Defs

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

Statistics

Metric	Count
Definitions `toVAdd`, `toVAddAddOpposite`, `AddAction`, `toAddSemigroupAction`, `toAddAction`, `AddSemigroupAction`, `toVAdd`, `addAction`, `mulAction`, `addAction`, `mulAction`, `IsCancelSMul`, `IsCancelVAdd`, `IsCentralScalar`, `IsCentralVAdd`, `IsLeftCancelSMul`, `IsLeftCancelVAdd`, `IsScalarTower`, `bundled_maps_over_different_rings`, `toMulAction`, `toSMul`, `toSMulMulOpposite`, `toSemigroupAction`, `MulDistribMulAction`, `toMulAction`, `comp`, `smul`, `SMulCommClass`, `SMulDistribClass`, `SemigroupAction`, `toSMul`, `comp`, `vadd`, `VAddAssocClass`, `VAddCommClass`	35
Theorems `ext`, `ext_iff`, `zero_vadd`, `vadd_left`, `vadd_right`, `vadd_eq_add_unop`, `vaddAssocClass`, `add_vadd`, `ext`, `ext_iff`, `smul_left`, `smul_left_iff`, `smul_right`, `smul_right_iff`, `smulCommClass`, `vaddCommClass`, `smulCommClass`, `vaddCommClass`, `eq_one_of_smul`, `left_cancel`, `right_cancel`, `right_cancel'`, `toIsLeftCancelSMul`, `eq_zero_of_vadd`, `left_cancel`, `right_cancel`, `right_cancel'`, `toIsLeftCancelVAdd`, `op_smul_eq_smul`, `unop_smul_eq_smul`, `op_vadd_eq_vadd`, `unop_vadd_eq_vadd`, `left_cancel`, `left_cancel'`, `left_cancel`, `left_cancel'`, `left`, `of_commMonoid`, `of_smul_one_mul`, `op_left`, `op_right`, `smul_assoc`, `to₁₂₄`, `to₁₃₄`, `to₂₃₄`, `ext`, `ext_iff`, `one_smul`, `ext`, `ext_iff`, `smul_mul`, `smul_one`, `smul_eq_mul_unop`, `isScalarTower`, `smulCommClass`, `smulCommClass'`, `of_commMonoid`, `of_mul_smul_one`, `op_left`, `op_right`, `smul_comm`, `smul_distrib_smul`, `isScalarTower`, `ext`, `ext_iff`, `mul_smul`, `vaddAssocClass`, `vaddCommClass`, `vaddCommClass'`, `left`, `of_vadd_zero_add`, `op_left`, `op_right`, `to₁₂₄`, `to₁₃₄`, `to₂₃₄`, `vadd_assoc`, `of_add_vadd_zero`, `op_left`, `op_right`, `vadd_comm`, `add_vadd_add_comm`, `add_vadd_comm`, `add_vadd_zero`, `comp_smul_left`, `comp_vadd_left`, `eq_inv_smul_iff`, `eq_neg_vadd_iff`, `instIsCancelSMul`, `instIsCancelVAdd`, `instIsLeftCancelSMul`, `instIsLeftCancelSMul_1`, `instIsLeftCancelVAdd`, `instIsLeftCancelVAdd_1`, `inv_smul_eq_iff`, `inv_smul_smul`, `isScalarTower_iff_smulCommClass_of_commMonoid`, `mul_smul_comm`, `mul_smul_mul_comm`, `mul_smul_one`, `neg_vadd_eq_iff`, `neg_vadd_vadd`, `one_smul`, `one_smul_eq_id`, `op_smul_eq_mul`, `op_vadd_eq_add`, `smulCommClass_self`, `smul_assoc`, `smul_div_assoc`, `smul_eq_mul`, `smul_inv`, `smul_inv_smul`, `smul_iterate`, `smul_iterate_apply`, `smul_mul'`, `smul_mul_assoc`, `smul_mul_smul`, `smul_mul_smul_comm`, `smul_one_mul`, `smul_one_smul`, `smul_pow`, `smul_smul`, `smul_smul_smul_comm`, `smul_zpow`, `vaddCommClass_self`, `vadd_add_assoc`, `vadd_add_vadd`, `vadd_add_vadd_comm`, `vadd_assoc`, `vadd_eq_add`, `vadd_iterate`, `vadd_iterate_apply`, `vadd_neg_vadd`, `vadd_sub_assoc`, `vadd_vadd`, `vadd_vadd_vadd_comm`, `vadd_zero_add`, `vadd_zero_vadd`, `zero_vadd`, `zero_vadd_eq_id`	140
Total	175

Add

Definitions

Name	Category	Theorems
`toVAdd` 📖	CompOp	41 math math: `AddSemigroupIdeal.mem_closure`, `AddSemigroup.vaddAssocClass`, `AddSemigroupIdeal.subset_closure`, `MeasureTheory.Measure.IsAddLeftInvariant.vaddInvariantMeasure`, `Set.op_vadd_set_add_eq_add_vadd_set`, `AddCommSemigroup.isCentralVAdd`, `AddSemigroupIdeal.closure_le`, `Finset.image_vadd_distrib`, `AddSemigroupIdeal.coe_closure`, `Set.add_subset_iff_left`, `AddSemigroup.opposite_vaddCommClass'`, `Set.image_vadd_distrib`, `AddSemigroupIdeal.coe_closure'`, `Additive.isIsIsometricVAdd'`, `Finset.op_vadd_finset_add_eq_add_vadd_finset`, `AddSemigroupIdeal.mem_closure''`, `AddSemigroupIdeal.instWellFoundedGT`, `Finset.add_subset_iff_left`, `Finset.singleton_add`, `AddSemigroupIdeal.mem_closure_of_mem`, `Set.range_add`, `Set.vadd_set_subset_add`, `mem_leftAddCoset`, `Finset.vadd_finset_subset_add`, `leftAddCoset_rightAddCoset`, `Finset.pairwiseDisjoint_vadd_iff`, `vadd_eq_add`, `AddSemigroup.opposite_vaddCommClass`, `AddSemigroupIdeal.mem_closure'`, `Set.pairwiseDisjoint_vadd_iff`, `AddSemigroupIdeal.closure_mono`, `measurableSMul₂_of_add`, `ContinuousAdd.to_continuousVAdd`, `measurableVAdd_of_add`, `Prod.vaddCommClassBoth`, `Absorbent.vadd_absorbs`, `leftAddCoset_assoc`, `instFaithfulVAddOfIsRightCancelAdd`, `instFaithfulVAdd`, `Prod.isIsometricVAdd'`, `Set.pair_add`
`toVAddAddOpposite` 📖	CompOp	32 math math: `Prod.isIsometricVAdd''`, `Finset.add_singleton`, `Set.op_vadd_set_add_eq_add_vadd_set`, `AddCommSemigroup.isCentralVAdd`, `VAddAssocClass.opposite_mid`, `Set.op_vadd_set_subset_add`, `mem_rightAddCoset`, `instFaithfulVAddAddOpposite`, `Finset.op_vadd_finset_subset_add`, `Set.image_op_vadd`, `AddSemigroup.opposite_vaddCommClass'`, `MeasureTheory.Measure.IsAddRightInvariant.toVAddInvariantMeasure_op`, `Finset.add_subset_iff_right`, `Set.iUnion_op_vadd_set`, `Finset.biUnion_op_vadd_finset`, `Set.add_pair`, `Finset.op_vadd_finset_add_eq_add_vadd_finset`, `ContinuousAdd.to_continuousVAdd_op`, `leftAddCoset_rightAddCoset`, `VAddCommClass.opposite_mid`, `AddOpposite.vadd_eq_add_unop`, `AddSemigroup.opposite_vaddCommClass`, `Set.add_subset_iff_right`, `op_vadd_eq_add`, `rightAddCoset_assoc`, `Additive.isIsIsometricVAdd''`, `measurableVAdd_opposite_of_add`, `instFaithfulVAddAddOppositeOfIsLeftCancelAdd`, `AddLeftCancelMonoid.to_faithfulVAdd_addOpposite`, `AddAction.Regular.isPretransitive_addOpposite`, `measurableSMul₂_opposite_of_add`, `Set.image_op_vadd_distrib`

AddAction

Definitions

Name	Category	Theorems
`toAddSemigroupAction` 📖	CompOp	868 math math: `Set.ncard_vadd_set`, `mem_stabilizer_set_iff_subset_vadd_set`, `ball_sub`, `NumberField.mixedEmbedding.fundamentalDomain_integerLattice`, `AffineIsometryEquiv.pointReflection_apply`, `Metric.vadd_closedBall`, `AddSubmonoid.continuousVAdd`, `EuclideanGeometry.dist_smul_vadd_sq`, `SubAddAction.map_ofFixingAddSubgroupUnion_bijective`, `IsOpen.vadd_left`, `isTopologicallyTransitive_iff_dense_iUnion_preimage`, `Equiv.coe_vaddConst`, `IsTrivialBlock.vadd_iff`, `SubAddAction.notMem_val_image`, `AddSubgroup.vadd_opposite_image_add_preimage'`, `IsPreprimitive.of_isTrivialBlock_base`, `EuclideanGeometry.reflection_orthogonal_vadd`, `Equiv.coe_constVSub_symm`, `orbit_eq_iff`, `fderivWithin_comp_add_left`, `rank_le_card_isVisible`, `isPeriodicPt_vadd_iff`, `AffineSubspace.sSameSide_vadd_right_iff`, `AddSubgroup.vaddCommClass_left`, `Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `IsOpen.iUnion_preimage_vadd`, `AffineSubspace.setOf_sSameSide_eq_image2`, `MeasureTheory.vadd_ae`, `IsUpperSet.vadd`, `VAddCommClass.of_add_vadd_zero`, `Homeomorph.vadd_symm_apply`, `AffineEquiv.constVAdd_apply`, `nsmul_vadd_mod_minimalPeriod`, `sub_add_vsub_comm`, `isAddQuotientCoveringMap_iff_isCoveringMap_and`, `mem_addSubgroup_orbit_iff`, `rightAddCoset_zero`, `zsmul_period_add_vadd`, `nhds_vadd`, `nonempty_orbit`, `Finset.vadd_finset_eq_univ`, `Convex.vadd`, `Finset.neg_op_vadd_finset_distrib`, `SetLike.vadd_of_tower_def`, `mapsTo_vadd_orbit`, `vadd_eq_vadd_iff_neg_add_eq_vsub`, `vadd_vsub_assoc`, `orbitRel_apply`, `vadd_mem_fixedPoints_of_normal`, `IsPretransitive.of_vaddAssocClass`, `vadd_eq_self_of_preimage_zsmul_eq_self`, `isTopologicallyTransitive_iff`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `rightAddCoset_mem_rightAddCoset`, `Affine.Simplex.centroid_eq_smul_sum_vsub_vadd`, `QuotientAddGroup.univ_eq_iUnion_vadd`, `Homeomorph.vaddConst_apply`, `Dense.vadd`, `derivWithin_comp_const_sub`, `Set.iUnion_neg_vadd`, `vadd_right_mem_affineSpan_pair`, `AddConstMap.coe_addLeftHom_apply`, `mem_const_vadd_affineSegment`, `AffineSubspace.wOppSide_smul_vsub_vadd_left`, `IsAddUnit.aemeasurable_const_vadd_iff`, `vsub_vadd_comm`, `SubAddAction.ofFixingAddSubgroup_of_singleton_bijective`, `Sbtw.vadd_const`, `AddCircle.isAddFundamentalDomain_of_ae_ball`, `orbit.pairwiseDisjoint`, `iteratedFDerivWithin_comp_add_right'`, `MeasureTheory.integral_vadd_eq_self`, `Supports.vadd`, `UpperHalfPlane.isometry_real_vadd`, `approxAddOrderOf.vadd_eq_of_mul_dvd`, `Multiset.vadd_sum`, `AffineSubspace.vadd_mem_mk'`, `Set.vadd_set_compl`, `MeasureTheory.mem_addFundamentalFrontier`, `EMetric.vadd_ball`, `AffineIsometryEquiv.coe_constVAdd`, `vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan`, `stabilizer_vadd_eq_stabilizer_map_conj`, `IsLowerSet.vadd_subset`, `pretransitive_iff_unique_quotient_of_nonempty`, `smul_vsub_rev_vadd_mem_affineSpan_pair`, `SubAddAction.mem_ofStabilizer_iff`, `tendsto_const_vadd_iff`, `EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection`, `QuotientAddGroup.measurableVAdd`, `affineSpan_singleton_union_vadd_eq_top_of_span_eq_top`, `Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter`, `Quotient.vadd_coe`, `EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint`, `threeAPFree_vadd_set`, `Finset.vadd_finset_univ`, `IsometryEquiv.constVSub_symm_apply`, `EuclideanGeometry.angle_vadd_const`, `isLinearSet_iff`, `Quotient.coe_vadd_out`, `vadd_vadd`, `isPretransitive_compHom`, `continuousVAdd_compHom`, `FreeAddMonoid.vadd_def`, `AffineSubspace.sOppSide_vadd_right_iff`, `Finset.vadd_addConvolution_eq_addConvolution_neg_add`, `MeasureTheory.measure_neg_vadd_inter`, `AffineIndependent.vadd`, `collinear_iff_of_mem`, `IsOpen.left_addCoset`, `AddSubmonoid.nsmul_vadd_mem_closure_vadd`, `Set.vadd_set_vsub_vadd_set`, `exists_disjoint_vadd_of_isCompact`, `AffineMap.map_vadd'`, `Set.vadd_set_sdiff`, `Finset.op_vadd_stabilizer_of_no_doubling`, `orbit_fixingAddSubgroup_compl_subset`, `SetLike.instVAddCommClassSubtypeMem_1`, `QuotientAddGroup.instContinuousVAdd`, `vsub_vadd_eq_vsub_sub`, `IsUniformAddGroup.to_uniformContinuousConstVAdd`, `IsLowerSet.vadd`, `EuclideanGeometry.orthogonalProjection_apply_mem`, `SetLike.instVAddCommClassSubtypeMem_2`, `AffineBasis.coe_vadd`, `isPreprimitive_ofFixingAddSubgroup_conj_iff`, `instIsOrderedVAddOfIsOrderedAddMonoid`, `AddSubgroup.vaddCommClass_right`, `orbitZMultiplesEquiv_symm_apply'`, `IsBlock.of_orbit`, `IsQuasiPreprimitive.isPretransitive_of_normal`, `orbitZMultiplesEquiv_symm_apply`, `Function.Embedding.vadd_apply`, `Finset.weightedVSubOfPoint_vadd`, `AffineSubspace.smul_vsub_vadd_mem`, `nndist_vadd_cancel_right`, `Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone`, `Set.vadd_set_pi_of_isAddUnit`, `mem_stabilizer_iff`, `IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd`, `Set.OrdConnected.vadd`, `Filter.vadd_tendsto_vadd_iff`, `sbtw_vadd_const_iff`, `IsAddUnit.preimage_vadd_setₛₗ`, `Set.neg_op_vadd_set_distrib`, `HomogeneousIdeal.toAddSubmonoid_irrelevant_le`, `IsAddQuotientCoveringMap.isCancelVAdd`, `vadd_vsub_eq_sub_vsub`, `iteratedFDerivWithin_comp_add_left`, `Set.vadd_sub_vadd_comm`, `Set.pairwise_disjoint_vadd_iff`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive'`, `isBlock_iff_vadd_eq_of_nonempty`, `SubAddAction.ofStabilizer.isPretransitive_iff`, `UpperHalfPlane.vadd_re`, `affinity_unitClosedBall`, `mem_orbit_vadd`, `IsAddUnit.vadd`, `vadd_eq_vadd_iff_sub_eq_vsub`, `vadd_neg_mem_fixedBy_iff_mem_fixedBy`, `Function.Periodic.map_vadd_multiples`, `ContinuousAffineMap.vadd_toAffineMap`, `SubAddAction.stabilizer_of_subMul.addSubmonoid`, `MeasureTheory.Measure.instVAddInvariantMeasureSubtypeMemAddSubmonoidOfIsAddLeftInvariant`, `IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPoints`, `AddOreLocalization.oreSub_eq_iff`, `EuclideanGeometry.orthogonalProjection_apply'`, `MeasureTheory.measure_vadd`, `pretransitive_iff_subsingleton_quotient`, `Metric.preimage_vadd_ball`, `instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid`, `op_vadd_add`, `Finite.to_properlyDiscontinuousVAdd`, `stabilizer_vadd_eq_right`, `Regular.isPretransitive`, `NumberField.mixedEmbedding.fundamentalDomain_idealLattice`, `IsTopologicallyTransitive.exists_vadd_inter`, `wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg`, `Finset.card_vadd_finset`, `Set.powersetCard.isPretransitive_of_isMultiplyPretransitive'`, `Metric.vadd_ball`, `dist_vadd_cancel_right`, `isAddFundamentalDomain_Ioc`, `Set.powersetCard.addActionHom_of_embedding_surjective`, `EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center`, `Set.vadd_mem_vadd_set_iff`, `Multiplicative.mulAction_isPretransitive`, `instIsLeftCancelVAdd_1`, `FreeAddMonoid.ofList_vadd`, `instErgodicVAddAddOppositeOfIsAddRightInvariant`, `Finset.vadd_finset_symmDiff`, `IsClosed.vadd_right_of_isCompact`, `Set.vadd_Icc`, `AffineSpace.asymptoticNhds_vadd_pure`, `measurableVAdd_iterateAddAct`, `Finset.vadd_finset_inter`, `vadd_eq_iff_eq_neg_vadd`, `IsAddFoelner.mean_vadd_eq_mean_vadd`, `orbit_addSubgroup_eq_self_of_mem`, `IsSemilinearSet.vadd`, `vadd_zero_vadd`, `convexHull_vadd`, `isPretransitive_of_is_two_pretransitive`, `sub_smul_slope_vadd`, `vadd_singleton_mem_nhds_of_sigmaCompact`, `NonarchimedeanAddGroup.exists_openAddSubgroup_separating`, `AddOreLocalization.vadd_oreSub`, `AffineSubspace.setOf_wOppSide_eq_image2`, `MeasureTheory.vadd_set_ae_le`, `IsCompact.exists_finite_cover_vadd`, `MeasureTheory.measure_sdiff_neg_vadd`, `nndist_vadd_left`, `Metric.preimage_vadd_closedEBall`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `HahnSeries.SummableFamily.embDomain_succ_smul_powers`, `isOpenMap_vadd`, `AddUnits.vaddAssocClass'`, `Finset.addDysonETransform_snd`, `vadd_fixedBy`, `Finset.vadd_finset_subset_iff`, `MeasureTheory.measure_neg_vadd_symmDiff`, `AffineSubspace.coe_pointwise_vadd`, `AffineEquiv.map_vadd`, `vadd_vsub_vadd_cancel_right`, `AffineSubspace.wSameSide_vadd_left_iff`, `Fin.partialSum_left_neg`, `SubAddAction.vaddAssocClass'`, `HahnSeries.of_symm_smul_of_eq_mul`, `mem_vadd_const_affineSegment`, `image_inter_image_iff`, `VAddAssocClass.left`, `AddTorsor.vadd_vsub'`, `vadd_mem_affineSpan_of_mem_affineSpan_of_mem_vectorSpan`, `continuousAt_const_vadd_iff`, `AffineMap.vadd_linear`, `isClosedMap_vadd`, `IsAddQuotientCoveringMap.apply_eq_iff_mem_orbit`, `IsAddUnit.vadd_tendsto_vadd_iff`, `Quotient.mk_vadd_out`, `measurable_const_vadd_iff`, `IsAddUnit.preimage_vadd_set`, `IsUpperSet.vadd_subset`, `ProperVAdd.isProperMap_vadd_pair`, `Filter.Tendsto.const_vadd_asymptoticNhds`, `SubAddAction.val_image_orbit`, `zmultiplesQuotientStabilizerEquiv_symm_apply`, `SubAddAction.SMulMemClass.coe_subtype`, `mem_fixingAddSubmonoid_iff`, `arrowAddAction_vadd`, `smul_vsub_vadd_mem_affineSpan_pair`, `IsOpen.dense_iUnion_preimage_vadd`, `MeasureTheory.tendsto_measure_vadd_diff_isCompact_isClosed`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero`, `Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one`, `HomogeneousIdeal.irrelevant_le`, `AddUnits.val_vadd`, `Set.vadd_univ`, `AddGroup.preimage_vadd_set`, `AffineMap.vadd_lineMap`, `op_vadd_coe_set`, `Set.vadd_graphOn_univ`, `affinity_unitBall`, `isSimplyConnected_vadd_set_iff`, `Affine.Triangle.circumsphere_eq_of_dist_of_oangle`, `Set.vadd_set_eq_univ`, `zeroEmbedding_isPretransitive_iff`, `surjective`, `AmpleSet.vadd`, `IsTrivialBlock.vadd`, `Set.vadd_set_subset_vadd_set_iff`, `Metric.vadd_sphere`, `Metric.preimage_vadd_sphere`, `StrictConvex.affinity`, `MeasureTheory.mem_addFundamentalInterior`, `op_vadd_op_vadd`, `iteratedFDerivWithin_comp_sub`, `orbit.coe_vadd`, `differentiableWithinAt_comp_sub`, `vadd_ball_zero`, `EuclideanGeometry.orthogonalProjection_vadd_eq_self`, `HahnModule.coeff_smul_order_add_order`, `HahnModule.instIsScalarTowerHahnSeries_1`, `isPretransitive_iff_orbit_eq_univ`, `nsmul_vadd_eq_iff_minimalPeriod_dvd`, `Set.vadd_inter_nonempty_iff'`, `IsClosed.vadd`, `AddSubgroup.instMeasurableVAdd`, `IsTopologicalAddTorsor.toContinuousVAdd`, `mem_orbit_self`, `AffineIsometryEquiv.coe_vaddConst`, `Set.preimage_vadd_neg`, `Ideal.homogeneousHull_eq_iSup`, `MeasureTheory.measure_vadd_eq_zero_iff`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `interior_vadd`, `mem_leftAddCoset_iff`, `VAddAssocClass.of_vadd_zero_add`, `signedDist_vadd_left_swap`, `mem_rightAddCoset_iff`, `VAddAssocClass.to₂₃₄`, `orbitRel.Quotient.mapsTo_vadd_orbit`, `Finset.add_mem_vadd_finset_iff`, `vadd_orbit_eq_orbit_vadd`, `EuclideanGeometry.reflection_apply_of_mem`, `isProperLinearSet_iff`, `vadd_orbit`, `minimalPeriod_eq_card`, `AddSubgroup.continuousVAdd`, `AddActionHom.map_mem_fixedBy`, `AddGroup.preimage_vadd_setₛₗ`, `Finset.vadd_finset_subsetSum_subset_subsetSum_insert`, `zsmul_vadd_eq_iff_minimalPeriod_dvd`, `Finset.card_inter_vadd`, `SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj`, `vadd_neg_vadd`, `MeasureTheory.measure_neg_vadd_sdiff`, `Seminorm.vadd_closedBall`, `instErgodicVAddOfIsAddLeftInvariant`, `LipschitzWith.vadd`, `Finset.addDysonETransform_fst`, `DilationEquiv.smulTorsor_apply`, `Set.vadd_set_univ`, `AffineSubspace.vadd_mem_iff_mem_of_mem_direction`, `NormedAddGroup.to_isIsometricVAdd_left`, `signedDist_vadd_right`, `neg_vadd_vadd`, `IsClosed.vadd_left_of_isCompact`, `NormedAddGroup.to_isIsometricVAdd_right`, `AffineMap.map_vadd`, `ZSpan.isAddFundamentalDomain'`, `affineSegment_const_vadd_image`, `Sbtw.const_vadd`, `EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center`, `vadd_closedBall''`, `Finset.mem_neg_vadd_finset_iff`, `AddSubgroup.vadd_leftQuotientEquiv`, `isInvariantBlock_iff_isFixedBlock`, `AffineMap.lineMap_vadd_apply`, `compHom_vadd_def`, `Metric.preimage_vadd_closedBall`, `measurableEmbedding_const_vadd`, `AddSubgroup.instFaithfulVAddSubtypeMem`, `HahnModule.SMulCommClass`, `mem_own_leftAddCoset`, `SubAddAction.nat_card_ofStabilizer_eq`, `vadd_orbit_subset`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `Finite.finite_addAction_orbit`, `continuousWithinAt_const_vadd_iff`, `AffineSubspace.coe_vadd`, `AddOreLocalization.vadd_cancel'`, `Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter`, `List.vadd_sum`, `IsBlock.of_subset`, `vadd_segment`, `AddSubgroup.instVAddAssocClassSubtypeMem`, `Set.powersetCard.faithfulVAdd`, `isBlock_iff_vadd_eq_or_disjoint`, `MeasureTheory.vadd_mem_ae`, `dist_vadd_left`, `ContinuousAffineMap.map_vadd`, `iteratedFDerivWithin_comp_add_right`, `vadd_mem_nhds_vadd`, `Finset.affineCombination_apply`, `orbit_addSubmonoid_subset`, `ProperVAdd.toContinuousVAdd`, `coe_aestabilizer`, `mem_stabilizer_finset'`, `AffineSpace.vadd_asymptoticNhds`, `zero_vadd_eq_id`, `midpoint_vadd_midpoint`, `Set.vadd_set_subset_iff_subset_neg_vadd_set`, `AffineSubspace.wSameSide_smul_vsub_vadd_left`, `IsFixedBlock.orbit`, `IsPreprimitive.exists_mem_vadd_and_notMem_vadd`, `translate_eq_domAddActMk_vadd`, `AddOreLocalization.expand`, `AmpleSet.vadd_iff`, `IsOpen.iUnion_vadd`, `Set.exists_vadd_inter_vadd_subset_vadd_neg_add_inter_neg_add`, `IsTrivialBlock.isBlock`, `SubAddAction.isCentralVAdd`, `vadd_mem_nhds_self`, `ZSpan.exist_unique_vadd_mem_fundamentalDomain`, `mem_stabilizer_set'`, `nsmul_vadd_eq_iff_period_dvd`, `Function.Periodic.map_vadd_zmultiples`, `dist_vadd_right`, `IsMinimal.dense_orbit`, `AddSubgroup.leftTransversals.vadd_diff_vadd`, `linearIndependent_set_iff_affineIndependent_vadd_union_singleton`, `AffineMap.lineMap_apply`, `Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd`, `differentiableWithinAt_comp_add_right`, `AddSubgroup.instMeasurableConstVAdd`, `SubAddAction.vadd_mem_iff'`, `Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one`, `Set.vadd_graphOn`, `AddSubgroup.leftCoset_cover_const_iff_surjOn`, `EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `IsAddUnit.vadd_left_cancel`, `Set.powersetCard.addActionHom_singleton_bijective`, `rightAddCoset_eq_iff`, `StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone`, `EuclideanGeometry.inversion_def`, `vadd_zsmul_movedBy_eq_of_addCommute`, `toFun_apply`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff`, `IsModuleFiltration.mk_int`, `zsmul_vadd_mod_minimalPeriod`, `comp_vadd_left`, `nsmul_period_vadd`, `ZSpan.isAddFundamentalDomain`, `properVAdd_iff`, `AddUnits.vaddAssocClass'_left`, `orbitRel.Quotient.orbit.coe_vadd`, `Affine.Simplex.centroid_eq_smul_vsub_vadd_point`, `period_eq_minimalPeriod`, `ergodic_vadd_of_denseRange_nsmul`, `Set.infinite_vadd_set`, `nndist_vadd_right`, `AddTorsor.vsub_vadd'`, `op_vadd_set_stabilizer_subset`, `leftAddCoset_eq_iff`, `vadd_iterate`, `zero_vadd`, `AffineSubspace.mem_affineSpan_insert_iff`, `AddOreLocalization.oreSub_vadd_char`, `Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter`, `isBlock_top`, `HahnModule.coeff_single_zero_smul`, `eq_addCosets_of_normal`, `addSubgroup_vadd_def`, `ProperVAdd.isProperMap_vadd_pair_set`, `MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt`, `mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd`, `mem_affineSpan_iff_exists`, `nsmul_add_period_vadd`, `MeasureTheory.vadd_set_ae_eq`, `AddMonoidHom.preimage_vadd_setₛₗ`, `Metric.vadd_closedEBall`, `aemeasurable_const_vadd_iff`, `Set.natCard_vadd_set`, `IsBlock.orbit`, `Measurable.measurableSMul₂_iterateAddAct`, `orbitRel.Quotient.mem_addSubgroup_orbit_iff'`, `isBlock_iff_disjoint_vadd_of_ne`, `preimage_vadd_setₛₗ_of_isAddUnit_isAddUnit`, `Set.powersetCard.coe_addActionHom_of_embedding`, `Finset.weightedVSub_vadd`, `AffineEquiv.ofLinearEquiv_apply`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero`, `vadd_zsmul_fixedBy_eq_of_addCommute`, `AffineEquiv.pointReflection_apply`, `period_eq_zero_iff`, `Homeomorph.vadd_apply`, `AffineSubspace.wOppSide_smul_vsub_vadd_right`, `isOpenMap_vadd_of_sigmaCompact`, `isCancelVAdd_iff_stabilizer_eq_bot`, `AddUnits.measurableVAdd`, `mem_fixedBy`, `AffineMap.coe_lineMap`, `Equiv.coe_constVAdd`, `AffineSubspace.vadd_mem_of_mem_direction`, `Set.op_vadd_inter_nonempty_iff`, `AffineEquiv.coe_constVSub_symm`, `Finset.op_vadd_addConvolution_eq_addConvolution_vadd`, `SubAddAction.val_preimage_orbit`, `vectorSpan_vadd`, `MeasureTheory.Subgroup.vaddInvariantMeasure`, `Bornology.IsVonNBounded.vadd`, `vadd_openSegment`, `toPerm_symm_apply`, `SubAddAction.image_inclusion`, `IsLinearSet.vadd`, `MeasureTheory.vaddInvariantMeasure_iterateAddAct`, `AddUnits.continuousVAdd`, `vadd_vsub_vadd_comm`, `ergodic_vadd_of_denseRange_zsmul`, `orbitEquivQuotientStabilizer_symm_apply`, `AddSubgroup.IsComplement.pairwiseDisjoint_vadd`, `AffineMap.vadd_apply`, `SubAddAction.mem_fixingAddSubgroup_insert_iff`, `AddSubgroup.vadd_def`, `Set.disjoint_vadd_set`, `AffineSubspace.sSameSide_smul_vsub_vadd_right`, `ball_add`, `lowerClosure_vadd`, `IsCompact.sub_closedBall`, `SubAddAction.mem_orbit_subAdd_iff`, `is_two_pretransitive_iff`, `Function.Embedding.coe_vadd`, `properVAdd_iff_continuousVAdd_ultrafilter_tendsto`, `MeasurableEquiv.vadd_apply`, `EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd`, `dense_orbit`, `signedDist_vadd_right_swap`, `Wbtw.vadd_const`, `card_orbit_mul_card_stabilizer_eq_card_addGroup`, `Wbtw.const_vadd`, `EMetric.vadd_closedBall`, `BlockMem.coe_top`, `Finsupp.mem_vaddAntidiagonal_of_addGroup`, `SubAddAction.compl_def`, `orbit.eq_or_disjoint`, `add_ball`, `AffineMap.homothety_apply`, `dist_vadd_cancel_left`, `hasFDerivWithinAt_comp_add_right`, `isMultiplyPreprimitive_succ_iff_ofStabilizer`, `ContinuousAffineMap.vadd_contLinear`, `orbit_addSubgroup_zero_eq_self`, `IsometryEquiv.vaddConst_apply`, `isLinearSet_iff_exists_fg_eq_vadd`, `slope_vadd_const`, `QuotientAddGroup.instContinuousConstVAdd`, `affineSegment_vadd_const_image`, `SubAddAction.ofStabilizer.snoc_castSucc`, `Set.Infinite.vadd_set`, `IsPretransitive.of_compHom`, `orbit_eq_univ`, `vadd_iterate_apply`, `AffineIsometry.map_vadd`, `isTopologicallyTransitive_iff_dense_iUnion`, `UpperHalfPlane.vadd_right_cancel_iff`, `quotient_preimage_image_eq_union_add`, `NormedAddTorsor.to_isIsIsometricVAdd`, `instIsPretransitiveOfSubsingleton`, `Prod.mk_vadd_mk`, `Cardinal.mk_vadd_set`, `vadd_mem_of_set_mem_fixedBy`, `SetLike.mk_vadd_of_tower_mk`, `signedDist_vadd_left`, `mem_stabilizer_finset_iff_subset_vadd_finset`, `isSimpleOrder_blockMem_iff_isPreprimitive`, `QuotientAddGroup.orbit_eq_out_vadd`, `Finset.weightedVSub_vadd_affineCombination`, `SetLike.GradedMul.toGradedSMul`, `iteratedFDerivWithin_comp_add_left'`, `Set.mem_vadd_set_neg`, `AddSubmonoid.instMeasurableConstVAdd`, `MeasureTheory.measure_inter_neg_vadd`, `SubAddAction.ENat_card_ofStabilizer_add_zero_eq`, `Finset.addETransformRight_snd`, `mem_own_rightAddCoset`, `Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `AddMonoidHom.vaddZeroHom_apply`, `isBlock_addSubgroup`, `SubAddAction.fixingAddSubgroup_of_insert`, `AffineSubspace.vadd_mem_iff_mem_direction`, `ext_iff`, `BlockMem.coe_bot`, `zero_vadd`, `edist_vadd_vadd_le`, `minimalPeriod_pos`, `is_zero_preprimitive_iff`, `IsOpen.exists_vadd_mem`, `ZLattice.isAddFundamentalDomain`, `MeasureTheory.measure_union_neg_vadd`, `SubAddAction.orbitRel_of_subAdd`, `vadd_closedBall_zero`, `AddSubgroup.vadd_toLeftFun`, `AffineSubspace.wSameSide_smul_vsub_vadd_right`, `SubAddAction.mem_ofFixingAddSubgroup_iff`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `HahnModule.one_smul'`, `Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone`, `injective`, `wbtw_smul_vadd_smul_vadd_of_nonneg_of_le`, `EuclideanGeometry.reflection_apply'`, `Finset.centroid_pair`, `Set.disjoint_vadd_set_left`, `vadd_closure_orbit_subset`, `AffineSubspace.sSameSide_vadd_left_iff`, `vadd_coe_set`, `SubAddAction.inclusion.coe_eq`, `subset_interior_vadd`, `AddOreLocalization.oreSub_zero_vadd`, `instProperConstVAddOfContinuousConstVAdd`, `vadd_left_cancel_iff`, `Finset.addETransformLeft_snd`, `SubAddAction.ofFixingAddSubgroup_carrier`, `HahnSeries.SummableFamily.hsum_smul`, `continuous_const_vadd_iff`, `AffineSubspace.wSameSide_vadd_right_iff`, `Finset.addDysonETransform.vadd_finset_snd_subset_fst`, `upperClosure_vadd`, `IsAddFoelner.mean_vadd_eq_mean`, `minimalPeriod_eq_one_iff_fixedBy`, `Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point`, `Quotient.vadd_mk`, `derivWithin_comp_add_const`, `IsometryEquiv.constVAdd_apply`, `vadd_vsub_vadd_cancel_left`, `wbtw_or_wbtw_smul_vadd_of_nonneg`, `SubAddAction.vaddAssocClass`, `Bornology.isVonNBounded_vadd`, `ofQuotientStabilizer_mem_orbit`, `Finset.addETransformLeft_fst`, `vsub_vadd`, `SlashInvariantForm.vAdd_width_periodic`, `UpperHalfPlane.coe_vadd`, `Ideal.univ_eq_iUnion_image_add`, `AddSubgroup.mk_vadd`, `vadd_uniformity`, `toPermHom_apply_apply`, `Set.neg_vadd_set_distrib`, `vadd_vsub`, `isPreprimitive_of_is_two_pretransitive`, `AffineMap.homothety_def`, `Finsupp.smul_apply_addAction`, `instIsPretransitiveElemOrbit`, `MeasureTheory.measure_symmDiff_neg_vadd`, `wbtw_const_vadd_iff`, `AffineIsometryEquiv.map_vadd`, `IsFixedBlock.univ`, `AffineEquiv.vaddConst_apply`, `neg_vadd_eq_iff`, `support_translate`, `isMultiplyPreprimitive_iff`, `HomogeneousIdeal.irrelevant_eq_iSup`, `Set.mem_neg_vadd_set_iff`, `amenable_of_maxAddFoelner_neBot`, `AffineSubspace.vadd_mem_pointwise_vadd_iff`, `AddOreLocalization.vadd_zero_vadd`, `disjoint_image_image_iff`, `Finset.vadd_univ`, `Finset.centroid_pair_fin`, `Finset.vadd_stabilizer_of_no_doubling`, `AddOreLocalization.vadd_sub_zero`, `zsmul_add_period_vadd`, `Seminorm.vadd_ball`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.covolume_ne_top`, `IsAddFoelner.tendsto_meas_vadd_symmDiff`, `zero_leftAddCoset`, `set_mem_fixedBy_iff`, `Set.disjoint_vadd_set_right`, `UpperHalfPlane.modular_T_zpow_smul`, `vadd_right_injective`, `mem_stabilizer_finset`, `AddUnits.vadd_neg`, `Metric.vadd_eball`, `mem_stabilizer_set_iff_vadd_set_subset`, `SubAddAction.ofFixingAddSubgroup.append_right`, `AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd`, `hasFDerivWithinAt_comp_sub`, `derivWithin_comp_sub_const`, `EuclideanGeometry.dist_smul_vadd_eq_dist`, `collinear_iff_exists_forall_eq_smul_vadd`, `vaddCommClass_self`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `MeasureTheory.measure_preimage_vadd`, `AffineIsometryEquiv.coe_vaddConst'`, `Set.vadd_set_symmDiff`, `uniformContinuous_vadd`, `wbtw_or_wbtw_smul_vadd_of_nonpos`, `AddOreLocalization.expand'`, `ofFixingSubgroup.isMultiplyPreprimitive`, `SubAddAction.nat_card_ofStabilizer_add_zero_eq`, `IsCompact.closedBall_add`, `AddMonoidHom.transfer_def`, `IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup`, `QuotientAction.inv_mul_mem`, `HomogeneousIdeal.irrelevant_eq_closure`, `IsPartition.of_orbits`, `Finset.vadd_mem_vadd_finset_iff`, `WithIdealFilter.mem_nhds_iff`, `orbit_addSubgroup_subset`, `AffineSpace.asymptoticNhds_eq_smul_vadd`, `QuotientAddGroup.eq_class_eq_leftCoset`, `FreeAddMonoid.of_vadd`, `SubAddAction.ofStabilizer_carrier`, `SubAddAction.disjoint_val_image`, `AddSubmonoid.instMeasurableVAdd`, `IsAddUnit.vadd_uniformity`, `MeasureTheory.measure_neg_vadd_union`, `Set.preimage_vadd`, `AddSubgroup.exists_leftTransversal_of_FiniteIndex`, `AddSubgroup.properlyDiscontinuousVAdd_of_tendsto_cofinite`, `AffineMap.homothety_add`, `orbit_addSubgroup_eq_rightCoset`, `wbtw_vadd_const_iff`, `Finset.card_vadd_inter`, `vadd_mem_nhds_vadd_iff`, `ZSpan.vadd_mem_fundamentalDomain`, `eq_neg_vadd_iff`, `differentiableWithinAt_comp_add_left`, `AffineSubspace.wOppSide_vadd_right_iff`, `AffineSubspace.sOppSide_smul_vsub_vadd_left`, `AddRightCancelMonoid.faithfulVAdd`, `MeasureTheory.MeasurePreserving.vaddInvariantMeasure_iterateAddAct`, `normal_iff_eq_addCosets`, `Finset.neg_vadd_mem_iff`, `Prod.snd_vadd`, `MeasureTheory.addFundamentalFrontier_vadd`, `Set.vadd_set_iInter`, `nsmul_mod_period_vadd`, `EuclideanGeometry.orthogonalProjection_apply`, `mem_aestabilizer`, `MeasureTheory.pairwise_disjoint_addFundamentalInterior`, `nsmul_period_add_vadd`, `derivWithin_comp_const_add`, `AffineSubspace.pointwise_vadd_span`, `mem_fixedPoints`, `convex_vadd`, `Filter.Tendsto.asymptoticNhds_vadd_const`, `AffineSubspace.setOf_sOppSide_eq_image2`, `AffineEquiv.map_vadd'`, `subset_interior_vadd_right`, `bijective`, `AddActionHom.map_mem_fixedPoints`, `Finset.vadd_finset_subset_vadd_finset_iff`, `denseRange_vadd`, `SubAddAction.val_vadd_of_tower`, `Set.vadd_inter_nonempty_iff`, `isCancelVAdd_iff_eq_zero_of_vadd_eq`, `Finset.subset_vadd_finset_iff`, `SubAddAction.ofStabilizer.isMultiplyPretransitive`, `nndist_vadd_cancel_left`, `Set.iUnion_vadd_eq_setOf_exists`, `ThreeAPFree.vadd_set`, `IsAddUnit.neg_vadd`, `mem_fixedPoints_iff_card_orbit_eq_one`, `AffineSubspace.setOf_wSameSide_eq_image2`, `le_stabilizer_iff_vadd_le`, `vadd_mem_fixedBy_iff_mem_fixedBy`, `vadd_right_cancel_iff`, `orbit_vadd`, `AddUnits.continuousConstVAdd`, `MeasureTheory.addFundamentalInterior_vadd`, `MeasureTheory.innerRegular_map_vadd`, `iteratedFDerivWithin_comp_sub'`, `AffineSubspace.sSameSide_smul_vsub_vadd_left`, `Finset.addConvolution_op_vadd_eq_addConvolution_add_neg`, `IsOpen.right_addCoset`, `IsAddUnit.vadd_bijective`, `mem_stabilizerAddSubmonoid_iff`, `IsAddUnit.measurable_const_vadd_iff`, `MeasureTheory.eventuallyConst_vadd_set_ae`, `vadd_ball''`, `fderivWithin_comp_add_right`, `mem_stabilizer_set`, `measurableSMul₂_iterateAddAct`, `IsBlock.univ`, `orbitRel.Quotient.orbit_eq_orbit_out`, `Metric.preimage_vadd_eball`, `faithfulVAdd_iff`, `Set.vadd_set_inter`, `IsOpen.vadd`, `SubAddAction.inclusion_injective`, `IsPreprimitive.mk'`, `Finset.vadd_finset_sdiff`, `Set.subset_vadd_set_iff`, `punctured_nhds_vadd`, `MeasureTheory.measure_vadd_null`, `nndist_vadd_vadd_le`, `stabilizerEquivStabilizer_zero`, `IsClosed.right_addCoset`, `stabilizer_orbit_eq`, `IsClosed.left_addCoset`, `approxAddOrderOf.vadd_subset_of_coprime`, `AffineSubspace.wOppSide_vadd_left_iff`, `MeasureTheory.Measure.isAddHaarMeasure_map_vadd`, `instIsPretransitiveElemOrbit_1`, `StrictConvex.vadd`, `IterateAddAct.mk_vadd`, `isBlock_addSubgroup'`, `Set.mem_vadd_set_iff_neg_vadd_mem`, `sub_ball`, `OpenPartialHomeomorph.unitBallBall_apply`, `AddUnits.instMeasurableConstVAdd`, `vadd_pi`, `eq_vadd_iff_vsub_eq`, `is_zero_pretransitive_iff`, `IsAddFoelner.amenable`, `totallyBounded_iff_subset_finite_iUnion_nhds_zero`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.vaddInvariantMeasure_quotient`, `leftAddCoset_mem_leftAddCoset`, `Affine.Simplex.ninePointCircle_center`, `orbitRel.Quotient.mem_addSubgroup_orbit_iff`, `AffineMap.lineMap_vadd`, `subsingleton_orbit_iff_mem_fixedPoints`, `IsOpen.dense_iUnion_vadd`, `wbtw_smul_vadd_smul_vadd_of_nonpos_of_le`, `isHomeomorph_vadd`, `ofQuotientStabilizer_vadd`, `Prod.fst_vadd`, `IsPreprimitive.of_prime_card`, `SubAddAction.stabilizer_of_subAdd`, `spectrum.vadd_eq`, `index_stabilizer`, `instIsCancelVAdd`, `instIsLeftCancelVAdd`, `MeasureTheory.vaddInvariantMeasure_tfae`, `Finset.addETransformRight_fst`, `isAddFoelner_iff`, `HahnSeries.SummableFamily.powerSeriesFamily_smul`, `isPreprimitive_fixingAddSubgroup_insert_iff`, `dist_vadd_vadd_le`, `Finset.card_vadd_inter_vadd`, `SlashInvariantForm.vAdd_apply_of_mem_strictPeriods`, `IsQuasiPreprimitive.toIsPretransitive`, `orbitRel.Quotient.orbit_mk`, `AddOreLocalization.oreSub_vadd_oreSub`, `toPerm_apply`, `isAddQuotientCoveringMap_iff`, `MeasureTheory.NullMeasurableSet.vadd`, `HahnSeries.SummableFamily.mul_eq_smul`, `isBlock_iff_vadd_eq_of_mem`, `fderivWithin_comp_sub`, `EuclideanGeometry.reflection_apply`, `isMultiplyPreprimitive_ofStabilizer`, `isBlock_subtypeVal`, `IsCompact.add_closedBall`, `vadd_set_stabilizer_subset`, `Set.finite_vadd_set`, `zsmul_mod_period_vadd`, `UpperHalfPlane.vadd_im`, `affineIndependent_vadd`, `SubAddAction.mem_ofFixingAddSubgroup_insert_iff`, `zsmul_vadd_eq_iff_period_dvd`, `ofQuotientStabilizer_mk`, `AffineMap.lineMap_vadd_lineMap`, `isCoatom_stabilizer_iff_preprimitive`, `UpperHalfPlane.modular_T_smul`, `EMetric.preimage_vadd_ball`, `vadd_mem_orbit_vadd`, `AffineSubspace.sOppSide_vadd_left_iff`, `QuotientAddGroup.orbit_mk_eq_vadd`, `Finset.dens_vadd_finset`, `closure_vadd`, `UpperHalfPlane.vadd_left_injective`, `sbtw_const_vadd_iff`, `isPreprimitive_of_fixingAddSubgroup_empty_iff`, `mem_orbit_symm`, `hasFDerivWithinAt_comp_add_left`, `SubAddAction.inclusion.toFun_eq_coe`, `Finset.neg_vadd_finset_distrib`, `IsBlock.orbit_of_normal`, `AddUnits.vaddCommClass'`, `wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos`, `continuousOn_const_vadd_iff`, `orbit_vadd_subset`, `Set.vadd_set_pi`, `vadd_left_mem_affineSpan_pair`, `IsAddQuotientCoveringMap.toContinuousConstVAdd`, `signedDist_vadd_vadd`, `AffineMap.coe_homothety`, `isPretransitive_quotient`, `HahnModule.single_zero_smul_eq_smul`, `Set.powersetCard.coe_vadd`, `ContinuousAffineMap.vadd_apply`, `MeasurableSet.const_vadd`, `mem_stabilizer_finset_iff_vadd_finset_subset`, `Set.encard_vadd_set`, `EuclideanGeometry.angle_const_vadd`, `Equiv.pointReflection_apply`, `isLinearSet_iff_exists_fin_addMonoidHom`, `SubAddAction.not_mem_of_mem_ofFixingAddSubgroup`, `IsBlockSystem.of_normal`, `mem_fixingAddSubgroup_iff`, `isPretransitive_iff_base`, `AffineSubspace.sOppSide_smul_vsub_vadd_right`, `IsCompact.closedBall_sub`, `SubAddAction.map_ofFixingAddSubgroupUnion_def`, `AddActionHom.zeroEmbeddingMap_bijective`, `EMetric.preimage_vadd_closedBall`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`ext` 📖	—	`VAdd.vadd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `toAddSemigroupAction`	—	—	—
`ext_iff` 📖	mathematical	—	`VAdd.vadd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `toAddSemigroupAction`	—	`ext`
`zero_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `toAddSemigroupAction` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	—

