRight_symm_coe`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_left`, `hasDerivWithinAt_zero`, `MeasureTheory.Measure.IsOpenPosMeasure.neg`, `MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le`, `ZMod.wilsons_lemma`, `ContDiffAt.hasStrictDerivAt`, `Seminorm.neg_ball`, `TrivSqZeroExt.inv_one`, `groupHomology.comp_d₂₁_eq`, `edist_zero_eq_enorm`, `Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero'`, `Differentiable.fun_neg`, `List.sum_int_mod`, `FormalMultilinearSeries.hasSum_of_finite`, `IntervalIntegrable.neg`, `conj_eq_zero_iff`, `QuaternionAlgebra.sub_re_self`, `Quaternion.imI_mul`, `hasDerivAtFilter_ofNat`, `groupHomology.mapCycles₁_comp_assoc`, `WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF`, `iteratedDerivWithin_const_zero`, `FormalMultilinearSeries.changeOriginSeries_summable_aux₃`, `curveIntegrable_smul_iff`, `sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent`, `CategoryTheory.Pretriangulated.invRotCompRot_inv_app_hom₃`, `add_eq_zero_iff_eq_neg'`, `CharZero.neg_eq_self_iff`, `IsNilpotent.exp_mul_exp_neg_self`, `HasFPowerSeriesOnBall.restrictScalars`, `smul_nonneg_iff_neg_imp_nonpos`, `QuaternionAlgebra.imK_intCast`, `Hyperreal.InfinitePos.neg`, `derivWithin_zero_of_frequently_const`, `ContinuousLinearMap.isometry_mul_flip`, `Quaternion.snd_re_dualNumberEquiv_symm`, `groupHomology.toCycles_comp_isoCycles₂_hom_assoc`, `AddSubgroup.coe_neg`, `negPart_eq_neg'`, `Finset.addETransformLeft_neg`, `Quaternion.coe_ratCast`, `Mathlib.Tactic.Module.NF.eval_neg`, `MeasureTheory.Integrable.exists_hasCompactSupport_lintegral_sub_le`, `HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt`, `Quaternion.imJ_one`, `CategoryTheory.Abelian.Ext.eq_zero_of_hasInjectiveDimensionLT`, `MeasureTheory.SimpleFunc.integral_neg`, `Finsupp.subtypeDomain_neg`, `Hyperreal.infinitesimal_def`, `ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective`, `ContinuousLinearMap.adjoint_id`, `ClosedSubmodule.inf_orthogonal`, `balanced_ball_zero`, `HasFDerivWithinAt.linear_multilinear_comp`, `iteratedFDerivWithin_succ_eq_comp_left`, `tendsto_birkhoffAverage_apply_sub_birkhoffAverage`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt`, `contDiffOn_iff_continuousOn_differentiableOn`, `ZMod.valMinAbs_neg_of_ne_half`, `IsNilpotent.neg`, `ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint`, `NonemptyInterval.length_nonneg`, `Finsupp.neLocus_self_add_left`, `CategoryTheory.ShortComplex.cyclesMap_neg`, `sum_cauchyPowerSeries_eq_integral`, `coe_neg_closedBall`, `SchwartzMap.laplacianCLM_eq`, `fderiv_fun_smul`, `instContinuousNegElemBallOfNat`, `Matrix.det_succ_row`, `Derivation.mapCoeffs_X`, `LinearIsometryEquiv.conjStarAlgEquiv_apply`, `Bundle.ContinuousLinearMap.vectorBundle`, `CochainComplex.HomComplex.Cochain.rightUnshift_neg`, `VectorField.mlieBracketWithin_const_smul_right`, `CochainComplex.mappingCone.inl_snd_assoc`, `Matrix.vecMul_neg`, `LipschitzOnWith.neg`, `EuclideanGeometry.oangle_self_left_right`, `RootPairing.coPolarization_apply_eq_zero_iff`, `StrictAntiOn.neg`, `MeasureTheory.ConvolutionExistsAt.integrable`, `MeasureTheory.lpNorm_fun_zero`, `AddGroupFilterBasis.neg'`, `AddGroupNorm.eq_zero_of_map_eq_zero'`, `abs_le_of_sq_le_sq'`, `HVertexOperator.coeff_isPWOsupport`, `Finsupp.filter_neg`, `Polynomial.map_sub_roots_sprod_eq_prod_map_eval`, `Asymptotics.isLittleOTVS_prodMk_left`, `InnerProductGeometry.angle_smul_left_of_neg`, `Module.exists_smul_eq_zero_and_mk_eq`, `LieSubalgebra.bot_coe`, `neg_eq_self`, `Matrix.adjugate_fin_succ_eq_det_submatrix`, `MeasureTheory.lpNorm_fun_neg`, `IsSl2Triple.lie_lie_smul_f`, `minpoly_neg_splits`, `QuaternionAlgebra.natCast_im`, `Orientation.two_zsmul_oangle_neg_self_right`, `Finset.weightedVSub_apply_const`, `IntervalIntegrable.zero`, `negPart_sub_posPart`, `smul_unitClosedBall`, `TestFunction.continuous_iff_continuous_comp`, `Quaternion.coe_pow`, `Module.FaithfullyFlat.rTensor_reflects_exact`, `MeasureTheory.Measure.toSphere_real_apply_univ`, `Asymptotics.isBigOWith_zero_right_iff`, `ContinuousLinearMap.opNorm_mul_flip_apply`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars`, `BoxIntegral.integral_zero`, `Quaternion.ratCast_re`, `NonemptyInterval.add_eq_zero_iff`, `Quaternion.imJ_fst_dualNumberEquiv`, `IsGLB.neg`, `InnerProductSpace.inner_left_rankOne_apply`, `integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable`, `TestFunction.toBoundedContinuousFunctionCLM_apply`, `IsAlgClosure.of_exist_roots`, `FreeAbelianGroup.support_zero`, `Orientation.oangle_neg_right`, `Set.neg_uIcc`, `Bornology.isVonNBounded_neg`, `LinearIsometryEquiv.map_zero`, `Finset.tendsto_Ioc_neg_atTop_atTop`, `ContinuousLinearMap.smul_compLp`, `Asymptotics.IsLittleO.tendsto_zero_of_tendsto`, `UniformConvergenceCLM.coe_zero`, `PowerSeries.derivative_inv'`, `WeierstrassCurve.Jacobian.negY_eq`, `DFinsupp.mk_neg`, `MeasureTheory.setToFun_undef`, `Matrix.exp_neg`, `LieModule.instIsTrivialOfSubsingleton'`, `Quaternion.im_re`, `leftInverse_add_right_neg_add`, `HasFPowerSeriesAt.add`, `ContinuousAlternatingMap.curryLeft_smul`, `PiLp.norm_toLp_single`, `TrivSqZeroExt.instNormOneClass`, `MeasureTheory.SimpleFunc.setToSimpleFunc_zero'`, `Matrix.neg_vecMul_neg`, `ContinuousLinearMap.hasBasis_nhds_zero`, `CategoryTheory.ShortComplex.ShortExact.d_eq_zero_of_f_eq_d_apply`, `HasFDerivAtFilter.isBigOTVS_sub`, `hasFDerivWithinAt_inv`, `groupCohomology.cocycles₂.d₂₃_apply`, `Seminorm.ball_mem_nhds`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn`, `ContMDiffAt.clm_postcomp`, `mapClusterPt_neg_atTop_nsmul`, `ContMDiffWithinAt.clm_postcomp`, `WithLp.neg_snd`, `NonUnitalStarSubalgebra.coe_neg`, `hasDerivWithinAt_pi`, `FreeAbelianGroup.seq_zero`, `AddSubgroup.closure_eq_bot_iff`, `Real.integrable_prod_sub`, `Seminorm.mem_closedBall_zero`, `Orientation.oangle_smul_left_of_neg`, `NormedSpace.isVonNBounded_ball`, `Height.logHeight₁_neg`, `deriv_const'`, `ContinuousLinearMap.eq_adjoint_iff`, `Finset.addConst_neg_right`, `LocallyLipschitzOn.neg`, `ZeroHom.sub_comp`, `groupHomology.d₃₂_single_one_thd`, `birkhoffAverage_neg`, `WeierstrassCurve.Jacobian.negAddY_of_Z_eq_zero_right`, `div_two_sub_self`, `PiTensorProduct.toDualContinuousMultilinearMap_apply_apply`, `MeasureTheory.Measure.addHaar_ball_of_pos`, `convexHull_union_neg_eq_absConvexHull`, `Ideal.Filtration.mem_submodule`, `WithTop.untop₀_le_untop₀`, `SubMulAction.neg_mem`, `IntermediateField.coe_neg`, `Polynomial.resultant_comm`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le`, `slope_pos_iff_of_le`, `smul_nonpos_iff`, `LieSubalgebra.mem_bot`, `HasFPowerSeriesAt.comp`, `LieModule.trivial_iff_le_maximal_trivial`, `WithTop.untop₀_min`, `CochainComplex.HomComplex.Cochain.toSingleMk_neg`, `ZeroAtInftyContinuousMap.instNormedStarGroup`, `Homeomorph.contDiff_unitBall`, `EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection`, `ContinuousLinearMap.IsPositive.smul_of_nonneg`, `AddAction.fixedBy_neg`, `ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀`, `InnerProductSpace.rankOne_apply`, `MeasureTheory.Measure.IsFiniteMeasureOnCompacts.neg`, `isClosed_nonneg`, `AddSemiconjBy.eq_zero_iff`, `DFinsupp.neLocus_self_sub_left`, `FormalMultilinearSeries.sum_of_finite`, `HurwitzZeta.hurwitzZetaEven_zero`, `CategoryTheory.Abelian.Ext.comp_zero`, `AddMonoid.Coprod.neg_def`, `extremePoints_pi`, `groupHomology.isoCycles₁_inv_comp_iCycles_apply`, `AddSubgroup.IsComplement.neg_toLeftFun_add_mem`, `CochainComplex.HomComplex.Cochain.comp_neg`, `smul_unitClosedBall_of_nonneg`, `HasFTaylorSeriesUpToOn.zero_eq'`, `CochainComplex.HomComplex.Cochain.map_zero`, `LieModule.instIsTrivialSubtypeMemLieSubmoduleMaxTrivSubmodule`, `finrank_zero_iff_forall_zero`, `stereographic'_source`, `neg_eq_iff_add_eq_zero`, `isHausdorff_iff`, `Quaternion.mul_imK`, `WeierstrassCurve.Jacobian.negAddY_of_X_eq`, `Polynomial.roots_degree_eq_one`, `Quaternion.star_re`, `LieModule.Cohomology.twoCochain_alt`, `Quaternion.coe_commutes`, `CliffordAlgebra.toProd_ι_tmul_one`, `deriv_fun_inv''`, `Matrix.isTotallyUnimodular_iff_fintype`, `ContinuousMap.toLp_norm_le`, `MeasureTheory.setIntegral_dirac`, `ContinuousMultilinearMap.norm_smulRightL_le`, `Matrix.trace_eq_neg_charpoly_coeff`, `balancedCore_nonempty_iff`, `comap_norm_nhdsGT_zero`, `IsAlgClosed.instIsAlgClosure`, `ContinuousLinearMap.precompL_apply`, `Seminorm.closedBall_smul_ball`, `IsSelfAdjoint.adjoint_eq`, `RingCon.coe_neg`, `Rep.finsuppToCoinvariantsTensorFree_single`, `FirstOrder.Field.realize_eqZero`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars`, `curveIntegralFun_segment`, `DifferentiableAt.hasDerivAt`, `ball_zero_eq`, `OrderDual.instIsStrictOrderedModule`, `fderivWithin_zero`, `LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top`, `MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part`, `hasSum_ite_sub_hasSum`, `groupHomology.chains₁ToCoinvariantsKer_surjective`, `HomologicalComplex₂.D₂_D₁_assoc`, `CircleIntegrable.neg`, `curveIntegral_neg`, `FormalMultilinearSeries.radius_le_smul`, `bddAbove_neg`, `Rep.coinvariantsTensorFreeLEquiv_symm_apply`, `AddSubgroup.coe_zero`, `CliffordAlgebra.contractRight_comm`, `MDifferentiable.clm_postcomp`, `IsRelPrime.neg_left`, `MonotoneOn.neg`, `ValueDistribution.logCounting_coe_eq_logCounting_sub_const_zero`, `deriv_zero_of_not_differentiableAt`, `CochainComplex.HomComplex.Cochain.shift_neg`, `ValueDistribution.proximity_coe_eq_proximity_sub_const_zero`, `OrderIso.addLeft_symm`, `CategoryTheory.DifferentialObject.shiftZero_hom_app_f`, `FiniteArchimedeanClass.lift_mk`, `intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right`, `neg_abs_le_neg`, `QuaternionAlgebra.imI_intCast`, `Meromorphic.neg`, `ContinuousLinearMap.isPositive_self_comp_adjoint`, `Continuous.exists_contDiff_approx_and_eqOn`, `Quaternion.imJ_zero`, `LinearMap.adjoint_toContinuousLinearMap`, `LinearIsometryEquiv.coe_neg`, `hasDerivAt_iff_isLittleO`, `MeasureTheory.VectorMeasure.neg_apply`, `tendsto_zero_iff_abs_tendsto_zero`, `ZeroHom.coe_sub`, `BoxIntegral.hasIntegral_zero`, `NormedSpace.isBounded_iff_subset_smul_closedBall`, `MeasureTheory.HasFiniteIntegral.tendsto_setIntegral_nhds_zero`, `Function.mulSupport_one_sub`, `Quaternion.instFree`, `AlternatingMap.neg_apply`, `hasFPowerSeriesAt_const`, `IsCompact.closedBall_zero_add`, `neg_pos`, `HasFDerivAtFilter.neg`, `IsLocalExtr.neg`, `CochainComplex.HomComplex.CohomologyClass.mk_eq_zero_iff`, `HasFPowerSeriesOnBall.const_smul`, `HahnEmbedding.Partial.archimedeanClassMk_eq_iff`, `ContinuousLinearMap.toSesqForm_apply_coe`, `Trivialization.zeroSection`, `signedDist_linear_apply_apply`, `DifferentiableAt.fun_neg`, `CategoryTheory.shift_shift_neg'`, `Quaternion.sub_imJ`, `ContinuousMultilinearMap.curry0_apply`, `HahnSeries.support_abs`, `neg_one_smul`, `neg_ball`, `ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear`, `MeasureTheory.MemLp.exist_eLpNorm_sub_le`, `FormalMultilinearSeries.radius_compNeg`, `neg_zsmul`, `AddSubgroup.IsComplement.neg_add_toLeftFun_mem`, `groupHomology.cycles₁_eq_top_of_isTrivial`, `LieAlgebra.IsKilling.apply_coroot_eq_cast'`, `hasFDerivAtFilter_zero`, `Polynomial.resultant_X_sub_C_right`, `quasispectrum.mem_iff_of_isUnit`, `MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zero`, `SchwartzMap.integral_bilin_fourierIntegral_eq`, `QuaternionAlgebra.im_ofNat`, `VectorField.lieBracketWithin_zero_right`, `IsLinearTopology.hasBasis_open_submodule`, `AbsolutelyContinuousOnInterval.fun_neg`, `ContinuousAffineMap.decomp`, `MeasureTheory.L1.SimpleFunc.setToL1S_neg`, `LinearIsometryEquiv.adjoint_eq_symm`, `Matrix.neg_mulVec_neg`, `extDeriv_fun_smul`, `Quaternion.im_smul`, `ContinuousAlternatingMap.toAlternatingMap_curryLeft`, `neg_add_eq_sub`, `Right.neg_pos_iff`, `ProbabilityTheory.HasGaussianLaw.neg`, `Orientation.neg_rotation_neg_pi_div_two`, `Finset.prod_sub`, `StrictConvex.neg`, `skewAdjoint.mem_iff`, `Quaternion.imI_fst_dualNumberEquiv`, `ContinuousAffineMap.zero_apply`, `LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt`, `groupHomology.d₃₂_comp_d₂₁_assoc`, `AddMonoidHom.fiberEquiv_symm_apply`, `groupCohomology.mem_cocycles₁_def`, `IsometryEquiv.addRight_symm`, `natAbs_nsmul_eq_zero`, `Finset.vadd_addConvolution_eq_addConvolution_neg_add`, `MeasureTheory.measure_neg_vadd_inter`, `ContinuousLinearMap.sSup_sphere_eq_nnnorm`, `infEDist_neg_neg`, `VectorFourier.fourierPowSMulRight_eq_comp`, `Matrix.isDiag_neg_iff`, `Quaternion.im_zero`, `CategoryTheory.Abelian.Ext.mk₀_neg`, `AddChar.sub_apply`, `ContinuousLinearMap.hasFDerivWithinAt_of_bilinear`, `LieAlgebra.derivedSeries_of_derivedLength_succ`, `LinearMap.BilinForm.nondegenerate_iff`, `MeasureTheory.ae_eq_zero_of_forall_inner`, `Finsupp.neLocus_eq_support_sub`, `AddSubgroup.mem_centralizer_iff_commutator_eq_zero`, `ZModModule.char_nsmul_eq_zero`, `memℓp_zero_iff`, `Asymptotics.isBigO_neg_right`, `RootPairing.zero_notMem_range_coroot`, `mul_neg_one_pow_eq_zero_iff`, `Quaternion.algebraMap_def`, `ContinuousAlternatingMap.constOfIsEmptyLIE_apply`, `Nat.eq_sq_add_sq_iff_eq_sq_mul`, `Left.neg_neg_iff`, `QuaternionAlgebra.imJ_intCast`, `comap_norm_nhds_zero`, `TemperedDistribution.smulLeftCLM_neg`, `analyticOrderAt_eq_top`, `MeasureTheory.SimpleFunc.integral_eq_sum_filter`, `egauge_zero_zero`, `sub_eq_zero`, `apply_abs_le_mul_of_one_le`, `Quaternion.imJ_coe`, `Matrix.IsHermitian.neg`, `OpenPartialHomeomorph.univUnitBall_symm_apply_zero`, `AnalyticOn.neg`, `AnalyticAt.frequently_zero_iff_eventually_zero`, `AddChar.map_neg_eq_inv`, `MDifferentiable.cle_arrowCongr`, `Finsupp.mapRange_neg'`, `Wbtw.oangle₃₁₂_eq_zero`, `QuadraticMap.polar_neg_left`, `HahnEmbedding.Seed.baseEmbedding_strictMono`, `ModuleCat.FilteredColimits.colimit_zero_eq`, `HahnSeries.map_neg`, `isScalarTower_closedBall_closedBall_closedBall`, `ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear`, `Algebra.Extension.Cotangent.smul_eq_zero_of_mem`, `Antivary.neg`, `MeasureTheory.Integrable.edist_toL1_zero`, `Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff`, `ediam_smul_le`, `HasFDerivAt.fun_smul`, `fderivWithin_fun_neg`, `Set.nonempty_image_addLeft_neg_inter_iff`, `ContinuousLinearMap.flipMultilinear_apply_apply`, `ContinuousMultilinearMap.uncurrySum_apply`, `isScalarTower_sphere_closedBall_closedBall`, `OpenPartialHomeomorph.univUnitBall_apply_zero`, `Quaternion.normSq_smul`, `HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope`, `add_add_neg_add_cancel`, `EuclideanGeometry.oangle_rev`, `Quaternion.coe_re`, `MeasureTheory.Lp.finStronglyMeasurable`, `CauSeq.const_neg`, `Real.Angle.sign_two_nsmul_eq_neg_sign_iff`, `Affine.Simplex.centroid_weighted_vsub_eq_zero`, `PiTensorProduct.mapL_smul`, `SchwartzMap.integral_sesq_fourier_eq`, `Right.nonneg_neg_iff`, `AddCircle.finite_torsion_of_isSMulRegular`, `CompactlySupportedContinuousMap.sub_apply`, `RCLike.I_mul_I`, `ContinuousLinearMap.adjointAux_norm`, `MeasureTheory.L1.setToL1_smul_left`, `ValueDistribution.logCounting_const_zero`, `analyticAt_neg`, `norm_sub_le_mul_volume_of_norm_lineDeriv_le`, `MeasureTheory.Measure.addHaar_ball_mul`, `Function.locallyFinsuppWithin.nsmul_posPart`, `CochainComplex.HomComplex.Cochain.neg_v`, `fderiv_neg`, `groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂`, `MeasureTheory.L1.setToL1_zero_left`, `neg_smul_neg`, `hasDerivAtFilter_natCast`, `ContinuousLinearMap.toContinuousAffineMap_map_zero`, `WithCStarModule.equiv_symm_neg`, `OreLocalization.neg_add_cancel`, `groupHomology.d₁₀ArrowIso_hom_left`, `MeasureTheory.SimpleFunc.setToSimpleFunc_zero_apply`, `WeierstrassCurve.Affine.polynomial_eq`, `intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip`, `AddChar.neg_apply`, `toIcoMod_sub_self_eq_mul`, `DualNumber.inv_eps`, `hasLineDerivWithinAt_zero`, `balancedHull_subset_convexHull_union_neg`, `Antivary.neg_right`, `ContinuousLinearMap.hasStrictFDerivAt_of_bilinear`, `Odd.neg_one_zpow`, `zpow_eq_neg_zpow_iff₀`, `VectorField.lieBracket_swap`, `groupHomology.cycles₁IsoOfIsTrivial_hom_apply`, `norm_curveIntegral_segment_le`, `derivWithin.fun_neg`, `DirectSum.lie_of_of_ne`, `Polynomial.resultant_X_pow_right`, `DFinsupp.Lex.isOrderedAddMonoid`, `ContinuousAffineMap.norm_def`, `LieSubmodule.coe_zero`, `Representation.coinvariantsFinsuppLEquiv_apply`, `CochainComplex.mappingCone.inl_v_triangle_mor₃_f`, `HasFDerivAtFilter.isThetaTVS_sub`, `abs_eq_max_neg`, `MeasureTheory.withDensityᵥ_neg'`, `InnerProductSpace.Core.inner_neg_left`, `RootPairing.Base.exists_root_eq_sum_nat_or_neg`, `TwoSidedIdeal.neg_mem`, `CharTwo.neg_eq`, `IncidenceAlgebra.neg_apply`, `CategoryTheory.Biprod.unipotentLower_inv`, `MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_regular`, `Orientation.oangle_neg_left_eq_neg_right`, `Int.cast_zero`, `neg_lt_sub_iff_lt_add`, `Quaternion.smul_imK`, `SchwartzMap.fourier_lineDerivOp_eq`, `Finsupp.sum_sub_index`, `Manifold.IsImmersionAtOfComplement.map_target_subset_target`, `Trivialization.localFrame_apply_of_notMem`, `WeierstrassCurve.ofJ0_Δ`, `WithZero.log_inv`, `TemperedDistribution.instLineDerivLeftSMulReal`, `meromorphicOrderAt_eq_top_iff`, `CategoryTheory.Abelian.Ext.mapExactFunctor_zero`, `MeasureTheory.VectorMeasure.coe_neg`, `MeasureTheory.Integrable.neg`, `groupHomology.d₂₁_single_inv_mul_ρ_add_single`, `LieModuleHom.mem_ker`, `MeasureTheory.AEEqFun.coeFn_neg`, `isBoundedBilinearMap_comp`, `Pi.linearIndependent_single_of_ne_zero`, `set_smul_sphere_zero`, `EuclideanGeometry.oangle_eq_zero_iff_angle_eq_zero`, `MeasureTheory.uniformIntegrable_iff`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx`, `Polynomial.algEquivCMulXAddC_symm_eq`, `NormedAddGroupHom.neg_apply`, `SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv`, `Polynomial.Chebyshev.T_eval_neg`, `hasStrictDerivAt_add_const_iff`, `TemperedDistribution.fourierInv_lineDerivOp_eq`, `IsAddUnit.add_eq_zero_iff_eq_neg`, `Int.cast_nonneg_iff`, `Int.cast_lt_zero`, `IsMIntegralCurveOn.hasDerivWithinAt`, `isSemireal_iff_not_isSumSq_neg_one`, `FormalMultilinearSeries.rightInv_removeZero`, `PresheafOfModules.Derivation.d_one`, `Finset.weightedVSubOfPoint_vadd`, `SModEq.zero`, `isCompactOperator_iff_isCompact_closure_image_ball`, `ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply`, `ClosedSubmodule.orthogonal_closure''`, `List.sum_set'`, `Quaternion.normSq_le_zero`, `abs_le`, `FreeAddGroup.lift_mk`, `QuaternionAlgebra.star_im`, `egauge_univ_pi`, `Orientation.eq_zero_or_eq_zero_of_kahler_eq_zero`, `SchwartzMap.smulLeftCLM_real_smul`, `DirichletCharacter.eval_modulus_sub`, `nhds_basis_zero_abs_lt`, `OreLocalization.neg_def`, `nhds_eq_iInf_abs_sub`, `groupHomology.d₁₀_comp_coinvariantsMk_apply`, `Orientation.kahler_eq_zero_iff`, `AddChar.sum_apply_eq_ite`, `IsAddUnit.zero_sub_add_cancel`, `even_neg_two`, `IsAddUnit.sub_add_left`, `norm_indicator_eq_indicator_norm`, `IsOfFinOrder.eq_neg_one`, `Quaternion.inv_def`, `TrivSqZeroExt.fst_invOf`, `hasDerivAtFilter_zero`, `HasMFDerivAt.neg`, `NormedAddGroupHom.isCentralScalar`, `Mathlib.Tactic.Ring.neg_zero`, `MeasureTheory.setToFun_measure_zero`, `SummationFilter.instLeAtTopSymmetricIco`, `DirectSum.lie_of`, `deriv.fun_neg'`, `PowerSeries.coeff_inv_aux`, `Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem`, `Orientation.oangle_smul_left_self_of_nonneg`, `UnitAddTorus.mFourierCoeff_toLp`, `AddSemiconjBy.neg_right`, `WeierstrassCurve.b₄_of_isShortNF_of_char_three`, `FirstOrder.Ring.realize_termOfFreeCommRing`, `DifferentiableAt.neg`, `lt_neg_add_iff_lt`, `CochainComplex.HomComplex.Cochain.single_zero`, `groupHomology.chainsMap_f_3_comp_chainsIso₃`, `groupHomology.mapCycles₁_id_comp_assoc`, `Multiset.sum_map_neg`, `curveIntegral_fun_smul`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum`, `Field.isSeparable_neg`, `ContinuousLinearMap.iInf_rayleigh_eq_iInf_rayleigh_sphere`, `taylor_tendsto`, `MeasureTheory.IntegrableAtFilter.smul`, `MeasureTheory.lintegral_lintegral_add_neg`, `Finset.small_alternating_nsmul_of_small_tripling`, `FreeRing.coe_neg`, `HasFDerivAt.curveIntegral_segment_source`, `MeasureTheory.rnDeriv_conv`, `ContinuousMultilinearMap.curryRight_norm`, `hasDerivWithinAt_Iic_of_tendsto_deriv`, `HahnEmbedding.Partial.toOrderAddMonoidHom_apply`, `norm_indicator_le_of_subset`, `mellin_hasDerivAt_of_isBigO_rpow`, `ContinuousLinearMap.analyticOn_bilinear`, `groupHomology.eq_d₂₁_comp_inv`, `MeasureTheory.memLp_const_iff`, `Commute.sq_eq_sq_iff_eq_or_eq_neg`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left'`, `OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single`, `WeierstrassCurve.Projective.negAddY_of_X_eq`, `MDifferentiableAt.clm_postcomp`, `Finsupp.mapRange_sub'`, `HurwitzZeta.completedSinZeta_neg`, `eq_or_eq_neg_of_sq_eq_sq`, `Bornology.isVonNBounded_iff_absorbing_le`, `VectorField.mlieBracket_zero_right`, `curveIntegral_fun_zero`, `Quaternion.zero_imJ`, `negPart_pos_iff`, `Bornology.isVonNBounded_covers`, `gradient_fun_const`, `Equiv.neg_addLeft`, `groupHomology.mapCycles₁_comp`, `Real.Angle.sign_eq_zero_iff`, `Matrix.frobenius_nnnorm_one`, `LucasLehmer.X.one_add_α_pow_q_succ`, `Orientation.rotation_pi_apply`, `mul_self_eq_mul_self_iff`, `WithCStarModule.zero_apply`, `cross_anticomm`, `Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splits`, `gauge_zero'`, `deriv_fderiv`, `Wbtw.oangle₂₁₃_eq_zero`, `Module.reflection_apply_self`, `AddSubgroup.list_sum_mem`, `ZMod.inv_neg_one`, `curveIntegralFun_symm_apply`, `QuotientAddGroup.leftRel_eq`, `inner_re_zero_right`, `ContinuousLinearMap.coe_neg'`, `CochainComplex.HomComplex.Cochain.neg_comp`, `LinearEquiv.toSpanNonzeroSingleton_homothety`, `LieAlgebra.abelian_radical_iff_solvable_is_abelian`, `Matrix.GeneralLinearGroup.upperRightHom_apply`, `TemperedDistribution.instFourierSMul`, `ZNum.of_intCast`, `Finset.preimage_add_left_zero`, `Module.exists_nontrivial_relation_of_finrank_lt_card`, `Algebra.discr_powerBasis_eq_norm`, `jacobiSum_one_nontrivial`, `MeasureTheory.setIntegral_support`, `Orientation.oangle_eq_angle_or_eq_neg_angle`, `Matrix.blockDiagonal'_neg`, `EuclideanGeometry.oangle_eq_zero_iff_oangle_rev_eq_zero`, `hasFPowerSeriesOnBall_const`, `HurwitzZeta.evenKernel_eq_cosKernel_of_zero`, `Asymptotics.isLittleO_zero`, `ContDiffMapSupportedIn.seminorm_le_iff`, `coe_neg_sphere`, `Set.neg_op_vadd_set_distrib`, `AdicCompletion.AdicCauchySequence.zero_apply`, `zsmul_zero`, `SignType.map_cast`, `ContinuousLinearMap.hasDerivAt`, `hasDerivAt_of_tendstoUniformly`, `MeasureTheory.condExp_zero`, `Right.neg_nonpos_iff`, `Algebra.Extension.H1Cotangent.val_zero`, `enorm_neg`, `Quaternion.smul_im`, `smul_nonpos_iff_pos_imp_nonpos`, `sub_eq_neg_add`, `monovaryOn_neg`, `IsPrimitiveRoot.norm_eq_neg_one_pow`, `PadicInt.fwdDiff_tendsto_zero`, `Real.Angle.sin_neg`, `MeasureTheory.integral_undef`, `HurwitzZeta.hurwitzZetaEven_apply_zero`, `MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall`, `WeierstrassCurve.b₈_of_isCharTwoJEqZeroNF`, `HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq`, `CategoryTheory.ShortComplex.moduleCat_zero_apply`, `Tactic.ReduceModChar.CharP.neg_eq_sub_one_mul`, `DFinsupp.neLocus_self_add_right`, `Quaternion.normSq_nonneg`, `Seminorm.ball_norm_mul_subset`, `Set.sub_mem_Ico_zero_iff_right`, `zero_eq_neg`, `Finset.Nonempty.zsmul`, `CategoryTheory.ShortComplex.Homotopy.neg_h₁`, `Quaternion.instNontrivial`, `ContinuousMultilinearMap.opNorm_smul_le`, `Module.Presentation.finsupp_R`, `Summable.neg`, `MeasureTheory.convolution_precompR_apply`, `DFinsupp.toFinsupp_sub`, `NormedSpace.eq_zero_iff_forall_dual_eq_zero`, `Set.pairwise_disjoint_vadd_iff`, `DirichletCharacter.Odd.to_fun`, `IncidenceAlgebra.moebius_inversion_bot`, `AddMonoidAlgebra.neg_apply`, `RootPairing.neg_mem_range_coroot_iff`, `VectorFourier.fourierIntegral_iteratedFDeriv`, `HasMFDerivWithinAt.neg`, `InnerProductGeometry.angle_neg_right`, `lp.coeFn_single`, `MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd`, `contMDiff_coe_sphere`, `InnerProductSpace.nnnorm_rankOne`, `HurwitzZeta.expZeta_one_sub`, `LinearEquiv.skewSwap_apply`, `neg_nsmul`, `LieSubmodule.bot_coe`, `Seminorm.closedBall_zero_eq_preimage_closedBall`, `fderiv_smul`, `IsLinearTopology.hasBasis_submodule`, `HahnSeries.single_sub`, `stereographic_apply_neg`, `groupHomology.mapCycles₁_comp_i`, `intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left`, `BoxIntegral.integral_neg`, `IsTopologicalAddGroup.ext_iff`, `CategoryTheory.Preadditive.comp_neg`, `MeasureTheory.Integrable.norm_toL1`, `CochainComplex.HomComplex.Cochain.shift_zero`, `ZNum.cast_succ`, `LieModule.genWeightSpaceChain_neg`, `Hyperreal.infinitePos_neg`, `hasDerivAt_of_tendstoLocallyUniformlyOn`, `hasDerivAtFilter_iff_tendsto_slope`, `MeasureTheory.Integrable.smul`, `ContinuousLinearMap.norm_toSpanSingleton`, `Complex.lift_apply`, `QuaternionAlgebra.sub_self_re`, `Finset.univ_of_card_le_three`, `FormalMultilinearSeries.continuousOn_of_finite`, `HahnEmbedding.Partial.isWF_support_evalCoeff`, `intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left`, `StrictMonoOn.neg`, `OrderDual.instSMulPosStrictMono`, `VectorField.lieBracketWithin_self`, `Quaternion.coe_zpow`, `FormalMultilinearSeries.ofScalars_series_of_subsingleton`, `Matrix.gram_zero`, `IsApproximateAddSubgroup.zero_mem`, `ContinuousAlternatingMap.curryLeft_apply_apply`, `NormedSpace.isVonNBounded_closedBall`, `HahnEmbedding.Partial.orderTop_eq_iff`, `affinity_unitClosedBall`, `exists_zsmul_eq_zero`, `ContinuousLinearMap.flip_smul`, `curveIntegralFun_refl`, `Finset.image_add_right`, `lie_neg`, `sub_neg_of_lt`, `Quaternion.im_one`, `HasFDerivAt.isBigOTVS_sub`, `tendsto_neg_nhdsGT_neg`, `Metric.preimage_add_left_closedBall`, `AddGroupSeminorm.neg'`, `InnerProductGeometry.angle_zero_right`, `AddSubgroup.single_mem_pi`, `DiffContOnCl.circleIntegral_eq_zero`, `IsLocalMinOn.neg`, `FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed`, `AffineMap.homothety_neg_one_apply`, `Matrix.TransvectionStruct.inv_c`, `InnerProductSpace.isSymmetricProjection_rankOne_self`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe`, `LinearIndependent.pair_neg_left_iff`, `hasDerivWithinAt_neg`, `HasFTaylorSeriesUpToOn.eventually_hasFDerivAt`, `Quaternion.imJ_nnratCast`, `ArchimedeanClass.top_eq_mk_iff`, `Ring.choose_neg`, `AddAction.vadd_neg_mem_fixedBy_iff_mem_fixedBy`, `WithTop.untop₀_nonneg`, `CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero`, `hasMFDerivAt_neg`, `LieModule.mem_genWeightSpace`, `Real.fourierIntegralInv_eq_fourierIntegral_neg`, `MeasureTheory.ConvolutionExistsAt.integrable_swap`, `Quaternion.re_zero`, `MeasureTheory.measure_neg_null`, `nndist_smul_le`, `RootPairing.pairing_reflectionPerm_self_left`, `Real.Angle.two_zsmul_coe_pi`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left`, `WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF`, `Polynomial.Chebyshev.U_eval_neg_one`, `LieAlgebra.LoopAlgebra.toFinsupp_symm_single`, `HahnSeries.one_minus_single_neg_mul`, `MeasureTheory.sub_ae_eq_zero`, `AddAut.conj_symm_apply`, `norm_zero`, `Matrix.adjugate_fin_three`, `Real.Angle.two_nsmul_eq_zero_iff`, `Subring.neg_mem'`, `Submodule.topologicalClosure_eq_self`, `LinearMap.hasStrictDerivAt`, `Finset.zero_mem_neg_add_iff`, `AffineMap.hasDerivAt_lineMap`, `IsometryEquiv.constVAdd_symm`, `IsRelPrime.neg_neg`, `WeierstrassCurve.toCharNeTwoNF_s`, `Summable.tendsto_alternating_series_tsum`, `QuaternionAlgebra.sub_im`, `sub_nonneg_of_le`, `cfcₙ_neg`, `ContinuousMapZero.hasFiniteIntegral_of_bound`, `iteratedFDerivWithin_neg_apply`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_const`, `Finset.weightedVSub_empty`, `PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decay`, `TendstoUniformlyOn.neg`, `Polynomial.nthRoots_two_one`, `Quaternion.re_add_im`, `Real.Angle.abs_toReal_neg`, `Seminorm.balanced_closedBall_zero`, `Finset.pluennecke_ruzsa_inequality_nsmul_add`, `Set.indicator_sub`, `Set.zsmul_singleton`, `Function.locallyFinsuppWithin.posPart_add`, `CentroidHom.neg_apply`, `isOpenEmbedding_stereographic_symm`, `LieModule.mem_ker`, `Polynomial.UniversalFactorizationRing.jacobian_resentation`, `LieModule.disjoint_lowerCentralSeries_maxTrivSubmodule_iff`, `intervalIntegral.integral_hasDerivWithinAt_left`, `IsTopologicalAddGroup.exists_antitone_basis_nhds_zero`, `LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional`, `HasFPowerSeriesOnBall.fderiv_eq`, `RCLike.wInner_neg_right`, `Set.image_neg_uIcc`, `RootPairing.pairing_reflectionPerm_self_right`, `CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_inv`, `exists_fun_of_mem_tangentConeAt`, `CochainComplex.HomComplex.