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, addConj_eq_zero_iff, 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, 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_bijective, 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_bijective, 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	439
Total	443

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	2650 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, mem_sphere_iff_norm_inv_mul_eq, 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, Function.csSup_div_semiconj, UpperSemicontinuousWithinAt.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', LowerSemicontinuousOn.inv, 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, Multipliable.hasFiniteMulSupport_of_discreteTopology, Filter.tendsto_comp_inv_atBot_iff, one_lt_inv_of_inv, AddAut.apply_inv_self, Lagrange.eval_interpolate_not_at_node', Valuation.mem_maximalIdeal_iff, Right.one_le_inv_iff, MeasureTheory.quasiMeasurePreserving_inv_mul, one_lt_zpow₀, 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, 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, NormedCommGroup.cauchySeq_iff, CauSeq.inv_aux, lt_inv_mul_iff_lt, GroupExtension.Section.mul_inv_mem_range_inl, MulAut.inv_apply, SeminormedGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_one, SeminormedGroup.disjoint_nhds, 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, one_lt_of_inv_lt_one, 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, WithVal.toVal_inv, 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, Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_mem, IsMulIndecomposable.mem_or_inv_mem_closure_baseOf, 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, Left.inv_le_self, le_inv_mul_iff_mul_le, Finset.inv_smul_finset_distrib, Lagrange.leadingCoeff_basis, oneLePart_one, GroupFilterBasis.nhds_one_eq, MeasureTheory.mlconvolution_assoc₀, LipschitzWith.norm_inv_mul_le_of_le, Int.ceil_div_ceil_inv_sub_one, conj_mul, isQuotientCoveringMap_iff, Set.smul_inter_ne_empty_iff, upperSemiContinuous_inv_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, Valuation.Integers.one_of_isUnit', 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, one_lt_mabs_pos_of_one_lt, 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, 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, LowerSemicontinuous.inv, Pell.Solution₁.eq_one_or_neg_one_iff_y_eq_zero, Finset.singleton_zpow, minpoly.eq_of_irreducible, spinGroup.star_eq_inv', Matrix.ProjGenLinGroup.mk_scalar, 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, Subgroup.eq_one_of_noncommProd_eq_one_of_iSupIndep, 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, RatFunc.irreducible_min_polynomial_valuation_lt_one_and_ne_zero, 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', MeasureTheory.Measure.pi.isInvInvariant, IsTopologicalGroup.mulInvClosureNhd.nhds, le_mul_inv_left, ValuationSubring.valuation_unit, monovary_inv_left, eventually_forall_conj_nhds_one, Commute.conj, Set.inv_Ioc, Representation.char_conj, DiffContOnCl.inv, isGLB_inv', Representation.char_dual, IsTopologicalGroup.ext_iff, NormedGroup.nhds_one_basis_norm_lt, GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity, eq_mul_inv_of_mul_eq, AnalyticOn.fun_inv, MulAction.QuotientAction.inv_mul_mem, 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, Subgroup.IsComplement.equiv_one, Commute.inv_left_iff, ball_div_one, lineMap_inv_two, MeasureTheory.Measure.IsHaarMeasure.isInvInvariant_of_regular, lowerClosure_one, Valuation.restrict_eq_one_iff, Subring.center.coe_inv, leOnePart_le_one, inv_natCast_smul_eq, Finset.subset_smul_finset_iff, LinearEquiv.coe_inv, Action.rightDual_ρ, leOnePart_of_one_le, 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, MeasureTheory.IntegrableOn.comp_inv_Ioi, Filter.Tendsto.op_one_isBoundedUnder_le, 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, cfc_ringInverse_id, 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, TopologicalGroup.IsSES.integral_pullback_invFun_apply, 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', leOnePart_of_le_one, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, IsOpen.mul_closure_one_eq, ClassGroup.mk0_eq_one_iff, Group.residuallyFinite_iff_forall_finiteIndex, 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, nndist_nnnorm_nnnorm_le_nnnorm_inv_mul, 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, TopologicalGroup.IsSES.pushforward_def, 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, mem_closedBall_iff_norm_inv_mul_le, 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, LowerSemicontinuousWithinAt.inv, 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, abs_norm_sub_norm_le_norm_inv_mul, AlgEquiv.aut_inv, Mathlib.Tactic.Ring.inv_congr, 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, Representation.card_inv_mul_sum_char_eq_finrank, 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, MeasureTheory.IsFundamentalDomain.covolume_eq_volume, antivaryOn_inv_left₀, leftInverse_inv_mul_mul_right, inv_mul', one_le_zpow₀, Derivation.leibniz_div, groupHomology.d₂₁_single_inv_mul_ρ_add_single, div_mul_cancel_left₀, NormedSpace.exp_eq_tsum, one_le_of_inv_le_one, TendstoLocallyUniformlyOn.fun_inv, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, mabs_le', Nonneg.inv_mk, mul_eq_one_iff_inv_eq₀, exists_nhds_split_inv, MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff, Ideal.pointwise_smul_subset_iff, mul_inv, isOfFinOrder_inv_iff, Finset.pow_right_strictMonoOn, 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, Representation.card_inv_mul_sum_char_mul_char_eq_finrank, Quaternion.inv_def, CategoryTheory.GrpObj.lift_conj_eq_mul_mul_inv, 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, Function.HasFiniteMulSupport.div, 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, Multipliable.one_lt_tprod, 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, EisensteinSeries.summable_inv_of_isBigO_rpow_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, lipschitzOnWith_iff_norm_inv_mul_le, 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, MeasureTheory.IsFundamentalDomain.mono, 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, MonoidHom.FixedPointFree.coe_eq_inv_of_involutive, isOfFinOrder_iff_zpow_eq_one, inv_mem_connectedComponent_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, ConjAct.toConjAct_inv_smul, Group.conj_mem_conjugatesOfSet, Set.mulIndicator_div, IntermediateField.inv_mem', Set.inv_Ioi, one_lt_ltOnePart, Function.HasFiniteMulSupport.inv, 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, Right.self_le_inv, Polynomial.natDegree_mul_leadingCoeff_self_inv, AddAut.coe_inv, isLUB_inv, CategoryTheory.GrpObj.inv_comp_assoc, Antivary.inv_right₀, eventually_cobounded_mapsTo, inv_zpow', MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum', Function.HasFiniteMulSupport.fun_div, LinearMap.GeneralLinearGroup.ofLinearEquiv_inv, Subgroup.mem_goursatFst, Matrix.conjTranspose_inv_natCast_smul, mul_eq_one_iff_eq_inv, MonoidHom.inv_apply, upperSemicontinuousOn_inv_iff, 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, MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum', powCoprime_inv, CommRing.Pic.inv_eq_dual, Group.residuallyFinite_iff_forall_finiteIndexNormalSubgroup, 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', nhds_basis_Ioo_one_lt_of_one_lt, 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, inv_lt_of_inv_lt₀, GroupCone.coe_oneLE, mabs_of_lt_one, Left.self_le_inv, lt_mul_inv_iff_lt, Circle.exp_two_pi, mul_notMem_of_exponent_two, singleton_div_closedBall_one, mulTSupport_fun_inv, inv_mem_nhds_one, monovaryOn_inv_right, Function.Antiperiodic.const_inv_smul₀, map_inv_mul, AnalyticWithinAt.inv, RatFunc.numDenom_div, groupCohomology.cocycles₂_map_one_snd, Real.Angle.toCircle_zero, powCoprime_one, fderivWithin_inv', dist_eq_norm_inv_mul, 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, inv_of_one_lt_inv, 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, zpow_lt_one_iff_right₀, 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, NormedGroup.tendsto_nhds_nhds, 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, lt_inv_of_lt_inv, RegularWreathProduct.left_inl, comap_mabs_nhds_one, inv_lt_of_mabs_lt, nndist_eq_nnnorm_inv_mul, MonovaryOn.inv_left₀, IsDiscrete.exists_nhds_eq_one_of_image_mulRight_inter_nonempty, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, tendsto_iff_norm_inv_mul_tendsto_zero, 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, one_le_zpow_iff_right_of_lt_one₀, CategoryTheory.Grp.Hom.hom_hom_inv, AddChar.neg_apply', Finset.one_mem_inv_mul_iff, Valuation.isEquiv_iff_val_le_one, Set.star_inv, CategoryTheory.GrpObj.lift_conj_eq_mul_mul_inv_assoc, 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, LipschitzOnWith.norm_inv_mul_le, AddCircle.equivAddCircle_apply_mk, Set.inv_zero, div_ball, MeasureTheory.Measure.map_mul_right_inv_eq_self, Multipliable.tprod_eq_mul_tprod_ite, Matrix.UnitaryGroup.map_star_inv_eq_transpose, uniformity_eq_comap_inv_mul_nhds_one, OrderIso.smulRight_symm_apply, sInf_inv, one_lt_div', LinearMap.GeneralLinearGroup.toLinearEquiv_inv, IsSquare.inv, HasCompactMulSupport.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, Sylow.conj_eq_normalizer_conj_of_mem, 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, MonoidHom.FixedPointFree.prod_pow_eq_one, comap_norm_nhdsGT_zero', Valuation.isEquiv_iff_val_eq_one, IsUnit.eq_inv_mul_iff_mul_eq, OpenSubgroup.mem_nhds_one, one_div_nonneg, Action.FintypeCat.toEndHom_apply, Subgroup.IsComplement.equiv_fst_eq_one_of_mem_of_one_mem, 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, Filter.HasBasis.uniformity_of_nhds_one_inv_mul_swapped, 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, meromorphicNFOn_fun_inv, 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, compl_mul_closure_one_eq, 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, tendsto_norm_inv_mul_self_nhdsNE, Set.inv_Icc, Bornology.IsBounded.inv, Subgroup.closure_mul_image_eq, 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, Valuation.restrict_lt_one_iff, star_inv_intCast_smul, LinearEquiv.det_symm, multipliable_const_iff, SeminormedGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_one, LinearEquiv.mem_transvections_iff_mem_dilatransvections_and_fixedReduce_eq_one, IsCompact.closedBall_one_mul, Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe, FractionalIdeal.mul_generator_self_inv, Subgroup.IsComplement.equiv_snd_eq_one_of_mem_of_one_mem, 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, ContinuousInv₀.of_nhds_one, GroupFilterBasis.conj', Set.subset_smul_set_iff, zpow_le_one_iff_right₀, 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, mabs_eq, Pell.Solution₁.x_one, List.prod_rotate_eq_one_of_prod_eq_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, one_lt_oneLePart, exists_closed_nhds_one_inv_eq_mul_subset, 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', Submonoid.coe_mulSupport, smul_mem_nhds_self, mul_inv_le_one_of_le₀, tendsto_norm_inv_mul_self, 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, Finset.doubling_lt_golden_ratio, 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, Subgroup.closure_mul_image_mul_eq_top, DifferentiableAt.inv, Filter.Tendsto.conj_nhds_one, 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, one_le_zpow_iff_right₀, Mathlib.Tactic.Ring.inv_mul, Metric.preimage_mul_left_ball, Finset.preimage_mul_right_one, ordinaryHypergeometric_eq_tsum, Subgroup.one_mem, Subgroup.normalizerMonoidHom_apply_apply_coe, UniformFun.hasBasis_nhds_one_of_basis, 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, Submonoid.IsMulPointed.eq_one_of_mem_of_inv_mem₂, 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, WithVal.ofVal_inv, 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, controlled_prod_of_mem_closure_range, RootPairing.Equiv.coweightEquiv_inv, Metric.preimage_smul_closedBall, IsUnit.div_mul_left, zpow_lt_one₀, mulAutArrow_apply_symm_apply, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv, Subgroup.disjoint_def, MeasureTheory.rnDeriv_mconv, Field.isSeparable_inv, Submonoid.val_inv_unitsEquivUnitsType_apply_coe, AddCircle.toCircle_zero, AntilipschitzWith.le_mul_norm_div, GroupCone.oneLE.hasMemOrInvMem, MeasureTheory.IntegrableOn.comp_inv_Ici, 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, upperSemicontinuousAt_inv_iff, EulerProduct.eulerProduct_completely_multiplicative_hasProd, norm_inv', lt_inv_of_lt_inv₀, 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, MeasureTheory.IsFundamentalDomain.setLIntegral_eq_tsum', 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, IsSelfAdjoint.inv_iff, commutatorElement_inv, lowerSemicontinuousWithinAt_inv_iff, zpow_le_one_iff_right_of_lt_one₀, Height.mulHeight₁_inv, Hyperreal.coe_inv, Subsemiring.mem_inv_pointwise_smul_iff₀, groupHomology.single_isCycle₁_iff, NormedField.continuousAt_inv, WithAbs.toAbs_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', lowerSemiContinuous_inv_iff, 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, Polynomial.valuation_le_one_of_valuation_X_le_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, inv_lt_one_of_one_lt₀, Left.self_lt_inv, GroupFilterBasis.nhds_one_hasBasis, Subgroup.exists_isLeast_one_lt, 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, inv_le_one_of_one_le, 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, AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀, UpperSemicontinuousAt.inv, mabs_of_le_one, 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, MeasureTheory.IsFundamentalDomain.smul, Function.HasFiniteMulSupport.zpow, MonoidHom.FixedPointFree.coe_eq_inv_of_sq_eq_one, MonoidWithZeroHom.snd_inl_apply_of_ne_zero, deriv_inv'', TendstoLocallyUniformly.fun_inv₀_of_disjoint, Right.inv_le_self, selfAdjoint.val_inv, NormedDivisionRing.to_continuousInv₀, Quandle.conj_act_eq_conj, Function.Periodic.const_smul₀, MulDistribMulActionHom.map_inv, 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, 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, mem_ball_iff_norm_inv_mul_lt', IsTopologicalGroup.t2Space_iff_one_closed, Mathlib.Tactic.Ring.inv_single, Submonoid.mem_pointwise_smul_iff_inv_smul_mem, Finset.zpow_eq_empty, Equiv.Perm.VectorsProdEqOne.one_eq, exists_zpow_eq_one, AddAut.coe_one, Function.HasFiniteMulSupport.fun_zpow, 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, one_lt_leOnePart, groupHomology.d₃₂_single_one_fst, existsUnique_zpow_near_of_one_lt', 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, 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, antitoneOn_inv_pos, 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, inv_lt_one_of_one_lt, 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, Set.inv_subset_div_right, Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_mem, 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, UniformOnFun.hasBasis_nhds_one_of_basis, GroupFilterBasis.inv, TannakaDuality.FiniteGroup.sumSMulInv_single_id, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Subgroup.inv_mem, UpperSemicontinuousOn.inv, 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, le_inv_of_le_inv₀, 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, PresentedGroup.to_group_eq_one_of_mem_closure, UniformFun.hasBasis_nhds_one, Set.zpow_eq_empty, one_le_zpow_of_nonpos₀, inv_mabs_le_inv, Positive.coe_inv, Subgroup.mem_normalizer_iff, mem_ball_iff_norm_inv_mul_lt, 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, one_lt_zpow_of_neg₀, 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, RatFunc.setOf_polynomial_valuation_lt_one_and_ne_zero_nonempty, 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, 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, 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', le_inv_of_le_inv, unitary.inv_mem, Function.Antiperiodic.const_smul, groupHomology.d₂₁_single_one_fst, GroupFilterBasis.N_one, Algebra.IsIntegral.inv_mem, Submonoid.IsMulPointed.eq_one_of_mem_of_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, MeasureTheory.Measure.instIsInvInvariantForallVolumeOfMeasurableInvOfSigmaFinite, leOnePart_eq_inv, TopologicalGroup.IsSES.inducedMeasure_lt_of_injOn, tendsto_div_comap_self, Representation.self_inv_apply, MonoidHom.eq_iff, IsUniformGroup.cauchy_iff_tendsto_swapped, Subgroup.zpowers_eq_bot, ball_eq_norm_inv_mul_lt, 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, MeasureTheory.IsFundamentalDomain.hasFundamentalDomain, iter_deriv_inv, Circle.exp_int_mul_two_pi, TendstoUniformly.fun_inv, PowerSeries.coeff_inv, inv_sub_inv', NormedGroup.tendsto_nhds_one, 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, one_lt_zpow_iff_right₀, 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, Rep.indResHomEquiv_apply, IsUnit.inv_mul_eq_one, Finset.smul_convolution_eq_convolution_inv_mul, inv_pow_sub₀, MonoidHom.transferSylow_eq_pow_aux, Set.apply_mulIndicator_symmDiff, 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, Right.self_lt_inv, 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, upperSemicontinuousWithinAt_inv_iff, 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, 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, Submonoid.IsMulSpanning.mem_or_inv_mem, NNRat.cast_inv, TendstoLocallyUniformly.inv₀_of_disjoint, Group.eq_one_iff_forall_finiteIndexNormalSubroup, singleton_mul_ball_one, smul_inv_le_iff_of_neg, leOnePart_eq_ite, Function.HasFiniteMulSupport.fun_inv, pinGroup.star_eq_inv, MulChar.inv_apply', Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_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, Filter.Tendsto.op_one_isBoundedUnder_le', 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, IsSelfAdjoint.inv₀_iff, Commute.conj_iff, SemiconjBy.inv_right_iff, pow_sub₀, smul_inv_lt_iff_of_neg, HasCompactSupport.div, 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, tendsto_norm_inv_mul_self_nhdsGE, 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, Valuation.restrict_le_one_iff, krullTopology_mem_nhds_one_iff_of_normal, CoxeterSystem.simple_mul_simple_self, Set.mulIndicator_diff, Set.inv_mem_center, Subgroup.closure_mul_image_eq_top, CommGroupWithZero.normalize_eq_one, MeasureTheory.IntegrableOn.comp_inv_Iic, 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, Subgroup.focalSubgroupOf.mk'_conj_eq, GroupTopology.continuous_inv', AdjoinRoot.minpoly_powerBasis_gen, AntivaryOn.inv, Finset.one_notMem_div_iff, dist_eq_norm_inv_mul', MulAut.inv_symm, ValuationSubring.mem_nonunits_iff, one_lt_leOnePart_iff, DilationEquiv.one_def, HasDerivAt.tendsto_slope_zero, sub_one_div_inv_le_two, inv_le_of_inv_le₀, Set.one_mem_div_iff, groupCohomology.map_inv_of_isMulCocycle₁, inverse_mfderiv_mul_left, Representation.leftRegular_norm_apply, totallyDisconnectedSpace_iff_connectedComponent_one, zpow_lt_one_iff_right_of_lt_one₀, 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, MeasureTheory.IsFundamentalDomain.fundamentalInterior, 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, SeminormedGroup.mem_closure_iff, 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, one_le_inv_of_le_one, 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', Representation.char_linHom, 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, oneLePart_of_le_one, groupHomology.isBoundary₀_iff, PowerSeries.C_inv, Subgroup.mem_inv_pointwise_smul_iff, one_div_mul_eq_div, CategoryTheory.ActionCategory.homOfPair.val, norm_le_norm_add_norm_inv_mul, 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, inv_le_of_inv_le', 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, Finset.small_pow_of_small_tripling, 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, zpow_le_one₀, LipschitzWith.norm_inv_mul_le, 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, one_lt_mabs_of_lt_one, Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply, rotation_symm, Rep.indResHomEquiv_symm_apply, 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, GroupCone.eq_one_of_mem_of_inv_mem', 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, Submonoid.mem_mulSupport, 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, Representation.char_orthonormal, TopologicalGroup.IsSES.mulExact, 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, Filter.HasBasis.uniformity_of_nhds_one_inv_mul, 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, Right.inv_lt_self, eq_inv_smul_iff₀, mulTSupport_inv, MeasureTheory.IsFundamentalDomain.preimage_of_equiv, monovary_inv_left₀, Left.inv_lt_self, groupHomology.single_one_mem_boundaries₁, Action.leftDual_ρ, Finset.pow_ssubset_pow_succ_of_pow_ne_closure, WithAbs.ofAbs_inv, 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, RatFunc.valuation_uniformizingPolynomial_lt_one, Subgroup.IsComplement.toRightFun_mul_inv_mem, Derivation.leibniz_div_const, MulAut.apply_inv_self, strictAntiOn_inv_pos, NumberField.ComplexEmbedding.IsConj.comp, mul_inv_eq_of_eq_mul, OrderIso.divLeft_symm_apply, one_le_mabs, IntermediateField.inv_mem, MulAction.stabilizerEquivStabilizer_inv, 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', MulArchimedeanClass.one_lt_of_one_lt_of_mk_lt, 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, le_one_of_one_le_inv, 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, lipschitzWith_iff_norm_inv_mul_le, 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, EMetric.preimage_smul_ball, inv_smul_le_iff_of_neg, Subgroup.closure_pow, one_div_neg_one_eq_neg_one, conj_eq_one_iff, fun_meromorphicOrderAt_inv, 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, 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, norm_sub_norm_le_norm_inv_mul, 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, NormedGroup.uniformity_basis_dist, 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, dist_norm_norm_le_norm_inv_mul, 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, Mathlib.Tactic.CancelDenoms.inv_subst, FDRep.scalar_product_char_eq_finrank_equivariant, CategoryTheory.PresheafOfGroups.OneCohomologyRelation.refl, spectrum.resolvent_isBigO_inv, GrpCat.FilteredColimits.colimit_one_eq, exists_lt_pow_of_lt_one, 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, Finset.inv_subset_div_right, RatFunc.single_inv, SignType.coe_zpow, closedBall_one_mul_singleton, TrivSqZeroExt.mul_inv_rev, one_lt_zpow_iff_right_of_lt_one₀, 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, MeasureTheory.IsFundamentalDomain.image_of_equiv, two_mul_le_add_mul_sq, zpow_lt_one_of_neg₀, Subgroup.IsComplement.equiv_snd_eq_inv_mul, gaussSum_mul_gaussSum_eq_card, edist_eq_enorm_inv_mul, Subgroup.le_pointwise_smul_iff₀, inv_eq_self_of_exponent_two, nhds_translation_inv_mul, Finset.add_one_le_card_pow, 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, Subgroup.conj_mem_sup_of_mem_inf_normalizer_of_mem_inf, Circle.coe_one, conjugate_commutatorElement, Equiv.inv_mulLeft, Int.neg_clog_inv_eq_log, hasFDerivAt_inv, map_mul_left_nhds_one, IsMulIndecomposable.apply_ne_one_iff_mem_closure, inv_lt_inv_iff, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, Differentiable.inv, inv_nonpos', tendsto_tprod_compl_atTop_one, Matrix.UnitaryGroup.transpose_inv_eq_map_star, Action.