Defs

📁 Source: Mathlib/Algebra/Group/Subgroup/Defs.lean

Statistics

Metric	Count
Definitions `AddSubgroup`, `Normal`, `add`, `copy`, `inclusion`, `instPartialOrder`, `instSetLike`, `neg`, `normalizer`, `nsmul`, `ofClass`, `ofSub`, `sub`, `subtype`, `toAddCommGroup`, `toAddGroup`, `toAddSubmonoid`, `zero`, `zsmul`, `AddSubgroupClass`, `inclusion`, `instZSMul`, `sub`, `subtype`, `toAddCommGroup`, `toAddGroup`, `HasMemOrInvMem`, `HasMemOrNegMem`, `InvMemClass`, `inv`, `NegMemClass`, `neg`, `Normal`, `copy`, `div`, `inclusion`, `instPartialOrder`, `instSetLike`, `inv`, `mul`, `normalizer`, `npow`, `ofClass`, `ofDiv`, `one`, `setNormalizer`, `subtype`, `toCommGroup`, `toGroup`, `toSubmonoid`, `zpow`, `SubgroupClass`, `div`, `inclusion`, `instZPow`, `subtype`, `toCommGroup`, `toGroup`	58
Theorems `addConj_mem'`, `conj_mem`, `mem_comm`, `mem_comm_iff`, `addCommGroup_isAddCommutative`, `add_comm_of_mem_isAddCommutative`, `add_mem`, `add_mem_cancel_left`, `add_mem_cancel_right`, `coe_add`, `coe_copy`, `coe_inclusion`, `coe_mk`, `coe_neg`, `coe_nonempty`, `coe_nsmul`, `coe_ofClass`, `coe_set_mk`, `coe_sub`, `coe_subtype`, `coe_toAddSubmonoid`, `coe_zero`, `coe_zsmul`, `copy_eq`, `exists_neg_mem_iff_exists_mem`, `ext`, `ext_iff`, `inclusion_inj`, `inclusion_injective`, `instAddSubgroupClass`, `instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallNeg`, `le_normalizer`, `mem_carrier`, `mem_mk`, `mem_normalizer_iff`, `mem_normalizer_iff'`, `mem_normalizer_iff''`, `mem_toAddSubmonoid`, `mk_eq_zero`, `mk_le_mk`, `neg_mem`, `neg_mem'`, `neg_mem_iff`, `normal_of_comm`, `nsmul_mem`, `sub_mem`, `subtype_apply`, `subtype_comp_inclusion`, `subtype_injective`, `toAddSubmonoid_inj`, `toAddSubmonoid_injective`, `toAddSubmonoid_le`, `toAddSubmonoid_mono`, `toAddSubmonoid_strictMono`, `zero_mem`, `zsmul_mem`, `coe_inclusion`, `coe_nsmul`, `coe_sub`, `coe_subtype`, `coe_zsmul`, `inclusion_mk`, `inclusion_right`, `inclusion_self`, `subset_union`, `subtype_apply`, `subtype_comp_inclusion`, `subtype_injective`, `toAddSubmonoidClass`, `toNegMemClass`, `inv_mem_of_notMem`, `mem_of_inv_notMem`, `mem_or_inv_mem`, `mem_of_neg_notMem`, `mem_or_neg_mem`, `neg_mem_of_notMem`, `coe_inv`, `inv_mem`, `coe_neg`, `neg_mem`, `injOn_iff_map_eq_one`, `injOn_iff_map_eq_zero`, `conj_mem`, `conj_mem'`, `mem_comm`, `mem_comm_iff`, `coe_copy`, `coe_div`, `coe_inclusion`, `coe_inv`, `coe_mk`, `coe_mul`, `coe_nonempty`, `coe_ofClass`, `coe_one`, `coe_pow`, `coe_set_mk`, `coe_subtype`, `coe_toSubmonoid`, `coe_zpow`, `commGroup_isMulCommutative`, `copy_eq`, `div_mem`, `exists_inv_mem_iff_exists_mem`, `ext`, `ext_iff`, `inclusion_inj`, `inclusion_injective`, `instCanLiftSetCoeAndMemOfNatForallForallForallForallHMulForallForallInv`, `instSubgroupClass`, `inv_mem`, `inv_mem'`, `inv_mem_iff`, `le_normalizer`, `mem_carrier`, `mem_mk`, `mem_normalizer_iff`, `mem_normalizer_iff'`, `mem_normalizer_iff''`, `mem_toSubmonoid`, `mk_eq_one`, `mk_le_mk`, `mul_comm_of_mem_isMulCommutative`, `mul_mem`, `mul_mem_cancel_left`, `mul_mem_cancel_right`, `normal_of_comm`, `one_mem`, `pow_mem`, `subtype_apply`, `subtype_comp_inclusion`, `subtype_injective`, `toSubmonoid_inj`, `toSubmonoid_injective`, `toSubmonoid_le`, `toSubmonoid_mono`, `toSubmonoid_strictMono`, `zpow_mem`, `coe_div`, `coe_inclusion`, `coe_pow`, `coe_subtype`, `coe_zpow`, `inclusion_inclusion`, `inclusion_mk`, `inclusion_right`, `inclusion_self`, `subset_union`, `subtype_apply`, `subtype_comp_inclusion`, `subtype_injective`, `toInvMemClass`, `toSubmonoidClass`, `add_mem_cancel_left`, `add_mem_cancel_right`, `div_mem`, `exists_inv_mem_iff_exists_mem`, `exists_neg_mem_iff_exists_mem`, `inv_mem_iff`, `mul_mem_cancel_left`, `mul_mem_cancel_right`, `neg_mem_iff`, `sub_mem`, `zpow_mem`, `zsmul_mem`	165
Total	223

