Documentation Verification Report

Defs

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

Statistics

MetricCount
DefinitionsHVAdd, hVAdd, VAdd, vadd, VSub, vsub, instHVAdd, «term_+ᵥ_», «term_-ᵥ_»
9
TheoremsinstNonempty, ext, ext_iff, eq_one, eq_zero, ext, ext_iff, instNonempty, add_dite, add_ite, dite_add, dite_add_dite, dite_div, dite_div_dite, dite_mul, dite_mul_dite, dite_sub, dite_sub_dite, div_dite, div_ite, ite_add, ite_add_ite, ite_div, ite_div_ite, ite_mul, ite_mul_ite, ite_sub, ite_sub_ite, mul_dite, mul_ite, sub_dite, sub_ite
32
Total41

HVAdd

Definitions

NameCategoryTheorems
hVAdd 📖CompOp
1132 mathmath: Set.ncard_vadd_set, AddAction.mem_stabilizer_set_iff_subset_vadd_set, Set.iUnion_vadd, ball_sub, AffineIsometryEquiv.pointReflection_apply, Metric.infEDist_vadd, Metric.vadd_closedBall, HahnModule.support_smul_subset_vadd_support', EuclideanGeometry.dist_smul_vadd_sq, MeasureTheory.vaddInvariantMeasure_iff, Fintype.piFinset_vadd_finset, IsOpen.vadd_left, DomAddAct.mk_vadd_indicatorConstLp, AddAction.isTopologicallyTransitive_iff_dense_iUnion_preimage, Finset.vadd_nonempty_iff, Equiv.coe_vaddConst, AddUnits.vadd_def, Measurable.vadd, Set.vadd_singleton, AddAction.IsTrivialBlock.vadd_iff, add_vadd_comm, AddSubgroup.vadd_opposite_image_add_preimage', DirectSum.Gmodule.smulAddMonoidHom_apply_of_of, EuclideanGeometry.reflection_orthogonal_vadd, Set.vadd_mem_vadd, Submodule.vadd_def, Set.vadd_set_iUnion₂, Equiv.coe_constVSub_symm, add_vadd_zero, fderivWithin_comp_add_left, dist_vadd, UniformSpace.Completion.vadd_def, rank_le_card_isVisible, AddAction.isPeriodicPt_vadd_iff, MeasureTheory.StronglyMeasurable.vadd_const, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'', MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum, AffineSubspace.sSameSide_vadd_right_iff, Filter.vadd_le_vadd, ContinuousAt.vadd, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Filter.mem_vadd, IsOpen.iUnion_preimage_vadd, AffineSubspace.setOf_sSameSide_eq_image2, AffineSubspace.map_pointwise_vadd, MeasureTheory.vadd_ae, Set.vadd_set_subset_vadd, AddOpposite.unop_vadd_eq_unop_vadd_unop, IsUpperSet.vadd, AddAction.exists_vadd_eq, Homeomorph.vadd_symm_apply, AffineEquiv.constVAdd_apply, AddAction.nsmul_vadd_mod_minimalPeriod, Set.vadd_set_inter_subset, sub_add_vsub_comm, rightAddCoset_zero, HahnModule.coeff_single_smul_vadd, AddAction.zsmul_period_add_vadd, nhds_vadd, Finset.vadd_finset_eq_univ, Convex.vadd, Finset.neg_op_vadd_finset_distrib, SetLike.vadd_of_tower_def, AddAction.mapsTo_vadd_orbit, image_vadd_setₛₗ, vadd_eq_vadd_iff_neg_add_eq_vsub, Option.vadd_some, vadd_vsub_assoc, Finset.vadd_eq_empty, vadd_mem_fixedPoints_of_normal, vadd_eq_self_of_preimage_zsmul_eq_self, AddAction.isTopologicallyTransitive_iff, rightAddCoset_mem_rightAddCoset, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, Finset.vadd_mem_vadd, Filter.EventuallyEq.fun_const_vadd, QuotientAddGroup.univ_eq_iUnion_vadd, AddCommute.vadd_left, Homeomorph.vaddConst_apply, Filter.pure_vadd_pure, Dense.vadd, Set.IsPWO.vadd, MeasureTheory.IsAddFundamentalDomain.sum_restrict, derivWithin_comp_const_sub, Set.iUnion_neg_vadd, vadd_right_mem_affineSpan_pair, MeasureTheory.IsAddFundamentalDomain.exists_ne_zero_vadd_eq, AddConstMap.coe_addLeftHom_apply, mem_const_vadd_affineSegment, Set.vadd_mem_vadd_set, ContinuousVAdd.continuous_vadd, AffineSubspace.wOppSide_smul_vsub_vadd_left, toColex_vadd, Set.vadd_subset_iff, IsAddUnit.aemeasurable_const_vadd_iff, Set.vadd_subset_vadd, Fintype.piFinset_vadd, vsub_vadd_comm, AEMeasurable.const_vadd, toDual_vadd', Sbtw.vadd_const, Inseparable.vadd, Set.vadd_inter_subset, Set.mem_vadd_set, ContinuousMap.vadd_comp, iteratedFDerivWithin_comp_add_right', MeasureTheory.integral_vadd_eq_self, Finset.coe_vadd_finset, vadd_sub_assoc, SetLike.val_vadd_of_tower, AddAction.Supports.vadd, AddOreLocalization.vadd_oreSub_zero, 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, Finset.vadd_finset_singleton, IsLowerSet.vadd_subset, SetLike.val_vadd, smul_vsub_rev_vadd_mem_affineSpan_pair, tendsto_const_vadd_iff, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, affineSpan_singleton_union_vadd_eq_top_of_span_eq_top, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, VAddCon.vadd, add_vadd_add_comm, Finset.add_singleton, Measurable.vadd_const, Finset.vadd_empty, AddAction.Quotient.vadd_coe, Set.op_vadd_set_add_eq_add_vadd_set, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, threeAPFree_vadd_set, Finset.card_vadd_le, Finset.vadd_finset_univ, ContinuousOn.vadd, IsometryEquiv.constVSub_symm_apply, EuclideanGeometry.angle_vadd_const, isLinearSet_iff, Finset.support_vaddAntidiagonal_subset_vadd, AddAction.Quotient.coe_vadd_out, vadd_vadd, FreeAddMonoid.vadd_def, AffineSubspace.sOppSide_vadd_right_iff, Finset.vadd_addConvolution_eq_addConvolution_neg_add, MeasureTheory.measure_neg_vadd_inter, Set.MapsTo.vadd_set, Pi.vadd_def', AffineIndependent.vadd, collinear_iff_of_mem, IsOpen.left_addCoset, AddSubmonoid.nsmul_vadd_mem_closure_vadd, AddAction.IsBlock.translate, 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, AddActionSemiHomClass.map_vaddₛₗ, DirectSum.Gmodule.of_smul_of, set_vadd_closure_subset, Set.op_vadd_set_subset_add, Set.vadd_set_univ_pi, vsub_vadd_eq_vsub_sub, IsLowerSet.vadd, EuclideanGeometry.orthogonalProjection_apply_mem, toLex_vadd', AffineBasis.coe_vadd, AddAction.isPreprimitive_ofFixingAddSubgroup_conj_iff, AddAction.orbitZMultiplesEquiv_symm_apply', VAddCommClass.vadd_comm, Set.sInter_vadd_subset, mem_rightAddCoset, Finset.inter_vadd_subset, AddAction.orbitZMultiplesEquiv_symm_apply, Function.Embedding.vadd_apply, vadd_assoc, Finset.weightedVSubOfPoint_vadd, AffineSubspace.smul_vsub_vadd_mem, Finset.mem_vadd, nndist_vadd_cancel_right, UniformContinuous.const_vadd, Set.vadd_nonempty, Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone, Set.iInter₂_vadd_subset, Finset.image_vadd_distrib, Set.vadd_set_pi_of_isAddUnit, MeasureTheory.measure_preimage_vadd_of_nullMeasurableSet, SubAddAction.vadd_mem, MeasureTheory.AEStronglyMeasurable.vadd, MeasureTheory.AEStronglyMeasurable.vadd_const, AddAction.mem_stabilizer_iff, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, ofColex_vadd', Set.OrdConnected.vadd, Finset.mem_vaddAntidiagonal, Filter.vadd_tendsto_vadd_iff, ContinuousMap.coe_vadd, IsCompact.vadd_set, AddAction.isBlock_iff_vadd_eq_vadd_of_nonempty, sbtw_vadd_const_iff, IsAddUnit.preimage_vadd_setₛₗ, MeasureTheory.IsAddFundamentalDomain.restrict_restrict, Set.neg_op_vadd_set_distrib, AddCommute.vadd_right, vadd_vsub_eq_sub_vsub, iteratedFDerivWithin_comp_add_left, Set.vadd_sub_vadd_comm, Set.pairwise_disjoint_vadd_iff, ofLex_vadd, AddAction.isBlock_iff_vadd_eq_of_nonempty, UpperHalfPlane.vadd_re, Filter.vadd_mem_vadd, MeasureTheory.IsAddFundamentalDomain.vadd_of_comm, Filter.bot_vadd, Finset.vadd_subset_iff, affinity_unitClosedBall, MeasureTheory.measurePreserving_vadd, 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, Filter.vadd_neBot_iff, ContinuousAffineMap.vadd_toAffineMap, DomAddAct.vadd_Lp_add, AddSemigroupAction.add_vadd, Filter.Tendsto.vadd_const, Function.extend_vadd, AddOreLocalization.oreSub_eq_iff, EuclideanGeometry.orthogonalProjection_apply', MeasureTheory.measure_vadd, Set.inter_vadd_union_subset_union, DirectLimit.vadd_def, Finset.union_vadd_inter_subset_union, Finset.vadd_inter_subset, Metric.preimage_vadd_ball, Filter.NeBot.vadd_filter, op_vadd_add, Set.vadd_set_insert, Filter.Tendsto.const_vadd, Set.vadd_set_eq_empty, AddAction.stabilizer_vadd_eq_right, AddAction.IsTopologicallyTransitive.exists_vadd_inter, vadd_add_vadd, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, toDual_vadd, ofMul_vadd, Finset.card_vadd_finset, Metric.vadd_ball, Set.vadd_set_range, MeasureTheory.IsAddFundamentalDomain.nullMeasurableSet_vadd, PUnit.vadd_eq, dist_vadd_cancel_right, Set.add_subset_iff_left, Finset.op_vadd_finset_subset_add, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, DirectSum.GdistribMulAction.smul_zero, Set.vadd_mem_vadd_set_iff, FreeAddMonoid.ofList_vadd, IsCentralVAdd.unop_vadd_eq_vadd, Finset.vadd_finset_symmDiff, IsClosed.vadd_right_of_isCompact, Measurable.fun_const_vadd, Set.vadd_Icc, AffineSpace.asymptoticNhds_vadd_pure, Filter.Germ.coe_vadd', Finset.vadd_finset_inter, vadd_eq_iff_eq_neg_vadd, IsAddFoelner.mean_vadd_eq_mean_vadd, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, MeasureTheory.isAddRightInvariant_map_vadd, Set.toFinset_vadd_set, IsSemilinearSet.vadd, Set.Nonempty.vadd, vadd_zero_vadd, convexHull_vadd, EMetric.infEdist_vadd, 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, UniformSpace.Completion.coe_vadd, Metric.preimage_vadd_closedEBall, Set.image_op_vadd, isOpenMap_vadd, Finset.vadd_union, Set.vadd_iInter₂_subset, Finset.addDysonETransform_snd, AddAction.vadd_fixedBy, Set.mem_vadd, Finset.vadd_finset_subset_iff, MeasureTheory.measure_neg_vadd_symmDiff, Finset.vadd_finset_nonempty, AffineSubspace.coe_pointwise_vadd, AffineEquiv.map_vadd, vadd_vsub_vadd_cancel_right, AffineSubspace.wSameSide_vadd_left_iff, Set.union_vadd_inter_subset_union, Fin.partialSum_left_neg, MeasurableConstVAdd.measurable_const_vadd, AddOpposite.op_vadd, mem_vadd_const_affineSegment, Set.Finite.toFinset_vadd_set, Set.vadd_set_singleton, AddAction.image_inter_image_iff, AddTorsor.vadd_vsub', vadd_mem_affineSpan_of_mem_affineSpan_of_mem_vectorSpan, continuousAt_const_vadd_iff, AffineMap.vadd_linear, isClosedMap_vadd, IsAddUnit.vadd_tendsto_vadd_iff, ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_self, MeasurableVAdd₂.measurable_vadd, Set.image2_vadd, AddAction.Quotient.mk_vadd_out, map_vadd, Set.vadd_iInter_subset, Finset.vadd_finset_def, AddAction.IsBlock.pairwiseDisjoint_range_vadd, measurable_const_vadd_iff, IsAddUnit.preimage_vadd_set, ContinuousWithinAt.vadd, Set.image_vadd, IsUpperSet.vadd_subset, IsCentralVAdd.op_vadd_eq_vadd, ProperVAdd.isProperMap_vadd_pair, Filter.Tendsto.const_vadd_asymptoticNhds, AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply, mem_fixingAddSubmonoid_iff, arrowAddAction_vadd, MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum, smul_vsub_vadd_mem_affineSpan_pair, Pi.vadd_def, 