ρ_inv_self_apply, mulSupport_comp_inv_smul₀, MeasureTheory.IsFundamentalDomain.integral_eq_tsum', HahnSeries.cardSupp_inv_le, UpperSemicontinuous.inv, mabs_div_le_one, Set.injOn_iff_map_eq_one, Sylow.conj_eq_normalizer_conj_of_mem_centralizer, ValueDistribution.logCounting_inv, Function.Antiperiodic.const_inv_smul, NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff, exists_one_lt', unitary.star_eq_inv, MulAut.one_def, Representation.mem_linHom_invariants_iff_isIntertwining, 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, pow_two_semiclosed, IsArithFrobAt.conj, lt_inv_mul_of_mul_lt, inv_le_one_of_one_le₀, Function.Periodic.const_mul, norm_inv_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', ContinuousInv.of_nhds_one, CauSeq.lim_inv, Valued.toNormedField.one_le_norm_iff, zpow_le_one_of_nonpos₀, ArchimedeanClass.stdPart_inv, SemiconjBy.inv_symm_left_iff₀, rat_inv_continuous_lemma, mapClusterPt_inv_atTop_pow, Finset.mulETransformLeft_snd, LipschitzOnWith.norm_inv_mul_le_of_le, 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, eq_one_of_inv_eq', 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, Units.mk0_one, MeasureTheory.IsFundamentalDomain.smul_of_comm, 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, MeasureTheory.IntegrableOn.comp_inv_Iio, 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, LowerSemicontinuousAt.inv, 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', lowerSemicontinuouAt_inv_iff, mabs_le_one, Subgroup.coe_bot, RCLike.inv_I, div_le_one₀, GenContFract.IntFractPair.succ_nth_stream_eq_some_iff, TrivSqZeroExt.inv_inr, Subgroup.closure_mul_image_eq_top', 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, cfc_comp_inv, 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, 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, Bound.one_le_inv₀, uniformity_eq_comap_nhds_one_left, Set.one_mem_inv_mul_iff, inv_mul_eq_one, RCLike.inv_re, GroupConeClass.eq_one_of_mem_of_inv_mem, 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, lowerSemicontinuousOn_inv_iff, 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, inv_lt_of_inv_lt', 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', NormedGroup.nhds_basis_norm_lt, NonemptyInterval.inv_mem_inv, Commute.inv_right, inv_eq_iff_mul_eq_one, fderiv_inv', controlled_prod_of_mem_closure, 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, mem_closedBall_iff_norm_inv_mul_le', 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	7069 math, 2 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, HasDerivAt.fun_neg, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, MeasureTheory.MemLp.eLpNorm_indicator_le_of_meas, ValueDistribution.logCounting_zero, TestFunction.lineDerivCLM_apply_of_le, Quaternion.normSq_eq_zero, norm_eq_zero, norm_eq_of_mem_sphere, 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, LieHom.inl_apply, nsmul_two_semiclosed, ContinuousMap.toLp_inj, LieHom.coe_zero, Real.hasDerivAt_fourier, HurwitzZeta.isBigO_atTop_evenKernel_sub, Matrix.isTotallyUnimodular_iff, Function.HasFiniteSupport.fun_sub, 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, totallyDisconnectedSpace_iff_connectedComponent_zero, LowerSemicontinuousWithinAt.neg, 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, HahnEmbedding.Seed.baseEmbedding_pos, 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, SeparatingDual.eq_zero_of_forall_dual_eq_zero, Bundle.ContMDiffRiemannianMetric.isVonNBounded, HasDerivWithinAt.clm_comp, SummationFilter.instLeAtTopSymmetricIoo, MvPolynomial.coeff_neg, Asymptotics.isBigO_neg_left, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, HasDerivWithinAt.congr_of_mem, 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, Left.self_le_neg, Seminorm.absorbent_closedBall_zero, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, 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, HasFDerivWithinAt.continuousMultilinearMap_apply, 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, HasCompactSupport.convolution_integrand_bound_left, Set.preimage_add_right_zero', lt_neg, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, Finset.zero_mem_sub_iff, Matrix.linfty_opNorm_diagonal, SchwartzMap.neg_apply, NonemptyInterval.length_zero, HasDerivAt.const_sub, hasDerivWithinAt_add_const_iff, Hyperreal.infinite_neg, comap_gauge_nhds_zero_le, AddGroupFilterBasis.t2Space_iff, FormalMultilinearSeries.comp_partialSum, tendsto_birkhoffAverage_apply_sub_birkhoffAverage', HasDerivAtFilter.sum, 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, Asymptotics.IsBigOTVS.congr', AnalyticOnNhd.eq_zero_or_eq_zero_of_smul_eq_zero, sub_lt_zero, neg_le_self_iff, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Function.Surjective.isLieAbelian, Filter.IsBoundedUnder.smul_tendsto_zero, AddMonoidHom.exact_of_comp_of_mem_range, Matrix.norm_diagonal, CompactlySupportedContinuousMap.coe_sub, Real.hasFDerivAt_fourierChar_neg_bilinear_left, HasDerivWithinAt.Iio_of_Iic, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, hasStrictDerivAt_intCast, CategoryTheory.ShiftedHom.neg_comp, Action.neg_hom, EuclideanGeometry.reflection_orthogonal_vadd, isSMulRegular_iff_mem_nonZeroSMulDivisors, MeasureTheory.convolution_eq_right', List.alternatingSum_append, MeasureTheory.eLpNorm_smul_le_mul_eLpNorm, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, groupCohomology.mem_cocycles₂_def, Quaternion.im_add, sq_eq_one_iff, DenseRange.eq_zero_of_inner_left, 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, MeasureTheory.condExp_bilin_of_stronglyMeasurable_left, 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, Asymptotics.IsThetaTVS.trans_isBigOTVS, AddCircle.coe_eq_zero_iff, StrongDual.norm_extendRCLike, 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, 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, Bornology.IsVonNBounded.of_sub_left, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, Polynomial.resultant_X_add_C_right, taylorWithinEval_hasDerivAt_Ioo, ContDiffMapSupportedIn.seminorm_monoLM_eq, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, fderivWithin_fun_smul, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, abs_add_eq_add_abs_iff, round_neg_two_inv, HasDerivWithinAt.congr_mono, complexOfReal_hasDerivWithinAt, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, GradedRingHom.map_neg, AddCircle.liftIoc_zero_continuous, AffineMap.hasDerivAtFilter, IsSemireal.of_not_isSumSq_neg_one, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, InnerProductGeometry.angle_neg_self_of_nonzero, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, VectorField.lieBracketWithin_zero_left, HasCompactSupport.integral_Ioi_deriv_eq, Set.indicator_neg, Quaternion.star_smul, hasDerivAt_integral_of_dominated_loc_of_lip, 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, ContinuousAffineMap.fst_decompLinearEquiv, 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, MeasureTheory.Measure.instIsNegInvariantForallVolumeOfMeasurableNegOfSigmaFinite, FormalMultilinearSeries.radius_pi_eq_iInf, LowerSemicontinuous.neg, 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, AddSubmonoid.coe_support, HahnSeries.order_neg, lineDerivWithin_zero_of_not_lineDifferentiableWithinAt, Finset.image_neg, Differentiable.clm_comp, AddSubgroup.closure_singleton_zero, LieAlgebra.Orthogonal.mem_so, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, TestFunction.coe_neg, HahnSeries.SummableFamily.coe_neg, Homeomorph.vadd_symm_apply, dist_smul_le, Filter.neg_atTop, Complex.eq_const_of_exists_le, 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, Asymptotics.isLittleOTVS_one, Quaternion.rank_eq_four, TopModuleCat.hom_zero_apply, SymplecticGroup.coe_inv, meromorphicOrderAt_const, Summable.finite_support_of_discreteTopology, HasDerivAt.hasDerivWithinAt, 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, HasDerivWithinAt.complexToReal_fderiv', groupHomology.mapCycles₁_comp_apply, isCompactOperator_id, 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, MeasureTheory.integral_nonneg, AnalyticOnNhd.eqOn_zero_of_preconnected_of_eventuallyEq_zero_aux, IsAddUnit.neg_add_eq_iff_eq_add, WithLp.ofLp_neg, NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded, Asymptotics.isTheta_const_const_iff, ContMDiffCovariantDerivativeOn.affine_combination, ZMod.intCast_cast_neg, LinearMap.IsSymmetric.diagonalization_apply_self_apply, BoundedContinuousFunction.char_neg, Memℓp.const_smul, MeasureTheory.Lp.eq_zero_iff_ae_eq_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, HasFDerivWithinAt.clm_apply, hasFPowerSeriesOnBall_pi_iff, ContinuousAffineMap.neg_apply, Set.nonempty_image_addRight_neg_inter_iff, Continuous.convolution_integrand_fst, BoxIntegral.Integrable.neg, MDifferentiableOn.smul_const_section, 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, MeasureTheory.setIntegral_measure_zero, QuotientAddGroup.eq, LieModule.traceForm_eq_sum_finrank_nsmul', deriv_comp_const_sub, HasFDerivWithinAt.comp_hasDerivWithinAt_of_eq, 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, Bornology.IsVonNBounded.of_neg, 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, Asymptotics.IsLittleOTVS.tendsto_div, LinearEquiv.skewSwap_symm_apply, existsUnique_zsmul_near_of_pos', LucasLehmer.X.zero_fst, IsCyclotomicExtension.discr_odd_prime, Finset.expect_neg_distrib, MeasureTheory.L1.SimpleFunc.setToL1S_nonneg, AntivaryOn.sub_smul_sub_nonpos, zero_memℓp, addConj_zsmul, 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, TemperedDistribution.fourierMultiplierCLM_smul, NormedRing.inverse_add_norm_diff_nth_order, Orientation.eq_rotation_self_iff_angle_eq_zero, Function.Periodic.zsmul_sub_eq, ProbabilityTheory.integral_id_stdGaussian, derivWithin_fderivWithin, groupCohomology.map_one_of_isCocycle₁, Fintype.balance_zero, WithLp.isBoundedSMulSeminormedAddCommGroupToProd, derivWithin_natCast, Orientation.two_zsmul_oangle_neg_left, zero_mem_ℓp', CompactConvergenceCLM.hasBasis_nhds_zero_of_basis, Set.instTietzeExtensionUnitBall, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, IsometryEquiv.toRealLinearIsometryEquiv_apply, StrictConvexOn.neg, Int.ceil_neg, AddSubgroup.closure_nsmul, MultilinearMap.mkContinuousMultilinear_apply, addCommutatorElement_neg, CharTwo.neg_eq', MeasureTheory.integral_non_aestronglyMeasurable, StrongDual.norm_extendRCLike_bound, 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, PiLp.dist_single_same, 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, ContDiffMapSupportedIn.fderivLM_eq_of_scalars, CategoryTheory.ShortComplex.RightHomologyMapData.neg_φQ, RingEquiv.map_neg, ContinuousMapZero.aeStronglyMeasurable_mkD_of_uncurry, 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, fderiv_clm_comp, Filter.eventually_sub_nonneg, StrictMono.neg, mdifferentiableWithinAt_smul_const_section, 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, fderiv_continuousAlternatingMap_apply_const, MeasureTheory.SimpleFunc.setToSimpleFunc_nonneg, tangentConeAt_eq_biInter_closure, Matrix.transpose_eq_intCast, neg_add_lt_iff_lt_add, EuclideanGeometry.oangle_eq_angle_or_eq_neg_angle, ContinuousLinearMap.nhds_zero_eq_of_basis, derivWithin_comp_const_sub, DifferentiableAt.continuousAlternatingMapCompContinuousLinearMap, add_neg_eq_zero, posPart_eq_self, AffineMap.hasDerivWithinAt, HahnSeries.single_zero_ofScientific, TrivSqZeroExt.inv_inl, HasFPowerSeriesAt.eventually_hasSum, HasDerivAt.clm_apply, neg_le, IncidenceAlgebra.moebius_inversion_top, Set.iUnion_neg_vadd, ContDiffMapSupportedIn.seminorm_fderivLM_le, instSMulCommClass_sphere_sphere_sphere, AddCircle.coe_neg, DFinsupp.neLocus_neg_neg, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, edist_zero_left, ContDiffMapSupportedIn.seminorm_fderivLM_top, 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, VertexOperator.of_coeff_apply_coeff, WeierstrassCurve.Jacobian.addZ_of_Z_eq_zero_right, neg_strictConvexOn_iff, upperSemiContinuous_neg_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, LieAlgebra.SemiDirectSum.projr_inl_apply, 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, MeasureTheory.Integrable.toL1_zero, hasStrictFDerivAt_iff_isLittleOTVS, groupHomology.cyclesMap_comp_isoCycles₂_hom, ZMod.natCast_natAbs_valMinAbs, Asymptotics.IsLittleOTVS.eventually_smallSets, 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, TestFunction.monoCLM_eq_zero, TopologicalGroup.IsSES.integral_inducedMeasure, ZMod.wilsons_lemma, hasDerivAt_star_conj_iff, 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, QuaternionAlgebra.sub_re_self, Quaternion.imI_mul, hasDerivAtFilter_ofNat, groupHomology.mapCycles₁_comp_assoc, WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF, VectorField.mlieBracket_smul_left, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear_of_le_one, iteratedDerivWithin_const_zero, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, MeasureTheory.memLp_indicator_const, 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, Asymptotics.IsBigOTVS.add, IsNilpotent.exp_mul_exp_neg_self, HasFPowerSeriesOnBall.restrictScalars, smul_nonneg_iff_neg_imp_nonpos, QuaternionAlgebra.imK_intCast, Hyperreal.InfinitePos.neg, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux1, 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, CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor, Quaternion.imJ_one, CategoryTheory.Abelian.Ext.eq_zero_of_hasInjectiveDimensionLT, MeasureTheory.SimpleFunc.integral_neg, Finsupp.subtypeDomain_neg, Hyperreal.infinitesimal_def, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, HasStrictFDerivAt.comp_hasStrictDerivAt, ContinuousLinearMap.adjoint_id, ClosedSubmodule.inf_orthogonal, balanced_ball_zero, RingCone.eq_zero_of_mem_of_neg_mem', HasFDerivWithinAt.linear_multilinear_comp, iteratedFDerivWithin_succ_eq_comp_left, tendsto_birkhoffAverage_apply_sub_birkhoffAverage, contDiffOn_iff_continuousOn_differentiableOn, ZMod.valMinAbs_neg_of_ne_half, IsNilpotent.neg, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, linearIndependent_neg_iff, 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, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, ae_eq_zero_of_integral_contMDiff_smul_eq_zero, Matrix.det_succ_row, ContinuousAffineMap.fst_decompEquiv, Derivation.mapCoeffs_X, LinearIsometryEquiv.conjStarAlgEquiv_apply, toIcoMod_add_toIocMod_zero, Bundle.ContinuousLinearMap.vectorBundle, CochainComplex.HomComplex.Cochain.rightUnshift_neg, VectorField.mlieBracketWithin_const_smul_right, HasDerivWithinAt.sub, 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, Matrix.BlockTriangular.sub_iff_right, HasFDerivWithinAt.continuousMultilinearMapCompContinuousLinearMap, Polynomial.map_sub_roots_sprod_eq_prod_map_eval, Asymptotics.isLittleOTVS_prodMk_left, Filter.Tendsto.op_zero_isBoundedUnder_le, InnerProductGeometry.angle_smul_left_of_neg, Module.exists_smul_eq_zero_and_mk_eq, LieSubalgebra.bot_coe, Asymptotics.IsBigOTVS.comp_tendsto, nonneg_and_nonneg_or_nonpos_and_nonpos_of_smul_nonneg, neg_eq_self, Matrix.adjugate_fin_succ_eq_det_submatrix, MeasureTheory.lpNorm_fun_neg, IsSl2Triple.lie_lie_smul_f, minpoly_neg_splits, Orientation.two_zsmul_oangle_neg_self_right, Finset.weightedVSub_apply_const, IntervalIntegrable.zero, negPart_sub_posPart, hasDerivAt_of_hasDerivAt_of_ne, smul_unitClosedBall, TestFunction.continuous_iff_continuous_comp, groupHomology.mem_cycles₁_of_comp_eq_d₂₁, HasFiniteFPowerSeriesOnBall.sum, Quaternion.coe_pow, Module.FaithfullyFlat.rTensor_reflects_exact, Distribution.IsVanishingOn.smulLeftCLM, 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, 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, LieAlgebra.Basis.symm_h', 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, HasDerivWithinAt.sub_const, ContinuousLinearMap.norm_extendTo𝕜, addCommutatorElement_zero_left, DFinsupp.mk_neg, MeasureTheory.setToFun_undef, Matrix.exp_neg, LieModule.instIsTrivialOfSubsingleton', leftInverse_add_right_neg_add, Seminorm.continuousAt_zero_of_forall', HasFPowerSeriesAt.add, ContinuousAlternatingMap.curryLeft_smul, PiLp.norm_toLp_single, TrivSqZeroExt.instNormOneClass, MeasureTheory.SimpleFunc.setToSimpleFunc_zero', norm_le_norm_add_norm_neg_add, Matrix.neg_vecMul_neg, ContinuousLinearMap.hasBasis_nhds_zero, CategoryTheory.ShortComplex.ShortExact.d_eq_zero_of_f_eq_d_apply, Bornology.IsVonNBounded.of_add_right, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, HasFDerivAtFilter.isBigOTVS_sub, groupHomology.δ₀_apply, hasFDerivWithinAt_inv, groupCohomology.cocycles₂.d₂₃_apply, Seminorm.ball_mem_nhds, TemperedDistribution.fourierMultiplierCLM_compL_fourierMultiplierCLM, 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', QuotientAddGroup.equivIocMod_zero, ContinuousLinearMap.eq_adjoint_iff, Finset.addConst_neg_right, LocallyLipschitzOn.neg, ZeroHom.sub_comp, groupHomology.d₃₂_single_one_thd, MeasureTheory.integral_eq_zero_of_mul_right_eq_neg, 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, MeasureTheory.integrable_fun_neg_iff, MeasureTheory.AEFinStronglyMeasurable.sub, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, slope_pos_iff_of_le, WithAbs.ofAbs_neg, smul_nonpos_iff, LieSubalgebra.mem_bot, HasFPowerSeriesAt.comp, LieModule.trivial_iff_le_maximal_trivial, WithTop.untop₀_min, CochainComplex.HomComplex.Cochain.toSingleMk_neg, HasFDerivAt.continuousMultilinear_apply_const, ZeroAtInftyContinuousMap.instNormedStarGroup, Homeomorph.contDiff_unitBall, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, HasFDerivWithinAt.continuousAlternatingMap_apply, 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, MeasureTheory.IsAddFundamentalDomain.hasAddFundamentalDomain, 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', Asymptotics.IsLittleOTVS.trans_isThetaTVS, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, CochainComplex.HomComplex.Cochain.map_zero, LieModule.instIsTrivialSubtypeMemLieSubmoduleMaxTrivSubmodule, finrank_zero_iff_forall_zero, stereographic'_source, neg_eq_iff_add_eq_zero, isHausdorff_iff, exists_closed_nhds_zero_neg_eq_add_subset, WeierstrassCurve.Jacobian.negAddY_of_X_eq, Polynomial.roots_degree_eq_one, HasStrictDerivAt.clm_comp, LieModule.Cohomology.twoCochain_alt, PiLp.isBoundedSMulSeminormedAddCommGroupToPi, Quaternion.coe_commutes, MeasureTheory.weightedSMul_nonneg, CliffordAlgebra.toProd_ι_tmul_one, deriv_fun_inv'', Matrix.isTotallyUnimodular_iff_fintype, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, MeasureTheory.setIntegral_dirac, TopologicalGroup.IsSES.integral_pullback_invFun_apply, ContDiffMapSupportedIn.monoLM_apply, HasDerivWithinAt.Iic_of_Iio, ContinuousMultilinearMap.norm_smulRightL_le, Matrix.trace_eq_neg_charpoly_coeff, balancedCore_nonempty_iff, comap_norm_nhdsGT_zero, IsAlgClosed.instIsAlgClosure, derivWithin_clm_comp, ContinuousLinearMap.precompL_apply, Seminorm.closedBall_smul_ball, IsSelfAdjoint.adjoint_eq, RingCon.coe_neg, Rep.finsuppToCoinvariantsTensorFree_single, MeasureTheory.ae_eq_zero_of_forall_setIntegral_eq_of_sigmaFinite, Asymptotics.IsLittleOTVS.prodMk, FirstOrder.Field.realize_eqZero, curveIntegralFun_segment, HasDerivWithinAt.clm_apply, DifferentiableAt.hasDerivAt, HahnEmbedding.Partial.baseEmbedding_le_sSupFun, ball_zero_eq, TopologicalGroup.IsSES.pullback_def, OrderDual.instIsStrictOrderedModule, MeasureTheory.IntegrableOn.comp_neg_Iio, fderivWithin_zero, RKHS.kernel_apply, HasDerivAt.finCons, 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, HasDerivAtFilter.add, MeasureTheory.condExp_ae_eq_restrict_zero, curveIntegral_neg, MeasureTheory.Integrable.fun_neg, FormalMultilinearSeries.radius_le_smul, bddAbove_neg, AddSubgroup.coe_zero, CliffordAlgebra.contractRight_comm, MDifferentiable.clm_postcomp, IsRelPrime.neg_left, MonotoneOn.neg, ValueDistribution.logCounting_coe_eq_logCounting_sub_const_zero, AddMonoidAlgebra.ofCoeff_neg, 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, Asymptotics.IsLittleOTVS.insert, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_right, MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero', ContinuousLinearMap.isPositive_self_comp_adjoint, MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Ioi, 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, MeasureTheory.AEFinStronglyMeasurable.ae_eq_zero_of_forall_setIntegral_eq_zero, BoxIntegral.hasIntegral_zero, circleIntegral.integral_eq_zero_of_hasDerivWithinAt', 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, HasFDerivAt.continuousMultilinearMapCompContinuousLinearMap, HasFDerivAtFilter.neg, IsLocalExtr.neg, CochainComplex.HomComplex.CohomologyClass.mk_eq_zero_iff, HasFPowerSeriesOnBall.const_smul, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, upperSemicontinuousAt_neg_iff, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, DifferentiableAt.fun_neg, CategoryTheory.shift_shift_neg', 