δ_zero`, `CFC.abs_neg`, `apply_abs_le_add_of_nonneg`, `RingEquiv.map_neg_one`, `Filter.map_neg_atTop`, `iteratedDerivWithin_const_sub`, `Quaternion.fst_imK_dualNumberEquiv_symm`, `Int.cast_neg_natCast`, `WithLp.zero_fst`, `posPart_nonneg`, `Asymptotics.IsLittleOTVS.zero`, `MvPolynomial.eval₂_neg`, `MeasureTheory.quasiMeasurePreserving_neg_add_swap`, `CategoryTheory.CommSq.shortComplex_f`, `abs_neg_one_pow`, `neg_abs_le`, `PowerSeries.coeff_invOfUnit`, `SchwartzMap.smulLeftCLM_sum`, `MeasureTheory.integral_integral_indicator`, `AddSubgroup.mem_normalizer_iff`, `QuaternionAlgebra.imK_swapEquiv_symm_apply`, `Metric.preimage_vadd_ball`, `LinearEquiv.coe_neg`, `Derivation.neg_apply`, `Quaternion.coe_zero`, `NonarchAddGroupSeminormClass.map_neg_eq_map'`, `AffineMap.hasDerivWithinAt_lineMap`, `MeasureTheory.LocallyIntegrable.neg`, `Finsupp.single_sub`, `edist_neg`, `lie_abelian_iff_equiv_lie_abelian`, `PowerBasis.leftMulMatrix`, `ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_three`, `Orientation.oangle_neg_self_left`, `ContinuousLinearMap.fderiv_of_bilinear`, `has_fderiv_at_filter_real_equiv`, `IsLinearMap.map_neg`, `CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_neg_f`, `MeasureTheory.posConvolution_eq_convolution_indicator`, `ContinuousMultilinearMap.neg_apply`, `Seminorm.gaugeSeminorm_ball`, `ContinuousLinearMap.nnnorm_toSpanSingleton`, `HahnSeries.coeff_sub`, `stereo_left_inv`, `Module.Presentation.finsupp_G`, `ContinuousAlternatingMap.alternatizeUncurryFin_smul`, `ProfiniteAddGrp.limit_zero_val`, `AddSubgroup.closure_singleton_neg`, `tendsto_integral_exp_smul_cocompact`, `Int.cast_negOnePow`, `Matrix.linftyOpIsBoundedSMul`, `Hamming.nnnorm_eq_hammingNorm`, `curveIntegral_segment`, `Asymptotics.isLittleOTVS_fun_neg_left`, `TestFunction.postcompCLM_apply`, `MeasureTheory.regular_neg_iff`, `hasDerivAt_iff_tendsto_slope_left_right`, `BoundedContinuousFunction.instStarModule`, `MeasureTheory.Integrable.neg'`, `HasFTaylorSeriesUpToOn.hasFDerivWithinAt`, `TensorProduct.neg_tmul`, `HomologicalComplex.homologyMap_neg`, `Asymptotics.isBigOTVS_iff_smallSets`, `Derivation.leibniz_inv`, `groupCohomology.map_inv_of_isCocycle₁`, `Orientation.rotation_symm`, `Homeomorph.coe_unitBall_apply_zero`, `multiplicity_neg`, `Submodule.adjoint_subtypeL`, `lp.coeFn_zero`, `TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf`, `MeasureTheory.UnifIntegrable.indicator`, `RingHom.IsIntegralElem.neg`, `Sbtw.oangle₂₃₁_eq_zero`, `inner_re_zero_left`, `IsSelfAdjoint.neg_algebraMap_norm_le_self`, `DFinsupp.update_eq_sub_add_single`, `QuotientAddGroup.norm_eq_infDist`, `Polynomial.smeval_neg_nat`, `IsAddKleinFour.neg_eq_self`, `ContinuousLinearMap.norm_smulRightL`, `Quaternion.star_eq_two_re_sub`, `AffineMap.decomp'`, `PiLp.nndist_toLp_single_same`, `Orientation.oangle_eq_zero_iff_sameRay`, `Submodule.reflection_orthogonalComplement_singleton_eq_neg`, `SModEq.neg`, `CategoryTheory.Preadditive.neg_iso_hom`, `ExistsContDiffBumpBase.u_neg`, `groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂`, `derivWithin.neg`, `HasFDerivWithinAt.fun_smul`, `BoundedContinuousFunction.nnnorm_def`, `iteratedDeriv_const_sub`, `Module.preReflection_apply_self`, `MeasureTheory.convolution_def`, `DirectLimit.neg_def`, `NonUnitalSubringClass.toNegMemClass`, `AddGrpCat.FilteredColimits.colimit_neg_mk_eq`, `Pretrivialization.continuousLinearMapCoordChange_apply`, `ContinuousMultilinearMap.curryLeft_norm`, `Seminorm.ball_zero_eq_preimage_ball`, `AddAction.toPerm_zero`, `WithLp.edist_toLp_snd`, `Polynomial.Splits.coeff_zero_eq_prod_roots_of_monic`, `IsApproximateAddSubgroup.nsmul_inter_nsmul`, `Quaternion.one_im`, `UniformFun.hasBasis_nhds_zero`, `InnerProductSpace.trace_rankOne`, `ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp`, `MDifferentiableWithinAt.cle_arrowCongr`, `deriv.neg`, `fourier_neg'`, `HasFPowerSeriesWithinOnBall.prod`, `MDifferentiableWithinAt.clm_precomp`, `sign_mul_abs`, `SemiNormedGrp.zero_apply`, `ContMDiffVectorBundle.continuousLinearMap`, `IsAddUnit.add_neg_eq_add_neg_iff`, `MeromorphicAt.meromorphicTrailingCoeffAt_of_order_eq_top`, `IsMIntegralCurveOn.comp_mul`, `TendstoLocallyUniformlyOn.neg`, `Quaternion.im_natCast`, `NonUnitalSubring.neg_mem`, `groupHomology.mapCycles₂_id_comp`, `Polynomial.coeff_zero_eq_leadingCoeff_mul_prod_roots_of_splits`, `Matrix.isBoundedSMul`, `WeierstrassCurve.Δ_of_char_three`, `deriv_zero`, `ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply`, `MonomialOrder.degree_neg`, `Polynomial.eq_neg_mul_add_of_aroots_quadratic_eq_pair`, `Quaternion.star_add_self`, `LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton'`, `HasFDerivWithinAt.neg`, `hasStrictDerivAt_const_add_iff`, `LinearMap.linearProjOfIsCompl_apply_right`, `MeasureTheory.setToFun_top_smul_measure`, `isBoundedBilinearMap_compMultilinear`, `PiLp.nnnorm_toLp_single`, `AddMonoidHom.fiberEquivKer_apply`, `Quaternion.sub_re_self`, `neg_convexOn_iff`, `SimpContFract.determinant`, `uniformContinuous_neg`, `derivWithin_ofNat`, `Asymptotics.isEquivalent_zero_iff_eventually_zero`, `ContinuousLinearMap.compL_apply`, `DirectSum.decompose_symm_neg`, `ContinuousLinearMap.lsmul_flip_inj`, `ContDiffMapSupportedIn.hasCompactSupport`, `WithLp.toLp_zero`, `Filter.tendsto_neg_atTop_atBot`, `HasFPowerSeriesOnBall.uniform_geometric_approx`, `SkewMonoidAlgebra.toFinsupp_sub`, `ProperCone.innerDual_zero`, `neg_sub_comm`, `Subring.neg_mem`, `Real.Angle.sign_zero`, `ArchimedeanClass.mk_monotoneOn`, `ContDiffMapSupportedIn.structureMapLM_eq_of_scalars`, `norm_sub_le_mul_volume_of_norm_deriv_le_of_le`, `Function.support_intCast`, `ball_zero_add_singleton`, `tsupport_neg`, `add_neg_le_iff_le_add'`, `Asymptotics.IsBigO.eq_zero_of_norm_pow_within`, `Asymptotics.isBigOTVS_fun_neg_left`, `Set.neg_mem_addCentralizer`, `HasFPowerSeriesWithinAt.fderivWithin_eq`, `nhds_zero_symm`, `inCoordinates_apply_eq₂`, `Asymptotics.isBigOTVS_fun_neg_right`, `isLUB_neg'`, `exists_homeomorph_image_interior_closure_frontier_eq_unitBall`, `FormalMultilinearSeries.id_comp'`, `MulSemiringActionHom.map_neg`, `eq_zero_or_norm_pos`, `associator_op`, `MeasureTheory.Measure.addModularCharacterFun_map_zero`, `groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv`, `AddSubmonoid.mem_neg`, `analyticOrderAt_ne_zero`, `AddGroupExtension.rightHom_inl`, `AddGroupCone.nonneg.hasMemOrNegMem`, `ContinuousMultilinearMap.range_toUniformOnFun`, `groupHomology.chainsMap_f_single`, `ContinuousLinearMap.IsPositive.conj_adjoint`, `ContinuousLinearMap.flip_apply`, `Real.Angle.coe_eq_zero_iff`, `derivWithin_inv`, `Matrix.toEuclideanCLM_toLp`, `Seminorm.smul_closedBall_zero`, `sub_smodEq_zero`, `Seminorm.balanced_ball_zero`, `FreeGroup.sum.map_one`, `DifferentiableWithinAt.hasDerivWithinAt`, `InnerProductSpace.Core.inner_neg_right`, `isSMulRegular_submodule_iff_right_eq_zero_of_smul`, `BoundedContinuousFunction.innerProbChar_zero`, `FormalMultilinearSeries.coeff_eq_zero`, `Ioo_smul_sphere_zero`, `MeasureTheory.condExp_neg`, `CochainComplex.HomComplex.Cochain.ofHom_neg`, `posPart_zero`, `WeierstrassCurve.b₄_of_char_three`, `SchwartzMap.smulLeftCLM_fun_neg`, `PiLp.instNormSMulClass`, `ContMDiffOn.clm_precomp`, `CharP.orderOf_eq_two_iff`, `hasGradientAt_iff_isLittleO_nhds_zero`, `contDiffOn_nat_iff_continuousOn_differentiableOn`, `Real.Angle.toReal_neg_eq_neg_toReal_iff`, `ImplicitFunctionData.leftDeriv_fderiv_implicitFunction`, `ContinuousLinearMap.bilinearRestrictScalars_apply_apply`, `Set.indicator_compl'`, `Homeomorph.subLeft_symm_apply`, `InnerProductSpace.adjoint_rankOne`, `FormalMultilinearSeries.compAlongComposition_nnnorm`, `Quaternion.imK_coe`, `stereoInvFun_apply`, `monovaryOn_iff_forall_smul_nonneg`, `locallyLipschitzOn_neg_iff`, `ContMDiffWithinAt.neg_section`, `TrivSqZeroExt.mul_left_eq_one`, `Summable.tendsto_atTop_zero`, `TendstoLocallyUniformly.neg`, `Int.ceil_eq_zero_iff`, `CochainComplex.HomComplex.Cochain.zero_v`, `lp.single_apply_ne`, `HurwitzZeta.sinKernel_neg`, `Filter.EventuallyEq.hasDerivAt_iff`, `Submodule.disjoint_span_singleton`, `Manifold.IsImmersionAt.writtenInCharts`, `InnerProductSpace.rankOne_eq_zero`, `card_nsmul_eq_zero`, `le_neg`, `IsAddCyclic.card_nsmul_eq_zero_le`, `ContMDiffSection.coe_zero`, `LieSubmodule.lieSpan_eq_bot_iff`, `HahnEmbedding.IsPartial.strictMono`, `MeasureTheory.Measure.addHaar_ball_center`, `hasDerivAt_deriv_iff`, `RCLike.mul_wInner_left`, `IsCoprime.neg_right_iff`, `IsStarNormal.neg`, `ContinuousAlternatingMap.norm_curryLeft`, `hasDerivAtFilter_neg`, `ContDiffBump.normed_neg`, `Real.Angle.toCircle_zero`, `Matrix.Pivot.listTransvecCol_getElem`, `WeierstrassCurve.Projective.negDblY_of_Z_eq_zero`, `MeasureTheory.Measure.toSphere_apply_univ`, `Antivary.neg_left`, `SeminormedAddGroup.disjoint_nhds_zero`, `vadd_eq_iff_eq_neg_vadd`, `MeasureTheory.martingale_zero`, `LinearMap.map_neg`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `div_neg_self`, `Filter.not_nonneg_sub_iff`, `InnerProductSpace.inner_right_rankOne_apply`, `CFC.negPart_eq_neg`, `MeromorphicAt.neg_iff`, `Rep.coinvariantsTensorFreeLEquiv_apply`, `strictMono_iff_map_pos`, `ContDiff.differentiable_iteratedFDeriv`, `SchwartzMap.pairing_apply`, `Asymptotics.isBigOTVS_iff_isBigO`, `hasGradientAt_const`, `Bornology.isVonNBounded_sub_of_nonempty`, `ZMod.val_neg_of_ne_zero`, `LineDeriv.iteratedLineDerivOp_zero`, `groupHomology.toCycles_comp_isoCycles₁_hom_apply`, `MeasureTheory.SimpleFunc.memLp_iff_finMeasSupp`, `WithSeminorms.isVonNBounded_iff_seminorm_bddAbove`, `CochainComplex.HomComplex.δ_ofHom`, `ball_add_zero`, `Asymptotics.IsBigO.neg_left`, `hasDerivAt_add_const_iff`, `HahnSeries.cardSuppLTSubfield_carrier`, `Module.FaithfullyFlat.rTensor_exact_iff_exact`, `max_zero_add_max_neg_zero_eq_abs_self`, `Quaternion.add_imI`, `MvPowerSeries.coeff_inv`, `EuclideanGeometry.oangle_eq_zero_iff_wbtw`, `PolynomialModule.single_apply`, `ContinuousLinearMap.fderivWithin_of_bilinear`, `LaurentSeries.derivative_iterate_coeff`, `QuadraticMap.toBilin_apply`, `HasFPowerSeriesOnBall.compContinuousLinearMap`, `StrongFEPair.hg₀`, `groupHomology.mapCycles₂_comp_i`, `Quaternion.smul_coe`, `neg_thickening`, `AlgebraicClosure.instIsAlgClosureOfIsAlgebraic`, `Set.injOn_iff_map_eq_zero`, `LinearMap.neg_apply`, `QuaternionAlgebra.im_natCast`, `gaugeSeminorm_ball_one`, `WithCStarModule.equiv_neg`, `AddSubgroup.isComplement_iff_existsUnique_neg_add_mem`, `ContDiffMapSupportedIn.uniformSpace_eq_iInf`, `SignType.coe_neg`, `Function.locallyFinsuppWithin.instIsOrderedAddMonoid`, `Pi.orthonormalBasis_apply`, `iteratedFDerivWithin_smul_const_apply`, `BddAbove.range_neg`, `neg_le_sub_iff_le_add'`, `LinearMap.IsSymmetric.diagonalization_symm_apply`, `PiTensorProduct.liftIsometry_tprodL`, `IsRightUniformAddGroup.uniformity_eq`, `VectorField.mpullback_smul_apply`, `CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff`, `Quaternion.instIsDomain`, `neg_one_pow_char`, `QuadraticAlgebra.norm_neg`, `stereographic'_target`, `curveIntegral_segment_const`, `hasDerivWithinAt_one`, `CategoryTheory.InjectiveResolution.extMk_zero`, `FourierTransform.fourierInv_neg`, `Continuous.exists_contMDiff_approx`, `CategoryTheory.ShortComplex.ab_exact_iff_function_exact`, `VectorBundleCore.localTriv_symm_apply`, `groupHomology.boundariesOfIsBoundary₁_coe`, `CategoryTheory.ShortComplex.homologyMap'_neg`, `AddSubgroup.neg_subset_closure`, `AddSubmonoid.mk_add_mk_neg_eq_zero`, `CliffordAlgebra.EquivEven.neg_e0_mul_v`, `TestFunction.coe_ofSupportedInCLM`, `MeasureTheory.measure_sdiff_neg_vadd`, `Quaternion.neg_imJ`, `ContDiffBump.normed_convolution_eq_right`, `CategoryTheory.Pretriangulated.Triangle.rotate_mor₃`, `continuousSMul_closedBall_ball`, `Matrix.det_eq_sum_column_mul_submatrix_succAbove_succAbove_det`, `Nonneg.instNontrivialSubtypeLeOfNatOfAddLeftMono`, `InnerProductSpace.rankOne_eq_rankOne_iff_comm`, `mdifferentiableWithinAt_neg_section`, `IsometryEquiv.addLeft_symm`, `VectorField.mpullbackWithin_neg_apply`, `AddCommute.neg_right`, `Left.neg_nonpos_iff`, `ContDiffMapSupportedIn.continuous_iff_comp_withOrder`, `CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φH`, `Metric.preimage_vadd_closedEBall`, `Function.locallyFinsuppWithin.coe_sub`, `CategoryTheory.Comonad.coalgebraPreadditive_homGroup_neg_f`, `Int.floor_neg`, `CategoryTheory.Preadditive.neg_comp_neg_assoc`, `AddGroupFilterBasis.conj'`, `LieModuleHom.coe_neg`, `IncidenceAlgebra.mu_apply`, `ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear`, `neg_div_self`, `ContinuousLinearMap.precompR_apply`, `sameRay_smul_left_iff`, `Quaternion.coe_smul`, `RootPairing.corootSpanMem_reflectionPerm_self`, `ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le`, `Matrix.blockDiagonal_neg`, `Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff`, `SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero`, `AddChar.forall_apply_eq_zero`, `Finset.subConst_neg_left`, `integral_smul_fderiv_eq_neg_fderiv_smul_of_integrable`, `Finset.addDysonETransform_snd`, `antitone_iff_map_nonpos`, `tendsto_zero_of_isBoundedUnder_smul_of_tendsto_cobounded`, `FormalMultilinearSeries.iteratedFDerivSeries_eq_zero`, `addInvariantVectorField_eq_mpullback`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd'`, `hasDerivAtFilter_one`, `AddAction.vadd_fixedBy`, `isScalarTower_sphere_sphere_sphere`, `AdicCompletion.val_neg_apply`, `CategoryTheory.Preadditive.neg_comp_neg`, `IncidenceAlgebra.mu_ofDual`, `DFinsupp.neLocus_neg`, `ContDiffBumpBase.support`, `ContMDiffSection.coe_smul`, `Quaternion.imI_neg`, `FiniteArchimedeanClass.liftOrderHom_mk`, `signedDist_zero`, `Asymptotics.IsLittleO.isLittleOTVS`, `MeasureTheory.hasFiniteIntegral_iff_edist`, `hasDerivAt_ofNat`, `Finset.vadd_finset_subset_iff`, `Orientation.oangle_eq_zero_iff_angle_eq_zero`, `Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero`, `Function.Injective.isLieAbelian`, `IsUpperSet.neg`, `neg_add_neg_iff`, `iteratedFDerivWithin_eq_equiv_comp`, `Asymptotics.IsTheta.eq_zero_iff`, `Function.HasTemperateGrowth.neg`, `DifferentiableAt.isBigOTVS_sub`, `MeasureTheory.measure_neg_vadd_symmDiff`, `nhds_basis_balanced`, `Matrix.mul_neg`, `IsRelPrime.neg_right`, `AlternatingMap.mkContinuousAlternating_norm_le`, `conjneg_neg`, `RingPreordering.mem_support`, `NormedAddGroupHom.mem_ker`, `ContDiffMapSupportedIn.structureMapCLM_zero_apply`, `VonNeumannAlgebra.centralizer_centralizer'`, `FormalMultilinearSeries.mkPiRing_coeff_eq`, `ZeroHom.sub_apply`, `mul_gaussSum_inv_eq_gaussSum`, `SchwartzMap.integral_bilinear_deriv_right_eq_neg_left`, `Finset.ruzsa_triangle_inequality_add_add_negAdd`, `Quaternion.mul_re`, `IsBoundedLinearMap.lim_zero_bounded_linear_map`, `ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap`, `MeasureTheory.eLpNorm'_neg`, `AddGrpCat.zero_apply`, `antivaryOn_neg_left`, `Quaternion.imI_nnratCast`, `Asymptotics.isLittleO_neg_right`, `ZNum.cast_add`, `MeasureTheory.Measure.sub_mem_nhds_zero_of_addHaar_pos`, `ZNum.cast_lt`, `Finset.subConst_neg_right`, `NormedSpace.polar_ball_subset_closedBall_div`, `EuclideanSpace.instIsManifoldSphere`, `Finset.tendsto_Ioo_neg`, `groupHomology.eq_d₃₂_comp_inv_apply`, `Set.neg_mem_Ioo_iff`, `InnerProductSpace.comp_rankOne`, `OrthonormalBasis.starProjection_eq_sum_rankOne`, `SeminormedAddGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_zero`, `HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum`, `Fin.partialSum_left_neg`, `neg_add`, `Quaternion.imK_fst_dualNumberEquiv`, `ProbabilityTheory.Kernel.setIntegral_deterministic`, `tendsto_neg_nhdsLT_neg`, `ContDiffMapSupportedIn.zero_on_compl'`, `Quaternion.imK_nnratCast`, `PerfectClosure.neg_mk`, `Mathlib.Meta.NormNum.IsInt.neg_to_eq`, `TotallyBounded.isVonNBounded`, `lp.single_neg`, `WeierstrassCurve.Δ_of_isShortNF`, `IsPrimitiveRoot.prod_pow_sub_one_eq_order`, `KaehlerDifferential.exact_mapBaseChange_map`, `Matrix.J_squared`, `IsAddFreimanHom.neg`, `CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg`, `Set.op_vadd_inter_ne_empty_iff`, `Function.Antiperiodic.sub_eq'`, `intervalIntegral.integral_cases`, `ContinuousLinearMap.adjoint_inner_left`, `IsLocalMaxOn.neg`, `AddSubgroup.disjoint_def`, `PointwiseConvergenceCLM.isInducing_inducingFn`, `FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le`, `star_neg`, `Orientation.oangle_rotation_oangle_right`, `ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf'`, `EuclideanGeometry.oangle_add_cyc3`, `Set.image_neg_Ioi`, `ContinuousLinearMap.isBoundedBilinearMap`, `ContinuousMultilinearMap.hasBasis_nhds_zero`, `HurwitzZeta.hurwitzEvenFEPair_zero_symm`, `CompactlySupportedContinuousMap.integrable`, `WithCStarModule.neg_apply`, `Nat.cast_card_eq_zero`, `HahnEmbedding.IsPartial.truncLT_mem_range`, `AddCommute.neg_add_cancel`, `MeasureTheory.integral_average_sub`, `groupHomology.single_one_fst_sub_single_one_fst_mem_boundaries₂`, `egauge_pi`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right`, `compContinuousLinearMap_zero`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply`, `MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere`, `FormalMultilinearSeries.le_radius_compContinuousLinearMap`, `odd_neg_one`, `Differentiable.fderiv_two`, `continuousMultilinearCurryFin0_symm_apply`, `DFinsupp.neLocus_sub_left`, `Asymptotics.isBigOTVS_congr`, `CochainComplex.HomComplex.Cochain.ofHomotopy_refl`, `inv_norm_smul_mem_unitClosedBall`, `slope_neg_fun`, `add_neg_nonpos_iff`, `Seminorm.neg_mem_ball_zero`, `CFC.abs_of_nonpos`, `DFinsupp.coe_neg`, `BoxIntegral.integralSum_neg`, `Orientation.oangle_add_oangle_rev`, `Asymptotics.isBigOTVS_neg_right`, `LieModule.Cohomology.twoCochain_skew`, `VectorField.lieBracketWithin_smul_left`, `inner_neg_right`, `VectorField.mlieBracketWithin_const_smul_left`, `sInf_neg`, `Orientation.oangle_self`, `Quaternion.re_fst_dualNumberEquiv`, `ContinuousAlternatingMap.ofSubsingletonLIE_apply`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply`, `LinearOrderedAddCommGroupWithTop.add_neg_cancel_iff_ne_top`, `FormalMultilinearSeries.compAlongComposition_bound`, `Quaternion.eq_re_of_eq_coe`, `continuousMultilinearCurryRightEquiv_symm_apply`, `Complex.liftAux_neg_I`, `MeasureTheory.average_zero`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le`, `Set.indicator_neg'`, `Function.HasTemperateGrowth.zero`, `WeierstrassCurve.VariableChange.inv_def`, `ContDiff.euclidean_dist`, `AddChar.neg_apply'`, `torusIntegral_neg`, `lp.single_zero`, `LaurentSeries.derivative_apply`, `MeasureTheory.integral_neg`, `Quaternion.imK_zero`, `LinearOrderedAddCommGroupWithTop.neg_pos`, `eq_on_neg`, `groupHomology.mapCycles₁_id_comp_apply`, `constFormalMultilinearSeries_apply_zero`, `IntermediateField.neg_mem`, `hasFTaylorSeriesUpToOn_top_iff'`, `ContinuousLinearMap.lsmul_apply`, `MeasureTheory.measurePreserving_add_prod_neg_right`, `LinearIsometryEquiv.conjStarAlgEquiv_trans`, `IsLocalMin.neg`, `FormalMultilinearSeries.radius_smul_eq`, `Set.image_neg_Ici`, `ContinuousMap.linearIsometryBoundedOfCompact_symm_apply`, `WittVector.mul_polyOfInterest_aux4`, `neg_one_pow_expChar`, `ContinuousLinearMap.bilinearComp_zero_right`, `neg_add_neg_iff_lt`, `Polynomial.roots_C_mul_X_add_C`, `Matrix.circulant_single_one`, `LinearMap.charpoly_eq_X_pow_iff`, `QuadraticAlgebra.star_mk`, `AlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq`, `LieModule.isTrivial_of_nilpotencyLength_le_one`, `MeasureTheory.eLpNorm'_smul_le_mul_eLpNorm'`, `hasDerivAtFilter_add_const_iff`, `ContDiffMapSupportedIn.zero_on_compl`, `isBounded_iff_asymptoticCone_subset_singleton`, `Basis.ofRankEqZero_apply`, `MeasureTheory.tendsto_indicator_ge`, `CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_hom_app`, `CochainComplex.HomComplex.Cocycle.toSingleMk_zero`, `InnerProductSpace.rank_rankOne`, `ContMDiffOn.cle_arrowCongr`, `AddSubgroup.torsionBy.nsmul_iff`, `Polynomial.coeff_sub_eq_neg_right_of_lt`, `neg_eq_zero`, `MeasureTheory.aemeasurable_lconvolution`, `MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zero`, `Quaternion.norm_coe`, `Quaternion.sub_self_im`, `neg_lt_neg`, `VertexOperator.ncoeff_apply`, `ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply`, `gauge_closure_zero`, `HahnSeries.mem_cardSuppLTAddSubgroup`, `MeasureTheory.SimpleFunc.memLp_approxOn_range`, `HahnSeries.order_abs`, `Pi.single_sub`, `AddCircle.equivIccQuot_comp_mk_eq_toIocMod`, `mdifferentiableAt_neg_section`, `VectorFourier.fourierIntegral_convergent_iff`, `eq_add_neg_of_add_eq`, `Algebra.Extension.Cotangent.mk_eq_zero_iff`, `Finset.image_add_right'`, `CochainComplex.HomComplex.Cocycle.coe_neg`, `ContinuousLinearMap.adjointAux_apply`, `FreeAbelianGroup.seq_neg`, `MvPolynomial.eval_neg`, `Module.Presentation.finsupp_var`, `isGLB_neg`, `Dense.eq_zero_of_mem_orthogonal`, `ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self`, `gauge_ball`, `HurwitzZeta.cosZeta_eq`, `NormedAddGroupHom.zero_apply`, `ZMod.natAbs_valMinAbs_eq_natAbs_valMinAbs`, `ExistsContDiffBumpBase.w_support`, `AbsolutelyContinuousOnInterval.neg`, `sub_eq_zero_of_eq`, `ZeroAtInftyContinuousMap.neg_apply`, `MeasureTheory.UniformIntegrable.spec'`, `RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem`, `HasFPowerSeriesWithinOnBall.sub`, `BooleanRing.neg_eq`, `Metric.preimage_add_left_closedEBall`, `ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear`, `infEDist_neg`, `PowerBasis.trace_gen_eq_nextCoeff_minpoly`, `ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall`, `monotone_iff_map_nonneg`, `AddMonoidAlgebra.supDegree_neg`, `OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply`, `hasFDerivAt_integral_of_dominated_loc_of_lip'`, `ConvexCone.coe_strictlyPositive`, `AddMonoidHom.neg_apply`, `arrowAddAction_vadd`, `InnerProductSpace.rankOne_def`, `HasDerivAt.smul_const`, `InnerProductSpace.Core.inner_self_eq_zero`, `Module.FaithfullyFlat.iff_exact_iff_rTensor_exact`, `slope_eq_zero_iff`, `ContinuousLinearMap.coe_flipₗᵢ'`, `add_add_neg_cancel'_right`, `MeasureTheory.tendsto_measure_vadd_diff_isCompact_isClosed`, `groupHomology.π_comp_H2Iso_hom`, `ContinuousLinearMap.adjointAux_inner_left`, `sub_sub_cancel_left`, `ZeroAtInftyContinuousMap.sub_apply`, `Filter.map_neg'`, `deriv_inv`, `CochainComplex.mappingCone.inl_snd`, `PowerSeries.evalNegHom_X`, `fderivWithin_fderivWithin_eq_of_mem_nhds`, `Char.card_pow_card`, `ContinuousLinearMap.norm_smulRight_apply`, `ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv`, `Interval.add_eq_zero_iff`, `contDiff_iff_continuous_differentiable`, `Int.cast_negSucc`, `hasDerivAt_const`, `AddSubmonoid.coe_negOrderIso_symm_apply`, `AddAction.stabilizerEquivStabilizer_symm_apply`, `nhds_basis_Ioo_pos`, `coe_set_eq_zero`, `HasFPowerSeriesWithinOnBall.uniform_geometric_approx'`, `neg_nonpos`, `add_eq_zero_iff_eq_neg`, `ball_sub_zero`, `Homeomorph.addRight_symm`, `UniformSpace.Completion.norm_toComplL`, `Real.zero_at_infty_fourierIntegral`, `QuaternionAlgebra.ofNat_imK`, `groupHomology.pOpcycles_comp_opcyclesIso_hom_apply`, `ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply`, `instSMulCommClass_sphere_closedBall_closedBall`, `ContinuousMap.toLp_def`, `ZMod.eq_neg_of_valMinAbs_eq_neg_valMinAbs`, `groupHomology.mapCycles₁_comp_i_apply`, `OrderDual.instSMulPosReflectLE`, `ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker`, `AddCommute.conj`, `VectorField.lieBracket_fmul_left`, `RootPairing.pairing_neg_one_neg_four_iff`, `SchwartzMap.integral_bilin_fourier_eq`, `Matrix.J_transpose`, `Orientation.oangle_rotation_self_left`, `Finset.tendsto_Icc_neg_atTop_atTop`, `SchwartzMap.zero_apply`, `intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right`, `smul_neg`, `MeasureTheory.integral_of_isEmpty`, `LinearMap.BilinForm.neg_left`, `groupHomology.mapCycles₂_comp`, `AddGroupSeminormClass.map_neg_eq_map`, `ContinuousMultilinearMap.prodL_apply`, `lt_add_neg_iff_lt`, `Matrix.IsTotallyUnimodular.apply`, `Finset.smul_neg`, `Filter.neg_nhdsGT`, `affinity_unitBall`, `IsTopologicalAddGroup.addNegClosureNhd.nhds`, `hasFTaylorSeriesUpToOn_succ_iff_right`, `sub_add_cancel_left`, `ContinuousLinearMap.coe_flipMultilinearEquiv`, `posPart_nonpos`, `ContinuousMultilinearMap.norm_map_init_le`, `SchwartzMap.tsupport_lineDerivOp_subset`, `Quaternion.one_imK`, `trace_eq_finrank_mul_minpoly_nextCoeff`, `SchwartzMap.smulRightCLM_apply_apply`, `MulChar.val_neg_one_eq_one_of_odd_order`, `DFinsupp.neLocus_self_sub_right`, `lie_self`, `MeasureTheory.setIntegral_tsupport`, `LinearIsometryEquiv.conjStarAlgEquiv_refl`, `CategoryTheory.DifferentialObject.shiftZero_inv_app_f`, `MeasureTheory.setToFun_smul_left`, `ArchimedeanClass.mk_zero`, `MeasureTheory.MemLp.const_smul`, `MeasureTheory.finStronglyMeasurable_of_measurable`, `AddSemiconjBy.neg_symm_left_iff`, `MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin`, `RCLike.ofReal_neg`, `Function.locallyFinsuppWithin.coe_zsmul`, `add_ball_zero`, `iteratedFDeriv_neg_apply`, `LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_sup`, `CategoryTheory.ShortComplex.opcyclesMap_neg`, `MeasureTheory.condExp_of_not_integrable`, `SchwartzMap.toTemperedDistributionCLM_apply_apply`, `VectorField.mpullback_zero`, `fderivWithin_fderivWithin_eq_of_eventuallyEq`, `ExistsContDiffBumpBase.u_exists`, `Function.support_fun_neg`, `AnalyticWithinAt.neg`, `MeasureTheory.condExp_of_not_le`, `card_nsmul_eq_zero'`, `curveIntegral_of_not_completeSpace`, `HahnSeries.cardSupp_neg`, `Metric.preimage_vadd_sphere`, `LieModule.nilpotencyLength_eq_one_iff`, `groupHomology.coe_mapCycles₂`, `AddSubgroup.coe_topologicalClosure_bot`, `PiTensorProduct.liftEquiv_symm_apply`, `lt_neg_add_iff_add_lt`, `coe_smulCardAddSubgroup`, `CategoryTheory.ShortComplex.Homotopy.symm_h₀`, `ArithmeticFunction.intCoe_mul`, `Quaternion.normSq_inv`, `TestFunction.coe_ofSupportedInLM`, `extDerivWithin_fun_smul`, `IsTopologicalAddGroup.toContinuousNeg`, `RCLike.wInner_zero_right`, `RootPairing.pairingIn_reflectionPerm_self_left`, `ZMod.neg_val`, `Monovary.neg_right`, `FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum`, `Asymptotics.isLittleOTVS_fun_neg_right`, `MeasureTheory.condExp_indicator`, `cfcₙ_neg_id`, `ConvexCone.strictlyPositive_le_positive`, `VectorField.mpullbackWithin_neg`, `groupHomology.comp_d₁₀_eq`, `preNormEDS_neg`, `Quaternion.imI_im`, `Orientation.oangle_sign_neg_left`, `Matrix.adjugate_fin_three_of`, `TemperedDistribution.smulLeftCLM_sub`, `groupHomology.H1π_comp_map_apply`, `MultilinearMap.map_update_neg`, `neg_one_pow_eq_pow_mod_two`, `FiniteField.isSquare_neg_two_iff`, `CategoryTheory.shift_equiv_triangle`, `add_abs_nonneg`, `AddGroupFilterBasis.N_zero`, `WeierstrassCurve.Projective.addXYZ_neg`, `iteratedFDerivWithin_comp_sub`, `intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae`, `IncidenceAlgebra.coe_neg`, `ContinuousLinearMapWOT.hasBasis_seminorms`, `tendsto_abs_nhdsNE_zero`, `ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear`, `EuclideanSpace.sphere_zero_eq`, `monovary_iff_forall_smul_nonneg`, `ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear`, `VectorField.mlieBracketWithin_zero_right`, `mem_closure_zero_iff_norm`, `NonarchAddGroupNormClass.eq_zero_of_map_eq_zero`, `ContinuousLinearMap.aestronglyMeasurable_comp₂`, `continuousSMul_sphere_closedBall`, `differentiableWithinAt_comp_sub`, `HurwitzZeta.completedHurwitzZetaEven_eq`, `lt_abs`, `SchwartzMap.smulLeftCLM_const`, `Finsupp.filter_sub`, `AddGroup.card_nsmul_eq_card_nsmul_card_univ`, `LieIdeal.isLieAbelian_iff`, `AddCon.mem_addSubgroup_iff`, `MeasureTheory.setToFun_indicator_const`, `neg_add_eq_of_eq_add`, `Set.sub_mem_Ioc_zero_iff_right`, `CategoryTheory.kernelCokernelCompSequence.inr_φ_fst_assoc`, `strictConvexSpace_iff`, `MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le`, `vadd_ball_zero`, `HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt`, `ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff`, `Odd.neg_zpow`, `neg_cthickening`, `LieModule.Cohomology.mem_twoCochain_iff`, `Function.locallyFinsuppWithin.toClosedBall_divisor`, `hasDerivAt_of_tendstoUniformlyOn`, `Summable.alternating`, `ZMod.isSquare_neg_one_iff`, `IsMaxFilter.neg`, `AffineMap.hasDerivAt`, `Matrix.toLin_apply_eq_zero_iff`, `hasDerivWithinAt_congr_set`, `le_abs`, `QuaternionAlgebra.imK_natCast`, `Finsupp.erase_eq_sub_single`, `TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf`, `FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq`, `ArithmeticFunction.coe_zeta_mul_coe_moebius`, `inner_zero_left`, `IsRelPrime.neg_left_iff`, `HasFDerivWithinAt.fun_neg`, `MeasureTheory.setToFun_zero_left`, `HVertexOperator.compHahnSeries_smul`, `Asymptotics.isBigOWith_zero`, `Equiv.addRight_symm_apply`, `IncidenceAlgebra.sum_Icc_mu_left`, `linearDepOn_iff`, `ZMod.lift_castAddHom`, `Quaternion.im_coe`, `Finset.weightedVSubVSubWeights_apply_right`, `Ideal.Cotangent.smul_eq_zero_of_mem`, `WithLp.toLp_listSum`, `Quaternion.re_exp`, `closedBall_zero_sub_singleton`, `ContinuousLinearMap.norm_precompR_le`, `ContDiffMapSupportedIn.structureMapLM_apply_withOrder`, `neg_rayOfNeZero`, `AddChar.div_apply`, `Quaternion.algebraMap_injective`, `hasStrictDerivAt_finCons'`, `Asymptotics.isLittleO_id_one`, `abs_mul_sign`, `MeasureTheory.quasiMeasurePreserving_neg_add`, `Pi.enorm_single`, `hasDerivWithinAt_taylorWithinEval_at_Icc`, `CategoryTheory.Preadditive.comp_neg_assoc`, `groupHomology.toCycles_comp_isoCycles₁_hom_assoc`, `meromorphicNFAt_iff_analyticAt_or`, `ContinuousLinearMap.isBoundedLinearMap_comp_right`, `quadratic_eq_zero_iff_of_discrim_eq_zero`, `RCLike.sqrt_eq_real_add_ite`, `LieAlgebra.abelian_iff_derived_one_eq_bot`, `Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg`, `ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear`, `HasFPowerSeriesWithinAt.pi`, `FormalMultilinearSeries.neg_apply`, `NormedSpace.isVonNBounded_iff'`, `zsmul_zero_sub`, `VonNeumannAlgebra.mem_carrier`, `MeasureTheory.hasFiniteIntegral_neg_iff`, `differentiableOn_fun_neg_iff`, `Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence`, `hasStrictDerivAt_finCons`, `PiTensorProduct.liftEquiv_apply`, `inner_neg_neg`, `HahnSeries.coe_cardSuppLTAddSubgroup`, `OpenPartialHomeomorph.univUnitBall_target`, `hasFTaylorSeriesUpTo_top_iff'`, `Set.neg_smul`, `IsIsotypicOfType.linearEquiv_finsupp`, `fderivWithin_iteratedFDerivWithin`, `Orientation.rotation_neg_orientation_eq_neg`, `MultilinearMap.mkContinuousLinear_norm_le`, `Orientation.eq_rotation_self_iff`, `HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff`, `WeierstrassCurve.