AddSubgroup

Definitions

Name	Category	Theorems
`Normal` 📖	CompData	64 math math: `inf_addSubgroupOf_inf_normal_of_left`, `AddMonoidHom.normal_ker`, `addCommutator_top_left_le_iff`, `normal_op`, `Normal.pathComponentZero`, `normal_bot`, `is_normal_topologicalClosure`, `Normal.of_addCommutator_le`, `IsSubnormal.lt_normal`, `normal_goursatSnd`, `prod_addSubgroupOf_prod_normal`, `normal_inf_normal`, `normalClosure_eq_iInf`, `addCommutator_top_right_le_iff`, `FiniteIndexNormalAddSubgroup.isNormal'`, `IsSubnormal.normal_of_isSimpleAddGroup`, `instNormalCenter`, `normal_goursatFst`, `normalizer_eq_top_iff`, `op.instNormal`, `OpenNormalAddSubgroup.instNormal`, `AddGroupExtension.normal_inl_range`, `Normal.map`, `Normal.addSubgroupOf`, `normal_of_characteristic`, `Normal.of_op`, `unop.instNormal`, `IsSubnormal.exists_normal_and_le_and_lt_top_of_ne`, `orderIsoAddCon_symm_apply_coe`, `normalClosure_normal`, `Normal.op`, `sup_normal`, `Normal.comap`, `normal_addSubgroupOf_iff`, `FiniteIndexNormalAddSubgroup.instNormal`, `normal_centralizer`, `normal_addSubgroupOf`, `orderIsoAddCon_apply`, `normal_top`, `Normal.unop`, `Normal.of_unop`, `OpenNormalAddSubgroup.isNormal'`, `normal_addSubgroupOf_of_le_normalizer`, `normal_addSubgroupOf_iff_le_normalizer`, `QuotientAddGroup.instNormalAddSubgroup`, `normal_iInf_normal`, `QuotientAddGroup.map_normal`, `normal_of_eq_addCosets`, `normalCore_normal`, `normal_of_comm`, `IsSubnormal.iff_eq_top_or_exists`, `normal_iff_eq_addCosets`, `inf_addSubgroupOf_inf_normal_of_right`, `normal_unop`, `goursat`, `addCommutator_normal`, `prod_normal`, `instNormalSubtypeMemFocalAddSubgroupOf`, `normal_addSubgroupOf_iff_le_normalizer_inf`, `normal_addSubgroupOf_sup_of_le_normalizer`, `normal_in_normalizer`, `IsSubnormal.isSubnormal_iff`, `normalCore_eq_iSup`, `normal_comap`
`add` 📖	CompOp	97 math math: `centerToAddOpposite_apply_coe`, `AddSubmonoid.val_addUnitsEquivAddUnitsType_symm_apply_coe`, `AddAction.stabilizerEquivStabilizer_symm`, `AddEquiv.addSubgroupMap_symm_apply`, `zmultiples_isAddCommutative`, `MeasureTheory.Lp.coeFn_add`, `addSubgroupOfContinuousAddEquivOfLe_apply`, `SubAddAction.ofStabilizer.addConjMap_apply`, `MeasureTheory.condExpIndL1_add`, `SubAddAction.addConjMap_ofFixingAddSubgroup_bijective`, `instIsAddCommutative_closure`, `AddEquiv.addSubgroupCongr_apply`, `MeasureTheory.condExpIndL1Fin_add`, `SubAddAction.ofStabilizer.addConjMap_comp_neg_apply`, `AddMonoidHom.apply_ofInjective_symm`, `MeasureTheory.L1.SimpleFunc.integral_add`, `AddMonoidHom.range_isAddCommutative`, `coe_equivMapOfInjective_apply`, `AddMonoidHom.ofLeftInverse_symm_apply`, `DomAddAct.vadd_Lp_add`, `addSubgroupOfEquivOfLe_apply_coe`, `coe_addEquiv_lpPiLp_symm`, `Int.addSubgroup_index_ne_zero_iff`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `MeasureTheory.Lp.dist_eq_norm`, `MeasureTheory.Lp.simpleFunc.add_toSimpleFunc`, `coe_ringEquiv_lpBCF`, `centerCongr_apply_coe`, `AddAction.stabilizerEquivStabilizer_symm_apply`, `lp.coeFn_add`, `MeasureTheory.condExpIndSMul_add`, `MeasureTheory.condExpL1_add`, `AddMonoidHom.ofLeftInverse_apply`, `addCommGroup_isAddCommutative`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `MeasureTheory.Lp_toLp_restrict_add`, `SubAddAction.ofStabilizer.addConjMap_comp`, `le_centralizer_iff_isAddCommutative`, `addSubgroupOfEquivOfLe_symm_apply_coe_coe`, `addSubgroupOf_isAddCommutative`, `ProfiniteAddGrp.limit_add_val`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `topEquiv_symm_apply_coe`, `SubAddAction.addConjMap_ofFixingAddSubgroup_coe_apply`, `AddAction.stabilizerEquivStabilizer_neg`, `MeasureTheory.Lp.add_smul`, `AddEquiv.coe_addSubgroupMap_apply`, `MeasureTheory.lpMeasSubgroupToLpTrim_add`, `map_isAddCommutative`, `MeasureTheory.Lp.instAddLeftMono`, `centerCongr_symm_apply_coe`, `coe_add`, `MeasureTheory.indicatorConstLp_add`, `MeasureTheory.Lp.instFourierInvAdd`, `AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_symm_apply_coe`, `coe_addEquiv_lpBCF_symm`, `SubAddAction.ofFixingAddSubgroup_insert_map_apply`, `MeasureTheory.condExpIndL1Fin_disjoint_union`, `coe_addEquiv_lpBCF`, `SubAddAction.ofStabilizer.addConjMap_comp_apply`, `Commute.expUnitary_add`, `SubAddAction.fixingAddSubgroupEquivFixingAddSubgroup_coe_apply`, `lp.single_add`, `centerToAddOpposite_symm_apply_coe`, `MeasureTheory.Lp.smul_add`, `MeasureTheory.L1.integral_add`, `MeasureTheory.condExpIndL1_disjoint_union`, `topEquiv_apply`, `ContinuousLinearMap.add_compLp`, `SubAddAction.ofStabilizer.neg_addConjMap_comp_apply`, `AddAction.stabilizerEquivStabilizer_apply`, `AddAction.stabilizerEquivStabilizer_trans`, `coe_addEquiv_lpPiLp`, `AddEquiv.addSubgroupCongr_symm_apply`, `MeasureTheory.MemLp.toLp_add`, `ContinuousLinearMap.holder_add_right`, `MeasureTheory.condExpInd_disjoint_union_apply`, `imaginaryPart_smul`, `coe_ringEquiv_lpBCF_symm`, `addSubgroupOfContinuousAddEquivOfLe_symm_apply`, `val_list_sum`, `MeasureTheory.L1.SimpleFunc.setToL1S_add`, `MeasureTheory.Integrable.toL1_add`, `isAddCommutative_closure`, `addSubgroupOfContinuousAddEquivOfLe_toAddEquiv`, `AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_apply_coe`, `AddAction.stabilizerEquivStabilizer_zero`, `comap_injective_isAddCommutative`, `MeasureTheory.indicatorConstLp_disjoint_union`, `SubAddAction.ofStabilizer.addConjMap_bijective`, `AddAction.stabilizerEquivStabilizer_compTriple`, `ContinuousLinearMap.holder_add_left`, `MeasureTheory.Lp.simpleFunc.toLp_add`, `MeasureTheory.Lp.instFourierAdd`, `AddMonoidHom.ofInjective_apply`, `DomMulAct.smul_Lp_add`, `AddSubmonoid.val_addUnitsEquivAddUnitsType_apply_coe`
`copy` 📖	CompOp	2 math math: `coe_copy`, `copy_eq`
`inclusion` 📖	CompOp	11 math math: `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `lp.toAddMonoidHom_linearMapOfLE`, `QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk`, `inclusion_inj`, `subtype_comp_inclusion`, `inclusion_range`, `inclusion_injective`, `comap_inclusion_addSubgroupOf`, `quotientAddSubgroupOfEmbeddingOfLE_apply_mk`, `coe_inclusion`, `ker_inclusion`
`instPartialOrder` 📖	CompOp	244 math math: `Submodule.toAddSubgroup_toZModSubmodule`, `NonUnitalSubring.toAddSubgroup_mono`, `addSubgroupOf_eq_top`, `addCommutator_comm_le`, `closure_le_normalClosure`, `addCommutator_top_left_le_iff`, `addCommutator_pi_pi_le`, `Normal.quotient_commutative_iff_addCommutator_le`, `AddMonoidHom.liftOfRightInverse_comp_apply`, `ArchimedeanClass.addSubgroup_antitone`, `normalClosure_le_normal`, `map_inf_le`, `mem_toSubgroup'`, `ofAddUnits_addUnits_gc`, `characteristic_iff_comap_le`, `le_prod_iff`, `le_centralizer_iff`, `zmultiples_le`, `prod_mono_left`, `map_eq_range_iff`, `addCommutator_le_focalAddSubgroupOf`, `MonoidHom.coe_toMultiplicative_range`, `Subring.toAddSubgroup_mono`, `AddEquiv.coe_comapAddSubgroup`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_apply₂`, `IsSubnormal.lt_normal`, `closure_le_centralizer_centralizer`, `addCommutator_le`, `AddAction.map_stabilizer_le`, `OpenAddSubgroup.toAddSubgroup_le`, `Valuation.ltAddSubgroup_monotone`, `focalAddSubgroup_le`, `op_le_iff`, `AddAction.stabilizer_le_aestabilizer`, `characteristic_iff_le_map`, `ofAddUnits_le_iff_le_addUnits`, `addCommutator_top_right_le_iff`, `Subring.toAddSubgroup_lt_toAddSubgroup`, `NumberField.Units.span_basisOfIsMaxRank`, `toZModSubmodule_toAddSubgroup`, `normal_le_normalCore`, `addCommutator_centralizer_addCommutator_le_center`, `topologicalClosure_minimal`, `AddAction.IsBlock.stabilizer_le`, `Subgroup.fg_iff_add_fg`, `Module.Basis.addSubgroupOfClosure_repr_apply`, `map_subtype_le`, `normalClosure_subset_iff`, `le_op_iff`, `ker_le_comap`, `toIntSubmodule_symm`, `QuotientAddGroup.strictMono_comap_prod_image`, `toSubgroup_closure`, `disjoint_def`, `AddEquiv.symm_mapAddSubgroup`, `op_le_op_iff`, `Submodule.toAddSubgroup_mono`, `map_le_map_iff`, `normalClosure_mono`, `closure_mono`, `NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion`, `Subgroup.mem_toAddSubgroup'`, `AddSubmonoid.addUnits_mono`, `MonoidHom.coe_toAdditive_map`, `map_subtype_lt_map_subtype`, `pi_le_iff`, `le_normalizer`, `QuotientAddGroup.ker_le_range_iff`, `Submodule.toIntSubmodule_toAddSubgroup`, `pointwise_smul_le_iff₀`, `AddEquiv.mapAddSubgroup_symm_apply`, `Subgroup.coe_toAddSubgroup_symm_apply`, `addCommutator_le_map_addCommutator`, `closure_add_le`, `QuotientAddGroup.strictMono_comap_prod_map`, `AddMonoidHom.liftOfRightInverse_comp`, `addSubgroupOf_mono`, `lp.monotone`, `map_eq_bot_iff`, `addCommutator_le_right`, `AddEquiv.comapAddSubgroup_apply`, `relIndex_eq_one`, `Submodule.toAddSubgroup_toIntSubmodule`, `le_centralizer_iff_isAddCommutative`, `comap_mono`, `map_le_map_iff_of_injective`, `IsSubnormal.exists_normal_and_le_and_lt_top_of_ne`, `fixedPoints_addSubgroup_antitone`, `toAddSubmonoid_strictMono`, `orderIsoAddCon_symm_apply_coe`, `normalCore_le`, `codisjoint_addSubgroupOf_sup`, `map_le_iff_le_comap`, `toZModSubmodule_symm`, `IsSimpleAddGroup.instIsSimpleOrderAddSubgroup`, `comap_le_comap_of_surjective`, `AddAction.fixingAddSubgroup_le_stabilizer`, `le_normalizer_map`, `RingSubgroupsBasis.inter`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_inter`, `opEquiv_symm_apply`, `ofAddUnits_mono`, `CategoryTheory.ShortComplex.ab_exact_iff_ker_le_range`, `AddMonoid.Coprod.codisjoint_range_inl_range_inr`, `Multiplicative.mem_toSubgroup`, `ArchimedeanClass.ballAddSubgroup_antitone`, `AddAction.le_stabilizer_vadd_right`, `Subgroup.toAddSubgroup_closure`, `Subring.toAddSubgroup_strictMono`, `AddEquiv.coe_mapAddSubgroup`, `MapSubtype.orderIso_apply_coe`, `characteristic_iff_le_comap`, `closure_nsmul_le`, `coe_toZModSubmodule`, `centralizer_le`, `Normal.addCommutator_le_of_self_sup_commutative_eq_top`, `Subgroup.coe_toAddSubgroup_apply`, `Submodule.toAddSubgroup_strictMono`, `map_mono`, `addCommutator_le_left`, `le_normalClosure`, `Subgroup.strictPeriods_le_periods`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_union`, `Subgroup.index_toAddSubgroup`, `AddMonoidHom.coe_toIntLinearMap_ker`, `gc_map_comap`, `map_subtype_le_map_subtype`, `coe_toIntSubmodule`, `zmultiples_le_of_mem`, `Valuation.ltAddSubgroup_le_leAddSubgroup`, `AddEquiv.mapAddSubgroup_apply`, `comap_lt_comap_of_surjective`, `MeasureTheory.Lp.antitone`, `MonoidHom.coe_toAdditive_range`, `disjoint_map`, `le_normalizer_of_normal`, `addCommutator_le_focalAddSubgroup`, `opEquiv_apply`, `le_pi_iff`, `MapSubtype.orderIso_symm_apply`, `FreeAddGroup.range_lift_le`, `gc_toAddSubmonoid_support`, `map_lt_map_iff_of_injective`, `AddMonoidHom.coe_toIntLinearMap_map`, `prod_le_iff`, `pointwise_smul_le_pointwise_smul_iff₀`, `orderIsoAddCon_apply`, `focalAddSubgroup_le_addCommutator`, `AddMonoidHom.coe_toIntLinearMap_range`, `AddMonoidHom.coe_toMultiplicative_map`, `prod_mono`, `ofAddUnits_strictMono`, `Subgroup.toAddSubgroup_comap`, `prod_mono_right`, `FiniteArchimedeanClass.addSubgroup_strictAnti`, `disjoint_iff_add_eq_zero`, `Submodule.AddMonoidHom.coe_toIntLinearMap_comap`, `finiteIndex_toSubgroup_iff`, `normal_addSubgroupOf_iff_le_normalizer`, `coe_toSubgroup_apply`, `fixingAddSubgroup_fixedPoints_gc`, `AddMonoidHom.closure_preimage_le`, `le_zmultiples_iff`, `Subring.toAddSubgroup_le_toAddSubgroup`, `normalizer_le_normalizer_sup_normal`, `NormedAddGroupHom.ker_le_ker_completion`, `topologicalClosure_mono`, `pointwise_smul_le_pointwise_smul_iff`, `fg_iff_mul_fg`, `normalCore_mono`, `mk_le_mk`, `fixingAddSubgroup_antitone`, `AddEquiv.symm_comapAddSubgroup`, `AddMonoidHom.range_le_ker_iff`, `toIntSubmodule_toAddSubgroup`, `FiniteArchimedeanClass.ballAddSubgroup_strictAnti`, `ArchimedeanClass.addSubgroup_strictAntiOn`, `le_comap_map`, `toSubgroup'_closure`, `pointwise_smul_le_iff`, `map_comap_le`, `normalizer_le_normalizer_sup_of_normalizer_le_left`, `NonUnitalSubring.toAddSubgroup_strictMono`, `disjoint_def'`, `addCommutator_le_inf`, `normalizer_inf_normalizer_le_normalizer_sup`, `addCommutator_mono`, `surjOn_iff_le_map`, `Subgroup.toAddSubgroup'_closure`, `IsSubnormal.iff_eq_top_or_exists`, `relIndex_eq_natAbs_det`, `AddMonoidHom.eq_liftOfRightInverse`, `iSup_comap_le`, `addCommutator_le_self`, `le_pointwise_smul_iff`, `goursatFst_prod_goursatSnd_le`, `index_toSubgroup`, `le_topologicalClosure`, `toIntSubmodule_closure`, `mem_toZModSubmodule`, `addSubgroupOf_eq_bot`, `toAddSubmonoid_le`, `Subgroup.finiteIndex_toAddSubgroup_iff`, `AddAction.le_stabilizer_iff_vadd_le`, `comap_sup_comap_le`, `QuotientAddGroup.con_le_iff`, `Valuation.leAddSubgroup_monotone`, `le_pointwise_smul_iff₀`, `unop_le_unop_iff`, `center_le_normalizer`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_ker`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_sdiff`, `normalizer_le_normalizer_sup_of_normalizer_le_right`, `Submodule.toAddSubgroup_le`, `center_le_centralizer`, `addCommutator_eq_bot_iff_le_centralizer`, `AddAction.le_stabilizer_vadd_left`, `le_normalizer_comap`, `toSubgroup_comap`, `coe_toSubgroup_symm_apply`, `le_normalizer_of_normal_addSubgroupOf`, `Module.Basis.addSubgroupOfClosure_apply`, `le_centralizer`, `codisjoint_map`, `inf_normalizer_le_normalizer_inf`, `closure_le`, `MonoidHom.coe_toAdditive_ker`, `AddAction.isCoatom_stabilizer_iff_preprimitive`, `comap_le_comap_of_le_range`, `AddAction.IsPreprimitive.isCoatom_stabilizer_of_isPreprimitive`, `map_le_map_iff'`, `characteristic_iff_map_le`, `Additive.mem_toAddSubgroup`, `normal_addSubgroupOf_iff_le_normalizer_inf`, `AddEquiv.comapAddSubgroup_symm_apply`, `Subgroup.relIndex_toAddSubgroup`, `IsSubnormal.isSubnormal_iff`, `QuotientAddGroup.le_comap_mk'`, `MonoidHom.coe_toMultiplicative_ker`, `map_le_range`, `toAddSubmonoid_mono`, `relIndex_toSubgroup`, `normalCore_eq_iSup`, `map_centralizer_le_centralizer_image`
`instSetLike` 📖	CompOp	1857 math math: `cfc_realPart`, `Unitary.openPartialHomeomorph_source`, `AddAction.mem_stabilizer_set_iff_subset_vadd_set`, `SchwartzMap.norm_toLp_le_seminorm`, `MeasureTheory.L1.setToL1_eq_setToL1'`, `continuous_decomposeProdAdjoint`, `MeasureTheory.Lp.instHasSolidNorm`, `coe_prod`, `MeasureTheory.integrable_indicatorConstLp`, `centerToAddOpposite_apply_coe`, `ContinuousMap.toLp_inj`, `inf_addSubgroupOf_inf_normal_of_left`, `IsFiniteRelIndex.to_finiteIndex_addSubgroupOf`, `noncommSum_mem`, `AddMonoidHom.coe_rangeRestrict`, `TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbing`, `MeasureTheory.Lp.toTemperedDistributionCLM_apply`, `StarModule.decomposeProdAdjointL_symm_apply`, `MeasureTheory.LpToLpRestrictCLM_coeFn`, `StarModule.selfAdjointPart_add_skewAdjointPart`, `mem_map_iff_mem`, `AddMonoidHom.coe_ker`, `MeasureTheory.L1.SimpleFunc.norm_Integral_le_one`, `lp.norm_apply_le_norm`, `Subgroup.isRegularAtInfty_iff`, `MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm''`, `MeasureTheory.condExpInd_of_measurable`, `SubAddAction.map_ofFixingAddSubgroupUnion_bijective`, `unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `normalClosure_closure_eq_normalClosure`, `MeasureTheory.Lp.mul_meas_ge_le_pow_enorm'`, `quotientEquivProdOfLE_symm_apply`, `isClosed_topologicalClosure`, `MeasureTheory.condExpL1_smul`, `lp.coe_linearMapOfLE_apply`, `MeasureTheory.Lp.instIsScalarTower`, `DomAddAct.mk_vadd_indicatorConstLp`, `imaginaryPart_eq_zero_iff`, `Commute.realPart_imaginaryPart`, `MeasureTheory.aestronglyMeasurable_condExpInd`, `AddSubmonoid.val_addUnitsEquivAddUnitsType_symm_apply_coe`, `CochainComplex.HomComplex.Cocycle.precomp_coe`, `QuotientAddGroup.leftRel_apply`, `MeasureTheory.mem_lpMeasSubgroup_iff_aestronglyMeasurable`, `CochainComplex.mappingCocone.inr_v_snd_v_assoc`, `Complex.coe_realPart`, `quasispectrum_imaginaryPart`, `lp.norm_le_of_tsum_le`, `AddAction.stabilizer_addSubgroup_op`, `ContinuousLinearMap.integral_compLp`, `addSubgroupOf_eq_top`, `ArchimedeanClass.subsemigroup_eq_addSubgroup_of_ne_top`, `lp.isLUB_norm`, `selfAdjoint.val_div`, `MeasureTheory.Lp.compMeasurePreserving_id_apply`, `SubAddAction.notMem_val_image`, `AddAction.stabilizerEquivStabilizer_symm`, `MeasureTheory.norm_indicatorConstLp_le`, `NormedAddGroupHom.Equalizer.ι_normNoninc`, `quotientiInfAddSubgroupOfEmbedding_apply_mk`, `isApproximateAddSubgroup_zero`, `AddGroup.closure_finite_fg`, `MeasureTheory.condExpInd_ae_eq_condExpIndSMul`, `Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `IsHilbertSum.surjective_isometry`, `MeasureTheory.L1.setToL1_indicatorConstLp`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left`, `cfc_im_id`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1`, `UnitAddTorus.coe_mFourierBasis`, `OrthogonalFamily.linearIsometry_apply_single`, `MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure`, `nsmul_finEquivZMultiples_symm_apply`, `realPart_idem`, `AddCircle.isAddQuotientCoveringMap_zsmul_of_ne_zero`, `SchwartzMap.inner_fourier_toL2_eq`, `SchwartzMap.toLp_fourierTransformInv_eq`, `MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral`, `FiniteArchimedeanClass.mem_addSubgroup_iff`, `MeasureTheory.Lp.mem_Lp_of_ae_bound`, `MeasureTheory.tendsto_condExpL1_of_dominated_convergence`, `exists_mem_sup`, `closure_preimage_eq_top`, `vaddCommClass_left`, `CochainComplex.Lifting.π_f_cochain₁_v_ι_f`, `CochainComplex.HomComplex.Cocycle.coe_smul`, `NormedAddGroupHom.incl_range`, `MeasureTheory.Lp.const_smul_mem_Lp`, `lp.instNormedStarGroupSubtypePreLpMemAddSubgroup`, `AddEquiv.addSubgroupMap_symm_apply`, `CochainComplex.mappingCone.id`, `MeasureTheory.norm_condExpL2_le`, `zmultiples_isAddCommutative`, `MeasureTheory.Lp.instIsOrderedAddMonoid`, `MeasureTheory.MemLp.toLp_val`, `AddSubmonoid.coe_support`, `mem_pi`, `lp.inner_eq_tsum`, `realPart_ofReal`, `MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm`, `ContinuousLinearMap.continuous_integral_comp_L1`, `MeasureTheory.Lp.edist_def`, `AddAction.mem_addSubgroup_orbit_iff`, `TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure`, `MeasureTheory.L1.norm_setToL1_le`, `CochainComplex.mappingCone.inr_f_fst_v`, `MeasureTheory.inner_condExpL2_left_eq_right`, `ContinuousMap.toLp_denseRange`, `FixedPoints.mem_addSubgroup`, `Unitary.mem_pathComponentOne_iff`, `MeasureTheory.Lp.coeFn_add`, `mem_closure_range_iff_of_fintype`, `ContinuousLinearMap.comp_memLp`, `CochainComplex.mappingCocone.inr_v_snd_v`, `coe_addSubgroupOf`, `MeasureTheory.Lp.eq_zero_iff_ae_eq_zero`, `lp.coeFn_star`, `imaginaryPart_I_smul`, `MeasureTheory.Lp.ext_iff`, `ContinuousLinearMap.norm_compLp_le`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff_of_addConj`, `lp.norm_eq_zero_iff`, `mem_toSubgroup'`, `image_addCommutatorSet_closureAddCommutatorRepresentatives`, `MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero`, `addSubgroupOfContinuousAddEquivOfLe_apply`, `QuotientAddGroup.eq`, `MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving`, `iSup_eq_closure`, `smul_mem_pointwise_smul_iff`, `MeasureTheory.Lp.coeFn_const`, `exists_isComplement_left`, `MeasureTheory.norm_setToFun_le_mul_norm'`, `LipschitzWith.lipschitzWith_compLp`, `coe_top`, `MeasureTheory.norm_indicatorConstLp`, `vadd_mem_fixedPoints_of_normal`, `ContinuousMap.range_toLp`, `CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero`, `top_addSubgroupOf`, `selfAdjoint.expUnitaryPathToOne_apply`, `Unitary.continuousOn_argSelfAdjoint`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `CochainComplex.HomComplex.Cocycle.coe_sub`, `CochainComplex.HomComplex.Cocycle.toCochainAddMonoidHom_apply`, `MeasureTheory.L1.ofReal_norm_eq_lintegral`, `IsSelfAdjoint.smul_mem_skewAdjoint`, `card_map_of_injective`, `rightAddCoset_mem_rightAddCoset`, `dense_of_no_min`, `MeasureTheory.condExpIndL1Fin_smul`, `le_centralizer_iff`, `mem_inv_pointwise_smul_iff`, `coe_comap`, `selfAdjoint.norm_sq_expUnitary_sub_one`, `card_comap_dvd_of_injective`, `QuotientAddGroup.univ_eq_iUnion_vadd`, `MeasureTheory.Lp.dist_def`, `MeasureTheory.Lp.aestronglyMeasurable`, `iSupIndep.dfinsuppSumAddHom_injective`, `mem_inertia`, `mem_sup_left`, `zmultiples_le`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_const`, `IsHilbertSum.linearIsometryEquiv_symm_apply`, `zsmul_mem`, `MeasureTheory.lpMeasSubgroupToLpTrim_neg`, `MeasureTheory.Lp.nnnorm_le_of_ae_bound`, `MeasureTheory.Lp.simpleFunc.uniformContinuous`, `coe_subtype`, `addCommutator_mem_addCommutator`, `SubgroupNormal.mem_comm`, `MeasureTheory.Lp.memLp`, `MeasureTheory.Lp.nnnorm_def`, `instNontrivialSubtypeMemTop`, `QuotientAddGroup.eq_iff_sub_mem`, `SubAddAction.ofStabilizer.addConjMap_apply`, `QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure`, `lp.eq_zero_iff_coeFn_eq_zero`, `MeasureTheory.Integrable.toL1_zero`, `addCommutator_def`, `noncommPiCoprod_single`, `SubAddAction.ofFixingAddSubgroup_of_singleton_bijective`, `MeasureTheory.Lp.mem_Lp_of_ae_le`, `MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq`, `AddCircle.isAddFundamentalDomain_of_ae_ball`, `relIndex_eq_two_iff_exists_notMem_and`, `normal_add`, `selfAdjoint.val_mul`, `multiset_noncommSum_mem`, `coe_neg`, `QuotientAddGroup.mk'_eq_mk'`, `lp.coeFnAddMonoidHom_apply`, `mem_prod`, `MeasureTheory.condExpIndL1_add`, `addCommutator_le_focalAddSubgroupOf`, `CochainComplex.mappingCone.d_snd_v`, `MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM`, `coe_unop`, `SubAddAction.addConjMap_ofFixingAddSubgroup_bijective`, `instIsAddCommutative_closure`, `AddCircle.isAddQuotientCoveringMap_nsmul_of_ne_zero`, `lp.sum_rpow_le_norm_rpow`, `MeasureTheory.norm_indicatorConstLp_top`, `lp.norm_le_of_forall_le'`, `CochainComplex.HomComplex.Cocycle.postcomp_coe`, `addSubgroupOf_self`, `lp.norm_sum_single`, `MeasureTheory.L1.integral_smul`, `MeasureTheory.Lp.instFourierInvSMul`, `CochainComplex.HomComplex.Cocycle.coe_units_smul`, `AddAction.finite_quotient_of_finite_quotient_of_finite_quotient`, `ContinuousLinearMap.smul_compLp`, `selfAdjointPart_comp_subtype_skewAdjoint`, `SubAddAction.ofStabilizer.isPretransitive_iff_of_addConj`, `sum_mem`, `Circle.isAddQuotientCoveringMap_exp`, `Nat.card_zmultiples`, `add_normal`, `AddCircle.isAddQuotientCoveringMap_nsmul`, `coe_copy`, `card_eq_iff_eq_top`, `mem_sup_of_normal_left`, `AddEquiv.addSubgroupCongr_apply`, `isFiniteRelIndex_iff_finiteIndex`, `MeasureTheory.AEEqFun.compMeasurePreserving_mem_Lp`, `MeasureTheory.L2.inner_def`, `MeasureTheory.Lp.enorm_toLp`, `SchwartzMap.toLpCLM_apply`, `SubAddAction.mem_ofStabilizer_iff`, `sub_mem_comm_iff`, `IsSelfAdjoint.selfAdjointPart_apply`, `isOpen_mono`, `IsComplement.neg_toLeftFun_add_mem`, `StarModule.decomposeProdAdjointL_apply`, `MeasureTheory.condExpIndL1Fin_add`, `discreteTopology_iff_of_isFiniteRelIndex`, `AddGroup.addConjugates_subset_normal`, `image_range_addOrderOf`, `coe_zmultiples`, `MeasureTheory.Lp.compMeasurePreservingₗ_apply`, `SubAddAction.ofStabilizer.addConjMap_comp_neg_apply`, `ContinuousMap.toLp_norm_le`, `mem_zmultiples_nsmul_iff`, `closure_le_centralizer_centralizer`, `CochainComplex.mappingCone.liftCocycle_coe`, `MeasureTheory.condExpL1_measure_zero`, `selfAdjoint.val_one`, `lp.toAddMonoidHom_linearMapOfLE`, `SchwartzMap.inner_toL2_toL2_eq`, `MeasureTheory.AEEqFun.integrable_iff_mem_L1`, `coe_zero`, `intCast_mem_zmultiples_one`, `MeasureTheory.Lp.simpleFunc.isDenseEmbedding`, `MeasureTheory.Integrable.toL1_coeFn`, `MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'`, `addCommutator_le`, `mem_zmultiples`, `subtype_range`, `CochainComplex.HomComplex.CohomologyClass.mk_eq_zero_iff`, `MeasureTheory.L1.SimpleFunc.norm_setToL1S_le`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp`, `AddMonoidHom.addSubgroupOf_range_eq_of_le`, `quotient_finite_of_isOpen'`, `IsComplement.neg_add_toLeftFun_mem`, `DomMulAct.smul_Lp_sub`, `SchwartzMap.norm_toLp_one`, `RingSubgroupsBasis.rightMul`, `MeasureTheory.L1.SimpleFunc.setToL1S_neg`, `SchwartzMap.toLp_fourierInv_eq`, `IsOfFinAddOrder.mem_zmultiples_iff_mem_range_addOrderOf`, `zmultiples_equiv_zmultiples_apply`, `card_eq_card_quotient_mul_card_addSubgroup`, `skewAdjoint.mem_iff`, `MeasureTheory.continuous_condExpIndL1`, `AddMonoidHom.rangeRestrict_surjective`, `IsHilbertSum.hasSum_linearIsometryEquiv_symm`, `MeasureTheory.Lp.nnnorm_eq_zero_iff`, `skewAdjoint.val_smul`, `AddMonoidHom.apply_ofInjective_symm`, `coe_equiv_lpPiLp_symm`, `selfAdjointPart_comp_subtype_selfAdjoint`, `MeasureTheory.dominatedFinMeasAdditive_condExpInd`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroupOp`, `AddCircle.isAddQuotientCoveringMap_coe`, `Finset.op_vadd_stabilizer_of_no_doubling`, `MeasureTheory.L1.SimpleFunc.integral_add`, `mem_iff_toAddUnits_mem_addUnits`, `MeasureTheory.Integrable.edist_toL1_zero`, `orbit_fixingAddSubgroup_compl_subset`, `IsAddCyclic.exists_generator`, `lp.inftyCStarRing`, `MeasureTheory.Lp.finStronglyMeasurable`, `MeasureTheory.aestronglyMeasurable_condExpL2`, `MeasureTheory.L1.setToL1_smul_left`, `isOpen_of_zero_mem_interior`, `noncommPiCoprod_range`, `MeasureTheory.L1.setToL1_zero_left`, `AddMonoidHom.ker_restrict`, `ContinuousAt.compMeasurePreservingLp`, `unop_normalizer`, `skewAdjoint.instIsStarNormalValMemAddSubgroup`, `MeasureTheory.condExpInd_nonneg`, `characteristic_centralizer`, `lp.evalₗ_apply`, `lp.norm_rpow_eq_tsum`, `AddMonoidHom.range_isAddCommutative`, `torsionBy.mod_self_nsmul`, `CochainComplex.mappingCone.lift_f_fst_v`, `isUniformAddGroup`, `FiniteArchimedeanClass.mem_ballAddSubgroup_iff`, `MeasureTheory.condExpL1_of_aestronglyMeasurable'`, `vaddCommClass_right`, `AddAction.orbitZMultiplesEquiv_symm_apply'`, `MeasureTheory.L1.continuous_integral`, `AddAction.IsBlock.of_orbit`, `card_range_dvd`, `CochainComplex.Lifting.exists_hom`, `AddAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `MeasureTheory.Lp.stronglyMeasurable`, `NormedAddGroupHom.Equalizer.map_normNoninc`, `exists_nsmul_mem_of_relIndex_ne_zero`, `MeasureTheory.L1.integrable_coeFn`, `SchwartzMap.injective_toLp`, `MeasureTheory.condExpL2_indicator_ae_eq_smul`, `AddAction.orbitZMultiplesEquiv_symm_apply`, `coe_equivMapOfInjective_apply`, `CategoryTheory.ShortComplex.abToCycles_apply_coe`, `MeasureTheory.condExpL1CLM_of_aestronglyMeasurable'`, `AddMonoidHom.rangeRestrict_injective_iff`, `UnitAddTorus.mFourierCoeff_toLp`, `CochainComplex.mappingCone.id_X`, `prod_addSubgroupOf_prod_normal`, `CochainComplex.mappingCocone.inr_v_desc_f_assoc`, `MeasureTheory.Lp.dist_edist`, `ContinuousLinearMap.holderₗ_apply_apply`, `MeasureTheory.Lp.edist_eq_eLpNorm_neg_add`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left'`, `coe_iSup_of_directed`, `index_eq_natAbs_det`, `OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single`, `MeasureTheory.Measure.IsAddLeftInvariant.addQuotientMeasureEqMeasurePreimage_of_set`, `MeasureTheory.Lp.coeFn_mk`, `AddAction.mem_stabilizer_iff`, `MeasureTheory.Lp.norm_zero`, `MeasureTheory.Lp.mem_Lp_of_ae_nnnorm_bound`, `card_subtype`, `MeasureTheory.continuous_setToFun`, `MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc`, `MeasureTheory.L1.dist_eq_integral_dist`, `noncommPiCoprod_apply`, `MeasureTheory.L1.norm_def`, `list_sum_mem`, `QuotientAddGroup.leftRel_eq`, `mem_closure_of_mem`, `MeasureTheory.integral_condExpL2_eq`, `DomAddAct.instIsIsometricVAddSubtypeAEEqFunMemAddAddSubgroupLp`, `Unitary.openPartialHomeomorph_symm_apply`, `op_normalizer`, `MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul`, `mem_map_of_mem`, `MeasureTheory.Lp.edist_toLp_toLp`, `CochainComplex.HomComplex.leftHomologyData_i_hom_apply`, `add_self_mem_of_index_two`, `addSubgroupOf_normalizer_eq`, `CochainComplex.mappingCone.d_snd_v'_assoc`, `orthonormal_fourier`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive`, `pi_mem_of_single_mem`, `normalClosure_eq_iInf`, `MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc`, `lp.coeFn_single`, `MeasureTheory.setIntegral_condExpL2_indicator`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive'`, `MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub`, `SubAddAction.ofStabilizer.isPretransitive_iff`, `AddMonoidHom.addSubgroupMap_apply_coe`, `MeasureTheory.Integrable.norm_toL1`, `AddMonoidHom.ofLeftInverse_symm_apply`, `add_mem_cancel_right`, `selfAdjoint.instNontrivialSubtypeMemAddSubgroup`, `ContinuousLinearMap.setIntegral_compLp`, `single_mem_pi`, `ProperlyDiscontinuousVAdd.finite_stabilizer`, `lp.summable_mul`, `MeasureTheory.Lp.edist_toLp_zero`, `rank_closure_finset_le_card`, `MeasureTheory.L1.setToL1_mono_left'`, `selfAdjoint.imaginaryPart_coe`, `AddCircle.dense_addSubgroup_iff_ne_zmultiples`, `tendsto_zmultiples_subtype_cofinite`, `DomAddAct.vadd_Lp_add`, `MeasureTheory.Integrable.toL1_eq_mk`, `mem_iSup_of_directed`, `Subring.coe_toAddSubgroup`, `lp.hasSum_single`, `selfAdjoint.val_zpow`, `cfcₙ_re_id`, `index_eq_two_iff_exists_notMem_and`, `isComplement_addSubgroup_left_iff_bijective`, `MeasureTheory.condExpIndSMul_empty`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le`, `ker_addSubgroupMap`, `index_ker`, `mem_normalizer_iff`, `MeasureTheory.setIntegral_condExpInd`, `AddSubmonoid.neg_mem_addUnits_iff`, `AddAction.stabilizer_add_self`, `RingSubgroupsBasis.hasBasis_nhds_zero`, `ProfiniteAddGrp.limit_zero_val`, `addCommutator_centralizer_addCommutator_le_center`, `MeasureTheory.edist_indicatorConstLp_eq_enorm`, `lp.memℓp`, `mem_ofAddUnits_iff_toAddUnits_mem`, `lp.coeFn_zero`, `CategoryTheory.ShortComplex.abLeftHomologyData_π`, `QuotientAddGroup.preimage_image_mk`, `add_mem_sup`, `continuous_decomposeProdAdjoint_symm`, `addSubgroupOfEquivOfLe_apply_coe`, `Submodule.span_int_eq`, `Normal.addConj_mem'`, `MeasureTheory.Lp.compMeasurePreserving_comp`, `MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero`, `MeasureTheory.L1.setToL1_eq_setToL1SCLM`, `MeasureTheory.norm_condExpL2_coe_le`, `MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le`, `lp.norm_const_smul`, `MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable`, `AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples`, `MeasureTheory.L1.setToL1_nonneg`, `MeasureTheory.aestronglyMeasurable_condExpL1`, `isAddFundamentalDomain_Ioc`, `AddAction.stabilizer_op_addSubgroup`, `SchwartzMap.norm_fourier_toL2_eq`, `MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure`, `AddMonoidHom.fiberEquivKer_apply`, `MeasureTheory.Lp.SecondCountableTopology`, `addConj_mem_sup_of_mem_inf_normalizer_of_mem_inf`, `ne_bot_iff_exists_ne_zero`, `card_le_of_le`, `AddMonoidHom.mem_graph`, `CochainComplex.mappingCone.lift_f_fst_v_assoc`, `MeasureTheory.Lp.instCompleteSpace`, `MeasureTheory.Lp.norm_toLp`, `CochainComplex.mappingCocone.id_X`, `MeasureTheory.Lp.instFourierPair`, `lp.zeroBasis_repr_apply`, `coe_addEquiv_lpPiLp_symm`, `CochainComplex.mappingCocone.descCocycle_coe`, `MeasureTheory.L1.integral_def`, `BoundedContinuousFunction.Lp_nnnorm_le`, `Module.Basis.addSubgroupOfClosure_repr_apply`, `map_subtype_addCommutator`, `exists_ne_zero_of_nontrivial`, `DomMulAct.edist_smul_Lp`, `hasSum_fourier_series_L2`, `isOpen_of_isClosed_of_finiteIndex`, `realPart.norm_le`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul_real`, `BoundedContinuousFunction.range_toLpHom`, `selfAdjoint.expUnitary_zero`, `BoundedContinuousFunction.toLp_inj`, `multiset_sum_mem`, `MeasureTheory.mem_lpMeas_indicatorConstLp`, `RingSubgroupsBasis.leftMul`, `normalizer_eq_top_iff`, `lp.single_apply_ne`, `AddMonoidHom.coe_graph`, `mem_fixingAddSubgroup_compl_iff_movedBy_subset`, `BoundedContinuousFunction.toLp_injective`, `lp.singleAddMonoidHom_apply`, `MeasureTheory.integral_indicatorConstLp`, `MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure`, `HilbertBasis.hasSum_repr`, `isOpen_of_mem_nhds`, `CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles`, `MeasureTheory.Lp.coeFn_compMeasurePreserving`, `orbit_addSubgroup_eq_self_of_mem`, `MeasureTheory.condExpIndSMul_smul`, `map_subtype_le`, `MeasureTheory.lintegral_nnnorm_condExpL2_le`, `finite_iff_addSubgroup_quotient`, `QuotientAddGroup.norm_mk`, `StrongDual.toLp_of_not_memLp`, `MeasureTheory.Lp.compMeasurePreservingₗᵢ_apply_coe`, `MeasureTheory.Lp.dist_eq_eLpNorm_neg_add`, `MeasureTheory.L1.setToFun_eq_setToL1`, `LinearMap.IsSymmetric.coe_toSelfAdjoint`, `SchwartzMap.norm_fourierTransformCLM_toL2_eq`, `Int.addSubgroup_index_ne_zero_iff`, `mem_sSup_of_directedOn`, `normalClosure_subset_iff`, `isAddQuotientCoveringMap_of_comm`, `MeasureTheory.enorm_indicatorConstLp_le`, `MeasureTheory.Lp.norm_neg`, `ModularFormClass.one_mem_strictPeriods_SL2Z`, `finite_quotient_of_pretransitive_of_index_ne_zero`, `AddMonoidHom.addSubgroupComap_surjective_of_surjective`, `CochainComplex.mappingCocone.inr_comp_descCochain`, `MeasureTheory.L1.integral_eq_setToL1`, `neg_subset_closure`, `MeasureTheory.Integrable.toL1_smul`, `lp.singleContinuousAddMonoidHom_apply`, `MeasureTheory.Lp.nnnorm_neg`, `int_mul_mem`, `realPart_add_I_smul_imaginaryPart`, `AddMonoidHom.subtype_comp_rangeRestrict`, `mem_sup'`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `ContinuousLinearMap.holder_smul_left`, `AddSubmonoid.mem_support`, `MeasureTheory.Lp.coeFn_smul`, `DomMulAct.mk_smul_toLp`, `MeasureTheory.condExpL1CLM_indicatorConstLp`, `CochainComplex.HomComplex.Cocycle.toSingleMk_mem_coboundaries_iff`, `addCommute_subtype_of_addCommute`, `isClosed_of_isOpen`, `lp.inner_single_right`, `NormedAddGroupHom.mem_ker`, `centralizer_closure`, `MeasureTheory.L1.setToL1_add_left'`, `comap_normalizer_eq_of_surjective`, `card_add_eq_card_addSubgroup_add_card_quotient`, `lp.norm_nonneg'`, `CochainComplex.HomComplex.Cocycle.cochain_ofHom_homOf_eq_coe`, `QuotientAddGroup.strictMono_comap_prod_image`, `IsSelfAdjoint.skewAdjointPart_apply`, `lp.single_neg`, `MeasureTheory.L1.SimpleFunc.coe_negPart`, `MeasureTheory.integrableOn_Lp_of_measure_ne_top`, `MeasureTheory.L1.setToL1_mono_left`, `MeasureTheory.Lp.dist_eq_norm`, `selfAdjoint.continuous_expUnitary`, `MeasureTheory.condExpInd_disjoint_union`, `MeasureTheory.Lp.coeFn_le`, `QuotientAddGroup.discreteTopology_iff`, `map_focalAddSubgroupOf`, `MeasureTheory.Lp.simpleFunc.add_toSimpleFunc`, `ComplexStarModule.ext_iff`, `coe_add_of_left_le_normalizer_right`, `range_subtype`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroup`, `UnitAddTorus.coeFn_mFourierLp`, `coe_ringEquiv_lpBCF`, `centerCongr_apply_coe`, `MeasureTheory.setIntegral_condExpIndSMul`, `goursat_surjective`, `nsmul_mem_of_relIndex_ne_zero_of_dvd`, `MeasureTheory.indicatorConstLp_univ`, `MeasureTheory.lpMeasToLpTrimLie_symm_indicator`, `lp.single_zero`, `MeasureTheory.norm_setToFun_le'`, `isClosed_of_discrete`, `selfAdjoint.unitarySelfAddISMul_coe`, `quasispectrum_imaginaryPart'`, `selfAdjoint.star_val_eq`, `StarModule.decomposeProdAdjoint_symm_apply`, `MeasureTheory.Lp.norm_const_le`, `TopologicalAddGroup.IsSES.ofClosedAddSubgroup`, `torsionBy.nsmul_iff`, `HahnSeries.mem_cardSuppLTAddSubgroup`, `Subgroup.mem_toAddSubgroup'`, `instIsAddTorsionFree`, `CochainComplex.HomComplex.Cocycle.coe_neg`, `cfcₙ_comp_re`, `MeasureTheory.Lp.coeFn_negPart_eq_max`, `coe_lpBCFₗᵢ`, `rank_closure_finite_le_nat_card`, `star_mul_self_eq_realPart_sq_add_imaginaryPart_sq`, `focalAddSubgroupOf_eq_closure`, `AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply`, `cfc_comp_im`, `ofAdd_image_zmultiples_eq_zpowers_ofAdd`, `lp.infty_coeFn_mul`, `MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'`, `MeasureTheory.condExpL1_undef`, `MeasureTheory.Lp.nnnorm_toLp`, `realPart_one`, `MeasureTheory.Measure.MeasureDense.indicatorConstLp_subset_closure`, `dense_iff_ne_zmultiples`, `Subring.mem_closure_iff`, `MeasureTheory.L1.SimpleFunc.setToL1S_sub`, `QuotientAddGroup.t1Space_iff`, `addSubgroupOf_map_subtype`, `AddAction.stabilizerEquivStabilizer_symm_apply`, `coe_set_eq_zero`, `vadd_opposite_add`, `card_dvd_of_le`, `ContinuousMap.toLp_def`, `isComplement_range_left`, `Normal.addSubgroupOf`, `pi_mem_of_single_mem_aux`, `MeasureTheory.L2.integral_inner_eq_sq_eLpNorm`, `norm_coe`, `map_subtype_lt_map_subtype`, `ContinuousWithinAt.compMeasurePreservingLp`, `lp.coeFn_add`, `MeasureTheory.Lp.norm_le_norm_of_ae_le`, `index_eq_two_iff_exists_notMem_and'`, `MeasureTheory.L2.inner_indicatorConstLp_one`, `MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp`, `MeasureTheory.L1.setToL1_smul_left'`, `MeasureTheory.Lp.boundedContinuousFunction_dense`, `LinearMap.IsSymmetric.toSelfAdjoint_apply`, `MeasureTheory.Lp.constₗ_apply`, `MeasureTheory.Lp.coe_nnnorm`, `le_normalizer`, `MeasureTheory.L1.SimpleFunc.toLp_one_eq_toL1`, `SubAddAction.mem_fixingAddSubgroup_union_iff`, `MeasureTheory.Lp.mem_boundedContinuousFunction_iff`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2`, `map_normalizer_eq_of_bijective`, `coe_topologicalClosure_bot`, `coe_smulCardAddSubgroup`, `MeasureTheory.condExpIndSMul_add`, `MeasureTheory.Lp.norm_fourier_eq`, `cfcₙ_comp_im`, `QuotientAddGroup.ker_le_range_iff`, `discrete_iff_addCyclic`, `card_mul_index`, `SchwartzMap.coeFn_toLp`, `CategoryTheory.ShortComplex.abLeftHomologyData_K_coe`, `MeasureTheory.Lp.instFourierSMul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left`, `AddCon.mem_addSubgroup_iff`, `card_addSubgroup_dvd_card`, `MeasureTheory.Lp.simpleFunc.toLp_eq_toLp`, `comap_normalizer_eq_of_le_range`, `CochainComplex.mappingCone.ofHom_lift`, `MeasureTheory.Lp.norm_const'`, `QuotientAddGroup.mk'_comp_subtype`, `MeasureTheory.norm_condExpIndL1_le`, `SchwartzMap.norm_toLp`, `IsUniformAddGroup.uniformContinuous_iff_isOpen_ker`, `CochainComplex.HomComplex.Cocycle.toSingleMk_coe`, `lp.norm_le_of_tendsto`, `AddMonoidHom.addSubgroupComap_apply_coe`, `Subgroup.coe_toAddSubgroup_symm_apply`, `FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff`, `dense_addSubmonoidClosure_iff_addSubgroupClosure`, `injective_noncommPiCoprod_of_iSupIndep`, `MeasureTheory.condExpL1_add`, `Real.Lp.fourierTransform_apply`, `CochainComplex.mappingCocone.ofHom_desc`, `MeasureTheory.Lp.smul_zero`, `MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul`, `CochainComplex.mappingCone.ext_to_iff`, `DomMulAct.mk_smul_indicatorConstLp`, `MeasureTheory.norm_condExpInd_apply_le`, `HahnSeries.coe_cardSuppLTAddSubgroup`, `QuotientAddGroup.strictMono_comap_prod_map`, `AddMonoidHom.ofLeftInverse_apply`, `inf_add_assoc`, `IsAddCyclic.card_nsmulAddMonoidHom_ker`, `coe_toAddSubmonoid`, `Complex.selfAdjointEquiv_apply`, `CochainComplex.mappingCone.lift_fst`, `ContinuousLinearMap.nnnorm_holder_apply_apply_le`, `OrthogonalFamily.hasSum_linearIsometry`, `addCommGroup_isAddCommutative`, `isComplement_addSubgroup_right_iff_bijective`, `mem_nullAddSubgroup_iff`, `ofMul_image_zpowers_eq_zmultiples_ofMul`, `map_equiv_normalizer_eq`, `DomAddAct.norm_vadd_Lp`, `lp.instSMulCommClassSubtypePreLpMemAddSubgroup`, `instMeasurableVAdd`, `MeasureTheory.condExpL1_neg`, `MeasureTheory.Lp.instTrivialStarSubtypeAEEqFunMemAddSubgroup`, `isComplement_addSubgroup_right_iff_existsUnique_quotientAddGroupMk`, `MeasureTheory.L1.nnnorm_integral_le`, `addSubgroupOf_mono`, `AddAction.finite_quotient_of_pretransitive_of_finite_quotient`, `CStarAlgebra.linear_combination_nonneg`, `MeasureTheory.Lp.norm_smul_le`, `CochainComplex.mappingCone.ext_cochain_to_iff`, `MeasureTheory.isClosed_aestronglyMeasurable`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary`, `star_mul_self_add_self_mul_star`, `MeasureTheory.Lp.coeFn_sup`, `NormedAddGroupHom.Equalizer.liftEquiv_apply`, `QuotientAddGroup.image_coe_inj`, `imaginaryPart.norm_le`, `mem_zmultiples_iff`, `NormedAddGroupHom.range_comp_incl_top`, `MeasureTheory.Lp_toLp_restrict_add`, `index_mul_card`, `lp.singleContinuousLinearMap_apply`, `LipschitzWith.coordinate`, `AddAction.vadd_orbit_eq_orbit_vadd`, `QuotientAddGroup.sound`, `quotientAddSubgroupOfMapOfLE_apply_mk`, `MeasureTheory.setIntegral_condExpL1`, `realPart_comp_subtype_selfAdjoint`, `add_injective_of_disjoint`, `mem_closure_range_iff`, `Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le`, `Orthonormal.linearIsometryEquiv_symm_apply_single_one`, `AddAction.minimalPeriod_eq_card`, `LipschitzOnWith.extend_lp_infty`, `continuousVAdd`, `discreteTopology_iff_of_finiteIndex`, `index_eq_two_iff'`, `mem_toAddSubmonoid`, `addUnit_of_mem_ofAddUnits_spec_mem`, `MeasureTheory.condExpIndL1_smul`, `UnitAddTorus.orthonormal_mFourier`, `FiniteArchimedeanClass.subsemigroup_eq_addSubgroup`, `ContinuousMap.toLp_norm_eq_toLp_norm_coe`, `closure_addSubmonoidClosure_eq_closure_addSubgroupClosure`, `SubAddAction.ofStabilizer.addConjMap_comp`, `mem_closure_singleton_iff_existsUnique_zsmul`, `nsmul_mem_of_index_ne_zero_of_dvd`, `RingSubgroupsBasis.mem_addGroupFilterBasis`, `CochainComplex.mappingCone.liftCochain_v_fst_v`, `coe_set_mk`, `AddAction.orbitRel_addSubgroup_le`, `MeasureTheory.Integrable.enorm_toL1`, `instFiniteIndex_addSubgroupOf`, `MeasureTheory.continuous_integral_integral`, `fourierCoeff_toLp`, `ArchimedeanClass.mem_addSubgroup_iff`, `OrthogonalFamily.summable_of_lp`, `coe_fourierBasis`, `coe_add_of_right_le_normalizer_left`, `NonUnitalSubring.coe_toAddSubgroup`, `Valuation.mem_leAddSubgroup_iff`, `spectrum_imaginaryPart`, `lp.coeFn_sub`, `CochainComplex.mappingCone.decomp_from`, `QuotientAddGroup.preimage_image_mk_eq_add`, `isSimpleAddGroup_iff`, `Complex.isAddQuotientCoveringMap_exp`, `coe_nsmul`, `le_centralizer_iff_isAddCommutative`, `addSubgroupOfEquivOfLe_symm_apply_coe_coe`, `card_le_one_iff_eq_bot`, `unitary.norm_argSelfAdjoint`, `skewAdjoint.negISMul_apply_coe`, `MeasureTheory.lpMeasSubgroupToLpTrim_sub`, `instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallNeg`, `MeasureTheory.Integrable.toL1_sub`, `NormedAddGroupHom.isClosed_ker`, `lp.ext_continuousAddMonoidHom_iff`, `relIndex_eq_two_iff_exists_notMem_and'`, `lp.infty_coeFn_pow`, `MeasureTheory.MemLp.toLp_neg`, `AddGroup.residuallyFinite_iff_exists_finiteIndex`, `lp.infty_smulCommClass`, `fixedPoints_addSubgroup_antitone`, `CochainComplex.HomComplex.mem_coboundaries_iff`, `coe_norm`, `coe_mk`, `normalClosure_eq_self`, `lp.norm_eq_card_dsupport`, `QuotientAddGroup.mk_out_eq_mul`, `RingSubgroupsBasis.hasBasis_nhds`, `QuotientAddGroup.rightRel_apply`, `ZSpan.isAddFundamentalDomain'`, `coe_op`, `ProbabilityTheory.Kernel.continuous_integral_integral`, `addSubgroupOf_isAddCommutative`, `DomMulAct.smul_Lp_neg`, `GromovHausdorff.ghDist_eq_hausdorffDist`, `toIsOrderedAddMonoid`, `vadd_leftQuotientEquiv`, `lp.lipschitzWith_one_eval`, `codisjoint_addSubgroupOf_sup`, `ProfiniteAddGrp.limit_add_val`, `MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one`, `imaginaryPart_realPart`, `lp.instStarModuleSubtypePreLpMemAddSubgroup`, `IsComplement.toRightFun_add_neg_mem`, `CochainComplex.HomComplex.Cocycle.fromSingleMk_coe`, `instFaithfulVAddSubtypeMem`, `MeasureTheory.integral_condExpL2_eq_of_fin_meas_real`, `coe_equiv_lpPiLp`, `lp.zeroBasis_apply`, `SubAddAction.nat_card_ofStabilizer_eq`, `addOrderOf_coe`, `coe_inf`, `neg_mem_iff`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `apply_coe_mem_map`, `IsSubnormal.trans'`, `CochainComplex.mappingCone.descCocycle_coe`, `MeasureTheory.Lp.simpleFunc.denseRange`, `MeasureTheory.memL1_smul_of_L1_withDensity`, `MeasureTheory.condExp_ae_eq_condExpL1`, `imaginaryPart_eq_neg_I_smul_skewAdjointPart`, `topEquiv_symm_apply_coe`, `mem_normalizer_iff''`, `selfAdjoint.isSelfAdjoint`, `NormedAddGroupHom.Equalizer.ι_comp_map`, `Int.mem_zmultiples_iff`, `SubAddAction.addConjMap_ofFixingAddSubgroup_coe_apply`, `MeasureTheory.condExpIndL1_smul'`, `skewAdjointPart_comp_subtype_selfAdjoint`, `instVAddAssocClassSubtypeMem`, `Set.nsmul_add_addSubgroupClosure`, `mem_op`, `le_normalizer_map`, `AddAction.stabilizerEquivStabilizer_neg`, `ker_subtype`, `mem_closure`, `BoundedContinuousFunction.mem_Lp`, `Submodule.mem_toAddSubgroup`, `NormedAddGroupHom.Equalizer.lift_normNoninc`, `lp.coeFn_sum`, `nsmul_exponent_eq_zero`, `MeasureTheory.lpMeasSubgroupToLpTrim_right_inv`, `Filter.Tendsto.compMeasurePreservingLp`, `mem_smul_pointwise_iff_exists`, `BoundedContinuousFunction.Lp_norm_le`, `CochainComplex.HomComplex.Cocycle.leftUnshift_coe`, `DomAddAct.vadd_Lp_ae_eq`, `MeasureTheory.Lp.norm_constL_le`, `AddAction.IsBlock.of_addSubgroup_of_conjugate`, `AddAction.coe_aestabilizer`, `exists_neg_mem_iff_exists_mem`, `AddAction.mem_stabilizer_finset'`, `span_selfAdjoint`, `MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc`, `realPart_I_smul`, `AddMonoidHom.addSubgroupMap_surjective`, `DomMulAct.norm_smul_Lp`, `CochainComplex.mappingCone.d_snd_v_assoc`, `lp.norm_compl_sum_single`, `card_top`, `KuratowskiEmbedding.embeddingOfSubset_isometry`, `selfAdjoint.realPart_unitarySelfAddISMul`, `MeasureTheory.condExpL2_indicator_of_measurable`, `mem_pointwise_smul_iff_inv_smul_mem`, `MeasureTheory.Lp.add_smul`, `MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top`, `MeasureTheory.condExp_ae_eq_condExpL1CLM`, `CochainComplex.mappingCone.d_snd_v'`, `AddMonoidHom.coe_comp_rangeRestrict`, `DomAddAct.vadd_Lp_sub`, `finEquivZMultiples_apply`, `mem_bot`, `BoundedContinuousFunction.coeFn_toLp`, `isAddQuotientCoveringMap`, `MeasureTheory.Integrable.toL1_smul'`, `NormedAddGroupHom.Equalizer.norm_map_le`, `UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp`, `MeasureTheory.Lp.instContinuousVAddDomAddAct`, `MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp`, `AddEquiv.coe_addSubgroupMap_apply`, `GromovHausdorff.eq_toGHSpace`, `infinite_zmultiples`, `CochainComplex.mappingCone.liftCochain_fst`, `MeasureTheory.L1.tendsto_setToL1`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le'`, `MeasureTheory.condExpL1CLM_indicatorConst`, `MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim`, `coe_center`, `isComplement_addSubgroup_left_iff_existsUnique_quotientMk''`, `tendsto_coe_cofinite_of_discrete`, `MeasureTheory.L1.nnnorm_Integral_le_one`, `cfcₙ_imaginaryPart`, `MeasureTheory.lpMeasSubgroupToLpTrim_add`, `MeasureTheory.L1.integral_eq_norm_posPart_sub`, `MeasureTheory.Lp.instContinuousFourierInv`, `imaginaryPart_apply_coe`, `mem_multiples_iff_mem_zmultiples`, `Unitary.openPartialHomeomorph_target`, `CochainComplex.HomComplex.Cocycle.homOf_f`, `UnitAddTorus.hasSum_mFourier_series_L2`, `MeasureTheory.Lp.norm_const`, `MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace`, `MeasureTheory.lpMeasSubgroupToLpTrim_left_inv`, `CategoryTheory.ShortComplex.abLeftHomologyData_f'`, `AddAction.mem_stabilizer_set'`, `CochainComplex.mappingCone.d_fst_v_assoc`, `CochainComplex.homOfDegreewiseSplit_f`, `CochainComplex.HomComplex.Cocycle.δ_eq_zero`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real`, `mem_ofAddUnits_iff_exists_isAddUnit`, `exists_zmultiples`, `MeasureTheory.L1.setToL1_unique`, `lp.single_sub`, `Function.Periodic.map_vadd_zmultiples`, `AddGroup.fg_iff_addSubgroup_fg`, `map_isAddCommutative`, `cfc_comp_re`, `coe_lpPiLpₗᵢ`, `imaginaryPart_comp_subtype_selfAdjoint`, `Multiplicative.mem_toSubgroup`, `CochainComplex.mappingCone.δ_snd`, `Subgroup.instDiscreteTopStrictPeriods`, `AddMonoidHom.restrict_range`, `forall_zmultiples`, `MeasureTheory.Lp.instAddLeftMono`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left`, `coe_matrix`, `quotient_norm_mk_eq`, `ContinuousLinearMap.lpPairing_eq_integral`, `coe_zsmul`, `MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc`, `instMeasurableConstVAdd`, `instProperVAddSubtypeMemAddSubgroupOfIsClosedCoe`, `ContinuousLinearMap.holder_smul_right`, `lp.lsingle_apply`, `ProfiniteAddGrp.limit_ext_iff`, `leftCoset_cover_const_iff_surjOn`, `CochainComplex.mappingCone.inl_v_fst_v`, `MeasureTheory.L2.eLpNorm_inner_lt_top`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left'`, `NormedAddGroupHom.incl_apply`, `rightAddCoset_eq_iff`, `MeasureTheory.condExpL1CLM_lpMeas`, `centerCongr_symm_apply_coe`, `mem_comap`, `selfAdjoint.val_inv`, `QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk`, `MeasureTheory.Lp.mem_Lp_iff_memLp`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff`, `selfAdjoint.val_smul`, `finite_quotient_of_finite_quotient_of_index_ne_zero`, `AddCommGrpCat.kernelIsoKer_inv_comp_ι`, `CochainComplex.Lifting.π_f_cochain₁_v_ι_f_assoc`, `SchwartzMap.norm_fourier_Lp_top_leq_toLp_one`, `realPart_surjective`, `StrongDual.toLpₗ_apply`, `MeasureTheory.L1.setToL1_apply_coeToLp`, `MeasureTheory.Lp.const_mem_Lp`, `NormedAddGroupHom.Equalizer.ι_comp_lift`, `MeasureTheory.Lp.compMeasurePreserving_comp_apply`, `MapSubtype.orderIso_apply_coe`, `coe_add`, `instIsTopologicalAddGroupSubtypeMem`, `coe_toZModSubmodule`, `Subgroup.two_mul_widthInfty_mem_strictPeriods`, `coe_bot`, `QuotientAddGroup.dense_image_mk`, `MeasureTheory.indicatorConstLp_add`, `mem_centralizer_iff_addCommutator_eq_zero`, `MeasureTheory.L1.setToL1_congr_left'`, `DomAddAct.vadd_Lp_neg`, `selfAdjoint.star_coe_unitarySelfAddISMul`, `MeasureTheory.Lp.simpleFunc.coeFn_le`, `MeasureTheory.Lp.instFourierPairInv`, `lp.norm_neg`, `AddMonoidHom.eqOn_closure`, `AddAction.op_vadd_set_stabilizer_subset`, `AddMonoid.le_minOrder_iff_forall_addSubgroup`, `Subgroup.coe_toAddSubgroup_apply`, `leftAddCoset_eq_iff`, `mem_goursatFst`, `index_map_subtype`, `Normal.mem_comm_iff`, `AddSubmonoid.mem_addUnits_of_val_mem_neg_val_mem`, `MeasureTheory.AddSubgroup.index_mul_measure`, `skewAdjoint.star_val_eq`, `MeasureTheory.Lp.norm_le_of_ae_bound`, `card_map_dvd`, `finEquivZMultiples_symm_apply`, `mem_closure_singleton_self`, `mem_mk`, `SchwartzMap.norm_toLp'`, `CochainComplex.mappingCocone.inr_v_fst_f_assoc`, `MeasureTheory.Lp.simpleFunc.toLp_zero`, `AddAction.isBlock_top`, `eq_addCosets_of_normal`, `MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner`, `MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral`, `cfcₙ_im_id`, `AddAction.addSubgroup_vadd_def`, `coe_eq_singleton`, `multiples_eq_zmultiples`, `MeasureTheory.Lp.coeFn_nonneg`, `MeasureTheory.Lp.toLp_coeFn`, `Valuation.mem_ltAddSubgroup_iff`, `TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_nonunital`, `MeasureTheory.nnnorm_indicatorConstLp_le`, `DomMulAct.dist_smul_Lp`, `MeasureTheory.Lp.instFourierInvAdd`, `quasispectrum_realPart`, `AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_symm_apply_coe`, `MeasureTheory.L1.setToL1_congr_left`, `HilbertBasis.repr_symm_single`, `HilbertBasis.repr_apply_apply`, `imaginaryPart_surjective`, `NormedAddGroupHom.SurjectiveOnWith.surjOn`, `AddCommGroup.coe_primaryComponent`, `MeasureTheory.L1.setToL1_smul`, `mem_sup_right`, `MeasureTheory.Lp.coeFn_lpSMul`, `sup_eq_closure`, `le_normalClosure`, `coe_sub`, `MeasureTheory.Lp.simpleFunc.coeFn_zero`, `lp.coeFn_smul`, `OpenAddSubgroup.coe_toAddSubgroup`, `MeasureTheory.condExpIndSMul_nonneg`, `nsmul_relIndex_mem`, `lp.summable_inner`, `selfAdjoint.val_pow`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'`, `nontrivial_iff_exists_ne_zero`, `lp.infty_coeFn_one`, `coe_addEquiv_lpBCF_symm`, `map_subtype_inj`, `MeasureTheory.L1.dist_def`, `mem_centralizer_iff`, `mem_of_mem_val_ofAddUnits`, `ContinuousLinearMap.coeFn_compLpL`, `NormedAddGroupHom.Equalizer.lift_apply_coe`, `Real.Lp.fourierTransformCLM_apply`, `StrongDual.norm_toLpₗ_le`, `MeasureTheory.Lp.coe_mk`, `Subfield.mem_toAddSubgroup`, `selfAdjoint.realPart_coe`, `MeasureTheory.Lp.instIsCentralScalar`, `lp.single_smul`, `pairwiseDisjoint_leftCoset_cover_const_of_index_eq`, `SubAddAction.ofFixingAddSubgroup_insert_map_apply`, `QuotientAddGroup.norm_mk_eq_zero`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left'`, `MeasureTheory.L1.norm_integral_le`, `MeasureTheory.setIntegral_indicatorConstLp`, `lp.ext_iff`, `saturated_iff_zsmul`, `lp.norm_zero`, `AddGroupExtension.Section.add_add_add_neg_mem_range_inl`, `NonUnitalSubring.mem_toAddSubgroup`, `NormedAddGroupHom.ker_completion`, `ProbabilityTheory.Kernel.continuous_integral_integral_comp`, `add_mem_iff_of_index_two`, `LipschitzOnWith.coordinate`, `lp.instIsCentralScalarSubtypePreLpMemAddSubgroup`, `addSubgroupOf_bot_eq_top`, `normal_addSubgroupOf_iff`, `ContinuousMap.toLp_injective`, `addSubgroupOf_map_nsmulAddMonoidHom_eq_range`, `CochainComplex.mappingCone.inr_f_fst_v_assoc`, `StrongDual.toLpₗ_of_not_memLp`, `MeasureTheory.indicatorConstLp_sub`, `map_subtype_le_map_subtype`, `finite_iff_finite_and_finiteIndex`, `bot_addSubgroupOf`, `CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v`, `coe_toIntSubmodule`, `normalizer_eq_top`, `DomAddAct.edist_vadd_Lp`, `MeasureTheory.L1.aemeasurable_coeFn`, `MeasureTheory.Subgroup.vaddInvariantMeasure`, `relIndex_addSubgroupOf`, `MeasureTheory.integrable_condExpL2_of_isFiniteMeasure`, `controlled_sum_of_mem_closure`, `CategoryTheory.ShortComplex.abLeftHomologyData_i`, `lp.inner_single_left`, `MeasureTheory.condExpIndL1Fin_disjoint_union`, `MeasureTheory.Lp.tendsto_Lp_of_tendsto_eLpNorm`, `MeasureTheory.Lp.instIsBoundedSMul`, `smul_mem_pointwise_smul`, `ContinuousMap.coe_toLp`, `skewAdjointPart_apply_coe`, `continuous_selfAdjointPart`, `lp.hasSum_norm`, `centralizer_eq_top_iff_subset`, `selfAdjoint.val_qsmul`, `DomMulAct.instIsIsometricSMulSubtypeAEEqFunMemAddSubgroupLp`, `SchwartzMap.norm_toLp_top_le`, `Finset.le_card_quotient_add_sq_inter_addSubgroup`, `lp.norm_le_of_forall_sum_le`, `ContinuousLinearMap.integral_comp_L1_comm`, `QuotientAddGroup.preimage_image_coe`, `span_fourierLp_closure_eq_top`, `selfAdjointPartL_apply_coe`, `isAddCyclic_iff_exists_zmultiples_eq_top`, `lp.norm_le_of_forall_le`, `mem_carrier`, `MeasureTheory.L1.measurable_coeFn`, `MeasureTheory.aestronglyMeasurable_condExpL1CLM`, `nsmul_mem_zmultiples_iff_exists_sub_div`, `mem_sup_of_normal_right`, `Subgroup.strictWidthInfty_mem_strictPeriods`, `SchwartzMap.inner_fourierTransformCLM_toL2_eq`, `SubAddAction.mem_fixingAddSubgroup_insert_iff`, `vadd_def`, `addOrderOf_dvd_natCard`, `MeasureTheory.continuous_integral`, `mem_inf`, `lp.infty_coeFn_intCast`, `MeasureTheory.Lp.simpleFunc.isBoundedSMul`, `mem_map_equiv`, `lp.tsum_mul_le_mul_norm'`, `le_normalizer_of_normal`, `AddMonoidHom.sub_mem_ker_iff`, `MeasureTheory.Lp.coe_posPart`, `MeasureTheory.integrable_condExpL2_indicator`, `addUnit_mem_of_mem_ofAddUnits`, `eq_top_iff'`, `MeasureTheory.Lp.zero_smul`, `exists_nsmul_mem_of_index_ne_zero`, `QuotientAddGroup.image_coe`, `coe_lpBCFₗᵢ_symm`, `coe_lpPiLpₗᵢ_symm`, `card_bot`, `lp.norm_single`, `mem_zmultiples_iff_mem_range_addOrderOf`, `relIindex_eq_two_iff'`, `DomMulAct.smul_Lp_zero`, `AddMonoidHom.fiberEquivKer_symm_apply`, `Complex.coe_selfAdjointEquiv`, `AddAction.card_orbit_mul_card_stabilizer_eq_card_addGroup`, `DomAddAct.mk_vadd_toLp`, `RingPreordering.mem_supportAddSubgroup`, `coe_addEquiv_lpBCF`, `MapSubtype.orderIso_symm_apply`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_isDiscrete_ker_addMonoidHom`, `MeasureTheory.lpMeasSubgroupToLpTrim_norm_map`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp'`, `imaginaryPart_ofReal`, `MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNorm`, `SubAddAction.ofStabilizer.addConjMap_comp_apply`, `MeasureTheory.Lp.simpleFunc.toLp_sub`, `RingPreordering.one_notMem_supportAddSubgroup`, `MeasureTheory.Lp.simpleFunc.coe_smul`, `intCast_mul_mem_zmultiples`, `normal_centralizer`, `MeasureTheory.Lp.smul_def`, `properlyDiscontinuousVAdd_opposite_of_tendsto_cofinite`, `MeasureTheory.Lp.norm_exponent_zero`, `MeasureTheory.Lp.smul_neg`, `Set.addConj_mem_fixingAddSubgroup`, `instDiscreteTopologyZMultiples`, `dense_addSubgroupClosure_pair_iff`, `AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `MeasureTheory.L1.stronglyMeasurable_coeFn`, `mem_sup`, `Commute.expUnitary_add`, `orbit_addSubgroup_zero_eq_self`, `ContinuousMap.coeFn_toLp`, `MeasureTheory.L1.norm_setToL1_le_mul_norm'`, `val_finset_sum`, `Normal.conj_mem`, `MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq`, `IsSelfAdjoint.coe_selfAdjointPart_apply`, `isOpen_of_openAddSubgroup`, `coe_even`, `nsmul_mem`, `lp.mem_lp_const_smul`, `MeasureTheory.tendstoInMeasure_of_tendsto_Lp`, `ProbabilityTheory.condVar_of_sigmaFinite`, `NormedAddGroupHom.IsQuotient.norm`, `SubAddAction.ofStabilizer.snoc_castSucc`, `lp.tsumCLM_apply`, `AddSubmonoid.isOpen_addUnits`, `MeasureTheory.Lp.instSMulCommClass`, `OrthogonalFamily.range_linearIsometry`, `MeasureTheory.Lp.simpleFunc.toLp_neg`, `mem_center_iff`, `inclusion_inj`, `SubAddAction.fixingAddSubgroupEquivFixingAddSubgroup_coe_apply`, `MeasureTheory.L1.SimpleFunc.integral_smul`, `MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one`, `closure_eq`, `MeasureTheory.lpTrimToLpMeas_ae_eq`, `mem_even`, `exists_mem_zmultiples`, `bot_or_nontrivial`, `lp.single_add`, `centerToAddOpposite_symm_apply_coe`, `DomAddAct.vadd_Lp_const`, `normal_addSubgroupOf`, `Set.addSubgroupClosure_add`, `smul_mem_pointwise_smul_iff₀`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le`, `ContinuousMap.toLp_comp_toContinuousMap`, `IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_AddHaarMeasure`, `sub_mem`, `NormedAddGroupHom.coe_ker`, `relIndex_dvd_two_iff`, `lp.norm_sub_norm_compl_sub_single`, `AddCommGroup.mem_torsion`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure`, `comap_subtype`, `MeasureTheory.Lp.smul_comm`, `SchwartzMap.continuous_toLp`, `selfAdjoint.val_ratCast`, `lp.infty_coeFn_natCast`, `MeasureTheory.isComplete_aestronglyMeasurable`, `AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume`, `MeasureTheory.Lp.simpleFunc.isUniformEmbedding`, `AddAction.mem_stabilizer_finset_iff_subset_vadd_finset`, `MeasureTheory.L1.integral_of_fun_eq_integral`, `MeasureTheory.L1.integral_zero`, `map_addSubgroupOf_eq_of_le`, `QuotientAddGroup.orbit_eq_out_vadd`, `CochainComplex.mappingCone.inl_fst`, `mem_iSup_of_mem`, `lp.hasSum_inner`, `CochainComplex.HomComplex.Cocycle.shift_coe`, `SchwartzMap.toLp_fourierTransform_eq`, `MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le`, `MeasureTheory.continuous_indicatorConstLp_set`, `closure_closure_coe_preimage`, `MeasureTheory.condExpIndL1_of_not_measurableSet`, `IsSubnormal.addSubgroupOf`, `MeasureTheory.Lp.smul_add`, `MeasureTheory.L1.norm_setToL1_le'`, `MeasureTheory.withDensitySMulLI_apply`, `one_lt_card_iff_ne_bot`, `CochainComplex.mappingCone.liftCochain_v_fst_v_assoc`, `nsmul_index_mem`, `NormedAddGroupHom.mem_range_self`, `MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq`, `CochainComplex.mappingCone.lift_desc_f`, `coe_iInf`, `skewAdjoint.conjugate'`, `ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite`, `UnitAddTorus.hasSum_prod_mFourierCoeff`, `instFiniteSubtypeMem`, `nontrivial_iff_ne_bot`, `Complex.selfAdjointEquiv_symm_apply`, `DomMulAct.smul_Lp_ae_eq`, `SubAddAction.ENat_card_ofStabilizer_add_zero_eq`, `NormedAddGroupHom.ker.incl_comp_lift`, `neg_mem`, `MeasureTheory.Lp.simpleFunc.isUniformInducing`, `IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single`, `MeasureTheory.L1.norm_of_fun_eq_integral_norm`, `Function.Exact.addMonoidHom_rangeRestrict`, `selfAdjointPart_apply_coe`, `MeasureTheory.L1.integral_add`, `MeasureTheory.Lp.mem_Lp_iff_eLpNorm_lt_top`, `add_inf_assoc`, `MeasureTheory.aestronglyMeasurable_condExpIndSMul`, `skewAdjointPartL_apply_coe`, `CochainComplex.mappingCone.desc_f`, `CochainComplex.mappingCone.d_fst_v'_assoc`, `CochainComplex.mappingCocone.inr_v_fst_f`, `MeasureTheory.Lp.constL_apply`, `SubAddAction.fixingAddSubgroup_of_insert`, `MeasureTheory.L2.mem_L1_inner`, `MeasureTheory.L1.integral_eq_integral`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp`, `two_smul_mem_of_index_two`, `subtype_injective`, `MeasureTheory.Integrable.coeFn_toL1`, `MeasureTheory.Lp.simpleFunc.coe_indicatorConst`, `normal_addSubgroupOf_of_le_normalizer`, `MeasureTheory.condExpIndL1_disjoint_union`, `topEquiv_apply`, `ContinuousLinearMap.add_compLp`, `MeasureTheory.Lp.inner_fourier_eq`, `ker_imaginaryPart`, `MeasureTheory.Integrable.norm_toL1_eq_lintegral_norm`, `coe_map`, `MeasureTheory.L1.aestronglyMeasurable_coeFn`, `AddAction.right_quotientAction`, `isAddCyclic`, `SubAddAction.of_fixingAddSubgroupEmpty_mapScalars_surjective`, `HilbertBasis.repr_self`, `exists_isComplement_right`, `SubAddAction.ofStabilizer.neg_addConjMap_comp_apply`, `val_mem_ofAddUnits_iff_mem`, `MeasureTheory.condExpInd_smul'`, `vadd_toLeftFun`, `MeasureTheory.L1.setToL1_add_left`, `AddAction.stabilizerEquivStabilizer_apply`, `SubAddAction.mem_ofFixingAddSubgroup_iff`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `normal_addSubgroupOf_iff_le_normalizer`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `isAddCyclic_of_le`, `mem_sSup_of_mem`, `MeasureTheory.Lp.eLpNorm_lt_top`, `AddMonoidHom.finite_iff_finite_ker_range`, `MeasureTheory.L2.integrable_inner`, `realPart_imaginaryPart`, `SchwartzMap.norm_fourier_toBoundedContinuousFunction_le_toLp_one`, `BoundedContinuousFunction.toLp_norm_le`, `quotientiInfAddSubgroupOfEmbedding_apply`, `coe_pi`, `normalClosure_idempotent`, `MeasureTheory.Lp.continuous_negPart`, `MeasureTheory.Lp.coeFn_negPart`, `AddAction.IsBlock.orbit_stabilizer_eq`, `AddAction.stabilizerEquivStabilizer_trans`, `lp.norm_tsum_le`, `selfAdjoint.mem_iff`, `Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples`, `coe_toSubgroup_apply`, `mem_zmultiples_zsmul_iff`, `addConjugatesOfSet_subset_normalClosure`, `coe_addEquiv_lpPiLp`, `CochainComplex.mappingCone.d_fst_v'`, `MeasureTheory.condExp_of_sigmaFinite`, `val_multiset_sum`, `mk_eq_zero`, `MeasureTheory.norm_setToFun_le_mul_norm`, `AddEquiv.addSubgroupCongr_symm_apply`, `lp.infty_isScalarTower`, `MeasureTheory.L1.SimpleFunc.norm_eq_integral`, `MeasureTheory.condExpIndL1_of_measure_eq_top`, `AddAction.stabilizer_addSubgroup`, `set_add_normalizer_comm`, `dense_or_cyclic`, `RingPreordering.coe_supportAddSubgroup`, `fixingAddSubgroup_fixedPoints_gc`, `zsmul_mem_zmultiples_iff_exists_sub_div`, `Fintype.card_zmultiples`, `NormedAddGroupHom.Equalizer.map_comp_map`, `skewAdjointPart_eq_I_smul_imaginaryPart`, `MeasureTheory.L1.SimpleFunc.norm_integral_le_norm`, `lp.linearMapOfLE_comp`, `AddSubmonoid.neg_mem_addUnits`, `SubAddAction.ofFixingAddSubgroup_carrier`, `Normal.mem_comm`, `MeasureTheory.Lp.simpleFunc.toLp_smul`, `instCountableSubtypeMemZMultiples`, `NormedAddGroupHom.Equalizer.comp_ι_eq`, `addCommutator_def'`, `MeasureTheory.L1.norm_setToL1_le_mul_norm`, `Subgroup.mem_strictPeriods_iff`, `normalizer_le_normalizer_sup_normal`, `mem_normalizer_iff'`, `MeasureTheory.MemLp.coeFn_toLp`, `mem_iSup_prop`, `IsTorsion.addSubgroup`, `coe_pointwise_smul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left'`, `CochainComplex.mappingCone.inl_fst_assoc`, `addSubgroupOf_bot_eq_bot`, `quotientEquivProdOfLE'_apply`, `MeasureTheory.Lp.neg_smul`, `CochainComplex.HomComplex.Cocycle.ext_iff`, `lp.eq_zero'`, `selfAdjoint.val_nnratCast`, `MeasureTheory.Lp.instOrderClosedTopologySubtypeAEEqFunMemAddSubgroupOfClosedIciTopology`, `MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le_mul`, `NormedAddGroupHom.ker_le_ker_completion`, `selfAdjoint.val_re_map_spectrum`, `exponent_top`, `Subring.mem_toAddSubgroup`, `mem_sInf`, `mem_addSubgroupOf`, `AddGroup.addConjugatesOfSet_subset`, `isAddCyclic_zmultiples`, `CochainComplex.HomComplex.Cocycle.ofHom_coe`, `lp.tendsto_lp_of_tendsto_pi`, `MeasureTheory.norm_condExpInd_le`, `AddGroup.closure_finset_fg`, `MeasureTheory.setToFun_mono_left`, `MeasureTheory.MemLp.toLp_add`, `star_mul_self_sub_self_mul_star`, `AddCircle.isAddQuotientCoveringMap_zsmul`, `mk_vadd`, `CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom`, `MeasureTheory.inner_condExpL2_eq_inner_fun`, `StrongDual.toLp_apply`, `MeasureTheory.Lp.coeFn_zero`, `index_eq_two_iff`, `AddGroup.fg_range`, `MeasureTheory.mem_lpMeas_self`, `subtype_comp_inclusion`, `MeasureTheory.norm_Lp_toLp_restrict_le`, `MeasureTheory.integrableOn_condExpL2_of_measure_ne_top`, `nsmul_mem_zmultiples`, `hasSum_sq_fourierCoeff`, `ContinuousLinearMap.holder_add_right`, `MeasureTheory.Lp.enorm_def`, `skewAdjoint.conjugate`, `MeasureTheory.condExpInd_disjoint_union_apply`, `NonUnitalSubring.mem_closure_iff`, `CochainComplex.HomComplex.