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, TopologicalGroup.IsSES.pushforward_def, VectorField.lieBracketWithin_zero_right, IsLinearTopology.hasBasis_open_submodule, AbsolutelyContinuousOnInterval.fun_neg, ContinuousAffineMap.decomp, HasStrictDerivAt.fun_sum, MeasureTheory.L1.SimpleFunc.setToL1S_neg, Char.card_pow_char_pow, LinearIsometryEquiv.adjoint_eq_symm, Matrix.neg_mulVec_neg, extDeriv_fun_smul, VectorField.mpullback_const_smul_apply, Quaternion.im_smul, ContinuousAlternatingMap.toAlternatingMap_curryLeft, neg_add_eq_sub, Right.neg_pos_iff, ProbabilityTheory.HasGaussianLaw.neg, abs_of_neg, Orientation.neg_rotation_neg_pi_div_two, Finset.prod_sub, StrictConvex.neg, skewAdjoint.mem_iff, Bornology.IsVonNBounded.image_multilinear', Quaternion.imI_fst_dualNumberEquiv, HasDerivAt.congr_of_eventuallyEq, 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, HasFPowerSeriesOnBall.tendsto_partialSum_prod, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, HahnSeries.le_orderTop_of_leadingCoeff_eq, LieAlgebra.derivedSeries_of_derivedLength_succ, LinearMap.BilinForm.nondegenerate_iff, MeasureTheory.ae_eq_zero_of_forall_inner, Finsupp.neLocus_eq_support_sub, ZModModule.char_nsmul_eq_zero, memℓp_zero_iff, Asymptotics.isBigO_neg_right, RootPairing.zero_notMem_range_coroot, ContDiffMapSupportedIn.fderivCLM_apply_of_gt, TestFunction.fderivCLM_apply_of_le, 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, UniformFun.hasBasis_nhds_zero_of_basis, AddChar.map_neg_eq_inv, TestFunction.lineDerivOpCLM_eq_lineDerivCLM, MDifferentiable.cle_arrowCongr, Asymptotics.IsLittleOTVS.neg_right, Finsupp.mapRange_neg', HahnEmbedding.Partial.truncLT_mem_range_extendFun, Wbtw.oangle₃₁₂_eq_zero, QuadraticMap.polar_neg_left, apply_abs_le_mul_of_one_le', HasFTaylorSeriesUpTo.fderiv_eq, 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, TestFunction.fderivCLM_ofSupportedIn, 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, fderiv_continuousAlternatingMapCompContinuousLinearMap, Quaternion.normSq_smul, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, MeasureTheory.IntegrableOn.fun_neg, add_add_neg_add_cancel, EuclideanGeometry.oangle_rev, MeasureTheory.Lp.finStronglyMeasurable, CauSeq.const_neg, Real.Angle.sign_two_nsmul_eq_neg_sign_iff, Affine.Simplex.centroid_weighted_vsub_eq_zero, mem_closedBall_iff_norm_neg_add_le, PiTensorProduct.mapL_smul, SchwartzMap.integral_sesq_fourier_eq, Right.nonneg_neg_iff, AddCircle.finite_torsion_of_isSMulRegular, CompactlySupportedContinuousMap.sub_apply, RCLike.I_mul_I, AddCommute.addConj_iff, HahnSeries.abs_lt_abs_of_orderTop_ofLex, MeasureTheory.integral_eq_zero_of_hasDerivAt_of_integrable, 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, Summable.tsum_pos, groupHomology.d₁₀ArrowIso_hom_left, MeasureTheory.SimpleFunc.setToSimpleFunc_zero_apply, AnalyticOnNhd.analyticOrderAt_eq_top_iff_eq_zero, WeierstrassCurve.Affine.polynomial_eq, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, AddChar.neg_apply, MeasureTheory.integral_nonpos, abs_pos_of_pos, toIcoMod_sub_self_eq_mul, upperSemicontinuousWithinAt_neg_iff, DualNumber.inv_eps, hasLineDerivWithinAt_zero, balancedHull_subset_convexHull_union_neg, Antivary.neg_right, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, Odd.neg_one_zpow, tendsto_setIntegral_peak_smul_of_integrableOn_of_tendsto_aux, 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, gauge_neg, AddMonoidAlgebra.coeff_sub, Representation.coinvariantsFinsuppLEquiv_apply, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, LinearPMap.graph_fst_eq_zero_snd, HasFDerivAtFilter.isThetaTVS_sub, abs_eq_max_neg, DenseRange.eq_zero_of_inner_right, 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, SchwartzMap.fourier_lineDerivOp_eq, Finsupp.sum_sub_index, HasFDerivWithinAt.isThetaTVS_sub, Manifold.IsImmersionAtOfComplement.map_target_subset_target, LinearMap.isBigOTVS_rev_comp, lowerSemicontinuousOn_neg_iff, WeierstrassCurve.ofJ0_Δ, WithZero.log_inv, TemperedDistribution.instLineDerivLeftSMulReal, meromorphicOrderAt_eq_top_iff, CategoryTheory.Abelian.Ext.mapExactFunctor_zero, le_neg_of_le_neg, MeasureTheory.VectorMeasure.coe_neg, MeasureTheory.Integrable.neg, groupHomology.d₂₁_single_inv_mul_ρ_add_single, LieModuleHom.mem_ker, toIocDiv_zsmul_sub_self, MeasureTheory.AEEqFun.coeFn_neg, Filter.EventuallyEq.ftaylorSeries, 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, Mathlib.Tactic.Ring.neg_congr, IsAddUnit.add_eq_zero_iff_eq_neg, Int.cast_nonneg_iff, Asymptotics.IsBigOTVS.neg_right, 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, HasDerivAt.add, Orientation.eq_zero_or_eq_zero_of_kahler_eq_zero, MeasureTheory.IsAddFundamentalDomain.mono, 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, NormedAddGroup.uniformity_basis_dist, even_neg_two, IsAddUnit.sub_add_left, norm_indicator_eq_indicator_norm, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable, IsOfFinOrder.eq_neg_one, Quaternion.inv_def, TrivSqZeroExt.fst_invOf, hasDerivAtFilter_zero, HasMFDerivAt.neg, NormedAddGroupHom.isCentralScalar, Function.HasFiniteSupport.fun_zsmul, 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, MeasureTheory.AEFinStronglyMeasurable.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, AddGroup.addConj_mem_addConjugatesOfSet, taylor_tendsto, MeasureTheory.Lp.edist_eq_eLpNorm_neg_add, MeasureTheory.IntegrableAtFilter.smul, MeasureTheory.lintegral_lintegral_add_neg, Finset.small_alternating_nsmul_of_small_tripling, FreeRing.coe_neg, HasFDerivAt.curveIntegral_segment_source, balancedCore_mem_nhds_zero, 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, iteratedFDeriv_comp_const_smul, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, WeierstrassCurve.Projective.negAddY_of_X_eq, MDifferentiableAt.clm_postcomp, Finsupp.mapRange_sub', fderiv_continuousAlternatingMap_apply, HurwitzZeta.completedSinZeta_neg, TemperedDistribution.laplacian_eq_fourierMultiplierCLM, eq_or_eq_neg_of_sq_eq_sq, Bornology.isVonNBounded_iff_absorbing_le, Set.neg_subset_sub_right, VectorField.mlieBracket_zero_right, curveIntegral_fun_zero, ContDiffMapSupportedIn.monoLM_eq_of_scalars, negPart_pos_iff, Bornology.isVonNBounded_covers, gradient_fun_const, iteratedFDeriv_zero, 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, posPart_of_nonpos, 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, addConj_add, 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, IsCovariantDerivativeOn.torsion_self, 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, TestFunction.limitCLM_apply, Orientation.oangle_eq_angle_or_eq_neg_angle, Matrix.blockDiagonal'_neg, EuclideanGeometry.oangle_eq_zero_iff_oangle_rev_eq_zero, hasFPowerSeriesOnBall_const, HasFDerivAt.clm_apply, 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, 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, AddGroup.eq_zero_iff_forall_finiteIndexNormalSubroup, Finset.Nonempty.zsmul, CategoryTheory.ShortComplex.Homotopy.neg_h₁, Quaternion.instNontrivial, ContinuousMultilinearMap.opNorm_smul_le, Module.Presentation.finsupp_R, Filter.HasBasis.isLittleOTVS_iff, HasFDerivAt.continuousAlternatingMap_apply, 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, SchwartzMap.compSubConstCLM_apply, IncidenceAlgebra.moebius_inversion_bot, AddMonoidAlgebra.neg_apply, RootPairing.neg_mem_range_coroot_iff, VectorFourier.fourierIntegral_iteratedFDeriv, HasMFDerivWithinAt.neg, InnerProductGeometry.angle_neg_right, TopologicalAddGroup.IsSES.pushforward_apply_apply, 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, gauge_eq_zero, fderiv_smul, tendsto_norm_neg_add_self_nhdsGE, InnerProductSpace.HarmonicContOnCl.neg, IsLinearTopology.hasBasis_submodule, HahnSeries.single_sub, stereographic_apply_neg, groupHomology.mapCycles₁_comp_i, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, LieAlgebra.Basis.linearIndepOn_root_baseSupp, 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, MeasureTheory.IsAddFundamentalDomain.vadd_of_comm, hasDerivAtFilter_iff_tendsto_slope, MeasureTheory.Integrable.smul, RootPairing.coroot_mem_or_neg_mem_closure_of_root, ContinuousLinearMap.norm_toSpanSingleton, Complex.lift_apply, Finset.univ_of_card_le_three, ContinuousLinearMap.rayleighQuotient_apply_zero, 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, HasDerivAtFilter.mono, 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, HasCompactSupport.hasDerivAt_convolution_right, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, LinearIndependent.pair_neg_left_iff, hasDerivWithinAt_neg, UpperSemicontinuousWithinAt.neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, HasDerivWithinAt.const_add, Quaternion.imJ_nnratCast, ArchimedeanClass.top_eq_mk_iff, Ring.choose_neg, LinearIndependent.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, HasFiniteFPowerSeriesOnBall.eq_partialSum, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF, Polynomial.Chebyshev.U_eval_neg_one, hasDerivAt_tsum_of_isPreconnected, 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, HahnEmbedding.Partial.lt_extend, Subring.neg_mem', Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, dist_eq_norm_neg_add', Finset.zero_mem_neg_add_iff, AffineMap.hasDerivAt_lineMap, IsometryEquiv.constVAdd_symm, fderivWithin_continuousAlternatingMap_apply_const_apply, range_stereographic_symm, IsRelPrime.neg_neg, LieAlgebra.Basis.coroot_eq_h', WeierstrassCurve.toCharNeTwoNF_s, Summable.tendsto_alternating_series_tsum, 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, toIcoMod_neg, Polynomial.nthRoots_two_one, PhragmenLindelof.eq_zero_on_vertical_strip, sign_sum, Quaternion.re_add_im, Real.Angle.abs_toReal_neg, HahnEmbedding.Partial.coeff_eq_of_mem, Seminorm.balanced_closedBall_zero, Finset.pluennecke_ruzsa_inequality_nsmul_add, Set.indicator_sub, PhragmenLindelof.eq_zero_on_quadrant_IV, LinearEquiv.mem_fixedSubmodule_transvection_iff, Set.zsmul_singleton, Function.locallyFinsuppWithin.posPart_add, CentroidHom.neg_apply, isOpenEmbedding_stereographic_symm, HahnEmbedding.Partial.extendFun_strictMono, 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, norm_sub_norm_le_norm_neg_add, toIocMod_neg, LipschitzOnWith.norm_neg_add_le, WithLp.zero_fst, IsCovariantDerivativeOn.smul_const, posPart_nonneg, Asymptotics.IsLittleOTVS.zero, MvPolynomial.eval₂_neg, MeasureTheory.quasiMeasurePreserving_neg_add_swap, CategoryTheory.CommSq.shortComplex_f, HasDerivAtFilter.fun_add, abs_neg_one_pow, neg_abs_le, PowerSeries.coeff_invOfUnit, SchwartzMap.smulLeftCLM_sum, MeasureTheory.integral_integral_indicator, AddSubgroup.mem_normalizer_iff, abs_eq, 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, Asymptotics.IsLittleOTVS.congr_left, 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, AddMonoidAlgebra.ofCoeff_sub, Matrix.linftyOpIsBoundedSMul, Hamming.nnnorm_eq_hammingNorm, ContDiffMapSupportedIn.monoCLM_eq_of_scalars, 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, MeasureTheory.setToFun_nonneg, addConj_neg, groupCohomology.map_inv_of_isCocycle₁, Orientation.rotation_symm, Homeomorph.coe_unitBall_apply_zero, multiplicity_neg, Submodule.adjoint_subtypeL, lp.coeFn_zero, IsCovariantDerivativeOn.torsion_antisymm, 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, HasDerivAtFilter.sub, Polynomial.smeval_neg_nat, IsAddKleinFour.neg_eq_self, ContinuousLinearMap.norm_smulRightL, AddSubgroup.Normal.addConj_mem', Quaternion.star_eq_two_re_sub, AffineMap.decomp', PiLp.nndist_toLp_single_same, Orientation.oangle_eq_zero_iff_sameRay, toIocDiv_neg', Submodule.reflection_orthogonalComplement_singleton_eq_neg, SModEq.neg, CategoryTheory.Preadditive.neg_iso_hom, MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero, ExistsContDiffBumpBase.u_neg, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, derivWithin.neg, HasFDerivWithinAt.fun_smul, abs_pos_of_neg, BoundedContinuousFunction.nnnorm_def, iteratedDeriv_const_sub, Module.preReflection_apply_self, MeasureTheory.convolution_def, WeierstrassCurve.Affine.slope_of_Y_ne', DirectLimit.neg_def, NonUnitalSubringClass.toNegMemClass, AddGrpCat.FilteredColimits.colimit_neg_mk_eq, 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, MonoidAlgebra.ofCoeff_sub, IsApproximateAddSubgroup.nsmul_inter_nsmul, UniformFun.hasBasis_nhds_zero, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MDifferentiableWithinAt.cle_arrowCongr, deriv.neg, MeasureTheory.L1.setToL1_nonneg, fourier_neg', HasFPowerSeriesWithinOnBall.prod, MDifferentiableWithinAt.clm_precomp, HasDerivAt.fun_add, HasDerivAt.neg, 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, HasDerivAt.star, 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', Bornology.IsVonNBounded.neg, HasFDerivWithinAt.neg, hasStrictDerivAt_const_add_iff, LinearMap.linearProjOfIsCompl_apply_right, MeasureTheory.setToFun_top_smul_measure, isBoundedBilinearMap_compMultilinear, Asymptotics.IsBigOTVS.fun_add, PiLp.nnnorm_toLp_single, AddMonoidHom.fiberEquivKer_apply, Quaternion.sub_re_self, neg_convexOn_iff, AddSubgroup.addConj_mem_sup_of_mem_inf_normalizer_of_mem_inf, 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, ContinuousAlternatingMap.continuous_compContinuousLinearMapCLM, norm_sub_le_mul_volume_of_norm_deriv_le_of_le, Function.support_intCast, MonoidAlgebra.coeff_neg, ball_zero_add_singleton, tsupport_neg, HasDerivAtFilter.const_smul, 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, ContDiffBump.convolution_tendsto_right, 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, AddCircle.liftIoc_zero_coe_apply, FormalMultilinearSeries.hasSum, 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, LieHom.coe_inl, Ioo_smul_sphere_zero, HasFPowerSeriesOnBall.sum, HasFDerivAt.comp_hasDerivAt, MeasureTheory.condExp_neg, Mathlib.Tactic.Abel.term_neg, IsCompactOperator.antilipschitz_of_not_hasEigenvalue, SeminormedAddGroup.mem_closure_iff, CochainComplex.HomComplex.Cochain.ofHom_neg, posPart_zero, WeierstrassCurve.b₄_of_char_three, SchwartzMap.smulLeftCLM_fun_neg, ClosedSubmodule.mulI_sup, PiLp.instNormSMulClass, ContMDiffOn.clm_precomp, CharP.orderOf_eq_two_iff, hasGradientAt_iff_isLittleO_nhds_zero, DifferentiableWithinAt.continuousAlternatingMapCompContinuousLinearMap, 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, NormedAddCommGroup.cauchySeq_iff, Manifold.IsImmersionAt.writtenInCharts, LieAlgebra.Basis.baseSupp_apply_smul_f, InnerProductSpace.rankOne_eq_zero, Distribution.delta_eq_zero_of_notMem, card_nsmul_eq_zero, le_neg, IsAddCyclic.card_nsmul_eq_zero_le, ContMDiffSection.coe_zero, fderivWithin_continuousMultilinear_apply_const_apply, LieSubmodule.lieSpan_eq_bot_iff, addCommutatorElement_self, 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, norm_neg_add, 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, hasDerivAt_of_hasDerivAt_of_ne', 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, IsSelfAdjoint.hasEigenvector_of_isMaxOn, Asymptotics.isBigOTVS_iff_isBigO, hasGradientAt_const, Bornology.isVonNBounded_sub_of_nonempty, ZMod.val_neg_of_ne_zero, LineDeriv.iteratedLineDerivOp_zero, MeasureTheory.ae_eq_zero_restrict_of_forall_setIntegral_eq_zero, groupHomology.toCycles_comp_isoCycles₁_hom_apply, fderivWithin_continuousAlternatingMapCompContinuousLinearMap, 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, IsOpen.forall_analyticOrderAt_eq_top_iff_eqOn_zero, HahnSeries.cardSuppLTSubfield_carrier, MeasureTheory.tendsto_integral_approxOn_of_measurable_of_range_subset, Module.FaithfullyFlat.rTensor_exact_iff_exact, max_zero_add_max_neg_zero_eq_abs_self, MvPowerSeries.coeff_inv, EuclideanGeometry.oangle_eq_zero_iff_wbtw, MeasureTheory.condExp_bilin_of_aestronglyMeasurable_left, PolynomialModule.single_apply, ContinuousLinearMap.fderivWithin_of_bilinear, LaurentSeries.derivative_iterate_coeff, QuadraticMap.toBilin_apply, HasFPowerSeriesOnBall.compContinuousLinearMap, StrongFEPair.hg₀, groupHomology.mapCycles₂_comp_i, MeasureTheory.Lp.dist_eq_eLpNorm_neg_add, 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, GeneralSchauderBasis.proj_apply_basis_mem, Pi.orthonormalBasis_apply, iteratedFDerivWithin_smul_const_apply, Finset.add_nonneg_card_nsmul, 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, Convex.second_derivative_within_at_symmetric, 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, ContDiffBump.normed_convolution_eq_right, exists_nhds_half_neg, 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, Asymptotics.IsLittleOTVS.fst, 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, tendsto_norm_neg_add_self_nhdsNE, 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, ContMDiffAt.const_smul_section, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, AddAction.vadd_fixedBy, isScalarTower_sphere_sphere_sphere, AdicCompletion.val_neg_apply, CategoryTheory.Preadditive.neg_comp_neg, AddSubmonoid.mem_support, IncidenceAlgebra.mu_ofDual, Mathlib.Tactic.Module.NF.sub_eq_eval₃, DFinsupp.neLocus_neg, MeasureTheory.hasFDerivAt_convolution_right_with_param, ContDiffBumpBase.support, ContMDiffSection.coe_smul, Quaternion.imI_neg, FiniteArchimedeanClass.liftOrderHom_mk, HahnSeries.leadingCoeff_sub, signedDist_zero, Asymptotics.IsLittleO.isLittleOTVS, MeasureTheory.hasFiniteIntegral_iff_edist, hasDerivAt_ofNat, SchwartzMap.postcompCLM_apply, Finset.vadd_finset_subset_iff, Orientation.oangle_eq_zero_iff_angle_eq_zero, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero, Asymptotics.IsLittleOTVS.neg_left, Function.Injective.isLieAbelian, IsUpperSet.neg, neg_add_neg_iff, DFinsupp.prod_neg_index, iteratedFDerivWithin_eq_equiv_comp, Asymptotics.IsTheta.eq_zero_iff, Function.HasTemperateGrowth.neg, PiLp.linearIndependent_single_of_ne_zero, DifferentiableAt.isBigOTVS_sub, MeasureTheory.measure_neg_vadd_symmDiff, nhds_basis_balanced, Matrix.mul_neg, IsRelPrime.neg_right, AlternatingMap.mkContinuousAlternating_norm_le, conjneg_neg, HasCompactSupport.hasFDerivAt_convolution_right, RingPreordering.mem_support, NormedAddGroupHom.mem_ker, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, 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, IsBoundedLinearMap.lim_zero_bounded_linear_map, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, MeasureTheory.eLpNorm'_neg, AddGrpCat.zero_apply, TemperedDistribution.fourierMultiplierCLM_fourierMultiplierCLM_apply, antivaryOn_neg_left, Quaternion.imI_nnratCast, HahnEmbedding.Partial.exists_sub_mem_ball, Asymptotics.isLittleO_neg_right, ZNum.cast_add, MeasureTheory.Measure.sub_mem_nhds_zero_of_addHaar_pos, ZNum.cast_lt, Finset.subConst_neg_right, Asymptotics.IsLittleOTVS.pi, 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, Left.neg_lt_self, Quaternion.imK_fst_dualNumberEquiv, ProbabilityTheory.Kernel.setIntegral_deterministic, tendsto_neg_nhdsLT_neg, ContDiffMapSupportedIn.zero_on_compl', Quaternion.imK_nnratCast, Bundle.Pretrivialization.continuousLinearMap.isLinear, 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, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, AddSubgroup.disjoint_def, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, star_neg, Orientation.oangle_rotation_oangle_right, Bornology.IsVonNBounded.image_multilinear, ProbabilityTheory.IndepFun.pdf_add_eq_lconvolution_pdf', EuclideanGeometry.oangle_add_cyc3, Set.image_neg_Ioi, ContDiffMapSupportedIn.seminorm_monoLM_le, ContinuousLinearMap.isBoundedBilinearMap, ContinuousMultilinearMap.hasBasis_nhds_zero, HurwitzZeta.hurwitzEvenFEPair_zero_symm, CompactlySupportedContinuousMap.integrable, WithCStarModule.neg_apply, HasFPowerSeriesWithinOnBall.sum, Nat.cast_card_eq_zero, MeasureTheory.IsAddFundamentalDomain.image_of_equiv, HasDerivAt.sub, 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, mdifferentiable_smul_const_section, HasStrictDerivAt.sum, fderivWithin_continuousMultilinear_apply_const, 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, ContinuousAffineMap.fst_decompAffineEquiv, 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, AddCommute.addCommutator_eq, 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, FiberBundle.exists_contMDiffOn_extend, TemperedDistribution.fourierMultiplierCLM_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, Set.indicator_neg', Function.HasTemperateGrowth.zero, WeierstrassCurve.VariableChange.inv_def, ContDiff.euclidean_dist, AddChar.neg_apply', MeasureTheory.integral_eq_zero_of_add_right_eq_neg, torusIntegral_neg, HasStrictDerivAt.smul, Mathlib.Tactic.Ring.neg_mul, 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, MeasureTheory.ae_eq_zero_of_forall_setIntegral_isCompact_eq_zero', hasDerivAt_tsum, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, MeasureTheory.measurePreserving_add_prod_neg_right, LinearIsometryEquiv.conjStarAlgEquiv_trans, IsLocalMin.neg, MeasureTheory.condExp_nonneg, FormalMultilinearSeries.radius_smul_eq, seminormFromBounded_neg, 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, controlled_sum_of_mem_closure_range, QuadraticAlgebra.star_mk, AlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, AddGroupFilterBasis.addConj, Matrix.BlockTriangular.add_iff_right, 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, HasDerivWithinAt.scomp_of_eq, Polynomial.coeff_sub_eq_neg_right_of_lt, neg_eq_zero, neg_pos_of_neg, MeasureTheory.aemeasurable_lconvolution, MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zero, Quaternion.norm_coe, HahnEmbedding.Partial.evalCoeff_eq_zero, neg_lt_neg, VertexOperator.ncoeff_apply, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, gauge_closure_zero, HahnSeries.mem_cardSuppLTAddSubgroup, MeasureTheory.SimpleFunc.memLp_approxOn_range, HahnSeries.order_abs, Convex.taylor_approx_two_segment, Pi.single_sub, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, ArithmeticFunction.dirichletInverseFun_apply_ne, 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, MeasureTheory.IntegrableOn.comp_neg_Iic, HurwitzZeta.cosZeta_eq, IsCompactOperator.hasEigenvalue_or_mem_resolventSet, NormedAddGroupHom.zero_apply, Left.self_lt_neg, ZMod.natAbs_valMinAbs_eq_natAbs_valMinAbs, ExistsContDiffBumpBase.w_support, VonNeumannAlgebra.coe_mk, 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, TemperedDistribution.fourierMultiplierCLM_const, Metric.preimage_add_left_closedEBall, infEDist_neg, PowerBasis.trace_gen_eq_nextCoeff_minpoly, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, monotone_iff_map_nonneg, AddMonoidAlgebra.supDegree_neg, CliffordAlgebra.mul_ι_mul_ι_mul_comm_of_isOrtho, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_integral_of_dominated_loc_of_lip', HasCompactSupport.neg, ConvexCone.coe_strictlyPositive, RKHS.kerFun_dense, VectorField.mpullback_const_smul, AddMonoidHom.neg_apply, arrowAddAction_vadd, InnerProductSpace.rankOne_def, HasDerivAt.smul_const, InnerProductSpace.Core.inner_self_eq_zero, Module.FaithfullyFlat.iff_exact_iff_rTensor_exact, HasDerivAtFilter.sub_const, slope_eq_zero_iff, smul_nonneg_of_nonpos_of_nonpos, ContinuousLinearMap.coe_flipₗᵢ', add_add_neg_cancel'_right, MeasureTheory.tendsto_measure_vadd_diff_isCompact_isClosed, groupHomology.