Δ_of_isShortNF_of_char_three`, `ExteriorAlgebra.liftAlternating_one`, `MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_le_of_meas`, `PolynomialModule.zero_apply`, `LinearIsometryEquiv.piLpCongrRight_single`, `antivary_neg`, `ContinuousLinearMap.deriv_of_bilinear`, `CochainComplex.HomComplex.Cochain.rightShift_zero`, `balanced_neg`, `Orientation.areaForm'_apply`, `Asymptotics.isBigO_const_iff`, `IsTopologicalAddGroup.isOpenMap_iff_nhds_zero`, `ZMod.lift_comp_coe`, `groupCohomology.cocycles₁_map_inv`, `ContinuousLinearMap.nnnorm_holder_apply_apply_le`, `TrivSqZeroExt.mul_inv_cancel`, `QuaternionAlgebra.coe_intCast`, `AddSubgroup.closure_toAddSubmonoid`, `Set.neg_Ici`, `TestFunctionClass.map_hasCompactSupport`, `tendsto_zero_of_meromorphicOrderAt_pos`, `AddSubmonoid.coe_neg`, `ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf`, `FormalMultilinearSeries.norm_compContinuousLinearMap_le`, `RootPairing.isReduced_iff'`, `Quaternion.normSq_eq_norm_mul_self`, `hasDerivAt_inv`, `MeasureTheory.Measure.Regular.neg`, `ContinuousLinearMap.bilinear_hasTemperateGrowth`, `AddSubgroup.zmultiples_zero_eq_bot`, `ascPochhammer_eval_eq_zero_iff`, `IsBoundedBilinearMap.isBoundedLinearMap_deriv`, `antitone_iff_map_nonneg`, `Bornology.isVonNBounded_iff_smul_tendsto_zero`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin`, `Representation.finsuppToCoinvariants_single_mk`, `neg_le_iff_add_nonneg'`, `groupHomology.H2π_comp_map_assoc`, `IsApproximateAddSubgroup.two_nsmul_covByVAdd`, `Submodule.neg_mem_iff`, `RestrictedProduct.single_sub`, `TrivSqZeroExt.inv_mul_cancel`, `CentroidHom.coe_neg`, `ContinuousLinearMap.prodMapL_apply`, `ContinuousLinearMap.uncurryLeft_apply`, `HilbertBasis.dense_span`, `sub_eq_self`, `edist_neg_neg`, `CategoryTheory.Preadditive.instMonoNegHom`, `Submodule.orthogonal_orthogonal_eq_closure`, `MeasureTheory.condExpL1_neg`, `ContMDiffAt.neg`, `AnalyticOnNhd.preimage_zero_mem_codiscrete`, `LieModule.mem_maxTrivSubmodule`, `Finset.zsmul_eq_empty`, `monovary_neg`, `CategoryTheory.Pretriangulated.Triangle.neg_hom₁`, `Set.preimage_vadd_neg`, `SeminormFamily.basisSets_neg`, `MeasureTheory.Measure.addHaar_real_closedBall'`, `ConvexOn.neg`, `intervalIntegral.integral_hasStrictFDerivAt`, `ContinuousAlternatingMap.curryLeft_compContinuousLinearMap`, `LieAlgebra.IsKilling.apply_coroot_eq_cast`, `nnnorm_neg`, `ZMod.invDFT_def'`, `contMDiffOn_continuousLinearMapCoordChange`, `fderivWithin_smul`, `RingHom.IsIntegralElem.neg_iff`, `VectorField.mpullbackWithin_zero`, `posPart_def`, `ContinuousMultilinearMap.curryFinFinset_apply_const`, `InnerProductSpace.enorm_rankOne`, `midpoint_neg_self`, `lineDifferentiableWithinAt_zero`, `mfderiv_coe_sphere_injective`, `ContinuousMultilinearMap.compContinuousLinearMapLRight_apply`, `Convex.exists_forall_hasDerivWithinAt`, `MvPolynomial.vars_neg`, `hasDerivWithinAt_taylor_coeff_within`, `AddGroupFilterBasis.neg`, `DFinsupp.single_neg`, `Set.image_neg_Iio`, `HasFPowerSeriesAt.hasStrictDerivAt`, `ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self`, `circleIntegral.integral_radius_zero`, `Set.neg_mem_Ioc_iff`, `MeasureTheory.setIntegral_indicator`, `IsAddKleinFour.eq_finset_univ`, `AddAut.conj_inv_apply`, `Function.Periodic.nat_mul_sub_eq`, `OpenPartialHomeomorph.univBall_apply_zero`, `InnerProductGeometry.angle_zero_left`, `LieModule.Cohomology.d₁₂_apply_apply_ofTrivial`, `QuaternionAlgebra.coe_neg`, `Set.indicator_diff'`, `Equiv.neg_addRight`, `ContDiff.smulRight`, `HurwitzZeta.completedCosZeta₀_neg`, `Equiv.addRight_zero`, `ContinuousMultilinearMap.flipLinear_apply_apply`, `mem_leftAddCoset_iff`, `HasStrictFDerivAt.neg`, `MeromorphicOn.fun_neg`, `ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall`, `LinearMap.hasDerivWithinAt`, `MeasureTheory.setToFun_neg`, `toMeromorphicNFOn_of_not_meromorphicOn`, `CStarModule.inner_self`, `FormalMultilinearSeries.comp_id`, `iteratedDeriv_const_zero`, `CategoryTheory.Pretriangulated.Triangle.neg_hom₃`, `Function.HasTemperateGrowth.fun_neg`, `ContinuousMap.nnnorm_smul_const`, `groupHomology.d₁₀ArrowIso_inv_right`, `CategoryTheory.ShortComplex.ShortExact.comp_extClass_assoc`, `signedDist_vadd_left_swap`, `FormalMultilinearSeries.cpolynomialAt_changeOrigin_of_finite`, `SeparationQuotient.mk_eq_zero_iff`, `TrivSqZeroExt.invOf_eq_inv`, `mem_rightAddCoset_iff`, `WithCStarModule.equiv_zero`, `hasFTaylorSeriesUpTo_succ_nat_iff_right`, `OpenPartialHomeomorph.contDiffOn_univUnitBall_symm`, `neg_concaveOn_iff`, `hasFDerivWithinAt_zero`, `IsAddUnit.sub_sub_cancel_left`, `LinearPMap.adjoint_apply_of_not_dense`, `ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun`, `AddMonoid.Coprod.mk_of_neg_add`, `VectorFourier.integral_sesq_fourierIntegral_eq_neg_flip`, `RCLike.wInner_smul_right`, `ordinaryHypergeometric_radius_top_of_neg_nat₂`, `neg_lt_iff_pos_add'`, `ClosedSubmodule.iInf_orthogonal`, `Quaternion.coe_imI`, `WeierstrassCurve.Jacobian.negDblY_of_Z_eq_zero`, `Asymptotics.isLittleOTVS_iff_smallSets`, `AffineSpace.asymptoticNhds_zero`, `Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero`, `AddMonoidHom.map_inv₂`, `WithCStarModule.zero_snd`, `Orientation.rotation_zero`, `nhds_hasBasis_absConvex`, `AddGroupSeminormClass.toZeroHomClass`, `HahnEmbedding.Partial.eval_smul`, `HasFPowerSeriesOnBall.neg`, `MeasureTheory.SimpleFunc.setToSimpleFunc_neg`, `contMDiff_neg`, `ContinuousLinearMap.uncurryBilinear_apply`, `WeierstrassCurve.Affine.addPolynomial_eq`, `HasFDerivWithinAt.smul_const`, `ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm`, `Finset.ruzsa_triangle_inequality_negAdd_negAdd_negAdd`, `Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le`, `MeasureTheory.integral_posConvolution`, `Asymptotics.isLittleOTVS_iff_tendsto_div`, `fourier_eval_zero`, `lipschitzOnWith_neg_iff`, `CategoryTheory.InjectiveResolution.extMk_eq_zero_iff`, `SchwartzMap.fourierInv_lineDerivOp_eq`, `VectorFourier.integral_fourierIntegral_swap`, `Finsupp.linearIndependent_single_of_ne_zero`, `ContDiffMapSupportedIn.tsupport_subset`, `Num.cast_sub'`, `CStarModule.inner_zero_left`, `IsCyclotomicExtension.Rat.Three.eta_sq`, `IsBoundedLinearMap.zero`, `Quaternion.imJ_neg`, `ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear`, `CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero`, `NormedSpace.isVonNBounded_of_isBounded`, `iteratedFDeriv_eq_equiv_comp`, `NumberField.Units.coe_neg_one`, `Function.locallyFinsuppWithin.mk_of_mem_toFun`, `MvPolynomial.totalDegree_neg`, `negPart_eq_ite`, `Int.cast_nonneg`, `List.sum_range_sub`, `instContinuousNegElemSphereOfNat`, `differentiableAt_zero`, `Filter.nonneg_sub_iff`, `IncidenceAlgebra.sum_Icc_mu_right`, `Function.Periodic.neg`, `neg_lt_of_abs_lt`, `ContinuousMap.toLp_norm_eq_toLp_norm_coe`, `Matrix.ofLp_toEuclideanCLM`, `hasFTaylorSeriesUpToOn_succ_nat_iff_right`, `neg_add_eq_neg_add_iff_add_eq_add`, `AddCircle.coe_zero`, `hasDerivAtFilter_iff_isLittleO`, `Quaternion.sub_self_re`, `AlgebraicClosure.instIsAlgClosure`, `Submodule.neg_mem`, `MvPolynomial.support_neg`, `Finset.card_inter_vadd`, `WithLp.ofLp_eq_zero`, `VectorField.lieBracket_zero_right`, `LinearPMap.map_zero`, `Differentiable.neg`, `le_neg_iff_add_nonpos_left`, `Asymptotics.IsLittleO.neg_left`, `MeasureTheory.Measure.IsAddHaarMeasure.isNegInvariant_of_innerRegular`, `isCompactOperator_iff_image_closedBall_subset_compact`, `Set.Nonempty.zsmul`, `HasFPowerSeriesWithinAt.sub`, `ClosedSubmodule.sup_orthogonal`, `neg_sup`, `Finsupp.erase_neg`, `quadraticChar_neg_two`, `MeasureTheory.measure_neg_vadd_sdiff`, `Asymptotics.isBigOTVS_neg_left`, `WithLp.norm_toLp_fst`, `HasFiniteFPowerSeriesAt.eventually_zero_of_bound_zero`, `Orientation.oangle_neg_left`, `CStarModule.norm_zero`, `ProbabilityTheory.Fernique.lintegral_closedBall_diff_exp_logRatio_mul_sq_le`, `groupHomology.d₁₀_comp_coinvariantsMk`, `ContDiffMapSupportedIn.locallyConvexSpace`, `hasFDerivWithinAt_comp_smul_smul_iff`, `MeasureTheory.finStronglyMeasurable_iff_measurable`, `groupHomology.d₂₁_comp_d₁₀_apply`, `fourierCoeff_toLp`, `Orientation.oangle_rotation_oangle_left`, `SummationFilter.symmetricIcc_le_Conditional`, `Subalgebra.neg_mem`, `ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense`, `monovaryOn_neg_right`, `MonomialOrder.sPolynomial_antisymm`, `QuadraticAlgebra.C_intCast`, `exists_jacobiSum_eq_neg_one_add`, `Matrix.neg_mulVec`, `LieDerivation.coe_neg`, `smul_unitBall_of_pos`, `LieSubmodule.mem_bot`, `Matrix.instNormOneClassOfNonempty`, `groupHomology.mapCycles₂_comp_apply`, `gauge_smul_left_of_nonneg`, `StrongFEPair.hf₀`, `le_add_neg_iff_add_le`, `strictAnti_iff_map_neg`, `Quaternion.intCast_imI`, `DifferentiableWithinAt.isBigOTVS_sub`, `uniformity_eq_comap_nhds_zero`, `LinearMap.isPositive_toContinuousLinearMap_iff`, `ValuationSubring.neg_mem`, `HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn'`, `zero_mem_asymptoticCone`, `exists_neg_mem_iff_exists_mem`, `AddChar.inv_apply`, `MonoidHom.map_neg`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd'`, `IsTopologicalAddGroup.addNegClosureNhd.neg`, `iteratedDerivWithin_one_div`, `norm_inner_eq_norm_tfae`, `derivWithin_zero_of_notMem_closure`, `CochainComplex.HomComplex.Cochain.fromSingleMk_zero`, `neg_add_le_iff_le_add`, `BddAbove.neg`, `Matrix.blockDiag'_neg`, `FormalMultilinearSeries.changeOrigin_eval_of_finite`, `Module.sum_smul_eq_zero_of_isTrivialRelation`, `WithLp.dist_toLp_snd`, `CategoryTheory.ShortComplex.homologyMap_neg`, `ZMod.dft_apply`, `Quaternion.fst_imJ_dualNumberEquiv_symm`, `DFinsupp.erase_eq_sub_single`, `Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff`, `lowerClosure_zero`, `MeasureTheory.condExp_def`, `IsCyclotomicExtension.discr_prime_pow_ne_two`, `CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc`, `iteratedFDerivWithin_two_apply'`, `curveIntegral_fun_neg`, `Set.image_neg_Ioc`, `mapClusterPt_zero_atTop_nsmul`, `Asymptotics.isLittleO_principal`, `HomologicalComplex.homotopyCofiber.d_fstX`, `CategoryTheory.unop_neg`, `squeeze_zero_norm'`, `Int.cast_nonpos`, `CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁`, `Projectivization.lift_mk`, `Quaternion.zero_imK`, `CStarModule.norm_zero_iff`, `NormedSpace.equicontinuous_TFAE`, `hasDerivAt_taylorWithinEval_succ`, `WeierstrassCurve.Projective.addZ_of_Z_eq_zero_right`, `CliffordAlgebra.EquivEven.neg_v_mul_e0`, `HVertexOperator.of_coeff_coeff`, `CategoryTheory.Abelian.Ext.neg_comp`, `Finsupp.sum_neg`, `AddSubgroup.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallNeg`, `CStarModule.inner_zero_right`, `neg_lt_zero`, `ZMod.natAbs_valMinAbs_neg`, `WeierstrassCurve.c₆_of_isCharTwoJEqZeroNF`, `SameRay.neg`, `CochainComplex.HomComplex.Cochain.leftShift_zero`, `IsLeftUniformAddGroup.uniformity_eq`, `intervalIntegral.deriv_integral_left`, `MeasureTheory.MemLp.toLp_neg`, `CategoryTheory.ShortComplex.Homotopy.symm_h₃`, `WithZero.log_zpow`, `analyticOrderAt_neg`, `ContinuousLinearMap.sSup_sphere_eq_norm`, `WithTop.untop₀_max`, `HVertexOperator.coeff_inj_iff`, `HasFPowerSeriesAt.fderiv_eq`, `HurwitzZeta.sinKernel_zero`, `FreeAbelianGroup.map_neg`, `NonUnitalSubring.val_neg`, `hasStrictFDerivAt_zero`, `CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero`, `RootPairing.coreflection_apply_self`, `Set.image_neg_Ioo`, `AlgebraicGeometry.StructureSheaf.const_zero`, `Polynomial.comp_neg_X_leadingCoeff_eq`, `ContinuousLinearMap.memLp_of_bilin`, `HasFPowerSeriesOnBall.tendstoUniformlyOn`, `lp.norm_eq_card_dsupport`, `AddCommute.neg_add_eq_neg_add_iff_of_isAddUnit`, `SchwartzMap.smulLeftCLM_smulLeftCLM_apply`, `QuotientAddGroup.rightRel_apply`, `IsAddUnit.add_add_sub`, `continuousMultilinearCurryFin0_apply`, `Metric.preimage_add_left_ball`, `sub_pow`, `HurwitzZeta.completedCosZeta₀_zero`, `HurwitzZeta.oddKernel_zero`, `mem_sphere_zero_iff_norm`, `Polynomial.Splits.nextCoeff_eq_neg_sum_roots_of_monic`, `PiTensorProduct.dualSeminorms_bounded`, `LinearMap.hasBasis_weakBilin`, `VectorField.mlieBracketWithin_self`, `FormalMultilinearSeries.radius_neg`, `DFinsupp.support_neg`, `ConjRootClass.mk_neg`, `neg_lie`, `Quaternion.imK_mul`, `Asymptotics.IsEquivalent.neg`, `CochainComplex.HomComplex.CohomologyClass.mk_zero`, `extDeriv_smul`, `EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear`, `homeomorphUnitSphereProd_symm_apply_coe`, `Orientation.rightAngleRotation_rightAngleRotation`, `groupHomology.H2π_eq_iff`, `QuotientAddGroup.nhds_zero_hasBasis`, `ContinuousLinearMap.opNorm_extend_le`, `Submodule.orthogonal_closure`, `intervalIntegral.integral_non_aestronglyMeasurable`, `IsSelfAdjoint.conj_adjoint`, `ContinuousMultilinearMap.curryMidEquiv_apply`, `Finset.mem_neg_vadd_finset_iff`, `AddCommGrpCat.zero_apply`, `StrictConvexSpace.strictConvex_closedBall`, `HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd`, `Matrix.val_planeConformalMatrix`, `AddGroupFilterBasis.nhds_zero_eq`, `Matrix.coeff_charpolyRev_eq_neg_trace`, `CategoryTheory.ShiftedHom.comp_neg`, `WithLp.nndist_toLp_snd`, `groupHomology.H1AddEquivOfIsTrivial_single`, `LaurentSeries.hasseDeriv_comp_coeff`, `SMulPosReflectLT.toSMulPosReflectLE`, `Quaternion.coe_div`, `Real.Angle.cos_eq_iff_coe_eq_or_eq_neg`, `sameRay_neg_smul_left_iff_of_ne`, `ContinuousLinearMap.analyticOnNhd_bilinear`, `WeierstrassCurve.Jacobian.addXYZ_of_Z_eq_zero_right`, `add_neg_lt_iff_le_add'`, `Metric.preimage_vadd_closedBall`, `DFinsupp.neLocus_sub_right`, `AddCircle.toCircle_zero`, `IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder`, `groupHomology.range_d₁₀_eq_coinvariantsKer`, `injective_iff_map_eq_zero'`, `cfc_neg`, `BoundedContinuousFunction.neg_apply`, `AddSubgroup.IsComplement.toRightFun_add_neg_mem`, `Finset.zsmul_singleton`, `CliffordAlgebra.contractLeft_comm`, `RootPairing.GeckConstruction.ω_mul_h`, `instContinuousNegMulOpposite`, `NormedSpace.invOf_exp`, `hasFiniteFPowerSeriesOnBall_const`, `ZMod.invDFT_apply'`, `iteratedFDerivWithin_succ_apply_left`, `MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le`, `HahnSeries.support_neg`, `AffineEquiv.constVAdd_zero`, `LatticeOrderedAddCommGroup.isSolid_ball`, `min_neg_neg`, `IsUniformAddGroup.cauchy_iff_tendsto_swapped`, `groupHomology.isoCycles₂_hom_comp_i_apply`, `support_deriv_subset`, `AddSubgroup.neg_mem_iff`, `ZNum.cast_inj`, `AffineIsometryEquiv.constVAdd_zero`, `ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear`, `SlashAction.neg_slash`, `Equiv.subLeft_symm_apply`, `MeasureTheory.setAverage_sub_setAverage`, `IsCauSeq.neg`, `MeasureTheory.absolutelyContinuous_neg`, `MvPowerSeries.coeff_inv_aux`, `nnnorm_indicator_eq_indicator_nnnorm`, `DFinsupp.zsmul_apply`, `MeasureTheory.L1.SimpleFunc.setToL1S_zero_left'`, `hasDerivWithinAt_natCast`, `RingNormClass.eq_zero_of_map_eq_zero`, `Matrix.invOf_fromBlocks_zero₁₂_eq`, `LieSubmodule.zero_mem`, `WeierstrassCurve.Jacobian.addXYZ_neg`, `IsPreconnected.eq_one_or_eq_neg_one_of_sq_eq`, `Orientation.oangle_zero_right`, `ProperCone.dual_zero`, `QuaternionAlgebra.imK_star`, `ContinuousLinearMap.bilinearComp_apply`, `Filter.neg_nhdsLT`, `neg_dotProduct`, `AddSubgroup.mem_normalizer_iff''`, `posPart_pos_iff`, `TemperedDistribution.instLineDerivSMulReal`, `intervalIntegral.integral_symm`, `iteratedDeriv_comp_neg`, `MeromorphicOn.neg`, `WeierstrassCurve.Affine.evalEval_polynomial_zero`, `MeasureTheory.setIntegral_empty`, `DFinsupp.erase_sub`, `Quaternion.im_imJ`, `Polynomial.resultant_X_sub_C_pow_right`, `HVertexOperator.compHahnSeries_add`, `Function.support_add_neg`, `intervalIntegral.integral_same`, `LieSubalgebra.mem_engel_iff`, `Finset.sum_smul_const_vsub_eq_neg_weightedVSub`, `DFinsupp.erase_neg`, `RootPairing.coroot_eq_neg_iff`, `Quaternion.intCast_imJ`, `Orientation.rotation_eq_self_iff_angle_eq_zero`, `InnerProductGeometry.angle_smul_right_of_neg`, `IsOpen.add_closure_zero_eq`, `Subfield.neg_mem`, `nndist_neg_neg`, `PowerSeries.IsRestricted.neg`, `circleEquivGen_symm_apply`, `PowerSeries.derivative_invOf`, `Polynomial.resultant_succ_left_deg`, `tendsto_integral_exp_smul_cocompact_of_inner_product`, `Quaternion.mul_star_eq_coe`, `LieModule.isFaithful_iff'`, `AddGroupFilterBasis.zero'`, `RootPairing.root_eq_neg_iff`, `QuaternionAlgebra.coe_im`, `HasFTaylorSeriesUpToOn.fderivWithin`, `uniformity_eq_comap_nhds_zero_left`, `groupHomology.eq_d₂₁_comp_inv_assoc`, `Quaternion.fst_imI_dualNumberEquiv_symm`, `posPart_eq_ite`, `BoxIntegral.HasIntegral.neg`, `LinearIsometry.map_neg`, `exists_nontrivial_relation_sum_zero_of_not_affine_ind`, `FormalMultilinearSeries.id_comp`, `ContinuousLinearMap.norm_map_tail_le`, `tangentConeAt_def`, `ZNum.cast_le`, `max_zero_sub_max_neg_zero_eq_self`, `HasFPowerSeriesAt.restrictScalars`, `hasDerivAt_integral_of_dominated_loc_of_deriv_le`, `DifferentiableWithinAt.fun_neg`, `intervalIntegral.integral_of_ge`, `ContinuousLinearMap.instStarModuleId`, `RCLike.wInner_smul_left`, `Wbtw.neg`, `monotone_iff_map_nonpos`, `Ring.choose_neg'`, `convexHull_neg`, `AddSubgroup.nsmul_exponent_eq_zero`, `sub_nsmul_neg`, `groupHomology.single_isCycle₁_iff`, `StrictAnti.neg`, `Finset.smul_finset_neg`, `PiTensorProduct.injectiveSeminorm_apply`, `Homeomorph.unitBall_apply_coe`, `groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc`, `ContinuousLinearMap.isBoundedLinearMap_comp_left`, `AddCommute.conj_iff`, `Besicovitch.SatelliteConfig.centerAndRescale_center`, `Set.image_add_right`, `MeasureTheory.setIntegral_neg_eq_setIntegral_nonpos`, `MeasurableSet.add_closure_zero_eq`, `differentiable_zero`, `norm_fderiv_iteratedFDeriv`, `isConnected_setOf_sameRay_and_ne_zero`, `CochainComplex.HomComplex.Cochain.equivHomotopy_apply_of_eq`, `curveIntegralFun_neg`, `AntitoneOn.slope_nonpos`, `Asymptotics.isLittleOTVS_map`, `IccLeftChart_extend_bot`, `ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply`, `PointedCone.dual_zero`, `AddSubgroup.exists_neg_mem_iff_exists_mem`, `BoundedContinuousFunction.mkOfCompact_neg`, `MeasureTheory.DominatedFinMeasAdditive.eq_zero_of_measure_zero`, `totallyBounded_neg`, `TemperedDistribution.fourier_lineDerivOp_eq`, `groupHomology.inhomogeneousChains.d_single`, `gaugeRescale_zero`, `Matrix.l2_opNNNorm_def`, `ContinuousMultilinearMap.instIsBoundedSMul`, `VectorField.mlieBracket_zero_left`, `RayVector.coe_neg`, `LocalizedModule.mk_neg`, `hasDerivAtFilter_sub_const_iff`, `alternating_series_error_bound`, `MonovaryOn.neg`, `VectorField.mlieBracket_swap_apply`, `spectrum.hasDerivAt_resolvent`, `TemperedDistribution.fourier_delta_zero`, `ContinuousLinearMap.adjointAux_adjointAux`, `ContDiffMapSupportedIn.seminorm_le_iff_withOrder`, `MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc`, `smul_nonpos_iff_neg_imp_nonneg`, `FreeAbelianGroup.neg_seq`, `ZMod.val_neg_one`, `Quaternion.normSq_add`, `NormedAddGroupHom.coe_neg`, `AddGroupFilterBasis.nhds_zero_hasBasis`, `LinearMap.hasEigenvalue_zero_tfae`, `hasFDerivAt_single`, `PolynomialModule.smul_apply`, `AddMonoidAlgebra.mul_apply_left`, `Finset.zero_notMem_sub_iff`, `iteratedDerivWithin_neg`, `ContMDiffAt.clm_precomp`, `CategoryTheory.ShortComplex.ShortExact.comp_extClass`, `inner_zero_right`, `LieAlgebra.Orthogonal.s_as_blocks`, `WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded`, `MvPolynomial.mul_esymm_eq_sum`, `Mathlib.Tactic.Module.NF.zero_sub_eq_eval`, `Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence`, `Quaternion.neg_im`, `AddCircle.card_torsion_le_of_isSMulRegular_int`, `inner_self_eq_zero`, `LinearOrderedAddCommGroup.Subgroup.negGen_neg`, `VectorField.mpullbackWithin_smul_apply`, `PositiveLinearMap.gnsStarAlgHom_apply`, `IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat`, `Polynomial.nextCoeff_X_sub_C`, `SchwartzMap.tsupport_iteratedLineDerivOp_subset`, `neg_le_iff_add_nonneg`, `ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin`, `hasDerivAt_iff_tendsto_slope_zero`, `SkewMonoidAlgebra.toFinsupp_neg`, `RootPairing.IsReduced.eq_or_eq_neg`, `OpenAddSubgroup.mem_nhds_zero`, `MeasureTheory.ProgMeasurable.neg`, `ContinuousAffineMap.coe_zero`, `Asymptotics.isLittleOTVS_iff_isLittleO`, `SemiNormedGrp.explicitCokernelπ_apply_dom_eq_zero`, `Matrix.trace_eq_neg_charpoly_nextCoeff`, `WeierstrassCurve.Projective.addXYZ_of_Z_eq_zero_right`, `WithSeminorms.equicontinuous_TFAE`, `Set.vadd_set_subset_iff_subset_neg_vadd_set`, `TrivSqZeroExt.inv_inv`, `MeasureTheory.MemLp.finStronglyMeasurable_of_stronglyMeasurable`, `SchwartzMap.integral_pow_mul_iteratedFDeriv_le`, `HasFTaylorSeriesUpToOn.hasFDerivAt`, `SeminormFamily.basisSets_mem_nhds`, `hasStrictFDerivAt_inv`, `AddSubgroup.mem_bot`, `groupHomology.isBoundary₂_iff`, `ContinuousLinearMap.flip_add`, `hasFiniteFPowerSeriesAt_const`, `inv_eq_self₀`, `odd_neg`, `ContinuousAlternatingMap.hasBasis_nhds_zero`, `lie_skew`, `abs_nonpos_iff`, `Bornology.isBounded_iff_isVonNBounded`, `deriv_neg''`, `ContinuousLinearMap.isSelfAdjoint_iff'`, `TendstoUniformly.fun_neg`, `translate_eq_domAddActMk_vadd`, `stereographic_neg_apply`, `LineDeriv.lineDerivOp_zero`, `RootPairing.pairingIn_reflectionPerm_self_right`, `TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq`, `MeasureTheory.withDensityᵥ_neg`, `MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp`, `Real.fourierInv_eq_fourier_comp_neg`, `ContinuousMultilinearMap.uncurryRight_apply`, `TestFunction.coe_zero`, `LieDerivation.neg_apply`, `Quaternion.imI_star`, `RingCon.neg`, `ContinuousLinearMap.isVonNBounded_iff`, `fderiv_inv`, `Asymptotics.isLittleO_norm_pow_norm_pow`, `WithLp.nnnorm_toLp_inl`, `NormedSpace.normalize_smul_of_neg`, `TrivSqZeroExt.exp_def`, `CharZero.eq_neg_self_iff`, `tangentConeAt.lim_zero`, `Matrix.SpecialLinearGroup.SL2_inv_expl`, `Algebra.Generators.Cotangent.exact`, `self_mul_sign`, `ContinuousLinearEquiv.coe_neg`, `Quaternion.imI_smul`, `derivWithin_zero_of_not_uniqueDiffWithinAt`, `curveIntegralFun_fun_zero`, `WeierstrassCurve.c₄_of_isShortNF`, `List.Vector.sum_set'`, `UniformCauchySeqOn.fun_neg`, `ContinuousLinearMap.bilinearComp_zero`, `MeasureTheory.integral_fun_norm_addHaar`, `SummationFilter.instLeAtTopSymmetricIoc`, `neg_add'`, `MeasureTheory.stoppedValue_sub_eq_sum'`, `isScalarTower_sphere_sphere_closedBall`, `le_neg_add_of_add_le`, `Set.exists_vadd_inter_vadd_subset_vadd_neg_add_inter_neg_add`, `iteratedDeriv_eq_equiv_comp`, `SchwartzMap.smulLeftCLM_add`, `RingPreordering.neg_one_notMem'`, `Set.neg_mem_Icc_iff`, `MultilinearMap.mkContinuousLinear_norm_le'`, `norm_fderivWithin_iteratedFDerivWithin`, `HasFTaylorSeriesUpToOn.shift_of_succ`, `Quaternion.imK_star`, `MeasureTheory.eLpNorm_indicator_le_of_bound`, `Module.Basis.norm_neg`, `NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply`, `MeasureTheory.eLpNorm_neg`, `WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF`, `MeromorphicAt.fun_neg`, `modelWithCornersEuclideanHalfSpace_zero`, `ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm`, `abs_choice`, `vadd_mem_nhds_self`, `groupHomology.mapCycles₂_id_comp_assoc`, `negPart_def`, `le_neg_self_iff`, `MeasureTheory.setToFun_measure_zero'`, `groupHomology.π_comp_H1Iso_hom_apply`, `MeasureTheory.integral_neg'`, `ZMod.dft_comp_neg`, `CochainComplex.mappingCone.d_fst_v_assoc`, `geom_sum_eq_zero_iff_neg_one`, `isOfFinAddOrder_neg_iff`, `ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap`, `Quaternion.normSq_exp`, `IsCompact.sub_closedBall_zero`, `ContinuousMultilinearMap.integral_apply`, `MeasureTheory.AEEqFun.neg_mk`, `Interval.length_nonneg`, `HasStrictDerivAt.smul_const`, `WithCStarModule.norm_single`, `ProbabilityTheory.HasGaussianLaw.fun_neg`, `groupHomology.single_isCycle₂_iff`, `LieModuleHom.zero_apply`, `CochainComplex.HomComplex.Cocycle.δ_eq_zero`, `ArchimedeanClass.stdPart_neg`, `Matrix.det_succ_column`, `HasFiniteFPowerSeriesOnBall.neg`, `derivWithin_intCast`, `ContinuousMapZero.norm_def`, `DFinsupp.filter_sub`, `Int.fract_sub_self`, `Polynomial.resultant_C_left`, `HahnSeries.single_neg`, `VectorField.lieBracket_self`, `LinearMap.charpoly_constantCoeff_eq_zero_iff`, `Finset.add_eq_zero_iff`, `Pi.norm_single`, `Rep.standardComplex.d_of`, `PowerSeries.coe_neg`, `Quaternion.star_add_self'`, `Derivation.map_neg`, `closure_zero_eq`, `AddGroupNormClass.eq_zero_of_map_eq_zero`, `Orientation.oangle_add_cyc3`, `LinearIsometry.inr_apply`, `ZMod.val_neg'`, `Seminorm.neg_closedBall`, `HurwitzZeta.completedHurwitzZetaOdd_neg`, `Function.support_neg`, `CochainComplex.mappingCone.