AddCommute

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`vadd_left` 📖	mathematical	`AddCommute`	`HVAdd.hVAdd` `instHVAdd`	—	`symm` `vadd_right`
`vadd_right` 📖	mathematical	`AddCommute`	`HVAdd.hVAdd` `instHVAdd`	—	`add_vadd_comm` `vadd_add_assoc`

AddMonoid

Definitions

Name	Category	Theorems
`toAddAction` 📖	CompOp	221 math math: `ball_sub`, `SubAddAction.map_ofFixingAddSubgroupUnion_bijective`, `AddAction.stabilizer_addSubgroup_op`, `IsUpperSet.vadd`, `VAddCommClass.of_add_vadd_zero`, `AddOreLocalization.oreSub_add_oreSub`, `Convex.vadd`, `Finset.neg_op_vadd_finset_distrib`, `vadd_eq_self_of_preimage_zsmul_eq_self`, `SubAddAction.ofStabilizer.conjMap_comp`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `AddOreLocalization.cardinalMk_le`, `QuotientAddGroup.univ_eq_iUnion_vadd`, `AddConstMap.coe_addLeftHom_apply`, `AddOreLocalization.sub_eq_zero'`, `SubAddAction.ofFixingAddSubgroup_of_singleton_bijective`, `approxAddOrderOf.vadd_eq_of_mul_dvd`, `IsLowerSet.vadd_subset`, `QuotientAddGroup.measurableVAdd`, `HahnSeries.SummableFamily.lsum_apply`, `threeAPFree_vadd_set`, `AddAction.map_stabilizer_le`, `isLinearSet_iff`, `Finset.vadd_addConvolution_eq_addConvolution_neg_add`, `IsOpen.left_addCoset`, `AddOreLocalization.sub_eq_zero`, `exists_disjoint_vadd_of_isCompact`, `Finset.op_vadd_stabilizer_of_no_doubling`, `SetLike.instVAddCommClassSubtypeMem_1`, `QuotientAddGroup.instContinuousVAdd`, `IsUniformAddGroup.to_uniformContinuousConstVAdd`, `IsLowerSet.vadd`, `SetLike.instVAddCommClassSubtypeMem_2`, `AddAction.isPreprimitive_ofFixingAddSubgroup_conj_iff`, `instIsOrderedVAddOfIsOrderedAddMonoid`, `SubAddAction.ofStabilizer.conjMap_comp_neg_apply`, `AddLocalization.mk_self`, `Set.OrdConnected.vadd`, `Set.neg_op_vadd_set_distrib`, `HomogeneousIdeal.toAddSubmonoid_irrelevant_le`, `AddOreLocalization.instVAddCommClass_1`, `AddAction.left_quotientAction`, `Set.vadd_sub_vadd_comm`, `SubAddAction.ofStabilizer.isPretransitive_iff`, `Function.Periodic.map_vadd_multiples`, `MeasureTheory.Measure.instVAddInvariantMeasureSubtypeMemAddSubmonoidOfIsAddLeftInvariant`, `SubAddAction.conjMap_ofFixingAddSubgroup_bijective`, `instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid`, `AddAction.stabilizer_add_self`, `AddAction.Regular.isPretransitive`, `AddOreLocalization.add_cancel`, `AddOreLocalization.numerator_isAddUnit`, `SubAddAction.conjMap_ofFixingAddSubgroup_coe_apply`, `Set.vadd_Icc`, `orbit_addSubgroup_eq_self_of_mem`, `IsSemilinearSet.vadd`, `AddSubgroup.isAddQuotientCoveringMap_of_comm`, `NonarchimedeanAddGroup.exists_openAddSubgroup_separating`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `HahnSeries.SummableFamily.embDomain_succ_smul_powers`, `Finset.addDysonETransform_snd`, `Fin.partialSum_left_neg`, `HahnSeries.of_symm_smul_of_eq_mul`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroup`, `AddOreLocalization.add_sub_zero`, `VAddAssocClass.left`, `AddLocalization.mk_self_mk`, `AddOreLocalization.oreSub_add_char`, `AddOreLocalization.instVAddAssocClass_1`, `IsUpperSet.vadd_subset`, `SubAddAction.val_image_orbit`, `MeasureTheory.tendsto_measure_vadd_diff_isCompact_isClosed`, `HomogeneousIdeal.irrelevant_le`, `Set.vadd_graphOn_univ`, `AddOreLocalization.numeratorHom_surjective_of_finite`, `vadd_ball_zero`, `HahnModule.coeff_smul_order_add_order`, `Set.vadd_inter_nonempty_iff'`, `IsApproximateAddSubgroup.two_nsmul_covByVAdd`, `Ideal.homogeneousHull_eq_iSup`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `mem_leftAddCoset_iff`, `VAddAssocClass.of_vadd_zero_add`, `Finset.add_mem_vadd_finset_iff`, `isProperLinearSet_iff`, `Finset.vadd_finset_subsetSum_subset_subsetSum_insert`, `Finset.card_inter_vadd`, `AddOreLocalization.add_zero`, `instErgodicVAddOfIsAddLeftInvariant`, `Finset.addDysonETransform_fst`, `NormedAddGroup.to_isIsometricVAdd_left`, `AddOreLocalization.vadd_zero_oreSub_zero_vadd`, `vadd_closedBall''`, `mem_own_leftAddCoset`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `AddOreLocalization.vadd_cancel'`, `AddOreLocalization.numeratorHom_apply`, `AddOreLocalization.add_vadd`, `translate_eq_domAddActMk_vadd`, `Set.exists_vadd_inter_vadd_subset_vadd_neg_add_inter_neg_add`, `vadd_mem_nhds_self`, `Function.Periodic.map_vadd_zmultiples`, `AddSubgroup.leftTransversals.vadd_diff_vadd`, `Set.vadd_graphOn`, `AddSubgroup.leftCoset_cover_const_iff_surjOn`, `IsModuleFiltration.mk_int`, `AddAction.op_vadd_set_stabilizer_subset`, `leftAddCoset_eq_iff`, `AddOreLocalization.oreSub_vadd_char`, `eq_addCosets_of_normal`, `AddOreLocalization.zero_vadd`, `MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt`, `SubAddAction.ofStabilizer.conjMap_bijective`, `SubAddAction.ofFixingAddSubgroup_insert_map_apply`, `AddLocalization.mk_zero`, `Finset.op_vadd_addConvolution_eq_addConvolution_vadd`, `SubAddAction.val_preimage_orbit`, `SubAddAction.image_inclusion`, `IsLinearSet.vadd`, `AddSubgroup.IsComplement.pairwiseDisjoint_vadd`, `ball_add`, `lowerClosure_vadd`, `IsCompact.sub_closedBall`, `SubAddAction.mem_orbit_subAdd_iff`, `Topology.IsQuotientMap.isAddQuotientCoveringMap_of_isDiscrete_ker_addMonoidHom`, `add_ball`, `orbit_addSubgroup_zero_eq_self`, `isLinearSet_iff_exists_fg_eq_vadd`, `QuotientAddGroup.instContinuousConstVAdd`, `AddOreLocalization.zero_add`, `QuotientAddGroup.orbit_eq_out_vadd`, `SetLike.GradedMul.toGradedSMul`, `Set.mem_vadd_set_neg`, `Finset.addETransformRight_snd`, `AddOreLocalization.universalAddHom_commutes`, `AddOreLocalization.add_assoc`, `vadd_closedBall_zero`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `AddOreLocalization.add_cancel'`, `AddAction.stabilizer_addSubgroup`, `vadd_coe_set`, `SubAddAction.inclusion.coe_eq`, `AddOreLocalization.oreSub_zero_vadd`, `AddOreLocalization.universalAddHom_apply`, `Finset.addETransformLeft_snd`, `HahnSeries.SummableFamily.hsum_smul`, `Finset.addDysonETransform.vadd_finset_snd_subset_fst`, `upperClosure_vadd`, `SubAddAction.ofStabilizer.neg_conjMap_comp_apply`, `AddLocalization.r_iff_oreEqv_r`, `AddOreLocalization.zero_sub_vadd`, `SubAddAction.vaddAssocClass`, `AddOreLocalization.eq_of_num_factor_eq`, `AddOreLocalization.oreSub_add_oreSub_comm`, `Ideal.univ_eq_iUnion_image_add`, `Set.neg_vadd_set_distrib`, `support_translate`, `AddAction.isMultiplyPreprimitive_iff`, `HomogeneousIdeal.irrelevant_eq_iSup`, `AddOreLocalization.vadd_zero_vadd`, `Finset.vadd_stabilizer_of_no_doubling`, `AddAction.stabilizer_image_coe_quotient`, `AddOreLocalization.vadd_sub_zero`, `AddOreLocalization.vadd_cancel`, `zero_leftAddCoset`, `AddOreLocalization.zero_sub_add`, `AddAction.stabilizer_finite`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `AddAction.add_stabilizer_self`, `IsCompact.closedBall_add`, `AddMonoidHom.transfer_def`, `AddAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup`, `HomogeneousIdeal.irrelevant_eq_closure`, `QuotientAddGroup.eq_class_eq_leftCoset`, `AddAction.IsBlock.subtype_val_preimage`, `AddSubgroup.exists_leftTransversal_of_FiniteIndex`, `AddSubgroup.properlyDiscontinuousVAdd_of_tendsto_cofinite`, `orbit_addSubgroup_eq_rightCoset`, `Finset.card_vadd_inter`, `AddOreLocalization.add_neg`, `AddRightCancelMonoid.faithfulVAdd`, `normal_iff_eq_addCosets`, `AddAction.stabilizer_subset_sub_right`, `SubAddAction.ofStabilizer.conjMap_comp_apply`, `Set.vadd_inter_nonempty_iff`, `ThreeAPFree.vadd_set`, `IsAddUnit.neg_vadd`, `IsApproximateAddSubgroup.nsmul_inter_nsmul_covByVAdd_sq_inter_sq`, `HahnModule.instIsTorsionFree`, `vadd_ball''`, `SubAddAction.inclusion_injective`, `IsClosed.left_addCoset`, `approxAddOrderOf.vadd_subset_of_coprime`, `sub_ball`, `totallyBounded_iff_subset_finite_iUnion_nhds_zero`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.vaddInvariantMeasure_quotient`, `leftAddCoset_mem_leftAddCoset`, `AddAction.ofQuotientStabilizer_vadd`, `spectrum.vadd_eq`, `instIsCancelVAdd`, `instIsLeftCancelVAdd`, `HahnSeries.SummableFamily.powerSeriesFamily_smul`, `AddAction.isPreprimitive_fixingAddSubgroup_insert_iff`, `Finset.card_vadd_inter_vadd`, `AddOreLocalization.oreSub_vadd_oreSub`, `HahnSeries.SummableFamily.mul_eq_smul`, `AddAction.isBlock_subtypeVal`, `IsCompact.add_closedBall`, `AddAction.vadd_set_stabilizer_subset`, `QuotientAddGroup.orbit_mk_eq_vadd`, `AddAction.isPreprimitive_of_fixingAddSubgroup_empty_iff`, `instProperVAddOfIsTopologicalAddGroup`, `SubAddAction.inclusion.toFun_eq_coe`, `Finset.neg_vadd_finset_distrib`, `AddAction.isPretransitive_quotient`, `isLinearSet_iff_exists_fin_addMonoidHom`, `AddAction.stabilizer_quotient`, `IsCompact.closedBall_sub`, `SubAddAction.ofStabilizer.isPretransitive_iff_of_conj`, `SubAddAction.map_ofFixingAddSubgroupUnion_def`, `SubAddAction.ofStabilizer.conjMap_apply`

AddOpposite

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`vadd_eq_add_unop` 📖	mathematical	—	`HVAdd.hVAdd` `AddOpposite` `instHVAdd` `Add.toVAddAddOpposite` `unop`	—	—

AddSemigroup

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`vaddAssocClass` 📖	mathematical	—	`VAddAssocClass` `Add.toVAdd` `toAdd`	—	`add_assoc`

AddSemigroupAction

Definitions

Name	Category	Theorems
`toVAdd` 📖	CompOp	870 math math: `Set.ncard_vadd_set`, `AddAction.mem_stabilizer_set_iff_subset_vadd_set`, `ball_sub`, `NumberField.mixedEmbedding.fundamentalDomain_integerLattice`, `AffineIsometryEquiv.pointReflection_apply`, `Metric.vadd_closedBall`, `AddSubmonoid.continuousVAdd`, `EuclideanGeometry.dist_smul_vadd_sq`, `SubAddAction.map_ofFixingAddSubgroupUnion_bijective`, `IsOpen.vadd_left`, `AddAction.isTopologicallyTransitive_iff_dense_iUnion_preimage`, `Equiv.coe_vaddConst`, `AddAction.IsTrivialBlock.vadd_iff`, `SubAddAction.notMem_val_image`, `AddSubgroup.vadd_opposite_image_add_preimage'`, `AddAction.IsPreprimitive.of_isTrivialBlock_base`, `EuclideanGeometry.reflection_orthogonal_vadd`, `Equiv.coe_constVSub_symm`, `AddAction.orbit_eq_iff`, `fderivWithin_comp_add_left`, `rank_le_card_isVisible`, `AddAction.isPeriodicPt_vadd_iff`, `AffineSubspace.sSameSide_vadd_right_iff`, `AddSubgroup.vaddCommClass_left`, `Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `IsOpen.iUnion_preimage_vadd`, `AffineSubspace.setOf_sSameSide_eq_image2`, `MeasureTheory.vadd_ae`, `IsUpperSet.vadd`, `VAddCommClass.of_add_vadd_zero`, `Homeomorph.vadd_symm_apply`, `AffineEquiv.constVAdd_apply`, `AddAction.nsmul_vadd_mod_minimalPeriod`, `sub_add_vsub_comm`, `isAddQuotientCoveringMap_iff_isCoveringMap_and`, `AddAction.mem_addSubgroup_orbit_iff`, `rightAddCoset_zero`, `AddAction.zsmul_period_add_vadd`, `nhds_vadd`, `AddAction.nonempty_orbit`, `Finset.vadd_finset_eq_univ`, `Convex.vadd`, `Finset.neg_op_vadd_finset_distrib`, `SetLike.vadd_of_tower_def`, `AddAction.mapsTo_vadd_orbit`, `vadd_eq_vadd_iff_neg_add_eq_vsub`, `vadd_vsub_assoc`, `AddAction.orbitRel_apply`, `vadd_mem_fixedPoints_of_normal`, `AddAction.IsPretransitive.of_vaddAssocClass`, `vadd_eq_self_of_preimage_zsmul_eq_self`, `AddAction.isTopologicallyTransitive_iff`, `SubAddAction.ofFixingAddSubgroup_of_inclusion_injective`, `rightAddCoset_mem_rightAddCoset`, `Affine.Simplex.centroid_eq_smul_sum_vsub_vadd`, `QuotientAddGroup.univ_eq_iUnion_vadd`, `Homeomorph.vaddConst_apply`, `Dense.vadd`, `derivWithin_comp_const_sub`, `Set.iUnion_neg_vadd`, `vadd_right_mem_affineSpan_pair`, `AddConstMap.coe_addLeftHom_apply`, `mem_const_vadd_affineSegment`, `AffineSubspace.wOppSide_smul_vsub_vadd_left`, `IsAddUnit.aemeasurable_const_vadd_iff`, `vsub_vadd_comm`, `SubAddAction.ofFixingAddSubgroup_of_singleton_bijective`, `Sbtw.vadd_const`, `AddCircle.isAddFundamentalDomain_of_ae_ball`, `AddAction.orbit.pairwiseDisjoint`, `iteratedFDerivWithin_comp_add_right'`, `MeasureTheory.integral_vadd_eq_self`, `AddAction.Supports.vadd`, `UpperHalfPlane.isometry_real_vadd`, `approxAddOrderOf.vadd_eq_of_mul_dvd`, `Multiset.vadd_sum`, `AffineSubspace.vadd_mem_mk'`, `Set.vadd_set_compl`, `MeasureTheory.mem_addFundamentalFrontier`, `EMetric.vadd_ball`, `AffineIsometryEquiv.coe_constVAdd`, `vadd_mem_spanPoints_of_mem_spanPoints_of_mem_vectorSpan`, `AddAction.stabilizer_vadd_eq_stabilizer_map_conj`, `IsLowerSet.vadd_subset`, `AddAction.pretransitive_iff_unique_quotient_of_nonempty`, `smul_vsub_rev_vadd_mem_affineSpan_pair`, `SubAddAction.mem_ofStabilizer_iff`, `tendsto_const_vadd_iff`, `EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection`, `QuotientAddGroup.measurableVAdd`, `affineSpan_singleton_union_vadd_eq_top_of_span_eq_top`, `Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter`, `AddAction.Quotient.vadd_coe`, `EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint`, `threeAPFree_vadd_set`, `Finset.vadd_finset_univ`, `IsometryEquiv.constVSub_symm_apply`, `EuclideanGeometry.angle_vadd_const`, `isLinearSet_iff`, `AddAction.Quotient.coe_vadd_out`, `vadd_vadd`, `AddAction.isPretransitive_compHom`, `AddAction.continuousVAdd_compHom`, `FreeAddMonoid.vadd_def`, `AffineSubspace.sOppSide_vadd_right_iff`, `Finset.vadd_addConvolution_eq_addConvolution_neg_add`, `MeasureTheory.measure_neg_vadd_inter`, `AffineIndependent.vadd`, `collinear_iff_of_mem`, `IsOpen.left_addCoset`, `AddSubmonoid.nsmul_vadd_mem_closure_vadd`, `Set.vadd_set_vsub_vadd_set`, `exists_disjoint_vadd_of_isCompact`, `AffineMap.map_vadd'`, `Set.vadd_set_sdiff`, `Finset.op_vadd_stabilizer_of_no_doubling`, `orbit_fixingAddSubgroup_compl_subset`, `SetLike.instVAddCommClassSubtypeMem_1`, `QuotientAddGroup.instContinuousVAdd`, `vsub_vadd_eq_vsub_sub`, `IsUniformAddGroup.to_uniformContinuousConstVAdd`, `IsLowerSet.vadd`, `EuclideanGeometry.orthogonalProjection_apply_mem`, `SetLike.instVAddCommClassSubtypeMem_2`, `AffineBasis.coe_vadd`, `AddAction.isPreprimitive_ofFixingAddSubgroup_conj_iff`, `instIsOrderedVAddOfIsOrderedAddMonoid`, `AddSubgroup.vaddCommClass_right`, `AddAction.orbitZMultiplesEquiv_symm_apply'`, `AddAction.IsBlock.of_orbit`, `AddAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `AddAction.orbitZMultiplesEquiv_symm_apply`, `Function.Embedding.vadd_apply`, `Finset.weightedVSubOfPoint_vadd`, `AffineSubspace.smul_vsub_vadd_mem`, `nndist_vadd_cancel_right`, `Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone`, `Set.vadd_set_pi_of_isAddUnit`, `AddAction.mem_stabilizer_iff`, `IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd`, `Set.OrdConnected.vadd`, `Filter.vadd_tendsto_vadd_iff`, `sbtw_vadd_const_iff`, `IsAddUnit.preimage_vadd_setₛₗ`, `Set.neg_op_vadd_set_distrib`, `HomogeneousIdeal.toAddSubmonoid_irrelevant_le`, `IsAddQuotientCoveringMap.isCancelVAdd`, `vadd_vsub_eq_sub_vsub`, `iteratedFDerivWithin_comp_add_left`, `Set.vadd_sub_vadd_comm`, `Set.pairwise_disjoint_vadd_iff`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive`, `SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive'`, `AddAction.isBlock_iff_vadd_eq_of_nonempty`, `SubAddAction.ofStabilizer.isPretransitive_iff`, `UpperHalfPlane.vadd_re`, `affinity_unitClosedBall`, `AddAction.mem_orbit_vadd`, `IsAddUnit.vadd`, `vadd_eq_vadd_iff_sub_eq_vsub`, `AddAction.vadd_neg_mem_fixedBy_iff_mem_fixedBy`, `Function.Periodic.map_vadd_multiples`, `ContinuousAffineMap.vadd_toAffineMap`, `add_vadd`, `SubAddAction.stabilizer_of_subMul.addSubmonoid`, `MeasureTheory.Measure.instVAddInvariantMeasureSubtypeMemAddSubmonoidOfIsAddLeftInvariant`, `AddAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPoints`, `AddOreLocalization.oreSub_eq_iff`, `EuclideanGeometry.orthogonalProjection_apply'`, `MeasureTheory.measure_vadd`, `AddAction.pretransitive_iff_subsingleton_quotient`, `Metric.preimage_vadd_ball`, `instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid`, `op_vadd_add`, `Finite.to_properlyDiscontinuousVAdd`, `AddAction.stabilizer_vadd_eq_right`, `AddAction.Regular.isPretransitive`, `NumberField.mixedEmbedding.fundamentalDomain_idealLattice`, `AddAction.IsTopologicallyTransitive.exists_vadd_inter`, `wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg`, `Finset.card_vadd_finset`, `Set.powersetCard.isPretransitive_of_isMultiplyPretransitive'`, `Metric.vadd_ball`, `dist_vadd_cancel_right`, `isAddFundamentalDomain_Ioc`, `Set.powersetCard.addActionHom_of_embedding_surjective`, `EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center`, `Set.vadd_mem_vadd_set_iff`, `Multiplicative.mulAction_isPretransitive`, `instIsLeftCancelVAdd_1`, `FreeAddMonoid.ofList_vadd`, `instErgodicVAddAddOppositeOfIsAddRightInvariant`, `Finset.vadd_finset_symmDiff`, `IsClosed.vadd_right_of_isCompact`, `Set.vadd_Icc`, `AffineSpace.asymptoticNhds_vadd_pure`, `measurableVAdd_iterateAddAct`, `Finset.vadd_finset_inter`, `vadd_eq_iff_eq_neg_vadd`, `IsAddFoelner.mean_vadd_eq_mean_vadd`, `orbit_addSubgroup_eq_self_of_mem`, `IsSemilinearSet.vadd`, `vadd_zero_vadd`, `convexHull_vadd`, `AddAction.isPretransitive_of_is_two_pretransitive`, `sub_smul_slope_vadd`, `vadd_singleton_mem_nhds_of_sigmaCompact`, `NonarchimedeanAddGroup.exists_openAddSubgroup_separating`, `AddOreLocalization.vadd_oreSub`, `AffineSubspace.setOf_wOppSide_eq_image2`, `MeasureTheory.vadd_set_ae_le`, `IsCompact.exists_finite_cover_vadd`, `MeasureTheory.measure_sdiff_neg_vadd`, `nndist_vadd_left`, `Metric.preimage_vadd_closedEBall`, `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `HahnSeries.SummableFamily.embDomain_succ_smul_powers`, `isOpenMap_vadd`, `AddUnits.vaddAssocClass'`, `Finset.addDysonETransform_snd`, `AddAction.vadd_fixedBy`, `Finset.vadd_finset_subset_iff`, `MeasureTheory.measure_neg_vadd_symmDiff`, `AffineSubspace.coe_pointwise_vadd`, `AffineEquiv.map_vadd`, `vadd_vsub_vadd_cancel_right`, `AffineSubspace.wSameSide_vadd_left_iff`, `Fin.partialSum_left_neg`, `SubAddAction.vaddAssocClass'`, `HahnSeries.of_symm_smul_of_eq_mul`, `mem_vadd_const_affineSegment`, `AddAction.image_inter_image_iff`, `VAddAssocClass.left`, `AddTorsor.vadd_vsub'`, `vadd_mem_affineSpan_of_mem_affineSpan_of_mem_vectorSpan`, `continuousAt_const_vadd_iff`, `AffineMap.vadd_linear`, `isClosedMap_vadd`, `IsAddQuotientCoveringMap.apply_eq_iff_mem_orbit`, `IsAddUnit.vadd_tendsto_vadd_iff`, `AddAction.Quotient.mk_vadd_out`, `measurable_const_vadd_iff`, `IsAddUnit.preimage_vadd_set`, `IsUpperSet.vadd_subset`, `ProperVAdd.isProperMap_vadd_pair`, `Filter.Tendsto.const_vadd_asymptoticNhds`, `SubAddAction.val_image_orbit`, `AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply`, `SubAddAction.SMulMemClass.coe_subtype`, `mem_fixingAddSubmonoid_iff`, `arrowAddAction_vadd`, `smul_vsub_vadd_mem_affineSpan_pair`, `IsOpen.dense_iUnion_preimage_vadd`, `MeasureTheory.tendsto_measure_vadd_diff_isCompact_isClosed`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero`, `Finset.affineCombination_eq_weightedVSubOfPoint_vadd_of_sum_eq_one`, `HomogeneousIdeal.irrelevant_le`, `AddUnits.val_vadd`, `Set.vadd_univ`, `AddGroup.preimage_vadd_set`, `AffineMap.vadd_lineMap`, `op_vadd_coe_set`, `Set.vadd_graphOn_univ`, `affinity_unitBall`, `isSimplyConnected_vadd_set_iff`, `Affine.Triangle.circumsphere_eq_of_dist_of_oangle`, `Set.vadd_set_eq_univ`, `AddAction.zeroEmbedding_isPretransitive_iff`, `AddAction.surjective`, `AmpleSet.vadd`, `AddAction.IsTrivialBlock.vadd`, `Set.vadd_set_subset_vadd_set_iff`, `Metric.vadd_sphere`, `Metric.preimage_vadd_sphere`, `StrictConvex.affinity`, `MeasureTheory.mem_addFundamentalInterior`, `op_vadd_op_vadd`, `iteratedFDerivWithin_comp_sub`, `AddAction.orbit.coe_vadd`, `differentiableWithinAt_comp_sub`, `vadd_ball_zero`, `EuclideanGeometry.orthogonalProjection_vadd_eq_self`, `HahnModule.coeff_smul_order_add_order`, `HahnModule.instIsScalarTowerHahnSeries_1`, `AddAction.isPretransitive_iff_orbit_eq_univ`, `AddAction.nsmul_vadd_eq_iff_minimalPeriod_dvd`, `Set.vadd_inter_nonempty_iff'`, `IsClosed.vadd`, `AddSubgroup.instMeasurableVAdd`, `IsTopologicalAddTorsor.toContinuousVAdd`, `AddAction.mem_orbit_self`, `AffineIsometryEquiv.coe_vaddConst`, `Set.preimage_vadd_neg`, `Ideal.homogeneousHull_eq_iSup`, `MeasureTheory.measure_vadd_eq_zero_iff`, `SubAddAction.ofFixingAddSubgroup_insert_map_bijective`, `interior_vadd`, `mem_leftAddCoset_iff`, `VAddAssocClass.of_vadd_zero_add`, `signedDist_vadd_left_swap`, `mem_rightAddCoset_iff`, `VAddAssocClass.to₂₃₄`, `AddAction.orbitRel.Quotient.mapsTo_vadd_orbit`, `Finset.add_mem_vadd_finset_iff`, `AddAction.vadd_orbit_eq_orbit_vadd`, `EuclideanGeometry.reflection_apply_of_mem`, `isProperLinearSet_iff`, `AddAction.vadd_orbit`, `AddAction.minimalPeriod_eq_card`, `AddSubgroup.continuousVAdd`, `AddActionHom.map_mem_fixedBy`, `AddGroup.preimage_vadd_setₛₗ`, `Finset.vadd_finset_subsetSum_subset_subsetSum_insert`, `AddAction.zsmul_vadd_eq_iff_minimalPeriod_dvd`, `Finset.card_inter_vadd`, `SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj`, `vadd_neg_vadd`, `MeasureTheory.measure_neg_vadd_sdiff`, `Seminorm.vadd_closedBall`, `instErgodicVAddOfIsAddLeftInvariant`, `LipschitzWith.vadd`, `Finset.addDysonETransform_fst`, `DilationEquiv.smulTorsor_apply`, `Set.vadd_set_univ`, `AffineSubspace.vadd_mem_iff_mem_of_mem_direction`, `NormedAddGroup.to_isIsometricVAdd_left`, `signedDist_vadd_right`, `neg_vadd_vadd`, `IsClosed.vadd_left_of_isCompact`, `NormedAddGroup.to_isIsometricVAdd_right`, `AffineMap.map_vadd`, `ZSpan.isAddFundamentalDomain'`, `affineSegment_const_vadd_image`, `Sbtw.const_vadd`, `EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center`, `vadd_closedBall''`, `Finset.mem_neg_vadd_finset_iff`, `AddSubgroup.vadd_leftQuotientEquiv`, `AddAction.isInvariantBlock_iff_isFixedBlock`, `AffineMap.lineMap_vadd_apply`, `AddAction.compHom_vadd_def`, `Metric.preimage_vadd_closedBall`, `measurableEmbedding_const_vadd`, `AddSubgroup.instFaithfulVAddSubtypeMem`, `HahnModule.SMulCommClass`, `mem_own_leftAddCoset`, `SubAddAction.nat_card_ofStabilizer_eq`, `AddAction.vadd_orbit_subset`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`, `Finite.finite_addAction_orbit`, `continuousWithinAt_const_vadd_iff`, `AffineSubspace.coe_vadd`, `AddOreLocalization.vadd_cancel'`, `Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter`, `List.vadd_sum`, `AddAction.IsBlock.of_subset`, `vadd_segment`, `AddSubgroup.instVAddAssocClassSubtypeMem`, `Set.powersetCard.faithfulVAdd`, `AddAction.isBlock_iff_vadd_eq_or_disjoint`, `MeasureTheory.vadd_mem_ae`, `dist_vadd_left`, `ContinuousAffineMap.map_vadd`, `iteratedFDerivWithin_comp_add_right`, `vadd_mem_nhds_vadd`, `Finset.affineCombination_apply`, `AddAction.orbit_addSubmonoid_subset`, `ProperVAdd.toContinuousVAdd`, `AddAction.coe_aestabilizer`, `AddAction.mem_stabilizer_finset'`, `AffineSpace.vadd_asymptoticNhds`, `zero_vadd_eq_id`, `midpoint_vadd_midpoint`, `Set.vadd_set_subset_iff_subset_neg_vadd_set`, `AffineSubspace.wSameSide_smul_vsub_vadd_left`, `AddAction.IsFixedBlock.orbit`, `AddAction.IsPreprimitive.exists_mem_vadd_and_notMem_vadd`, `translate_eq_domAddActMk_vadd`, `AddOreLocalization.expand`, `AmpleSet.vadd_iff`, `IsOpen.iUnion_vadd`, `Set.exists_vadd_inter_vadd_subset_vadd_neg_add_inter_neg_add`, `AddAction.IsTrivialBlock.isBlock`, `SubAddAction.isCentralVAdd`, `vadd_mem_nhds_self`, `ZSpan.exist_unique_vadd_mem_fundamentalDomain`, `AddAction.mem_stabilizer_set'`, `AddAction.nsmul_vadd_eq_iff_period_dvd`, `Function.Periodic.map_vadd_zmultiples`, `dist_vadd_right`, `AddAction.IsMinimal.dense_orbit`, `AddSubgroup.leftTransversals.vadd_diff_vadd`, `linearIndependent_set_iff_affineIndependent_vadd_union_singleton`, `AffineMap.lineMap_apply`, `Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd`, `differentiableWithinAt_comp_add_right`, `AddSubgroup.instMeasurableConstVAdd`, `SubAddAction.vadd_mem_iff'`, `Finset.weightedVSubOfPoint_vadd_eq_of_sum_eq_one`, `Set.vadd_graphOn`, `AddSubgroup.leftCoset_cover_const_iff_surjOn`, `EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `IsAddUnit.vadd_left_cancel`, `Set.powersetCard.addActionHom_singleton_bijective`, `rightAddCoset_eq_iff`, `StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone`, `EuclideanGeometry.inversion_def`, `AddAction.vadd_zsmul_movedBy_eq_of_addCommute`, `AddAction.toFun_apply`, `SubAddAction.ofStabilizer.isMultiplyPretransitive_iff`, `IsModuleFiltration.mk_int`, `AddAction.zsmul_vadd_mod_minimalPeriod`, `comp_vadd_left`, `AddAction.nsmul_period_vadd`, `ZSpan.isAddFundamentalDomain`, `properVAdd_iff`, `AddUnits.vaddAssocClass'_left`, `AddAction.orbitRel.Quotient.orbit.coe_vadd`, `Affine.Simplex.centroid_eq_smul_vsub_vadd_point`, `AddAction.period_eq_minimalPeriod`, `ergodic_vadd_of_denseRange_nsmul`, `Set.infinite_vadd_set`, `nndist_vadd_right`, `AddTorsor.vsub_vadd'`, `AddAction.op_vadd_set_stabilizer_subset`, `leftAddCoset_eq_iff`, `vadd_iterate`, `zero_vadd`, `AffineSubspace.mem_affineSpan_insert_iff`, `AddOreLocalization.oreSub_vadd_char`, `Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter`, `AddAction.isBlock_top`, `HahnModule.coeff_single_zero_smul`, `eq_addCosets_of_normal`, `AddAction.addSubgroup_vadd_def`, `ProperVAdd.isProperMap_vadd_pair_set`, `MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt`, `mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd`, `mem_affineSpan_iff_exists`, `AddAction.nsmul_add_period_vadd`, `MeasureTheory.vadd_set_ae_eq`, `AddMonoidHom.preimage_vadd_setₛₗ`, `Metric.vadd_closedEBall`, `aemeasurable_const_vadd_iff`, `Set.natCard_vadd_set`, `AddAction.IsBlock.orbit`, `Measurable.measurableSMul₂_iterateAddAct`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff'`, `AddAction.isBlock_iff_disjoint_vadd_of_ne`, `preimage_vadd_setₛₗ_of_isAddUnit_isAddUnit`, `Set.powersetCard.coe_addActionHom_of_embedding`, `Finset.weightedVSub_vadd`, `AffineEquiv.ofLinearEquiv_apply`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero`, `AddAction.vadd_zsmul_fixedBy_eq_of_addCommute`, `AffineEquiv.pointReflection_apply`, `AddAction.period_eq_zero_iff`, `Homeomorph.vadd_apply`, `AffineSubspace.wOppSide_smul_vsub_vadd_right`, `isOpenMap_vadd_of_sigmaCompact`, `isCancelVAdd_iff_stabilizer_eq_bot`, `AddUnits.measurableVAdd`, `AddAction.mem_fixedBy`, `AffineMap.coe_lineMap`, `Equiv.coe_constVAdd`, `AffineSubspace.vadd_mem_of_mem_direction`, `Set.op_vadd_inter_nonempty_iff`, `AffineEquiv.coe_constVSub_symm`, `Finset.op_vadd_addConvolution_eq_addConvolution_vadd`, `SubAddAction.val_preimage_orbit`, `vectorSpan_vadd`, `MeasureTheory.Subgroup.vaddInvariantMeasure`, `Bornology.IsVonNBounded.vadd`, `vadd_openSegment`, `AddAction.toPerm_symm_apply`, `ext_iff`, `SubAddAction.image_inclusion`, `IsLinearSet.vadd`, `MeasureTheory.vaddInvariantMeasure_iterateAddAct`, `AddUnits.continuousVAdd`, `vadd_vsub_vadd_comm`, `ergodic_vadd_of_denseRange_zsmul`, `AddAction.orbitEquivQuotientStabilizer_symm_apply`, `AddSubgroup.IsComplement.pairwiseDisjoint_vadd`, `AffineMap.vadd_apply`, `SubAddAction.mem_fixingAddSubgroup_insert_iff`, `AddSubgroup.vadd_def`, `Set.disjoint_vadd_set`, `AffineSubspace.sSameSide_smul_vsub_vadd_right`, `ball_add`, `lowerClosure_vadd`, `IsCompact.sub_closedBall`, `SubAddAction.mem_orbit_subAdd_iff`, `AddAction.is_two_pretransitive_iff`, `Function.Embedding.coe_vadd`, `properVAdd_iff_continuousVAdd_ultrafilter_tendsto`, `MeasurableEquiv.vadd_apply`, `EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd`, `AddAction.dense_orbit`, `signedDist_vadd_right_swap`, `Wbtw.vadd_const`, `AddAction.card_orbit_mul_card_stabilizer_eq_card_addGroup`, `Wbtw.const_vadd`, `EMetric.vadd_closedBall`, `AddAction.BlockMem.coe_top`, `Finsupp.mem_vaddAntidiagonal_of_addGroup`, `SubAddAction.compl_def`, `AddAction.orbit.eq_or_disjoint`, `add_ball`, `AffineMap.homothety_apply`, `dist_vadd_cancel_left`, `hasFDerivWithinAt_comp_add_right`, `AddAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `ContinuousAffineMap.vadd_contLinear`, `orbit_addSubgroup_zero_eq_self`, `IsometryEquiv.vaddConst_apply`, `isLinearSet_iff_exists_fg_eq_vadd`, `slope_vadd_const`, `QuotientAddGroup.instContinuousConstVAdd`, `affineSegment_vadd_const_image`, `SubAddAction.ofStabilizer.snoc_castSucc`, `Set.Infinite.vadd_set`, `AddAction.IsPretransitive.of_compHom`, `AddAction.orbit_eq_univ`, `vadd_iterate_apply`, `AffineIsometry.map_vadd`, `AddAction.isTopologicallyTransitive_iff_dense_iUnion`, `UpperHalfPlane.vadd_right_cancel_iff`, `AddAction.quotient_preimage_image_eq_union_add`, `NormedAddTorsor.to_isIsIsometricVAdd`, `AddAction.instIsPretransitiveOfSubsingleton`, `Prod.mk_vadd_mk`, `Cardinal.mk_vadd_set`, `AddAction.vadd_mem_of_set_mem_fixedBy`, `SetLike.mk_vadd_of_tower_mk`, `signedDist_vadd_left`, `AddAction.mem_stabilizer_finset_iff_subset_vadd_finset`, `AddAction.isSimpleOrder_blockMem_iff_isPreprimitive`, `QuotientAddGroup.orbit_eq_out_vadd`, `Finset.weightedVSub_vadd_affineCombination`, `SetLike.GradedMul.toGradedSMul`, `iteratedFDerivWithin_comp_add_left'`, `Set.mem_vadd_set_neg`, `AddSubmonoid.instMeasurableConstVAdd`, `MeasureTheory.measure_inter_neg_vadd`, `SubAddAction.ENat_card_ofStabilizer_add_zero_eq`, `Finset.addETransformRight_snd`, `mem_own_rightAddCoset`, `Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection`, `AddMonoidHom.vaddZeroHom_apply`, `AddAction.isBlock_addSubgroup`, `SubAddAction.fixingAddSubgroup_of_insert`, `AffineSubspace.vadd_mem_iff_mem_direction`, `AddAction.ext_iff`, `AddAction.BlockMem.coe_bot`, `AddAction.zero_vadd`, `edist_vadd_vadd_le`, `AddAction.minimalPeriod_pos`, `AddAction.is_zero_preprimitive_iff`, `IsOpen.exists_vadd_mem`, `ZLattice.isAddFundamentalDomain`, `MeasureTheory.measure_union_neg_vadd`, `SubAddAction.orbitRel_of_subAdd`, `vadd_closedBall_zero`, `AddSubgroup.vadd_toLeftFun`, `AffineSubspace.wSameSide_smul_vsub_vadd_right`, `SubAddAction.mem_ofFixingAddSubgroup_iff`, `SubAddAction.ofFixingAddSubgroupEmpty_equivariantMap_bijective`, `HahnModule.one_smul'`, `Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone`, `AddAction.injective`, `wbtw_smul_vadd_smul_vadd_of_nonneg_of_le`, `EuclideanGeometry.reflection_apply'`, `Finset.centroid_pair`, `Set.disjoint_vadd_set_left`, `vadd_closure_orbit_subset`, `AffineSubspace.sSameSide_vadd_left_iff`, `vadd_coe_set`, `SubAddAction.inclusion.coe_eq`, `subset_interior_vadd`, `AddOreLocalization.oreSub_zero_vadd`, `instProperConstVAddOfContinuousConstVAdd`, `vadd_left_cancel_iff`, `Finset.addETransformLeft_snd`, `SubAddAction.ofFixingAddSubgroup_carrier`, `HahnSeries.SummableFamily.hsum_smul`, `continuous_const_vadd_iff`, `AffineSubspace.wSameSide_vadd_right_iff`, `Finset.addDysonETransform.vadd_finset_snd_subset_fst`, `upperClosure_vadd`, `IsAddFoelner.mean_vadd_eq_mean`, `AddAction.minimalPeriod_eq_one_iff_fixedBy`, `Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point`, `AddAction.Quotient.vadd_mk`, `derivWithin_comp_add_const`, `IsometryEquiv.constVAdd_apply`, `vadd_vsub_vadd_cancel_left`, `wbtw_or_wbtw_smul_vadd_of_nonneg`, `SubAddAction.vaddAssocClass`, `Bornology.isVonNBounded_vadd`, `AddAction.ofQuotientStabilizer_mem_orbit`, `Finset.addETransformLeft_fst`, `vsub_vadd`, `SlashInvariantForm.vAdd_width_periodic`, `UpperHalfPlane.coe_vadd`, `Ideal.univ_eq_iUnion_image_add`, `AddSubgroup.mk_vadd`, `vadd_uniformity`, `AddAction.toPermHom_apply_apply`, `Set.neg_vadd_set_distrib`, `vadd_vsub`, `AddAction.isPreprimitive_of_is_two_pretransitive`, `AffineMap.homothety_def`, `Finsupp.smul_apply_addAction`, `AddAction.instIsPretransitiveElemOrbit`, `MeasureTheory.measure_symmDiff_neg_vadd`, `wbtw_const_vadd_iff`, `AffineIsometryEquiv.map_vadd`, `AddAction.IsFixedBlock.univ`, `AffineEquiv.vaddConst_apply`, `neg_vadd_eq_iff`, `support_translate`, `AddAction.isMultiplyPreprimitive_iff`, `HomogeneousIdeal.irrelevant_eq_iSup`, `Set.mem_neg_vadd_set_iff`, `amenable_of_maxAddFoelner_neBot`, `AffineSubspace.vadd_mem_pointwise_vadd_iff`, `AddOreLocalization.vadd_zero_vadd`, `AddAction.disjoint_image_image_iff`, `Finset.vadd_univ`, `Finset.centroid_pair_fin`, `Finset.vadd_stabilizer_of_no_doubling`, `AddOreLocalization.vadd_sub_zero`, `AddAction.zsmul_add_period_vadd`, `Seminorm.vadd_ball`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.covolume_ne_top`, `IsAddFoelner.tendsto_meas_vadd_symmDiff`, `zero_leftAddCoset`, `AddAction.set_mem_fixedBy_iff`, `Set.disjoint_vadd_set_right`, `UpperHalfPlane.modular_T_zpow_smul`, `vadd_right_injective`, `AddAction.mem_stabilizer_finset`, `AddUnits.vadd_neg`, `Metric.vadd_eball`, `AddAction.mem_stabilizer_set_iff_vadd_set_subset`, `SubAddAction.ofFixingAddSubgroup.append_right`, `AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd`, `hasFDerivWithinAt_comp_sub`, `derivWithin_comp_sub_const`, `EuclideanGeometry.dist_smul_vadd_eq_dist`, `collinear_iff_exists_forall_eq_smul_vadd`, `vaddCommClass_self`, `SubAddAction.ofFixingAddSubgroup_equivariantMap_injective`, `MeasureTheory.measure_preimage_vadd`, `AffineIsometryEquiv.coe_vaddConst'`, `Set.vadd_set_symmDiff`, `uniformContinuous_vadd`, `wbtw_or_wbtw_smul_vadd_of_nonpos`, `AddOreLocalization.expand'`, `AddAction.ofFixingSubgroup.isMultiplyPreprimitive`, `SubAddAction.nat_card_ofStabilizer_add_zero_eq`, `IsCompact.closedBall_add`, `AddMonoidHom.transfer_def`, `AddAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingAddSubgroup`, `AddAction.QuotientAction.inv_mul_mem`, `HomogeneousIdeal.irrelevant_eq_closure`, `AddAction.IsPartition.of_orbits`, `Finset.vadd_mem_vadd_finset_iff`, `WithIdealFilter.mem_nhds_iff`, `AddAction.orbit_addSubgroup_subset`, `AffineSpace.asymptoticNhds_eq_smul_vadd`, `QuotientAddGroup.eq_class_eq_leftCoset`, `FreeAddMonoid.of_vadd`, `SubAddAction.ofStabilizer_carrier`, `SubAddAction.disjoint_val_image`, `AddSubmonoid.instMeasurableVAdd`, `IsAddUnit.vadd_uniformity`, `MeasureTheory.measure_neg_vadd_union`, `Set.preimage_vadd`, `AddSubgroup.exists_leftTransversal_of_FiniteIndex`, `AddSubgroup.properlyDiscontinuousVAdd_of_tendsto_cofinite`, `AffineMap.homothety_add`, `orbit_addSubgroup_eq_rightCoset`, `wbtw_vadd_const_iff`, `Finset.card_vadd_inter`, `vadd_mem_nhds_vadd_iff`, `ZSpan.vadd_mem_fundamentalDomain`, `eq_neg_vadd_iff`, `differentiableWithinAt_comp_add_left`, `AffineSubspace.wOppSide_vadd_right_iff`, `AffineSubspace.sOppSide_smul_vsub_vadd_left`, `AddRightCancelMonoid.faithfulVAdd`, `MeasureTheory.MeasurePreserving.vaddInvariantMeasure_iterateAddAct`, `normal_iff_eq_addCosets`, `Finset.neg_vadd_mem_iff`, `Prod.snd_vadd`, `MeasureTheory.addFundamentalFrontier_vadd`, `Set.vadd_set_iInter`, `AddAction.nsmul_mod_period_vadd`, `EuclideanGeometry.orthogonalProjection_apply`, `AddAction.mem_aestabilizer`, `MeasureTheory.pairwise_disjoint_addFundamentalInterior`, `AddAction.nsmul_period_add_vadd`, `derivWithin_comp_const_add`, `AffineSubspace.pointwise_vadd_span`, `AddAction.mem_fixedPoints`, `convex_vadd`, `Filter.Tendsto.asymptoticNhds_vadd_const`, `AffineSubspace.setOf_sOppSide_eq_image2`, `AffineEquiv.map_vadd'`, `subset_interior_vadd_right`, `AddAction.bijective`, `AddActionHom.map_mem_fixedPoints`, `Finset.vadd_finset_subset_vadd_finset_iff`, `denseRange_vadd`, `SubAddAction.val_vadd_of_tower`, `Set.vadd_inter_nonempty_iff`, `isCancelVAdd_iff_eq_zero_of_vadd_eq`, `Finset.subset_vadd_finset_iff`, `SubAddAction.ofStabilizer.isMultiplyPretransitive`, `nndist_vadd_cancel_left`, `Set.iUnion_vadd_eq_setOf_exists`, `ThreeAPFree.vadd_set`, `IsAddUnit.neg_vadd`, `AddAction.mem_fixedPoints_iff_card_orbit_eq_one`, `AffineSubspace.setOf_wSameSide_eq_image2`, `AddAction.le_stabilizer_iff_vadd_le`, `AddAction.vadd_mem_fixedBy_iff_mem_fixedBy`, `vadd_right_cancel_iff`, `AddAction.orbit_vadd`, `AddUnits.continuousConstVAdd`, `MeasureTheory.addFundamentalInterior_vadd`, `MeasureTheory.innerRegular_map_vadd`, `iteratedFDerivWithin_comp_sub'`, `AffineSubspace.sSameSide_smul_vsub_vadd_left`, `Finset.addConvolution_op_vadd_eq_addConvolution_add_neg`, `IsOpen.right_addCoset`, `IsAddUnit.vadd_bijective`, `AddAction.mem_stabilizerAddSubmonoid_iff`, `IsAddUnit.measurable_const_vadd_iff`, `MeasureTheory.eventuallyConst_vadd_set_ae`, `vadd_ball''`, `fderivWithin_comp_add_right`, `AddAction.mem_stabilizer_set`, `measurableSMul₂_iterateAddAct`, `AddAction.IsBlock.univ`, `AddAction.orbitRel.Quotient.orbit_eq_orbit_out`, `Metric.preimage_vadd_eball`, `faithfulVAdd_iff`, `Set.vadd_set_inter`, `IsOpen.vadd`, `SubAddAction.inclusion_injective`, `AddAction.IsPreprimitive.mk'`, `Finset.vadd_finset_sdiff`, `Set.subset_vadd_set_iff`, `punctured_nhds_vadd`, `MeasureTheory.measure_vadd_null`, `nndist_vadd_vadd_le`, `AddAction.stabilizerEquivStabilizer_zero`, `IsClosed.right_addCoset`, `AddAction.stabilizer_orbit_eq`, `IsClosed.left_addCoset`, `approxAddOrderOf.vadd_subset_of_coprime`, `AffineSubspace.wOppSide_vadd_left_iff`, `MeasureTheory.Measure.isAddHaarMeasure_map_vadd`, `AddAction.instIsPretransitiveElemOrbit_1`, `StrictConvex.vadd`, `IterateAddAct.mk_vadd`, `AddAction.isBlock_addSubgroup'`, `Set.mem_vadd_set_iff_neg_vadd_mem`, `sub_ball`, `OpenPartialHomeomorph.unitBallBall_apply`, `AddUnits.instMeasurableConstVAdd`, `vadd_pi`, `eq_vadd_iff_vsub_eq`, `AddAction.is_zero_pretransitive_iff`, `IsAddFoelner.amenable`, `totallyBounded_iff_subset_finite_iUnion_nhds_zero`, `MeasureTheory.AddQuotientMeasureEqMeasurePreimage.vaddInvariantMeasure_quotient`, `leftAddCoset_mem_leftAddCoset`, `Affine.Simplex.ninePointCircle_center`, `AddAction.orbitRel.Quotient.mem_addSubgroup_orbit_iff`, `AffineMap.lineMap_vadd`, `AddAction.subsingleton_orbit_iff_mem_fixedPoints`, `IsOpen.dense_iUnion_vadd`, `wbtw_smul_vadd_smul_vadd_of_nonpos_of_le`, `isHomeomorph_vadd`, `AddAction.ofQuotientStabilizer_vadd`, `Prod.fst_vadd`, `AddAction.IsPreprimitive.of_prime_card`, `SubAddAction.stabilizer_of_subAdd`, `spectrum.vadd_eq`, `AddAction.index_stabilizer`, `instIsCancelVAdd`, `instIsLeftCancelVAdd`, `MeasureTheory.vaddInvariantMeasure_tfae`, `Finset.addETransformRight_fst`, `isAddFoelner_iff`, `HahnSeries.SummableFamily.powerSeriesFamily_smul`, `AddAction.isPreprimitive_fixingAddSubgroup_insert_iff`, `dist_vadd_vadd_le`, `Finset.card_vadd_inter_vadd`, `SlashInvariantForm.vAdd_apply_of_mem_strictPeriods`, `AddAction.IsQuasiPreprimitive.toIsPretransitive`, `AddAction.orbitRel.Quotient.orbit_mk`, `AddOreLocalization.oreSub_vadd_oreSub`, `AddAction.toPerm_apply`, `isAddQuotientCoveringMap_iff`, `MeasureTheory.NullMeasurableSet.vadd`, `HahnSeries.SummableFamily.mul_eq_smul`, `AddAction.isBlock_iff_vadd_eq_of_mem`, `fderivWithin_comp_sub`, `EuclideanGeometry.reflection_apply`, `AddAction.isMultiplyPreprimitive_ofStabilizer`, `AddAction.isBlock_subtypeVal`, `IsCompact.add_closedBall`, `AddAction.vadd_set_stabilizer_subset`, `Set.finite_vadd_set`, `AddAction.zsmul_mod_period_vadd`, `UpperHalfPlane.vadd_im`, `affineIndependent_vadd`, `SubAddAction.mem_ofFixingAddSubgroup_insert_iff`, `AddAction.zsmul_vadd_eq_iff_period_dvd`, `AddAction.ofQuotientStabilizer_mk`, `AffineMap.lineMap_vadd_lineMap`, `AddAction.isCoatom_stabilizer_iff_preprimitive`, `UpperHalfPlane.modular_T_smul`, `EMetric.preimage_vadd_ball`, `AddAction.vadd_mem_orbit_vadd`, `AffineSubspace.sOppSide_vadd_left_iff`, `QuotientAddGroup.orbit_mk_eq_vadd`, `Finset.dens_vadd_finset`, `closure_vadd`, `UpperHalfPlane.vadd_left_injective`, `sbtw_const_vadd_iff`, `AddAction.isPreprimitive_of_fixingAddSubgroup_empty_iff`, `AddAction.mem_orbit_symm`, `hasFDerivWithinAt_comp_add_left`, `SubAddAction.inclusion.toFun_eq_coe`, `Finset.neg_vadd_finset_distrib`, `AddAction.IsBlock.orbit_of_normal`, `AddUnits.vaddCommClass'`, `wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos`, `continuousOn_const_vadd_iff`, `AddAction.orbit_vadd_subset`, `Set.vadd_set_pi`, `vadd_left_mem_affineSpan_pair`, `IsAddQuotientCoveringMap.toContinuousConstVAdd`, `signedDist_vadd_vadd`, `AffineMap.coe_homothety`, `AddAction.isPretransitive_quotient`, `HahnModule.single_zero_smul_eq_smul`, `Set.powersetCard.coe_vadd`, `ContinuousAffineMap.vadd_apply`, `MeasurableSet.const_vadd`, `AddAction.mem_stabilizer_finset_iff_vadd_finset_subset`, `Set.encard_vadd_set`, `EuclideanGeometry.angle_const_vadd`, `Equiv.pointReflection_apply`, `isLinearSet_iff_exists_fin_addMonoidHom`, `SubAddAction.not_mem_of_mem_ofFixingAddSubgroup`, `AddAction.IsBlockSystem.of_normal`, `mem_fixingAddSubgroup_iff`, `AddAction.isPretransitive_iff_base`, `AffineSubspace.sOppSide_smul_vsub_vadd_right`, `IsCompact.closedBall_sub`, `SubAddAction.map_ofFixingAddSubgroupUnion_def`, `AddActionHom.zeroEmbeddingMap_bijective`, `EMetric.preimage_vadd_closedBall`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`add_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `toVAdd` `AddSemigroup.toAdd`	—	—
`ext` 📖	—	`VAdd.vadd` `toVAdd`	—	—	—
`ext_iff` 📖	mathematical	—	`VAdd.vadd` `toVAdd`	—	`ext`