δ_comp_zero_cocycle`, `ContinuousLinearMap.add_compLpL`, `imaginaryPart_imaginaryPart`, `MeasureTheory.L1.setToL1_simpleFunc_indicatorConst`, `lp.instNormOneClassSubtypePreLpMemAddSubgroupTopENNRealOfNonempty`, `IsHilbertSum.linearIsometryEquiv_symm_apply_single`, `MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'`, `fixedPoints_addSubgroup_iSup`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left`, `UnitAddTorus.mFourierBasis_repr`, `NormedAddGroupHom.Equalizer.map_id`, `MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul`, `MeasureTheory.Lp.norm_measure_zero`, `AddMonoidHom.ker_rangeRestrict`, `skewAdjoint.smul_mem`, `MeasureTheory.tendsto_indicatorConstLp_set`, `mem_addUnits_iff_val_mem`, `instIsAddCommutativeQuotientSubtypeMemFocalAddSubgroupOf`, `LipschitzWith.coeFn_compLp`, `MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot`, `CochainComplex.HomComplex.Cocycle.coe_zero`, `fourierBasis_repr`, `quasispectrum_realPart'`, `AddAction.isMultiplyPreprimitive_iff`, `MeasureTheory.L1.setToL1_zero_left'`, `MeasureTheory.BoundedContinuousFunction.inner_toLp`, `cfc_re_id`, `MeasureTheory.condExpL1_mono`, `index_range`, `MeasureTheory.Lp.coeFn_neg`, `MeasureTheory.L1.norm_Integral_le_one`, `AddCommGrpCat.kernelIsoKer_hom_comp_subtype`, `ArchimedeanClass.mem_ballAddSubgroup_iff`, `MeasureTheory.Lp.toLp_compMeasurePreserving`, `MeasureTheory.Lp.coeFn_abs`, `MeasureTheory.Lp.norm_eq_zero_iff`, `Finset.vadd_stabilizer_of_no_doubling`, `lp.single_apply`, `normalizer_le_normalizer_sup_of_normalizer_le_left`, `imaginaryPart_smul`, `Commensurable.discreteTopology_iff`, `QuotientAddGroup.preimage_image_mk_eq_iUnion_image`, `quotientEquivProdOfLE'_symm_apply`, `lp.isometry_single`, `KuratowskiEmbedding.embeddingOfSubset_dist_le`, `mem_inv_pointwise_smul_iff₀`, `MeasureTheory.Lp.coeFn_sub`, `leftCoset_cover_filter_FiniteIndex_aux`, `AddAction.IsBlock.addSubgroup`, `NormedAddGroupHom.ker.lift_apply_coe`, `AddAction.mem_stabilizer_finset`, `MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le`, `mem_closure_iff_of_fintype`, `MeasureTheory.Lp.meas_ge_le_mul_pow_enorm`, `cfcₙ_realPart`, `Unitary.norm_argSelfAdjoint`, `UnitAddTorus.hasSum_sq_mFourierCoeff`, `AddAction.stabilizer_finite`, `AddAction.mem_stabilizer_set_iff_vadd_set_subset`, `SubAddAction.ofFixingAddSubgroup.append_right`, `coe_sInf`, `realPart_apply_coe`, `normalizer_inf_normalizer_le_normalizer_sup`, `ContinuousLinearMap.coeFn_compLp`, `DomMulAct.nnnorm_smul_Lp`, `isLeast_of_closure_iff_eq_abs`, `vadd_apply_eq_vadd_apply_neg_vadd`, `MeasureTheory.L1.setToL1_mono`, `coe_pathComponentZero`, `mem_zmultiples_of_prime_card`, `CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff`, `AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples`, `coe_ringEquiv_lpBCF_symm`, `MeasureTheory.lintegral_nnnorm_condExpIndSMul_le`, `subset_normalizer_of_normal`, `LipschitzWith.continuous_compLp`, `QuotientAddGroup.eq_zero_iff`, `surjOn_iff_le_map`, `lp.norm_eq_tsum_rpow`, `spectrum_realPart`, `MeasureTheory.Lp.smul_assoc`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `MeasureTheory.integrable_condExpIndSMul`, `lp.coeFn_neg`, `spectrum_imaginaryPart'`, `Subfield.coe_toAddSubgroup`, `Valuation.coe_ltAddSubgroup`, `AddAction.add_stabilizer_self`, `CochainComplex.mappingCone.δ_descCochain`, `MeasureTheory.Lp.toTemperedDistribution_apply`, `addSubgroupOfContinuousAddEquivOfLe_symm_apply`, `val_list_sum`, `LipschitzWith.compLp_zero`, `AddAction.isPreprimitive_ofFixingAddSubgroup_addConj_iff`, `exists_right_transversal_of_le`, `AddAction.ofFixingSubgroup.isMultiplyPreprimitive`, `add_mem_cancel_left`, `quotientEquivProdOfLE_apply`, `MeasureTheory.condExpL1_zero`, `SubAddAction.nat_card_ofStabilizer_add_zero_eq`, `MeasureTheory.Lp.compMeasurePreserving_continuous`, `AddAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup`, `MeasureTheory.Lp.coeFn_posPart`, `lp.zeroBasis_repr_symm_apply_coe`, `NormedAddGroupHom.mem_range`, `AddAction.QuotientAction.inv_mul_mem`, `index_dvd_two_iff'`, `AddAction.card_eq_sum_card_addGroup_sub_card_stabilizer`, `MeasureTheory.L1.SimpleFunc.setToL1S_add`, `AddAction.orbit_addSubgroup_subset`, `MeasureTheory.Lp.mem_Lp_of_ae_le_mul`, `QuotientAddGroup.eq_class_eq_leftCoset`, `MeasureTheory.L1.norm_sub_eq_lintegral`, `mem_map`, `IsSubnormal.iff_eq_top_or_exists`, `AddMonoidHom.eq_iff`, `MeasureTheory.norm_indicatorConstLp'`, `SubAddAction.ofStabilizer_carrier`, `lp.norm_toNorm`, `exists_isLeast_pos`, `sup_eq_closure_add`, `SubAddAction.disjoint_val_image`, `lp.norm_const_smul_le`, `MeasureTheory.Lp.neg_smul_neg`, `relIndex_eq_natAbs_det`, `exists_leftTransversal_of_FiniteIndex`, `MeasureTheory.isometry_lpMeasSubgroupToLpTrim`, `MeasureTheory.integrable_condExpL1`, `ContinuousLinearMap.smul_compLpL`, `isClosed_nullAddSubgroup`, `properlyDiscontinuousVAdd_of_tendsto_cofinite`, `mem_unop`, `MeasureTheory.Integrable.toL1_add`, `equivOp_apply_coe`, `orbit_addSubgroup_eq_rightCoset`, `AddSubmonoid.mem_addUnits_iff`, `ContinuousLinearMap.norm_compLpL_le`, `CochainComplex.mappingCocone.inr_v_descCochain_v_assoc`, `DomMulAct.smul_Lp_const`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left`, `isAddCommutative_closure`, `MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq`, `QuotientAddGroup.exists_norm_add_lt`, `Set.add_addSubgroupClosure`, `IsLinearTopology.hasBasis_subbimodule`, `MeasureTheory.setIntegral_condExpL1CLM`, `MeasureTheory.L1.hasFiniteIntegral_coeFn`, `lp.norm_eq_ciSup`, `card_eq_one`, `inclusion_range`, `eq_bot_iff_card`, `tsum_sq_fourierCoeff`, `MeasureTheory.lpMeasToLpTrim_ae_eq`, `MeasureTheory.eLpNorm_condExpL2_le`, `IsSelfAdjoint.coe_realPart`, `normal_iff_eq_addCosets`, `AddAction.card_eq_sum_card_addGroup_sub_card_stabilizer'`, `realPart_smul`, `RingSubgroupsBasis.mem_addGroupFilterBasis_iff`, `exponent_toAddSubmonoid`, `lp.completeSpace`, `AddGroup.rank_range_le`, `MeasureTheory.L1.integral_eq'`, `CochainComplex.HomComplex.Cocycle.fromSingleMk_mem_coboundaries_iff`, `MeasureTheory.lpMeasToLpTrim_smul`, `bot_or_exists_ne_zero`, `CochainComplex.mappingCocone.δ_liftCochain`, `unitary.norm_argSelfAdjoint_le_pi`, `addSubgroupOfContinuousAddEquivOfLe_toAddEquiv`, `MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg`, `focalAddSubgroupOf.mk'_addConj_eq`, `CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero`, `mem_toZModSubmodule`, `isComplement'_def`, `inf_addSubgroupOf_inf_normal_of_right`, `KuratowskiEmbedding.exists_isometric_embedding`, `AddAction.mem_aestabilizer`, `card_le_card_addGroup`, `Set.addSubgroupClosure_add_nsmul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono`, `mem_ofAddUnits_iff`, `AddAction.stabilizer_subset_sub_right`, `lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup`, `fixedPoints_addSubgroup_sup`, `IsOfFinAddOrder.mem_multiples_iff_mem_zmultiples`, `KuratowskiEmbedding.embeddingOfSubset_coe`, `lp.star_apply`, `vadd_opposite_image_add_preimage`, `inclusion_injective`, `Unitary.norm_argSelfAdjoint_le_pi`, `instAddSubgroupClass`, `comap_inclusion_addSubgroupOf`, `MeasureTheory.Lp.compMeasurePreserving_id`, `selfAdjoint.isStarNormal`, `NormedAddGroupHom.Equalizer.norm_lift_le`, `MeasureTheory.condExpIndSMul_ae_eq_smul`, `IsOfFinAddOrder.multiples_eq_zmultiples`, `MeasureTheory.Lp.simpleFunc.isDenseInducing`, `mapClusterPt_atTop_nsmul_iff_mem_topologicalClosure_zmultiples`, `MeasureTheory.Lp.dense_hasCompactSupport_contDiff`, `addSubgroupOf_eq_bot`, `SubAddAction.ofStabilizer.isMultiplyPretransitive`, `instProperVAddSubtypeAddOppositeMemAddSubgroupOpOfIsTopologicalAddGroupOfIsClosedCoe`, `equiv_lpPiLp_norm`, `ContinuousLinearMap.norm_holderL_le`, `lp.uniformContinuous_coe`, `relIindex_dvd_two_iff'`, `coe_algEquiv_lpBCF_symm`, `MeasureTheory.lpMeas.ae_fin_strongly_measurable'`, `dense_of_not_isolated_zero`, `exists_left_transversal_of_le`, `CochainComplex.HomComplex.Cocycle.leftShift_coe`, `addOrderOf_mk`, `MeasureTheory.L1.setToL1'_eq_setToL1SCLM`, `RingPreordering.HasIdealSupport.smul_mem_support`, `spectrum_realPart'`, `OpenAddSubgroup.mem_toAddSubgroup`, `CochainComplex.HomComplex.Cocycle.coe_add`, `MeasureTheory.condExpL1_sub`, `rank_congr`, `MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpLpMeasSubgroupOfFactLeMeasurableSpace`, `Real.Lp.coe_fourierTransform`, `quotientAddSubgroupOfEmbeddingOfLE_apply_mk`, `IsOfFinAddOrder.finite_zmultiples`, `AddGroupExtension.Section.add_neg_mem_range_inl`, `lp.norm_mono`, `goursat`, `MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq`, `addSubgroupOf_isOpen`, `CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero_assoc`, `Unitary.openPartialHomeomorph_apply`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg`, `MeasureTheory.L1.integral_sub`, `MeasureTheory.L1.ofReal_norm_sub_eq_lintegral`, `Unitary.argSelfAdjoint_coe`, `MeasureTheory.Lp.coeFn_inf`, `MeasureTheory.ContinuousMap.inner_toLp`, `skewAdjoint.I_smul_neg_I`, `AddSubmonoid.add_mem_addUnits`, `MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral`, `MeasureTheory.Lp.simpleFunc.toLp_eq_mk`, `mem_closure_singleton`, `DomAddAct.dist_vadd_Lp`, `QuotientAddGroup.rightRel_eq`, `OrthogonalFamily.linearIsometry_apply`, `AddAction.mem_stabilizer_set`, `mem_goursatSnd`, `subset_normalClosure`, `ContinuousLinearMap.holderL_apply_apply`, `MeasureTheory.Lp.instContinuousFourier`, `center_le_normalizer`, `DomAddAct.vadd_Lp_zero`, `MeasureTheory.condExpInd_empty`, `SchwartzMap.norm_fourier_apply_le_toLp_one`, `MeasureTheory.condExpL1CLM_smul`, `CochainComplex.HomComplex.Cocycle.diff_coe`, `Subgroup.widthInfty_mem_periods`, `LipschitzWith.norm_compLp_le`, `normalizer_le_normalizer_sup_of_normalizer_le_right`, `subtype_apply`, `MeasureTheory.L1.edist_def`, `relIndex_ker`, `MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun`, `zsmul_mem_zmultiples`, `MeasureTheory.continuous_setIntegral`, `focalAddSubgroup_def`, `MeasureTheory.MemLp.toLp_zero`, `lp.single_apply_self`, `addCommutator_eq_bot_iff_le_centralizer`, `CochainComplex.Lifting.comp_coe_cocycle₁_comp`, `AddMonoidHom.coe_range`, `torsionBy.nsmul`, `CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero_assoc`, `CategoryTheory.ShortComplex.abLeftHomologyData_H_coe`, `AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_apply_coe`, `UnitAddTorus.span_mFourierLp_closure_eq_top`, `AddAction.stabilizerEquivStabilizer_zero`, `CochainComplex.HomComplex.Cocycle.rightUnshift_coe`, `leftCoset_cover_filter_FiniteIndex`, `skewAdjointPart_comp_subtype_skewAdjoint`, `continuous_skewAdjointPart`, `set_add_normal_comm`, `AddAction.stabilizer_orbit_eq`, `IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single`, `MeasureTheory.Lp.pow_mul_meas_ge_le_enorm`, `CochainComplex.mappingCone.lift_f`, `MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero`, `comap_injective_isAddCommutative`, `MeasureTheory.condExpIndL1Fin_smul'`, `ContinuousLinearMap.norm_holder_apply_apply_le`, `MeasureTheory.Lp.edist_dist`, `IsSelfAdjoint.imaginaryPart`, `FiniteIndexNormalAddSubgroup.mem_toAddSubgroup_iff`, `AddMonoidHom.mem_ker`, `BoundedContinuousFunction.range_toLp`, `MeasureTheory.indicatorConstLp_disjoint_union`, `zero_mem`, `QuotientAddGroup.rangeKerLift_injective`, `coe_eq_univ`, `SubAddAction.ofStabilizer.addConjMap_bijective`, `mem_closure_pair`, `MeasureTheory.L1.integral_eq`, `MeasureTheory.indicatorConstLp_coeFn`, `AddAction.stabilizerEquivStabilizer_compTriple`, `le_normalizer_comap`, `SubAddAction.exists_vadd_of_last_eq`, `Continuous.compMeasurePreservingLp`, `MeasureTheory.Lp.fourier_toTemperedDistribution_eq`, `CochainComplex.mappingCone.inl_v_fst_v_assoc`, `MeasureTheory.Lp.const_val`, `coe_toSubgroup_symm_apply`, `leftAddCoset_mem_leftAddCoset`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff`, `unitary.mem_pathComponentOne_iff`, `MeasureTheory.Lp.simpleFunc.coeFn_nonneg`, `mem_unitary_iff_isStarNormal_and_realPart_sq_add_imaginaryPart_sq_eq_one`, `isAddFundamentalDomain_Ioc'`, `MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp`, `Subgroup.instDiscreteTopPeriods`, `MeasureTheory.L1.setToL1'_apply_coeToLp`, `relIndex_dvd_card`, `addSubgroupOf_sup`, `SchwartzMap.denseRange_toLpCLM`, `ContinuousOn.compMeasurePreservingLp`, `mem_fixingAddSubgroup_iff_subset_fixedBy`, `MeasureTheory.memLp_trim_of_mem_lpMeasSubgroup`, `SchwartzMap.toLp_fourier_eq`, `coe_ofClass`, `DomMulAct.smul_Lp_val`, `IsComplement.add_neg_toRightFun_mem`, `NormedSpace.discreteTopology_zmultiples`, `RingSubgroupsBasis.mul`, `AddMonoidHom.mem_range`, `DomAddAct.nnnorm_vadd_Lp`, `le_normalizer_of_normal_addSubgroupOf`, `MeasureTheory.L1.setToL1_const`, `addOrderOf_le_card`, `iSupIndep_iff_dfinsuppSumAddHom_injective`, `MeasureTheory.norm_condExpIndL1Fin_le`, `MeasureTheory.lpMeasToLpTrimLie_symm_toLp`, `MeasureTheory.continuous_L1_toL1`, `CochainComplex.mappingCocone.inr_v_descCochain_v`, `AddAction.isPreprimitive_fixingAddSubgroup_insert_iff`, `MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm`, `ProfiniteAddGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemAddSubgroupLimitConePtAux`, `MeasureTheory.indicatorConstLp_empty`, `pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero`, `instNormalSubtypeMemFocalAddSubgroupOf`, `MeasureTheory.Integrable.edist_toL1_toL1`, `MeasureTheory.MemLp.toLp_const_smul`, `MeasureTheory.Lp.norm_le_mul_norm_of_ae_le_mul`, `coe_algEquiv_lpBCF`, `MeasureTheory.L1.setToL1_lipschitz`, `MeasureTheory.Integrable.toL1_neg`, `MeasureTheory.norm_condExpL2_le_one`, `GromovHausdorff.eq_toGHSpace_iff`, `MeasureTheory.setToFun_eq`, `MeasureTheory.condExpL2_comp_continuousLinearMap`, `NormedAddGroupHom.Equalizer.liftEquiv_symm_apply_coe`, `MeasureTheory.Lp.coeFn_star`, `MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top`, `AddMonoid.minOrder_le_natCard`, `coe_nonempty`, `ContinuousLinearMap.holder_add_left`, `lp.toNorm_coe`, `ArchimedeanClass.mem_closedBallAddSubgroup_iff`, `CochainComplex.mappingCocone.liftCocycle_coe`, `CochainComplex.HomComplex.Cocycle.mk_coe`, `le_centralizer`, `AddGroupExtension.Section.neg_add_mem_range_inl`, `AddAction.orbitRel_addSubgroupOf`, `ext_iff`, `AddAction.isMultiplyPreprimitive_ofStabilizer`, `MeasureTheory.dist_indicatorConstLp_eq_norm`, `LipschitzWith.norm_compLp_sub_le`, `MeasureTheory.Lp.simpleFunc.toLp_add`, `mem_top`, `BoundedContinuousFunction.toLp_denseRange`, `MeasureTheory.condExpL2_const_inner`, `lp.instIsScalarTowerSubtypePreLpMemAddSubgroup`, `AddAction.vadd_set_stabilizer_subset`, `Unitary.path_apply`, `inf_normalizer_le_normalizer_inf`, `unitary.two_mul_one_sub_cos_norm_argSelfAdjoint`, `MeasureTheory.Lp.isometry_compMeasurePreserving`, `CochainComplex.mappingCone.inr_fst`, `closure_le`, `QuotientAddGroup.rangeKerLift_surjective`, `CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv`, `coeFn_fourierLp`, `MeasureTheory.Lp.simpleFunc.dense`, `SubAddAction.mem_ofFixingAddSubgroup_insert_iff`, `MeasureTheory.Lp.instFourierAdd`, `mem_iInf`, `index_dvd_two_iff`, `MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc`, `MeasureTheory.norm_setToFun_le`, `topologicalClosure_coe`, `MeasureTheory.Lp.toTemperedDistribution_smul_eq`, `CochainComplex.HomComplex.Cocycle.mem_iff`, `MeasureTheory.Lp_toLp_restrict_smul`, `mem_centralizer_singleton_iff`, `MeasureTheory.condExpL1_eq`, `DomAddAct.vadd_Lp_val`, `QuotientAddGroup.preimage_mk_zero`, `MeasureTheory.L1.SimpleFunc.coe_posPart`, `Additive.mem_toAddSubgroup`, `MeasureTheory.Lp.compMeasurePreserving_val`, `QuotientAddGroup.orbit_mk_eq_vadd`, `Submodule.coe_toAddSubgroup`, `CochainComplex.HomComplex.Cocycle.rightShift_coe`, `ContinuousLinearMap.coeFn_holder`, `CochainComplex.mappingCone.d_fst_v`, `HilbertBasis.hasSum_repr_symm`, `AddAction.isPreprimitive_of_fixingAddSubgroup_empty_iff`, `mem_biSup_of_directedOn`, `MeasureTheory.Lp.instContinuousSMulDomMulAct`, `MeasureTheory.Lp.norm_compMeasurePreserving`, `IsAddQuotientCoveringMap.addSubgroup_congr`, `MeasureTheory.Lp.nnnorm_zero`, `MeasureTheory.setToFun_toL1`, `AddMonoidHom.ofInjective_apply`, `normal_addSubgroupOf_iff_le_normalizer_inf`, `MeasureTheory.condExpL2_indicator_nonneg`, `NormedAddGroupHom.norm_incl`, `selfAdjoint.expUnitary_coe`, `selfAdjoint.val_nnqsmul`, `AddAction.IsBlock.orbit_of_normal`, `MeasureTheory.L1.integral_neg`, `instCountableSubtypeAddOppositeMemOp`, `subset_closure`, `normal_addSubgroupOf_sup_of_le_normalizer`, `MeasureTheory.MemLp.toLp_sub`, `coe_inclusion`, `add_mem`, `AddGroupExtension.Section.add_neg_add_add_mem_range_inl`, `normal_in_normalizer`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left'`, `dense_xor'_cyclic`, `StarModule.decomposeProdAdjoint_apply`, `MeasureTheory.Lp.mul_meas_ge_le_pow_enorm`, `MeasureTheory.Lp.simpleFunc.norm_toLp`, `AddAction.orbitRel.Quotient.addSubgroup_quotient_eq_iff`, `CochainComplex.mappingCone.inr_fst_assoc`, `DomMulAct.smul_Lp_add`, `IsSubnormal.isSubnormal_iff`, `card_zmultiples_le`, `kuratowskiEmbedding.isometry`, `isStarNormal_iff_commute_realPart_imaginaryPart`, `relIndex_bot_left`, `lp.tsum_mul_le_mul_norm`, `MeasureTheory.Lp.continuous_posPart`, `AddAction.mem_stabilizer_finset_iff_vadd_finset_subset`, `IsLinearTopology.hasBasis_open_subbimodule`, `MeasureTheory.Lp.norm_def`, `isComplement_range_right`, `lp.ext_continuousLinearMap_iff`, `exists_mem_ofAddUnits_val_eq`, `IsAddCyclic.card_nsmulAddMonoidHom_range`, `ker_inclusion`, `SubAddAction.not_mem_of_mem_ofFixingAddSubgroup`, `AddSubmonoid.val_addUnitsEquivAddUnitsType_apply_coe`, `AddAction.IsBlockSystem.of_normal`, `mem_fixingAddSubgroup_iff`, `equivOp_symm_apply_coe`, `Function.locallyFinsuppWithin.memAddSubgroup`, `mem_pointwise_smul_iff_inv_smul_mem₀`, `ContinuousLinearMap.coeFn_compLp'`, `Finset.nsmul_right_strictMonoOn`, `CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles`, `CochainComplex.mappingCocone.inr_v_desc_f`, `MeasureTheory.MemLp.toLp_const`, `unitary.continuousOn_argSelfAdjoint`, `MeasureTheory.lpMeas.aestronglyMeasurable`, `MeasureTheory.leftInvariantIsAddQuotientMeasureEqMeasurePreimage`, `cfc_imaginaryPart`, `IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul`, `CochainComplex.HomComplex.δ_zero_cocycle_comp`, `finite_zmultiples`, `SubAddAction.map_ofFixingAddSubgroupUnion_def`, `MeasureTheory.Lp.compMeasurePreserving_iterate`, `MeasureTheory.L1.norm_eq_integral_norm`, `Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint`, `relIndex_eq_two_iff`, `Bot.isAddCyclic`
`neg` 📖	CompOp	22 math math: `MeasureTheory.lpMeasSubgroupToLpTrim_neg`, `coe_neg`, `MeasureTheory.L1.SimpleFunc.setToL1S_neg`, `MeasureTheory.Lp.norm_neg`, `MeasureTheory.Lp.nnnorm_neg`, `lp.single_neg`, `MeasureTheory.Lp.dist_eq_norm`, `MeasureTheory.condExpL1_neg`, `MeasureTheory.MemLp.toLp_neg`, `DomMulAct.smul_Lp_neg`, `MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc`, `realPart_I_smul`, `DomAddAct.vadd_Lp_neg`, `lp.norm_neg`, `MeasureTheory.Lp.smul_neg`, `MeasureTheory.Lp.simpleFunc.toLp_neg`, `MeasureTheory.Lp.neg_smul`, `MeasureTheory.Lp.coeFn_neg`, `lp.coeFn_neg`, `MeasureTheory.Lp.neg_smul_neg`, `MeasureTheory.Integrable.toL1_neg`, `MeasureTheory.L1.integral_neg`
`normalizer` 📖	CompOp	28 math math: `unop_normalizer`, `op_normalizer`, `addSubgroupOf_normalizer_eq`, `mem_normalizer_iff`, `normalizer_eq_top_iff`, `comap_normalizer_eq_of_surjective`, `le_normalizer`, `map_normalizer_eq_of_bijective`, `comap_normalizer_eq_of_le_range`, `map_equiv_normalizer_eq`, `mem_normalizer_iff''`, `le_normalizer_map`, `normalizer_eq_top`, `le_normalizer_of_normal`, `AddAction.right_quotientAction`, `normal_addSubgroupOf_iff_le_normalizer`, `normalizer_le_normalizer_sup_normal`, `mem_normalizer_iff'`, `normalizer_le_normalizer_sup_of_normalizer_le_left`, `normalizer_inf_normalizer_le_normalizer_sup`, `subset_normalizer_of_normal`, `center_le_normalizer`, `normalizer_le_normalizer_sup_of_normalizer_le_right`, `le_normalizer_comap`, `le_normalizer_of_normal_addSubgroupOf`, `inf_normalizer_le_normalizer_inf`, `normal_addSubgroupOf_iff_le_normalizer_inf`, `normal_in_normalizer`
`nsmul` 📖	CompOp	3 math math: `torsionBy.mod_self_nsmul`, `coe_nsmul`, `torsionBy.nsmul`
`ofClass` 📖	CompOp	1 math math: `coe_ofClass`
`ofSub` 📖	CompOp	—
`sub` 📖	CompOp	21 math math: `DomMulAct.smul_Lp_sub`, `MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc`, `MeasureTheory.L1.SimpleFunc.setToL1S_sub`, `lp.coeFn_sub`, `MeasureTheory.lpMeasSubgroupToLpTrim_sub`, `MeasureTheory.Integrable.toL1_sub`, `lp.norm_compl_sum_single`, `DomAddAct.vadd_Lp_sub`, `lp.single_sub`, `coe_sub`, `MeasureTheory.indicatorConstLp_sub`, `MeasureTheory.Lp.simpleFunc.toLp_sub`, `lp.norm_sub_norm_compl_sub_single`, `MeasureTheory.Lp.coeFn_sub`, `MeasureTheory.L1.norm_sub_eq_lintegral`, `realPart_smul`, `MeasureTheory.condExpL1_sub`, `MeasureTheory.L1.integral_sub`, `MeasureTheory.L1.ofReal_norm_sub_eq_lintegral`, `LipschitzWith.norm_compLp_sub_le`, `MeasureTheory.MemLp.toLp_sub`
`subtype` 📖	CompOp	44 math math: `closure_preimage_eq_top`, `coe_addSubgroupOf`, `image_addCommutatorSet_closureAddCommutatorRepresentatives`, `iSupIndep.dfinsuppSumAddHom_injective`, `coe_subtype`, `subtype_range`, `card_subtype`, `tendsto_zmultiples_subtype_cofinite`, `map_subtype_addCommutator`, `map_subtype_le`, `AddMonoidHom.subtype_comp_rangeRestrict`, `addCommute_subtype_of_addCommute`, `QuotientAddGroup.strictMono_comap_prod_image`, `map_focalAddSubgroupOf`, `range_subtype`, `goursat_surjective`, `TopologicalAddGroup.IsSES.ofClosedAddSubgroup`, `addSubgroupOf_map_subtype`, `map_subtype_lt_map_subtype`, `QuotientAddGroup.ker_le_range_iff`, `QuotientAddGroup.mk'_comp_subtype`, `QuotientAddGroup.strictMono_comap_prod_map`, `IsSubnormal.trans'`, `ker_subtype`, `AddCommGrpCat.kernelIsoKer_inv_comp_ι`, `MapSubtype.orderIso_apply_coe`, `index_map_subtype`, `map_subtype_inj`, `map_subtype_le_map_subtype`, `CategoryTheory.ShortComplex.abLeftHomologyData_i`, `comap_subtype`, `map_addSubgroupOf_eq_of_le`, `Function.Exact.addMonoidHom_rangeRestrict`, `SubAddAction.fixingAddSubgroup_of_insert`, `subtype_injective`, `SubAddAction.of_fixingAddSubgroupEmpty_mapScalars_surjective`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `subtype_comp_inclusion`, `AddCommGrpCat.kernelIsoKer_hom_comp_subtype`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `goursat`, `subtype_apply`, `iSupIndep_iff_dfinsuppSumAddHom_injective`
`toAddCommGroup` 📖	CompOp	205 math math: `cfc_realPart`, `continuous_decomposeProdAdjoint`, `StarModule.decomposeProdAdjointL_symm_apply`, `StarModule.selfAdjointPart_add_skewAdjointPart`, `MeasureTheory.L1.SimpleFunc.norm_Integral_le_one`, `lp.coe_linearMapOfLE_apply`, `MeasureTheory.Lp.instIsScalarTower`, `imaginaryPart_eq_zero_iff`, `Commute.realPart_imaginaryPart`, `Complex.coe_realPart`, `quasispectrum_imaginaryPart`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left`, `cfc_im_id`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1`, `realPart_idem`, `MeasureTheory.norm_condExpL2_le`, `MeasureTheory.Lp.instIsOrderedAddMonoid`, `realPart_ofReal`, `MeasureTheory.inner_condExpL2_left_eq_right`, `imaginaryPart_I_smul`, `MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero`, `ContinuousMap.range_toLp`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_const`, `MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM`, `lp.norm_sum_single`, `ContinuousLinearMap.smul_compLp`, `selfAdjointPart_comp_subtype_skewAdjoint`, `IsSelfAdjoint.selfAdjointPart_apply`, `StarModule.decomposeProdAdjointL_apply`, `MeasureTheory.Lp.compMeasurePreservingₗ_apply`, `lp.toAddMonoidHom_linearMapOfLE`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp`, `selfAdjointPart_comp_subtype_selfAdjoint`, `MeasureTheory.aestronglyMeasurable_condExpL2`, `lp.evalₗ_apply`, `MeasureTheory.condExpL2_indicator_ae_eq_smul`, `ContinuousLinearMap.holderₗ_apply_apply`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left'`, `index_eq_natAbs_det`, `MeasureTheory.integral_condExpL2_eq`, `MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc`, `MeasureTheory.setIntegral_condExpL2_indicator`, `selfAdjoint.imaginaryPart_coe`, `cfcₙ_re_id`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le`, `CategoryTheory.ShortComplex.abLeftHomologyData_π`, `continuous_decomposeProdAdjoint_symm`, `MeasureTheory.L1.setToL1_eq_setToL1SCLM`, `MeasureTheory.norm_condExpL2_coe_le`, `MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le`, `lp.norm_const_smul`, `MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable`, `lp.zeroBasis_repr_apply`, `realPart.norm_le`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul_real`, `MeasureTheory.mem_lpMeas_indicatorConstLp`, `MeasureTheory.lintegral_nnnorm_condExpL2_le`, `realPart_add_I_smul_imaginaryPart`, `ContinuousLinearMap.holder_smul_left`, `MeasureTheory.Lp.coeFn_smul`, `IsSelfAdjoint.skewAdjointPart_apply`, `ComplexStarModule.ext_iff`, `MeasureTheory.lpMeasToLpTrimLie_symm_indicator`, `quasispectrum_imaginaryPart'`, `StarModule.decomposeProdAdjoint_symm_apply`, `cfcₙ_comp_re`, `star_mul_self_eq_realPart_sq_add_imaginaryPart_sq`, `cfc_comp_im`, `realPart_one`, `MeasureTheory.Lp.constₗ_apply`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2`, `cfcₙ_comp_im`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left`, `lp.instSMulCommClassSubtypePreLpMemAddSubgroup`, `CStarAlgebra.linear_combination_nonneg`, `CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary`, `star_mul_self_add_self_mul_star`, `imaginaryPart.norm_le`, `realPart_comp_subtype_selfAdjoint`, `spectrum_imaginaryPart`, `skewAdjoint.negISMul_apply_coe`, `toIsOrderedAddMonoid`, `imaginaryPart_realPart`, `lp.instStarModuleSubtypePreLpMemAddSubgroup`, `MeasureTheory.integral_condExpL2_eq_of_fin_meas_real`, `lp.zeroBasis_apply`, `imaginaryPart_eq_neg_I_smul_skewAdjointPart`, `skewAdjointPart_comp_subtype_selfAdjoint`, `lp.coeFn_sum`, `realPart_I_smul`, `lp.norm_compl_sum_single`, `selfAdjoint.realPart_unitarySelfAddISMul`, `MeasureTheory.condExpL2_indicator_of_measurable`, `MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le'`, `cfcₙ_imaginaryPart`, `imaginaryPart_apply_coe`, `MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace`, `CategoryTheory.ShortComplex.abLeftHomologyData_f'`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real`, `cfc_comp_re`, `imaginaryPart_comp_subtype_selfAdjoint`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left`, `ContinuousLinearMap.lpPairing_eq_integral`, `ContinuousLinearMap.holder_smul_right`, `lp.lsingle_apply`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left'`, `MeasureTheory.condExpL1CLM_lpMeas`, `AddCommGrpCat.kernelIsoKer_inv_comp_ι`, `realPart_surjective`, `StrongDual.toLpₗ_apply`, `MeasureTheory.L1.setToL1_apply_coeToLp`, `cfcₙ_im_id`, `quasispectrum_realPart`, `imaginaryPart_surjective`, `lp.coeFn_smul`, `StrongDual.norm_toLpₗ_le`, `selfAdjoint.realPart_coe`, `MeasureTheory.Lp.instIsCentralScalar`, `lp.single_smul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left'`, `lp.instIsCentralScalarSubtypePreLpMemAddSubgroup`, `addSubgroupOf_map_nsmulAddMonoidHom_eq_range`, `StrongDual.toLpₗ_of_not_memLp`, `MeasureTheory.integrable_condExpL2_of_isFiniteMeasure`, `CategoryTheory.ShortComplex.abLeftHomologyData_i`, `skewAdjointPart_apply_coe`, `continuous_selfAdjointPart`, `selfAdjointPartL_apply_coe`, `MeasureTheory.integrable_condExpL2_indicator`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp'`, `imaginaryPart_ofReal`, `MeasureTheory.Lp.simpleFunc.coe_smul`, `val_finset_sum`, `IsSelfAdjoint.coe_selfAdjointPart_apply`, `MeasureTheory.Lp.instSMulCommClass`, `MeasureTheory.L1.SimpleFunc.integral_smul`, `MeasureTheory.lpTrimToLpMeas_ae_eq`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le`, `lp.norm_sub_norm_compl_sub_single`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure`, `MeasureTheory.Lp.smul_comm`, `selfAdjointPart_apply_coe`, `skewAdjointPartL_apply_coe`, `ker_imaginaryPart`, `realPart_imaginaryPart`, `val_multiset_sum`, `skewAdjointPart_eq_I_smul_imaginaryPart`, `lp.linearMapOfLE_comp`, `MeasureTheory.Lp.simpleFunc.toLp_smul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left'`, `star_mul_self_sub_self_mul_star`, `MeasureTheory.inner_condExpL2_eq_inner_fun`, `MeasureTheory.mem_lpMeas_self`, `MeasureTheory.integrableOn_condExpL2_of_measure_ne_top`, `imaginaryPart_imaginaryPart`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left`, `quasispectrum_realPart'`, `cfc_re_id`, `AddCommGrpCat.kernelIsoKer_hom_comp_subtype`, `imaginaryPart_smul`, `cfcₙ_realPart`, `realPart_apply_coe`, `spectrum_realPart`, `MeasureTheory.Lp.smul_assoc`, `spectrum_imaginaryPart'`, `lp.zeroBasis_repr_symm_apply_coe`, `lp.norm_const_smul_le`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left`, `MeasureTheory.lpMeasToLpTrim_ae_eq`, `MeasureTheory.eLpNorm_condExpL2_le`, `IsSelfAdjoint.coe_realPart`, `realPart_smul`, `MeasureTheory.lpMeasToLpTrim_smul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono`, `MeasureTheory.condExpIndSMul_ae_eq_smul`, `ContinuousLinearMap.norm_holderL_le`, `MeasureTheory.lpMeas.ae_fin_strongly_measurable'`, `MeasureTheory.L1.setToL1'_eq_setToL1SCLM`, `spectrum_realPart'`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg`, `skewAdjoint.I_smul_neg_I`, `ContinuousLinearMap.holderL_apply_apply`, `skewAdjointPart_comp_subtype_skewAdjoint`, `continuous_skewAdjointPart`, `MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero`, `IsSelfAdjoint.imaginaryPart`, `BoundedContinuousFunction.range_toLp`, `mem_unitary_iff_isStarNormal_and_realPart_sq_add_imaginaryPart_sq_eq_one`, `MeasureTheory.L1.setToL1'_apply_coeToLp`, `MeasureTheory.lpMeasToLpTrimLie_symm_toLp`, `MeasureTheory.MemLp.toLp_const_smul`, `MeasureTheory.norm_condExpL2_le_one`, `MeasureTheory.condExpL2_comp_continuousLinearMap`, `MeasureTheory.condExpL2_const_inner`, `lp.instIsScalarTowerSubtypePreLpMemAddSubgroup`, `MeasureTheory.Lp_toLp_restrict_smul`, `MeasureTheory.condExpL2_indicator_nonneg`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left'`, `StarModule.decomposeProdAdjoint_apply`, `isStarNormal_iff_commute_realPart_imaginaryPart`, `CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles`, `MeasureTheory.lpMeas.aestronglyMeasurable`, `cfc_imaginaryPart`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul`
`toAddGroup` 📖	CompOp	406 math math: `inf_addSubgroupOf_inf_normal_of_left`, `IsFiniteRelIndex.to_finiteIndex_addSubgroupOf`, `AddMonoidHom.coe_rangeRestrict`, `MeasureTheory.L1.SimpleFunc.norm_Integral_le_one`, `SubAddAction.map_ofFixingAddSubgroupUnion_bijective`, `quotientEquivProdOfLE_symm_apply`, `MeasureTheory.Lp.instIsScalarTower`, `MeasureTheory.mem_lpMeasSubgroup_iff_aestronglyMeasurable`, `addSubgroupOf_eq_top`, `MeasureTheory.Lp.compMeasurePreserving_id_apply`, `SubAddAction.notMem_val_image`, `quotientiInfAddSubgroupOfEmbedding_apply_mk`, `AddGroup.closure_finite_fg`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1`, `AddCircle.isAddQuotientCoveringMap_zsmul_of_ne_zero`, `closure_preimage_eq_top`, `vaddCommClass_left`, `AddAction.mem_addSubgroup_orbit_iff`, `coe_addSubgroupOf`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff_of_addConj`, `image_addCommutatorSet_closureAddCommutatorRepresentatives`, `addSubgroupOfContinuousAddEquivOfLe_apply`, `MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving`, `MeasureTheory.Lp.coeFn_const`, `vadd_mem_fixedPoints_of_normal`, `top_addSubgroupOf`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `iSupIndep.dfinsuppSumAddHom_injective`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_const`, `MeasureTheory.lpMeasSubgroupToLpTrim_neg`, `MeasureTheory.Lp.simpleFunc.uniformContinuous`, `coe_subtype`, `SubAddAction.ofStabilizer.addConjMap_apply`, `noncommPiCoprod_single`, `SubAddAction.ofFixingAddSubgroup_of_singleton_bijective`, `MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq`, `lp.coeFnAddMonoidHom_apply`, `addCommutator_le_focalAddSubgroupOf`, `MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM`, `SubAddAction.addConjMap_ofFixingAddSubgroup_bijective`, `AddCircle.isAddQuotientCoveringMap_nsmul_of_ne_zero`, `addSubgroupOf_self`, `AddAction.finite_quotient_of_finite_quotient_of_finite_quotient`, `ContinuousLinearMap.smul_compLp`, `SubAddAction.ofStabilizer.isPretransitive_iff_of_addConj`, `Circle.isAddQuotientCoveringMap_exp`, `AddCircle.isAddQuotientCoveringMap_nsmul`, `isFiniteRelIndex_iff_finiteIndex`, `SubAddAction.mem_ofStabilizer_iff`, `MeasureTheory.Lp.compMeasurePreservingₗ_apply`, `SubAddAction.ofStabilizer.addConjMap_comp_neg_apply`, `MeasureTheory.Lp.simpleFunc.isDenseEmbedding`, `subtype_range`, `MeasureTheory.L1.SimpleFunc.norm_setToL1S_le`, `AddMonoidHom.addSubgroupOf_range_eq_of_le`, `quotient_finite_of_isOpen'`, `MeasureTheory.L1.SimpleFunc.setToL1S_neg`, `AddMonoidHom.rangeRestrict_surjective`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroupOp`, `AddCircle.isAddQuotientCoveringMap_coe`, `MeasureTheory.L1.SimpleFunc.integral_add`, `orbit_fixingAddSubgroup_compl_subset`, `noncommPiCoprod_range`, `AddMonoidHom.ker_restrict`, `ContinuousAt.compMeasurePreservingLp`, `isUniformAddGroup`, `vaddCommClass_right`, `AddAction.orbitZMultiplesEquiv_symm_apply'`, `AddAction.IsBlock.of_orbit`, `AddAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `AddAction.orbitZMultiplesEquiv_symm_apply`, `CategoryTheory.ShortComplex.abToCycles_apply_coe`, `AddMonoidHom.rangeRestrict_injective_iff`, `prod_addSubgroupOf_prod_normal`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left'`, `MeasureTheory.Measure.IsAddLeftInvariant.addQuotientMeasureEqMeasurePreimage_of_set`, `card_subtype`, `MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc`, `noncommPiCoprod_apply`, `addSubgroupOf_normalizer_eq`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive`, `MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive'`, `MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub`, `SubAddAction.ofStabilizer.isPretransitive_iff`, `AddMonoidHom.addSubgroupMap_apply_coe`, `rank_closure_finset_le_card`, `tendsto_zmultiples_subtype_cofinite`, `ker_addSubgroupMap`, `CategoryTheory.ShortComplex.abLeftHomologyData_π`, `addSubgroupOfEquivOfLe_apply_coe`, `MeasureTheory.Lp.compMeasurePreserving_comp`, `MeasureTheory.L1.setToL1_eq_setToL1SCLM`, `lp.norm_const_smul`, `MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure`, `map_subtype_addCommutator`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul_real`, `lp.singleAddMonoidHom_apply`, `CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles`, `MeasureTheory.Lp.coeFn_compMeasurePreserving`, `orbit_addSubgroup_eq_self_of_mem`, `map_subtype_le`, `isAddQuotientCoveringMap_of_comm`, `finite_quotient_of_pretransitive_of_index_ne_zero`, `AddMonoidHom.addSubgroupComap_surjective_of_surjective`, `AddMonoidHom.subtype_comp_rangeRestrict`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `ContinuousLinearMap.holder_smul_left`, `MeasureTheory.Lp.coeFn_smul`, `addCommute_subtype_of_addCommute`, `QuotientAddGroup.strictMono_comap_prod_image`, `MeasureTheory.L1.SimpleFunc.coe_negPart`, `MeasureTheory.condExpInd_disjoint_union`, `map_focalAddSubgroupOf`, `MeasureTheory.Lp.simpleFunc.add_toSimpleFunc`, `range_subtype`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroup`, `goursat_surjective`, `MeasureTheory.indicatorConstLp_univ`, `MeasureTheory.Lp.norm_const_le`, `TopologicalAddGroup.IsSES.ofClosedAddSubgroup`, `instIsAddTorsionFree`, `rank_closure_finite_le_nat_card`, `focalAddSubgroupOf_eq_closure`, `AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply`, `MeasureTheory.L1.SimpleFunc.setToL1S_sub`, `addSubgroupOf_map_subtype`, `Normal.addSubgroupOf`, `map_subtype_lt_map_subtype`, `ContinuousWithinAt.compMeasurePreservingLp`, `MeasureTheory.Lp.boundedContinuousFunction_dense`, `MeasureTheory.Lp.constₗ_apply`, `MeasureTheory.L1.SimpleFunc.toLp_one_eq_toL1`, `MeasureTheory.Lp.mem_boundedContinuousFunction_iff`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2`, `QuotientAddGroup.ker_le_range_iff`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left`, `MeasureTheory.Lp.simpleFunc.toLp_eq_toLp`, `MeasureTheory.Lp.norm_const'`, `QuotientAddGroup.mk'_comp_subtype`, `AddMonoidHom.addSubgroupComap_apply_coe`, `injective_noncommPiCoprod_of_iSupIndep`, `MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul`, `QuotientAddGroup.strictMono_comap_prod_map`, `lp.instSMulCommClassSubtypePreLpMemAddSubgroup`, `instMeasurableVAdd`, `addSubgroupOf_mono`, `AddAction.finite_quotient_of_pretransitive_of_finite_quotient`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `AddAction.vadd_orbit_eq_orbit_vadd`, `quotientAddSubgroupOfMapOfLE_apply_mk`, `AddAction.minimalPeriod_eq_card`, `continuousVAdd`, `SubAddAction.ofStabilizer.addConjMap_comp`, `AddAction.orbitRel_addSubgroup_le`, `instFiniteIndex_addSubgroupOf`, `isSimpleAddGroup_iff`, `Complex.isAddQuotientCoveringMap_exp`, `addSubgroupOfEquivOfLe_symm_apply_coe_coe`, `MeasureTheory.lpMeasSubgroupToLpTrim_sub`, `fixedPoints_addSubgroup_antitone`, `addSubgroupOf_isAddCommutative`, `codisjoint_addSubgroupOf_sup`, `lp.instStarModuleSubtypePreLpMemAddSubgroup`, `instFaithfulVAddSubtypeMem`, `SubAddAction.nat_card_ofStabilizer_eq`, `addOrderOf_coe`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `IsSubnormal.trans'`, `MeasureTheory.Lp.simpleFunc.denseRange`, `SubAddAction.addConjMap_ofFixingAddSubgroup_coe_apply`, `instVAddAssocClassSubtypeMem`, `ker_subtype`, `nsmul_exponent_eq_zero`, `MeasureTheory.lpMeasSubgroupToLpTrim_right_inv`, `Filter.Tendsto.compMeasurePreservingLp`, `AddAction.IsBlock.of_addSubgroup_of_conjugate`, `MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc`, `AddMonoidHom.addSubgroupMap_surjective`, `AddMonoidHom.coe_comp_rangeRestrict`, `isAddQuotientCoveringMap`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le'`, `MeasureTheory.condExpL1CLM_indicatorConst`, `MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim`, `MeasureTheory.lpMeasSubgroupToLpTrim_add`, `MeasureTheory.Lp.norm_const`, `MeasureTheory.lpMeasSubgroupToLpTrim_left_inv`, `Function.Periodic.map_vadd_zmultiples`, `AddGroup.fg_iff_addSubgroup_fg`, `AddMonoidHom.restrict_range`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left`, `MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc`, `instMeasurableConstVAdd`, `instProperVAddSubtypeMemAddSubgroupOfIsClosedCoe`, `ContinuousLinearMap.holder_smul_right`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left'`, `QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff`, `finite_quotient_of_finite_quotient_of_index_ne_zero`, `MeasureTheory.L1.setToL1_apply_coeToLp`, `MeasureTheory.Lp.compMeasurePreserving_comp_apply`, `MapSubtype.orderIso_apply_coe`, `instIsTopologicalAddGroupSubtypeMem`, `MeasureTheory.Lp.simpleFunc.coeFn_le`, `index_map_subtype`, `MeasureTheory.Lp.simpleFunc.toLp_zero`, `AddAction.isBlock_top`, `MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral`, `AddAction.addSubgroup_vadd_def`, `MeasureTheory.Lp.simpleFunc.coeFn_zero`, `lp.coeFn_smul`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'`, `map_subtype_inj`, `MeasureTheory.Lp.instIsCentralScalar`, `lp.single_smul`, `SubAddAction.ofFixingAddSubgroup_insert_map_apply`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left'`, `lp.instIsCentralScalarSubtypePreLpMemAddSubgroup`, `addSubgroupOf_bot_eq_top`, `normal_addSubgroupOf_iff`, `addSubgroupOf_map_nsmulAddMonoidHom_eq_range`, `map_subtype_le_map_subtype`, `bot_addSubgroupOf`, `MeasureTheory.Subgroup.vaddInvariantMeasure`, `relIndex_addSubgroupOf`, `span_fourierLp_closure_eq_top`, `vadd_def`, `MeasureTheory.Lp.simpleFunc.isBoundedSMul`, `MapSubtype.orderIso_symm_apply`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_isDiscrete_ker_addMonoidHom`, `MeasureTheory.lpMeasSubgroupToLpTrim_norm_map`, `SubAddAction.ofStabilizer.addConjMap_comp_apply`, `MeasureTheory.Lp.simpleFunc.toLp_sub`, `MeasureTheory.Lp.simpleFunc.coe_smul`, `AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `orbit_addSubgroup_zero_eq_self`, `MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq`, `SubAddAction.ofStabilizer.snoc_castSucc`, `MeasureTheory.Lp.instSMulCommClass`, `MeasureTheory.Lp.simpleFunc.toLp_neg`, `inclusion_inj`, `MeasureTheory.L1.SimpleFunc.integral_smul`, `DomAddAct.vadd_Lp_const`, `normal_addSubgroupOf`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le`, `IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_AddHaarMeasure`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure`, `comap_subtype`, `MeasureTheory.Lp.smul_comm`, `AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume`, `MeasureTheory.Lp.simpleFunc.isUniformEmbedding`, `map_addSubgroupOf_eq_of_le`, `QuotientAddGroup.orbit_eq_out_vadd`, `closure_closure_coe_preimage`, `IsSubnormal.addSubgroupOf`, `SubAddAction.ENat_card_ofStabilizer_add_zero_eq`, `MeasureTheory.Lp.simpleFunc.isUniformInducing`, `Function.Exact.addMonoidHom_rangeRestrict`, `MeasureTheory.Lp.constL_apply`, `SubAddAction.fixingAddSubgroup_of_insert`, `subtype_injective`, `MeasureTheory.Lp.simpleFunc.coe_indicatorConst`, `normal_addSubgroupOf_of_le_normalizer`, `AddAction.right_quotientAction`, `SubAddAction.of_fixingAddSubgroupEmpty_mapScalars_surjective`, `SubAddAction.ofStabilizer.neg_addConjMap_comp_apply`, `SubAddAction.mem_ofFixingAddSubgroup_iff`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `normal_addSubgroupOf_iff_le_normalizer`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `quotientiInfAddSubgroupOfEmbedding_apply`, `AddAction.IsBlock.orbit_stabilizer_eq`, `MeasureTheory.L1.SimpleFunc.norm_eq_integral`, `fixingAddSubgroup_fixedPoints_gc`, `MeasureTheory.L1.SimpleFunc.norm_integral_le_norm`, `SubAddAction.ofFixingAddSubgroup_carrier`, `MeasureTheory.Lp.simpleFunc.toLp_smul`, `IsTorsion.addSubgroup`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left'`, `addSubgroupOf_bot_eq_bot`, `quotientEquivProdOfLE'_apply`, `exponent_top`, `mem_addSubgroupOf`, `AddGroup.closure_finset_fg`, `AddCircle.isAddQuotientCoveringMap_zsmul`, `mk_vadd`, `AddGroup.fg_range`, `subtype_comp_inclusion`, `ContinuousLinearMap.add_compLpL`, `MeasureTheory.L1.setToL1_simpleFunc_indicatorConst`, `fixedPoints_addSubgroup_iSup`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left`, `AddMonoidHom.ker_rangeRestrict`, `instIsAddCommutativeQuotientSubtypeMemFocalAddSubgroupOf`, `AddAction.isMultiplyPreprimitive_iff`, `MeasureTheory.Lp.toLp_compMeasurePreserving`, `MeasureTheory.Lp.coeFn_abs`, `quotientEquivProdOfLE'_symm_apply`, `AddAction.IsBlock.addSubgroup`, `SubAddAction.ofFixingAddSubgroup.append_right`, `MeasureTheory.Lp.smul_assoc`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `addSubgroupOfContinuousAddEquivOfLe_symm_apply`, `AddAction.isPreprimitive_ofFixingAddSubgroup_addConj_iff`, `AddAction.ofFixingSubgroup.isMultiplyPreprimitive`, `quotientEquivProdOfLE_apply`, `SubAddAction.nat_card_ofStabilizer_add_zero_eq`, `MeasureTheory.Lp.compMeasurePreserving_continuous`, `AddAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup`, `MeasureTheory.L1.SimpleFunc.setToL1S_add`, `AddAction.orbit_addSubgroup_subset`, `IsSubnormal.iff_eq_top_or_exists`, `SubAddAction.ofStabilizer_carrier`, `SubAddAction.disjoint_val_image`, `lp.norm_const_smul_le`, `exists_leftTransversal_of_FiniteIndex`, `MeasureTheory.isometry_lpMeasSubgroupToLpTrim`, `properlyDiscontinuousVAdd_of_tendsto_cofinite`, `orbit_addSubgroup_eq_rightCoset`, `DomMulAct.smul_Lp_const`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left`, `inclusion_range`, `exponent_toAddSubmonoid`, `AddGroup.rank_range_le`, `MeasureTheory.lpMeasToLpTrim_smul`, `addSubgroupOfContinuousAddEquivOfLe_toAddEquiv`, `MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg`, `focalAddSubgroupOf.mk'_addConj_eq`, `inf_addSubgroupOf_inf_normal_of_right`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono`, `fixedPoints_addSubgroup_sup`, `inclusion_injective`, `comap_inclusion_addSubgroupOf`, `MeasureTheory.Lp.compMeasurePreserving_id`, `MeasureTheory.Lp.simpleFunc.isDenseInducing`, `addSubgroupOf_eq_bot`, `SubAddAction.ofStabilizer.isMultiplyPretransitive`, `instProperVAddSubtypeAddOppositeMemAddSubgroupOpOfIsTopologicalAddGroupOfIsClosedCoe`, `ContinuousLinearMap.norm_holderL_le`, `addOrderOf_mk`, `MeasureTheory.L1.setToL1'_eq_setToL1SCLM`, `rank_congr`, `MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpLpMeasSubgroupOfFactLeMeasurableSpace`, `quotientAddSubgroupOfEmbeddingOfLE_apply_mk`, `goursat`, `MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq`, `addSubgroupOf_isOpen`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg`, `MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral`, `MeasureTheory.Lp.simpleFunc.toLp_eq_mk`, `ContinuousLinearMap.holderL_apply_apply`, `subtype_apply`, `MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun`, `CategoryTheory.ShortComplex.abLeftHomologyData_H_coe`, `UnitAddTorus.span_mFourierLp_closure_eq_top`, `AddAction.stabilizer_orbit_eq`, `QuotientAddGroup.rangeKerLift_injective`, `SubAddAction.ofStabilizer.addConjMap_bijective`, `SubAddAction.exists_vadd_of_last_eq`, `Continuous.compMeasurePreservingLp`, `MeasureTheory.Lp.const_val`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff`, `MeasureTheory.Lp.simpleFunc.coeFn_nonneg`, `MeasureTheory.L1.setToL1'_apply_coeToLp`, `addSubgroupOf_sup`, `ContinuousOn.compMeasurePreservingLp`, `MeasureTheory.memLp_trim_of_mem_lpMeasSubgroup`, `iSupIndep_iff_dfinsuppSumAddHom_injective`, `AddAction.isPreprimitive_fixingAddSubgroup_insert_iff`, `instNormalSubtypeMemFocalAddSubgroupOf`, `MeasureTheory.MemLp.toLp_const_smul`, `AddAction.orbitRel_addSubgroupOf`, `AddAction.isMultiplyPreprimitive_ofStabilizer`, `MeasureTheory.Lp.simpleFunc.toLp_add`, `lp.instIsScalarTowerSubtypePreLpMemAddSubgroup`, `MeasureTheory.Lp.isometry_compMeasurePreserving`, `QuotientAddGroup.rangeKerLift_surjective`, `MeasureTheory.Lp.simpleFunc.dense`, `SubAddAction.mem_ofFixingAddSubgroup_insert_iff`, `MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc`, `MeasureTheory.Lp_toLp_restrict_smul`, `MeasureTheory.L1.SimpleFunc.coe_posPart`, `MeasureTheory.Lp.compMeasurePreserving_val`, `QuotientAddGroup.orbit_mk_eq_vadd`, `AddAction.isPreprimitive_of_fixingAddSubgroup_empty_iff`, `MeasureTheory.Lp.norm_compMeasurePreserving`, `IsAddQuotientCoveringMap.addSubgroup_congr`, `normal_addSubgroupOf_iff_le_normalizer_inf`, `AddAction.IsBlock.orbit_of_normal`, `normal_addSubgroupOf_sup_of_le_normalizer`, `coe_inclusion`, `normal_in_normalizer`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left'`, `MeasureTheory.Lp.simpleFunc.norm_toLp`, `AddAction.orbitRel.Quotient.addSubgroup_quotient_eq_iff`, `IsSubnormal.isSubnormal_iff`, `ker_inclusion`, `SubAddAction.not_mem_of_mem_ofFixingAddSubgroup`, `AddAction.IsBlockSystem.of_normal`, `MeasureTheory.MemLp.toLp_const`, `MeasureTheory.leftInvariantIsAddQuotientMeasureEqMeasurePreimage`, `IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul`, `SubAddAction.map_ofFixingAddSubgroupUnion_def`, `MeasureTheory.Lp.compMeasurePreserving_iterate`
`toAddSubmonoid` 📖	CompOp	50 math math: `map_toAddSubmonoid`, `ClosedAddSubgroup.ext_iff`, `bot_toAddSubmonoid`, `FixedPoints.addSubgroup_toAddSubmonoid`, `mem_iff_toAddUnits_mem_addUnits`, `AddMonoidHom.addSubgroupMap_apply_coe`, `fg_iff_addSubmonoid_fg`, `Submodule.toAddSubgroup_toAddSubmonoid`, `HahnSeries.cardSuppLTSubfield_carrier`, `op_toAddSubmonoid`, `AddMonoidHom.graph_toAddSubmonoid`, `op_toSubsemigroup`, `ClosedAddSubgroup.isClosed'`, `AddMonoidHom.addSubgroupComap_apply_coe`, `FiniteIndexNormalAddSubgroup.ext_iff`, `coe_toAddSubmonoid`, `closure_toAddSubmonoid`, `unop_toSubsemigroup`, `mem_toAddSubmonoid`, `toAddSubmonoid_strictMono`, `comap_toAddSubmonoid`, `pointwise_smul_toAddSubmonoid`, `center_toAddSubmonoid`, `mul_toAddSubmonoid`, `topologicalClosure_addSubgroupClosure_toAddSubmonoid`, `top_toAddSubmonoid`, `toAddSubmonoid_injective`, `closure_toAddSubmonoid_of_finite`, `saturated_iff_zsmul`, `AddSubmonoid.ker_saturated`, `mem_carrier`, `closure_toAddSubmonoid_of_isOfFinAddOrder`, `gc_toAddSubmonoid_support`, `OpenAddSubgroup.isOpen'`, `AddSubmonoid.multiples_le_zmultiples`, `AddSubmonoid.support_toAddSubmonoid`, `ker_saturated`, `toAddSubmonoid_zmultiples`, `le_closure_toAddSubmonoid`, `mem_addUnits_iff_val_mem`, `AddMonoidHom.ker_toAddSubmonoid`, `even_toAddSubmonoid`, `unop_toAddSubmonoid`, `toAddSubmonoid_inj`, `exponent_toAddSubmonoid`, `neg_mem'`, `toAddSubmonoid_le`, `OpenNormalAddSubgroup.ext_iff`, `toAddSubmonoid_mono`, `AddCommGroup.add_torsion_eq_add_torsion_submonoid`
`zero` 📖	CompOp	68 math math: `imaginaryPart_eq_zero_iff`, `MeasureTheory.Lp.eq_zero_iff_ae_eq_zero`, `lp.norm_eq_zero_iff`, `lp.eq_zero_iff_coeFn_eq_zero`, `MeasureTheory.Integrable.toL1_zero`, `noncommPiCoprod_single`, `AddCircle.isAddFundamentalDomain_of_ae_ball`, `MeasureTheory.condExpL1_measure_zero`, `coe_zero`, `MeasureTheory.Lp.nnnorm_eq_zero_iff`, `MeasureTheory.Integrable.edist_toL1_zero`, `MeasureTheory.condExpInd_nonneg`, `MeasureTheory.Lp.norm_zero`, `MeasureTheory.Lp.edist_toLp_zero`, `selfAdjoint.imaginaryPart_coe`, `MeasureTheory.condExpIndSMul_empty`, `ProfiniteAddGrp.limit_zero_val`, `lp.coeFn_zero`, `AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples`, `isAddFundamentalDomain_Ioc`, `selfAdjoint.expUnitary_zero`, `StrongDual.toLp_of_not_memLp`, `IsSelfAdjoint.skewAdjointPart_apply`, `lp.single_zero`, `MeasureTheory.condExpL1_undef`, `MeasureTheory.Lp.smul_zero`, `ZSpan.isAddFundamentalDomain'`, `imaginaryPart_realPart`, `Unitary.openPartialHomeomorph_target`, `MeasureTheory.Lp.simpleFunc.toLp_zero`, `MeasureTheory.Lp.coeFn_nonneg`, `MeasureTheory.Lp.simpleFunc.coeFn_zero`, `lp.norm_zero`, `StrongDual.toLpₗ_of_not_memLp`, `MeasureTheory.Lp.instIsBoundedSMul`, `span_fourierLp_closure_eq_top`, `MeasureTheory.Lp.simpleFunc.isBoundedSMul`, `MeasureTheory.Lp.zero_smul`, `DomMulAct.smul_Lp_zero`, `imaginaryPart_ofReal`, `MeasureTheory.L1.integral_zero`, `MeasureTheory.condExpIndL1_of_not_measurableSet`, `Function.Exact.addMonoidHom_rangeRestrict`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `mk_eq_zero`, `MeasureTheory.condExpIndL1_of_measure_eq_top`, `lp.eq_zero'`, `MeasureTheory.Lp.coeFn_zero`, `imaginaryPart_imaginaryPart`, `MeasureTheory.Lp.norm_eq_zero_iff`, `val_list_sum`, `LipschitzWith.compLp_zero`, `MeasureTheory.condExpL1_zero`, `ContinuousLinearMap.smul_compLpL`, `MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg`, `lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup`, `ContinuousLinearMap.norm_holderL_le`, `ContinuousLinearMap.holderL_apply_apply`, `DomAddAct.vadd_Lp_zero`, `MeasureTheory.MemLp.toLp_zero`, `torsionBy.nsmul`, `UnitAddTorus.span_mFourierLp_closure_eq_top`, `IsSelfAdjoint.imaginaryPart`, `MeasureTheory.Lp.simpleFunc.coeFn_nonneg`, `isAddFundamentalDomain_Ioc'`, `MeasureTheory.indicatorConstLp_empty`, `MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc`, `MeasureTheory.Lp.nnnorm_zero`
`zsmul` 📖	CompOp	9 math math: `AddAction.orbitZMultiplesEquiv_symm_apply'`, `AddAction.orbitZMultiplesEquiv_symm_apply`, `discrete_iff_addCyclic`, `coe_zsmul`, `isAddCyclic_iff_exists_zmultiples_eq_top`, `isAddCyclic`, `isAddCyclic_of_le`, `isAddCyclic_zmultiples`, `Bot.isAddCyclic`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`addCommGroup_isAddCommutative` 📖	mathematical	—	`IsAddCommutative` `AddSubgroup` `AddCommGroup.toAddGroup` `SetLike.instMembership` `instSetLike` `add`	—	`AddCommMagma.to_isCommutative` `AddSubmonoidClass.toAddMemClass` `AddSubgroupClass.toAddSubmonoidClass` `instAddSubgroupClass`
`add_comm_of_mem_isAddCommutative` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`setLike_add_comm` `AddSubmonoidClass.toAddMemClass` `AddSubgroupClass.toAddSubmonoidClass` `instAddSubgroupClass`
`add_mem` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`AddMemClass.add_mem` `AddSubmonoidClass.toAddMemClass` `AddSubgroupClass.toAddSubmonoidClass` `instAddSubgroupClass`
`add_mem_cancel_left` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`add_mem_cancel_left` `instAddSubgroupClass`
`add_mem_cancel_right` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`add_mem_cancel_right` `instAddSubgroupClass`
`coe_add` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `add` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	—
`coe_copy` 📖	mathematical	`SetLike.coe` `AddSubgroup` `instSetLike`	`SetLike.coe` `AddSubgroup` `instSetLike` `copy`	—	—
`coe_inclusion` 📖	mathematical	`AddSubgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `DFunLike.coe` `AddMonoidHom` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion`	—	`Set.coe_inclusion`
`coe_mk` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike`	—	—
`coe_neg` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `neg` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—
`coe_nonempty` 📖	mathematical	—	`Set.Nonempty` `SetLike.coe` `AddSubgroup` `instSetLike`	—	`ZeroMemClass.zero_mem` `AddSubmonoidClass.toZeroMemClass` `AddSubgroupClass.toAddSubmonoidClass` `instAddSubgroupClass`
`coe_nsmul` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `nsmul` `AddMonoid.toNSMul` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	—
`coe_ofClass` 📖	mathematical	—	`SetLike.coe` `AddSubgroup` `instSetLike` `ofClass`	—	—
`coe_set_mk` 📖	mathematical	`Set` `Set.instMembership` `AddSubsemigroup.carrier` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.toAddSubsemigroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	`SetLike.coe` `AddSubgroup` `instSetLike` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.instSetLike`	—	—
`coe_sub` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `sub` `SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	—
`coe_subtype` 📖	mathematical	—	`DFunLike.coe` `AddMonoidHom` `AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `subtype`	—	—
`coe_toAddSubmonoid` 📖	mathematical	—	`SetLike.coe` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.instSetLike` `toAddSubmonoid` `AddSubgroup` `instSetLike`	—	—
`coe_zero` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `zero` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—
`coe_zsmul` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `zsmul` `SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid`	—	—
`copy_eq` 📖	mathematical	`SetLike.coe` `AddSubgroup` `instSetLike`	`copy`	—	`SetLike.coe_injective`
`exists_neg_mem_iff_exists_mem` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`exists_neg_mem_iff_exists_mem` `instAddSubgroupClass`
`ext` 📖	—	`AddSubgroup` `SetLike.instMembership` `instSetLike`	—	—	`SetLike.ext`
`ext_iff` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike`	—	`ext`
`inclusion_inj` 📖	mathematical	`AddSubgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`DFunLike.coe` `AddMonoidHom` `AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion`	—	`inclusion_injective`
`inclusion_injective` 📖	mathematical	`AddSubgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `DFunLike.coe` `AddMonoidHom` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion`	—	`Set.inclusion_injective`
`instAddSubgroupClass` 📖	mathematical	—	`AddSubgroupClass` `AddSubgroup` `AddGroup.toSubNegMonoid` `instSetLike`	—	`AddSubsemigroup.add_mem'` `AddSubmonoid.zero_mem'` `neg_mem'`
`instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallNeg` 📖	mathematical	—	`CanLift` `Set` `AddSubgroup` `SetLike.coe` `instSetLike` `Set.instMembership` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—
`le_normalizer` 📖	mathematical	—	`AddSubgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder` `normalizer` `SetLike.coe` `instSetLike`	—	`SetLike.mem_coe` `add_mem_cancel_right` `neg_mem` `add_mem_cancel_left`
`mem_carrier` 📖	mathematical	—	`Set` `Set.instMembership` `AddSubsemigroup.carrier` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.toAddSubsemigroup` `toAddSubmonoid` `AddSubgroup` `SetLike.instMembership` `instSetLike`	—	—
`mem_mk` 📖	mathematical	`Set` `Set.instMembership` `AddSubsemigroup.carrier` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.toAddSubsemigroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.instSetLike`	—	—
`mem_normalizer_iff` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `normalizer` `SetLike.coe` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—
`mem_normalizer_iff'` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `normalizer` `SetLike.coe` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`SetLike.mem_coe` `add_assoc` `add_neg_cancel_right` `neg_add_cancel_right`
`mem_normalizer_iff''` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `normalizer` `SetLike.coe` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_mem_iff` `AddSubgroupClass.toNegMemClass` `instAddSubgroupClass` `mem_normalizer_iff` `neg_neg`
`mem_toAddSubmonoid` 📖	mathematical	—	`AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `SetLike.instMembership` `AddSubmonoid.instSetLike` `toAddSubmonoid` `AddSubgroup` `instSetLike`	—	—
`mk_eq_zero` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `zero` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`AddSubmonoid.mk_eq_zero`
`mk_le_mk` 📖	mathematical	`Set` `Set.instMembership` `AddSubsemigroup.carrier` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.toAddSubsemigroup` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	`AddSubgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.instPartialOrder`	—	—
`neg_mem` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`NegMemClass.neg_mem` `AddSubgroupClass.toNegMemClass` `instAddSubgroupClass`
`neg_mem'` 📖	mathematical	`Set` `Set.instMembership` `AddSubsemigroup.carrier` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.toAddSubsemigroup` `toAddSubmonoid`	`Set` `Set.instMembership` `AddSubsemigroup.carrier` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddSubmonoid.toAddSubsemigroup` `toAddSubmonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—
`neg_mem_iff` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_mem_iff` `AddSubgroupClass.toNegMemClass` `instAddSubgroupClass`
`normal_of_comm` 📖	mathematical	—	`Normal` `AddCommGroup.toAddGroup`	—	`add_comm` `add_neg_cancel_right` `Zero.instNonempty`
`nsmul_mem` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `AddMonoid.toNSMul` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`nsmul_mem` `AddSubgroupClass.toAddSubmonoidClass` `instAddSubgroupClass`
`sub_mem` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `SubNegMonoid.toSub` `AddGroup.toSubNegMonoid`	—	`sub_mem` `instAddSubgroupClass`
`subtype_apply` 📖	mathematical	—	`DFunLike.coe` `AddMonoidHom` `AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `subtype`	—	—
`subtype_comp_inclusion` 📖	mathematical	`AddSubgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`AddMonoidHom.comp` `AddSubgroup` `SetLike.instMembership` `instSetLike` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `subtype` `inclusion`	—	—
`subtype_injective` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `DFunLike.coe` `AddMonoidHom` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `subtype`	—	`Subtype.coe_injective`
`toAddSubmonoid_inj` 📖	mathematical	—	`toAddSubmonoid`	—	`toAddSubmonoid_injective`
`toAddSubmonoid_injective` 📖	mathematical	—	`AddSubgroup` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddSubmonoid`	—	`SetLike.ext'_iff` `coe_toAddSubmonoid`
`toAddSubmonoid_le` 📖	mathematical	—	`AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `Preorder.toLE` `PartialOrder.toPreorder` `AddSubmonoid.instPartialOrder` `toAddSubmonoid` `AddSubgroup` `instPartialOrder`	—	—
`toAddSubmonoid_mono` 📖	mathematical	—	`Monotone` `AddSubgroup` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `PartialOrder.toPreorder` `instPartialOrder` `AddSubmonoid.instPartialOrder` `toAddSubmonoid`	—	`StrictMono.monotone` `toAddSubmonoid_strictMono`
`toAddSubmonoid_strictMono` 📖	mathematical	—	`StrictMono` `AddSubgroup` `AddSubmonoid` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `PartialOrder.toPreorder` `instPartialOrder` `AddSubmonoid.instPartialOrder` `toAddSubmonoid`	—	—
`zero_mem` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `instSetLike` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`ZeroMemClass.zero_mem` `AddSubmonoidClass.toZeroMemClass` `AddSubgroupClass.toAddSubmonoidClass` `instAddSubgroupClass`
`zsmul_mem` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `instSetLike`	`AddSubgroup` `SetLike.instMembership` `instSetLike` `SubNegMonoid.toZSMul` `AddGroup.toSubNegMonoid`	—	`zsmul_mem` `instAddSubgroupClass`