δ_snd`, `RootPairing.EmbeddedG2.pairing_long_short`, `groupHomology.toCycles_comp_isoCycles₂_hom`, `SkewMonoidAlgebra.ofFinsupp_neg`, `Real.fourier_bilin_convolution_eq`, `CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact`, `isLUB_neg`, `sub_one_zsmul`, `IsLocalization.mk'_neg`, `MeasureTheory.MemLp.exists_hasCompactSupport_eLpNorm_sub_le`, `cmp_sub_zero`, `Finsupp.neLocus_sub_left`, `ZMod.lift_comp_castAddHom`, `LaurentSeries.hasseDeriv_coeff`, `Set.zero_mem_neg_add_iff`, `homeomorphSphereProd_symm_apply_coe`, `RCLike.sqrt_neg_one`, `le_add_neg_iff_le`, `nsmulCoprime_neg`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left`, `WeierstrassCurve.Projective.negDblY_eq`, `ContinuousLinearMap.le_opNorm₂`, `ContinuousLinearMap.lpPairing_eq_integral`, `TrivSqZeroExt.snd_invOf`, `Matrix.coe_toEuclideanCLM_eq_toEuclideanLin`, `groupHomology.cyclesMap_comp_isoCycles₂_hom_apply`, `InnerProductSpace.Core.inner_zero_right`, `PresheafOfModules.Derivation'.d_app`, `Seminorm.continuous_iff`, `HasFDerivAt.smul_const`, `ContinuousLinearMap.norm_uncurryMid`, `real_inner_self_nonpos`, `quadratic_eq_zero_iff`, `DifferentiableWithinAt.neg`, `InnerProductSpace.rankOne_def'`, `SchwartzMap.tendsto_cocompact`, `ContinuousLinearMap.uncurryLeft_norm`, `tendsto_sub_comap_self`, `UniformSpace.Completion.coe_neg`, `WeierstrassCurve.Projective.addY_of_Z_eq_zero_right`, `IsBoundedLinearMap.neg`, `circleIntegral.integral_undef`, `MeasureTheory.Measure.map_add_right_neg_eq_self`, `groupHomology.mapCycles₁_id_comp`, `Finset.addETransformLeft_zero`, `HasFPowerSeriesOnBall.tendstoUniformlyOn'`, `Pretrivialization.continuousLinearMap.isLinear`, `HasFPowerSeriesWithinOnBall.const_smul`, `HVertexOperator.coeff_inj`, `PolynomialModule.smul_single_apply`, `sub_zsmul`, `isScalarTower_sphere_sphere_ball`, `Quaternion.sub_im`, `Orientation.oangle_neg_self_right`, `HasFPowerSeriesOnBall.sub`, `SchwartzMap.integral_sesq_fourierIntegral_eq`, `AddGroupSeminorm.apply_one`, `ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left`, `HurwitzZeta.oddKernel_neg`, `MeasureTheory.sub_nonneg_ae`, `MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd`, `Set.zsmul_eq_empty`, `Int.fract_neg`, `monovaryOn_neg_left`, `Nat.prime_iff_fac_equiv_neg_one`, `LieModuleHom.neg_apply`, `MeasureTheory.Integrable.convolution_integrand`, `FormalMultilinearSeries.radius_compContinuousLinearMap_eq`, `VectorField.mlieBracketWithin_swap_apply`, `Module.reflection_mul_reflection_pow_apply_self`, `Quaternion.im_exp`, `Module.FaithfullyFlat.lTensor_reflects_exact`, `CliffordAlgebra.evenToNeg_ι`, `rightAddCoset_eq_iff`, `Filter.tendsto_neg_atBot_iff`, `AddGroupFilterBasis.zero`, `HurwitzZeta.evenKernel_neg`, `Quaternion.re_one`, `List.sum_neg`, `deriv_inv''`, `LieAlgebra.of_zero`, `IsSl2Triple.symm`, `ArchimedeanClass.out_top`, `NormedSpace.vonNBornology_eq`, `Subring.exists_list_of_mem_closure`, `Module.Presentation.finsupp_relation`, `UpperSet.coe_zero`, `ZeroAtInftyContinuousMap.norm_toBCF_eq_norm`, `neg_lt_self_iff`, `curveIntegral_symm`, `HomologicalComplex.homotopyCofiber.inlX_d`, `tendsto_neg_nhdsLE_neg`, `SchwartzMap.integral_bilinear_laplacian_right_eq_left`, `instContinuousNegElemClosedBallOfNat`, `MeasureTheory.IsAddFundamentalDomain.mk'`, `neg_nonneg`, `abs_cases`, `hasDerivWithinAt_const`, `FormalMultilinearSeries.compAlongComposition_norm`, `Finsupp.neLocus_self_sub_left`, `LinearPMap.map_neg`, `NonarchAddGroupSeminorm.apply_one`, `NormedSpace.normalize_eq_zero_iff`, `ZMod.cast_neg_one`, `MeasureTheory.eLpNorm_indicator_sub_indicator`, `CochainComplex.HomComplex.Cocycle.fromSingleMk_neg`, `HurwitzZeta.cosZeta_zero`, `Filter.Tendsto.uniformity_neg_iff`, `homeomorphUnitSphereProd_apply_fst_coe`, `LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace`, `MeasureTheory.unifTight_iff_ennreal`, `QuotientAddGroup.btw_coe_iff`, `LeftInvariantDerivation.coe_neg`, `WeierstrassCurve.Jacobian.addY_of_Z_eq_zero_right`, `dist_neg`, `WeierstrassCurve.Projective.add_of_Z_eq_zero_right`, `IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrder`, `FreeLieAlgebra.Rel.neg`, `iteratedDerivWithin_const`, `Asymptotics.isBigOWith_zero'`, `curveIntegral_refl`, `ContinuousLinearEquiv.map_neg`, `MeasureTheory.Pi.isNegInvariant_volume`, `groupHomology.eq_d₁₀_comp_inv`, `WithTop.LinearOrderedAddCommGroup.coe_neg`, `constFormalMultilinearSeries_apply_of_nonzero`, `egauge_ball_one_le_of_one_lt_norm`, `Quaternion.zero_re`, `HasFTaylorSeriesUpToOn.add`, `ModuleCat.Derivation.d_map`, `differentiableOn_neg`, `ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM`, `abs_pos`, `ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff`, `AlternatingMap.map_update_neg`, `Asymptotics.isBigOTVS_pi`, `LieAlgebra.LoopAlgebra.toFinsupp_single_tmul`, `SignType.intCast_cast`, `PiLp.smul_apply`, `TrivSqZeroExt.hasSum_expSeries_of_smul_comm`, `Homeomorph.addLeft_symm`, `AddMonoidAlgebra.single_mul_apply`, `groupHomology.isoShortComplexH1_inv`, `MDifferentiableOn.cle_arrowCongr`, `PiLp.normSMulClassSeminormedAddCommGroupToPi`, `AddSubgroup.coe_bot`, `differentiableAt_fun_neg_iff`, `ContinuousMultilinearMap.isEmbedding_toUniformOnFun`, `MultilinearMap.mkContinuousMultilinear_norm_le'`, `add_neg_le_add_neg_iff`, `WithCStarModule.inner_single_right`, `DirichletCharacter.IsPrimitive.fourierTransform_eq_inv_mul_gaussSum`, `ZMod.cast_zero`, `neg_add_le_of_le_add`, `MeasureTheory.neg_vadd_ae_eq_self`, `RingQuot.Rel.neg`, `differentiableOn_neg_iff`, `tendsto_neg_nhdsGE`, `groupHomology.eq_d₁₀_comp_inv_assoc`, `MeasureTheory.Measure.addHaar_real_closedBall_center`, `lie_jacobi`, `IsLinearTopology.hasBasis_submodule'`, `QuaternionAlgebra.imI_ofNat`, `QuaternionAlgebra.intCast_im`, `Filter.tendsto_comp_neg_atBot_iff`, `frobenius_neg`, `EuclideanGeometry.oangle_self_right`, `Submodule.det_reflection`, `round_eq_zero_iff`, `deriv_neg'`, `deriv_zero_of_frequently_const`, `Orientation.kahler_rotation_left'`, `fderivWithin_neg`, `hasFDerivAtFilter_iff_isLittleOTVS`, `Quaternion.smul_re`, `AffineMap.toConstProdLinearMap_apply`, `FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp`, `Quaternion.self_add_star'`, `lineDeriv_zero`, `derivWithin_zero_of_not_accPt`, `ContinuousAlternatingMap.curryLeft_same`, `IsLocalizedModule.mk'_neg`, `ContinuousMultilinearMap.curryRight_apply`, `Homotopy.symm_hom`, `groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc`, `slope_neg`, `MeasureTheory.eLpNorm_const_smul_le`, `Polynomial.resultant_X_add_C_left`, `ContinuousLinearMap.sSup_unit_ball_eq_nnnorm`, `Module.End.mem_iInf_maxGenEigenspace_iff`, `HasFPowerSeriesOnBall.uniform_geometric_approx'`, `neg_npow_assoc`, `groupHomology.isoCycles₁_hom_comp_i_apply`, `Quaternion.coe_mul_eq_smul`, `Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent`, `InnerProductGeometry.angle_self_neg_of_nonzero`, `contDiff_neg`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars`, `ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const`, `Real.Angle.sign_two_zsmul_eq_neg_sign_iff`, `neg_lt_iff_pos_add`, `MeasureTheory.SimpleFunc.setToSimpleFunc_indicator`, `Quaternion.instIsStarNormal`, `leftAddCoset_eq_iff`, `AddSubgroup.mem_goursatFst`, `MeasureTheory.SignedMeasure.toMeasureOfLEZero_apply`, `CompactConvergenceCLM.hasBasis_nhds_zero`, `Derivation.leibniz_of_mul_eq_one`, `IsMinFilter.neg`, `nnnorm_zero`, `MeasureTheory.DominatedFinMeasAdditive.eq_zero`, `LieSubmodule.mk_eq_zero`, `ascPochhammer_eval_neg_coe_nat_of_lt`, `QuaternionAlgebra.sub_self_im`, `skewAdjoint.star_val_eq`, `LieModule.traceForm_eq_sum_finrank_nsmul`, `ArithmeticFunction.log_mul_moebius_eq_vonMangoldt`, `ContinuousLinearEquiv.neg_apply`, `Set.image_neg_Icc`, `SymplecticGroup.inv_left_mul_aux`, `groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply`, `Ring.multichoose_succ_neg_natCast`, `isScalarTower_sphere_closedBall_ball`, `IsBoundedSMul.of_enorm_smul_le`, `ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq`, `neg_neg_sub_neg`, `HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope`, `MeasureTheory.Lp.simpleFunc.toLp_zero`, `MulRingNormClass.eq_zero_of_map_eq_zero`, `LieModule.instIsTrivialOfSubsingleton`, `groupCohomology.H1π_eq_zero_iff`, `MDifferentiableAt.clm_precomp`, `Set.image_add_left`, `Quaternion.summable_coe`, `ContDiffMapSupportedIn.postcompCLM_apply`, `TemperedDistribution.smulLeftCLM_add`, `AddCircle.eq_coe_Ico`, `ContinuousAlternatingMap.curryLeft_zero`, `signedDist_neg`, `UniformCauchySeqOn.neg`, `ContinuousMultilinearMap.analyticOn_uncurry_of_linear`, `WeierstrassCurve.Projective.negAddY_of_Z_eq_zero_right`, `AddSubgroup.Normal.conj_mem'`, `Quaternion.zero_imI`, `ContinuousAlternatingMap.restrictScalarsLI_apply`, `Ideal.toCotangent_eq_zero`, `Complex.UnitDisc.mk_neg`, `MeasureTheory.Measure.neg.instIsAddRightInvariant`, `QuaternionAlgebra.Basis.k_mul_k`, `Asymptotics.IsTheta.isThetaTVS`, `MeasureTheory.Lp.coeFn_nonneg`, `Quaternion.sub_imI`, `Set.neg_Ioc`, `strictAnti_iff_map_pos`, `groupHomology.d₃₂_single_one_fst`, `dist_zero_left`, `inhomogeneousCochains.d_hom_apply`, `MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt`, `ZMod.dft_dft`, `Quaternion.imJ_snd_dualNumberEquiv`, `IsSl2Triple.HasPrimitiveVectorWith.lie_e`, `MeasureTheory.Martingale.neg`, `Quaternion.star_im`, `gauge_unit_ball`, `Filter.Tendsto.zero_smul_isBoundedUnder_le`, `MeasureTheory.setToFun_non_aestronglyMeasurable`, `CategoryTheory.Abelian.Ext.zero_hom`, `sameRay_neg_swap`, `ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft`, `neg_one_eq_invOf_mul_add_invOf_mul_iff`, `HasFPowerSeriesWithinAt.prod`, `Matrix.frobenius_nnnorm_diagonal`, `Set.neg_smul_set`, `Matrix.blockDiagonal_sub`, `Quaternion.re_natCast`, `singleton_add_closedBall_zero`, `ZMod.neg_eq_self_iff`, `FormalMultilinearSeries.leftInv_coeff_one`, `LaurentSeries.hasseDeriv_single_add`, `AddGroupNorm.apply_one`, `Matrix.det_succ_column_zero`, `FiniteMultiplicity.neg_iff`, `apply_eq_zero_of_analyticOrderAt_ne_zero`, `Set.preimage_add_left_singleton`, `WeierstrassCurve.c₆_of_isCharNeTwoNF`, `sameRay_iff_inv_norm_smul_eq`, `mdifferentiableOn_continuousLinearMapCoordChange`, `derivWithin_one`, `hasDerivAtFilter_intCast`, `MeasureTheory.Submartingale.neg`, `groupHomology.d₂₁_comp_d₁₀`, `LinearOrderedAddCommGroupWithTop.sub_eq_zero`, `Function.Periodic.sub_antiperiod_eq`, `IsModuleTopology.continuousNeg`, `MDifferentiableAt.neg`, `hasFPowerSeriesAt_pi_iff`, `CategoryTheory.Adjunction.homAddEquiv_symm_neg`, `LieAlgebra.IsKilling.span_weight_isNonZero_eq_top`, `MeasureTheory.Lp.coeFn_lpSMul`, `CategoryTheory.Abelian.Ext.mk₀_zero`, `groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self`, `MeasureTheory.MemLp.integral_indicator_norm_ge_nonneg_le`, `KaehlerDifferential.exact_kerCotangentToTensor_mapBaseChange`, `TestFunction.tsupport_subset`, `hasDerivWithinAt_univ`, `LinearMap.det_eq_sign_charpoly_coeff`, `neg_sub'`, `Asymptotics.isLittleOTVS_neg_right`, `Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub`, `MeasureTheory.IntegrableAtFilter.neg`, `MvPowerSeries.weightedOrder_neg`, `TrivSqZeroExt.isUnit_inv_iff`, `MeasureTheory.Lp.simpleFunc.coeFn_zero`, `Seminorm.ball_zero_absorbs_ball_zero`, `IsNilpotent.exp_neg_mul_exp_self`, `eq_neg_add_iff_add_eq`, `iteratedDeriv_fun_const_zero`, `gradient_const`, `groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc`, `Filter.isBoundedUnder_le_neg`, `PiLp.dist_toLp_single_same`, `FreeAbelianGroup.support_neg`, `groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁`, `Function.locallyFinsuppWithin.negPart_add`, `OrderDual.instSMulPosMono`, `ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff`, `groupHomology.H1ToTensorOfIsTrivial_H1π_single`, `LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff`, `ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear`, `Orientation.neg_rotation_pi_div_two`, `InnerProductSpace.isStarProjection_rankOne_self`, `ProperCone.relative_hyperplane_separation`, `OrderedFinpartition.compAlongOrderedFinpartitionL_apply`, `ContinuousAlternatingMap.piLIE_symm_apply_apply`, `ContinuousMapZero.instContinuousNeg`, `DifferentiableOn.neg`, `Quaternion.snd_imK_dualNumberEquiv_symm`, `Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff`, `HasFPowerSeriesAt.hasFDerivAt`, `FormalMultilinearSeries.comp_coeff_zero'`, `LipschitzWith.neg`, `WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope`, `QuaternionAlgebra.ofNat_imI`, `antivary_neg_left`, `Int.cast_list_sum`, `IsAddQuotientCoveringMap.disjoint`, `HahnSeries.archimedeanClassOrderIsoWithTop_apply`, `IsMaxOn.neg`, `Module.length_finsupp`, `SetTheory.PGame.Domineering.shiftRight_symm_apply`, `HasFPowerSeriesWithinOnBall.compContinuousLinearMap`, `HasFPowerSeriesOnBall.eventually_hasSum`, `LinearMap.mkContinuous₂_norm_le`, `nhds_translation_add_neg`, `signedDist_linear_apply`, `UpperHalfPlane.isZeroAtImInfty_iff`, `Fintype.balance_neg`, `FormalMultilinearSeries.zero_radius`, `Finset.tendsto_Icc_neg`, `smul_unitBall`, `Quaternion.sq_eq_neg_normSq`, `QuotientAddGroup.mk_zero`, `mul_self_eq_one_iff`, `ContinuousLinearMap.hasFPowerSeriesAt_bilinear`, `TrivSqZeroExt.inv_neg`, `Quaternion.imK_neg`, `Monotone.neg`, `BoundedContinuousFunction.norm_def`, `VertexOperator.ext_iff`, `hasStrictDerivAt_const`, `nnnorm_smul_le`, `negPart_lt`, `MeasureTheory.measure_add_closure_zero`, `PosSMulMono.toSMulPosMono`, `Quaternion.coe_one`, `groupHomology.cyclesOfIsCycle₁_coe`, `QuaternionAlgebra.natCast_imK`, `DFinsupp.sum_neg`, `IsPrimitiveRoot.norm_pow_sub_one_two`, `ZMod.lift_coe`, `Hyperreal.lt_neg_of_pos_of_infinitesimal`, `Quaternion.imK_ratCast`, `ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_coprime`, `HasFPowerSeriesWithinAt.restrictScalars`, `Module.Basis.parallelepiped_eq_map`, `ContDiffMapSupportedIn.norm_apply_le_seminorm`, `IsAddUnit.eq_neg_add_iff_add_eq`, `SchwartzMap.hasDerivAt`, `AddValuation.map_neg`, `LieAddGroup.contMDiff_neg`, `PiTensorProduct.mapLMultilinear_apply_apply`, `Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero`, `Matrix.transpose_intCast`, `AddSubmonoid.mk_neg_add_mk_eq_zero`, `Units.neg_smul`, `IsAddUnit.sub_add_right`, `FreeAddGroup.sum_mk`, `lineDeriv_zero_of_not_lineDifferentiableAt`, `Multiset.sum_map_neg'`, `jacobiSum_nontrivial_inv`, `isBoundedBilinearMap_apply`, `FormalMultilinearSeries.analyticOnNhd`, `WithConv.toConv_neg`, `Mathlib.Tactic.RingNF.add_neg`, `abs_zero`, `ContMDiffMap.coe_neg`, `exteriorPower.presentation_relation`, `hasDerivAtFilter_iff_tendsto`, `Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero`, `CochainComplex.HomComplex.Cocycle.fromSingleMk_zero`, `MeasureTheory.Integrable.aefinStronglyMeasurable`, `HVertexOperator.ext_iff`, `LieAlgebra.isLieAbelian_iff_center_eq_top`, `DFinsupp.single_sub`, `OrderDual.instSMulPosReflectLT`, `groupHomology.d₂₁_apply_mem_cycles₁`, `stereographic_target`, `MeromorphicNFOn.zero_set_eq_divisor_support`, `AddGroupExtension.Section.add_add_add_neg_mem_range_inl`, `CategoryTheory.ProjectiveResolution.extMk_zero`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn`, `MeasureTheory.convolution_zero`, `LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply`, `MeasureTheory.integral_indicator₀`, `InnerProductSpace.rankOne_comp_rankOne`, `NormedSpace.eq_zero_of_forall_dual_eq_zero`, `Real.circleAverage.integral_undef`, `mdifferentiableAt_neg`, `CategoryTheory.ShortComplex.zero_apply`, `singleton_sub_ball_zero`, `Quaternion.tsum_coe`, `Summable.tendsto_cofinite_zero`, `TrivSqZeroExt.norm_inl`, `Subalgebra.coe_neg`, `AddSubgroup.normal_addSubgroupOf_iff`, `hasDerivAtFilter_finCons'`, `groupHomology.cyclesMap_comp_isoCycles₁_hom_apply`, `Fintype.expect_balance`, `RootPairing.reflection_apply_self`, `MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero`, `SetTheory.PGame.Domineering.shiftUp_symm_apply`, `ContinuousMap.toLp_injective`, `groupHomology.toCycles_comp_isoCycles₂_hom_apply`, `groupCohomology.H2π_eq_zero_iff`, `MeasureTheory.setIntegral_dirac'`, `MeasureTheory.Filtration.memLp_limitProcess_of_eLpNorm_bdd`, `Polynomial.ofFinsupp_neg`, `LaurentSeries.hasseDeriv_comp`, `Module.FaithfullyFlat.one_tmul_eq_zero_iff`, `WeierstrassCurve.Δ_of_isCharNeTwoNF`, `isConformalMap_complex_linear_conj`, `fderiv_smul_const`, `MeasureTheory.Measure.measurePreserving_add_right_neg`, `hasDerivWithinAt_finCons'`, `Cubic.prod_X_sub_C_eq`, `Set.neg_Iio`, `TrivSqZeroExt.instL1IsBoundedSMul`, `Quaternion.continuous_im`, `AddAut.conj_apply`, `BoundedContinuousFunction.instIsBoundedSMul_1`, `MeasureTheory.MemLp.integral_indicator_norm_ge_le`, `deriv.fun_neg`, `Asymptotics.Filter.Tendsto.isBigOTVS_one`, `Quaternion.sq_eq_normSq`, `support_iteratedFDeriv_subset`, `MeromorphicOn.neg_iff`, `MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball`, `MulActionHom.coe_neg`, `Wbtw.oangle₂₃₁_eq_zero`, `Finset.centerMass_empty`, `CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v`, `uniformity_eq_comap_neg_add_nhds_zero`, `fderiv_fun_neg`, `curveIntegral_zero`, `Matrix.det_neg`, `Quaternion.re_coe`, `Set.op_vadd_inter_nonempty_iff`, `gradient_const'`, `InnerProductSpace.rankOne_comp`, `Polynomial.multiset_prod_X_sub_C_nextCoeff`, `add_neg_lt_neg_add_iff`, `inner_eq_neg_one_iff_of_norm_eq_one`, `ContinuousAffineMap.norm_image_zero_le`, `Matrix.circulant_col_zero_eq`, `WeierstrassCurve.Jacobian.negDblY_of_Y_eq`, `Affine.Simplex.eq_centroid_iff_sum_vsub_eq_zero`, `derivWithin_inv'`, `Asymptotics.isLittleOTVS_fun_comm`, `nsmul_neg_comm`, `AffineEquiv.coe_constVSub_symm`, `neg_one_pow_char_pow`, `Asymptotics.isLittleO_zero_right_iff`, `IsCompact.add_closure_zero_eq_closure`, `ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq`, `Asymptotics.isLittleOTVS_comm`, `intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le`, `groupCohomology.cocycles₁_map_one`, `MeasureTheory.MemLp.neg`, `hasFPowerSeriesWithinAt_pi_iff`, `isCompactOperator_iff_isCompact_closure_image_closedBall`, `groupHomology.eq_d₃₂_comp_inv_assoc`, `neg_one_geom_sum`, `hasDerivWithinAt_comp_mul_left_smul_iff`, `hasDerivAt_iff_isLittleO_nhds_zero`, `SchwartzMap.tsupport_smulLeftCLM_subset`, `InnerProductSpace.toMatrix_rankOne`, `CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app`, `nnnorm_eq_zero`, `IncidenceAlgebra.mu_eq_neg_sum_Ioc_of_ne`, `add_neg_lt_add_neg_iff`, `deriv_const`, `ContMDiff.neg_section`, `Real.Angle.toReal_eq_zero_iff`, `ContDiffMapSupportedIn.structureMapCLM_apply_withOrder`, `MeasureTheory.lpNorm_zero`, `Quaternion.imJ_mul`, `zsmul_smul_addOrderOf`, `LieAlgebra.Extension.ofTwoCocycle_incl_apply`, `LieAlgebra.IsKilling.eq_zero_of_isNilpotent_ad_of_mem_isCartanSubalgebra`, `Finsupp.update_eq_sub_add_single`, `PiTensorProduct.liftIsometry_comp_mapL`, `CliffordAlgebra.star_ι`, `Set.preimage_add_left_zero'`, `iteratedFDeriv_smul_const_apply`, `AddAction.toPerm_symm_apply`, `Sbtw.oangle₃₁₂_eq_zero`, `Hyperreal.not_infinite_neg`, `Quaternion.im_nnratCast`, `Function.locallyFinsuppWithin.coe_nsmul`, `InnerProductSpace.isSymmetric_rankOne_self`, `Finsupp.toDFinsupp_neg`, `Orientation.oangle_smul_right_of_neg`, `RingNorm.eq_zero_of_map_eq_zero'`, `tendsto_zero_iff_norm_tendsto_zero`, `Seminorm.ball_smul_ball`, `ContinuousMap.coe_toLp`, `CliffordAlgebra.involute_ι`, `continuousMultilinearCurryLeftEquiv_apply`, `tsupport_fderiv_subset`, `CategoryTheory.ShortComplex.Homotopy.neg_h₃`, `tendsto_neg_nhdsGE_neg`, `AddChar.expect_apply_ne_zero_iff_eq_zero`, `nndist_zero_right`, `LinearMap.exact_zero_iff_injective`, `Module.Dual.lie_apply`, `LieSubmodule.coe_neg`, `MeasureTheory.Supermartingale.neg`, `Orientation.two_zsmul_oangle_neg_self_left`, `MeasureTheory.conv_withDensity_eq_lconvolution`, `Representation.Coinvariants.mk_eq_zero`, `MeasureTheory.SimpleFunc.integrable_approxOn_range`, `LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff`, `nsmul_zero_sub`, `Asymptotics.IsBigOTVS.rfl`, `Polynomial.sum_roots_eq_nextCoeff_of_monic_of_split`, `IsTopologicalAddGroup.exist_add_closure_nhds`, `Asymptotics.isLittleO_pure`, `Filter.comap_neg_atBot`, `summable_const_iff`, `Asymptotics.IsLittleOTVS.bot`, `IsSemisimpleModule.exists_end_algEquiv`, `SchwartzMap.tsupport_fderivCLM_subset`, `ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv`, `ContinuousLinearMap.isBigOTVS_comp`, `Continuous.exists_contMDiff_approx_and_eqOn`, `Quaternion.coe_sub`, `WeierstrassCurve.Projective.negDblY_eq'`, `Submodule.IsCompl.projection_apply_eq_zero_iff`, `MonomialOrder.leadingCoeff_neg`, `QuadraticMap.map_neg`, `tendsto_neg_nhdsGT`, `ContinuousLinearMap.intervalIntegral_apply`, `RingCone.nonneg.hasMemOrNegMem`, `IsIntegral.neg_iff`, `Function.noZeroSMulDivisors`, `Quaternion.natCast_im`, `SummationFilter.instLeAtTopSymmetricIcc`, `hasDerivAt_intCast`, `EuclideanGeometry.angle_eq_iff_oangle_eq_neg_of_sign_eq_neg`, `le_sub_self_iff`, `Seminorm.absorbent_ball_zero`, `NonemptyInterval.fst_neg`, `FiniteMultiplicity.neg`, `HasDerivWithinAt.inv`, `HasFDerivAtFilter.fun_neg`, `PiTensorProduct.liftIsometry_symm_apply`, `comap_abs_nhds_zero`, `SchwartzMap.smulLeftCLM_neg`, `CategoryTheory.ShortComplex.neg_τ₂`, `ContinuousMultilinearMap.iteratedFDerivComponent_apply`, `CategoryTheory.kernelCokernelCompSequence.δ_fac`, `add_neg_nonpos_iff_le`, `RootPairing.pairingIn_neg_one_neg_four_iff`, `Quaternion.self_mul_star`, `ContinuousLinearMap.toContinuousAddMonoidHom_neg`, `RootPairing.neg_root_mem`, `ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear`, `deriv_one`, `WithLp.neg_fst`, `Set.image_add_left'`, `DFinsupp.neLocus_eq_support_sub`, `QuaternionAlgebra.im_coe`, `HasFPowerSeriesAt.const_smul`, `ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder`, `CStarModule.inner_neg_right`, `iteratedFDeriv_succ_eq_comp_right`, `ArithmeticFunction.moebius_mul_log_eq_vonMangoldt`, `Quaternion.imJ_ratCast`, `ContinuousMultilinearMap.changeOriginSeries_support`, `ZModModule.neg_eq_self`, `Set.preimage_add_right_singleton`, `IsAlgClosure.ofAlgebraic`, `IsApproximateAddSubgroup.neg_eq_self`, `MeasureTheory.SimpleFunc.setToSimpleFunc_zero`, `ZNum.cast_bit0`, `Asymptotics.isBigOTVS_fun_comm`, `ContDiffMapSupportedIn.seminorm_apply`, `tsupport_iteratedFDeriv_subset`, `NormedAddCommGroup.tendsto_nhds_zero`, `QuaternionAlgebra.imK_ofNat`, `LieAlgebra.IsKilling.coroot_neg`, `Real.zero_at_infty_fourier`, `logDeriv_inv`, `Fintype.not_linearIndependent_iff`, `ZNum.cast_bitm1`, `ODE.hasDerivWithinAt_picard_Icc`, `MeasureTheory.condExp_of_not_sigmaFinite`, `IsCoprime.neg_left`, `VectorField.lieBracket_smul_left`, `Seminorm.smul_closedBall_subset`, `Polynomial.nextCoeff_eq_neg_sum_roots_of_monic_of_splits`, `ContinuousAddMonoidHom.neg_toFun`, `SimpleGraph.circulantGraph_eq_erase_zero`, `hasDerivWithinAt_diff_singleton`, `DFinsupp.neg_apply`, `fderiv_continuousLinearEquiv_comp`, `FiniteField.pow_dichotomy`, `ContinuousLinearMap.adjoint_toSpanSingleton`, `gaussSum_mul_gaussSum_pow_orderOf_sub_one`, `tendsto_tsum_compl_atTop_zero`, `HurwitzZeta.completedHurwitzZetaEven_zero`, `IsCompact.sub_closedBall`, `Quaternion.im_neg`, `neg_le_negPart`, `nhds_translation_sub`, `Balanced.zero_insert_interior`, `CFC.negPart_neg`, `tendsto_conj_nhds_zero`, `Set.instTietzeExtensionUnitClosedBall`, `Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card`, `Finset.preimage_add_right_singleton`, `half_sub`, `groupHomology.mapCycles₂_hom`, `Quaternion.im_imK`, `HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow`, `HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk`, `Polynomial.Chebyshev.U_eval_neg`, `Finsupp.toDFinsupp_sub`, `Quaternion.neg_imK`, `ContDiffMapSupportedIn.seminorm_eq_bot_of_gt`, `groupHomology.isoCycles₂_inv_comp_iCycles_apply`, `IsRelPrime.neg_right_iff`, `Quaternion.imK_intCast`, `toSpanSingleton_derivWithin`, `stereoInvFunAux_mem`, `ZMod.cast_descFactorial`, `isMIntegralCurveAt_comp_mul_ne_zero`, `groupHomology.isoCycles₂_inv_comp_iCycles_assoc`, `LieAlgebra.IsSemisimple.non_abelian_of_isAtom`, `EuclideanSpace.ball_zero_eq`, `Function.Periodic.sub_eq'`, `AddMonoidHom.fiberEquiv_apply`, `HasFiniteFPowerSeriesOnBall.eq_partialSum'`, `VectorField.mlieBracket_const_smul_left`, `QuotientAddGroup.btw_coe_iff'`, `sSup_neg`, `injective_iff_map_eq_zero`, `negPart_nonpos'`, `QuotientAddGroup.image_coe`, `CategoryTheory.Pretriangulated.Triangle.neg_hom₂`, `Filter.BoundedAtFilter.neg`, `abs_neg_one_zpow`, `range_mfderiv_coe_sphere`, `IsMIntegralCurve.comp_mul`, `MeasureTheory.Integrable.smul_essSup`, `IsBoundedBilinearMap.toContinuousLinearMap_apply`, `AddCommute.neg_neg`, `QuadraticMap.polar_neg`, `Bornology.isVonNBounded_sub`, `AnalyticAt.fun_neg`, `BoundedContinuousFunction.coe_zsmulRec`, `HasFDerivWithinAt.curveIntegral_segment_source`, `MeasureTheory.Integrable.comp_neg`, `HasFPowerSeriesOnBall.pi`, `ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply`, `WithLp.idemSnd_apply`, `LieAlgebra.abelian_of_le_center`, `HasFPowerSeriesWithinOnBall.fderivWithin_eq`, `nhds_basis_closed_balanced`, `MeasureTheory.Measure.addHaar_closedBall_mul_of_pos`, `stereographic_source`, `ContinuousMultilinearMap.piₗᵢ_symm_apply`, `orderOf_neg_one`, `TendstoLocallyUniformly.fun_neg`, `Interval.length_zero`, `MeasurableEquiv.symm_addRight`, `CategoryTheory.Biprod.unipotentUpper_inv`, `Asymptotics.isBigOWith_neg_left`, `NumberField.linearDisjoint_of_isGalois_isCoprime_discr`, `LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul`, `deriv.neg'`, `Quaternion.normSq_def'`, `SchwartzMap.pairing_continuous_left`, `AddCommute.neg_right_iff`, `signedDist_vadd_right_swap`, `Complex.integral_boundary_rect_eq_zero_of_differentiable_on_off_countable`, `CFC.posPart_neg`, `Filter.Tendsto.isVonNBounded_range`, `HahnSeries.map_sub`, `Quaternion.imI_add`, `QuadraticMap.coeFn_neg`, `intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left`, `SchwartzMap.integralCLM_apply`, `csInf_neg`, `UniformConvergenceCLM.hasBasis_nhds_zero`, `InnerProductSpace.rankOne_one_right_eq_toSpanSingleton`, `LieAlgebra.IsKilling.eq_zero_of_apply_eq_zero_of_mem_corootSpace`, `Filter.Tendsto.neg_neg`, `hasDerivAt_one`, `NonarchAddGroupSeminorm.toZeroHom_eq_coe`, `groupHomology.cyclesMk₂_eq`, `AffineMap.decomp`, `groupHomology.chainsMap_f_1_comp_chainsIso₁`, `add_eq_zero_iff_neg_eq`, `Matrix.Module.single_smul`, `intervalIntegral.integral_zero`, `IsBoundedSMul.of_nnnorm_smul_le`, `add_neg_le_neg_add_iff`, `Quaternion.ratCast_im`, `LieAlgebra.LoopAlgebra.residuePairing_apply_apply`, `Left.neg_pos_iff`, `NormedSpace.polar_ball`, `HasFTaylorSeriesUpToOn.hasStrictFDerivAt`, `AddSubmonoid.closure_neg`, `ContinuousLinearMap.neg_apply`, `smul_nonneg_iff`, `PolynomialLaw.neg_def`, `AddSubgroup.eq_bot_iff_forall`, `PresheafOfModules.Derivation.d_app`, `FormalMultilinearSeries.div_le_radius_compContinuousLinearMap`, `RingPreordering.mem_supportAddSubgroup`, `self_eq_neg`, `WithLp.toLp_neg`, `Complex.arg_conj_coe_angle`, `Set.indicator_compl`, `RCLike.sqrt_neg_I`, `groupHomology.H1π_eq_zero_iff`, `AnalyticAt.neg`, `QuaternionAlgebra.im_star`, `isGLB_neg'`, `Algebra.normalizedTrace_minpoly`, `map_add_right_nhds_zero`, `Finsupp.mem_vaddAntidiagonal_of_addGroup`, `groupHomology.isoCycles₁_inv_comp_iCycles_assoc`, `CategoryTheory.ProjectiveResolution.extMk_eq_zero_iff`, `IsUniformAddGroup.cauchy_iff_tendsto`, `groupHomology.