Commute

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`smul_left` 📖	—	`Commute`	—	—	`symm` `smul_right`
`smul_left_iff` 📖	mathematical	—	`Commute` `SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction`	—	`symm_iff` `smul_right_iff`
`smul_right` 📖	—	`Commute`	—	—	`mul_smul_comm` `smul_mul_assoc`
`smul_right_iff` 📖	mathematical	—	`Commute` `SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction`	—	`smul_right` `inv_smul_smul`

Function.Injective

Definitions

Name	Category	Theorems
`addAction` 📖	CompOp	—
`mulAction` 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`smulCommClass` 📖	mathematical	—	`SMulCommClass`	—	`SMulCommClass.smul_comm`
`vaddCommClass` 📖	mathematical	`HVAdd.hVAdd` `instHVAdd`	`VAddCommClass`	—	`VAddCommClass.vadd_comm`

Function.Surjective

Definitions

Name	Category	Theorems
`addAction` 📖	CompOp	—
`mulAction` 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`smulCommClass` 📖	mathematical	—	`SMulCommClass`	—	`forall` `SMulCommClass.smul_comm`
`vaddCommClass` 📖	mathematical	`HVAdd.hVAdd` `instHVAdd`	`VAddCommClass`	—	`forall` `VAddCommClass.vadd_comm`

IsCancelSMul

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`eq_one_of_smul` 📖	mathematical	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction`	`MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`right_cancel` `one_smul`
`left_cancel` 📖	—	—	—	—	`IsLeftCancelSMul.left_cancel'` `toIsLeftCancelSMul`
`right_cancel` 📖	—	—	—	—	`right_cancel'`
`right_cancel'` 📖	—	—	—	—	—
`toIsLeftCancelSMul` 📖	mathematical	—	`IsLeftCancelSMul`	—	—

IsCancelVAdd

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`eq_zero_of_vadd` 📖	mathematical	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction`	`AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`right_cancel` `zero_vadd`
`left_cancel` 📖	—	`HVAdd.hVAdd` `instHVAdd`	—	—	`IsLeftCancelVAdd.left_cancel'` `toIsLeftCancelVAdd`
`right_cancel` 📖	—	`HVAdd.hVAdd` `instHVAdd`	—	—	`right_cancel'`
`right_cancel'` 📖	—	`HVAdd.hVAdd` `instHVAdd`	—	—	—
`toIsLeftCancelVAdd` 📖	mathematical	—	`IsLeftCancelVAdd`	—	—

IsCentralScalar

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`op_smul_eq_smul` 📖	mathematical	—	`MulOpposite` `MulOpposite.op`	—	—
`unop_smul_eq_smul` 📖	mathematical	—	`MulOpposite.unop` `MulOpposite`	—	`op_smul_eq_smul`

IsCentralVAdd

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`op_vadd_eq_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `AddOpposite` `instHVAdd` `AddOpposite.op`	—	—
`unop_vadd_eq_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddOpposite.unop` `AddOpposite`	—	`op_vadd_eq_vadd`

IsLeftCancelSMul

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`left_cancel` 📖	—	—	—	—	`left_cancel'`
`left_cancel'` 📖	—	—	—	—	—

IsLeftCancelVAdd

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`left_cancel` 📖	—	`HVAdd.hVAdd` `instHVAdd`	—	—	`left_cancel'`
`left_cancel'` 📖	—	`HVAdd.hVAdd` `instHVAdd`	—	—	—

IsScalarTower

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`left` 📖	mathematical	—	`IsScalarTower` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `Monoid.toMulAction`	—	`SemigroupAction.mul_smul`
`of_commMonoid` 📖	mathematical	—	`IsScalarTower` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `CommMonoid.toMonoid` `Monoid.toMulAction`	—	`smul_eq_mul` `mul_comm` `SMulCommClass.smul_comm`
`of_smul_one_mul` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	`IsScalarTower` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `Monoid.toMulAction`	—	`smul_eq_mul` `mul_assoc`
`op_left` 📖	mathematical	—	`IsScalarTower` `MulOpposite`	—	`IsCentralScalar.unop_smul_eq_smul` `smul_assoc`
`op_right` 📖	mathematical	—	`IsScalarTower` `MulOpposite` `MulOpposite.instSMul`	—	`IsCentralScalar.unop_smul_eq_smul` `MulOpposite.unop_smul` `smul_assoc`
`smul_assoc` 📖	—	—	—	—	—
`to₁₂₄` 📖	mathematical	—	`IsScalarTower`	—	`smul_one_smul` `smul_assoc`
`to₁₃₄` 📖	mathematical	—	`IsScalarTower`	—	`smul_one_smul` `smul_assoc`
`to₂₃₄` 📖	mathematical	`MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	`IsScalarTower` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction`	—	`smul_one_smul` `smul_assoc`

LibraryNote

Definitions

Name	Category	Theorems
`bundled_maps_over_different_rings` 📖	CompOp	—

Monoid

Definitions

Name	Category	Theorems
`toMulAction` 📖	CompOp	325 math math: `SubMulAction.ofStabilizer.isPretransitive_iff_of_conj`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset`, `instIsOrderedCancelSMulOfIsOrderedCancelMonoid`, `MulAction.isPreprimitive_of_fixingSubgroup_empty_iff`, `SubMulAction.ofStabilizer.conjMap_comp_apply`, `OreLocalization.numeratorHom_surjective_of_finite`, `SubMulAction.ofFixingSubgroup_insert_map_apply`, `IsLowerSet.smul`, `mul_ball`, `Representation.ofMulActionSelfAsModuleEquiv_symm_apply`, `Rep.diagonalSuccIsoFree_inv_hom_single`, `instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl`, `SubMulAction.ofFixingSubgroup_equivariantMap_injective`, `FractionRing.instIsScalarTower`, `Set.smul_graphOn_univ`, `LocalizedModule.restrictScalars_map_eq`, `SubMulAction.ofStabilizer.conjMap_comp_inv_apply`, `OreLocalization.mul_smul`, `Finset.inv_smul_finset_distrib`, `Finset.doubling_lt_three_halves`, `Set.mem_smul_set_inv`, `IsCompact.closedBall_mul`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left`, `instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeComplFractionRing`, `mem_leftCoset_iff`, `DoubleCoset.doubleCoset_union_leftCoset`, `MulAction.stabilizer_mul_self`, `SubMulAction.ofFixingSubgroup_of_inclusion_injective`, `RatFunc.mk_smul`, `Subgroup.center.smulCommClass_right`, `Complex.isQuotientCoveringMap_npow`, `Localization.liftOn_zero`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity`, `instIsScalarTowerAtPrimeFractionRing_1`, `OreLocalization.smul_cancel'`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity`, `SubMulAction.ofStabilizer.inv_conjMap_comp_apply`, `one_leftCoset`, `Finset.inv_op_smul_finset_distrib`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single`, `SubMulAction.map_ofFixingSubgroupUnion_def`, `Finset.mulDysonETransform_snd`, `HomogeneousLocalization.val_zero`, `MulAction.op_smul_set_stabilizer_subset`, `HomogeneousLocalization.val_one`, `MulAction.mul_stabilizer_self`, `orbit_subgroup_eq_self_of_mem`, `instIsPushoutFractionRingPolynomial_1`, `OreLocalization.oreDiv_mul_oreDiv`, `Rep.diagonalSuccIsoFree_inv_hom_single_single`, `Set.exists_smul_inter_smul_subset_smul_inv_mul_inter_inv_mul`, `Complex.UnitDisc.instIsScalarTower_circle_circle`, `Finset.smul_inv_mul_eq_inv_mul_opSMul`, `IsUnit.inv_smul`, `OreLocalization.one_smul`, `Localization.algHom_ext_iff`, `Representation.ofMulAction_self_smul_eq_mul`, `LocalizedModule.equivTensorProduct_symm_apply_tmul_one`, `SubMulAction.ofStabilizer.isPretransitive_iff`, `OreLocalization.eq_of_num_factor_eq`, `HomogeneousLocalization.val_smul`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_subgroup`, `OreLocalization.mul_div_one`, `coeSubmodule_differentIdeal_fractionRing`, `Ideal.Fiber.lift_residueField_surjective`, `OreLocalization.smul_cancel`, `OreLocalization.numeratorHom_inj`, `smul_ball''`, `Finset.mul_mem_smul_finset_iff`, `Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure`, `smul_closedBall_one`, `IsScalarTower.of_smul_one_mul`, `Set.OrdConnected.smul`, `Subgroup.leftCoset_cover_const_iff_surjOn`, `Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomial`, `OreLocalization.mul_assoc`, `instProperSMulOfIsTopologicalGroup`, `NonarchimedeanGroup.exists_openSubgroup_separating`, `ball_mul`, `OreLocalization.div_eq_one`, `IsCompact.div_closedBall`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1`, `QuotientGroup.eq_class_eq_leftCoset`, `StarMul.toStarModule`, `IsLocalization.instIsScalarTowerLocalizationAtPrime`, `RatFunc.ofFractionRing_one`, `MonoidHom.transfer_def`, `approxOrderOf.smul_subset_of_coprime`, `MulAction.isPreprimitive_ofFixingSubgroup_conj_iff`, `smul_coe_set`, `QuotientGroup.univ_eq_iUnion_smul`, `RatFunc.smul_eq_C_mul`, `leftCoset_eq_iff`, `Circle.isQuotientCoveringMap_zpow`, `RatFunc.ofFractionRing_zero`, `RightCancelMonoid.faithfulSMul`, `Subgroup.leftTransversals.smul_diff_smul`, `GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_range`, `isQuotientCoveringMap_npow`, `Ideal.ResidueField.liftₐ_comp_toAlgHom`, `SubMulAction.inclusion.toFun_eq_coe`, `div_ball`, `smul_eq_self_of_preimage_zpow_eq_self`, `OreLocalization.numeratorRingHom_apply`, `Action.FintypeCat.toEndHom_apply`, `IsCompact.mul_closedBall`, `classifyingSpaceUniversalCover_map`, `Action.diagonalSuccIsoTensorTrivial_inv_hom_apply`, `MulAction.stabilizer_subgroup`, `Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂`, `Localization.instNoZeroDivisors`, `GradedMonoid.smulCommClass_right`, `IsCompact.closedBall_div`, `ball_div`, `instIsCancelSMul`, `ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule`, `SubMulAction.inclusion_injective`, `OreLocalization.mul_cancel`, `map_equiv_traceDual`, `MulAction.smul_set_stabilizer_subset`, `OreLocalization.mul_one`, `HomogeneousLocalization.instIsScalarTowerSubtypeMemOfNatLocalization`, `SubMulAction.mem_orbit_subMul_iff`, `SubMulAction.val_image_orbit`, `MulAction.isPretransitive_quotient`, `RatFunc.smul_eq_C_smul`, `smul_mem_nhds_self`, `normal_iff_eq_cosets`, `MulAction.stabilizer_subset_div_right`, `IsOpen.leftCoset`, `MulAction.isPreprimitive_fixingSubgroup_insert_iff`, `QuotientGroup.measurableSMul`, `Subgroup.exists_leftTransversal_of_FiniteIndex`, `MeasureTheory.QuotientMeasureEqMeasurePreimage.smulInvariantMeasure_quotient`, `RatFunc.instIsScalarTowerOfIsDomainOfPolynomial`, `SubMulAction.ofFixingSubgroup_of_eq_apply`, `MulAction.stabilizer_subgroup_op`, `IsClosed.leftCoset`, `RatFunc.one_def`, `RatFunc.div_smul`, `Representation.ofMulActionSelfAsModuleEquiv_apply`, `Fin.partialProd_left_inv`, `instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient`, `RatFunc.faithfulSMul`, `Finset.card_smul_inter`, `IsScalarTower.left`, `Subgroup.quotientEquivSigmaZMod_apply`, `Subgroup.IsComplement.pairwiseDisjoint_smul`, `Action.FintypeCat.quotientToEndHom_mk`, `RatFunc.instIsScalarTowerPolynomial`, `Finset.mulDysonETransform_fst`, `QuotientGroup.orbit_eq_out_smul`, `OreLocalization.one_div_mul`, `IsLowerSet.smul_subset`, `Finset.mulDysonETransform.smul_finset_snd_subset_fst`, `OreLocalization.smul_one_oreDiv_one_smul`, `smul_closedBall''`, `Circle.isQuotientCoveringMap_npow`, `isQuotientCoveringMap_zpow`, `Localization.mk_list_sum`, `MulAction.stabilizer_quotient`, `Topology.IsQuotientMap.isQuotientCoveringMap_of_isDiscrete_ker_monoidHom`, `RatFunc.zero_def`, `MulAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingSubgroup`, `Subgroup.center.smulCommClass_left`, `OreLocalization.mul_cancel'`, `OreLocalization.numeratorHom_apply`, `MulAction.isMultiplyPreprimitive_iff`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset'`, `Localization.mk_self`, `MulAction.map_stabilizer_le`, `Set.inv_smul_set_distrib`, `Subgroup.transferTransversal_apply'`, `QuotientGroup.instContinuousSMul`, `AlgebraicIndependent.liftAlgHom_comp_reprField`, `OreLocalization.universalMulHom_apply`, `OreLocalization.mul_inv`, `MulActionHom.toQuotient_apply`, `Submonoid.center.smulCommClass_left`, `instIsReducedLocalization`, `instIsLeftCancelSMul`, `Equiv.Perm.isPretransitive_of_isCycle_mem`, `OreLocalization.instIsScalarTower_1`, `leftCoset_mem_leftCoset`, `RatFunc.instIsScalarTowerOfPolynomial`, `Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule`, `SubMulAction.ofStabilizer.conjMap_comp`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure`, `OreLocalization.div_eq_one'`, `Ideal.ResidueField.algHom_ext_iff`, `Localization.instSMulCommClassOfIsScalarTower`, `OreLocalization.oreDiv_mul_char`, `Submonoid.center.smulCommClass_right`, `IsUpperSet.smul`, `WittVector.StandardOneDimIsocrystal.frobenius_apply`, `Finset.op_smul_convolution_eq_convolution_smul`, `Localization.mk_one`, `MulAction.stabilizer_image_coe_quotient`, `SMulCommClass.of_mul_smul_one`, `IsLocalization.instIsScalarTowerAtPrimeFractionRing`, `mem_own_leftCoset`, `Localization.AtPrime.instIsScalarTower`, `Localization.smul_mk`, `MeasureTheory.eventually_nhds_one_measure_smul_diff_lt`, `Finset.smul_convolution_eq_convolution_inv_mul`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset`, `CategoryTheory.PreGaloisCategory.has_decomp_quotients`, `SetLike.GradedMul.toGradedSMul`, `Finset.card_inter_smul`, `Action.FintypeCat.quotientToQuotientOfLE_hom_mk`, `HomogeneousLocalization.Away.eventually_smul_mem`, `Set.smul_inter_nonempty_iff`, `orbit_subgroup_eq_rightCoset`, `OreLocalization.oreDiv_smul_oreDiv`, `instIsPushoutFractionRingPolynomial`, `OreLocalization.smul_add`, `SubMulAction.inclusion.coe_eq`, `Subgroup.isQuotientCoveringMap_of_comm`, `Set.inv_op_smul_set_distrib`, `Set.smul_div_smul_comm`, `Localization.instFaithfulSMulAtPrimeOfNoZeroDivisors`, `SubMulAction.ofFixingSubgroup_of_singleton_bijective`, `Subgroup.normalCore_eq_ker`, `OreLocalization.oreDiv_mul_oreDiv_comm`, `threeGPFree_smul_set`, `SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective`, `ModularGroup.T_S_rel`, `Set.smul_inter_nonempty_iff'`, `IsRightCancelMulZero.faithfulSMul`, `IsApproximateSubgroup.sq_covBySMul`, `OreLocalization.instSMulCommClass_1`, `MeasureTheory.Measure.instSMulInvariantMeasureSubtypeMemSubmonoidOfIsMulLeftInvariant`, `RatFunc.mk_zero`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range`, `OreLocalization.numerator_isUnit`, `SubMulAction.map_ofFixingSubgroupUnion_bijective`, `HomogeneousLocalization.den_smul_val`, `Subgroup.properlyDiscontinuousSMul_of_tendsto_cofinite`, `Finset.card_smul_inter_smul`, `Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq`, `SubMulAction.ofFixingSubgroup_of_eq_bijective`, `QuotientGroup.orbit_mk_eq_smul`, `IsScalarTower.of_commMonoid`, `QuotientGroup.instContinuousConstSMul`, `eq_cosets_of_normal`, `Subgroup.transferFunction_apply`, `Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero`, `GradedMonoid.isScalarTower_right`, `OreLocalization.universalMulHom_commutes`, `Finset.mulETransformRight_snd`, `MulAction.stabilizer_finite`, `SubMulAction.val_preimage_orbit`, `SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter`, `NormedGroup.to_isIsometricSMul_left`, `OreLocalization.smul_div_one`, `Finset.op_smul_stabilizer_of_no_doubling`, `RatFunc.isScalarTower_liftAlgebra`, `totallyBounded_iff_subset_finite_iUnion_nhds_one`, `Set.smul_Icc`, `lowerClosure_smul`, `FractionRing.isScalarTower_liftAlgebra`, `Subgroup.transferTransversal_apply''`, `OreLocalization.one_mul`, `MeasureTheory.tendsto_measure_smul_diff_isCompact_isClosed`, `isScalarTower_iff_smulCommClass_of_commMonoid`, `instIsScalarTowerLocalizationAlgebraMapSubmonoid`, `OreLocalization.one_div_smul`, `MulAction.IsBlock.subtype_val_preimage`, `OreLocalization.oreDiv_smul_char`, `ThreeGPFree.smul_set`, `IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq`, `SubMulAction.ofStabilizer.conjMap_bijective`, `TrivSqZeroExt.inl_mul_eq_smul`, `SubMulAction.isScalarTower`, `Subgroup.quotientEquivSigmaZMod_symm_apply`, `CategoryTheory.PreGaloisCategory.exists_lift_of_quotient_openSubgroup`, `Localization.r_iff_oreEqv_r`, `MulAction.left_quotientAction`, `smul_ball_one`, `orbit_subgroup_one_eq_self`, `IsUniformGroup.to_uniformContinuousConstSMul`, `exists_disjoint_smul_of_isCompact`, `Units.smul_eq_mul`, `GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset`, `Localization.mk_self_mk`, `FractionRing.instFaithfulSMul`, `Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1`, `OreLocalization.cardinalMk_le`, `SetLike.instSMulCommClassSubtypeMem_1`, `OreLocalization.smul_zero`, `instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl_1`, `Localization.mk_zero`, `SubMulAction.ofStabilizer.conjMap_apply`, `SetLike.instIsScalarTowerSubtypeMem`, `Set.smul_graphOn`, `approxOrderOf.smul_eq_of_mul_dvd`, `OreLocalization.smul_one_smul`, `MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot`, `MulAction.ofQuotientStabilizer_smul`, `OreLocalization.universalHom_commutes`, `SubMulAction.image_inclusion`, `Finset.mulETransformLeft_snd`, `instIsOrderedSMulOfIsOrderedMonoid`, `MulAction.Regular.isPretransitive`, `SubMulAction.ofFixingSubgroup_insert_map_bijective`, `OreLocalization.oreDiv_one_smul`, `SubMulAction.conjMap_ofFixingSubgroup_bijective`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset'`, `upperClosure_smul`, `Finset.smul_stabilizer_of_no_doubling`, `Finset.smul_inv_mul_opSMul_eq_mul_of_doubling_lt_three_halves`, `IsUpperSet.smul_subset`, `SetLike.instSMulCommClassSubtypeMem_2`, `SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter`, `instIsPushoutFractionRingMvPolynomial_1`, `classifyingSpaceUniversalCover_obj`, `Action.FintypeCat.toEndHom_trivial_of_mem`, `SubMulAction.conjMap_ofFixingSubgroup_coe_apply`, `MulAction.isBlock_subtypeVal`, `QuotientGroup.out_conj_pow_minimalPeriod_mem`, `instIsPushoutFractionRingMvPolynomial`, `AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero`, `instErgodicSMulOfIsMulLeftInvariant`

Mul

Definitions

Name	Category	Theorems
`toSMul` 📖	CompOp	—
`toSMulMulOpposite` 📖	CompOp	40 math math: `MeasureTheory.Measure.IsMulRightInvariant.toSMulInvariantMeasure_op`, `Multiplicative.isIsIsometricVAdd''`, `Finset.mul_subset_iff_right`, `LefttCancelMonoid.to_faithfulSMul_mulOpposite`, `Finset.op_smul_finset_mul_eq_mul_smul_finset`, `IsScalarTower.opposite_mid`, `Finset.op_smul_finset_subset_mul`, `LeftCancelMonoid.to_faithfulSMul_mulOpposite`, `op_smul_eq_mul`, `Matrix.vecMulVec_update`, `Semigroup.opposite_smulCommClass'`, `measurableSMul_opposite_of_mul`, `MulAction.Regular.isPretransitive_mulOpposite`, `mem_rightCoset`, `Set.op_smul_set_mul_eq_mul_smul_set`, `Prod.isIsometricSMul''`, `Matrix.map_op_smul'`, `SMulCommClass.opposite_mid`, `Matrix.vecMulVec_smul'`, `Set.iUnion_op_smul_set`, `Set.mul_pair`, `measurableSMul₂_opposite_of_mul`, `Set.mul_subset_iff_right`, `Semigroup.opposite_smulCommClass`, `isRightRegular_iff`, `Set.image_op_smul`, `Set.op_smul_set_subset_mul`, `Set.image_op_smul_distrib`, `MulOpposite.smul_eq_mul_unop`, `Finset.biUnion_op_smul_finset`, `IsRightRegular.isSMulRegular`, `leftCoset_rightCoset`, `Matrix.conjTranspose_smul_self`, `instFaithfulSMulMulOppositeOfIsLeftCancelMul`, `rightCoset_assoc`, `Finset.mul_singleton`, `ContinuousMul.to_continuousSMul_op`, `instFaithfulSMulMulOpposite`, `CommSemigroup.isCentralScalar`, `Matrix.col_vecMulVec`