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, AddUnits.val_vadd, AddSubgroup.vadd_opposite_add, Set.vadd_univ, MeasureTheory.StronglyMeasurable.vadd, AddGroup.preimage_vadd_set, AffineMap.vadd_lineMap, op_vadd_coe_set, Set.vadd_graphOn_univ, affinity_unitBall, isSimplyConnected_vadd_set_iff, MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'', Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Set.vadd_set_eq_univ, AddAction.surjective, AmpleSet.vadd, AddAction.IsTrivialBlock.vadd, Set.vadd_set_subset_vadd_set_iff, VAddMemClass.vadd_mem, Metric.vadd_sphere, Finset.add_subset_iff_right, Metric.preimage_vadd_sphere, StrictConvex.affinity, MeasureTheory.mem_addFundamentalInterior, AddOpposite.unop_vadd, op_vadd_op_vadd, iteratedFDerivWithin_comp_sub, Set.image_vadd_distrib, AddAction.orbit.coe_vadd, Finset.singleton_vadd_singleton, differentiableWithinAt_comp_sub, Sum.vadd_inr, vadd_ball_zero, vadd_preimage_set_subset, EuclideanGeometry.orthogonalProjection_vadd_eq_self, MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum', Filter.map₂_vadd, AEMeasurable.vadd_const, MeasureTheory.IsAddFundamentalDomain.iUnion_vadd_ae_eq, MeasureTheory.IsAddFundamentalDomain.pairwise_aedisjoint_of_ac, AddAction.nsmul_vadd_eq_iff_minimalPeriod_dvd, ofAdd_smul, Finset.Nonempty.vadd, VAddAssocClass.vadd_assoc, Set.vadd_inter_nonempty_iff', MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum', IsClosed.vadd, AddCon.vadd, Finset.mem_vadd_finset, SubAddAction.vadd_mem', DomAddAct.norm_vadd_Lp, edist_vadd_left, AffineIsometryEquiv.coe_vaddConst, Set.preimage_vadd_neg, Measurable.const_vadd, MeasureTheory.measure_vadd_eq_zero_iff, interior_vadd, mem_leftAddCoset_iff, signedDist_vadd_left_swap, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum, mem_rightAddCoset_iff, Set.mem_vaddAntidiagonal, AddAction.orbitRel.Quotient.mapsTo_vadd_orbit, Finset.add_mem_vadd_finset_iff, AddAction.vadd_orbit_eq_orbit_vadd, QuotientAddGroup.sound, AddAction.IsBlock.not_vadd_set_ssubset_vadd_set, Pi.vadd_comp, EuclideanGeometry.reflection_apply_of_mem, isProperLinearSet_iff, Set.vadd_set_prod, AddAction.vadd_orbit, AddAction.minimalPeriod_eq_card, Set.iUnion_op_vadd_set, AddGroup.preimage_vadd_setₛₗ, MeasureTheory.SimpleFunc.vadd_apply, Finset.vadd_finset_subsetSum_subset_subsetSum_insert, Filter.vadd_le_vadd_left, AddAction.zsmul_vadd_eq_iff_minimalPeriod_dvd, Finset.card_inter_vadd, IsCompact.preimage_vadd, SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj, vadd_neg_vadd, ContinuousConstVAdd.continuous_const_vadd, MeasureTheory.measure_neg_vadd_sdiff, Seminorm.vadd_closedBall, ContinuousMap.vadd_apply, MeasureTheory.SimpleFunc.coe_vadd, LipschitzWith.vadd, Finset.addDysonETransform_fst, DilationEquiv.smulTorsor_apply, Set.vadd_set_univ, AffineSubspace.vadd_mem_iff_mem_of_mem_direction, Set.vadd_iUnion₂, signedDist_vadd_right, Finset.biUnion_op_vadd_finset, neg_vadd_vadd, IsClosed.vadd_left_of_isCompact, Inseparable.const_vadd, DomAddAct.vadd_aeeqFun_const, AddOreLocalization.vadd_zero_oreSub_zero_vadd, ProperConstVAdd.isProperMap_vadd, Set.vadd_set_sUnion, AffineMap.map_vadd, affineSegment_const_vadd_image, Finset.vadd_finset_card_le, 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, AffineMap.lineMap_vadd_apply, AddAction.compHom_vadd_def, Metric.preimage_vadd_closedBall, measurableEmbedding_const_vadd, Finset.coe_vadd, Filter.Tendsto.vadd, mem_own_leftAddCoset, ContinuousAt.const_vadd, AddAction.vadd_orbit_subset, Set.add_pair, AddAction.IsBlock.isBlockSystem, Set.sUnion_vadd, 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, toColex_vadd', AddAction.IsBlock.of_subset, vadd_segment, DomAddAct.vadd_aeeqFun_aeeq, AddAction.isBlock_iff_vadd_eq_or_disjoint, MeasureTheory.vadd_mem_ae, image_vadd_set, AddOreLocalization.add_vadd, dist_vadd_left, RestrictedProduct.vadd_apply, ContinuousAffineMap.map_vadd, iteratedFDerivWithin_comp_add_right, vadd_mem_nhds_vadd, Finset.affineCombination_apply, faithfulVAdd_iff_injective_vadd_zero, Option.vadd_def, DomAddAct.vadd_Lp_ae_eq, AddAction.IsBlock.of_addSubgroup_of_conjugate, AddAction.coe_aestabilizer, AddAction.mem_stabilizer_finset', AffineSpace.vadd_asymptoticNhds, MeasureTheory.AEStronglyMeasurable.const_vadd, Finset.op_vadd_finset_add_eq_add_vadd_finset, zero_vadd_eq_id, toAdd_vadd, midpoint_vadd_midpoint, AffineSubspace.pointwise_vadd_direction, AddAction.mem_orbit_iff, Set.vadd_set_subset_iff_subset_neg_vadd_set, AffineSubspace.wSameSide_smul_vsub_vadd_left, DomAddAct.vadd_Lp_sub, Finset.add_subset_iff_left, Filter.vadd_pure, AddCon.coe_vadd, 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, Finset.singleton_add, vadd_mem_nhds_self, ZSpan.exist_unique_vadd_mem_fundamentalDomain, AddAction.mem_stabilizer_set', vadd_set_closure_subset, AddAction.nsmul_vadd_eq_iff_period_dvd, Finset.image_vadd, Set.singleton_vadd, Function.Periodic.map_vadd_zmultiples, dist_vadd_right, AddSubgroup.leftTransversals.vadd_diff_vadd, linearIndependent_set_iff_affineIndependent_vadd_union_singleton, AddAction.IsBlock.disjoint_vadd_of_ne, AffineMap.lineMap_apply, Finset.vadd_finset_union, LocallyConstant.vadd_apply, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Filter.vadd_le_vadd_right, Set.vadd_set_subset_iff, Prod.vadd_mk, differentiableWithinAt_comp_add_right, Set.vadd_union, 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, Set.range_vadd_range, IsAddUnit.vadd_left_cancel, rightAddCoset_eq_iff, isProperMap_vadd, StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, EuclideanGeometry.inversion_def, AddAction.vadd_zsmul_movedBy_eq_of_addCommute, AddAction.toFun_apply, AddAction.le_stabilizer_vadd_right, AddAction.zsmul_vadd_mod_minimalPeriod, IsIsometricVAdd.isometry_vadd, Set.range_vadd, comp_vadd_left, Set.range_add, AddAction.nsmul_period_vadd, properVAdd_iff, ProperlyDiscontinuousVAdd.finite_disjoint_inter_image, ediam_vadd, AddAction.orbitRel.Quotient.orbit.coe_vadd, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, DomAddAct.vadd_Lp_neg, AddAction.period_eq_minimalPeriod, ergodic_vadd_of_denseRange_nsmul, Set.infinite_vadd_set, nndist_vadd_right, AddTorsor.vsub_vadd', Set.inter_vadd_subset, AddAction.op_vadd_set_stabilizer_subset, leftAddCoset_eq_iff, vadd_iterate, zero_vadd, Filter.vadd_filter_bot, AffineSubspace.mem_affineSpan_insert_iff, AddOreLocalization.oreSub_vadd_char, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, MeasurableVAdd.measurable_vadd_const, vadd_ite, eq_addCosets_of_normal, Filter.HasBasis.vadd, AddAction.addSubgroup_vadd_def, Filter.NeBot.vadd, AddOreLocalization.zero_vadd, ProperVAdd.isProperMap_vadd_pair_set, Set.vadd_set_subset_add, MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt, Sigma.vadd_mk, mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd, AddActionHom.map_vadd, mem_affineSpan_iff_exists, AddAction.nsmul_add_period_vadd, MeasureTheory.vadd_set_ae_eq, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_ac, AddMonoidHom.preimage_vadd_setₛₗ, Metric.vadd_closedEBall, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum, Prod.vadd_def, Function.update_vadd, toLex_vadd, vadd_closure_subset, aemeasurable_const_vadd_iff, Set.natCard_vadd_set, Finset.vadd_finset_insert, AddAction.isBlock_iff_disjoint_vadd_of_ne, Prod.vadd_snd, preimage_vadd_setₛₗ_of_isAddUnit_isAddUnit, IsOrderedVAdd.vadd_le_vadd, Filter.Germ.const_vadd, Set.vadd_sUnion, Finset.weightedVSub_vadd, AffineEquiv.ofLinearEquiv_apply, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, AddAction.vadd_zsmul_fixedBy_eq_of_addCommute, MeasureTheory.tendsto_vadd_ae, AffineEquiv.pointReflection_apply, AddAction.period_eq_zero_iff, Homeomorph.vadd_apply, AffineSubspace.wOppSide_smul_vsub_vadd_right, Function.Periodic.vadd, isOpenMap_vadd_of_sigmaCompact, Filter.vadd_filter_le_vadd_filter, PUnit.vadd_eq', AddAction.mem_fixedBy, AffineMap.coe_lineMap, dite_vadd, Equiv.coe_constVAdd, AffineSubspace.vadd_mem_of_mem_direction, DomAddAct.edist_vadd_Lp, Set.op_vadd_inter_nonempty_iff, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, AffineEquiv.coe_constVSub_symm, Finset.op_vadd_addConvolution_eq_addConvolution_vadd, vectorSpan_vadd, AffineSubspace.pointwise_vadd_eq_map, Filter.covariant_vadd, Continuous.vadd, Filter.mem_vadd_filter, Bornology.IsVonNBounded.vadd, ofColex_vadd, vadd_openSegment, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, AddAction.toPerm_symm_apply, AddSubmonoid.vadd_def, Specializes.const_vadd, IsLinearSet.vadd, Set.empty_vadd, Prod.vadd_swap, AddAction.mem_orbit, vadd_vsub_vadd_comm, ite_vadd, SubAddAction.vadd_of_tower_mem, ergodic_vadd_of_denseRange_zsmul, AddAction.orbitEquivQuotientStabilizer_symm_apply, AffineSubspace.pointwise_vadd_bot, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, Finset.vadd_finset_empty, 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, AddAction.is_two_pretransitive_iff, Function.Embedding.coe_vadd, properVAdd_iff_continuousVAdd_ultrafilter_tendsto, MeasurableEquiv.vadd_apply, Set.vadd_image_prod, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum, Set.vadd_set_iUnion, vadd_zero_add, signedDist_vadd_right_swap, Wbtw.vadd_const, SetLike.vadd_def, DomAddAct.mk_vadd_toLp, Wbtw.const_vadd, VAdd.vadd_lt_vadd_of_le_of_lt, mem_leftAddCoset, EMetric.vadd_closedBall, Finsupp.mem_vaddAntidiagonal_of_addGroup, Finset.vadd_finset_subset_add, add_ball, AffineMap.homothety_apply, SetLike.GradedSMul.smul_mem, dist_vadd_cancel_left, vadd_univ_pi, IsOrderedVAdd.vadd_le_vadd_right, Function.vadd_const, hasFDerivWithinAt_comp_add_right, AffineSubspace.pointwise_vadd_top, ContinuousAffineMap.vadd_contLinear, IsometryEquiv.vaddConst_apply, Finset.biUnion_vadd_finset, MeasureTheory.IsAddFundamentalDomain.sum_restrict_of_ac, isLinearSet_iff_exists_fg_eq_vadd, slope_vadd_const, affineSegment_vadd_const_image, Set.Infinite.vadd_set, vadd_vadd_vadd_comm, Filter.vadd_bot, MeasureTheory.measure_preimage_vadd_le, vadd_iterate_apply, AffineIsometry.map_vadd, AddAction.isTopologicallyTransitive_iff_dense_iUnion, UpperHalfPlane.vadd_right_cancel_iff, AddAction.quotient_preimage_image_eq_union_add, DomAddAct.vadd_Lp_const, Prod.mk_vadd_mk, AddAction.mem_orbit_of_mem_orbit, Cardinal.mk_vadd_set, Filter.vadd_eq_bot_iff, UniformContinuousConstVAdd.uniformContinuous_const_vadd, MeasureTheory.IsAddFundamentalDomain.ae_covers, vadd_left_injective', AddAction.vadd_mem_of_set_mem_fixedBy, Set.vadd_set_mono, DirectSum.Gmodule.zero_smul, leftAddCoset_rightAddCoset, Finset.pairwiseDisjoint_vadd_iff, SetLike.mk_vadd_of_tower_mk, signedDist_vadd_left, AddAction.mem_stabilizer_finset_iff_subset_vadd_finset, QuotientAddGroup.orbit_eq_out_vadd, Finset.vadd_subset_vadd_right, Set.vadd_set_empty, Finset.weightedVSub_vadd_affineCombination, iteratedFDerivWithin_comp_add_left', toMul_smul, Set.mem_vadd_set_neg, vadd_eq_add, MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum_of_ac, AddOpposite.vadd_eq_add_unop, AddOpposite.op_vadd_eq_op_vadd_op, vadd_pi_subset, MeasureTheory.measure_inter_neg_vadd, Finset.vadd_finset_inter_subset, Set.iUnion_vadd_right_image, Finset.addETransformRight_snd, mem_own_rightAddCoset, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, AddMonoidHom.vaddZeroHom_apply, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum', AffineSubspace.vadd_mem_iff_mem_direction, instContravariantClassHVAddLeOfIsOrderedCancelVAdd, AddAction.zero_vadd, edist_vadd_vadd_le, AddAction.minimalPeriod