AddSubgroup.Normal

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`addConj_mem'` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike`	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`neg_neg` `conj_mem`
`conj_mem` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike`	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike` `AddSemigroup.toAdd` `AddMonoid.toAddSemigroup` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	—
`mem_comm` 📖	mathematical	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`conj_mem` `neg_add_cancel_left` `neg_neg`
`mem_comm_iff` 📖	mathematical	—	`AddSubgroup` `SetLike.instMembership` `AddSubgroup.instSetLike` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`mem_comm`

AddSubgroupClass

Definitions

Name	Category	Theorems
`inclusion` 📖	CompOp	5 math math: `inclusion_self`, `inclusion_mk`, `coe_inclusion`, `subtype_comp_inclusion`, `inclusion_right`
`instZSMul` 📖	CompOp	2 math math: `coe_zsmul`, `ZLattice.sum_piFinset_Icc_rpow_le`
`sub` 📖	CompOp	12 math math: `coe_sub`, `LieSubmodule.coe_sub`, `Subalgebra.coe_sub`, `NumberField.RingOfIntegers.mk_sub_mk`, `NonUnitalSubalgebra.coe_sub`, `Submodule.coe_sub`, `LinearPMap.map_sub`, `LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplitting`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle`, `NonUnitalStarSubalgebra.coe_sub`, `Subfield.coe_sub`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle'`
`subtype` 📖	CompOp	4 math math: `subtype_apply`, `subtype_comp_inclusion`, `subtype_injective`, `coe_subtype`
`toAddCommGroup` 📖	CompOp	88 math math: `DirectSum.decompose_sub`, `LieSubmodule.coe_smul`, `LieModule.shiftedGenWeightSpace.shift_apply`, `TensorProduct.LieModule.mapIncl_def`, `LieModule.traceForm_eq_sum_genWeightSpaceOf`, `LieModule.traceForm_eq_sum_finrank_nsmul'`, `LieModule.shiftedGenWeightSpace.instSubtypeMemLieSubmodule`, `LieModule.isNilpotent_toEnd_genWeightSpace_zero`, `LieSubmodule.isNilpotent_iff_exists_lcs_eq_bot`, `LieModule.trace_toEnd_genWeightSpace`, `LieModule.trivial_iff_le_maximal_trivial`, `LieModule.shiftedGenWeightSpace.toEnd_eq`, `LieModule.instIsTrivialSubtypeMemLieSubmoduleMaxTrivSubmodule`, `LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom`, `LieModule.instIsTriangularizableSubtypeMemLieSubmodule_1`, `LieSubmodule.traceForm_eq_of_le_idealizer`, `DirectSum.decompose_symm_sub`, `LieSubmodule.incl_apply`, `LieAlgebra.Extension.toKer_bracket`, `LieSubmodule.lowerCentralSeries_eq_bot_iff_lcs_eq_bot`, `LieSubmodule.lowerCentralSeries_map_eq_lcs`, `LieSubmodule.map_incl_top`, `LieSubmodule.subsingleton_of_bot`, `LieSubmodule.isNilpotent_iff_exists_self_le_ucs`, `LieSubmodule.comap_incl_eq_top`, `LieAlgebra.coe_rootSpaceWeightSpaceProduct_tmul`, `LieSubmodule.comap_incl_eq_bot`, `LieSubmodule.ucs_comap_incl`, `DirectSum.decompose_symm_neg`, `LieSubmodule.instIsTorsionFreeSubtypeMem`, `LieSubmodule.range_incl`, `LieSubmodule.map_incl_lt_iff_lt_top`, `LieSubmodule.trace_eq_trace_restrict_of_le_idealizer`, `LieAlgebra.Extension.ringModuleOf_bracket`, `LieSubmodule.ker_incl`, `LieSubmodule.instIsArtinianSubtypeMem`, `LieSubmodule.toEnd_restrict_eq_toEnd`, `LieSubmodule.map_restrictLie_incl_top`, `LieModuleHom.codRestrict_apply`, `LieModule.toLinearMap_maxTrivLinearMapEquivLieModuleHom_symm`, `LieModule.trace_comp_toEnd_genWeightSpace_eq`, `LieModule.instMaxNilpotentSubmoduleIsNilpotent`, `LieSubmodule.coe_inclusion`, `LieModuleHom.comp_ker_incl`, `LieSubmodule.map_incl_le`, `LieModule.maxTrivEquiv_of_equiv_symm_eq_symm`, `LieModule.shiftedGenWeightSpace.coe_lie_shiftedGenWeightSpace_apply`, `LieSubmodule.lowerCentralSeries_eq_lcs_comap`, `LieModule.traceForm_eq_sum_finrank_nsmul`, `LieModule.shiftedGenWeightSpace.instIsNilpotentSubtypeMemLieSubmoduleOfIsNoetherian`, `LieModule.isNilpotent_of_top_iff'`, `LieSubmodule.coe_toEnd`, `LieSubmodule.coe_bracket`, `LieModuleEquiv.ofTop_apply`, `LieModule.isNilpotent_toEnd_sub_algebraMap`, `LieSubmodule.incl_eq_val`, `LieModule.maxTrivEquiv_of_refl_eq_refl`, `LieSubmodule.inclusion_apply`, `LieModule.isNilpotent_iff_le_maxNilpotentSubmodule`, `LieModule.traceForm_genWeightSpace_eq`, `LieModule.instIsNilpotentSup`, `LieAlgebra.IsKilling.finrank_rootSpace_eq_one`, `LieModule.instIsNilpotentSubtypeMemLieSubmoduleGenWeightSpaceOfNatForallOfIsNoetherian`, `LieModule.trace_toEnd_genWeightSpaceChain_eq_zero`, `LieModule.zero_lt_finrank_genWeightSpace`, `LieSubmodule.lieIdeal_oper_eq_tensor_map_range`, `LieModule.coe_maxTrivLinearMapEquivLieModuleHom_symm`, `LieAlgebra.Extension.lie_apply_proj_of_leftInverse_eq`, `LieAlgebra.Extension.ringModuleOf_bracket_proj`, `LieSubmodule.coe_toEnd_pow`, `LieModule.traceForm_eq_sum_finrank_nsmul_mul`, `LieModule.coe_maxTrivEquiv_apply`, `instIsLieTowerSubtypeMemLieSubmodule_1`, `LieSubmodule.instIsNoetherianSubtypeMem`, `LieSubmodule.inclusion_injective`, `LieSubmodule.incl_coe`, `LieModule.coe_maxTrivHom_apply`, `LieSubmodule.instLieModule`, `LieSubmodule.injective_incl`, `LieSubmodule.map_comap_incl`, `DirectSum.decompose_neg`, `LieModule.shiftedGenWeightSpace.shift_symm_apply`, `LieModule.isNilpotent_of_le`, `LieSubmodule.comap_incl_self`, `LieAlgebra.rootSpaceProduct_tmul`, `LieModule.posFittingComp_map_incl_sup_of_codisjoint`, `LieModule.coe_maxTrivLinearMapEquivLieModuleHom`, `LieModule.genWeightSpace_genWeightSpaceOf_map_incl`
`toAddGroup` 📖	CompOp	9 math math: `inclusion_self`, `subtype_apply`, `inclusion_mk`, `coe_inclusion`, `subtype_comp_inclusion`, `subtype_injective`, `inclusion_right`, `AddSubgroup.instFiniteQuotientSubtypeMemOpenAddSubgroupOfIsTopologicalAddGroupOfCompactSpace`, `coe_subtype`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`coe_inclusion` 📖	mathematical	—	`SetLike.instMembership` `DFunLike.coe` `AddMonoidHom` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion`	—	`Set.coe_inclusion` `SetLike.coe_subset_coe`
`coe_nsmul` 📖	mathematical	—	`SetLike.instMembership` `AddSubmonoidClass.instNSMul` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddSubmonoidClass` `AddMonoid.toNSMul`	—	`toAddSubmonoidClass`
`coe_sub` 📖	mathematical	—	`SetLike.instMembership` `sub` `AddGroup.toSubNegMonoid` `SubNegMonoid.toSub`	—	—
`coe_subtype` 📖	mathematical	—	`DFunLike.coe` `AddMonoidHom` `SetLike.instMembership` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `subtype`	—	—
`coe_zsmul` 📖	mathematical	—	`SetLike.instMembership` `instZSMul` `AddGroup.toSubNegMonoid` `SubNegMonoid.toZSMul`	—	—
`inclusion_mk` 📖	mathematical	`SetLike.instMembership`	`DFunLike.coe` `AddMonoidHom` `SetLike.instMembership` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion` `mem_of_le_of_mem`	—	—
`inclusion_right` 📖	mathematical	`SetLike.instMembership`	`DFunLike.coe` `AddMonoidHom` `SetLike.instMembership` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion`	—	—
`inclusion_self` 📖	mathematical	—	`DFunLike.coe` `AddMonoidHom` `SetLike.instMembership` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `inclusion` `Preorder.toLE` `le_rfl`	—	`le_rfl`
`subset_union` 📖	mathematical	—	`Set` `Set.instHasSubset` `SetLike.coe` `Set.instUnion`	—	`SetLike.not_le_iff_exists` `SetLike.coe_subset_coe` `AddMemClass.add_mem` `AddSubmonoidClass.toAddMemClass` `toAddSubmonoidClass` `add_mem_cancel_right` `add_mem_cancel_left` `mem_of_le_of_mem`
`subtype_apply` 📖	mathematical	—	`DFunLike.coe` `AddMonoidHom` `SetLike.instMembership` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `subtype`	—	—
`subtype_comp_inclusion` 📖	mathematical	—	`AddMonoidHom.comp` `SetLike.instMembership` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `subtype` `inclusion`	—	—
`subtype_injective` 📖	mathematical	—	`SetLike.instMembership` `DFunLike.coe` `AddMonoidHom` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `toAddGroup` `AddMonoidHom.instFunLike` `subtype`	—	`Subtype.coe_injective`
`toAddSubmonoidClass` 📖	mathematical	—	`AddSubmonoidClass` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid`	—	—
`toNegMemClass` 📖	mathematical	—	`NegMemClass` `SubNegMonoid.toNeg`	—	—

HasMemOrInvMem

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`inv_mem_of_notMem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership`	—	`mem_or_inv_mem`
`mem_of_inv_notMem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership`	—	`mem_or_inv_mem`
`mem_or_inv_mem` 📖	mathematical	—	`SetLike.instMembership`	—	—

HasMemOrNegMem

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`mem_of_neg_notMem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership`	—	`mem_or_neg_mem`
`mem_or_neg_mem` 📖	mathematical	—	`SetLike.instMembership`	—	—
`neg_mem_of_notMem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership`	—	`mem_or_neg_mem`

InvMemClass

Definitions

Name	Category	Theorems
`inv` 📖	CompOp	2 math math: `coe_inv`, `IntermediateField.coe_inv`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`coe_inv` 📖	mathematical	—	`SetLike.instMembership` `inv` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid` `SubgroupClass.toInvMemClass` `Group.toDivInvMonoid`	—	`SubgroupClass.toInvMemClass`
`inv_mem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership`	—	—

NegMemClass

Definitions

Name	Category	Theorems
`neg` 📖	CompOp	17 math math: `LieAlgebra.Basis.symm_h'`, `NonUnitalStarSubalgebra.coe_neg`, `IntermediateField.coe_neg`, `RootPairing.corootSpanMem_reflectionPerm_self`, `NonUnitalSubring.val_neg`, `CliffordAlgebra.evenToNeg_ι`, `LinearPMap.map_neg`, `Subalgebra.coe_neg`, `LieSubmodule.coe_neg`, `LieAlgebra.IsKilling.coroot_neg`, `RootPairing.rootSpanMem_reflectionPerm_self`, `Subring.coe_neg`, `Submodule.coe_neg`, `NonUnitalSubalgebra.coe_neg`, `ZSpan.vadd_mem_fundamentalDomain`, `Subfield.coe_neg`, `coe_neg`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`coe_neg` 📖	mathematical	—	`SetLike.instMembership` `neg` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid` `AddSubgroupClass.toNegMemClass` `AddGroup.toSubNegMonoid`	—	`AddSubgroupClass.toNegMemClass`
`neg_mem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership`	—	—

Set

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`injOn_iff_map_eq_one` 📖	mathematical	—	`InjOn` `DFunLike.coe` `SetLike.coe` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`OneMemClass.one_mem` `map_one` `MonoidHomClass.toOneHomClass` `mul_inv_eq_one` `MulMemClass.mul_mem` `InvMemClass.inv_mem` `map_mul` `MonoidHomClass.toMulHomClass` `map_inv` `mul_inv_cancel`
`injOn_iff_map_eq_zero` 📖	mathematical	—	`InjOn` `DFunLike.coe` `SetLike.coe` `NegZeroClass.toZero` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`ZeroMemClass.zero_mem` `map_zero` `AddMonoidHomClass.toZeroHomClass` `add_neg_eq_zero` `AddMemClass.add_mem` `SetLike.mem_coe` `NegMemClass.neg_mem` `map_add` `AddMonoidHomClass.toAddHomClass` `map_neg` `add_neg_cancel`