π_comp_H1Iso_hom_assoc`, `DistribMulActionHom.map_neg`, `Finset.tendsto_Ioo_neg_atTop_atTop`, `Polynomial.Chebyshev.C_eval_neg_two`, `abs_eq_zero`, `groupHomology.chainsMap_f_2_comp_chainsIso₂`, `groupHomology.d₂₁_single_one_fst`, `HasDerivWithinAt.smul_const`, `antivaryOn_neg`, `HasFDerivAt.fun_neg`, `LieSubalgebra.engel_zero`, `Asymptotics.IsBigO.eq_zero_of_norm_pow`, `contDiff_nat_iff_continuous_differentiable`, `MeasureTheory.L1.SimpleFunc.setToL1S_zero_left`, `Finset.addConst_neg_left`, `HomogeneousLocalization.NumDenSameDeg.num_neg`, `HurwitzZeta.hurwitzZetaOdd_eq`, `SchwartzMap.lineDerivOp_fourierInv_eq`, `LinearIsometryEquiv.symm_conjStarAlgEquiv`, `HahnSeries.coeff_sub'`, `Submodule.topologicalClosure_eq_top_iff`, `groupHomology.H2π_comp_map`, `IsAddUnit.neg_add_eq_zero`, `MeasureTheory.Measure.addHaar_real_ball_center`, `Asymptotics.isLittleO_neg_left`, `HasFiniteFPowerSeriesOnBall.add`, `SubringClass.toNegMemClass`, `Quaternion.imK_smul`, `MeasureTheory.Lp.smul_def`, `iteratedDeriv_comp_const_sub`, `Polynomial.monomial_neg`, `RootPairing.rootSpanMem_reflectionPerm_self`, `negPart_nonneg`, `QuadraticMap.polar_neg_right`, `ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply`, `ContinuousLinearMap.opNorm_lsmul_le`, `gauge_neg_set_eq_gauge_neg`, `SkewMonoidAlgebra.support_neg`, `RCLike.conj_I`, `intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae`, `Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two`, `MultilinearMap.mkContinuousMultilinear_norm_le`, `Quaternion.star_imK`, `CategoryTheory.ShortComplex.Homotopy.neg_h₀`, `PolynomialModule.lsingle_apply`, `hasDerivAt_natCast`, `orbit_addSubgroup_zero_eq_self`, `ContinuousMap.coeFn_toLp`, `intervalIntegral.integral_non_aestronglyMeasurable_of_le`, `Quaternion.im_star`, `IsAddUnit.sub_eq_zero_iff_eq`, `IsModuleTopology.continuous_neg`, `AddSubgroup.Normal.conj_mem`, `MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq`, `HurwitzZeta.hurwitzZeta_zero`, `lt_neg_iff_add_neg'`, `Function.locallyFinsuppWithin.posPart_apply`, `tsum_neg`, `Quaternion.coe_mul`, `uniformity_eq_comap_nhds_zero'`, `LinearMap.exact_subtype_ker_map`, `Real.fourier_bilin_convolution_eq_integral`, `Quaternion.ratCast_imI`, `Matrix.det_eq_sum_row_mul_submatrix_succAbove_succAbove_det`, `HomologicalComplex₂.D₂_D₁`, `HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding`, `Orientation.oangle_add_cyc3_neg_left`, `QuaternionAlgebra.natCast_imI`, `EuclideanGeometry.oangle_eq_or_eq_neg_of_angle_eq`, `OpenPartialHomeomorph.unitBallBall_source`, `iter_deriv_inv`, `uniformity_eq_comap_neg_add_nhds_zero_swapped`, `PowerSeries.coeff_inv`, `Complex.lift_symm_apply_coe`, `ContinuousLinearMap.norm_compL_le`, `MeasureTheory.measure_lintegral_sub_measure`, `ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap`, `SeminormFamily.withSeminorms_iff_nhds_eq_iInf`, `Polynomial.aeval_neg`, `LieModule.chainTop_neg`, `StrictAntiOn.slope_neg`, `IsIntegral.neg`, `deriv_natCast`, `WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval`, `torusIntegral_radius_zero`, `abs_eq_neg_self`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars`, `HahnSeries.SummableFamily.neg_apply`, `sameRay_neg_smul_right_iff_of_ne`, `Polynomial.taylorEquiv_symm`, `Bornology.isVonNBounded_add`, `groupHomology.H1π_comp_map_assoc`, `HasFPowerSeriesAt.sub`, `abs_sub_nonpos`, `OrderDual.instIsOrderedModule`, `HasStrictFDerivAt.fun_neg`, `FreeAbelianGroup.map_zero`, `norm_le_zero_iff`, `OrthogonalFamily.range_linearIsometry`, `CategoryTheory.Pretriangulated.rotCompInvRot_inv_app_hom₁`, `Real.tendsto_integral_exp_smul_cocompact`, `AffineEquiv.constVAdd_symm`, `groupHomology.instEpiModuleCatH1π`, `Units.val_set_image_rootsOfUnity_two`, `RootPairing.Base.root_mem_or_neg_mem`, `LieModule.chainBot_neg`, `neg_add_lt_of_lt_add`, `fderivWithin_inv`, `MeasureTheory.Lp.simpleFunc.toLp_neg`, `LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional`, `Matrix.of_mem_specialOrthogonalGroup_fin_two_iff`, `nsmulCoprime_zero`, `Sbtw.oangle₁₃₂_eq_zero`, `SemiNormedGrp₁.zero_apply`, `Real.Angle.eq_neg_self_iff`, `SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left`, `Mathlib.Meta.Positivity.abs_pos_of_ne_zero`, `ofBoolRing_neg`, `Quaternion.normSq_zpow`, `Asymptotics.IsBigOWith.neg_left`, `Real.fourierIntegralInv_eq_fourierIntegral_comp_neg`, `MeasureTheory.ae_eq_zero_of_forall_dual`, `Quaternion.coe_nnratCast`, `ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv`, `IsCompact.closedBall_zero_sub`, `ContinuousLinearMap.opNNNorm_mul_flip_apply`, `Sbtw.oangle₂₁₃_eq_zero`, `translate_zero`, `Module.Relations.toQuotient_map_apply`, `InnerProductSpace.gramSchmidt_zero`, `AffineMap.coe_neg`, `HasFPowerSeriesOnBall.hasFDerivAt`, `MeasureTheory.rnDeriv_conv'`, `neg_add_lt_iff_lt_add'`, `NumberField.RingOfIntegers.neg_mk`, `AddGroupFilterBasis.conj`, `Polynomial.coe_neg`, `QuaternionAlgebra.neg_im`, `SeminormFamily.basisSets_zero`, `differentiableAt_neg_iff`, `Submodule.starProjection_orthogonalComplement_singleton_eq_zero`, `HahnEmbedding.Partial.mem_domain`, `DFinsupp.filter_neg`, `Orientation.oangle_smul_smul_self_of_nonneg`, `Archimedean.embedRealFun_zero`, `zero_mem_absConvexHull`, `FirstOrder.Field.instModelField`, `CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero`, `tsupport_fun_neg`, `ContinuousMultilinearMap.curryMid_apply`, `Polynomial.evalEval_neg`, `Quaternion.coe_starAe`, `iter_deriv_inv'`, `ClosedSubmodule.sInf_orthogonal`, `intervalIntegral.fderivWithin_integral_of_tendsto_ae`, `AddSubmonoid.fromLeftNeg_eq_neg`, `ContinuousMap.toLp_comp_toContinuousMap`, `PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm`, `spectrum.add_mem_iff`, `contDiff_single`, `MeasureTheory.integrable_const_iff`, `LieModule.isLieAbelian_of_ker_traceForm_eq_bot`, `neg_add_le_iff_le_add'`, `HasStrictFDerivAt.isBigOTVS_sub`, `Module.Relations.Solution.π_relation`, `TrivSqZeroExt.nnnorm_inl`, `MeasureTheory.Measure.addHaar_ball_mul_of_pos`, `Finset.box_succ_eq_sdiff`, `ContMDiff.clm_postcomp`, `NormedAddGroupHom.coe_ker`, `PolynomialModule.eval_apply`, `Int.fract_neg_eq_zero`, `balanced_closedBall_zero`, `iteratedFDeriv_zero_fun`, `TrivSqZeroExt.isUnit_or_isNilpotent_of_isMaximal_isNilpotent`, `Finset.neg_smul_finset`, `WeierstrassCurve.twoTorsionPolynomial_of_char_three`, `Quaternion.sub_im_self`, `CochainComplex.HomComplex.δ_δ`, `Quaternion.inner_self`, `CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg`, `groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂`, `mem_tangentConeAt_iff_exists_seq`, `Manifold.IsImmersionAt.target_subset_preimage_target`, `RootPairing.eq_baseOf_iff`, `LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace`, `AddCommute.neg_left_iff`, `CategoryTheory.CommSq.shortComplex'_g`, `Matrix.SpecialLinearGroup.SL2_inv_expl_det`, `HahnEmbedding.Seed.mem_domain_baseEmbedding`, `mapsTo_tangentConeAt_pi`, `Valuation.map_neg`, `Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero`, `TestFunction.hasCompactSupport'`, `IsTopologicalRing.toContinuousNeg`, `gradient_fun_const'`, `Module.reflection_mul_reflection_zpow_apply_self`, `QuaternionAlgebra.ofNat_imJ`, `MeasureTheory.hasFiniteIntegral_const_iff`, `MeromorphicAt.neg`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn`, `Function.Periodic.neg_eq`, `LieSubmodule.Quotient.mk_eq_zero'`, `parallelepiped_eq_sum_segment`, `MDifferentiableWithinAt.clm_postcomp`, `EuclideanGeometry.oangle_add_oangle_rev`, `MeasureTheory.L1.integral_zero`, `MeasureTheory.Measure.sub_mem_nhds_zero_of_addHaar_pos_ne_top`, `groupHomology.instEpiModuleCatH2π`, `ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear`, `Matrix.mulVec_neg`, `NormedSpace.sInter_polar_eq_closedBall`, `ContDiffBump.convolution_eq_right`, `TemperedDistribution.instFourierInvSMul`, `sameRay_neg_smul_right_iff`, `MeasureTheory.AEEqFun.Integrable.smul`, `ZMod.neg_eq_self_mod_two`, `add_neg_eq_of_eq_add`, `HurwitzZeta.hurwitzZeta_one_sub`, `pow_eq_one_iff_of_ne_zero`, `MeasureTheory.neg_absolutelyContinuous`, `LieAlgebra.Extension.proj_incl`, `ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity`, `List.alternatingSum_reverse`, `LieHom.mem_ker`, `FormalMultilinearSeries.analyticAt_changeOrigin`, `FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card`, `AddSemiconjBy.neg_symm_left`, `DFinsupp.neLocus_self_add_left`, `intervalIntegral.integral_hasFDerivWithinAt`, `HasFPowerSeriesAt.tendsto_partialSum`, `RCLike.wInner_zero_left`, `ContinuousLinearMap.orthogonal_range`, `NormedDivisionRing.toNormSMulClass`, `HasFiniteFPowerSeriesAt.add`, `sub_nsmul`, `HasFPowerSeriesAt.hasDerivAt`, `neg_dotProduct_neg`, `hasDerivWithinAt_congr_set'`, `dist_indicator`, `HomologicalComplex₂.D₁_D₂_assoc`, `neg_le_abs`, `Submodule.Quotient.mk_neg`, `Quaternion.im_imI`, `LieAlgebra.IsKilling.chainTopCoeff_zero_right`, `deriv_comp_neg`, `ContinuousLinearMap.isThetaTVS_comp`, `StrictConcaveOn.neg`, `fourierIntegral_half_period_translate`, `ordinaryHypergeometricSeries_eq_zero_iff`, `RingPreordering.IsOrdering.toHasMemOrNegMem`, `MeasureTheory.withDensityᵥ_zero`, `ZMod.isSquare_neg_one_iff'`, `EuclideanGeometry.Sphere.secondInter_zero`, `HasFDerivAt.linear_multilinear_comp`, `qExpansion_neg`, `Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero`, `ContinuousLinearMap.opNorm_smul_le`, `Asymptotics.isLittleOTVS_congr`, `HasStrictFDerivAt.isThetaTVS_sub`, `Quaternion.self_add_star`, `Quaternion.normSq_def`, `fderiv_zero`, `hasDerivWithinAt_const_add_iff`, `Quaternion.continuous_coe`, `sameRay_or_sameRay_neg_iff_not_linearIndependent`, `Quaternion.imK_one`, `Quaternion.ratCast_imK`, `Real.Angle.neg_coe_pi`, `EuclideanGeometry.hasFDerivAt_inversion`, `MeasureTheory.neg_ae`, `sub_eq_neg_self`, `MeasureTheory.convolutionExistsAt_iff_integrable_swap`, `self_eq_inv₀`, `TendstoUniformlyOn.fun_neg`, `Set.mem_vadd_set_neg`, `AddChar.sum_apply_ne_zero_iff_eq_zero`, `MeasureTheory.setToFun_zero`, `Quaternion.coe_commute`, `ConcaveOn.neg`, `VectorField.mpullback_smul`, `IncidenceAlgebra.mu_mul_zeta`, `LocallyLipschitz.neg`, `Quaternion.coe_injective`, `groupHomology.H1π_comp_map`, `groupHomology.chainsMap_f_hom`, `QuaternionAlgebra.imI_natCast`, `groupHomology.d₃₂_apply_mem_cycles₂`, `Asymptotics.IsBigO.neg_right`, `LucasLehmer.X.neg_fst`, `addInvariantVector_mlieBracket`, `addOrderOf_dvd_iff_zsmul_eq_zero`, `CochainComplex.mappingCone.δ_liftCochain`, `TendstoUniformlyOnFilter.neg`, `uniformity_eq_comap_add_neg_nhds_zero_swapped`, `ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply`, `FiniteField.sum_pow_units`, `Set.sub_mem_Ioo_zero_iff_right`, `HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff`, `Set.zero_notMem_sub_iff`, `Quaternion.ratCast_imJ`, `negPart_zero`, `ContinuousMultilinearMap.compContinuousLinearMapL_apply`, `ZMod.lift_injective`, `NormedSpace.exp_neg`, `Module.isTorsionFree_iff_smul_eq_zero`, `SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul`, `posPart_lt`, `AddSubgroup.closure_neg`, `Function.locallyFinsuppWithin.restrict_posPart`, `AnalyticAt.eventually_eq_zero_or_eventually_ne_zero`, `MeasureTheory.measure_inter_neg_vadd`, `Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero`, `ContinuousLinearMap.norm_bilinearRestrictScalars`, `Finset.addETransformRight_snd`, `inseparable_zero_iff_norm`, `ContinuousLinearMap.nhds_zero_eq`, `posPart_inf_negPart_eq_zero`, `PiTensorProduct.liftIsometry_apply_apply`, `ContinuousMultilinearMap.prodL_symm_apply`, `List.alternatingSum_cons`, `Bornology.IsBounded.neg`, `LeftInvariantDerivation.map_neg`, `derivWithin_fun_const`, `AddSubgroup.neg_mem`, `Multiset.esymm_neg`, `ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear`, `WeierstrassCurve.Projective.neg_of_Z_eq_zero`, `ProbabilityTheory.covarianceBilin_map`, `IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single`, `LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker`, `zero_mem_tangentConeAt`, `HahnSeries.inv_def`, `HasFPowerSeriesOnBall.prod`, `Orientation.two_zsmul_oangle_smul_right_self`, `HasFDerivAt.curveIntegral_segment_source'`, `Subring.coe_neg`, `groupHomology.boundariesOfIsBoundary₂_coe`, `HasFPowerSeriesWithinOnBall.neg`, `Set.image_add_right'`, `DFinsupp.coe_sub`, `IsLocalMax.neg`, `zero_lie`, `norm_neg`, `MeasureTheory.measure_add_lintegral_eq`, `groupHomology.cyclesMk₁_eq`, `CochainComplex.mappingCone.d_fst_v'_assoc`, `IsAddUnit.add_neg_eq_zero`, `Orientation.oangle_sign_neg_right`, `ContinuousLinearMap.bilinearComp_zero_left`, `ContinuousLinearMap.nnnorm_smulRight_apply`, `RootPairing.pairing_neg_one_neg_four_iff'`, `hasFPowerSeriesWithinOnBall_pi_iff`, `Quaternion.re_neg`, `sub_abs_eq_neg_two_nsmul_negPart`, `hasDerivAt_zero`, `SchwartzMap.fderivCLM_fourier_eq`, `MvPowerSeries.coeff_invOfUnit`, `HurwitzZeta.completedHurwitzZetaEven₀_neg`, `Quaternion.re_im`, `Quaternion.imI_intCast`, `CochainComplex.HomComplex.Cochain.toSingleMk_zero`, `ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt`, `PiLp.edist_toLp_single_same`, `Quaternion.star_mul_eq_coe`, `SchwartzMap.derivCLM_apply`, `intervalIntegral.integral_indicator`, `Seminorm.gauge_ball`, `List.sum_neg_reverse`, `ArchimedeanClass.mk_neg`, `groupHomology.mapCycles₂_comp_i_assoc`, `Real.Angle.neg_eq_self_iff`, `sub_nonpos_of_le`, `CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_cancel_inv_app`, `lie_zero`, `LieDerivation.map_neg`, `Function.locallyFinsuppWithin.restrictMonoidHom_apply`, `HurwitzZeta.completedHurwitzZetaEven₀_zero`, `isLinearTopology_iff_hasBasis_open_submodule`, `IncidenceAlgebra.zeta_mul_mu`, `MeasureTheory.MemLp.eLpNorm_indicator_le`, `slope_nonpos_iff_of_le`, `Real.Angle.toCircle_neg`, `add_neg_add_add_cancel`, `hasDerivWithinAt_inter'`, `Pi.single_zsmul`, `FirstOrder.realize_genericPolyMapSurjOnOfInjOn`, `CategoryTheory.Adjunction.homAddEquiv_neg`, `ContDiffBump.dist_normed_convolution_le`, `MDifferentiableOn.clm_precomp`, `ContDiffWithinAt.neg`, `MeasureTheory.eLpNormEssSup_indicator_eq_eLpNormEssSup_restrict`, `Summable.tsum_eq_add_tsum_ite`, `ContinuousMap.linearIsometryBoundedOfCompact_apply_apply`, `AdicCompletion.val_neg`, `differentiable_neg`, `RCLike.wInner_neg_left`, `hasDerivAt_neg`, `Filter.neg_cobounded`, `hasDerivAtFilter_finCons`, `ContinuousLinearMap.adjoint_comp`, `iteratedFDeriv_zero_eq_comp`, `isCompactOperator_iff_image_ball_subset_compact`, `LieModule.toEnd_eq_zero_iff`, `OrthonormalBasis.adjustToOrientation_apply_eq_or_eq_neg`, `intervalIntegral.integral_hasDerivAt_right`, `RootPairing.EmbeddedG2.pairing_short_long`, `tsupport_fderiv_apply_subset`, `hasFTaylorSeriesUpToOn_succ_iff_left`, `WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded`, `Absorbs.neg_neg`, `eq_neg_add_of_add_eq`, `MvPolynomial.C_neg`, `Balanced.starConvex`, `LinearMap.map_neg₂`, `IsPreconnected.eq_or_eq_neg_of_sq_eq`, `VectorFourier.integral_bilin_fourierIntegral_eq_flip`, `zero_at_infty_of_norm_le`, `Matrix.inv_fromBlocks_zero₂₁_of_isUnit_iff`, `dist_neg_neg`, `SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left`, `MultilinearMap.neg_apply`, `HasFPowerSeriesWithinOnBall.add`, `LieAlgebra.IsKilling.coroot_eq_zero_iff`, `RayVector.equiv_neg_iff`, `minpoly.neg`, `AffineMap.hasStrictDerivAt`, `AddSubgroup.disjoint_iff_add_eq_zero`, `InnerProductSpace.toLinearMap_rankOne`, `ContinuousLinearMap.comp_hasFPowerSeriesOnBall`, `LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem`, `Matrix.sum_single_intCast`, `MeasureTheory.measure_union_neg_vadd`, `ContinuousLinearMap.adjointAux_inner_right`, `HasDerivWithinAt.Ioi_iff_Ioo`, `ArchimedeanClass.FiniteElement.mk_neg`, `LinearIsometryEquiv.map_eq_zero_iff`, `AddSemiconjBy.neg_neg_symm_iff`, `CategoryTheory.Preadditive.inv_def`, `IsAddUnit.eq_on_neg`, `Quaternion.normSq_neg`, `Equiv.addRight_symm`, `QuadraticAlgebra.coe_intCast`, `TemperedDistribution.instLineDerivSMulComplex`, `HomologicalComplex.mapBifunctorMapHomotopy.comm₁_aux`, `summable_indicator_mod_iff_summable`, `QuaternionAlgebra.imJ_star`, `Tactic.ReduceModChar.CharP.neg_mul_eq_sub_one_mul`, `abs_lt`, `groupHomology.mapCycles₂_id_comp_apply`, `Orientation.oangle_rev`, `vadd_closedBall_zero`, `CategoryTheory.ShortComplex.Homotopy.symm_h₂`, `eq_or_eq_neg_of_abs_eq`, `negPart_eq_zero`, `Real.Angle.sin_zero`, `deriv_intCast`, `CategoryTheory.Preadditive.neg_comp`, `CliffordAlgebra.ι_mul_ι_comm_of_isOrtho`, `Polynomial.toFinsupp_neg`, `CategoryTheory.Abelian.Ext.neg_hom`, `IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end`, `continuousMultilinearCurryRightEquiv_symm_apply'`, `IsAddKleinFour.add_self`, `Polynomial.resultant_deriv`, `IsSepClosure.isAlgClosure_of_perfectField_top`, `ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply`, `Orientation.oangle_add_oangle_rev_neg_left`, `TendstoLocallyUniformlyOn.fun_neg`, `ContDiffMapSupportedIn.continuousSMul`, `Matrix.circulant_single`, `ContDiffMapSupportedIn.structureMapLM_zero_injective`, `AddSemiconjBy.neg_right_iff`, `toSpanSingleton_deriv`, `CategoryTheory.Abelian.Ext.eq_zero_of_projective`, `CategoryTheory.ShortComplex.ab_zero_apply`, `LinearMap.isStarProjection_toContinuousLinearMap_iff`, `Submodule.coe_neg`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `MeasureTheory.UnifTight.exists_measurableSet_indicator`, `WithLp.idemFst_apply`, `HahnSeries.orderTop_neg`, `ZNum.cast_bit1`, `HasFDerivAtFilter.isLittleOTVS`, `CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff`, `edist_zero_right`, `iteratedDerivWithin_eq_equiv_comp`, `Mathlib.Tactic.Abel.zero_smulg`, `conjneg_apply`, `Finset.image_add_left'`, `BoxIntegral.integrable_zero`, `AddGroup.exponent_dvd_iff_forall_zsmul_eq_zero`, `Matrix.J_inv`, `Quaternion.one_imJ`, `IsPrimitiveRoot.pow_sub_one_eq`, `FreeCommRing.isSupported_neg`, `iteratedFDerivWithin_two_apply`, `extDerivWithin_smul`, `ZModModule.add_self`, `Pretrivialization.continuousOn_continuousLinearMapCoordChange`, `ContDiffMapSupportedIn.seminorm_postcompLM_le`, `MeasureTheory.integrable_smul_iff`, `sq_eq_sq_iff_eq_or_eq_neg`, `Module.End.mem_maxGenEigenspace`, `HasStrictFDerivAt.fun_smul`, `HurwitzZeta.sinZeta_neg`, `tendsto_neg_nhdsLE`, `IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt`, `WittVector.wittNeg_zero`, `groupHomology.H2π_comp_map_apply`, `MeasureTheory.integrable_neg_iff`, `LocallyConvexSpace.convex_open_basis_zero`, `Submodule.adjoint_orthogonalProjection`, `squeeze_zero_norm`, `uniformity_eq_comap_nhds_zero_swapped`, `Polynomial.Splits.coeff_zero_eq_leadingCoeff_mul_prod_roots`, `MeasureTheory.Integrable.fun_smul`, `CochainComplex.HomComplex.Cocycle.toSingleMk_neg`, `LieSubalgebra.coe_zero_iff_zero`, `Orientation.two_zsmul_oangle_neg_right`, `Polynomial.eval₂_neg`, `IsCompactOperator.neg`, `MeasureTheory.lintegral_enorm_eq_lintegral_edist`, `SkewMonoidAlgebra.intCast_def`, `CochainComplex.mappingCone.d_fst_v'`, `MeasureTheory.condExp_of_sigmaFinite`, `MeasureTheory.integral_sub_average`, `Complex.IsConservativeOn.hasDerivAt_wedgeIntegral`, `CurveIntegrable.smul`, `QuaternionAlgebra.natCast_imJ`, `HurwitzZeta.completedCosZeta_eq`, `Prod.card_box_succ`, `intervalIntegral.integral_zero_ae`, `QuaternionAlgebra.intCast_imI`, `AddSubgroup.mk_eq_zero`, `Continuous.exists_contDiff_approx`, `CategoryTheory.ShortComplex.LeftHomologyMapData.neg_φK`, `isMIntegralCurveOn_comp_mul_ne_zero`, `ContinuousLinearMap.hasFDerivAt_of_bilinear`, `ContinuousAlternatingMap.neg_apply`, `Set.disjoint_vadd_set_left`, `ContinuousNeg.of_continuousConstSMul`, `FormalMultilinearSeries.min_radius_le_radius_add`, `le_neg_add_iff_le`, `hasStrictDerivAt_one`, `FormalMultilinearSeries.ofScalars_comp_neg_id`, `MeasureTheory.HasFiniteIntegral.smul`, `LieAlgebra.of_symm_zero`, `gaussSum_pow_eq_prod_jacobiSum`, `ContinuousAffineMap.norm_comp_le`, `Quaternion.coe_imK`, `SchwartzMap.instZeroAtInftyContinuousMapClass`, `ContinuousLinearMap.closed_range_of_antilipschitz`, `AddSubgroup.leftTransversals.diff_neg`, `LieModuleHom.coe_zero`, `RootPairing.neg_coroot_mem`, `VonNeumannAlgebra.coe_toStarSubalgebra`, `SeminormFamily.basisSets_singleton_mem`, `MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter`, `WithLp.zero_snd`, `Asymptotics.isLittleOTVS_iff_tendsto_inv_smul`, `IsPrimitiveRoot.neg_one`, `FirstOrder.Field.model_hasChar_of_charP`, `ContinuousAlternatingMap.curryLeft_add`, `hasFDerivAt_integral_of_dominated_of_fderiv_le`, `neg_sub_neg`, `map_eq_zero_iff_eq_zero`, `HasFPowerSeriesAt.pi`, `WeierstrassCurve.Jacobian.addY_of_X_eq'`, `HahnSeries.leadingCoeff_neg`, `HasFPowerSeriesWithinOnBall.tendstoUniformlyOn'`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply`, `hasStrictDerivAt_pi`, `hasLineDerivAt_zero`, `ZNum.cast_mul`, `Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero'`, `ContDiff.hasStrictDerivAt`, `LieModule.isTrivial_iff_max_triv_eq_top`, `Submodule.starProjection_orthogonal_apply_eq_zero`, `HasFDerivWithinAt.smul`, `MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_pos_le`, `Filter.tendsto_comp_neg_atTop_iff`, `ContinuousAlternatingMap.prodLIE_apply`, `MeasureTheory.Measure.neg.instIsAddLeftInvariant`, `Finset.addETransformRight_neg`, `HurwitzZeta.hurwitzEvenFEPair_neg`, `LieAlgebra.IsKilling.chainBotCoeff_of_eq_zsmul_add`, `add_notMem_of_exponent_two`, `Manifold.IsImmersionAtOfComplement.writtenInCharts`, `LinearIsometry.inl_apply`, `Finset.addETransformLeft_snd`, `WithCStarModule.inner_single_left`, `MDifferentiableOn.neg`, `AddCircle.finite_torsion`, `Even.neg`, `Asymptotics.isLittleO_norm_pow_id`, `LucasLehmer.ω_pow_eq_neg_one`, `PadicInt.mahlerEquiv_apply`, `Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul`, `groupHomology.inhomogeneousChains.d_comp_d`, `instSMulPosStrictMonoIntOfIsOrderedAddMonoid`, `Finset.addETransformRight_zero`, `continuousSMul_closedBall_closedBall`, `ContinuousLinearMap.opNorm_flip`, `Module.Basis.parallelepiped_map`, `isNilpotent_neg_iff`, `NonemptyInterval.length_pure`, `CliffordAlgebra.EquivEven.e0_mul_e0`, `MvPolynomial.psum_eq_mul_esymm_sub_sum`, `sub_lt_self_iff`, `Polynomial.coeffList_neg`, `UniqueFactorizationDomain.radical_neg_one`, `FormalMultilinearSeries.radius_compContinuousLinearMap_le`, `hasDerivWithinAt_derivWithin_iff`, `hasDerivAt_sub_const_iff`, `AddSubgroup.mem_iSup_prop`, `ContinuousLinearMap.IsPositive.adjoint_conj`, `compl_add_closure_zero_eq_iff`, `ArchimedeanClass.mk_eq_top_iff`, `IsUniformAddGroup.cauchy_map_iff_tendsto_swapped`, `RootPairing.Base.coroot_mem_or_neg_mem`, `IsConformalMap.smul`, `sub_add_eq_sub_add_zero_sub`, `Set.add_eq_zero_iff`, `DivisibleHull.neg_mk`, `MeasureTheory.eLpNorm'_const_smul_le`, `List.sum_map_ite_eq`, `OrderIso.subLeft_symm_apply`, `CliffordAlgebra.toProd_one_tmul_ι`, `Polynomial.coeff_neg`, `AddSubgroup.quotientEquivProdOfLE'_apply`, `Set.neg_mem_Ico_iff`, `FormalMultilinearSeries.derivSeries_eq_zero`, `HahnSeries.min_orderTop_le_orderTop_sub`, `Projectivization.mk'_eq_mk`, `LinearMap.linearProjOfIsCompl_apply_right'`, `HurwitzZeta.completedHurwitzZetaEven_neg`, `Real.Angle.cos_eq_iff_eq_or_eq_neg`, `LieIdeal.isLieAbelian_of_trivial`, `ContDiffWithinAt.smulRight`, `Quaternion.coe_imJ`, `MeasureTheory.integral_zero'`, `PowerSeries.rescale_neg_one_X`, `ContinuousLinearMap.star_eq_adjoint`, `LinearMap.BilinForm.neg_apply`, `EMetric.preimage_add_left_ball`, `PolynomialLaw.toFun_neg`, `ContinuousMultilinearMap.curryLeft_apply`, `ZMod.abs_valMinAbs_eq_abs_valMinAbs`, `QuadraticMap.IsOrtho.polar_eq_zero`, `Derivation.mapCoeffs_apply`, `Function.locallyFinsuppWithin.nsmul_negPart`, `neg_eq_self_of_exponent_two`, `LineDeriv.lineDerivOp_neg`, `HasFPowerSeriesWithinAt.neg`, `EuclideanGeometry.angle_neg`, `CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f`, `HahnModule.of_sub`, `WithZero.exp_zsmul`, 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`Filter.map_neg_atBot`, `bddBelow_neg`, `CStarModule.inner_neg_left`, `sameRay_neg_smul_left_iff`, `groupHomology.d₁₀ArrowIso_hom_right`, `tendsto_neg_nhdsLT`, `apply_eq_zero_of_analyticOrderNatAt_ne_zero`, `IsCoprime.neg_neg_iff`, `DFinsupp.Colex.isOrderedAddMonoid`, `TestFunction.instContinuousSMulReal`, `FourierTransform.fourier_neg`, `MeasureTheory.measure_neg_vadd_union`, `Set.preimage_vadd`, `EuclideanGeometry.oangle_self_left`, `WithLp.norm_toLp_snd`, `Quaternion.re_sub`, `Dense.eq_zero_of_inner_right`, `Finsupp.neLocus_self_add_right`, `MeasureTheory.integral_mul_deriv_eq_deriv_mul_of_integrable`, `QuaternionAlgebra.intCast_imK`, `ContinuousMap.norm_smul_const`, `iteratedFDeriv_succ_eq_comp_left`, `Seminorm.closedBall_zero_eq`, `ContinuousMapZero.toNNReal_neg_smul`, `antivary_iff_forall_smul_nonpos`, `ContinuousLinearMap.smul_compLpL`, `groupHomology.single_one_mem_boundaries₁`, `VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral`, `AddMonoidHom.exact_iff`, `Finsupp.subtypeDomain_sub`, `add_neg_neg_iff`, `Filter.isBoundedUnder_ge_neg`, `AntivaryOn.neg`, `RootPairing.neg_mem_range_root_iff`, `Algebra.Generators.cotangentCompLocalizationAwayEquiv_symm_inl`, `PiLp.zero_apply`, `IncidenceAlgebra.sub_apply`, `Balanced.neg_mem_iff`, `Polynomial.Chebyshev.T_eval_neg_one`, `eq_neg_iff_add_eq_zero`, `DivisibleHull.zero_qsmul`, `convexHull_list_sum`, `quadraticChar_neg_one`, `Finset.card_vadd_inter`, `ClosedSubmodule.orthogonal_closure`, `BoxIntegral.integrable_neg`, `ZSpan.vadd_mem_fundamentalDomain`, `CategoryTheory.ShiftedHom.mk₀_neg`, `Hyperreal.infinitesimal_neg`, `AddChar.map_neg_eq_conj`, `Complex.arg_inv_coe_angle`, `Polynomial.C_neg`, `AddMonoidAlgebra.antipode_single`, `ContDiffMapSupportedIn.structureMapCLM_zero_injective`, `Finset.pluennecke_ruzsa_inequality_nsmul_sub`, `AddGroupSeminorm.map_zero'`, `Hyperreal.coe_neg`, `Real.Angle.cos_neg`, `Finset.ruzsa_triangle_inequality_addNeg_addNeg_addNeg`, `HasFDerivWithinAt.curveIntegral_segment_source'`, `IsLinearTopology.hasBasis_subbimodule`, `ContinuousMultilinearMap.piₗᵢ_apply`, `Algebra.SubmersivePresentation.sectionCotangent_zero_of_notMem_range`, `QuaternionAlgebra.im_neg`, `Polynomial.prod_X_sub_C_coeff_card_pred`, `Module.Basis.opNNNorm_le`, `nndist_zero_left`, `Polynomial.resultant_one_left`, `ContMDiffWithinAt.clm_precomp`, `LinearOrderedAddCommGroupWithTop.sub_self_nonneg`, `ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply`, `LieAlgebra.mem_corootSpace`, `Quaternion.mul_imI`, `MeasureTheory.UnifIntegrable.neg`, `ContMDiffWithinAt.neg`, `MeasureTheory.lconvolution_assoc₀`, `continuousMultilinearCurryFin1_symm_apply`, `CauSeq.coe_neg`, `AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff`, `MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound`, `FormalMultilinearSeries.radius_pi_le`, `Set.zero_mem_sub_iff`, `MeasureTheory.HasFiniteIntegral.neg`, `groupHomology.d₂₁_single`, `PadicInt.mahlerEquiv_symm_apply`, `ContinuousLinearMap.lsmul_flip_apply`, `Quaternion.re_ratCast`, `mem_closedBall_zero_iff`, `Finset.preimage_add_left_zero'`, `hasDerivAt_iff_tendsto`, `Quaternion.intCast_re`, `HasStrictFDerivAt.smul_const`, `MeasureTheory.Measure.addHaar_ball`, `IncidenceAlgebra.mu_eq_neg_sum_Ico_of_ne`, `Quaternion.coe_im`, `ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply`, `Fin.neg_partialSum_add_eq_contractNth`, `QuaternionAlgebra.im_intCast`, `List.alternatingSum_cons'`, `SchwartzMap.smulLeftCLM_ofReal`, `OrderIso.addRight_symm`, `zsmul_neg'`, `Finset.neg_vadd_mem_iff`, `groupHomology.inhomogeneousChains.d_eq`, `ContDiffAt.differentiableAt_iteratedFDeriv`, `groupHomology.cycles₁IsoOfIsTrivial_inv_apply`, `TrivSqZeroExt.inv_zero`, `max_zero_sub_eq_self`, `groupHomology.eq_d₂₁_comp_inv_apply`, `AddCommute.add_neg_eq_add_neg_iff_of_isAddUnit`, `Complex.integral_boundary_rect_eq_zero_of_continuousOn_of_differentiableOn`, `ContinuousLinearMap.sSup_unitClosedBall_eq_norm`, `ZNum.cast_sub`, `ContinuousMultilinearMap.nnnorm_smulRight`, `spectrum.neg_eq`, `Cubic.d_eq_three_roots`, `Quaternion.zero_im`, `CategoryTheory.ShortComplex.cyclesMap'_neg`, `intervalIntegral.integral_hasDerivAt_left`, `ContinuousLinearMap.norm_map_iff_adjoint_comp_self`, `zero_mem_tangentConeAt_iff`, `map_addUnits_neg`, `ContDiffOn.smulRight`, `groupHomology.d₁₀_comp_coinvariantsMk_assoc`, `CategoryTheory.op_neg`, `ContinuousLinearMap.norm_adjoint_comp_self`, `zpow_eq_one_iff_cases₀`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith`, `DirichletCharacter.Even.to_fun`, `complEDS_neg`, `Real.Angle.two_zsmul_eq_zero_iff`, `hasDerivWithinAt_intCast`, `MeasureTheory.IsAddFundamentalDomain.mk''`, `Matrix.circulant_isSymm_apply`, `ContMDiff.clm_precomp`, `Function.locallyFinsuppWithin.restrictLatticeHom_apply`, `locallyConvexSpace_iff_zero`, `MeasureTheory.exists_eLpNorm_indicator_le`, `HasFPowerSeriesWithinAt.compContinuousLinearMap`, `Rep.indToCoindAux_of_not_rel`, `summable_neg_iff`, `pow_eq_pow_iff_of_ne_zero`, `Quaternion.instIsScalarTower`, `Finset.centerMass_neg_left`, `LieAlgebra.IsKilling.chainTopCoeff_le_chainLength`, `ContinuousMultilinearMap.norm_smulRight`, `Equiv.subRight_eq_addRight_neg`, `groupHomology.isoCycles₁_hom_comp_i`, `instSMulCommClass_sphere_closedBall_ball`, `AddGroupCone.nonneg.isMaxCone`, `MeasureTheory.eventuallyConst_neg_set_ae`, `IsLinearMap.isLinearMap_neg`, `ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm`, `Real.hasDerivAt_fourierIntegral`, `Equiv.addLeft_zero`, `IntervalIntegrable.smul`, `MeasureTheory.integral_neg_eq_self`, `MeasureTheory.Measure.toSphere_eq_zero_iff_finrank`, `Module.Relations.Solution.IsPresentation.exact`, `antilipschitzWith_neg_iff`, `MonoidHom.map_neg_one`, `Finset.coe_zsmul`, `neg_add_eq_zero`, `ContinuousLinearMap.hasDerivWithinAt`, `IsAddTorsionFree.to_noZeroSMulDivisors_int`, `Antivary.sub_smul_sub_nonpos`, `AddSubmonoid.coe_negOrderIso_apply`, `FormalMultilinearSeries.derivSeries_apply_diag`, `NormedSpace.polar_closedBall`, `wbtw_neg_iff`, `monovary_neg_right`, `Set.vadd_inter_ne_empty_iff`, `MeasureTheory.Measure.instIsNegInvariantCount`, `fderiv_comp_smul`, `groupHomology.chainsMap_f_0_comp_chainsIso₀_apply`, `AddConstMap.coe_conjNeg_apply`, `Finset.weightedVSub_sdiff_sub`, `MeasureTheory.predictablePart_zero`, `ContinuousLinearMap.opNorm_lsmul`, `IsClosed.add_closure_zero_eq`, `zpow_eq_zpow_iff_cases₀`, `iteratedDeriv_neg`, `FormalMultilinearSeries.norm_changeOriginSeriesTerm`, `HurwitzZeta.completedHurwitzZetaEven_residue_zero`, `TemperedDistribution.smulLeftCLM_smul`, `ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply`, `NormedRing.inverse_add_nth_order`, `TrivSqZeroExt.isUnit_inl_iff`, `isScalarTower_closedBall_closedBall_ball`, `Complex.circleIntegral_eq_zero_of_differentiable_on_off_countable`, `isometry_neg`, `Polynomial.roots_X_add_C`, `DFinsupp.toFinsupp_neg`, `GenContFract.sub_convs_eq`, `HasFTaylorSeriesUpTo.zero_eq'`, `InnerProductGeometry.angle_neg_neg`, `groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁`, `Module.End.mem_genEigenspace_zero`, `ZMod.prod_Ico_one_prime`, `Finset.preimage_add_right_zero`, `Function.Periodic.zsmul_eq`, `AddGrpCat.FilteredColimits.colimit_zero_eq`, `WeierstrassCurve.Jacobian.add_of_Z_eq_zero_right`, `Matrix.cstar_norm_def`, `PointwiseConvergenceCLM.withSeminorms`, `integral_eq_zero_of_forall_integral_inner_eq_zero`, `WeierstrassCurve.b₈_of_isShortNF`, `abs_sub_pos`, `Quaternion.imJ_star`, `MeasureTheory.convolution_eq_swap`, `ContMDiffOn.neg_section`, `Int.sign_eq_sign`, `CategoryTheory.ShortComplex.neg_τ₃`, `ContinuousLinearMap.map_zero₂`, `Module.Basis.opNorm_le`, `WittVector.mul_polyOfInterest_aux3`, `ContDiffBumpBase.symmetric`, `UniformCauchySeqOnFilter.one_smulRight`, `isConformalMap_complex_linear`, `mulInvariantVectorField_smul`, `Real.zero_at_infty_vector_fourierIntegral`, `AnalyticOnNhd.preimage_zero_mem_codiscreteWithin`, `Summable.tendsto_zero_of_even_summable_symmetricIcc`, `hasDerivAt_const_add_iff`, `Matrix.trace_neg`, `ContinuousMultilinearMap.curryFinFinset_symm_apply`, `HasFPowerSeriesWithinOnBall.pi`, `SchwartzMap.smulLeftCLM_apply`, `MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix`, `ContDiffMapSupportedIn.withSeminorms'`, `MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant`, `ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply`, `discreteTopology_iff_isOpen_singleton_zero`, `Set.sub_mem_Icc_zero_iff_right`, `Polynomial.shiftedLegendre_eval_symm`, `TestFunctionClass.tsupport_map_subset`, `Balanced.neg_eq`, `TrivSqZeroExt.inl_intCast`, `isOfFinAddOrder_iff_zsmul_eq_zero`, `HasFTaylorSeriesUpTo.fderiv`, `CPolynomialAt.neg`, `QuaternionAlgebra.imJ_ofNat`, `AddSubgroup.neg_mem'`, `MDifferentiable.neg`, `MeasureTheory.Measure.addHaar_closedBall_center`, `MeasureTheory.Lp.dense_hasCompactSupport_contDiff`, `IsSepClosure.isAlgClosure_of_perfectField`, `neg_strictConcaveOn_iff`, `LieAlgebra.IsKilling.span_weight_eq_top`, `Set.vadd_inter_nonempty_iff`, `isCancelVAdd_iff_eq_zero_of_vadd_eq`, `Finset.subset_vadd_finset_iff`, `Mathlib.Tactic.RingNF.int_rawCast_neg`, `parallelepiped_eq_convexHull`, `support_fderiv_subset`, `Dense.eq_zero_of_inner_left`, `ContinuousLinearMap.norm_holderL_le`, `ModuleCat.span_rightExact`, `HahnSeries.inv_single`, `MvPolynomial.IsHomogeneous.neg`, `hammingDist_eq_hammingNorm`, `LucasLehmer.X.zero_snd`, `SchwartzMap.smulLeftCLM_compL_smulLeftCLM`, `DirectSum.toAddMonoidAlgebra_neg`, `coe_neg_ball`, `Rat.cast_neg`, `hasDerivWithinAt_inv`, `ContinuousAffineMap.toConstProdContinuousLinearMap_fst`, `Asymptotics.isBigOTVS_prodMk_left`, `NonarchAddGroupSeminorm.add_le_max'`, `MeasureTheory.lpMeas.ae_fin_strongly_measurable'`, `CancelDenoms.neg_subst`, `IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq`, `gaugeSeminormFamily_ball`, `IsNonarchimedean.finset_powerset_image_add`, `CochainComplex.HomComplex.Cochain.rightUnshift_zero`, `HahnModule.instIsTorsionFree`, `SubMulAction.neg_mem_iff`, `WeierstrassCurve.Jacobian.addX_of_Z_eq_zero_right`, `DFinsupp.subtypeDomain_neg`, `Polynomial.multiset_prod_X_sub_C_coeff_card_pred`, `slope_nonneg_iff_of_le`, `Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add`, `TorusIntegrable.neg`, `intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip`, `AlgebraicGeometry.tilde.map_neg`, `TemperedDistribution.derivCLM_apply_apply`, `DirichletCharacter.fourierTransform_eq_gaussSum_mulShift`, `Unitization.inl_sub`, `Finset.sum_neg_distrib`, `FirstOrder.Ring.mvPolynomial_zeroLocus_definable`, `deriv_neg`, `intervalIntegral.derivWithin_integral_left`, `posPart_neg`, `AddGroupCone.coe_nonneg`, `ContMDiffSection.coe_neg`, `hasDerivWithinAt_Ici_of_tendsto_deriv`, `Module.Relations.Solution.