Documentation Verification Report

CompleteBooleanAlgebra

πŸ“ Source: Mathlib/Order/CompleteBooleanAlgebra.lean

Statistics

MetricCount
DefinitionstoDistribLattice, CompleteAtomicBooleanAlgebra, toCompleteBooleanAlgebra, toCompletelyDistribLattice, CompleteBooleanAlgebra, toBooleanAlgebra, toCompl, toCompleteDistribLattice, toCompleteLattice, toHImp, toSDiff, CompleteDistribLattice, of, toCoframe, toCoframeMinimalAxioms, toCompleteLattice, toFrame, toFrameMinimalAxioms, ofMinimalAxioms, toBiheytingAlgebra, toCoframe, toFrame, toHNot, toSDiff, toCompletelyDistribLattice, CompletelyDistribLattice, of, toCompleteDistribLattice, toCompleteLattice, ofMinimalAxioms, toBiheytingAlgebra, toCompl, toCompleteDistribLattice, toCompleteLattice, toHImp, toHNot, toSDiff, toDistribLattice, coframe, coframeMinimalAxioms, completeAtomicBooleanAlgebra, completeBooleanAlgebra, completeDistribLattice, completeDistribLatticeMinimalAxioms, completelyDistribLattice, completelyDistribLatticeMinimalAxioms, frame, frameMinimalAxioms, Coframe, of, toCompleteLattice, ofMinimalAxioms, toCoheytingAlgebra, toCompleteLattice, toHNot, toSDiff, Frame, of, toCompleteLattice, ofMinimalAxioms, toCompl, toCompleteLattice, toHImp, toHeytingAlgebra, instCoframe, instCompleteAtomicBooleanAlgebra, instCompleteBooleanAlgebra, instCompleteDistribLattice, instCompletelyDistribLattice, instFrame, instCompleteAtomicBooleanAlgebra, instCompleteBooleanAlgebra, instCoframe, instCompleteAtomicBooleanAlgebra, instCompleteBooleanAlgebra, instCompleteDistribLattice, instCompletelyDistribLattice, instFrame, instCoframe, instCompleteAtomicBooleanAlgebra, instCompleteBooleanAlgebra, instCompleteDistribLattice, instCompletelyDistribLattice, instFrame, instCompleteAtomicBooleanAlgebra, instCompleteBooleanAlgebra
86
TheoremsiInf_iSup_eq, himp_eq, inf_compl_le_bot, le_sup_inf, sdiff_eq, top_le_sup_compl, iInf_sup_le_sup_sInf, inf_sSup_le_iSup_inf, sdiff_le_iff, top_sdiff, iInf_iSup_eq, iInf_iSup_eq', iSup_iInf_eq, himp_bot, iInf_iSup_eq, le_himp_iff, sdiff_le_iff, top_sdiff, iInf_sup_eq, iInf_sup_le_sup_sInf, sInf_sup_eq, sup_iInf_eq, sup_iInfβ‚‚_eq, sup_sInf_eq, sdiff_le_iff, top_sdiff, iSup_inf_eq, inf_iSup_eq, inf_iSupβ‚‚_eq, inf_sSup_eq, inf_sSup_le_iSup_inf, sSup_inf_eq, himp_bot, le_himp_iff, sInf_eq, sSup_eq, biInf_sup_biInf, biSup_iInter_of_pairwise_disjoint, biSup_inf_biSup, biSup_inter_of_pairwise_disjoint, biSup_symmDiff_biSup_le, compl_eq_sSup_disjoint, compl_iInf, compl_iSup, compl_sInf, compl_sInf', compl_sSup, compl_sSup', disjoint_iSup_iff, disjoint_iSupβ‚‚_iff, disjoint_sSup_iff, himp_eq_sSup, himp_iInf_eq, himp_le_iff, hnot_eq_sInf_codisjoint, iInf_iSup_eq, iInf_sup_eq, iInf_sup_iInf, iInf_sup_of_antitone, iInf_sup_of_monotone, iInfβ‚‚_sup_eq, iSup_disjoint_iff, iSup_himp_eq, iSup_iInf_eq, iSup_iInf_le, iSup_inf_eq, iSup_inf_iSup, iSup_inf_of_antitone, iSup_inf_of_monotone, iSup_sdiff_eq, iSup_symmDiff_iSup_le, iSupβ‚‚_disjoint_iff, iSupβ‚‚_inf_eq, inf_iSup_eq, inf_iSupβ‚‚_eq, inf_sSup_eq, le_iInf_iSup, le_sdiff_iff, sInf_sup_eq, sInf_sup_sInf, sSup_disjoint_iff, sSup_inf_eq, sSup_inf_sSup, sdiff_eq_sInf, sdiff_iSup_eq, sup_iInf_eq, sup_iInfβ‚‚_eq, sup_sInf_eq
88
Total174

Coframe

Definitions

NameCategoryTheorems
toDistribLattice πŸ“–CompOpβ€”

CompleteAtomicBooleanAlgebra

Definitions

NameCategoryTheorems
toCompleteBooleanAlgebra πŸ“–CompOp
1154 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, upperBounds_supClosure, SimpleGraph.locallyLinear_bot, MeasureTheory.Measure.MeasureDense.approx, Dynamics.netEntropyEntourage_monotone, Dynamics.netMaxcard_monotone_subset, Set.Finite.t2_separation, TopCat.binaryCofan_isColimit_iff, SimpleGraph.cliqueSet_bot, Set.ncard_mono, Matroid.exists_isBasis_disjoint_isBasis_of_subset, Metric.ball_disjoint_ball, NonUnitalAlgebra.gc, Set.pairwiseDisjoint_pair_insert, fixingSubgroup_antitone, Metric.disjoint_ball_infDist, convexIndependent_set_iff_inter_convexHull_subset, Dynamics.coverEntropyInfEntourage_antitone, Set.disjoint_ordT5Nhd, LowerAdjoint.closure_iUnionβ‚‚_closure, Set.smul_set_symmDiff, Set.preimage_kernImage, Language.iSup_add, IsLinearMap.image_convexHull, ProbabilityTheory.measure_limsup_eq_one, Language.reverse_iInf, LocalizedModule.subsingleton_iff_disjoint, FirstOrder.Language.Substructure.closure_eq_of_isRelational, Finpartition.isPartition_parts, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, convexHull_insert, Antitone.Icc, SimpleGraph.killCopies_bot, subset_closedConvexHull, SimpleGraph.TopEdgeLabeling.labelGraph_adj, Geometry.SimplicialComplex.vertex_mem_convexHull_iff, SimpleGraph.isBipartiteWith_neighborSet_disjoint, closedConvexHull_min, SeparatedNhds.disjoint, PrimeSpectrum.localization_specComap_range, Language.iSup_sub, convexHull_multiset_sum, Geometry.SimplicialComplex.convexHull_subset_space, MeasureTheory.liminf_ae_eq_of_forall_ae_eq, disjoint_or_subset_of_isClopen, BoxIntegral.Box.disjoint_splitCenterBox, Finset.inf_id_set_eq_sInter, SimpleGraph.cliqueFree_two, Matroid.isBase_compl_iff_maximal_disjoint_isBase, LowerAdjoint.mem_iff, Set.iUnionLift_unary, supClosure_eq_