MulAction

Definitions

Name	Category	Theorems
`toSemigroupAction` 📖	CompOp	1769 math math: `AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀`, `IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPoints`, `Matrix.l2_opNorm_toEuclideanCLM`, `Quotient.coe_smul_out`, `units_inv_smul`, `LeftPreLieAlgebra.toSMulCommClass`, `compHom_smul_def`, `DoubleCoset.doubleCoset_union_rightCoset`, `DomMulAct.smul_monoidHom_apply`, `aestronglyMeasurable_const_smul_iff`, `continuousSMul_sphere_ball`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset`, `pow_add_period_smul`, `IsSMulRegular.of_mul_eq_one`, `instIsOrderedCancelSMulOfIsOrderedCancelMonoid`, `isPreprimitive_of_fixingSubgroup_empty_iff`, `isHomeomorph_smul₀`, `Homeomorph.smulOfNeZero_symm_apply`, `Subgroup.smul_mem_pointwise_smul_iff₀`, `CategoryTheory.PreGaloisCategory.mulAction_def`, `interior_smul₀`, `ModularGroup.SLOnGLPos_smul_apply`, `dot_self_cross`, `Subgroup.pointwise_smul_le_pointwise_smul_iff`, `Matrix.toLin'_symm`, `MeasureTheory.smulInvariantMeasure_iterateMulAct`, `NormedGroup.to_isIsometricSMul_right`, `LinearMap.toMatrixAlgEquiv'_mul`, `Matrix.kroneckerTMulStarAlgEquiv_symm_apply`, `IsUnit.isSMulRegular`, `properSMul_iff`, `Monoid.PushoutI.NormalWord.base_smul_def`, `IsLowerSet.smul`, `smul_pow'`, `IsTrivialBlock.smul`, `Set.smul_set_symmDiff`, `instProperConstSMulOfContinuousConstSMul`, `Finset.smul_finset_subset_smul_finset_iff`, `mul_ball`, `MeasurableEquiv.smul_apply`, `Subgroup.equivSMul_apply_coe`, `Finset.smul_finset_sdiff`, `AffineMap.coe_smul`, `Metric.smul_ball`, `FreeMonoid.ofList_smul`, `ErgodicSMul.of_aestabilizer`, `isTopologicallyTransitive_iff_dense_iUnion_preimage`, `MeasureTheory.measure_sdiff_inv_smul`, `MeasurableEquiv.coe_smul₀`, `IsClosed.smul_of_ne_zero`, `Subgroup.coe_pointwise_smul`, `Mathlib.Tactic.Module.NF.eval_algebraMap`, `NonUnitalCStarAlgebra.toStarModule`, `Finset.inv_smul_mem_iff`, `IsBlock.of_subset`, `HNNExtension.NormalWord.prod_group_smul`, `Subring.pointwise_smul_def`, `Complex.UnitDisc.instIsScalarTower_circle`, `AddSubgroup.zero_smul`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `MulSemiringAction.toRingHom_apply`, `Polynomial.Gal.smul_def`, `nonempty_orbit`, `Matrix.toLinearMapRight'_mul`, `Equiv.Perm.smul_def`, `Filter.smul_tendsto_smul_iff₀`, `MonoidHom.preimage_smul_setₛₗ`, `Rep.diagonalSuccIsoFree_inv_hom_single`, `mem_own_rightCoset`, `continuousSMul_sphere_sphere`, `Equiv.Perm.Basis.toCentralizer_equivariant`, `punctured_nhds_smul`, `support_comp_inv_smul₀`, `Matrix.spectrum_toEuclideanLin`, `Matrix.iSup_eigenspace_toLin'_diagonal_eq_top`, `SubMulAction.ofStabilizer_carrier`, `Matrix.cstar_nnnorm_def`, `Submonoid.smul_mem_pointwise_smul_iff₀`, `MeasureTheory.Subgroup.smulInvariantMeasure`, `LinearMap.mapMatrixLinear_apply`, `Filter.mem_absorbing`, `smul_mem_nhds_smul₀`, `SubMulAction.ofFixingSubgroup_equivariantMap_injective`, `Matrix.toLinearMap₂'_comp`, `Sylow.pointwise_smul_def`, `kroneckerTMulAlgEquiv_symm_single_tmul`, `smul_zpow`, `UpperHalfPlane.re_smul`, `Subgroup.pointwise_smul_subset_iff`, `Action.ofMulAction_apply`, `RelIso.smul_def`, `OrderIso.smulRight_apply`, `Set.smul_graphOn_univ`, `Function.Embedding.coe_smul`, `OnePoint.isBoundedAt_iff_exists_SL2Z`, `alternatingGroup.isPreprimitive_of_three_le_card`, `SubMulAction.fixingSubgroup_smul_eq_fixingSubgroup_map_conj`, `Ideal.coe_smul_primesOver_mk_eq_map_galRestrict`, `isPretransitive_iff_orbit_eq_univ`, `Function.Embedding.smul_apply`, `LocalizedModule.restrictScalars_map_eq`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar`, `HNNExtension.NormalWord.group_smul_toList`, `Subring.instSMulCommClassSubtypeMemCenter`, `set_mem_fixedBy_iff`, `CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected`, `Subgroup.subset_pointwise_smul_iff`, `OreLocalization.oreDiv_eq_iff`, `inv_smul_smul₀`, `Units.isSMulRegular`, `Module.Ray.neg_units_smul`, `Set.infinite_smul_set`, `IsCusp.smul_of_mem`, `Finset.inv_smul_finset_distrib`, `AddSubgroup.smul_mem_pointwise_smul_iff`, `isQuotientCoveringMap_iff`, `Finset.doubling_lt_three_halves`, `Set.mem_smul_set_inv`, `smulMulHom_apply`, `Subgroup.exists_smul_eq`, `CongruenceSubgroup.exists_Gamma_le_conj'`, `UpperHalfPlane.tendsto_smul_atImInfty`, `Set.powersetCard.isPretransitive`, `NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm`, `ofQuotientStabilizer_mem_orbit`, `Subgroup.conj_smul_subgroupOf`, `IsCompact.closedBall_mul`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left`, `Supports.smul`, `inv_smul_eq_iff`, `QuotSMulTop.equivTensorQuot_naturality`, `MeasureTheory.pairwise_disjoint_fundamentalInterior`, `IsClosed.smul_left_of_isCompact`, `AddSubgroup.mem_inv_pointwise_smul_iff`, `Complex.UnitDisc.instSMulCommClass_closedBall_circle`, `Units.smul_coe`, `CongruenceSubgroup.conjGL_coe`, `Dense.smul`, `Module.Basis.groupSMul_span_eq_top`, `mem_leftCoset_iff`, `cross_cross`, `Complex.UnitDisc.instSMulCommClass_closedBall_left`, `Subsemiring.mem_smul_pointwise_iff_exists`, `Matrix.spectrum_toLpLin`, `EMetric.smul_ball`, `Submodule.top_eq_ofList_cons_smul_iff`, `UpperHalfPlane.im_smul_eq_div_normSq`, `AddSubgroup.mem_inertia`, `OreLocalization.nsmul_eq_nsmul`, `UpperHalfPlane.specialLinearGroup_apply`, `smul_mem_orbit_smul`, `Set.smul_set_inter`, `instSMulCommClass_sphere_sphere_sphere`, `Sylow.coe_smul`, `NumberField.InfinitePlace.exists_smul_eq_of_comap_eq`, `DoubleCoset.doubleCoset_union_leftCoset`, `AddSubmonoid.le_pointwise_smul_iff`, `MeasureTheory.Measure.domSMul_apply`, `isClosedMap_smul_of_ne_zero`, `Equiv.Perm.exists_mem_stabilizer_smul_eq`, `IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply`, `Module.FinitePresentation.exists_notMem_bijective`, `Set.mem_inv_smul_set_iff₀`, `Set.finite_smul_set`, `ContinuousAlternatingMap.piLIE_apply_apply`, `Set.preimage_smul_inv₀`, `Subsemiring.smul_mem_pointwise_smul_iff`, `SubMulAction.ofFixingSubgroup_of_inclusion_injective`, `ENNReal.smul_def`, `cross_self`, `mem_aestabilizer`, `Set.smul_set_inter₀`, `Subgroup.center.smulCommClass_right`, `quotient_out_smul_fixedPoints`, `Set.smul_set_subset_smul_set_iff₀`, `ContinuousMultilinearMap.piLinearEquiv_symm_apply`, `MulDistribMulAction.toMulEquiv_apply`, `Submonoid.smul_mem_pointwise_smul`, `Equidecomp.restr_refl_symm`, `Module.Ray.units_smul_of_neg`, `Matrix.intrinsicStar_toLin'`, `RelEmbedding.smul_def`, `InnerProductSpace.smul_left`, `zpow_smul_mod_minimalPeriod`, `MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv`, `IsQuasiPreprimitive.isPretransitive_of_normal`, `MeasureTheory.mem_fundamentalInterior`, `Finset.smul_finset_inter`, `MeasureTheory.mem_fundamentalFrontier`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity`, `QuotientAction.inv_mul_mem`, `Finset.smul_finset_univ`, `ModularGroup.one_lt_normSq_T_zpow_smul`, `QuadraticMap.toMatrix'_comp`, `Set.powersetCard.mem_mulActionHom_compl`, `OnePoint.smul_infty_eq_self_iff`, `HNNExtension.NormalWord.t_smul_eq_unitsSMul`, `SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix`, `isPreprimitive_of_is_two_pretransitive`, `SubMulAction.subset_coe_pow`, `Finset.subset_smul_finset_iff`, `cfcₙHom_nnreal_eq_restrict`, `OreLocalization.smul_cancel'`, `unitary.smul_mem_of_mem`, `isBlock_iff_smul_eq_of_mem`, `SubMulAction.nat_card_ofStabilizer_add_one_eq`, `groupCohomology.isMulCoboundary₁_of_mem_coboundaries₁`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right`, `absorbent_univ`, `mulSupport_comp_inv_smul`, `cfcₙ_map_pi`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity`, `Representation.ofMulAction_apply`, `RightPreLieAlgebra.toIsScalarTower`, `hasDerivWithinAt_pi`, `LinearMap.spectrum_toMatrix'`, `Real.smul_map_diagonal_volume_pi`, `Submonoid.pointwise_smul_le_pointwise_smul_iff₀`, `AlgHom.mulLeftRightMatrix.inv_comp`, `Submonoid.mem_smul_pointwise_iff_exists`, `one_leftCoset`, `KaehlerDifferential.quotKerTotalEquiv_symm_comp_D`, `Unitary.smul_mem`, `QuotSMulTop.equivTensorQuot_naturality_mk`, `dot_cross_self`, `MeasureTheory.fundamentalFrontier_smul`, `Subring.mem_pointwise_smul_iff_inv_smul_mem`, `Matrix.toLpLin_mul_same`, `mem_orbit_smul`, `jacobiTheta_T_sq_smul`, `Submonoid.instMeasurableSMul`, `DistribMulAction.smul_add`, `orbit_subgroup_subset`, `Subalgebra.coe_pointwise_smul`, `smul_zpow_movedBy_eq_of_commute`, `SlashInvariantForm.quotientFunc_smul`, `IsUnit.tendsto_const_smul_iff`, `Equiv.swap_smul_involutive`, `NonUnitalSubalgebra.prod_inf_prod`, `CStarMatrix.toCLM_injective`, `Submonoid.pointwise_smul_le_pointwise_smul_iff`, `ModularGroup.sl_moeb`, `is_one_preprimitive_iff`, `MeasureTheory.Measure.IsAddHaarMeasure.domSMul`, `Subgroup.smulCommClass_right`, `NumberField.InfinitePlace.smul_apply`, `Finset.inv_op_smul_finset_distrib`, `rightCoset_eq_iff`, `le_stabilizer_iff_smul_le`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single`, `MulAut.smul_def`, `absorbs_inter`, `MeasureTheory.measure_smul_eq_zero_iff`, `Subring.mem_pointwise_smul_iff_inv_smul_mem₀`, `IsUnit.stronglyMeasurable_const_smul_iff`, `LinearMap.rank_diagonal`, `bijective`, `QuotSMulTop.map_comp_mkQ`, `BlockMem.coe_top`, `OnePoint.isZeroAt_iff_exists_SL2Z`, `AlternatingGroup.isPreprimitive_of_three_le_card`, `Finset.prod_smul`, `lt_inv_smul_iff_of_pos`, `Matrix.toEuclideanLin_apply`, `orbitRel.Quotient.mem_subgroup_orbit_iff'`, `LinearIndependent.group_smul_iff`, `LinearMap.toMatrixAlgEquiv'_id`, `toPerm_apply`, `smul_rayOfNeZero`, `UpperHalfPlane.glPos_smul_def`, `Subgroup.instCovariantClassHSMulLe`, `IsCusp.of_isFiniteRelIndex_conj`, `Finset.smul_finset_subset_smul_finset_iff₀`, `Metric.smul_closedEBall`, `UpperHalfPlane.coe_pos_real_smul`, `isScalarTower_closedBall_closedBall_closedBall`, `Matrix.liftLinear_singleLinearMap`, `NonUnitalSubalgebra.prod_top`, `ModularGroup.coe_T_zpow_smul_eq`, `smul_uniformity₀`, `SubMulAction.map_ofFixingSubgroupUnion_def`, `AddSubmonoid.smul_bot`, `isScalarTower_sphere_closedBall_closedBall`, `Set.powersetCard.faithfulSMul`, `LocalizedModule.divBy_mul_by`, `Submodule.pointwise_smul_toAddSubgroup`, `LinearMap.toMatrix₂'_compl₁₂`, `LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle`, `LinearMap.prodEquiv_apply`, `CStarMatrix.norm_def'`, `MulActionWithZero.zero_smul`, `Representation.ofMulAction_single`, `Finset.mulDysonETransform_snd`, `LocalizedModule.map_surjective`, `AddSubmonoid.smul_sup`, `SubMulAction.ofStabilizer.isMultiplyPretransitive_iff`, `Matrix.toLin'_mul_apply`, `Complex.UnitDisc.coe_smul_circle`, `Quotient.smul_mk`, `UpperHalfPlane.denom_cocycle_σ`, `Submonoid.mem_inv_pointwise_smul_iff`, `MeasureTheory.eventuallyConst_smul_set_ae`, `SkewMonoidAlgebra.comapSMul_def`, `Finset.smul_mem_smul_finset_iff`, `CliffordAlgebra.foldr'Aux_foldr'Aux`, `LieAdmissibleAlgebra.toSMulCommClass`, `isBlock_iff_smul_eq_or_disjoint`, `Finsupp.comapSMul_single`, `CStarMatrix.inner_toCLM_conjTranspose_left`, `LinearMap.toMatrix'_toLin'`, `op_smul_set_stabilizer_subset`, `Subsemiring.smul_mem_pointwise_smul`, `IsUnit.aemeasurable_const_smul_iff`, `Sylow.smul_eq_iff_mem_normalizer`, `Subgroup.pointwise_smul_le_pointwise_smul_iff₀`, `Finset.smul_mem_smul_finset_iff₀`, `pow_smul_mod_minimalPeriod`, `TrivSqZeroExt.lift_comp_inrHom`, `NNReal.instPosSMulStrictMono`, `smul_lt_of_lt_one_left`, `isBlock_top`, `orbit_subgroup_eq_self_of_mem`, `CategoryTheory.End.smul_left`, `Subsemiring.pointwise_smul_toAddSubmonoid`, `instIsPushoutFractionRingPolynomial_1`, `OrderIso.smulRightDual_apply`, `isCoprime_group_smul_right`, `ModularGroup.tendsto_abs_re_smul`, `Rep.diagonalSuccIsoFree_inv_hom_single_single`, `MDifferentiableAt.clm_prodMap`, `smul_div'`, `Matrix.toAlgEquiv_kroneckerStarAlgEquiv`, `Polynomial.instSMulCommClassElemRootSet`, `Set.exists_smul_inter_smul_subset_smul_inv_mul_inter_inv_mul`, `Module.add_smul`, `ofFixingSubgroup.isMultiplyPreprimitive`, `smul_inv_smul₀`, `CategoryTheory.actionAsFunctor_map`, `IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective`, `Complex.UnitDisc.instIsScalarTower_circle_circle`, `Subgroup.Normal.conj_smul_eq_self`, `Monoid.PushoutI.NormalWord.base_smul_eq_smul`, `closure_smul₀'`, `Set.smul_univ₀`, `Finset.smul_inv_mul_eq_inv_mul_opSMul`, `Pi.intrinsicStar_comul_commSemiring`, `IsUnit.inv_smul`, `Matrix.det_kroneckerMapBilinear`, `Monoid.PushoutI.NormalWord.base_smul_def'`, `Finset.smul_finset_symmDiff`, `SlashInvariantForm.coe_translate`, `Localization.algHom_ext_iff`, `Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap`, `Finset.smul_finset_univ₀`, `measurableEmbedding_const_smul₀`, `Matrix.vecMulBilin_apply`, `HasCompactMulSupport.comp_smul`, `cross_anticomm`, `Subgroup.Normal.conjAct`, `ModularGroup.exists_max_im`, `Finite.finite_mulAction_orbit`, `SubMulAction.ofStabilizer.isPretransitive_iff`, `CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM`, `Subsemiring.smul_bot`, `minimalPeriod_eq_one_iff_fixedBy`, `DistribMulAction.toLinearEquiv_symm_apply`, `cross_cross_eq_smul_sub_smul`, `Real.map_matrix_volume_pi_eq_smul_volume_pi`, `TrivSqZeroExt.algHom_ext'_iff`, `index_stabilizer`, `Submonoid.coe_pointwise_smul`, `instIsPretransitiveElemOrbit_1`, `LocalizedModule.map_injective`, `Monoid.CoprodI.Word.prod_smul`, `NumberField.InfinitePlace.smul_eq_comap`, `IsOpen.iUnion_smul`, `Complex.UnitDisc.instSMulCommClass_circle_left`, `Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv`, `Subgroup.smul_leftQuotientEquiv`, `groupCohomology.isMulCoboundary₂_of_mem_coboundaries₂`, `mem_orbit_symm`, `KaehlerDifferential.mulActionBaseChange_smul_add`, `Subgroup.Commensurable.commensurable_conj`, `NumberField.InfinitePlace.smul_mk`, `SubMulAction.stabilizer_of_subMul`, `isCusp_SL2Z_iff'`, `Subgroup.pointwise_smul_def`, `coeSubmodule_differentIdeal_fractionRing`, `QuotSMulTop.map_surjective`, `Ideal.Fiber.lift_residueField_surjective`, `Subgroup.conjAct_pointwise_smul_iff`, `IsCompact.exists_finite_cover_smul`, `Set.smul_set_univ₀`, `MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar`, `Metric.preimage_smul_closedEBall`, `IsFoelner.tendsto_meas_smul_symmDiff`, `nhds_smul₀`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe`, `Matrix.isNilpotent_toLin'_iff`, `unitary.coe_smul`, `RegularWreathProduct.smul_def`, `ModularGroup.im_T_smul`, `MeasureTheory.measure_inv_smul_sdiff`, `smul_ball''`, `Finset.mul_mem_smul_finset_iff`, `orbitRel.Quotient.mem_subgroup_orbit_iff`, `Finset.mem_inv_smul_finset_iff`, `Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure`, `isInvariantBlock_iff_isFixedBlock`, `ProperSMul.isProperMap_smul_pair`, `Matrix.toLinearEquiv'_symm_apply`, `smul_closedBall_one`, `LinearMap.BilinForm.mul_toMatrix'_mul`, `Subring.pointwise_smul_toAddSubgroup`, `OnePoint.smul_some_eq_ite`, `Subring.coe_pointwise_smul`, `IsBlock.orbit_of_normal`, `IsScalarTower.of_smul_one_mul`, `CategoryTheory.PreGaloisCategory.toAut_hom_app_apply`, `InnerProductGeometry.norm_toLp_symm_crossProduct`, `mem_closure_isSwap`, `WithConv.toConv_smul`, `SubMulAction.mem_mul`, `Set.OrdConnected.smul`, `Set.powersetCard.isPretransitive_alternatingGroup`, `FreeMonoid.of_smul`, `Set.smul_set_pi`, `Set.Finite.absorbs_sInter`, `Multiset.smul_prod'`, `CFC.sqrt_map_prod`, `AffineMap.smul_linear`, `Subgroup.leftCoset_cover_const_iff_surjOn`, `SubMulAction.fixingSubgroup_of_insert`, `MeasureTheory.Measure.addHaarScalarFactor_smul_congr`, `MonoidHom.smulOneHom_apply`, `Matrix.det_smul_of_tower`, `NonarchimedeanGroup.exists_openSubgroup_separating`, `Module.Ray.linearEquiv_smul_eq_map`, `Submonoid.smul_mem_pointwise_smul_iff`, `ball_mul`, `SubMulAction.ofFixingSubgroup_carrier`, `Homeomorph.smul_symm_apply`, `IsCompact.div_closedBall`, `MatrixEquivTensor.toFunBilinear_apply`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1`, `groupCohomology.isMulCocycle₁_of_mem_cocycles₁`, `Subgroup.smul_diff_smul'`, `QuotientGroup.eq_class_eq_leftCoset`, `PosSMulMono.nnrat_of_rat`, `HNNExtension.NormalWord.prod_smul`, `Monoid.PushoutI.NormalWord.instFaithfulSMul`, `StarMul.toStarModule`, `IntermediateField.continuousSMul`, `units_smul_eq_self_iff`, `Matrix.toLpLin_symm_pow`, `TensorProduct.prodLeft_tmul`, `denseRange_smul`, `units_smul_eq_neg_iff`, `smul_inv_mem_fixedBy_iff_mem_fixedBy`, `Matrix.linfty_opNNNorm_toMatrix`, `disjoint_image_image_iff`, `Subgroup.Commensurable.commensurator_mem_iff`, `MonoidHom.transfer_def`, `Finset.smul_univ`, `Matrix.toEuclideanCLM_toLp`, `approxOrderOf.smul_subset_of_coprime`, `isClosedMap_smul`, `isPreprimitive_ofFixingSubgroup_conj_iff`, `ProperSMul.toContinuousSMul`, `cross_anticomm'`, `smul_inv'`, `ENNReal.instIsScalarTowerNNReal`, `Set.disjoint_smul_set`, `Pi.intrinsicStar_comul`, `MeasureTheory.innerRegular_map_smul`, `NumberField.InfinitePlace.isUnramified_smul_iff`, `Homeomorph.smulOfNeZero_apply`, `Units.coe_smul`, `Projectivization.cross_mk_of_cross_ne_zero`, `Matrix.toLpLin_one`, `Monoid.PushoutI.NormalWord.prod_summand_smul`, `CFC.nnrpow_map_pi`, `toFun_apply`, `SubMulAction.mem_fixingSubgroup_insert_iff`, `isCancelSMul_iff_stabilizer_eq_bot`, `OreLocalization.expand'`, `CategoryTheory.PreGaloisCategory.IsFundamentalGroup.transitive_of_isGalois`, `Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix`, `TensorProduct.prodLeft_symm_tmul`, `EisensteinSeries.G2_S_transform`, `smul_coe_set`, `ModularGroup.SL_to_GL_tower`, `QuotientGroup.univ_eq_iUnion_smul`, `Matrix.piLp_ofLp_toEuclideanLin`, `OnePoint.map_smul`, `MeasureTheory.Measure.isHaarMeasure_map_smul`, `Submonoid.smul_sup`, `lieEquivMatrix'_apply`, `leftCoset_eq_iff`, `Set.smul_mem_smul_set_iff₀`, `Homeomorph.smul_apply`, `SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux`, `continuousSMul_closedBall_ball`, `Sylow.orbit_eq_top`, `MulSemiringAction.toAlgEquiv_symm_apply`, `Ideal.Quotient.smul_top`, `Submonoid.le_pointwise_smul_iff₀`, `smul_subset_of_set_mem_fixedBy`, `Commute.smul_left_iff`, `LinearMap.minpoly_toMatrix'`, `Submodule.pointwise_smul_toAddSubmonoid`, `List.smul_prod`, `isScalarTower_sphere_sphere_sphere`, `toPerm_symm_apply`, `jacobiTheta_S_smul`, `isPretransitive_iff_base`, `smul_smul`, `RightCancelMonoid.faithfulSMul`, `RightPreLieAlgebra.toSMulCommClass`, `isCoatom_stabilizer_iff_preprimitive`, `Subgroup.leftTransversals.smul_diff_smul`, `GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_range`, `ModularGroup.re_T_smul`, `IsFoelner.mean_smul_eq_mean_smul`, `NNReal.smulCommClass_left`, `OreLocalization.expand`, `SubMulAction.stabilizer_of_subMul.submonoid`, `smul_orbit`, `LinearMap.prodEquiv_symm_apply`, `absorbs_iInter`, `Subring.mem_inv_pointwise_smul_iff`, `Matrix.toLpLin_pow`, `Module.ext_iff`, `Set.ncard_smul_set`, `CongruenceSubgroup.IsArithmetic.conj`, `DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem`, `Matrix.isUnit_toLin'_iff`, `Subalgebra.instCovariantClassHSMulLe`, `LinearMap.CompatibleSMul.units`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem`, `Polynomial.adjSylvester_comp_sylveserMap`, `Ideal.ResidueField.liftₐ_comp_toAlgHom`, `HNNExtension.NormalWord.smul_ofGroup`, `Submonoid.pointwise_smul_le_iff₀`, `Matrix.toLin'_mul`, `hasDerivAt_update`, `CongruenceSubgroup.Gamma_cong_eq_self`, `UpperHalfPlane.coe_smul_of_det_pos`, `ext_iff`, `AddSubmonoid.pointwise_isCentralScalar`, `op_smul_coe_set`, `SubMulAction.inclusion.toFun_eq_coe`, `Complex.UnitDisc.coe_closedBall_smul`, `Matrix.ofLp_toLpLin`, `div_ball`, `zpow_mod_period_smul`, `smul_eq_self_of_preimage_zpow_eq_self`, `Rep.ofMulDistribMulAction_ρ_apply_apply`, `MeasureTheory.MeasurePreserving.smulInvariantMeasure_iterateMulAct`, `OrderIso.smulRight_symm_apply`, `isCoprime_group_smul_left`, `IsQuotientCoveringMap.apply_eq_iff_mem_orbit`, `MDifferentiableOn.clm_prodMap`, `Subgroup.pointwise_isCentralScalar`, `LinearMap.det_toLin'`, `Monoid.CoprodI.Word.mem_smul_iff_of_ne`, `MulActionWithZero.smul_zero`, `CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois`, `Monoid.CoprodI.Word.of_smul_def`, `Representation.norm_ofMulDistribMulAction_eq`, `Matrix.kroneckerMapBilinear_apply_apply`, `orbit.eq_or_disjoint`, `NumberField.InfinitePlace.smul_coe_apply`, `Finite.to_properlyDiscontinuousSMul`, `Subgroup.smul_apply_eq_smul_apply_inv_smul`, `Subsemiring.pointwise_central_scalar`, `Matrix.toLinearMapRight'_mul_apply`, `interior_smul`, `Finset.smul_finset_subset_iff₀`, `oneEmbedding_isPretransitive_iff`, `measurableSMul₂_iterateMulAct`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero`, `Subring.pointwise_smul_subset_iff`, `unitary.smul_mem`, `SubMulAction.disjoint_val_image`, `UpperHalfPlane.modular_S_smul`, `isBlock_subgroup'`, `instSMulCommClass_sphere_closedBall_closedBall`, `Subgroup.mem_inv_pointwise_smul_iff₀`, `kroneckerTMulLinearEquiv_one`, `ModularGroup.re_T_inv_smul`, `ContinuousMultilinearMap.prodL_apply`, `Subgroup.normalCore_eq_iInf_conjAct`, `preimage_smul_setₛₗ_of_isUnit_isUnit`, `Metric.preimage_smul_eball`, `Sylow.smul_eq_of_normal`, `hasEigenvector_toLin'_diagonal`, `mem_stabilizer_finset`, `IsCompact.mul_closedBall`, `IsFixedBlock.orbit`, `LinearMap.toMatrixAlgEquiv'_apply`, `CongruenceSubgroup.isArithmetic_conj_SL2Z`, `Module.Ray.units_smul_of_pos`, `arrowAction_smul`, `mem_fixedPoints`, `Orientation.map_eq_det_inv_smul`, `LinearMap.toMatrix'_algebraMap`, `IsUnit.smul_mem_nhds_smul_iff`, `IsPartition.of_orbits`, `Cardinal.mk_smul_set`, `LocalizedModule.coe_map_eq`, `HNNExtension.NormalWord.unitsSMul_one_group_smul`, `SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux`, `Set.mem_invOf_smul_set`, `stabilizer_smul_eq_stabilizer_map_conj`, `Monoid.PushoutI.NormalWord.prod_base_smul`, `Finset.smul_finset_symmDiff₀`, `AddSubmonoid.smul_mem_pointwise_smul`, `Action.diagonalSuccIsoTensorTrivial_inv_hom_apply`, `ValuationSubring.pointwise_smul_toSubring`, `SubMulAction.nat_card_ofStabilizer_eq`, `Unitary.smul_mem_of_mem`, `instIsLeftCancelSMul_1`, `RootPairing.GeckConstruction.span_range_h'_eq_top`, `IsOpen.dense_iUnion_preimage_smul`, `continuousSMul_sphere_closedBall`, `coe_quotient_smul_fixedPoints`, `OreLocalization.zsmul_eq_zsmul`, `AddSubgroup.pointwise_smul_le_iff₀`, `Monoid.CoprodI.Word.cons_eq_smul`, `smul_orbit_subset`, `smul_iterate`, `isQuotientCoveringMap_iff_isCoveringMap_and`, `Submonoid.instSMulCommClassSubtypeMemCenter_1`, `Subring.mem_smul_pointwise_iff_exists`, `MulActionHom.coe_one`, `Matrix.toLin'_reindex`, `hasStrictDerivAt_finCons'`, `isScalarTower_closedBall_ball_ball`, `LinearMap.BilinForm.toMatrix'_compLeft`, `Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂`, `hasStrictDerivAt_finCons`, `IsTrivialBlock.isBlock`, `Set.subset_smul_set_iff`, `orbitRel.Quotient.orbit.coe_smul`, `ContinuousMultilinearMap.piLinearEquiv_apply`, `GradedMonoid.smulCommClass_right`, `orbit_smul_subset`, `inv_smul_smul`, `UpperHalfPlane.im_smul`, `mem_stabilizer_set_iff_subset_smul_set`, `IsCompact.closedBall_div`, `NumberField.InfinitePlace.isComplex_smul_iff`, `AffineMap.isCentralScalar`, `ball_div`, `DiscreteTiling.PlacedTile.coe_mk_mk`, `OnePoint.IsZeroAt.smul_iff`, `SkewMonoidAlgebra.comapSMul_single`, `instIsCancelSMul`, `LinearMap.toMatrix'_apply`, `ModularGroup.normSq_S_smul_lt_one`, `SubMulAction.inclusion_injective`, `Matrix.toLpLin_toLp`, `ContinuousLinearMap.prodMapL_apply`, `Subsemiring.smul_mem_pointwise_smul_iff₀`, `map_equiv_traceDual`, `HNNExtension.NormalWord.instFaithfulSMul_1`, `isPretransitive_compHom`, `UpperHalfPlane.coe_smul`, `pow_period_smul`, `MeasureTheory.measure_symmDiff_inv_smul`, `smul_set_stabilizer_subset`, `ModularGroup.exists_row_one_eq_and_min_re`, `AddSubmonoid.pointwise_smul_le_iff`, `NNRat.instContinuousSMulOfIsScalarTowerOfRat`, `Unitary.coe_smul`, `SubMulAction.mem_orbit_subMul_iff`, `Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff`, `mem_stabilizerSubmonoid_iff`, `Subgroup.mem_smul_pointwise_iff_exists`, `HNNExtension.NormalWord.group_smul_def`, `RelEmbedding.apply_faithfulSMul`, `Equiv.Perm.applyFaithfulSMul`, `image_inter_image_iff`, `CStarMatrix.toCLM_apply_single`, `Subring.smul_bot`, `continuousWithinAt_const_smul_iff`, `SubMulAction.val_image_orbit`, `isCoprime_group_smul`, `Circle.instContinuousSMul`, `isHomeomorph_smul`, `mulAutArrow_apply_apply`, `QuotSMulTop.equivQuotTensor_naturality`, `ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors`, `LinearMap.toMatrix'_symm`, `isPretransitive_quotient`, `smul_inv_smul`, `smul_mem_nhds_self`, `Monoid.PushoutI.NormalWord.prod_smul_empty`, `normal_iff_eq_cosets`, `MeasureTheory.Measure.Regular.domSMul`, `isSimplyConnected_smul_set_iff`, `LinearMap.mapMatrix_smul`, `InnerProductGeometry.norm_ofLp_crossProduct`, `AdicCompletion.transitionMap_comp_reduceModIdeal`, `Subsemiring.pointwise_smul_subset_iff`, `Metric.preimage_smul_sphere`, `Subring.smul_closure`, `DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem`, `measurableEmbedding_const_smul`, `IsOpen.leftCoset`, `SubMulAction.mem_one`, `ModularGroup.re_T_zpow_smul`, `isPreprimitive_fixingSubgroup_insert_iff`, `QuotientGroup.measurableSMul`, `MeasureTheory.measure_inter_inv_smul`, `instIsPretransitiveOfSubsingleton`, `Matrix.kroneckerTMulAlgEquiv_symm_apply`, `continuousWithinAt_const_smul_iff₀`, `Matrix.ofLp_toEuclideanCLM`, `isUnit_smul_iff`, `ergodic_smul_of_denseRange_pow`, `mem_stabilizer_set'`, `groupCohomology.isMulCocycle₂_of_mem_cocycles₂`, `CStarMatrix.toCLM_apply_eq_sum`, `IsPGroup.card_orbit`, `op_smul_op_smul`, `stronglyMeasurable_const_smul_iff`, `Equiv.Perm.OnCycleFactors.val_centralizer_smul`, `Submonoid.instSMulCommClassSubtypeMemCenter`, `Matrix.kroneckerTMulStarAlgEquiv_apply`, `dense_orbit`, `Subgroup.exists_leftTransversal_of_FiniteIndex`, `ContinuousMultilinearMap.smul_prod_smul`, `Matrix.range_toLin'`, `Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff`, `LinearMap.prodMapLinear_apply`, `MulActionHom.coe_mul`, `Submonoid.mem_inv_pointwise_smul_iff₀`, `smul_le_iff_le_one_left`, `CuspForm.coe_translate`, `MeasureTheory.smul_ae`, `smul_algebraMap`, `LinearMap.mul_toMatrix'`, `continuousAt_const_smul_iff₀`, `IsBaseChange.pi`, `zpow_smul_eq_iff_period_dvd`, `MeasureTheory.QuotientMeasureEqMeasurePreimage.smulInvariantMeasure_quotient`, `Commute.smul_right_iff`, `Metric.smul_sphere`, `Matrix.toLpLin_symm_id`, `SubMulAction.ofFixingSubgroup_of_eq_apply`, `Finset.smul_finset_subset_iff`, `Set.iUnion_inv_smul`, `ModularGroup.im_lt_im_S_smul`, `Matrix.isPositive_toEuclideanLin_iff`, `Set.op_smul_inter_nonempty_iff`, `IsClosed.leftCoset`, `Set.natCard_smul_set`, `Subring.instCovariantClassHSMulLe`, `HNNExtension.NormalWord.instFaithfulSMul`, `absorbs_iff_eventually_cobounded_mapsTo`, `Subgroup.instMeasurableConstSMul`, `Submodule.mulRightMap_eq_mulMap_comp`, `Set.powersetCard.mulActionHom_compl_mulActionHom_compl`, `pow_smul_eq_iff_minimalPeriod_dvd`, `Metric.preimage_smul_closedBall`, `IsBaseChange.prodMap`, `kroneckerTMulLinearEquiv_mul`, `swap_mem_closure_isSwap`, `QuadraticMap.discr_comp`, `CategoryTheory.PreGaloisCategory.continuousSMul_aut_fiber`, `Subfield.continuousSMul`, `mulAutArrow_apply_symm_apply`, `Equidecomp.refl_toPartialEquiv`, `kroneckerTMulLinearEquiv_symm_kroneckerTMul`, `SubMulAction.nat_card_ofStabilizer_eq_add_one`, `AddSubgroup.relIndex_pointwise_smul`, `LinearMap.lsum_single`, `Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality`, `ConvexCone.smul_mem_iff`, `Units.measurableSMul`, `IsScalarTower.to₂₃₄`, `LinearMap.toMatrix'_mul`, `isFoelner_iff`, `Units.instMeasurableConstSMul`, `MeasureTheory.measure_smul_null`, `IsBlock.univ`, `amenable_of_maxFoelner_neBot`, `AddSubmonoid.mem_inv_pointwise_smul_iff₀`, `SubMulAction.coe_mul`, `LieAlgebra.lie_smul`, `IsFoelner.tendsto_meas_smul_symmDiff_smul`, `Fin.partialProd_left_inv`, `Projectivization.mk_eq_mk_iff_crossProduct_eq_zero`, `Matrix.diagonal_toLin'`, `CStarMatrix.toCLM_apply`, `AddSubmonoid.smul_closure`, `ModularGroup.im_T_zpow_smul`, `AddSubgroup.pointwise_smul_toAddSubmonoid`, `smul_closure_orbit_subset`, `Matrix.charpoly_toLin'`, `properSMul_iff_continuousSMul_ultrafilter_tendsto_t2`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive`, `Subsemiring.mem_inv_pointwise_smul_iff₀`, `Matrix.toLin'_pow`, `AddSubgroup.mem_smul_pointwise_iff_exists`, `LieAdmissibleAlgebra.toIsScalarTower`, `RelIso.apply_faithfulSMul`, `instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient`, `continuousOn_const_smul_iff₀`, `Matrix.toLinAlgEquiv'_apply`, `Matrix.l2_opNNNorm_def`, `smul_mem_of_set_mem_fixedBy`, `Finset.card_smul_inter`, `smul_mem_nhds_smul_iff₀`, `HNNExtension.NormalWord.group_smul_head`, `IsScalarTower.left`, `SubMulAction.ENat_card_ofStabilizer_add_one_eq`, `Ideal.isPretransitive_of_isGalois`, `Subgroup.quotientEquivSigmaZMod_apply`, `Ideal.coe_smul_primesOver_mk`, `Matrix.minpoly_toLin'`, `CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem`, `ModularForm.slash_action_eq'_iff`, `PositiveLinearMap.gnsStarAlgHom_apply`, `MulSemiringAction.toRingEquiv_symm_apply`, `smulCommClass_self`, `Subgroup.IsComplement.pairwiseDisjoint_smul`, `one_smul`, `SetLike.forall_smul_mem_iff`, `LinearMap.toMatrix'_intrinsicStar`, `Set.preimage_smul`, `MDifferentiable.clm_prodMap`, `UpperHalfPlane.pos_real_smul_injective`, `IterateMulAct.mk_smul`, `coe_smul_fixedPoints_of_normal`, `cross_apply`, `zpow_smul_eq_iff_minimalPeriod_dvd`, `ENNReal.smulCommClass_left`, `Finset.mulDysonETransform_fst`, `Set.powersetCard.mulActionHom_compl_bijective`, `UpperHalfPlane.J_smul`, `IsUnit.aestronglyMeasurable_const_smul_iff`, `IsQuotientCoveringMap.toContinuousConstSMul`, `SlashInvariantForm.slash_action_eqn''`, `LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv'`, `IsQuasiPreprimitive.toIsPretransitive`, `kroneckerTMulLinearEquiv_tmul`, `isScalarTower_sphere_sphere_closedBall`, `QuotientGroup.orbit_eq_out_smul`, `Complex.UnitDisc.instSMulCommClass_closedBall_right`, `mem_subgroup_orbit_iff`, `Set.preimage_smul_inv`, `IsSMulRegular.of_smul_eq_one`, `vecMulVecBilin_apply_apply`, `isAdjointPair_toLinearMap₂'`, `Matrix.toLin'_apply'`, `QuotSMulTop.map_exact`, `IsOpen.dense_iUnion_smul`, `Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero`, `Matrix.ker_toLin'_eq_bot_iff`, `LinearMap.vecCons₂_apply`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `period_eq_one_iff`, `bijective₀`, `inv_smul_lt_iff_of_pos`, `MulSemiringAction.smul_mul`, `UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal`, `Ideal.isPretransitive_of_isGaloisGroup`, `orbitRel_apply`, `Subgroup.conj_smul_le_of_le`, `IsPretransitive.of_isScalarTower`, `Set.mem_inv_smul_set_iff`, `Subring.le_pointwise_smul_iff₀`, `MulDistribMulAction.toMulEquiv_symm_apply`, `IsLowerSet.smul_subset`, `Complex.UnitDisc.instIsScalarTower_closedBall`, `LinearMap.BilinForm.mul_toMatrix'`, `cfcₙ_map_prod`, `Set.smul_set_iInter`, `isOpenMap_smul₀`, `CStarMatrix.mul_entry_mul_eq_inner_toCLM`, `Subring.smul_mem_pointwise_smul_iff₀`, `SubMulAction.notMem_val_image`, `Finset.mulDysonETransform.smul_finset_snd_subset_fst`, `Set.smul_set_compl`, `Matrix.coe_toEuclideanCLM_eq_toEuclideanLin`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `Subsemiring.pointwise_smul_def`, `Function.End.smul_def`, `IsPGroup.smul_mul_inv_trivial_or_surjective`, `LeftPreLieAlgebra.ext_iff`, `LinearMap.toMatrixRight'_id`, `leibniz_cross`, `orbitZPowersEquiv_symm_apply`, `IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite`, `Subalgebra.smul_mem_pointwise_smul`, `isScalarTower_sphere_sphere_ball`, `inv_smul_le_iff_of_pos`, `Units.smul_inv`, `Subgroup.Commensurable.commensurable_inv`, `ModularGroup.exists_one_half_le_im_smul`, `Subgroup.instIsScalarTowerSubtypeMem`, `MulDistribMulAction.ext_iff`, `IsScalarTower.algebraMap_smul`, `measurableSMul_iterateMulAct`, `NonUnitalCommCStarAlgebra.toStarModule`, `Set.smul_set_sdiff`, `instIsPretransitiveElemOrbit`, `LinearMap.prodMapAlgHom_apply_apply`, `smul_closedBall''`, `Subalgebra.inclusion.isScalarTower_right`, `orbitRel.Quotient.orbit_mk`, `Submonoid.pointwise_smul_subset_iff`, `mem_stabilizer_set`, `IsMultiplyPreprimitive.isPreprimitive_ofFixingSubgroup`, `surjective₀`, `Subgroup.center.smulCommClass_left`, `UpperHalfPlane.petersson_slash_SL`, `pow_smul_eq_iff_period_dvd`, `smul_pi`, `Matrix.ker_diagonal_toLin'`, `IsFixedBlock.univ`, `Subsemiring.instSMulCommClassSubtypeMemCenter_1`, `mem_stabilizer_finset_iff_smul_finset_subset`, `IsPreprimitive.of_prime_card`, `Subgroup.Commensurable.conj`, `isMultiplyPreprimitive_iff`, `Quotient.mk_smul_out`, `Finsupp.comapSMul_def`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem`, `IsSMulRegular.pow_iff`, `Set.smul_set_pi_of_isUnit`, `Units.val_smul`, `MulActionHom.map_mem_fixedPoints`, `isScalarTower_sphere_closedBall_ball`, `Subsemiring.pointwise_smul_le_pointwise_smul_iff`, `CategoryTheory.PreGaloisCategory.isPretransitive_of_surjective`, `AddSubmonoid.smul_mem_pointwise_smul_iff₀`, `smul_mem_nhds_smul`, `ModularForm.SL_slash_def`, `Matrix.toLin'_one`, `Commute.smul_right_iff₀`, `smul_finprod'`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset'`, `OnePoint.smul_infty_eq_ite`, `NNReal.smul_def`, `inv_smul_eq_iff₀`, `MultilinearMap.piFamilyₗ_apply`, `le_smul_of_one_le_left`, `Finsupp.comapSMul_apply`, `DistribMulAction.ext_iff`, `Set.inv_smul_set_distrib`, `NonUnitalStarSubalgebra.prod_inf_prod`, `Subgroup.transferTransversal_apply'`, `AddAut.apply_faithfulSMul`, `cfcHom_nnreal_eq_restrict`, `IsOpen.rightCoset`, `Subgroup.continuousSMul`, `NNReal.smulCommClass_right`, `NumberField.InfinitePlace.isReal_smul_iff`, `Subring.pointwise_central_scalar`, `QuotientGroup.instContinuousSMul`, `Algebra.smul_units_def`, `Subgroup.smul_closure`, `UpperHalfPlane.coe_J_smul`, `orbitEquivQuotientStabilizer_symm_apply`, `ContinuousAlternatingMap.piLIE_symm_apply_apply`, `endVecAlgEquivMatrixEnd_apply_apply`, `alternatingGroup.exists_mem_stabilizer_smul_eq`, `Subring.pointwise_smul_le_pointwise_smul_iff`, `IsPreprimitive.of_isTrivialBlock_base`, `IsOpen.smul`, `AlgebraicIndependent.liftAlgHom_comp_reprField`, `isSimpleOrder_blockMem_iff_isPreprimitive`, `Matrix.trace_toLin'_eq`, `MulDistribMulAction.smul_one`, `rightCoset_mem_rightCoset`, `Units.continuousConstSMul`, `invOf_smul_smul`, `Units.smulCommClass'`, `tendsto_const_smul_iff`, `List.smul_prod'`, `Submonoid.pointwise_isCentralScalar`, `Rat.cast_smul_eq_qsmul`, `IsClosed.smul_right_of_isCompact`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero`, `smul_mem_nhds_smul_iff`, `Submodule.smul_mem_iff'`, `PosSMulStrictMono.nnrat_of_rat`, `Units.coe_inv_smul`, `MulActionHom.toQuotient_apply`, `Module.FinitePresentation.linearEquivMapExtendScalars_apply`, `SubMulAction.mem_ofStabilizer_iff`, `BlockMem.coe_bot`, `isBlock_subgroup`, `ContinuousAlternatingMap.piLinearEquiv_symm_apply`, `SubMulAction.ofStabilizer.snoc_castSucc`, `OnePoint.IsBoundedAt.smul_iff`, `Submonoid.center.smulCommClass_left`, `IsPretransitive.of_compHom`, `CategoryTheory.ActionCategory.curry_apply_left`, `Set.iUnion_smul_eq_setOf_exists`, `FixedPoints.mem_subgroup`, `instIsLeftCancelSMul`, `Complex.UnitDisc.coe_smul_closedBall`, `MeasureTheory.smulInvariantMeasure_tfae`, `UpperHalfPlane.pos_real_re`, `DiscreteTiling.PlacedTile.coe_smul`, `SubMulAction.mem_ofFixingSubgroup_insert_iff`, `coe_aestabilizer`, `LinearMap.toMatrix'_comp`, `Matrix.toLinearEquiv'_apply`, `LinearMap.isUnit_toMatrix'_iff`, `hasDerivAtFilter_finCons'`, `CategoryTheory.End.smul_right`, `Equiv.Perm.isPretransitive_of_isCycle_mem`, `isMultiplyPreprimitive_succ_iff_ofStabilizer`, `ArithmeticFunction.coe_zeta_smul_apply`, `AddAction.toPermHom_apply_symm_apply`, `IsUnit.preimage_smul_set`, `Finset.smul_univ₀'`, `hasDerivWithinAt_finCons'`, `Matrix.toBilin'_comp`, `Matrix.isHermitian_iff_isSymmetric`, `MeasureTheory.smul_mem_ae`, `IsFoelner.mean_smul_eq_mean`, `leftCoset_mem_leftCoset`, `ofQuotientStabilizer_mk`, `Subsemiring.instCovariantClassHSMulLe`, `algebraMap.coe_smul'`, `Subring.pointwise_smul_le_iff₀`, `MeasureTheory.measure_inv_smul_symmDiff`, `ergodic_smul_of_denseRange_zpow`, `CategoryTheory.PreGaloisCategory.instIsPretransitiveCarrierObjFintypeCatOfIsConnected`, `CategoryTheory.FintypeCat.Action.isConnected_iff_transitive`, `Subgroup.pointwise_smul_le_iff₀`, `isSMulRegular_of_group`, `Complex.UnitDisc.instSMulCommClass_circle_right`, `Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule`, `MeasureTheory.ergodicSMul_iterateMulAct`, `AddSubgroup.smul_mem_pointwise_smul`, `Metric.smul_closedBall`, `Metric.smul_eball`, `SlashInvariantForm.slash_action_eqn_SL''`, `Monoid.PushoutI.NormalWord.summand_smul_def'`, `Subgroup.smul_sup`, `Matrix.toEuclideanLin_conjTranspose_eq_adjoint`, `Set.smul_univ`, `ContMDiffAt.clm_prodMap`, `zpow_add_period_smul`, `smul_one_smul`, `isBlock_iff_disjoint_smul_of_ne`, `Set.smul_set_sdiff₀`, `MeasurableSet.const_smul_of_ne_zero`, `IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective`, `mem_stabilizer_set_iff_smul_set_subset`, `QuotSMulTop.equivQuotTensor_naturality_mk`, `Ideal.ResidueField.algHom_ext_iff`, `Matrix.toLpLinAlgEquiv_apply_apply_ofLp`, `Localization.instSMulCommClassOfIsScalarTower`, `LinearMap.toMatrix'_id`, `Equiv.Perm.instIsPreprimitive`, `Set.smul_set_univ`, `LocalizedModule.mul_by_divBy`, `Projectivization.cross_mk`, `support_comp_inv_smul`, `zpowersQuotientStabilizerEquiv_symm_apply`, `IsScalarTower.of_compHom`, `Subgroup.smul_def`, `Submodule.mem_smul_top_iff`, `UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStrip`, `LinearMap.BilinForm.toMatrix'_comp`, `Submonoid.center.smulCommClass_right`, `continuousOn_const_smul_iff`, `Subgroup.instMeasurableSMul`, `mulLinearMap_apply_apply`, `UpperHalfPlane.coe_specialLinearGroup_apply`, `OreLocalization.smul_oreDiv`, `IsUpperSet.smul`, `AlternatingGroup.isPretransitive_of_three_le_card`, `triple_product_eq_det`, `mem_fixedPoints_iff_card_orbit_eq_one`, `KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination`, `tangentConeAt_mono_field`, `smul_fixedBy`, `IsPreprimitive.exists_mem_smul_and_notMem_smul`, `MeasureTheory.measure_smul`, `orbit.coe_smul`, `Finset.smul_finset_eq_univ`, `Finset.op_smul_convolution_eq_convolution_smul`, `DiscreteTiling.PlacedTile.smul_mem_smul_iff`, `Monoid.CoprodI.Word.equivPair_head_smul_equivPair_tail`, `Equiv.smulRight_symm_apply`, `Matrix.toLinearMapRight'_apply`, `is_two_pretransitive_iff`, `smul_pow`, `Subsemiring.coe_pointwise_smul`, `ContinuousMultilinearMap.piₗᵢ_symm_apply`, `orbitZPowersEquiv_symm_apply'`, `CategoryTheory.PreGaloisCategory.IsFundamentalGroup.continuous_smul`, `MeasureTheory.NullMeasurableSet.smul`, `MeasureTheory.measure_inv_smul_union`, `Units.isScalarTower'`, `Set.smul_set_eq_univ`, `LieAlgebra.SpecialLinear.val_single`, `Matrix.ofLp_toEuclideanLin_apply`, `NNReal.instContinuousSMulOfReal`, `Subgroup.smul_inf`, `Monoid.CoprodI.Word.equivPair_smul_same`, `Equidecomp.symm_involutive`, `SubMulAction.ofStabilizer.isMultiplyPretransitive`, `CFC.nnrpow_eq_nnrpow_pi`, `SubMulAction.ofFixingSubgroup.append_right`, `SMulCommClass.of_mul_smul_one`, `Matrix.mulVecBilin_apply`, `nat_smul_eq_nsmul`, `MultilinearMap.piFamily_smul`, `lieEquivMatrix'_symm_apply`, `Projectivization.smul_def`, `Matrix.proj_diagonal`, `ModularGroup.im_smul_eq_div_normSq`, `isPretransitive_of_is_two_pretransitive`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle`, `isOpenMap_smul`, `Submonoid.instCovariantClassHSMulLe`, `mem_own_leftCoset`, `LocalizedModule.map_id`, `IsUnit.smul_uniformity`, `Matrix.linfty_opNorm_toMatrix`, `isSimplyConnected_smul_set₀_iff`, `Subgroup.smul_opposite_image_mul_preimage'`, `CategoryTheory.PreGaloisCategory.isGalois_iff_pretransitive`, `Subring.continuousSMul`, `Module.IsTorsionBySet.isScalarTower`, `SubMulAction.subset_coe_one`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀`, `NumberField.InfinitePlace.comap_smul`, `FreeGroup.startsWith.smul_def`, `NNRat.cast_smul_eq_nnqsmul`, `tendsto_const_smul_iff₀`, `Ideal.coe_smul_primesOver_eq_map_galRestrict`, `Matrix.SpecialLinearGroup.toLin'_to_linearMap`, `LinearMap.mul_toMatrix₂'_mul`, `LinearMap.toMatrix₂'_mul`, `MeasureTheory.eventually_nhds_one_measure_smul_diff_lt`, `Finset.smul_convolution_eq_convolution_inv_mul`, `IsUnit.smul_left_cancel`, `OnePoint.smul_infty_def`, `AddSubgroup.smul_mem_pointwise_smul_iff₀`, `EisensteinSeries.tendsto_double_sum_S_act`, `Subsemiring.instSMulCommClassSubtypeMemCenter`, `LinearMap.intrinsicStar_single`, `Module.Basis.map_orientation_eq_det_inv_smul`, `StarSemigroup.toOpposite_starModule`, `triple_product_permutation`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset`, `instSMulCommClass_sphere_ball_ball`, `Group.preimage_smul_set`, `HNNExtension.NormalWord.smul_cons`, `cosetToCuspOrbit_apply_mk`, `SubMulAction.SMulMemClass.coe_subtype`, `Matrix.kroneckerMapBilinear_mul_mul`, `ContMDiff.clm_prodMap`, `SubMulAction.isCentralScalar`, `stabilizerEquivStabilizer_one`, `Submonoid.continuousSMul`, `NormedSpace.norm_smul_le`, `RelHom.smul_def`, `orbit.pairwiseDisjoint`, `SetLike.GradedMul.toGradedSMul`, `IsUnit.continuousOn_const_smul_iff`, `OnePoint.exists_mem_SL2`, `Monoid.PushoutI.NormalWord.cons_eq_smul`, `LinearEquiv.smulOfNeZero_symm_apply`, `Submonoid.subset_pointwise_smul_iff`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem`, `Subgroup.conjAct_pointwise_smul_eq_self`, `IsTopologicallyTransitive.exists_smul_inter`, `SubMulAction.compl_def`, `DistribMulAction.toAddEquiv_symm_apply`, `orbit_smul`, `Finset.card_inter_smul`, `HasDerivAtFilter.prodMk`, `ContinuousMultilinearMap.prodL_symm_apply`, `CliffordAlgebra.foldr'Aux_apply_apply`, `le_smul_iff_one_le_left`, `QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last`, `EMetric.preimage_smul_closedBall`, `orbit_submonoid_subset`, `LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix'`, `Matrix.toLin_finTwoProd_toContinuousLinearMap`, `Set.smul_inter_nonempty_iff`, `Finset.mulETransformRight_fst`, `injective₀`, `orbit_subgroup_eq_rightCoset`, `pow_mod_period_smul`, `LinearMap.toMatrixAlgEquiv'_symm`, `AddSubmonoid.mem_inv_pointwise_smul_iff`, `OreLocalization.oreDiv_smul_oreDiv`, `Set.powersetCard.isPreprimitive_perm`, `instIsPushoutFractionRingPolynomial`, `MeasureTheory.measure_inv_smul_inter`, `hasDerivAtFilter_finCons`, `HasStrictDerivAt.prodMk`, `SubMulAction.SMulMemClass.subtype_apply`, `Set.encard_smul_set`, `SubMulAction.coe_one`, `SubMulAction.inclusion.coe_eq`, `lt_smul_of_one_lt_left`, `IsOpen.smul₀`, `Matrix.kroneckerTMulBilinear_apply`, `comp_smul_left`, `RingHom.smulOneHom_apply`, `IsOpen.smul_left`, `Set.powersetCard.isPretransitive_of_isMultiplyPretransitive`, `LinearMap.prodMap_smul`, `Finset.smul_prod`, `SetLike.mk_smul_of_tower_mk`, `Set.inv_op_smul_set_distrib`, `one_smul`, `hasEigenvalue_toLin'_diagonal_iff`, `ContinuousLinearMap.prodL_apply`, `IsLocalizedModule.map_injective_iff_localizedModuleMap_injective`, `Sylow.coe_subgroup_smul`, `MeasureTheory.smul_set_ae_eq`, `Set.smul_div_smul_comm`, `pow_period_add_smul`, `subset_interior_smul_right`, `IsCyclic.mulAutMulEquiv_symm_apply_symm_apply`, `Matrix.toLpLin_mul`, `IsBlock.orbit`, `Matrix.toLin'_submatrix`, `Polynomial.instIsScalarTowerElemRootSet`, `MulSemiringAction.smul_one`, `HasDerivAt.prodMk`, `Subring.pointwise_smul_le_pointwise_smul_iff₀`, `punctured_nhds_smul₀`, `pretransitive_iff_subsingleton_quotient`, `isTopologicallyTransitive_iff_dense_iUnion`, `cross_dot_cross`, `SetLike.smul_of_tower_def`, `SubMulAction.ofFixingSubgroup_of_singleton_bijective`, `Subsemiring.subset_pointwise_smul_iff`, `orbit_eq_iff`, `Equiv.Perm.OnCycleFactors.toPermHom_apply`, `lt_smul_iff_one_lt_left`, `Monoid.PushoutI.NormalWord.of_smul_eq_smul`, `Sylow.smul_subtype`, `Matrix.toEuclideanLin_apply_piLp_toLp`, `Set.powersetCard.isPreprimitive_alternatingGroup`, `continuousSMul_iff_stabilizer_isOpen`, `LieAlgebra.ext_iff`, `hasStrictDerivAt_pi`, `Submonoid.smul_closure`, `AlgEquiv.smul_units_def`, `Sylow.isPretransitive_of_finite`, `ContinuousAlternatingMap.prodLIE_apply`, `Subring.smul_sup`, `Finset.smul_prod'`, `subgroup_smul_def`, `threeGPFree_smul_set`, `SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective`, `ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le`, `DistribMulAction.smul_zero`, `Module.zero_smul`, `MulDistribMulAction.smul_mul`, `continuousSMul_closedBall_closedBall`, `ModularGroup.T_S_rel`, `Submonoid.instMeasurableConstSMul`, `HasDerivWithinAt.prodMk`, `Set.smul_inter_nonempty_iff'`, `Equiv.swap_smul_self_smul`, `AddSubgroup.coe_pointwise_smul`, `LinearMap.vecEmpty₂_apply`, `IsRightCancelMulZero.faithfulSMul`, `IsUnit.isHomeomorph_smul`, `aemeasurable_const_smul_iff`, `IsGalois.map_fixingSubgroup`, `Matrix.toLinAlgEquiv'_toMatrixAlgEquiv'`, `AddSubmonoid.coe_pointwise_smul`, `IsUnit.smul_tendsto_smul_iff`, `MeasureTheory.measure_preimage_smul`, `MeasureTheory.Measure.instSMulInvariantMeasureSubtypeMemSubmonoidOfIsMulLeftInvariant`, `QuotSMulTop.map_comp`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff`, `Projectivization.cross_mk_of_ne`, `Matrix.kroneckerTMulAlgEquiv_apply`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range`, `LieAdmissibleAlgebra.ext_iff`, `endVecAlgEquivMatrixEnd_symm_apply_apply`, `IsUnit.smul_bijective`, `properSMul_iff_continuousSMul_ultrafilter_tendsto`, `Matrix.trace_kroneckerMapBilinear`, `Polynomial.rootSet.coe_smul`, `IsometryEquiv.constSMul_apply`, `Matrix.toLinAlgEquiv'_one`, `IsUnit.isClosedMap_smul`, `IsMinimal.dense_orbit`, `SubMulAction.map_ofFixingSubgroupUnion_bijective`, `faithfulSMul_iff`, `Subgroup.Commensurable.commensurator'_mem_iff`, `ModularGroup.exists_smul_mem_fd`, `Ideal.pointwise_smul_toAddSubgroup`, `hasDerivAtFilter_pi`, `Set.powersetCard.mulActionHom_singleton_bijective`, `Subgroup.properlyDiscontinuousSMul_of_tendsto_cofinite`, `isBlock_iff_smul_eq_of_nonempty`, `CategoryTheory.PreGaloisCategory.mulAction_naturality`, `Finset.card_smul_inter_smul`, `instErgodicSMulMulOppositeOfIsMulRightInvariant`, `Monoid.CoprodI.Word.mem_smul_iff`, `Matrix.toLpLin_symm_comp`, `instSMulCommClass_closedBall_closedBall_ball`, `alternatingGroup.isPretransitive_of_three_le_card`, `SubMulAction.ofFixingSubgroup_of_eq_bijective`, `Complex.UnitDisc.instSMulCommClass_circle_closedBall`, `Monoid.CoprodI.Word.smul_eq_of_smul`, `QuotientGroup.orbit_mk_eq_smul`, `Set.preimage_smul₀`, `SubMulAction.SMulMemClass.subtype_injective`, `NonUnitalCStarAlgebra.toIsScalarTower`, `IsScalarTower.of_commMonoid`, `QuotientGroup.instContinuousConstSMul`, `Equiv.Perm.instIsPretransitive`, `eq_cosets_of_normal`, `Subgroup.transferFunction_apply`, `ModularForm.slash_def`, `ProperSMul.isProperMap_smul_pair_set`, `SubMulAction.smul_mem_iff'`, `Finset.dens_smul_finset`, `hasDerivAt_finCons'`, `Monoid.PushoutI.NormalWord.instFaithfulSMul_2`, `UpperHalfPlane.instContinuousGLSMul`, `mem_stabilizer_iff`, `isScalarTower_sphere_ball_ball`, `GradedMonoid.isScalarTower_right`, `continuousSMul_compHom`, `smul_uniformity`, `Module.Basis.orientation_unitsSMul`, `CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality`, `Finset.inv_smul_mem_iff₀`, `Subsemiring.smul_sup`, `orbit_nonempty`, `Subgroup.mem_inv_pointwise_smul_iff`, `CategoryTheory.ActionCategory.homOfPair.val`, `CongruenceSubgroup.conj_cong_is_cong`, `LinearMap.BilinForm.toMatrix'_mul`, `AddSubgroup.pointwise_smul_le_iff`, `Set.powersetCard.coe_mulActionHom_compl`, `hasDerivAt_single`, `SubMulAction.not_mem_of_mem_ofFixingSubgroup`, `ModularGroup.im_T_inv_smul`, `Finset.mulETransformRight_snd`, `MeasureTheory.Measure.addHaarScalarFactor_domSMul`, `LinearMap.toMatrix₂'_compl₂`, `IsPreprimitive.mk'`, `AddSubmonoid.smul_mem_pointwise_smul_iff`, `orbitRel.Quotient.mapsTo_smul_orbit`, `Matrix.toLinAlgEquiv'_symm`, `SlashInvariantFormClass.norm_petersson_smul`, `MulDistribMulAction.toMonoidHomZModOfIsCyclic_apply`, `NonUnitalCommCStarAlgebra.toSMulCommClass`, `stabilizer_orbit_eq`, `AddSubgroup.mem_inv_pointwise_smul_iff₀`, `Monoid.PushoutI.NormalWord.prod_smul`, `SubMulAction.val_preimage_orbit`, `smul_invOf_smul`, `absorbent_iff_inv_smul`, `continuous_const_smul_iff₀`, `AddSubmonoid.pointwise_smul_le_pointwise_smul_iff`, `Filter.smul_tendsto_smul_iff`, `UpperHalfPlane.modular_T_zpow_smul`, `CFC.nnrpow_eq_nnrpow_prod`, `Metric.preimage_smul_ball`, `isPeriodicPt_smul_iff`, `SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter`, `NormedGroup.to_isIsometricSMul_left`, `OreLocalization.smul_div_one`, `MeasurableSet.const_smul`, `MulActionHom.oneEmbeddingMap_bijective`, `Subring.subset_pointwise_smul_iff`, `IsUnit.continuousAt_const_smul_iff`, `FreeMonoid.smul_def`, `QuotSMulTop.map_apply_mk`, `Matrix.cramer_smul`, `Finset.op_smul_stabilizer_of_no_doubling`, `ContMDiffWithinAt.clm_prodMap`, `smul_pi₀`, `subset_interior_smul`, `isMultiplyPreprimitive_ofStabilizer`, `Subgroup.conj_smul_eq_self_of_mem`, `FreeGroup.Orbit.duplicate`, `Finset.mem_inv_smul_finset_iff₀`, `CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isGalois`, `Set.pairwise_disjoint_smul_iff`, `Set.smul_mem_smul_set_iff`, `Subring.instSMulCommClassSubtypeMemCenter_1`, `NumberField.InfinitePlace.mem_orbit_iff`, `invOf_smul_eq_iff`, `HNNExtension.NormalWord.of_smul_eq_smul`, `Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1`, `totallyBounded_iff_subset_finite_iUnion_nhds_one`, `Set.mem_smul_set_iff_inv_smul_mem`, `IsUnit.measurable_const_smul_iff`, `Set.smul_Icc`, `Set.smul_set_subset_smul_set_iff`, `Subalgebra.continuousSMul`, `lowerClosure_smul`, `exists_bijective_map_powers`, `OrderIso.smulRightDual_symm_apply`, `Set.Infinite.smul_set`, `jacobi_cross`, `SubMulAction.orbitRel_of_subMul`, `DiscreteTiling.PlacedTile.coe_mk_coe`, `Finset.subset_smul_finset_iff₀`, `UpperHalfPlane.pos_real_im`, `Subring.smul_mem_pointwise_smul`, `Subgroup.transferTransversal_apply''`, `Representation.ofMulDistribMulAction_apply_apply`, `WithConv.ofConv_smul`, `minimalPeriod_pos`, `Subsemiring.pointwise_smul_le_pointwise_smul_iff₀`, `neg_cross`, `Projectivization.generalLinearGroup_smul_def`, `LocalizedModule.map_mk`, `MeasureTheory.tendsto_measure_smul_diff_isCompact_isClosed`, `isScalarTower_iff_smulCommClass_of_commMonoid`, `aestronglyMeasurable_const_smul_iff₀`, `Monoid.CoprodI.Word.smul_def`, `smul_eq_iff_eq_invOf_smul`, `AddAut.mulLeft_apply_symm_apply`, `LinearMap.det_toMatrix'`, `IsQuotientCoveringMap.isCancelSMul`, `CFC.sqrt_map_pi`, `Subgroup.smul_mem_pointwise_smul`, `SubMulAction.smul_mem_iff`, `smul_eq_iff_eq_inv_smul`, `Absorbs.univ`, `Equidecomp.trans_toPartialEquiv`, `Finset.smul_finset_inter₀`, `eq_inv_smul_iff₀`, `Subgroup.relIndex_pointwise_smul`, `smul_zpow'`, `ModularForm.SL_slash_apply`, `OreLocalization.oreDiv_smul_char`, `MeasureTheory.Measure.addHaarScalarFactor_smul_congr'`, `Subalgebra.pointwise_smul_toSubsemiring`, `ThreeGPFree.smul_set`, `NormedSpace.ext_iff`, `smul_mem_fixedBy_iff_mem_fixedBy`, `SubMulAction.mem_ofFixingSubgroup_iff`, `EisensteinSeries.eisSummand_SL2_apply`, `AddSubgroup.le_pointwise_smul_iff`, `Subsemiring.continuousSMul`, `ContinuousMultilinearMap.piₗᵢ_apply`, `TrivSqZeroExt.inl_mul_eq_smul`, `Commute.smul_left_iff₀`, `DualNumber.algHom_ext'_iff`, `Matrix.range_diagonal`, `SubMulAction.isScalarTower`, `Subgroup.quotientEquivSigmaZMod_symm_apply`, `mem_fixingSubgroup_iff`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive'`, `MulActionHom.map_mem_fixedBy`, `Monoid.CoprodI.Word.rcons_eq_smul`, `UniformOnFun.continuousSMul_submodule_of_image_bounded`, `continuous_const_smul_iff`, `Group.preimage_smul_setₛₗ`, `Finset.smul_finset_sdiff₀`, `ContinuousLinearMap.prodₗ_apply`, `orbit_eq_univ`, `SlashInvariantForm.slash_action_eqn'`, `Subgroup.equivSMul_symm_apply_coe`, `Units.continuousSMul`, `Subgroup.smul_toLeftFun`, `IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1`, `LinearMap.toMatrix₂'_comp`, `NNReal.instSMulPosStrictMono`, `NonUnitalStarSubalgebra.prod_top`, `LinearPMap.closure_inverse_graph`, `instSMulCommClass_sphere_closedBall_ball`, `isOpenMap_smul_of_sigmaCompact`, `ContMDiffOn.clm_prodMap`, `Submonoid.pow_smul_mem_closure_smul`, `Matrix.SpecialLinearGroup.toLin'_symm_apply`, `MeasureTheory.smul_set_ae_le`, `LeftPreLieAlgebra.toIsScalarTower`, `Subsemiring.smul_closure`, `isScalarTower_closedBall_closedBall_ball`, `rightCoset_one`, `Set.disjoint_smul_set_left`, `LinearMap.toMatrix'_one`, `LieAlgebra.SpecialLinear.val_singleSubSingle`, `Subsemiring.pointwise_smul_le_iff₀`, `SubMulAction.val_smul_of_tower`, `Matrix.cstar_norm_def`, `EMetric.preimage_smul_ball`, `Monoid.CoprodI.lift_word_ping_pong`, `ModularForm.coe_translate`, `Equiv.Perm.moves_in`, `MulAut.apply_faithfulSMul`, `Set.smul_set_subset_iff₀`, `smul_ball_one`, `UpperHalfPlane.neg_smul`, `cross_cross_eq_smul_sub_smul'`, `Set.disjoint_smul_set_right`, `Equiv.smulRight_apply`, `orbit_subgroup_one_eq_self`, `quotient_preimage_image_eq_union_mul`, `MeasureTheory.fundamentalInterior_smul`, `Matrix.toLinearMapRight'_one`, `Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace`, `zpow_period_add_smul`, `Set.Finite.absorbs_biInter`, `IsUniformGroup.to_uniformContinuousConstSMul`, `IwasawaStructure.is_conj`, `IsSMulRegular.one`, `SlashInvariantFormClass.petersson_smul`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem`, `smul_finprod_perm`, `AddCommGroup.smul_top_eq_top_of_divisibleBy_int`, `Submodule.topologicalClosure_iSup_map_single`, `period_eq_minimalPeriod`, `exists_disjoint_smul_of_isCompact`, `Subalgebra.pointwise_smul_toSubmodule`, `CategoryTheory.PreGaloisCategory.isPretransitive_of_isGalois`, `smul_lt_iff_lt_one_left`, `Matrix.toLpLin_apply`, `EMetric.smul_closedBall`, `properlyDiscontinuousSMul_iff_properSMul`, `Matrix.toLin'_apply`, `QuotSMulTop.map_id`, `RelHom.apply_faithfulSMul`, `KaehlerDifferential.mulActionBaseChange_smul_zero`, `Multiset.smul_prod`, `Units.smul_eq_mul`, `hasDerivAt_pi`, `GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset`, `ModuleCat.sMulCommClass_mk`, `is_one_pretransitive_iff`, `hasDerivWithinAt_finCons`, `HNNExtension.NormalWord.prod_smul_empty`, `Finset.smul_prod_perm`, `stabilizer_smul_eq_right`, `OpenPartialHomeomorph.unitBallBall_symm_apply`, `card_orbit_mul_card_stabilizer_eq_card_group`, `AddSubgroup.le_pointwise_smul_iff₀`, `Sylow.smul_le`, `one_smul_eq_id`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset`, `instSMulCommClass_sphere_sphere_closedBall`, `UpperHalfPlane.contMDiff_smul`, `mem_rightCoset_iff`, `Matrix.l2_opNorm_def`, `Subgroup.smul_bot`, `AddSubgroup.pointwise_smul_def`, `AddSubmonoid.le_pointwise_smul_iff₀`, `Matrix.toEuclideanLin_toLp`, `AddAut.smul_def`, `FixedPoints.mem_submonoid`, `IsFoelner.amenable`, `Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1`, `Ideal.coe_smul_primesOver`, `stronglyMeasurable_const_smul_iff₀`, `IsBaseChange.finitePow`, `Equidecomp.symm_bijective`, `MeasureTheory.measure_union_inv_smul`, `Sylow.smul_def`, `ENNReal.smulCommClass_right`, `HasCompactSupport.comp_smul`, `Matrix.toLin'_toMatrix'`, `ContinuousAlternatingMap.prodLIE_symm_apply`, `Subring.smul_mem_pointwise_smul_iff`, `Set.smul_set_subset_iff_subset_inv_smul_set`, `UpperHalfPlane.isometry_pos_mul`, `DomMulAct.mk_smul_monoidHom_apply`, `PosSMulMono.toPosSMulReflectLE`, `instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation`, `closure_smul`, `instSMulCommClass_closedBall_closedBall_closedBall`, `smul_mem_fixedPoints_of_normal`, `SMul.smul_stabilizer_def`, `Set.smul_set_pi₀'`, `isTopologicallyTransitive_iff`, `SetLike.instSMulCommClassSubtypeMem_1`, `CategoryTheory.ActionCategory.hom_as_subtype`, `Subgroup.le_pointwise_smul_iff₀`, `injective`, `Monoid.PushoutI.NormalWord.summand_smul_def`, `Equidecomp.symm_toPartialEquiv`, `IsUnit.continuous_const_smul_iff`, `RightPreLieAlgebra.ext_iff`, `Subgroup.smulCommClass_left`, `Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff`, `Additive.addAction_isPretransitive`, `Matrix.kroneckerStarAlgEquiv_apply`, `minimalPeriod_eq_card`, `mem_stabilizer_finset'`, `subsingleton_orbit_iff_mem_fixedPoints`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀`, `AddSubgroup.pointwise_isCentralScalar`, `Projectivization.smul_mk`, `Real.volume_preserving_transvectionStruct`, `mulSupport_comp_inv_smul₀`, `ContinuousAlternatingMap.piLinearEquiv_apply`, `Matrix.toLpLinAlgEquiv_symm_apply`, `MDifferentiableWithinAt.clm_prodMap`, `smul_iterate_apply`, `ModularGroup.SL_neg_smul`, `OpenPartialHomeomorph.unitBallBall_apply`, `Subring.pointwise_smul_toSubsemiring`, `LinearMap.toMatrix'_mulVec`, `IsBlockSystem.of_normal`, `IsTrivialBlock.smul_iff`, `SetLike.instIsScalarTowerSubtypeMem`, `Set.mem_smul_set_iff_inv_smul_mem₀`, `Set.smul_graphOn`, `smul_zpow_fixedBy_eq_of_commute`, `SubMulAction.isScalarTower'`, `pretransitive_iff_unique_quotient_of_nonempty`, `approxOrderOf.smul_eq_of_mul_dvd`, `HNNExtension.NormalWord.t_pow_smul_eq_unitsSMul`, `Units.isScalarTower'_left`, `OreLocalization.smul_one_smul`, `MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot`, `Set.powersetCard.coe_mulActionHom_of_embedding`, `instSMulCommClass_sphere_sphere_ball`, `Flag.coe_smul`, `AddSubgroup.index_smul`, `IsBlock.of_orbit`, `Matrix.diagonal_comp_single`, `ofQuotientStabilizer_smul`, `measurable_const_smul_iff₀`, `Finset.smul_univ₀`, `NonUnitalCStarAlgebra.toSMulCommClass`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply`, `SubMulAction.image_inclusion`, `Finset.card_smul_finset`, `Finset.mulETransformLeft_snd`, `Monoid.PushoutI.NormalWord.instFaithfulSMul_1`, `IsUnit.smul`, `orbitRel.Quotient.orbit_eq_orbit_out`, `Set.smul_univ₀'`, `mem_fixingSubmonoid_iff`, `instIsOrderedSMulOfIsOrderedMonoid`, `Subgroup.smul_diff'`, `Regular.isPretransitive`, `Set.powersetCard.mulActionHom_of_embedding_surjective`, `SubMulAction.ofFixingSubgroup_insert_map_bijective`, `Subalgebra.pointwise_smul_toSubring`, `Set.smul_set_symmDiff₀`, `IsUnit.preimage_smul_setₛₗ`, `InnerProductSpace.symm_toEuclideanLin_rankOne`, `LinearMap.BilinForm.toMatrix'_compRight`, `MulDistribMulAction.toMonoidHom_apply`, `Algebra.Extension.Cotangent.ker_mk`, `CategoryTheory.PreGaloisCategory.instIsPretransitiveAutCarrierVFintypeCatFunctorObjActionFunctorToActionOfIsGalois`, `EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act`, `Finset.mulETransformLeft_fst`, `TrivSqZeroExt.mul_inl_eq_op_smul`, `Ideal.pointwise_smul_toAddSubmonoid`, `Complex.UnitDisc.instIsScalarTower_closedBall_closedBall`, `LinearPMap.IsClosable.graph_closure_eq_closure_graph`, `isBoundedLinearMap_prod_multilinear`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle'`, `Subgroup.IsArithmetic.conj`, `Subgroup.instFaithfulSMulSubtypeMem`, `op_smul_mul`, `Subring.mem_inv_pointwise_smul_iff₀`, `OreLocalization.oreDiv_one_smul`, `ModularGroup.exists_eq_T_zpow_of_c_eq_zero`, `Matrix.rank_vecMulVec`, `Monoid.CoprodI.Word.equivPair_tail_eq_inv_smul`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset'`, `Subsemiring.mem_inv_pointwise_smul_iff`, `le_inv_smul_iff_of_pos`, `Quotient.smul_coe`, `hasDerivAt_finCons`, `upperClosure_smul`, `Complex.UnitDisc.coe_circle_smul`, `Set.powersetCard.coe_smul`, `IsOpen.iUnion_preimage_smul`, `CFC.nnrpow_map_prod`, `LinearMap.toMatrixRight'_comp`, `Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul`, `smul_left_cancel_iff`, `Matrix.kroneckerStarAlgEquiv_symm_apply`, `smul_inv`, `IsUnit.isOpenMap_smul`, `MeasureTheory.integral_smul_eq_self`, `orbit_fixingSubgroup_compl_subset`, `UpperHalfPlane.modular_T_smul`, `measurable_const_smul_iff`, `Subgroup.pointwise_smul_toSubmonoid`, `Finset.smul_stabilizer_of_no_doubling`, `Submonoid.smul_bot`, `NonUnitalCommCStarAlgebra.toIsScalarTower`, `NNReal.instIsScalarTowerOfReal`, `IsCusp.smul`, `Set.smul_set_pi₀`, `KaehlerDifferential.mulActionBaseChange_smul_tmul`, `SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent`, `Finset.smul_inv_mul_opSMul_eq_mul_of_doubling_lt_three_halves`, `isCancelSMul_iff_eq_one_of_smul_eq`, `mem_stabilizer_finset_iff_subset_smul_finset`, `ModularGroup.smul_eq_lcRow0_add`, `Submodule.span_singleton_group_smul_eq`, `Matrix.SpecialLinearGroup.toLin'_apply`, `Module.Finite.of_isComplemented_codomain`, `nhds_smul`, `Subgroup.mk_smul`, `IsUpperSet.smul_subset`, `CStarMatrix.norm_def`, `mem_orbit_self`, `AddSubmonoid.mem_smul_pointwise_iff_exists`, `IsSelfAdjoint.smul_iff`, `Equiv.Perm.OnCycleFactors.centralizer_smul_def`, `Measurable.measurableSMul₂_iterateMulAct`, `mapsTo_smul_orbit`, `AlgHom.mulLeftRightMatrix.comp_inv`, `SetLike.instSMulCommClassSubtypeMem_2`, `surjective`, `SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter`, `instIsPushoutFractionRingMvPolynomial_1`, `Set.subset_smul_set_iff₀`, `int_smul_eq_zsmul`, `LinearMap.toMatrixAlgEquiv'_comp`, `smul_orbit_eq_orbit_smul`, `smul_mul'`, `mem_fixedBy`, `LinearPMap.IsClosable.existsUnique`, `aemeasurable_const_smul_iff₀`, `CStarMatrix.inner_toCLM_conjTranspose_right`, `SlashInvariantForm.T_zpow_width_invariant`, `AddSubmonoid.pointwise_smul_le_iff₀`, `LieModule.toEnd_matrix`, `isBlock_subtypeVal`, `CStarMatrix.toCLM_apply_single_apply`, `MeasureTheory.QuotientMeasureEqMeasurePreimage.covolume_ne_top`, `SubMulAction.coe_pow`, `QuotientGroup.out_conj_pow_minimalPeriod_mem`, `UpperHalfPlane.mdifferentiable_smul`, `eq_inv_smul_iff`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `ModularForm.slash_apply`, `Subsemiring.le_pointwise_smul_iff₀`, `Subgroup.smul_coe`, `Action.FintypeCat.ofMulAction_apply`, `Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply`, `IsClosed.rightCoset`, `continuousAt_const_smul_iff`, `smul_singleton_mem_nhds_of_sigmaCompact`, `IsUnit.continuousWithinAt_const_smul_iff`, `instIsPushoutFractionRingMvPolynomial`, `Finset.convolution_op_smul_eq_convolution_mul_inv`, `Representation.ofMulAction_def`, `smul_le_of_le_one_left`, `AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero`, `instErgodicSMulOfIsMulLeftInvariant`, `UpperHalfPlane.petersson_slash`, `Matrix.spectrum_toLin'`, `IsOpen.exists_smul_mem`, `Subgroup.smul_mem_pointwise_smul_iff`, `Function.End.apply_FaithfulSMul`, `IsClosed.smul`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`ext` 📖	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `toSemigroupAction`	—	—	—
`ext_iff` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `toSemigroupAction`	—	`ext`
`one_smul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `toSemigroupAction` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	—