π_comp_map_apply`, `Finset.indicator_biUnion_eq_sum_powerset`, `isCauSeq_neg`, `LinearMap.hasDerivAt`, `ZeroAtInftyContinuousMap.coe_sub`, `intervalIntegral.deriv_integral_of_tendsto_ae_left`, `Matrix.blockDiag_neg`, `TopologicalGroup.isOpenMap_iff_nhds_zero`, `groupHomology.single_mem_cycles₂_iff`, `LieModule.traceForm_apply_lie_apply'`, `MeasureTheory.weightedSMul_smul_measure`, `neg_one_pow_mul_eq_zero_iff`, `AddSemiconjBy.neg_neg_symm`, `LinearMap.hasDerivAtFilter`, `InnerProductSpace.Core.definite`, `CategoryTheory.hasProjectiveDimensionLT_iff`, `intervalIntegral.integral_hasFDerivAt`, `FreeAbelianGroup.zero_seq`, `tendsto_norm_zero`, `Quaternion.sub_imK`, `HasFiniteFPowerSeriesOnBall.fderiv_eq`, `WeierstrassCurve.Projective.addX_of_Z_eq_zero_right`, `finsum_neg_distrib`, `Memℓp.neg`, `Real.Angle.two_nsmul_coe_pi`, `PointedCone.to_isOrderedModule`, `ArchimedeanClass.mk_antitoneOn`, `MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound`, `HahnSeries.cardSupp_sub_le`, `mem_eball_zero_iff`, `WithSeminorms.isVonNBounded_iff_seminorm_bounded`, `HurwitzZeta.sinZeta_eq`, `InnerProductSpace.Core.normSq_eq_zero`, `groupHomology.boundaries₁_le_cycles₁`, `HasFPowerSeriesAt.locally_zero_iff`, `hasDerivAt_iff_tendsto_slope`, `Function.locallyFinsuppWithin.restrict_negPart`, `TrivSqZeroExt.isUnit_or_isNilpotent`, `intervalIntegral.fderiv_integral`, `ContinuousLinearMap.analyticAt_bilinear`, `Asymptotics.isBigO_pure`, `Matrix.det_succ_row_zero`, `hasCompactSupport_norm_iff`, `abs_eq_abs`, `dist_zero_right`, `Set.image_neg_Iic`, `HasFPowerSeriesAt.hasStrictFDerivAt`, `VectorField.mlieBracketWithin_zero_left`, `LieHom.le_ker_iff`, `AddGroupExtension.Section.add_neg_mem_range_inl`, `Quaternion.im_sq`, `ZMod.dft_odd_iff`, `WithSeminorms.hasBasis`, `HahnEmbedding.Partial.exists_domain_eq_top`, `Summable.indicator`, `zsmul_eq_zero_iff_modEq`, `AddGroupFilterBasis.mem_nhds_zero`, `ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right`, `FirstOrder.Field.model_fieldOfChar_of_charP`, `UniformConvergenceCLM.nhds_zero_eq`, `isBoundedLinearMap_continuousMultilinearMap_comp_linear`, `IsMinOn.neg`, `FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm`, `iteratedFDerivWithin_comp_sub'`, `Cubic.C_mul_prod_X_sub_C_eq`, `AddGroupSeminormClass.map_zero`, `ZMod.neg_val'`, `WithConv.ofConv_neg`, `ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp`, `Quaternion.imJ_natCast`, `Derivation.leibniz_invOf`, `Function.locallyFinsuppWithin.coe_zero`, `Orientation.oangle_neg_neg`, `smul_neg_iff_of_neg_left`, `strictMono_iff_map_neg`, `Finset.addConvolution_op_vadd_eq_addConvolution_add_neg`, `LieModule.Weight.toLinear_neg`, `FreeAbelianGroup.lift_neg`, `Orientation.oangle_smul_right_self_of_nonneg`, `HolderWith.smul`, `PresheafOfModules.Sheafify.smul_zero`, `Function.locallyFinsuppWithin.negPart_apply`, `ZSpan.fract_eq_fract`, `Quaternion.natCast_imJ`, `AddChar.injective_iff`, `hasDerivAt_pi`, `MeasureTheory.ContinuousMap.inner_toLp`, `Int.cast_pos`, `Polynomial.Chebyshev.S_eval_neg_two`, `IsPrimitiveRoot.eq_neg_one_of_two_right`, `posPart_eq_zero`, `ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars`, `derivWithin_fun_inv'`, `Set.abs_indicator_symmDiff`, `SchwartzMap.toZeroAtInfty_apply`, `sub_nonneg`, `abs_eq_self`, `SeminormFamily.basisSets_mem`, `lt_neg_self_iff`, `MeasureTheory.ae_eq_zero_of_forall_dual_of_isSeparable`, `DirectSum.GRing.intCast_negSucc_ofNat`, `MeasureTheory.innerRegular_neg_iff`, `hasDerivWithinAt_finCons`, `Quaternion.coe_neg`, `neg_le_sub_iff_le_add`, `WithTop.untop₀_le_untop₀_iff`, `exists_continuousLinearEquiv_fderiv_symm_eq`, `CategoryTheory.CatCenter.app_neg`, `FormalMultilinearSeries.rightInv_coeff`, `IsPrimitiveRoot.norm_of_cyclotomic_irreducible`, `tangentMap_prod_right`, `Metric.instTietzeExtensionBall`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand'`, `MeasureTheory.quasiMeasurePreserving_neg`, `Orientation.oangle_neg_orientation_eq_neg`, `AddGroupFilterBasis.t2Space_iff_sInter_subset`, `IncidenceAlgebra.mu_toDual`, `mfderiv_neg`, `ContinuousLinearMap.map_neg`, `normEDS_neg`, `QuotientAddGroup.rightRel_eq`, `LieModule.chainTopCoeff_neg`, `ContinuousLinearMap.isPositive_adjoint_comp_self`, `SchwartzMap.integral_clm_comp_laplacian_right_eq_left`, `instSMulCommClass_sphere_sphere_closedBall`, `neg_inf`, `ContDiffOn.differentiableOn_iteratedFDerivWithin`, `EuclideanSpace.single_eq_zero_iff`, `differentiableAt_iff_comp_const_add`, `ValueDistribution.log_counting_zero_sub_logCounting_top`, `PosSMulStrictMono.toSMulPosStrictMono`, `HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn'`, `ClosedSubmodule.orthogonal_closure'`, `ContinuousLinearMap.map_neg₂`, `Matrix.l2_opNorm_def`, `Int.cast_negOfNat`, `Quaternion.hasSum_coe`, `Filter.tendsto_neg_atTop_iff`, `ContinuousNeg.induced`, `AddGroupTopology.continuous_neg'`, `HomologicalComplex.neg_f_apply`, `ConvexBody.coe_nsmul`, `HasFiniteFPowerSeriesOnBall.sub`, `CochainComplex.HomComplex.CohomologyClass.mk_neg`, `ContinuousMultilinearMap.norm_compContinuousLinearMapL_le`, `Bornology.isVonNBounded_singleton`, `Bundle.RiemannianMetric.continuousAt`, `IsCompact.add_closedBall_zero`, `QuaternionAlgebra.re_add_im`, `AddSubgroup.mem_goursatSnd`, `MeasureTheory.charFun_zero`, `WithTop.untop₀_neg`, `continuous_stereoInvFun`, `Filter.tendsto_neg_cobounded`, `AnalyticAt.analyticOrderAt_ne_zero`, `abs_nonneg`, `ContMDiffOn.neg`, `linearDepOn_iff'`, `QuaternionAlgebra.sub_im_self`, `FormalMultilinearSeries.comp_rightInv_aux2`, `Filter.comap_neg_atTop`, `MeasureTheory.tendsto_integral_norm_approxOn_sub`, `TrivSqZeroExt.mul_inv_rev`, `AddChar.expect_apply_eq_ite`, `add_neg_le_iff_le_add`, `Quaternion.intCast_im`, `Cubic.b_eq_three_roots`, `MeasureTheory.hasFiniteIntegral_smul_iff`, `VectorField.mlieBracketWithin_swap`, `Quaternion.imI_coe`, `MeasureTheory.DominatedFinMeasAdditive.zero`, `IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt`, `ContDiffMapSupportedIn.compact_supp`, `MeasureTheory.integrable_fun_smul_iff`, `isConformalMap_const_smul`, `IsExtrOn.neg`, `MeasureTheory.MemLp.eLpNorm_indicator_le'`, `ArithmeticFunction.intCoe_apply`, `hasDerivWithinAt_iff_tendsto_slope'`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand`, `CategoryTheory.ProjectiveResolution.neg_extMk`, `SeminormFamily.basisSets_iff`, `Function.locallyFinsuppWithin.coe_neg`, `exists_zero_lt`, `VectorFourier.hasFDerivAt_fourierChar_smul`, `Hyperreal.IsSt.neg`, `PEquiv.toMatrix_swap`, `Finset.neg_smul`, `Metric.preimage_vadd_eball`, `AddAut.neg_conj_apply`, `tangentMap_prod_left`, `ContMDiffWithinAt.cle_arrowCongr`, `MeasureTheory.lpNorm_eq_zero`, `Quaternion.hom_ext_iff`, `PowerSeries.rescale_neg_one_invOneSubPow`, `FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm`, `MeasureTheory.measure_unitBall_eq_integral_div_gamma`, `groupHomology.single_isCycle₁_of_mem_fixedPoints`, `DFinsupp.sub_apply`, `continuousMultilinearCurryRightEquiv_apply`, `NormedAddGroupHom.coe_zero`, `SeminormedAddGroup.tendstoUniformlyOn_zero`, `ContinuousLinearMap.integrable_of_bilin_of_bdd_right`, `NonarchAddGroupSeminormClass.map_zero`, `HasFDerivAt.neg`, `ZMod.exists_sq_eq_neg_two_iff`, `ZeroAtInftyContinuousMap.coe_neg`, `Module.Presentation.tautologicalRelations_relation`, `ContDiffMapSupportedIn.structureMapLM_zero_apply`, `Right.sign_neg`, `LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero`, `gauge_closedBall`, `Submodule.Quotient.eq'`, `ContinuousAlternatingMap.prodLIE_symm_apply`, `NormedSpace.normalize_neg`, `sub_le_self_iff`, `VectorField.lieBracket_zero_left`, `MeasureTheory.integral_zero`, `DifferentiableOn.hasDerivAt`, `ContinuousLinearMapWOT.instContinuousNeg`, `CochainComplex.HomComplex.Cochain.ofHoms_zero`, `EMetric.preimage_add_left_closedBall`, `Bornology.sUnion_isVonNBounded_eq_univ`, `DirectSum.decompose_neg`, `Set.subset_vadd_set_iff`, `SchwartzMap.integral_smul_deriv_right_eq_neg_left`, `NonemptyInterval.neg_mem_neg`, `ContinuousLinearMap.apply_apply'`, `HasFPowerSeriesWithinAt.hasFDerivWithinAt`, `Set.zsmul_empty`, `abs_le'`, `IsSemireal.not_isSumSq_neg_one`, `IsCoprime.neg_neg`, `MeasureTheory.support_convolution_subset`, `EuclideanGeometry.oangle_eq_neg_angle_of_sign_eq_neg_one`, `Orientation.two_zsmul_oangle_smul_smul_self`, `Polynomial.roots_C_mul_X_add_C_of_IsUnit`, `Submodule.starProjection_apply_eq_zero_iff`, `Algebra.Extension.exact_cotangentComplex_toKaehler`, `SchwartzMap.fourier_convolution`, `Quaternion.re_intCast`, `Polynomial.smeval_neg`, `fderivWithin_comp_smul`, `ZMod.LFunction_dft`, `TestFunction.tsupport_subset'`, `MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp`, `ArchimedeanClass.FiniteElement.neg_mk`, `MvPolynomial.degreeOf_neg`, `ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear`, `instSMulCommClass_closedBall_closedBall_closedBall`, `Finset.zero_notMem_neg_add_iff`, `ContinuousLinearMap.flipₗᵢ_symm`, `AnalyticOnNhd.neg`, `HasFPowerSeriesAt.compContinuousLinearMap`, `Asymptotics.IsBigOTVS.refl`, `Metric.preimage_add_left_eball`, `Mathlib.Tactic.Ring.neg_one_mul`, `gauge_zero`, `TopModuleCat.hom_neg`, `IsRelPrime.neg_neg_iff`, `exists_continuousLinearEquiv_fderivWithin_symm_eq`, `Quaternion.re_mul`, `ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz`, `hasDerivAt_of_tendsto_locally_uniformly_on'`, `Quaternion.normSq_div`, `dist_zero`, `Matrix.conjTranspose_circulant`, `AlternatingMap.mkContinuousLinear_norm_le_max`, `WithLp.nndist_toLp_fst`, `FormalMultilinearSeries.rightInv_coeff_one`, `lt_neg_iff_add_neg`, `IsExtrFilter.neg`, `WithLp.instProdIsBoundedSMul`, `neg_eq_self_of_addOrderOf_eq_two`, `Seminorm.ball_zero_eq`, `WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF_of_char_three`, `IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single`, `ContMDiff.neg`, `WeierstrassCurve.c₆_of_isShortNF`, `Finsupp.neLocus_self_sub_right`, `MeasureTheory.zero_convolution`, `Real.log_of_ne_zero`, `absorbs_neg_neg`, `ContinuousLinearMap.isBigOTVS_id`, `groupHomology.d₁₀ArrowIso_inv_left`, `QuaternionAlgebra.imI_star`, `groupHomology.H1AddEquivOfIsTrivial_symm_tmul`, `ContinuousLinearMap.norm_holder_apply_apply_le`, `lipschitzWith_smul`, `WeierstrassCurve.Jacobian.negY_of_Z_eq_zero`, `neg_one_pow_expChar_pow`, `groupHomology.single_mem_cycles₁_iff`, `MeasureTheory.LocallyIntegrable.smul`, `TensorProduct.tmul_neg`, `UniformConvergenceCLM.isVonNBounded_iff`, `groupHomology.d₂₁_single_ρ_add_single_inv_mul`, `Finset.image_add_left`, `absorbent_ball_zero`, `edist_smul_le`, `StrictMonoOn.slope_pos`, `ContinuousLinearMap.hasStrictDerivAt`, `ContinuousLinearMap.analyticAt_uncurry_of_multilinear`, `hasDerivWithinAt_iff_tendsto_slope`, `FreeAbelianGroup.zero_bind`, `Function.Periodic.neg_nat_mul`, `Quaternion.instFinite`, `constFormalMultilinearSeries_apply_succ`, `Finset.card_add_neg_eq_addConvolution_neg`, `FormalMultilinearSeries.continuousOn`, `LieAlgebra.IsSimple.non_abelian`, `hasFDerivAt_inv`, `HahnEmbedding.Partial.exists_isMax`, `le_neg_add_iff_add_le`, `add_neg_lt_iff_lt_add`, `Finset.box_succ_union_prod`, `AddSubgroup.zero_mem`, `pow_eq_pow_iff_cases`, `Wbtw.oangle₁₃₂_eq_zero`, `VectorField.mlieBracket_self`, `discrim_neg`, `ContinuousMultilinearMap.isUniformInducing_toUniformOnFun`, `MeasureTheory.setIntegral_eq_zero_of_ae_eq_zero`, `Disjoint.zero_notMem_sub_set`, `List.sum_drop_succ`, `Derivation.coe_neg`, `VectorFourier.fourierIntegral_fderiv`, `ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv`, `ContinuousLinearMap.fpowerSeries_apply_one`, `Set.neg_Iic`, `fderiv_continuousLinearEquiv_comp'`, `ContinuousLinearMap.smulRightL_apply_apply`, `MeasureTheory.indicatorConstLp_coeFn`, `WeakFEPair.Λ_residue_zero`, `IccRightChart_extend_top`, `Finset.preimage_add_right_zero'`, `TendstoUniformlyOnFilter.fun_neg`, `norm_indicator_le_norm_self`, `addGroup_inseparable_iff`, `infEdist_neg_neg`, `intervalIntegral.integral_add_adjacent_intervals_cancel`, `unitary.coe_neg`, `WeierstrassCurve.Affine.evalEval_polynomialX_zero`, `Set.mem_vadd_set_iff_neg_vadd_mem`, `add_neg_eq_iff_eq_add`, `ContinuousAffineMap.coe_neg`, `constFormalMultilinearSeries_zero`, `sub_ball`, `QuaternionAlgebra.star_mk`, `IncidenceAlgebra.mu_self`, `Set.Nonempty.zero_mem_sub`, `Asymptotics.IsBigO.isBigOTVS`, `isSMulRegular_iff_right_eq_zero_of_smul`, `Ring.inverse_exp`, `Asymptotics.isLittleOTVS_neg_left`, `FreeGroup.sum.map_inv`, `LinearIsometryEquiv.toContinuousLinearEquiv_smul`, `ContinuousAlternatingMap.compContinuousLinearMapCLM_apply`, `Orientation.eq_zero_or_angle_eq_zero_or_pi_of_sign_oangle_eq_zero`, `IsDiscrete.exists_nhds_eq_zero_of_image_addRight_inter_nonempty`, `ContinuousMultilinearMap.curryFinFinset_apply`, `groupHomology.eq_d₁₀_comp_inv_apply`, `Quaternion.normSq_star`, `deriv_zero_of_frequently_mem`, `ContDiffAt.smulRight`, `Interval.length_pure`, `Quaternion.imK_sub`, `TestFunction.injective_toBoundedContinuousFunctionCLM`, `VertexOperator.coeff_eq_ncoeff`, `Matrix.invOf_fromBlocks₁₁_eq`, `MeasureTheory.Lp.simpleFunc.coeFn_nonneg`, `FormalMultilinearSeries.changeOriginSeriesTerm_bound`, `ContMDiffAt.neg_section`, `Hyperreal.st_neg`, `AddMonoidAlgebra.mul_apply_right`, `CharP.intCast_eq_zero_iff`, `Real.Angle.coe_pi_add_coe_pi`, `Meromorphic.fun_neg`, `MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp`, `derivWithin_const_sub`, `Matrix.linfty_opNNNorm_diagonal`, `RCLike.I_mul_I_of_nonzero`, `Set.neg_Ico`, `isMIntegralCurve_comp_mul_ne_zero`, `SchwartzMap.toZeroAtInftyCLM_apply`, `FormalMultilinearSeries.constFormalMultilinearSeries_radius`, `Asymptotics.isLittleOTVS_sup`, `Height.mulHeight₁_neg`, `DihedralGroup.inv_r`, `zero_sub_add_eq_sub`, `lineDeriv_neg`, `zpow_eq_one_iff_of_ne_zero₀`, `edist_indicator`, `Num.cast_toZNumNeg`, `MeromorphicAt.frequently_zero_iff_eventuallyEq_zero`, `QuaternionAlgebra.star_eq_neg`, `QuadraticMap.polar_zero_right`, `VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le`, `AddSubgroup.IsComplement.add_neg_toRightFun_mem`, `LineDeriv.iteratedLineDerivOp_neg`, `ContinuousLinearMap.norm_precompL_le`, `HasFTaylorSeriesUpToOn.restrictScalars`, `ZMod.dft_def`, `ContinuousLinearMap.apply_apply`, `Rep.barComplex.d_single`, `egauge_zero_right`, `Module.Presentation.tautological_relation`, `Asymptotics.isThetaTVS_iff_isTheta`, `ContinuousLinearMap.norm_map_removeNth_le`, `Left.sign_neg`, `CategoryTheory.ShortComplex.Homotopy.symm_h₁`, `LowerSet.Iic_zero`, `ContinuousMultilinearMap.hasStrictFDerivAt_uncurry`, `iteratedFDeriv_neg`, `AddCircle.toCircle_neg`, `ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply`, `instSMulCommClass_sphere_sphere_ball`, `HVertexOperator.comp_apply`, `tsupport_sub`, `AlternatingMap.mkContinuousAlternating_apply`, `IsSymmSndFDerivWithinAt.eq`, `PiTensorProduct.mapLMultilinear_opNorm`, `hasDerivWithinAt_inter`, `Quaternion.normSq_ratCast`, `StarConvex.neg`, `RootPairing.isReduced_iff`, `Quaternion.imK_im`, `IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀`, `CategoryTheory.NatTrans.app_neg`, `MeasureTheory.Measure.toSphere.instIsOpenPosMeasure`, `LinearIsometryEquiv.conjStarAlgEquiv_apply_apply`, `groupHomology.d₂₁_comp_d₁₀_assoc`, `midpoint_zero_add`, `meromorphicOrderAt_ne_top_iff_eventually_ne_zero`, `WithLp.dist_toLp_fst`, `Polynomial.leadingCoeff_neg`, `Quaternion.imK_add`, `MulRingNorm.eq_zero_of_map_eq_zero'`, `closedBall_zero_add_singleton`, `CochainComplex.HomComplex.Cochain.leftShift_neg`, `CategoryTheory.Abelian.Ext.comp_neg`, `LieSubmodule.lie_eq_bot_iff`, `Matrix.det_eq_sign_charpoly_coeff`, `MeasureTheory.Measure.addHaar_singleton`, `Orientation.rightAngleRotation_neg_orientation`, `LieModule.genWeightSpace_neg_add_chainBot`, `exteriorPower.presentation.relations_relation`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply`, `fderiv_single`, `InnerProductSpace.gramSchmidtNormed_orthonormal'`, `abs_zsmul_eq_zero`, `Quaternion.fst_re_dualNumberEquiv_symm`, `PowerSeries.derivative_inv`, `gaussSum_sq`, `WeierstrassCurve.ofJ1728_Δ`, `RootPairing.GeckConstruction.lie_e_f_mul_ω`, `Orientation.oangle_eq_neg_angle_of_sign_eq_neg_one`, `Function.Periodic.int_mul_sub_eq`, `Set.Finite.isVonNBounded`, `Orientation.oangle_add_cyc3_neg_right`, `Quaternion.continuous_normSq`, `HomologicalComplex₂.D₁_D₂`, `even_neg`, `Finset.card_vadd_inter_vadd`, `QuaternionAlgebra.im_sub`, `Module.End.eigenspace_aeval_polynomial_degree_1`, `le_egauge_closedBall_one`, `affineSpan_insert_zero`, `Quaternion.imI_snd_dualNumberEquiv`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd`, `iteratedDerivWithin_fun_neg`, `CliffordAlgebra.map_mul_map_eq_neg_of_isOrtho_of_mem_evenOdd_one`, `MeasureTheory.Integrable.toL1_neg`, `LieHom.range_eq_ker_iff`, `ContDiffOn.neg`, `AddSubgroup.isComplement_iff_existsUnique_add_neg_mem`, `intervalIntegral.integral_neg`, `CategoryTheory.kernelCokernelCompSequence.inr_φ_fst`, `HasFPowerSeriesWithinOnBall.hasFDerivWithinAt`, `MeasurableEquiv.symm_vadd`, `LieSubmodule.eq_bot_iff`, `tsupport_add_neg`, `groupHomology.chainsMap_f_1_comp_chainsIso₁_apply`, `neg_add_nonpos_iff`, `Asymptotics.isBigOTVS_comm`, `MonovaryOn.neg_left`, `HahnEmbedding.Seed.domain_baseEmbedding`, `CFC.neg_negPart_le`, `InnerProductSpace.symm_toEuclideanLin_rankOne`, `isBoundedBilinearMap_smulRight`, `MvPolynomial.IsSymmetric.neg`, `QuadraticAlgebra.im_star`, `Right.neg_neg_iff`, `QuaternionAlgebra.imK_swapEquiv_apply`, `CategoryTheory.ShortComplex.opcyclesMap'_neg`, `antivary_neg_right`, `Submodule.coe_set_neg`, `sub_neg_eq_add`, `ContMDiffAt.cle_arrowCongr`, `groupHomology.isBoundary₁_iff`, `isAddQuotientCoveringMap_iff`, `mdifferentiableOn_neg_section`, `ContinuousLinearMap.adjoint_innerSL_apply`, `Subfield.coe_neg`, `Submodule.span_neg_eq_neg`, `Balanced.zero_mem`, `slope_same`, `Ring.eq_self_iff_eq_zero_of_char_ne_two`, `hasFDerivAt_iff_isLittleO_nhds_zero`, `fderivWithin_comp_sub`, `negPart_neg`, `Int.cast_negOnePow_natCast`, `Asymptotics.isLittleOTVS_pi`, `neg_one_eq_one_iff`, `Module.finrank_eq_zero_iff`, `ContDiffMapSupportedIn.structureMapLM_apply`, `AddGroupExtension.Section.neg_add_mem_range_inl`, `monovary_neg_left`, `MeasureTheory.aefinStronglyMeasurable_of_aemeasurable`, `CochainComplex.HomComplex.Cochain.leftUnshift_neg`, `trace_adjoinSimpleGen`, `negPart_eq_ite_lt`, `isBoundedLinearMap_prod_multilinear`, `Module.reflection_mul_reflection_mul_reflection_pow_apply_self`, `UniqueFactorizationDomain.radical_neg`, `deriv_const_sub`, `gradient_eq_zero_of_not_differentiableAt`, `HasStrictDerivAt_ofNat`, `groupHomology.mapCycles₁_quotientGroupMk'_epi`, `Matrix.adjugate_fin_two_of`, `MeasureTheory.measurePreserving_prod_neg_add_swap`, `Real.Angle.tan_zero`, `Quaternion.imJ_intCast`, `Module.reflection_mul_reflection_mul_reflection_zpow_apply_self`, `mem_ball_zero_iff`, `inverse_mfderiv_add_left`, `groupHomology.mapCycles₁_comp_i_assoc`, `Quaternion.smul_imJ`, `HasFiniteFPowerSeriesAt.comp`, `AddSubgroup.zmultiples_eq_bot`, `SymplecticGroup.inv_eq_symplectic_inv`, `CategoryTheory.Preadditive.neg_comp_assoc`, `RCLike.sqrt_neg_of_nonneg`, `hasDerivWithinAt_iff_tendsto`, `LinearPMap.zero_apply`, `CategoryTheory.Preadditive.instEpiNegHom`, `MonoidAlgebra.neg_apply`, `CliffordAlgebra.EquivEven.involute_v`, `ascPochhammer_eval_neg_eq_descPochhammer`, `midpoint_self_neg`, `CategoryTheory.Preadditive.neg_iso_inv`, `TemperedDistribution.laplacianCLM_apply`, `LieAlgebra.IsKilling.rootSystem_root_apply`, `InnerProductSpace.Core.inner_zero_left`, `CochainComplex.mappingCone.inr_fst`, `Monovary.sub_smul_sub_nonneg`, `WithCStarModule.equiv_symm_zero`, `Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single`, `CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁`, `RingQuot.neg_quot`, `RootPairing.polarization_apply_eq_zero_iff`, `MeasureTheory.Submartingale.condExp_sub_nonneg`, `HurwitzZeta.hurwitzZetaEven_neg`, `ContinuousLinearMap.norm_smulRightL_apply`, `ContinuousAlternatingMap.alternatizeUncurryFin_apply`, `hasDerivAt_finCons`, `Asymptotics.IsThetaTVS.rfl`, `HasFDerivAt.smul`, `le_abs'`, `tendsto_sub_nhds_zero_iff`, `FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin`, `Algebra.H1Cotangent.exact_δ_mapBaseChange`, `ConvexBody.coe_zero`, `SchwartzMap.smulLeftCLM_smul`, `IsAbsoluteValue.abv_neg`, `MeasureTheory.measurePreserving_add_prod_neg`, `differentiableAt_iff_comp_neg`, `isClosed_setOf_isCompactOperator`, `Submodule.span_neg`, `Quaternion.one_re`, `DoubleCentralizer.coe_snd`, `sbtw_neg_iff`, `WeierstrassCurve.Jacobian.neg_of_Z_eq_zero`, `Quaternion.exp_coe`, `ContinuousLinearMap.fpowerSeriesBilinear_apply_one`, `dotProduct_neg`, `AddChar.inv_mulShift`, `HasFiniteFPowerSeriesOnBall.eq_zero_of_bound_zero`, `MeasureTheory.integral_convolution`, `HomologicalComplex.homotopyCofiber.d_fstX_assoc`, `OpenPartialHomeomorph.univBall_symm_apply_center`, `TrivialLieModule.instIsTrivial`, `Quaternion.star_coe`, `derivWithin_mem_iff`, `Submodule.Quotient.mk_zero`, `DifferentiableOn.fun_neg`, `RCLike.conj_neg_I`, `ContinuousMultilinearMap.norm_curryMid`, `zero_mem_tangentCone`, `Quaternion.smul_imI`, `Submodule.mem_neg`, `AnalyticOnNhd.eqOn_zero_or_eventually_ne_zero_of_preconnected`, `UpperHalfPlane.IsZeroAtImInfty.of_exp_decay`, `add_notMem_of_addOrderOf_eq_two`, `CategoryTheory.ShortComplex.ShortExact.ab_exact_iff_function_exact`, `WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three`, `Real.arcsin_projIcc`, `Left.nonneg_neg_iff`, `Quaternion.imI_one`, `RCLike.inv_I`, `Submodule.starProjection_tendsto_closure_iSup`, `IsRealClosed.isSquare_neg_of_not_isSquare`, `MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_top_mul_eLpNorm`, `AddSubmonoid.leftNegEquiv_symm_eq_neg`, `SimpContFract.determinant_aux`, `TrivSqZeroExt.inv_inr`, `MeasureTheory.Lp.toTemperedDistribution_smul_eq`, `Quaternion.exp_eq`, `Polynomial.homogenize_neg`, `map_add_left_nhds_zero`, `CochainComplex.HomComplex.Cocycle.mem_iff`, `Submodule.reflection_mem_subspace_orthogonalComplement_eq_neg`, `NegMemClass.coe_neg`, `finiteDimensional_finsupp`, `HasDerivAt.inv`, `differentiableWithinAt_zero`, `groupHomology.mem_cycles₁_iff`, `AddSubgroup.leftTransversals.diff_self`, `EMetric.preimage_vadd_ball`, `Filter.EventuallyEq.hasDerivAtFilter_iff`, `LaurentSeries.hasseDeriv_single`, `natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zero`, `LinearMap.IsAlt.neg`, `MeasureTheory.Measure.toSphere_apply_univ'`, `HasMFDerivAt.const_smul`, `instIsSemisimpleModuleFinsupp`, `LieModule.Weight.coe_neg`, `AddCommute.neg_left`, `Matrix.Pivot.listTransvecRow_getElem`, `FormalMultilinearSeries.hasFPowerSeriesOnBall`, `Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff`, `iteratedDeriv_const`, `lipschitzWith_neg_iff`, `Quaternion.imJ_sub`, `SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left`, `Quaternion.normSq_coe`, `QuotientAddGroup.preimage_mk_zero`, `groupHomology.boundariesToCycles₁_apply`, `groupHomology.single_mem_cycles₂_iff_inv`, `egauge_pi'`, `groupHomology.d₁₀_single`, `Finset.ruzsa_triangle_inequality_negAdd_add_add`, `ContinuousLinearMap.innerSL_apply_comp`, `iteratedDeriv_fun_neg`, `Finset.ruzsa_triangle_inequality_addNeg_add_add`, `surjective_stereographic`, `LieSubalgebra.eq_bot_iff`, `cfc_neg_id`, `neg_add_eq_mul_invOf_mul_same_iff`, `neg_le_neg_iff`, `ContinuousLinearMap.toSesqForm_apply_norm_le`, `MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd`, `ContinuousLinearMap.coeFn_holder`, `Polynomial.algEquivAevalXAddC_symm`, `CochainComplex.mappingCone.d_fst_v`, `deriv_ofNat`, `ContDiffMapSupportedIn.structureMapLM_eq`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul_left`, `NonarchAddGroupSeminorm.neg'`, `Memℓp.finite_dsupport`, `PosSMulStrictMono.toPosSMulReflectLT`, `ProbabilityTheory.instIsGaussianMapNeg`, `inner_neg_left`, `FirstOrder.Field.charP_iff_model_fieldOfChar`, `LineDeriv.lineDerivOp_left_neg`, `ContMDiff.cle_arrowCongr`, `ContinuousLinearMap.coe_deriv₂`, `IsMIntegralCurveAt.eventually_hasDerivAt`, `OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le`, `Algebra.Extension.Cotangent.of_zero`, `LipschitzWith.integral_lineDeriv_mul_eq`, `DiffContOnCl.neg`, `Function.Antiperiodic.neg_eq`, `HurwitzZeta.hurwitzZetaEven_eq`, `balanced_iff_neg_mem`, `ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply`, `ContinuousLinearMap.adjoint_adjoint`, `Finsupp.erase_sub`, `HasDerivWithinAt.fun_inv`, `MeasureTheory.MemLp.eLpNorm_indicator_norm_ge_le`, `groupCohomology.cocycles₁.d₁₂_apply`, `CochainComplex.HomComplex.Cochain.leftUnshift_zero`, `Quaternion.re_nnratCast`, `Bundle.ContinuousRiemannianMetric.isVonNBounded`, `MeasureTheory.conv_withDensity_eq_mlconvolution₀`, `MonovaryOn.sub_smul_sub_nonneg`, `HurwitzKernelBounds.isBigO_atTop_F_int_zero_sub`, `Finset.neg_vadd_finset_distrib`, `TemperedDistribution.smulLeftCLM_apply_apply`, `MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp_eLpNorm`, `sub_pos_of_lt`, `groupHomology.isoCycles₂_hom_comp_i_assoc`, `inv_eq_of_root_of_coeff_zero_ne_zero`, `AddAction.period_neg`, `zpow_eq_neg_one_iff₀`, `MeasureTheory.L1.integral_neg`, `Ideal.span_singleton_neg`, `List.sum_range_sub'`, `WithZero.exp_neg`, `groupHomology.comp_d₃₂_eq`, `WithSeminorms.hasBasis_zero_ball`, `eq_add_neg_iff_add_eq`, `InnerProductGeometry.angle_neg_left`, `Asymptotics.IsTheta.tendsto_zero_iff`, `Set.indicator_diff`, `MeasureTheory.Measure.addHaar_closedBall'`, `groupHomology.H2π_eq_zero_iff`, `Finset.weightedVSubOfPoint_sdiff_sub`, `toIocDiv_mul_sub_self`, `locallyConvexSpace_iff_exists_convex_subset_zero`, `AddGroupExtension.Section.add_neg_add_add_mem_range_inl`, `Quaternion.natCast_imI`, `derivWithin_comp_neg`, `addInvariantVectorField_add`, `RCLike.div_I`, `sameRay_neg_iff`, `IsCyclotomicExtension.discr_prime_pow`, `BddBelow.range_neg`, `CochainComplex.HomComplex.Cochain.map_neg`, `HasStrictFDerivAt.smul`, `Finsupp.support_sub`, `ContinuousLinearMap.orthogonal_ker`, `MeasureTheory.MemLp.exists_eLpNorm_indicator_compl_lt`, `posPart_eq_ite_lt`, `Module.Relations.Solution.linearCombination_var_relation`, `AnalyticAt.hasStrictDerivAt`, `Fin.insertNth_sub_same`, `Asymptotics.IsThetaTVS.refl`, `Monovary.neg_left`, `ContDiffMapSupportedIn.norm_toBoundedContinuousFunction`, `WeierstrassCurve.Projective.negDblY_of_Y_eq`, `ContDiffMapSupportedInClass.map_zero_on_compl`, `Filter.EventuallyEq.hasDerivWithinAt_iff`, `HahnSeries.leadingCoeff_abs`, `MeasureTheory.IntegrableAtFilter.eq_zero_of_tendsto`, `Quaternion.nnnorm_coe`, `Seminorm.neg_mem_closedBall_zero`, `AddSubgroup.closure_union_zero`, `IsLowerSet.neg`, `algebraMap.coe_neg`, `InnerProductSpace.norm_rankOne`, `CochainComplex.mappingCone.inr_fst_assoc`, `CategoryTheory.ShortComplex.ShortExact.extClass_comp`, `hasFDerivAt_integral_of_dominated_loc_of_lip`, `CategoryTheory.shift_neg_shift'`, `ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le`, `Real.Angle.toReal_zero`, `PiTensorProduct.mapLMultilinear_toFun_apply`, `le_neg_iff_add_nonpos_right`, `Derivation.map_intCast`, `Quaternion.mul_imJ`, `contDiff_zero_fun`, `Seminorm.closedBall_smul_closedBall`, `AddCommute.neg_add_cancel_assoc`, `ContinuousAffineMap.toConstProdContinuousLinearMap_snd`, `TrivSqZeroExt.snd_intCast`, `MeasureTheory.Measure.toSphere_eq_zero_iff`, `IsAddUnit.neg_add_eq_neg_add_iff`, `circleEquivGen_apply`, `Equiv.addLeft_symm`, `Polynomial.coeff_zero_eq_prod_roots_of_monic_of_splits`, `UniformConvergenceCLM.neg_apply`, `Mathlib.Tactic.Abel.term_atom_pfg`, `ContinuousMultilinearMap.curryMidEquiv_symm_apply`, `FormalMultilinearSeries.comp_summable_nnreal`, `ContDiffMapSupportedIn.coe_zero`, `HahnModule.of_symm_sub`, `intGCD_nsmul_eq_zero`, `HurwitzZeta.hasSum_int_evenKernel₀`, `MeasureTheory.eLpNorm_smul_le_eLpNorm_mul_eLpNorm_top`, `hasGradientWithinAt_const`, `bernsteinPolynomial.iterate_derivative_at_1`, `ContinuousMultilinearMap.uncurryRight_norm`, `ContinuousLinearMap.flipAlternating_apply_apply`, `AddValuation.map_inv`, `IsLinearTopology.hasBasis_open_subbimodule`, `PointedCone.salient_iff_inter_neg_eq_singleton`, `MeasureTheory.Measure.addHaar_real_closedBall`, `CliffordAlgebra.