self, MonotoneOn.Icc, Geometry.SimplicialComplex.mem_space_iff, MeasureTheory.measureReal_symmDiff_le, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, SimpleGraph.eccent_bot, MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt, Disjoint.of_spanβ‚€, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRing, antitone_continuousOn, isSublattice_latticeClosure, strictMono_nhdsSet, Descriptive.Tree.take_mem, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, lowerPolar_anti, Monotone.Ici, Convex.convex_remove_iff_notMem_convexHull_remove, ProjectiveSpectrum.gc_homogeneousIdeal, LowerAdjoint.closure_union_closure, Finset.ordConnected_range_coe, AntitoneOn.Ici, AlgebraicGeometry.IsAffineOpen.isCompact_pullback_inf, Matroid.eRk_mono, inf_mem_infClosure, convexHull_eq_iInter, SimpleGraph.copyCount_bot, SimpleGraph.turanGraph_eq_top, UpperSet.sdiff_eq_left, latticeClosure_univ, FirstOrder.Language.Substructure.fg_closure_singleton, monotone_hausdorffEntourage, NFA.pumping_lemma, MeasureTheory.pairwise_disjoint_fundamentalInterior, SimpleGraph.bot_not_connected, SimpleGraph.isExtremal_top_free_iff_isTuranMaximal, MeasureTheory.monotone_spanningSets, SeparatedNhds.disjoint_closure_left, Set.Iio_disjoint_Ioi_of_not_lt, LinearMap.polar_antitone, HasCardinalLT.Set.functor_obj, Filter.Realizer.map_F, PrimeSpectrum.gc, Complex.convexHull_reProdIm, SimpleGraph.toTopEdgeLabeling_labelGraph_compl, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, IsUltrametricDist.ball_subset_trichotomy, Matroid.IsBasis.contract_dep_iff, SimpleGraph.edgeFinset_top, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, isGLB_infClosure, SimpleGraph.isClique_iff_induce_eq, Monotone.Ioo, LowerAdjoint.le_iff_subset, SimpleGraph.ComponentCompl.disjoint_right, LowerSet.disjoint_coe, AddAction.orbit.pairwiseDisjoint, MeasureTheory.measure_symmDiff_eq_top, Language.instMulRightMono, EMetric.ball_disjoint, Topology.RelCWComplex.pairwiseDisjoint', convexJoin_segments, Matroid.contract_isCocircuit_iff, FirstOrder.Language.Substructure.small_closure, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, Topology.RelCWComplex.disjoint_openCell_of_ne, FirstOrder.Language.Substructure.cg_def, IsCompact.separation_of_notMem, Cardinal.mk_monotone, Finset.isWF_sup, IsSublattice.latticeClosure_eq, AddAction.IsBlock.disjoint_vadd_left, Language.mem_iSup, OrderedFinpartition.disjoint, biUnion_range_succ_disjointed, Set.Iio_disjoint_Ioi_iff, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, exists_dist_slope_lt_pairwiseDisjoint_hasSum, LinearEquiv.dilatransvections_pow_mono, FirstOrder.Language.Substructure.mem_closure, Besicovitch.exist_disjoint_covering_families, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.exists_null_pairwise_disjoint_diff, convexHull_union_neg_eq_absConvexHull, BoxIntegral.Box.Ioo_subset_coe, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', SimpleGraph.bot_not_preconnected, SimpleGraph.Copy.topEmbedding_apply, Localization.localRingHom_injective_of_primesOver_eq_singleton, MeasureTheory.measure_liminf_cofinite_eq_zero, interior_convexHull_nonempty_iff_affineSpan_eq_top, SummationFilter.support_eq_limsInf, Matroid.IsBasis.contract_indep_iff, Descriptive.Tree.mem_pullSub_long, separated_by_continuous, SimpleGraph.UnitDistEmbedding.bot_p, Antitone.pairwise_disjoint_on_Ioo_pred, mem_absConvexHull_iff, Language.reverse_iSup, Perfect.small_diam_splitting, SimpleGraph.ComponentCompl.pairwise_disjoint, Set.Iic_disjoint_Ioi, Geometry.SimplicialComplex.convexHull_inter_convexHull, HasCardinalLT.Set.cocone_pt, Set.disjoint_pi_univ_Ioc_update_left_right, disjoint_nested_nhds_of_not_inseparable, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, AffineBasis.convexHull_eq_nonneg_coord, FirstOrder.Language.Substructure.fg_closure, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', exists_disjoint_vadd_of_isCompact, AntitoneOn.Icc, segment_subset_convexHull, MeasureTheory.measureReal_symmDiff_eq, SimpleGraph.cycleGraph_one_eq_bot, convexHull_toCone_eq_sInf, MulAction.IsBlock.disjoint_smul_of_ne, Balanced.convexHull, Disjoint.of_span, subset_absConvexHull, Matroid.IsMinor.exists_eq_contract_delete_disjoint, SimpleGraph.edgeDisjointTriangles_bot, balancedHull_subset_convexHull_union_neg, SSet.Subcomplex.degenerate_eq_top_iff, TopologicalSpace.Closeds.gc, isEmbedding_sumElim, Matroid.delete_eq_self_iff, Convex.convexHull_union, closedConvexHull_eq_closure_convexHull, MonotoneOn.Iio, Finset.mem_convexHull', subset_convexHull, Dynamics.coverEntropy_monotone, MulAction.isBlock_iff_smul_eq_or_disjoint, disjoint_interior_frontier, blimsup_thickening_mul_ae_eq_aux, SimpleGraph.emptyGraph_eq_bot, Convex.convexHull_subset_iff, SimpleGraph.chromaticNumber_top, AffineBasis.interior_convexHull, Filter.Realizer.ne_bot_iff, Matroid.contract_eq_self_iff, antitone_Ioi, Finset.sup_set_eq_biUnion, AlgebraicIndependent.adjoin_iff_disjoint, Set.Finite.infClosure, ofDual_preimage_latticeClosure, SimpleGraph.center_bot, MeasureTheory.IsSetSemiring.disjointOfUnion_props, MeasureTheory.Measure.QuasiMeasurePreserving.liminf_preimage_iterate_ae_