MulDistribMulAction

Definitions

Name	Category	Theorems
`toMulAction` 📖	CompOp	72 math math: `DomMulAct.smul_monoidHom_apply`, `Subgroup.smul_mem_pointwise_smul_iff₀`, `ConjAct.fixedPoints_eq_center`, `smul_pow'`, `Subgroup.equivSMul_apply_coe`, `Subgroup.coe_pointwise_smul`, `MulSemiringAction.toRingHom_apply`, `ConjAct.stabilizer_eq_centralizer`, `Submonoid.smul_mem_pointwise_smul_iff₀`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `toMulEquiv_apply`, `Submonoid.smul_mem_pointwise_smul`, `groupCohomology.isMulCoboundary₁_of_mem_coboundaries₁`, `Submonoid.mem_smul_pointwise_iff_exists`, `val_unitsCentralizerEquiv_apply_coe`, `Submonoid.mem_inv_pointwise_smul_iff`, `smul_div'`, `Submonoid.coe_pointwise_smul`, `groupCohomology.isMulCoboundary₂_of_mem_coboundaries₂`, `Multiset.smul_prod'`, `Submonoid.smul_mem_pointwise_smul_iff`, `groupCohomology.isMulCocycle₁_of_mem_cocycles₁`, `smul_inv'`, `Units.coe_smul`, `Rep.ofMulDistribMulAction_ρ_apply_apply`, `Representation.norm_ofMulDistribMulAction_eq`, `Subgroup.mem_inv_pointwise_smul_iff₀`, `MulActionHom.coe_one`, `Subgroup.mem_smul_pointwise_iff_exists`, `mulAutArrow_apply_apply`, `groupCohomology.isMulCocycle₂_of_mem_cocycles₂`, `MulActionHom.coe_mul`, `Submonoid.mem_inv_pointwise_smul_iff₀`, `smul_algebraMap`, `mulAutArrow_apply_symm_apply`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `toMulEquiv_symm_apply`, `val_unitsCentralizerEquiv_symm_apply_coe`, `IsPGroup.smul_mul_inv_trivial_or_surjective`, `ext_iff`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem`, `smul_finprod'`, `Algebra.smul_units_def`, `Subgroup.smul_closure`, `smul_one`, `List.smul_prod'`, `Units.coe_inv_smul`, `FixedPoints.mem_subgroup`, `algebraMap.coe_smul'`, `Submonoid.smul_closure`, `AlgEquiv.smul_units_def`, `Finset.smul_prod'`, `smul_mul`, `Subgroup.mem_inv_pointwise_smul_iff`, `toMonoidHomZModOfIsCyclic_apply`, `Representation.ofMulDistribMulAction_apply_apply`, `ConjAct.orbitRel_conjAct`, `Subgroup.smul_mem_pointwise_smul`, `smul_zpow'`, `Subgroup.equivSMul_symm_apply_coe`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem`, `smul_finprod_perm`, `Finset.smul_prod_perm`, `FixedPoints.mem_submonoid`, `ConjClasses.card_carrier`, `DomMulAct.mk_smul_monoidHom_apply`, `Subgroup.nat_card_centralizer_nat_card_stabilizer`, `toMonoidHom_apply`, `smul_mul'`, `Subgroup.centralizer_eq_comap_stabilizer`, `Subgroup.smul_coe`, `Subgroup.smul_mem_pointwise_smul_iff`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`ext` 📖	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `toMulAction`	—	—	—
`ext_iff` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `toMulAction`	—	`ext`
`smul_mul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `toMulAction` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	—
`smul_one` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `toMulAction` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	—

MulOpposite

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`smul_eq_mul_unop` 📖	mathematical	—	`MulOpposite` `Mul.toSMulMulOpposite` `unop`	—	—

SMul

Definitions

Name	Category	Theorems
`comp` 📖	CompOp	3 math math: `comp.smulCommClass'`, `comp.smulCommClass`, `comp.isScalarTower`

SMul.comp

Definitions

Name	Category	Theorems
`smul` 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`isScalarTower` 📖	mathematical	—	`IsScalarTower` `SMul.comp`	—	`smul_assoc`
`smulCommClass` 📖	mathematical	—	`SMulCommClass` `SMul.comp`	—	`SMulCommClass.smul_comm`
`smulCommClass'` 📖	mathematical	—	`SMulCommClass` `SMul.comp`	—	`SMulCommClass.smul_comm`

SMulCommClass

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`of_commMonoid` 📖	mathematical	—	`SMulCommClass`	—	`one_smul` `smul_assoc` `smul_comm` `smulCommClass_self`
`of_mul_smul_one` 📖	mathematical	`MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass` `MulOne.toOne`	`SMulCommClass` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `Monoid.toMulAction`	—	`smul_eq_mul` `mul_assoc`
`op_left` 📖	mathematical	—	`SMulCommClass` `MulOpposite`	—	`IsCentralScalar.unop_smul_eq_smul` `smul_comm`
`op_right` 📖	mathematical	—	`SMulCommClass` `MulOpposite`	—	`IsCentralScalar.unop_smul_eq_smul` `smul_comm`
`smul_comm` 📖	—	—	—	—	—

SMulDistribClass

Theorems

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

Semigroup

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`isScalarTower` 📖	mathematical	—	`IsScalarTower` `toMul`	—	`mul_assoc`