_pos, IsOpen.exists_vadd_mem, Sigma.vadd_def, MeasureTheory.measure_union_neg_vadd, ofLex_vadd', vadd_closedBall_zero, AddSubgroup.vadd_toLeftFun, AffineSubspace.wSameSide_smul_vsub_vadd_right, Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, diam_vadd, AddAction.injective, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, EuclideanGeometry.reflection_apply', SeparationQuotient.mk_vadd, Finset.centroid_pair, Set.disjoint_vadd_set_left, Set.vadd_set_nonempty, Filter.vadd.instNeBot, DomAddAct.mk_vadd_mk_aeeqFun, VAdd.vadd_lt_vadd_of_lt_of_le, vadd_closure_orbit_subset, AffineSubspace.sSameSide_vadd_left_iff, Filter.le_vadd_iff, vadd_coe_set, subset_interior_vadd, AddOreLocalization.oreSub_zero_vadd, Set.Nonempty.vadd_set, Set.piecewise_vadd, vadd_left_cancel_iff, MeasureTheory.AEStronglyMeasurable.const_vadd', Finset.addETransformLeft_snd, Set.pairwiseDisjoint_vadd_iff, continuous_const_vadd_iff, MeasureTheory.IsAddFundamentalDomain.vadd, AffineSubspace.wSameSide_vadd_right_iff, AddAction.surjective_vadd, Finsupp.mem_vaddAntidiagonal_iff, Finset.addDysonETransform.vadd_finset_snd_subset_fst, upperClosure_vadd, IsAddFoelner.mean_vadd_eq_mean, AddAction.minimalPeriod_eq_one_iff_fixedBy, Filter.Germ.coe_vadd, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, AddAction.Quotient.vadd_mk, Set.add_subset_iff_right, derivWithin_comp_add_const, Finset.vadd_finset_eq_empty, AddOreLocalization.zero_sub_vadd, IsometryEquiv.constVAdd_apply, vadd_vsub_vadd_cancel_left, Sum.vadd_def, wbtw_or_wbtw_smul_vadd_of_nonneg, Bornology.isVonNBounded_vadd, Finset.addETransformLeft_fst, vsub_vadd, LinearPMap.vadd_apply, SlashInvariantForm.vAdd_width_periodic, UpperHalfPlane.coe_vadd, Ideal.univ_eq_iUnion_image_add, AffineBasis.coord_vadd, AddSubgroup.mk_vadd, vadd_uniformity, AddAction.toPermHom_apply_apply, Set.neg_vadd_set_distrib, vadd_vsub, AffineMap.homothety_def, Finsupp.smul_apply_addAction, MeasureTheory.measure_symmDiff_neg_vadd, wbtw_const_vadd_iff, AffineIsometryEquiv.map_vadd, op_vadd_eq_add, IsCompact.vadd, rightAddCoset_assoc, AffineEquiv.vaddConst_apply, neg_vadd_eq_iff, HahnModule.support_smul_subset_vadd_support, support_translate, nndist_vadd, Set.mem_neg_vadd_set_iff, amenable_of_maxAddFoelner_neBot, AffineSubspace.vadd_mem_pointwise_vadd_iff, AddConstMap.coe_vadd, AddOreLocalization.vadd_zero_vadd, AddAction.disjoint_image_image_iff, Sum.vadd_swap, vadd_add_vadd_comm, Set.vadd_iUnion, Finset.vadd_univ, Option.vadd_none, Finset.centroid_pair_fin, SetLike.mk_vadd_mk, Finset.vadd_stabilizer_of_no_doubling, Continuous.const_vadd, AddOreLocalization.vadd_sub_zero, AddOreLocalization.vadd_cancel, Set.vadd_subset_vadd_right, AddAction.isPretransitive_iff, Specializes.vadd, AddAction.zsmul_add_period_vadd, Seminorm.vadd_ball, IsAddFoelner.tendsto_meas_vadd_symmDiff, zero_leftAddCoset, AddAction.set_mem_fixedBy_iff, MeasureTheory.isAddLeftInvariant_map_vadd, Set.disjoint_vadd_set_right, UpperHalfPlane.modular_T_zpow_smul, Finset.vadd_finset_subset_vadd, vadd_right_injective, AddAction.mem_stabilizer_finset, AddUnits.vadd_neg, MeasureTheory.map_vadd, Metric.vadd_eball, AddAction.mem_stabilizer_set_iff_vadd_set_subset, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, Set.toFinset_vadd, hasFDerivWithinAt_comp_sub, derivWithin_comp_sub_const, EuclideanGeometry.dist_smul_vadd_eq_dist, vadd_preimage_set_subsetₛₗ, MeasureTheory.StronglyMeasurable.const_vadd', Filter.covariant_vadd_filter, collinear_iff_exists_forall_eq_smul_vadd, Set.iUnion₂_vadd, Set.union_vadd, SetLike.coe_GSMul, MeasureTheory.measure_preimage_vadd, vadd_dite, AffineIsometryEquiv.coe_vaddConst', Set.vadd_set_symmDiff, uniformContinuous_vadd, wbtw_or_wbtw_smul_vadd_of_nonpos, Equiv.vadd_def, Set.Finite.toFinset_vadd, AddOreLocalization.expand', Set.vadd_eq_empty, Filter.vadd_filter_neBot_iff, SubAddAction.val_vadd, LinearPMap.vadd_domain, IsCompact.closedBall_add, Set.Finite.vadd_set, AddMonoidHom.transfer_def, Finset.Nonempty.vadd_finset, AddAction.QuotientAction.inv_mul_mem, DomAddAct.vadd_apply, Finset.vadd_mem_vadd_finset_iff, WithIdealFilter.mem_nhds_iff, AffineSpace.asymptoticNhds_eq_smul_vadd, QuotientAddGroup.eq_class_eq_leftCoset, FreeAddMonoid.of_vadd, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum', IsAddUnit.vadd_uniformity, Set.iUnion_vadd_set, MeasureTheory.measure_neg_vadd_union, Set.preimage_vadd, AddSubgroup.exists_leftTransversal_of_FiniteIndex, Prod.vadd_fst, Filter.EventuallyEq.vadd, MeasureTheory.IsAddFundamentalDomain.aedisjoint, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, AffineMap.homothety_add, orbit_addSubgroup_eq_rightCoset, Set.vadd_set_union, wbtw_vadd_const_iff, IsOrderedVAdd.vadd_le_vadd_left, 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, Set.IsWF.min_vadd, Finset.inter_vadd_union_subset_union, normal_iff_eq_addCosets, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac, Finset.neg_vadd_mem_iff, Prod.snd_vadd, MeasureTheory.addFundamentalFrontier_vadd, Set.vadd_set_iInter, ULift.vadd_down, AEMeasurable.fun_const_vadd, AddAction.nsmul_mod_period_vadd, EuclideanGeometry.orthogonalProjection_apply, Set.vadd_sInter_subset, 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, Set.Finite.vadd, AddActionHom.map_vadd', Set.singleton_vadd_singleton, AddSubgroup.vadd_opposite_image_add_preimage, Filter.Tendsto.asymptoticNhds_vadd_const, vadd_add_assoc, AffineSubspace.setOf_sOppSide_eq_image2, Set.IsWF.vadd, AffineEquiv.map_vadd', ofDual_vadd', subset_interior_vadd_right, AddAction.bijective, LinearPMap.coe_vadd, AddAction.isMultiplyPretransitive_iff, Finset.vadd_finset_subset_vadd_finset_iff, denseRange_vadd, SubAddAction.val_vadd_of_tower, Set.vadd_inter_nonempty_iff, Finset.subset_vadd_finset_iff, nndist_vadd_cancel_left, Finset.vaddAntidiagonal_min_vadd_min, Set.iUnion_vadd_eq_setOf_exists, Finset.vadd_singleton, ThreeAPFree.vadd_set, IsAddUnit.neg_vadd, AffineSubspace.setOf_wSameSide_eq_image2, AddAction.le_stabilizer_iff_vadd_le, Finset.vadd_subset_vadd, AddAction.vadd_mem_fixedBy_iff_mem_fixedBy, vadd_right_cancel_iff, Set.vadd_empty, AddAction.orbit_vadd, Finset.vadd_mem_vadd_finset, MeasureTheory.VAddInvariantMeasure.measure_preimage_vadd, MeasureTheory.addFundamentalInterior_vadd, MeasureTheory.innerRegular_map_vadd, iteratedFDerivWithin_comp_sub', AffineSubspace.sSameSide_smul_vsub_vadd_left, GradedMonoid.mk_smul_mk, Finset.addConvolution_op_vadd_eq_addConvolution_add_neg, MeasureTheory.measure_preimage_vadd_null, Filter.vadd_filter_eq_bot_iff, AEMeasurable.vadd, IsOpen.right_addCoset, IsAddUnit.vadd_bijective, MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum', DomAddAct.dist_vadd_Lp, AddAction.mem_stabilizerAddSubmonoid_iff, IsAddUnit.measurable_const_vadd_iff, MeasureTheory.eventuallyConst_vadd_set_ae, vadd_ball'', ULift.vadd_def, fderivWithin_comp_add_right, ContinuousWithinAt.const_vadd, DirectSum.gsmulHom_apply_apply, Sum.vadd_inl, AddAction.mem_stabilizer_set, Finset.vadd_finset_subset_vadd_finset, DomAddAct.vadd_Lp_zero, Metric.preimage_vadd_eball, Filter.EventuallyEq.const_vadd, Set.vadd_set_inter, IsOpen.vadd, Set.MapsTo.vadd_setₛₗ, DirectSum.GdistribMulAction.smul_add, Finset.vadd_finset_sdiff, Set.subset_vadd_set_iff, punctured_nhds_vadd, MeasureTheory.measure_vadd_null, Finset.empty_vadd, LocallyConstant.coe_vadd, nndist_vadd_vadd_le, AddAction.stabilizerEquivStabilizer_zero, IsClosed.right_addCoset, IsClosed.left_addCoset, approxAddOrderOf.vadd_subset_of_coprime, instCovariantClassHVAddLeOfIsOrderedVAdd, Absorbent.vadd_absorbs, AffineSubspace.wOppSide_vadd_left_iff, Finset.vadd_def, MeasureTheory.Measure.isAddHaarMeasure_map_vadd, StrictConvex.vadd, ofDual_vadd, IterateAddAct.mk_vadd, AddAction.le_stabilizer_vadd_left, Filter.vadd_filter.instNeBot, Set.iUnion_vadd_left_image, Set.mem_vadd_set_iff_neg_vadd_mem, MeasureTheory.vaddInvariantMeasure_map_vadd, SubAddAction.exists_vadd_of_last_eq, Set.vadd_set_iInter₂_subset, sub_ball, OpenPartialHomeomorph.unitBallBall_apply, vadd_pi, eq_vadd_iff_vsub_eq, Finset.union_vadd, IsAddFoelner.amenable, totallyBounded_iff_subset_finite_iUnion_nhds_zero, leftAddCoset_mem_leftAddCoset, Affine.Simplex.ninePointCircle_center, Set.vadd_subset_vadd_left, AffineMap.lineMap_vadd, IsOpen.dense_iUnion_vadd, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, isHomeomorph_vadd, AddAction.ofQuotientStabilizer_vadd, Prod.fst_vadd, DomAddAct.nnnorm_vadd_Lp, spectrum.vadd_eq, AddUnits.vadd_mk_apply, Finset.addETransformRight_fst, isAddFoelner_iff, Bornology.IsBounded.vadd, Filter.map_vadd, dist_vadd_vadd_le, Finset.vadd_subset_vadd_left, Finset.card_vadd_inter_vadd, AddAction.IsPretransitive.exists_vadd_eq, Finset.image_vadd_product, SlashInvariantForm.vAdd_apply_of_mem_strictPeriods, leftAddCoset_assoc, AddOreLocalization.oreSub_vadd_oreSub, AddAction.toPerm_apply, MeasureTheory.NullMeasurableSet.vadd, Set.vadd_set_sInter_subset, AddAction.isBlock_iff_vadd_eq_of_mem, fderivWithin_comp_sub, AddSubmonoid.mk_vadd, EuclideanGeometry.reflection_apply, Filter.vadd_set_mem_vadd_filter, IsCompact.add_closedBall, AddAction.vadd_set_stabilizer_subset, Function.Embedding.vadd_def, Set.finite_vadd_set, AddAction.zsmul_mod_period_vadd, AffineBasis.basisOf_vadd, Pi.vadd_apply', UpperHalfPlane.vadd_im, affineIndependent_vadd, AddAction.zsmul_vadd_eq_iff_period_dvd, AddAction.ofQuotientStabilizer_mk, AffineMap.lineMap_vadd_lineMap, Monotone.vadd, UpperHalfPlane.modular_T_smul, AddAction.IsBlock.vadd_eq_or_disjoint, EMetric.preimage_vadd_ball, Set.iInter_vadd_subset, AddAction.vadd_mem_orbit_vadd, DomAddAct.vadd_Lp_val, AffineSubspace.sOppSide_vadd_left_iff, QuotientAddGroup.orbit_mk_eq_vadd, Finset.dens_vadd_finset, closure_vadd, UpperHalfPlane.vadd_left_injective, sbtw_const_vadd_iff, hasFDerivWithinAt_comp_add_left, MeasureTheory.StronglyMeasurable.const_vadd, ProperlyDiscontinuousVAdd.finite_stabilizer', AddActionHom.coe_vadd, Finset.neg_vadd_finset_distrib, Finset.singleton_vadd, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, continuousOn_const_vadd_iff, AddAction.orbit_vadd_subset, ContinuousOn.const_vadd, Set.vadd_set_pi, vadd_left_mem_affineSpan_pair, signedDist_vadd_vadd, AffineMap.coe_homothety, Set.powersetCard.coe_vadd, Pi.vadd_apply, ContinuousAffineMap.vadd_apply, MeasurableSet.const_vadd, Set.image_op_vadd_distrib, AddAction.mem_stabilizer_finset_iff_vadd_finset_subset, Set.encard_vadd_set, EuclideanGeometry.angle_const_vadd, Equiv.pointReflection_apply, isLinearSet_iff_exists_fin_addMonoidHom, mem_fixingAddSubgroup_iff, Set.vadd_set_iInter_subset, AddAction.isPretransitive_iff_base, AffineSubspace.sOppSide_smul_vsub_vadd_right, IsCompact.closedBall_sub, Measurable.vadd', Filter.pure_vadd, VAddCommClass.toAddActionHom_apply, Set.pair_add, DirectSum.Gmodule.add_smul, EMetric.preimage_vadd_closedBall