eq, SimpleGraph.edgeSet_top, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_fst, SimpleGraph.deleteEdges_univ, Finset.coe_wcovBy_coe, Set.Ioc_disjoint_Ioc, SimpleGraph.girth_bot, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, UpperSet.codisjoint_coe, Geometry.SimplicialComplex.inter_subset_convexHull, convexJoin_segment_singleton, Matroid.isClosed_iff_isFlat, beattySeq'_symmDiff_beattySeq_pos, SimpleGraph.support_top_of_nontrivial, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, SimpleGraph.neighborFinset_completeEquipartiteGraph, gc_upperPolar_lowerPolar, Concept.isCompl_extent_intent, convexJoin_singleton_segment, convexHull_diam, TopologicalSpace.Opens.frameHom_toFun, Matroid.Coindep.delete_spanning_iff, Antitone.Ico, Monotone.pairwise_disjoint_on_Ioc_pred, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', SimpleGraph.toTopEdgeLabeling_get, Set.disjoint_right_ordSeparatingSet, SimpleGraph.cycleGraph_two_eq_top, LowerSet.sdiff_eq_left, Antitone.pairwise_disjoint_on_Ioo_succ, subset_closedAbsConvexHull, gc_upperBounds_lowerBounds, Dynamics.netEntropyEntourage_antitone, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Ξ΅NFA.pumping_lemma, Finset.centerMass_id_mem_convexHull, Set.pairwise_disjoint_vadd_iff, latticeClosure_mono, Set.Finite.isCompact_convexHull, image_latticeClosure', Finset.centerMass_id_mem_convexHull_of_nonpos, CompleteLatticeHom.setPreimage_apply, convexHull_add, IsFoelner.tendsto_meas_smul_symmDiff, Filter.cofinite.limsup_set_eq, Language.instMulLeftMono, SimpleGraph.IsSRGWith.top, Set.disjoint_iUnion_left, SimpleGraph.degree_completeEquipartiteGraph, upperHemicontinuousWithinAt_iff_preimage_Iic, Set.definable_finset_sup, affineSpan_convexHull, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, MeasureTheory.IsSetSemiring.isSetRing_supClosure, Cardinal.mk_strictMonoOn, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Besicovitch.TauPackage.monotone_iUnionUpTo, SimpleGraph.free_bot, Set.PairwiseDisjoint.exists_mem_filter, Antitone.Ioc, MeasureTheory.hittingBtwn_apply_anti, Set.encard_strictMono, MeasureTheory.Measure.MeasureDense.fin_meas_approx, NonarchimedeanGroup.exists_openSubgroup_separating, Subgroup.leftCoset_cover_filter_FiniteIndex_aux, MeasureTheory.edist_indicatorConstLp_eq_enorm, Digraph.default_def, convexHull_basis_eq_stdSimplex, fixingAddSubmonoid_fixedPoints_gc, Ideal.disjoint_powers_iff_notMem, Matroid.Indep.contract_dep_iff, Language.sub_iSup, blimsup_cthickening_ae_le_of_eventually_mul_le_aux, Convex.radon_partition, instIsCoatomistic, Digraph.bot_adj, SimpleGraph.edist_top, IsOpen.exists_iUnion_isClosed, Language.le_iff, SimpleGraph.cycleGraph_three_eq_top, SimpleGraph.disjoint_edge, SimpleGraph.edgeSet_bot, Ctop.Realizer.nhds_F, lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl, Matroid.cRk_mono, ConvexOn.bddAbove_convexHull, MeasureTheory.IsSetSemiring.mem_supClosure_iff, FirstOrder.Language.Substructure.fg_def, SupClosed.infClosure, disjoint_nhdsSet_principal, BoxIntegral.Box.iUnion_Ioo_of_tendsto, Language.IsRegular_compl, iInf_iSup_eq, Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, MulAction.disjoint_image_image_iff, t2_separation_nhds, CompleteSublattice.mem_subtype, SimpleGraph.disjoint_edgeFinset, Setoid.IsPartition.finpartition_parts, MonotoneOn.Ici, Set.disjoint_smul_set, AddAction.IsBlock.disjoint_vadd_vadd_set, SimpleGraph.edge_self_eq_bot, Matroid.closure_eq_subtypeClosure, SimpleGraph.cliqueFree_bot, infClosed_infClosure, Filter.disjoint_iff, Ideal.disjoint_map_primeCompl_iff_comap_le, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, MeasureTheory.measure_symmDiff_le, ConvexIndependent.mem_convexHull_iff, not_disjoint_segment_convexHull_triple, AffineSubspace.inf_coe, Digraph.toSimpleGraphStrict_top, Language.add_iSup, convexHull_vadd, Filter.monotone_mem, Matroid.closure_mono, FirstOrder.Language.Substructure.lift_card_closure_le_card_term, MeasureTheory.dense_of_generateFrom_isSetSemiring, Set.disjoint_sUnion_left, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, SimpleGraph.Subgraph.spanningCoe_bot, AffineSubspace.coe_inf, Set.isCoatom_iff, Monotone.Iio, exists_mem_interior_convexHull_affineBasis, LowerSet.sdiff_lt_left, SimpleGraph.disjoint_edgeSet, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, MeasureTheory.measure_neg_vadd_symmDiff, supClosure_empty, SimpleGraph.preconnected_top, FirstOrder.Language.Substructure.mem_closure_iff_exists_term, IsRetrocompact.finsetInf', Besicovitch.exist_finset_disjoint_balls_large_measure, blimsup_cthickening_ae_le_of_eventually_mul_le, isInducing_sumElim, BoxIntegral.Box.Ioo_ae_eq_Icc, QuotientAddGroup.strictMono_comap_prod_image, compl_image_latticeClosure, closedAbsConvexHull_min, Order.Ideal.PrimePair.isCompl_I_F, TopologicalSpace.Opens.gc, Filter.cofinite.bliminf_set_eq, PrimitiveSpectrum.gc_closureOperator, beattySeq_symmDiff_beattySeq'_pos, Irrational.beattySeq_symmDiff_beattySeq_pos, upperHemicontinuousOn_iff_preimage_Iic, totallyBounded_absConvexHull, Set.Ioi_disjoint_Iio_iff, Matroid.dual_indep_iff_exists', infClosure_singleton, MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, absConvexHull_nonempty, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, SimpleGraph.fromEdgeSet_not_isDiag, Descriptive.Tree.take_coe, absConvexHull_empty, SimpleGraph.ConnectedComponent.top_supp_eq_univ, AddAction.IsBlock.pairwiseDisjoint_range_vadd, Set.isAtom_singleton, Set.PairwiseDisjoint.exists_mem_filter_basis, absConvexHull_eq_self, Set.kernImage_mono, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, SimpleGraph.preconnected_bot, Set.monotone_accumulate, MulAction.orbit.eq_or_disjoint, Topology.IsInducing.disjoint_of_sumElim_aux, Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, latticeClosure_prod, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, IsLocalization.isPrime_iff_isPrime_disjoint, SubMulAction.disjoint_val_image, Monotone.Ico, InfClosed.infClosure_eq, SimpleGraph.chromaticNumber_eq_card_iff, MeasureTheory.measure_limsup_cofinite_eq_zero, Dynamics.coverMincard_antitone, SimpleGraph.egirth_bot, SimpleGraph.support_eq_bot_iff, NonUnitalStarAlgebra.gc, Dynamics.netMaxcard_antitone, AddAction.IsBlock.disjoint_vadd_set_vadd, AlgebraicGeometry.isCompl_range_inl_inr, Antitone.Iio, Metric.disjoint_closedEBall_of_lt_infEDist, upperHemicontinuousAt_iff_preimage_Iic, exists_nhds_disjoint_closure, Seminorm.closedBall_finset_sup, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, ProjectiveSpectrum.gc_set, convexHull_add_subset, TopologicalSpace.Opens.coe_finset_sup, SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph, SimpleGraph.extremalNumber_top, MeasureTheory.IsSetSemiring.diff_mem_supClosure, isNowhereDense_iff_disjoint, ConvexCone.disjoint_hull_left_of_convex, EisensteinSeries.pairwise_disjoint_gammaSet, Descriptive.Tree.pullSub_adjunction, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, Topology.IsLocallyConstructible.finsetInf, infClosure_eq_self, closedConvexHull_closure_eq_closedConvexHull, SimpleGraph.isVertexCover_bot, SimpleGraph.dist_top_of_ne, SimpleGraph.top_adj, MulAction.IsBlock.disjoint_smul_right, compl_image_latticeClosure_eq_of_compl_image_eq_self, partialSups_eq_sUnion_image, Polynomial.rootSet_derivative_subset_convexHull_rootSet, BoxIntegral.unitPartition.disjoint, latticeClosure_singleton, closure_convexHull_extremePoints, SimpleGraph.maxDegree_bot_eq_zero, MulAction.IsBlock.disjoint_smul_smul_set, MeasureTheory.le_measure_symmDiff, TopologicalSpace.Closeds.coe_finset_inf, CompleteSublattice.mem_sInf, MeasurableSet.bihimp, Dynamics.coverEntropyEntourage_monotone, Descriptive.coe_def, Set.Finite.isClosed_convexHull, Descriptive.Tree.pullSub_subAt, MeasureTheory.measure_symmDiff_inv_smul, convexHull_empty, Set.disjoint_iUnion_right, SimpleGraph.card_edgeFinset_top_eq_card_choose_two, Set.image_preimage, absConvexHull_add_subset, Finset.centerMass_mem_convexHull, exists_open_nhds_disjoint_closure, SimpleGraph.fromEdgeSet_univ, SimpleGraph.vertexCoverNum_eq_zero, Sublattice.setLike_mem_inf, SimpleGraph.isExtremal_top_free_turanGraph, SimpleGraph.ediam_top, disjoint_measurableAtom_of_notMem, convexHull_pair, MeasureTheory.disjoint_cylinder_iff, MonotoneOn.Iic, Descriptive.Tree.take_eq_take, preCantorSet_antitone, MeasureTheory.hittingBtwn_anti, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, NFA.disjoint_evalFrom_reverse_iff, Matroid.contract_spanning_iff, FirstOrder.Language.Substructure.mem_closed_of_isRelational, SimpleGraph.not_connected_bot, Topology.CWComplex.pairwiseDisjoint', Filter.antitone_seq_of_seq, infClosure_univ, Dynamics.coverEntropyInf_monotone, FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_family, Sublattice.ext_mem_iff, MulAction.IsBlock.disjoint_smul_set_smul, fixingSubmonoid_antitone, TopologicalSpace.Opens.coe_finset_inf, subset_latticeClosure, SimpleGraph.default_def, convexJoin_subset_convexHull, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, subset_infClosure, SimpleGraph.Subgraph.verts_monotone, convexHull_eq_empty, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, FirstOrder.Language.ClosedUnder.inf, FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, disjoint_frontier_iff_isOpen, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, MvPolynomial.supported_strictMono, IsGenericPoint.disjoint_iff, Sublattice.mem_subtype, AddAction.IsBlock.disjoint_vadd_right, Digraph.toSimpleGraphInclusive_bot, SimpleGraph.top_isIndContained_iff_top_isContained, convexHull_singleton, fixedPoints_addSubgroup_antitone, MeasureTheory.hittingAfter_apply_anti, MeasureTheory.IsSetSemiring.diff_eq_sUnion', SimpleGraph.ediam_eq_one, AntitoneOn.Ioi, Antitone.pairwise_disjoint_on_Ioc_succ, dist_mulIndicator, SimpleGraph.diam_eq_one, CompleteSublattice.mem_sup, Filter.Realizer.mem_sets, SimpleGraph.toTopEdgeLabeling_labelGraph, exists_seq_infinite_isOpen_pairwise_disjoint, LowerAdjoint.closure_union_closure_subset, BooleanSubalgebra.latticeClosure_subset_closure, Set.disjoint_iUnionβ‚‚_right, isFoelner_iff, Antitone.Ioi, convex_convexHull, convexHull_sum, Set.limsup_eq_tendsto_sum_indicator_atTop, Finset.inf_set_eq_iInter, IsUltrametricDist.ball_eq_or_disjoint, Filter.HasBasis.disjoint_iff, IsFoelner.tendsto_meas_smul_symmDiff_smul, FirstOrder.Language.Substructure.closure_insert, isBounded_convexHull, Digraph.top_adj, AddAction.isBlock_iff_vadd_eq_or_disjoint, Dynamics.netEntropyInfEntourage_monotone, Set.exists_union_disjoint_cardinal_eq_of_even, SimpleGraph.pairwise_disjoint_supp_connectedComponent, Language.instOrderedSub, Finset.mem_convexHull, BooleanSubalgebra.closure_latticeClosure, convexHull_neg, upperHemicontinuous_iff_isOpen_preimage_Iic, convexIndependent_set_iff_notMem_convexHull_diff, IsRetrocompact.finsetSup, upperHemicontinuous_iff_preimage_Iic, Set.Ioi_disjoint_Iio_of_le, BoxIntegral.Prepartition.pairwiseDisjoint, Antitone.Ici, LinearEquiv.transvections_pow_mono, Concept.codisjoint_extent_intent, convexHull_sphere_eq_closedBall, SimpleGraph.IsContained.bot, Metric.ball_disjoint_closedBall, SimpleGraph.edist_bot, mem_add_wellApproximable_iff, LinearMap.polar_gc, AntitoneOn.Iic, LowerAdjoint.subset_closure, Matroid.IsCircuit.disjoint_coloops, UpperSet.lt_sdiff_left, MeasureTheory.tendsto_measure_symmDiff_preimage_nhds_zero, Set.Finite.supClosure, Subgroup.IsComplement.pairwiseDisjoint_smul, Convex.exists_subset_interior_convexHull_finset_of_isCompact, Filter.Realizer.ofEquiv_F, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, MeasurableSet.measurableSet_bliminf, convexHull_mono, SimpleGraph.bot_isContained_iff_card_le, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, convex_absConvexHull, CauchyFilter.monotone_gen, Set.isCoatom_singleton_compl, Cardinal.mk_strictMono, convexHullAddMonoidHom_apply, Finset.intervalGapsWithin_pairwiseDisjoint_Ioc, absConvexHull_mono, biUnion_Iic_disjointed, Finset.convexHull_eq, SimpleGraph.dist_bot, SimpleGraph.EdgeLabeling.pairwiseDisjoint_univ_labelGraph, MulAction.IsBlock.smul_eq_smul_or_disjoint, ConvexCone.disjoint_coe, totallyBounded_convexHull, Set.Nonempty.absConvexHull, TopologicalSpace.Compacts.coe_finset_sup, CompleteSublattice.mem_inf, Filter.disjoint_principal_principal, connectedComponent_disjoint, AddAction.IsBlock.disjoint_vadd_of_ne, MeasureTheory.IsSetRing.partialSups_mem, sup_mem_supClosure, lowerBounds_infClosure, SimpleGraph.diam_bot, gc_nhdsKer_interior, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, LowerAdjoint.closure_union_closure_right, Topology.RelCWComplex.disjoint_interior_base_closedCell, absConvex_convexClosedHull, Set.Iic_disjoint_Ioc, convexHull_eq_singleton, convexHull_eq_zero, SimpleGraph.nonempty_dart_top, DFA.accepts_compl, Set.encard_mono, nndist_mulIndicator, SimpleGraph.IsBipartiteWith.disjoint, MeasureTheory.eLpNorm_indicator_sub_indicator, SeparatedNhds.disjoint_closure_right, Set.Ioc_disjoint_Ioi, SimpleGraph.turanGraph_zero, FirstOrder.Language.Substructure.closure_empty, QuotientGroup.strictMono_comap_prod_image, monotone_Iio, isCompact_closedAbsConvexHull_of_totallyBounded, supClosure_isClosed, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, absConvexHull_subset_closedAbsConvexHull, Matroid.setOf_indep_eq, toWeakSpace_closedConvexHull_eq, Set.Iic_disjoint_Ici, convexHull_pi, FirstOrder.Language.monotone_distinctConstantsTheory, Set.isAtom_iff, Monotone.Ioc, Language.IsRegular.inf, MeasureTheory.measure_liminf_atTop_eq_zero, Finset.coe_covBy_coe, gc_upperClosure_coe, FirstOrder.Language.Substructure.iSup_eq_closure, disjoint_ball_closedBall_iff, MeasurableSet.symmDiff, Filter.EventuallyEq.symmDiff, SimpleGraph.fromEdgeSet_disjoint, supClosure_singleton, SimpleGraph.isBipartiteWith_neighborSet_disjoint', image_latticeClosure, doublyStochastic_eq_convexHull_permMatrix, SimpleGraph.support_bot, SimpleGraph.fromEdgeSet_empty, latticeClosure_eq_self, SimpleGraph.connected_bot_iff, Interval.disjoint_coe, absConvexHull_eq_iInter, CFilter.mem_toFilter_sets, Set.Ioi_disjoint_Iio_of_not_lt, latticeClosure_empty, VitaliFamily.covering, BoxIntegral.Box.Ioo_subset_Icc, Finset.isPWO_sup, Finset.partiallyWellOrderedOn_sup, MeasurableSet.measurableSet_liminf, exists_open_convex_of_notMem, Language.iSup_mul, BoxIntegral.Box.exists_seq_mono_tendsto, Finset.centroid_mem_convexHull, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, supClosure_mono, AddAction.isBlock_iff_disjoint_vadd_of_ne, Vitali.exists_disjoint_subfamily_covering_enlargement, Matroid.coindep_contract_iff, t2_separation_compact_nhds, AbsConvex.absConvexHull_subset_iff, IndexedPartition.disjoint, SimpleGraph.induce_singleton_eq_top, SimpleGraph.pathGraph_two_eq_top, lowerHemicontinuous_iff_isClosed_preimage_Iic, Set.Ico_disjoint_Ico, AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, Topology.RelCWComplex.disjointBase, SupClosed.supClosure_eq, SimpleGraph.cycleGraph_one_eq_top, MeasureTheory.Egorov.notConvergentSeq_antitone, ClosedSubmodule.coe_inf, Projectivization.Subspace.monotone_span, Locale.openOfElementHom_toFun, FirstOrder.Language.Substructure.subset_closure, PrimitiveSpectrum.closedsGC_closureOperator, Filter.cofinite.liminf_set_eq, Monotone.pairwise_disjoint_on_Ico_pred, FirstOrder.Language.Substructure.closure_iUnion, Metric.disjoint_closedBall_of_lt_infDist, absConvex_absConvexHull, monotone_Iic, AntitoneOn.Ioo, mem_wellApproximable_iff, DFA.acceptsFrom_inter, Metric.frontier_thickening_disjoint, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, ProjectiveSpectrum.gc_ideal, TopologicalSpace.Closeds.coe_finset_sup, MeasureTheory.measure_inv_smul_symmDiff, Vitali.exists_disjoint_covering_ae, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, Monotone.pairwise_disjoint_on_Ioo_succ, Metric.AreSeparated.disjoint, Set.Ioi_disjoint_Iio_same, BoxIntegral.Box.disjoint_coe, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, LinearMap.image_convexHull, SimpleGraph.lineGraph_bot, IsLowerSet.disjoint_upperClosure_left, FirstOrder.Language.Substructure.closure_union, MulAction.isBlock_iff_disjoint_smul_of_ne, ContinuousMap.ideal_gc, SimpleGraph.reachable_bot, IsRetrocompact.finsetSup', Dynamics.coverEntropyEntourage_antitone, DFA.pumping_lemma, Besicovitch.exists_disjoint_closedBall_covering_ae, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, PrimeSpectrum.gc_set, IsLocalization.orderIsoOfPrime_symm_apply_coe, StarAlgebra.gc, Matroid.dual_indep_iff_exists, convexHull_univ, FreeGroup.startsWith.disjoint_iff_ne, Set.disjoint_vadd_set, convexHull_ediam, disjoint_closedBall_closedBall_iff, Finsupp.codisjoint_supported_supported_iff, SimpleGraph.isNClique_map_copy_top, Set.disjoint_sUnion_right, FirstOrder.Language.Structure.cg_iff, T2Space.t2, Monotone.Ioi, infClosure_min, absConvexHull_min, Filter.ker_mono, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, Descriptive.Tree.tree_eq_bot, Metric.closedBall_disjoint_ball, HasCardinalLT.Set.cocone_ΞΉ_app, IsLocalization.disjoint_comap_iff, SimpleGraph.bot_preconnected_iff_subsingleton, AffineIndependent.convexHull_inter', AntitoneOn.Iio, SimpleGraph.bot_adj, Filter.Realizer.le_iff, SimpleGraph.isClique_bot_iff, AddAction.orbit.eq_or_disjoint, latticeClosure_idem, SimpleGraph.diam_top, convexHull_zero, t2Space_iff_nhds, IsLowerSet.disjoint_upperClosure_right, convexHull_eq_union_convexHull_finite_subsets, Monotone.pairwise_disjoint_on_Ioo_pred, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, SimpleGraph.isClique_range_copy_top, Set.ncard_union_eq_iff, Concept.strictAnti_intent, Monotone.pairwise_disjoint_on_Ioc_succ, Language.IsRegular.compl, MeasurableSet.measurableSet_limsup, SimpleGraph.eq_bot_iff_forall_not_adj, SimpleGraph.edgeFinset_bot, Matroid.delete_dep_iff, fixingSubmonoid_fixedPoints_gc, SimpleGraph.eq_top_iff_forall_eccent_eq_one, CompleteSublattice.mem_iSup, MeasureTheory.exists_subordinate_pairwise_disjoint, zero_mem_absConvexHull, MeasureTheory.MeasuredSets.dist_def, Language.mem_inf, DFA.acceptsFrom_compl, disjoint_principal_nhdsSet, Matroid.contract_spanning_iff', Filter.Realizer.principal_F, infClosure_prod, Set.exists_union_disjoint_cardinal_eq_iff, HasCardinalLT.Set.functor_map_coe, affineCombination_mem_convexHull, Digraph.completeDigraph_eq_top, MeasureTheory.ae_mem_limsup_atTop_iff, Matroid.Indep.contract_indep_iff, mem_convexHull_iff_exists_fintype, Metric.frontier_cthickening_disjoint, dist_indicator, MulAction.orbit.pairwiseDisjoint, Set.antitone_dissipate, absConvexHull_univ, Set.Iio_disjoint_Ioi_same, Topology.RelCWComplex.disjoint_skeleton_openCell, convexHull_toCone_isLeast, Set.partialSups_eq_accumulate, RootedTree.subtrees_disjoint, posTangentConeAt_mono, fixedPoints_subgroup_antitone, Language.compl_compl, Set.iUnionLift_binary, SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling, Metric.eball_disjoint, CompleteSublattice.mem_top, Filter.mem_limsup_iff_frequently_mem, MeasureTheory.AEDisjoint.exists_disjoint_diff, fixingAddSubmonoid_antitone, MeasurableSpace.generateMeasurableRec_mono, disjoint_ball_ball_iff, Set.Finite.latticeClosure, extremePoints_convexHull_subset, MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection, Topology.RelCWComplex.disjointBase', SimpleGraph.completeGraph_eq_top, MeasurableSet.measurableSet_blimsup, TopologicalSpace.gc_generateFrom, TopologicalSpace.Closeds.isAtom_coe, SimpleGraph.center_top, SimpleGraph.completeEquipartiteGraph_eq_bot_iff, SimpleGraph.disjoint_left, disjoint_memPartition, Geometry.SimplicialComplex.face_subset_face_iff, Convex.convexHull_eq, Descriptive.Tree.mem_subAt, Set.monotone_preimage, SimpleGraph.not_isHamiltonian_bot_of_card_ne_one, convexHull_convexHull_union_right, Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one, NFA.disjoint_stepSet_reverse, MeasureTheory.measure_limsup_atTop_eq_zero, fixedPoints_antitone_addSubmonoid, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, PiNat.disjoint_cylinder_of_longestPrefix_lt, IsUpperSet.disjoint_lowerClosure_left, HasCardinalLT.Set.instIsCardinalFiltered, IsUltrametricDist.closedBall_subset_trichotomy, Set.disjoint_vadd_set_left, MonotoneOn.Ico, SimpleGraph.disjoint_image_val_universalVerts, MeasureTheory.measure_symmDiff_eq, fixingAddSubgroup_fixedPoints_gc, ConvexCone.disjoint_hull_right_of_convex, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_snd, Set.Ioc_disjoint_Ioc_of_le, SimpleGraph.chromaticNumber_top_eq_top_of_infinite, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, EMetric