SemigroupAction

Definitions

Name	Category	Theorems
`toSMul` 📖	CompOp	1771 math math: `AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀`, `MulAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPoints`, `Matrix.l2_opNorm_toEuclideanCLM`, `MulAction.Quotient.coe_smul_out`, `units_inv_smul`, `LeftPreLieAlgebra.toSMulCommClass`, `MulAction.compHom_smul_def`, `DoubleCoset.doubleCoset_union_rightCoset`, `DomMulAct.smul_monoidHom_apply`, `aestronglyMeasurable_const_smul_iff`, `continuousSMul_sphere_ball`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset`, `MulAction.pow_add_period_smul`, `IsSMulRegular.of_mul_eq_one`, `instIsOrderedCancelSMulOfIsOrderedCancelMonoid`, `MulAction.isPreprimitive_of_fixingSubgroup_empty_iff`, `isHomeomorph_smul₀`, `Homeomorph.smulOfNeZero_symm_apply`, `Subgroup.smul_mem_pointwise_smul_iff₀`, `CategoryTheory.PreGaloisCategory.mulAction_def`, `interior_smul₀`, `ModularGroup.SLOnGLPos_smul_apply`, `dot_self_cross`, `Subgroup.pointwise_smul_le_pointwise_smul_iff`, `Matrix.toLin'_symm`, `MeasureTheory.smulInvariantMeasure_iterateMulAct`, `NormedGroup.to_isIsometricSMul_right`, `LinearMap.toMatrixAlgEquiv'_mul`, `Matrix.kroneckerTMulStarAlgEquiv_symm_apply`, `IsUnit.isSMulRegular`, `properSMul_iff`, `Monoid.PushoutI.NormalWord.base_smul_def`, `IsLowerSet.smul`, `smul_pow'`, `MulAction.IsTrivialBlock.smul`, `Set.smul_set_symmDiff`, `instProperConstSMulOfContinuousConstSMul`, `Finset.smul_finset_subset_smul_finset_iff`, `mul_ball`, `MeasurableEquiv.smul_apply`, `Subgroup.equivSMul_apply_coe`, `Finset.smul_finset_sdiff`, `AffineMap.coe_smul`, `Metric.smul_ball`, `FreeMonoid.ofList_smul`, `ErgodicSMul.of_aestabilizer`, `MulAction.isTopologicallyTransitive_iff_dense_iUnion_preimage`, `MeasureTheory.measure_sdiff_inv_smul`, `MeasurableEquiv.coe_smul₀`, `IsClosed.smul_of_ne_zero`, `Subgroup.coe_pointwise_smul`, `Mathlib.Tactic.Module.NF.eval_algebraMap`, `NonUnitalCStarAlgebra.toStarModule`, `Finset.inv_smul_mem_iff`, `MulAction.IsBlock.of_subset`, `HNNExtension.NormalWord.prod_group_smul`, `Subring.pointwise_smul_def`, `Complex.UnitDisc.instIsScalarTower_circle`, `AddSubgroup.zero_smul`, `TrivSqZeroExt.lift_inlAlgHom_inrHom`, `MulSemiringAction.toRingHom_apply`, `Polynomial.Gal.smul_def`, `MulAction.nonempty_orbit`, `Matrix.toLinearMapRight'_mul`, `Equiv.Perm.smul_def`, `Filter.smul_tendsto_smul_iff₀`, `MonoidHom.preimage_smul_setₛₗ`, `Rep.diagonalSuccIsoFree_inv_hom_single`, `mem_own_rightCoset`, `continuousSMul_sphere_sphere`, `Equiv.Perm.Basis.toCentralizer_equivariant`, `punctured_nhds_smul`, `support_comp_inv_smul₀`, `Matrix.spectrum_toEuclideanLin`, `Matrix.iSup_eigenspace_toLin'_diagonal_eq_top`, `SubMulAction.ofStabilizer_carrier`, `Matrix.cstar_nnnorm_def`, `Submonoid.smul_mem_pointwise_smul_iff₀`, `MeasureTheory.Subgroup.smulInvariantMeasure`, `LinearMap.mapMatrixLinear_apply`, `Filter.mem_absorbing`, `smul_mem_nhds_smul₀`, `SubMulAction.ofFixingSubgroup_equivariantMap_injective`, `Matrix.toLinearMap₂'_comp`, `Sylow.pointwise_smul_def`, `kroneckerTMulAlgEquiv_symm_single_tmul`, `smul_zpow`, `UpperHalfPlane.re_smul`, `Subgroup.pointwise_smul_subset_iff`, `Action.ofMulAction_apply`, `RelIso.smul_def`, `OrderIso.smulRight_apply`, `Set.smul_graphOn_univ`, `Function.Embedding.coe_smul`, `OnePoint.isBoundedAt_iff_exists_SL2Z`, `alternatingGroup.isPreprimitive_of_three_le_card`, `SubMulAction.fixingSubgroup_smul_eq_fixingSubgroup_map_conj`, `Ideal.coe_smul_primesOver_mk_eq_map_galRestrict`, `MulAction.isPretransitive_iff_orbit_eq_univ`, `Function.Embedding.smul_apply`, `LocalizedModule.restrictScalars_map_eq`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `MeasureTheory.addHaarScalarFactor_smul_inv_eq_distribHaarChar`, `HNNExtension.NormalWord.group_smul_toList`, `Subring.instSMulCommClassSubtypeMemCenter`, `MulAction.set_mem_fixedBy_iff`, `CategoryTheory.FintypeCat.Action.pretransitive_of_isConnected`, `Subgroup.subset_pointwise_smul_iff`, `OreLocalization.oreDiv_eq_iff`, `inv_smul_smul₀`, `Units.isSMulRegular`, `Module.Ray.neg_units_smul`, `Set.infinite_smul_set`, `IsCusp.smul_of_mem`, `Finset.inv_smul_finset_distrib`, `AddSubgroup.smul_mem_pointwise_smul_iff`, `isQuotientCoveringMap_iff`, `Finset.doubling_lt_three_halves`, `Set.mem_smul_set_inv`, `smulMulHom_apply`, `Subgroup.exists_smul_eq`, `CongruenceSubgroup.exists_Gamma_le_conj'`, `UpperHalfPlane.tendsto_smul_atImInfty`, `Set.powersetCard.isPretransitive`, `NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm`, `MulAction.ofQuotientStabilizer_mem_orbit`, `Subgroup.conj_smul_subgroupOf`, `IsCompact.closedBall_mul`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left`, `MulAction.Supports.smul`, `inv_smul_eq_iff`, `QuotSMulTop.equivTensorQuot_naturality`, `MeasureTheory.pairwise_disjoint_fundamentalInterior`, `IsClosed.smul_left_of_isCompact`, `AddSubgroup.mem_inv_pointwise_smul_iff`, `Complex.UnitDisc.instSMulCommClass_closedBall_circle`, `Units.smul_coe`, `CongruenceSubgroup.conjGL_coe`, `Dense.smul`, `Module.Basis.groupSMul_span_eq_top`, `mem_leftCoset_iff`, `cross_cross`, `Complex.UnitDisc.instSMulCommClass_closedBall_left`, `Subsemiring.mem_smul_pointwise_iff_exists`, `Matrix.spectrum_toLpLin`, `EMetric.smul_ball`, `Submodule.top_eq_ofList_cons_smul_iff`, `UpperHalfPlane.im_smul_eq_div_normSq`, `AddSubgroup.mem_inertia`, `OreLocalization.nsmul_eq_nsmul`, `UpperHalfPlane.specialLinearGroup_apply`, `MulAction.smul_mem_orbit_smul`, `Set.smul_set_inter`, `instSMulCommClass_sphere_sphere_sphere`, `Sylow.coe_smul`, `NumberField.InfinitePlace.exists_smul_eq_of_comap_eq`, `DoubleCoset.doubleCoset_union_leftCoset`, `AddSubmonoid.le_pointwise_smul_iff`, `MeasureTheory.Measure.domSMul_apply`, `isClosedMap_smul_of_ne_zero`, `Equiv.Perm.exists_mem_stabilizer_smul_eq`, `IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply`, `Module.FinitePresentation.exists_notMem_bijective`, `Set.mem_inv_smul_set_iff₀`, `Set.finite_smul_set`, `ContinuousAlternatingMap.piLIE_apply_apply`, `Set.preimage_smul_inv₀`, `Subsemiring.smul_mem_pointwise_smul_iff`, `SubMulAction.ofFixingSubgroup_of_inclusion_injective`, `ENNReal.smul_def`, `cross_self`, `MulAction.mem_aestabilizer`, `Set.smul_set_inter₀`, `Subgroup.center.smulCommClass_right`, `MulAction.quotient_out_smul_fixedPoints`, `Set.smul_set_subset_smul_set_iff₀`, `ContinuousMultilinearMap.piLinearEquiv_symm_apply`, `MulDistribMulAction.toMulEquiv_apply`, `Submonoid.smul_mem_pointwise_smul`, `Equidecomp.restr_refl_symm`, `Module.Ray.units_smul_of_neg`, `Matrix.intrinsicStar_toLin'`, `RelEmbedding.smul_def`, `InnerProductSpace.smul_left`, `MulAction.zpow_smul_mod_minimalPeriod`, `MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar_inv`, `MulAction.IsQuasiPreprimitive.isPretransitive_of_normal`, `MeasureTheory.mem_fundamentalInterior`, `Finset.smul_finset_inter`, `MeasureTheory.mem_fundamentalFrontier`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity`, `MulAction.QuotientAction.inv_mul_mem`, `Finset.smul_finset_univ`, `ModularGroup.one_lt_normSq_T_zpow_smul`, `QuadraticMap.toMatrix'_comp`, `Set.powersetCard.mem_mulActionHom_compl`, `OnePoint.smul_infty_eq_self_iff`, `HNNExtension.NormalWord.t_smul_eq_unitsSMul`, `SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix`, `MulAction.isPreprimitive_of_is_two_pretransitive`, `SubMulAction.subset_coe_pow`, `Finset.subset_smul_finset_iff`, `cfcₙHom_nnreal_eq_restrict`, `OreLocalization.smul_cancel'`, `unitary.smul_mem_of_mem`, `MulAction.isBlock_iff_smul_eq_of_mem`, `SubMulAction.nat_card_ofStabilizer_add_one_eq`, `groupCohomology.isMulCoboundary₁_of_mem_coboundaries₁`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right`, `absorbent_univ`, `mulSupport_comp_inv_smul`, `cfcₙ_map_pi`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_infinity`, `Representation.ofMulAction_apply`, `RightPreLieAlgebra.toIsScalarTower`, `hasDerivWithinAt_pi`, `LinearMap.spectrum_toMatrix'`, `Real.smul_map_diagonal_volume_pi`, `Submonoid.pointwise_smul_le_pointwise_smul_iff₀`, `AlgHom.mulLeftRightMatrix.inv_comp`, `Submonoid.mem_smul_pointwise_iff_exists`, `one_leftCoset`, `KaehlerDifferential.quotKerTotalEquiv_symm_comp_D`, `Unitary.smul_mem`, `QuotSMulTop.equivTensorQuot_naturality_mk`, `dot_cross_self`, `MeasureTheory.fundamentalFrontier_smul`, `Subring.mem_pointwise_smul_iff_inv_smul_mem`, `Matrix.toLpLin_mul_same`, `MulAction.mem_orbit_smul`, `jacobiTheta_T_sq_smul`, `Submonoid.instMeasurableSMul`, `DistribMulAction.smul_add`, `MulAction.orbit_subgroup_subset`, `Subalgebra.coe_pointwise_smul`, `MulAction.smul_zpow_movedBy_eq_of_commute`, `SlashInvariantForm.quotientFunc_smul`, `IsUnit.tendsto_const_smul_iff`, `Equiv.swap_smul_involutive`, `NonUnitalSubalgebra.prod_inf_prod`, `CStarMatrix.toCLM_injective`, `Submonoid.pointwise_smul_le_pointwise_smul_iff`, `ModularGroup.sl_moeb`, `MulAction.is_one_preprimitive_iff`, `MeasureTheory.Measure.IsAddHaarMeasure.domSMul`, `Subgroup.smulCommClass_right`, `NumberField.InfinitePlace.smul_apply`, `Finset.inv_op_smul_finset_distrib`, `rightCoset_eq_iff`, `MulAction.le_stabilizer_iff_smul_le`, `Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single`, `MulAut.smul_def`, `absorbs_inter`, `MeasureTheory.measure_smul_eq_zero_iff`, `Subring.mem_pointwise_smul_iff_inv_smul_mem₀`, `IsUnit.stronglyMeasurable_const_smul_iff`, `LinearMap.rank_diagonal`, `MulAction.bijective`, `QuotSMulTop.map_comp_mkQ`, `MulAction.BlockMem.coe_top`, `OnePoint.isZeroAt_iff_exists_SL2Z`, `AlternatingGroup.isPreprimitive_of_three_le_card`, `Finset.prod_smul`, `lt_inv_smul_iff_of_pos`, `Matrix.toEuclideanLin_apply`, `MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff'`, `LinearIndependent.group_smul_iff`, `LinearMap.toMatrixAlgEquiv'_id`, `MulAction.toPerm_apply`, `smul_rayOfNeZero`, `UpperHalfPlane.glPos_smul_def`, `Subgroup.instCovariantClassHSMulLe`, `IsCusp.of_isFiniteRelIndex_conj`, `Finset.smul_finset_subset_smul_finset_iff₀`, `Metric.smul_closedEBall`, `UpperHalfPlane.coe_pos_real_smul`, `isScalarTower_closedBall_closedBall_closedBall`, `Matrix.liftLinear_singleLinearMap`, `NonUnitalSubalgebra.prod_top`, `ModularGroup.coe_T_zpow_smul_eq`, `smul_uniformity₀`, `SubMulAction.map_ofFixingSubgroupUnion_def`, `AddSubmonoid.smul_bot`, `isScalarTower_sphere_closedBall_closedBall`, `Set.powersetCard.faithfulSMul`, `LocalizedModule.divBy_mul_by`, `Submodule.pointwise_smul_toAddSubgroup`, `LinearMap.toMatrix₂'_compl₁₂`, `LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle`, `LinearMap.prodEquiv_apply`, `CStarMatrix.norm_def'`, `MulActionWithZero.zero_smul`, `Representation.ofMulAction_single`, `Finset.mulDysonETransform_snd`, `LocalizedModule.map_surjective`, `AddSubmonoid.smul_sup`, `SubMulAction.ofStabilizer.isMultiplyPretransitive_iff`, `Matrix.toLin'_mul_apply`, `Complex.UnitDisc.coe_smul_circle`, `MulAction.Quotient.smul_mk`, `UpperHalfPlane.denom_cocycle_σ`, `Submonoid.mem_inv_pointwise_smul_iff`, `MeasureTheory.eventuallyConst_smul_set_ae`, `SkewMonoidAlgebra.comapSMul_def`, `Finset.smul_mem_smul_finset_iff`, `CliffordAlgebra.foldr'Aux_foldr'Aux`, `LieAdmissibleAlgebra.toSMulCommClass`, `MulAction.isBlock_iff_smul_eq_or_disjoint`, `Finsupp.comapSMul_single`, `CStarMatrix.inner_toCLM_conjTranspose_left`, `LinearMap.toMatrix'_toLin'`, `MulAction.op_smul_set_stabilizer_subset`, `Subsemiring.smul_mem_pointwise_smul`, `IsUnit.aemeasurable_const_smul_iff`, `Sylow.smul_eq_iff_mem_normalizer`, `Subgroup.pointwise_smul_le_pointwise_smul_iff₀`, `Finset.smul_mem_smul_finset_iff₀`, `MulAction.pow_smul_mod_minimalPeriod`, `TrivSqZeroExt.lift_comp_inrHom`, `NNReal.instPosSMulStrictMono`, `smul_lt_of_lt_one_left`, `MulAction.isBlock_top`, `orbit_subgroup_eq_self_of_mem`, `CategoryTheory.End.smul_left`, `Subsemiring.pointwise_smul_toAddSubmonoid`, `instIsPushoutFractionRingPolynomial_1`, `OrderIso.smulRightDual_apply`, `isCoprime_group_smul_right`, `ModularGroup.tendsto_abs_re_smul`, `Rep.diagonalSuccIsoFree_inv_hom_single_single`, `MDifferentiableAt.clm_prodMap`, `smul_div'`, `Matrix.toAlgEquiv_kroneckerStarAlgEquiv`, `Polynomial.instSMulCommClassElemRootSet`, `Set.exists_smul_inter_smul_subset_smul_inv_mul_inter_inv_mul`, `Module.add_smul`, `MulAction.ofFixingSubgroup.isMultiplyPreprimitive`, `smul_inv_smul₀`, `CategoryTheory.actionAsFunctor_map`, `IsLocalizedModule.map_surjective_iff_localizedModuleMap_surjective`, `Complex.UnitDisc.instIsScalarTower_circle_circle`, `Subgroup.Normal.conj_smul_eq_self`, `Monoid.PushoutI.NormalWord.base_smul_eq_smul`, `closure_smul₀'`, `Set.smul_univ₀`, `Finset.smul_inv_mul_eq_inv_mul_opSMul`, `Pi.intrinsicStar_comul_commSemiring`, `IsUnit.inv_smul`, `Matrix.det_kroneckerMapBilinear`, `Monoid.PushoutI.NormalWord.base_smul_def'`, `Finset.smul_finset_symmDiff`, `SlashInvariantForm.coe_translate`, `Localization.algHom_ext_iff`, `Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap`, `Finset.smul_finset_univ₀`, `measurableEmbedding_const_smul₀`, `Matrix.vecMulBilin_apply`, `HasCompactMulSupport.comp_smul`, `cross_anticomm`, `Subgroup.Normal.conjAct`, `ModularGroup.exists_max_im`, `Finite.finite_mulAction_orbit`, `SubMulAction.ofStabilizer.isPretransitive_iff`, `CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM`, `Subsemiring.smul_bot`, `MulAction.minimalPeriod_eq_one_iff_fixedBy`, `DistribMulAction.toLinearEquiv_symm_apply`, `cross_cross_eq_smul_sub_smul`, `Real.map_matrix_volume_pi_eq_smul_volume_pi`, `TrivSqZeroExt.algHom_ext'_iff`, `MulAction.index_stabilizer`, `Submonoid.coe_pointwise_smul`, `MulAction.instIsPretransitiveElemOrbit_1`, `LocalizedModule.map_injective`, `Monoid.CoprodI.Word.prod_smul`, `NumberField.InfinitePlace.smul_eq_comap`, `IsOpen.iUnion_smul`, `Complex.UnitDisc.instSMulCommClass_circle_left`, `Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv`, `Subgroup.smul_leftQuotientEquiv`, `groupCohomology.isMulCoboundary₂_of_mem_coboundaries₂`, `MulAction.mem_orbit_symm`, `KaehlerDifferential.mulActionBaseChange_smul_add`, `Subgroup.Commensurable.commensurable_conj`, `NumberField.InfinitePlace.smul_mk`, `SubMulAction.stabilizer_of_subMul`, `isCusp_SL2Z_iff'`, `Subgroup.pointwise_smul_def`, `coeSubmodule_differentIdeal_fractionRing`, `QuotSMulTop.map_surjective`, `Ideal.Fiber.lift_residueField_surjective`, `Subgroup.conjAct_pointwise_smul_iff`, `IsCompact.exists_finite_cover_smul`, `Set.smul_set_univ₀`, `MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar`, `Metric.preimage_smul_closedEBall`, `IsFoelner.tendsto_meas_smul_symmDiff`, `nhds_smul₀`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe`, `Matrix.isNilpotent_toLin'_iff`, `unitary.coe_smul`, `RegularWreathProduct.smul_def`, `ModularGroup.im_T_smul`, `MeasureTheory.measure_inv_smul_sdiff`, `smul_ball''`, `Finset.mul_mem_smul_finset_iff`, `MulAction.orbitRel.Quotient.mem_subgroup_orbit_iff`, `Finset.mem_inv_smul_finset_iff`, `Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure`, `MulAction.isInvariantBlock_iff_isFixedBlock`, `ProperSMul.isProperMap_smul_pair`, `Matrix.toLinearEquiv'_symm_apply`, `smul_closedBall_one`, `LinearMap.BilinForm.mul_toMatrix'_mul`, `Subring.pointwise_smul_toAddSubgroup`, `OnePoint.smul_some_eq_ite`, `Subring.coe_pointwise_smul`, `MulAction.IsBlock.orbit_of_normal`, `IsScalarTower.of_smul_one_mul`, `CategoryTheory.PreGaloisCategory.toAut_hom_app_apply`, `InnerProductGeometry.norm_toLp_symm_crossProduct`, `mem_closure_isSwap`, `WithConv.toConv_smul`, `SubMulAction.mem_mul`, `Set.OrdConnected.smul`, `Set.powersetCard.isPretransitive_alternatingGroup`, `FreeMonoid.of_smul`, `Set.smul_set_pi`, `Set.Finite.absorbs_sInter`, `Multiset.smul_prod'`, `CFC.sqrt_map_prod`, `AffineMap.smul_linear`, `Subgroup.leftCoset_cover_const_iff_surjOn`, `SubMulAction.fixingSubgroup_of_insert`, `MeasureTheory.Measure.addHaarScalarFactor_smul_congr`, `MonoidHom.smulOneHom_apply`, `Matrix.det_smul_of_tower`, `NonarchimedeanGroup.exists_openSubgroup_separating`, `Module.Ray.linearEquiv_smul_eq_map`, `Submonoid.smul_mem_pointwise_smul_iff`, `ball_mul`, `SubMulAction.ofFixingSubgroup_carrier`, `Homeomorph.smul_symm_apply`, `IsCompact.div_closedBall`, `MatrixEquivTensor.toFunBilinear_apply`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1`, `groupCohomology.isMulCocycle₁_of_mem_cocycles₁`, `Subgroup.smul_diff_smul'`, `QuotientGroup.eq_class_eq_leftCoset`, `PosSMulMono.nnrat_of_rat`, `HNNExtension.NormalWord.prod_smul`, `Monoid.PushoutI.NormalWord.instFaithfulSMul`, `StarMul.toStarModule`, `IntermediateField.continuousSMul`, `units_smul_eq_self_iff`, `Matrix.toLpLin_symm_pow`, `TensorProduct.prodLeft_tmul`, `denseRange_smul`, `units_smul_eq_neg_iff`, `MulAction.smul_inv_mem_fixedBy_iff_mem_fixedBy`, `Matrix.linfty_opNNNorm_toMatrix`, `MulAction.disjoint_image_image_iff`, `Subgroup.Commensurable.commensurator_mem_iff`, `MonoidHom.transfer_def`, `Finset.smul_univ`, `Matrix.toEuclideanCLM_toLp`, `approxOrderOf.smul_subset_of_coprime`, `isClosedMap_smul`, `MulAction.isPreprimitive_ofFixingSubgroup_conj_iff`, `ProperSMul.toContinuousSMul`, `cross_anticomm'`, `smul_inv'`, `ENNReal.instIsScalarTowerNNReal`, `Set.disjoint_smul_set`, `Pi.intrinsicStar_comul`, `MeasureTheory.innerRegular_map_smul`, `NumberField.InfinitePlace.isUnramified_smul_iff`, `Homeomorph.smulOfNeZero_apply`, `Units.coe_smul`, `Projectivization.cross_mk_of_cross_ne_zero`, `Matrix.toLpLin_one`, `Monoid.PushoutI.NormalWord.prod_summand_smul`, `CFC.nnrpow_map_pi`, `MulAction.toFun_apply`, `SubMulAction.mem_fixingSubgroup_insert_iff`, `isCancelSMul_iff_stabilizer_eq_bot`, `OreLocalization.expand'`, `CategoryTheory.PreGaloisCategory.IsFundamentalGroup.transitive_of_isGalois`, `Algebra.PreSubmersivePresentation.aevalDifferential_toMatrix'_eq_mapMatrix_jacobiMatrix`, `TensorProduct.prodLeft_symm_tmul`, `EisensteinSeries.G2_S_transform`, `smul_coe_set`, `ModularGroup.SL_to_GL_tower`, `QuotientGroup.univ_eq_iUnion_smul`, `Matrix.piLp_ofLp_toEuclideanLin`, `OnePoint.map_smul`, `MeasureTheory.Measure.isHaarMeasure_map_smul`, `Submonoid.smul_sup`, `lieEquivMatrix'_apply`, `leftCoset_eq_iff`, `Set.smul_mem_smul_set_iff₀`, `Homeomorph.smul_apply`, `SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux`, `continuousSMul_closedBall_ball`, `Sylow.orbit_eq_top`, `MulSemiringAction.toAlgEquiv_symm_apply`, `Ideal.Quotient.smul_top`, `Submonoid.le_pointwise_smul_iff₀`, `MulAction.smul_subset_of_set_mem_fixedBy`, `Commute.smul_left_iff`, `LinearMap.minpoly_toMatrix'`, `Submodule.pointwise_smul_toAddSubmonoid`, `List.smul_prod`, `isScalarTower_sphere_sphere_sphere`, `MulAction.toPerm_symm_apply`, `jacobiTheta_S_smul`, `MulAction.isPretransitive_iff_base`, `smul_smul`, `RightCancelMonoid.faithfulSMul`, `RightPreLieAlgebra.toSMulCommClass`, `MulAction.isCoatom_stabilizer_iff_preprimitive`, `Subgroup.leftTransversals.smul_diff_smul`, `GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_range`, `ModularGroup.re_T_smul`, `IsFoelner.mean_smul_eq_mean_smul`, `NNReal.smulCommClass_left`, `OreLocalization.expand`, `SubMulAction.stabilizer_of_subMul.submonoid`, `MulAction.smul_orbit`, `LinearMap.prodEquiv_symm_apply`, `absorbs_iInter`, `Subring.mem_inv_pointwise_smul_iff`, `Matrix.toLpLin_pow`, `Module.ext_iff`, `Set.ncard_smul_set`, `CongruenceSubgroup.IsArithmetic.conj`, `DiscreteTiling.PlacedTile.mem_inv_smul_iff_smul_mem`, `Matrix.isUnit_toLin'_iff`, `Subalgebra.instCovariantClassHSMulLe`, `LinearMap.CompatibleSMul.units`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem`, `Polynomial.adjSylvester_comp_sylveserMap`, `Ideal.ResidueField.liftₐ_comp_toAlgHom`, `HNNExtension.NormalWord.smul_ofGroup`, `Submonoid.pointwise_smul_le_iff₀`, `Matrix.toLin'_mul`, `hasDerivAt_update`, `CongruenceSubgroup.Gamma_cong_eq_self`, `UpperHalfPlane.coe_smul_of_det_pos`, `MulAction.ext_iff`, `AddSubmonoid.pointwise_isCentralScalar`, `op_smul_coe_set`, `SubMulAction.inclusion.toFun_eq_coe`, `Complex.UnitDisc.coe_closedBall_smul`, `Matrix.ofLp_toLpLin`, `div_ball`, `MulAction.zpow_mod_period_smul`, `smul_eq_self_of_preimage_zpow_eq_self`, `Rep.ofMulDistribMulAction_ρ_apply_apply`, `MeasureTheory.MeasurePreserving.smulInvariantMeasure_iterateMulAct`, `OrderIso.smulRight_symm_apply`, `isCoprime_group_smul_left`, `IsQuotientCoveringMap.apply_eq_iff_mem_orbit`, `MDifferentiableOn.clm_prodMap`, `Subgroup.pointwise_isCentralScalar`, `LinearMap.det_toLin'`, `Monoid.CoprodI.Word.mem_smul_iff_of_ne`, `MulActionWithZero.smul_zero`, `CategoryTheory.PreGaloisCategory.toAut_surjective_isGalois`, `Monoid.CoprodI.Word.of_smul_def`, `Representation.norm_ofMulDistribMulAction_eq`, `Matrix.kroneckerMapBilinear_apply_apply`, `MulAction.orbit.eq_or_disjoint`, `NumberField.InfinitePlace.smul_coe_apply`, `Finite.to_properlyDiscontinuousSMul`, `Subgroup.smul_apply_eq_smul_apply_inv_smul`, `Subsemiring.pointwise_central_scalar`, `Matrix.toLinearMapRight'_mul_apply`, `interior_smul`, `Finset.smul_finset_subset_iff₀`, `MulAction.oneEmbedding_isPretransitive_iff`, `measurableSMul₂_iterateMulAct`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_ne_zero`, `Subring.pointwise_smul_subset_iff`, `unitary.smul_mem`, `SubMulAction.disjoint_val_image`, `UpperHalfPlane.modular_S_smul`, `MulAction.isBlock_subgroup'`, `instSMulCommClass_sphere_closedBall_closedBall`, `Subgroup.mem_inv_pointwise_smul_iff₀`, `kroneckerTMulLinearEquiv_one`, `ModularGroup.re_T_inv_smul`, `ContinuousMultilinearMap.prodL_apply`, `Subgroup.normalCore_eq_iInf_conjAct`, `preimage_smul_setₛₗ_of_isUnit_isUnit`, `Metric.preimage_smul_eball`, `Sylow.smul_eq_of_normal`, `hasEigenvector_toLin'_diagonal`, `MulAction.mem_stabilizer_finset`, `IsCompact.mul_closedBall`, `MulAction.IsFixedBlock.orbit`, `LinearMap.toMatrixAlgEquiv'_apply`, `CongruenceSubgroup.isArithmetic_conj_SL2Z`, `Module.Ray.units_smul_of_pos`, `arrowAction_smul`, `MulAction.mem_fixedPoints`, `Orientation.map_eq_det_inv_smul`, `LinearMap.toMatrix'_algebraMap`, `IsUnit.smul_mem_nhds_smul_iff`, `MulAction.IsPartition.of_orbits`, `Cardinal.mk_smul_set`, `LocalizedModule.coe_map_eq`, `HNNExtension.NormalWord.unitsSMul_one_group_smul`, `SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux`, `Set.mem_invOf_smul_set`, `MulAction.stabilizer_smul_eq_stabilizer_map_conj`, `Monoid.PushoutI.NormalWord.prod_base_smul`, `Finset.smul_finset_symmDiff₀`, `AddSubmonoid.smul_mem_pointwise_smul`, `Action.diagonalSuccIsoTensorTrivial_inv_hom_apply`, `ValuationSubring.pointwise_smul_toSubring`, `SubMulAction.nat_card_ofStabilizer_eq`, `Unitary.smul_mem_of_mem`, `instIsLeftCancelSMul_1`, `RootPairing.GeckConstruction.span_range_h'_eq_top`, `IsOpen.dense_iUnion_preimage_smul`, `continuousSMul_sphere_closedBall`, `MulAction.coe_quotient_smul_fixedPoints`, `OreLocalization.zsmul_eq_zsmul`, `AddSubgroup.pointwise_smul_le_iff₀`, `Monoid.CoprodI.Word.cons_eq_smul`, `MulAction.smul_orbit_subset`, `smul_iterate`, `isQuotientCoveringMap_iff_isCoveringMap_and`, `Submonoid.instSMulCommClassSubtypeMemCenter_1`, `Subring.mem_smul_pointwise_iff_exists`, `MulActionHom.coe_one`, `Matrix.toLin'_reindex`, `hasStrictDerivAt_finCons'`, `isScalarTower_closedBall_ball_ball`, `LinearMap.BilinForm.toMatrix'_compLeft`, `Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂`, `hasStrictDerivAt_finCons`, `MulAction.IsTrivialBlock.isBlock`, `Set.subset_smul_set_iff`, `MulAction.orbitRel.Quotient.orbit.coe_smul`, `ContinuousMultilinearMap.piLinearEquiv_apply`, `GradedMonoid.smulCommClass_right`, `MulAction.orbit_smul_subset`, `inv_smul_smul`, `UpperHalfPlane.im_smul`, `MulAction.mem_stabilizer_set_iff_subset_smul_set`, `IsCompact.closedBall_div`, `NumberField.InfinitePlace.isComplex_smul_iff`, `AffineMap.isCentralScalar`, `ball_div`, `DiscreteTiling.PlacedTile.coe_mk_mk`, `OnePoint.IsZeroAt.smul_iff`, `SkewMonoidAlgebra.comapSMul_single`, `instIsCancelSMul`, `LinearMap.toMatrix'_apply`, `ModularGroup.normSq_S_smul_lt_one`, `SubMulAction.inclusion_injective`, `Matrix.toLpLin_toLp`, `ContinuousLinearMap.prodMapL_apply`, `Subsemiring.smul_mem_pointwise_smul_iff₀`, `map_equiv_traceDual`, `HNNExtension.NormalWord.instFaithfulSMul_1`, `MulAction.isPretransitive_compHom`, `UpperHalfPlane.coe_smul`, `MulAction.pow_period_smul`, `MeasureTheory.measure_symmDiff_inv_smul`, `MulAction.smul_set_stabilizer_subset`, `ModularGroup.exists_row_one_eq_and_min_re`, `AddSubmonoid.pointwise_smul_le_iff`, `NNRat.instContinuousSMulOfIsScalarTowerOfRat`, `Unitary.coe_smul`, `SubMulAction.mem_orbit_subMul_iff`, `Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff`, `MulAction.mem_stabilizerSubmonoid_iff`, `Subgroup.mem_smul_pointwise_iff_exists`, `HNNExtension.NormalWord.group_smul_def`, `RelEmbedding.apply_faithfulSMul`, `Equiv.Perm.applyFaithfulSMul`, `MulAction.image_inter_image_iff`, `CStarMatrix.toCLM_apply_single`, `Subring.smul_bot`, `continuousWithinAt_const_smul_iff`, `SubMulAction.val_image_orbit`, `isCoprime_group_smul`, `Circle.instContinuousSMul`, `isHomeomorph_smul`, `mulAutArrow_apply_apply`, `QuotSMulTop.equivQuotTensor_naturality`, `ArithmeticFunction.sum_divisorsAntidiagonal_eq_sum_divisors`, `LinearMap.toMatrix'_symm`, `MulAction.isPretransitive_quotient`, `smul_inv_smul`, `smul_mem_nhds_self`, `Monoid.PushoutI.NormalWord.prod_smul_empty`, `normal_iff_eq_cosets`, `MeasureTheory.Measure.Regular.domSMul`, `isSimplyConnected_smul_set_iff`, `LinearMap.mapMatrix_smul`, `InnerProductGeometry.norm_ofLp_crossProduct`, `AdicCompletion.transitionMap_comp_reduceModIdeal`, `Subsemiring.pointwise_smul_subset_iff`, `Metric.preimage_smul_sphere`, `Subring.smul_closure`, `DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem`, `measurableEmbedding_const_smul`, `IsOpen.leftCoset`, `SubMulAction.mem_one`, `ModularGroup.re_T_zpow_smul`, `MulAction.isPreprimitive_fixingSubgroup_insert_iff`, `QuotientGroup.measurableSMul`, `MeasureTheory.measure_inter_inv_smul`, `MulAction.instIsPretransitiveOfSubsingleton`, `Matrix.kroneckerTMulAlgEquiv_symm_apply`, `continuousWithinAt_const_smul_iff₀`, `Matrix.ofLp_toEuclideanCLM`, `isUnit_smul_iff`, `ergodic_smul_of_denseRange_pow`, `MulAction.mem_stabilizer_set'`, `groupCohomology.isMulCocycle₂_of_mem_cocycles₂`, `CStarMatrix.toCLM_apply_eq_sum`, `IsPGroup.card_orbit`, `op_smul_op_smul`, `stronglyMeasurable_const_smul_iff`, `Equiv.Perm.OnCycleFactors.val_centralizer_smul`, `Submonoid.instSMulCommClassSubtypeMemCenter`, `Matrix.kroneckerTMulStarAlgEquiv_apply`, `MulAction.dense_orbit`, `Subgroup.exists_leftTransversal_of_FiniteIndex`, `ContinuousMultilinearMap.smul_prod_smul`, `Matrix.range_toLin'`, `Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff`, `LinearMap.prodMapLinear_apply`, `MulActionHom.coe_mul`, `Submonoid.mem_inv_pointwise_smul_iff₀`, `smul_le_iff_le_one_left`, `CuspForm.coe_translate`, `MeasureTheory.smul_ae`, `smul_algebraMap`, `LinearMap.mul_toMatrix'`, `continuousAt_const_smul_iff₀`, `IsBaseChange.pi`, `MulAction.zpow_smul_eq_iff_period_dvd`, `MeasureTheory.QuotientMeasureEqMeasurePreimage.smulInvariantMeasure_quotient`, `Commute.smul_right_iff`, `Metric.smul_sphere`, `Matrix.toLpLin_symm_id`, `SubMulAction.ofFixingSubgroup_of_eq_apply`, `Finset.smul_finset_subset_iff`, `Set.iUnion_inv_smul`, `ModularGroup.im_lt_im_S_smul`, `Matrix.isPositive_toEuclideanLin_iff`, `Set.op_smul_inter_nonempty_iff`, `IsClosed.leftCoset`, `Set.natCard_smul_set`, `Subring.instCovariantClassHSMulLe`, `HNNExtension.NormalWord.instFaithfulSMul`, `absorbs_iff_eventually_cobounded_mapsTo`, `Subgroup.instMeasurableConstSMul`, `Submodule.mulRightMap_eq_mulMap_comp`, `Set.powersetCard.mulActionHom_compl_mulActionHom_compl`, `MulAction.pow_smul_eq_iff_minimalPeriod_dvd`, `Metric.preimage_smul_closedBall`, `IsBaseChange.prodMap`, `kroneckerTMulLinearEquiv_mul`, `swap_mem_closure_isSwap`, `QuadraticMap.discr_comp`, `CategoryTheory.PreGaloisCategory.continuousSMul_aut_fiber`, `Subfield.continuousSMul`, `mulAutArrow_apply_symm_apply`, `Equidecomp.refl_toPartialEquiv`, `kroneckerTMulLinearEquiv_symm_kroneckerTMul`, `SubMulAction.nat_card_ofStabilizer_eq_add_one`, `AddSubgroup.relIndex_pointwise_smul`, `LinearMap.lsum_single`, `Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality`, `ConvexCone.smul_mem_iff`, `Units.measurableSMul`, `IsScalarTower.to₂₃₄`, `LinearMap.toMatrix'_mul`, `isFoelner_iff`, `Units.instMeasurableConstSMul`, `MeasureTheory.measure_smul_null`, `MulAction.IsBlock.univ`, `amenable_of_maxFoelner_neBot`, `AddSubmonoid.mem_inv_pointwise_smul_iff₀`, `SubMulAction.coe_mul`, `LieAlgebra.lie_smul`, `IsFoelner.tendsto_meas_smul_symmDiff_smul`, `Fin.partialProd_left_inv`, `Projectivization.mk_eq_mk_iff_crossProduct_eq_zero`, `Matrix.diagonal_toLin'`, `CStarMatrix.toCLM_apply`, `AddSubmonoid.smul_closure`, `ModularGroup.im_T_zpow_smul`, `AddSubgroup.pointwise_smul_toAddSubmonoid`, `smul_closure_orbit_subset`, `Matrix.charpoly_toLin'`, `properSMul_iff_continuousSMul_ultrafilter_tendsto_t2`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive`, `Subsemiring.mem_inv_pointwise_smul_iff₀`, `Matrix.toLin'_pow`, `AddSubgroup.mem_smul_pointwise_iff_exists`, `LieAdmissibleAlgebra.toIsScalarTower`, `RelIso.apply_faithfulSMul`, `instIsLocalizedModuleQuotientSubmoduleLocalizedModuleLocalizationLocalizedToLocalizedQuotient`, `continuousOn_const_smul_iff₀`, `Matrix.toLinAlgEquiv'_apply`, `Matrix.l2_opNNNorm_def`, `MulAction.smul_mem_of_set_mem_fixedBy`, `Finset.card_smul_inter`, `smul_mem_nhds_smul_iff₀`, `HNNExtension.NormalWord.group_smul_head`, `IsScalarTower.left`, `SubMulAction.ENat_card_ofStabilizer_add_one_eq`, `Ideal.isPretransitive_of_isGalois`, `Subgroup.quotientEquivSigmaZMod_apply`, `Ideal.coe_smul_primesOver_mk`, `Matrix.minpoly_toLin'`, `CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isConnected`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem`, `ModularForm.slash_action_eq'_iff`, `PositiveLinearMap.gnsStarAlgHom_apply`, `MulSemiringAction.toRingEquiv_symm_apply`, `smulCommClass_self`, `Subgroup.IsComplement.pairwiseDisjoint_smul`, `one_smul`, `SetLike.forall_smul_mem_iff`, `LinearMap.toMatrix'_intrinsicStar`, `Set.preimage_smul`, `MDifferentiable.clm_prodMap`, `UpperHalfPlane.pos_real_smul_injective`, `IterateMulAct.mk_smul`, `coe_smul_fixedPoints_of_normal`, `cross_apply`, `MulAction.zpow_smul_eq_iff_minimalPeriod_dvd`, `ENNReal.smulCommClass_left`, `Finset.mulDysonETransform_fst`, `Set.powersetCard.mulActionHom_compl_bijective`, `UpperHalfPlane.J_smul`, `IsUnit.aestronglyMeasurable_const_smul_iff`, `IsQuotientCoveringMap.toContinuousConstSMul`, `SlashInvariantForm.slash_action_eqn''`, `LinearMap.toMatrixAlgEquiv'_toLinAlgEquiv'`, `MulAction.IsQuasiPreprimitive.toIsPretransitive`, `kroneckerTMulLinearEquiv_tmul`, `isScalarTower_sphere_sphere_closedBall`, `QuotientGroup.orbit_eq_out_smul`, `Complex.UnitDisc.instSMulCommClass_closedBall_right`, `MulAction.mem_subgroup_orbit_iff`, `Set.preimage_smul_inv`, `IsSMulRegular.of_smul_eq_one`, `vecMulVecBilin_apply_apply`, `isAdjointPair_toLinearMap₂'`, `Matrix.toLin'_apply'`, `QuotSMulTop.map_exact`, `IsOpen.dense_iUnion_smul`, `Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zero`, `Matrix.ker_toLin'_eq_bot_iff`, `LinearMap.vecCons₂_apply`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `MulAction.period_eq_one_iff`, `MulAction.bijective₀`, `inv_smul_lt_iff_of_pos`, `MulSemiringAction.smul_mul`, `UpperHalfPlane.instIsIsometricSMulSpecialLinearGroupFinOfNatNatReal`, `Ideal.isPretransitive_of_isGaloisGroup`, `MulAction.orbitRel_apply`, `Subgroup.conj_smul_le_of_le`, `MulAction.IsPretransitive.of_isScalarTower`, `Set.mem_inv_smul_set_iff`, `Subring.le_pointwise_smul_iff₀`, `MulDistribMulAction.toMulEquiv_symm_apply`, `IsLowerSet.smul_subset`, `Complex.UnitDisc.instIsScalarTower_closedBall`, `LinearMap.BilinForm.mul_toMatrix'`, `cfcₙ_map_prod`, `Set.smul_set_iInter`, `isOpenMap_smul₀`, `CStarMatrix.mul_entry_mul_eq_inner_toCLM`, `Subring.smul_mem_pointwise_smul_iff₀`, `SubMulAction.notMem_val_image`, `Finset.mulDysonETransform.smul_finset_snd_subset_fst`, `Set.smul_set_compl`, `Matrix.coe_toEuclideanCLM_eq_toEuclideanLin`, `AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀`, `Subsemiring.pointwise_smul_def`, `Function.End.smul_def`, `IsPGroup.smul_mul_inv_trivial_or_surjective`, `LeftPreLieAlgebra.ext_iff`, `LinearMap.toMatrixRight'_id`, `leibniz_cross`, `MulAction.orbitZPowersEquiv_symm_apply`, `IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite`, `Subalgebra.smul_mem_pointwise_smul`, `isScalarTower_sphere_sphere_ball`, `inv_smul_le_iff_of_pos`, `Units.smul_inv`, `Subgroup.Commensurable.commensurable_inv`, `ModularGroup.exists_one_half_le_im_smul`, `Subgroup.instIsScalarTowerSubtypeMem`, `MulDistribMulAction.ext_iff`, `IsScalarTower.algebraMap_smul`, `measurableSMul_iterateMulAct`, `NonUnitalCommCStarAlgebra.toStarModule`, `Set.smul_set_sdiff`, `MulAction.instIsPretransitiveElemOrbit`, `LinearMap.prodMapAlgHom_apply_apply`, `smul_closedBall''`, `Subalgebra.inclusion.isScalarTower_right`, `MulAction.orbitRel.Quotient.orbit_mk`, `Submonoid.pointwise_smul_subset_iff`, `MulAction.mem_stabilizer_set`, `MulAction.IsMultiplyPreprimitive.isPreprimitive_ofFixingSubgroup`, `MulAction.surjective₀`, `Subgroup.center.smulCommClass_left`, `UpperHalfPlane.petersson_slash_SL`, `MulAction.pow_smul_eq_iff_period_dvd`, `smul_pi`, `Matrix.ker_diagonal_toLin'`, `MulAction.IsFixedBlock.univ`, `Subsemiring.instSMulCommClassSubtypeMemCenter_1`, `MulAction.mem_stabilizer_finset_iff_smul_finset_subset`, `MulAction.IsPreprimitive.of_prime_card`, `Subgroup.Commensurable.conj`, `MulAction.isMultiplyPreprimitive_iff`, `MulAction.Quotient.mk_smul_out`, `Finsupp.comapSMul_def`, `Submonoid.mem_pointwise_smul_iff_inv_smul_mem`, `IsSMulRegular.pow_iff`, `Set.smul_set_pi_of_isUnit`, `Units.val_smul`, `MulActionHom.map_mem_fixedPoints`, `isScalarTower_sphere_closedBall_ball`, `Subsemiring.pointwise_smul_le_pointwise_smul_iff`, `CategoryTheory.PreGaloisCategory.isPretransitive_of_surjective`, `AddSubmonoid.smul_mem_pointwise_smul_iff₀`, `smul_mem_nhds_smul`, `ModularForm.SL_slash_def`, `Matrix.toLin'_one`, `Commute.smul_right_iff₀`, `smul_finprod'`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset'`, `OnePoint.smul_infty_eq_ite`, `NNReal.smul_def`, `inv_smul_eq_iff₀`, `MultilinearMap.piFamilyₗ_apply`, `le_smul_of_one_le_left`, `Finsupp.comapSMul_apply`, `DistribMulAction.ext_iff`, `Set.inv_smul_set_distrib`, `NonUnitalStarSubalgebra.prod_inf_prod`, `Subgroup.transferTransversal_apply'`, `AddAut.apply_faithfulSMul`, `cfcHom_nnreal_eq_restrict`, `IsOpen.rightCoset`, `Subgroup.continuousSMul`, `NNReal.smulCommClass_right`, `NumberField.InfinitePlace.isReal_smul_iff`, `Subring.pointwise_central_scalar`, `QuotientGroup.instContinuousSMul`, `Algebra.smul_units_def`, `Subgroup.smul_closure`, `UpperHalfPlane.coe_J_smul`, `MulAction.orbitEquivQuotientStabilizer_symm_apply`, `ContinuousAlternatingMap.piLIE_symm_apply_apply`, `endVecAlgEquivMatrixEnd_apply_apply`, `alternatingGroup.exists_mem_stabilizer_smul_eq`, `Subring.pointwise_smul_le_pointwise_smul_iff`, `MulAction.IsPreprimitive.of_isTrivialBlock_base`, `IsOpen.smul`, `AlgebraicIndependent.liftAlgHom_comp_reprField`, `MulAction.isSimpleOrder_blockMem_iff_isPreprimitive`, `Matrix.trace_toLin'_eq`, `MulDistribMulAction.smul_one`, `rightCoset_mem_rightCoset`, `Units.continuousConstSMul`, `invOf_smul_smul`, `Units.smulCommClass'`, `tendsto_const_smul_iff`, `List.smul_prod'`, `Submonoid.pointwise_isCentralScalar`, `Rat.cast_smul_eq_qsmul`, `IsClosed.smul_right_of_isCompact`, `UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero`, `smul_mem_nhds_smul_iff`, `Submodule.smul_mem_iff'`, `PosSMulStrictMono.nnrat_of_rat`, `Units.coe_inv_smul`, `MulActionHom.toQuotient_apply`, `Module.FinitePresentation.linearEquivMapExtendScalars_apply`, `SubMulAction.mem_ofStabilizer_iff`, `MulAction.BlockMem.coe_bot`, `MulAction.isBlock_subgroup`, `ContinuousAlternatingMap.piLinearEquiv_symm_apply`, `SubMulAction.ofStabilizer.snoc_castSucc`, `OnePoint.IsBoundedAt.smul_iff`, `Submonoid.center.smulCommClass_left`, `MulAction.IsPretransitive.of_compHom`, `CategoryTheory.ActionCategory.curry_apply_left`, `Set.iUnion_smul_eq_setOf_exists`, `FixedPoints.mem_subgroup`, `instIsLeftCancelSMul`, `Complex.UnitDisc.coe_smul_closedBall`, `MeasureTheory.smulInvariantMeasure_tfae`, `UpperHalfPlane.pos_real_re`, `DiscreteTiling.PlacedTile.coe_smul`, `SubMulAction.mem_ofFixingSubgroup_insert_iff`, `MulAction.coe_aestabilizer`, `LinearMap.toMatrix'_comp`, `Matrix.toLinearEquiv'_apply`, `LinearMap.isUnit_toMatrix'_iff`, `hasDerivAtFilter_finCons'`, `CategoryTheory.End.smul_right`, `Equiv.Perm.isPretransitive_of_isCycle_mem`, `MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizer`, `ArithmeticFunction.coe_zeta_smul_apply`, `AddAction.toPermHom_apply_symm_apply`, `IsUnit.preimage_smul_set`, `Finset.smul_univ₀'`, `hasDerivWithinAt_finCons'`, `Matrix.toBilin'_comp`, `Matrix.isHermitian_iff_isSymmetric`, `MeasureTheory.smul_mem_ae`, `IsFoelner.mean_smul_eq_mean`, `leftCoset_mem_leftCoset`, `MulAction.ofQuotientStabilizer_mk`, `Subsemiring.instCovariantClassHSMulLe`, `algebraMap.coe_smul'`, `Subring.pointwise_smul_le_iff₀`, `MeasureTheory.measure_inv_smul_symmDiff`, `ergodic_smul_of_denseRange_zpow`, `CategoryTheory.PreGaloisCategory.instIsPretransitiveCarrierObjFintypeCatOfIsConnected`, `CategoryTheory.FintypeCat.Action.isConnected_iff_transitive`, `Subgroup.pointwise_smul_le_iff₀`, `isSMulRegular_of_group`, `Complex.UnitDisc.instSMulCommClass_circle_right`, `Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModule`, `MeasureTheory.ergodicSMul_iterateMulAct`, `AddSubgroup.smul_mem_pointwise_smul`, `Metric.smul_closedBall`, `Metric.smul_eball`, `SlashInvariantForm.slash_action_eqn_SL''`, `Monoid.PushoutI.NormalWord.summand_smul_def'`, `Subgroup.smul_sup`, `Matrix.toEuclideanLin_conjTranspose_eq_adjoint`, `Set.smul_univ`, `ContMDiffAt.clm_prodMap`, `MulAction.zpow_add_period_smul`, `smul_one_smul`, `MulAction.isBlock_iff_disjoint_smul_of_ne`, `Set.smul_set_sdiff₀`, `MeasurableSet.const_smul_of_ne_zero`, `IsLocalizedModule.map_bijective_iff_localizedModuleMap_bijective`, `MulAction.mem_stabilizer_set_iff_smul_set_subset`, `QuotSMulTop.equivQuotTensor_naturality_mk`, `Ideal.ResidueField.algHom_ext_iff`, `Matrix.toLpLinAlgEquiv_apply_apply_ofLp`, `Localization.instSMulCommClassOfIsScalarTower`, `LinearMap.toMatrix'_id`, `Equiv.Perm.instIsPreprimitive`, `Set.smul_set_univ`, `LocalizedModule.mul_by_divBy`, `Projectivization.cross_mk`, `support_comp_inv_smul`, `MulAction.zpowersQuotientStabilizerEquiv_symm_apply`, `IsScalarTower.of_compHom`, `Subgroup.smul_def`, `Submodule.mem_smul_top_iff`, `UpperHalfPlane.ModularGroup_T_zpow_mem_verticalStrip`, `LinearMap.BilinForm.toMatrix'_comp`, `Submonoid.center.smulCommClass_right`, `continuousOn_const_smul_iff`, `Subgroup.instMeasurableSMul`, `mulLinearMap_apply_apply`, `UpperHalfPlane.coe_specialLinearGroup_apply`, `OreLocalization.smul_oreDiv`, `IsUpperSet.smul`, `AlternatingGroup.isPretransitive_of_three_le_card`, `triple_product_eq_det`, `MulAction.mem_fixedPoints_iff_card_orbit_eq_one`, `KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination`, `tangentConeAt_mono_field`, `MulAction.smul_fixedBy`, `MulAction.IsPreprimitive.exists_mem_smul_and_notMem_smul`, `MeasureTheory.measure_smul`, `MulAction.orbit.coe_smul`, `Finset.smul_finset_eq_univ`, `Finset.op_smul_convolution_eq_convolution_smul`, `DiscreteTiling.PlacedTile.smul_mem_smul_iff`, `Monoid.CoprodI.Word.equivPair_head_smul_equivPair_tail`, `Equiv.smulRight_symm_apply`, `Matrix.toLinearMapRight'_apply`, `MulAction.is_two_pretransitive_iff`, `smul_pow`, `Subsemiring.coe_pointwise_smul`, `ContinuousMultilinearMap.piₗᵢ_symm_apply`, `MulAction.orbitZPowersEquiv_symm_apply'`, `CategoryTheory.PreGaloisCategory.IsFundamentalGroup.continuous_smul`, `MeasureTheory.NullMeasurableSet.smul`, `MeasureTheory.measure_inv_smul_union`, `Units.isScalarTower'`, `Set.smul_set_eq_univ`, `LieAlgebra.SpecialLinear.val_single`, `Matrix.ofLp_toEuclideanLin_apply`, `NNReal.instContinuousSMulOfReal`, `Subgroup.smul_inf`, `Monoid.CoprodI.Word.equivPair_smul_same`, `Equidecomp.symm_involutive`, `SubMulAction.ofStabilizer.isMultiplyPretransitive`, `CFC.nnrpow_eq_nnrpow_pi`, `SubMulAction.ofFixingSubgroup.append_right`, `SMulCommClass.of_mul_smul_one`, `Matrix.mulVecBilin_apply`, `nat_smul_eq_nsmul`, `MultilinearMap.piFamily_smul`, `lieEquivMatrix'_symm_apply`, `Projectivization.smul_def`, `Matrix.proj_diagonal`, `ModularGroup.im_smul_eq_div_normSq`, `MulAction.isPretransitive_of_is_two_pretransitive`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle`, `isOpenMap_smul`, `Submonoid.instCovariantClassHSMulLe`, `mem_own_leftCoset`, `LocalizedModule.map_id`, `IsUnit.smul_uniformity`, `Matrix.linfty_opNorm_toMatrix`, `isSimplyConnected_smul_set₀_iff`, `Subgroup.smul_opposite_image_mul_preimage'`, `CategoryTheory.PreGaloisCategory.isGalois_iff_pretransitive`, `Subring.continuousSMul`, `Module.IsTorsionBySet.isScalarTower`, `SubMulAction.subset_coe_one`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff₀`, `NumberField.InfinitePlace.comap_smul`, `FreeGroup.startsWith.smul_def`, `NNRat.cast_smul_eq_nnqsmul`, `tendsto_const_smul_iff₀`, `Ideal.coe_smul_primesOver_eq_map_galRestrict`, `Matrix.SpecialLinearGroup.toLin'_to_linearMap`, `LinearMap.mul_toMatrix₂'_mul`, `LinearMap.toMatrix₂'_mul`, `MeasureTheory.eventually_nhds_one_measure_smul_diff_lt`, `Finset.smul_convolution_eq_convolution_inv_mul`, `IsUnit.smul_left_cancel`, `OnePoint.smul_infty_def`, `AddSubgroup.smul_mem_pointwise_smul_iff₀`, `EisensteinSeries.tendsto_double_sum_S_act`, `Subsemiring.instSMulCommClassSubtypeMemCenter`, `LinearMap.intrinsicStar_single`, `Module.Basis.map_orientation_eq_det_inv_smul`, `StarSemigroup.toOpposite_starModule`, `triple_product_permutation`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset`, `instSMulCommClass_sphere_ball_ball`, `Group.preimage_smul_set`, `HNNExtension.NormalWord.smul_cons`, `cosetToCuspOrbit_apply_mk`, `SubMulAction.SMulMemClass.coe_subtype`, `Matrix.kroneckerMapBilinear_mul_mul`, `ContMDiff.clm_prodMap`, `SubMulAction.isCentralScalar`, `MulAction.stabilizerEquivStabilizer_one`, `Submonoid.continuousSMul`, `NormedSpace.norm_smul_le`, `RelHom.smul_def`, `MulAction.orbit.pairwiseDisjoint`, `SetLike.GradedMul.toGradedSMul`, `IsUnit.continuousOn_const_smul_iff`, `OnePoint.exists_mem_SL2`, `Monoid.PushoutI.NormalWord.cons_eq_smul`, `LinearEquiv.smulOfNeZero_symm_apply`, `Submonoid.subset_pointwise_smul_iff`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem`, `Subgroup.conjAct_pointwise_smul_eq_self`, `MulAction.IsTopologicallyTransitive.exists_smul_inter`, `SubMulAction.compl_def`, `DistribMulAction.toAddEquiv_symm_apply`, `MulAction.orbit_smul`, `Finset.card_inter_smul`, `HasDerivAtFilter.prodMk`, `ContinuousMultilinearMap.prodL_symm_apply`, `CliffordAlgebra.foldr'Aux_apply_apply`, `le_smul_iff_one_le_left`, `QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last`, `EMetric.preimage_smul_closedBall`, `MulAction.orbit_submonoid_subset`, `LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix'`, `Matrix.toLin_finTwoProd_toContinuousLinearMap`, `Set.smul_inter_nonempty_iff`, `Finset.mulETransformRight_fst`, `MulAction.injective₀`, `orbit_subgroup_eq_rightCoset`, `MulAction.pow_mod_period_smul`, `LinearMap.toMatrixAlgEquiv'_symm`, `AddSubmonoid.mem_inv_pointwise_smul_iff`, `OreLocalization.oreDiv_smul_oreDiv`, `Set.powersetCard.isPreprimitive_perm`, `instIsPushoutFractionRingPolynomial`, `MeasureTheory.measure_inv_smul_inter`, `hasDerivAtFilter_finCons`, `HasStrictDerivAt.prodMk`, `SubMulAction.SMulMemClass.subtype_apply`, `Set.encard_smul_set`, `SubMulAction.coe_one`, `SubMulAction.inclusion.coe_eq`, `lt_smul_of_one_lt_left`, `IsOpen.smul₀`, `Matrix.kroneckerTMulBilinear_apply`, `comp_smul_left`, `RingHom.smulOneHom_apply`, `IsOpen.smul_left`, `Set.powersetCard.isPretransitive_of_isMultiplyPretransitive`, `LinearMap.prodMap_smul`, `Finset.smul_prod`, `SetLike.mk_smul_of_tower_mk`, `Set.inv_op_smul_set_distrib`, `MulAction.one_smul`, `hasEigenvalue_toLin'_diagonal_iff`, `ContinuousLinearMap.prodL_apply`, `IsLocalizedModule.map_injective_iff_localizedModuleMap_injective`, `Sylow.coe_subgroup_smul`, `MeasureTheory.smul_set_ae_eq`, `Set.smul_div_smul_comm`, `MulAction.pow_period_add_smul`, `subset_interior_smul_right`, `IsCyclic.mulAutMulEquiv_symm_apply_symm_apply`, `Matrix.toLpLin_mul`, `MulAction.IsBlock.orbit`, `Matrix.toLin'_submatrix`, `Polynomial.instIsScalarTowerElemRootSet`, `MulSemiringAction.smul_one`, `HasDerivAt.prodMk`, `Subring.pointwise_smul_le_pointwise_smul_iff₀`, `punctured_nhds_smul₀`, `MulAction.pretransitive_iff_subsingleton_quotient`, `MulAction.isTopologicallyTransitive_iff_dense_iUnion`, `cross_dot_cross`, `SetLike.smul_of_tower_def`, `SubMulAction.ofFixingSubgroup_of_singleton_bijective`, `Subsemiring.subset_pointwise_smul_iff`, `MulAction.orbit_eq_iff`, `Equiv.Perm.OnCycleFactors.toPermHom_apply`, `lt_smul_iff_one_lt_left`, `Monoid.PushoutI.NormalWord.of_smul_eq_smul`, `Sylow.smul_subtype`, `Matrix.toEuclideanLin_apply_piLp_toLp`, `Set.powersetCard.isPreprimitive_alternatingGroup`, `continuousSMul_iff_stabilizer_isOpen`, `LieAlgebra.ext_iff`, `hasStrictDerivAt_pi`, `Submonoid.smul_closure`, `AlgEquiv.smul_units_def`, `Sylow.isPretransitive_of_finite`, `ContinuousAlternatingMap.prodLIE_apply`, `Subring.smul_sup`, `Finset.smul_prod'`, `MulAction.subgroup_smul_def`, `threeGPFree_smul_set`, `SubMulAction.ofFixingSubgroupEmpty_equivariantMap_bijective`, `ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le`, `DistribMulAction.smul_zero`, `Module.zero_smul`, `MulDistribMulAction.smul_mul`, `continuousSMul_closedBall_closedBall`, `ModularGroup.T_S_rel`, `Submonoid.instMeasurableConstSMul`, `HasDerivWithinAt.prodMk`, `Set.smul_inter_nonempty_iff'`, `Equiv.swap_smul_self_smul`, `AddSubgroup.coe_pointwise_smul`, `LinearMap.vecEmpty₂_apply`, `IsRightCancelMulZero.faithfulSMul`, `IsUnit.isHomeomorph_smul`, `aemeasurable_const_smul_iff`, `IsGalois.map_fixingSubgroup`, `Matrix.toLinAlgEquiv'_toMatrixAlgEquiv'`, `AddSubmonoid.coe_pointwise_smul`, `IsUnit.smul_tendsto_smul_iff`, `MeasureTheory.measure_preimage_smul`, `MeasureTheory.Measure.instSMulInvariantMeasureSubtypeMemSubmonoidOfIsMulLeftInvariant`, `QuotSMulTop.map_comp`, `AddSubgroup.pointwise_smul_le_pointwise_smul_iff`, `Projectivization.cross_mk_of_ne`, `Matrix.kroneckerTMulAlgEquiv_apply`, `GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range`, `LieAdmissibleAlgebra.ext_iff`, `endVecAlgEquivMatrixEnd_symm_apply_apply`, `IsUnit.smul_bijective`, `properSMul_iff_continuousSMul_ultrafilter_tendsto`, `Matrix.trace_kroneckerMapBilinear`, `Polynomial.rootSet.coe_smul`, `IsometryEquiv.constSMul_apply`, `Matrix.toLinAlgEquiv'_one`, `IsUnit.isClosedMap_smul`, `MulAction.IsMinimal.dense_orbit`, `SubMulAction.map_ofFixingSubgroupUnion_bijective`, `faithfulSMul_iff`, `Subgroup.Commensurable.commensurator'_mem_iff`, `ModularGroup.exists_smul_mem_fd`, `Ideal.pointwise_smul_toAddSubgroup`, `hasDerivAtFilter_pi`, `Set.powersetCard.mulActionHom_singleton_bijective`, `Subgroup.properlyDiscontinuousSMul_of_tendsto_cofinite`, `MulAction.isBlock_iff_smul_eq_of_nonempty`, `CategoryTheory.PreGaloisCategory.mulAction_naturality`, `Finset.card_smul_inter_smul`, `instErgodicSMulMulOppositeOfIsMulRightInvariant`, `Monoid.CoprodI.Word.mem_smul_iff`, `Matrix.toLpLin_symm_comp`, `instSMulCommClass_closedBall_closedBall_ball`, `alternatingGroup.isPretransitive_of_three_le_card`, `SubMulAction.ofFixingSubgroup_of_eq_bijective`, `Complex.UnitDisc.instSMulCommClass_circle_closedBall`, `Monoid.CoprodI.Word.smul_eq_of_smul`, `QuotientGroup.orbit_mk_eq_smul`, `Set.preimage_smul₀`, `SubMulAction.SMulMemClass.subtype_injective`, `NonUnitalCStarAlgebra.toIsScalarTower`, `IsScalarTower.of_commMonoid`, `QuotientGroup.instContinuousConstSMul`, `Equiv.Perm.instIsPretransitive`, `eq_cosets_of_normal`, `Subgroup.transferFunction_apply`, `ModularForm.slash_def`, `ProperSMul.isProperMap_smul_pair_set`, `SubMulAction.smul_mem_iff'`, `Finset.dens_smul_finset`, `hasDerivAt_finCons'`, `Monoid.PushoutI.NormalWord.instFaithfulSMul_2`, `UpperHalfPlane.instContinuousGLSMul`, `MulAction.mem_stabilizer_iff`, `isScalarTower_sphere_ball_ball`, `GradedMonoid.isScalarTower_right`, `MulAction.continuousSMul_compHom`, `smul_uniformity`, `Module.Basis.orientation_unitsSMul`, `CategoryTheory.PreGaloisCategory.IsNaturalSMul.naturality`, `Finset.inv_smul_mem_iff₀`, `Subsemiring.smul_sup`, `MulAction.orbit_nonempty`, `Subgroup.mem_inv_pointwise_smul_iff`, `CategoryTheory.ActionCategory.homOfPair.val`, `CongruenceSubgroup.conj_cong_is_cong`, `LinearMap.BilinForm.toMatrix'_mul`, `AddSubgroup.pointwise_smul_le_iff`, `Set.powersetCard.coe_mulActionHom_compl`, `hasDerivAt_single`, `SubMulAction.not_mem_of_mem_ofFixingSubgroup`, `ModularGroup.im_T_inv_smul`, `Finset.mulETransformRight_snd`, `MeasureTheory.Measure.addHaarScalarFactor_domSMul`, `LinearMap.toMatrix₂'_compl₂`, `MulAction.IsPreprimitive.mk'`, `AddSubmonoid.smul_mem_pointwise_smul_iff`, `MulAction.orbitRel.Quotient.mapsTo_smul_orbit`, `Matrix.toLinAlgEquiv'_symm`, `SlashInvariantFormClass.norm_petersson_smul`, `MulDistribMulAction.toMonoidHomZModOfIsCyclic_apply`, `NonUnitalCommCStarAlgebra.toSMulCommClass`, `MulAction.stabilizer_orbit_eq`, `AddSubgroup.mem_inv_pointwise_smul_iff₀`, `Monoid.PushoutI.NormalWord.prod_smul`, `SubMulAction.val_preimage_orbit`, `smul_invOf_smul`, `absorbent_iff_inv_smul`, `continuous_const_smul_iff₀`, `AddSubmonoid.pointwise_smul_le_pointwise_smul_iff`, `Filter.smul_tendsto_smul_iff`, `UpperHalfPlane.modular_T_zpow_smul`, `CFC.nnrpow_eq_nnrpow_prod`, `Metric.preimage_smul_ball`, `MulAction.isPeriodicPt_smul_iff`, `SubMulAction.IsPreprimitive.isPreprimitive_ofFixingSubgroup_inter`, `NormedGroup.to_isIsometricSMul_left`, `OreLocalization.smul_div_one`, `MeasurableSet.const_smul`, `MulActionHom.oneEmbeddingMap_bijective`, `Subring.subset_pointwise_smul_iff`, `IsUnit.continuousAt_const_smul_iff`, `FreeMonoid.smul_def`, `QuotSMulTop.map_apply_mk`, `Matrix.cramer_smul`, `Finset.op_smul_stabilizer_of_no_doubling`, `ContMDiffWithinAt.clm_prodMap`, `smul_pi₀`, `subset_interior_smul`, `MulAction.isMultiplyPreprimitive_ofStabilizer`, `Subgroup.conj_smul_eq_self_of_mem`, `FreeGroup.Orbit.duplicate`, `Finset.mem_inv_smul_finset_iff₀`, `CategoryTheory.PreGaloisCategory.FiberFunctor.isPretransitive_of_isGalois`, `Set.pairwise_disjoint_smul_iff`, `Set.smul_mem_smul_set_iff`, `Subring.instSMulCommClassSubtypeMemCenter_1`, `NumberField.InfinitePlace.mem_orbit_iff`, `invOf_smul_eq_iff`, `HNNExtension.NormalWord.of_smul_eq_smul`, `Module.Finite.instLinearMapIdSubtypeMemSubmoduleOfIsSemisimpleModule_1`, `totallyBounded_iff_subset_finite_iUnion_nhds_one`, `Set.mem_smul_set_iff_inv_smul_mem`, `IsUnit.measurable_const_smul_iff`, `Set.smul_Icc`, `Set.smul_set_subset_smul_set_iff`, `Subalgebra.continuousSMul`, `lowerClosure_smul`, `exists_bijective_map_powers`, `OrderIso.smulRightDual_symm_apply`, `Set.Infinite.smul_set`, `jacobi_cross`, `SubMulAction.orbitRel_of_subMul`, `DiscreteTiling.PlacedTile.coe_mk_coe`, `Finset.subset_smul_finset_iff₀`, `UpperHalfPlane.pos_real_im`, `Subring.smul_mem_pointwise_smul`, `Subgroup.transferTransversal_apply''`, `Representation.ofMulDistribMulAction_apply_apply`, `WithConv.ofConv_smul`, `MulAction.minimalPeriod_pos`, `Subsemiring.pointwise_smul_le_pointwise_smul_iff₀`, `neg_cross`, `Projectivization.generalLinearGroup_smul_def`, `LocalizedModule.map_mk`, `MeasureTheory.tendsto_measure_smul_diff_isCompact_isClosed`, `isScalarTower_iff_smulCommClass_of_commMonoid`, `aestronglyMeasurable_const_smul_iff₀`, `Monoid.CoprodI.Word.smul_def`, `smul_eq_iff_eq_invOf_smul`, `AddAut.mulLeft_apply_symm_apply`, `LinearMap.det_toMatrix'`, `IsQuotientCoveringMap.isCancelSMul`, `CFC.sqrt_map_pi`, `Subgroup.smul_mem_pointwise_smul`, `SubMulAction.smul_mem_iff`, `smul_eq_iff_eq_inv_smul`, `Absorbs.univ`, `Equidecomp.trans_toPartialEquiv`, `Finset.smul_finset_inter₀`, `eq_inv_smul_iff₀`, `Subgroup.relIndex_pointwise_smul`, `smul_zpow'`, `ModularForm.SL_slash_apply`, `OreLocalization.oreDiv_smul_char`, `MeasureTheory.Measure.addHaarScalarFactor_smul_congr'`, `Subalgebra.pointwise_smul_toSubsemiring`, `ThreeGPFree.smul_set`, `NormedSpace.ext_iff`, `MulAction.smul_mem_fixedBy_iff_mem_fixedBy`, `SubMulAction.mem_ofFixingSubgroup_iff`, `EisensteinSeries.eisSummand_SL2_apply`, `AddSubgroup.le_pointwise_smul_iff`, `Subsemiring.continuousSMul`, `ContinuousMultilinearMap.piₗᵢ_apply`, `TrivSqZeroExt.inl_mul_eq_smul`, `Commute.smul_left_iff₀`, `DualNumber.algHom_ext'_iff`, `Matrix.range_diagonal`, `SubMulAction.isScalarTower`, `Subgroup.quotientEquivSigmaZMod_symm_apply`, `mem_fixingSubgroup_iff`, `SubMulAction.ofFixingSubgroup.isMultiplyPretransitive'`, `MulActionHom.map_mem_fixedBy`, `Monoid.CoprodI.Word.rcons_eq_smul`, `UniformOnFun.continuousSMul_submodule_of_image_bounded`, `continuous_const_smul_iff`, `Group.preimage_smul_setₛₗ`, `Finset.smul_finset_sdiff₀`, `ContinuousLinearMap.prodₗ_apply`, `MulAction.orbit_eq_univ`, `SlashInvariantForm.slash_action_eqn'`, `Subgroup.equivSMul_symm_apply_coe`, `Units.continuousSMul`, `Subgroup.smul_toLeftFun`, `IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1`, `LinearMap.toMatrix₂'_comp`, `NNReal.instSMulPosStrictMono`, `NonUnitalStarSubalgebra.prod_top`, `LinearPMap.closure_inverse_graph`, `instSMulCommClass_sphere_closedBall_ball`, `isOpenMap_smul_of_sigmaCompact`, `ContMDiffOn.clm_prodMap`, `Submonoid.pow_smul_mem_closure_smul`, `ext_iff`, `Matrix.SpecialLinearGroup.toLin'_symm_apply`, `MeasureTheory.smul_set_ae_le`, `LeftPreLieAlgebra.toIsScalarTower`, `Subsemiring.smul_closure`, `isScalarTower_closedBall_closedBall_ball`, `rightCoset_one`, `Set.disjoint_smul_set_left`, `LinearMap.toMatrix'_one`, `LieAlgebra.SpecialLinear.val_singleSubSingle`, `Subsemiring.pointwise_smul_le_iff₀`, `SubMulAction.val_smul_of_tower`, `Matrix.cstar_norm_def`, `EMetric.preimage_smul_ball`, `Monoid.CoprodI.lift_word_ping_pong`, `ModularForm.coe_translate`, `Equiv.Perm.moves_in`, `MulAut.apply_faithfulSMul`, `Set.smul_set_subset_iff₀`, `smul_ball_one`, `UpperHalfPlane.neg_smul`, `cross_cross_eq_smul_sub_smul'`, `Set.disjoint_smul_set_right`, `Equiv.smulRight_apply`, `orbit_subgroup_one_eq_self`, `MulAction.quotient_preimage_image_eq_union_mul`, `MeasureTheory.fundamentalInterior_smul`, `Matrix.toLinearMapRight'_one`, `Matrix.maxGenEigenspace_toLin'_diagonal_eq_eigenspace`, `MulAction.zpow_period_add_smul`, `Set.Finite.absorbs_biInter`, `IsUniformGroup.to_uniformContinuousConstSMul`, `MulAction.IwasawaStructure.is_conj`, `IsSMulRegular.one`, `SlashInvariantFormClass.petersson_smul`, `Subgroup.mem_pointwise_smul_iff_inv_smul_mem`, `smul_finprod_perm`, `AddCommGroup.smul_top_eq_top_of_divisibleBy_int`, `Submodule.topologicalClosure_iSup_map_single`, `MulAction.period_eq_minimalPeriod`, `exists_disjoint_smul_of_isCompact`, `Subalgebra.pointwise_smul_toSubmodule`, `CategoryTheory.PreGaloisCategory.isPretransitive_of_isGalois`, `smul_lt_iff_lt_one_left`, `Matrix.toLpLin_apply`, `EMetric.smul_closedBall`, `properlyDiscontinuousSMul_iff_properSMul`, `Matrix.toLin'_apply`, `QuotSMulTop.map_id`, `RelHom.apply_faithfulSMul`, `KaehlerDifferential.mulActionBaseChange_smul_zero`, `Multiset.smul_prod`, `Units.smul_eq_mul`, `hasDerivAt_pi`, `GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset`, `ModuleCat.sMulCommClass_mk`, `MulAction.is_one_pretransitive_iff`, `hasDerivWithinAt_finCons`, `HNNExtension.NormalWord.prod_smul_empty`, `Finset.smul_prod_perm`, `MulAction.stabilizer_smul_eq_right`, `OpenPartialHomeomorph.unitBallBall_symm_apply`, `MulAction.card_orbit_mul_card_stabilizer_eq_card_group`, `AddSubgroup.le_pointwise_smul_iff₀`, `Sylow.smul_le`, `one_smul_eq_id`, `GrpCat.SurjectiveOfEpiAuxs.τ_symm_apply_fromCoset`, `instSMulCommClass_sphere_sphere_closedBall`, `UpperHalfPlane.contMDiff_smul`, `mem_rightCoset_iff`, `Matrix.l2_opNorm_def`, `Subgroup.smul_bot`, `AddSubgroup.pointwise_smul_def`, `AddSubmonoid.le_pointwise_smul_iff₀`, `Matrix.toEuclideanLin_toLp`, `AddAut.smul_def`, `FixedPoints.mem_submonoid`, `IsFoelner.amenable`, `Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1`, `Ideal.coe_smul_primesOver`, `stronglyMeasurable_const_smul_iff₀`, `IsBaseChange.finitePow`, `Equidecomp.symm_bijective`, `MeasureTheory.measure_union_inv_smul`, `Sylow.smul_def`, `ENNReal.smulCommClass_right`, `HasCompactSupport.comp_smul`, `Matrix.toLin'_toMatrix'`, `ContinuousAlternatingMap.prodLIE_symm_apply`, `Subring.smul_mem_pointwise_smul_iff`, `Set.smul_set_subset_iff_subset_inv_smul_set`, `UpperHalfPlane.isometry_pos_mul`, `DomMulAct.mk_smul_monoidHom_apply`, `PosSMulMono.toPosSMulReflectLE`, `instIsLocalizedModuleLinearMapIdLocalizationLocalizedModuleMapOfFinitePresentation`, `closure_smul`, `instSMulCommClass_closedBall_closedBall_closedBall`, `smul_mem_fixedPoints_of_normal`, `SMul.smul_stabilizer_def`, `Set.smul_set_pi₀'`, `MulAction.isTopologicallyTransitive_iff`, `SetLike.instSMulCommClassSubtypeMem_1`, `CategoryTheory.ActionCategory.hom_as_subtype`, `Subgroup.le_pointwise_smul_iff₀`, `MulAction.injective`, `Monoid.PushoutI.NormalWord.summand_smul_def`, `Equidecomp.symm_toPartialEquiv`, `IsUnit.continuous_const_smul_iff`, `RightPreLieAlgebra.ext_iff`, `Subgroup.smulCommClass_left`, `Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff`, `Additive.addAction_isPretransitive`, `Matrix.kroneckerStarAlgEquiv_apply`, `MulAction.minimalPeriod_eq_card`, `MulAction.mem_stabilizer_finset'`, `MulAction.subsingleton_orbit_iff_mem_fixedPoints`, `Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀`, `AddSubgroup.pointwise_isCentralScalar`, `Projectivization.smul_mk`, `Real.volume_preserving_transvectionStruct`, `mulSupport_comp_inv_smul₀`, `ContinuousAlternatingMap.piLinearEquiv_apply`, `Matrix.toLpLinAlgEquiv_symm_apply`, `MDifferentiableWithinAt.clm_prodMap`, `smul_iterate_apply`, `ModularGroup.SL_neg_smul`, `OpenPartialHomeomorph.unitBallBall_apply`, `Subring.pointwise_smul_toSubsemiring`, `LinearMap.toMatrix'_mulVec`, `MulAction.IsBlockSystem.of_normal`, `MulAction.IsTrivialBlock.smul_iff`, `SetLike.instIsScalarTowerSubtypeMem`, `Set.mem_smul_set_iff_inv_smul_mem₀`, `Set.smul_graphOn`, `MulAction.smul_zpow_fixedBy_eq_of_commute`, `SubMulAction.isScalarTower'`, `MulAction.pretransitive_iff_unique_quotient_of_nonempty`, `approxOrderOf.smul_eq_of_mul_dvd`, `HNNExtension.NormalWord.t_pow_smul_eq_unitsSMul`, `Units.isScalarTower'_left`, `OreLocalization.smul_one_smul`, `MonoidHom.transfer_eq_prod_quotient_orbitRel_zpowers_quot`, `Set.powersetCard.coe_mulActionHom_of_embedding`, `mul_smul`, `instSMulCommClass_sphere_sphere_ball`, `Flag.coe_smul`, `AddSubgroup.index_smul`, `MulAction.IsBlock.of_orbit`, `Matrix.diagonal_comp_single`, `MulAction.ofQuotientStabilizer_smul`, `measurable_const_smul_iff₀`, `Finset.smul_univ₀`, `NonUnitalCStarAlgebra.toSMulCommClass`, `PositiveLinearMap.gnsNonUnitalStarAlgHom_apply`, `SubMulAction.image_inclusion`, `Finset.card_smul_finset`, `Finset.mulETransformLeft_snd`, `Monoid.PushoutI.NormalWord.instFaithfulSMul_1`, `IsUnit.smul`, `MulAction.orbitRel.Quotient.orbit_eq_orbit_out`, `Set.smul_univ₀'`, `mem_fixingSubmonoid_iff`, `instIsOrderedSMulOfIsOrderedMonoid`, `Subgroup.smul_diff'`, `MulAction.Regular.isPretransitive`, `Set.powersetCard.mulActionHom_of_embedding_surjective`, `SubMulAction.ofFixingSubgroup_insert_map_bijective`, `Subalgebra.pointwise_smul_toSubring`, `Set.smul_set_symmDiff₀`, `IsUnit.preimage_smul_setₛₗ`, `InnerProductSpace.symm_toEuclideanLin_rankOne`, `LinearMap.BilinForm.toMatrix'_compRight`, `MulDistribMulAction.toMonoidHom_apply`, `Algebra.Extension.Cotangent.ker_mk`, `CategoryTheory.PreGaloisCategory.instIsPretransitiveAutCarrierVFintypeCatFunctorObjActionFunctorToActionOfIsGalois`, `EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act`, `Finset.mulETransformLeft_fst`, `TrivSqZeroExt.mul_inl_eq_op_smul`, `Ideal.pointwise_smul_toAddSubmonoid`, `Complex.UnitDisc.instIsScalarTower_closedBall_closedBall`, `LinearPMap.IsClosable.graph_closure_eq_closure_graph`, `isBoundedLinearMap_prod_multilinear`, `LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle'`, `Subgroup.IsArithmetic.conj`, `Subgroup.instFaithfulSMulSubtypeMem`, `op_smul_mul`, `Subring.mem_inv_pointwise_smul_iff₀`, `OreLocalization.oreDiv_one_smul`, `ModularGroup.exists_eq_T_zpow_of_c_eq_zero`, `Matrix.rank_vecMulVec`, `Monoid.CoprodI.Word.equivPair_tail_eq_inv_smul`, `GrpCat.SurjectiveOfEpiAuxs.τ_apply_fromCoset'`, `Subsemiring.mem_inv_pointwise_smul_iff`, `le_inv_smul_iff_of_pos`, `MulAction.Quotient.smul_coe`, `hasDerivAt_finCons`, `upperClosure_smul`, `Complex.UnitDisc.coe_circle_smul`, `Set.powersetCard.coe_smul`, `IsOpen.iUnion_preimage_smul`, `CFC.nnrpow_map_prod`, `LinearMap.toMatrixRight'_comp`, `Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul`, `smul_left_cancel_iff`, `Matrix.kroneckerStarAlgEquiv_symm_apply`, `smul_inv`, `IsUnit.isOpenMap_smul`, `MeasureTheory.integral_smul_eq_self`, `orbit_fixingSubgroup_compl_subset`, `UpperHalfPlane.modular_T_smul`, `measurable_const_smul_iff`, `Subgroup.pointwise_smul_toSubmonoid`, `Finset.smul_stabilizer_of_no_doubling`, `Submonoid.smul_bot`, `NonUnitalCommCStarAlgebra.toIsScalarTower`, `NNReal.instIsScalarTowerOfReal`, `IsCusp.smul`, `Set.smul_set_pi₀`, `KaehlerDifferential.mulActionBaseChange_smul_tmul`, `SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent`, `Finset.smul_inv_mul_opSMul_eq_mul_of_doubling_lt_three_halves`, `isCancelSMul_iff_eq_one_of_smul_eq`, `MulAction.mem_stabilizer_finset_iff_subset_smul_finset`, `ModularGroup.smul_eq_lcRow0_add`, `Submodule.span_singleton_group_smul_eq`, `Matrix.SpecialLinearGroup.toLin'_apply`, `Module.Finite.of_isComplemented_codomain`, `nhds_smul`, `Subgroup.mk_smul`, `IsUpperSet.smul_subset`, `CStarMatrix.norm_def`, `MulAction.mem_orbit_self`, `AddSubmonoid.mem_smul_pointwise_iff_exists`, `IsSelfAdjoint.smul_iff`, `Equiv.Perm.OnCycleFactors.centralizer_smul_def`, `Measurable.measurableSMul₂_iterateMulAct`, `MulAction.mapsTo_smul_orbit`, `AlgHom.mulLeftRightMatrix.comp_inv`, `SetLike.instSMulCommClassSubtypeMem_2`, `MulAction.surjective`, `SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_inter`, `instIsPushoutFractionRingMvPolynomial_1`, `Set.subset_smul_set_iff₀`, `int_smul_eq_zsmul`, `LinearMap.toMatrixAlgEquiv'_comp`, `MulAction.smul_orbit_eq_orbit_smul`, `smul_mul'`, `MulAction.mem_fixedBy`, `LinearPMap.IsClosable.existsUnique`, `aemeasurable_const_smul_iff₀`, `CStarMatrix.inner_toCLM_conjTranspose_right`, `SlashInvariantForm.T_zpow_width_invariant`, `AddSubmonoid.pointwise_smul_le_iff₀`, `LieModule.toEnd_matrix`, `MulAction.isBlock_subtypeVal`, `CStarMatrix.toCLM_apply_single_apply`, `MeasureTheory.QuotientMeasureEqMeasurePreimage.covolume_ne_top`, `SubMulAction.coe_pow`, `QuotientGroup.out_conj_pow_minimalPeriod_mem`, `UpperHalfPlane.mdifferentiable_smul`, `eq_inv_smul_iff`, `AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀`, `ModularForm.slash_apply`, `Subsemiring.le_pointwise_smul_iff₀`, `Subgroup.smul_coe`, `Action.FintypeCat.ofMulAction_apply`, `Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply`, `IsClosed.rightCoset`, `continuousAt_const_smul_iff`, `smul_singleton_mem_nhds_of_sigmaCompact`, `IsUnit.continuousWithinAt_const_smul_iff`, `instIsPushoutFractionRingMvPolynomial`, `Finset.convolution_op_smul_eq_convolution_mul_inv`, `Representation.ofMulAction_def`, `smul_le_of_le_one_left`, `AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero`, `instErgodicSMulOfIsMulLeftInvariant`, `UpperHalfPlane.petersson_slash`, `Matrix.spectrum_toLin'`, `IsOpen.exists_smul_mem`, `Subgroup.smul_mem_pointwise_smul_iff`, `Function.End.apply_FaithfulSMul`, `IsClosed.smul`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`ext` 📖	—	`toSMul`	—	—	—
`ext_iff` 📖	mathematical	—	`toSMul`	—	`ext`
`mul_smul` 📖	mathematical	—	`toSMul` `Semigroup.toMul`	—	—