One

Theorems

NameKindAssumesProvesValidatesDepends On
instNonempty 📖

SMul

Theorems

NameKindAssumesProvesValidatesDepends On
ext 📖
ext_iff 📖ext

Subsingleton

Theorems

NameKindAssumesProvesValidatesDepends On
eq_one 📖
eq_zero 📖

VAdd

Definitions

NameCategoryTheorems
vadd 📖CompOp
4 mathmath: ext_iff, arrowAddAction_vadd, AddSemigroupAction.ext_iff, AddAction.ext_iff

Theorems

NameKindAssumesProvesValidatesDepends On
ext 📖vadd
ext_iff 📖mathematicalvaddext

VSub

Definitions

NameCategoryTheorems
vsub 📖CompOp
407 mathmath: AffineSubspace.sOppSide_iff_exists_right, Set.vsub_subset_vsub_right, AffineIsometryEquiv.coe_constVSub, vsub_midpoint, AffineIsometryEquiv.pointReflection_apply, EuclideanGeometry.dist_smul_vadd_sq, Equiv.right_vsub_pointReflection, Set.Finite.toFinset_vsub, AffineSubspace.coe_vsub, Finset.affineCombination_vsub, AffineMap.lineMap_vsub_left, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, vectorSpan_range_eq_span_range_vsub_left_ne, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, inner_vsub_right_eq_zero_symm, Finset.empty_vsub, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, Set.vsub_subset_vsub_left, AffineMap.lineMap_linear, vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPoints, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, Finset.weightedVSubOfPoint_apply, Filter.NeBot.vsub, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul', AffineSubspace.mem_perpBisector_iff_inner_eq_zero', Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, AffineSubspace.setOf_sSameSide_eq_image2, Finset.vsub_subset_vsub_left, EuclideanGeometry.Sphere.wbtw_secondInter, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, sub_add_vsub_comm, vsub_mem_vectorSpan, Filter.vsub.instNeBot, Finset.affineCombination_sdiff_sub, vsub_mem_vectorSpan_pair, DilationEquiv.smulTorsor_symm_apply, Set.vsub_singleton, vadd_eq_vadd_iff_neg_add_eq_vsub, vadd_vsub_assoc, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, Filter.map₂_vsub, Set.iUnion_vsub_left_image, Filter.vsub_le_vsub_left, Filter.bot_vsub, vadd_right_mem_affineSpan_pair, AffineSubspace.wOppSide_smul_vsub_vadd_left, vectorSpan_eq_span_vsub_set_right_ne, vsub_vadd_comm, Set.vsub_nonempty, Finset.singleton_vsub_singleton, smul_vsub_rev_vadd_mem_affineSpan_pair, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, Prod.mk_vsub_mk, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, affineIndependent_set_iff_linearIndependent_vsub, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, wbtw_const_vsub_iff, AffineSubspace.sSameSide_iff_exists_left, vsub_right_injective, Set.vadd_set_vsub_vadd_set, Finset.vsub_mem_vsub, AffineSubspace.vsub_mem_direction, Set.Finite.vsub, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, Affine.Simplex.centroid_weighted_vsub_eq_zero, Filter.vsub_bot, EuclideanGeometry.Sphere.secondInter_collinear, vsub_vadd_eq_vsub_sub, EuclideanGeometry.orthogonalProjection_apply_mem, Finset.sum_smul_vsub_eq_weightedVSubOfPoint_sub, AffineSubspace.sOppSide_iff_exists_left, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, Filter.vsub_eq_bot_iff, EuclideanGeometry.inversion_vsub_center, Finset.image_vsub_product, AffineSubspace.smul_vsub_vadd_mem, signedDist_apply_apply, vectorSpan_range_eq_span_range_vsub_right, Set.sUnion_vsub, AffineSubspace.direction_affineSpan_insert, Filter.le_vsub_iff, EuclideanGeometry.angle_vsub_const, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, vadd_vsub_eq_sub_vsub, AffineIsometryEquiv.map_vsub, vsub_eq_zero_iff_eq, dist_vsub_cancel_left, Equiv.pointReflection_vsub_right, vadd_eq_vadd_iff_sub_eq_vsub, vsub_rev_mem_vectorSpan_pair, Wbtw.sameRay_vsub_right, sbtw_const_vsub_iff, Set.inter_vsub_subset, EuclideanGeometry.orthogonalProjection_apply', Finset.sum_smul_const_vsub_eq_vsub_affineCombination, Filter.pure_vsub_pure, AffineMap.left_vsub_lineMap, Set.mem_vsub, Finset.weightedVSub_weightedVSubVSubWeights, AffineMap.lineMap_vsub_right, Set.vsub_sUnion, vsub_add_vsub_cancel, Finset.vsub_subset_vsub, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Filter.mem_vsub, Sbtw.vsub_const, Finset.vsub_subset_iff, AffineSubspace.wOppSide_iff_exists_left, AffineSubspace.signedInfDist_eq_signedDist_of_mem, Filter.Tendsto.vsub, Prod.fst_vsub, vectorSpan_image_eq_span_vsub_set_left_ne, AffineSubspace.setOf_wOppSide_eq_image2, Affine.Simplex.signedInfDist_apply_self, EuclideanGeometry.Sphere.IsTangentAt.inner_right_eq_zero_of_mem, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, AffineEquiv.coe_constVSub, AffineSubspace.coe_direction_eq_vsub_set, vadd_vsub_vadd_cancel_right, Set.vsub_iInter₂_subset, Set.toFinset_vsub, Finset.inter_vsub_subset, Pi.vsub_apply, uniformContinuous_vsub, AddTorsor.vadd_vsub', Affine.Simplex.mongePlane_def, dist_eq_norm_vsub', AffineMap.right_vsub_lineMap, vectorSpan_eq_span_vsub_finset_right_ne, AffineSubspace.mem_direction_iff_eq_vsub, Finset.vsub_eq_empty, Set.vsub_subset_iff, Wbtw.sameRay_vsub_left, smul_vsub_vadd_mem_affineSpan_pair, AffineMap.linearMap_vsub, EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius, vectorSpan_pair_rev, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, EuclideanGeometry.Sphere.sbtw_secondInter, Pi.vsub_def, EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_mem, Set.inter_vsub_union_subset_union, Filter.vsub_pure, AffineMap.vsub_lineMap, AffineMap.vsub_apply, Set.vsub_iUnion, vectorSpan_eq_span_vsub_set_left_ne, Set.singleton_vsub_singleton, Finset.vsub_empty, Sbtw.const_vsub, EuclideanGeometry.reflection_apply_of_mem, AffineSubspace.direction_sup, Equiv.coe_vaddConst_symm, AffineMap.lineMap_vsub, AffineIsometry.map_vsub, vectorSpan_pair, Finset.union_vsub, nndist_vsub_vsub_le, Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, affineSegment_const_vsub_image, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior_faceOpposite, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Homeomorph.vaddConst_symm_apply, Set.vsub_iInter_subset, inner_vsub_vsub_right_eq_dist_sq_left_iff, Affine.Simplex.direction_mongePlane, Set.sInter_vsub_subset, dist_vsub_cancel_right, midpoint_vsub_left, Finset.sum_smul_const_vsub_eq_neg_weightedVSub, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, EuclideanGeometry.Sphere.sOppSide_faceOpposite_secondInter_of_mem_interior, vsub_sub_vsub_comm, sbtw_vsub_const_iff, Continuous.vsub, Set.vsub_eq_empty, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, Finset.vsub_nonempty, AffineSubspace.wSameSide_iff_exists_left, Set.Nonempty.vsub, vectorSpan_eq_span_vsub_set_left, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, AffineSubspace.wSameSide_smul_vsub_vadd_left, Finset.vsub_union, vectorSpan_segment, Set.empty_vsub, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, AffineMap.lineMap_apply, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, slope_fun_def, mem_vectorSpan_pair_rev, Finset.mem_vsub, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, vsub_left_injective, Wbtw.const_vsub, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, EuclideanGeometry.inversion_def, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, Set.union_vsub, abs_signedDist_eq_dist_iff_vsub_mem_span, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, Set.union_vsub_inter_subset_union, AddTorsor.vsub_vadd', LipschitzWith.vsub, AffineSubspace.mem_affineSpan_insert_iff, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, Equiv.left_vsub_pointReflection, nndist_eq_nnnorm_vsub, Equiv.coe_constVSub, Set.vsub_self_mono, Set.singleton_vsub, signedDist_vsub_self_rev, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Set.iUnion_vsub, midpoint_vsub_midpoint, Filter.pure_vsub, AffineEquiv.ofLinearEquiv_apply, AffineMap.vsub_linear, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, AffineIsometryEquiv.coe_vaddConst_symm, AffineEquiv.pointReflection_apply, Finset.weightedVSubOfPoint_apply_const, signedDist_vsub_self, AffineSubspace.wOppSide_smul_vsub_vadd_right, ContinuousAt.vsub, midpoint_vsub_right, AffineMap.coe_lineMap, Set.iInter₂_vsub_subset, vectorSpan_range_eq_span_range_vsub_right_ne, Finset.Nonempty.vsub, vsub_sub_vsub_cancel_left, Affine.Simplex.eq_centroid_iff_sum_vsub_eq_zero, IsTopologicalAddTorsor.continuous_vsub, vadd_vsub_vadd_comm, Finset.centroid_vsub_const, AffineSubspace.sSameSide_smul_vsub_vadd_right, Set.vsub_mem_vsub, vsub_sub_vsub_cancel_right, Set.vsub_empty, vectorSpan_def, AffineMap.homothety_apply, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, dist_vsub_vsub_le, EuclideanGeometry.inner_nonneg_of_dist_le_radius, smul_vsub_rev_mem_vectorSpan_pair, AffineSubspace.direction_affineSpan_pair_le_iff_exists_smul, Set.image_vsub_prod, inner_vsub_vsub_left_eq_dist_sq_right_iff, AffineSubspace.coe_direction_eq_vsub_set_left, Set.vsub_union, Finset.singleton_vsub, EuclideanGeometry.orthogonalProjection_vsub_mem_direction, mem_const_vsub_affineSegment, vsub_right_cancel_iff, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, nndist_vsub_cancel_left, Filter.vsub_neBot_iff, AffineSubspace.sSameSide_iff_exists_right, mem_vectorSpan_pair, affineSegment_vsub_const_image, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, EuclideanGeometry.angle_const_vsub, EuclideanGeometry.vsub_orthogonalProjection_mem_direction, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, AffineSubspace.signedInfDist_singleton, vectorSpan_image_eq_span_vsub_set_right_ne, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Finset.weightedVSub_apply, AffineSubspace.wSameSide_iff_exists_right, neg_vsub_eq_vsub_rev, IsometryEquiv.constVSub_apply, wbtw_vsub_const_iff, AffineSubspace.wSameSide_smul_vsub_vadd_right, ContinuousAffineMap.contLinear_map_vsub, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, EuclideanGeometry.reflection_apply', Finset.centroid_pair, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, mem_vsub_const_affineSegment, sub_smul_slope, ContinuousAffineMap.vsub_toAffineMap, Set.iUnion_vsub_right_image, AffineSubspace.mem_direction_iff_eq_vsub_right, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Finset.vsub_card_le, vadd_vsub_vadd_cancel_left, vsub_vadd, Set.image2_vsub, nndist_vsub_cancel_right, vadd_vsub, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, AffineMap.homothety_def, IsometryEquiv.vaddConst_symm_apply, midpoint_vsub, AffineEquiv.vaddConst_symm_apply, AffineSubspace.signedInfDist_def, affineIndependent_iff_linearIndependent_vsub, dist_eq_norm_vsub, Finset.centroid_pair_fin, ContinuousAffineMap.vsub_apply, AffineSubspace.mem_mk', Affine.Simplex.signedInfDist_affineCombination, Finset.vsub_subset_vsub_right, signedDist_apply, signedDist_eq_dist_iff_vsub_mem_span, AffineSubspace.direction_perpBisector, Finset.sum_smul_vsub_const_eq_weightedVSub, Finset.sum_smul_vsub_const_eq_affineCombination_vsub, vsub_left_cancel_iff, ContinuousOn.vsub, EuclideanGeometry.dist_smul_vadd_eq_dist, Set.iUnion₂_vsub, Set.vsub_inter_subset, AffineSubspace.mem_perpBisector_iff_inner_eq, Set.vsub_sInter_subset, Set.vsub_iUnion₂, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, vectorSpan_eq_span_vsub_set_right, Set.iInter_vsub_subset, AffineMap.homothety_add, Finset.sum_smul_vsub_eq_affineCombination_vsub, AffineSubspace.wOppSide_iff_exists_right, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, AffineSubspace.vsub_right_mem_direction_iff_mem, Wbtw.sameRay_vsub, AffineSubspace.sOppSide_smul_vsub_vadd_left, smul_vsub_mem_vectorSpan_pair, Set.vsub_subset_vsub, Finset.sum_smul_const_vsub_eq_sub_weightedVSubOfPoint, exists_eq_smul_of_parallel, vsub_mem_vectorSpan_of_mem_affineSpan_of_mem_affineSpan, ContinuousAffineMap.vsub_contLinear, EuclideanGeometry.orthogonalProjection_apply, EuclideanGeometry.Sphere.direction_orthRadius, Prod.snd_vsub, EuclideanGeometry.inner_pos_of_dist_lt_radius, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, AffineSubspace.setOf_sOppSide_eq_image2, inner_vsub_vsub_left_eq_dist_sq_left_iff, AffineSubspace.mem_direction_iff_eq_vsub_left, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere, Filter.vsub_le_vsub_right, AffineSubspace.setOf_wSameSide_eq_image2, ContinuousWithinAt.vsub, vsub_set_subset_vectorSpan, edist_vsub_vsub_le, Finset.sum_smul_vsub_const_eq_weightedVSubOfPoint_sub, midpoint_vsub_midpoint_same_left, right_vsub_midpoint, AffineSubspace.sSameSide_smul_vsub_vadd_left, Filter.vsub_le_vsub, OpenPartialHomeomorph.unitBallBall_symm_apply, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, EuclideanGeometry.Sphere.secondInter_eq_lineMap, vsub_eq_sub, midpoint_eq_midpoint_iff_vsub_eq_vsub, AffineMap.image_vsub_image, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, vectorSpan_range_eq_span_range_vsub_left, Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, Affine.Simplex.affineSpan_pair_eq_altitude_iff, Finset.coe_vsub, vsub_self, eq_vadd_iff_vsub_eq, EuclideanGeometry.orthogonalProjection_eq_iff_mem, Affine.Simplex.ninePointCircle_center, EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq, AffineIsometryEquiv.dist_pointReflection_self', AffineSubspace.vsub_left_mem_direction_iff_mem, EuclideanGeometry.reflection_apply, Finset.vsub_singleton, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, EuclideanGeometry.Sphere.secondInter_eq_self_iff, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, nndist_eq_nnnorm_vsub', wbtw_iff_sameRay_vsub, Affine.Simplex.points_vsub_eulerPoint, Equiv.pointReflection_vsub_left, inner_vsub_vsub_right_eq_dist_sq_right_iff, EuclideanGeometry.Sphere.eq_or_eq_secondInter_iff_mem_of_mem_affineSpan_pair, inner_vsub_left_eq_zero_symm, midpoint_vsub_midpoint_same_right, Affine.Simplex.centroid_vsub_eq, AffineMap.lineMap_vsub_lineMap, NormedAddTorsor.dist_eq_norm', Wbtw.vsub_const, Finset.sum_smul_vsub_eq_weightedVSub_sub, AffineSubspace.coe_direction_eq_vsub_set_right, vadd_left_mem_affineSpan_pair, left_vsub_midpoint, AffineMap.coe_homothety, Finset.vsub_def, Filter.vsub_mem_vsub, Equiv.pointReflection_apply, Set.singleton_vsub_self, Finset.vsub_inter_subset, AffineSubspace.sOppSide_smul_vsub_vadd_right, AffineBasis.basisOf_apply, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq

Zero

Theorems

NameKindAssumesProvesValidatesDepends On
instNonempty 📖

(root)

Definitions

NameCategoryTheorems
HVAdd 📖CompData
VAdd 📖CompData
VSub 📖CompData
instHVAdd 📖CompOp
1132 mathmath: Set.ncard_vadd_set, AddAction.mem_stabilizer_set_iff_subset_vadd_set, Set.iUnion_vadd, ball_sub, AffineIsometryEquiv.pointReflection_apply, Metric.infEDist_vadd, Metric.vadd_closedBall, HahnModule.support_smul_subset_vadd_support', EuclideanGeometry.dist_smul_vadd_sq, MeasureTheory.vaddInvariantMeasure_iff, Fintype.piFinset_vadd_finset, IsOpen.vadd_left, DomAddAct.mk_vadd_indicatorConstLp, AddAction.isTopologicallyTransitive_iff_dense_iUnion_preimage, Finset.vadd_nonempty_iff, Equiv.coe_vaddConst, AddUnits.vadd_def, Measurable.vadd, Set.vadd_singleton, AddAction.IsTrivialBlock.vadd_iff, add_vadd_comm, AddSubgroup.vadd_opposite_image_add_preimage', DirectSum.Gmodule.smulAddMonoidHom_apply_of_of, EuclideanGeometry.reflection_orthogonal_vadd, Set.vadd_mem_vadd, Submodule.vadd_def, Set.vadd_set_iUnion₂, Equiv.coe_constVSub_symm, add_vadd_zero, fderivWithin_comp_add_left, dist_vadd, UniformSpace.Completion.vadd_def, rank_le_card_isVisible, AddAction.isPeriodicPt_vadd_iff, MeasureTheory.StronglyMeasurable.vadd_const, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'', MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum, AffineSubspace.sSameSide_vadd_right_iff, Filter.vadd_le_vadd, ContinuousAt.vadd, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Filter.mem_vadd, IsOpen.iUnion_preimage_vadd, AffineSubspace.setOf_sSameSide_eq_image2, AffineSubspace.map_pointwise_vadd, MeasureTheory.vadd_ae, Set.vadd_set_subset_vadd, AddOpposite.unop_vadd_eq_unop_vadd_unop, IsUpperSet.vadd, AddAction.exists_vadd_eq, Homeomorph.vadd_symm_apply, AffineEquiv.constVAdd_apply, AddAction.nsmul_vadd_mod_minimalPeriod, Set.vadd_set_inter_subset, sub_add_vsub_comm, rightAddCoset_zero, HahnModule.coeff_single_smul_vadd, AddAction.zsmul_period_add_vadd, nhds_vadd, Finset.vadd_finset_eq_univ, Convex.vadd, Finset.neg_op_vadd_finset_distrib, SetLike.vadd_of_tower_def, AddAction.mapsTo_vadd_orbit, image_vadd_setₛₗ, vadd_eq_vadd_iff_neg_add_eq_vsub, Option.vadd_some, vadd_vsub_assoc, Finset.vadd_eq_empty, vadd_mem_fixedPoints_of_normal, vadd_eq_self_of_preimage_zsmul_eq_self, AddAction.isTopologicallyTransitive_iff, rightAddCoset_mem_rightAddCoset, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, Finset.vadd_mem_vadd, Filter.EventuallyEq.fun_const_vadd, QuotientAddGroup.univ_eq_iUnion_vadd, AddCommute.vadd_left, Homeomorph.vaddConst_apply, Filter.pure_vadd_pure, Dense.vadd, Set.IsPWO.vadd, MeasureTheory.IsAddFundamentalDomain.sum_restrict, derivWithin_comp_const_sub, Set.iUnion_neg_vadd, vadd_right_mem_affineSpan_pair, MeasureTheory.IsAddFundamentalDomain.exists_ne_zero_vadd_eq, AddConstMap.coe_addLeftHom_apply, mem_const_vadd_affineSegment, Set.vadd_mem_vadd_set, ContinuousVAdd.continuous_vadd, AffineSubspace.wOppSide_smul_vsub_vadd_left, toColex_vadd, Set.vadd_subset_iff, IsAddUnit.aemeasurable_const_vadd_iff, Set.vadd_subset_vadd, Fintype.piFinset_vadd, vsub_vadd_comm, AEMeasurable.const_vadd, toDual_vadd', Sbtw.vadd_const, Inseparable.vadd, Set.vadd_inter_subset, Set.mem_vadd_set, ContinuousMap.vadd_comp, iteratedFDerivWithin_comp_add_right', MeasureTheory.integral_vadd_eq_self, Finset.coe_vadd_finset, vadd_sub_assoc, SetLike.val_vadd_of_tower, AddAction.Supports.vadd, AddOreLocalization.vadd_oreSub_zero, 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, Finset.vadd_finset_singleton, IsLowerSet.vadd_subset, SetLike.val_vadd, smul_vsub_rev_vadd_mem_affineSpan_pair, tendsto_const_vadd_iff, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, affineSpan_singleton_union_vadd_eq_top_of_span_eq_top, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, VAddCon.vadd, add_vadd_add_comm, Finset.add_singleton, Measurable.vadd_const, Finset.vadd_empty, AddAction.Quotient.vadd_coe, Set.op_vadd_set_add_eq_add_vadd_set, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, threeAPFree_vadd_set, Finset.card_vadd_le, Finset.vadd_finset_univ, ContinuousOn.vadd, IsometryEquiv.constVSub_symm_apply, EuclideanGeometry.angle_vadd_const, isLinearSet_iff, Finset.support_vaddAntidiagonal_subset_vadd, AddAction.Quotient.coe_vadd_out, vadd_vadd, FreeAddMonoid.vadd_def, AffineSubspace.sOppSide_vadd_right_iff, Finset.vadd_addConvolution_eq_addConvolution_neg_add, MeasureTheory.measure_neg_vadd_inter, Set.MapsTo.vadd_set, Pi.vadd_def', AffineIndependent.vadd, collinear_iff_of_mem, IsOpen.left_addCoset, AddSubmonoid.nsmul_vadd_mem_closure_vadd, AddAction.IsBlock.translate, 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, AddActionSemiHomClass.map_vaddₛₗ, DirectSum.Gmodule.of_smul_of, set_vadd_closure_subset, Set.op_vadd_set_subset_add, Set.vadd_set_univ_pi, vsub_vadd_eq_vsub_sub, IsLowerSet.vadd, EuclideanGeometry.orthogonalProjection_apply_mem, toLex_vadd', AffineBasis.coe_vadd, AddAction.isPreprimitive_ofFixingAddSubgroup_conj_iff, AddAction.orbitZMultiplesEquiv_symm_apply', VAddCommClass.vadd_comm, Set.sInter_vadd_subset, mem_rightAddCoset, Finset.inter_vadd_subset, AddAction.orbitZMultiplesEquiv_symm_apply, Function.Embedding.vadd_apply, vadd_assoc, Finset.weightedVSubOfPoint_vadd, AffineSubspace.smul_vsub_vadd_mem, Finset.mem_vadd, nndist_vadd_cancel_right, UniformContinuous.const_vadd, Set.vadd_nonempty, Convex.smul_vadd_mem_of_mem_nhds_of_mem_asymptoticCone, Set.iInter₂_vadd_subset, Finset.image_vadd_distrib, Set.vadd_set_pi_of_isAddUnit, MeasureTheory.measure_preimage_vadd_of_nullMeasurableSet, SubAddAction.vadd_mem, MeasureTheory.AEStronglyMeasurable.vadd, MeasureTheory.AEStronglyMeasurable.vadd_const, AddAction.mem_stabilizer_iff, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, ofColex_vadd', Set.OrdConnected.vadd, Finset.mem_vaddAntidiagonal, Filter.vadd_tendsto_vadd_iff, ContinuousMap.coe_vadd, IsCompact.vadd_set, AddAction.isBlock_iff_vadd_eq_vadd_of_nonempty, sbtw_vadd_const_iff, IsAddUnit.preimage_vadd_setₛₗ, MeasureTheory.IsAddFundamentalDomain.restrict_restrict, Set.neg_op_vadd_set_distrib, AddCommute.vadd_right, vadd_vsub_eq_sub_vsub, iteratedFDerivWithin_comp_add_left, Set.vadd_sub_vadd_comm, Set.pairwise_disjoint_vadd_iff, ofLex_vadd, AddAction.isBlock_iff_vadd_eq_of_nonempty, UpperHalfPlane.vadd_re, Filter.vadd_mem_vadd, MeasureTheory.IsAddFundamentalDomain.vadd_of_comm, Filter.bot_vadd, Finset.vadd_subset_iff, affinity_unitClosedBall, MeasureTheory.measurePreserving_vadd, 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, Filter.vadd_neBot_iff, ContinuousAffineMap.vadd_toAffineMap, DomAddAct.vadd_Lp_add, AddSemigroupAction.add_vadd, Filter.Tendsto.vadd_const, Function.extend_vadd, AddOreLocalization.oreSub_eq_iff, EuclideanGeometry.orthogonalProjection_apply', MeasureTheory.measure_vadd, Set.inter_vadd_union_subset_union, DirectLimit.vadd_def, Finset.union_vadd_inter_subset_union, Finset.vadd_inter_subset, Metric.preimage_vadd_ball, Filter.NeBot.vadd_filter, op_vadd_add, Set.vadd_set_insert, Filter.Tendsto.const_vadd, Set.vadd_set_eq_empty, AddAction.stabilizer_vadd_eq_right, AddAction.IsTopologicallyTransitive.exists_vadd_inter, vadd_add_vadd, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, toDual_vadd, ofMul_vadd, Finset.card_vadd_finset, Metric.vadd_ball, Set.vadd_set_range, MeasureTheory.IsAddFundamentalDomain.nullMeasurableSet_vadd, PUnit.vadd_eq, dist_vadd_cancel_right, Set.add_subset_iff_left, Finset.op_vadd_finset_subset_add, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, DirectSum.GdistribMulAction.smul_zero, Set.vadd_mem_vadd_set_iff, FreeAddMonoid.ofList_vadd, IsCentralVAdd.unop_vadd_eq_vadd, Finset.vadd_finset_symmDiff, IsClosed.vadd_right_of_isCompact, Measurable.fun_const_vadd, Set.vadd_Icc, AffineSpace.asymptoticNhds_vadd_pure, Filter.Germ.coe_vadd', Finset.vadd_finset_inter, vadd_eq_iff_eq_neg_vadd, IsAddFoelner.mean_vadd_eq_mean_vadd, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, MeasureTheory.isAddRightInvariant_map_vadd, Set.toFinset_vadd_set, IsSemilinearSet.vadd, Set.Nonempty.vadd, vadd_zero_vadd, convexHull_vadd, EMetric.infEdist_vadd, 