Subgroup

Definitions

Name	Category	Theorems
`Normal` 📖	CompData	90 math math: `InfiniteGalois.normal_iff_isGalois`, `instNormalSubtypeMemFocalSubgroupOf`, `GroupExtension.normal_inl_range`, `prod_subgroupOf_prod_normal`, `normal_goursatSnd`, `Normal.of_map_injective`, `normal_subgroupOf_iff`, `normalCore_eq_iSup`, `InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois`, `OpenNormalSubgroup.instNormal`, `Sylow.normal_of_normalizerCondition`, `IsSubnormal.iff_eq_top_or_exists`, `CongruenceSubgroup.Gamma_normal`, `normal_of_index_eq_minFac_card`, `normal_comap`, `normal_subgroupOf_sup_of_le_normalizer`, `Sylow.normal_of_all_max_subgroups_normal`, `normal_bot`, `normal_goursatFst`, `IsSubnormal.exists_normal_and_le_and_lt_top_of_ne`, `OpenNormalSubgroup.isNormal'`, `Sylow.normal_of_subsingleton`, `instNormalCommutatorClosure`, `Normal.of_commutator_le`, `Field.absoluteGaloisGroup.commutator_closure_isNormal`, `Normal.of_unop`, `normal_subgroupOf_iff_le_normalizer_inf`, `normal_op`, `normal_top`, `normal_of_index_eq_one`, `normal_of_characteristic`, `instNormalCenter`, `NormalizerCondition.normal_of_coatom`, `inf_subgroupOf_inf_normal_of_left`, `FiniteIndexNormalSubgroup.instNormal`, `PrincipalIdeals.normal`, `normal_inf_normal`, `normal_iInf_normal`, `orderIsoCon_apply`, `normal_iff_eq_cosets`, `Normal.op`, `normalClosure_eq_iInf`, `QuotientGroup.instNormalSubgroup`, `ConjAct.normal_of_characteristic_of_normal`, `normal_of_index_eq_two`, `normal_subgroupOf`, `commutator_top_right_le_iff`, `normal_subgroupOf_iff_le_normalizer`, `QuotientGroup.map_normal`, `Normal.map`, `Normal.subgroupOf`, `commutator_top_left_le_iff`, `normalizer_eq_top_iff`, `alternatingGroup.normal`, `alternatingGroup.normal_kleinFour`, `normalClosure_normal`, `CategoryTheory.Subgroupoid.IsNormal.vertexSubgroup`, `Normal.of_map_subtype`, `unop.instNormal`, `sup_normal`, `MonoidHom.normal_ker`, `CategoryTheory.PreGaloisCategory.stabilizer_normal_of_isGalois`, `Normal.pathComponentOne`, `Normal.of_op`, `normal_subgroupOf_of_le_normalizer`, `orderIsoCon_symm_apply_coe`, `Sylow.normal_of_normalizer_normal`, `derivedSeries_normal`, `normal_of_eq_cosets`, `IsGalois.fixingSubgroup_normal_of_isGalois`, `FiniteIndexNormalSubgroup.isNormal'`, `normal_in_normalizer`, `normalCore_normal`, `op.instNormal`, `Normal.unop`, `normal_of_comm`, `IsSubnormal.lt_normal`, `is_normal_topologicalClosure`, `Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia`, `Normal.comap`, `IsSubnormal.normal_of_isSimpleGroup`, `normal_unop`, `IsSubnormal.isSubnormal_iff`, `goursat`, `normal_centralizer`, `prod_normal`, `commutator_normal`, `Normal.of_conjugate_fixed`, `IsSubnormal.exists_chain`, `inf_subgroupOf_inf_normal_of_right`
`copy` 📖	CompOp	2 math math: `coe_copy`, `copy_eq`
`div` 📖	CompOp	5 math math: `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `Valuation.exists_div_eq_of_unit`, `coe_div`, `Valuation.restrict_exists_div_eq`
`inclusion` 📖	CompOp	13 math math: `subtype_comp_inclusion`, `coe_inclusion`, `SubMulAction.ofFixingSubgroup_of_inclusion_injective`, `quotientSubgroupOfEmbeddingOfLE_apply_mk`, `ker_inclusion`, `QuotientGroup.quotientMapSubgroupOfOfLe_mk`, `inclusion_inj`, `comap_inclusion_subgroupOf`, `inclusion_range`, `SemidirectProduct.mulEquivSubgroup_apply`, `SemidirectProduct.mulEquivSubgroup_symm_apply`, `inclusion_injective`, `SemidirectProduct.monoidHomSubgroup_apply`
`instPartialOrder` 📖	CompOp	306 math math: `fixingSubgroup_antitone`, `MulAction.IwasawaStructure.commutator_le`, `pointwise_smul_le_pointwise_smul_iff`, `gc_map_comap`, `MonoidHom.ker_transferSylow_disjoint`, `toSubmonoid_le`, `MapSubtype.orderIso_apply_coe`, `MulArchimedeanClass.subgroup_strictAntiOn`, `IsSolvable.commutator_lt_of_ne_bot`, `pointwise_smul_subset_iff`, `IsPGroup.sylow_mem_fixedPoints_iff`, `subset_pointwise_smul_iff`, `le_normalClosure`, `AddSubgroup.mem_toSubgroup'`, `op_le_op_iff`, `normalCore_eq_iSup`, `CongruenceSubgroup.exists_Gamma_le_conj'`, `Equiv.Perm.disjoint_of_disjoint_support`, `ofUnits_le_iff_le_units`, `isCoatom_map`, `map_le_range`, `lowerCentralSeries_antitone`, `upperCentralSeries_mono`, `frattini_le_comap_frattini_of_surjective`, `MulEquiv.comapSubgroup_symm_apply`, `pi_le_iff`, `derivedSeries_le_map_derivedSeries`, `subgroupOf_eq_top`, `frattini_le_coatom`, `MonoidHom.coe_toMultiplicative_range`, `le_centralizer_iff`, `ofUnits_strictMono`, `commutator_mono`, `IsSubnormal.iff_eq_top_or_exists`, `toSubmonoid_mono`, `OpenSubgroup.toSubgroup_le`, `descending_central_series_ge_lower`, `MulAction.le_stabilizer_iff_smul_le`, `commutator_le_right`, `le_normalizer_comap`, `MulAction.stabilizer_inf_stabilizer_le_stabilizer_sdiff`, `Equiv.Perm.disjoint_closure_of_disjoint_support`, `instCovariantClassHSMulLe`, `Equiv.Perm.alternatingGroup_le_of_index_le_two`, `Normal.quotient_commutative_iff_commutator_le`, `MulEquiv.mapSubgroup_apply`, `disjoint_rootsOfUnity_of_coprime`, `QuotientGroup.con_le_iff`, `normalizer_le_normalizer_sup_normal`, `pointwise_smul_le_pointwise_smul_iff₀`, `map_inf_le`, `alternatingGroup.isCoatom_stabilizer_singleton`, `MulAction.IsBlock.stabilizer_le`, `ofUnits_le_ofUnits_iff`, `map_le_map_iff_of_injective`, `MonoidHom.closure_preimage_le`, `MulAction.le_stabilizer_smul_left`, `IsSolvable.commutator_lt_top_of_nontrivial`, `upperCentralSeries.StrictMonoOn`, `upperCentralSeries.map`, `isCoatom_comap_of_surjective`, `IsComplement'.isCompl`, `derivedSeries_antitone`, `IsSubnormal.exists_normal_and_le_and_lt_top_of_ne`, `NumberField.Units.span_basisOfIsMaxRank`, `closure_le`, `IsGalois.intermediateFieldEquivSubgroup_apply`, `ProfiniteGrp.closedSubgroup_eq_sInf_open`, `normalClosure_subset_iff`, `normalizer_le_normalizer_sup_of_normalizer_le_right`, `fg_iff_add_fg`, `le_topologicalClosure`, `map_derivedSeries_le_derivedSeries`, `IsDedekindDomain.selmerGroup.monotone`, `le_centralizer`, `toSubmonoid_strictMono`, `zpowers_le`, `characteristic_iff_comap_le`, `normal_subgroupOf_iff_le_normalizer_inf`, `characteristic_iff_map_le`, `ValuationSubring.principalUnitGroup_le_principalUnitGroup`, `comap_lt_comap_of_surjective`, `IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup`, `IsGaloisGroup.fixingSubgroup_le_of_le`, `commutator_le`, `IntermediateField.fixedField_antitone`, `MulAction.isCoatom_stabilizer_iff_preprimitive`, `CommGroup.mem_subgroupOrderIsoSubgroupMonoidHom_iff`, `AddSubgroup.toSubgroup_closure`, `sylow_mem_fixedPoints_iff`, `CommGroup.mem_subgroupOrderIsoSubgroupMonoidHom_symm_iff`, `le_pi_iff`, `NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion`, `IsSimpleGroup.instIsSimpleOrderSubgroup`, `MulEquiv.coe_comapSubgroup`, `mem_toAddSubgroup'`, `Ideal.inertia_le_stabilizer`, `subgroupOf_eq_bot`, `MulAction.IsPreprimitive.isCoatom_stabilizer_of_isPreprimitive`, `MonoidHom.coe_toAdditive_map`, `map_lt_map_iff_of_injective`, `PresentedGroup.closure_rels_subset_ker`, `normal_le_normalCore`, `Sylow.exists_subgroup_card_pow_prime_le`, `map_subtype_le_map_subtype`, `mk_le_mk`, `coe_toAddSubgroup_symm_apply`, `prod_mono`, `codisjoint_map`, `center_le_normalizer`, `MulEquiv.coe_mapSubgroup`, `Sylow.normalizer_le_centralizer_or_le_commutator`, `commutator_pi_pi_le`, `le_normalizer`, `disjoint_def'`, `orderIsoCon_apply`, `IntermediateField.fixingSubgroup_le`, `map_eq_bot_iff`, `IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply`, `characteristic_iff_le_comap`, `iSup_comap_le`, `Sylow.le_center_or_le_commutator`, `IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual`, `closure_mono`, `commutator_le_self`, `MulArchimedeanClass.ballSubgroup_antitone`, `commutator_eq_bot_iff_le_centralizer`, `disjoint_def`, `map_centralizer_le_centralizer_image`, `MulChar.mem_subgroupOrderIsoSubgroupMulChar_symm_iff`, `MulEquiv.mapSubgroup_symm_apply`, `IntermediateField.fixingSubgroup_antitone`, `comap_sup_comap_le`, `IsPGroup.bot_lt_center`, `ValuationSubring.unitGroup_strictMono`, `normalClosure_mono`, `subgroupOf_mono`, `ofUnits_units_gc`, `Equiv.Perm.centralizer_le_alternating_iff`, `le_prod_iff`, `IsPGroup.exists_le_sylow`, `map_subtype_lt_map_subtype`, `normalCore_mono`, `map_le_map_iff`, `MulChar.mem_subgroupOrderIsoSubgroupMulChar_iff`, `closure_le_centralizer_centralizer`, `Sylow.exists_subgroup_le_card_pow_prime_of_le_card`, `MulAction.stabilizer_le_aestabilizer`, `conj_smul_le_of_le`, `Multiplicative.mem_toSubgroup`, `IsPGroup.disjoint_of_ne`, `lowerCentralSeries_pi_le`, `lowerCentralSeries.map`, `ofUnits_mono`, `IsCyclotomicExtension.Rat.galEquivZMod_stabilizer`, `ker_le_comap`, `toAddSubgroup_closure`, `QuotientGroup.strictMono_comap_prod_image`, `map_le_map_iff'`, `MulEquiv.comapSubgroup_apply`, `le_normalizer_of_normal_subgroupOf`, `coe_toAddSubgroup_apply`, `ValuationSubring.unitGroup_le_unitGroup`, `commutator_le_inf`, `ValuationSubring.principal_units_le_units`, `disjoint_map`, `commutator_top_right_le_iff`, `comap_le_comap_of_surjective`, `Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_mem`, `IsGalois.intermediateFieldEquivSubgroup_symm_apply`, `MulAction.map_stabilizer_le`, `commutator_le_focalSubgroup`, `normal_subgroupOf_iff_le_normalizer`, `normalizer_le_normalizer_sup_of_normalizer_le_left`, `IsZGroup.commutator_lt`, `commutator_centralizer_commutator_le_center`, `map_subtype_le`, `index_toAddSubgroup`, `IsPGroup.le_or_disjoint_of_coprime`, `lowerCentralSeries_map_subtype_le`, `le_comap_map`, `pointwise_smul_le_iff₀`, `MonoidHom.coe_toAdditive_range`, `map_eq_range_iff`, `prod_le_iff`, `prod_mono_left`, `topologicalClosure_minimal`, `derived_le_lower_central`, `map_le_iff_le_comap`, `CongruenceSubgroup.Gamma1_in_Gamma0`, `focalSubgroup_le_commutator`, `IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply`, `opEquiv_symm_apply`, `relIndex_eq_one`, `commutator_top_left_le_iff`, `commutator_le_map_commutator`, `closure_mul_le`, `normalizer_inf_normalizer_le_normalizer_sup`, `isComplement'_iff_card_mul_and_disjoint`, `MonoidHom.eq_liftOfRightInverse`, `topologicalClosure_mono`, `center_le_centralizer`, `goursatFst_prod_goursatSnd_le`, `AddMonoidHom.coe_toMultiplicative_map`, `alternatingGroup.isCoatom_stabilizer`, `centralizer_le`, `fixedPoints_subgroup_antitone`, `toAddSubgroup_comap`, `le_adjoinNegOne`, `FiniteMulArchimedeanClass.ballSubgroup_strictAnti`, `Normal.commutator_le_of_self_sup_commutative_eq_top`, `map_comap_le`, `AddSubgroup.finiteIndex_toSubgroup_iff`, `isSolvable_iff_commutator_lt`, `AddSubgroup.coe_toSubgroup_apply`, `comap_mono`, `IsGaloisGroup.intermediateFieldEquivSubgroup_apply`, `Equiv.Perm.isCoatom_stabilizer`, `normalClosure_le_normal`, `closure_le_normalClosure`, `orderIsoCon_symm_apply_coe`, `MulArchimedeanClass.subgroup_antitone`, `le_normalizer_of_normal`, `ascending_central_series_le_upper`, `rootsOfUnity_le_of_dvd`, `AddSubgroup.fg_iff_mul_fg`, `fixingSubgroup_fixedPoints_gc`, `alternatingGroup.commutator_perm_le`, `map_mono`, `IsMultiplyPretransitive.alternatingGroup_le`, `IntermediateField.le_iff_le`, `AddSubgroup.toSubgroup'_closure`, `MulAction.le_stabilizer_smul_right`, `codisjoint_subgroupOf_sup`, `SemidirectProduct.mulEquivSubgroup_apply`, `DirichletCharacter.factorsThrough_iff_ker_unitsMap`, `MulAction.stabilizer_inf_stabilizer_le_stabilizer_inter`, `MulAction.stabilizer_inf_stabilizer_le_stabilizer_apply₂`, `Sylow.exists_subgroup_card_pow_succ`, `Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer`, `SemidirectProduct.mulEquivSubgroup_symm_apply`, `MulAction.stabilizer_inf_stabilizer_le_stabilizer_union`, `Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_compl`, `le_centralizer_iff_isMulCommutative`, `prod_mono_right`, `commutator_le_focalSubgroupOf`, `toAddSubgroup'_closure`, `MulAction.fixingSubgroup_le_stabilizer`, `MonoidHom.liftOfRightInverse_comp`, `AddSubgroup.index_toSubgroup`, `QuotientGroup.ker_le_range_iff`, `MonoidHom.range_le_ker_iff`, `zpowers_le_of_mem`, `closure_pow_le`, `commutator_comm_le`, `focalSubgroup_le`, `gc_toSubmonoid_mulSupport`, `Equiv.Perm.alternatingGroup_le_of_isPreprimitive`, `Sylow.exists_subgroup_le_card_le`, `Monoid.Coprod.codisjoint_range_inl_range_inr`, `finiteIndex_toAddSubgroup_iff`, `le_op_iff`, `normalCore_le`, `unop_le_unop_iff`, `MulEquiv.symm_comapSubgroup`, `FiniteMulArchimedeanClass.subgroup_strictAnti`, `MulEquiv.symm_mapSubgroup`, `disjoint_iff_mul_eq_one`, `IsSubnormal.lt_normal`, `Sylow.smul_le`, `Monoid.CoprodI.lift_range_le`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_ker`, `surjOn_iff_le_map`, `QuotientGroup.strictMono_comap_prod_map`, `commutator_le_left`, `inf_normalizer_le_normalizer_inf`, `le_pointwise_smul_iff₀`, `op_le_iff`, `comap_le_comap_of_le_range`, `QuotientGroup.le_comap_mk'`, `FreeGroup.range_lift_le`, `AddSubgroup.toSubgroup_comap`, `AddSubgroup.coe_toSubgroup_symm_apply`, `IsCyclic.normalizer_le_centralizer`, `map_rootsOfUnity`, `le_normalizer_map`, `Submonoid.units_mono`, `IsSubnormal.isSubnormal_iff`, `MonoidHom.liftOfRightInverse_comp_apply`, `MonoidHom.noncommCoprod_injective`, `MonoidHom.coe_toAdditive_ker`, `Abelianization.commutator_subset_ker`, `characteristic_iff_le_map`, `IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual`, `Additive.mem_toAddSubgroup`, `le_zpowers_iff`, `relIndex_toAddSubgroup`, `IsComplement'.disjoint`, `IsSubnormal.exists_chain`, `opEquiv_apply`, `MonoidHom.coe_toMultiplicative_ker`, `IsGalois.ofDual_intermediateFieldEquivSubgroup_apply`, `alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl`, `MapSubtype.orderIso_symm_apply`, `AddSubgroup.relIndex_toSubgroup`, `isCoatom_comap`
`instSetLike` 📖	CompOp	1643 math math: `map_focalSubgroupOf`, `card_map_of_injective`, `IsPGroup.center_nontrivial`, `SubMulAction.ofStabilizer.isPretransitive_iff_of_conj`, `Valuation.mem_nhds_zero_iff`, `DoubleCoset.doubleCoset_union_rightCoset`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset`, `Sylow.isPGroup'`, `mem_centralizer_iff_commutator_eq_one`, `mulSingle_mem_pi`, `MulAction.isPreprimitive_of_fixingSubgroup_empty_iff`, `Valued.isOpen_closedball`, `smul_mem_pointwise_smul_iff₀`, `instFiniteSubtypeMem`, `card_eq_card_quotient_mul_card_subgroup`, `SubMulAction.ofStabilizer.conjMap_comp_apply`, `ConjAct.fixedPoints_eq_center`, `ModularGroup.SLOnGLPos_smul_apply`, `SubMulAction.ofFixingSubgroup_insert_map_apply`, `MonoidWithZeroHom.mem_valueGroup`, `characteristic_centralizer`, `instNormalSubtypeMemFocalSubgroupOf`, `mem_rootsOfUnity`, `Matrix.GLPos.coe_neg_apply`, `sup_eq_closure_mul`, `ValuationSubring.coe_mem_principalUnitGroup_iff`, `Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_apply`, `adjoinNegOne_eq_self_iff`, `IsComplement.equiv_fst_eq_iff_leftCosetEquivalence`, `exists_mem_sup`, `mem_normalizer_iff''`, `closure_eq`, `FiniteIndexNormalSubgroup.mem_toSubgroup_iff`, `mem_zpowers_iff_mem_range_orderOf`, `Ideal.Quotient.map_ker_stabilizer_subtype`, `WithVal.valueGroupOrderIso₀_symm_apply`, `prod_subgroupOf_prod_normal`, `equivSMul_apply_coe`, `QuotientGroup.norm_mk`, `QuotientGroup.image_coe_inj`, `MonoidHom.ker_transferSylow_disjoint`, `Fintype.card_coeSort_range`, `IsPGroup.card_center_eq_prime_pow`, `Valuation.isClopen_closedBall`, `IsCyclic.isComplement'`, `coe_pointwise_smul`, `subgroupOfContinuousMulEquivOfLe_toMulEquiv`, `centerCongr_symm_apply_coe`, `modularCyclotomicCharacter.id`, `rootsOfUnityEquivOfPrimitiveRoots_apply_coe_inv_val`, `MonoidHom.transferSylow_eq_pow`, `subtype_comp_inclusion`, `IsOfFinOrder.mem_powers_iff_mem_zpowers`, `NumberField.Units.instNonemptySubtypeUnitsRingOfIntegersMemSubgroupTorsion`, `CongruenceSubgroup.Gamma_mem'`, `autAdjoinRootXPowSubCEquiv_root`, `eq_one_of_smul_eq_one`, `MapSubtype.orderIso_apply_coe`, `Equiv.Perm.Basis.toCentralizer_equivariant`, `Group.IsPerfect.mem_commutator`, `MonoidHom.restrictHomKerEquiv_apply_coe`, `isOpen_of_isClosed_of_finiteIndex`, `subgroupOf_normalizer_eq`, `NumberField.IsCMField.unitsComplexConj_torsion`, `SubMulAction.ofStabilizer_carrier`, `Rep.coindResAdjunction_counit_app`, `finEquivZPowers_symm_apply`, `relIndex_eq_two_iff_exists_notMem_and'`, `dense_of_not_isolated_one`, `MeasureTheory.Subgroup.smulInvariantMeasure`, `SubMulAction.ofFixingSubgroup_equivariantMap_injective`, `transferTransversal_apply`, `GroupExtension.Section.mul_inv_mem_range_inl`, `Rep.coindToInd_of_support_subset_orbit`, `IsPGroup.sylow_mem_fixedPoints_iff`, `DiscreteTiling.PlacedTile.ext_iff_of_preimage`, `NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two`, `IsOfFinOrder.finite_zpowers`, `MulAut.conjNormal_symm_apply`, `instCountableSubtypeMulOppositeMemOp`, `alternatingGroup.isPreprimitive_of_three_le_card`, `Sylow.normalizer_normalizer`, `NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one`, `index_dvd_two_iff'`, `normal_subgroupOf_iff`, `AddSubgroup.subgroupOf_inertia`, `QuotientGroup.norm_mk_eq_zero`, `equivOp_symm_apply_coe`, `fixedPoints_subgroup_iSup`, `Matrix.SpecialLinearGroup.toGLPos_injective`, `ProfiniteGrp.limit_one_val`, `mem_pointwise_smul_iff_inv_smul_mem₀`, `QuotientGroup.leftRel_r_eq_leftCosetEquivalence`, `SubMulAction.ofStabilizer.conjMap_comp_inv_apply`, `val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe`, `le_normalClosure`, `coe_inclusion`, `IsUniformGroup.uniformContinuous_iff_isOpen_ker`, `isOpen_of_mem_nhds`, `AddSubgroup.mem_toSubgroup'`, `Rep.indToCoindAux_self`, `Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar`, `Finset.doubling_lt_three_halves`, `MulAut.conjNormal_val`, `exists_smul_eq`, `DoubleCoset.eq_of_not_disjoint`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst`, `isClosed_topologicalClosure`, `DoubleCoset.mem_doubleCoset_self`, `focalSubgroupOf.pow_index_surjective`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk`, `normalClosure_of_stabilizer_eq_top`, `Rep.indCoindNatIso_hom_app`, `card_top`, `conj_smul_subgroupOf`, `mem_biSup_of_directedOn`, `instSubgroupClass`, `Equiv.Perm.Basis.toCentralizer_apply`, `QuotientGroup.preimage_image_mk`, `MulAction.stabilizerEquivStabilizer_symm_apply`, `Group.IsPerfect.top_iff`, `SlashInvariantForm.quotientFunc_mk`, `map_subtype_inj`, `CongruenceSubgroup.mem_Gamma_one`, `SpecialLinearGroup.mem_center_iff_spec`, `isCoatom_map`, `WithVal.valueGroupOrderIso₀_restrict`, `mem_iSup_of_mem`, `cyclotomicCharacter.toZModPow`, `Sylow.exists_subgroup_card_pow_prime_of_le_card`, `GroupExtension.Section.mul_inv_mul_mul_mem_range_inl`, `conjugatesOfSet_subset_normalClosure`, `AddSubgroup.mem_inertia`, `Submonoid.inv_mem_units_iff`, `commutator_def'`, `IsZGroup.coprime_commutator_index`, `QuotientGroup.rangeKerLift_injective`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `Equiv.Perm.isThreeCycle_subset_alternatingGroup`, `mem_square`, `subgroup_solvable_of_solvable`, `Normal.mem_comm_iff`, `Equiv.Perm.disjoint_ofSubtype_noncommPiCoprod`, `transferFocal_surjective`, `subgroupOf_isMulCommutative`, `DoubleCoset.doubleCoset_union_leftCoset`, `Valuation.IsRankOneDiscrete.generator_mem_valueGroup`, `MonoidWithZeroHom.ValueGroup₀.monoidWithZeroHom_strictMono`, `WithVal.valueGroupOrderIso₀_apply`, `RootPairing.span_orbit_eq_top`, `Rep.coindToInd_indToCoind`, `groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top`, `DoubleCoset.iUnion_image_mk_rightRel`, `IsGaloisGroup.fixedPoints_top`, `Equiv.Perm.exists_mem_stabilizer_smul_eq`, `Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff'`, `MulAction.stabilizer_mul_self`, `Set.unitEquivUnitsInteger_symm_apply_coe`, `alternatingGroup.card_two_sylow_of_card_eq_four`, `SubMulAction.ofFixingSubgroup_of_inclusion_injective`, `val_unitarySubgroupUnitsEquiv_symm_apply_coe`, `Rep.instIsLeftAdjointSubtypeMemSubgroupCoindFunctorSubtype`, `MonoidHom.ker_transferSylow_isComplement'`, `SpecialLinearGroup.mem_center_iff`, `MulAction.mem_aestabilizer`, `Valued.toUniformSpace_eq`, `RootPairing.range_weylGroup_coweightHom`, `center.smulCommClass_right`, `MulAction.quotient_out_smul_fixedPoints`, `Ideal.torsionMapQuot_apply`, `DomMulAct.mem_stabilizer_iff`, `NumberField.HeightOneSpectrum.rankOne_hom'_def`, `IsGalois.card_fixingSubgroup_eq_finrank`, `IsPrimitiveRoot.val_toRootsOfUnity_coe`, `Complex.isQuotientCoveringMap_npow`, `mem_ofUnits_iff_exists_isUnit`, `MulAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `alternatingGroup.kleinFour_card_of_card_eq_four`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity`, `subgroupOf_eq_top`, `MulAction.QuotientAction.inv_mul_mem`, `rootsOfUnity.integer_power_of_ringEquiv`, `mem_principal_ideals_iff`, `WithVal.valueGroupEquiv_symm_apply`, `subgroup_units_cyclic`, `FiniteGaloisIntermediateField.mem_fixingSubgroup_iff`, `Valuation.restrict_eq_one_iff`, `CommGroup.forall_monoidHom_apply_eq_one_iff`, `le_centralizer_iff`, `Submonoid.val_inv_unitsEquivUnitsType_symm_apply_coe`, `mem_centralizer_iff`, `apply_coe_mem_map`, `SubMulAction.nat_card_ofStabilizer_add_one_eq`, `rootsOfUnity.isCyclic`, `IsCyclic.exists_generator`, `ModularForm.norm_eq_zero_iff`, `Valuation.IsRankOneDiscrete.generator'_lt_one`, `mem_unitarySubgroup_iff`, `Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe`, `IsSubnormal.iff_eq_top_or_exists`, `Equiv.Perm.OnCycleFactors.kerParam_range_card`, `MulAction.stabilizerEquivStabilizer_trans`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity`, `mul_normal`, `autAdjoinRootXPowSubCEquiv_symm_smul`, `MonoidHom.ofLeftInverse_symm_apply`, `instCountableSubtypeMemZpowers`, `coe_mk`, `Monoid.PushoutI.NormalWord.Transversal.compl`, `Equiv.Perm.exists_mem_stabilizer_isThreeCycle_of_two_lt_ncard`, `Equiv.Perm.OnCycleFactors.kerParam_injective`, `MulAction.right_quotientAction`, `IsCyclic.monoidHom_mulEquiv_rootsOfUnity`, `index_eq_sum_minimalPeriod`, `isComplement_range_right`, `SubMulAction.ofStabilizer.inv_conjMap_comp_apply`, `NumberField.InfinitePlace.card_stabilizer`, `coe_pi`, `Bot.isCyclic`, `quotientEquivProdOfLE_apply`, `isFiniteRelIndex_iff_finiteIndex`, `exists_left_transversal_of_le`, `coe_mul_of_left_le_normalizer_right`, `isOpen_of_one_mem_interior`, `ModularGroup.coe_apply_complex`, `IsArithFrobAt.mul_inv_mem_inertia`, `MulAction.orbit_subgroup_subset`, `DoubleCoset.mem_doubleCoset_of_not_disjoint`, `HNNExtension.equiv_eq_conj`, `subgroupOf_isOpen`, `SlashInvariantForm.quotientFunc_smul`, `instIsMulTorsionFree`, `MonoidHom.subgroupOf_range_eq_of_le`, `subgroupOf_self`, `one_lt_card_iff_ne_bot`, `Function.MulExact.monoidHom_rangeRestrict`, `smulCommClass_right`, `MonoidHom.fiberEquivKer_symm_apply`, `tendsto_coe_cofinite_of_discrete`, `rightCoset_eq_iff`, `MonoidWithZeroHom.valueGroup.mk_mul`, `card_le_of_le`, `Sylow.normalizer_sup_eq_top'`, `MonoidHom.ker_rangeRestrict`, `le_normalizer_comap`, `card_eq_one`, `AlternatingGroup.isPreprimitive_of_three_le_card`, `IsComplement'.index_eq_card`, `InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois`, `mem_rootsOfUnity_prime_pow_mul_iff'`, `MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff'`, `finite_zpowers`, `val_unitsCentralizerEquiv_apply_coe`, `Equiv.Perm.IsCycle.commute_iff'`, `SpecialLinearGroup.centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq`, `Complex.mem_rootsOfUnity`, `Equiv.altCongrHom_apply_coe`, `Representation.Coinvariants.le_comap_ker`, `CuspForm.coe_trace`, `Ideal.rootsOfUnityMapQuot_injective`, `NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk`, `groupHomology.H1CoresCoinfOfTrivial_X₁`, `mem_op`, `mem_rootsOfUnity_iff_mem_nthRoots`, `QuotientGroup.norm_mk_eq_zero_iff_mem_closure`, `SubMulAction.map_ofFixingSubgroupUnion_def`, `Valued.isClopen_ball`, `CongruenceSubgroup.exists_Gamma_le_conj`, `DiscreteTiling.PlacedTile.ext_iff_of_exists`, `exists_ne_one_of_nontrivial`, `exists_zpowers`, `ValuativeRel.ValueGroupWithZero.embed_strictMono`, `finite_iff_subgroup_quotient`, `pow_mem_of_index_ne_zero_of_dvd`, `rootsOfUnity.coe_injective`, `unop_normalizer`, `card_bot`, `bot_or_nontrivial`, `spinGroup.units_mem_lipschitzGroup`, `SubMulAction.ofStabilizer.isMultiplyPretransitive_iff`, `Ideal.Quotient.stabilizerHom_surjective`, `MonoidHom.transfer_eq_pow_aux`, `modularCyclotomicCharacter.toFun_spec'`, `Equiv.Perm.OnCycleFactors.nat_card_range_toPermHom`, `IsGaloisGroup.quotientMap`, `normal_subgroupOf_sup_of_le_normalizer`, `rank_closure_finite_le_nat_card`, `alternatingGroup.normalClosure_swap_mul_swap_five`, `normalizer_le_normalizer_sup_normal`, `coe_map`, `MulAction.op_smul_set_stabilizer_subset`, `mem_adjoinNegOne_iff`, `Valuation.hasBasis_nhds_zero`, `IsPGroup.coprime_card_of_ne`, `NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply`, `Sylow.smul_eq_iff_mem_normalizer`, `MulAction.mul_stabilizer_self`, `IsTorsion.subgroup`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff`, `Representation.instIsTrivialSubtypeMemSubgroupSubmoduleInvariantsCompLinearMapIdSubtypeToInvariants`, `MulArchimedeanClass.mem_subgroup_iff`, `Finset.pow_right_strictMonoOn`, `MulAction.isBlock_top`, `orbit_subgroup_eq_self_of_mem`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `HNNExtension.inv_t_mul_of`, `HNNExtension.toSubgroupEquiv_neg_one`, `alternatingGroup.subsingleton_two_sylow`, `val_list_prod`, `MulArchimedeanClass.subsemigroup_eq_subgroup_of_ne_top`, `Equiv.Perm.mul_mem_alternatingGroup_of_isSwap`, `IsPGroup.comap_of_ker_isPGroup`, `CongruenceSubgroup.Gamma1_mem'`, `Valuation.restrict_le_iff`, `mem_mk`, `QuotientGroup.preimage_image_mk_eq_mul`, `MulAction.ofFixingSubgroup.isMultiplyPreprimitive`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_strictMono`, `alternatingGroup.isCoatom_stabilizer_singleton`, `DoubleCoset.left_bot_eq_left_quot`, `pow_finEquivZPowers_symm_apply`, `Valued.is_topological_valuation`, `QuotientGroup.leftRel_eq`, `Equiv.Perm.commute_iff_of_mem_cycleFactorsFinset`, `IsValuativeTopology.isOpen_ball`, `Equiv.Perm.IsThreeCycle.mem_commutator_alternatingGroup`, `coe_equivMapOfInjective_apply`, `SubMulAction.ofStabilizer.isPretransitive_iff`, `mem_ofUnits_iff`, `IsComplement.mul_inv_toRightFun_mem`, `exists_pow_mem_of_relIndex_ne_zero`, `Valuation.restrict_eq_zero_iff`, `Sylow.prime_pow_dvd_card_normalizer`, `MonoidHom.not_dvd_card_ker_transferSylow`, `IsComplement.equiv_mul_left_of_mem`, `smul_leftQuotientEquiv`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroup`, `RestrictedProduct.coe_unitsEquiv_apply`, `Group.IsPerfect.instSubtypeMemSubgroupTop`, `Valuation.restrict_eq_mk`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `HasEnoughRootsOfUnity.natCard_rootsOfUnity`, `MonoidHom.transferSylow_restrict_eq_pow`, `alternatingGroup.closure_isThreeCycles_eq_top`, `Equiv.Perm.sumCongrHom.card_range`, `conjAct_pointwise_smul_iff`, `MulAction.stabilizerEquivStabilizer_compTriple`, `IsGaloisGroup.fixedPoints_of_isGaloisGroup`, `quotientSubgroupOfEmbeddingOfLE_apply_mk`, `NumberField.mixedEmbedding.fundamentalCone.integerSetEquiv_apply_fst`, `isUniformGroup`, `Sylow.stabilizer_eq_normalizer`, `Group.conjugates_subset_normal`, `index_ker`, `normalCore_isClosed`, `rootsOfUnity.val_mkOfPowEq_coe`, `Monoid.minOrder_le_natCard`, `DoubleCoset.right_bot_eq_right_quot`, `IsGaloisGroup.of_fixedPoints_eq`, `list_prod_mem`, `centerCongr_apply_coe`, `MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff`, `mem_map_equiv`, `RootPairing.weylGroup_apply_root`, `MulAction.card_eq_sum_card_group_div_card_stabilizer`, `unitarySubgroupUnitsEquiv_apply_coe`, `alternatingGroup.characteristic_kleinFour`, `mem_iSup_prop`, `nontrivial_iff_exists_ne_one`, `Valuation.restrict_lt_iff_lt_embedding`, `eq_bot_iff_card`, `MulEquiv.restrictRootsOfUnity_symm`, `MulAction.IsBlock.orbit_of_normal`, `IsPrimitiveRoot.coe_autToPow_apply`, `Valued.extension_eq_zero_iff`, `coe_inv`, `finite_iff_finite_and_finiteIndex`, `DiscreteTiling.PlacedTile.smul_mk_mk`, `closure_le`, `mem_closure_isSwap`, `mem_iInf`, `IsDecompositionField.toIsGaloisGroup`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `div_mem_comm_iff`, `set_mul_normalizer_comm`, `Equiv.Perm.mem_range_ofSubtype_iff`, `rank_congr`, `comap_injective_isMulCommutative`, `Set.powersetCard.isPretransitive_alternatingGroup`, `ProfiniteGrp.denseRange_toLimit`, `DiscreteTiling.PlacedTile.ext_iff`, `alternatingGroup.kleinFour_isKleinFour`, `exists_mem_ofUnits_val_eq`, `ProfiniteGrp.closedSubgroup_eq_sInf_open`, `AlternatingGroup.card_of_cycleType_singleton`, `IsSubnormal.trans'`, `leftCoset_cover_const_iff_surjOn`, `SubMulAction.fixingSubgroup_of_insert`, `coe_square`, `alternatingGroup.mem_range_ofSubtype_iff`, `IsComplement.equiv_snd_eq_iff_rightCosetEquivalence`, `ne_bot_iff_exists_ne_one`, `CommGroup.coe_primaryComponent`, `leftCoset_cover_filter_FiniteIndex_aux`, `MulEquiv.subgroupCongr_apply`, `closure_closure_coe_preimage`, `Con.mem_subgroup_iff`, `orderOf_mk`, `subtype_apply`, `SubMulAction.ofFixingSubgroup_carrier`, `alternatingGroup.normalClosure_finRotate_five`, `normalClosure_subset_iff`, `groupHomology.H1CoresCoinf_X₁`, `subset_normalizer_of_normal`, `smul_diff_smul'`, `mem_of_mem_val_ofUnits`, `coe_subtype`, `QuotientGroup.eq_class_eq_leftCoset`, `normalizer_le_normalizer_sup_of_normalizer_le_right`, `centerToMulOpposite_apply_coe`, `rank_le_index_mul_rank`, `NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_smul_coe`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_of_ne_zero`, `map_subgroupOf_eq_of_le`, `Set.coe_unit`, `Ideal.card_stabilizer_eq`, `mem_goursatFst`, `subtype_injective`, `DoubleCoset.iUnion_finset_leftRel_eq_univ_of_leftRel`, `index_mul_card`, `Valuation.subgroups_basis`, `alternatingGroup.kleinFour_eq_commutator`, `Rep.indToCoindAux_fst_mul_inv`, `set_mul_normal_comm`, `pairwiseDisjoint_leftCoset_cover_const_of_index_eq`, `Ideal.stabilizerEquiv_symm_apply_smul`, `Commensurable.commensurator_mem_iff`, `infinite_zpowers`, `Valuation.mem_unitGroup_iff`, `GroupExtension.Section.inv_mul_mem_range_inl`, `DiscreteTiling.Prototile.ext_iff`, `Valuation.restrict_le_iff_le_embedding`, `HasEnoughRootsOfUnity.rootsOfUnity_isCyclic`, `Set.subgroupClosure_mul_pow`, `mem_pi`, `MulAction.isPreprimitive_ofFixingSubgroup_conj_iff`, `le_centralizer`, `instIsTopologicalGroupSubtypeMem`, `Submonoid.inv_mem_units`, `instFiniteIndex_subgroupOf`, `mem_map_of_mem`, `isComplement_subgroup_left_iff_existsUnique_quotientMk''`, `card_commutator_le_of_finite_commutatorSet`, `zpowers_le`, `IsPGroup.to_subgroup`, `Equiv.Perm.Basis.card_ofPermHom_support`, `SubMulAction.exists_smul_of_last_eq`, `mem_center_iff`, `QuotientGroup.rightRel_r_eq_rightCosetEquivalence`, `IsPrimitiveRoot.card_rootsOfUnity'`, `alternatingGroup.center_eq_bot`, `alternatingGroup.stabilizer.surjective_toPerm`, `mem_sSup_of_directedOn`, `coe_ofClass`, `IsGaloisGroup.fixedPoints_fixingSubgroup`, `SubMulAction.mem_fixingSubgroup_insert_iff`, `prod_mem`, `NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def`, `centralizer_eq_top_iff_subset`, `negOne_mem_adjoinNegOne`, `smul_opposite_image_mul_preimage`, `Units.val_set_image_rootsOfUnity_one`, `Equiv.Perm.Basis.ofPermHom_apply`, `Valuation.nonempty_rankOne_iff_mulArchimedean`, `subgroupOf_map_powMonoidHom_eq_range`, `FiniteField.sum_subgroup_units_eq_zero`, `ModularGroup.SL_to_GL_tower`, `coe_pow`, `QuotientGroup.univ_eq_iUnion_smul`, `normal_subgroupOf_iff_le_normalizer_inf`, `SubMulAction.ofStabilizer.isMultiplyPretransitive_iff_of_conj`, `MulArchimedeanClass.mem_closedBallSubgroup_iff`, `FiniteMulArchimedeanClass.mem_ballSubgroup_iff`, `SubgroupNormal.mem_comm`, `relIndex_subgroupOf`, `Group.IsPerfect.map`, `leftCoset_eq_iff`, `IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup`, `Rep.indToCoindAux_comm`, `MonoidHom.restrictHomKerEquiv_symm_coe_apply`, `op_normalizer`, `Valuation.RankOne.exists_val_lt`, `Circle.isQuotientCoveringMap_zpow`, `MonoidWithZeroHom.valueGroup_eq_range`, `commutator_le`, `noncommPiCoprod_apply`, `normalizerMonoidHom_ker`, `MonoidHom.restrict_range`, `FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff`, `Valued.hasBasis_nhds_zero`, `Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup`, `CommGroup.mem_subgroupOrderIsoSubgroupMonoidHom_iff`, `MulAction.card_eq_sum_card_group_div_card_stabilizer'`, `GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_range`, `MonoidHom.range_isMulCommutative`, `ker_subtype`, `Sylow.instFiniteQuotientSubgroupNormalizer`, `Equiv.Perm.OnCycleFactors.mem_range_toPermHom'_iff`, `Sylow.not_dvd_card_commutator_or_not_dvd_index_commutator`, `sylow_mem_fixedPoints_iff`, `comap_normalizer_eq_of_surjective`, `isInertiaField_iff`, `card_commutatorSet_closureCommutatorRepresentatives`, `InfiniteGalois.mulEquivToLimit_symm_continuous`, `modularCyclotomicCharacter.toFun_spec`, `isQuotientCoveringMap_npow`, `coe_norm`, `centralizer_closure`, `isDecompositionField_iff`, `MulChar.apply_mem_rootsOfUnity_of_pow_eq_one`, `Rep.coindResAdjunction_unit_app`, `alternatingGroup.closure_cycleType_eq_two_two_eq_top`, `IsComplement.leftCosetEquivalence_equiv_fst`, `MulAction.IsBlock.orbit_stabilizer_eq`, `subgroup_mul_singleton`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroupOp`, `CommGroup.mem_subgroupOrderIsoSubgroupMonoidHom_symm_iff`, `Equiv.Perm.swap_mem_stabilizer`, `WithVal.strictMono_valueGroupOrderIso₀`, `QuotientGroup.eq`, `Monoid.PushoutI.NormalWord.cons_head`, `MulEquiv.restrictRootsOfUnity_coe_apply`, `discrete_iff_cyclic`, `IsOfFinOrder.mem_zpowers_iff_mem_range_orderOf`, `NumberField.IsCMField.indexRealUnits_mul_eq`, `mem_zpowers`, `IsPrimitiveRoot.card_rootsOfUnity`, `MulAction.stabilizerEquivStabilizer_apply`, `InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup`, `WithVal.strictMono_valueGroupOrderIso₀_symm`, `HasEnoughRootsOfUnity.cyc`, `normalizer_eq_top`, `instCanLiftSetCoeAndMemOfNatForallForallForallForallHMulForallForallInv`, `mem_toAddSubgroup'`, `MonoidHom.subtype_comp_rangeRestrict`, `MeasureTheory.Measure.IsMulLeftInvariant.quotientMeasureEqMeasurePreimage_of_set`, `Ideal.Quotient.stabilizerHom_surjective_of_profinite`, `NumberField.mixedEmbedding.fundamentalCone.unit_smul_mem_iff_mem_torsion`, `isClosed_nullSubgroup`, `ValuationSubring.coe_unitGroupMulEquiv_apply`, `coe_top`, `TopologicalGroup.IsSES.ofClosedSubgroup`, `Sylow.conj_eq_normalizer_conj_of_mem`, `NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer`, `ofAdd_image_zmultiples_eq_zpowers_ofAdd`, `smul_apply_eq_smul_apply_inv_smul`, `IsComplement'.card_mul`, `subgroupOfEquivOfLe_symm_apply_coe_coe`, `isCyclic_zpowers`, `inf_subgroupOf_inf_normal_of_left`, `SubMulAction.disjoint_val_image`, `Units.val_set_image_rootsOfUnity`, `WithVal.valueGroupEquiv_apply`, `multiset_prod_mem`, `mul_mem_cancel_left`, `QuotientGroup.rangeKerLift_surjective`, `IsPGroup.to_le`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow'`, `mem_map_iff_mem`, `Rep.coindToInd_apply`, `mem_inv_pointwise_smul_iff₀`, `Valuation.RankOne.strictMono`, `subgroupOf_eq_bot`, `alternatingGroup.coe_kleinFour_of_card_eq_four`, `Equiv.Perm.subtypeCongrHom.card_range`, `card_range_dvd`, `MulChar.restrict_ofUnitHom`, `ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀`, `Valued.coe_valuation_eq_rankOne_hom_comp_valuation`, `MulAction.mem_stabilizer_finset`, `ValuationSubring.mem_unitGroup_iff`, `relIndex_eq_two_iff_exists_notMem_and`, `HNNExtension.NormalWord.unitsSMulGroup_snd`, `subgroupIsFreeOfIsFree`, `Rep.resIndAdjunction_homEquiv_symm_apply`, `relIndex_eq_two_iff`, `quotientEquivProdOfLE_symm_apply`, `mem_closure_range_iff_of_fintype`, `GrpCat.SurjectiveOfEpiAuxs.agree`, `HNNExtension.NormalWord.unitsSMul_one_group_smul`, `fg_of_index_ne_zero`, `powers_eq_zpowers`, `Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux`, `SubMulAction.nat_card_ofStabilizer_eq`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `MonoidHom.fiberEquivKer_apply`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_range_eq_top`, `Finset.invMulSubgroup_eq_mul_inv`, `commGroup_isMulCommutative`, `rank_commutator_le_card`, `Sylow.exists_subgroup_card_pow_prime_le`, `ker_inclusion`, `MulAction.coe_quotient_smul_fixedPoints`, `Valued.isClosed_ball`, `MulAction.IsBlock.of_subgroup_of_conjugate`, `GroupExtension.Section.mul_mul_mul_inv_mem_range_inl`, `QuotientGroup.eq_iff_div_mem`, `MulAction.stabilizer_subgroup`, `isOpen_mono`, `Ideal.inertiaEquiv_apply_smul`, `NumberField.IsCMField.unitsMulComplexConjInv_apply_torsion`, `map_subtype_le_map_subtype`, `Valuation.restrict_lt_one_iff`, `coe_toAddSubgroup_symm_apply`, `Equiv.Perm.Basis.ofPermHom_mem_centralizer`, `MulAction.finite_quotient_of_finite_quotient_of_finite_quotient`, `mem_sup_of_normal_right`, `coe_zpow`, `IsGaloisGroup.fixingSubgroup_fixedPoints`, `IsFractionRing.stabilizerHom_surjective`, `Submonoid.units_isCompact`, `mem_closure_singleton`, `pow_index_mem`, `coe_pathComponentOne`, `groupCohomology.H1InfRes_X₃`, `index_eq_two_iff`, `SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `IsZGroup.instSubtypeMemSubgroup`, `properlyDiscontinuousSMul_opposite_of_tendsto_cofinite`, `MulAction.mem_stabilizer_set_iff_subset_smul_set`, `Units.mem_posSubgroup`, `bot_or_exists_ne_one`, `Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe`, `DiscreteTiling.PlacedTile.coe_mk_mk`, `ProfiniteGrp.limit_mul_val`, `MonoidHom.mem_ker`, `Ideal.Quotient.stabilizerHom_apply`, `center_le_normalizer`, `ofMul_image_zpowers_eq_zmultiples_ofMul`, `NumberField.mixedEmbedding.fundamentalCone.quotIntNorm_apply`, `IsValuativeTopology.isClosed_closedBall`, `Rep.indToCoindAux_mul_fst`, `mem_closure_range_iff`, `Finset.doubling_lt_two`, `NumberField.Units.mem_torsion`, `Group.IsPerfect.range`, `Submonoid.isOpen_units`, `IsPGroup.to_sup_of_normal_left'`, `Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe`, `quotientEquivProdOfLE'_symm_apply`, `map_rootsOfUnity_eq_pow_self`, `MulAction.smul_set_stabilizer_subset`, `card_map_dvd`, `Equiv.Perm.support_zpowers_of_mem_cycleFactorsFinset_le`, `mem_sup_left`, `QuotientGroup.mk'_comp_subtype`, `Sylow.normalizer_le_centralizer_or_le_commutator`, `IsCyclic.card_powMonoidHom_ker`, `mem_lowerCentralSeries_succ_iff`, `mem_smul_pointwise_iff_exists`, `Equiv.Perm.stabilizer_isPreprimitive`, `val_centerUnitsEquivUnitsCenter_symm_apply_coe`, `ext_iff`, `QuotientGroup.mk'_eq_mk'`, `IsPGroup.ker_isPGroup_of_injective`, `IsGaloisGroup.fixedPoints_bot`, `zpowers_isMulCommutative`, `Valuation.cauchy_iff`, `relIndex_bot_left`, `le_normalizer`, `Equiv.Perm.mem_alternatingGroup`, `instFiniteSubtypeMemCommutatorOfElemCommutatorSet`, `IsCyclotomicExtension.Rat.mem_zpowers_galEquivZMod_of_mem_stabilizer`, `relIindex_dvd_two_iff'`, `IsPGroup.to_inf_left`, `Submonoid.coe_mulSupport`, `injective_noncommPiCoprod_of_iSupIndep`, `normal_iff_eq_cosets`, `index_dvd_two_iff`, `MulAction.stabilizer_subset_div_right`, `PresentedGroup.mk_eq_one_iff`, `isClosed_of_discrete`, `map_normalizer_eq_of_bijective`, `Finset.doubling_lt_golden_ratio`, `Valuation.IsRankOneDiscrete.generator_zpowers_eq_range`, `Matrix.SpecialLinearGroup.scalar_eq_coe_self_center`, `MulAction.isPreprimitive_fixingSubgroup_insert_iff`, `closure_mul_image_mul_eq_top`, `QuotientGroup.quotientMapSubgroupOfOfLe_mk`, `alternatingGroup.isConj_of`, `HNNExtension.of_mul_t`, `Rep.resIndAdjunction_homEquiv_apply`, `MulAction.mem_stabilizer_set'`, `Valuation.IsRankOneDiscrete.embedding_generator'`, `Equiv.Perm.OnCycleFactors.val_centralizer_smul`, `one_mem`, `topEquiv_symm_apply_coe`, `FiniteField.sum_subgroup_pow_eq_zero`, `normalizerMonoidHom_apply_apply_coe`, `card_commutator_dvd_index_center_pow`, `IsQuotientCoveringMap.subgroup_congr`, `exists_leftTransversal_of_FiniteIndex`, `exists_isComplement_left`, `topologicalClosure_coe`, `rank_closure_finset_le_card`, `IsComplement.inv_mul_toLeftFun_mem`, `singleton_mul_subgroup`, `ProperlyDiscontinuousSMul.finite_stabilizer`, `HNNExtension.of_mul_inv_t`, `AddChar.val_mem_rootsOfUnity`, `bijective_rootsOfUnityAddChar`, `NumberField.Units.instIsCyclicSubtypeUnitsRingOfIntegersMemSubgroupTorsion`, `DoubleCoset.rel_bot_eq_right_group_rel`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `Set.val_unitEquivUnitsInteger_apply_coe`, `SubMulAction.ofFixingSubgroup_of_eq_apply`, `Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk`, `MulAction.stabilizer_subgroup_op`, `MonoidHom.div_mem_ker_iff`, `MonoidHom.transfer_center_eq_pow`, `Submonoid.val_unitsEquivUnitsType_apply_coe`, `commutator_eq_bot_iff_le_centralizer`, `instMeasurableConstSMul`, `Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_apply`, `noncommPiCoprod_mulSingle`, `swap_mem_closure_isSwap`, `subgroupOf_sup`, `MulChar.mem_subgroupOrderIsoSubgroupMulChar_symm_iff`, `Submonoid.val_inv_unitsEquivUnitsType_apply_coe`, `SubMulAction.nat_card_ofStabilizer_eq_add_one`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `Rep.coindResAdjunction_homEquiv_apply`, `mem_fixingSubgroup_compl_iff_movedBy_subset`, `coe_set_mk`, `MonoidHom.coe_comp_rangeRestrict`, `instIsDecompositionFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupStabilizerIdealOfIsGalois`, `Valuation.embedding_restrict`, `mem_ofUnits_iff_toUnits_mem`, `quotientSubgroupOfMapOfLE_apply_mk`, `rootsOfUnity.coe_mkOfPowEq`, `RootPairing.isSimpleModule_weylGroupRootRep`, `AlternatingGroup.card_of_cycleType`, `mem_comap`, `QuotientGroup.discreteTopology_iff`, `Rep.coinvariantsShortComplex_f`, `isCyclic_subgroup_units`, `normalClosure_eq_iInf`, `mem_sSup_of_mem`, `Rep.resIndAdjunction_counit_app`, `DiscreteTiling.PlacedTile.smul_mk_coe`, `RootPairing.InvariantForm.apply_weylGroup_smul`, `Equiv.Perm.Basis.toPermHom_apply_toCentralizer`, `quotientiInfSubgroupOfEmbedding_apply_mk`, `coe_copy`, `dense_or_cyclic`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive`, `instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient`, `RootPairing.isSimpleModule_weylGroupRootRep_iff`, `subgroupOf_mono`, `MonoidWithZeroHom.ValueGroup₀.mk_eq_of_ne_zero`, `MulAction.finite_quotient_of_pretransitive_of_finite_quotient`, `coe_iInf`, `QuotientGroup.mk_out_eq_mul`, `IsPGroup.to_sup_of_normal_right`, `MulAction.isPreprimitive_stabilizer_subgroup`, `commutator_mem_commutator`, `isClosed_of_isOpen`, `Equiv.Perm.finRotate_bit1_mem_alternatingGroup`, `SubMulAction.ENat_card_ofStabilizer_add_one_eq`, `quotientEquivSigmaZMod_apply`, `Valued.cauchy_iff`, `pinGroup.units_mem_iff`, `exponent_toSubmonoid`, `exponent_top`, `mem_centralizer_singleton_iff`, `Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iff`, `NumberField.Units.torsion_eq_one_or_neg_one_of_odd_finrank`, `instIsMulCommutativeSubtypeMemSubgroupOfIsCyclic`, `surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar`, `IsComplement.rightCosetEquivalence_equiv_snd`, `Set.pow_mul_subgroupClosure`, `Equiv.Perm.Basis.ofPermHom_support`, `map_subtype_lt_map_subtype`, `IntermediateField.fixingSubgroup_isClosed`, `MulAction.orbitRel.Quotient.subgroup_quotient_eq_iff`, `coe_smul_fixedPoints_of_normal`, `RootPairing.reflection_mem_weylGroup`, `MulAction.stabilizer_op_subgroup`, `Action.FintypeCat.quotientToEndHom_mk`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow`, `MulChar.mem_subgroupOrderIsoSubgroupMulChar_iff`, `normal_mul`, `CategoryTheory.PreGaloisCategory.nhds_one_has_basis_stabilizers`, `HahnSeries.binomial_power`, `QuotientGroup.orbit_eq_out_smul`, `coe_iSup_of_directed`, `MulAction.mem_subgroup_orbit_iff`, `NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two`, `eq_top_iff'`, `closure_le_centralizer_centralizer`, `Equiv.Perm.mem_sumCongrHom_range_of_perm_mapsTo_inl`, `subgroupOf_map_subtype`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_eq_zero_iff`, `Sylow.exists_subgroup_le_card_pow_prime_of_le_card`, `QuotientGroup.preimage_image_mk_eq_iUnion_image`, `exists_isLeast_one_lt`, `ConjAct.normal_of_characteristic_of_normal`, `Valuation.IsRankOneDiscrete.generator'_zpowers_eq_top`, `IsConj.normalClosure_eq_top_of`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm'`, `mem_sup`, `alternatingGroup.subgroup_eq_top_of_isPreprimitive`, `Sylow.exists_subgroup_card_pow_prime`, `conj_smul_le_of_le`, `Multiplicative.mem_toSubgroup`, `commutator_def`, `exists_mem_zpowers`, `val_unitsCentralizerEquiv_symm_apply_coe`, `isNilpotent_of_finite_tfae`, `card_le_card_group`, `SubMulAction.notMem_val_image`, `Submodule.unitsQuotEquivRelPic_symm_apply`, `DoubleCoset.eq''`, `MulAction.orbitZPowersEquiv_symm_apply`, `Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants`, `isPretransitive_of_stabilizer_lt`, `Rep.indToCoindAux_mul_snd`, `Ideal.inertiaEquiv_symm_apply_smul`, `HNNExtension.t_mul_of`, `sq_mem_of_index_two`, `mul_mem_cancel_right`, `val_centerUnitsEquivUnitsCenter_apply_coe`, `Valuation.restrict_pos_iff`, `instIsScalarTowerSubtypeMem`, `Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff`, `IsValuativeTopology.isClopen_ball`, `PresentedGroup.generated_by`, `Equiv.Perm.cycleType_eq_two_two_subset_alternatingGroup`, `isPerfect_iff`, `exists_inv_mem_iff_exists_mem`, `alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_four`, `QuotientGroup.strictMono_comap_prod_image`, `mem_zpowers_pow_iff`, `Matrix.SpecialLinearGroup.coe_GLPos_neg`, `Circle.isQuotientCoveringMap_npow`, `MonoidHom.mem_range`, `alternatingGroup.nontrivial_of_three_le_card`, `isQuotientCoveringMap_zpow`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_isDiscrete_ker_monoidHom`, `MulAction.mem_stabilizer_set`, `Valuation.restrict_def`, `coe_mul`, `isZGroup_iff_exists_mulEquiv`, `MulAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingSubgroup`, `center.smulCommClass_left`, `le_normalizer_of_normal_subgroupOf`, `HahnSeries.pow_add`, `exists_finset_card_le_mul`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_surjective`, `mem_upperCentralSeriesStep`, `mul_self_mem_of_index_two`, `NumberField.IsCMField.unitsMulComplexConjInv_ker`, `sup_subgroupOf_eq`, `normal_subgroupOf`, `MulAction.mem_stabilizer_finset_iff_smul_finset_subset`, `coe_toAddSubgroup_apply`, `MulAction.isMultiplyPreprimitive_iff`, `forall_zpowers`, `Set.conj_mem_fixingSubgroup`, `Equiv.swap_mem_stabilizer`, `Equiv.Perm.IsCycle.zpowersEquivSupport_apply`, `isNilpotent`, `subset_closure`, `CongruenceSubgroup.ModularGroup_T_pow_mem_Gamma`, `Valuation.IsEquiv.orderMonoidIso_trans`, `WithVal.strictMono_valueGroupEquiv_symm`, `mem_goursatSnd`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset'`, `Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply`, `MonoidHom.rangeRestrict_surjective`, `MonoidHom.coe_graph`, `Valuation.isClosed_closedBall`, `transferTransversal_apply'`, `Sylow.card_eq_multiplicity`, `pinGroup.units_mem_lipschitzGroup`, `normal_subgroupOf_iff_le_normalizer`, `continuousSMul`, `subgroupOfContinuousMulEquivOfLe_apply`, `pi_mem_of_mulSingle_mem`, `RootPairing.range_weylGroupToPerm`, `Function.MulExact.iff_monoidHom_rangeRestrict`, `AlternatingGroup.isMultiplyPretransitive`, `Matrix.GeneralLinearGroup.mem_center_iff_val_eq_scalar`, `mem_closure_of_mem`, `alternatingGroup.exists_mem_stabilizer_smul_eq`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply`, `normalizer_le_normalizer_sup_of_normalizer_le_left`, `FiniteMulArchimedeanClass.mem_subgroup_iff`, `alternatingGroup.coe_two_sylow_of_card_eq_four`, `Group.rank_range_le`, `NumberField.IsCMField.unitsMulComplexConjInv_apply`, `rightCoset_mem_rightCoset`, `Set.unit_valuation_eq_one`, `commutator_centralizer_commutator_le_center`, `MulAction.orbitRel_subgroupOf`, `lowerCentralSeries_succ`, `SubMulAction.mem_ofStabilizer_iff`, `map_subtype_le`, `IsValuativeTopology.isOpen_closedBall`, `SubMulAction.ofStabilizer.snoc_castSucc`, `stabilizer_isOpen_of_isIntegral`, `card_subgroup_dvd_card`, `IsFiniteRelIndex.to_finiteIndex_subgroupOf`, `FixedPoints.mem_subgroup`, `mem_sInf`, `relIindex_eq_two_iff'`, `IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_HaarMeasure`, `lowerCentralSeries_map_subtype_le`, `discreteTopology_iff_of_isFiniteRelIndex`, `SubMulAction.mem_ofFixingSubgroup_insert_iff`, `MulAction.coe_aestabilizer`, `Equiv.Perm.isPretransitive_of_isCycle_mem`, `MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iff`, `Valuation.toTopologicalSpace_eq`, `SlashInvariantForm.coe_trace`, `Equiv.Perm.OnCycleFactors.coe_toPermHom`, `dense_submonoidClosure_iff_subgroupClosure`, `leftCoset_mem_leftCoset`, `isComplement_range_left`, `Equiv.Perm.exists_mem_stabilizer_isThreeCycle`, `closure_submonoidClosure_eq_closure_subgroupClosure`, `IsFractionRing.stabilizerHom_apply_apply_mk`, `inv_mem`, `MonoidHom.transferCenterPow_apply`, `mem_closure_singleton_iff_existsUnique_zpow`, `ClassGroup.equivPic_symm_apply`, `isOpen_of_openSubgroup`, `mul_mem_sup`, `NumberField.IsCMField.mem_realUnits_iff`, `two_mul_card_alternatingGroup`, `commutator_alternatingGroup_eq_top`, `Monoid.le_minOrder_iff_forall_subgroup`, `MonoidHom.coe_rangeRestrict`, `Finset.le_card_quotient_mul_sq_inter_subgroup`, `mem_normalizer_iff`, `SubMulAction.ofStabilizer.conjMap_comp`, `groupCohomology.H1InfRes_g`, `instFGSubtypeMemCommutator`, `Equiv.Perm.sigmaCongrRightHom.card_range`, `IsGaloisGroup.subgroup_iff`, `RootPairing.weylGroup.ofIdx_smul`, `RestrictedProduct.unitsEquiv_apply`, `MulAction.mem_stabilizer_set_iff_smul_set_subset`, `ConjClasses.mk_bijOn`, `mem_upperCentralSeries_succ_iff`, `Representation.le_comap_invariants`, `Group.fg_iff_subgroup_fg`, `Rep.indCoindNatIso_inv_app`, `QuotientGroup.rightRel_apply`, `instIsMulCommutativeQuotientSubtypeMemFocalSubgroupOf`, `MulAction.zpowersQuotientStabilizerEquiv_symm_apply`, `smul_def`, `NumberField.IsCMField.unitsComplexConj_eq_self_iff`, `quotient_finite_of_isOpen'`, `HNNExtension.toSubgroupEquiv_neg_apply`, `ValuationSubring.surjective_unitGroupToResidueFieldUnits`, `Equiv.Perm.swap_mul_swap_same_mem_closure_three_cycles`, `alternatingGroup.range_ofSubtype`, `instMeasurableSMul`, `AlternatingGroup.isPretransitive_of_three_le_card`, `coe_one`, `IsGaloisGroup.intermediateField`, `mem_closure_pair`, `finite_quotient_of_pretransitive_of_index_ne_zero`, `Valuation.isClopen_ball`, `DoubleCoset.rel_iff`, `coe_unop`, `Rep.coindResAdjunction_homEquiv_symm_apply`, `ValuationSubring.principalUnitGroupEquiv_apply`, `coe_inf`, `bot_subgroupOf`, `coe_topologicalClosure_bot`, `equivOp_apply_coe`, `Normal.subgroupOf`, `card_alternatingGroup`, `Rep.indCoindIso_hom_hom_toLinearMap`, `IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply`, `MulAction.orbitZPowersEquiv_symm_apply'`, `alternatingGroup.stabilizer_isPreprimitive`, `Nat.card_zpowers`, `index_eq_two_iff_exists_notMem_and'`, `Submonoid.mem_units_iff`, `smul_opposite_mul`, `IsDedekindDomain.selmerGroup.fromUnit_ker`, `ConjAct.Subgroup.val_conj_smul`, `Equiv.Perm.prod_list_swap_mem_alternatingGroup_iff_even_length`, `SubMulAction.ofStabilizer.isMultiplyPretransitive`, `coe_set_eq_one`, `CongruenceSubgroup.Gamma1_mem`, `SubMulAction.ofFixingSubgroup.append_right`, `mapClusterPt_atTop_pow_iff_mem_topologicalClosure_zpowers`, `unit_mem_of_mem_ofUnits`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow'`, `IntermediateField.finrank_fixedField_eq_card`, `toIsOrderedMonoid`, `goursat_surjective`, `MulAction.isPreprimitive_stabilizer_of_surjective`, `discreteTopology_iff_of_finiteIndex`, `two_mul_nat_card_alternatingGroup`, `Valued.isOpen_closedBall`, `Ideal.card_inertia_eq_ramificationIdxIn`, `Valuation.instNontrivialSubtypeUnitsMemSubgroupValueGroupOfIsNontrivial`, `Equiv.Perm.IsSwap.mul_mem_closure_three_cycles`, `Ideal.rootsOfUnityMapQuot_apply`, `Valuation.hasBasis_nhds`, `MonoidHom.ofLeftInverse_apply`, `card_dvd_of_le`, `mem_zpowers_zpow_iff`, `MonoidHom.eq_iff`, `Equiv.Perm.IsThreeCycle.alternating_normalClosure`, `Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity`, `coe_center`, `IsComplement.inv_toLeftFun_mul_mem`, `isMulCommutative_closure`, `mem_zpowers_of_prime_card`, `normalizer_eq_top_iff`, `CongruenceSubgroup.mem_conjGL`, `Valued.mem_nhds_zero`, `Valuation.RankLeOne.exists_val_lt`, `instFiniteElemSubtypeMemSubgroupClosureCommutatorRepresentativesCommutatorSet`, `normalizer_inf_normalizer_le_normalizer_sup`, `NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two`, `Valued.isOpen_ball`, `ker_subgroupMap`, `mem_iSup_of_directed`, `isComplement_subgroup_left_iff_bijective`, `Matrix.SpecialLinearGroup.coe_to_GLPos_to_GL_det`, `Units.val_set_image_rootsOfUnity_two`, `ValuationSubring.mem_principalUnitGroup_iff`, `QuotientGroup.exists_norm_mul_lt`, `inclusion_inj`, `DoubleCoset.finite_quotient_iff_exists_finset_iUnion_eq_univ`, `Valued.mem_nhds`, `alternatingGroup.normal_kleinFour`, `isComplement'_iff_card_mul_and_disjoint`, `mul_injective_of_disjoint`, `card_commutator_closureCommutatorRepresentatives`, `DoubleCoset.iUnion_quotToDoubleCoset`, `DoubleCoset.eq`, `Ideal.Quotient.ker_stabilizerHom`, `mem_closure_isSwap'`, `DomMulAct.stabilizerMulEquiv_apply`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset`, `IsPGroup.mem_toSylow`, `finEquivZPowers_apply`, `Normal.mem_comm`, `ConjAct.coe_smul`, `MonoidHom.rangeRestrict_injective_iff`, `inv_subset_closure`, `Valuation.isOpen_ball`, `cosetToCuspOrbit_apply_mk`, `transferFocal_eq_pow`, `leftCoset_cover_filter_FiniteIndex`, `Group.isNilpotent_top`, `MulAction.stabilizerEquivStabilizer_one`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply`, `index_eq_two_iff_exists_notMem_and`, `Rep.indCoindIso_inv_hom_toLinearMap`, `alternatingGroup.isSimpleGroup_five`, `Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff`, `Normal.of_map_subtype`, `isSimpleGroup_iff`, `IsDedekindDomain.selmerGroup.fromUnitLift_injective`, `comap_inclusion_subgroupOf`, `alternatingGroup.isCoatom_stabilizer`, `IsPGroup.to_sup_of_normal_right'`, `relIndex_dvd_two_iff`, `fixedPoints_subgroup_sup`, `subgroupOfContinuousMulEquivOfLe_symm_apply`, `isApproximateSubgroup_one`, `fixedPoints_subgroup_antitone`, `inclusion_range`, `cyclotomicCharacter.toZModPow_toFun`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure`, `ValuationSubring.coe_unitGroupMulEquiv_symm_apply`, `MonoidWithZeroHom.valueMonoid_eq_valueGroup'`, `exists_right_transversal_of_le`, `Matrix.mem_glpos`, `IsValuativeTopology.isClosed_ball`, `Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one`, `coe_eq_univ`, `Ideal.torsionMapQuot_injective`, `groupHomology.H1CoresCoinfOfTrivial_f`, `index_eq_two_iff'`, `zpow_mem_zpowers`, `ProfiniteGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemSubgroupLimitConePtAux`, `MulAction.stabilizerEquivStabilizer_symm`, `Equiv.Perm.IsCycle.zpowersEquivSupport_symm_apply`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `MulAction.orbitRel_subgroup_le`, `orbit_subgroup_eq_rightCoset`, `Rep.instPreservesProjectiveObjectsSubtypeMemSubgroupResFunctorSubtype`, `image_range_orderOf`, `inv_mem_iff`, `focalSubgroupOf_eq_closure`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `card_zpowers_le`, `alternatingGroup.exponent_kleinFour_of_card_eq_four`, `LinearEquiv.mem_stabilizer_fixedSubmodule`, `isQuotientCoveringMap_of_comm`, `ModularGroup.coe_one`, `mul_inf_assoc`, `pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one`, `mem_nullSubgroup_iff`, `Valuation.hasBasis_uniformity`, `OpenSubgroup.mem_toSubgroup`, `Int.subgroup_index_ne_zero_iff`, `mem_top`, `Valued.toNormedField.norm_def`, `Finset.card_pow_quotient_mul_pow_inter_subgroup_le`, `ModularForm.coe_norm`, `CongruenceSubgroup.Gamma1_to_Gamma0_mem`, `IsGaloisGroup.subgroup`, `Ideal.card_stabilizer_eq_card_inertia_mul_finrank`, `Valuation.toUniformSpace_eq`, `AddSubgroup.coe_toSubgroup_apply`, `mem_closure`, `Rep.instPreservesEpimorphismsSubtypeMemSubgroupCoindFunctorSubtype`, `IsPGroup.to_inf_right`, `Sylow.coe_subtype`, `krullTopology_mem_nhds_one_iff`, `SubMulAction.ofFixingSubgroup_of_singleton_bijective`, `Valuation.norm_def`, `Equiv.Perm.Basis.ofPermHomFun_apply_of_cycleOf_mem`, `Equiv.Perm.OnCycleFactors.toPermHom_apply`, `Finset.card_mul_finset_lt_two`, `modularCyclotomicCharacter.comp`, `Sylow.smul_subtype`, `focalSubgroup_def`, `OpenSubgroup.coe_toSubgroup`, `Group.closure_finset_fg`, `Set.powersetCard.isPreprimitive_alternatingGroup`, `continuousSMul_iff_stabilizer_isOpen`, `alternatingGroup.instNontrivialSubtypePermFinHAddNatOfNatMemSubgroup`, `normalClosure_closure_eq_normalClosure`, `Sylow.normalizer_sup_eq_top`, `MonoidHom.finite_iff_finite_ker_range`, `Sylow.card_quotient_normalizer_modEq_card_quotient`, `lipschitzGroup.coe_mem_iff_mem`, `IsPGroup.of_bot`, `MulAction.subgroup_smul_def`, `SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective`, `pow_relIndex_mem`, `saturated_iff_zpow`, `quotientiInfSubgroupOfEmbedding_apply`, `mem_strictPeriods_iff`, `MulArchimedeanClass.mem_ballSubgroup_iff`, `Sylow.dvd_card_of_dvd_card`, `normal_subgroupOf_of_le_normalizer`, `Valuation.exists_div_eq_of_unit`, `instProperSMulSubtypeMulOppositeMemSubgroupOpOfIsTopologicalGroupOfIsClosedCoe`, `Valuation.restrict_le_one_iff`, `SubMulAction.fixingSubgroupEquivFixingSubgroup_coe_apply`, `Representation.toCoinvariants_mk`, `krullTopology_mem_nhds_one_iff_of_normal`, `mem_map`, `Valuation.isClosed_ball`, `inf_mul_assoc`, `CommGroup.primaryComponent.isPGroup`, `MonoidWithZeroHom.mem_valueGroup_iff_of_comm`, `subset_normalClosure`, `Rep.quotientToCoinvariantsFunctor_map_hom_toLinearMap`, `closure_mul_image_eq_top`, `Sylow.exists_comap_subtype_eq`, `Finset.invMulSubgroup_eq_inv_mul`, `IntermediateField.fixingSubgroup_isOpen`, `ker_restrict_transferFocal_eq_focalSubgroupOf`, `le_normalizer_of_normal`, `val_mem_ofUnits_iff_mem`, `commProb_subgroup_le`, `Matrix.SpecialLinearGroup.coe_GLPos_coe_GL_coe_matrix`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range`, `MonoidHom.ofInjective_apply`, `MulEquiv.coe_subgroupMap_apply`, `focalSubgroupOf.mk'_conj_eq`, `pow_mem`, `SubMulAction.mem_fixingSubgroup_union_iff`, `Valuation.IsEquiv.orderMonoidIso_eq_refl`, `rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val`, `ker_transferFocal_inf_eq_focalSubgroup`, `fixingSubgroup_fixedPoints_gc`, `mem_normalizer_fintype`, `SubMulAction.map_ofFixingSubgroupUnion_bijective`, `IsComplement.equiv_mul_right_of_mem`, `Commensurable.commensurator'_mem_iff`, `SubMulAction.of_fixingSubgroupEmpty_mapScalars_surjective`, `Valuation.RankOne.zero_of_hom_zero`, `properlyDiscontinuousSMul_of_tendsto_cofinite`, `Set.mul_subgroupClosure`, `Submodule.mem_stabilizer_submodule_iff_map_eq`, `MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀`, `Valuation.IsEquiv.valueGroup₀Fun_zero`, `Valuation.IsEquiv.valueGroup₀Fun_spec`, `NumberField.InfinitePlace.mem_stabilizer_mk_iff`, `alternatingGroup.isPretransitive_of_three_le_card`, `SubMulAction.ofFixingSubgroup_of_eq_bijective`, `QuotientGroup.orbit_mk_eq_smul`, `pi_mem_of_mulSingle_mem_aux`, `HNNExtension.ReducedWord.map_fst_eq_and_of_prod_eq`, `Equiv.Perm.Basis.ofPermHomFun_mul`, `eq_cosets_of_normal`, `Equiv.Perm.IsThreeCycle.mem_commutatorSet_alternatingGroup`, `mul_mem_iff_of_index_two`, `Valued.hasBasis_uniformity`, `transferFunction_apply`, `rootsOfUnityEquivNthRoots_apply`, `QuotientGroup.card_preimage_mk`, `coe_div`, `IsInertiaField.toIsGaloisGroup`, `normalClosure_idempotent`, `quotientEquivProdOfLE'_apply`, `Rep.resIndAdjunction_unit_app`, `MulAction.mem_stabilizer_iff`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `NumberField.IsCMField.indexRealUnits_eq_two_iff`, `card_rootsOfUnity_eq_iff_exists_isPrimitiveRoot`, `rootsOfUnityCircleEquiv_apply`, `QuotientGroup.preimage_image_coe`, `Complex.card_rootsOfUnity`, `mem_inv_pointwise_smul_iff`, `IsComplement'.QuotientMulEquiv_symm_apply`, `codisjoint_subgroupOf_sup`, `coe_mul_of_right_le_normalizer_left`, `LinearEquiv.reduce_mk`, `SubMulAction.not_mem_of_mem_ofFixingSubgroup`, `alternatingGroup.isMultiplyPretransitive`, `Group.residuallyFinite_iff_exists_finiteIndex`, `DoubleCoset.disjoint_out`, `Rep.indToCoind_coindToInd`, `pow_mem_of_relIndex_ne_zero_of_dvd`, `subtype_range`, `SemidirectProduct.mulEquivSubgroup_apply`, `FiniteMulArchimedeanClass.subsemigroup_eq_subgroup`, `MulAction.stabilizer_orbit_eq`, `MonoidHom.coe_range`, `MulAction.stabilizer_finite`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `instProperSMulSubtypeMemSubgroupOfIsClosedCoe`, `IsPrimitiveRoot.mem_rootsOfUnity`, `SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter`, `IsPGroup.map`, `IsComplement.equiv_mul_right`, `IsPGroup.inf_normalizer_sylow`, `mem_iff_toUnits_mem_units`, `closure_preimage_eq_top`, `Sylow.exists_subgroup_card_pow_succ`, `NumberField.Units.exist_unique_eq_mul_prod`, `Equiv.Perm.IsCycle.forall_commute_iff`, `mem_sup_of_normal_left`, `mem_normalizer_iff'`, `MulAut.conjNormal_inv_apply`, `unit_of_mem_ofUnits_spec_mem`, `subgroupOfEquivOfLe_apply_coe`, `MonoidHom.subgroupMap_surjective`, `Finset.op_smul_stabilizer_of_no_doubling`, `Valuation.restrict_lt_iff`, `IsGaloisGroup.fixedPoints_le_of_le`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `MonoidHom.restrict_surjective`, `modularCyclotomicCharacter'.spec'`, `MulAction.isMultiplyPreprimitive_ofStabilizer`, `NumberField.Units.rootsOfUnity_eq_one`, `MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mk'`, `Equiv.Perm.stabilizer.surjective_toPerm`, `mem_toSubmonoid`, `HNNExtension.NormalWord.TransversalPair.compl`, `Valued.isClosed_closedBall`, `Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer`, `autEquivRootsOfUnity_apply_rootOfSplit`, `HahnSeries.coeff_toOrderTopSubOnePos_pow`, `ProfiniteGrp.toLimitFun_continuous`, `Valuation.isOpen_closedBall`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply`, `coe_toSubmonoid`, `DiscreteTiling.PlacedTile.coe_mk_coe`, `Submonoid.mem_mulSupport`, `IsZGroup.isCyclic_commutator`, `SemidirectProduct.mulEquivSubgroup_symm_apply`, `rootsOfUnity.coe_pow`, `finite_quotient_of_finite_quotient_of_index_ne_zero`, `card_le_one_iff_eq_bot`, `coe_subgroupOf`, `Rep.indToCoindAux_snd_mul_inv`, `transferTransversal_apply''`, `restrictRootsOfUnity_coe_apply`, `multiset_noncommProd_mem`, `card_subtype`, `QuotientGroup.preimage_mk_one`, `IsPGroup.comap_subtype`, `le_centralizer_iff_isMulCommutative`, `IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat`, `HasEnoughRootsOfUnity.finite_rootsOfUnity`, `image_commutatorSet_closureCommutatorRepresentatives`, `commutator_le_focalSubgroupOf`, `IsPGroup.comap_of_injective`, `range_subtype`, `Equiv.Perm.IsCycle.commute_iff`, `Ideal.ncard_primesOver_mul_card_inertia_mul_finrank`, `InfiniteGalois.algEquivToLimit_continuous`, `DoubleCoset.doubleCoset_eq_of_mem`, `coe_op`, `CommGroup.mem_torsion`, `QuotientGroup.rightRel_eq`, `smul_mem_pointwise_smul`, `ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eq`, `top_subgroupOf`, `IsPrimitiveRoot.val_inv_toRootsOfUnity_coe`, `exists_pow_mem_of_index_ne_zero`, `mem_rootsOfUnity'`, `inclusion_injective`, `isComplement_subgroup_right_iff_existsUnique_quotientGroupMk`, `card_mul_eq_card_subgroup_mul_card_quotient`, `DoubleCoset.bot_rel_eq_leftRel`, `mem_fixingSubgroup_iff_subset_fixedBy`, `zpowersEquivZPowers_apply`, `Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange`, `mul_mem`, `normalClosure_eq_self`, `dense_of_no_min`, `SubMulAction.mem_ofFixingSubgroup_iff`, `SubMulAction.ofStabilizer.conjMap_bijective`, `rank_closureCommutatorRepresentatives_le`, `Sylow.prime_dvd_card_quotient_normalizer`, `IsComplement.toRightFun_mul_inv_mem`, `ValuativeRel.restrict_lt_orderMonoidIso`, `orderOf_le_card`, `MulAction.stabilizerEquivStabilizer_inv`, `quotientEquivSigmaZMod_symm_apply`, `mem_prod`, `mem_fixingSubgroup_iff`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive'`, `MulAction.IwasawaStructure.is_comm`, `QuotientGroup.ker_le_range_iff`, `relIndex_ker`, `IsPGroup.to_sup_of_normal_left`, `IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one`, `mem_zpowers_iff`, `QuotientGroup.image_coe`, `card_rootsOfUnity`, `equivSMul_symm_apply_coe`, `smul_toLeftFun`, `isCyclic`, `mem_carrier`, `MonoidWithZeroHom.inv_mem_valueGroup`, `IsZGroup.isZGroup`, `MonoidHom.subgroupComap_apply_coe`, `Lagrange.nodal_subgroup_eq_X_pow_card_sub_one`, `Rep.indToCoindAux_of_not_rel`, `normal_in_normalizer`, `coe_powCardSubgroup`, `ModularGroup.det_coe`, `FiniteField.sum_subgroup_units`, `IsComplement'.QuotientMulEquiv_apply`, `MonoidHom.mem_graph`, `isZGroup_iff`, `ValuationSubring.ker_unitGroupToResidueFieldUnits`, `instIsInertiaFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupInertiaOfIsGalois`, `HNNExtension.equiv_symm_eq_conj`, `orderOf_dvd_natCard`, `Sylow.pow_dvd_card_of_pow_dvd_card`, `MulChar.apply_mem_rootsOfUnity_orderOf`, `val_finset_prod`, `IsCyclic.card_powMonoidHom_range`, `Equiv.Perm.moves_in`, `subgroupOf_bot_eq_top`, `isCyclic_iff_exists_zpowers_eq_top`, `mem_closure_singleton_self`, `card_mul_index`, `MonoidHom.transfer_eq_pow`, `Sylow.exists_subgroup_le_card_le`, `MulEquiv.subgroupMap_symm_apply`, `orbit_subgroup_one_eq_self`, `stabilizer_isOpen`, `MeasureTheory.leftInvariantIsQuotientMeasureEqMeasurePreimage`, `val_rootsOfUnityEquivOfPrimitiveRoots_apply_coe`, `exists_isComplement_right`, `commute_subtype_of_commute`, `mem_sup_right`, `Group.nat_card_center_add_sum_card_noncenter_eq_card`, `alternatingGroup.card_of_card_eq_four`, `ClassGroup.equivPic_apply`, `DoubleCoset.out_eq'`, `Valuation.restrict_exists_div_eq`, `mem_pointwise_smul_iff_inv_smul_mem`, `alternatingGroup.isThreeCycle_isConj`, `Rep.instIsRightAdjointSubtypeMemSubgroupIndFunctorSubtype`, `Submonoid.val_unitsEquivUnitsType_symm_apply_coe`, `mem_sup'`, `frattini_nilpotent`, `RootPairing.range_weylGroup_weightHom`, `Sylow.card_eq_card_quotient_normalizer`, `Valuation.IsEquiv.orderMonoidIso_spec`, `ModularForm.coe_trace`, `IsGaloisGroup.card_fixingSubgroup_eq_finrank`, `isCyclic_of_le`, `Valuation.RankOne.hom_eq_zero_iff`, `Fintype.card_zpowers`, `AlternatingGroup.map_subtype_of_cycleType`, `IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup`, `normalizerMonoidHom_apply_symm_apply_coe`, `Matrix.GLPos.coe_neg_GL`, `mem_powers_iff_mem_zpowers`, `Valued.isClopen_closedBall`, `groupHomology.H1CoresCoinf_f`, `Valuation.RankOne.restrict_RankOne_hom_eq`, `GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset`, `QuotientGroup.dense_image_mk`, `index_range`, `instIsMulCommutative_closure`, `Unitization.val_unitsFstOne_mulEquiv_quasiregular_apply`, `IsComplement.equiv_mul_left`, `index_map_subtype`, `MulAction.card_orbit_mul_card_stabilizer_eq_card_group`, `QuotientGroup.eq_one_iff`, `mem_unop`, `Sylow.smul_le`, `SchurZassenhausInduction.step7`, `centerToMulOpposite_symm_apply_coe`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset`, `Equiv.Perm.OnCycleFactors.kerParam_range_eq`, `coe_comap`, `autAdjoinRootXPowSubC_root`, `mem_subgroupOf`, `nat_card_alternatingGroup`, `Equiv.Perm.ofSubtype_mem_stabilizer`, `WithVal.strictMono_valueGroupEquiv`, `coe_nonempty`, `Group.card_center_add_sum_card_noncenter_eq_card`, `MulAction.IsBlock.subgroup`, `mem_inf`, `dense_xor'_cyclic`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `commProb_quotient_le`, `ConjClasses.card_carrier`, `mem_units_iff_val_mem`, `instDiscreteTopologyZMultiples`, `MonoidHom.subgroupMap_apply_coe`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zero`, `NumberField.IsCMField.map_unitsMulComplexConjInv_torsion`, `LinearEquiv.mem_stabilizer_submodule_of_le_fixedSubmodule`, `CongruenceSubgroup.Gamma_mem`, `mem_rootsOfUnity_iff_isRoot`, `surjOn_iff_le_map`, `QuotientGroup.strictMono_comap_prod_map`, `HahnSeries.val_toOrderTopSubOnePos_coe`, `Valuation.RankLeOne.strictMono'`, `instNontrivialSubtypeMemTop`, `Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia`, `smul_mem_fixedPoints_of_normal`, `IsPGroup.isCyclic_of_isZGroup`, `inf_normalizer_le_normalizer_inf`, `HahnSeries.mem_orderTopSubOnePos_iff`, `rootsOfUnityEquivNthRoots_symm_apply`, `SMul.smul_stabilizer_def`, `norm_coe`, `comap_normalizer_eq_of_le_range`, `ModularGroup.coeHom_apply`, `MonoidHom.apply_ofInjective_symm`, `npow_mem_zpowers`, `Valuation.exists_setOf_restrict_le_iff`, `smulCommClass_left`, `HahnSeries.val_inv_toOrderTopSubOnePos_coe`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono`, `ProfiniteGrp.limit_ext_iff`, `isLeast_of_closure_iff_eq_mabs`, `Unitization.unitsFstOne_val_val_fst`, `conj_mem_sup_of_mem_inf_normalizer_of_mem_inf`, `Equiv.Perm.Basis.ofPermHomFun_one`, `noncommProd_mem`, `MulAction.minimalPeriod_eq_card`, `MulAction.mem_stabilizer_finset'`, `MonoidHom.eqOn_closure`, `IntermediateField.mem_fixingSubgroup_iff`, `SubMulAction.ofStabilizer.conjMap_apply`, `IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int`, `relIndex_dvd_card`, `Sylow.conj_eq_normalizer_conj_of_mem_centralizer`, `nontrivial_iff_ne_bot`, `closureCommutatorRepresentatives_fg`, `InfiniteGalois.fixingSubgroup_isClosed`, `AddSubgroup.coe_toSubgroup_symm_apply`, `MulAction.IsBlockSystem.of_normal`, `isComplement_subgroup_right_iff_bijective`, `instSubsingletonSubtypeUnitsMemSubgroupRootsOfUnityOfNatNat`, `IsCyclic.normalizer_le_centralizer`, `topEquiv_apply`, `Commensurable.discreteTopology_iff`, `iSup_eq_closure`, `MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot`, `NumberField.IsCMField.complexConj_torsion`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `MulChar.apply_mem_rootsOfUnity`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk`, `instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra`, `Sylow.mem_fixedPoints_mul_left_cosets_iff_mem_normalizer`, `MulAction.IsBlock.of_orbit`, `rootsOfUnityEquivOfPrimitiveRoots_symm_apply`, `IsArithmetic.discreteTopology`, `AddSubgroup.inertia_map_subtype`, `MonoidHom.subgroupComap_surjective_of_surjective`, `alternatingGroup.stabilizer_subgroup_isPreprimitive`, `ValuationSubring.coe_unitGroupToResidueFieldUnits_apply`, `le_normalizer_map`, `div_mem`, `nat_card_centralizer_nat_card_stabilizer`, `smul_diff'`, `Sylow.card_normalizer_modEq_card`, `QuotientGroup.sound`, `isComplement'_def`, `MonoidWithZeroHom.ValueGroup₀.embedding_strictMono`, `SubMulAction.ofFixingSubgroup_insert_map_bijective`, `modularCyclotomicCharacter.aux_spec`, `Equiv.Perm.IsThreeCycle.mem_alternatingGroup`, `IsSubnormal.isSubnormal_iff`, `Equiv.Perm.OnCycleFactors.kerParam_apply`, `coe_zpowers`, `AlternatingGroup.card_of_cycleType_mul_eq`, `modularCyclotomicCharacter'.unique'`, `mem_bot`, `zpow_mem`, `Group.fg_range`, `LinearEquiv.reduce_mkQ`, `MulEquiv.subgroupCongr_symm_apply`, `SlashInvariantForm.coe_norm`, `Equiv.Perm.has_swap_mem_of_lt_stabilizer`, `instFaithfulSMulSubtypeMem`, `noncommPiCoprod_range`, `ZMod.rootsOfUnityAddChar_val`, `inv_card_commutator_le_commProb`, `coe_eq_singleton`, `SubMulAction.conjMap_ofFixingSubgroup_bijective`, `DoubleCoset.iUnion_finset_rightRel_eq_univ_of_rightRel`, `IsOfFinOrder.powers_eq_zpowers`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset'`, `MonoidHom.coe_ker`, `IsValuativeTopology.isClopen_closedBall`, `Sylow.card_eq_index_normalizer`, `DoubleCoset.iUnion_image_mk_leftRel`, `Valuation.mem_nhds_iff`, `Equiv.Perm.nat_card_centralizer`, `goursat`, `comap_subtype`, `Set.subgroupClosure_mul`, `modularCyclotomicCharacter.toFun_spec''`, `NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvd`, `normal_centralizer`, `coe_bot`, `MeasureTheory.Subgroup.index_mul_measure`, `instDiscreteTopologySubtypeGeneralLinearGroupMemSubgroupAdjoinNegOneOfIsTopologicalRingOfT2Space`, `orbit_fixingSubgroup_compl_subset`, `coe_prod`, `closure_mul_image_eq_top'`, `Unitization.mem_unitsFstOne`, `nilpotencyClass_le`, `IsSubnormal.subgroupOf`, `card_eq_iff_eq_top`, `Finset.smul_stabilizer_of_no_doubling`, `Submonoid.mem_units_of_val_mem_inv_val_mem`, `cyclotomicCharacter.toFun_spec`, `HNNExtension.ReducedWord.exists_normalWord_prod_eq`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply_of_finrank_le_one`, `pow_exponent_eq_one`, `MulAction.mem_stabilizer_finset_iff_subset_smul_finset`, `orderOf_coe`, `Valuation.is_topological_valuation`, `IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual`, `Additive.mem_toAddSubgroup`, `IsZGroup.instIsCyclicSubtypeMemSubgroupOfFactPrime`, `val_multiset_prod`, `map_equiv_normalizer_eq`, `Submonoid.mul_mem_units`, `Monoid.PushoutI.NormalWord.cons_toList`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow`, `mk_smul`, `Normal.conj_mem'`, `IsDedekindDomain.selmerGroup.valuation_ker_eq`, `Equiv.Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom'`, `Valuation.IsEquiv.orderMonoidIso_symm`, `Unitization.unitsFstOne_val_inv_val_fst`, `ValuationSubring.principalUnitGroup_symm_apply`, `Equiv.Perm.OnCycleFactors.centralizer_smul_def`, `Group.conjugatesOfSet_subset`, `Matrix.SpecialLinearGroup.mem_center_iff`, `mem_closure_iff_of_fintype`, `MonoidHom.ker_restrict`, `SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter`, `alternatingGroup.conj_smul_range_ofSubtype`, `map_isMulCommutative`, `Normal.conj_mem`, `subgroupOf_bot_eq_bot`, `mem_rootsOfUnity_prime_pow_mul_iff`, `SemidirectProduct.monoidHomSubgroup_apply`, `isQuotientCoveringMap`, `MulAction.smul_orbit_eq_orbit_smul`, `SubMulAction.conjMap_ofFixingSubgroup_coe_apply`, `Ideal.stabilizerEquiv_apply_smul`, `Submodule.unitsQuotEquivRelPic_apply_coe`, `Equiv.Perm.commute_ofSubtype_noncommPiCoprod`, `IsSubnormal.exists_chain`, `Sylow.card_coprime_index`, `QuotientGroup.t1Space_iff`, `QuotientGroup.out_conj_pow_minimalPeriod_mem`, `Sylow.instFiniteSubtypeMemSubgroup`, `smul_coe`, `center.isMulCommutative`, `alternatingGroup.ofSubtype_comp_subtype`, `alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl`, `inf_subgroupOf_inf_normal_of_right`, `Valued.extensionValuation_toFun`, `QuotientGroup.leftRel_apply`, `Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply`, `rootsOfUnity.eq_one`, `MapSubtype.orderIso_symm_apply`, `Matrix.GLPos.coe_neg`, `CongruenceSubgroup.Gamma0_mem`, `controlled_prod_of_mem_closure`, `Rep.quotientToCoinvariantsFunctor_obj_V`, `map_subtype_commutator`, `mk_eq_one`, `card_comap_dvd_of_injective`, `sup_eq_closure`, `coe_sInf`, `autEquivRootsOfUnity_smul`, `LinearOrderedCommGroup.Subgroup.genLTOne_mem`, `Group.closure_finite_fg`, `smul_mem_pointwise_smul_iff`, `MulAut.conjNormal_apply`, `DoubleCoset.mk_out_eq_mul`, `dense_iff_ne_zpowers`
`inv` 📖	CompOp	9 math math: `NumberField.IsCMField.unitsComplexConj_torsion`, `SlashInvariantForm.quotientFunc_smul`, `coe_inv`, `Equiv.Perm.OnCycleFactors.val_centralizer_smul`, `Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_apply`, `Action.FintypeCat.quotientToEndHom_mk`, `InfiniteGalois.limitToAlgEquiv_symm_apply`, `Equiv.Perm.OnCycleFactors.centralizer_smul_def`, `smul_coe`
`mul` 📖	CompOp	184 math math: `SubMulAction.ofStabilizer.conjMap_comp_apply`, `ModularGroup.SLOnGLPos_smul_apply`, `SubMulAction.ofFixingSubgroup_insert_map_apply`, `ValuationSubring.coe_mem_principalUnitGroup_iff`, `Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_apply`, `WithVal.valueGroupOrderIso₀_symm_apply`, `equivSMul_apply_coe`, `subgroupOfContinuousMulEquivOfLe_toMulEquiv`, `centerCongr_symm_apply_coe`, `rootsOfUnityEquivOfPrimitiveRoots_apply_coe_inv_val`, `autAdjoinRootXPowSubCEquiv_root`, `MonoidHom.restrictHomKerEquiv_apply_coe`, `MulAut.conjNormal_symm_apply`, `SubMulAction.ofStabilizer.conjMap_comp_inv_apply`, `val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe`, `MulAut.conjNormal_val`, `MulAction.stabilizerEquivStabilizer_symm_apply`, `isCoatom_map`, `WithVal.valueGroupOrderIso₀_restrict`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_restrict_apply_of_surjective`, `subgroupOf_isMulCommutative`, `WithVal.valueGroupOrderIso₀_apply`, `Set.unitEquivUnitsInteger_symm_apply_coe`, `val_unitarySubgroupUnitsEquiv_symm_apply_coe`, `WithVal.valueGroupEquiv_symm_apply`, `Submonoid.val_inv_unitsEquivUnitsType_symm_apply_coe`, `Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe`, `MulAction.stabilizerEquivStabilizer_trans`, `autAdjoinRootXPowSubCEquiv_symm_smul`, `MonoidHom.ofLeftInverse_symm_apply`, `IsCyclic.monoidHom_mulEquiv_rootsOfUnity`, `SubMulAction.ofStabilizer.inv_conjMap_comp_apply`, `HNNExtension.equiv_eq_conj`, `MonoidWithZeroHom.valueGroup.mk_mul`, `val_unitsCentralizerEquiv_apply_coe`, `SpecialLinearGroup.centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq`, `Equiv.altCongrHom_apply_coe`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `HNNExtension.inv_t_mul_of`, `HNNExtension.toSubgroupEquiv_neg_one`, `val_list_prod`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_strictMono`, `coe_equivMapOfInjective_apply`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `MulAction.stabilizerEquivStabilizer_compTriple`, `centerCongr_apply_coe`, `unitarySubgroupUnitsEquiv_apply_coe`, `MulEquiv.restrictRootsOfUnity_symm`, `comap_injective_isMulCommutative`, `MulEquiv.subgroupCongr_apply`, `centerToMulOpposite_apply_coe`, `Ideal.stabilizerEquiv_symm_apply_smul`, `MonoidHom.restrictHomKerEquiv_symm_coe_apply`, `normalizerMonoidHom_ker`, `MonoidHom.range_isMulCommutative`, `InfiniteGalois.mulEquivToLimit_symm_continuous`, `WithVal.strictMono_valueGroupOrderIso₀`, `Monoid.PushoutI.NormalWord.cons_head`, `MulEquiv.restrictRootsOfUnity_coe_apply`, `MulAction.stabilizerEquivStabilizer_apply`, `InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup`, `WithVal.strictMono_valueGroupOrderIso₀_symm`, `ValuationSubring.coe_unitGroupMulEquiv_apply`, `subgroupOfEquivOfLe_symm_apply_coe_coe`, `WithVal.valueGroupEquiv_apply`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow'`, `MulChar.restrict_ofUnitHom`, `HNNExtension.NormalWord.unitsSMul_one_group_smul`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `commGroup_isMulCommutative`, `Ideal.inertiaEquiv_apply_smul`, `SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply`, `Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe`, `ProfiniteGrp.limit_mul_val`, `Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe`, `val_centerUnitsEquivUnitsCenter_symm_apply_coe`, `zpowers_isMulCommutative`, `HNNExtension.of_mul_t`, `topEquiv_symm_apply_coe`, `normalizerMonoidHom_apply_apply_coe`, `HNNExtension.of_mul_inv_t`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `Set.val_unitEquivUnitsInteger_apply_coe`, `SubMulAction.ofFixingSubgroup_of_eq_apply`, `Submonoid.val_unitsEquivUnitsType_apply_coe`, `Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_apply`, `Submonoid.val_inv_unitsEquivUnitsType_apply_coe`, `instIsMulCommutativeSubtypeMemSubgroupOfIsCyclic`, `surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow`, `val_unitsCentralizerEquiv_symm_apply_coe`, `isNilpotent_of_finite_tfae`, `Submodule.unitsQuotEquivRelPic_symm_apply`, `Ideal.inertiaEquiv_symm_apply_smul`, `HNNExtension.t_mul_of`, `val_centerUnitsEquivUnitsCenter_apply_coe`, `coe_mul`, `isZGroup_iff_exists_mulEquiv`, `HahnSeries.pow_add`, `Valuation.IsEquiv.orderMonoidIso_trans`, `WithVal.strictMono_valueGroupEquiv_symm`, `subgroupOfContinuousMulEquivOfLe_apply`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply`, `ClassGroup.equivPic_symm_apply`, `SubMulAction.ofStabilizer.conjMap_comp`, `HNNExtension.toSubgroupEquiv_neg_apply`, `ValuationSubring.principalUnitGroupEquiv_apply`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow'`, `MonoidHom.ofLeftInverse_apply`, `Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity`, `isMulCommutative_closure`, `DomMulAct.stabilizerMulEquiv_apply`, `MulAction.stabilizerEquivStabilizer_one`, `subgroupOfContinuousMulEquivOfLe_symm_apply`, `ValuationSubring.coe_unitGroupMulEquiv_symm_apply`, `MulAction.stabilizerEquivStabilizer_symm`, `WithVal.valueGroupOrderIso₀_symm_restrict`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `Int.subgroup_index_ne_zero_iff`, `SubMulAction.fixingSubgroupEquivFixingSubgroup_coe_apply`, `commProb_subgroup_le`, `MonoidHom.ofInjective_apply`, `MulEquiv.coe_subgroupMap_apply`, `Valuation.IsEquiv.orderMonoidIso_eq_refl`, `rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val`, `SubMulAction.ofFixingSubgroup_of_eq_bijective`, `Equiv.Perm.Basis.ofPermHomFun_mul`, `ValuativeRel.valuation_lt_symm_orderMonoidIso`, `rootsOfUnityCircleEquiv_apply`, `IsComplement'.QuotientMulEquiv_symm_apply`, `SemidirectProduct.mulEquivSubgroup_apply`, `MulAut.conjNormal_inv_apply`, `subgroupOfEquivOfLe_apply_coe`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `autEquivRootsOfUnity_apply_rootOfSplit`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply`, `SemidirectProduct.mulEquivSubgroup_symm_apply`, `le_centralizer_iff_isMulCommutative`, `IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat`, `SubMulAction.ofStabilizer.conjMap_bijective`, `ValuativeRel.restrict_lt_orderMonoidIso`, `MulAction.stabilizerEquivStabilizer_inv`, `MulAction.IwasawaStructure.is_comm`, `equivSMul_symm_apply_coe`, `IsComplement'.QuotientMulEquiv_apply`, `HNNExtension.equiv_symm_eq_conj`, `MulEquiv.subgroupMap_symm_apply`, `val_rootsOfUnityEquivOfPrimitiveRoots_apply_coe`, `ClassGroup.equivPic_apply`, `Submonoid.val_unitsEquivUnitsType_symm_apply_coe`, `Valuation.IsEquiv.orderMonoidIso_spec`, `normalizerMonoidHom_apply_symm_apply_coe`, `instIsMulCommutative_closure`, `Unitization.val_unitsFstOne_mulEquiv_quasiregular_apply`, `IsComplement.equiv_mul_left`, `SchurZassenhausInduction.step7`, `centerToMulOpposite_symm_apply_coe`, `WithVal.strictMono_valueGroupEquiv`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zero`, `MonoidHom.apply_ofInjective_symm`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_strictMono`, `SubMulAction.ofStabilizer.conjMap_apply`, `IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int`, `topEquiv_apply`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `rootsOfUnityEquivOfPrimitiveRoots_symm_apply`, `ValuationSubring.coe_unitGroupToResidueFieldUnits_apply`, `smul_diff'`, `SubMulAction.ofFixingSubgroup_insert_map_bijective`, `MulEquiv.subgroupCongr_symm_apply`, `SubMulAction.conjMap_ofFixingSubgroup_bijective`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply_of_finrank_le_one`, `IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow`, `Valuation.IsEquiv.orderMonoidIso_symm`, `ValuationSubring.principalUnitGroup_symm_apply`, `map_isMulCommutative`, `SemidirectProduct.monoidHomSubgroup_apply`, `SubMulAction.conjMap_ofFixingSubgroup_coe_apply`, `Ideal.stabilizerEquiv_apply_smul`, `Submodule.unitsQuotEquivRelPic_apply_coe`, `center.isMulCommutative`, `autEquivRootsOfUnity_smul`, `MulAut.conjNormal_apply`
`normalizer` 📖	CompOp	56 math math: `mem_normalizer_iff''`, `subgroupOf_normalizer_eq`, `Sylow.normalizer_normalizer`, `MulAction.right_quotientAction`, `Sylow.normalizer_sup_eq_top'`, `le_normalizer_comap`, `unop_normalizer`, `normalizer_le_normalizer_sup_normal`, `Sylow.smul_eq_iff_mem_normalizer`, `Sylow.prime_pow_dvd_card_normalizer`, `conjAct_pointwise_smul_iff`, `Sylow.stabilizer_eq_normalizer`, `subset_normalizer_of_normal`, `normalizer_le_normalizer_sup_of_normalizer_le_right`, `normal_subgroupOf_iff_le_normalizer_inf`, `op_normalizer`, `normalizerMonoidHom_ker`, `Sylow.instFiniteQuotientSubgroupNormalizer`, `sylow_mem_fixedPoints_iff`, `comap_normalizer_eq_of_surjective`, `normalizer_eq_top`, `Sylow.conj_eq_normalizer_conj_of_mem`, `center_le_normalizer`, `Sylow.normalizer_le_centralizer_or_le_commutator`, `le_normalizer`, `map_normalizer_eq_of_bijective`, `normalizerMonoidHom_apply_apply_coe`, `le_normalizer_of_normal_subgroupOf`, `normal_subgroupOf_iff_le_normalizer`, `normalizer_le_normalizer_sup_of_normalizer_le_left`, `mem_normalizer_iff`, `normalizer_eq_top_iff`, `normalizer_inf_normalizer_le_normalizer_sup`, `Sylow.normalizer_sup_eq_top`, `Sylow.card_quotient_normalizer_modEq_card_quotient`, `le_normalizer_of_normal`, `mem_normalizer_fintype`, `SemidirectProduct.mulEquivSubgroup_apply`, `IsPGroup.inf_normalizer_sylow`, `mem_normalizer_iff'`, `SemidirectProduct.mulEquivSubgroup_symm_apply`, `Sylow.prime_dvd_card_quotient_normalizer`, `normal_in_normalizer`, `Sylow.card_eq_card_quotient_normalizer`, `normalizerMonoidHom_apply_symm_apply_coe`, `inf_normalizer_le_normalizer_inf`, `comap_normalizer_eq_of_le_range`, `Sylow.conj_eq_normalizer_conj_of_mem_centralizer`, `IsCyclic.normalizer_le_centralizer`, `Sylow.mem_fixedPoints_mul_left_cosets_iff_mem_normalizer`, `le_normalizer_map`, `Sylow.card_normalizer_modEq_card`, `Sylow.card_eq_index_normalizer`, `map_equiv_normalizer_eq`, `SemidirectProduct.monoidHomSubgroup_apply`, `smul_coe`
`npow` 📖	CompOp	3 math math: `coe_pow`, `rootsOfUnity.coe_pow`, `smul_diff'`
`ofClass` 📖	CompOp	1 math math: `coe_ofClass`
`ofDiv` 📖	CompOp	—
`one` 📖	CompOp	19 math math: `eq_one_of_smul_eq_one`, `ProfiniteGrp.limit_one_val`, `Valuation.restrict_eq_one_iff`, `Valuation.IsRankOneDiscrete.generator'_lt_one`, `Function.MulExact.monoidHom_rangeRestrict`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff`, `val_list_prod`, `alternatingGroup.coe_kleinFour_of_card_eq_four`, `Valuation.restrict_lt_one_iff`, `noncommPiCoprod_mulSingle`, `Function.MulExact.iff_monoidHom_rangeRestrict`, `alternatingGroup.coe_two_sylow_of_card_eq_four`, `coe_one`, `ModularGroup.coe_one`, `Valuation.restrict_le_one_iff`, `Equiv.Perm.Basis.ofPermHomFun_one`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply_of_finrank_le_one`, `mk_eq_one`
`setNormalizer` 📖	CompOp	—
`subtype` 📖	CompOp	95 math math: `map_focalSubgroupOf`, `Ideal.Quotient.map_ker_stabilizer_subtype`, `subtype_comp_inclusion`, `MapSubtype.orderIso_apply_coe`, `Rep.coindResAdjunction_counit_app`, `SubMulAction.ofFixingSubgroup_equivariantMap_injective`, `Rep.coindToInd_of_support_subset_orbit`, `DiscreteTiling.PlacedTile.ext_iff_of_preimage`, `Rep.indCoindNatIso_hom_app`, `map_subtype_inj`, `Rep.coindToInd_indToCoind`, `groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top`, `Rep.instIsLeftAdjointSubtypeMemSubgroupCoindFunctorSubtype`, `Function.MulExact.monoidHom_rangeRestrict`, `Representation.Coinvariants.le_comap_ker`, `groupHomology.H1CoresCoinfOfTrivial_X₁`, `DiscreteTiling.PlacedTile.ext_iff_of_exists`, `Representation.instIsTrivialSubtypeMemSubgroupSubmoduleInvariantsCompLinearMapIdSubtypeToInvariants`, `DiscreteTiling.PlacedTile.smul_mk_mk`, `DiscreteTiling.PlacedTile.ext_iff`, `IsSubnormal.trans'`, `SubMulAction.fixingSubgroup_of_insert`, `subtype_apply`, `groupHomology.H1CoresCoinf_X₁`, `coe_subtype`, `map_subgroupOf_eq_of_le`, `subtype_injective`, `ker_subtype`, `Rep.coindResAdjunction_unit_app`, `MonoidHom.subtype_comp_rangeRestrict`, `TopologicalGroup.IsSES.ofClosedSubgroup`, `Rep.coindToInd_apply`, `Rep.resIndAdjunction_homEquiv_symm_apply`, `map_subtype_le_map_subtype`, `groupCohomology.H1InfRes_X₃`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `DiscreteTiling.PlacedTile.coe_mk_mk`, `QuotientGroup.mk'_comp_subtype`, `Rep.resIndAdjunction_homEquiv_apply`, `Rep.coindResAdjunction_homEquiv_apply`, `Rep.coinvariantsShortComplex_f`, `Rep.resIndAdjunction_counit_app`, `DiscreteTiling.PlacedTile.smul_mk_coe`, `map_subtype_lt_map_subtype`, `subgroupOf_map_subtype`, `ConjAct.normal_of_characteristic_of_normal`, `Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants`, `QuotientGroup.strictMono_comap_prod_image`, `Function.MulExact.iff_monoidHom_rangeRestrict`, `map_subtype_le`, `lowerCentralSeries_map_subtype_le`, `groupCohomology.H1InfRes_g`, `Representation.le_comap_invariants`, `Rep.indCoindNatIso_inv_app`, `Rep.coindResAdjunction_homEquiv_symm_apply`, `Rep.indCoindIso_hom_hom_toLinearMap`, `goursat_surjective`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply`, `Rep.indCoindIso_inv_hom_toLinearMap`, `groupHomology.H1CoresCoinfOfTrivial_f`, `Rep.instPreservesProjectiveObjectsSubtypeMemSubgroupResFunctorSubtype`, `Rep.instPreservesEpimorphismsSubtypeMemSubgroupCoindFunctorSubtype`, `Sylow.normalizer_sup_eq_top`, `Sylow.card_quotient_normalizer_modEq_card_quotient`, `SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective`, `Representation.toCoinvariants_mk`, `Rep.quotientToCoinvariantsFunctor_map_hom_toLinearMap`, `Sylow.exists_comap_subtype_eq`, `SubMulAction.of_fixingSubgroupEmpty_mapScalars_surjective`, `Rep.resIndAdjunction_unit_app`, `Rep.indToCoind_coindToInd`, `subtype_range`, `closure_preimage_eq_top`, `DiscreteTiling.PlacedTile.coe_mk_coe`, `coe_subgroupOf`, `card_subtype`, `IsPGroup.comap_subtype`, `image_commutatorSet_closureCommutatorRepresentatives`, `range_subtype`, `Sylow.prime_dvd_card_quotient_normalizer`, `QuotientGroup.ker_le_range_iff`, `ValuationSubring.ker_unitGroupToResidueFieldUnits`, `commute_subtype_of_commute`, `Rep.instIsRightAdjointSubtypeMemSubgroupIndFunctorSubtype`, `groupHomology.H1CoresCoinf_f`, `index_map_subtype`, `Equiv.Perm.OnCycleFactors.kerParam_range_eq`, `QuotientGroup.strictMono_comap_prod_map`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk`, `AddSubgroup.inertia_map_subtype`, `goursat`, `comap_subtype`, `alternatingGroup.ofSubtype_comp_subtype`, `Rep.quotientToCoinvariantsFunctor_obj_V`, `map_subtype_commutator`
`toCommGroup` 📖	CompOp	7 math math: `Valuation.nonempty_rankOne_iff_mulArchimedean`, `subgroupOf_map_powMonoidHom_eq_range`, `toIsOrderedMonoid`, `val_finset_prod`, `MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid`, `NumberField.IsCMField.map_unitsMulComplexConjInv_torsion`, `val_multiset_prod`
`toGroup` 📖	CompOp	650 math math: `map_focalSubgroupOf`, `SubMulAction.ofStabilizer.isPretransitive_iff_of_conj`, `Valuation.mem_nhds_zero_iff`, `Sylow.isPGroup'`, `MulAction.isPreprimitive_of_fixingSubgroup_empty_iff`, `SubMulAction.ofStabilizer.conjMap_comp_apply`, `ModularGroup.SLOnGLPos_smul_apply`, `SubMulAction.ofFixingSubgroup_insert_map_apply`, `instNormalSubtypeMemFocalSubgroupOf`, `Ideal.Quotient.map_ker_stabilizer_subtype`, `WithVal.valueGroupOrderIso₀_symm_apply`, `prod_subgroupOf_prod_normal`, `MonoidHom.ker_transferSylow_disjoint`, `IsCyclic.isComplement'`, `subgroupOfContinuousMulEquivOfLe_toMulEquiv`, `MonoidHom.transferSylow_eq_pow`, `subtype_comp_inclusion`, `MapSubtype.orderIso_apply_coe`, `Equiv.Perm.Basis.toCentralizer_equivariant`, `MonoidHom.restrictHomKerEquiv_apply_coe`, `subgroupOf_normalizer_eq`, `SubMulAction.ofStabilizer_carrier`, `Rep.coindResAdjunction_counit_app`, `MeasureTheory.Subgroup.smulInvariantMeasure`, `SubMulAction.ofFixingSubgroup_equivariantMap_injective`, `Rep.coindToInd_of_support_subset_orbit`, `IsPGroup.sylow_mem_fixedPoints_iff`, `DiscreteTiling.PlacedTile.ext_iff_of_preimage`, `alternatingGroup.isPreprimitive_of_three_le_card`, `normal_subgroupOf_iff`, `AddSubgroup.subgroupOf_inertia`, `fixedPoints_subgroup_iSup`, `Matrix.SpecialLinearGroup.toGLPos_injective`, `SubMulAction.ofStabilizer.conjMap_comp_inv_apply`, `coe_inclusion`, `Rep.indToCoindAux_self`, `MulAut.conjNormal_val`, `exists_smul_eq`, `focalSubgroupOf.pow_index_surjective`, `Rep.indCoindNatIso_hom_app`, `conj_smul_subgroupOf`, `Equiv.Perm.Basis.toCentralizer_apply`, `Group.IsPerfect.top_iff`, `SlashInvariantForm.quotientFunc_mk`, `map_subtype_inj`, `isCoatom_map`, `QuotientGroup.rangeKerLift_injective`, `subgroup_solvable_of_solvable`, `Equiv.Perm.disjoint_ofSubtype_noncommPiCoprod`, `transferFocal_surjective`, `subgroupOf_isMulCommutative`, `MonoidWithZeroHom.ValueGroup₀.monoidWithZeroHom_strictMono`, `WithVal.valueGroupOrderIso₀_apply`, `RootPairing.span_orbit_eq_top`, `Rep.coindToInd_indToCoind`, `groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top`, `IsGaloisGroup.fixedPoints_top`, `Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff'`, `alternatingGroup.card_two_sylow_of_card_eq_four`, `SubMulAction.ofFixingSubgroup_of_inclusion_injective`, `Rep.instIsLeftAdjointSubtypeMemSubgroupCoindFunctorSubtype`, `MonoidHom.ker_transferSylow_isComplement'`, `Valued.toUniformSpace_eq`, `RootPairing.range_weylGroup_coweightHom`, `center.smulCommClass_right`, `MulAction.quotient_out_smul_fixedPoints`, `Ideal.torsionMapQuot_apply`, `NumberField.HeightOneSpectrum.rankOne_hom'_def`, `Complex.isQuotientCoveringMap_npow`, `MulAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `alternatingGroup.kleinFour_card_of_card_eq_four`, `subgroupOf_eq_top`, `SubMulAction.nat_card_ofStabilizer_add_one_eq`, `ModularForm.norm_eq_zero_iff`, `Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe`, `IsSubnormal.iff_eq_top_or_exists`, `Equiv.Perm.OnCycleFactors.kerParam_range_card`, `Equiv.Perm.OnCycleFactors.kerParam_injective`, `MulAction.right_quotientAction`, `index_eq_sum_minimalPeriod`, `SubMulAction.ofStabilizer.inv_conjMap_comp_apply`, `quotientEquivProdOfLE_apply`, `isFiniteRelIndex_iff_finiteIndex`, `MulAction.orbit_subgroup_subset`, `subgroupOf_isOpen`, `SlashInvariantForm.quotientFunc_smul`, `instIsMulTorsionFree`, `MonoidHom.subgroupOf_range_eq_of_le`, `subgroupOf_self`, `Function.MulExact.monoidHom_rangeRestrict`, `InfiniteGalois.toAlgEquivAux_eq_proj_of_mem`, `smulCommClass_right`, `MonoidHom.ker_rangeRestrict`, `AlternatingGroup.isPreprimitive_of_three_le_card`, `MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff'`, `Representation.Coinvariants.le_comap_ker`, `CuspForm.coe_trace`, `Ideal.rootsOfUnityMapQuot_injective`, `groupHomology.H1CoresCoinfOfTrivial_X₁`, `SubMulAction.map_ofFixingSubgroupUnion_def`, `DiscreteTiling.PlacedTile.ext_iff_of_exists`, `ValuativeRel.ValueGroupWithZero.embed_strictMono`, `SubMulAction.ofStabilizer.isMultiplyPretransitive_iff`, `Ideal.Quotient.stabilizerHom_surjective`, `Equiv.Perm.OnCycleFactors.nat_card_range_toPermHom`, `IsGaloisGroup.quotientMap`, `normal_subgroupOf_sup_of_le_normalizer`, `rank_closure_finite_le_nat_card`, `alternatingGroup.normalClosure_swap_mul_swap_five`, `Valuation.hasBasis_nhds_zero`, `NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_apply`, `IsTorsion.subgroup`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_one_iff`, `Representation.instIsTrivialSubtypeMemSubgroupSubmoduleInvariantsCompLinearMapIdSubtypeToInvariants`, `MulAction.isBlock_top`, `orbit_subgroup_eq_self_of_mem`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_valuation_eq_restrict₀`, `alternatingGroup.subsingleton_two_sylow`, `IsPGroup.comap_of_ker_isPGroup`, `CongruenceSubgroup.Gamma1_mem'`, `MulAction.ofFixingSubgroup.isMultiplyPreprimitive`, `alternatingGroup.isCoatom_stabilizer_singleton`, `Valued.is_topological_valuation`, `Equiv.Perm.IsThreeCycle.mem_commutator_alternatingGroup`, `SubMulAction.ofStabilizer.isPretransitive_iff`, `MonoidHom.not_dvd_card_ker_transferSylow`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroup`, `Group.IsPerfect.instSubtypeMemSubgroupTop`, `ValuativeRel.ValueGroupWithZero.leftInverse_embedding_orderMonoidIso`, `MonoidHom.transferSylow_restrict_eq_pow`, `alternatingGroup.closure_isThreeCycles_eq_top`, `IsGaloisGroup.fixedPoints_of_isGaloisGroup`, `quotientSubgroupOfEmbeddingOfLE_apply_mk`, `isUniformGroup`, `IsGaloisGroup.of_fixedPoints_eq`, `MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff`, `RootPairing.weylGroup_apply_root`, `alternatingGroup.characteristic_kleinFour`, `Valuation.restrict_lt_iff_lt_embedding`, `MulAction.IsBlock.orbit_of_normal`, `DiscreteTiling.PlacedTile.smul_mk_mk`, `mem_closure_isSwap`, `IsDecompositionField.toIsGaloisGroup`, `MonoidWithZeroHom.ValueGroup₀.embedding_unit_pos`, `rank_congr`, `Set.powersetCard.isPretransitive_alternatingGroup`, `DiscreteTiling.PlacedTile.ext_iff`, `alternatingGroup.kleinFour_isKleinFour`, `IsSubnormal.trans'`, `SubMulAction.fixingSubgroup_of_insert`, `alternatingGroup.mem_range_ofSubtype_iff`, `closure_closure_coe_preimage`, `orderOf_mk`, `subtype_apply`, `SubMulAction.ofFixingSubgroup_carrier`, `alternatingGroup.normalClosure_finRotate_five`, `groupHomology.H1CoresCoinf_X₁`, `smul_diff_smul'`, `coe_subtype`, `rank_le_index_mul_rank`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_of_ne_zero`, `map_subgroupOf_eq_of_le`, `subtype_injective`, `Valuation.subgroups_basis`, `alternatingGroup.kleinFour_eq_commutator`, `Rep.indToCoindAux_fst_mul_inv`, `Ideal.stabilizerEquiv_symm_apply_smul`, `DiscreteTiling.Prototile.ext_iff`, `Valuation.restrict_le_iff_le_embedding`, `MulAction.isPreprimitive_ofFixingSubgroup_conj_iff`, `instIsTopologicalGroupSubtypeMem`, `instFiniteIndex_subgroupOf`, `IsPGroup.to_subgroup`, `Equiv.Perm.Basis.card_ofPermHom_support`, `SubMulAction.exists_smul_of_last_eq`, `alternatingGroup.center_eq_bot`, `alternatingGroup.stabilizer.surjective_toPerm`, `IsGaloisGroup.fixedPoints_fixingSubgroup`, `NumberField.HeightOneSpectrum.NumberField.rankOne_hom'_def`, `Equiv.Perm.Basis.ofPermHom_apply`, `subgroupOf_map_powMonoidHom_eq_range`, `ModularGroup.SL_to_GL_tower`, `normal_subgroupOf_iff_le_normalizer_inf`, `SubMulAction.ofStabilizer.isMultiplyPretransitive_iff_of_conj`, `relIndex_subgroupOf`, `Group.IsPerfect.map`, `IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup`, `Rep.indToCoindAux_comm`, `MonoidHom.restrictHomKerEquiv_symm_coe_apply`, `Valuation.RankOne.exists_val_lt`, `Circle.isQuotientCoveringMap_zpow`, `noncommPiCoprod_apply`, `normalizerMonoidHom_ker`, `MonoidHom.restrict_range`, `Valued.hasBasis_nhds_zero`, `ker_subtype`, `sylow_mem_fixedPoints_iff`, `isInertiaField_iff`, `card_commutatorSet_closureCommutatorRepresentatives`, `isQuotientCoveringMap_npow`, `isDecompositionField_iff`, `Rep.coindResAdjunction_unit_app`, `alternatingGroup.closure_cycleType_eq_two_two_eq_top`, `MulAction.IsBlock.orbit_stabilizer_eq`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroupOp`, `NumberField.IsCMField.indexRealUnits_mul_eq`, `MonoidHom.subtype_comp_rangeRestrict`, `MeasureTheory.Measure.IsMulLeftInvariant.quotientMeasureEqMeasurePreimage_of_set`, `Ideal.Quotient.stabilizerHom_surjective_of_profinite`, `TopologicalGroup.IsSES.ofClosedSubgroup`, `NumberField.mixedEmbedding.fundamentalCone.integerSetTorsionSMul_stabilizer`, `subgroupOfEquivOfLe_symm_apply_coe_coe`, `inf_subgroupOf_inf_normal_of_left`, `SubMulAction.disjoint_val_image`, `QuotientGroup.rangeKerLift_surjective`, `IsPGroup.to_le`, `Rep.coindToInd_apply`, `Valuation.RankOne.strictMono`, `subgroupOf_eq_bot`, `alternatingGroup.coe_kleinFour_of_card_eq_four`, `MulChar.restrict_ofUnitHom`, `ValuativeRel.ValueGroupWithZero.embed_valuation_eq_restrict₀`, `Valued.coe_valuation_eq_rankOne_hom_comp_valuation`, `subgroupIsFreeOfIsFree`, `Rep.resIndAdjunction_homEquiv_symm_apply`, `quotientEquivProdOfLE_symm_apply`, `fg_of_index_ne_zero`, `Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux`, `SubMulAction.nat_card_ofStabilizer_eq`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_mk`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_range_eq_top`, `rank_commutator_le_card`, `ker_inclusion`, `MulAction.coe_quotient_smul_fixedPoints`, `MulAction.IsBlock.of_subgroup_of_conjugate`, `Ideal.inertiaEquiv_apply_smul`, `NumberField.IsCMField.unitsMulComplexConjInv_apply_torsion`, `map_subtype_le_map_subtype`, `Equiv.Perm.Basis.ofPermHom_mem_centralizer`, `MulAction.finite_quotient_of_finite_quotient_of_finite_quotient`, `IsGaloisGroup.fixingSubgroup_fixedPoints`, `IsFractionRing.stabilizerHom_surjective`, `InfiniteGalois.proj_adjoin_singleton_val`, `groupCohomology.H1InfRes_X₃`, `SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply`, `MonoidWithZeroHom.ValueGroup₀.embedding_apply`, `IsZGroup.instSubtypeMemSubgroup`, `DiscreteTiling.PlacedTile.coe_mk_mk`, `Ideal.Quotient.stabilizerHom_apply`, `NumberField.mixedEmbedding.fundamentalCone.quotIntNorm_apply`, `Rep.indToCoindAux_mul_fst`, `Group.IsPerfect.range`, `IsPGroup.to_sup_of_normal_left'`, `quotientEquivProdOfLE'_symm_apply`, `QuotientGroup.mk'_comp_subtype`, `IsPGroup.ker_isPGroup_of_injective`, `IsGaloisGroup.fixedPoints_bot`, `Valuation.cauchy_iff`, `IsPGroup.to_inf_left`, `injective_noncommPiCoprod_of_iSupIndep`, `MulAction.isPreprimitive_fixingSubgroup_insert_iff`, `QuotientGroup.quotientMapSubgroupOfOfLe_mk`, `alternatingGroup.isConj_of`, `Rep.resIndAdjunction_homEquiv_apply`, `Valuation.IsRankOneDiscrete.embedding_generator'`, `Equiv.Perm.OnCycleFactors.val_centralizer_smul`, `normalizerMonoidHom_apply_apply_coe`, `IsQuotientCoveringMap.subgroup_congr`, `exists_leftTransversal_of_FiniteIndex`, `rank_closure_finset_le_card`, `bijective_rootsOfUnityAddChar`, `ValuativeRel.ValueGroupWithZero.orderMonoidIso_embed`, `SubMulAction.ofFixingSubgroup_of_eq_apply`, `Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk`, `MonoidHom.transfer_center_eq_pow`, `instMeasurableConstSMul`, `noncommPiCoprod_mulSingle`, `swap_mem_closure_isSwap`, `subgroupOf_sup`, `SubMulAction.nat_card_ofStabilizer_eq_add_one`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_eq_zero_iff`, `Rep.coindResAdjunction_homEquiv_apply`, `MonoidHom.coe_comp_rangeRestrict`, `instIsDecompositionFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupStabilizerIdealOfIsGalois`, `Valuation.embedding_restrict`, `quotientSubgroupOfMapOfLE_apply_mk`, `RootPairing.isSimpleModule_weylGroupRootRep`, `Rep.coinvariantsShortComplex_f`, `Rep.resIndAdjunction_counit_app`, `DiscreteTiling.PlacedTile.smul_mk_coe`, `RootPairing.InvariantForm.apply_weylGroup_smul`, `Equiv.Perm.Basis.toPermHom_apply_toCentralizer`, `quotientiInfSubgroupOfEmbedding_apply_mk`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive`, `instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient`, `RootPairing.isSimpleModule_weylGroupRootRep_iff`, `subgroupOf_mono`, `MulAction.finite_quotient_of_pretransitive_of_finite_quotient`, `IsPGroup.to_sup_of_normal_right`, `MulAction.isPreprimitive_stabilizer_subgroup`, `SubMulAction.ENat_card_ofStabilizer_add_one_eq`, `quotientEquivSigmaZMod_apply`, `Valued.cauchy_iff`, `exponent_toSubmonoid`, `exponent_top`, `Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iff`, `surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar`, `Equiv.Perm.Basis.ofPermHom_support`, `map_subtype_lt_map_subtype`, `MulAction.orbitRel.Quotient.subgroup_quotient_eq_iff`, `coe_smul_fixedPoints_of_normal`, `Action.FintypeCat.quotientToEndHom_mk`, `QuotientGroup.orbit_eq_out_smul`, `MulAction.mem_subgroup_orbit_iff`, `subgroupOf_map_subtype`, `ConjAct.normal_of_characteristic_of_normal`, `Valuation.IsRankOneDiscrete.generator'_zpowers_eq_top`, `IsConj.normalClosure_eq_top_of`, `alternatingGroup.subgroup_eq_top_of_isPreprimitive`, `SubMulAction.notMem_val_image`, `MulAction.orbitZPowersEquiv_symm_apply`, `Representation.instIsTrivialSubtypeMemSubgroupCoinvariantsCompLinearMapIdSubtypeToCoinvariants`, `isPretransitive_of_stabilizer_lt`, `Rep.indToCoindAux_mul_snd`, `Ideal.inertiaEquiv_symm_apply_smul`, `instIsScalarTowerSubtypeMem`, `isPerfect_iff`, `alternatingGroup.two_sylow_eq_kleinFour_of_card_eq_four`, `QuotientGroup.strictMono_comap_prod_image`, `Matrix.SpecialLinearGroup.coe_GLPos_neg`, `Circle.isQuotientCoveringMap_npow`, `isQuotientCoveringMap_zpow`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_isDiscrete_ker_monoidHom`, `Valuation.restrict_def`, `isZGroup_iff_exists_mulEquiv`, `MulAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingSubgroup`, `center.smulCommClass_left`, `exists_finset_card_le_mul`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_surjective`, `NumberField.IsCMField.unitsMulComplexConjInv_ker`, `sup_subgroupOf_eq`, `normal_subgroupOf`, `MulAction.isMultiplyPreprimitive_iff`, `isNilpotent`, `Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply`, `MonoidHom.rangeRestrict_surjective`, `transferTransversal_apply'`, `normal_subgroupOf_iff_le_normalizer`, `continuousSMul`, `subgroupOfContinuousMulEquivOfLe_apply`, `RootPairing.range_weylGroupToPerm`, `Function.MulExact.iff_monoidHom_rangeRestrict`, `AlternatingGroup.isMultiplyPretransitive`, `alternatingGroup.exists_mem_stabilizer_smul_eq`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply`, `alternatingGroup.coe_two_sylow_of_card_eq_four`, `Group.rank_range_le`, `NumberField.IsCMField.unitsMulComplexConjInv_apply`, `MulAction.orbitRel_subgroupOf`, `SubMulAction.mem_ofStabilizer_iff`, `map_subtype_le`, `SubMulAction.ofStabilizer.snoc_castSucc`, `IsFiniteRelIndex.to_finiteIndex_subgroupOf`, `IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_HaarMeasure`, `lowerCentralSeries_map_subtype_le`, `SubMulAction.mem_ofFixingSubgroup_insert_iff`, `Equiv.Perm.isPretransitive_of_isCycle_mem`, `MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `Valuation.toTopologicalSpace_eq`, `SlashInvariantForm.coe_trace`, `Equiv.Perm.OnCycleFactors.coe_toPermHom`, `IsFractionRing.stabilizerHom_apply_apply_mk`, `MonoidHom.transferCenterPow_apply`, `commutator_alternatingGroup_eq_top`, `MonoidHom.coe_rangeRestrict`, `SubMulAction.ofStabilizer.conjMap_comp`, `groupCohomology.H1InfRes_g`, `instFGSubtypeMemCommutator`, `IsGaloisGroup.subgroup_iff`, `RootPairing.weylGroup.ofIdx_smul`, `Representation.le_comap_invariants`, `Group.fg_iff_subgroup_fg`, `Rep.indCoindNatIso_inv_app`, `instIsMulCommutativeQuotientSubtypeMemFocalSubgroupOf`, `MulAction.zpowersQuotientStabilizerEquiv_symm_apply`, `smul_def`, `quotient_finite_of_isOpen'`, `ValuationSubring.surjective_unitGroupToResidueFieldUnits`, `alternatingGroup.range_ofSubtype`, `instMeasurableSMul`, `AlternatingGroup.isPretransitive_of_three_le_card`, `IsGaloisGroup.intermediateField`, `finite_quotient_of_pretransitive_of_index_ne_zero`, `Rep.coindResAdjunction_homEquiv_symm_apply`, `bot_subgroupOf`, `Normal.subgroupOf`, `Rep.indCoindIso_hom_hom_toLinearMap`, `IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply`, `MulAction.orbitZPowersEquiv_symm_apply'`, `alternatingGroup.stabilizer_isPreprimitive`, `IsDedekindDomain.selmerGroup.fromUnit_ker`, `SubMulAction.ofStabilizer.isMultiplyPretransitive`, `SubMulAction.ofFixingSubgroup.append_right`, `goursat_surjective`, `InfiniteGalois.toAlgEquivAux_eq_liftNormal`, `Ideal.rootsOfUnityMapQuot_apply`, `Valuation.hasBasis_nhds`, `Equiv.Perm.IsThreeCycle.alternating_normalClosure`, `Valued.mem_nhds_zero`, `Valuation.RankLeOne.exists_val_lt`, `instFiniteElemSubtypeMemSubgroupClosureCommutatorRepresentativesCommutatorSet`, `ker_subgroupMap`, `Matrix.SpecialLinearGroup.coe_to_GLPos_to_GL_det`, `inclusion_inj`, `Valued.mem_nhds`, `alternatingGroup.normal_kleinFour`, `card_commutator_closureCommutatorRepresentatives`, `Ideal.Quotient.ker_stabilizerHom`, `ConjAct.coe_smul`, `MonoidHom.rangeRestrict_injective_iff`, `cosetToCuspOrbit_apply_mk`, `transferFocal_eq_pow`, `Group.isNilpotent_top`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply`, `Rep.indCoindIso_inv_hom_toLinearMap`, `alternatingGroup.isSimpleGroup_five`, `Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff`, `Normal.of_map_subtype`, `isSimpleGroup_iff`, `IsDedekindDomain.selmerGroup.fromUnitLift_injective`, `comap_inclusion_subgroupOf`, `alternatingGroup.isCoatom_stabilizer`, `IsPGroup.to_sup_of_normal_right'`, `fixedPoints_subgroup_sup`, `subgroupOfContinuousMulEquivOfLe_symm_apply`, `fixedPoints_subgroup_antitone`, `inclusion_range`, `ValuativeRel.ValueGroupWithZero.embed_mk`, `IsFundamentalDomain.QuotientMeasureEqMeasurePreimage_smulHaarMeasure`, `Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one`, `Ideal.torsionMapQuot_injective`, `groupHomology.H1CoresCoinfOfTrivial_f`, `MulAction.orbitRel_subgroup_le`, `orbit_subgroup_eq_rightCoset`, `Rep.instPreservesProjectiveObjectsSubtypeMemSubgroupResFunctorSubtype`, `focalSubgroupOf_eq_closure`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_symm_apply`, `ValuativeRel.ValueGroupWithZero.embedding_orderMonoidIso_valuation_eq`, `InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj`, `alternatingGroup.exponent_kleinFour_of_card_eq_four`, `isQuotientCoveringMap_of_comm`, `Valuation.hasBasis_uniformity`, `Valued.toNormedField.norm_def`, `ModularForm.coe_norm`, `CongruenceSubgroup.Gamma1_to_Gamma0_mem`, `IsGaloisGroup.subgroup`, `Valuation.toUniformSpace_eq`, `Rep.instPreservesEpimorphismsSubtypeMemSubgroupCoindFunctorSubtype`, `IsPGroup.to_inf_right`, `Sylow.coe_subtype`, `SubMulAction.ofFixingSubgroup_of_singleton_bijective`, `Valuation.norm_def`, `Equiv.Perm.OnCycleFactors.toPermHom_apply`, `Sylow.smul_subtype`, `Group.closure_finset_fg`, `Set.powersetCard.isPreprimitive_alternatingGroup`, `Sylow.normalizer_sup_eq_top`, `Sylow.card_quotient_normalizer_modEq_card_quotient`, `IsPGroup.of_bot`, `MulAction.subgroup_smul_def`, `SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective`, `quotientiInfSubgroupOfEmbedding_apply`, `normal_subgroupOf_of_le_normalizer`, `Valuation.exists_div_eq_of_unit`, `instProperSMulSubtypeMulOppositeMemSubgroupOpOfIsTopologicalGroupOfIsClosedCoe`, `Representation.toCoinvariants_mk`, `CommGroup.primaryComponent.isPGroup`, `Rep.quotientToCoinvariantsFunctor_map_hom_toLinearMap`, `closure_mul_image_eq_top`, `Sylow.exists_comap_subtype_eq`, `ker_restrict_transferFocal_eq_focalSubgroupOf`, `Matrix.SpecialLinearGroup.coe_GLPos_coe_GL_coe_matrix`, `focalSubgroupOf.mk'_conj_eq`, `rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val`, `ker_transferFocal_inf_eq_focalSubgroup`, `fixingSubgroup_fixedPoints_gc`, `SubMulAction.map_ofFixingSubgroupUnion_bijective`, `SubMulAction.of_fixingSubgroupEmpty_mapScalars_surjective`, `properlyDiscontinuousSMul_of_tendsto_cofinite`, `MonoidWithZeroHom.ValueGroup₀.embedding_restrict₀`, `alternatingGroup.isPretransitive_of_three_le_card`, `SubMulAction.ofFixingSubgroup_of_eq_bijective`, `QuotientGroup.orbit_mk_eq_smul`, `InfiniteGalois.mk_toAlgEquivAux`, `Equiv.Perm.IsThreeCycle.mem_commutatorSet_alternatingGroup`, `Valued.hasBasis_uniformity`, `transferFunction_apply`, `IsInertiaField.toIsGaloisGroup`, `quotientEquivProdOfLE'_apply`, `Rep.resIndAdjunction_unit_app`, `NumberField.IsCMField.indexRealUnits_eq_two_iff`, `codisjoint_subgroupOf_sup`, `LinearEquiv.reduce_mk`, `SubMulAction.not_mem_of_mem_ofFixingSubgroup`, `alternatingGroup.isMultiplyPretransitive`, `Rep.indToCoind_coindToInd`, `subtype_range`, `SemidirectProduct.mulEquivSubgroup_apply`, `MulAction.stabilizer_orbit_eq`, `InfiniteGalois.proj_of_le`, `MonoidWithZeroHom.ValueGroup₀.restrict₀_apply`, `instProperSMulSubtypeMemSubgroupOfIsClosedCoe`, `SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter`, `IsPGroup.map`, `closure_preimage_eq_top`, `subgroupOfEquivOfLe_apply_coe`, `MonoidHom.subgroupMap_surjective`, `IsGaloisGroup.fixedPoints_le_of_le`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply`, `MulAction.isMultiplyPreprimitive_ofStabilizer`, `Equiv.Perm.stabilizer.surjective_toPerm`, `Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer`, `autEquivRootsOfUnity_apply_rootOfSplit`, `ProfiniteGrp.toLimitFun_continuous`, `SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply`, `DiscreteTiling.PlacedTile.coe_mk_coe`, `SemidirectProduct.mulEquivSubgroup_symm_apply`, `finite_quotient_of_finite_quotient_of_index_ne_zero`, `coe_subgroupOf`, `Rep.indToCoindAux_snd_mul_inv`, `transferTransversal_apply''`, `restrictRootsOfUnity_coe_apply`, `card_subtype`, `IsPGroup.comap_subtype`, `image_commutatorSet_closureCommutatorRepresentatives`, `commutator_le_focalSubgroupOf`, `IsPGroup.comap_of_injective`, `range_subtype`, `InfiniteGalois.algEquivToLimit_continuous`, `ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eq`, `top_subgroupOf`, `inclusion_injective`, `SubMulAction.mem_ofFixingSubgroup_iff`, `SubMulAction.ofStabilizer.conjMap_bijective`, `rank_closureCommutatorRepresentatives_le`, `Sylow.prime_dvd_card_quotient_normalizer`, `quotientEquivSigmaZMod_symm_apply`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive'`, `QuotientGroup.ker_le_range_iff`, `IsPGroup.to_sup_of_normal_left`, `MonoidHom.subgroupComap_apply_coe`, `Rep.indToCoindAux_of_not_rel`, `normal_in_normalizer`, `ValuationSubring.ker_unitGroupToResidueFieldUnits`, `instIsInertiaFieldSubtypeMemIntermediateFieldIntermediateFieldAlgEquivSubgroupInertiaOfIsGalois`, `subgroupOf_bot_eq_top`, `MonoidHom.transfer_eq_pow`, `orbit_subgroup_one_eq_self`, `MeasureTheory.leftInvariantIsQuotientMeasureEqMeasurePreimage`, `commute_subtype_of_commute`, `Valuation.restrict_exists_div_eq`, `alternatingGroup.isThreeCycle_isConj`, `Rep.instIsRightAdjointSubtypeMemSubgroupIndFunctorSubtype`, `frattini_nilpotent`, `RootPairing.range_weylGroup_weightHom`, `ModularForm.coe_trace`, `Valuation.RankOne.hom_eq_zero_iff`, `IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup`, `normalizerMonoidHom_apply_symm_apply_coe`, `groupHomology.H1CoresCoinf_f`, `Valuation.RankOne.restrict_RankOne_hom_eq`, `index_map_subtype`, `Sylow.smul_le`, `Equiv.Perm.OnCycleFactors.kerParam_range_eq`, `autAdjoinRootXPowSubC_root`, `mem_subgroupOf`, `MulAction.IsBlock.subgroup`, `MonoidHom.subgroupMap_apply_coe`, `NumberField.IsCMField.map_unitsMulComplexConjInv_torsion`, `QuotientGroup.strictMono_comap_prod_map`, `Valuation.RankLeOne.strictMono'`, `Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia`, `smul_mem_fixedPoints_of_normal`, `ModularGroup.coeHom_apply`, `Valuation.exists_setOf_restrict_le_iff`, `smulCommClass_left`, `MulAction.minimalPeriod_eq_card`, `SubMulAction.ofStabilizer.conjMap_apply`, `closureCommutatorRepresentatives_fg`, `MulAction.IsBlockSystem.of_normal`, `MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot`, `ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk`, `instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra`, `Sylow.mem_fixedPoints_mul_left_cosets_iff_mem_normalizer`, `MulAction.IsBlock.of_orbit`, `AddSubgroup.inertia_map_subtype`, `MonoidHom.subgroupComap_surjective_of_surjective`, `alternatingGroup.stabilizer_subgroup_isPreprimitive`, `ValuationSubring.coe_unitGroupToResidueFieldUnits_apply`, `smul_diff'`, `MonoidWithZeroHom.ValueGroup₀.embedding_strictMono`, `SubMulAction.ofFixingSubgroup_insert_map_bijective`, `IsSubnormal.isSubnormal_iff`, `Equiv.Perm.OnCycleFactors.kerParam_apply`, `Group.fg_range`, `LinearEquiv.reduce_mkQ`, `SlashInvariantForm.coe_norm`, `instFaithfulSMulSubtypeMem`, `noncommPiCoprod_range`, `ZMod.rootsOfUnityAddChar_val`, `SubMulAction.conjMap_ofFixingSubgroup_bijective`, `Valuation.mem_nhds_iff`, `goursat`, `comap_subtype`, `NumberField.IsCMField.index_unitsMulComplexConjInv_range_dvd`, `orbit_fixingSubgroup_compl_subset`, `closure_mul_image_eq_top'`, `nilpotencyClass_le`, `IsSubnormal.subgroupOf`, `pow_exponent_eq_one`, `orderOf_coe`, `Valuation.is_topological_valuation`, `IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual`, `mk_smul`, `IsDedekindDomain.selmerGroup.valuation_ker_eq`, `Equiv.Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom'`, `Equiv.Perm.OnCycleFactors.centralizer_smul_def`, `MonoidHom.ker_restrict`, `SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter`, `alternatingGroup.conj_smul_range_ofSubtype`, `subgroupOf_bot_eq_bot`, `SemidirectProduct.monoidHomSubgroup_apply`, `isQuotientCoveringMap`, `MulAction.smul_orbit_eq_orbit_smul`, `SubMulAction.conjMap_ofFixingSubgroup_coe_apply`, `Ideal.stabilizerEquiv_apply_smul`, `Equiv.Perm.commute_ofSubtype_noncommPiCoprod`, `IsSubnormal.exists_chain`, `Sylow.instFiniteSubtypeMemSubgroup`, `smul_coe`, `alternatingGroup.ofSubtype_comp_subtype`, `alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl`, `inf_subgroupOf_inf_normal_of_right`, `Valued.extensionValuation_toFun`, `Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply`, `MapSubtype.orderIso_symm_apply`, `Rep.quotientToCoinvariantsFunctor_obj_V`, `map_subtype_commutator`, `autEquivRootsOfUnity_smul`, `Group.closure_finite_fg`
`toSubmonoid` 📖	CompOp	56 math math: `equivSMul_apply_coe`, `toSubmonoid_le`, `InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois`, `RootPairing.weylGroup_toSubmonoid`, `comap_toSubmonoid`, `toSubmonoid_mono`, `closure_toSubmonoid`, `ClosedSubgroup.isClosed'`, `FiniteIndexNormalSubgroup.ext_iff`, `fg_iff_submonoid_fg`, `top_toSubmonoid`, `toSubmonoid_strictMono`, `MonoidWithZeroHom.valueMonoid_eq_valueGroup`, `op_toSubsemigroup`, `toSubmonoid_zpowers`, `Submonoid.powers_le_zpowers`, `map_toSubmonoid`, `exponent_toSubmonoid`, `topologicalClosure_subgroupClosure_toSubmonoid`, `le_closure_toSubmonoid`, `MonoidHom.graph_toSubmonoid`, `CommGroup.torsion_eq_torsion_submonoid`, `ClosedSubgroup.ext_iff`, `OpenSubgroup.isOpen'`, `unop_toSubsemigroup`, `bot_toSubmonoid`, `InfiniteGalois.isOpen_iff_finite`, `pinGroup.mem_lipschitzGroup`, `FixedPoints.subgroup_toSubmonoid`, `inv_mem'`, `unitarySubgroup_toSubmonoid`, `pinGroup.mem_iff`, `OpenNormalSubgroup.ext_iff`, `lipschitzGroup.coe_mem_iff_mem`, `saturated_iff_zpow`, `toSubmonoid_injective`, `mem_galBasis_iff`, `op_toSubmonoid`, `mem_iff_toUnits_mem_units`, `mem_toSubmonoid`, `coe_toSubmonoid`, `equivSMul_symm_apply_coe`, `mem_carrier`, `MonoidHom.subgroupComap_apply_coe`, `gc_toSubmonoid_mulSupport`, `mem_units_iff_val_mem`, `MonoidHom.subgroupMap_apply_coe`, `toSubmonoid_inj`, `Submonoid.mulSupport_toSubmonoid`, `closure_toSubmonoid_of_isOfFinOrder`, `MonoidHom.ker_toSubmonoid`, `unop_toSubmonoid`, `closure_toSubmonoid_of_finite`, `pointwise_smul_toSubmonoid`, `center_toSubmonoid`, `square_toSubmonoid`
`zpow` 📖	CompOp	23 math math: `subgroup_units_cyclic`, `rootsOfUnity.isCyclic`, `Bot.isCyclic`, `HasEnoughRootsOfUnity.rootsOfUnity_isCyclic`, `Valuation.IsRankOneDiscrete.instIsCyclicSubtypeUnitsMemSubgroupValueGroup`, `discrete_iff_cyclic`, `HasEnoughRootsOfUnity.cyc`, `isCyclic_zpowers`, `coe_zpow`, `NumberField.Units.instIsCyclicSubtypeUnitsRingOfIntegersMemSubgroupTorsion`, `isCyclic_subgroup_units`, `MulAction.orbitZPowersEquiv_symm_apply`, `isZGroup_iff_exists_mulEquiv`, `MulAction.orbitZPowersEquiv_symm_apply'`, `IsZGroup.isCyclic_commutator`, `isCyclic`, `IsZGroup.isZGroup`, `isZGroup_iff`, `isCyclic_iff_exists_zpowers_eq_top`, `isCyclic_of_le`, `IsPGroup.isCyclic_of_isZGroup`, `Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt_apply_zpow`, `IsZGroup.instIsCyclicSubtypeMemSubgroupOfFactPrime`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`coe_copy` 📖	mathematical	`SetLike.coe` `Subgroup` `instSetLike`	`SetLike.coe` `Subgroup` `instSetLike` `copy`	—	—
`coe_div` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `div` `DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	—
`coe_inclusion` 📖	mathematical	`Subgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`Subgroup` `SetLike.instMembership` `instSetLike` `DFunLike.coe` `MonoidHom` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion`	—	`Set.coe_inclusion`
`coe_inv` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `inv` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—
`coe_mk` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike`	—	—
`coe_mul` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `mul` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	—
`coe_nonempty` 📖	mathematical	—	`Set.Nonempty` `SetLike.coe` `Subgroup` `instSetLike`	—	`OneMemClass.one_mem` `SubmonoidClass.toOneMemClass` `SubgroupClass.toSubmonoidClass` `instSubgroupClass`
`coe_ofClass` 📖	mathematical	—	`SetLike.coe` `Subgroup` `instSetLike` `ofClass`	—	—
`coe_one` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `one` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—
`coe_pow` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `npow` `Monoid.toPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	—
`coe_set_mk` 📖	mathematical	`Set` `Set.instMembership` `Subsemigroup.carrier` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.toSubsemigroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	`SetLike.coe` `Subgroup` `instSetLike` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.instSetLike`	—	—
`coe_subtype` 📖	mathematical	—	`DFunLike.coe` `MonoidHom` `Subgroup` `SetLike.instMembership` `instSetLike` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `subtype`	—	—
`coe_toSubmonoid` 📖	mathematical	—	`SetLike.coe` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.instSetLike` `toSubmonoid` `Subgroup` `instSetLike`	—	—
`coe_zpow` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `zpow` `DivInvMonoid.toZPow` `Group.toDivInvMonoid`	—	—
`commGroup_isMulCommutative` 📖	mathematical	—	`IsMulCommutative` `Subgroup` `CommGroup.toGroup` `SetLike.instMembership` `instSetLike` `mul`	—	`CommMagma.to_isCommutative` `SubmonoidClass.toMulMemClass` `SubgroupClass.toSubmonoidClass` `instSubgroupClass`
`copy_eq` 📖	mathematical	`SetLike.coe` `Subgroup` `instSetLike`	`copy`	—	`SetLike.coe_injective`
`div_mem` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `DivInvMonoid.toDiv` `Group.toDivInvMonoid`	—	`div_mem` `instSubgroupClass`
`exists_inv_mem_iff_exists_mem` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`exists_inv_mem_iff_exists_mem` `instSubgroupClass`
`ext` 📖	—	`Subgroup` `SetLike.instMembership` `instSetLike`	—	—	`SetLike.ext`
`ext_iff` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike`	—	`ext`
`inclusion_inj` 📖	mathematical	`Subgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`DFunLike.coe` `MonoidHom` `Subgroup` `SetLike.instMembership` `instSetLike` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion`	—	`inclusion_injective`
`inclusion_injective` 📖	mathematical	`Subgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`Subgroup` `SetLike.instMembership` `instSetLike` `DFunLike.coe` `MonoidHom` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion`	—	`Set.inclusion_injective`
`instCanLiftSetCoeAndMemOfNatForallForallForallForallHMulForallForallInv` 📖	mathematical	—	`CanLift` `Set` `Subgroup` `SetLike.coe` `instSetLike` `Set.instMembership` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—
`instSubgroupClass` 📖	mathematical	—	`SubgroupClass` `Subgroup` `Group.toDivInvMonoid` `instSetLike`	—	`Subsemigroup.mul_mem'` `Submonoid.one_mem'` `inv_mem'`
`inv_mem` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`InvMemClass.inv_mem` `SubgroupClass.toInvMemClass` `instSubgroupClass`
`inv_mem'` 📖	mathematical	`Set` `Set.instMembership` `Subsemigroup.carrier` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.toSubsemigroup` `toSubmonoid`	`Set` `Set.instMembership` `Subsemigroup.carrier` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.toSubsemigroup` `toSubmonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—
`inv_mem_iff` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mem_iff` `SubgroupClass.toInvMemClass` `instSubgroupClass`
`le_normalizer` 📖	mathematical	—	`Subgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder` `normalizer` `SetLike.coe` `instSetLike`	—	`SetLike.mem_coe` `mul_mem_cancel_right` `inv_mem` `mul_mem_cancel_left`
`mem_carrier` 📖	mathematical	—	`Set` `Set.instMembership` `Subsemigroup.carrier` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.toSubsemigroup` `toSubmonoid` `Subgroup` `SetLike.instMembership` `instSetLike`	—	—
`mem_mk` 📖	mathematical	`Set` `Set.instMembership` `Subsemigroup.carrier` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.toSubsemigroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	`Subgroup` `SetLike.instMembership` `instSetLike` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.instSetLike`	—	—
`mem_normalizer_iff` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `normalizer` `SetLike.coe` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—
`mem_normalizer_iff'` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `normalizer` `SetLike.coe` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`SetLike.mem_coe` `mul_assoc` `mul_inv_cancel_right` `inv_mul_cancel_right`
`mem_normalizer_iff''` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `normalizer` `SetLike.coe` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_mem_iff` `SubgroupClass.toInvMemClass` `instSubgroupClass` `mem_normalizer_iff` `inv_inv`
`mem_toSubmonoid` 📖	mathematical	—	`Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `SetLike.instMembership` `Submonoid.instSetLike` `toSubmonoid` `Subgroup` `instSetLike`	—	—
`mk_eq_one` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `one` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`Submonoid.mk_eq_one`
`mk_le_mk` 📖	mathematical	`Set` `Set.instMembership` `Subsemigroup.carrier` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.toSubsemigroup` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	`Subgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Submonoid.instPartialOrder`	—	—
`mul_comm_of_mem_isMulCommutative` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`setLike_mul_comm` `SubmonoidClass.toMulMemClass` `SubgroupClass.toSubmonoidClass` `instSubgroupClass`
`mul_mem` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`MulMemClass.mul_mem` `SubmonoidClass.toMulMemClass` `SubgroupClass.toSubmonoidClass` `instSubgroupClass`
`mul_mem_cancel_left` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`mul_mem_cancel_left` `instSubgroupClass`
`mul_mem_cancel_right` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`mul_mem_cancel_right` `instSubgroupClass`
`normal_of_comm` 📖	mathematical	—	`Normal` `CommGroup.toGroup`	—	`mul_comm` `mul_inv_cancel_right` `One.instNonempty`
`one_mem` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `InvOneClass.toOne` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`OneMemClass.one_mem` `SubmonoidClass.toOneMemClass` `SubgroupClass.toSubmonoidClass` `instSubgroupClass`
`pow_mem` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `Monoid.toPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`pow_mem` `SubgroupClass.toSubmonoidClass` `instSubgroupClass`
`subtype_apply` 📖	mathematical	—	`DFunLike.coe` `MonoidHom` `Subgroup` `SetLike.instMembership` `instSetLike` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `subtype`	—	—
`subtype_comp_inclusion` 📖	mathematical	`Subgroup` `Preorder.toLE` `PartialOrder.toPreorder` `instPartialOrder`	`MonoidHom.comp` `Subgroup` `SetLike.instMembership` `instSetLike` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `subtype` `inclusion`	—	—
`subtype_injective` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `instSetLike` `DFunLike.coe` `MonoidHom` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `subtype`	—	`Subtype.coe_injective`
`toSubmonoid_inj` 📖	mathematical	—	`toSubmonoid`	—	`toSubmonoid_injective`
`toSubmonoid_injective` 📖	mathematical	—	`Subgroup` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toSubmonoid`	—	`SetLike.ext'_iff` `coe_toSubmonoid`
`toSubmonoid_le` 📖	mathematical	—	`Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `Preorder.toLE` `PartialOrder.toPreorder` `Submonoid.instPartialOrder` `toSubmonoid` `Subgroup` `instPartialOrder`	—	—
`toSubmonoid_mono` 📖	mathematical	—	`Monotone` `Subgroup` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `PartialOrder.toPreorder` `instPartialOrder` `Submonoid.instPartialOrder` `toSubmonoid`	—	`StrictMono.monotone` `toSubmonoid_strictMono`
`toSubmonoid_strictMono` 📖	mathematical	—	`StrictMono` `Subgroup` `Submonoid` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `PartialOrder.toPreorder` `instPartialOrder` `Submonoid.instPartialOrder` `toSubmonoid`	—	—
`zpow_mem` 📖	mathematical	`Subgroup` `SetLike.instMembership` `instSetLike`	`Subgroup` `SetLike.instMembership` `instSetLike` `DivInvMonoid.toZPow` `Group.toDivInvMonoid`	—	`zpow_mem` `instSubgroupClass`