VAdd

Definitions

Name	Category	Theorems
`comp` 📖	CompOp	3 math math: `comp.vaddCommClass`, `comp.vaddCommClass'`, `comp.vaddAssocClass`

VAdd.comp

Definitions

Name	Category	Theorems
`vadd` 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`vaddAssocClass` 📖	mathematical	—	`VAddAssocClass` `VAdd.comp`	—	`vadd_assoc`
`vaddCommClass` 📖	mathematical	—	`VAddCommClass` `VAdd.comp`	—	`VAddCommClass.vadd_comm`
`vaddCommClass'` 📖	mathematical	—	`VAddCommClass` `VAdd.comp`	—	`VAddCommClass.vadd_comm`

VAddAssocClass

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`left` 📖	mathematical	—	`VAddAssocClass` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddMonoid.toAddAction`	—	`AddSemigroupAction.add_vadd`
`of_vadd_zero_add` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `HVAdd.hVAdd` `instHVAdd` `AddZero.toZero`	`VAddAssocClass` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddMonoid.toAddAction`	—	`vadd_eq_add` `add_assoc`
`op_left` 📖	mathematical	—	`VAddAssocClass` `AddOpposite`	—	`IsCentralVAdd.unop_vadd_eq_vadd` `vadd_assoc`
`op_right` 📖	mathematical	—	`VAddAssocClass` `AddOpposite` `AddOpposite.instVAdd`	—	`IsCentralVAdd.unop_vadd_eq_vadd` `AddOpposite.unop_vadd` `vadd_assoc`
`to₁₂₄` 📖	mathematical	—	`VAddAssocClass`	—	`vadd_zero_vadd` `vadd_assoc`
`to₁₃₄` 📖	mathematical	—	`VAddAssocClass`	—	`vadd_zero_vadd` `vadd_assoc`
`to₂₃₄` 📖	mathematical	`HVAdd.hVAdd` `instHVAdd` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	`VAddAssocClass` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction`	—	`vadd_zero_vadd` `vadd_assoc`
`vadd_assoc` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	—

VAddCommClass

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`of_add_vadd_zero` 📖	mathematical	`AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass` `HVAdd.hVAdd` `instHVAdd` `AddZero.toZero`	`VAddCommClass` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddMonoid.toAddAction`	—	`vadd_eq_add` `add_assoc`
`op_left` 📖	mathematical	—	`VAddCommClass` `AddOpposite`	—	`IsCentralVAdd.unop_vadd_eq_vadd` `vadd_comm`
`op_right` 📖	mathematical	—	`VAddCommClass` `AddOpposite`	—	`IsCentralVAdd.unop_vadd_eq_vadd` `vadd_comm`
`vadd_comm` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	—

(root)