π_comp_H2Iso_hom, AddCircle.coe_eq_zero_iff_of_mem_Ico, ContinuousLinearMap.adjointAux_inner_left, sub_sub_cancel_left, ZeroAtInftyContinuousMap.sub_apply, Filter.map_neg', IsHausdorff.haus, deriv_inv, MeasureTheory.tendsto_setToFun_approxOn_of_measurable_of_range_subset, 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, Asymptotics.IsLittleOTVS.exists_eventuallyLE_mul_ennreal, 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', PiLp.single_sub, neg_nonpos, add_eq_zero_iff_eq_neg, ball_sub_zero, Homeomorph.addRight_symm, Filter.EventuallyEq.ftaylorSeriesWithin, UniformSpace.Completion.norm_toComplL, Real.zero_at_infty_fourierIntegral, Mathlib.Tactic.Ring.neg_add, Bornology.IsVonNBounded.tendsto_smallSets_nhds, 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, VectorField.lieBracket_fmul_left, Asymptotics.IsBigOTVS.snd, 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, DifferentiableOn.clm_comp, groupHomology.mapCycles₂_comp, ContDiffMapSupportedIn.monoCLM_apply, AddGroupSeminormClass.map_neg_eq_map, ftaylorSeriesWithin_zero, 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, ae_eq_zero_of_integral_contDiff_smul_eq_zero, posPart_nonpos, ContinuousMultilinearMap.norm_map_init_le, addCommutatorElement_zero_right, SchwartzMap.compCLMOfAntilipschitz_apply, SchwartzMap.tsupport_lineDerivOp_subset, SchwartzMap.fourierInv_apply_eq, trace_eq_finrank_mul_minpoly_nextCoeff, SchwartzMap.smulRightCLM_apply_apply, HasDerivWithinAt.fun_neg, 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, HasDerivAt.complexToReal_fderiv', MeasureTheory.finStronglyMeasurable_of_measurable, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, 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, one_div_lt_neg_one, CategoryTheory.ShortComplex.opcyclesMap_neg, Asymptotics.IsBigOTVS.fun_symm, MeasureTheory.condExp_of_not_integrable, SchwartzMap.toTemperedDistributionCLM_apply_apply, Seminorm.continuousAt_zero', VectorField.mpullback_zero, Function.Antiperiodic.nat_mul_sub_eq, fderivWithin_fderivWithin_eq_of_eventuallyEq, ExistsContDiffBumpBase.u_exists, Function.support_fun_neg, AnalyticWithinAt.neg, StandardSubspace.IsCyclic, MeasureTheory.condExp_of_not_le, card_nsmul_eq_zero', PhragmenLindelof.eq_zero_on_horizontal_strip, curveIntegral_of_not_completeSpace, HasDerivWithinAt.Ici_of_Ioi, 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, InnerProductSpace.HarmonicOnNhd.neg, 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, zero_mem_addCommutatorSet, Asymptotics.isLittleOTVS_fun_neg_right, ftaylorSeries_fun_zero, MeasureTheory.condExp_indicator, cfcₙ_neg_id, ConvexCone.strictlyPositive_le_positive, HasDerivAt.add_const, VectorField.mpullbackWithin_neg, groupHomology.comp_d₁₀_eq, preNormEDS_neg, Quaternion.imI_im, Asymptotics.IsLittleOTVS.triangle, Orientation.oangle_sign_neg_left, Matrix.adjugate_fin_three_of, TemperedDistribution.smulLeftCLM_sub, fromTangentSpace_mfderiv_smul', HasDerivAt.of_isLittleO, HasFDerivWithinAt.continuousAlternatingMapCompContinuousLinearMap, groupHomology.H1π_comp_map_apply, MultilinearMap.map_update_neg, neg_one_pow_eq_pow_mod_two, FiniteField.isSquare_neg_two_iff, LieAlgebra.SemiDirectSum.zero_eq_mk, CategoryTheory.shift_equiv_triangle, SchwartzMap.postcompCLM_postcompCLM, 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, map_neg_add, HasDerivAt.sub_const, LieAlgebra.Basis.instIsLieAbelianSubtypeMemLieSubalgebraCartan, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, VectorField.mlieBracketWithin_zero_right, mem_closure_zero_iff_norm, NonarchAddGroupNormClass.eq_zero_of_map_eq_zero, CompactlySupportedContinuousMap.pullback_addMonoidHom_def, ContinuousLinearMap.aestronglyMeasurable_comp₂, continuousSMul_sphere_closedBall, AddGroupCone.eq_zero_of_mem_of_neg_mem', differentiableWithinAt_comp_sub, HurwitzZeta.completedHurwitzZetaEven_eq, lt_abs, SchwartzMap.smulLeftCLM_const, MeasureTheory.integral_eq_zero_of_mul_left_eq_neg, Finsupp.filter_sub, AddGroup.card_nsmul_eq_card_nsmul_card_univ, LieIdeal.isLieAbelian_iff, AddCon.mem_addSubgroup_iff, MDifferentiableAt.smul_section, MeasureTheory.setToFun_indicator_const, Asymptotics.IsBigOTVS.congr_left, 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, Asymptotics.IsLittleOTVS.smul_left, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Odd.neg_zpow, neg_cthickening, LieModule.Cohomology.mem_twoCochain_iff, Function.locallyFinsuppWithin.toClosedBall_divisor, Matrix.IsDiag.neg, hasDerivAt_of_tendstoUniformlyOn, Summable.alternating, ZMod.isSquare_neg_one_iff, Finsupp.sum_neg_index, IsMaxFilter.neg, Balanced.smul_mem_mono, Asymptotics.IsBigOTVS.proj, 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, VectorField.mlieBracketWithin_eq_zero_of_eq_zero, HasStrictDerivAt.scomp_of_eq, Equiv.addRight_symm_apply, DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap, IncidenceAlgebra.sum_Icc_mu_left, FiberBundle.mdifferentiableAt_extend, Bornology.IsVonNBounded.of_sub_right, linearDepOn_iff, ZMod.lift_castAddHom, Quaternion.im_coe, Finset.weightedVSubVSubWeights_apply_right, Matrix.inner_toEuclideanCLM, Ideal.Cotangent.smul_eq_zero_of_mem, WithLp.toLp_listSum, Quaternion.re_exp, closedBall_zero_sub_singleton, ContinuousLinearMap.norm_precompR_le, neg_rayOfNeZero, HasFPowerSeriesAt.eventually_eq_zero, MeasureTheory.Integrable.ae_eq_zero_of_forall_setIntegral_eq_zero, MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum', 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, TestFunction.lineDerivCLM_add, differentiableOn_fun_neg_iff, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, hasStrictDerivAt_finCons, PiTensorProduct.liftEquiv_apply, inner_neg_neg, Asymptotics.IsLittleOTVS.trans_isBigOTVS, WeakDual.isBounded_iff_isVonNBounded, HasDerivWithinAt.congr_of_eventuallyEq_of_mem, MeromorphicAt.eventuallyEq_zero_nhdsNE_of_eventuallyEq_zero_codiscreteWithin, HahnSeries.coe_cardSuppLTAddSubgroup, OpenPartialHomeomorph.univUnitBall_target, hasFTaylorSeriesUpTo_top_iff', Set.neg_smul, IsIsotypicOfType.linearEquiv_finsupp, fderivWithin_iteratedFDerivWithin, Convex.isLittleO_alternate_sum_square, 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, neg_le_self, 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, AnalyticOnNhd.eqOn_zero_of_preconnected_of_mem_closure, 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, Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange, RootPairing.isReduced_iff', Quaternion.normSq_eq_norm_mul_self, HasDerivAtFilter.star, hasDerivAt_inv, Function.HasFiniteSupport.sub, MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum', 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, ContinuousLinearMap.rayleighQuotient_apply_neg, 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, HasDerivAtFilter.scomp, CategoryTheory.Preadditive.instMonoNegHom, Submodule.orthogonal_orthogonal_eq_closure, MeasureTheory.condExpL1_neg, SnakeLemma.exact_δ_right, ContMDiffAt.neg, AnalyticOnNhd.preimage_zero_mem_codiscrete, ae_eq_zero_of_integral_smooth_smul_eq_zero, LieModule.mem_maxTrivSubmodule, Finset.zsmul_eq_empty, cfcₙ_comp_neg, 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, HasDerivWithinAt.fun_smul, LieAlgebra.IsKilling.apply_coroot_eq_cast, nnnorm_neg, ZMod.invDFT_def', TestFunction.lineDerivOp_eq_lineDerivCLM, InnerProductSpace.laplacianWithin_neg, contMDiffOn_continuousLinearMapCoordChange, fderivWithin_smul, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, 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, SchwartzMap.fourierMultiplierCLM_apply, HasCompactSupport.convolution, 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, dist_eq_norm_neg_add, Asymptotics.IsBigOTVS.trans_isLittleOTVS, 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, AnalyticOnNhd.eqOn_zero_of_preconnected_of_frequently_eq_zero, groupHomology.d₁₀ArrowIso_inv_right, MeasureTheory.integral_nonpos_of_ae, 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, IsCovariantDerivativeOn.leibniz, SchwartzMap.compSubConstCLM_zero, comap_addConj_nhds_zero, ContDiffMapSupportedIn.seminorm_top_le_iff, 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, 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, nhds_basis_Ioo_pos_of_pos, HahnEmbedding.Partial.eval_smul, HasDerivAt.clm_comp, LinearMap.coe_neg, HasFPowerSeriesOnBall.neg, MeasureTheory.SimpleFunc.setToSimpleFunc_neg, contMDiff_neg, MeasureTheory.continuous_integral_apply_neg_add, ContinuousLinearMap.uncurryBilinear_apply, WeierstrassCurve.Affine.addPolynomial_eq, HasFDerivWithinAt.smul_const, 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, IsOpen.smul_sphere, toIcoMod_zero_sub_comm, 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, AddGroup.residuallyFinite_iff_forall_finiteIndexNormalAddSubgroup, iteratedFDeriv_eq_equiv_comp, NumberField.Units.coe_neg_one, MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Iic, MvPolynomial.totalDegree_neg, negPart_eq_ite, Int.cast_nonneg, List.sum_range_sub, instContinuousNegElemSphereOfNat, differentiableAt_zero, PointedCone.coe_lineal, Filter.nonneg_sub_iff, Differentiable.continuousMultilinearMapCompContinuousLinearMap, 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, AlgebraicClosure.instIsAlgClosure, Submodule.neg_mem, MvPolynomial.support_neg, HasDerivAt.fun_const_smul, Finset.card_inter_vadd, WithLp.ofLp_eq_zero, HasDerivAt.fun_sub, Mathlib.Meta.NormNum.isInt_neg, UniformConvergenceCLM.hasBasis_nhds_zero_of_basis, 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, UpperSemicontinuousOn.neg, Set.Nonempty.zsmul, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, neg_sup, Finsupp.erase_neg, HasDerivAtFilter.add_const, 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, HasStrictDerivAt.congr_deriv, groupHomology.mapCycles₂_comp_apply, gauge_smul_left_of_nonneg, StrongFEPair.hf₀, HahnEmbedding.Partial.le_sSupFun, le_add_neg_iff_add_le, strictAnti_iff_map_neg, DifferentiableWithinAt.isBigOTVS_sub, uniformity_eq_comap_nhds_zero, LinearMap.isPositive_toContinuousLinearMap_iff, ValuationSubring.neg_mem, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', HasFPowerSeriesAt.apply_eq_zero, zero_mem_asymptoticCone, exists_neg_mem_iff_exists_mem, AddChar.inv_apply, MonoidHom.map_neg, Asymptotics.IsLittleOTVS.congr', 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, SeparatingDual.eq_zero_iff_forall_dual_eq_zero, CategoryTheory.ShortComplex.homologyMap_neg, ZMod.dft_apply, NormedAddGroup.tendsto_nhds_nhds, 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', HasDerivAt.const_smul, curveIntegral_fun_neg, Set.image_neg_Ioc, mapClusterPt_zero_atTop_nsmul, Asymptotics.isLittleO_principal, HasStrictDerivAt.add, HomologicalComplex.homotopyCofiber.d_fstX, CategoryTheory.unop_neg, squeeze_zero_norm', Int.cast_nonpos, CategoryTheory.Pretriangulated.Triangle.invRotate_mor₁, Projectivization.lift_mk, 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, HasFTaylorSeriesUpTo.tsupport_subset, neg_lt_zero, ZMod.natAbs_valMinAbs_neg, WeierstrassCurve.c₆_of_isCharTwoJEqZeroNF, SameRay.neg, CochainComplex.HomComplex.Cochain.leftShift_zero, Height.mulHeight_neg, IsLeftUniformAddGroup.uniformity_eq, intervalIntegral.deriv_integral_left, MeasureTheory.MemLp.toLp_neg, nndist_nnnorm_nnnorm_le_nnnorm_neg_add, CategoryTheory.ShortComplex.Homotopy.symm_h₃, WithZero.log_zpow, analyticOrderAt_neg, ContinuousLinearMap.sSup_sphere_eq_norm, WithTop.untop₀_max, toIcoMod_eq_sub, HVertexOperator.coeff_inj_iff, HasFPowerSeriesAt.fderiv_eq, HurwitzZeta.sinKernel_zero, FreeAbelianGroup.map_neg, NonUnitalSubring.val_neg, hasStrictFDerivAt_zero, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, HasDerivAtFilter.scomp_of_eq, RootPairing.coreflection_apply_self, HasDerivWithinAt.deriv_eq_zero, Set.image_neg_Ioo, AlgebraicGeometry.StructureSheaf.const_zero, Polynomial.comp_neg_X_leadingCoeff_eq, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, HasDerivAt.scomp_hasDerivWithinAt_of_eq, lp.norm_eq_card_dsupport, AddCommute.neg_add_eq_neg_add_iff_of_isAddUnit, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, VectorField.mlieBracketWithin_smul_left, ContinuousLinearMap.isometry_iff_adjoint_comp_self, QuotientAddGroup.rightRel_apply, IsAddUnit.add_add_sub, continuousMultilinearCurryFin0_apply, Metric.preimage_add_left_ball, Function.zero_of_even_and_odd, sub_pow, HurwitzZeta.completedCosZeta₀_zero, HurwitzZeta.oddKernel_zero, mem_sphere_zero_iff_norm, MeasureTheory.integrableOn_fun_neg_iff, 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, LinearMap.injective_range_liftQ_of_exact, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, homeomorphUnitSphereProd_symm_apply_coe, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, Orientation.rightAngleRotation_rightAngleRotation, HasDerivAt.comp_const_sub, groupHomology.H2π_eq_iff, QuotientAddGroup.nhds_zero_hasBasis, ContinuousLinearMap.opNorm_extend_le, Submodule.orthogonal_closure, intervalIntegral.integral_non_aestronglyMeasurable, HasDerivWithinAt.add, 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, HasStrictFDerivAt.continuousMultilinear_apply_const, Matrix.coeff_charpolyRev_eq_neg_trace, CategoryTheory.ShiftedHom.comp_neg, WithLp.nndist_toLp_snd, groupHomology.H1AddEquivOfIsTrivial_single, Asymptotics.IsLittleOTVS.sup, LaurentSeries.hasseDeriv_comp_coeff, ContDiffMapSupportedIn.monoLM_eq_zero, 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, Mathlib.Tactic.Module.NF.sub_eq_eval₁, 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, Filter.Tendsto.op_zero_isBoundedUnder_le', HahnEmbedding.Seed.coeff_baseEmbedding, MeasureTheory.MemLp.exists_hasCompactSupport_integral_rpow_sub_le, CovariantDerivative.zero, 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, mem_ball_iff_norm_neg_add_lt, AddSubgroup.neg_mem_iff, ZNum.cast_inj, AffineIsometryEquiv.constVAdd_zero, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, SlashAction.neg_slash, Asymptotics.IsBigOTVS.prodMk, Equiv.subLeft_symm_apply, MeasureTheory.setAverage_sub_setAverage, IsCauSeq.neg, MeasureTheory.absolutelyContinuous_neg, MvPowerSeries.coeff_inv_aux, nnnorm_indicator_eq_indicator_nnnorm, neg_mem_nhds_zero, 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, PiLp.nndist_single_same, Filter.neg_nhdsLT, neg_dotProduct, AddSubgroup.mem_normalizer_iff'', MeasureTheory.Measure.toSphere_apply', posPart_pos_iff, TemperedDistribution.instLineDerivSMulReal, intervalIntegral.integral_symm, iteratedDeriv_comp_neg, MeromorphicOn.neg, WeierstrassCurve.Affine.evalEval_polynomial_zero, MeasureTheory.setIntegral_empty, DFinsupp.erase_sub, 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, iteratedFDerivWithin_zero, 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, TopologicalGroup.IsSES.integrate_apply, tendsto_integral_exp_smul_cocompact_of_inner_product, Quaternion.mul_star_eq_coe, Set.apply_indicator_symmDiff, LieModule.isFaithful_iff', AddGroupFilterBasis.zero', RootPairing.root_eq_neg_iff, HasFTaylorSeriesUpToOn.fderivWithin, uniformity_eq_comap_nhds_zero_left, LieAlgebra.IsKilling.isLieAbelian_iff_subsingleton, groupHomology.eq_d₂₁_comp_inv_assoc, continuousMultilinearCurryFin0_symm_apply_apply, HasDerivWithinAt.fun_const_smul, ContinuousLinearMap.ker_self_comp_adjoint, 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, AddAction.stabilizerEquivStabilizer_neg, 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, VectorField.mlieBracketWithin_smul_right, AddSubgroup.nsmul_exponent_eq_zero, sub_nsmul_neg, groupHomology.single_isCycle₁_iff, HasFDerivAt.continuousAlternatingMap_apply_const, StrictAnti.neg, WithVal.toVal_neg, Finset.smul_finset_neg, PiTensorProduct.injectiveSeminorm_apply, Homeomorph.unitBall_apply_coe, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, ContinuousLinearMap.isBoundedLinearMap_comp_left, 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, mem_closedBall_iff_norm_neg_add_le', AntitoneOn.slope_nonpos, TestFunction.lineDerivCLM_eq_fderivCLM, TopologicalAddGroup.IsSES.integrate_mono, Asymptotics.isLittleOTVS_map, Bornology.IsVonNBounded.sub, IccLeftChart_extend_bot, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, 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, MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc, smul_nonpos_iff_neg_imp_nonneg, HasStrictDerivAt.const_add, FreeAbelianGroup.neg_seq, fderivWithin_continuousMultilinearMapCompContinuousLinearMap, ZMod.val_neg_one, Quaternion.normSq_add, NormedAddGroupHom.coe_neg, AddGroupFilterBasis.nhds_zero_hasBasis, LinearMap.hasEigenvalue_zero_tfae, mem_ball_iff_norm_neg_add_lt', Bundle.Trivialization.zeroSection, hasFDerivAt_single, PolynomialModule.smul_apply, AddMonoidAlgebra.mul_apply_left, Finset.zero_notMem_sub_iff, iteratedDerivWithin_neg, ContMDiffAt.clm_precomp, CategoryTheory.ShortComplex.ShortExact.comp_extClass, TestFunction.lineDerivCLM_apply, 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, 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, Asymptotics.IsBigOTVS.symm, 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, toIcoDiv_zsmul_sub_self, 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, Function.Antiperiodic.zsmul_sub_eq, hasFiniteFPowerSeriesAt_const, inv_eq_self₀, odd_neg, MonoidAlgebra.ofCoeff_neg, ContinuousAlternatingMap.hasBasis_nhds_zero, lie_skew, abs_nonpos_iff, Bornology.isBounded_iff_isVonNBounded, neg_of_neg_pos, HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', TendstoUniformly.fun_neg, translate_eq_domAddActMk_vadd, LipschitzWith.norm_neg_add_le_of_le, stereographic_neg_apply, LineDeriv.lineDerivOp_zero, RootPairing.pairingIn_reflectionPerm_self_right, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, continuousAt_gauge_zero, MeasureTheory.withDensityᵥ_neg, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Real.fourierInv_eq_fourier_comp_neg, ContinuousMultilinearMap.uncurryRight_apply, LinearEquiv.transvection.symm_eq, CharacterModule.eq_zero_of_ofSpanSingleton_apply_self, TestFunction.coe_zero, LieDerivation.neg_apply, HasDerivAt.comp_const_add, 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', HasDerivWithinAt.scomp_hasDerivAt_of_eq, isScalarTower_sphere_sphere_closedBall, Function.HasFiniteSupport.neg, ContinuousLinearMap.isVonNBounded_image2_apply, 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, addConj_injective, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF, MeasureTheory.condExp_nonpos, MeromorphicAt.fun_neg, modelWithCornersEuclideanHalfSpace_zero, abs_choice, vadd_mem_nhds_self, groupHomology.mapCycles₂_id_comp_assoc, negPart_def, HasDerivWithinAt.neg, le_neg_self_iff, integral_bilinear_hasLineDerivAt_right_eq_neg_left_of_integrable_aux2, MeasureTheory.setToFun_measure_zero', ContinuousLinearMap.norm_extendTo𝕜'_bound, groupHomology.π_comp_H1Iso_hom_apply, MeasureTheory.integral_neg', nndist_eq_nnnorm_neg_add, ZMod.dft_comp_neg, ball_eq_norm_neg_add_lt, 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, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, WithCStarModule.norm_single, ProbabilityTheory.HasGaussianLaw.fun_neg, HasStrictDerivAt.sub, groupHomology.single_isCycle₂_iff, LieModuleHom.zero_apply, CochainComplex.HomComplex.Cocycle.