ι_mul_ι_mul_of_isOrtho`, `Monovary.neg`, `MeasureTheory.lconvolution_assoc`, `AddAction.stabilizer_quotient`, `sub_add_cancel_right`, `Matrix.gram_single`, `Quaternion.star_eq_self`, `IsAddTorsionFree.zsmul_eq_zero_iff`, `Function.locallyFinsuppWithin.memAddSubgroup`, `coe_negAddMonoidHom`, `Set.singleton_vsub_self`, `Multiset.prod_X_sub_C_coeff`, `NormedSpace.Core.norm_eq_zero_iff`, `Real.Angle.coe_neg`, `Nat.cast_eq_neg_cast`, `IsCyclotomicExtension.discr_prime_pow_ne_two'`, `WeierstrassCurve.Projective.negDblY_of_Y_eq'`, `CategoryTheory.ShortComplex.leftHomologyMap_neg`, `List.alternatingSum_eq_finset_sum`, `curveIntegralFun_zero`, `Function.Periodic.neg_nsmul`, `WeierstrassCurve.ofJ1728_c₄`, `csSup_neg`, `iteratedFDeriv_succ_apply_left`, `hahnEmbedding_isOrderedModule`, `IsSymmSndFDerivAt.eq`, `MeasureTheory.stoppedValue_piecewise_const'`, `groupHomology.H1π_eq_iff`, `ContDiffAt.neg`, `hasDerivWithinAt_sub_const_iff`, `ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux`, `ball_zero_subset_range_iff_surjective`, `Hyperreal.Infinitesimal.neg`, `ContinuousLinearMapWOT.zero_apply`, `groupHomology.d₃₂_comp_d₂₁_apply`, `Homeomorph.unitBall_symm_apply`, `Complex.restrictScalars_toSpanSingleton'`, `AddSubgroup.zmultiples_eq_zmultiples_iff`, `CategoryTheory.hasInjectiveDimensionLT_iff`, `Matrix.GLPos.coe_neg`, `DirichletCharacter.Even.eval_neg`, `ContinuousAlgHom.map_neg`, `CategoryTheory.Abelian.Ext.eq_zero_of_injective`, `Quaternion.imK_snd_dualNumberEquiv`, `MDifferentiableWithinAt.neg`, `Quaternion.neg_imI`, `ContinuousLinearMapWOT.ext_inner_iff`, `groupHomology.chainsMap_f`, `AddMonoid.Coprod.con_neg_add_cancel`, `LieAlgebra.IsKilling.instIsLieAbelianOfIsCartanSubalgebra`, `ZMod.pow_div_two_eq_neg_one_or_one`, `Quaternion.imI_ratCast`, `VectorField.mlieBracket_const_smul_right`, `Submodule.disjoint_span_singleton''`, `lie_swap_lie`, `Quaternion.natCast_re`, `groupHomology.chainsMap_f_2_comp_chainsIso₂_apply`, `CauSeq.Completion.ofRat_neg`, `TendstoUniformly.neg`, `FormalMultilinearSeries.comp_assoc`, `HasFPowerSeriesWithinAt.comp`, `Quaternion.ext_iff`, `Asymptotics.IsLittleO.neg_right`, `differentiable_neg_iff`, `CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg`, `Polynomial.eq_neg_mul_add_of_roots_quadratic_eq_pair`, `groupHomology.cyclesMap_comp_isoCycles₁_hom`, `Polynomial.nextCoeff_eq_neg_sum_roots_mul_leadingCoeff_of_splits`, `Set.image_neg`, `balanced_zero`, `continuousMultilinearCurryFin1_apply`, `MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed`, `hasStrictDerivAt_neg`, `WeierstrassCurve.Jacobian.neg_of_Z_eq_zero'`, `Mathlib.Meta.NormNum.IsRat.neg_to_eq`, `RootPairing.reflectionPerm_eq_iff_smul_coroot`, `CochainComplex.HomComplex.Cochain.ofHomotopy_ofEq`, `RootPairing.pairing_neg_two_neg_two_iff`, `HilbertBasis.finite_spans_dense`, `Module.notMem_support_iff'`, `EMetric.preimage_vadd_closedBall`, `emultiplicity_neg`, `Summable.countable_support`, `ProbabilityTheory.Kernel.integral_indicator₂`, `Orientation.oangle_add_oangle_rev_neg_right`, `HahnEmbedding.Partial.toOrderAddMonoidHom_injective` bridge: `BoxIntegral.hasIntegralIndicatorConst`

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`add_add_add_comm` 📖	mathematical	—	`AddCommMagma.toAdd` `AddCommSemigroup.toAddCommMagma`	—	`add_left_comm` `add_assoc`
`add_add_add_comm'` 📖	mathematical	—	`AddCommMagma.toAdd` `AddCommSemigroup.toAddCommMagma`	—	—
`add_add_neg_add_cancel` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_assoc` `add_neg_cancel` `zero_add`
`add_add_neg_cancel'_right` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid`	—	`sub_eq_add_neg` `add_sub_cancel`
`add_add_sub_cancel` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `SubNegMonoid.toSub`	—	`add_assoc` `add_sub_cancel`
`add_comm_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_comm` `add_left_comm`
`add_eq_left` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	`add_zero` `add_left_cancel_iff`
`add_eq_of_eq_add_neg` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—	`add_assoc` `neg_add_cancel` `add_zero`
`add_eq_of_eq_neg_add` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—	`add_neg_cancel_left`
`add_eq_of_eq_sub` 📖	mathematical	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_add_cancel`
`add_eq_of_eq_sub'` 📖	mathematical	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `add_comm` `add_neg_cancel_left`
`add_eq_right` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	`zero_add` `add_right_cancel_iff`
`add_eq_zero_iff_eq_neg` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toNeg`	—	`eq_neg_of_add_eq_zero_left` `neg_add_cancel`
`add_eq_zero_iff_eq_neg'` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toNeg`	—	`add_eq_zero_iff_neg_eq`
`add_eq_zero_iff_neg_eq` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toNeg`	—	`add_eq_zero_iff_eq_neg` `neg_eq_iff_eq_neg`
`add_eq_zero_iff_neg_eq'` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toNeg`	—	`add_eq_zero_iff_eq_neg`
`add_left_comm` 📖	mathematical	—	`AddCommMagma.toAdd` `AddCommSemigroup.toAddCommMagma`	—	`add_assoc` `add_comm`
`add_left_iterate` 📖	mathematical	—	`Nat.iterate` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`zero_nsmul` `zero_add` `comp_add_left` `add_assoc` `succ_nsmul`
`add_left_iterate_apply` 📖	mathematical	—	`Nat.iterate` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`add_left_iterate`
`add_left_iterate_apply_zero` 📖	mathematical	—	`Nat.iterate` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero` `AddMonoid.toNatSMul`	—	`add_left_iterate` `add_zero`
`add_left_surjective` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`add_neg_cancel_left`
`add_ne_left` 📖	—	—	—	—	`Iff.not` `add_eq_left`
`add_ne_right` 📖	—	—	—	—	`Iff.not` `add_eq_right`
`add_neg_add_add_cancel` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_assoc` `neg_add_cancel` `zero_add`
`add_neg_eq_add_neg_iff_add_eq_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid`	—	`sub_eq_add_neg` `sub_eq_sub_iff_add_eq_add`
`add_neg_eq_iff_eq_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_add_cancel_right` `add_neg_cancel_right`
`add_neg_eq_of_eq_add` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_assoc` `add_neg_cancel` `add_zero`
`add_neg_eq_zero` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toZero`	—	`add_eq_zero_iff_eq_neg` `neg_neg`
`add_one_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`natCast_zsmul` `succ_nsmul` `zero_zsmul` `neg_zsmul` `one_zsmul` `neg_add_cancel` `negSucc_zsmul` `succ_nsmul'` `neg_add_rev` `neg_add_cancel_right`
`add_right_comm` 📖	mathematical	—	`AddCommMagma.toAdd` `AddCommSemigroup.toAddCommMagma`	—	`add_assoc` `add_comm`
`add_right_iterate` 📖	mathematical	—	`Nat.iterate` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`zero_nsmul` `add_zero` `comp_add_right` `succ_nsmul'`
`add_right_iterate_apply` 📖	mathematical	—	`Nat.iterate` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`add_right_iterate`
`add_right_iterate_apply_zero` 📖	mathematical	—	`Nat.iterate` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero` `AddMonoid.toNatSMul`	—	`add_right_iterate` `zero_add`
`add_right_surjective` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`neg_add_cancel_right`
`add_rotate` 📖	mathematical	—	`AddCommMagma.toAdd` `AddCommSemigroup.toAddCommMagma`	—	`add_comm` `add_left_comm`
`add_rotate'` 📖	mathematical	—	`AddCommMagma.toAdd` `AddCommSemigroup.toAddCommMagma`	—	`add_comm` `add_left_comm`
`add_self_zsmul` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SubNegMonoid.toZSMul`	—	`add_one_zsmul`
`add_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_assoc`
`add_sub_add_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `add_comm` `add_assoc` `add_left_comm`
`add_sub_add_left_eq_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`add_comm` `sub_eq_add_neg` `neg_add_rev` `add_assoc` `add_neg_cancel_comm_assoc`
`add_sub_add_right_eq_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_add_eq_sub_sub_swap` `add_sub_cancel_right`
`add_sub_assoc'` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubNegMonoid.toSub`	—	`add_sub_assoc`
`add_sub_cancel` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `SubNegMonoid.toSub`	—	`add_sub_assoc` `add_sub_cancel_left`
`add_sub_cancel_left` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_neg_add` `neg_add_cancel_left`
`add_sub_left_comm` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_left_comm`
`add_sub_one_nsmul` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`succ_nsmul`
`add_sub_right_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `add_assoc` `add_comm` `add_left_comm`
`add_sub_sub_cancel` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_add` `add_sub_cancel_left`
`add_zero_eq_id` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddZero.toZero`	—	`add_zero`
`add_zero_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubNegMonoid.toSub` `AddZero.toZero`	—	`sub_eq_add_neg` `zero_add`
`add_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`Int.induction_on` `zero_zsmul` `add_zero` `add_one_zsmul` `add_assoc` `sub_one_zsmul`
`add_zsmul_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SubNegMonoid.toZSMul`	—	`natCast_zsmul` `add_nsmul_add` `negSucc_zsmul` `eq_add_neg_iff_add_eq` `add_assoc` `neg_add_eq_iff_eq_add`
`add_zsmul_self` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SubNegMonoid.toZSMul`	—	`add_zsmul` `one_zsmul`
`additive_of_isTotal` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	—	`additive_of_total`
`additive_of_symmetric_of_isTotal` 📖	—	`Symmetric` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	—	`additive_of_symmetric_of_total`
`additive_of_symmetric_of_total` 📖	—	`Symmetric` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	—	`total_of` `zero_add` `add_assoc` `add_zero`
`additive_of_total` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	—	`additive_of_symmetric_of_total`
`boole_nsmul` 📖	mathematical	—	`AddMonoid.toNatSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`ite_smul` `one_nsmul` `zero_nsmul`
`comp_add_left` 📖	mathematical	—	`AddSemigroup.toAdd`	—	`add_assoc`
`comp_add_right` 📖	mathematical	—	`AddSemigroup.toAdd`	—	`add_assoc`
`comp_mul_left` 📖	mathematical	—	`Semigroup.toMul`	—	`mul_assoc`
`comp_mul_right` 📖	mathematical	—	`Semigroup.toMul`	—	`mul_assoc`
`conj_eq_one_iff` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toOne`	—	`mul_inv_eq_one` `mul_eq_left` `LeftCancelSemigroup.toIsLeftCancelMul`
`conj_eq_zero_iff` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toZero`	—	`add_neg_eq_zero` `add_eq_left` `AddLeftCancelSemigroup.toIsLeftCancelAdd`
`const_div_involutive` 📖	mathematical	—	`Function.Involutive` `DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	—	`div_div_cancel`
`const_sub_involutive` 📖	mathematical	—	`Function.Involutive` `SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	—	`sub_sub_cancel`
`dite_pow` 📖	—	—	—	—	—
`dite_smul` 📖	—	—	—	—	—
`dite_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	—
`div_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_assoc` `mul_inv_rev` `mul_comm`
`div_div_cancel` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	—	`div_div_self'`
`div_div_cancel_left` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroup.toDivisionCommMonoid`	—	`div_eq_mul_inv` `mul_comm` `mul_left_comm` `mul_inv_cancel_left`
`div_div_div_cancel_left` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	—	`inv_div` `div_inv_eq_mul` `mul_comm` `div_mul_div_cancel`
`div_div_div_cancel_right` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	`inv_div` `div_inv_eq_mul` `div_mul_div_cancel`
`div_div_div_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv` `mul_left_comm` `mul_assoc` `mul_comm`
`div_div_div_eq` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv` `mul_left_comm` `mul_assoc` `mul_comm`
`div_div_eq_mul_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv` `mul_assoc`
`div_div_self'` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv` `mul_inv_cancel_comm_assoc`
`div_eq_div_iff_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid`	—	`inv_div`
`div_eq_div_iff_div_eq_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	—	`div_eq_iff_eq_mul` `div_mul_eq_mul_div` `div_eq_iff_eq_mul'` `mul_div_assoc`
`div_eq_div_iff_mul_eq_mul` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_iff_eq_mul` `div_mul_eq_mul_div` `div_eq_iff_eq_mul'` `mul_comm`
`div_eq_div_mul_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_left_comm` `mul_assoc` `mul_inv_cancel` `mul_one`
`div_eq_iff_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	—	`div_eq_iff_eq_mul'` `div_eq_iff_eq_mul`
`div_eq_iff_eq_mul` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_eq_iff_eq_mul`
`div_eq_iff_eq_mul'` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_iff_eq_mul` `mul_comm`
`div_eq_inv_mul` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`div_eq_mul_inv` `mul_comm`
`div_eq_inv_self` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toOne`	—	`div_eq_mul_inv` `mul_eq_right` `RightCancelSemigroup.toIsRightCancelMul`
`div_eq_mul_one_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `MulOne.toOne`	—	`div_eq_mul_inv` `one_div`
`div_eq_of_eq_mul'` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup`	`DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_comm` `inv_mul_cancel_left`
`div_eq_of_eq_mul''` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`DivInvMonoid.toDiv`	—	`mul_div_cancel_right`
`div_eq_one` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`eq_of_div_eq_one` `div_self'`
`div_eq_one_of_eq` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`div_eq_one`
`div_eq_self` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`div_eq_mul_inv` `mul_eq_left` `LeftCancelSemigroup.toIsLeftCancelMul` `inv_eq_one`
`div_inv_eq_mul` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `inv_inv`
`div_left_inj` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	`div_eq_mul_inv` `RightCancelSemigroup.toIsRightCancelMul`
`div_left_injective` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	`div_eq_mul_inv` `mul_left_injective` `RightCancelSemigroup.toIsRightCancelMul`
`div_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_comm` `mul_left_comm` `mul_inv_rev` `inv_inv`
`div_mul_cancel_left` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroup.toDivisionCommMonoid`	—	`inv_div` `mul_div_cancel_left`
`div_mul_cancel_right` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_div` `mul_div_cancel_right`
`div_mul_comm` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_comm` `mul_left_comm`
`div_mul_div_cancel` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `DivInvMonoid.toDiv`	—	`mul_div_assoc` `div_mul_cancel`
`div_mul_div_cancel'` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `DivInvMonoid.toDiv`	—	`mul_comm` `div_mul_div_cancel`
`div_mul_div_comm` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_left_comm` `mul_assoc` `mul_inv_rev` `mul_comm`
`div_mul_eq_div_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `mul_comm` `mul_assoc`
`div_mul_eq_div_div_swap` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `mul_assoc`
`div_mul_eq_div_mul_one_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `mul_comm` `mul_one` `mul_assoc`
`div_mul_eq_mul_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_comm` `mul_left_comm` `mul_assoc`
`div_mul_mul_cancel` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `DivInvMonoid.toDiv`	—	`mul_left_comm` `div_mul_cancel` `mul_comm`
`div_ne_one` 📖	—	—	—	—	`div_eq_one`
`div_ne_one_of_ne` 📖	—	—	—	—	`eq_of_div_eq_one`
`div_one` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivInvOneMonoid.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass`	—	`div_eq_mul_inv` `inv_one` `mul_one`
`div_pow` 📖	mathematical	—	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_pow` `inv_pow`
`div_right_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid`	—	`div_eq_mul_inv` `mul_assoc` `mul_comm` `mul_left_comm`
`div_right_inj` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	`div_right_injective`
`div_right_injective` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	`div_eq_mul_inv` `inv_injective` `mul_right_injective` `LeftCancelSemigroup.toIsLeftCancelMul`
`div_zpow` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_zpow` `inv_zpow`
`eq_add_neg_iff_add_eq` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_add_cancel_right` `add_neg_cancel_right`
`eq_add_neg_of_add_eq` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_assoc` `add_neg_cancel` `add_zero`
`eq_add_of_add_neg_eq` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—	`add_assoc` `neg_add_cancel` `add_zero`
`eq_add_of_neg_add_eq` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—	`add_neg_cancel_left`
`eq_add_of_sub_eq` 📖	mathematical	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_add_cancel`
`eq_add_of_sub_eq'` 📖	mathematical	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `add_left_comm` `add_neg_cancel` `add_zero`
`eq_div_iff_mul_eq'` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `eq_mul_inv_iff_mul_eq`
`eq_div_iff_mul_eq''` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`eq_div_iff_mul_eq'` `mul_comm`
`eq_div_of_mul_eq'` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`DivInvMonoid.toDiv`	—	`mul_div_cancel_right`
`eq_div_of_mul_eq''` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup`	`DivInvMonoid.toDiv`	—	`mul_comm` `div_eq_mul_inv` `mul_assoc` `mul_inv_cancel` `mul_one`
`eq_iff_eq_of_add_eq_add` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddCommMonoid.toAddMonoid` `AddCancelCommMonoid.toAddCommMonoid`	—	—	`AddLeftCancelSemigroup.toIsLeftCancelAdd` `AddRightCancelSemigroup.toIsRightCancelAdd`
`eq_iff_eq_of_div_eq_div` 📖	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	—	`div_eq_one`
`eq_iff_eq_of_mul_eq_mul` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `CommMonoid.toMonoid` `CancelCommMonoid.toCommMonoid`	—	—	`LeftCancelSemigroup.toIsLeftCancelMul` `RightCancelSemigroup.toIsRightCancelMul`
`eq_iff_eq_of_sub_eq_sub` 📖	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	—	`sub_eq_zero`
`eq_inv_iff_mul_eq_one` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne`	—	`mul_eq_one_iff_eq_inv`
`eq_inv_mul_iff_mul_eq` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_inv_cancel_left` `inv_mul_cancel_left`
`eq_inv_mul_of_mul_eq` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mul_cancel_left`
`eq_inv_of_mul_eq_one_right` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `MulOne.toOne`	`DivInvMonoid.toInv`	—	`inv_eq_of_mul_eq_one_right`
`eq_mul_inv_iff_mul_eq` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mul_cancel_right` `mul_inv_cancel_right`
`eq_mul_inv_of_mul_eq` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_assoc` `mul_inv_cancel` `mul_one`
`eq_mul_of_div_eq` 📖	mathematical	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_mul_cancel`
`eq_mul_of_div_eq'` 📖	mathematical	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_left_comm` `mul_inv_cancel` `mul_one`
`eq_mul_of_inv_mul_eq` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—	`mul_inv_cancel_left`
`eq_mul_of_mul_inv_eq` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—	`mul_assoc` `inv_mul_cancel` `mul_one`
`eq_neg_add_iff_add_eq` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_neg_cancel_left` `neg_add_cancel_left`
`eq_neg_add_of_add_eq` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_add_cancel_left`
`eq_neg_iff_add_eq_zero` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero`	—	`add_eq_zero_iff_eq_neg`
`eq_neg_of_add_eq_zero_right` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `AddZero.toZero`	`SubNegMonoid.toNeg`	—	`neg_eq_of_add_eq_zero_right`
`eq_of_add_neg_eq_zero` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toNeg` `AddZero.toZero`	—	—	`neg_neg` `eq_neg_of_add_eq_zero_left`
`eq_of_div_eq_one` 📖	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	—	`inv_injective` `inv_eq_of_mul_eq_one_right` `div_eq_mul_inv`
`eq_of_inv_mul_eq_one` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toInv` `MulOne.toOne`	—	—	`eq_inv_of_mul_eq_one_left`
`eq_of_mul_inv_eq_one` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toInv` `MulOne.toOne`	—	—	`inv_inv` `eq_inv_of_mul_eq_one_left`
`eq_of_neg_add_eq_zero` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toNeg` `AddZero.toZero`	—	—	`eq_neg_of_add_eq_zero_left`
`eq_of_one_div_eq_one_div` 📖	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	—	`one_div_one_div`
`eq_of_sub_eq_zero` 📖	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	—	`neg_injective` `neg_eq_of_add_eq_zero_right` `sub_eq_add_neg`
`eq_of_zero_sub_eq_zero_sub` 📖	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	—	`zero_sub_zero_sub`
`eq_one_div_of_mul_eq_one_left` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `MulOne.toOne`	`DivInvMonoid.toDiv`	—	`eq_inv_of_mul_eq_one_left` `one_div`
`eq_one_div_of_mul_eq_one_right` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `MulOne.toOne`	`DivInvMonoid.toDiv`	—	`eq_inv_of_mul_eq_one_right` `one_div`
`eq_one_iff_eq_one_of_mul_eq_one` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	—	`one_mul` `mul_one`
`eq_sub_iff_add_eq` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `eq_add_neg_iff_add_eq`
`eq_sub_iff_add_eq'` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`eq_sub_iff_add_eq` `add_comm`
`eq_sub_of_add_eq` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`SubNegMonoid.toSub`	—	`add_sub_cancel_right`
`eq_sub_of_add_eq'` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	`SubNegMonoid.toSub`	—	`add_comm` `sub_eq_add_neg` `add_assoc` `add_neg_cancel` `add_zero`
`eq_zero_iff_eq_zero_of_add_eq_zero` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddZero.toZero`	—	—	`zero_add` `add_zero`
`eq_zero_sub_of_add_eq_zero_left` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `AddZero.toZero`	`SubNegMonoid.toSub`	—	`eq_neg_of_add_eq_zero_left` `zero_sub`
`eq_zero_sub_of_add_eq_zero_right` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `AddZero.toZero`	`SubNegMonoid.toSub`	—	`eq_neg_of_add_eq_zero_right` `zero_sub`
`hom_coe_nsmul` 📖	mathematical	`AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toAdd`	`AddMonoid.toNatSMul` `Nat.iterate`	—	`zero_nsmul` `succ_nsmul` `Function.iterate_succ`
`hom_coe_pow` 📖	mathematical	`MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toMul`	`Monoid.toNatPow` `Nat.iterate`	—	`pow_zero` `pow_succ` `Function.iterate_succ`
`inv_comp_inv` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`Function.Involutive.comp_self` `inv_involutive`
`inv_div` 📖	mathematical	—	`DivInvMonoid.toInv` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv`
`inv_div'` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv` `mul_comm`
`inv_div_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`div_eq_mul_inv` `mul_comm`
`inv_div_inv` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`div_eq_mul_inv` `inv_inv` `mul_comm`
`inv_div_left` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toInv` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev`
`inv_eq_iff_eq_inv` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`inv_inv`
`inv_eq_iff_mul_eq_one` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne`	—	`mul_eq_one_iff_inv_eq`
`inv_eq_one` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `InvOneClass.toOne`	—	`inv_injective` `inv_one`
`inv_inj` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`inv_injective`
`inv_injective` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`Function.Involutive.injective` `inv_involutive`
`inv_inv_div_inv` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid`	—	`div_eq_mul_inv` `inv_inv` `mul_comm` `mul_inv_rev`
`inv_involutive` 📖	mathematical	—	`Function.Involutive` `InvolutiveInv.toInv`	—	`inv_inv`
`inv_mul'` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toDiv`	—	`mul_inv_rev` `mul_comm` `div_eq_mul_inv`
`inv_mul_eq_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivInvMonoid.toDiv`	—	`mul_comm` `div_eq_mul_inv`
`inv_mul_eq_iff_eq_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_inv_cancel_left` `inv_mul_cancel_left`
`inv_mul_eq_inv_mul_iff_mul_eq_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroup.toDivisionCommMonoid`	—	`div_eq_inv_mul` `div_eq_div_iff_mul_eq_mul`
`inv_mul_eq_of_eq_mul` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mul_cancel_left`
`inv_mul_eq_one` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toOne`	—	`mul_eq_one_iff_eq_inv`
`inv_ne_one` 📖	—	—	—	—	`Iff.not` `inv_eq_one`
`inv_pow` 📖	mathematical	—	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`pow_zero` `inv_one` `pow_succ'` `pow_succ` `mul_inv_rev`
`inv_pow_sub` 📖	mathematical	—	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`pow_sub` `inv_pow` `inv_inv`
`inv_surjective` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`Function.Involutive.surjective` `inv_involutive`
`inv_unique` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `CommMonoid.toMonoid` `MulOne.toOne`	—	—	`left_inv_eq_right_inv` `mul_comm`
`inv_zpow` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`zpow_natCast` `inv_pow` `zpow_negSucc`
`inv_zpow'` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`inv_zpow` `zpow_neg`
`ite_add_zero` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddZero.toZero`	—	`add_zero`
`ite_mul_one` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	`mul_one`