Definitions

Name	Category	Theorems
`AddAction` 📖	CompData	2 math math: `SubAddAction.ofFixingAddSubgroup_of_eq_bijective`, `SubAddAction.ofFixingAddSubgroup_of_eq_apply`
`AddSemigroupAction` 📖	CompData	—
`IsCancelSMul` 📖	CompData	8 math math: `Submonoid.instIsCancelSMulSubtypeMem`, `instIsCancelSMulOfIsOrderedCancelSMul`, `isCancelSMul_iff_stabilizer_eq_bot`, `SetLike.instIsCancelSMulSubtypeMem`, `isQuotientCoveringMap_iff_isCoveringMap_and`, `instIsCancelSMul`, `IsQuotientCoveringMap.isCancelSMul`, `isCancelSMul_iff_eq_one_of_smul_eq`
`IsCancelVAdd` 📖	CompData	8 math math: `isAddQuotientCoveringMap_iff_isCoveringMap_and`, `AddSubmonoid.instIsCancelVAddSubtypeMem`, `IsAddQuotientCoveringMap.isCancelVAdd`, `instIsCancelVAddOfIsOrderedCancelVAdd`, `isCancelVAdd_iff_stabilizer_eq_bot`, `isCancelVAdd_iff_eq_zero_of_vadd_eq`, `instIsCancelVAdd`, `SetLike.instIsCancelVAddSubtypeMem`
`IsCentralScalar` 📖	CompData	69 math math: `Matrix.isCentralScalar`, `ZeroAtInftyContinuousMap.instIsCentralScalar`, `Prod.isCentralScalar`, `Function.Embedding.instIsCentralScalar`, `BoundedContinuousFunction.instIsCentralScalar`, `Filter.isCentralScalar`, `NormedAddGroupHom.isCentralScalar`, `ZeroHom.instIsCentralScalar`, `AdicCompletion.instIsCentralScalar`, `LinearMap.instIsCentralScalar`, `Set.isCentralScalar`, `MeasureTheory.AEEqFun.instIsCentralScalar`, `Equiv.isCentralScalar`, `AddSubmonoid.pointwise_isCentralScalar`, `Subgroup.pointwise_isCentralScalar`, `Subsemiring.pointwise_central_scalar`, `AffineMap.isCentralScalar`, `Sum.instIsCentralScalar`, `ValuationSubring.pointwise_central_scalar`, `SeparationQuotient.instIsCentralScalar`, `MeasureTheory.OuterMeasure.instIsCentralScalar`, `Polynomial.isCentralScalar`, `Finset.isCentralScalar`, `AddMonoid.End.isCentralScalar`, `MulOpposite.instIsCentralScalar`, `Option.instIsCentralScalar`, `DoubleCentralizer.instIsCentralScalar`, `OreLocalization.instIsCentralScalar`, `CompactlySupportedContinuousMap.instIsCentralScalar`, `Finsupp.isCentralScalar`, `CStarMatrix.instIsCentralScalar`, `TrivSqZeroExt.isCentralScalar`, `LieSubmodule.Quotient.isCentralScalar`, `Derivation.instIsCentralScalar`, `AddMonoidHom.instIsCentralScalar`, `Subring.pointwise_central_scalar`, `Submonoid.pointwise_isCentralScalar`, `MeasureTheory.Lp.instIsCentralScalar`, `Complex.instIsCentralScalarOfReal`, `Unitization.instIsCentralScalar`, `Submodule.Quotient.isCentralScalar`, `Submodule.isCentralScalar`, `SubMulAction.isCentralScalar`, `PUnit.instIsCentralScalar`, `ContinuousMap.instIsCentralScalar`, `CentroidHom.instIsCentralScalar`, `Ideal.pointwise_central_scalar`, `FreeLieAlgebra.instIsCentralScalar`, `SkewMonoidAlgebra.instIsCentralScalar`, `ContinuousAlternatingMap.instIsCentralScalar`, `RingCon.instIsCentralScalarQuotient`, `ContinuousMultilinearMap.instIsCentralScalar`, `UniformSpace.Completion.instIsCentralScalar`, `MonoidAlgebra.isCentralScalar`, `MvPolynomial.isCentralScalar`, `Con.instIsCentralScalar`, `ContinuousLinearMap.isCentralScalar`, `MeasureTheory.Measure.instIsCentralScalar`, `RestrictScalars.isCentralScalar`, `ULift.instIsCentralScalar`, `AddSubgroup.pointwise_isCentralScalar`, `LieSubalgebra.instIsCentralScalarSubtypeMem`, `AddMonoidAlgebra.isCentralScalar`, `QuadraticAlgebra.instIsCentralScalar`, `ContinuousAffineMap.instIsCentralScalar`, `TensorProduct.instIsCentralScalar`, `AlternatingMap.instIsCentralScalar`, `Submodule.pointwiseCentralScalar`, `CommSemigroup.isCentralScalar`
`IsCentralVAdd` 📖	CompData	14 math math: `Finset.isCentralVAdd`, `AddCommSemigroup.isCentralVAdd`, `PUnit.instIsCentralVAdd`, `AddOpposite.instIsCentralVAdd`, `SeparationQuotient.instIsCentralVAdd`, `Filter.isCentralVAdd`, `SubAddAction.isCentralVAdd`, `UniformSpace.Completion.instIsCentralVAdd`, `Option.instIsCentralVAdd`, `AddOreLocalization.instIsCentralVAdd`, `Prod.isCentralVAdd`, `Sum.instIsCentralVAdd`, `Equiv.isCentralVAdd`, `Set.isCentralVAdd`
`IsLeftCancelSMul` 📖	CompData	5 math math: `instIsLeftCancelSMul_1`, `Submonoid.instIsLeftCancelSMulSubtypeMem`, `instIsLeftCancelSMul`, `SetLike.instIsLeftCancelSMulSubtypeMem`, `IsCancelSMul.toIsLeftCancelSMul`
`IsLeftCancelVAdd` 📖	CompData	5 math math: `instIsLeftCancelVAdd_1`, `AddSubmonoid.instIsLeftCancelVAddSubtypeMem`, `IsCancelVAdd.toIsLeftCancelVAdd`, `instIsLeftCancelVAdd`, `SetLike.instIsLeftCancelVAddSubtypeMem`
`IsScalarTower` 📖	CompData	342 math math: `Submodule.instIsScalarTowerQuotientIdealSubtypeMemTorsionBySetCoe`, `Ideal.Quotient.isScalarTower`, `Nonneg.instIsScalarTower`, `Finset.isScalarTower`, `AlgebraicGeometry.StructureSheaf.instIsScalarTowerCarrierStalkCommRingCatStructurePresheafInCommRingCatCarrierAbPresheafOpensCarrierTopModuleStructurePresheaf`, `QuaternionAlgebra.instIsScalarTower`, `Module.Basis.instIsScalarTower`, `MeasureTheory.Lp.instIsScalarTower`, `NonUnitalNonAssocSemiring.nat_isScalarTower`, `NumberField.RingOfIntegers.inst_isScalarTower`, `Submodule.isScalarTower`, `QuadraticAlgebra.instIsScalarTower`, `Complex.UnitDisc.instIsScalarTower_circle`, `MvPolynomial.isScalarTower_right`, `OrderDual.instIsScalarTower'`, `instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl`, `AddCommGroup.intIsScalarTower`, `NonUnitalSubalgebra.instIsScalarTower'`, `IntermediateField.isScalarTower_mid'`, `ContinuousMap.instIsScalarTower`, `FractionRing.instIsScalarTower`, `AddMonoidAlgebra.isScalarTower_self`, `ContinuousMapZero.instIsScalarTower`, `instIsScalarTowerPolynomial_1`, `MulOpposite.instIsScalarTower`, `instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeComplFractionRing`, `Complex.instIsScalarTowerOfReal`, `AdicCompletion.instIsScalarTower_1`, `ZeroAtInftyContinuousMap.instIsScalarTower`, `Submonoid.isScalarTower`, `Module.Basis.isScalarTower_of_nonempty`, `Finset.isScalarTower''`, `IsScalarTower.opposite_mid`, `IsScalarTower.right`, `TrivSqZeroExt.isScalarTower`, `MvPolynomial.instIsScalarTower`, `Lex.instIsScalarTower''`, `instIsScalarTowerAtPrimeFractionRing_1`, `Lex.instIsScalarTower`, `TensorProduct.isScalarTower_right`, `RightPreLieAlgebra.toIsScalarTower`, `instIsScalarTowerAtPrimeLocalizationAlgebraMapSubmonoidPrimeCompl`, `Ideal.Quotient.tower_quotient_map_quotient`, `KaehlerDifferential.isScalarTower'`, `RingCon.isScalarTower_right`, `Con.instIsScalarTower`, `IntermediateField.isScalarTower`, `Matrix.isScalarTower`, `QuadraticMap.instIsScalarTower`, `AlgebraicGeometry.functionField_isScalarTower`, `IsScalarTower.subsemiring`, `Subalgebra.inclusion.isScalarTower_left`, `IsScalarTower.to₁₃₄`, `DoubleCentralizer.instIsScalarTower`, `Circle.instIsScalarTower`, `instIsScalarTowerAtPrimeLocalizationAlgebraMapSubmonoidPrimeComplFractionRing`, `LinearPMap.instIsScalarTower`, `isScalarTower_closedBall_closedBall_closedBall`, `isScalarTower_sphere_closedBall_closedBall`, `IncidenceAlgebra.instIsScalarTower`, `IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower'`, `KaehlerDifferential.instIsScalarTowerTensorProduct`, `Option.instIsScalarTowerOfSMul`, `LieDerivation.instIsScalarTower`, `Algebra.Extension.instIsScalarTowerH1CotangentOfCotangent`, `Subsemiring.isScalarTower`, `WeierstrassCurve.Affine.CoordinateRing.instIsScalarTowerPolynomial`, `Prod.isScalarTowerBoth`, `Complex.UnitDisc.instIsScalarTower_circle_circle`, `IntermediateField.instIsScalarTowerSubtypeMem`, `AlgebraicGeometry.instIsScalarTowerObjOppositeOpensCarrierTopValStructureSheafInType`, `Module.AEval.instIsScalarTowerOrigPolynomial`, `IntermediateField.isScalarTower_bot`, `SemimoduleCat.Algebra.instIsScalarTowerCarrier`, `Finset.isScalarTower'`, `Algebra.Presentation.instIsScalarTowerCore`, `Polynomial.isScalarTower`, `FiniteField.instIsScalarTowerZModExtension`, `Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure`, `TestFunction.instIsScalarTower`, `IsScalarTower.of_smul_one_mul`, `Units.instIsScalarTower`, `ULift.isScalarTower`, `FractionRing.instIsScalarTower_1`, `Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomial`, `RingQuot.instIsScalarTower`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1`, `IsLocalization.instIsScalarTowerLocalizationAtPrime`, `SeparationQuotient.instIsScalarTower`, `RingCon.instIsScalarTowerQuotient`, `ENNReal.instIsScalarTowerNNReal`, `Module.Basis.isScalarTower_finsupp`, `Subalgebra.isScalarTower_right`, `NonUnitalNonAssocRing.int_isScalarTower`, `Algebra.Extension.instIsScalarTowerRing`, `KaehlerDifferential.isScalarTower_of_tower`, `RatFunc.instIsScalarTowerOfPolynomial_1`, `AddMonoidAlgebra.isScalarTower`, `ModularGroup.SL_to_GL_tower`, `Algebra.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetCoeRingHomAlgebraMap`, `Seminorm.instIsScalarTowerOfReal`, `LieRinehartAlgebra.toIsScalarTower`, `PowerSeries.instIsScalarTower`, `Algebra.Extension.instIsScalarTowerCotangent`, `PUnit.instIsScalarTowerOfSMul`, `Ideal.instIsScalarTowerQuotientHPowKerRingHomAlgebraMapOfNat`, `isScalarTower_sphere_sphere_sphere`, `Algebra.Extension.isScalarTower`, `IsLocalRing.ResidueField.instIsScalarTower_1`, `Ideal.Factors.isScalarTower`, `LinearMap.isScalarTower_of_injective`, `ModularForm.instIsScalarTowerComplex`, `Polynomial.Gal.instIsScalarTowerSplittingField`, `BoundedContinuousFunction.instIsScalarTower_1`, `Algebra.TensorProduct.isScalarTower_right`, `instIsScalarTowerPolynomial`, `instIsScalarTowerUniformOnFun`, `IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap`, `Polynomial.SplittingFieldAux.scalar_tower'`, `normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1`, `instIsScalarTowerAtPrimeFractionRing`, `ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt`, `PolynomialModule.isScalarTower'`, `instIsScalarTowerUniformFun`, `Derivation.instIsScalarTower`, `SkewMonoidAlgebra.instIsScalarTower`, `isScalarTower_closedBall_ball_ball`, `AffineBasis.instIsScalarTower`, `HahnModule.instIsScalarTowerHahnSeries_1`, `ModuleCat.instIsScalarTowerLocalizationCarrierLocalizedModule`, `IsDedekindDomain.FiniteAdeleRing.instIsScalarTower`, `HomogeneousLocalization.instIsScalarTowerSubtypeMemOfNatLocalization`, `Algebra.Generators.instIsScalarTowerRing`, `Representation.instIsScalarTowerMonoidAlgebraAsModule`, `AdjoinRoot.isScalarTower_right`, `CentroidHom.instIsScalarTower`, `Submodule.isScalarTower'`, `MonoidAlgebra.isScalarTower_monoidAlgebra`, `AdicCompletion.instIsScalarTowerQuotientIdealHSMulTopSubmodule`, `IsScalarTower.rat`, `Semigroup.isScalarTower`, `RatFunc.instIsScalarTowerOfIsDomainOfPolynomial`, `Filter.isScalarTower`, `IsScalarTower.subalgebra`, `Submonoid.instIsScalarTowerSubtypeMem`, `WithLp.instIsScalarTower`, `IsScalarTower.op_right`, `WeakBilin.instIsScalarTower`, `IsScalarTower.to₂₃₄`, `normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure`, `Subalgebra.isScalarTower_left`, `WithVal.instIsScalarTower`, `WithVal.instIsScalarTower_1`, `Matrix.Module.instIsScalarTowerForall`, `Submodule.instIsScalarTowerQuotientSpanSingletonSetSubtypeMemTorsionBy`, `LieAdmissibleAlgebra.toIsScalarTower`, `Valuation.HasExtension.instIsScalarTower_valuationSubring'`, `IsScalarTower.of_algebraMap_eq'`, `CyclotomicRing.instIsScalarTowerCyclotomicField`, `IsScalarTower.left`, `SetLike.instIsScalarTower`, `OrderDual.instIsScalarTower''`, `AdjoinRoot.instIsScalarTower`, `RatFunc.instIsScalarTowerPolynomial`, `Real.isScalarTower`, `isScalarTower_sphere_sphere_closedBall`, `PointedContMDiffMap.instIsScalarTowerSomeENatTop`, `IntermediateField.instIsScalarTowerSubtypeMem_1`, `CentroidHom.instIsScalarTower_1`, `Equiv.isScalarTower`, `Complex.UnitDisc.instIsScalarTower_closedBall`, `isScalarTower_sphere_sphere_ball`, `PadicComplex.instIsScalarTowerPadicPadicAlgCl`, `Subgroup.instIsScalarTowerSubtypeMem`, `SMul.comp.isScalarTower`, `ContinuousMultilinearMap.instIsScalarTower`, `Subalgebra.inclusion.isScalarTower_right`, `Ideal.Quotient.isScalarTower_of_liesOver`, `isScalarTower_sphere_closedBall_ball`, `Subalgebra.isScalarTower_mid`, `PolynomialModule.instIsScalarTower`, `TensorProduct.isScalarTower_left`, `Set.isScalarTower`, `Module.End.instIsScalarTower`, `OreLocalization.instIsScalarTower_1`, `RatFunc.instIsScalarTowerOfPolynomial`, `IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace`, `Lex.instIsScalarTower'`, `Algebra.Extension.instIsScalarTowerRing_1`, `PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf`, `Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure`, `ULift.isScalarTower''`, `Rat.instIsScalarTowerRight`, `ValuationSubring.ofPrime_scalar_tower`, `IsScalarTower.of_compHom`, `instIsScalarTowerCyclotomicField`, `IsScalarTower.to₁₂₃`, `LinearMap.instIsScalarTower`, `CuspForm.instIsScalarTowerComplex`, `MatrixModCat.isScalarTower_toModuleCat`, `Matrix.instIsScalarTowerForall`, `Units.isScalarTower'`, `ContinuousLinearMap.isScalarTower`, `IsLocalization.instIsScalarTowerAtPrimeFractionRing`, `Ring.instIsScalarTowerNormalClosure`, `IsLocalizedModule.isScalarTower_module`, `Localization.AtPrime.instIsScalarTower_1`, `Localization.AtPrime.instIsScalarTower`, `IntermediateField.isScalarTower_over_bot`, `Submodule.Quotient.isScalarTower`, `Module.IsTorsionBySet.isScalarTower`, `LocalizedModule.instIsScalarTower`, `RestrictScalars.isScalarTower`, `LieAlgebra.isScalarTower`, `Submodule.restrictScalars.isScalarTower`, `IsScalarTower.of_mclosure_eq_top`, `AddCommMonoid.nat_isScalarTower`, `OrderDual.instIsScalarTower`, `AddGroupSeminorm.isScalarTower`, `PUnit.instIsScalarTower`, `Algebra.TensorProduct.right_isScalarTower`, `MvPowerSeries.instIsScalarTower`, `MvPolynomial.isScalarTower`, `IsScalarTower.of_algebraMap_eq`, `instIsScalarTowerTensorAlgebra`, `LinearEquiv.isScalarTower`, `SkewMonoidAlgebra.isScalarTower_self`, `AlgebraicClosure.instIsScalarTower`, `Matrix.Semiring.isScalarTower`, `Polynomial.instIsScalarTowerElemRootSet`, `IsLocalRing.ResidueField.instIsScalarTower`, `Subfield.instIsScalarTowerSubtypeMem`, `instIsScalarTowerQuotientIdealResidueField`, `IntermediateField.fixedField.isScalarTower`, `Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure`, `NormedAddGroupHom.isScalarTower`, `IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin`, `IsScalarTower.complexToReal`, `Subalgebra.instIsScalarTowerSubtypeMem`, `Filter.isScalarTower''`, `PiTensorProduct.isScalarTower'`, `LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime`, `MeasureTheory.Measure.instIsScalarTower`, `AddMonoid.End.isScalarTower`, `NumberField.RingOfIntegers.instIsScalarTower`, `HahnSeries.instIsScalarTower`, `WithCStarModule.instIsScalarTower`, `NumberField.RingOfIntegers.instIsScalarTower_1`, `NonUnitalCStarAlgebra.toIsScalarTower`, `IsScalarTower.of_commMonoid`, `Unitary.instIsScalarTowerSubtypeMemSubmonoidUnitary`, `isScalarTower_sphere_ball_ball`, `GradedMonoid.isScalarTower_right`, `NonarchAddGroupSeminorm.instIsScalarTowerOfReal`, `CauSeq.instIsScalarTower`, `BoundedContinuousFunction.instIsScalarTower`, `ZeroHom.instIsScalarTower`, `MonoidAlgebra.isScalarTower_self`, `NNRat.instIsScalarTowerRight`, `minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure`, `Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass`, `IsScalarTower.op_left`, `NonUnitalStarSubalgebra.instIsScalarTower`, `NonUnitalSubalgebra.instIsScalarTowerSubtypeMem`, `Unitization.instIsScalarTower`, `HahnModule.instIsScalarTowerHahnSeries`, `isScalarTower_of_section_of_ker_sqZero`, `RatFunc.isScalarTower_liftAlgebra`, `Prod.isScalarTower`, `FractionRing.isScalarTower_liftAlgebra`, `IsScalarTower.to₁₂₄`, `OreLocalization.instIsScalarTower`, `IsScalarTower.subalgebra'`, `isScalarTower_iff_smulCommClass_of_commMonoid`, `instIsScalarTowerLocalizationAlgebraMapSubmonoid`, `Module.End.apply_isScalarTower`, `LieSubalgebra.instIsScalarTowerSubtypeMem`, `MonoidAlgebra.isScalarTower`, `AdicCompletion.instIsScalarTower`, `SubMulAction.isScalarTower`, `SkewPolynomial.instIsScalarTower`, `WeakSpace.instIsScalarTower`, `KaehlerDifferential.instIsScalarTowerTensorProduct_1`, `IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1`, `Quaternion.instIsScalarTower`, `ULift.isScalarTower'`, `Valuation.HasExtension.instIsScalarTower_valuationSubring`, `LeftPreLieAlgebra.toIsScalarTower`, `Algebra.Extension.instIsScalarTowerRing_2`, `TrivSqZeroExt.instIsScalarTower`, `isScalarTower_closedBall_closedBall_ball`, `ContinuousMapZero.instIsScalarTower'`, `CliffordAlgebra.instIsScalarTower`, `Polynomial.isScalarTower_right`, `IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap`, `MeasureTheory.AEEqFun.instIsScalarTower`, `MeasureTheory.SimpleFunc.instIsScalarTower`, `IsLocalization.localization_isScalarTower_of_submonoid_le`, `AddMonoidHom.instIsScalarTower`, `Function.Embedding.instIsScalarTower`, `GroupSeminorm.instIsScalarTowerOfReal`, `ZMod.instIsScalarTower`, `ModuleCat.isScalarTower_of_algebra_moduleCat`, `SchwartzMap.instIsScalarTower`, `ModuleCat.Algebra.instIsScalarTowerCarrier`, `IsScalarTower.of_algebraMap_smul`, `Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1`, `MeasureTheory.OuterMeasure.instIsScalarTower`, `Ideal.Quotient.isScalarTower_right`, `instIsScalarTowerLocalizationAlgebraMapSubmonoidPrimeCompl_1`, `Finsupp.isScalarTower`, `IsScalarTower.nnrat`, `FreeAlgebra.instIsScalarTower`, `LaurentPolynomial.instIsScalarTowerPolynomial`, `SetLike.instIsScalarTowerSubtypeMem`, `IsLocalRing.instIsScalarTowerResidueField`, `SubMulAction.isScalarTower'`, `Units.isScalarTower'_left`, `TensorProduct.isScalarTower`, `CompactlySupportedContinuousMap.instIsScalarTower`, `ContinuousAlternatingMap.instIsScalarTower`, `smooth_functions_tower`, `CentroidHom.isScalarTowerRight`, `Complex.UnitDisc.instIsScalarTower_closedBall_closedBall`, `Sum.instIsScalarTower`, `NonUnitalStarSubalgebra.instIsScalarTower'`, `KaehlerDifferential.instIsScalarTowerTensorProduct_2`, `Subring.instIsScalarTowerSubtypeMem`, `IsScalarTower.of_algHom`, `Filter.isScalarTower'`, `NonUnitalCommCStarAlgebra.toIsScalarTower`, `PiTensorProduct.instIsScalarTower`, `NNReal.instIsScalarTowerOfReal`, `UniformSpace.Completion.instIsScalarTower`, `ContinuousMap.instIsScalarTower_1`, `Set.isScalarTower''`, `Submodule.instIsScalarTower`, `IntermediateField.isScalarTower_mid`, `CStarMatrix.instIsScalarTower`, `AddMonoidAlgebra.vaddAssocClass_addMonoidAlgebra`, `Valuation.HasExtension.instIsScalarTowerInteger`, `Set.isScalarTower'`
`MulDistribMulAction` 📖	CompData	—
`SMulCommClass` 📖	CompData	271 math math: `SetLike.instSMulCommClass`, `LeftPreLieAlgebra.toSMulCommClass`, `OrderDual.instSMulCommClass''`, `Prod.smulCommClass`, `Algebra.TensorProduct.instSMulCommClassTensorProduct`, `Quaternion.instSMulCommClass`, `RingCon.smulCommClass`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1`, `Subring.center.smulCommClass_right`, `Function.Injective.smulCommClass`, `RingCon.instSMulCommClassQuotient`, `ContinuousMapZero.instSMulCommClass`, `Rat.instSMulCommClass`, `ZeroHom.instSMulCommClass`, `IsScalarTower.to_smulCommClass'`, `TwoSidedIdeal.instSMulCommClassMulOppositeSubtypeMem`, `Subring.instSMulCommClassSubtypeMemCenter`, `Algebra.to_smulCommClass`, `SMul.comp.smulCommClass'`, `Matrix.Semiring.smulCommClass`, `Complex.UnitDisc.instSMulCommClass_closedBall_circle`, `Complex.UnitDisc.instSMulCommClass_closedBall_left`, `Filter.smulCommClass`, `instSMulCommClass_sphere_sphere_sphere`, `ConjAct.unitsSMulCommClass'`, `AlgEquiv.apply_smulCommClass'`, `BoundedContinuousFunction.instSMulCommClass_1`, `Set.smulCommClass`, `MeasureTheory.AEEqFun.instSMulCommClass`, `ContinuousLinearMap.applySMulCommClass'`, `LieDerivation.instSMulCommClass`, `Finsupp.smulCommClass`, `Subgroup.center.smulCommClass_right`, `DomMulAct.instSMulCommClassMonoidHom`, `SMulCommClass.of_commMonoid`, `NNRat.instSMulCommClass'`, `NormedAddGroupHom.smulCommClass`, `Module.End.apply_smulCommClass'`, `ConjAct.unitsSMulCommClass`, `HahnSeries.instSMulCommClass`, `MonoidAlgebra.smulCommClass`, `Subgroup.smulCommClass_right`, `Algebra.TensorProduct.sMulCommClass_right`, `BoundedContinuousFunction.instSMulCommClass_2`, `Unitization.instSMulCommClass`, `Sum.instSMulCommClass`, `instSMulCommClassMatrixFinOfNatNatProd`, `Units.smulCommClass_left`, `AddMonoid.nat_smulCommClass'`, `MonoidAlgebra.smulCommClass_self`, `LieAdmissibleAlgebra.toSMulCommClass`, `ConjAct.smulCommClass₀`, `UniformSpace.Completion.instSMulCommClassOfUniformContinuousConstSMul`, `IntermediateField.smulCommClass_left`, `LinearMap.instSMulCommClass`, `Polynomial.instSMulCommClassElemRootSet`, `Submodule.instSMulCommClass`, `CentroidHom.instSMulCommClass_2`, `AddMonoidAlgebra.smulCommClass`, `Matrix.instSMulCommClassForall_1`, `FreeAlgebra.instSMulCommClass`, `Complex.UnitDisc.instSMulCommClass_circle_left`, `MvPolynomial.smulCommClass`, `Function.smulCommClass`, `AddMonoidHom.instSMulCommClass`, `Subfield.smulCommClass_left`, `FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield`, `Finset.smulCommClass_finset`, `SMul.comp.smulCommClass`, `PiTensorProduct.instSMulCommClass`, `SMulCommClass.op_left`, `Finset.smulCommClass_finset''`, `Algebra.TensorProduct.instSMulCommClassTensorProduct_1`, `CompactlySupportedContinuousMap.instSMulCommClass`, `ConjAct.smulCommClass₀'`, `AddMonoidAlgebra.smulCommClass_symm_self`, `ConjAct.smulCommClass'`, `Filter.smulCommClass_filter''`, `Semigroup.opposite_smulCommClass'`, `RightPreLieAlgebra.toSMulCommClass`, `NNReal.smulCommClass_left`, `DomMulAct.instSMulCommClassForall_1`, `instSMulCommClassUniformOnFun`, `Circle.instSMulCommClass_left`, `Filter.smulCommClass_filter`, `OreLocalization.instSMulCommClass`, `Rat.instSMulCommClass'`, `ContinuousLinearMap.smulCommClass`, `RingQuot.instSMulCommClass`, `instSMulCommClass_sphere_closedBall_closedBall`, `DomMulAct.instSMulCommClassDistribMulActionHomId`, `Con.instSMulCommClass`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2`, `Subring.smulCommClass_right`, `Submonoid.instSMulCommClassSubtypeMemCenter_1`, `DomMulAct.instSMulCommClassMulActionHomId`, `Function.Embedding.instSMulCommClass`, `GradedMonoid.smulCommClass_right`, `SMulCommClass.symm`, `BoundedContinuousFunction.instSMulCommClass`, `SMulCommClass.complexToReal`, `MvPolynomial.smulCommClass_right`, `Circle.instSMulCommClass_right`, `QuadraticMap.instSMulCommClass`, `DomMulAct.instSMulCommClassForall_2`, `MeasureTheory.OuterMeasure.instSMulCommClass`, `NonUnitalSubalgebra.instSMulCommClass`, `instSMulCommClassUniformFun`, `Submonoid.instSMulCommClassSubtypeMemCenter`, `Subalgebra.smulCommClass_right`, `Subfield.smulCommClass_right`, `MeasureTheory.Measure.instSMulCommClassDomMulActNNReal`, `CliffordAlgebra.instSMulCommClass`, `LinearEquiv.apply_smulCommClass`, `KaehlerDifferential.instSMulCommClassTensorProduct_1`, `AddGroup.int_smulCommClass'`, `HahnModule.SMulCommClass`, `RingCon.smulCommClass'`, `LieAlgebra.smulCommClass`, `PUnit.instSMulCommClass`, `Subsemiring.center.smulCommClass_right`, `Units.smulCommClass_right`, `Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1`, `ConjAct.smulCommClass`, `TrivSqZeroExt.smulCommClass`, `smulCommClass_self`, `Set.smulCommClass_set`, `Complex.instSMulCommClassOfReal`, `ENNReal.smulCommClass_left`, `PiTensorProduct.smulCommClass'`, `Complex.UnitDisc.instSMulCommClass_closedBall_right`, `CentroidHom.instSMulCommClass_1`, `SemimoduleCat.Algebra.instSMulCommClassCarrier`, `Matrix.smulCommClass`, `SMulCommClass.rat'`, `ContinuousMap.instSMulCommClass_2`, `KaehlerDifferential.instSMulCommClassTensorProduct`, `Set.smulCommClass_set'`, `SMulCommClass.opposite_mid`, `AffineBasis.instSMulCommClass`, `Subgroup.center.smulCommClass_left`, `DomMulAct.instSMulCommClassAddMonoidHom`, `Subsemiring.instSMulCommClassSubtypeMemCenter_1`, `ZeroAtInftyContinuousMap.instSMulCommClass`, `MeasureTheory.Measure.instSMulCommClassNNRealDomMulAct`, `ContinuousLinearMap.applySMulCommClass`, `NNRat.instSMulCommClass`, `Lex.instSMulCommClass'`, `NNReal.smulCommClass_right`, `SMulCommClass.op_right`, `OrderDual.instSMulCommClass'`, `Units.smulCommClass'`, `Submonoid.center.smulCommClass_left`, `CentroidHom.instSMulCommClass`, `AddMonoid.End.smulCommClass`, `Subsemiring.smulCommClass_left`, `LinearEquiv.apply_smulCommClass'`, `Module.End.instSMulCommClass'`, `Module.End.apply_smulCommClass`, `Complex.UnitDisc.instSMulCommClass_circle_right`, `Finset.smulCommClass`, `RootPairing.Equiv.instSMulCommClassAut`, `Submonoid.smulCommClass_left`, `ContinuousMapZero.instSMulCommClass'`, `NonUnitalSubalgebra.instSMulCommClass'`, `Localization.instSMulCommClassOfIsScalarTower`, `Submonoid.center.smulCommClass_right`, `Derivation.instSMulCommClass`, `IsScalarTower.to_smulCommClass`, `Unitary.instSMulCommClassSubtypeMemSubmonoidUnitary`, `ContinuousMap.instSMulCommClass_1`, `PUnit.instSMulCommClass_1`, `DomMulAct.instSMulCommClassForall`, `DomMulAct.instSMulCommClassAddMonoidHom_1`, `SMulCommClass.of_mul_smul_one`, `Filter.smulCommClass_filter'`, `OrderDual.instSMulCommClass`, `Semigroup.opposite_smulCommClass`, `QuadraticAlgebra.instSMulCommClass`, `Prod.smulCommClassBoth`, `Subalgebra.smulCommClass_left`, `MeasureTheory.Lp.instSMulCommClass`, `NonUnitalStarSubalgebra.instSMulCommClass'`, `Subsemiring.instSMulCommClassSubtypeMemCenter`, `instSMulCommClass_sphere_ball_ball`, `Module.End.instSMulCommClass`, `instSMulCommClass`, `Equiv.smulCommClass`, `WithLp.instSMulCommClass`, `AddGroup.int_smulCommClass`, `Subring.center.smulCommClass_left`, `Matrix.instSMulCommClassForall`, `MonoidAlgebra.smulCommClass_symm_self`, `Option.instSMulCommClass`, `CStarMatrix.instSMulCommClass`, `DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp`, `AdjoinRoot.instSMulCommClass`, `DomMulAct.instSMulCommClassAEEqFun_2`, `Ideal.Quotient.smulCommClass'`, `Submonoid.instSMulCommClassSubtypeMem_1`, `DomMulAct.instSMulCommClassAEEqFun_1`, `SeparationQuotient.instSMulCommClass`, `ContinuousMultilinearMap.instSMulCommClass`, `Function.Surjective.smulCommClass`, `SkewMonoidAlgebra.instSMulCommClass`, `OreLocalization.instSMulCommClass_1`, `Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower`, `instSMulCommClass_closedBall_closedBall_ball`, `Complex.UnitDisc.instSMulCommClass_circle_closedBall`, `LinearMap.instSMulCommClassDomMulAct`, `NonUnitalCommCStarAlgebra.toSMulCommClass`, `Ideal.Quotient.smulCommClass`, `IntermediateField.smulCommClass_right`, `instSMulCommClassSubtypeMemSubalgebraIntegralClosure`, `Subring.instSMulCommClassSubtypeMemCenter_1`, `Submonoid.smulCommClass_right`, `isScalarTower_iff_smulCommClass_of_commMonoid`, `ModuleCat.Algebra.instSMulCommClassCarrier`, `Submodule.Quotient.smulCommClass`, `AlternatingMap.instSMulCommClass`, `Polynomial.smulCommClass`, `Submodule.instSMulCommClass_1`, `SkewPolynomial.instSMulCommClass`, `ContinuousAlternatingMap.instSMulCommClass`, `FixedPoints.smulCommClass'`, `Set.smulCommClass_set''`, `SMulCommClass.nnrat`, `instSMulCommClass_sphere_closedBall_ball`, `Subsemiring.smulCommClass_right`, `MeasureTheory.Measure.instSMulCommClass`, `LinearPMap.instSMulCommClass`, `WithCStarModule.instSMulCommClass`, `SchwartzMap.instSMulCommClass`, `ModuleCat.sMulCommClass_mk`, `Submonoid.instSMulCommClassSubtypeMem`, `instSMulCommClass_sphere_sphere_closedBall`, `DomMulAct.instSMulCommClassAEEqFun`, `AdicCompletion.instSMulCommClass`, `ENNReal.smulCommClass_right`, `instSMulCommClassTensorAlgebra`, `instSMulCommClass_closedBall_closedBall_closedBall`, `NonUnitalStarSubalgebra.instSMulCommClass`, `SetLike.instSMulCommClassSubtypeMem_1`, `Subgroup.smulCommClass_left`, `SMulCommClass.nnrat'`, `RootPairing.Equiv.instSMulCommClassMulOppositeAut`, `Submodule.instSMulCommClassSubtypeMemTorsion'`, `Lex.instSMulCommClass''`, `Multiplicative.smulCommClass`, `AddMonoid.nat_smulCommClass`, `instSMulCommClass_sphere_sphere_ball`, `instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra`, `QuaternionAlgebra.instSMulCommClass`, `NonUnitalCStarAlgebra.toSMulCommClass`, `Finset.smulCommClass_finset'`, `AddMonoidAlgebra.smulCommClass_self`, `SMulCommClass.of_mclosure_eq_top`, `IsGaloisGroup.commutes`, `DoubleCentralizer.instSMulCommClass`, `Module.Basis.instSMulCommClass`, `Subring.smulCommClass_left`, `SMulCommClass.rat`, `ContinuousMap.instSMulCommClass`, `SetLike.instSMulCommClassSubtypeMem`, `MeasureTheory.SimpleFunc.instSMulCommClass`, `SetLike.instSMulCommClassSubtypeMem_2`, `TensorProduct.smulCommClass_left`, `AlgEquiv.apply_smulCommClass`, `Lex.instSMulCommClass`, `Subsemiring.center.smulCommClass_left`, `MulOpposite.instSMulCommClass`
`SMulDistribClass` 📖	CompData	2 math math: `NumberField.RingOfIntegers.instSMulDistribClass`, `instSMulDistribClassSubtypeMemSubalgebraIntegralClosure`
`SemigroupAction` 📖	CompData	—
`VAddAssocClass` 📖	CompData	45 math math: `VAddAssocClass.of_mclosure_eq_top`, `AddSemigroup.vaddAssocClass`, `Finset.vaddAssocClass''`, `Lex.instVAddAssocClass'`, `VAddAssocClass.to₁₂₃`, `AddOpposite.instVAddAssocClass`, `VAddAssocClass.opposite_mid`, `Filter.vaddAssocClass`, `VAddAssocClass.to₁₃₄`, `Filter.vaddAssocClass''`, `AddOreLocalization.instVAddAssocClass`, `PUnit.instVAddAssocClassOfVAdd`, `VAddAssocClass.op_right`, `Equiv.vaddAssocClass`, `Finset.vaddAssocClass`, `AddUnits.vaddAssocClass'`, `SubAddAction.vaddAssocClass'`, `VAddAssocClass.left`, `AddOreLocalization.instVAddAssocClass_1`, `VAddAssocClass.op_left`, `VAddAssocClass.of_vadd_zero_add`, `VAddAssocClass.to₂₃₄`, `Set.vaddAssocClass`, `Option.instVAddAssocClassOfVAdd`, `AddSubgroup.instVAddAssocClassSubtypeMem`, `Lex.instVAddAssocClass''`, `AddUnits.vaddAssocClass'_left`, `UniformSpace.Completion.instVAddAssocClass`, `AddSubmonoid.instVAddAssocClassSubtypeMem`, `Lex.instVAddAssocClass`, `OrderDual.instVAddAssocClass`, `Set.vaddAssocClass''`, `AddSubmonoid.vaddAssocClass`, `Prod.vaddAssocClass`, `SubAddAction.vaddAssocClass`, `VAdd.comp.vaddAssocClass`, `Finset.vaddAssocClass'`, `Set.vaddAssocClass'`, `OrderDual.instVAddAssocClass''`, `VAddAssocClass.to₁₂₄`, `AddUnits.instVAddAssocClass`, `WithLp.instVAddAssocClass`, `SeparationQuotient.instVAddAssocClass`, `Filter.vaddAssocClass'`, `OrderDual.instVAddAssocClass'`
`VAddCommClass` 📖	CompData	65 math math: `VAdd.comp.vaddCommClass`, `AddSubgroup.vaddCommClass_left`, `VAdd.comp.vaddCommClass'`, `VAddCommClass.of_add_vadd_zero`, `Filter.vaddCommClass_filter''`, `DomAddAct.instVAddCommClassAEEqFun_2`, `Additive.vaddCommClass`, `DomAddAct.instVAddCommClassForall_1`, `Function.vaddCommClass`, `Option.instVAddCommClass`, `SetLike.instVAddCommClassSubtypeMem_1`, `SetLike.instVAddCommClassSubtypeMem_2`, `AddSubgroup.vaddCommClass_right`, `Lex.instVAddCommClass''`, `AddSubmonoid.instVAddCommClassSubtypeMem_1`, `AddOreLocalization.instVAddCommClass_1`, `PUnit.instVAddCommClass`, `Lex.instVAddCommClass'`, `Prod.vaddCommClass`, `AddSemigroup.opposite_vaddCommClass'`, `AddSubmonoid.instVAddCommClassSubtypeMem`, `OrderDual.instVAddCommClass''`, `Lex.instVAddCommClass`, `ContinuousMap.instVAddCommClass`, `Function.Surjective.vaddCommClass`, `DomAddAct.instVAddCommClassForall_2`, `Finset.vaddCommClass_finset''`, `Set.vaddCommClass`, `AddUnits.vaddCommClass_left`, `Function.Embedding.instVAddCommClass`, `DomAddAct.instVAddCommClassForall`, `Filter.vaddCommClass_filter`, `Finset.vaddCommClass_finset`, `Filter.vaddCommClass`, `SetLike.instVAddCommClassSubtypeMem`, `Equiv.vaddCommClass`, `AddSubmonoid.vaddCommClass_left`, `OrderDual.instVAddCommClass'`, `PUnit.instVAddCommClass_1`, `OrderDual.instVAddCommClass`, `Function.Injective.vaddCommClass`, `VAddCommClass.opposite_mid`, `Set.vaddCommClass_set''`, `AddSemigroup.opposite_vaddCommClass`, `Sum.instVAddCommClass`, `Set.vaddCommClass_set`, `VAddCommClass.of_mclosure_eq_top`, `WithLp.instVAddCommClass`, `Set.vaddCommClass_set'`, `Submodule.vaddCommClass`, `AddUnits.vaddCommClass_right`, `vaddCommClass_self`, `AddOreLocalization.instVAddCommClass`, `VAddCommClass.op_right`, `SeparationQuotient.instVAddCommClass`, `AddOpposite.instVAddCommClass`, `Finset.vaddCommClass_finset'`, `Prod.vaddCommClassBoth`, `UniformSpace.Completion.instVAddCommClassOfUniformContinuousConstVAdd`, `AddSubmonoid.vaddCommClass_right`, `VAddCommClass.op_left`, `VAddCommClass.symm`, `AddUnits.vaddCommClass'`, `Finset.vaddCommClass`, `Filter.vaddCommClass_filter'`

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
`add_vadd_add_comm` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`vadd_vadd_vadd_comm`
`add_vadd_comm` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`VAddCommClass.vadd_comm`
`add_vadd_zero` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `HVAdd.hVAdd` `instHVAdd` `AddZero.toZero`	—	`vadd_eq_add` `VAddCommClass.vadd_comm` `add_zero`
`comp_smul_left` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`SemigroupAction.mul_smul`
`comp_vadd_left` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`AddSemigroupAction.add_vadd`
`eq_inv_smul_iff` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction` `DivInvMonoid.toInv`	—	`smul_inv_smul` `inv_smul_smul`
`eq_neg_vadd_iff` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddAction.toAddSemigroupAction` `SubNegMonoid.toNeg`	—	`vadd_neg_vadd` `neg_vadd_vadd`
`instIsCancelSMul` 📖	mathematical	—	`IsCancelSMul` `SemigroupAction.toSMul` `Monoid.toSemigroup` `RightCancelMonoid.toMonoid` `CancelMonoid.toRightCancelMonoid` `MulAction.toSemigroupAction` `Monoid.toMulAction`	—	`IsLeftCancelMul.mul_left_cancel` `LeftCancelSemigroup.toIsLeftCancelMul` `mul_right_cancel` `RightCancelSemigroup.toIsRightCancelMul`
`instIsCancelVAdd` 📖	mathematical	—	`IsCancelVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddRightCancelMonoid.toAddMonoid` `AddCancelMonoid.toAddRightCancelMonoid` `AddAction.toAddSemigroupAction` `AddMonoid.toAddAction`	—	`IsLeftCancelAdd.add_left_cancel` `AddLeftCancelSemigroup.toIsLeftCancelAdd` `add_right_cancel` `AddRightCancelSemigroup.toIsRightCancelAdd`
`instIsLeftCancelSMul` 📖	mathematical	—	`IsLeftCancelSMul` `SemigroupAction.toSMul` `Monoid.toSemigroup` `LeftCancelMonoid.toMonoid` `MulAction.toSemigroupAction` `Monoid.toMulAction`	—	`IsLeftCancelMul.mul_left_cancel` `LeftCancelSemigroup.toIsLeftCancelMul`
`instIsLeftCancelSMul_1` 📖	mathematical	—	`IsLeftCancelSMul` `SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction`	—	`inv_smul_smul`
`instIsLeftCancelVAdd` 📖	mathematical	—	`IsLeftCancelVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddLeftCancelMonoid.toAddMonoid` `AddAction.toAddSemigroupAction` `AddMonoid.toAddAction`	—	`IsLeftCancelAdd.add_left_cancel` `AddLeftCancelSemigroup.toIsLeftCancelAdd`
`instIsLeftCancelVAdd_1` 📖	mathematical	—	`IsLeftCancelVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddAction.toAddSemigroupAction`	—	`neg_vadd_vadd`
`inv_smul_eq_iff` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction` `DivInvMonoid.toInv`	—	`smul_inv_smul` `inv_smul_smul`
`inv_smul_smul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction` `DivInvMonoid.toInv`	—	`smul_smul` `inv_mul_cancel` `one_smul`
`isScalarTower_iff_smulCommClass_of_commMonoid` 📖	mathematical	—	`SMulCommClass` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `CommMonoid.toMonoid` `Monoid.toMulAction` `IsScalarTower`	—	`IsScalarTower.of_commMonoid` `SMulCommClass.of_commMonoid` `IsScalarTower.left`
`mul_smul_comm` 📖	—	—	—	—	`SMulCommClass.smul_comm`
`mul_smul_mul_comm` 📖	—	—	—	—	`smul_smul_smul_comm`
`mul_smul_one` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	`smul_eq_mul` `SMulCommClass.smul_comm` `mul_one`
`neg_vadd_eq_iff` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddAction.toAddSemigroupAction` `SubNegMonoid.toNeg`	—	`vadd_neg_vadd` `neg_vadd_vadd`
`neg_vadd_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddAction.toAddSemigroupAction` `SubNegMonoid.toNeg`	—	`vadd_vadd` `neg_add_cancel` `zero_vadd`
`one_smul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`MulAction.one_smul`
`one_smul_eq_id` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`one_smul`
`op_smul_eq_mul` 📖	mathematical	—	`MulOpposite` `Mul.toSMulMulOpposite` `MulOpposite.op`	—	—
`op_vadd_eq_add` 📖	mathematical	—	`HVAdd.hVAdd` `AddOpposite` `instHVAdd` `Add.toVAddAddOpposite` `AddOpposite.op`	—	—
`smulCommClass_self` 📖	mathematical	—	`SMulCommClass` `SemigroupAction.toSMul` `Monoid.toSemigroup` `CommMonoid.toMonoid` `MulAction.toSemigroupAction`	—	`SemigroupAction.mul_smul` `mul_comm`
`smul_assoc` 📖	—	—	—	—	`IsScalarTower.smul_assoc`
`smul_div_assoc` 📖	mathematical	—	`DivInvMonoid.toDiv`	—	`div_eq_mul_inv` `smul_mul_assoc`
`smul_eq_mul` 📖	—	—	—	—	—
`smul_inv` 📖	mathematical	—	`DivInvMonoid.toInv` `Group.toDivInvMonoid` `SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `MulAction.toSemigroupAction`	—	`inv_eq_of_mul_eq_one_right` `smul_mul_smul_comm` `IsScalarTower.left` `mul_inv_cancel` `one_smul`
`smul_inv_smul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `Group.toDivInvMonoid` `MulAction.toSemigroupAction` `DivInvMonoid.toInv`	—	`smul_smul` `mul_inv_cancel` `one_smul`
`smul_iterate` 📖	mathematical	—	`Nat.iterate` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `Monoid.toNatPow`	—	`pow_zero` `one_smul` `smul_smul` `pow_succ`
`smul_iterate_apply` 📖	mathematical	—	`Nat.iterate` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `Monoid.toNatPow`	—	`smul_iterate`
`smul_mul'` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `MulDistribMulAction.toMulAction` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`MulDistribMulAction.smul_mul`
`smul_mul_assoc` 📖	—	—	—	—	`smul_assoc`
`smul_mul_smul` 📖	—	—	—	—	`smul_mul_smul_comm`
`smul_mul_smul_comm` 📖	—	—	—	—	`SMulCommClass.symm` `smul_smul_smul_comm`
`smul_one_mul` 📖	mathematical	—	`MulOne.toMul` `MulOneClass.toMulOne` `MulOne.toOne`	—	`smul_mul_assoc` `one_mul`
`smul_one_smul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `MulOne.toOne` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`smul_assoc` `one_smul`
`smul_pow` 📖	mathematical	—	`Monoid.toNatPow` `SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction`	—	`pow_zero` `one_smul` `pow_succ'` `smul_mul_smul_comm` `IsScalarTower.left`
`smul_smul` 📖	mathematical	—	`SemigroupAction.toSMul` `Monoid.toSemigroup` `MulAction.toSemigroupAction` `MulOne.toMul` `MulOneClass.toMulOne` `Monoid.toMulOneClass`	—	`SemigroupAction.mul_smul`
`smul_smul_smul_comm` 📖	—	—	—	—	`smul_assoc` `SMulCommClass.smul_comm`
`smul_zpow` 📖	mathematical	—	`DivInvMonoid.toZPow` `Group.toDivInvMonoid` `SemigroupAction.toSMul` `Monoid.toSemigroup` `DivInvMonoid.toMonoid` `MulAction.toSemigroupAction`	—	`zpow_natCast` `smul_pow` `zpow_negSucc` `smul_inv`
`vaddCommClass_self` 📖	mathematical	—	`VAddCommClass` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddCommMonoid.toAddMonoid` `AddAction.toAddSemigroupAction`	—	`AddSemigroupAction.add_vadd` `add_comm`
`vadd_add_assoc` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`vadd_assoc`
`vadd_add_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`vadd_add_vadd_comm`
`vadd_add_vadd_comm` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`VAddCommClass.symm` `vadd_vadd_vadd_comm`
`vadd_assoc` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`VAddAssocClass.vadd_assoc`
`vadd_eq_add` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `Add.toVAdd`	—	—
`vadd_iterate` 📖	mathematical	—	`Nat.iterate` `HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddMonoid.toNatSMul`	—	`zero_nsmul` `zero_vadd` `vadd_vadd` `succ_nsmul`
`vadd_iterate_apply` 📖	mathematical	—	`Nat.iterate` `HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddMonoid.toNatSMul`	—	`vadd_iterate`
`vadd_neg_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `SubNegMonoid.toAddMonoid` `AddGroup.toSubNegMonoid` `AddAction.toAddSemigroupAction` `SubNegMonoid.toNeg`	—	`vadd_vadd` `add_neg_cancel` `zero_vadd`
`vadd_sub_assoc` 📖	mathematical	—	`SubNegMonoid.toSub` `HVAdd.hVAdd` `instHVAdd`	—	`sub_eq_add_neg` `vadd_add_assoc`
`vadd_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddZero.toAdd` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`AddSemigroupAction.add_vadd`
`vadd_vadd_vadd_comm` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd`	—	`vadd_assoc` `VAddCommClass.vadd_comm`
`vadd_zero_add` 📖	mathematical	—	`AddZero.toAdd` `AddZeroClass.toAddZero` `HVAdd.hVAdd` `instHVAdd` `AddZero.toZero`	—	`vadd_add_assoc` `zero_add`
`vadd_zero_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`vadd_assoc` `zero_vadd`
`zero_vadd` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`AddAction.zero_vadd`
`zero_vadd_eq_id` 📖	mathematical	—	`HVAdd.hVAdd` `instHVAdd` `AddSemigroupAction.toVAdd` `AddMonoid.toAddSemigroup` `AddAction.toAddSemigroupAction` `AddZero.toZero` `AddZeroClass.toAddZero` `AddMonoid.toAddZeroClass`	—	`zero_vadd`

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