δ_eq_zero, ArchimedeanClass.stdPart_neg, MeasureTheory.SimpleFunc.setToSimpleFunc_smul, Matrix.det_succ_column, HasFiniteFPowerSeriesOnBall.neg, derivWithin_intCast, ContinuousMapZero.norm_def, DFinsupp.filter_sub, HasDerivWithinAt.Ioo_of_Ioi, 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, Asymptotics.IsBigOTVS.congr_right, 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, Asymptotics.IsThetaTVS.isBigOTVS, 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, FormalMultilinearSeries.le_comp_radius_of_summable, 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, TopologicalGroup.IsSES.pushforward_apply_apply, 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, TestFunction.instLineDerivLeftSMulRealTopENat, MeasureTheory.Measure.map_add_right_neg_eq_self, groupHomology.mapCycles₁_id_comp, Finset.addETransformLeft_zero, HasFDerivAt.comp_hasDerivWithinAt, HasFPowerSeriesOnBall.tendstoUniformlyOn', HasFPowerSeriesWithinOnBall.const_smul, HVertexOperator.coeff_inj, PolynomialModule.smul_single_apply, sub_zsmul, Asymptotics.IsLittleOTVS.comp_tendsto, isScalarTower_sphere_sphere_ball, Orientation.oangle_neg_self_right, Mathlib.Tactic.Module.NF.neg_eq_eval, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, Distribution.IsVanishingOn.iteratedLineDerivOp, AddCommute.addConj, AddGroupSeminorm.apply_one, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, TestFunction.monoCLM_eq_of_scalars, UniformConvergenceCLM.isVonNBounded_image2_apply, HurwitzZeta.oddKernel_neg, MeasureTheory.sub_nonneg_ae, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, HasStrictDerivAt.of_notMem_tsupport, fderiv_continuousMultilinear_apply_const_apply, Set.zsmul_eq_empty, Asymptotics.IsLittleOTVS.congr, 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, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, HurwitzZeta.evenKernel_neg, Quaternion.re_one, List.sum_neg, deriv_inv'', LieAlgebra.of_zero, NormedAddGroup.tendsto_nhds_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, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, instContinuousNegElemClosedBallOfNat, MeasureTheory.IsAddFundamentalDomain.mk', neg_nonneg, abs_cases, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Finsupp.neLocus_self_sub_left, LinearPMap.map_neg, NonarchAddGroupSeminorm.apply_one, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, 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, Int.coe_negOnePow, WeierstrassCurve.Jacobian.addY_of_Z_eq_zero_right, negPart_of_nonneg, dist_neg, WeierstrassCurve.Projective.add_of_Z_eq_zero_right, IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrder, ContinuousNeg.of_nhds_zero, FreeLieAlgebra.Rel.neg, iteratedDerivWithin_const, LipschitzWith.norm_neg_add_le, HasStrictFDerivAt.continuousAlternatingMap_apply, Asymptotics.isBigOWith_zero', curveIntegral_refl, ContinuousLinearEquiv.map_neg, MeasureTheory.Pi.isNegInvariant_volume, groupHomology.eq_d₁₀_comp_inv, WithTop.LinearOrderedAddCommGroup.coe_neg, HasDerivAtFilter.congr_of_eventuallyEq, HasStrictDerivAt.complexToReal_fderiv', Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetric, constFormalMultilinearSeries_apply_of_nonzero, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', 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, DifferentiableWithinAt.clm_comp, AddMonoidAlgebra.single_mul_apply, groupHomology.isoShortComplexH1_inv, MDifferentiableOn.cle_arrowCongr, PiLp.normSMulClassSeminormedAddCommGroupToPi, AddSubgroup.coe_bot, differentiableAt_fun_neg_iff, Asymptotics.IsLittleO.trans_tendsto, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, MultilinearMap.mkContinuousMultilinear_norm_le', addConj_nsmul, add_neg_le_add_neg_iff, WithCStarModule.inner_single_right, AddSubgroup.mem_centralizer_iff_addCommutator_eq_zero, 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, tendsto_gauge_nhds_zero_nhdsGE, IsLinearTopology.hasBasis_submodule', QuaternionAlgebra.imI_ofNat, Function.Antiperiodic.add_nat_mul_eq, Filter.tendsto_comp_neg_atBot_iff, frobenius_neg, EuclideanGeometry.oangle_self_right, Submodule.det_reflection, round_eq_zero_iff, HasStrictDerivAt.const_smul, deriv_neg', HasDerivAt.fun_sum, deriv_zero_of_frequently_const, Orientation.kahler_rotation_left', fderivWithin_neg, hasFDerivAtFilter_iff_isLittleOTVS, AffineMap.toConstProdLinearMap_apply, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, Quaternion.self_add_star', lineDeriv_zero, neg_nonpos_of_nonneg, derivWithin_zero_of_not_accPt, second_derivative_symmetric, ContinuousAlternatingMap.curryLeft_same, IsLocalizedModule.mk'_neg, ContinuousMultilinearMap.curryRight_apply, Homotopy.symm_hom, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, Distribution.dsupport_smulLeftCLM_subset, 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, TopologicalAddGroup.IsSES.integral_pullback_invFun_apply, 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, HasFDerivAt.comp_hasDerivWithinAt_of_eq, 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, 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, Right.neg_le_self, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, MeasureTheory.IntegrableOn.comp_neg_Ioi, ContinuousLinearMap.norm_extendTo𝕜', neg_neg_sub_neg, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, MeasureTheory.Lp.simpleFunc.toLp_zero, MulRingNormClass.eq_zero_of_map_eq_zero, tendsto_addConj_nhds_zero, LieModule.instIsTrivialOfSubsingleton, Asymptotics.IsLittleOTVS.fun_symm, HasDerivAtFilter.const_add, groupCohomology.H1π_eq_zero_iff, CharacterModule.eq_zero_of_character_apply, HasDerivWithinAt.of_notMem_tsupport, FiberBundle.contMDiffAt_extend', not_linearIndependent_iff_finsupp, MDifferentiableAt.clm_precomp, Set.image_add_left, Quaternion.summable_coe, ContDiffMapSupportedIn.postcompCLM_apply, SchwartzMap.compSubConstCLM_comp, HasDerivWithinAt.mono_of_mem_nhdsWithin, 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, ContinuousAlternatingMap.restrictScalarsLI_apply, Ideal.toCotangent_eq_zero, Complex.UnitDisc.mk_neg, MeasureTheory.Measure.neg.instIsAddRightInvariant, QuaternionAlgebra.Basis.k_mul_k, Ideal.span_insert_neg, Asymptotics.IsTheta.isThetaTVS, MeasureTheory.Lp.coeFn_nonneg, lowerSemicontinuouAt_neg_iff, Set.neg_Ioc, strictAnti_iff_map_pos, groupHomology.d₃₂_single_one_fst, HasFPowerSeriesOnBall.tendsto_partialSum, dist_zero_left, inhomogeneousCochains.d_hom_apply, MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt, ZMod.dft_dft, Quaternion.imJ_snd_dualNumberEquiv, HasDerivWithinAt.Ioi_of_Ioo, IsSl2Triple.HasPrimitiveVectorWith.lie_e, MeasureTheory.Martingale.neg, DifferentiableOn.continuousMultilinearMapCompContinuousLinearMap, Quaternion.star_im, gauge_unit_ball, Filter.Tendsto.zero_smul_isBoundedUnder_le, MeasureTheory.setToFun_non_aestronglyMeasurable, CategoryTheory.Abelian.Ext.zero_hom, sameRay_neg_swap, InnerProductSpace.HarmonicAt.neg, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, neg_one_eq_invOf_mul_add_invOf_mul_iff, HasFPowerSeriesWithinAt.prod, Matrix.frobenius_nnnorm_diagonal, ZMod.isSquare_neg_one_of_dvd, Set.neg_smul_set, Matrix.blockDiagonal_sub, Quaternion.re_natCast, singleton_add_closedBall_zero, ZMod.neg_eq_self_iff, ContinuousLinearMap.adjoint_comp_self_injective_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, ContDiffMapSupportedIn.fderivCLM_eq_of_scalars, MeasureTheory.Submartingale.neg, groupHomology.d₂₁_comp_d₁₀, LinearOrderedAddCommGroupWithTop.sub_eq_zero, Asymptotics.IsThetaTVS.symm, 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, PiLp.single_eq_zero_iff, 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, AddCircle.coe_eq_zero_of_pos_iff, Function.locallyFinsuppWithin.negPart_add, OrderDual.instSMulPosMono, PiLp.nnnorm_single, 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, lp.coeFn_smul, 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, MeasureTheory.condExpIndSMul_nonneg, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, HasFPowerSeriesAt.hasFDerivAt, FormalMultilinearSeries.comp_coeff_zero', LipschitzWith.neg, WeierstrassCurve.Affine.CoordinateRing.C_addPolynomial_slope, Bornology.IsVonNBounded.extend_scalars, antivary_neg_left, Asymptotics.IsBigOTVS.congr, Int.cast_list_sum, IsAddQuotientCoveringMap.disjoint, HahnSeries.archimedeanClassOrderIsoWithTop_apply, IsMaxOn.neg, Module.length_finsupp, 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, MeasureTheory.integral_nonneg_of_ae, PiLp.single_neg, 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, toIocMod_eq_sub, ContinuousLinearMap.self_comp_adjoint_injective_iff, groupHomology.cyclesOfIsCycle₁_coe, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff_of_orderTop_ofLex, DFinsupp.sum_neg, addConj_eq_zero_iff, IsPrimitiveRoot.norm_pow_sub_one_two, ZMod.lift_coe, Hyperreal.lt_neg_of_pos_of_infinitesimal, Quaternion.imK_ratCast, HasStrictDerivAt.scomp, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_coprime, HasFPowerSeriesWithinAt.restrictScalars, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, Finsupp.prod_neg_index, fderiv_continuousAlternatingMap_apply_apply, IsAddUnit.eq_neg_add_iff_add_eq, SchwartzMap.hasDerivAt, AddValuation.map_neg, HasDerivWithinAt.fun_sub, 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, HasStrictFDerivAt.comp_hasStrictDerivAt_of_eq, Units.neg_smul, HasFDerivWithinAt.clm_comp, IsAddUnit.sub_add_right, FreeAddGroup.sum_mk, lineDeriv_zero_of_not_lineDifferentiableAt, Multiset.sum_map_neg', jacobiSum_nontrivial_inv, isBoundedBilinearMap_apply, PiTensorProduct.projectiveSeminorm_zero, FormalMultilinearSeries.analyticOnNhd, WithConv.toConv_neg, Mathlib.Tactic.RingNF.add_neg, abs_zero, ContMDiffMap.coe_neg, exteriorPower.presentation_relation, AddCircle.liftIco_zero_coe_apply, 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, fromTangentSpace_mfderiv_smul, 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, TestFunction.mkCLM_apply, SchauderBasis.proj_apply_basis_mem, CategoryTheory.ShortComplex.zero_apply, singleton_sub_ball_zero, Quaternion.tsum_coe, Summable.tendsto_cofinite_zero, TrivSqZeroExt.norm_inl, Subalgebra.coe_neg, lp.instIsCentralScalarSubtypePreLpMemAddSubgroup, Antitone.tendsto_le_alternating_series, AddSubgroup.normal_addSubgroupOf_iff, hasDerivAtFilter_finCons', Asymptotics.IsBigOTVS.eventually_smallSets, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, Fintype.expect_balance, RootPairing.reflection_apply_self, MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero, ContinuousMap.toLp_injective, groupHomology.toCycles_comp_isoCycles₂_hom_apply, TestFunction.fderivCLM_eq_of_scalars, AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_iSupIndep, 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, VectorField.mpullbackWithin_const_smul_apply, 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, TestFunction.lineDerivCLM_eq_of_scalars, Wbtw.oangle₂₃₁_eq_zero, Finset.centerMass_empty, CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v, uniformity_eq_comap_neg_add_nhds_zero, fderiv_fun_neg, isCompactOperator_of_locallyCompactSpace_rng, 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, HasDerivWithinAt.scomp, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, MeasureTheory.MemLp.neg, Asymptotics.IsLittleOTVS.snd, 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, HahnEmbedding.Partial.coeff_eq_zero_of_mem, abs_of_nonpos, InnerProductSpace.toMatrix_rankOne, HasFDerivWithinAt.continuousMultilinear_apply_const, Bornology.IsVonNBounded.vadd, CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_cancel_inv_app, nnnorm_eq_zero, dist_norm_norm_le_norm_neg_add, controlled_sum_of_mem_closure, 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, 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, UnitAddTorus.coe_measurableEquivPiIoc_apply, HasStrictDerivAt.fun_const_smul, AddAction.toPerm_symm_apply, Sbtw.oangle₃₁₂_eq_zero, Hyperreal.not_infinite_neg, HasDerivWithinAt.congr_deriv, Quaternion.im_nnratCast, 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, pos_of_neg_neg, 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, IsIntegralCurveAt.hasDerivAt, MeasureTheory.Supermartingale.neg, Orientation.two_zsmul_oangle_neg_self_left, MeasureTheory.conv_withDensity_eq_lconvolution, Representation.Coinvariants.mk_eq_zero, tendsto_gauge_nhds_zero, MeasureTheory.SimpleFunc.integrable_approxOn_range, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero_aux, nsmul_zero_sub, Asymptotics.IsBigOTVS.rfl, neg_le_of_neg_le, 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, groupHomology.mem_cycles₁_of_mem_boundaries₁, 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, HasFDerivWithinAt.comp_hasDerivWithinAt, 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, fderivWithin_continuousAlternatingMap_apply_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, FormalMultilinearSeries.leftInv_comp, deriv_one, WithLp.neg_fst, Set.image_add_left', MeasureTheory.convolution_neg_of_neg_eq, DFinsupp.neLocus_eq_support_sub, addCommutatorElement_eq_zero_iff_add_comm, QuaternionAlgebra.im_coe, HasFPowerSeriesAt.const_smul, 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, LieAlgebra.SemiDirectSum.inl_eq_mk, ContDiffMapSupportedIn.seminorm_apply, tsupport_iteratedFDeriv_subset, NormedAddCommGroup.tendsto_nhds_zero, deriv_of_notMem_tsupport, QuaternionAlgebra.imK_ofNat, LieAlgebra.IsKilling.coroot_neg, Real.zero_at_infty_fourier, logDeriv_inv, HasFDerivAt.isThetaTVS_sub, DifferentiableAt.clm_comp, Fintype.not_linearIndependent_iff, posPart_pos, LieHom.inr_apply, ZNum.cast_bitm1, ODE.hasDerivWithinAt_picard_Icc, PiLp.linearIndependent_single, 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, TopologicalAddGroup.IsSES.pushforward_def, hasDerivWithinAt_diff_singleton, DFinsupp.neg_apply, fderiv_continuousLinearEquiv_comp, FiniteField.pow_dichotomy, deriv_clm_comp, ContinuousLinearMap.adjoint_toSpanSingleton, gaussSum_mul_gaussSum_pow_orderOf_sub_one, tendsto_tsum_compl_atTop_zero, Bornology.IsVonNBounded.of_topologicalSpace_le, HurwitzZeta.completedHurwitzZetaEven_zero, IsCompact.sub_closedBall, Quaternion.im_neg, neg_le_negPart, Height.logHeight_neg, ContDiffMapSupportedIn.structureMapCLM_top_apply, nhds_translation_sub, Balanced.zero_insert_interior, Summable.hasFiniteSupport_of_discreteTopology, CFC.negPart_neg, Set.instTietzeExtensionUnitClosedBall, Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card, Finset.preimage_add_right_singleton, half_sub, groupHomology.mapCycles₂_hom, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Polynomial.Chebyshev.U_eval_neg, Finsupp.toDFinsupp_sub, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, groupHomology.isoCycles₂_inv_comp_iCycles_apply, IsRelPrime.neg_right_iff, Quaternion.imK_intCast, toSpanSingleton_derivWithin, Asymptotics.IsBigOTVS.triangle, IsOrderedModule.of_smul_nonneg, 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', HasCompactSupport.sub, sSup_neg, injective_iff_map_eq_zero, MeasureTheory.FinStronglyMeasurable.neg, 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, MeasureTheory.ae_eq_zero_of_forall_setIntegral_eq_of_finStronglyMeasurable_trim, BoundedContinuousFunction.coe_zsmulRec, HasFDerivWithinAt.curveIntegral_segment_source, MeasureTheory.Integrable.comp_neg, HasFPowerSeriesOnBall.pi, 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, HasDerivAt.scomp, CategoryTheory.Biprod.unipotentUpper_inv, Asymptotics.isBigOWith_neg_left, LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul, ContDiffMapSupportedIn.structureMapLM_top_apply, deriv.neg', ContinuousLinearMap.ker_adjoint_comp_self, Quaternion.normSq_def', SchwartzMap.pairing_continuous_left, AddCommute.neg_right_iff, signedDist_vadd_right_swap, LowerSemicontinuousOn.neg, Function.HasFiniteSupport.zsmul, 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, HasDerivWithinAt.congr, 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, HasDerivAtFilter.fun_neg, NonarchAddGroupSeminorm.toZeroHom_eq_coe, groupHomology.cyclesMk₂_eq, AffineMap.decomp, IsAddIndecomposable.apply_ne_zero_iff_mem_closure, groupHomology.chainsMap_f_1_comp_chainsIso₁, add_eq_zero_iff_neg_eq, Matrix.Module.single_smul, hasFDerivAt_iff_isLittleOTVS, neg_nonneg_of_nonpos, intervalIntegral.integral_zero, IsBoundedSMul.of_nnnorm_smul_le, add_neg_le_neg_add_iff, Right.neg_lt_self, 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, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, AddSubgroup.eq_bot_iff_forall, PresheafOfModules.Derivation.d_app, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, RingPreordering.mem_supportAddSubgroup, self_eq_neg, WithLp.toLp_neg, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, Complex.arg_conj_coe_angle, Set.indicator_compl, RCLike.sqrt_neg_I, groupHomology.H1π_eq_zero_iff, AnalyticAt.neg, QuaternionAlgebra.im_star, ContinuousMultilinearMap.isVonNBounded_image2_apply, Submodule.disjoint_iff_add_eq_zero, isGLB_neg', LieAlgebra.Basis.lie_h_h, 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, Function.Even.smul_odd, IsUniformAddGroup.cauchy_iff_tendsto, groupHomology.π_comp_H1Iso_hom_assoc, DistribMulActionHom.map_neg, fderiv_continuousMultilinearMapCompContinuousLinearMap, Finset.tendsto_Ioo_neg_atTop_atTop, VectorField.lieBracketWithin_eq_zero_of_eq_zero, 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, ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, 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, UniformOnFun.hasBasis_nhds_zero_of_basis, 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, groupHomology.mem_cycles₂_of_mem_boundaries₂, ContinuousLinearMap.opNorm_lsmul_le, LieAlgebra.Basis.cartanMatrix_base_eq, gauge_neg_set_eq_gauge_neg, SkewMonoidAlgebra.support_neg, RCLike.conj_I, AntilipschitzWith.le_mul_norm_sub, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, MultilinearMap.mkContinuousMultilinear_norm_le, CategoryTheory.ShortComplex.Homotopy.neg_h₀, ContDiffMapSupportedIn.monoCLM_eq_zero, eq_zero_of_sameRay_self_neg, PolynomialModule.lsingle_apply, Matrix.BlockTriangular.sub_iff_left, HasFPowerSeriesAt.eventually_hasSum_of_comp, hasDerivAt_natCast, orbit_addSubgroup_zero_eq_self, HasDerivAtFilter.fun_sub, ContinuousMap.coeFn_toLp, intervalIntegral.integral_non_aestronglyMeasurable_of_le, HasDerivWithinAt.union, 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, ContinuousMapZero.aeStronglyMeasurable_restrict_mkD_restrict_of_uncurry, 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, HasDerivWithinAt.add_const, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_of_symmetric, 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, Bornology.IsVonNBounded.of_add_left, ContinuousLinearMap.norm_compL_le, MeasureTheory.measure_lintegral_sub_measure, Seminorm.continuousAt_zero_of_forall, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, Polynomial.aeval_neg, Asymptotics.IsBigO.continuousMultilinearMap_apply_eq_zero, LieModule.chainTop_neg, StrictAntiOn.slope_neg, IsIntegral.neg, deriv_natCast, WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval, torusIntegral_radius_zero, fderivWithin_clm_comp, RootPairing.eq_zero_iff_forall_coroot'_eq_zero, abs_eq_neg_self, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, cfc_comp_neg, HahnSeries.SummableFamily.neg_apply, sameRay_neg_smul_right_iff_of_ne, HasDerivWithinAt.congr_set, Polynomial.taylorEquiv_symm, SnakeLemma.exact_δ_left, 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, HasCompactSupport.fderiv_apply, MeasureTheory.Lp.simpleFunc.toLp_neg, fderiv_continuousMultilinear_apply_const, SchauderBasis.succSub_ortho, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, HasDerivWithinAt.smul, 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, PhragmenLindelof.eq_zero_on_quadrant_II, 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, Polynomial.coe_neg, SeminormFamily.basisSets_zero, differentiableAt_neg_iff, CovariantDerivative.torsion_antisymm, eq_zero_of_neg_eq, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, HasDerivWithinAt.mono, 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, HasFDerivWithinAt.comp_hasDerivAt, SchwartzMap.compCLM_apply, Quaternion.coe_starAe, iter_deriv_inv', TemperedDistribution.fourierMultiplierCLM_apply_apply, ClosedSubmodule.sInf_orthogonal, intervalIntegral.fderivWithin_integral_of_tendsto_ae, AddSubmonoid.fromLeftNeg_eq_neg, ContinuousMap.toLp_comp_toContinuousMap, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, MeasureTheory.IsAddFundamentalDomain.covolume_eq_volume, 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, Asymptotics.IsLittleOTVS.tendsto_inv_smul, 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, fderivWithin_continuousAlternatingMap_apply_const, 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, WithVal.ofVal_neg, Asymptotics.IsLittleOTVS.isBigOTVS, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, TestFunction.hasCompactSupport', IsTopologicalRing.toContinuousNeg, gradient_fun_const', Module.reflection_mul_reflection_zpow_apply_self, MeasureTheory.hasFiniteIntegral_const_iff, MeromorphicAt.neg, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, Function.Periodic.neg_eq, LieSubmodule.Quotient.mk_eq_zero', toIcoMod_neg', 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, HasDerivWithinAt.const_sub, 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, Function.locallyFinsuppWithin.mk_of_mem_addSubgroup_toFun, pow_eq_one_iff_of_ne_zero, HasDerivWithinAt.const_smul, 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, HasDerivWithinAt.hasDerivAt, 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, TopologicalGroup.IsSES.pushforward_mono, 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, LieAlgebra.IsKilling.chainTopCoeff_zero_right, tendsto_iff_norm_neg_add_tendsto_zero, 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, HasStrictFDerivAt.continuousMultilinearMapCompContinuousLinearMap, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, ContinuousLinearMap.opNorm_smul_le, Matrix.compl_of_one_sub_one, TestFunction.fderivCLM_apply_of_gt, 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, Real.Angle.neg_coe_pi, ContinuousLinearMap.spectralRadius_eq_nnnorm, Distribution.dsupport_iteratedLineDerivOp_subset, 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, UnitAddTorus.coe_measurableEquivPiIoc, QuaternionAlgebra.imI_natCast, groupHomology.d₃₂_apply_mem_cycles₂, Asymptotics.IsBigO.neg_right, ContinuousLinearMap.spectrum_eq, Mathlib.Meta.NormNum.isRat_neg, LucasLehmer.X.neg_fst, addInvariantVector_mlieBracket, addOrderOf_dvd_iff_zsmul_eq_zero, addCommutatorElement_eq_zero_iff_addCommute, CochainComplex.mappingCone.