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, UniformSpace.Completion.coe_vadd, Metric.preimage_vadd_closedEBall, Set.image_op_vadd, isOpenMap_vadd, Finset.vadd_union, Set.vadd_iInter₂_subset, Finset.addDysonETransform_snd, AddAction.vadd_fixedBy, Set.mem_vadd, Finset.vadd_finset_subset_iff, MeasureTheory.measure_neg_vadd_symmDiff, Finset.vadd_finset_nonempty, AffineSubspace.coe_pointwise_vadd, AffineEquiv.map_vadd, vadd_vsub_vadd_cancel_right, AffineSubspace.wSameSide_vadd_left_iff, Set.union_vadd_inter_subset_union, Fin.partialSum_left_neg, MeasurableConstVAdd.measurable_const_vadd, AddOpposite.op_vadd, mem_vadd_const_affineSegment, Set.Finite.toFinset_vadd_set, Set.vadd_set_singleton, AddAction.image_inter_image_iff, AddTorsor.vadd_vsub', vadd_mem_affineSpan_of_mem_affineSpan_of_mem_vectorSpan, continuousAt_const_vadd_iff, AffineMap.vadd_linear, isClosedMap_vadd, IsAddUnit.vadd_tendsto_vadd_iff, ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_self, MeasurableVAdd₂.measurable_vadd, Set.image2_vadd, AddAction.Quotient.mk_vadd_out, map_vadd, Set.vadd_iInter_subset, Finset.vadd_finset_def, AddAction.IsBlock.pairwiseDisjoint_range_vadd, measurable_const_vadd_iff, IsAddUnit.preimage_vadd_set, ContinuousWithinAt.vadd, Set.image_vadd, IsUpperSet.vadd_subset, IsCentralVAdd.op_vadd_eq_vadd, ProperVAdd.isProperMap_vadd_pair, Filter.Tendsto.const_vadd_asymptoticNhds, AddAction.zmultiplesQuotientStabilizerEquiv_symm_apply, mem_fixingAddSubmonoid_iff, arrowAddAction_vadd, MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum, smul_vsub_vadd_mem_affineSpan_pair, Pi.vadd_def, 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, AddUnits.val_vadd, AddSubgroup.vadd_opposite_add, Set.vadd_univ, MeasureTheory.StronglyMeasurable.vadd, AddGroup.preimage_vadd_set, AffineMap.vadd_lineMap, op_vadd_coe_set, Set.vadd_graphOn_univ, affinity_unitBall, isSimplyConnected_vadd_set_iff, MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'', Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Set.vadd_set_eq_univ, AddAction.surjective, AmpleSet.vadd, AddAction.IsTrivialBlock.vadd, Set.vadd_set_subset_vadd_set_iff, VAddMemClass.vadd_mem, Metric.vadd_sphere, Finset.add_subset_iff_right, Metric.preimage_vadd_sphere, StrictConvex.affinity, MeasureTheory.mem_addFundamentalInterior, AddOpposite.unop_vadd, op_vadd_op_vadd, iteratedFDerivWithin_comp_sub, Set.image_vadd_distrib, AddAction.orbit.coe_vadd, Finset.singleton_vadd_singleton, differentiableWithinAt_comp_sub, Sum.vadd_inr, vadd_ball_zero, vadd_preimage_set_subset, EuclideanGeometry.orthogonalProjection_vadd_eq_self, MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum', Filter.map₂_vadd, AEMeasurable.vadd_const, MeasureTheory.IsAddFundamentalDomain.iUnion_vadd_ae_eq, MeasureTheory.IsAddFundamentalDomain.pairwise_aedisjoint_of_ac, AddAction.nsmul_vadd_eq_iff_minimalPeriod_dvd, ofAdd_smul, Finset.Nonempty.vadd, VAddAssocClass.vadd_assoc, Set.vadd_inter_nonempty_iff', MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum', IsClosed.vadd, AddCon.vadd, Finset.mem_vadd_finset, SubAddAction.vadd_mem', DomAddAct.norm_vadd_Lp, edist_vadd_left, AffineIsometryEquiv.coe_vaddConst, Set.preimage_vadd_neg, Measurable.const_vadd, MeasureTheory.measure_vadd_eq_zero_iff, interior_vadd, mem_leftAddCoset_iff, signedDist_vadd_left_swap, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum, mem_rightAddCoset_iff, Set.mem_vaddAntidiagonal, AddAction.orbitRel.Quotient.mapsTo_vadd_orbit, Finset.add_mem_vadd_finset_iff, AddAction.vadd_orbit_eq_orbit_vadd, QuotientAddGroup.sound, AddAction.IsBlock.not_vadd_set_ssubset_vadd_set, Pi.vadd_comp, EuclideanGeometry.reflection_apply_of_mem, isProperLinearSet_iff, Set.vadd_set_prod, AddAction.vadd_orbit, AddAction.minimalPeriod_eq_card, Set.iUnion_op_vadd_set, AddGroup.preimage_vadd_setₛₗ, MeasureTheory.SimpleFunc.vadd_apply, Finset.vadd_finset_subsetSum_subset_subsetSum_insert, Filter.vadd_le_vadd_left, AddAction.zsmul_vadd_eq_iff_minimalPeriod_dvd, Finset.card_inter_vadd, IsCompact.preimage_vadd, SubAddAction.fixingAddSubgroup_vadd_eq_fixingAddSubgroup_map_conj, vadd_neg_vadd, ContinuousConstVAdd.continuous_const_vadd, MeasureTheory.measure_neg_vadd_sdiff, Seminorm.vadd_closedBall, ContinuousMap.vadd_apply, MeasureTheory.SimpleFunc.coe_vadd, LipschitzWith.vadd, Finset.addDysonETransform_fst, DilationEquiv.smulTorsor_apply, Set.vadd_set_univ, AffineSubspace.vadd_mem_iff_mem_of_mem_direction, Set.vadd_iUnion₂, signedDist_vadd_right, Finset.biUnion_op_vadd_finset, neg_vadd_vadd, IsClosed.vadd_left_of_isCompact, Inseparable.const_vadd, DomAddAct.vadd_aeeqFun_const, AddOreLocalization.vadd_zero_oreSub_zero_vadd, ProperConstVAdd.isProperMap_vadd, Set.vadd_set_sUnion, AffineMap.map_vadd, affineSegment_const_vadd_image, Finset.vadd_finset_card_le, 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, AffineMap.lineMap_vadd_apply, AddAction.compHom_vadd_def, Metric.preimage_vadd_closedBall, measurableEmbedding_const_vadd, Finset.coe_vadd, Filter.Tendsto.vadd, mem_own_leftAddCoset, ContinuousAt.const_vadd, AddAction.vadd_orbit_subset, Set.add_pair, AddAction.IsBlock.isBlockSystem, Set.sUnion_vadd, 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, toColex_vadd', AddAction.IsBlock.of_subset, vadd_segment, DomAddAct.vadd_aeeqFun_aeeq, AddAction.isBlock_iff_vadd_eq_or_disjoint, MeasureTheory.vadd_mem_ae, image_vadd_set, AddOreLocalization.add_vadd, dist_vadd_left, RestrictedProduct.vadd_apply, ContinuousAffineMap.map_vadd, iteratedFDerivWithin_comp_add_right, vadd_mem_nhds_vadd, Finset.affineCombination_apply, faithfulVAdd_iff_injective_vadd_zero, Option.vadd_def, DomAddAct.vadd_Lp_ae_eq, AddAction.IsBlock.of_addSubgroup_of_conjugate, AddAction.coe_aestabilizer, AddAction.mem_stabilizer_finset', AffineSpace.vadd_asymptoticNhds, MeasureTheory.AEStronglyMeasurable.const_vadd, Finset.op_vadd_finset_add_eq_add_vadd_finset, zero_vadd_eq_id, toAdd_vadd, midpoint_vadd_midpoint, AffineSubspace.pointwise_vadd_direction, AddAction.mem_orbit_iff, Set.vadd_set_subset_iff_subset_neg_vadd_set, AffineSubspace.wSameSide_smul_vsub_vadd_left, DomAddAct.vadd_Lp_sub, Finset.add_subset_iff_left, Filter.vadd_pure, AddCon.coe_vadd, 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, Finset.singleton_add, vadd_mem_nhds_self, ZSpan.exist_unique_vadd_mem_fundamentalDomain, AddAction.mem_stabilizer_set', vadd_set_closure_subset, AddAction.nsmul_vadd_eq_iff_period_dvd, Finset.image_vadd, Set.singleton_vadd, Function.Periodic.map_vadd_zmultiples, dist_vadd_right, AddSubgroup.leftTransversals.vadd_diff_vadd, linearIndependent_set_iff_affineIndependent_vadd_union_singleton, AddAction.IsBlock.disjoint_vadd_of_ne, AffineMap.lineMap_apply, Finset.vadd_finset_union, LocallyConstant.vadd_apply, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Filter.vadd_le_vadd_right, Set.vadd_set_subset_iff, Prod.vadd_mk, differentiableWithinAt_comp_add_right, Set.vadd_union, 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, Set.range_vadd_range, IsAddUnit.vadd_left_cancel, rightAddCoset_eq_iff, isProperMap_vadd, StarConvex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, EuclideanGeometry.inversion_def, AddAction.vadd_zsmul_movedBy_eq_of_addCommute, AddAction.toFun_apply, AddAction.le_stabilizer_vadd_right, AddAction.zsmul_vadd_mod_minimalPeriod, IsIsometricVAdd.isometry_vadd, Set.range_vadd, comp_vadd_left, Set.range_add, AddAction.nsmul_period_vadd, properVAdd_iff, ProperlyDiscontinuousVAdd.finite_disjoint_inter_image, ediam_vadd, AddAction.orbitRel.Quotient.orbit.coe_vadd, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, DomAddAct.vadd_Lp_neg, AddAction.period_eq_minimalPeriod, ergodic_vadd_of_denseRange_nsmul, Set.infinite_vadd_set, nndist_vadd_right, AddTorsor.vsub_vadd', Set.inter_vadd_subset, AddAction.op_vadd_set_stabilizer_subset, leftAddCoset_eq_iff, vadd_iterate, zero_vadd, Filter.vadd_filter_bot, AffineSubspace.mem_affineSpan_insert_iff, AddOreLocalization.oreSub_vadd_char, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, MeasurableVAdd.measurable_vadd_const, vadd_ite, eq_addCosets_of_normal, Filter.HasBasis.vadd, AddAction.addSubgroup_vadd_def, Filter.NeBot.vadd, AddOreLocalization.zero_vadd, ProperVAdd.isProperMap_vadd_pair_set, Set.vadd_set_subset_add, MeasureTheory.eventually_nhds_zero_measure_vadd_diff_lt, Sigma.vadd_mk, mem_affineSpan_iff_eq_weightedVSubOfPoint_vadd, AddActionHom.map_vadd, mem_affineSpan_iff_exists, AddAction.nsmul_add_period_vadd, MeasureTheory.vadd_set_ae_eq, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_ac, AddMonoidHom.preimage_vadd_setₛₗ, Metric.vadd_closedEBall, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum, Prod.vadd_def, Function.update_vadd, toLex_vadd, vadd_closure_subset, aemeasurable_const_vadd_iff, Set.natCard_vadd_set, Finset.vadd_finset_insert, AddAction.isBlock_iff_disjoint_vadd_of_ne, Prod.vadd_snd, preimage_vadd_setₛₗ_of_isAddUnit_isAddUnit, IsOrderedVAdd.vadd_le_vadd, Filter.Germ.const_vadd, Set.vadd_sUnion, Finset.weightedVSub_vadd, AffineEquiv.ofLinearEquiv_apply, UpperHalfPlane.exists_SL2_smul_eq_of_apply_zero_one_eq_zero, AddAction.vadd_zsmul_fixedBy_eq_of_addCommute, MeasureTheory.tendsto_vadd_ae, AffineEquiv.pointReflection_apply, AddAction.period_eq_zero_iff, Homeomorph.vadd_apply, AffineSubspace.wOppSide_smul_vsub_vadd_right, Function.Periodic.vadd, isOpenMap_vadd_of_sigmaCompact, Filter.vadd_filter_le_vadd_filter, PUnit.vadd_eq', AddAction.mem_fixedBy, AffineMap.coe_lineMap, dite_vadd, Equiv.coe_constVAdd, AffineSubspace.vadd_mem_of_mem_direction, DomAddAct.edist_vadd_Lp, Set.op_vadd_inter_nonempty_iff, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, AffineEquiv.coe_constVSub_symm, Finset.op_vadd_addConvolution_eq_addConvolution_vadd, vectorSpan_vadd, AffineSubspace.pointwise_vadd_eq_map, Filter.covariant_vadd, Continuous.vadd, Filter.mem_vadd_filter, Bornology.IsVonNBounded.vadd, ofColex_vadd, vadd_openSegment, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, AddAction.toPerm_symm_apply, AddSubmonoid.vadd_def, Specializes.const_vadd, IsLinearSet.vadd, Set.empty_vadd, Prod.vadd_swap, AddAction.mem_orbit, vadd_vsub_vadd_comm, ite_vadd, SubAddAction.vadd_of_tower_mem, ergodic_vadd_of_denseRange_zsmul, AddAction.orbitEquivQuotientStabilizer_symm_apply, AffineSubspace.pointwise_vadd_bot, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, Finset.vadd_finset_empty, 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, AddAction.is_two_pretransitive_iff, Function.Embedding.coe_vadd, properVAdd_iff_continuousVAdd_ultrafilter_tendsto, MeasurableEquiv.vadd_apply, Set.vadd_image_prod, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum, Set.vadd_set_iUnion, vadd_zero_add, signedDist_vadd_right_swap, Wbtw.vadd_const, SetLike.vadd_def, DomAddAct.mk_vadd_toLp, Wbtw.const_vadd, VAdd.vadd_lt_vadd_of_le_of_lt, mem_leftAddCoset, EMetric.vadd_closedBall, Finsupp.mem_vaddAntidiagonal_of_addGroup, Finset.vadd_finset_subset_add, add_ball, AffineMap.homothety_apply, SetLike.GradedSMul.smul_mem, dist_vadd_cancel_left, vadd_univ_pi, IsOrderedVAdd.vadd_le_vadd_right, Function.vadd_const, hasFDerivWithinAt_comp_add_right, AffineSubspace.pointwise_vadd_top, ContinuousAffineMap.vadd_contLinear, IsometryEquiv.vaddConst_apply, Finset.biUnion_vadd_finset, MeasureTheory.IsAddFundamentalDomain.sum_restrict_of_ac, isLinearSet_iff_exists_fg_eq_vadd, slope_vadd_const, affineSegment_vadd_const_image, Set.Infinite.vadd_set, vadd_vadd_vadd_comm, Filter.vadd_bot, MeasureTheory.measure_preimage_vadd_le, vadd_iterate_apply, AffineIsometry.map_vadd, AddAction.isTopologicallyTransitive_iff_dense_iUnion, UpperHalfPlane.vadd_right_cancel_iff, AddAction.quotient_preimage_image_eq_union_add, DomAddAct.vadd_Lp_const, Prod.mk_vadd_mk, AddAction.mem_orbit_of_mem_orbit, Cardinal.mk_vadd_set, Filter.vadd_eq_bot_iff, UniformContinuousConstVAdd.uniformContinuous_const_vadd, MeasureTheory.IsAddFundamentalDomain.ae_covers, vadd_left_injective', AddAction.vadd_mem_of_set_mem_fixedBy, Set.vadd_set_mono, DirectSum.Gmodule.zero_smul, leftAddCoset_rightAddCoset, Finset.pairwiseDisjoint_vadd_iff, SetLike.mk_vadd_of_tower_mk, signedDist_vadd_left, AddAction.mem_stabilizer_finset_iff_subset_vadd_finset, QuotientAddGroup.orbit_eq_out_vadd, Finset.vadd_subset_vadd_right, Set.vadd_set_empty, Finset.weightedVSub_vadd_affineCombination, iteratedFDerivWithin_comp_add_left', toMul_smul, Set.mem_vadd_set_neg, vadd_eq_add, MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum_of_ac, AddOpposite.vadd_eq_add_unop, AddOpposite.op_vadd_eq_op_vadd_op, vadd_pi_subset, MeasureTheory.measure_inter_neg_vadd, Finset.vadd_finset_inter_subset, Set.iUnion_vadd_right_image, Finset.addETransformRight_snd, mem_own_rightAddCoset, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, AddMonoidHom.vaddZeroHom_apply, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum', AffineSubspace.vadd_mem_iff_mem_direction, instContravariantClassHVAddLeOfIsOrderedCancelVAdd, AddAction.zero_vadd, edist_vadd_vadd_le, AddAction.minimalPeriod_pos, IsOpen.exists_vadd_mem, Sigma.vadd_def, MeasureTheory.measure_union_neg_vadd, ofLex_vadd', vadd_closedBall_zero, AddSubgroup.vadd_toLeftFun, AffineSubspace.wSameSide_smul_vsub_vadd_right, Convex.smul_vadd_mem_of_isClosed_of_mem_asymptoticCone, diam_vadd, AddAction.injective, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, EuclideanGeometry.reflection_apply', SeparationQuotient.mk_vadd, Finset.centroid_pair, Set.disjoint_vadd_set_left, Set.vadd_set_nonempty, Filter.vadd.instNeBot, DomAddAct.mk_vadd_mk_aeeqFun, VAdd.vadd_lt_vadd_of_lt_of_le, vadd_closure_orbit_subset, AffineSubspace.sSameSide_vadd_left_iff, Filter.le_vadd_iff, vadd_coe_set, subset_interior_vadd, AddOreLocalization.oreSub_zero_vadd, Set.Nonempty.vadd_set, Set.piecewise_vadd, vadd_left_cancel_iff, MeasureTheory.AEStronglyMeasurable.const_vadd', Finset.addETransformLeft_snd, Set.pairwiseDisjoint_vadd_iff, continuous_const_vadd_iff, MeasureTheory.IsAddFundamentalDomain.vadd, AffineSubspace.wSameSide_vadd_right_iff, AddAction.surjective_vadd, Finsupp.mem_vaddAntidiagonal_iff, Finset.addDysonETransform.vadd_finset_snd_subset_fst, upperClosure_vadd, IsAddFoelner.mean_vadd_eq_mean, AddAction.minimalPeriod_eq_one_iff_fixedBy, Filter.Germ.coe_vadd, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, AddAction.Quotient.vadd_mk, Set.add_subset_iff_right, derivWithin_comp_add_const, Finset.vadd_finset_eq_empty, AddOreLocalization.zero_sub_vadd, IsometryEquiv.constVAdd_apply, vadd_vsub_vadd_cancel_left, Sum.vadd_def, wbtw_or_wbtw_smul_vadd_of_nonneg, Bornology.isVonNBounded_vadd, Finset.addETransformLeft_fst, vsub_vadd, LinearPMap.vadd_apply, SlashInvariantForm.vAdd_width_periodic, UpperHalfPlane.coe_vadd, Ideal.univ_eq_iUnion_image_add, AffineBasis.coord_vadd, AddSubgroup.mk_vadd, vadd_uniformity, AddAction.toPermHom_apply_apply, Set.neg_vadd_set_distrib, vadd_vsub, AffineMap.homothety_def, Finsupp.smul_apply_addAction, MeasureTheory.measure_symmDiff_neg_vadd, wbtw_const_vadd_iff, AffineIsometryEquiv.map_vadd, op_vadd_eq_add, IsCompact.vadd, rightAddCoset_assoc, AffineEquiv.vaddConst_apply, neg_vadd_eq_iff, HahnModule.support_smul_subset_vadd_support, support_translate, nndist_vadd, Set.mem_neg_vadd_set_iff, amenable_of_maxAddFoelner_neBot, AffineSubspace.vadd_mem_pointwise_vadd_iff, AddConstMap.coe_vadd, AddOreLocalization.vadd_zero_vadd, AddAction.disjoint_image_image_iff, Sum.vadd_swap, vadd_add_vadd_comm, Set.vadd_iUnion, Finset.vadd_univ, Option.vadd_none, Finset.centroid_pair_fin, SetLike.mk_vadd_mk, Finset.vadd_stabilizer_of_no_doubling, Continuous.const_vadd, AddOreLocalization.vadd_sub_zero, AddOreLocalization.vadd_cancel, Set.vadd_subset_vadd_right, AddAction.isPretransitive_iff, Specializes.vadd, AddAction.zsmul_add_period_vadd, Seminorm.vadd_ball, IsAddFoelner.tendsto_meas_vadd_symmDiff, zero_leftAddCoset, AddAction.set_mem_fixedBy_iff, MeasureTheory.isAddLeftInvariant_map_vadd, Set.disjoint_vadd_set_right, UpperHalfPlane.modular_T_zpow_smul, Finset.vadd_finset_subset_vadd, vadd_right_injective, AddAction.mem_stabilizer_finset, AddUnits.vadd_neg, MeasureTheory.map_vadd, Metric.vadd_eball, AddAction.mem_stabilizer_set_iff_vadd_set_subset, AddSubgroup.vadd