Subgroup.Normal

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`conj_mem` 📖	mathematical	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike`	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	—
`conj_mem'` 📖	mathematical	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike`	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`inv_inv` `conj_mem`
`mem_comm` 📖	mathematical	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`conj_mem` `inv_mul_cancel_left` `inv_inv`
`mem_comm_iff` 📖	mathematical	—	`Subgroup` `SetLike.instMembership` `Subgroup.instSetLike` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`mem_comm`

SubgroupClass

Definitions

Name	Category	Theorems
`div` 📖	CompOp	2 math math: `coe_div`, `IntermediateField.coe_div`
`inclusion` 📖	CompOp	6 math math: `subtype_comp_inclusion`, `inclusion_mk`, `inclusion_inclusion`, `coe_inclusion`, `inclusion_right`, `inclusion_self`
`instZPow` 📖	CompOp	1 math math: `coe_zpow`
`subtype` 📖	CompOp	4 math math: `subtype_injective`, `subtype_comp_inclusion`, `subtype_apply`, `coe_subtype`
`toCommGroup` 📖	CompOp	—
`toGroup` 📖	CompOp	14 math math: `subtype_injective`, `subtype_comp_inclusion`, `Subgroup.IsComplement.equiv_mul_left_of_mem`, `subtype_apply`, `inclusion_mk`, `Subgroup.instFiniteQuotientSubtypeMemOpenSubgroupOfIsTopologicalGroupOfCompactSpace`, `inclusion_inclusion`, `coe_subtype`, `coe_inclusion`, `inclusion_right`, `Subgroup.ker_restrict_transferFocal_eq_focalSubgroupOf`, `Subgroup.IsComplement.equiv_mul_right_of_mem`, `Subgroup.IsComplement.equiv_mul_right`, `inclusion_self`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`coe_div` 📖	mathematical	—	`SetLike.instMembership` `div` `Group.toDivInvMonoid` `DivInvMonoid.toDiv`	—	—
`coe_inclusion` 📖	mathematical	—	`SetLike.instMembership` `DFunLike.coe` `MonoidHom` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion`	—	`Set.coe_inclusion` `SetLike.coe_subset_coe`
`coe_pow` 📖	mathematical	—	`SetLike.instMembership` `SubmonoidClass.instPow` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toSubmonoidClass` `Monoid.toPow`	—	`toSubmonoidClass`
`coe_subtype` 📖	mathematical	—	`DFunLike.coe` `MonoidHom` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `subtype`	—	—
`coe_zpow` 📖	mathematical	—	`SetLike.instMembership` `instZPow` `Group.toDivInvMonoid` `DivInvMonoid.toZPow`	—	—
`inclusion_inclusion` 📖	mathematical	`Preorder.toLE`	`DFunLike.coe` `MonoidHom` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion` `Preorder.toLE` `LE.le.trans`	—	`LE.le.trans`
`inclusion_mk` 📖	mathematical	`SetLike.instMembership`	`DFunLike.coe` `MonoidHom` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion` `mem_of_le_of_mem`	—	—
`inclusion_right` 📖	mathematical	`SetLike.instMembership`	`DFunLike.coe` `MonoidHom` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion`	—	—
`inclusion_self` 📖	mathematical	—	`DFunLike.coe` `MonoidHom` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `inclusion` `Preorder.toLE` `le_rfl`	—	`le_rfl`
`subset_union` 📖	mathematical	—	`Set` `Set.instHasSubset` `SetLike.coe` `Set.instUnion`	—	`SetLike.not_le_iff_exists` `SetLike.coe_subset_coe` `MulMemClass.mul_mem` `SubmonoidClass.toMulMemClass` `toSubmonoidClass` `mul_mem_cancel_right` `mul_mem_cancel_left` `mem_of_le_of_mem`
`subtype_apply` 📖	mathematical	—	`DFunLike.coe` `MonoidHom` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `subtype`	—	—
`subtype_comp_inclusion` 📖	mathematical	—	`MonoidHom.comp` `SetLike.instMembership` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `subtype` `inclusion`	—	—
`subtype_injective` 📖	mathematical	—	`SetLike.instMembership` `DFunLike.coe` `MonoidHom` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `toGroup` `MonoidHom.instFunLike` `subtype`	—	`Subtype.coe_injective`
`toInvMemClass` 📖	mathematical	—	`InvMemClass` `DivInvMonoid.toInv`	—	—
`toSubmonoidClass` 📖	mathematical	—	`SubmonoidClass` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid`	—	—

(root)