`ite_one_mul` 📖	mathematical	—	`MulOne.toOne` `MulOneClass.toMulOne` `MulOne.toMul`	—	`mul_one`
`ite_pow` 📖	—	—	—	—	`dite_pow`
`ite_smul` 📖	—	—	—	—	`dite_smul`
`ite_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`dite_vadd`
`ite_zero_add` 📖	mathematical	—	`AddZero.toZero` `AddZeroClass.toAddZero` `AddZero.toAdd`	—	`add_zero`
`leftInverse_add_left_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SubNegMonoid.toSub`	—	`sub_add_cancel`
`leftInverse_add_right_neg_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_neg_cancel_left`
`leftInverse_div_mul_left` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`mul_div_cancel_right`
`leftInverse_inv` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`inv_inv`
`leftInverse_inv_mul_mul_right` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mul_cancel_left`
`leftInverse_mul_left_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `DivInvMonoid.toDiv`	—	`div_mul_cancel`
`leftInverse_mul_right_inv_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_inv_cancel_left`
`leftInverse_neg` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`neg_neg`
`leftInverse_neg_add_add_right` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_add_cancel_left`
`leftInverse_sub_add_left` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`add_sub_cancel_right`
`left_eq_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	`add_eq_left`
`left_eq_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	`mul_eq_left`
`left_ne_add` 📖	—	—	—	—	`Iff.not` `left_eq_add`
`left_ne_mul` 📖	—	—	—	—	`Iff.not` `left_eq_mul`
`mul_comm_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_comm` `mul_left_comm`
`mul_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_assoc`
`mul_div_assoc'` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivInvMonoid.toDiv`	—	`mul_div_assoc`
`mul_div_cancel` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `DivInvMonoid.toDiv`	—	`mul_div_assoc` `mul_div_cancel_left`
`mul_div_cancel_left` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_inv_mul` `inv_mul_cancel_left`
`mul_div_div_cancel` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_mul` `mul_div_cancel_left`
`mul_div_left_comm` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `mul_left_comm`
`mul_div_mul_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `mul_comm` `mul_assoc` `mul_left_comm`
`mul_div_mul_left_eq_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`mul_comm` `div_eq_mul_inv` `mul_inv_rev` `mul_assoc` `mul_inv_cancel_comm_assoc`
`mul_div_mul_right_eq_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_mul_eq_div_div_swap` `mul_div_cancel_right`
`mul_div_right_comm` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_assoc` `mul_comm` `mul_left_comm`
`mul_eq_left` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	`mul_one` `mul_left_cancel_iff`
`mul_eq_of_eq_div` 📖	mathematical	`DivInvMonoid.toDiv` `Group.toDivInvMonoid`	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_mul_cancel`
`mul_eq_of_eq_div'` 📖	mathematical	`DivInvMonoid.toDiv` `Group.toDivInvMonoid` `CommGroup.toGroup`	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_comm` `mul_inv_cancel_left`
`mul_eq_of_eq_inv_mul` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—	`mul_inv_cancel_left`
`mul_eq_of_eq_mul_inv` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—	`mul_assoc` `inv_mul_cancel` `mul_one`
`mul_eq_one_iff_eq_inv` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toInv`	—	`eq_inv_of_mul_eq_one_left` `inv_mul_cancel`
`mul_eq_one_iff_eq_inv'` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toInv`	—	`mul_eq_one_iff_inv_eq`
`mul_eq_one_iff_inv_eq` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toInv`	—	`mul_eq_one_iff_eq_inv` `inv_eq_iff_eq_inv`
`mul_eq_one_iff_inv_eq'` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toInv`	—	`mul_eq_one_iff_eq_inv`
`mul_eq_right` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	`one_mul` `mul_right_cancel_iff`
`mul_inv` 📖	mathematical	—	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid`	—	`mul_inv_rev` `mul_comm`
`mul_inv_eq_iff_eq_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mul_cancel_right` `mul_inv_cancel_right`
`mul_inv_eq_mul_inv_iff_mul_eq_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroup.toDivisionCommMonoid`	—	`div_eq_mul_inv` `div_eq_div_iff_mul_eq_mul`
`mul_inv_eq_of_eq_mul` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_assoc` `mul_inv_cancel` `mul_one`
`mul_inv_eq_one` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `InvOneClass.toOne`	—	`mul_eq_one_iff_eq_inv` `inv_inv`
`mul_inv_mul_mul_cancel` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_assoc` `inv_mul_cancel` `one_mul`
`mul_left_comm` 📖	mathematical	—	`CommMagma.toMul` `CommSemigroup.toCommMagma`	—	`mul_assoc` `mul_comm`
`mul_left_iterate` 📖	mathematical	—	`Nat.iterate` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`pow_zero` `one_mul` `comp_mul_left` `mul_assoc` `pow_succ`
`mul_left_iterate_apply` 📖	mathematical	—	`Nat.iterate` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`mul_left_iterate`
`mul_left_iterate_apply_one` 📖	mathematical	—	`Nat.iterate` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne` `Monoid.toNatPow`	—	`mul_left_iterate` `mul_one`
`mul_left_surjective` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`mul_inv_cancel_left`
`mul_mul_div_cancel` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `DivInvMonoid.toDiv`	—	`mul_assoc` `mul_div_cancel`
`mul_mul_inv_cancel'_right` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `CommGroup.toGroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `DivisionCommMonoid.toDivisionMonoid` `CommGroup.toDivisionCommMonoid`	—	`div_eq_mul_inv` `mul_div_cancel`
`mul_mul_inv_mul_cancel` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_assoc` `mul_inv_cancel` `one_mul`
`mul_mul_mul_comm` 📖	mathematical	—	`CommMagma.toMul` `CommSemigroup.toCommMagma`	—	`mul_left_comm` `mul_assoc`
`mul_mul_mul_comm'` 📖	mathematical	—	`CommMagma.toMul` `CommSemigroup.toCommMagma`	—	—
`mul_ne_left` 📖	—	—	—	—	`Iff.not` `mul_eq_left`
`mul_ne_right` 📖	—	—	—	—	`Iff.not` `mul_eq_right`
`mul_one_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivInvMonoid.toDiv` `MulOne.toOne`	—	`div_eq_mul_inv` `one_mul`
`mul_one_eq_id` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	`mul_one`
`mul_pow` 📖	mathematical	—	`Monoid.toNatPow` `CommMonoid.toMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`pow_zero` `one_mul` `pow_succ'` `mul_mul_mul_comm`
`mul_pow_sub_one` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`pow_succ'`
`mul_right_comm` 📖	mathematical	—	`CommMagma.toMul` `CommSemigroup.toCommMagma`	—	`mul_assoc` `mul_comm`
`mul_right_iterate` 📖	mathematical	—	`Nat.iterate` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`pow_zero` `mul_one` `comp_mul_right` `pow_succ'`
`mul_right_iterate_apply` 📖	mathematical	—	`Nat.iterate` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`mul_right_iterate`
`mul_right_iterate_apply_one` 📖	mathematical	—	`Nat.iterate` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne` `Monoid.toNatPow`	—	`mul_right_iterate` `one_mul`
`mul_right_surjective` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`inv_mul_cancel_right`
`mul_rotate` 📖	mathematical	—	`CommMagma.toMul` `CommSemigroup.toCommMagma`	—	`mul_comm` `mul_left_comm`
`mul_rotate'` 📖	mathematical	—	`CommMagma.toMul` `CommSemigroup.toCommMagma`	—	`mul_comm` `mul_left_comm`
`mul_self_zpow` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `DivInvMonoid.toZPow`	—	`zpow_add` `zpow_one`
`mul_zpow` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`zpow_natCast` `mul_pow` `zpow_negSucc` `mul_inv`
`mul_zpow_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `DivInvMonoid.toZPow`	—	`zpow_natCast` `mul_pow_mul` `zpow_negSucc` `mul_assoc`
`mul_zpow_neg_one` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`zpow_neg` `zpow_one` `mul_inv_rev`
`mul_zpow_self` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `DivInvMonoid.toZPow`	—	`zpow_add_one`
`mul_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid`	—	`mul_zsmul'`
`mul_zsmul'` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid`	—	`natCast_zsmul` `mul_nsmul` `negSucc_zsmul` `neg_zsmul` `neg_nsmul` `neg_neg`
`multiplicative_of_isTotal` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	—	`multiplicative_of_total`
`multiplicative_of_symmetric_of_isTotal` 📖	—	`Symmetric` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	—	`multiplicative_of_symmetric_of_total`
`multiplicative_of_symmetric_of_total` 📖	—	`Symmetric` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	—	`total_of` `one_mul` `mul_assoc` `mul_one`
`multiplicative_of_total` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	—	`multiplicative_of_symmetric_of_total`
`natAbs_nsmul_eq_zero` 📖	mathematical	—	`AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `SubNegMonoid.toZSMul`	—	`natCast_zsmul` `negSucc_zsmul` `neg_eq_zero`
`natCast_sub_natCast_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `SubNegMonoid.toSub` `AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `natCast_zsmul` `sub_zsmul`
`natCast_sub_one_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `SubNegMonoid.toSub` `AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `natCast_zsmul` `one_zsmul` `sub_zsmul`
`ne_iff_ne_of_add_eq_add` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddCommMonoid.toAddMonoid` `AddCancelCommMonoid.toAddCommMonoid`	—	—	`AddRightCancelSemigroup.toIsRightCancelAdd` `AddLeftCancelSemigroup.toIsLeftCancelAdd`
`ne_iff_ne_of_mul_eq_mul` 📖	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `CommMonoid.toMonoid` `CancelCommMonoid.toCommMonoid`	—	—	`RightCancelSemigroup.toIsRightCancelMul` `LeftCancelSemigroup.toIsLeftCancelMul`
`neg_add` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid`	—	`neg_add_rev` `add_comm`
`neg_add'` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toSub`	—	`neg_add_rev` `add_comm` `sub_eq_add_neg`
`neg_add_eq_iff_eq_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_neg_cancel_left` `neg_add_cancel_left`
`neg_add_eq_neg_add_iff_add_eq_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid`	—	`sub_eq_neg_add` `sub_eq_sub_iff_add_eq_add`
`neg_add_eq_of_eq_add` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_add_cancel_left`
`neg_add_eq_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubNegMonoid.toSub`	—	`add_comm` `sub_eq_add_neg`
`neg_add_eq_zero` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toZero`	—	`add_eq_zero_iff_eq_neg`
`neg_comp_neg` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`Function.Involutive.comp_self` `neg_involutive`
`neg_eq_iff_add_eq_zero` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero`	—	`add_eq_zero_iff_neg_eq`
`neg_eq_iff_eq_neg` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`neg_neg`
`neg_eq_zero` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `NegZeroClass.toZero`	—	`neg_injective` `neg_zero`
`neg_inj` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`neg_injective`
`neg_injective` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`Function.Involutive.injective` `neg_involutive`
`neg_involutive` 📖	mathematical	—	`Function.Involutive` `InvolutiveNeg.toNeg`	—	`neg_neg`
`neg_ne_zero` 📖	—	—	—	—	`Iff.not` `neg_eq_zero`
`neg_neg_sub_neg` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid`	—	`sub_eq_add_neg` `neg_neg` `add_comm` `neg_add_rev`
`neg_nsmul` 📖	mathematical	—	`AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`zero_nsmul` `neg_zero` `succ_nsmul'` `succ_nsmul` `neg_add_rev`
`neg_one_zsmul_add` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`neg_zsmul` `one_zsmul` `neg_add_rev`
`neg_sub` 📖	mathematical	—	`SubNegMonoid.toNeg` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg`
`neg_sub'` 📖	mathematical	—	`NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg` `add_comm`
`neg_sub_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`sub_eq_add_neg` `add_comm`
`neg_sub_left` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toNeg` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev`
`neg_sub_neg` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`sub_eq_add_neg` `neg_neg` `add_comm`
`neg_surjective` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`Function.Involutive.surjective` `neg_involutive`
`neg_unique` 📖	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddCommMonoid.toAddMonoid` `AddZero.toZero`	—	—	`left_neg_eq_right_neg` `add_comm`
`neg_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`SubNegMonoid.zsmul_neg'` `zero_zsmul` `neg_zero` `negSucc_zsmul` `neg_neg` `natCast_zsmul`
`nsmul_add` 📖	mathematical	—	`AddMonoid.toNatSMul` `AddCommMonoid.toAddMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`zero_nsmul` `zero_add` `succ_nsmul'` `add_add_add_comm`
`nsmul_add_nsmul_eq_zero` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	`AddMonoid.toNatSMul`	—	`zero_nsmul` `add_zero` `succ_nsmul` `succ_nsmul'` `add_assoc`
`nsmul_add_sub_nsmul` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`add_nsmul`
`nsmul_eq_mod_nsmul` 📖	—	`AddMonoid.toNatSMul` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	—	`add_nsmul` `mul_nsmul` `nsmul_zero` `add_zero`
`nsmul_iterate` 📖	mathematical	—	`Nat.iterate` `AddMonoid.toNatSMul`	—	`one_nsmul` `mul_nsmul`
`nsmul_sub` 📖	mathematical	—	`AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `nsmul_add` `neg_nsmul`
`nsmul_zero_sub` 📖	mathematical	—	`AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toSub` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`zero_sub` `neg_nsmul`
`one_add_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`add_zsmul` `one_zsmul`
`one_div_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `mul_inv_rev` `inv_inv` `one_mul`
`one_div_mul_eq_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`div_eq_mul_inv` `mul_comm` `mul_one`
`one_div_mul_one_div` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivisionCommMonoid.toDivisionMonoid` `DivInvMonoid.toDiv` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`div_eq_mul_inv` `mul_comm` `mul_one` `mul_inv_rev`
`one_div_mul_one_div_rev` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toDiv` `MulOne.toOne`	—	`div_eq_mul_inv` `one_mul` `mul_inv_rev`
`one_div_one` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivInvOneMonoid.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass`	—	`div_one`
`one_div_one_div` 📖	mathematical	—	`DivInvMonoid.toDiv` `DivisionMonoid.toDivInvMonoid` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `one_mul` `inv_inv`
`one_div_pow` 📖	mathematical	—	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toDiv` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`one_div` `inv_pow`
`one_div_zpow` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `DivInvMonoid.toDiv` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`one_div` `inv_zpow`
`one_eq_inv` 📖	mathematical	—	`InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `InvOneClass.toInv`	—	`inv_eq_one`
`one_mul_eq_id` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	`one_mul`
`one_sub_natCast_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `SubNegMonoid.toSub` `AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `one_zsmul` `natCast_zsmul` `sub_zsmul`
`one_zpow` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`zpow_natCast` `one_pow` `zpow_negSucc` `inv_one`
`pow_boole` 📖	mathematical	—	`Monoid.toNatPow` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`pow_ite` `pow_one` `pow_zero`
`pow_dite` 📖	—	—	—	—	—
`pow_eq_pow_mod` 📖	—	`Monoid.toNatPow` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	—	`pow_add` `pow_mul` `one_pow` `mul_one`
`pow_ite` 📖	—	—	—	—	`pow_dite`
`pow_iterate` 📖	mathematical	—	`Nat.iterate` `Monoid.toNatPow`	—	`pow_one` `pow_mul`
`pow_mul_pow_eq_one` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	`Monoid.toNatPow`	—	`pow_zero` `mul_one` `pow_succ` `pow_succ'` `mul_assoc`
`pow_mul_pow_sub` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`pow_add`
`pow_natAbs_eq_one` 📖	mathematical	—	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `DivInvMonoid.toZPow`	—	`zpow_natCast` `zpow_negSucc`
`pow_sub` 📖	mathematical	—	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`eq_mul_inv_of_mul_eq` `pow_add`
`pow_sub_mul_pow` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`pow_add`
`pow_sub_one_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `Monoid.toNatPow`	—	`pow_succ`
`rightInverse_inv` 📖	mathematical	—	`InvolutiveInv.toInv`	—	`inv_inv`
`rightInverse_neg` 📖	mathematical	—	`InvolutiveNeg.toNeg`	—	`neg_neg`
`right_eq_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddZero.toZero`	—	`add_eq_right`
`right_eq_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	—	`mul_eq_right`
`right_ne_add` 📖	—	—	—	—	`Iff.not` `right_eq_add`
`right_ne_mul` 📖	—	—	—	—	`Iff.not` `right_eq_mul`
`smul_dite` 📖	—	—	—	—	—
`smul_ite` 📖	—	—	—	—	`smul_dite`
`sub_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_comm` `add_left_comm` `neg_add_rev` `neg_neg`
`sub_add_add_cancel` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `SubNegMonoid.toSub`	—	`add_left_comm` `sub_add_cancel` `add_comm`
`sub_add_cancel_left` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid`	—	`neg_sub` `add_sub_cancel_left`
`sub_add_cancel_right` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_sub` `add_sub_cancel_right`
`sub_add_comm` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_comm` `add_left_comm`
`sub_add_eq_add_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_comm` `add_left_comm` `add_assoc`
`sub_add_eq_sub_add_zero_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `add_comm` `add_zero` `add_assoc`
`sub_add_eq_sub_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `add_comm` `add_assoc`
`sub_add_eq_sub_sub_swap` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `add_assoc`
`sub_add_sub_cancel` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SubNegMonoid.toSub`	—	`add_sub_assoc` `sub_add_cancel`
`sub_add_sub_cancel'` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `SubNegMonoid.toSub`	—	`add_comm` `sub_add_sub_cancel`
`sub_add_sub_comm` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_left_comm` `add_assoc` `neg_add_rev` `add_comm`
`sub_eq_add_zero_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddZero.toZero`	—	`sub_eq_add_neg` `zero_sub`
`sub_eq_iff_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	—	`sub_eq_iff_eq_add'` `sub_eq_iff_eq_add`
`sub_eq_iff_eq_add` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `add_neg_eq_iff_eq_add`
`sub_eq_iff_eq_add'` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_iff_eq_add` `add_comm`
`sub_eq_neg_add` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`sub_eq_add_neg` `add_comm`
`sub_eq_neg_self` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `NegZeroClass.toZero`	—	`sub_eq_add_neg` `add_eq_right` `AddRightCancelSemigroup.toIsRightCancelAdd`
`sub_eq_of_eq_add` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`SubNegMonoid.toSub`	—	`add_sub_cancel_right`
`sub_eq_of_eq_add'` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	`SubNegMonoid.toSub`	—	`sub_eq_add_neg` `add_comm` `neg_add_cancel_left`
`sub_eq_self` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`sub_eq_add_neg` `add_eq_left` `AddLeftCancelSemigroup.toIsLeftCancelAdd` `neg_eq_zero`
`sub_eq_sub_add_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `add_left_comm` `add_assoc` `add_neg_cancel` `add_zero`
`sub_eq_sub_iff_add_eq_add` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_iff_eq_add` `sub_add_eq_add_sub` `sub_eq_iff_eq_add'` `add_comm`
`sub_eq_sub_iff_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid`	—	`neg_sub`
`sub_eq_sub_iff_sub_eq_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	—	`sub_eq_iff_eq_add` `sub_add_eq_add_sub` `sub_eq_iff_eq_add'` `add_sub_assoc`
`sub_eq_zero` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`eq_of_sub_eq_zero` `sub_self`
`sub_eq_zero_of_eq` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`sub_eq_zero`
`sub_left_inj` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	`sub_eq_add_neg` `AddRightCancelSemigroup.toIsRightCancelAdd`
`sub_left_injective` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	`sub_eq_add_neg` `add_left_injective` `AddRightCancelSemigroup.toIsRightCancelAdd`
`sub_ne_zero` 📖	—	—	—	—	`sub_eq_zero`
`sub_ne_zero_of_ne` 📖	—	—	—	—	`eq_of_sub_eq_zero`
`sub_neg_eq_add` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_neg`
`sub_nsmul` 📖	mathematical	—	`AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`eq_add_neg_of_add_eq` `add_nsmul`
`sub_nsmul_neg` 📖	mathematical	—	`AddMonoid.toNatSMul` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`sub_nsmul` `neg_nsmul` `neg_neg`
`sub_nsmul_nsmul_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`add_nsmul`
`sub_one_nsmul_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `AddMonoid.toNatSMul`	—	`succ_nsmul'`
`sub_one_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_neg_cancel_right` `add_one_zsmul`
`sub_right_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid`	—	`sub_eq_add_neg` `add_assoc` `add_comm` `add_left_comm`
`sub_right_inj` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	`sub_right_injective`
`sub_right_injective` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	`sub_eq_add_neg` `neg_injective` `add_right_injective` `AddLeftCancelSemigroup.toIsLeftCancelAdd`
`sub_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `add_assoc` `neg_add_rev` `add_comm`
`sub_sub_cancel` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	—	`sub_sub_self`
`sub_sub_cancel_left` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddCommGroup.toDivisionAddCommMonoid`	—	`sub_eq_add_neg` `add_comm` `add_left_comm` `add_neg_cancel_left`
`sub_sub_eq_add_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg` `add_assoc`
`sub_sub_self` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg` `add_neg_cancel_comm_assoc`
`sub_sub_sub_cancel_left` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid` `AddCommGroup.toAddGroup`	—	`neg_sub` `sub_neg_eq_add` `add_comm` `sub_add_sub_cancel`
`sub_sub_sub_cancel_right` 📖	mathematical	—	`SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	`neg_sub` `sub_neg_eq_add` `sub_add_sub_cancel`
`sub_sub_sub_comm` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg` `add_left_comm` `add_assoc` `add_comm`
`sub_sub_sub_eq` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg` `add_left_comm` `add_assoc` `add_comm`
`sub_zero` 📖	mathematical	—	`SubNegMonoid.toSub` `SubNegZeroMonoid.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass`	—	`sub_eq_add_neg` `neg_zero` `add_zero`
`sub_zsmul` 📖	mathematical	—	`SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`add_zsmul` `neg_zsmul`
`vadd_dite` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	—
`vadd_ite` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`vadd_dite`
`zero_add_eq_id` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddZero.toZero`	—	`zero_add`
`zero_eq_neg` 📖	mathematical	—	`NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `NegZeroClass.toNeg`	—	`neg_eq_zero`
`zero_sub_add_eq_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`sub_eq_add_neg` `add_comm` `add_zero`
`zero_sub_add_zero_sub` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`sub_eq_add_neg` `add_comm` `add_zero` `neg_add_rev`
`zero_sub_add_zero_sub_rev` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toSub` `AddZero.toZero`	—	`sub_eq_add_neg` `zero_add` `neg_add_rev`
`zero_sub_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `neg_add_rev` `neg_neg` `zero_add`
`zero_sub_zero` 📖	mathematical	—	`SubNegMonoid.toSub` `SubNegZeroMonoid.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass`	—	`sub_zero`
`zero_sub_zero_sub` 📖	mathematical	—	`SubNegMonoid.toSub` `SubtractionMonoid.toSubNegMonoid` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`sub_eq_add_neg` `zero_add` `neg_neg`
`zpow_add` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`Int.induction_on` `zpow_zero` `mul_one` `zpow_add_one` `mul_assoc` `zpow_sub_one`
`zpow_add_one` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`zpow_natCast` `pow_succ` `zpow_zero` `zpow_neg` `zpow_one` `inv_mul_cancel` `zpow_negSucc` `pow_succ'` `mul_inv_rev` `inv_mul_cancel_right`
`zpow_comm` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid`	—	`zpow_mul` `zpow_mul'`
`zpow_eq_zpow_emod` 📖	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—	`zpow_add` `zpow_mul` `one_zpow` `mul_one`
`zpow_eq_zpow_emod'` 📖	mathematical	`Monoid.toNatPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	`DivInvMonoid.toZPow`	—	`zpow_eq_zpow_emod` `zpow_natCast`
`zpow_induction_left` 📖	mathematical	`InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv`	`DivInvMonoid.toZPow`	—	`Int.induction_on` `zpow_zero` `zpow_add` `zpow_one` `zpow_neg_one`
`zpow_induction_right` 📖	mathematical	`InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv`	`DivInvMonoid.toZPow`	—	`Int.induction_on` `zpow_zero` `zpow_add_one` `zpow_sub_one`
`zpow_iterate` 📖	mathematical	—	`Nat.iterate` `DivInvMonoid.toZPow` `Group.toDivInvMonoid`	—	`zpow_one` `zpow_mul`
`zpow_mul` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid`	—	`zpow_natCast` `pow_mul` `zpow_negSucc` `zpow_neg` `inv_pow` `inv_inv`
`zpow_mul'` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid`	—	`zpow_mul`
`zpow_mul_comm` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `DivInvMonoid.toZPow`	—	`zpow_add`
`zpow_natCast_sub_natCast` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `DivInvMonoid.toDiv` `Monoid.toNatPow` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `zpow_natCast` `zpow_sub`
`zpow_natCast_sub_one` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `DivInvMonoid.toDiv` `Monoid.toNatPow` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `zpow_natCast` `zpow_one` `zpow_sub`
`zpow_neg` 📖	mathematical	—	`DivInvMonoid.toZPow` `DivisionMonoid.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid`	—	`DivInvMonoid.zpow_neg'` `zpow_zero` `inv_one` `zpow_negSucc` `inv_inv` `zpow_natCast`
`zpow_one_add` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	`zpow_add` `zpow_one`
`zpow_one_sub_natCast` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `DivInvMonoid.toDiv` `Monoid.toNatPow` `DivInvMonoid.toMonoid`	—	`div_eq_mul_inv` `zpow_one` `zpow_natCast` `zpow_sub`
`zpow_sub` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`zpow_add` `zpow_neg`
`zpow_sub_one` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`mul_inv_cancel_right` `zpow_add_one`
`zsmul_add` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	`natCast_zsmul` `nsmul_add` `negSucc_zsmul` `neg_nsmul` `neg_add`
`zsmul_add_comm` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SubNegMonoid.toZSMul`	—	`add_zsmul`
`zsmul_comm` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid`	—	`mul_zsmul'` `mul_zsmul`
`zsmul_induction_left` 📖	mathematical	`NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg`	`SubNegMonoid.toZSMul`	—	`Int.induction_on` `zero_zsmul` `add_zsmul` `one_zsmul` `neg_one_zsmul`
`zsmul_induction_right` 📖	mathematical	`NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg`	`SubNegMonoid.toZSMul`	—	`Int.induction_on` `zero_zsmul` `add_one_zsmul` `sub_one_zsmul`
`zsmul_iterate` 📖	mathematical	—	`Nat.iterate` `SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid`	—	`one_zsmul` `mul_zsmul'`
`zsmul_neg` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`natCast_zsmul` `neg_nsmul` `negSucc_zsmul`
`zsmul_neg'` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`zsmul_neg` `neg_zsmul`
`zsmul_sub` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `SubtractionCommMonoid.toSubtractionMonoid` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `zsmul_add` `zsmul_neg`
`zsmul_zero` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`natCast_zsmul` `nsmul_zero` `negSucc_zsmul` `neg_zero`
`zsmul_zero_sub` 📖	mathematical	—	`SubNegMonoid.toZSMul` `SubtractionMonoid.toSubNegMonoid` `SubNegMonoid.toSub` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid`	—	`zero_sub` `zsmul_neg`

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