δ_liftCochain, Finset.neg_subset_sub_right, TendstoUniformlyOnFilter.neg, uniformity_eq_comap_add_neg_nhds_zero_swapped, FiniteField.sum_pow_units, Set.sub_mem_Ioo_zero_iff_right, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, HasStrictDerivAt.fun_sub, Set.zero_notMem_sub_iff, HasDerivWithinAt.star, negPart_zero, 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, AnalyticAt.eventually_eq_zero_or_eventually_ne_zero, MeasureTheory.measure_inter_neg_vadd, HasDerivAtFilter.prodMk, 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, Function.Antiperiodic.nsmul_sub_eq, ContinuousMapZero.hasFiniteIntegral_mkD_restrict_of_bound, LeftInvariantDerivation.map_neg, derivWithin_fun_const, AddSubgroup.neg_mem, IsSelfAdjoint.hasEigenvector_of_isMinOn, Multiset.esymm_neg, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HasDerivAt.sum, 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, HasStrictDerivAt.finCons, 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.fun_smul, hasDerivAt_zero, SchwartzMap.fderivCLM_fourier_eq, MvPowerSeries.coeff_invOfUnit, Bundle.Trivialization.localFrame_apply_of_notMem, HurwitzZeta.completedHurwitzZetaEven₀_neg, ZMod.isSquare_neg_one_mul, Quaternion.re_im, Quaternion.imI_intCast, HasFDerivWithinAt.isLittleOTVS, CochainComplex.HomComplex.Cochain.toSingleMk_zero, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, PiLp.edist_toLp_single_same, ContMDiffOn.const_smul_section, Quaternion.star_mul_eq_coe, SchwartzMap.derivCLM_apply, intervalIntegral.integral_indicator, Filter.ZeroAtFilter.neg, Seminorm.gauge_ball, List.sum_neg_reverse, ArchimedeanClass.mk_neg, IsCompactOperator.image_closedBall_subset_compact, 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, HasDerivWithinAt.scomp_hasDerivAt, CategoryTheory.Adjunction.homAddEquiv_neg, ContDiffBump.dist_normed_convolution_le, MDifferentiableOn.clm_precomp, isCompactOperator_of_tendsto, 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, HahnEmbedding.Partial.eval_lt, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, HasStrictDerivAt.prodMk, LieModule.toEnd_eq_zero_iff, OrthonormalBasis.adjustToOrientation_apply_eq_or_eq_neg, intervalIntegral.integral_hasDerivAt_right, RootPairing.EmbeddedG2.pairing_short_long, abs_norm_sub_norm_le_norm_neg_add, tsupport_fderiv_apply_subset, hasFTaylorSeriesUpToOn_succ_iff_left, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Absorbs.neg_neg, eq_neg_add_of_add_eq, HasCompactSupport.hasDerivAt_convolution_left, DFinsupp.sum_neg_index, MvPolynomial.C_neg, Balanced.starConvex, LinearMap.map_neg₂, IsPreconnected.eq_or_eq_neg_of_sq_eq, VectorFourier.integral_bilin_fourierIntegral_eq_flip, deriv_clm_apply, 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, comap_gauge_nhds_zero, minpoly.neg, AffineMap.hasStrictDerivAt, AddSubgroup.disjoint_iff_add_eq_zero, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, HasDerivWithinAt.Ioi_of_Ici, 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, VectorField.mpullbackWithin_const_smul, 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, HasStrictFDerivAt.clm_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, ContDiffMapSupportedIn.fderivLM_apply, 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, IsCovariantDerivativeOn.zero, 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, MeasureTheory.Measure.pi.isNegInvariant, CategoryTheory.Abelian.Ext.eq_zero_of_projective, CategoryTheory.ShortComplex.ab_zero_apply, HasDerivWithinAt.fun_add, LinearMap.isStarProjection_toContinuousLinearMap_iff, Submodule.coe_neg, SnakeLemma.exact_δ'_right, Function.Exact.iff_addMonoidHom_rangeRestrict, MeasureTheory.UnifTight.exists_measurableSet_indicator, WithLp.idemFst_apply, IsSelfAdjoint.linearly_dependent_of_isLocalExtrOn, HahnSeries.orderTop_neg, ZNum.cast_bit1, HasFDerivAtFilter.isLittleOTVS, lipschitzOnWith_iff_norm_neg_add_le, CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff, edist_zero_right, isCompactOperator_id_iff_finiteDimensional, iteratedDerivWithin_eq_equiv_comp, Mathlib.Tactic.Abel.zero_smulg, conjneg_apply, Finset.image_add_left', HasDerivAt.const_add, BoxIntegral.integrable_zero, AddGroup.exponent_dvd_iff_forall_zsmul_eq_zero, Matrix.J_inv, IsPrimitiveRoot.pow_sub_one_eq, FreeCommRing.isSupported_neg, iteratedFDerivWithin_two_apply, Matrix.map_intCast, extDerivWithin_smul, ZModModule.add_self, ContDiffMapSupportedIn.seminorm_postcompLM_le, toIocDiv_neg, MeasureTheory.integrable_smul_iff, sq_eq_sq_iff_eq_or_eq_neg, Module.End.mem_maxGenEigenspace, HasDerivAt.prodMk, HasStrictFDerivAt.fun_smul, MeasureTheory.IntegrableOn.comp_neg_Ici, HurwitzZeta.sinZeta_neg, iteratedFDeriv_fun_zero, 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, Filter.HasBasis.isBigOTVS_iff, 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, Function.Odd.smul_even, SkewMonoidAlgebra.intCast_def, CochainComplex.mappingCone.d_fst_v', MeasureTheory.condExp_of_sigmaFinite, MeasureTheory.integral_sub_average, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, CurveIntegrable.smul, isAddConj_iff, HurwitzZeta.completedCosZeta_eq, Prod.card_box_succ, intervalIntegral.integral_zero_ae, 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, HasDerivWithinAt.of_isLittleO, ContinuousAffineMap.norm_comp_le, SchwartzMap.instZeroAtInftyContinuousMapClass, IsCompactOperator.image_ball_subset_compact, ContinuousLinearMap.closed_range_of_antilipschitz, AddSubgroup.leftTransversals.diff_neg, LieModuleHom.coe_zero, tendsto_integral_comp_smul_smul_of_integrable, RootPairing.neg_coroot_mem, HasDerivAt.scomp_of_eq, 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, ContDiffMapSupportedIn.continuous_iff_comp_order_le, MeasureTheory.SimpleFunc.norm_approxOn_zero_le, iteratedFDerivWithin_fun_zero, Mathlib.Tactic.Module.NF.sub_eq_eval₂, toIcoDiv_neg, TopologicalAddGroup.IsSES.inducedMeasure_lt_of_injOn, ContinuousAlternatingMap.curryLeft_add, hasFDerivAt_integral_of_dominated_of_fderiv_le, neg_sub_neg, TopologicalAddGroup.IsSES.integral_inducedMeasure, map_eq_zero_iff_eq_zero, HasFPowerSeriesAt.pi, neg_mem_connectedComponent_zero, WeierstrassCurve.Jacobian.addY_of_X_eq', HahnSeries.leadingCoeff_neg, AddSubmonoid.IsSpanning.mem_or_neg_mem, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', TensorialAt.mkHom_apply_eq_extend, 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, ProbabilityTheory.HasIndepIncrements.neg, Asymptotics.isLittleO_norm_pow_id, LucasLehmer.ω_pow_eq_neg_one, ftaylorSeries_zero, PadicInt.mahlerEquiv_apply, Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul, Distribution.dsupport_lineDerivOp_subset, 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, HasDerivWithinAt.prodMk, Polynomial.coeffList_neg, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, MeasureTheory.IsAddFundamentalDomain.vadd, 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, ConvexBody.zero_mem_of_symmetric, CliffordAlgebra.toProd_one_tmul_ι, MeasureTheory.integral_bilinear_hasDerivAt_right_eq_sub, Polynomial.coeff_neg, TemperedDistribution.fourierMultiplierCLM_sum, AddSubgroup.quotientEquivProdOfLE'_apply, Set.neg_mem_Ico_iff, FormalMultilinearSeries.derivSeries_eq_zero, HahnSeries.min_orderTop_le_orderTop_sub, HasFPowerSeriesOnBall.eventually_eq_zero, Projectivization.mk'_eq_mk, LinearMap.linearProjOfIsCompl_apply_right', HurwitzZeta.completedHurwitzZetaEven_neg, Function.Odd.add, Real.Angle.cos_eq_iff_eq_or_eq_neg, LieIdeal.isLieAbelian_of_trivial, TestFunction.lineDerivCLM_smul, ContDiffWithinAt.smulRight, HasDerivWithinAt.congr_of_eventuallyEq, MeasureTheory.integral_zero', PowerSeries.rescale_neg_one_X, MeasureTheory.integral_eq_zero_of_ae, ContinuousLinearMap.star_eq_adjoint, LinearMap.BilinForm.neg_apply, EMetric.preimage_add_left_ball, FormalMultilinearSeries.comp_rightInv, MeasureTheory.IsAddFundamentalDomain.preimage_of_equiv, 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, HasStrictDerivAt.fun_neg, LineDeriv.lineDerivOp_neg, HasFPowerSeriesWithinAt.neg, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_of_le_one, Function.Antiperiodic.smul, Bornology.IsVonNBounded.closure, EuclideanGeometry.angle_neg, CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f, HahnModule.of_sub, WithZero.exp_zsmul, SymplecticGroup.neg_mem, MeasureTheory.UniformIntegrable.spec, volume_euclideanSpace_eq_dirac, differentiableOn_zero, AddCommute.neg_neg_iff, Asymptotics.isThetaTVS_comm, hasStrictDerivAt_inv, Projectivization.cross_mk_of_ne, ExistsContDiffBumpBase.y_neg, Matrix.conjTranspose_neg, AlternatingMap.mkContinuousLinear_norm_le, HurwitzZeta.cosKernel_neg, asymptoticCone_subset_singleton_of_bounded, SkewMonoidAlgebra.ofFinsupp_sub, Asymptotics.isTheta_zero_left, ProperCone.hyperplane_separation_of_notMem, Finsupp.support_neg, Module.Basis.adjustToOrientation_apply_eq_or_eq_neg, CategoryTheory.ShortComplex.rightHomologyMap_neg, abs_lt_of_sq_lt_sq', ExistsContDiffBumpBase.y_support, one_div_le_neg_one, fderiv_clm_apply, MeasureTheory.setToFun_zero_left', derivWithin_zero, VectorField.mpullback_neg_apply, ContinuousAlternatingMap.curryLeftLI_apply, smul_pos_iff_of_neg_left, lineDifferentiableAt_zero, re_inner_self_nonpos, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, DFinsupp.coe_zsmul, ContMDiffWithinAt.const_smul_section, groupHomology.isoCycles₁_hom_comp_i_assoc, mdifferentiable_neg_section, Complex.eq_const_of_exists_max, MeasureTheory.AddContent.onIocAux_empty, iteratedFDerivWithin_zero_eq_comp, CompactlySupportedContinuousMap.neg_apply, HasFiniteFPowerSeriesAt.sub, Matrix.frobenius_norm_diagonal, Matrix.mem_specialOrthogonalGroup_fin_two_iff, ContinuousLinearMap.norm_compSL_le, toIcoDiv_neg', TestFunction.monoCLM_apply, AddCircle.nsmul_eq_zero_iff, fderivWithin_smul_const, Balanced.neg, MonoidAlgebra.single_neg, Asymptotics.isLittleO_one_iff, ContDiffMapSupportedIn.withSeminorms, CochainComplex.HomComplex.δ_shape, isArtinian_finsupp, Int.cast_eq_zero, ConvexCone.mem_strictlyPositive, LieDerivation.IsKilling.ad_apply_eq_zero_iff, FiniteArchimedeanClass.mk_neg, MeasureTheory.withDensityᵥ_smul, ContDiffAt.exists_eventually_eq_hasDerivAt, TopologicalAddGroup.IsSES.pushforward_mono, Fin.partialSum_right_neg, Bornology.isVonNBounded_vadd, Function.Antiperiodic.int_mul_eq_of_eq_zero, LieAlgebra.mem_corootSpace', mem_openSegment_of_gauge_lt_one, HasFDerivWithinAt.isBigOTVS_sub, ContDiffMapSupportedIn.support_subset, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, CentroidHom.toEnd_neg, LinearOrderedAddCommGroupWithTop.sub_self_eq_zero_of_ne_top, fourier_zero', stereo_right_inv, IsAddUnit.eq_add_neg_iff_add_eq, Orientation.eq_iff_oangle_eq_zero_of_norm_eq, IsMIntegralCurveAt.comp_mul_ne_zero, InnerProductSpace.isIdempotentElem_rankOne_self_iff, LucasLehmer.X.pow_ω, fderivWithin_continuousLinearEquiv_comp, ContinuousMultilinearMap.toUniformOnFun_toFun, Quaternion.re_snd_dualNumberEquiv, Matrix.invOf_fromBlocks_zero₂₁_eq, UpperSemicontinuousAt.neg, QuaternionAlgebra.coe_natCast, gauge_neg_set_neg, Quaternion.re_add, LipschitzOnWith.norm_neg_add_le_of_le, div_le_egauge_ball, hasDerivAtFilter_pi, stereographic_apply, groupHomology.d₁₀_eq_zero_of_isTrivial, AddCircle.coe_period, Asymptotics.IsThetaTVS.trans, ContinuousLinearMap.coe_flipₗᵢ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, IsConjRoot.neg, IsSelfAdjoint.neg, MeasureTheory.Lp.coeFn_zero, AddCircle.finite_torsion_of_isSMulRegular_int, not_linearIndepOn_finset_iff, HomologicalComplex.homotopyCofiber.inlX_d_assoc, MeasureTheory.setIntegral_setAverage_sub, NonarchimedeanAddGroup.summable_iff_tendsto_cofinite_zero, instIsSemisimpleModuleDFinsupp, Representation.coinvariantsToFinsupp_mk_single, hasDerivAtFilter_const_add_iff, homeomorphSphereProd_apply_snd_coe, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, derivWithin_zero_of_not_differentiableWithinAt, IsTopologicalSemiring.continuousNeg_of_mul, Fintype.sum_balance, SMulPosMono.toSMulPosStrictMono, MeasureTheory.Lp.coe_LpSubmodule, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, Bornology.isVonNBounded_insert, Polynomial.coeff_eq_esymm_roots_of_card, TestFunction.instLocallyConvexSpaceReal, AddSubgroup.closure_insert_zero, CategoryTheory.Pretriangulated.invRotCompRot_hom_app_hom₃, Hyperreal.infiniteNeg_neg, AddSubgroup.toAddSubmonoid_zmultiples, instSMulCommClass_closedBall_closedBall_ball, Set.neg_vadd_set_distrib, ball_zero_sub_singleton, FormalMultilinearSeries.ofScalars_series_eq_zero, MonovaryOn.neg_right, Asymptotics.IsLittleOTVS.mono, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, FormalMultilinearSeries.changeOrigin_eval, VertexOperator.ncoeff_of_coeff, LinearMap.toSeminorm_ball_zero, SchwartzMap.norm_toZeroAtInfty, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, WithCStarModule.zero_fst, Asymptotics.IsBigO.trans_tendsto, ExteriorAlgebra.liftAlternating_algebraMap, Finsupp.smul_apply_addAction, MeasureTheory.measure_symmDiff_neg_vadd, iter_deriv_inv_linear_sub, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, add_neg_eq_add_neg_iff_add_eq_add, groupHomology.d₂₁_single_one_snd, neg_neg_of_pos, MeasureTheory.integral_indicator_const, Asymptotics.IsThetaTVS.trans_isLittleOTVS, Quaternion.mul_coe_eq_smul, LieSubalgebra.zero_mem, List.sum_reverse_noncomm, VectorField.lieBracketWithin_swap, LinearIsometry.map_zero, nhds_zero_symm', VertexOperator.ncoeff_eq_zero_of_lt_order, RestrictedProduct.single_zsmul, IsSelfAdjoint.adjoint_conj, SchwartzMap.toZeroAtInfty_toBCF, Asymptotics.IsBigOTVS.trans_isThetaTVS, Bornology.IsVonNBounded.image, not_linearIndependent_iff, enorm_smul_le, TrivSqZeroExt.exp_inl, RingPreordering.neg_one_notMem, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, tendsto_sum_nat_add, AffineMap.coe_zero, HasFPowerSeriesAt.prod, Asymptotics.isTheta_zero_right, LieAlgebra.Basis.lie_e_f_ne, CategoryTheory.ShortComplex.rightHomologyMap'_neg, hasStrictDerivAt_natCast, pow_eq_one_iff_cases, CategoryTheory.Abelian.Ext.eq_zero_of_hasProjectiveDimensionLT, NormedSpace.normalize_zero_eq_zero, PowerSeries.order_neg, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, IsSl2Triple.lie_h_f_nsmul, IsCovariantDerivativeOn.torsion_apply_eq_extend, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, FourierTransform.fourier_zero, IsTopologicalAddGroup.t2Space_iff_zero_closed, AlternatingMap.mkContinuousAlternating_norm_le_max, Asymptotics.isLittleO_id_const, algebraicClosure.isAlgClosure, LieAlgebra.abelian_derivedAbelianOfIdeal, ContinuousMapZero.aeStronglyMeasurable_mkD_restrict_of_uncurry, OrthonormalBasis.sum_rankOne_eq_id, Real.Angle.coe_two_pi, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, Ideal.neg_mem_iff, SnakeLemma.exact_δ'_left, Right.self_lt_neg, WithLp.toLp_eq_zero, hasDerivAt_finCons', Quaternion.im_ratCast, HasStrictDerivAt.hasDerivAt, CategoryTheory.InjectiveResolution.neg_extMk, CochainComplex.HomComplex.Cocycle.coe_zero, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, Representation.coinvariantsFinsuppLEquiv_symm_apply, Asymptotics.IsLittleOTVS.trans, closedBall_rpow_sub_one_eq_empty_aux, HurwitzZeta.completedCosZeta_zero, CategoryTheory.Functor.map_neg, LinearIndependent.pair_neg_right_iff, Localization.neg_mk, support_translate, MeasureTheory.Measure.addHaar_closedBall, ContDiffBump.neg, groupHomology.d₃₂_comp_d₂₁, HahnSeries.orderTop_abs, groupHomology.d₃₂_single_one_snd, HasFPowerSeriesWithinAt.add, LieAlgebra.abelian_iff_derived_succ_eq_bot, LinearIsometryEquiv.piLpCongrLeft_single, Quaternion.imJ_add, FiberBundle.exists_mdifferentiableOn_extend, neg_closedBall, MeasureTheory.L1.setToL1_zero_left', ContDiffMapSupportedIn.fderivCLM_apply_of_le, Set.mem_neg_vadd_set_iff, ContinuousLinearMap.adjoint_inner_right, Matrix.circulant_isSymm_iff, IsCoprime.neg_left_iff, Finset.tendsto_Ico_neg, AlternatingMap.map_swap, HVertexOperator.compHahnSeries_coeff, SimpleGraph.adjMatrix_completeGraph_eq_of_one_sub_one, CliffordAlgebra.EquivEven.involute_e0, MeasureTheory.submartingale_iff_condExp_sub_nonneg, groupHomology.π_comp_H2Iso_hom_apply, Quaternion.im_sub, Finset.addConvolution_neg, neg_le_neg, Matrix.blockDiagonal'_sub, MeasureTheory.Lp.coeFn_neg, MvPowerSeries.order_neg, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, Algebra.Extension.Cotangent.val_zero, HurwitzZeta.completedCosZeta_neg, NonUnitalSubalgebra.coe_neg, groupHomology.isBoundary₀_iff, AddMonoidAlgebra.toDirectSum_neg, Pi.update_eq_sub_add_single, HasStrictFDerivAt.continuousAlternatingMap_apply_const, MeasureTheory.condExp_bilin_of_stronglyMeasurable_right, NormedSpace.closedBall_inv_subset_polar_closedBall, IsAddUnit.add_neg_cancel_right, nndist_indicator, ContDiffMapSupportedIn.postcompLM_apply, CovariantDerivative.torsion_self, neg_lt_sub_iff_lt_add', Matrix.det_neg_eq_smul, ContinuousLinearMap.norm_smulRightL_le, LaurentSeries.derivative_iterate, derivWithin_neg, MeasureTheory.withDensityᵥ_smul', Quaternion.imI_natCast, Algebra.discr_powerBasis_eq_prod'', Finset.zsmul_empty, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, hasDerivAtFilter_const, SchwartzMap.tsupport_derivCLM_subset, IsRealClosed.isSquare_or_isSquare_neg, ContinuousAffineMap.fst_decompLinearIsometryEquiv, SubMulAction.val_neg, tendsto_integral_exp_inner_smul_cocompact, Flow.image_eq_preimage_symm, QuaternionAlgebra.imJ_natCast, DFinsupp.subtypeDomain_sub, CochainComplex.HomComplex.Cochain.zero_comp, MellinConvergent.const_smul, isLinearTopology_iff_hasBasis_submodule, Equiv.addLeft_symm_apply, PiLp.neg_apply, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, UniformOnFun.hasBasis_nhds_zero, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, LieModule.mem_genWeightSpaceOf, LieAlgebra.IsKilling.coe_invtSubmoduleToLieIdeal_eq_iSup, Function.Odd.finset_sum_eq_zero, infEdist_neg, neg_le_of_abs_le, groupHomology.mapCycles₁_hom, nhds_translation_neg_add, intervalIntegral.integral_undef, lp.single_apply, Pi.single_neg, isCompactOperator_id_iff_locallyCompactSpace, Polynomial.eval_neg, Polynomial.coeff_eq_esymm_roots_of_splits, AntivaryOn.neg_right, FormalMultilinearSeries.radius_prod_eq_min, tendsto_norm_nhdsNE_zero, Quaternion.snd_imI_dualNumberEquiv_symm, RCLike.re_le_neg_norm_iff_eq_neg_norm, MeasureTheory.integral_zero_measure, hasFDerivAt_zero, neg_one_lt_zero, HurwitzZeta.cosZeta_neg, circleIntegral.integral_eq_zero_of_hasDerivWithinAt, AddMonoidAlgebra.map_neg, DFinsupp.sum_sub_index, groupHomology.isoCycles₁_inv_comp_iCycles, lt_neg_of_lt_neg, Matrix.nnnorm_diagonal, lowerSemiContinuous_neg_iff, IsOfFinAddOrder.neg, isAlgClosure_iff, Set.smul_neg, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_isCoprime, LieAlgebra.IsKilling.traceForm_coroot, neg_add_eq_iff_eq_add, Set.neg_mem_center, Orientation.two_zsmul_oangle_smul_left_self, ContinuousLinearMap.le_of_opNorm₂_le_of_le, PointwiseConvergenceCLM.hasBasis_nhds_zero, RestrictedProduct.single_neg, slope_neg_iff_of_le, eq_zero_of_sameRay_neg_smul_right, uzpow_neg, AddSubgroup.disjoint_def', Fourier.fourierIntegral_def, MeasureTheory.AddQuotientMeasureEqMeasurePreimage.covolume_ne_top, ContDiffMapSupportedIn.coe_neg, Cubic.eq_sum_three_roots, Complex.IsExactOn.with_val_at, Matrix.SpecialLinearGroup.coe_neg, ContinuousMultilinearMap.currySum_apply, MeasureTheory.MemLp.aefinStronglyMeasurable, MeasureTheory.setIntegral_eq_zero_of_forall_eq_zero, CochainComplex.HomComplex.Cochain.ofHom_zero, NormSMulClass.toIsBoundedSMul, Orientation.angle_eq_iff_oangle_eq_neg_of_sign_eq_neg, Polynomial.taylorLinearEquiv_symm, CategoryTheory.ShortComplex.ShortExact.extClass_comp_assoc, QuotientAddGroup.equivIcoMod_zero, FormalMultilinearSeries.ofScalars_comp_neg, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, neg_lt, LieModule.chainBotCoeff_neg, MeasureTheory.conv_eq_withDensity_lconvolution_rnDeriv, Set.disjoint_vadd_set_right, mem_emetric_ball_zero_iff, Unitary.coe_neg, LieDerivation.coe_zero, Set.zero_notMem_neg_add_iff, Matrix.neg_mul, MeasureTheory.memLp_neg_iff, LieModule.traceForm_eq_sum_finrank_nsmul_mul, IsAddUnit.add_neg_eq_iff_eq_add, WithLp.edist_toLp_fst, Antitone.alternating_series_le_tendsto, groupHomology.single_mem_cycles₁_of_mem_invariants, NonUnitalSubring.neg_mem', continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, AddUnits.vadd_neg, groupHomology.isoShortComplexH2_inv, groupHomology.coe_mapCycles₁, le_egauge_ball_one, AddMonoidAlgebra.single_neg, sub_ball_zero, TestFunction.instLineDerivSMulTopENat, rank_eq_zero_iff, TensorialAt.zero, LieAlgebra.IsKilling.coroot_zero, TemperedDistribution.lineDerivOp_fourierInv_eq, groupHomology.toCycles_comp_isoCycles₁_hom, Finset.tendsto_Ioc_neg, IsAlgebraic.neg, DivisibleHull.instIsStrictOrderedModuleRat, sphere_ext_iff, antivaryOn_neg_right, CompactlySupportedContinuousMap.coe_neg, Module.Relations.toQuotient_relation, ProbabilityTheory.Kernel.integral_integral_indicator, nonpos_of_neg_nonneg, VectorField.pullback_eq_of_not_isInvertible, HasFiniteFPowerSeriesOnBall.hasFDerivAt, LinearMap.BilinForm.neg_right, homeomorphUnitSphereProd_apply_snd_coe, Matrix.neg_vecMul, PiLp.norm_single, LieAlgebra.instIsLieAbelianSubtypeMemLieSubmoduleCenter, WeierstrassCurve.Jacobian.dblU_of_Z_eq_zero, birkhoffSum_neg, ordinaryHypergeometric_radius_top_of_neg_nat₁, hasStrictDerivAt_zero, ContinuousAlternatingMap.alternatizeUncurryFin_add, ZNum.cast_to_int, ContinuousLinearMap.isBigOTVS_fun_comp, iSupIndep_iff_finset_sum_eq_zero_imp_eq_zero, HasDerivAtFilter.finCons, HahnEmbedding.Partial.archimedeanClassMk_le_of_eval_eq, negPart_of_nonpos, Finset.ruzsa_triangle_inequality_add_addNeg_add, TestFunction.hasCompactSupport, IsBoundedSMul.of_norm_smul_le, curveIntegralFun_symm, RootPairing.pairingIn_neg_two_neg_two_iff, AddConstMapClass.map_zsmul_const, Finset.disjoint_box_succ_prod, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesAt.eq_zero, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq, LinearOrderedAddCommGroup.Subgroup.exists_neg_generator, IsSl2Triple.symm_iff, AddSubgroup.isLeast_of_closure_iff_eq_abs, Orientation.oangle_eq_neg_of_angle_eq_of_sign_eq_neg, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, LieAlgebra.IsKilling.chainBotCoeff_zero_right, Filter.NeBot.nonneg_sub, negPart_eq_neg, VectorField.mpullback_neg, AddSubgroup.zmultiples_neg, ContDiffMapSupportedIn.fderivCLM_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, AddSubmonoid.IsUnit.Submonoid.coe_neg, ContDiff.neg, tangentConeAt_subset_zero, HahnEmbedding.Partial.baseEmbedding_le_extendFun, hasFDerivWithinAt_comp_sub, derivWithin_comp_sub_const, TestFunction.fderivCLM_apply, MeasureTheory.UnifTight.neg, ContinuousLinearMap.isAdjointPair_inner, AddSubmonoid.mem_closure_neg, MeasureTheory.FinStronglyMeasurable.sub, upperSemicontinuousOn_neg_iff, groupHomology.mapCycles₂_comp_i_apply, Finsupp.neLocus_sub_right, PolynomialModule.monomial_smul_apply, WeierstrassCurve.c₆_of_char_three, lt_neg_add_of_add_lt, WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF, WeierstrassCurve.c₄_of_isCharTwoJEqZeroNF, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, CategoryTheory.Monad.algebraPreadditive_homGroup_neg_f, complexOfReal_hasDerivAt, MeasureTheory.SimpleFunc.integrable_iff_finMeasSupp, Quaternion.coe_intCast, HVertexOperator.coeff_comp, LaurentSeries.hasseDeriv_zero, QuotientAddGroup.eq_zero_iff, ZMod.cast_neg, apply_abs_le_add_of_nonneg', CauchySeq.neg, PadicInt.coe_neg, NonemptyInterval.neg_pure, HasSum.neg, groupHomology.boundariesToCycles₂_apply, RingEquiv.map_eq_neg_one_iff, IsAddTorsionFree.zsmul_eq_zero_iff_left, WeakFEPair.f_modif_aux1, MDifferentiableAt.smul_const_section, toMeromorphicNFAt_of_not_meromorphicAt, ContDiffMapSupportedIn.continuous_iff_comp, LieAlgebra.Basis.root_mem_or_mem_neg, finsum_mem_neg_distrib, ContMDiffOn.smul_section_of_tsupport, groupHomology.cyclesOfIsCycle₂_coe, ContMDiffWithinAt.smul_section, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite, VectorField.mlieBracket_swap, lp.coeFn_neg, negPart_eq_neg_inf_zero, Set.neg_mem_addCenter, HahnSeries.coeff_toOrderTopSubOnePos_pow, TrivSqZeroExt.mul_right_eq_one, fderivWithin_continuousAlternatingMap_apply, groupHomology.isoCycles₂_hom_comp_i, CauSeq.neg_apply, stereographic'_symm_apply, InnerProductSpace.laplacian_neg, HasDerivAt.fun_inv, neg_lt_of_neg_lt, LieAlgebra.IsKilling.chainTopCoeff_of_eq_zsmul_add, MeasureTheory.IntegrableOn.neg, Quaternion.re_smul, NormedAddCommGroup.nhds_zero_basis_norm_lt, HasFPowerSeriesAt.eq_zero_of_eventually, MeasureTheory.eLpNorm_const_lt_top_iff, Function.HasFiniteSupport.fun_neg, HVertexOperator.coeff_apply_apply, PosNum.cast_sub', div_le_egauge_closedBall, Real.Angle.coe_zero, CauSeq.lim_neg, AddCircle.liftIco_zero_continuous, groupHomology.