Definitions

Name	Category	Theorems
`AddSubgroup` 📖	CompData	2509 math math: `cfc_realPart`, `Unitary.openPartialHomeomorph_source`, `AddAction.mem_stabilizer_set_iff_subset_vadd_set`, `SchwartzMap.norm_toLp_le_seminorm`, `QuotientAddGroup.kerLift_mk`, `MeasureTheory.L1.setToL1_eq_setToL1'`, `continuous_decomposeProdAdjoint`, `MeasureTheory.Lp.instHasSolidNorm`, `AddSubgroup.ofAddUnits_right_inverse`, `AddSubgroup.coe_prod`, `MeasureTheory.integrable_indicatorConstLp`, `AddSubgroup.centerToAddOpposite_apply_coe`, `ContinuousMap.toLp_inj`, `AddSubgroup.inf_addSubgroupOf_inf_normal_of_left`, `AddSubgroup.IsFiniteRelIndex.to_finiteIndex_addSubgroupOf`, `AddSubgroup.noncommSum_mem`, `Submodule.toAddSubgroup_toZModSubmodule`, `AddMonoidHom.coe_rangeRestrict`, `AddCircle.not_isOfFinAddOrder_iff_forall_rat_ne_div`, `TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbing`, `MeasureTheory.Lp.toTemperedDistributionCLM_apply`, `StarModule.decomposeProdAdjointL_symm_apply`, `MeasureTheory.LpToLpRestrictCLM_coeFn`, `StarModule.selfAdjointPart_add_skewAdjointPart`, `AddSubgroup.mem_map_iff_mem`, `AddMonoidHom.coe_ker`, `MeasureTheory.L1.SimpleFunc.norm_Integral_le_one`, `lp.norm_apply_le_norm`, `AddSubgroup.closure_empty`, `Subgroup.isRegularAtInfty_iff`, `MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm''`, `MeasureTheory.condExpInd_of_measurable`, `SubAddAction.map_ofFixingAddSubgroupUnion_bijective`, `unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `AddSubgroup.normalClosure_closure_eq_normalClosure`, `MeasureTheory.Lp.mul_meas_ge_le_pow_enorm'`, `AddSubgroup.quotientEquivProdOfLE_symm_apply`, `AddSubgroup.isClosed_topologicalClosure`, `MeasureTheory.condExpL1_smul`, `lp.coe_linearMapOfLE_apply`, `MeasureTheory.Lp.instIsScalarTower`, `DomAddAct.mk_vadd_indicatorConstLp`, `imaginaryPart_eq_zero_iff`, `QuotientAddGroup.exists_norm_mk_lt`, `Int.zmultiples_one`, `AddSubgroup.ofAddUnits_bot`, `Commute.realPart_imaginaryPart`, `MeasureTheory.aestronglyMeasurable_condExpInd`, `AddSubmonoid.val_addUnitsEquivAddUnitsType_symm_apply_coe`, `CochainComplex.HomComplex.Cocycle.precomp_coe`, `QuotientAddGroup.leftRel_apply`, `MeasureTheory.mem_lpMeasSubgroup_iff_aestronglyMeasurable`, `NonUnitalSubring.toAddSubgroup_mono`, `CochainComplex.mappingCocone.inr_v_snd_v_assoc`, `Complex.coe_realPart`, `quasispectrum_imaginaryPart`, `lp.norm_le_of_tsum_le`, `AddAction.stabilizer_addSubgroup_op`, `ContinuousLinearMap.integral_compLp`, `AddSubgroup.addSubgroupOf_eq_top`, `ArchimedeanClass.subsemigroup_eq_addSubgroup_of_ne_top`, `lp.isLUB_norm`, `QuotientAddGroup.instT3Space`, `selfAdjoint.val_div`, `AddSubgroup.IsSubnormal.quotient`, `MeasureTheory.Lp.compMeasurePreserving_id_apply`, `SubAddAction.notMem_val_image`, `AddAction.stabilizerEquivStabilizer_symm`, `MeasureTheory.norm_indicatorConstLp_le`, `NormedAddGroupHom.Equalizer.ι_normNoninc`, `AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply_mk`, `isApproximateAddSubgroup_zero`, `AddGroup.closure_finite_fg`, `MeasureTheory.condExpInd_ae_eq_condExpIndSMul`, `Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le`, `IsHilbertSum.surjective_isometry`, `MeasureTheory.L1.setToL1_indicatorConstLp`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left`, `cfc_im_id`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1`, `UnitAddTorus.coe_mFourierBasis`, `OrthogonalFamily.linearIsometry_apply_single`, `AddSubgroup.addCommutator_comm_le`, `AddCircle.coe_eq_zero_iff`, `MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_lt_measure`, `AddSubgroup.closure_le_normalClosure`, `nsmul_finEquivZMultiples_symm_apply`, `realPart_idem`, `AddCircle.isAddQuotientCoveringMap_zsmul_of_ne_zero`, `SchwartzMap.inner_fourier_toL2_eq`, `SchwartzMap.toLp_fourierTransformInv_eq`, `AddSubgroup.zero_smul`, `MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral`, `FiniteArchimedeanClass.mem_addSubgroup_iff`, `AddSubgroup.map_eq_map_iff`, `AddSubgroup.addCommutator_top_left_le_iff`, `MeasureTheory.Lp.mem_Lp_of_ae_bound`, `MeasureTheory.tendsto_condExpL1_of_dominated_convergence`, `AddSubgroup.exists_mem_sup`, `AddSubgroup.closure_preimage_eq_top`, `AddSubgroup.vaddCommClass_left`, `CochainComplex.Lifting.π_f_cochain₁_v_ι_f`, `QuotientAddGroup.completeSpace_right'`, `AddSubgroup.centralizer_eq_iInf`, `CochainComplex.HomComplex.Cocycle.coe_smul`, `NormedAddGroupHom.incl_range`, `MeasureTheory.Lp.const_smul_mem_Lp`, `lp.instNormedStarGroupSubtypePreLpMemAddSubgroup`, `AddEquiv.addSubgroupMap_symm_apply`, `CochainComplex.mappingCone.id`, `MeasureTheory.norm_condExpL2_le`, `AddSubgroup.addCommutator_pi_pi_le`, `AddSubgroup.zmultiples_isAddCommutative`, `AddSubgroup.Normal.quotient_commutative_iff_addCommutator_le`, `MeasureTheory.Lp.instIsOrderedAddMonoid`, `MeasureTheory.MemLp.toLp_val`, `AddSubmonoid.coe_support`, `AddSubgroup.closure_singleton_zero`, `AddSubgroup.mem_pi`, `lp.inner_eq_tsum`, `realPart_ofReal`, `MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm`, `ContinuousLinearMap.continuous_integral_comp_L1`, `AddMonoidHom.liftOfRightInverse_comp_apply`, `MeasureTheory.Lp.edist_def`, `AddAction.mem_addSubgroup_orbit_iff`, `TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure`, `MeasureTheory.L1.norm_setToL1_le`, `AddSubgroup.norm_normedMk_le`, `CochainComplex.mappingCone.inr_f_fst_v`, `QuotientAddGroup.addEquivPiModRangeNSMulAddMonoidHom_apply`, `MeasureTheory.inner_condExpL2_left_eq_right`, `ArchimedeanClass.closedBallAddSubgroup_top`, `ArchimedeanClass.addSubgroup_antitone`, `ContinuousMap.toLp_denseRange`, `AddSubgroup.normalClosure_le_normal`, `FixedPoints.mem_addSubgroup`, `Unitary.mem_pathComponentOne_iff`, `MeasureTheory.Lp.coeFn_add`, `AddSubgroup.pi_top`, `AddSubgroup.mem_closure_range_iff_of_fintype`, `ContinuousLinearMap.comp_memLp`, `CochainComplex.mappingCocone.inr_v_snd_v`, `AddSubgroup.map_inf_le`, `AddSubgroup.coe_addSubgroupOf`, `MeasureTheory.Lp.eq_zero_iff_ae_eq_zero`, `lp.coeFn_star`, `imaginaryPart_I_smul`, `MeasureTheory.Lp.ext_iff`, `ContinuousLinearMap.norm_compLp_le`, `AddSubgroup.index_eq_zero_iff_infinite`, `AddMonoidHom.noncommPiCoprod_range`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff_of_addConj`, `lp.norm_eq_zero_iff`, `AddSubgroup.mem_toSubgroup'`, `image_addCommutatorSet_closureAddCommutatorRepresentatives`, `MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero`, `AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_apply`, `QuotientAddGroup.eq`, `AddCircle.coe_real_preimage_closedBall_eq_iUnion`, `MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving`, `AddSubgroup.iSup_eq_closure`, `AddSubgroup.bot_toAddSubmonoid`, `AddSubgroup.smul_mem_pointwise_smul_iff`, `MeasureTheory.Lp.coeFn_const`, `AddSubgroup.exists_isComplement_left`, `MeasureTheory.norm_setToFun_le_mul_norm'`, `ofAddUnits_addUnits_gc`, `OpenAddSubgroup.toAddSubgroup_injective`, `LipschitzWith.lipschitzWith_compLp`, `AddSubgroup.coe_top`, `AddSubmonoid.addUnits_iInf₂`, `MeasureTheory.norm_indicatorConstLp`, `AddSubgroup.IsComplement.quotientAddGroupMk_leftQuotientEquiv`, `AddSubgroup.characteristic_iff_comap_le`, `vadd_mem_fixedPoints_of_normal`, `AddSubgroup.addCommutator_comm`, `ContinuousMap.range_toLp`, `CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero`, `AddSubgroup.le_prod_iff`, `AddSubgroup.normalClosure_empty`, `AddSubgroup.top_addSubgroupOf`, `selfAdjoint.expUnitaryPathToOne_apply`, `Unitary.continuousOn_argSelfAdjoint`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `CochainComplex.HomComplex.Cocycle.coe_sub`, `CochainComplex.HomComplex.Cocycle.toCochainAddMonoidHom_apply`, `MeasureTheory.L1.ofReal_norm_eq_lintegral`, `IsSelfAdjoint.smul_mem_skewAdjoint`, `AddSubgroup.card_map_of_injective`, `rightAddCoset_mem_rightAddCoset`, `AddSubgroup.dense_of_no_min`, `MeasureTheory.condExpIndL1Fin_smul`, `AddSubgroup.le_centralizer_iff`, `AddSubgroup.mem_inv_pointwise_smul_iff`, `AddSubgroup.coe_comap`, `selfAdjoint.norm_sq_expUnitary_sub_one`, `OpenNormalAddSubgroup.toAddSubgroup_injective`, `AddSubgroup.card_comap_dvd_of_injective`, `QuotientAddGroup.univ_eq_iUnion_vadd`, `AddSubgroup.pi_bot`, `MeasureTheory.Lp.dist_def`, `MeasureTheory.Lp.aestronglyMeasurable`, `iSupIndep.dfinsuppSumAddHom_injective`, `AddSubgroup.mem_inertia`, `AddSubgroup.mem_sup_left`, `AddSubgroup.zmultiples_le`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_const`, `IsHilbertSum.linearIsometryEquiv_symm_apply`, `AddSubgroup.zsmul_mem`, `AddSubgroup.prod_mono_left`, `MeasureTheory.lpMeasSubgroupToLpTrim_neg`, `MeasureTheory.Lp.nnnorm_le_of_ae_bound`, `AddCircle.coe_neg`, `MeasureTheory.Lp.simpleFunc.uniformContinuous`, `AddSubgroup.coe_subtype`, `AddSubgroup.addCommutator_mem_addCommutator`, `AddSubgroup.normal_bot`, `AddSubgroup.SubgroupNormal.mem_comm`, `MeasureTheory.Lp.memLp`, `AddSubgroup.inf_addSubgroupOf_left`, `QuotientAddGroup.le_norm_iff`, `AddSubgroup.eq_bot_of_card_eq`, `MeasureTheory.Lp.nnnorm_def`, `AddSubgroup.instNontrivialSubtypeMemTop`, `QuotientAddGroup.eq_iff_sub_mem`, `SubAddAction.ofStabilizer.addConjMap_apply`, `AddSubgroup.map_eq_range_iff`, `QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure`, `lp.eq_zero_iff_coeFn_eq_zero`, `MeasureTheory.Integrable.toL1_zero`, `AddSubgroup.addCommutator_def`, `AddSubgroup.op_inf`, `AddSubgroup.noncommPiCoprod_single`, `AddSubgroup.comap_map_eq`, `QuotientAddGroup.equivQuotientZSMulOfEquiv_symm`, `SubAddAction.ofFixingAddSubgroup_of_singleton_bijective`, `MeasureTheory.Lp.mem_Lp_of_ae_le`, `MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq`, `AddSubgroup.inf_addSubgroupOf_right`, `AddCircle.isAddFundamentalDomain_of_ae_ball`, `AddSubgroup.relIndex_eq_two_iff_exists_notMem_and`, `QuotientAddGroup.leftRel_eq_top`, `AddSubgroup.normal_add`, `selfAdjoint.val_mul`, `AddSubgroup.multiset_noncommSum_mem`, `AddSubgroup.bot_prod_bot`, `AddSubgroup.coe_neg`, `QuotientAddGroup.mk'_eq_mk'`, `lp.coeFnAddMonoidHom_apply`, `AddSubgroup.mem_prod`, `MeasureTheory.condExpIndL1_add`, `AddSubgroup.addCommutator_le_focalAddSubgroupOf`, `CochainComplex.mappingCone.d_snd_v`, `MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM`, `AddSubgroup.coe_unop`, `SubAddAction.addConjMap_ofFixingAddSubgroup_bijective`, `AddSubgroup.instIsAddCommutative_closure`, `AddCircle.isAddQuotientCoveringMap_nsmul_of_ne_zero`, `lp.sum_rpow_le_norm_rpow`, `NormedAddGroupHom.lift_mk`, `MeasureTheory.norm_indicatorConstLp_top`, `lp.norm_le_of_forall_le'`, `CochainComplex.HomComplex.Cocycle.postcomp_coe`, `QuotientAddGroup.mk_surjective`, `AddSubgroup.addSubgroupOf_self`, `lp.norm_sum_single`, `MonoidHom.coe_toMultiplicative_range`, `MeasureTheory.L1.integral_smul`, `QuotientAddGroup.isOpenQuotientMap_mk`, `Subring.toAddSubgroup_mono`, `MeasureTheory.Lp.instFourierInvSMul`, `CochainComplex.HomComplex.Cocycle.coe_units_smul`, `AddAction.finite_quotient_of_finite_quotient_of_finite_quotient`, `ContinuousLinearMap.smul_compLp`, `selfAdjointPart_comp_subtype_skewAdjoint`, `SubAddAction.ofStabilizer.isPretransitive_iff_of_addConj`, `AddSubgroup.sum_mem`, `QuotientAddGroup.ker_map`, `QuotientAddGroup.subsingleton_quotient_top`, `Circle.isAddQuotientCoveringMap_exp`, `Nat.card_zmultiples`, `AddSubgroup.add_normal`, `AddCircle.isAddQuotientCoveringMap_nsmul`, `QuotientAddGroup.coe_mk'`, `AddSubgroup.coe_copy`, `AddSubgroup.card_eq_iff_eq_top`, `AddSubgroup.mem_sup_of_normal_left`, `QuotientAddGroup.completeSpace_left`, `AddEquiv.coe_comapAddSubgroup`, `AddMonoidHom.ker_fst`, `AddSubgroup.closure_eq_bot_iff`, `AddEquiv.addSubgroupCongr_apply`, `AddSubgroup.isFiniteRelIndex_iff_finiteIndex`, `MeasureTheory.AEEqFun.compMeasurePreserving_mem_Lp`, `QuotientAddGroup.equivIocMod_zero`, `AddSubgroup.eq_top_of_card_eq`, `MeasureTheory.L2.inner_def`, `MeasureTheory.Lp.enorm_toLp`, `SchwartzMap.toLpCLM_apply`, `SubAddAction.mem_ofStabilizer_iff`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_apply₂`, `QuotientAddGroup.instSecondCountableTopology`, `AddSubgroup.sub_mem_comm_iff`, `IsSelfAdjoint.selfAdjointPart_apply`, `AddSubgroup.addCommutator_sum_sum`, `AddSubmonoid.addUnits_sInf`, `QuotientAddGroup.measurableVAdd`, `AddSubgroup.isOpen_mono`, `AddSubgroup.IsComplement.neg_toLeftFun_add_mem`, `StarModule.decomposeProdAdjointL_apply`, `MeasureTheory.condExpIndL1Fin_add`, `AddSubgroup.IsSubnormal.inf`, `AddSubgroup.discreteTopology_iff_of_isFiniteRelIndex`, `AddGroup.addConjugates_subset_normal`, `image_range_addOrderOf`, `AddSubgroup.coe_zmultiples`, `MeasureTheory.Lp.compMeasurePreservingₗ_apply`, `SubAddAction.ofStabilizer.addConjMap_comp_neg_apply`, `AddAction.aestabilizer_empty`, `ContinuousMap.toLp_norm_le`, `AddSubgroup.IsSubnormal.lt_normal`, `mem_zmultiples_nsmul_iff`, `AddSubgroup.closure_le_centralizer_centralizer`, `CochainComplex.mappingCone.liftCocycle_coe`, `MeasureTheory.condExpL1_measure_zero`, `AddAction.Quotient.vadd_coe`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.addInvariantMeasure_quotient`, `selfAdjoint.val_one`, `lp.toAddMonoidHom_linearMapOfLE`, `SchwartzMap.inner_toL2_toL2_eq`, `AddAction.injective_ofQuotientStabilizer`, `MeasureTheory.AEEqFun.integrable_iff_mem_L1`, `AddSubgroup.coe_zero`, `AddSubgroup.intCast_mem_zmultiples_one`, `MeasureTheory.Lp.simpleFunc.isDenseEmbedding`, `MeasureTheory.Integrable.toL1_coeFn`, `MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'`, `AddSubgroup.addCommutator_bot_left`, `AddSubgroup.addCommutator_le`, `QuotientAddGroup.liftEquiv_coe`, `AddMonoidHom.ker_eq_bot_iff`, `AddSubgroup.mem_zmultiples`, `AddSubgroup.subtype_range`, `CochainComplex.HomComplex.CohomologyClass.mk_eq_zero_iff`, `MeasureTheory.L1.SimpleFunc.norm_setToL1S_le`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp`, `AddMonoidHom.addSubgroupOf_range_eq_of_le`, `AddCircle.coe_zsmul`, `AddSubgroup.quotient_finite_of_isOpen'`, `AddAction.map_stabilizer_le`, `OpenAddSubgroup.toAddSubgroup_le`, `AddGroup.fg_iff'`, `AddSubgroup.IsComplement.neg_add_toLeftFun_mem`, `DomMulAct.smul_Lp_sub`, `AddAction.Quotient.coe_vadd_out`, `SchwartzMap.norm_toLp_one`, `RingSubgroupsBasis.rightMul`, `MeasureTheory.L1.SimpleFunc.setToL1S_neg`, `SchwartzMap.toLp_fourierInv_eq`, `IsOfFinAddOrder.mem_zmultiples_iff_mem_range_addOrderOf`, `zmultiples_equiv_zmultiples_apply`, `AddSubgroup.card_eq_card_quotient_mul_card_addSubgroup`, `skewAdjoint.mem_iff`, `MeasureTheory.continuous_condExpIndL1`, `AddMonoidHom.rangeRestrict_surjective`, `IsHilbertSum.hasSum_linearIsometryEquiv_symm`, `MeasureTheory.Lp.nnnorm_eq_zero_iff`, `QuotientAddGroup.ker_mk'`, `skewAdjoint.val_smul`, `AddMonoidHom.apply_ofInjective_symm`, `coe_equiv_lpPiLp_symm`, `selfAdjointPart_comp_subtype_selfAdjoint`, `Valuation.ltAddSubgroup_monotone`, `AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div`, `AddSubgroup.map_zero_eq_bot`, `AddSubgroup.relIndex_inf_mul_relIndex`, `MeasureTheory.dominatedFinMeasAdditive_condExpInd`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroupOp`, `AddCircle.isAddQuotientCoveringMap_coe`, `Finset.op_vadd_stabilizer_of_no_doubling`, `AddSubgroup.index_iInf_le`, `MeasureTheory.L1.SimpleFunc.integral_add`, `AddCircle.isLocalHomeomorph_coe`, `AddSubgroup.mem_iff_toAddUnits_mem_addUnits`, `MeasureTheory.Integrable.edist_toL1_zero`, `orbit_fixingAddSubgroup_compl_subset`, `IsAddCyclic.exists_generator`, `Submodule.pointwise_smul_toAddSubgroup`, `AdjoinRoot.evalEval_apply`, `QuotientAddGroup.instContinuousVAdd`, `lp.inftyCStarRing`, `MeasureTheory.Lp.finStronglyMeasurable`, `MeasureTheory.aestronglyMeasurable_condExpL2`, `MeasureTheory.L1.setToL1_smul_left`, `AddSubgroup.isOpen_of_zero_mem_interior`, `AddSubgroup.noncommPiCoprod_range`, `MeasureTheory.L1.setToL1_zero_left`, `AddMonoidHom.ker_restrict`, `ContinuousAt.compMeasurePreservingLp`, `AddSubgroup.unop_normalizer`, `skewAdjoint.instIsStarNormalValMemAddSubgroup`, `MeasureTheory.condExpInd_nonneg`, `AddSubgroup.characteristic_centralizer`, `lp.evalₗ_apply`, `lp.norm_rpow_eq_tsum`, `AddMonoidHom.range_isAddCommutative`, `AddSubgroup.index_inf_le`, `AddSubgroup.torsionBy.mod_self_nsmul`, `AddSubgroup.focalAddSubgroup_le`, `CochainComplex.mappingCone.lift_f_fst_v`, `AddSubgroup.isUniformAddGroup`, `FiniteArchimedeanClass.mem_ballAddSubgroup_iff`, `MeasureTheory.condExpL1_of_aestronglyMeasurable'`, `AddSubgroup.vaddCommClass_right`, `AddAction.orbitZMultiplesEquiv_symm_apply'`, `MeasureTheory.L1.continuous_integral`, `AddSubgroup.unop_sInf`, `AddAction.IsBlock.of_orbit`, `AddSubgroup.card_range_dvd`, `CochainComplex.Lifting.exists_hom`, `AddAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `MeasureTheory.Lp.stronglyMeasurable`, `NormedAddGroupHom.Equalizer.map_normNoninc`, `AddSubgroup.exists_nsmul_mem_of_relIndex_ne_zero`, `AddSubgroup.norm_trivial_quotient_mk`, `AddSubgroup.op_le_iff`, `MeasureTheory.L1.integrable_coeFn`, `SchwartzMap.injective_toLp`, `MeasureTheory.condExpL2_indicator_ae_eq_smul`, `AddAction.orbitZMultiplesEquiv_symm_apply`, `AddSubgroup.coe_equivMapOfInjective_apply`, `AddMonoidHom.ker_prod`, `AddAction.stabilizer_le_aestabilizer`, `AddCircle.norm_div_natCast`, `CategoryTheory.ShortComplex.abToCycles_apply_coe`, `AddMonoidHom.range_eq_map`, `AddGroup.residuallyFinite_def`, `MeasureTheory.condExpL1CLM_of_aestronglyMeasurable'`, `AddAction.aestabilizer_univ`, `AddMonoidHom.rangeRestrict_injective_iff`, `UnitAddTorus.mFourierCoeff_toLp`, `CochainComplex.mappingCone.id_X`, `AddSubgroup.prod_addSubgroupOf_prod_normal`, `CochainComplex.mappingCocone.inr_v_desc_f_assoc`, `MeasureTheory.Lp.dist_edist`, `AddSubgroup.characteristic_iff_le_map`, `ContinuousLinearMap.holderₗ_apply_apply`, `MeasureTheory.Lp.edist_eq_eLpNorm_neg_add`, `AddSubgroup.relIndex_map_map`, `ofAddUnits_le_iff_le_addUnits`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left'`, `AddSubgroup.coe_iSup_of_directed`, `AddSubgroup.index_eq_natAbs_det`, `OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single`, `MeasureTheory.Measure.IsAddLeftInvariant.addQuotientMeasureEqMeasurePreimage_of_set`, `LinearOrderedAddCommGroup.negGen_eq_of_top`, `MeasureTheory.Lp.coeFn_mk`, `AddAction.mem_stabilizer_iff`, `MeasureTheory.Lp.norm_zero`, `MeasureTheory.Lp.mem_Lp_of_ae_nnnorm_bound`, `AddSubgroup.card_subtype`, `MeasureTheory.continuous_setToFun`, `QuotientAddGroup.isOpenMap_coe`, `MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc`, `MeasureTheory.L1.dist_eq_integral_dist`, `AddSubgroup.noncommPiCoprod_apply`, `MeasureTheory.L1.norm_def`, `AddSubgroup.list_sum_mem`, `QuotientAddGroup.leftRel_eq`, `AddSubgroup.Normal.eq_bot_or_eq_top`, `AddSubgroup.mem_closure_of_mem`, `MeasureTheory.integral_condExpL2_eq`, `AddSubgroup.normal_inf_normal`, `AddSubgroup.op_sInf`, `DomAddAct.instIsIsometricVAddSubtypeAEEqFunMemAddAddSubgroupLp`, `AddAction.stabilizer_finset_univ`, `Unitary.openPartialHomeomorph_symm_apply`, `AddSubgroup.op_normalizer`, `MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul`, `AddSubgroup.mem_map_of_mem`, `MeasureTheory.Lp.edist_toLp_toLp`, `CochainComplex.HomComplex.leftHomologyData_i_hom_apply`, `QuotientAddGroup.equivQuotientZSMulOfEquiv_trans`, `AddSubgroup.add_self_mem_of_index_two`, `AddSubgroup.topCharacteristic`, `AddSubgroup.addSubgroupOf_normalizer_eq`, `CochainComplex.mappingCone.d_snd_v'_assoc`, `orthonormal_fourier`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive`, `AddSubgroup.pi_mem_of_single_mem`, `AddSubgroup.normalClosure_eq_iInf`, `fixingAddSubgroup_iUnion`, `MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc`, `lp.coeFn_single`, `AddAction.stabilizer_univ`, `MeasureTheory.setIntegral_condExpL2_indicator`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive'`, `MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub`, `SubAddAction.ofStabilizer.isPretransitive_iff`, `AddMonoidHom.addSubgroupMap_apply_coe`, `MeasureTheory.Integrable.norm_toL1`, `AddMonoidHom.ofLeftInverse_symm_apply`, `AddSubgroup.add_mem_cancel_right`, `selfAdjoint.instNontrivialSubtypeMemAddSubgroup`, `AddSubgroup.addCommutator_top_right_le_iff`, `ContinuousLinearMap.setIntegral_compLp`, `Subring.toAddSubgroup_lt_toAddSubgroup`, `fixingAddSubgroup_empty`, `AddSubgroup.single_mem_pi`, `ProperlyDiscontinuousVAdd.finite_stabilizer`, `lp.summable_mul`, `MeasureTheory.Lp.edist_toLp_zero`, `AddSubgroup.rank_closure_finset_le_card`, `MeasureTheory.L1.setToL1_mono_left'`, `selfAdjoint.imaginaryPart_coe`, `AddCircle.dense_addSubgroup_iff_ne_zmultiples`, `AddSubgroup.tendsto_zmultiples_subtype_cofinite`, `DomAddAct.vadd_Lp_add`, `MeasureTheory.Integrable.toL1_eq_mk`, `AddSubgroup.mem_iSup_of_directed`, `NumberField.Units.span_basisOfIsMaxRank`, `Subring.coe_toAddSubgroup`, `Subring.pointwise_smul_toAddSubgroup`, `NormedAddGroupHom.lift_normNoninc`, `lp.hasSum_single`, `selfAdjoint.val_zpow`, `cfcₙ_re_id`, `QuotientAddGroup.completeSpace_right`, `AddSubgroup.unop_inf`, `AddSubgroup.index_eq_two_iff_exists_notMem_and`, `AddSubgroup.isComplement_addSubgroup_left_iff_bijective`, `AddSubgroup.relIndex_sup_left`, `QuotientAddGroup.norm_lt_iff`, `MeasureTheory.condExpIndSMul_empty`, `AddSubgroup.toZModSubmodule_toAddSubgroup`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le`, `AddSubgroup.ker_addSubgroupMap`, `fixingAddSubgroup_union`, `AddGroup.fg_iff`, `AddAction.stabilizer_empty`, `AddSubgroup.index_ker`, `AddSubgroup.mem_normalizer_iff`, `AddSubgroup.map_top_of_surjective`, `MeasureTheory.setIntegral_condExpInd`, `AddCircle.add_projection_respects_measure`, `AddSubmonoid.addUnits_iInf`, `AddSubmonoid.neg_mem_addUnits_iff`, `AddAction.stabilizer_add_self`, `RingSubgroupsBasis.hasBasis_nhds_zero`, `ProfiniteAddGrp.limit_zero_val`, `AddSubgroup.normal_le_normalCore`, `addCommutator_centralizer_addCommutator_le_center`, `MeasureTheory.edist_indicatorConstLp_eq_enorm`, `AddSubgroup.topologicalClosure_minimal`, `lp.memℓp`, `AddSubgroup.mem_ofAddUnits_iff_toAddUnits_mem`, `lp.coeFn_zero`, `CategoryTheory.ShortComplex.abLeftHomologyData_π`, `QuotientAddGroup.preimage_image_mk`, `QuotientAddGroup.norm_eq_infDist`, `AddSubgroup.add_mem_sup`, `QuotientAddGroup.liftEquiv_mk`, `continuous_decomposeProdAdjoint_symm`, `AddSubgroup.addSubgroupOfEquivOfLe_apply_coe`, `Submodule.span_int_eq`, `AddSubgroup.Normal.addConj_mem'`, `MeasureTheory.Lp.compMeasurePreserving_comp`, `MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero`, `AddSubgroup.map_inf_eq`, `AddSubgroup.pi_empty`, `MeasureTheory.L1.setToL1_eq_setToL1SCLM`, `AddSubgroup.isComplement'_top_bot`, `MeasureTheory.norm_condExpL2_coe_le`, `MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le`, `lp.norm_const_smul`, `MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable`, `AddCircle.instHasAddFundamentalDomainSubtypeAddOppositeRealMemAddSubgroupOpZmultiples`, `QuotientAddGroup.finite`, `MeasureTheory.L1.setToL1_nonneg`, `AddMonoidHom.ker_id`, `AddAction.IsBlock.stabilizer_le`, `QuotientAddGroup.nontrivial_iff`, `MeasureTheory.aestronglyMeasurable_condExpL1`, `isAddFundamentalDomain_Ioc`, `AddAction.stabilizer_op_addSubgroup`, `SchwartzMap.norm_fourier_toL2_eq`, `MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure`, `AddMonoidHom.fiberEquivKer_apply`, `MeasureTheory.Lp.SecondCountableTopology`, `AddSubgroup.addConj_mem_sup_of_mem_inf_normalizer_of_mem_inf`, `AddSubgroup.ne_bot_iff_exists_ne_zero`, `AddSubgroup.card_le_of_le`, `AddMonoidHom.mem_graph`, `CochainComplex.mappingCone.lift_f_fst_v_assoc`, `AddSubgroup.addCommutator_bot_right`, `MeasureTheory.Lp.instCompleteSpace`, `MeasureTheory.Lp.norm_toLp`, `CochainComplex.mappingCocone.id_X`, `AddCircle.norm_coe_mul`, `Subgroup.fg_iff_add_fg`, `MeasureTheory.Lp.instFourierPair`, `lp.zeroBasis_repr_apply`, `coe_addEquiv_lpPiLp_symm`, `CochainComplex.mappingCocone.descCocycle_coe`, `MeasureTheory.L1.integral_def`, `BoundedContinuousFunction.Lp_nnnorm_le`, `Module.Basis.addSubgroupOfClosure_repr_apply`, `AddSubgroup.map_subtype_addCommutator`, `AddSubgroup.exists_ne_zero_of_nontrivial`, `DomMulAct.edist_smul_Lp`, `hasSum_fourier_series_L2`, `AddSubgroup.isOpen_of_isClosed_of_finiteIndex`, `realPart.norm_le`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul_real`, `BoundedContinuousFunction.range_toLpHom`, `selfAdjoint.expUnitary_zero`, `AddCircle.norm_half_period_eq`, `BoundedContinuousFunction.toLp_inj`, `AddSubgroup.multiset_sum_mem`, `MeasureTheory.mem_lpMeas_indicatorConstLp`, `RingSubgroupsBasis.leftMul`, `AddSubgroup.normalizer_eq_top_iff`, `lp.single_apply_ne`, `AddSubgroup.comap_inf`, `AddMonoidHom.coe_graph`, `mem_fixingAddSubgroup_compl_iff_movedBy_subset`, `BoundedContinuousFunction.toLp_injective`, `AddSubgroup.closure_univ`, `lp.singleAddMonoidHom_apply`, `MeasureTheory.integral_indicatorConstLp`, `MeasureTheory.exists_ne_zero_mem_lattice_of_measure_mul_two_pow_le_measure`, `HilbertBasis.hasSum_repr`, `AddSubgroup.isOpen_of_mem_nhds`, `CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles`, `MeasureTheory.Lp.coeFn_compMeasurePreserving`, `orbit_addSubgroup_eq_self_of_mem`, `AddGroup.exponent_quotient_dvd`, `Topology.IsQuotientMap.isCoveringMapOn_of_properlyDiscontinuousVAdd`, `MeasureTheory.condExpIndSMul_smul`, `AddSubgroup.map_subtype_le`, `MeasureTheory.lintegral_nnnorm_condExpL2_le`, `finite_iff_addSubgroup_quotient`, `QuotientAddGroup.norm_mk`, `StrongDual.toLp_of_not_memLp`, `MeasureTheory.Lp.compMeasurePreservingₗᵢ_apply_coe`, `MeasureTheory.Lp.dist_eq_eLpNorm_neg_add`, `MeasureTheory.L1.setToFun_eq_setToL1`, `AddSubgroup.isComplement'_top_left`, `LinearMap.IsSymmetric.coe_toSelfAdjoint`, `SchwartzMap.norm_fourierTransformCLM_toL2_eq`, `Int.addSubgroup_index_ne_zero_iff`, `AddSubgroup.mem_sSup_of_directedOn`, `AddSubgroup.map_equiv_top`, `AddSubgroup.normalClosure_subset_iff`, `AddSubgroup.isAddQuotientCoveringMap_of_comm`, `MeasureTheory.enorm_indicatorConstLp_le`, `MeasureTheory.Lp.norm_neg`, `ModularFormClass.one_mem_strictPeriods_SL2Z`, `AddSubgroup.finite_quotient_of_pretransitive_of_index_ne_zero`, `AddMonoidHom.addSubgroupComap_surjective_of_surjective`, `CochainComplex.mappingCocone.inr_comp_descCochain`, `MeasureTheory.L1.integral_eq_setToL1`, `AddSubgroup.le_op_iff`, `AddSubgroup.neg_subset_closure`, `MeasureTheory.Integrable.toL1_smul`, `lp.singleContinuousAddMonoidHom_apply`, `AddCircle.addOrderOf_div_of_gcd_eq_one`, `MeasureTheory.Lp.nnnorm_neg`, `AddSubgroup.int_mul_mem`, `realPart_add_I_smul_imaginaryPart`, `AddMonoidHom.subtype_comp_rangeRestrict`, `AddSubgroup.unop_iSup`, `AddSubgroup.mem_sup'`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `ArchimedeanClass.ballAddSubgroup_top`, `ContinuousLinearMap.holder_smul_left`, `ClosedAddSubgroup.toAddSubgroup_injective`, `AddSubgroup.op_top`, `AddSubmonoid.mem_support`, `MeasureTheory.Lp.coeFn_smul`, `DomMulAct.mk_smul_toLp`, `MeasureTheory.condExpL1CLM_indicatorConstLp`, `AddSubgroup.ker_le_comap`, `CochainComplex.HomComplex.Cocycle.toSingleMk_mem_coboundaries_iff`, `AddSubgroup.addCommute_subtype_of_addCommute`, `AddSubgroup.isClosed_of_isOpen`, `AddSubgroup.toIntSubmodule_symm`, `lp.inner_single_right`, `NormedAddGroupHom.mem_ker`, `AddSubgroup.centralizer_closure`, `MeasureTheory.L1.setToL1_add_left'`, `Submodule.top_toAddSubgroup`, `AddSubgroup.comap_normalizer_eq_of_surjective`, `AddSubgroup.card_add_eq_card_addSubgroup_add_card_quotient`, `lp.norm_nonneg'`, `CochainComplex.HomComplex.Cocycle.cochain_ofHom_homOf_eq_coe`, `QuotientAddGroup.strictMono_comap_prod_image`, `AddSubgroup.toSubgroup_closure`, `IsSelfAdjoint.skewAdjointPart_apply`, `lp.single_neg`, `MeasureTheory.L1.SimpleFunc.coe_negPart`, `MeasureTheory.integrableOn_Lp_of_measure_ne_top`, `MeasureTheory.L1.setToL1_mono_left`, `MeasureTheory.Lp.dist_eq_norm`, `selfAdjoint.continuous_expUnitary`, `MeasureTheory.condExpInd_disjoint_union`, `MeasureTheory.Lp.coeFn_le`, `AddSubgroup.disjoint_def`, `AddCircle.coe_sub`, `QuotientAddGroup.discreteTopology_iff`, `AddSubgroup.map_focalAddSubgroupOf`, `MeasureTheory.Lp.simpleFunc.add_toSimpleFunc`, `ComplexStarModule.ext_iff`, `AddSubgroup.coe_add_of_left_le_normalizer_right`, `AddSubgroup.range_subtype`, `AddEquiv.symm_mapAddSubgroup`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroup`, `UnitAddTorus.coeFn_mFourierLp`, `coe_ringEquiv_lpBCF`, `AddSubgroup.op_le_op_iff`, `AddSubgroup.centerCongr_apply_coe`, `AddMonoidHom.ker_eq_bot_of_cancel`, `essSup_comp_quotientAddGroup_mk`, `Submodule.toAddSubgroup_mono`, `iSupIndep_of_dfinsuppSumAddHom_injective'`, `MeasureTheory.setIntegral_condExpIndSMul`, `AddSubgroup.goursat_surjective`, `AddSubgroup.nsmul_mem_of_relIndex_ne_zero_of_dvd`, `AddSubgroup.map_le_map_iff`, `AddSubgroup.instDiscreteTopologyQuotientOfSeparatelyContinuousAdd`, `MeasureTheory.indicatorConstLp_univ`, `AddSubgroup.normalClosure_mono`, `AddSubgroup.closure_mono`, `MeasureTheory.lpMeasToLpTrimLie_symm_indicator`, `lp.single_zero`, `MeasureTheory.norm_setToFun_le'`, `NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion`, `AddSubgroup.isClosed_of_discrete`, `selfAdjoint.unitarySelfAddISMul_coe`, `quasispectrum_imaginaryPart'`, `AddAction.Quotient.mk_vadd_out`, `selfAdjoint.star_val_eq`, `StarModule.decomposeProdAdjoint_symm_apply`, `MeasureTheory.Lp.norm_const_le`, `TopologicalAddGroup.IsSES.ofClosedAddSubgroup`, `AddSubgroup.torsionBy.nsmul_iff`, `AddSubgroup.op_bot`, `AddSubgroup.quotientiInfEmbedding_apply_mk`, `QuotientAddGroup.lift_mk'`, `AddSubgroup.relIndex_inf_le`, `HahnSeries.mem_cardSuppLTAddSubgroup`, `Subgroup.mem_toAddSubgroup'`, `AddSubgroup.instIsAddTorsionFree`, `CochainComplex.HomComplex.Cocycle.coe_neg`, `cfcₙ_comp_re`, `MeasureTheory.Lp.coeFn_negPart_eq_max`, `coe_lpBCFₗᵢ`, `AddSubgroup.rank_closure_finite_le_nat_card`, `AddSubgroup.index_map`, `AddSubgroup.unop_injective`, `star_mul_self_eq_realPart_sq_add_imaginaryPart_sq`, `AddSubgroup.focalAddSubgroupOf_eq_closure`, `AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply`, `cfc_comp_im`, `ofAdd_image_zmultiples_eq_zpowers_ofAdd`, `lp.infty_coeFn_mul`, `MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'`, `AddSubmonoid.addUnits_mono`, `MeasureTheory.condExpL1_undef`, `MeasureTheory.Lp.nnnorm_toLp`, `AddGroup.rank_spec`, `QuotientAddGroup.subsingleton_iff`, `realPart_one`, `QuotientAddGroup.rightRel_eq_top`, `QuotientAddGroup.map_comp_map`, `AddCircle.coe_eq_zero_iff_of_mem_Ico`, `MeasureTheory.Measure.MeasureDense.indicatorConstLp_subset_closure`, `AddSubgroup.dense_iff_ne_zmultiples`, `Subring.mem_closure_iff`, `NonUnitalSubring.toAddSubgroup_eq_top`, `AddMonoid.Coprod.range_eq`, `MeasureTheory.L1.SimpleFunc.setToL1S_sub`, `AddCommGrpCat.range_eq_top_of_epi`, `QuotientAddGroup.t1Space_iff`, `AddSubgroup.addSubgroupOf_map_subtype`, `AddSubmonoid.addUnits_bot`, `AddAction.stabilizerEquivStabilizer_symm_apply`, `coe_set_eq_zero`, `AddSubgroup.vadd_opposite_add`, `QuotientAddGroup.instIsTopologicalAddGroup`, `AddSubgroup.card_dvd_of_le`, `ContinuousMap.toLp_def`, `QuotientAddGroup.instT2Space`, `AddSubgroup.isComplement_range_left`, `AddSubgroup.Normal.addSubgroupOf`, `AddSubgroup.pi_mem_of_single_mem_aux`, `QuotientAddGroup.measurable_from_quotient`, `MeasureTheory.L2.integral_inner_eq_sq_eLpNorm`, `AddSubgroup.norm_coe`, `MonoidHom.coe_toAdditive_map`, `AddSubgroup.op_sup`, `AddSubgroup.map_subtype_lt_map_subtype`, `ContinuousWithinAt.compMeasurePreservingLp`, `lp.coeFn_add`, `MeasureTheory.Lp.norm_le_norm_of_ae_le`, `AddSubgroup.pi_le_iff`, `AddSubgroup.index_eq_two_iff_exists_notMem_and'`, `MeasureTheory.L2.inner_indicatorConstLp_one`, `MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp`, `MeasureTheory.L1.setToL1_smul_left'`, `MeasureTheory.Lp.boundedContinuousFunction_dense`, `LinearMap.IsSymmetric.toSelfAdjoint_apply`, `MeasureTheory.Lp.constₗ_apply`, `MeasureTheory.Lp.coe_nnnorm`, `QuotientAddGroup.fg`, `AddSubgroup.le_normalizer`, `MeasureTheory.L1.SimpleFunc.toLp_one_eq_toL1`, `SubAddAction.mem_fixingAddSubgroup_union_iff`, `MeasureTheory.Lp.mem_boundedContinuousFunction_iff`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2`, `AddSubgroup.map_normalizer_eq_of_bijective`, `AddSubgroup.coe_topologicalClosure_bot`, `coe_smulCardAddSubgroup`, `MeasureTheory.condExpIndSMul_add`, `quotient_norm_add_le`, `MeasureTheory.Lp.norm_fourier_eq`, `cfcₙ_comp_im`, `QuotientAddGroup.ker_le_range_iff`, `AddSubgroup.discrete_iff_addCyclic`, `AddMonoidHom.range_eq_top`, `AddSubgroup.card_mul_index`, `SchwartzMap.coeFn_toLp`, `CategoryTheory.ShortComplex.abLeftHomologyData_K_coe`, `MeasureTheory.Lp.instFourierSMul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left`, `AddCon.mem_addSubgroup_iff`, `AddSubgroup.card_addSubgroup_dvd_card`, `MeasureTheory.Lp.simpleFunc.toLp_eq_toLp`, `AddSubgroup.comap_normalizer_eq_of_le_range`, `CochainComplex.mappingCone.ofHom_lift`, `MeasureTheory.Lp.norm_const'`, `QuotientAddGroup.mk'_comp_subtype`, `Submodule.toIntSubmodule_toAddSubgroup`, `MeasureTheory.norm_condExpIndL1_le`, `AddSubgroup.pointwise_smul_le_iff₀`, `AddSubgroup.discreteTopology`, `SchwartzMap.norm_toLp`, `IsUniformAddGroup.uniformContinuous_iff_isOpen_ker`, `CochainComplex.HomComplex.Cocycle.toSingleMk_coe`, `lp.norm_le_of_tendsto`, `AddEquiv.mapAddSubgroup_symm_apply`, `AddMonoidHom.addSubgroupComap_apply_coe`, `AddGroup.FG.out`, `Subgroup.coe_toAddSubgroup_symm_apply`, `FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff`, `dense_addSubmonoidClosure_iff_addSubgroupClosure`, `AddSubgroup.injective_noncommPiCoprod_of_iSupIndep`, `MeasureTheory.condExpL1_add`, `Real.Lp.fourierTransform_apply`, `AddSubgroup.addCommutator_le_map_addCommutator`, `CochainComplex.mappingCocone.ofHom_desc`, `AddCircle.coe_nsmul`, `MeasureTheory.Lp.smul_zero`, `AddSubgroup.prod_top`, `AddSubgroup.comap_sup_eq_of_le_range`, `AddSubgroup.pi_eq_bot_iff`, `MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul`, `AddSubgroup.nontrivial_iff`, `AddSubgroup.closure_add_le`, `CochainComplex.mappingCone.ext_to_iff`, `DomMulAct.mk_smul_indicatorConstLp`, `MeasureTheory.norm_condExpInd_apply_le`, `HahnSeries.coe_cardSuppLTAddSubgroup`, `QuotientAddGroup.strictMono_comap_prod_map`, `AddMonoidHom.ofLeftInverse_apply`, `AddSubgroup.inf_add_assoc`, `IsAddCyclic.card_nsmulAddMonoidHom_ker`, `AddSubgroup.coe_toAddSubmonoid`, `AddMonoidHom.ker_snd`, `QuotientAddGroup.mk_add`, `Complex.selfAdjointEquiv_apply`, `CochainComplex.mappingCone.lift_fst`, `ContinuousLinearMap.nnnorm_holder_apply_apply_le`, `AddMonoidHom.range_eq_bot_iff`, `OrthogonalFamily.hasSum_linearIsometry`, `AddSubgroup.addCommGroup_isAddCommutative`, `Submodule.toAddSubgroup_injective`, `addCommutator_eq_bot_iff_center_eq_top`, `AddSubgroup.Characteristic.comap_quotient_mk`, `AddSubgroup.isComplement_addSubgroup_right_iff_bijective`, `AddSubgroup.zmultiples_zero_eq_bot`, `mem_nullAddSubgroup_iff`, `ofMul_image_zpowers_eq_zmultiples_ofMul`, `AddMonoidHom.liftOfRightInverse_comp`, `AddSubgroup.map_equiv_normalizer_eq`, `DomAddAct.norm_vadd_Lp`, `lp.instSMulCommClassSubtypePreLpMemAddSubgroup`, `AddSubgroup.instMeasurableVAdd`, `MeasureTheory.condExpL1_neg`, `MeasureTheory.Lp.instTrivialStarSubtypeAEEqFunMemAddSubgroup`, `AddSubgroup.isComplement_addSubgroup_right_iff_existsUnique_quotientAddGroupMk`, `MeasureTheory.L1.nnnorm_integral_le`, `AddSubgroup.addSubgroupOf_mono`, `AddAction.finite_quotient_of_pretransitive_of_finite_quotient`, `CStarAlgebra.linear_combination_nonneg`, `MeasureTheory.Lp.norm_smul_le`, `CochainComplex.mappingCone.ext_cochain_to_iff`, `AddSubgroup.ofAddUnits_injective`, `MeasureTheory.isClosed_aestronglyMeasurable`, `lp.monotone`, `isAddCyclic_iff_exists_zmultiples_eq_top`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary`, `QuotientAddGroup.equivIcoMod_symm_apply`, `star_mul_self_add_self_mul_star`, `AddSubgroup.map_eq_bot_iff`, `MeasureTheory.Lp.coeFn_sup`, `NormedAddGroupHom.Equalizer.liftEquiv_apply`, `AddSubgroup.ofAddUnits_sSup`, `QuotientAddGroup.image_coe_inj`, `AddSubgroup.map_comap_eq`, `QuotientAddGroup.comap_map_mk'`, `imaginaryPart.norm_le`, `AddSubgroup.mem_zmultiples_iff`, `NormedAddGroupHom.range_comp_incl_top`, `MeasureTheory.Lp_toLp_restrict_add`, `AddSubgroup.index_mul_card`, `lp.singleContinuousLinearMap_apply`, `LipschitzWith.coordinate`, `AddAction.vadd_orbit_eq_orbit_vadd`, `QuotientAddGroup.instCompactSpaceQuotientAddSubgroup`, `QuotientAddGroup.sound`, `AddMonoidHom.range_eq_top_of_surjective`, `AddSubgroup.quotientAddSubgroupOfMapOfLE_apply_mk`, `MeasureTheory.setIntegral_condExpL1`, `realPart_comp_subtype_selfAdjoint`, `AddSubgroup.add_injective_of_disjoint`, `AddSubgroup.mem_closure_range_iff`, `Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le`, `Orthonormal.linearIsometryEquiv_symm_apply_single_one`, `AddAction.minimalPeriod_eq_card`, `LipschitzOnWith.extend_lp_infty`, `AddSubgroup.continuousVAdd`, `AddSubgroup.discreteTopology_iff_of_finiteIndex`, `NonUnitalSubring.toAddSubgroup_injective`, `AddSubgroup.index_eq_two_iff'`, `AddSubgroup.mem_toAddSubmonoid`, `AddSubgroup.addUnit_of_mem_ofAddUnits_spec_mem`, `MeasureTheory.condExpIndL1_smul`, `UnitAddTorus.orthonormal_mFourier`, `FiniteArchimedeanClass.subsemigroup_eq_addSubgroup`, `ContinuousMap.toLp_norm_eq_toLp_norm_coe`, `QuotientAddGroup.homQuotientZSMulOfHom_comp_of_rightInverse`, `closure_addSubmonoidClosure_eq_closure_addSubgroupClosure`, `SubAddAction.ofStabilizer.addConjMap_comp`, `AddSubgroup.mem_closure_singleton_iff_existsUnique_zsmul`, `AddSubgroup.nsmul_mem_of_index_ne_zero_of_dvd`, `RingSubgroupsBasis.mem_addGroupFilterBasis`, `AddSubgroup.addCommutator_le_right`, `CochainComplex.mappingCone.liftCochain_v_fst_v`, `AddSubgroup.coe_set_mk`, `AddSubgroup.center_eq_infi'`, `AddAction.orbitRel_addSubgroup_le`, `MeasureTheory.Integrable.enorm_toL1`, `AddSubgroup.instFiniteIndex_addSubgroupOf`, `MeasureTheory.continuous_integral_integral`, `fourierCoeff_toLp`, `AddSubgroup.map_eq_bot_iff_of_injective`, `ArchimedeanClass.mem_addSubgroup_iff`, `OrthogonalFamily.summable_of_lp`, `ArchimedeanClass.addSubgroup_eq_bot`, `coe_fourierBasis`, `AddSubgroup.coe_add_of_right_le_normalizer_left`, `NonUnitalSubring.coe_toAddSubgroup`, `Valuation.mem_leAddSubgroup_iff`, `spectrum_imaginaryPart`, `lp.coeFn_sub`, `AddEquiv.comapAddSubgroup_apply`, `CochainComplex.mappingCone.decomp_from`, `AddCircle.coe_image_Icc_eq`, `AddSubgroup.relIndex_eq_one`, `QuotientAddGroup.preimage_image_mk_eq_add`, `AddSubgroup.isSimpleAddGroup_iff`, `Complex.isAddQuotientCoveringMap_exp`, `Submodule.toAddSubgroup_toIntSubmodule`, `AddSubgroup.coe_nsmul`, `AddSubgroup.unop_sup`, `AddSubgroup.le_centralizer_iff_isAddCommutative`, `AddSubgroup.addSubgroupOfEquivOfLe_symm_apply_coe_coe`, `AddSubgroup.card_le_one_iff_eq_bot`, `AddSubgroup.comap_mono`, `unitary.norm_argSelfAdjoint`, `skewAdjoint.negISMul_apply_coe`, `MeasureTheory.lpMeasSubgroupToLpTrim_sub`, `AddSubgroup.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallNeg`, `MeasureTheory.Integrable.toL1_sub`, `NormedAddGroupHom.isClosed_ker`, `lp.ext_continuousAddMonoidHom_iff`, `AddSubgroup.relIndex_eq_two_iff_exists_notMem_and'`, `AddSubgroup.map_le_map_iff_of_injective`, `lp.infty_coeFn_pow`, `AddSubgroup.IsSubnormal.exists_normal_and_le_and_lt_top_of_ne`, `MeasureTheory.MemLp.toLp_neg`, `AddGroup.residuallyFinite_iff_exists_finiteIndex`, `lp.infty_smulCommClass`, `fixedPoints_addSubgroup_antitone`, `CochainComplex.HomComplex.mem_coboundaries_iff`, `AddSubgroup.coe_norm`, `AddSubgroup.coe_mk`, `AddSubgroup.toAddSubmonoid_strictMono`, `AddSubgroup.normalClosure_eq_self`, `AddSubgroup.orderIsoAddCon_symm_apply_coe`, `lp.norm_eq_card_dsupport`, `QuotientAddGroup.mk_out_eq_mul`, `RingSubgroupsBasis.hasBasis_nhds`, `QuotientAddGroup.rightRel_apply`, `ZSpan.isAddFundamentalDomain'`, `AddGroup.fg_def`, `AddSubgroup.coe_op`, `AddSubgroup.index_ne_zero_iff_finite`, `ProbabilityTheory.Kernel.continuous_integral_integral`, `AddSubgroup.addSubgroupOf_isAddCommutative`, `DomMulAct.smul_Lp_neg`, `QuotientAddGroup.nhds_zero_hasBasis`, `GromovHausdorff.ghDist_eq_hausdorffDist`, `AddSubgroup.normalCore_le`, `AddCircle.coe_real_preimage_closedBall_inter_eq`, `AddSubgroup.toIsOrderedAddMonoid`, `AddSubgroup.vadd_leftQuotientEquiv`, `lp.lipschitzWith_one_eval`, `AddSubgroup.codisjoint_addSubgroupOf_sup`, `ProfiniteAddGrp.limit_add_val`, `MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one`, `imaginaryPart_realPart`, `AddSubgroup.relIndex_pointwise_smul`, `lp.instStarModuleSubtypePreLpMemAddSubgroup`, `AddSubgroup.IsComplement.toRightFun_add_neg_mem`, `AddSubgroup.map_le_iff_le_comap`, `CochainComplex.HomComplex.Cocycle.fromSingleMk_coe`, `AddSubgroup.ofAddUnits_inf`, `AddSubgroup.instFaithfulVAddSubtypeMem`, `MeasureTheory.integral_condExpL2_eq_of_fin_meas_real`, `coe_equiv_lpPiLp`, `lp.zeroBasis_apply`, `SubAddAction.nat_card_ofStabilizer_eq`, `AddSubgroup.toZModSubmodule_symm`, `AddSubgroup.addOrderOf_coe`, `AddSubgroup.coe_inf`, `AddSubgroup.neg_mem_iff`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `AddSubgroup.apply_coe_mem_map`, `AddSubgroup.IsSubnormal.trans'`, `CochainComplex.mappingCone.descCocycle_coe`, `MeasureTheory.Lp.simpleFunc.denseRange`, `IsSimpleAddGroup.instIsSimpleOrderAddSubgroup`, `MeasureTheory.memL1_smul_of_L1_withDensity`, `MeasureTheory.condExp_ae_eq_condExpL1`, `imaginaryPart_eq_neg_I_smul_skewAdjointPart`, `AddSubgroup.topEquiv_symm_apply_coe`, `AddSubgroup.mem_normalizer_iff''`, `selfAdjoint.isSelfAdjoint`, `AddSubgroup.comap_le_comap_of_surjective`, `AddCircle.coe_image_Ioc_eq`, `NormedAddGroupHom.Equalizer.ι_comp_map`, `Int.mem_zmultiples_iff`, `SubAddAction.addConjMap_ofFixingAddSubgroup_coe_apply`, `MeasureTheory.condExpIndL1_smul'`, `skewAdjointPart_comp_subtype_selfAdjoint`, `AddSubgroup.isComplement'_top_right`, `AddSubgroup.instVAddAssocClassSubtypeMem`, `IsSimpleAddGroup.eq_bot_or_eq_top_of_normal`, `AddSubgroup.top_prod_top`, `QuotientAddGroup.quotientAddEquivOfEq_mk`, `AddSubgroup.pointwise_smul_toAddSubmonoid`, `AddAction.fixingAddSubgroup_le_stabilizer`, `Set.nsmul_add_addSubgroupClosure`, `QuotientAddGroup.ker_lift`, `AddSubgroup.mem_op`, `AddSubgroup.le_normalizer_map`, `AddAction.stabilizerEquivStabilizer_neg`, `AddSubgroup.ker_subtype`, `AddSubgroup.mem_closure`, `BoundedContinuousFunction.mem_Lp`, `Submodule.mem_toAddSubgroup`, `NormedAddGroupHom.Equalizer.lift_normNoninc`, `lp.coeFn_sum`, `AddSubgroup.nsmul_exponent_eq_zero`, `MeasureTheory.lpMeasSubgroupToLpTrim_right_inv`, `Filter.Tendsto.compMeasurePreservingLp`, `AddSubgroup.mem_smul_pointwise_iff_exists`, `RingSubgroupsBasis.inter`, `BoundedContinuousFunction.Lp_norm_le`, `CochainComplex.HomComplex.Cocycle.leftUnshift_coe`, `DomAddAct.vadd_Lp_ae_eq`, `MeasureTheory.Lp.norm_constL_le`, `AddAction.IsBlock.of_addSubgroup_of_conjugate`, `AddAction.coe_aestabilizer`, `AddSubgroup.exists_neg_mem_iff_exists_mem`, `AddAction.mem_stabilizer_finset'`, `span_selfAdjoint`, `MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc`, `realPart_I_smul`, `AddMonoidHom.addSubgroupMap_surjective`, `DomMulAct.norm_smul_Lp`, `CochainComplex.mappingCone.d_snd_v_assoc`, `lp.norm_compl_sum_single`, `AddSubgroup.card_top`, `KuratowskiEmbedding.embeddingOfSubset_isometry`, `selfAdjoint.realPart_unitarySelfAddISMul`, `MeasureTheory.condExpL2_indicator_of_measurable`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem`, `MeasureTheory.Lp.add_smul`, `MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top`, `MeasureTheory.condExp_ae_eq_condExpL1CLM`, `QuotientAddGroup.lift_comp_mk'`, `CochainComplex.mappingCone.d_snd_v'`, `AddMonoidHom.coe_comp_rangeRestrict`, `DomAddAct.vadd_Lp_sub`, `finEquivZMultiples_apply`, `AddSubgroup.mem_bot`, `BoundedContinuousFunction.coeFn_toLp`, `AddSubgroup.isAddQuotientCoveringMap`, `MeasureTheory.Integrable.toL1_smul'`, `NormedAddGroupHom.Equalizer.norm_map_le`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_inter`, `UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp`, `MeasureTheory.Lp.instContinuousVAddDomAddAct`, `MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp`, `AddEquiv.coe_addSubgroupMap_apply`, `GromovHausdorff.eq_toGHSpace`, `isSimpleAddGroup_iff`, `infinite_zmultiples`, `CochainComplex.mappingCone.liftCochain_fst`, `MeasureTheory.L1.tendsto_setToL1`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le'`, `MeasureTheory.condExpL1CLM_indicatorConst`, `MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim`, `AddSubgroup.coe_center`, `AddSubgroup.isComplement_addSubgroup_left_iff_existsUnique_quotientMk''`, `AddSubgroup.tendsto_coe_cofinite_of_discrete`, `MeasureTheory.L1.nnnorm_Integral_le_one`, `cfcₙ_imaginaryPart`, `MeasureTheory.lpMeasSubgroupToLpTrim_add`, `AddSubgroup.opEquiv_symm_apply`, `MeasureTheory.L1.integral_eq_norm_posPart_sub`, `MeasureTheory.Lp.instContinuousFourierInv`, `imaginaryPart_apply_coe`, `mem_multiples_iff_mem_zmultiples`, `Unitary.openPartialHomeomorph_target`, `AddSubgroup.ofAddUnits_mono`, `CochainComplex.HomComplex.Cocycle.homOf_f`, `CategoryTheory.ShortComplex.ab_exact_iff_ker_le_range`, `QuotientAddGroup.lift_mk`, `UnitAddTorus.hasSum_mFourier_series_L2`, `MeasureTheory.Lp.norm_const`, `MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace`, `MeasureTheory.lpMeasSubgroupToLpTrim_left_inv`, `CategoryTheory.ShortComplex.abLeftHomologyData_f'`, `AddAction.mem_stabilizer_set'`, `CochainComplex.mappingCone.d_fst_v_assoc`, `QuotientAddGroup.mk_sub`, `CochainComplex.homOfDegreewiseSplit_f`, `CochainComplex.HomComplex.Cocycle.δ_eq_zero`, `MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real`, `AddSubmonoid.addUnits_inf`, `AddSubgroup.mem_ofAddUnits_iff_exists_isAddUnit`, `AddSubgroup.relIndex_top_right`, `AddSubgroup.exists_zmultiples`, `MeasureTheory.L1.setToL1_unique`, `AddMonoid.Coprod.codisjoint_range_inl_range_inr`, `lp.single_sub`, `Function.Periodic.map_vadd_zmultiples`, `AddGroup.fg_iff_addSubgroup_fg`, `AddSubgroup.map_isAddCommutative`, `cfc_comp_re`, `coe_lpPiLpₗᵢ`, `imaginaryPart_comp_subtype_selfAdjoint`, `Multiplicative.mem_toSubgroup`, `QuotientAddGroup.quotientKerEquivOfRightInverse_symm_apply`, `CochainComplex.mappingCone.δ_snd`, `Subgroup.instDiscreteTopStrictPeriods`, `AddMonoidHom.restrict_range`, `AddSubgroup.forall_zmultiples`, `MeasureTheory.Lp.instAddLeftMono`, `AddSubgroup.mul_toAddSubmonoid`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left`, `AddSubgroup.coe_matrix`, `quotient_norm_mk_eq`, `ContinuousLinearMap.lpPairing_eq_integral`, `AddSubgroup.map_bot`, `AddSubgroup.coe_zsmul`, `ArchimedeanClass.ballAddSubgroup_antitone`, `MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc`, `AddSubgroup.op_sSup`, `AddSubgroup.instMeasurableConstVAdd`, `instProperVAddSubtypeMemAddSubgroupOfIsClosedCoe`, `ContinuousLinearMap.holder_smul_right`, `lp.lsingle_apply`, `AddSubgroup.quotientiInfEmbedding_apply`, `OpenAddSubgroup.toAddSubgroup_sup`, `ProfiniteAddGrp.limit_ext_iff`, `AddCircle.norm_coe_eq_abs_iff`, `AddSubgroup.leftCoset_cover_const_iff_surjOn`, `CochainComplex.mappingCone.inl_v_fst_v`, `MeasureTheory.L2.eLpNorm_inner_lt_top`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left'`, `NormedAddGroupHom.incl_apply`, `QuotientAddGroup.measurable_coe`, `rightAddCoset_eq_iff`, `MeasureTheory.condExpL1CLM_lpMeas`, `AddSubgroup.centerCongr_symm_apply_coe`, `AddSubgroup.mem_comap`, `selfAdjoint.val_inv`, `QuotientAddGroup.quotientMapAddSubgroupOfOfLe_mk`, `AddSubgroup.comap_injective`, `AddSubgroup.unop_eq_top`, `MeasureTheory.Lp.mem_Lp_iff_memLp`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff`, `selfAdjoint.val_smul`, `QuotientAddGroup.integral_eq_integral_automorphize`, `AddSubgroup.finite_quotient_of_finite_quotient_of_index_ne_zero`, `AddAction.le_stabilizer_vadd_right`, `AddCommGrpCat.kernelIsoKer_inv_comp_ι`, `CochainComplex.Lifting.π_f_cochain₁_v_ι_f_assoc`, `Subgroup.toAddSubgroup_closure`, `QuotientAddGroup.btw_coe_iff`, `SchwartzMap.norm_fourier_Lp_top_leq_toLp_one`, `Subring.toAddSubgroup_strictMono`, `realPart_surjective`, `StrongDual.toLpₗ_apply`, `MeasureTheory.L1.setToL1_apply_coeToLp`, `MeasureTheory.Lp.const_mem_Lp`, `AddEquiv.coe_mapAddSubgroup`, `NormedAddGroupHom.Equalizer.ι_comp_lift`, `MeasureTheory.Lp.compMeasurePreserving_comp_apply`, `AddSubgroup.MapSubtype.orderIso_apply_coe`, `AddSubgroup.characteristic_iff_le_comap`, `AddSubgroup.closure_nsmul_le`, `AddSubgroup.coe_add`, `AddSubgroup.instIsTopologicalAddGroupSubtypeMem`, `AddSubgroup.unop_eq_bot`, `QuotientAddGroup.addSubgroup_eq_top_of_subsingleton`, `AddSubgroup.coe_toZModSubmodule`, `Subgroup.two_mul_widthInfty_mem_strictPeriods`, `AddSubgroup.coe_bot`, `QuotientAddGroup.dense_image_mk`, `MeasureTheory.indicatorConstLp_add`, `AddSubgroup.mem_centralizer_iff_addCommutator_eq_zero`, `MeasureTheory.L1.setToL1_congr_left'`, `DomAddAct.vadd_Lp_neg`, `AddSubgroup.centralizer_le`, `selfAdjoint.star_coe_unitarySelfAddISMul`, `MeasureTheory.Lp.simpleFunc.coeFn_le`, `AddSubgroup.Normal.addCommutator_le_of_self_sup_commutative_eq_top`, `AddSubgroup.map_injective`, `FreeAddGroup.closure_range_of`, `MeasureTheory.Lp.instFourierPairInv`, `lp.norm_neg`, `AddMonoidHom.eqOn_closure`, `AddAction.op_vadd_set_stabilizer_subset`, `AddMonoid.le_minOrder_iff_forall_addSubgroup`, `AddSubgroup.top_toAddSubmonoid`, `AddSubgroup.finiteIndex_iInf`, `Subgroup.coe_toAddSubgroup_apply`, `AddCommGrpCat.epi_iff_range_eq_top`, `leftAddCoset_eq_iff`, `AddSubgroup.mem_goursatFst`, `AddSubgroup.index_map_subtype`, `AddSubgroup.IsSubnormal.bot`, `AddSubgroup.Normal.mem_comm_iff`, `AddSubmonoid.mem_addUnits_of_val_mem_neg_val_mem`, `MeasureTheory.AddSubgroup.index_mul_measure`, `skewAdjoint.star_val_eq`, `MeasureTheory.Lp.norm_le_of_ae_bound`, `AddSubgroup.card_map_dvd`, `QuotientAddGroup.mk_nat_mul`, `AddCircle.denseRange_zsmul_coe_iff`, `finEquivZMultiples_symm_apply`, `AddSubgroup.mem_closure_singleton_self`, `AddSubgroup.mem_mk`, `SchwartzMap.norm_toLp'`, `CochainComplex.mappingCocone.inr_v_fst_f_assoc`, `AddSubgroup.FG.iSup`, `AddSubgroup.eq_top_of_le_card`, `MeasureTheory.Lp.simpleFunc.toLp_zero`, `AddAction.isBlock_top`, `eq_addCosets_of_normal`, `AddSubgroup.toAddSubmonoid_injective`, `MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner`, `Submodule.toAddSubgroup_strictMono`, `MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral`, `cfcₙ_im_id`, `AddAction.addSubgroup_vadd_def`, `AddSubgroup.coe_eq_singleton`, `multiples_eq_zmultiples`, `MeasureTheory.Lp.coeFn_nonneg`, `AddSubgroup.sup_normal`, `MeasureTheory.Lp.toLp_coeFn`, `AddSubgroup.unop_bot`, `AddSubgroup.FG.finset_sup`, `QuotientAddGroup.norm_lift_apply_le`, `Valuation.mem_ltAddSubgroup_iff`, `TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_nonunital`, `MeasureTheory.nnnorm_indicatorConstLp_le`, `DomMulAct.dist_smul_Lp`, `QuotientAddGroup.instDiscreteMeasurableSpace`, `MeasureTheory.Lp.instFourierInvAdd`, `quasispectrum_realPart`, `AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_symm_apply_coe`, `AddSubgroup.map_mono`, `AddSubgroup.ofAddUnits_iSup₂`, `MeasureTheory.L1.setToL1_congr_left`, `AddSubgroup.addCommutator_le_left`, `HilbertBasis.repr_symm_single`, `HilbertBasis.repr_apply_apply`, `imaginaryPart_surjective`, `NormedAddGroupHom.SurjectiveOnWith.surjOn`, `AddCommGroup.coe_primaryComponent`, `MeasureTheory.L1.setToL1_smul`, `AddSubgroup.mem_sup_right`, `MeasureTheory.Lp.coeFn_lpSMul`, `AddSubgroup.sup_eq_closure`, `AddSubgroup.le_normalClosure`, `Subgroup.strictPeriods_le_periods`, `AddSubgroup.coe_sub`, `MeasureTheory.Lp.simpleFunc.coeFn_zero`, `AddCircle.coe_eq_zero_of_pos_iff`, `lp.coeFn_smul`, `OpenAddSubgroup.coe_toAddSubgroup`, `MeasureTheory.condExpIndSMul_nonneg`, `QuotientAddGroup.map_surjective_of_surjective`, `AddSubgroup.nsmul_relIndex_mem`, `lp.summable_inner`, `selfAdjoint.val_pow`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'`, `AddSubgroup.nontrivial_iff_exists_ne_zero`, `AddSubgroup.top_prod`, `lp.infty_coeFn_one`, `AddSubgroup.finite_quotient_of_finiteIndex`, `coe_addEquiv_lpBCF_symm`, `QuotientAddGroup.mk_zero`, `AddSubgroup.map_subtype_inj`, `MeasureTheory.L1.dist_def`, `AddSubgroup.mem_centralizer_iff`, `AddSubgroup.mem_of_mem_val_ofAddUnits`, `ContinuousLinearMap.coeFn_compLpL`, `NormedAddGroupHom.Equalizer.lift_apply_coe`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_union`, `Real.Lp.fourierTransformCLM_apply`, `QuotientAddGroup.instLocallyCompactSpace`, `AddSubgroup.eq_bot_or_eq_top_of_prime_card`, `StrongDual.norm_toLpₗ_le`, `MeasureTheory.Lp.coe_mk`, `Subfield.mem_toAddSubgroup`, `selfAdjoint.realPart_coe`, `Subgroup.index_toAddSubgroup`, `AddMonoidHom.coe_toIntLinearMap_ker`, `MeasureTheory.Lp.instIsCentralScalar`, `lp.single_smul`, `AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq`, `AddSubgroup.gc_map_comap`, `Subring.sInf_toAddSubgroup`, `SubAddAction.ofFixingAddSubgroup_insert_map_apply`, `QuotientAddGroup.norm_mk_eq_zero`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left'`, `MeasureTheory.L1.norm_integral_le`, `MeasureTheory.setIntegral_indicatorConstLp`, `lp.ext_iff`, `AddSubgroup.saturated_iff_zsmul`, `lp.norm_zero`, `AddGroupExtension.Section.add_add_add_neg_mem_range_inl`, `NonUnitalSubring.mem_toAddSubgroup`, `NormedAddGroupHom.ker_completion`, `ProbabilityTheory.Kernel.continuous_integral_integral_comp`, `isCancelVAdd_iff_stabilizer_eq_bot`, `AddSubgroup.add_mem_iff_of_index_two`, `LipschitzOnWith.coordinate`, `lp.instIsCentralScalarSubtypePreLpMemAddSubgroup`, `AddSubgroup.addSubgroupOf_bot_eq_top`, `AddSubgroup.normal_addSubgroupOf_iff`, `ContinuousMap.toLp_injective`, `AddSubgroup.addSubgroupOf_map_nsmulAddMonoidHom_eq_range`, `CochainComplex.mappingCone.inr_f_fst_v_assoc`, `StrongDual.toLpₗ_of_not_memLp`, `MeasureTheory.indicatorConstLp_sub`, `AddSubgroup.map_subtype_le_map_subtype`, `AddSubgroup.finite_iff_finite_and_finiteIndex`, `AddSubgroup.op_iInf`, `AddSubgroup.bot_addSubgroupOf`, `CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v`, `AddSubgroup.coe_toIntSubmodule`, `AddSubgroup.normalizer_eq_top`, `AddSubgroup.zmultiples_le_of_mem`, `AddMonoid.Coprod.range_swap`, `DomAddAct.edist_vadd_Lp`, `AddCircle.norm_neg_period`, `QuotientAddGroup.quotientBot_apply`, `MeasureTheory.L1.aemeasurable_coeFn`, `QuotientAddGroup.equivIocMod_symm_apply`, `Valuation.ltAddSubgroup_le_leAddSubgroup`, `MeasureTheory.Subgroup.vaddInvariantMeasure`, `AddSubgroup.relIndex_addSubgroupOf`, `MeasureTheory.integrable_condExpL2_of_isFiniteMeasure`, `AddEquiv.mapAddSubgroup_apply`, `controlled_sum_of_mem_closure`, `CategoryTheory.ShortComplex.abLeftHomologyData_i`, `lp.inner_single_left`, `MeasureTheory.condExpIndL1Fin_disjoint_union`, `instIsModularLatticeAddSubgroup`, `MeasureTheory.Lp.tendsto_Lp_of_tendsto_eLpNorm`, `map_addCommutator_eq`, `MeasureTheory.Lp.instIsBoundedSMul`, `AddSubgroup.smul_mem_pointwise_smul`, `AddSubgroup.unop_iInf`, `ContinuousMap.coe_toLp`, `skewAdjointPart_apply_coe`, `AddSubgroup.comap_lt_comap_of_surjective`, `QuotientAddGroup.quotientKerEquivOfRightInverse_apply`, `UnitAddCircle.norm_eq`, `continuous_selfAdjointPart`, `lp.hasSum_norm`, `AddSubgroup.centralizer_eq_top_iff_subset`, `selfAdjoint.val_qsmul`, `DomMulAct.instIsIsometricSMulSubtypeAEEqFunMemAddSubgroupLp`, `MeasureTheory.Lp.antitone`, `SchwartzMap.norm_toLp_top_le`, `AddSubgroup.inf_relIndex_right`, `Finset.le_card_quotient_add_sq_inter_addSubgroup`, `lp.norm_le_of_forall_sum_le`, `MonoidHom.coe_toAdditive_range`, `ContinuousLinearMap.integral_comp_L1_comm`, `QuotientAddGroup.preimage_image_coe`, `addCommutator_def`, `AddSubgroup.comap_iInf`, `AddCommGroup.isTorsion_quotient_range_nsmulAddMonoidHom`, `AddSubgroup.ofAddUnits_inf_addUnits`, `AddAction.orbitEquivQuotientStabilizer_symm_apply`, `AddSubgroup.surjective_normedMk`, `span_fourierLp_closure_eq_top`, `selfAdjointPartL_apply_coe`, `AddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_top`, `lp.norm_le_of_forall_le`, `AddSubgroup.mem_carrier`, `MeasureTheory.L1.measurable_coeFn`, `QuotientAddGroup.mk_zsmul`, `MeasureTheory.aestronglyMeasurable_condExpL1CLM`, `AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div`, `AddSubgroup.mem_sup_of_normal_right`, `AddSubgroup.disjoint_map`, `Subgroup.strictWidthInfty_mem_strictPeriods`, `SchwartzMap.inner_fourierTransformCLM_toL2_eq`, `QuotientAddGroup.mk_nsmul`, `SubAddAction.mem_fixingAddSubgroup_insert_iff`, `AddSubgroup.vadd_def`, `AddSubgroup.FG.biSup_finset`, `AddSubgroup.addOrderOf_dvd_natCard`, `MeasureTheory.continuous_integral`, `AddSubgroup.mem_inf`, `lp.infty_coeFn_intCast`, `MeasureTheory.Lp.simpleFunc.isBoundedSMul`, `AddSubgroup.mem_map_equiv`, `lp.tsum_mul_le_mul_norm'`, `AddSubgroup.le_normalizer_of_normal`, `AddMonoidHom.sub_mem_ker_iff`, `MeasureTheory.Lp.coe_posPart`, `Int.addSubgroupClosure_one`, `AddSubgroup.addCommutator_le_focalAddSubgroup`, `MeasureTheory.integrable_condExpL2_indicator`, `AddSubgroup.addUnit_mem_of_mem_ofAddUnits`, `AddSubgroup.eq_top_iff'`, `MeasureTheory.Lp.zero_smul`, `QuotientAddGroup.btw_coe_iff'`, `AddSubgroup.exists_nsmul_mem_of_index_ne_zero`, `AddSubgroup.addCommutator_addCommutator_eq_bot_of_rotate`, `QuotientAddGroup.image_coe`, `AddMonoid.Coprod.range_lift`, `coe_lpBCFₗᵢ_symm`, `coe_lpPiLpₗᵢ_symm`, `AddSubgroup.card_bot`, `lp.norm_single`, `QuotientAddGroup.instFirstCountableTopology`, `mem_zmultiples_iff_mem_range_addOrderOf`, `AddSubgroup.relIindex_eq_two_iff'`, `AddSubgroup.opEquiv_apply`, `DomMulAct.smul_Lp_zero`, `AddCircle.continuous_mk'`, `AddMonoidHom.fiberEquivKer_symm_apply`, `AddSubgroup.relIndex_bot_right`, `Complex.coe_selfAdjointEquiv`, `AddAction.card_orbit_mul_card_stabilizer_eq_card_addGroup`, `AddCircle.coe_real_preimage_closedBall_period_zero`, `DomAddAct.mk_vadd_toLp`, `AddSubgroup.eq_bot_iff_forall`, `QuotientAddGroup.dense_preimage_mk`, `AddSubgroup.le_pi_iff`, `RingPreordering.mem_supportAddSubgroup`, `AddSubgroup.closure_iUnion`, `coe_addEquiv_lpBCF`, `AddSubgroup.MapSubtype.orderIso_symm_apply`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_isDiscrete_ker_addMonoidHom`, `MeasureTheory.lpMeasSubgroupToLpTrim_norm_map`, `MeasureTheory.MemLp.condExpL2_ae_eq_condExp'`, `imaginaryPart_ofReal`, `MeasureTheory.Lp.completeSpace_lp_of_cauchy_complete_eLpNorm`, `SubAddAction.ofStabilizer.addConjMap_comp_apply`, `MeasureTheory.Lp.simpleFunc.toLp_sub`, `RingPreordering.one_notMem_supportAddSubgroup`, `MeasureTheory.Lp.simpleFunc.coe_smul`, `FreeAddGroup.range_lift_le`, `AddEquiv.range_eq_top`, `AddSubgroup.gc_toAddSubmonoid_support`, `AddSubgroup.intCast_mul_mem_zmultiples`, `QuotientAddGroup.comap_comap_center`, `AddSubgroup.normal_centralizer`, `MeasureTheory.Lp.smul_def`, `AddSubgroup.map_lt_map_iff_of_injective`, `AddSubgroup.properlyDiscontinuousVAdd_opposite_of_tendsto_cofinite`, `MeasureTheory.Lp.norm_exponent_zero`, `MeasureTheory.Lp.smul_neg`, `Set.addConj_mem_fixingAddSubgroup`, `AddSubgroup.instDiscreteTopologyZMultiples`, `dense_addSubgroupClosure_pair_iff`, `AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `MeasureTheory.L1.stronglyMeasurable_coeFn`, `AddSubgroup.mem_sup`, `Commute.expUnitary_add`, `orbit_addSubgroup_zero_eq_self`, `ContinuousMap.coeFn_toLp`, `MeasureTheory.L1.norm_setToL1_le_mul_norm'`, `AddSubgroup.val_finset_sum`, `AddSubgroup.Normal.conj_mem`, `MeasureTheory.Lp.simpleFunc.exists_simpleFunc_nonneg_ae_eq`, `AddSubgroup.addSubgroupOf_inj`, `IsSelfAdjoint.coe_selfAdjointPart_apply`, `AddSubgroup.op_injective`, `AddSubgroup.isOpen_of_openAddSubgroup`, `AddSubgroup.coe_even`, `QuotientAddGroup.instContinuousConstVAdd`, `AddSubgroup.nsmul_mem`, `lp.mem_lp_const_smul`, `AddMonoidHom.coe_toIntLinearMap_map`, `AddSubgroup.ker_normedMk`, `QuotientAddGroup.isQuotientMap_mk`, `MeasureTheory.tendstoInMeasure_of_tendsto_Lp`, `AddSubgroup.prod_le_iff`, `ProbabilityTheory.condVar_of_sigmaFinite`, `NormedAddGroupHom.IsQuotient.norm`, `SubAddAction.ofStabilizer.snoc_castSucc`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀`, `lp.tsumCLM_apply`, `AddSubmonoid.isOpen_addUnits`, `MeasureTheory.Lp.instSMulCommClass`, `OrthogonalFamily.range_linearIsometry`, `MeasureTheory.Lp.simpleFunc.toLp_neg`, `AddSubgroup.mem_center_iff`, `AddSubgroup.inclusion_inj`, `SubAddAction.fixingAddSubgroupEquivFixingAddSubgroup_coe_apply`, `MeasureTheory.L1.SimpleFunc.integral_smul`, `AddSubgroup.isComplement'_bot_left`, `isPointed_iff_support_eq_bot`, `MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one`, `AddSubgroup.closure_eq`, `MeasureTheory.lpTrimToLpMeas_ae_eq`, `AddSubgroup.mem_even`, `AddSubgroup.exists_mem_zmultiples`, `QuotientAddGroup.mk_sum`, `AddSubgroup.bot_or_nontrivial`, `lp.single_add`, `AddSubgroup.centerToAddOpposite_symm_apply_coe`, `DomAddAct.vadd_Lp_const`, `AddSubgroup.normal_addSubgroupOf`, `AddSubgroup.orderIsoAddCon_apply`, `Set.addSubgroupClosure_add`, `AddSubgroup.smul_mem_pointwise_smul_iff₀`, `MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le`, `ContinuousMap.toLp_comp_toContinuousMap`, `IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_AddHaarMeasure`, `QuotientAddGroup.map_mk'`, `AddSubgroup.sub_mem`, `NormedAddGroupHom.coe_ker`, `AddSubgroup.relIndex_dvd_two_iff`, `lp.norm_sub_norm_compl_sub_single`, `AddCommGroup.mem_torsion`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_measure`, `AddSubgroup.comap_subtype`, `MeasureTheory.Lp.smul_comm`, `SchwartzMap.continuous_toLp`, `selfAdjoint.val_ratCast`, `zmultiples_eq_top_of_prime_card`, `lp.infty_coeFn_natCast`, `MeasureTheory.isComplete_aestronglyMeasurable`, `AddCircle.instAddQuotientMeasureEqMeasurePreimageSubtypeAddOppositeRealMemAddSubgroupOpZmultiplesVolume`, `MeasureTheory.Lp.simpleFunc.isUniformEmbedding`, `AddAction.mem_stabilizer_finset_iff_subset_vadd_finset`, `AddSubgroup.focalAddSubgroup_le_addCommutator`, `MeasureTheory.L1.integral_of_fun_eq_integral`, `MeasureTheory.L1.integral_zero`, `QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff`, `AddSubgroup.map_addSubgroupOf_eq_of_le`, `QuotientAddGroup.orbit_eq_out_vadd`, `CochainComplex.mappingCone.inl_fst`, `AddMonoidHom.coe_toIntLinearMap_range`, `AddSubgroup.mem_iSup_of_mem`, `lp.hasSum_inner`, `CochainComplex.HomComplex.Cocycle.shift_coe`, `AddSubgroup.normal_top`, `SchwartzMap.toLp_fourierTransform_eq`, `MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le`, `MeasureTheory.continuous_indicatorConstLp_set`, `AddSubgroup.closure_closure_coe_preimage`, `MeasureTheory.condExpIndL1_of_not_measurableSet`, `AddSubgroup.IsSubnormal.addSubgroupOf`, `MeasureTheory.Lp.smul_add`, `MeasureTheory.L1.norm_setToL1_le'`, `MeasureTheory.withDensitySMulLI_apply`, `AddSubgroup.one_lt_card_iff_ne_bot`, `NormedAddGroupHom.lift_norm_le`, `AddMonoidHom.coe_toMultiplicative_map`, `CochainComplex.mappingCone.liftCochain_v_fst_v_assoc`, `AddSubgroup.nsmul_index_mem`, `NormedAddGroupHom.mem_range_self`, `MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq`, `CochainComplex.mappingCone.lift_desc_f`, `AddSubgroup.coe_iInf`, `skewAdjoint.conjugate'`, `ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite`, `UnitAddTorus.hasSum_prod_mFourierCoeff`, `AddSubgroup.botCharacteristic`, `AddSubgroup.instFiniteSubtypeMem`, `AddSubgroup.nontrivial_iff_ne_bot`, `Complex.selfAdjointEquiv_symm_apply`, `DomMulAct.smul_Lp_ae_eq`, `SubAddAction.ENat_card_ofStabilizer_add_zero_eq`, `OpenAddSubgroup.toAddSubgroup_inf`, `NormedAddGroupHom.ker.incl_comp_lift`, `AddSubgroup.neg_mem`, `MeasureTheory.Lp.simpleFunc.isUniformInducing`, `IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single`, `AddSubgroup.prod_mono`, `AddSubgroup.ofAddUnits_strictMono`, `Subgroup.toAddSubgroup_comap`, `isCoveringMapOn_quotientMk_of_properlyDiscontinuousVAdd`, `MeasureTheory.L1.norm_of_fun_eq_integral_norm`, `Function.Exact.addMonoidHom_rangeRestrict`, `selfAdjointPart_apply_coe`, `MeasureTheory.L1.integral_add`, `MeasureTheory.Lp.mem_Lp_iff_eLpNorm_lt_top`, `AddSubgroup.add_inf_assoc`, `MeasureTheory.aestronglyMeasurable_condExpIndSMul`, `skewAdjointPartL_apply_coe`, `CochainComplex.mappingCone.desc_f`, `CochainComplex.mappingCone.d_fst_v'_assoc`, `CochainComplex.mappingCocone.inr_v_fst_f`, `MeasureTheory.Lp.constL_apply`, `SubAddAction.fixingAddSubgroup_of_insert`, `MeasureTheory.L2.mem_L1_inner`, `QuotientAddGroup.exists_mk`, `MeasureTheory.L1.integral_eq_integral`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp`, `AddSubgroup.two_smul_mem_of_index_two`, `AddSubgroup.subtype_injective`, `MeasureTheory.Integrable.coeFn_toL1`, `AddSubgroup.prod_mono_right`, `MeasureTheory.Lp.simpleFunc.coe_indicatorConst`, `FiniteArchimedeanClass.addSubgroup_strictAnti`, `AddSubgroup.normal_addSubgroupOf_of_le_normalizer`, `MeasureTheory.condExpIndL1_disjoint_union`, `AddSubgroup.instFiniteIndexTop`, `AddSubgroup.topEquiv_apply`, `ContinuousLinearMap.add_compLp`, `AddSubgroup.map_iInf`, `MeasureTheory.Lp.inner_fourier_eq`, `ker_imaginaryPart`, `MeasureTheory.Integrable.norm_toL1_eq_lintegral_norm`, `AddSubgroup.disjoint_iff_add_eq_zero`, `Submodule.AddMonoidHom.coe_toIntLinearMap_comap`, `AddSubgroup.coe_map`, `MeasureTheory.L1.aestronglyMeasurable_coeFn`, `AddAction.right_quotientAction`, `AddSubgroup.isAddCyclic`, `SubAddAction.of_fixingAddSubgroupEmpty_mapScalars_surjective`, `HilbertBasis.repr_self`, `AddSubgroup.exists_isComplement_right`, `SubAddAction.ofStabilizer.neg_addConjMap_comp_apply`, `AddSubgroup.val_mem_ofAddUnits_iff_mem`, `MeasureTheory.condExpInd_smul'`, `AddSubgroup.vadd_toLeftFun`, `MeasureTheory.L1.setToL1_add_left`, `AddAction.stabilizerEquivStabilizer_apply`, `SubAddAction.mem_ofFixingAddSubgroup_iff`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `AddSubgroup.finiteIndex_toSubgroup_iff`, `AddSubgroup.normal_addSubgroupOf_iff_le_normalizer`, `Function.Exact.iff_addMonoidHom_rangeRestrict`, `AddSubgroup.isAddCyclic_of_le`, `AddSubgroup.mem_sSup_of_mem`, `MeasureTheory.Lp.eLpNorm_lt_top`, `AddMonoidHom.finite_iff_finite_ker_range`, `MeasureTheory.L2.integrable_inner`, `realPart_imaginaryPart`, `SchwartzMap.norm_fourier_toBoundedContinuousFunction_le_toLp_one`, `QuotientAddGroup.quotientBot_symm_apply`, `BoundedContinuousFunction.toLp_norm_le`, `AddSubgroup.quotientiInfAddSubgroupOfEmbedding_apply`, `AddSubgroup.center_eq_iInf`, `AddSubgroup.coe_pi`, `AddSubgroup.normalClosure_idempotent`, `MeasureTheory.Lp.continuous_negPart`, `MeasureTheory.Lp.coeFn_negPart`, `AddAction.IsBlock.orbit_stabilizer_eq`, `AddAction.stabilizerEquivStabilizer_trans`, `lp.norm_tsum_le`, `selfAdjoint.mem_iff`, `QuotientAddGroup.addMonoidHom_ext_iff`, `OpenAddSubgroup.toAddSubgroup_top`, `Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples`, `AddSubgroup.coe_toSubgroup_apply`, `mem_zmultiples_zsmul_iff`, `QuotientAddGroup.isClosedMap_coe`, `AddSubgroup.addConjugatesOfSet_subset_normalClosure`, `coe_addEquiv_lpPiLp`, `CochainComplex.mappingCone.d_fst_v'`, `MeasureTheory.condExp_of_sigmaFinite`, `NormedAddGroupHom.norm_lift_le`, `AddSubgroup.val_multiset_sum`, `AddSubgroup.mk_eq_zero`, `MeasureTheory.norm_setToFun_le_mul_norm`, `AddEquiv.addSubgroupCongr_symm_apply`, `lp.infty_isScalarTower`, `MeasureTheory.L1.SimpleFunc.norm_eq_integral`, `MeasureTheory.condExpIndL1_of_measure_eq_top`, `AddAction.stabilizer_addSubgroup`, `AddSubgroup.set_add_normalizer_comm`, `AddSubgroup.dense_or_cyclic`, `RingPreordering.coe_supportAddSubgroup`, `fixingAddSubgroup_fixedPoints_gc`, `AddMonoidHom.closure_preimage_le`, `AddSubgroup.le_zmultiples_iff`, `AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div`, `Fintype.card_zmultiples`, `NormedAddGroupHom.Equalizer.map_comp_map`, `skewAdjointPart_eq_I_smul_imaginaryPart`, `QuotientAddGroup.range_mk'`, `MeasureTheory.L1.SimpleFunc.norm_integral_le_norm`, `lp.linearMapOfLE_comp`, `AddSubmonoid.neg_mem_addUnits`, `AddSubgroup.instNontrivial`, `SubAddAction.ofFixingAddSubgroup_carrier`, `AddSubgroup.Normal.mem_comm`, `MeasureTheory.Lp.simpleFunc.toLp_smul`, `AddSubgroup.instCountableSubtypeMemZMultiples`, `NormedAddGroupHom.Equalizer.comp_ι_eq`, `AddSubgroup.addCommutator_def'`, `Subring.toAddSubgroup_le_toAddSubgroup`, `MeasureTheory.L1.norm_setToL1_le_mul_norm`, `Subgroup.mem_strictPeriods_iff`, `AddSubgroup.normalizer_le_normalizer_sup_normal`, `AddSubgroup.mem_normalizer_iff'`, `MeasureTheory.MemLp.coeFn_toLp`, `AddSubgroup.mem_iSup_prop`, `QuotientAddGroup.map_mk`, `IsTorsion.addSubgroup`, `AddSubmonoid.addUnits_left_inverse`, `AddSubgroup.coe_pointwise_smul`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left'`, `NonUnitalSubring.sInf_toAddSubgroup`, `CochainComplex.mappingCone.inl_fst_assoc`, `AddSubgroup.addSubgroupOf_bot_eq_bot`, `AddSubgroup.quotientEquivProdOfLE'_apply`, `MeasureTheory.Lp.neg_smul`, `AddGrpCat.epi_iff_range_eq_top`, `QuotientAddGroup.lift_surjective_of_surjective`, `Submodule.toAddSubgroup_eq_top`, `CochainComplex.HomComplex.Cocycle.ext_iff`, `lp.eq_zero'`, `selfAdjoint.val_nnratCast`, `MeasureTheory.Lp.instOrderClosedTopologySubtypeAEEqFunMemAddSubgroupOfClosedIciTopology`, `AddSubgroup.FG.biSup`, `MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le_mul`, `AddAction.Quotient.vadd_mk`, `Valuation.leAddSubgroup_zero`, `NormedAddGroupHom.ker_le_ker_completion`, `AddSubgroup.topologicalClosure_mono`, `selfAdjoint.val_re_map_spectrum`, `AddMonoidHom.eqLocus_same`, `QuotientAddGroup.equivQuotientZSMulOfEquiv_refl`, `QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff`, `AddSubgroup.exponent_top`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff`, `QuotientAddGroup.norm_eq_addGroupSeminorm`, `Subring.mem_toAddSubgroup`, `AddSubgroup.mem_sInf`, `AddSubgroup.mem_addSubgroupOf`, `AddGroup.addConjugatesOfSet_subset`, `AddSubgroup.isAddCyclic_zmultiples`, `AddSubgroup.op_iSup`, `CochainComplex.HomComplex.Cocycle.ofHom_coe`, `QuotientAddGroup.continuous_mk`, `lp.tendsto_lp_of_tendsto_pi`, `MeasureTheory.norm_condExpInd_le`, `AddSubgroup.comap_top`, `AddGroup.closure_finset_fg`, `MeasureTheory.setToFun_mono_left`, `AddSubgroup.normal_iInf_normal`, `MeasureTheory.MemLp.toLp_add`, `AddSubgroup.fg_iff_mul_fg`, `AddSubgroup.ofAddUnits_sup_addUnits`, `star_mul_self_sub_self_mul_star`, `AddSubgroup.normalCore_mono`, `AddSubgroup.mk_le_mk`, `fixingAddSubgroup_antitone`, `AddCircle.isAddQuotientCoveringMap_zsmul`, `Ideal.pointwise_smul_toAddSubgroup`, `AddEquiv.symm_comapAddSubgroup`, `AddSubgroup.mk_vadd`, `QuotientAddGroup.map_normal`, `CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom`, `MeasureTheory.inner_condExpL2_eq_inner_fun`, `StrongDual.toLp_apply`, `AddCircle.coe_period`, `QuotientAddGroup.map_id`, `MeasureTheory.Lp.coeFn_zero`, `AddSubgroup.index_eq_two_iff`, `AddGroup.fg_range`, `MeasureTheory.mem_lpMeas_self`, `AddMonoidHom.range_le_ker_iff`, `AddSubgroup.subtype_comp_inclusion`, `MeasureTheory.norm_Lp_toLp_restrict_le`, `MeasureTheory.integrableOn_condExpL2_of_measure_ne_top`, `AddSubgroup.nsmul_mem_zmultiples`, `hasSum_sq_fourierCoeff`, `ContinuousLinearMap.holder_add_right`, `MeasureTheory.Lp.enorm_def`, `skewAdjoint.conjugate`, `MeasureTheory.condExpInd_disjoint_union_apply`, `NonUnitalSubring.mem_closure_iff`, `AddSubgroup.toIntSubmodule_toAddSubgroup`, `CochainComplex.HomComplex.δ_comp_zero_cocycle`, `ContinuousLinearMap.add_compLpL`, `imaginaryPart_imaginaryPart`, `MeasureTheory.L1.setToL1_simpleFunc_indicatorConst`, `FiniteArchimedeanClass.ballAddSubgroup_strictAnti`, `lp.instNormOneClassSubtypePreLpMemAddSubgroupTopENNRealOfNonempty`, `IsHilbertSum.linearIsometryEquiv_symm_apply_single`, `MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm'`, `fixedPoints_addSubgroup_iSup`, `QuotientAddGroup.map_map`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left`, `UnitAddTorus.mFourierBasis_repr`, `NormedAddGroupHom.Equalizer.map_id`, `MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul`, `MeasureTheory.Lp.norm_measure_zero`, `QuotientAddGroup.lift_quot_mk`, `ArchimedeanClass.addSubgroup_strictAntiOn`, `AddMonoidHom.ker_rangeRestrict`, `skewAdjoint.smul_mem`, `MeasureTheory.tendsto_indicatorConstLp_set`, `AddSubgroup.mem_addUnits_iff_val_mem`, `AddSubgroup.instIsAddCommutativeQuotientSubtypeMemFocalAddSubgroupOf`, `LipschitzWith.coeFn_compLp`, `MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot`, `CochainComplex.HomComplex.Cocycle.coe_zero`, `fourierBasis_repr`, `quasispectrum_realPart'`, `AddGroup.ResiduallyFinite.iInf_eq_bot`, `AddSubgroup.le_comap_map`, `QuotientAddGroup.nhds_eq`, `AddAction.isMultiplyPreprimitive_iff`, `NormedAddGroupHom.isQuotientQuotient`, `MeasureTheory.L1.setToL1_zero_left'`, `MeasureTheory.BoundedContinuousFunction.inner_toLp`, `cfc_re_id`, `QuotientAddGroup.norm_mk_le_norm`, `MeasureTheory.condExpL1_mono`, `AddSubgroup.index_range`, `MeasureTheory.Lp.coeFn_neg`, `MeasureTheory.L1.norm_Integral_le_one`, `AddCommGrpCat.kernelIsoKer_hom_comp_subtype`, `AddCircle.addOrderOf_period_div`, `AddSubgroup.toSubgroup'_closure`, `AddSubgroup.pointwise_smul_le_iff`, `measurePreserving_quotientAddGroup_mk_of_AddQuotientMeasureEqMeasurePreimage`, `ArchimedeanClass.mem_ballAddSubgroup_iff`, `MeasureTheory.Lp.toLp_compMeasurePreserving`, `MeasureTheory.Lp.coeFn_abs`, `AddSubgroup.map_comap_le`, `AddMonoidHom.ker_eq_top_iff`, `AddSubgroup.comap_sup_eq`, `AddSubgroup.map_inf`, `MeasureTheory.Lp.norm_eq_zero_iff`, `Finset.vadd_stabilizer_of_no_doubling`, `lp.single_apply`, `AddSubgroup.normalizer_le_normalizer_sup_of_normalizer_le_left`, `AddAction.stabilizer_image_coe_quotient`, `AddSubgroup.inf_eq_bot_of_coprime`, `imaginaryPart_smul`, `NonUnitalSubring.toAddSubgroup_strictMono`, `AddSubgroup.Commensurable.discreteTopology_iff`, `AddSubgroup.map_addCommutator`, `AddMonoidHom.comap_bot`, `QuotientAddGroup.preimage_image_mk_eq_iUnion_image`, `AddSubgroup.quotientEquivProdOfLE'_symm_apply`, `lp.isometry_single`, `KuratowskiEmbedding.embeddingOfSubset_dist_le`, `AddSubgroup.mem_inv_pointwise_smul_iff₀`, `AddSubgroup.disjoint_def'`, `AddMonoid.Coprod.closure_range_inl_union_inr`, `QuotientAddGroup.kerLift_mk'`, `AddSubgroup.index_eq_card`, `QuotientAddGroup.equivIcoMod_zero`, `MeasureTheory.Lp.coeFn_sub`, `AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux`, `AddSubgroup.addCommutator_le_inf`, `AddAction.IsBlock.addSubgroup`, `Subring.toAddSubgroup_eq_top`, `NormedAddGroupHom.ker.lift_apply_coe`, `AddAction.mem_stabilizer_finset`, `AddCircle.norm_eq`, `MeasureTheory.Lp.mem_Lp_of_nnnorm_ae_le`, `AddSubgroup.mem_closure_iff_of_fintype`, `AddMonoidHom.range_zero`, `fourier_coe_apply'`, `MeasureTheory.Lp.meas_ge_le_mul_pow_enorm`, `cfcₙ_realPart`, `Unitary.norm_argSelfAdjoint`, `UnitAddTorus.hasSum_sq_mFourierCoeff`, `QuotientAddGroup.automorphize_smul_left`, `AddAction.stabilizer_finite`, `AddAction.mem_stabilizer_set_iff_vadd_set_subset`, `SubAddAction.ofFixingAddSubgroup.append_right`, `AddSubgroup.coe_sInf`, `realPart_apply_coe`, `AddSubgroup.normalizer_inf_normalizer_le_normalizer_sup`, `ContinuousLinearMap.coeFn_compLp`, `DomMulAct.nnnorm_smul_Lp`, `AddSubgroup.isLeast_of_closure_iff_eq_abs`, `AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd`, `QuotientAddGroup.equivIcoMod_coe`, `QuotientAddGroup.quotientQuotientEquivQuotientAux_mk`, `MeasureTheory.L1.setToL1_mono`, `AddSubgroup.coe_pathComponentZero`, `mem_zmultiples_of_prime_card`, `CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff`, `AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples`, `coe_ringEquiv_lpBCF_symm`, `AddSubgroup.addCommutator_mono`, `AddSubgroup.subsingleton_iff`, `MeasureTheory.lintegral_nnnorm_condExpIndSMul_le`, `AddSubgroup.subset_normalizer_of_normal`, `LipschitzWith.continuous_compLp`, `QuotientAddGroup.eq_zero_iff`, `AddCommGroup.isAddTorsionFree_iff_torsion_eq_bot`, `AddSubgroup.surjOn_iff_le_map`, `lp.norm_eq_tsum_rpow`, `AddCircle.addOrderOf_div_of_gcd_eq_one'`, `spectrum_realPart`, `MeasureTheory.Lp.smul_assoc`, `QuotientAddGroup.mk_int_mul`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `AddSubgroup.inf_relIndex_left`, `MeasureTheory.integrable_condExpIndSMul`, `lp.coeFn_neg`, `AddMonoidHom.independent_range_of_coprime_order`, `spectrum_imaginaryPart'`, `AddSubgroup.FG.bot`, `Subfield.coe_toAddSubgroup`, `Valuation.coe_ltAddSubgroup`, `AddCircle.coe_image_Ico_eq`, `AddAction.add_stabilizer_self`, `CochainComplex.mappingCone.δ_descCochain`, `QuotientAddGroup.mk'_surjective`, `MeasureTheory.Lp.toTemperedDistribution_apply`, `AddSubgroup.unop_top`, `AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_symm_apply`, `AddSubgroup.val_list_sum`, `LipschitzWith.compLp_zero`, `AddAction.isPreprimitive_ofFixingAddSubgroup_addConj_iff`, `AddSubgroup.exists_right_transversal_of_le`, `AddAction.ofFixingSubgroup.isMultiplyPreprimitive`, `AddSubgroup.add_mem_cancel_left`, `AddSubgroup.quotientEquivProdOfLE_apply`, `MeasureTheory.condExpL1_zero`, `SubAddAction.nat_card_ofStabilizer_add_zero_eq`, `MeasureTheory.Lp.compMeasurePreserving_continuous`, `AddSubgroup.closure_eq_top_of_mclosure_eq_top`, `Subgroup.toAddSubgroup'_closure`, `AddSubgroup.addCommutator_characteristic`, `AddAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup`, `MeasureTheory.Lp.coeFn_posPart`, `lp.zeroBasis_repr_symm_apply_coe`, `NormedAddGroupHom.mem_range`, `AddAction.QuotientAction.inv_mul_mem`, `AddSubgroup.index_dvd_two_iff'`, `FiniteIndexNormalAddSubgroup.toAddSubgroup_injective`, `AddAction.card_eq_sum_card_addGroup_sub_card_stabilizer`, `QuotientAddGroup.discreteTopology`, `MeasureTheory.L1.SimpleFunc.setToL1S_add`, `AddAction.orbit_addSubgroup_subset`, `MeasureTheory.Lp.mem_Lp_of_ae_le_mul`, `QuotientAddGroup.integral_mul_eq_integral_automorphize_mul`, `QuotientAddGroup.kerLift_injective`, `QuotientAddGroup.eq_class_eq_leftCoset`, `QuotientAddGroup.mk_neg`, `MeasureTheory.L1.norm_sub_eq_lintegral`, `AddSubgroup.mem_map`, `AddSubgroup.IsSubnormal.iff_eq_top_or_exists`, `QuotientAddGroup.map_mk'_self`, `AddMonoidHom.eq_iff`, `MeasureTheory.norm_indicatorConstLp'`, `SubAddAction.ofStabilizer_carrier`, `lp.norm_toNorm`, `AddSubgroup.exists_isLeast_pos`, `AddSubgroup.sup_eq_closure_add`, `SubAddAction.disjoint_val_image`, `AddSubgroup.finiteIndex_iff_finite_quotient`, `AddSubgroup.norm_normedMk`, `lp.norm_const_smul_le`, `MeasureTheory.Lp.neg_smul_neg`, `AddSubgroup.relIndex_eq_natAbs_det`, `AddSubgroup.exists_leftTransversal_of_FiniteIndex`, `AddMonoidHom.eq_liftOfRightInverse`, `MeasureTheory.isometry_lpMeasSubgroupToLpTrim`, `AddSubgroup.iSup_comap_le`, `MeasureTheory.integrable_condExpL1`, `ContinuousLinearMap.smul_compLpL`, `isClosed_nullAddSubgroup`, `AddSubgroup.properlyDiscontinuousVAdd_of_tendsto_cofinite`, `AddSubgroup.mem_unop`, `MeasureTheory.Integrable.toL1_add`, `AddSubgroup.equivOp_apply_coe`, `orbit_addSubgroup_eq_rightCoset`, `DirectSum.IsInternal.addSubgroup_iSupIndep`, `AddSubmonoid.mem_addUnits_iff`, `AddAction.stabilizer_finset_empty`, `ContinuousLinearMap.norm_compLpL_le`, `CochainComplex.mappingCocone.inr_v_descCochain_v_assoc`, `AddSubgroup.addCommutator_le_self`, `DomMulAct.smul_Lp_const`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left`, `AddSubgroup.le_pointwise_smul_iff`, `AddSubgroup.isAddCommutative_closure`, `MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq`, `QuotientAddGroup.exists_norm_add_lt`, `Set.add_addSubgroupClosure`, `AddSubgroup.goursatFst_prod_goursatSnd_le`, `IsLinearTopology.hasBasis_subbimodule`, `AddSubgroup.index_toSubgroup`, `MeasureTheory.setIntegral_condExpL1CLM`, `MeasureTheory.L1.hasFiniteIntegral_coeFn`, `AddCircle.intCast_div_mul_eq_zsmul`, `lp.norm_eq_ciSup`, `AddSubgroup.card_eq_one`, `AddSubgroup.inclusion_range`, `AddSubgroup.eq_bot_iff_card`, `AddSubgroup.op_eq_bot`, `tsum_sq_fourierCoeff`, `MeasureTheory.lpMeasToLpTrim_ae_eq`, `MeasureTheory.eLpNorm_condExpL2_le`, `IsSelfAdjoint.coe_realPart`, `AddSubgroup.le_topologicalClosure`, `normal_iff_eq_addCosets`, `AddAction.card_eq_sum_card_addGroup_sub_card_stabilizer'`, `realPart_smul`, `RingSubgroupsBasis.mem_addGroupFilterBasis_iff`, `AddSubgroup.exponent_toAddSubmonoid`, `lp.completeSpace`, `AddGroup.rank_range_le`, `AddSubgroup.unop_sSup`, `MeasureTheory.L1.integral_eq'`, `CochainComplex.HomComplex.Cocycle.fromSingleMk_mem_coboundaries_iff`, `AddSubgroup.toIntSubmodule_closure`, `MeasureTheory.lpMeasToLpTrim_smul`, `AddSubgroup.bot_or_exists_ne_zero`, `CochainComplex.mappingCocone.δ_liftCochain`, `unitary.norm_argSelfAdjoint_le_pi`, `AddSubgroup.addSubgroupOfContinuousAddEquivOfLe_toAddEquiv`, `MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg`, `AddSubgroup.focalAddSubgroupOf.mk'_addConj_eq`, `CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero`, `AddSubgroup.mem_toZModSubmodule`, `AddSubgroup.isComplement'_def`, `AddSubgroup.inf_addSubgroupOf_inf_normal_of_right`, `KuratowskiEmbedding.exists_isometric_embedding`, `AddCircle.addOrderOf_coe_rat`, `AddAction.mem_aestabilizer`, `AddSubgroup.card_le_card_addGroup`, `Set.addSubgroupClosure_add_nsmul`, `AddMonoid.Coprod.range_inl_sup_range_inr`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono`, `AddSubgroup.mem_ofAddUnits_iff`, `AddAction.stabilizer_subset_sub_right`, `lp.instIsBoundedSMulSubtypePreLpMemAddSubgroup`, `fixedPoints_addSubgroup_sup`, `IsOfFinAddOrder.mem_multiples_iff_mem_zmultiples`, `KuratowskiEmbedding.embeddingOfSubset_coe`, `lp.star_apply`, `AddSubgroup.vadd_opposite_image_add_preimage`, `AddSubgroup.inclusion_injective`, `Unitary.norm_argSelfAdjoint_le_pi`, `AddSubgroup.instAddSubgroupClass`, `AddSubgroup.comap_inclusion_addSubgroupOf`, `AddSubgroup.quotient_finite_of_isOpen`, `QuotientAddGroup.borelSpace`, `MeasureTheory.Lp.compMeasurePreserving_id`, `AddGrpCat.ker_eq_bot_of_mono`, `selfAdjoint.isStarNormal`, `AddCircle.norm_eq'`, `NormedAddGroupHom.Equalizer.norm_lift_le`, `MeasureTheory.condExpIndSMul_ae_eq_smul`, `IsOfFinAddOrder.multiples_eq_zmultiples`, `MeasureTheory.Lp.simpleFunc.isDenseInducing`, `mapClusterPt_atTop_nsmul_iff_mem_topologicalClosure_zmultiples`, `MeasureTheory.Lp.dense_hasCompactSupport_contDiff`, `AddSubgroup.addSubgroupOf_eq_bot`, `AddSubgroup.index_top`, `SubAddAction.ofStabilizer.isMultiplyPretransitive`, `instProperVAddSubtypeAddOppositeMemAddSubgroupOpOfIsTopologicalAddGroupOfIsClosedCoe`, `equiv_lpPiLp_norm`, `ContinuousLinearMap.norm_holderL_le`, `lp.uniformContinuous_coe`, `AddSubgroup.relIindex_dvd_two_iff'`, `coe_algEquiv_lpBCF_symm`, `MeasureTheory.lpMeas.ae_fin_strongly_measurable'`, `AddSubgroup.dense_of_not_isolated_zero`, `AddSubgroup.exists_left_transversal_of_le`, `AddSubgroup.toAddSubmonoid_le`, `AddSubgroup.instFiniteQuotientOfSeparatelyContinuousAddOfCompactSpace`, `CochainComplex.HomComplex.Cocycle.leftShift_coe`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.addHaarMeasure_quotient`, `AddSubgroup.addOrderOf_mk`, `MeasureTheory.L1.setToL1'_eq_setToL1SCLM`, `Subgroup.finiteIndex_toAddSubgroup_iff`, `RingPreordering.HasIdealSupport.smul_mem_support`, `AddAction.le_stabilizer_iff_vadd_le`, `spectrum_realPart'`, `AddSubgroup.comap_sup_comap_le`, `QuotientAddGroup.instT1Space`, `AddCommGroup.smul_top_eq_top_of_divisibleBy_int`, `OpenAddSubgroup.mem_toAddSubgroup`, `CochainComplex.HomComplex.Cocycle.coe_add`, `MeasureTheory.condExpL1_sub`, `AddSubgroup.rank_congr`, `MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpLpMeasSubgroupOfFactLeMeasurableSpace`, `AddSubgroup.finiteIndex_iInf'`, `Real.Lp.coe_fourierTransform`, `QuotientAddGroup.con_le_iff`, `AddSubgroup.quotientAddSubgroupOfEmbeddingOfLE_apply_mk`, `IsOfFinAddOrder.finite_zmultiples`, `RingPreordering.supportAddSubgroup_eq_bot`, `AddGroupExtension.Section.add_neg_mem_range_inl`, `lp.norm_mono`, `AddSubgroup.goursat`, `AddSubgroup.eq_bot_of_card_le`, `MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq`, `AddSubgroup.addSubgroupOf_isOpen`, `CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zero_assoc`, `Unitary.openPartialHomeomorph_apply`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_nonneg`, `MeasureTheory.L1.integral_sub`, `AddSubgroup.relIndex_top_left`, `MeasureTheory.L1.ofReal_norm_sub_eq_lintegral`, `Unitary.argSelfAdjoint_coe`, `Topology.IsQuotientMap.isCoveringMapOn_of_vadd_disjoint`, `MeasureTheory.Lp.coeFn_inf`, `MeasureTheory.ContinuousMap.inner_toLp`, `AddCircle.coe_add`, `skewAdjoint.I_smul_neg_I`, `AddSubmonoid.add_mem_addUnits`, `MeasureTheory.IsAddFundamentalDomain.absolutelyContinuous_map`, `Valuation.leAddSubgroup_monotone`, `AddSubgroup.le_pointwise_smul_iff₀`, `MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral`, `MeasureTheory.Lp.simpleFunc.toLp_eq_mk`, `AddSubgroup.mem_closure_singleton`, `AddSubgroup.normedMk.apply`, `Subring.toAddSubgroup_injective`, `DomAddAct.dist_vadd_Lp`, `QuotientAddGroup.rightRel_eq`, `AddSubgroup.unop_le_unop_iff`, `NormedAddGroupHom.ker_zero`, `AddSubgroup.pointwise_smul_def`, `AddSubgroup.addCommutator_normal`, `OrthogonalFamily.linearIsometry_apply`, `AddAction.mem_stabilizer_set`, `AddSubgroup.mem_goursatSnd`, `AddSubgroup.subset_normalClosure`, `ContinuousLinearMap.holderL_apply_apply`, `MeasureTheory.Lp.instContinuousFourier`, `AddSubgroup.center_le_normalizer`, `NumberField.Units.dirichletUnitTheorem.logEmbedding_ker`, `DomAddAct.vadd_Lp_zero`, `MeasureTheory.condExpInd_empty`, `AddAction.stabilizer_inf_stabilizer_le_stabilizer_sdiff`, `SchwartzMap.norm_fourier_apply_le_toLp_one`, `MeasureTheory.condExpL1CLM_smul`, `CochainComplex.HomComplex.Cocycle.diff_coe`, `Subgroup.widthInfty_mem_periods`, `LipschitzWith.norm_compLp_le`, `AddSubgroup.normalizer_le_normalizer_sup_of_normalizer_le_right`, `AddSubgroup.subtype_apply`, `MeasureTheory.L1.edist_def`, `AddSubgroup.relIndex_ker`, `MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun`, `AddSubgroup.zsmul_mem_zmultiples`, `MeasureTheory.continuous_setIntegral`, `Submodule.toAddSubgroup_le`, `AddMonoidHom.range_eq_top_of_cancel`, `AddCircle.isCoveringMap_coe`, `AddSubgroup.map_iSup`, `AddSubgroup.center_le_centralizer`, `AddSubgroup.focalAddSubgroup_def`, `MeasureTheory.MemLp.toLp_zero`, `lp.single_apply_self`, `AddSubgroup.addCommutator_eq_bot_iff_le_centralizer`, `CochainComplex.Lifting.comp_coe_cocycle₁_comp`, `AddMonoidHom.coe_range`, `AddSubgroup.torsionBy.nsmul`, `CochainComplex.Lifting.coe_cocycle₁'_v_comp_eq_zero_assoc`, `CategoryTheory.ShortComplex.abLeftHomologyData_H_coe`, `AddSubmonoid.val_neg_addUnitsEquivAddUnitsType_apply_coe`, `AddSubgroup.prod_eq_bot_iff`, `AddSubgroup.isComplement'_bot_top`, `UnitAddTorus.span_mFourierLp_closure_eq_top`, `AddSubgroup.FG.sup`, `AddAction.stabilizerEquivStabilizer_zero`, `CochainComplex.HomComplex.Cocycle.rightUnshift_coe`, `AddSubgroup.ofAddUnits_iSup`, `AddSubgroup.leftCoset_cover_filter_FiniteIndex`, `skewAdjointPart_comp_subtype_skewAdjoint`, `AddCommGrpCat.ker_eq_bot_of_mono`, `continuous_skewAdjointPart`, `AddSubmonoid.addUnits_surjective`, `AddSubgroup.set_add_normal_comm`, `AddAction.stabilizer_orbit_eq`, `AddSubgroup.closure_union`, `IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single`, `MeasureTheory.Lp.pow_mul_meas_ge_le_enorm`, `CochainComplex.mappingCone.lift_f`, `MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero`, `AddSubgroup.comap_injective_isAddCommutative`, `MeasureTheory.condExpIndL1Fin_smul'`, `ContinuousLinearMap.norm_holder_apply_apply_le`, `MeasureTheory.Lp.edist_dist`, `IsSelfAdjoint.imaginaryPart`, `FiniteIndexNormalAddSubgroup.mem_toAddSubgroup_iff`, `DenseRange.topologicalClosure_map_addSubgroup`, `AddMonoidHom.mem_ker`, `FiniteArchimedeanClass.addSubgroup_eq_bot`, `BoundedContinuousFunction.range_toLp`, `QuotientAddGroup.card_quotient_rightRel`, `MeasureTheory.indicatorConstLp_disjoint_union`, `AddSubgroup.zero_mem`, `AddAction.le_stabilizer_vadd_left`, `QuotientAddGroup.rangeKerLift_injective`, `AddSubgroup.pointwise_isCentralScalar`, `AddSubgroup.coe_eq_univ`, `SubAddAction.ofStabilizer.addConjMap_bijective`, `AddSubgroup.mem_closure_pair`, `MeasureTheory.L1.integral_eq`, `MeasureTheory.indicatorConstLp_coeFn`, `AddAction.stabilizerEquivStabilizer_compTriple`, `AddSubgroup.le_normalizer_comap`, `AddSubgroup.independent_of_coprime_order`, `AddCommGrpCat.mono_iff_ker_eq_bot`, `AddSubgroup.Commensurable.equivalence`, `SubAddAction.exists_vadd_of_last_eq`, `AddMonoidHom.ker_zero`, `AddSubgroup.toSubgroup_comap`, `Continuous.compMeasurePreservingLp`, `AddSubgroup.isComplement'_bot_right`, `AddSubgroup.relIndex_iInf_le`, `MeasureTheory.Lp.fourier_toTemperedDistribution_eq`, `AddSubgroup.card_quotient_dvd_card`, `CochainComplex.mappingCone.inl_v_fst_v_assoc`, `MeasureTheory.Lp.const_val`, `AddSubgroup.coe_toSubgroup_symm_apply`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.vaddInvariantMeasure_quotient`, `leftAddCoset_mem_leftAddCoset`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff`, `unitary.mem_pathComponentOne_iff`, `MeasureTheory.Lp.simpleFunc.coeFn_nonneg`, `KaehlerDifferential.quotKerTotalEquiv_apply`, `mem_unitary_iff_isStarNormal_and_realPart_sq_add_imaginaryPart_sq_eq_one`, `isAddFundamentalDomain_Ioc'`, `MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp`, `Subgroup.instDiscreteTopPeriods`, `MeasureTheory.L1.setToL1'_apply_coeToLp`, `AddSubgroup.relIndex_dvd_card`, `AddSubgroup.addSubgroupOf_sup`, `AddSubgroup.op_eq_top`, `SchwartzMap.denseRange_toLpCLM`, `ContinuousOn.compMeasurePreservingLp`, `mem_fixingAddSubgroup_iff_subset_fixedBy`, `MeasureTheory.memLp_trim_of_mem_lpMeasSubgroup`, `SchwartzMap.toLp_fourier_eq`, `AddSubgroup.coe_ofClass`, `DomMulAct.smul_Lp_val`, `AddAction.ofQuotientStabilizer_vadd`, `AddSubgroup.IsComplement.add_neg_toRightFun_mem`, `AddSubmonoid.addUnits_top`, `AddSubgroup.relIndex_sup_right`, `NormedSpace.discreteTopology_zmultiples`, `RingSubgroupsBasis.mul`, `AddMonoidHom.mem_range`, `Submodule.sup_toAddSubgroup`, `DomAddAct.nnnorm_vadd_Lp`, `AddSubgroup.le_normalizer_of_normal_addSubgroupOf`, `AddSubgroup.map_sup`, `MeasureTheory.L1.setToL1_const`, `NonUnitalSubring.toAddSubgroup_top`, `AddSubgroup.addOrderOf_le_card`, `QuotientAddGroup.instIsAddTorsionFree`, `iSupIndep_iff_dfinsuppSumAddHom_injective`, `AddCircle.norm_eq_of_zero`, `MeasureTheory.norm_condExpIndL1Fin_le`, `AddSubgroup.index_smul`, `MeasureTheory.lpMeasToLpTrimLie_symm_toLp`, `MeasureTheory.continuous_L1_toL1`, `CochainComplex.mappingCocone.inr_v_descCochain_v`, `AddAction.isPreprimitive_fixingAddSubgroup_insert_iff`, `MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm`, `AddSubgroup.instFiniteIndexMin`, `ProfiniteAddGrp.instCompactSpaceSubtypeForallCarrierToTopTotallyDisconnectedSpaceToProfiniteObjMemAddSubgroupLimitConePtAux`, `MeasureTheory.indicatorConstLp_empty`, `AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero`, `AddSubgroup.instNormalSubtypeMemFocalAddSubgroupOf`, `MeasureTheory.Integrable.edist_toL1_toL1`, `MeasureTheory.MemLp.toLp_const_smul`, `MeasureTheory.Lp.norm_le_mul_norm_of_ae_le_mul`, `coe_algEquiv_lpBCF`, `MeasureTheory.L1.setToL1_lipschitz`, `IsCancelVAdd.stabilizer_eq_bot`, `MeasureTheory.Integrable.toL1_neg`, `MeasureTheory.norm_condExpL2_le_one`, `GromovHausdorff.eq_toGHSpace_iff`, `MeasureTheory.setToFun_eq`, `Module.Basis.addSubgroupOfClosure_apply`, `MeasureTheory.condExpL2_comp_continuousLinearMap`, `NormedAddGroupHom.Equalizer.liftEquiv_symm_apply_coe`, `MeasureTheory.Lp.coeFn_star`, `MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top`, `AddMonoid.minOrder_le_natCard`, `AddSubgroup.coe_nonempty`, `Submodule.bot_toAddSubgroup`, `Subring.toAddSubgroup_top`, `AddSubgroup.eq_bot_of_subsingleton`, `ContinuousLinearMap.holder_add_left`, `lp.toNorm_coe`, `ArchimedeanClass.mem_closedBallAddSubgroup_iff`, `CochainComplex.mappingCocone.liftCocycle_coe`, `CochainComplex.HomComplex.Cocycle.mk_coe`, `AddSubgroup.le_centralizer`, `AddGroupExtension.Section.neg_add_mem_range_inl`, `AddAction.orbitRel_addSubgroupOf`, `AddSubgroup.ext_iff`, `QuotientAddGroup.range_mk`, `AddAction.isMultiplyPreprimitive_ofStabilizer`, `MeasureTheory.dist_indicatorConstLp_eq_norm`, `LipschitzWith.norm_compLp_sub_le`, `AddSubgroup.zmultiples_eq_bot`, `MeasureTheory.Lp.simpleFunc.toLp_add`, `AddSubgroup.codisjoint_map`, `AddSubgroup.mem_top`, `BoundedContinuousFunction.toLp_denseRange`, `MeasureTheory.condExpL2_const_inner`, `lp.instIsScalarTowerSubtypePreLpMemAddSubgroup`, `AddAction.vadd_set_stabilizer_subset`, `Unitary.path_apply`, `AddSubgroup.inf_normalizer_le_normalizer_inf`, `unitary.two_mul_one_sub_cos_norm_argSelfAdjoint`, `MeasureTheory.Lp.isometry_compMeasurePreserving`, `CochainComplex.mappingCone.inr_fst`, `AddSubgroup.closure_le`, `QuotientAddGroup.rangeKerLift_surjective`, `QuotientAddGroup.quotientQuotientEquivQuotientAux_mk_mk`, `CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv`, `coeFn_fourierLp`, `MeasureTheory.Lp.simpleFunc.dense`, `SubAddAction.mem_ofFixingAddSubgroup_insert_iff`, `AddSubgroup.index_eq_one`, `MeasureTheory.Lp.instFourierAdd`, `MonoidHom.coe_toAdditive_ker`, `AddSubgroup.mem_iInf`, `QuotientAddGroup.mk'_apply`, `AddSubgroup.index_dvd_two_iff`, `AddAction.isCoatom_stabilizer_iff_preprimitive`, `MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc`, `MeasureTheory.norm_setToFun_le`, `AddSubgroup.topologicalClosure_coe`, `MeasureTheory.Lp.toTemperedDistribution_smul_eq`, `CochainComplex.HomComplex.Cocycle.mem_iff`, `MeasureTheory.Lp_toLp_restrict_smul`, `AddSubgroup.comap_le_comap_of_le_range`, `AddSubgroup.mem_centralizer_singleton_iff`, `AddCosetSpace.borelSpace`, `AddAction.IsPreprimitive.isCoatom_stabilizer_of_isPreprimitive`, `AddSubgroup.instFiniteQuotientSubtypeMemOpenAddSubgroupOfIsTopologicalAddGroupOfCompactSpace`, `AddSubgroup.map_le_map_iff'`, `AddSubgroup.index_bot`, `AddSubgroup.IsSubnormal.eq_bot_or_top_of_isSimpleAddGroup`, `AddSubgroup.IsComplement.leftQuotientEquiv_apply`, `MeasureTheory.condExpL1_eq`, `DomAddAct.vadd_Lp_val`, `QuotientAddGroup.preimage_mk_zero`, `MeasureTheory.L1.SimpleFunc.coe_posPart`, `QuotientAddGroup.homQuotientZSMulOfHom_comp`, `AddSubgroup.characteristic_iff_map_le`, `Additive.mem_toAddSubgroup`, `MeasureTheory.Lp.compMeasurePreserving_val`, `QuotientAddGroup.orbit_mk_eq_vadd`, `Submodule.coe_toAddSubgroup`, `CochainComplex.HomComplex.Cocycle.rightShift_coe`, `ContinuousLinearMap.coeFn_holder`, `CochainComplex.mappingCone.d_fst_v`, `HilbertBasis.hasSum_repr_symm`, `AddAction.isPreprimitive_of_fixingAddSubgroup_empty_iff`, `AddSubgroup.mem_biSup_of_directedOn`, `MeasureTheory.Lp.instContinuousSMulDomMulAct`, `MeasureTheory.Lp.norm_compMeasurePreserving`, `IsAddQuotientCoveringMap.addSubgroup_congr`, `MeasureTheory.Lp.nnnorm_zero`, `MeasureTheory.setToFun_toL1`, `AddMonoidHom.ofInjective_apply`, `AddSubgroup.normal_addSubgroupOf_iff_le_normalizer_inf`, `MeasureTheory.condExpL2_indicator_nonneg`, `NormedAddGroupHom.norm_incl`, `QuotientAddGroup.completeSpace_left'`, `selfAdjoint.expUnitary_coe`, `AddEquiv.comapAddSubgroup_symm_apply`, `selfAdjoint.val_nnqsmul`, `AddAction.IsBlock.orbit_of_normal`, `MeasureTheory.L1.integral_neg`, `AddSubgroup.instCountableSubtypeAddOppositeMemOp`, `AddSubgroup.subset_closure`, `AddSubgroup.normal_addSubgroupOf_sup_of_le_normalizer`, `MeasureTheory.MemLp.toLp_sub`, `AddSubgroup.coe_inclusion`, `AddSubgroup.add_mem`, `AddGroupExtension.Section.add_neg_add_add_mem_range_inl`, `AddSubgroup.normal_in_normalizer`, `AddCircle.gcd_mul_addOrderOf_div_eq`, `MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left'`, `QuotientAddGroup.homQuotientZSMulOfHom_id`, `QuotientAddGroup.equivIocMod_coe`, `AddSubgroup.dense_xor'_cyclic`, `StarModule.decomposeProdAdjoint_apply`, `MeasureTheory.Lp.mul_meas_ge_le_pow_enorm`, `AddAction.isPretransitive_quotient`, `Subgroup.relIndex_toAddSubgroup`, `MeasureTheory.Lp.simpleFunc.norm_toLp`, `AddAction.orbitRel.Quotient.addSubgroup_quotient_eq_iff`, `CochainComplex.mappingCone.inr_fst_assoc`, `DomMulAct.smul_Lp_add`, `AddSubgroup.IsSubnormal.isSubnormal_iff`, `card_zmultiples_le`, `QuotientAddGroup.le_comap_mk'`, `kuratowskiEmbedding.isometry`, `isStarNormal_iff_commute_realPart_imaginaryPart`, `AddSubgroup.relIndex_bot_left`, `lp.tsum_mul_le_mul_norm`, `HurwitzZeta.hasSum_int_evenKernel₀`, `MeasureTheory.Lp.continuous_posPart`, `AddAction.mem_stabilizer_finset_iff_vadd_finset_subset`, `AddGrpCat.mono_iff_ker_eq_bot`, `MonoidHom.coe_toMultiplicative_ker`, `IsLinearTopology.hasBasis_open_subbimodule`, `MeasureTheory.Lp.norm_def`, `AddSubgroup.isComplement_range_right`, `lp.ext_continuousLinearMap_iff`, `AddSubgroup.exists_mem_ofAddUnits_val_eq`, `IsAddCyclic.card_nsmulAddMonoidHom_range`, `AddSubgroup.ker_inclusion`, `AddAction.stabilizer_quotient`, `SubAddAction.not_mem_of_mem_ofFixingAddSubgroup`, `AddSubmonoid.val_addUnitsEquivAddUnitsType_apply_coe`, `AddAction.IsBlockSystem.of_normal`, `mem_fixingAddSubgroup_iff`, `AddSubgroup.equivOp_symm_apply_coe`, `Function.locallyFinsuppWithin.memAddSubgroup`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `ContinuousLinearMap.coeFn_compLp'`, `Finset.nsmul_right_strictMonoOn`, `AddSubgroup.map_le_range`, `CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles`, `Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply`, `CochainComplex.mappingCocone.inr_v_desc_f`, `AddSubgroup.toAddSubmonoid_mono`, `MeasureTheory.MemLp.toLp_const`, `AddCircle.natCast_div_mul_eq_nsmul`, `unitary.continuousOn_argSelfAdjoint`, `AddSubgroup.relIndex_toSubgroup`, `MeasureTheory.lpMeas.aestronglyMeasurable`, `MeasureTheory.leftInvariantIsAddQuotientMeasureEqMeasurePreimage`, `cfc_imaginaryPart`, `IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_vaddAddHaarMeasure`, `MeasureTheory.L1.SimpleFunc.setToL1S_smul`, `CochainComplex.HomComplex.δ_zero_cocycle_comp`, `AddSubgroup.normalCore_eq_iSup`, `AddSubmonoid.IsPointed.support_eq_bot`, `AddSubgroup.map_centralizer_le_centralizer_image`, `finite_zmultiples`, `SubAddAction.map_ofFixingAddSubgroupUnion_def`, `MeasureTheory.Lp.compMeasurePreserving_iterate`, `MeasureTheory.L1.norm_eq_integral_norm`, `Unitary.two_mul_one_sub_cos_norm_argSelfAdjoint`, `AddSubgroup.relIndex_eq_two_iff`, `Bot.isAddCyclic`, `QuotientAddGroup.map_id_apply`
`AddSubgroupClass` 📖	CompData	11 math math: `Submodule.addSubgroupClass`, `OpenNormalAddSubgroup.instAddSubgroupClass`, `ClosedAddSubgroup.instAddSubgroupClass`, `NonUnitalSubringClass.addSubgroupClass`, `FiniteIndexNormalAddSubgroup.instAddSubgroupClass`, `SubringClass.addSubgroupClass`, `LieSubmodule.instAddSubgroupClass`, `AddSubgroup.instAddSubgroupClass`, `OpenAddSubgroup.instAddSubgroupClass`, `LieSubalgebra.instAddSubgroupClass`, `TwoSidedIdeal.instAddSubgroupClass`
`HasMemOrInvMem` 📖	CompData	1 math math: `GroupCone.oneLE.hasMemOrInvMem`
`HasMemOrNegMem` 📖	CompData	3 math math: `AddGroupCone.nonneg.hasMemOrNegMem`, `RingCone.nonneg.hasMemOrNegMem`, `RingPreordering.IsOrdering.toHasMemOrNegMem`
`InvMemClass` 📖	CompData	2 math math: `SubgroupClass.toInvMemClass`, `SubfieldClass.toInvMemClass`
`NegMemClass` 📖	CompData	3 math math: `NonUnitalSubringClass.toNegMemClass`, `AddSubgroupClass.toNegMemClass`, `SubringClass.toNegMemClass`
`SubgroupClass` 📖	CompData	7 math math: `Subgroup.instSubgroupClass`, `OpenNormalSubgroup.instSubgroupClass`, `FiniteIndexNormalSubgroup.instSubgroupClass`, `ClosedSubgroup.instSubgroupClass`, `OpenSubgroup.instSubgroupClass`, `SubfieldClass.toSubgroupClass`, `Sylow.instSubgroupClass`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`add_mem_cancel_left` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`neg_add_cancel_left` `AddMemClass.add_mem` `AddSubmonoidClass.toAddMemClass` `AddSubgroupClass.toAddSubmonoidClass` `NegMemClass.neg_mem` `AddSubgroupClass.toNegMemClass`
`add_mem_cancel_right` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid`	—	`add_neg_cancel_right` `AddMemClass.add_mem` `AddSubmonoidClass.toAddMemClass` `AddSubgroupClass.toAddSubmonoidClass` `NegMemClass.neg_mem` `AddSubgroupClass.toNegMemClass`
`div_mem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `MulMemClass.mul_mem` `SubmonoidClass.toMulMemClass` `SubgroupClass.toSubmonoidClass` `InvMemClass.inv_mem` `SubgroupClass.toInvMemClass`
`exists_inv_mem_iff_exists_mem` 📖	mathematical	—	`SetLike.instMembership` `InvOneClass.toInv` `DivInvOneMonoid.toInvOneClass` `DivisionMonoid.toDivInvOneMonoid` `Group.toDivisionMonoid`	—	`InvMemClass.inv_mem` `SubgroupClass.toInvMemClass` `inv_inv`
`exists_neg_mem_iff_exists_mem` 📖	mathematical	—	`SetLike.instMembership` `NegZeroClass.toNeg` `SubNegZeroMonoid.toNegZeroClass` `SubtractionMonoid.toSubNegZeroMonoid` `AddGroup.toSubtractionMonoid`	—	`NegMemClass.neg_mem` `AddSubgroupClass.toNegMemClass` `neg_neg`
`inv_mem_iff` 📖	mathematical	—	`SetLike.instMembership` `InvolutiveInv.toInv`	—	`InvMemClass.inv_mem` `inv_inv`
`mul_mem_cancel_left` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`inv_mul_cancel_left` `MulMemClass.mul_mem` `SubmonoidClass.toMulMemClass` `SubgroupClass.toSubmonoidClass` `InvMemClass.inv_mem` `SubgroupClass.toInvMemClass`
`mul_mem_cancel_right` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid`	—	`mul_inv_cancel_right` `MulMemClass.mul_mem` `SubmonoidClass.toMulMemClass` `SubgroupClass.toSubmonoidClass` `InvMemClass.inv_mem` `SubgroupClass.toInvMemClass`
`neg_mem_iff` 📖	mathematical	—	`SetLike.instMembership` `InvolutiveNeg.toNeg`	—	`NegMemClass.neg_mem` `neg_neg`
`sub_mem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `SubNegMonoid.toSub`	—	`sub_eq_add_neg` `AddMemClass.add_mem` `AddSubmonoidClass.toAddMemClass` `AddSubgroupClass.toAddSubmonoidClass` `NegMemClass.neg_mem` `AddSubgroupClass.toNegMemClass`
`zpow_mem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `DivInvMonoid.toZPow`	—	`zpow_natCast` `pow_mem` `SubgroupClass.toSubmonoidClass` `zpow_negSucc` `InvMemClass.inv_mem` `SubgroupClass.toInvMemClass`
`zsmul_mem` 📖	mathematical	`SetLike.instMembership`	`SetLike.instMembership` `SubNegMonoid.toZSMul`	—	`natCast_zsmul` `nsmul_mem` `AddSubgroupClass.toAddSubmonoidClass` `negSucc_zsmul` `NegMemClass.neg_mem` `AddSubgroupClass.toNegMemClass`

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