_apply_eq_vadd_apply_neg_vadd, Set.toFinset_vadd, hasFDerivWithinAt_comp_sub, derivWithin_comp_sub_const, EuclideanGeometry.dist_smul_vadd_eq_dist, vadd_preimage_set_subsetₛₗ, MeasureTheory.StronglyMeasurable.const_vadd', Filter.covariant_vadd_filter, collinear_iff_exists_forall_eq_smul_vadd, Set.iUnion₂_vadd, Set.union_vadd, SetLike.coe_GSMul, MeasureTheory.measure_preimage_vadd, vadd_dite, AffineIsometryEquiv.coe_vaddConst', Set.vadd_set_symmDiff, uniformContinuous_vadd, wbtw_or_wbtw_smul_vadd_of_nonpos, Equiv.vadd_def, Set.Finite.toFinset_vadd, AddOreLocalization.expand', Set.vadd_eq_empty, Filter.vadd_filter_neBot_iff, SubAddAction.val_vadd, LinearPMap.vadd_domain, IsCompact.closedBall_add, Set.Finite.vadd_set, AddMonoidHom.transfer_def, Finset.Nonempty.vadd_finset, AddAction.QuotientAction.inv_mul_mem, DomAddAct.vadd_apply, Finset.vadd_mem_vadd_finset_iff, WithIdealFilter.mem_nhds_iff, AffineSpace.asymptoticNhds_eq_smul_vadd, QuotientAddGroup.eq_class_eq_leftCoset, FreeAddMonoid.of_vadd, MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum', IsAddUnit.vadd_uniformity, Set.iUnion_vadd_set, MeasureTheory.measure_neg_vadd_union, Set.preimage_vadd, AddSubgroup.exists_leftTransversal_of_FiniteIndex, Prod.vadd_fst, Filter.EventuallyEq.vadd, MeasureTheory.IsAddFundamentalDomain.aedisjoint, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, AffineMap.homothety_add, orbit_addSubgroup_eq_rightCoset, Set.vadd_set_union, wbtw_vadd_const_iff, IsOrderedVAdd.vadd_le_vadd_left, 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, Set.IsWF.min_vadd, Finset.inter_vadd_union_subset_union, normal_iff_eq_addCosets, MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac, Finset.neg_vadd_mem_iff, Prod.snd_vadd, MeasureTheory.addFundamentalFrontier_vadd, Set.vadd_set_iInter, ULift.vadd_down, AEMeasurable.fun_const_vadd, AddAction.nsmul_mod_period_vadd, EuclideanGeometry.orthogonalProjection_apply, Set.vadd_sInter_subset, 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, Set.Finite.vadd, AddActionHom.map_vadd', Set.singleton_vadd_singleton, AddSubgroup.vadd_opposite_image_add_preimage, Filter.Tendsto.asymptoticNhds_vadd_const, vadd_add_assoc, AffineSubspace.setOf_sOppSide_eq_image2, Set.IsWF.vadd, AffineEquiv.map_vadd', ofDual_vadd', subset_interior_vadd_right, AddAction.bijective, LinearPMap.coe_vadd, AddAction.isMultiplyPretransitive_iff, Finset.vadd_finset_subset_vadd_finset_iff, denseRange_vadd, SubAddAction.val_vadd_of_tower, Set.vadd_inter_nonempty_iff, Finset.subset_vadd_finset_iff, nndist_vadd_cancel_left, Finset.vaddAntidiagonal_min_vadd_min, Set.iUnion_vadd_eq_setOf_exists, Finset.vadd_singleton, ThreeAPFree.vadd_set, IsAddUnit.neg_vadd, AffineSubspace.setOf_wSameSide_eq_image2, AddAction.le_stabilizer_iff_vadd_le, Finset.vadd_subset_vadd, AddAction.vadd_mem_fixedBy_iff_mem_fixedBy, vadd_right_cancel_iff, Set.vadd_empty, AddAction.orbit_vadd, Finset.vadd_mem_vadd_finset, MeasureTheory.VAddInvariantMeasure.measure_preimage_vadd, MeasureTheory.addFundamentalInterior_vadd, MeasureTheory.innerRegular_map_vadd, iteratedFDerivWithin_comp_sub', AffineSubspace.sSameSide_smul_vsub_vadd_left, GradedMonoid.mk_smul_mk, Finset.addConvolution_op_vadd_eq_addConvolution_add_neg, MeasureTheory.measure_preimage_vadd_null, Filter.vadd_filter_eq_bot_iff, AEMeasurable.vadd, IsOpen.right_addCoset, IsAddUnit.vadd_bijective, MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum', DomAddAct.dist_vadd_Lp, AddAction.mem_stabilizerAddSubmonoid_iff, IsAddUnit.measurable_const_vadd_iff, MeasureTheory.eventuallyConst_vadd_set_ae, vadd_ball'', ULift.vadd_def, fderivWithin_comp_add_right, ContinuousWithinAt.const_vadd, DirectSum.gsmulHom_apply_apply, Sum.vadd_inl, AddAction.mem_stabilizer_set, Finset.vadd_finset_subset_vadd_finset, DomAddAct.vadd_Lp_zero, Metric.preimage_vadd_eball, Filter.EventuallyEq.const_vadd, Set.vadd_set_inter, IsOpen.vadd, Set.MapsTo.vadd_setₛₗ, DirectSum.GdistribMulAction.smul_add, Finset.vadd_finset_sdiff, Set.subset_vadd_set_iff, punctured_nhds_vadd, MeasureTheory.measure_vadd_null, Finset.empty_vadd, LocallyConstant.coe_vadd, nndist_vadd_vadd_le, AddAction.stabilizerEquivStabilizer_zero, IsClosed.right_addCoset, IsClosed.left_addCoset, approxAddOrderOf.vadd_subset_of_coprime, instCovariantClassHVAddLeOfIsOrderedVAdd, Absorbent.vadd_absorbs, AffineSubspace.wOppSide_vadd_left_iff, Finset.vadd_def, MeasureTheory.Measure.isAddHaarMeasure_map_vadd, StrictConvex.vadd, ofDual_vadd, IterateAddAct.mk_vadd, AddAction.le_stabilizer_vadd_left, Filter.vadd_filter.instNeBot, Set.iUnion_vadd_left_image, Set.mem_vadd_set_iff_neg_vadd_mem, MeasureTheory.vaddInvariantMeasure_map_vadd, SubAddAction.exists_vadd_of_last_eq, Set.vadd_set_iInter₂_subset, sub_ball, OpenPartialHomeomorph.unitBallBall_apply, vadd_pi, eq_vadd_iff_vsub_eq, Finset.union_vadd, IsAddFoelner.amenable, totallyBounded_iff_subset_finite_iUnion_nhds_zero, leftAddCoset_mem_leftAddCoset, Affine.Simplex.ninePointCircle_center, Set.vadd_subset_vadd_left, AffineMap.lineMap_vadd, IsOpen.dense_iUnion_vadd, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, isHomeomorph_vadd, AddAction.ofQuotientStabilizer_vadd, Prod.fst_vadd, DomAddAct.nnnorm_vadd_Lp, spectrum.vadd_eq, AddUnits.vadd_mk_apply, Finset.addETransformRight_fst, isAddFoelner_iff, Bornology.IsBounded.vadd, Filter.map_vadd, dist_vadd_vadd_le, Finset.vadd_subset_vadd_left, Finset.card_vadd_inter_vadd, AddAction.IsPretransitive.exists_vadd_eq, Finset.image_vadd_product, SlashInvariantForm.vAdd_apply_of_mem_strictPeriods, leftAddCoset_assoc, AddOreLocalization.oreSub_vadd_oreSub, AddAction.toPerm_apply, MeasureTheory.NullMeasurableSet.vadd, Set.vadd_set_sInter_subset, AddAction.isBlock_iff_vadd_eq_of_mem, fderivWithin_comp_sub, AddSubmonoid.mk_vadd, EuclideanGeometry.reflection_apply, Filter.vadd_set_mem_vadd_filter, IsCompact.add_closedBall, AddAction.vadd_set_stabilizer_subset, Function.Embedding.vadd_def, Set.finite_vadd_set, AddAction.zsmul_mod_period_vadd, AffineBasis.basisOf_vadd, Pi.vadd_apply', UpperHalfPlane.vadd_im, affineIndependent_vadd, AddAction.zsmul_vadd_eq_iff_period_dvd, AddAction.ofQuotientStabilizer_mk, AffineMap.lineMap_vadd_lineMap, Monotone.vadd, UpperHalfPlane.modular_T_smul, AddAction.IsBlock.vadd_eq_or_disjoint, EMetric.preimage_vadd_ball, Set.iInter_vadd_subset, AddAction.vadd_mem_orbit_vadd, DomAddAct.vadd_Lp_val, AffineSubspace.sOppSide_vadd_left_iff, QuotientAddGroup.orbit_mk_eq_vadd, Finset.dens_vadd_finset, closure_vadd, UpperHalfPlane.vadd_left_injective, sbtw_const_vadd_iff, hasFDerivWithinAt_comp_add_left, MeasureTheory.StronglyMeasurable.const_vadd, ProperlyDiscontinuousVAdd.finite_stabilizer', AddActionHom.coe_vadd, Finset.neg_vadd_finset_distrib, Finset.singleton_vadd, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, continuousOn_const_vadd_iff, AddAction.orbit_vadd_subset, ContinuousOn.const_vadd, Set.vadd_set_pi, vadd_left_mem_affineSpan_pair, signedDist_vadd_vadd, AffineMap.coe_homothety, Set.powersetCard.coe_vadd, Pi.vadd_apply, ContinuousAffineMap.vadd_apply, MeasurableSet.const_vadd, Set.image_op_vadd_distrib, AddAction.mem_stabilizer_finset_iff_vadd_finset_subset, Set.encard_vadd_set, EuclideanGeometry.angle_const_vadd, Equiv.pointReflection_apply, isLinearSet_iff_exists_fin_addMonoidHom, mem_fixingAddSubgroup_iff, Set.vadd_set_iInter_subset, AddAction.isPretransitive_iff_base, AffineSubspace.sOppSide_smul_vsub_vadd_right, IsCompact.closedBall_sub, Measurable.vadd', Filter.pure_vadd, VAddCommClass.toAddActionHom_apply, Set.pair_add, DirectSum.Gmodule.add_smul, EMetric.preimage_vadd_closedBall
«term_+ᵥ_» 📖CompOp
«term_-ᵥ_» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
add_dite 📖
add_ite 📖add_dite
dite_add 📖
dite_add_dite 📖
dite_div 📖
dite_div_dite 📖
dite_mul 📖
dite_mul_dite 📖
dite_sub 📖
dite_sub_dite 📖
div_dite 📖
div_ite 📖div_dite
ite_add 📖dite_add
ite_add_ite 📖
ite_div 📖dite_div
ite_div_ite 📖dite_div_dite
ite_mul 📖dite_mul
ite_mul_ite 📖
ite_sub 📖dite_sub
ite_sub_ite 📖dite_sub_dite
mul_dite 📖
mul_ite 📖mul_dite
sub_dite 📖
sub_ite 📖sub_dite

---

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