π_comp_H1Iso_hom, Memℓp.neg_iff, Quaternion.eq_re_iff_mem_range_coe, homeomorphSphereProd_apply_fst_coe, Algebra.discr_powerBasis_eq_prod', LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, HasDerivAt.scomp_hasDerivWithinAt, AddGroupCone.mem_nonneg, CochainComplex.HomComplex.Cochain.comp_zero, SchwartzMap.smulLeftCLM_sub, MeasureTheory.support_convolution_subset_swap, CategoryTheory.ShortComplex.neg_τ₁, groupHomology.isoCycles₂_inv_comp_iCycles, TemperedDistribution.smulLeftCLM_const, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', AddSubgroup.val_list_sum, HasStrictDerivAt.add_const, MeasureTheory.ae_eq_zero_of_forall_setIntegral_isCompact_eq_zero, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, LinearEquiv.neg_apply, Bornology.IsVonNBounded.smul_tendsto_zero, intervalIntegral.integral_hasStrictDerivAt_right, Orientation.oangle_eq_pi_iff_sameRay_neg, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, Quaternion.coe_add, HVertexOperator.of_coeff_apply, MDifferentiableOn.smul_section, MeasureTheory.lintegral_norm_eq_lintegral_edist, CochainComplex.HomComplex.Cochain.rightShift_neg, Seminorm.smul_ball_zero, Set.preimage_add_left_zero, AddSubgroup.quotientEquivProdOfLE_apply, Asymptotics.isBigOTVS_map, MeasureTheory.condExpL1_zero, neg_cross, Polynomial.leadingCoeff_sub_of_degree_lt', iteratedFDeriv_two_apply, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, Asymptotics.isLittleO_top, MeasureTheory.lconvolution_comm, pow_eq_neg_one_iff, HahnEmbedding.Partial.eval_zero, HurwitzZeta.hurwitzZetaOdd_neg, max_neg_zero, Quaternion.normSq_intCast, LieAlgebra.Orthogonal.pso_inv, iteratedFDerivWithin_zero_fun, add_eq_zero_iff_neg_eq', LieAlgebra.mem_zeroRootSubalgebra, TemperedDistribution.smulLeftCLM_sum, sub_nonpos, LinearPMap.mem_inverse_graph_snd_eq_zero, LieAlgebra.Extension.instIsLieAbelianSubtypeLMemLieSubmoduleKerProj, IsAddTorsionFree.zsmul_eq_zero_iff_right, NormedAddGroup.nhds_zero_basis_norm_lt, Asymptotics.IsBigOWith.neg_right, intervalIntegral.integral_hasStrictDerivAt_left, iter_deriv_inv_linear, resolventSet_neg, Asymptotics.IsBigOTVS.neg_left, HahnEmbedding.Partial.eval_eq_truncLT, Representation.IntertwiningMap.coe_neg, CategoryTheory.ShortComplex.Homotopy.neg_h₂, LieAlgebra.IsKilling.restr_invtSubmoduleToLieIdeal_eq_iSup, antivaryOn_iff_forall_smul_nonpos, meromorphicTrailingCoeffAt_of_not_MeromorphicAt, AddAction.QuotientAction.inv_mul_mem, DFinsupp.mk_sub, ProbabilityTheory.multivariateGaussian_zero_one, PresheafOfModules.Sheafify.zero_smul, MDifferentiable.clm_precomp, WithLp.ofLp_zero, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, DilationEquiv.smulTorsor_preimage_ball, Finsupp.single_neg, ContDiffMapSupportedIn.fderivLM_apply_of_le, MeasureTheory.average_neg, sameRay_smul_right_iff, HahnSeries.finiteArchimedeanClassOrderIso_apply, UniformConvergenceCLM.eventually_nhds_zero_mapsTo, Unitization.inl_neg, Asymptotics.isEquivalent_zero_iff_isBigO_zero, Asymptotics.isLittleO_const_const_iff, FormalMultilinearSeries.le_radius_pi, continuousMultilinearCurryLeftEquiv_symm_apply, MeasureTheory.integral_def, NonarchAddGroupNorm.apply_one, MeasureTheory.Measure.addHaar_closedBall_mul, IsUnit.integrable_smul_iff, AddChar.doubleDualEmb_eq_zero, TrivSqZeroExt.exp_def_of_smul_comm, RootPairing.eq_zero_of_mem_rootSpan_of_rootForm_self_eq_zero, AddMonoidHom.exact_of_comp_eq_zero_of_ker_le_range, QuotientAddGroup.mk_neg, FreeAbelianGroup.lift_neg_apply, MeasureTheory.Measure.integral_isAddLeftInvariant_isAddRightInvariant_combo, Nat.neg_cast_eq_cast, IsAddUnit.add_eq_zero_iff_neg_eq, singleton_add_ball_zero, ZMod.toAddCircle_eq_zero, ContinuousMultilinearMap.smulRightL_apply, FourierTransform.fourierInv_zero, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, AddSubmonoid.IsPointed.eq_zero_of_mem_of_neg_mem, AddMonoidHom.eq_iff, Matrix.intCast_apply, smul_nonneg_iff_pos_imp_nonneg, Convex.second_derivative_within_at_symmetric_of_mem_interior, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum', AddSubgroup.exists_isLeast_pos, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, IsLUB.neg, ContinuousAlternatingMap.coe_neg, 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, Asymptotics.IsLittleOTVS.congr_right, FourierTransform.fourier_neg, MeasureTheory.measure_neg_vadd_union, Set.preimage_vadd, EuclideanGeometry.oangle_self_left, WithLp.norm_toLp_snd, negPart_pos, Quaternion.re_sub, Dense.eq_zero_of_inner_right, Finsupp.neLocus_self_add_right, MeasureTheory.integral_mul_deriv_eq_deriv_mul_of_integrable, ContinuousMap.norm_smul_const, iteratedFDeriv_succ_eq_comp_left, Seminorm.closedBall_zero_eq, toIcoDiv_eq_sub, 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, CovariantDerivative.torsion_apply_eq_extend, PiLp.zero_apply, ArchimedeanClass.pos_of_pos_of_mk_lt, ContDiffMapSupportedIn.fderivLM_apply_of_gt, HasDerivAt.hasDerivAtFilter, 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, LieAlgebra.Basis.symm_h, ClosedSubmodule.orthogonal_closure, TopologicalAddGroup.IsSES.pullback_def, BoxIntegral.integrable_neg, HasCompactSupport.exist_eLpNorm_sub_le_of_continuous, 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', HahnEmbedding.Partial.evalCoeff_eq, 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, MeasureTheory.UnifIntegrable.neg, ContMDiffWithinAt.neg, MeasureTheory.lconvolution_assoc₀, continuousMultilinearCurryFin1_symm_apply, CauSeq.coe_neg, HasStrictDerivAt.fun_add, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, balancedCore_zero_mem, HahnEmbedding.Partial.sSupFun_strictMono, FormalMultilinearSeries.radius_pi_le, Set.zero_mem_sub_iff, InnerProductSpace.HarmonicContOnCl.fun_neg, MeasureTheory.HasFiniteIntegral.neg, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, 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, IsSemitopologicalSemiring.continuousNeg_of_mul, HasStrictFDerivAt.smul_const, MeasureTheory.Measure.addHaar_ball, IncidenceAlgebra.mu_eq_neg_sum_Ico_of_ne, MeasureTheory.SimpleFunc.integral_nonneg, Fin.neg_partialSum_add_eq_contractNth, QuaternionAlgebra.im_intCast, ContinuousMapZero.aeStronglyMeasurable_restrict_mkD_of_uncurry, PhragmenLindelof.eq_zero_on_quadrant_I, 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, CategoryTheory.ShortComplex.cyclesMap'_neg, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, zero_mem_tangentConeAt_iff, map_addUnits_neg, ContDiffOn.smulRight, MDifferentiableOn.smul_section_of_tsupport, groupHomology.d₁₀_comp_coinvariantsMk_assoc, CategoryTheory.op_neg, ContinuousLinearMap.norm_adjoint_comp_self, IsSemitopologicalRing.toContinuousNeg, LieAlgebra.SemiDirectSum.neg_eq_mk, 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.integral_bilinear_hasDerivAt_eq_sub, MeasureTheory.IsAddFundamentalDomain.mk'', Matrix.circulant_isSymm_apply, AddSubgroup.focalAddSubgroupOf.mk'_addConj_eq, ContMDiff.clm_precomp, IsLinearTopology.tendsto_smul_zero, Function.locallyFinsuppWithin.restrictLatticeHom_apply, locallyConvexSpace_iff_zero, MeasureTheory.exists_eLpNorm_indicator_le, Left.neg_le_self, HasFPowerSeriesWithinAt.compContinuousLinearMap, Rep.indToCoindAux_of_not_rel, LowerSemicontinuousAt.neg, 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, MeasureTheory.eventuallyConst_neg_set_ae, IsLinearMap.isLinearMap_neg, 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, Mathlib.Tactic.Module.NF.sub_eq_eval, IsCompactOperator.isCompact_closure_image_ball, FormalMultilinearSeries.derivSeries_apply_diag, NormedSpace.polar_closedBall, Monotone.alternating_series_le_tendsto, wbtw_neg_iff, ClosedSubmodule.symplComp_sup, neg_lt_self, 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, Asymptotics.IsLittleOTVS.add, 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', toIocMod_neg', 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, integral_bilinear_hasFDerivAt_right_eq_neg_left_of_integrable, Function.Periodic.zsmul_eq, HasCompactSupport.deriv, 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, ContMDiff.codRestrict_sphere, 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, AddGroupConeClass.eq_zero_of_mem_of_neg_mem, Summable.tendsto_zero_of_even_summable_symmetricIcc, hasDerivAt_const_add_iff, Matrix.trace_neg, MeasureTheory.integral_Icc_deriv_smul_of_deriv_nonpos, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, HasFPowerSeriesWithinOnBall.tendsto_partialSum, SchwartzMap.smulLeftCLM_apply, MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix, ContDiffMapSupportedIn.withSeminorms', MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, UpperSemicontinuous.neg, 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, ContinuousMapZero.hasFiniteIntegral_mkD_of_bound, Dense.eq_zero_of_inner_left, ContinuousLinearMap.norm_holderL_le, ModuleCat.span_rightExact, HahnSeries.inv_single, MvPolynomial.IsHomogeneous.neg, Module.Basis.span_neg, hammingDist_eq_hammingNorm, LucasLehmer.X.zero_snd, Asymptotics.IsLittleOTVS.fun_add, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, DirectSum.toAddMonoidAlgebra_neg, coe_neg_ball, Rat.cast_neg, hasFDerivWithinAt_iff_isLittleOTVS, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, NonarchAddGroupSeminorm.add_le_max', MeasureTheory.lpMeas.ae_fin_strongly_measurable', PointedCone.dual_neg, IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq, gaugeSeminormFamily_ball, IsNonarchimedean.finset_powerset_image_add, CochainComplex.HomComplex.Cochain.rightUnshift_zero, not_linearIndependent_iff_linearCombination, HahnModule.instIsTorsionFree, mdifferentiable_smul_section, 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, lipschitzWith_iff_norm_neg_add_le, PointwiseConvergenceCLM.hasBasis_nhds_zero_of_basis, posPart_neg, AddGroupCone.coe_nonneg, ContMDiffSection.coe_neg, hasDerivWithinAt_Ici_of_tendsto_deriv, exists_lt_nsmul_of_neg, spectrum.hasDerivAt_resolvent_const_left, Module.Relations.Solution.π_comp_map_apply, Finset.indicator_biUnion_eq_sum_powerset, isCauSeq_neg, LinearMap.hasDerivAt, Monotone.tendsto_le_alternating_series, ZeroAtInftyContinuousMap.coe_sub, intervalIntegral.deriv_integral_of_tendsto_ae_left, Matrix.blockDiag_neg, IsCovariantDerivativeOn.affine_combination, 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, 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, TestFunction.lineDerivCLM_apply_of_gt, WithSeminorms.isVonNBounded_iff_seminorm_bounded, HurwitzZeta.sinZeta_eq, InnerProductSpace.Core.normSq_eq_zero, groupHomology.boundaries₁_le_cycles₁, HasFPowerSeriesAt.locally_zero_iff, LieAlgebra.Basis.coe_linearMap_baseSupp', hasDerivAt_iff_tendsto_slope, 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, HasFDerivWithinAt.comp_hasDerivAt_of_eq, 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', Finset.small_nsmul_of_small_tripling, WithConv.ofConv_neg, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, Quaternion.imJ_natCast, Derivation.leibniz_invOf, Orientation.oangle_neg_neg, smul_neg_iff_of_neg_left, ContMDiff.const_smul_section, strictMono_iff_map_neg, Finset.addConvolution_op_vadd_eq_addConvolution_add_neg, HasDerivWithinAt.fun_sum, HasStrictFDerivAt.continuousAlternatingMapCompContinuousLinearMap, LieModule.Weight.toLinear_neg, RKHS.coe_neg, MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg, FreeAbelianGroup.lift_neg, Orientation.oangle_smul_right_self_of_nonneg, HolderWith.smul, PresheafOfModules.Sheafify.smul_zero, TopologicalGroup.IsSES.integrate_mono, Function.locallyFinsuppWithin.negPart_apply, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_gt, ZSpan.fract_eq_fract, 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, HasDerivAt.of_notMem_tsupport, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, derivWithin_fun_inv', integral_bilinear_fderiv_right_eq_neg_left_of_integrable, 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, HasStrictDerivAt.const_sub, hasDerivWithinAt_finCons, Quaternion.coe_neg, neg_le_sub_iff_le_add, WithTop.untop₀_le_untop₀_iff, PiLp.single_add, exists_continuousLinearEquiv_fderiv_symm_eq, Finsupp.mapDomain_sub, HasDerivAt.smul, CategoryTheory.CatCenter.app_neg, FormalMultilinearSeries.rightInv_coeff, IsPrimitiveRoot.norm_of_cyclotomic_irreducible, tangentMap_prod_right, Metric.instTietzeExtensionBall, TensorialAt.mkHom₂_apply_eq_extend, MeasureTheory.AEStronglyMeasurable.convolution_integrand', MeasureTheory.quasiMeasurePreserving_neg, Orientation.oangle_neg_orientation_eq_neg, AddGroupFilterBasis.t2Space_iff_sInter_subset, IncidenceAlgebra.mu_toDual, MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum', mfderiv_neg, ContinuousLinearMap.map_neg, normEDS_neg, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, QuotientAddGroup.rightRel_eq, Asymptotics.IsBigOTVS.mono, LieModule.chainTopCoeff_neg, Asymptotics.IsLittleOTVS.proj, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, instSMulCommClass_sphere_sphere_closedBall, AddGroup.residuallyFinite_iff_forall_finiteIndex, 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, Asymptotics.IsBigOTVS.trans, 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, NonarchAddGroupNorm.eq_zero_of_map_eq_zero', QuaternionAlgebra.re_add_im, Filter.HasBasis.uniformity_of_nhds_zero_neg_add_swapped, AddSubgroup.mem_goursatSnd, MeasureTheory.charFun_zero, WithTop.untop₀_neg, continuous_stereoInvFun, Filter.tendsto_neg_cobounded, HasStrictDerivAt.neg, AnalyticAt.analyticOrderAt_ne_zero, abs_nonneg, ContMDiffOn.neg, linearDepOn_iff', QuaternionAlgebra.sub_im_self, MeasureTheory.condExp_indicator_aux, 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, 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, Asymptotics.isLittleOTVS_insert, 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, SeminormedAddGroup.disjoint_nhds, AddAut.neg_conj_apply, tangentMap_prod_left, ContMDiffWithinAt.cle_arrowCongr, MeasureTheory.lpNorm_eq_zero, Quaternion.hom_ext_iff, PowerSeries.rescale_neg_one_invOneSubPow, MeasureTheory.integrableOn_neg_iff, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, MeasureTheory.measure_unitBall_eq_integral_div_gamma, groupHomology.single_isCycle₁_of_mem_fixedPoints, IsHausdorff.haus', DFinsupp.sub_apply, continuousMultilinearCurryRightEquiv_apply, NormedAddGroupHom.coe_zero, SeminormedAddGroup.tendstoUniformlyOn_zero, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, HasDerivAt.comp_add_const, NonarchAddGroupSeminormClass.map_zero, HasFDerivAt.neg, ZMod.exists_sq_eq_neg_two_iff, ZeroAtInftyContinuousMap.coe_neg, Bornology.isVonNBounded_of_smul_tendsto_zero, Module.Presentation.tautologicalRelations_relation, ContDiffMapSupportedIn.structureMapLM_zero_apply, Right.sign_neg, LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero, gauge_closedBall, Function.Antiperiodic.int_mul_sub_eq, AddSubmonoid.IsPointed.eq_zero_of_mem_of_neg_mem₂, 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, MeasureTheory.MemLp.toLp_zero, EMetric.preimage_add_left_closedBall, Bornology.sUnion_isVonNBounded_eq_univ, DirectSum.decompose_neg, Matrix.isHermitian_neg_iff, 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, AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_apply_coe, nonneg_of_neg_nonpos, Polynomial.roots_C_mul_X_add_C_of_IsUnit, Submodule.starProjection_apply_eq_zero_iff, ContMDiffAt.smul_section, Algebra.Extension.exact_cotangentComplex_toKaehler, SchwartzMap.fourier_convolution, toIocDiv_eq_sub, 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, AddMonoidAlgebra.coeff_neg, Finset.zero_notMem_neg_add_iff, ContinuousLinearMap.flipₗᵢ_symm, AnalyticOnNhd.neg, HasFPowerSeriesAt.compContinuousLinearMap, Asymptotics.IsBigOTVS.refl, Mathlib.Tactic.Abel.subst_into_negg, Metric.preimage_add_left_eball, CompactlySupportedContinuousMap.pullback_monoidHom_def, Mathlib.Tactic.Ring.neg_one_mul, gauge_zero, fderivWithin_clm_apply, 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, tendsto_norm_neg_add_self, 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, fderiv_continuousAlternatingMap_apply_const_apply, 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, HasFDerivAt.continuousAlternatingMapCompContinuousLinearMap, Function.Odd.sum_eq_zero, ContMDiff.neg, WeierstrassCurve.c₆_of_isShortNF, Finsupp.neLocus_self_sub_right, Rep.standardComplex.d_single, MeasureTheory.zero_convolution, toIcoMod_mem_Ico', Real.log_of_ne_zero, absorbs_neg_neg, MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero, ContinuousLinearMap.isBigOTVS_id, groupHomology.d₁₀ArrowIso_inv_left, QuaternionAlgebra.imI_star, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, ContinuousLinearMap.norm_holder_apply_apply_le, lipschitzWith_smul, ClosedSubmodule.symplComp_inf, 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, Asymptotics.IsBigOTVS.fst, 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, edist_eq_enorm_neg_add, constFormalMultilinearSeries_apply_succ, Finset.card_add_neg_eq_addConvolution_neg, LieAlgebra.Basis.coe_baseSupportEquiv_apply, ContinuousAlternatingMap.alternatizeUncurryFin_fderivCompContinuousLinearMap_eq_zero, FormalMultilinearSeries.continuousOn, LieAlgebra.IsSimple.non_abelian, hasFDerivAt_inv, HahnEmbedding.Partial.exists_isMax, HasStrictFDerivAt.clm_comp, 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, Filter.Tendsto.addConj_nhds_zero, Derivation.coe_neg, Function.Odd.const_smul, VectorFourier.fourierIntegral_fderiv, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, TemperedDistribution.lineDeriv_eq_fourierMultiplierCLM, Set.neg_Iic, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, MeasureTheory.indicatorConstLp_coeFn, HahnEmbedding.Partial.apply_of_mem_stratum, 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, Rep.finsupp_V, 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, Asymptotics.IsBigOTVS.of_egauge_le_mul, Asymptotics.IsLittleOTVS.symm, MeasureTheory.integral_eq_zero_of_add_left_eq_neg, QuaternionAlgebra.star_mk, IncidenceAlgebra.mu_self, HasStrictFDerivAt.continuousMultilinearMap_apply, 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, ContDiffBump.convolution_tendsto_right_of_continuous, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_top, LinearIsometryEquiv.toContinuousLinearEquiv_smul, 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, HasDerivWithinAt.sum, CategoryTheory.SimplicialObject.Homotopy.ToChainHomotopy.hom_eq, 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, Asymptotics.IsLittleOTVS.of_tendsto_div, 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, smul_pos_of_neg_of_neg, AddSubgroup.IsComplement.add_neg_toRightFun_mem, LineDeriv.iteratedLineDerivOp_neg, ContinuousLinearMap.norm_precompL_le, HasFTaylorSeriesUpToOn.restrictScalars, ZMod.dft_def, HasDerivAtFilter.neg, ContinuousLinearMap.apply_apply, Rep.barComplex.d_single, egauge_zero_right, lowerSemicontinuousWithinAt_neg_iff, Module.Presentation.tautological_relation, Asymptotics.isThetaTVS_iff_isTheta, ContinuousLinearMap.norm_map_removeNth_le, Function.Odd.map_zero, Left.sign_neg, CategoryTheory.ShortComplex.Homotopy.symm_h₁, PhragmenLindelof.eq_zero_on_quadrant_III, LowerSet.Iic_zero, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, iteratedFDeriv_neg, eq_zero_of_abs_deriv_le_mul_abs_self_of_eq_zero_right, 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, fderivWithin_restrictScalars_comp, PiLp.instIsBoundedSMul, Ideal.span_pair_neg, Quaternion.normSq_ratCast, StarConvex.neg, RootPairing.isReduced_iff, Quaternion.imK_im, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, CategoryTheory.NatTrans.app_neg, Mathlib.Tactic.CancelDenoms.neg_subst, MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, groupHomology.d₂₁_comp_d₁₀_assoc, midpoint_zero_add, meromorphicOrderAt_ne_top_iff_eventually_ne_zero, IsAddIndecomposable.mem_or_neg_mem_closure_baseOf, 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, HahnSeries.orderTop_sub, LieSubmodule.lie_eq_bot_iff, Matrix.det_eq_sign_charpoly_coeff, LieAlgebra.SemiDirectSum.inr_eq_mk, toIocMod_zero_sub_comm, MeasureTheory.Measure.addHaar_singleton, Orientation.rightAngleRotation_neg_orientation, LieModule.genWeightSpace_neg_add_chainBot, exteriorPower.presentation.relations_relation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, derivWithin_clm_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, LieHom.coe_inr, QuaternionAlgebra.im_sub, LinearEquiv.transvection.inv_eq, Module.End.eigenspace_aeval_polynomial_degree_1, HasStrictDerivAt.congr_of_eventuallyEq, le_egauge_closedBall_one, affineSpan_insert_zero, Quaternion.imI_snd_dualNumberEquiv, MeasureTheory.SimpleFunc.setToSimpleFunc_nonneg', MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, iteratedDerivWithin_fun_neg, compl_add_closure_zero_eq, CliffordAlgebra.map_mul_map_eq_neg_of_isOrtho_of_mem_evenOdd_one, NormedAddGroup.nhds_basis_norm_lt, MeasureTheory.Integrable.toL1_neg, HasCompactSupport.convolution_integrand_bound_right, 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, HasDerivAt.comp_semilinear, HahnEmbedding.Seed.domain_baseEmbedding, CFC.neg_negPart_le, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, MvPolynomial.IsSymmetric.neg, QuadraticAlgebra.im_star, HasDerivAt.comp_sub_const, 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, VertexOperator.coeff_eq_zero_of_lt_order, groupHomology.isBoundary₁_iff, isAddQuotientCoveringMap_iff, mdifferentiableOn_neg_section, HasFDerivAt.clm_comp, 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, Distribution.IsVanishingOn.lineDerivOp, Int.cast_negOnePow_natCast, Asymptotics.isLittleOTVS_pi, neg_one_eq_one_iff, Module.finrank_eq_zero_iff, Bundle.Pretrivialization.continuousLinearMapCoordChange_apply, ContDiffMapSupportedIn.structureMapLM_apply, AddGroupExtension.Section.neg_add_mem_range_inl, monovary_neg_left, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, MonoidAlgebra.map_neg, MeasureTheory.aefinStronglyMeasurable_of_aemeasurable, IsCompactOperator.hasEigenvalue_iff_mem_spectrum, 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, HasCompactSupport.convolution_integrand_bound_right_of_subset, deriv_const_sub, tsupport_deriv_subset, gradient_eq_zero_of_not_differentiableAt, hasStrictDerivAt_of_hasDerivAt_of_continuousAt, HasStrictDerivAt_ofNat, groupHomology.mapCycles₁_quotientGroupMk'_epi, Matrix.adjugate_fin_two_of, MeasureTheory.measurePreserving_prod_neg_add_swap, Real.Angle.tan_zero, Filter.HasBasis.uniformity_of_nhds_zero_neg_add, 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, HasFiniteFPowerSeriesAt.comp, AddSubgroup.zmultiples_eq_bot, SymplecticGroup.inv_eq_symplectic_inv, CategoryTheory.Preadditive.neg_comp_assoc, RCLike.sqrt_neg_of_nonneg, second_derivative_symmetric_of_eventually_of_real, hasDerivWithinAt_iff_tendsto, LinearPMap.zero_apply, CategoryTheory.Preadditive.instEpiNegHom, Finset.nsmul_ssubset_nsmul_succ_of_nsmul_ne_closure, MonoidAlgebra.neg_apply, ContDiffAt.hasStrictDerivAt', 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, HasDerivAt.star_conj, WithCStarModule.equiv_symm_zero, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, Bornology.IsVonNBounded.insert, CategoryTheory.Pretriangulated.rotCompInvRot_hom_app_hom₁, RingQuot.neg_quot, RootPairing.polarization_apply_eq_zero_iff, MeasureTheory.Submartingale.condExp_sub_nonneg, HurwitzZeta.hurwitzZetaEven_neg, Seminorm.continuousAt_zero, ftaylorSeriesWithin_fun_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, HasFDerivAt.smul, le_abs', WithAbs.toAbs_neg, tendsto_sub_nhds_zero_iff, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, Algebra.H1Cotangent.exact_δ_mapBaseChange, ConvexBody.coe_zero, SchwartzMap.smulLeftCLM_smul, IsAbsoluteValue.abv_neg, RKHS.coe_zero, MeasureTheory.measurePreserving_add_prod_neg, differentiableAt_iff_comp_neg, isClosed_setOf_isCompactOperator, Submodule.span_neg, DoubleCentralizer.coe_snd, sbtw_neg_iff, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, ContinuousLinearMap.opNorm_le_bound₂, Quaternion.exp_coe, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, dotProduct_neg, AddChar.inv_mulShift, HasFiniteFPowerSeriesOnBall.eq_zero_of_bound_zero, MeasureTheory.integral_convolution, QuadraticMap.mem_radical_iff', 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, Submodule.mem_neg, AnalyticOnNhd.eqOn_zero_or_eventually_ne_zero_of_preconnected, UpperHalfPlane.IsZeroAtImInfty.of_exp_decay, add_notMem_of_addOrderOf_eq_two, TopologicalAddGroup.IsSES.integrate_apply, 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, hasDerivAt_of_tendstoUniformlyOnFilter, 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, Asymptotics.IsBigOTVS.pi, HasFDerivAt.isLittleOTVS, HasDerivAt.inv, differentiableWithinAt_zero, HVertexOperator.coeff_of_coeff, conjugate_addCommutatorElement, 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, HasDerivAtFilter.fun_sum, LieModule.Weight.coe_neg, AddCommute.neg_left, Matrix.Pivot.listTransvecRow_getElem, FormalMultilinearSeries.hasFPowerSeriesOnBall, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, HasCompactSupport.abs, iteratedDeriv_const, lipschitzWith_neg_iff, Quaternion.imJ_sub, SchwartzMap.integral_mul_lineDerivOp_right_eq_neg_left, Quaternion.normSq_coe, QuotientAddGroup.preimage_mk_zero, Matrix.IsDiag.sub, groupHomology.boundariesToCycles₁_apply, groupHomology.single_mem_cycles₂_iff_inv, Right.self_le_neg, egauge_pi', groupHomology.d₁₀_single, Finset.ruzsa_triangle_inequality_negAdd_add_add, HasFDerivWithinAt.continuousAlternatingMap_apply_const, ContinuousLinearMap.innerSL_apply_comp, iteratedDeriv_fun_neg, Finset.ruzsa_triangle_inequality_addNeg_add_add, surjective_stereographic, LieSubalgebra.eq_bot_iff, Balanced.smul_mono, 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, InnerProductSpace.laplacian_const, ProbabilityTheory.instIsGaussianMapNeg, inner_neg_left, FirstOrder.Field.charP_iff_model_fieldOfChar, Function.Antiperiodic.sub_nat_mul_eq, LineDeriv.lineDerivOp_left_neg, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_deriv₂, MonoidAlgebra.coeff_sub, 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, DifferentiableWithinAt.continuousMultilinearMapCompContinuousLinearMap, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, 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, toIocMod_add_toIcoMod_zero, HasDerivWithinAt.finCons, HasStrictDerivAt.clm_apply, Finset.neg_vadd_finset_distrib, TemperedDistribution.smulLeftCLM_apply_apply, HasDerivAt.congr_deriv, MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp_eLpNorm, IsCompactOperator.isCompact_closure_image_closedBall, 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, ContinuousLinearMap.hasDerivAt_of_bilinear, mem_sphere_iff_norm_neg_add_eq, 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, second_derivative_symmetric_of_eventually, HasFDerivAt.comp_hasDerivAt_of_eq, AddGroupExtension.Section.add_neg_add_add_mem_range_inl, derivWithin_comp_neg, addInvariantVectorField_add, RCLike.div_I, sameRay_neg_iff, IsCyclotomicExtension.discr_prime_pow, BddBelow.range_neg, CochainComplex.HomComplex.Cochain.map_neg, HasDerivAtFilter.const_sub, 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, PointedCone.mem_lineal, Asymptotics.IsThetaTVS.refl, Monovary.neg_left, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, ContMDiff.smul_section, WeierstrassCurve.Projective.negDblY_of_Y_eq, ContDiffMapSupportedInClass.map_zero_on_compl, Matrix.BlockTriangular.add_iff_left, 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, Pi.noZeroSMulDivisors, CategoryTheory.ShortComplex.ShortExact.extClass_comp, hasFDerivAt_integral_of_dominated_loc_of_lip, UniformConvergenceCLM.nhds_zero_eq_of_basis, CategoryTheory.shift_neg_shift', Real.Angle.toReal_zero, PiTensorProduct.mapLMultilinear_toFun_apply, le_neg_iff_add_nonpos_right, AnalyticOnNhd.eqOn_zero_of_preconnected_of_eventuallyEq_zero, VectorField.mlieBracket_smul_right, MeasureTheory.ae_eq_zero_of_forall_setIntegral_isClosed_eq_zero, HasDerivAtFilter.fun_const_smul, Derivation.map_intCast, 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, Matrix.compl_zero_eq_of_one_sub_one, 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, LinearMap.continuousAt_zero_of_locally_bounded, CliffordAlgebra.ι_mul_ι_mul_of_isOrtho, Monovary.neg, MeasureTheory.lconvolution_assoc, AddAction.stabilizer_quotient, sub_add_cancel_right, Matrix.gram_single, groupHomology.δ₁_apply, Quaternion.star_eq_self, IsAddTorsionFree.zsmul_eq_zero_iff, Function.locallyFinsuppWithin.memAddSubgroup, HasStrictDerivAt.fun_smul, Function.locallyFinsuppWithin.toClosedBall_eval_within, coe_negAddMonoidHom, Set.singleton_vsub_self, Finset.nsmul_right_strictMonoOn, 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', MeasureTheory.integral_bilinear_hasDerivAt_right_eq_neg_left_of_integrable, CategoryTheory.ShortComplex.leftHomologyMap_neg, MDifferentiableWithinAt.smul_section, ContMDiffOn.smul_section, 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, VectorField.lieBracket_eq_zero_of_eq_zero, HasFDerivAt.continuousMultilinearMap_apply, ContinuousAlgHom.map_neg, PiLp.edist_single_same, CategoryTheory.Abelian.Ext.eq_zero_of_injective, Quaternion.imK_snd_dualNumberEquiv, MDifferentiableWithinAt.neg, ContinuousLinearMapWOT.ext_inner_iff, groupHomology.chainsMap_f, AddMonoid.Coprod.con_neg_add_cancel, ContDiffMapSupportedIn.iteratedFDerivLM_apply_of_le, Module.Baer.ExtensionOfMaxAdjoin.extendIdealTo_wd', LieAlgebra.IsKilling.instIsLieAbelianOfIsCartanSubalgebra, ZMod.pow_div_two_eq_neg_one_or_one, Quaternion.imI_ratCast, VectorField.mlieBracket_const_smul_right, Submodule.disjoint_span_singleton'', HasStrictDerivAt.star, lie_swap_lie, 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, TopologicalAddGroup.IsSES.exact, Set.image_neg, balanced_zero, continuousMultilinearCurryFin1_apply, MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed, LieAlgebra.SemiDirectSum.projl_inr_apply, hasStrictDerivAt_neg, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero', RingPreordering.HasIdealSupport.neg_smul_mem, 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, TensorialAt.smul, HilbertBasis.finite_spans_dense, Module.notMem_support_iff', EMetric.preimage_vadd_closedBall, LinearIsometry.adjoint_comp_self, emultiplicity_neg, Summable.countable_support, ProbabilityTheory.Kernel.integral_indicator₂, Orientation.oangle_add_oangle_rev_neg_right, Function.Periodic.exists_mem_Ico₀, HahnEmbedding.Partial.toOrderAddMonoidHom_injective bridge: BoxIntegral.hasIntegralIndicatorConst, BoxIntegral.HasIntegral.of_aeEq_zero

(root)

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
addConj_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
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 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid AddGroup.toSubtractionMonoid	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid	—	add_assoc neg_add_cancel add_zero
add_eq_of_eq_neg_add 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid AddGroup.toSubtractionMonoid	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid	—	add_neg_cancel_left
add_eq_of_eq_sub 📖	mathematical	SubNegMonoid.toSub AddGroup.toSubNegMonoid	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid	—	sub_add_cancel
add_eq_of_eq_sub' 📖	mathematical	SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	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.toNSMul	—	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.toNSMul	—	add_left_iterate
add_left_iterate_apply_zero 📖	mathematical	—	Nat.iterate AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toZero AddMonoid.toNSMul	—	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	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.toNSMul	—	zero_nsmul add_zero comp_add_right succ_nsmul'
add_right_iterate_apply 📖	mathematical	—	Nat.iterate AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoid.toNSMul	—	add_right_iterate
add_right_iterate_apply_zero 📖	mathematical	—	Nat.iterate AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toZero AddMonoid.toNSMul	—	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.toNSMul	—	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 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toZero	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass	—	additive_of_total
additive_of_symmetric_of_isTotal 📖	mathematical	Symmetric AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toZero	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass	—	additive_of_symmetric_of_total
additive_of_symmetric_of_total 📖	mathematical	Symmetric AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toZero	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass	—	total_of zero_add add_assoc add_zero
additive_of_total 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toZero	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass	—	additive_of_symmetric_of_total
boole_nsmul 📖	mathematical	—	AddMonoid.toNSMul 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
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 Group.toDivInvMonoid CommGroup.toGroup	—	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 Group.toDivInvMonoid	—	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.toPow 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	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 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid AddGroup.toSubtractionMonoid	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid	—	add_assoc neg_add_cancel add_zero
eq_add_of_neg_add_eq 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid AddGroup.toSubtractionMonoid	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid	—	add_neg_cancel_left
eq_add_of_sub_eq 📖	mathematical	SubNegMonoid.toSub AddGroup.toSubNegMonoid	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid	—	sub_add_cancel
eq_add_of_sub_eq' 📖	mathematical	SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	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 Group.toDivInvMonoid	—	mul_div_cancel_right
eq_div_of_mul_eq'' 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup	DivInvMonoid.toDiv Group.toDivInvMonoid CommGroup.toGroup	—	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	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 DivisionMonoid.toDivInvMonoid	—	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	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 Group.toDivInvMonoid	—	div_mul_cancel
eq_mul_of_div_eq' 📖	mathematical	DivInvMonoid.toDiv Group.toDivInvMonoid CommGroup.toGroup	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup	—	div_eq_mul_inv mul_left_comm mul_inv_cancel mul_one
eq_mul_of_inv_mul_eq 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid	—	mul_inv_cancel_left
eq_mul_of_mul_inv_eq 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid	—	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	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 SubtractionMonoid.toSubNegMonoid	—	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 DivisionMonoid.toDivInvMonoid MulOne.toOne MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid	—	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 DivisionMonoid.toDivInvMonoid MulOne.toOne MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid	—	eq_inv_of_mul_eq_one_right one_div
eq_one_iff_eq_one_of_mul_eq_one 📖	mathematical	MulOne.toMul MulOneClass.toMulOne MulOne.toOne	MulOne.toOne MulOneClass.toMulOne	—	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 AddGroup.toSubNegMonoid	—	add_sub_cancel_right
eq_sub_of_add_eq' 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	add_comm sub_eq_add_neg add_assoc add_neg_cancel add_zero
eq_zero_iff_eq_zero_of_add_eq_zero 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddZero.toZero	AddZero.toZero AddZeroClass.toAddZero	—	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 SubtractionMonoid.toSubNegMonoid AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid	—	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 SubtractionMonoid.toSubNegMonoid AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid	—	eq_neg_of_add_eq_zero_right zero_sub
hom_coe_nsmul 📖	mathematical	AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddZero.toAdd	AddMonoid.toNSMul Nat.iterate	—	zero_nsmul succ_nsmul Function.iterate_succ
hom_coe_pow 📖	mathematical	MulOne.toOne MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toMul	Monoid.toPow Nat.iterate	—	pow_zero pow_succ Function.iterate_succ
inv_bijective 📖	mathematical	—	Function.Bijective InvolutiveInv.toInv	—	Function.Involutive.bijective inv_involutive
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	—	Function.Involutive.eq_iff inv_involutive
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	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.toPow 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.toPow 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 Group.toDivInvMonoid	—	div_mul_cancel
mul_eq_of_eq_div' 📖	mathematical	DivInvMonoid.toDiv Group.toDivInvMonoid CommGroup.toGroup	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid CommGroup.toGroup	—	div_eq_mul_inv mul_comm mul_inv_cancel_left
mul_eq_of_eq_inv_mul 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid	—	mul_inv_cancel_left
mul_eq_of_eq_mul_inv 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid InvOneClass.toInv DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass DivInvMonoid.toMonoid Group.toDivInvMonoid	—	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	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.toPow	—	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.toPow	—	mul_left_iterate
mul_left_iterate_apply_one 📖	mathematical	—	Nat.iterate MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne Monoid.toPow	—	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.toPow 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.toPow	—	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.toPow	—	pow_zero mul_one comp_mul_right pow_succ'
mul_right_iterate_apply 📖	mathematical	—	Nat.iterate MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass Monoid.toPow	—	mul_right_iterate
mul_right_iterate_apply_one 📖	mathematical	—	Nat.iterate MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne Monoid.toPow	—	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 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass	—	multiplicative_of_total
multiplicative_of_symmetric_of_isTotal 📖	mathematical	Symmetric MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass	—	multiplicative_of_symmetric_of_total
multiplicative_of_symmetric_of_total 📖	mathematical	Symmetric MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass	—	total_of one_mul mul_assoc mul_one
multiplicative_of_total 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass	—	multiplicative_of_symmetric_of_total
natAbs_nsmul_eq_zero 📖	mathematical	—	AddMonoid.toNSMul 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.toNSMul SubNegMonoid.toAddMonoid	—	sub_eq_add_neg natCast_zsmul sub_zsmul
natCast_sub_one_zsmul 📖	mathematical	—	SubNegMonoid.toZSMul AddGroup.toSubNegMonoid SubNegMonoid.toSub AddMonoid.toNSMul 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	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_bijective 📖	mathematical	—	Function.Bijective InvolutiveNeg.toNeg	—	Function.Involutive.bijective neg_involutive
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	—	Function.Involutive.eq_iff neg_involutive
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.toNSMul 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.toNSMul 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	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoid.toNSMul AddZero.toZero	—	zero_nsmul add_zero succ_nsmul succ_nsmul' add_assoc
nsmul_add_sub_nsmul 📖	mathematical	—	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoid.toNSMul	—	add_nsmul
nsmul_eq_mod_nsmul 📖	mathematical	AddMonoid.toNSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass	AddMonoid.toNSMul	—	add_nsmul mul_nsmul nsmul_zero add_zero
nsmul_iterate 📖	mathematical	—	Nat.iterate AddMonoid.toNSMul	—	one_nsmul mul_nsmul
nsmul_sub 📖	mathematical	—	AddMonoid.toNSMul SubNegMonoid.toAddMonoid SubtractionMonoid.toSubNegMonoid SubtractionCommMonoid.toSubtractionMonoid SubNegMonoid.toSub	—	sub_eq_add_neg nsmul_add neg_nsmul
nsmul_zero_sub 📖	mathematical	—	AddMonoid.toNSMul 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.toPow 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.toNSMul 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.toPow MulOne.toOne MulOneClass.toMulOne Monoid.toMulOneClass	—	pow_ite pow_one pow_zero
pow_dite 📖	—	—	—	—	—
pow_eq_pow_mod 📖	mathematical	Monoid.toPow MulOne.toOne MulOneClass.toMulOne Monoid.toMulOneClass	Monoid.toPow	—	pow_add pow_mul one_pow mul_one
pow_ite 📖	—	—	—	—	pow_dite
pow_iterate 📖	mathematical	—	Nat.iterate Monoid.toPow	—	pow_one pow_mul
pow_mul_pow_eq_one 📖	mathematical	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass MulOne.toOne	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass Monoid.toPow MulOne.toOne	—	pow_zero mul_one pow_succ pow_succ' mul_assoc
pow_mul_pow_sub 📖	mathematical	—	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass Monoid.toPow	—	pow_add
pow_natAbs_eq_one 📖	mathematical	—	Monoid.toPow DivInvMonoid.toMonoid Group.toDivInvMonoid InvOneClass.toOne DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid DivInvMonoid.toZPow	—	zpow_natCast zpow_negSucc
pow_sub 📖	mathematical	—	Monoid.toPow 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.toPow	—	pow_add
pow_sub_one_mul 📖	mathematical	—	MulOne.toMul MulOneClass.toMulOne Monoid.toMulOneClass Monoid.toPow	—	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 AddGroup.toSubNegMonoid	—	add_sub_cancel_right
sub_eq_of_eq_add' 📖	mathematical	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	SubNegMonoid.toSub AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	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.toNSMul 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.toNSMul 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.toNSMul	—	add_nsmul
sub_one_nsmul_add 📖	mathematical	—	AddZero.toAdd AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoid.toNSMul	—	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 📖	mathematical	DivInvMonoid.toZPow Group.toDivInvMonoid InvOneClass.toOne DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid	DivInvMonoid.toZPow Group.toDivInvMonoid	—	zpow_add zpow_mul one_zpow mul_one
zpow_eq_zpow_emod' 📖	mathematical	Monoid.toPow DivInvMonoid.toMonoid Group.toDivInvMonoid InvOneClass.toOne DivInvOneMonoid.toInvOneClass DivisionMonoid.toDivInvOneMonoid Group.toDivisionMonoid	DivInvMonoid.toZPow Group.toDivInvMonoid	—	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 Group.toDivInvMonoid	—	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 Group.toDivInvMonoid	—	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.toPow DivInvMonoid.toMonoid	—	div_eq_mul_inv zpow_natCast zpow_sub
zpow_natCast_sub_one 📖	mathematical	—	DivInvMonoid.toZPow Group.toDivInvMonoid DivInvMonoid.toDiv Monoid.toPow 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.toPow 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 AddGroup.toSubNegMonoid	—	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 AddGroup.toSubNegMonoid	—	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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