.disjoint_closedBall_of_lt_infEdist, FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize, Set.pairwiseDisjoint_vadd_iff, Ideal.disjoint_primeCompl_of_liesOver, MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative, FirstOrder.Language.Substructure.closed, blimsup_cthickening_ae_eq_blimsup_thickening, supClosure_infClosure, Composition.disjoint_range, MulAction.IsBlock.pairwiseDisjoint_range_smul, MulAction.isBlock_iff_pairwiseDisjoint_range_smul, absConvexHull_isClosed, Set.instIsCoatomistic, infClosure_mono, SimpleGraph.top_preconnected, isSeparatedMap_iff_nhds, Set.exists_union_disjoint_ncard_eq_of_even, convexHull_convexHull_union_left, SimpleGraph.card_commonNeighbors_top, MonotoneOn.Ioc, Set.mabs_mulIndicator_symmDiff, Set.Ici_disjoint_Iic, convexHull_min, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, fixingSubgroup_fixedPoints_gc, convexHull_isClosed, fixingAddSubgroup_antitone, Matroid.delete_isBasis_iff, MeasureTheory.AddContent.supClosure_apply_of_mem, monotone_nhdsSet, SimpleGraph.eq_top_iff_forall_ne_adj, InfClosed.supClosure, antitone_Ici, Language.mul_iSup, MeasureTheory.measure_symmDiff_neg_vadd, MeasureTheory.limsup_ae_eq_of_forall_ae_eq, Filter.cofinite.blimsup_set_eq, SimpleGraph.edgeFinset_eq_empty, Set.pairwiseDisjoint_iff, closedAbsConvexHull_eq_closure_absConvexHull, Seminorm.closedBall_finset_sup', Digraph.toSimpleGraphInclusive_top, SimpleGraph.disjoint_fromEdgeSet, TopologicalSpace.Opens.coe_disjoint, SimpleGraph.bot_degree, Matroid.isFlat_iff_isClosed, instIsAtomistic, BoxIntegral.Box.measurableSet_Ioo, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, CompleteSublattice.mem_sSup, nndist_indicator, PMF.toOuterMeasure_apply_eq_zero_iff, SimpleGraph.bot_isCompleteMultipartite, ConvexCone.gc_hull_coe, AddAction.disjoint_image_image_iff, convexHull_prod, SimpleGraph.radius_top, MeasureTheory.OuterMeasure.isCaratheodory_partialSups, DoubleCoset.disjoint_out, Antitone.Iic, FirstOrder.Language.Substructure.closure_withConstants_eq, blimsup_thickening_mul_ae_eq, Filter.IsAntitoneBasis.antitone, IsAddFoelner.tendsto_meas_vadd_symmDiff, Finset.wellFoundedOn_sup, CompleteSublattice.ext_iff, AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux, Set.disjoint_vadd_set_right, MonotoneOn.Ioo, infClosure_supClosure, convexHull_eq_union, Digraph.toSimpleGraphStrict_bot, Set.Iio_disjoint_Ici, Topology.RelCWComplex.disjoint_skeletonLT_openCell, convexHull_eq, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, SimpleGraph.commonNeighbors_top_eq, Filter.Realizer.bot_F, Monotone.Iic, supClosure_idem, Set.pairwise_disjoint_smul_iff, CompleteLatticeHom.coe_setPreimage, SimpleGraph.minDegree_bot_eq_zero, convexHull_smul, Setoid.IsPartition.pairwiseDisjoint, ModelWithCorners.disjoint_interior_boundary, CompleteLatticeHom.setPreimage_id, Filter.Realizer.top_F, Set.Nonempty.convexHull, SimpleGraph.preconnected_bot_iff_subsingleton, absConvexHull_eq_convexHull_balancedHull, FirstOrder.Language.Substructure.map_closure, Set.Ico_disjoint_Ico_same, Set.Finite.convexHull_eq_image, Set.vadd_set_symmDiff, Filter.HasAntitoneBasis.antitone, SimpleGraph.card_edgeFinset_completeEquipartiteGraph, infClosure_idem, SimpleGraph.radius_bot, Disjoint.edgeSet, mem_convexHull_of_exists_fintype, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring, convexHull_rangle_single_eq_stdSimplex, FirstOrder.Language.Substructure.closure_le, AffineBasis.centroid_mem_interior_convexHull, AffineMap.image_convexHull, convexHull_union, convexHull_sub, FirstOrder.Language.Substructure.mem_closed_iff, upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl, SubAddAction.disjoint_val_image, Monotone.Icc, WCovBy.finset_coe, closure_subset_closedConvexHull, ConcaveOn.bddBelow_convexHull, BoxIntegral.Prepartition.disjoint_coe_of_mem, blimsup_cthickening_mul_ae_eq, Set.Countable.substructure_closure, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, FirstOrder.Language.Substructure.subset_closure_withConstants, DFA.accepts_inter, Antitone.pairwise_disjoint_on_Ico_pred, convexHull_list_sum, Matroid.Indep.contract_isBase_iff, Set.definable_finset_inf, Set.Finite.ncard_strictMonoOn, IntermediateField.gc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', Submodule.span_monotone, partialSups_eq_biUnion_range, Filter.exists_antitone_seq, Pairwise.exists_mem_filter_basis_of_disjoint, Set.pairwiseDisjoint_smul_iff, MulAction.IsBlock.smul_eq_or_disjoint, CompleteSublattice.mem_iInf, Concept.strictMono_extent, Set.Ioo_disjoint_Ioo, Perfect.splitting, convexHull_nonempty_iff, CovBy.finset_coe, Metric.sphere_disjoint_ball, infClosure_isClosed, SimpleGraph.eq_top_of_chromaticNumber_eq_card, RealRMK.range_cut_partition, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, Topology.IsLocallyConstructible.finsetInf', Ideal.exists_disjoint_powers_of_span_eq_top, subset_supClosure, Dynamics.netEntropyInfEntourage_antitone, Descriptive.Tree.mem_pullSub_self, SimpleGraph.edgeSet_eq_empty, MeasureTheory.pairwise_disjoint_addFundamentalInterior, upperPolar_anti, Topology.RelCWComplex.pairwiseDisjoint, Matroid.Coindep.delete_isBase_iff, closedAbsConvexHull_isClosed, AntitoneOn.Ioc, HasCardinalLT.Set.instIsFilteredOfFactIsRegular, Set.disjoint_smul_set_left, disjoint_nhdsWithin_of_mem_discrete, finsetInf'_mem_infClosure, mem_convexHull_iff, Dynamics.dynEntourage_antitone, AntitoneOn.Ico, Filter.NeBot.not_disjoint, Seminorm.ball_finset_sup, SimpleGraph.not_preconnected_bot, Set.disjoint_smul_set_right, Matroid.dualIndepMatroid_Indep, parallelepiped_eq_convexHull, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, nhdsKer_mono, PrimeSpectrum.localization_comap_range, latticeClosure_isClosed, IsLocalization.orderIsoOfPrime_apply_coe, Digraph.emptyDigraph_eq_bot, MeasurableSpace.disjoint_countablePartition, VitaliFamily.FineSubfamilyOn.covering_disjoint, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, MeasurableSet.exists_isOpen_symmDiff_lt, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, absConvexHull_eq_empty, Matroid.IsBasis'.contract_dep_iff, Matroid.delete_indep_iff, Submodule.sup_set_smul, Descriptive.Tree.mem_pullSub_short, MeasureTheory.IsSetRing.finsetSup_mem, SimpleGraph.killCopies_def, MonotoneOn.Ioi, FirstOrder.Language.Substructure.cg_iff_empty_or_exists_nat_generating_family, Pairwise.exists_mem_filter_of_disjoint, Set.disjoint_left_ordSeparatingSet, fixedPoints_antitone, MeasureTheory.IsSetSemiring.exists_finpartition_diff, SimpleGraph.IsRegularOfDegree.top, Set.abs_indicator_symmDiff, isLUB_supClosure, Matroid.Indep.disjoint_loops, SimpleGraph.isAcyclic_bot, Set.Iio_disjoint_Ioi_of_le, SimpleGraph.Hom.injective_of_top_hom, Finset.pairwiseDisjoint_pair_insert, gc_lowerClosure_coe, CompleteLatticeHom.setPreimage_comp, Finsupp.disjoint_supported_supported_iff, Set.instIsAtomistic, SimpleGraph.isNClique_bot_iff, SimpleGraph.bot_preconnected, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, isClosed_closedAbsConvexHull, MeasureTheory.MeasuredSets.edist_def, Sublattice.setLike_mem_coe, supClosure_prod, SimpleGraph.ediam_bot, AffineIndependent.convexHull_inter, Set.sUnion_powerset_gc, MeasureTheory.measure_symmDiff_eq_zero_iff, SimpleGraph.card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph, finsetSup'_mem_supClosure, Urysohns.CU.disjoint_C_support_lim, Language.kstar_eq_iSup_pow, IsUpperSet.disjoint_lowerClosure_right, infClosure_empty, Order.Ideal.PrimePair.disjoint, Disjoint.exists_mem_filter_basis, convex_closedConvexHull, IsRetrocompact.finsetInf, closure_subset_closedAbsConvexHull, SimpleGraph.edist_top_of_ne, IsLocalization.map_algebraMap_ne_top_iff_disjoint, AlgebraicGeometry.Scheme.codisjoint_zeroLocus, Descriptive.Tree.drop_coe, FirstOrder.Language.Hom.eqOn_closure, SimpleGraph.deleteEdges_eq_self, HasCardinalLT.Set.isFiltered_of_aleph0_le, Submodule.coe_scott_continuous, Seminorm.ball_finset_sup', Matroid.delete_isCircuit_iff, Set.disjoint_iUnionβ‚‚_left, Set.Finite.convexHull_eq, Sublattice.setLike_mem_sup, supClosed_supClosure, MeasureTheory.hittingAfter_anti, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, Set.ncard_strictMono, r1_separation, isClosed_closedConvexHull, edist_indicator, SimpleGraph.cliqueFree_iff_top_free, OnePoint.isCompl_range_coe_infty, SimpleGraph.cycleGraph_zero_eq_bot, SimpleGraph.chromaticNumber_eq_one_iff, Finset.sup_id_set_eq_sUnion, MeasureTheory.NullMeasurableSet.symmDiff, isAddFoelner_iff, NumberField.InfinitePlace.disjoint_isReal_isComplex, PrimitiveSpectrum.gc, Antitone.Ioo, Vitali.exists_disjoint_covering_ae', Set.Finite.encard_strictMonoOn, AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero, Matroid.IsBasis'.contract_indep_iff, Dynamics.coverEntropyInfEntourage_monotone, Set.smul_set_symmDiffβ‚€, balanced_absConvexHull, convexHull_subset_affineSpan, convexHull_eq_self, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, disjoint_closedBall_ball_iff, MeasureTheory.Measure.QuasiMeasurePreserving.limsup_preimage_iterate_ae_eq, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, CompleteSublattice.notMem_bot, supClosure_univ, MeasureTheory.dist_indicatorConstLp_eq_norm, SimpleGraph.bot_strongly_regular, lowerClosure_mono, balancedHull_convexHull_subseteq_absConvexHull, SimpleGraph.card_topEdgeLabeling, PiNat.exists_disjoint_cylinder, t2_separation, SimpleGraph.cycleGraph_zero_eq_top, Algebra.gc, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, Filter.Realizer.tendsto_iff, Set.Ioc_disjoint_Ioi_same, latticeClosure_min, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, convexHull_range_eq_exists_affineCombination, convexIndependent_iff_notMem_convexHull_diff, Topology.RelCWComplex.disjoint_base_iUnion_openCell, AddAction.IsBlock.vadd_eq_or_disjoint, FirstOrder.Language.Substructure.lift_card_closure_le, FirstOrder.Language.Substructure.closure_eq, SimpleGraph.isVertexCover_empty, FirstOrder.Language.Substructure.mem_closure_iff_of_isRelational, Descriptive.Tree.mem_pullSub_append, FirstOrder.Language.Substructure.closure_mono, IsUltrametricDist.closedBall_eq_or_disjoint, Concept.disjoint_extent_intent, SimpleGraph.edist_bot_of_ne, Dynamics.dynEntourage_monotone, monotone_closure, SimpleGraph.dist_top, FirstOrder.Language.Substructure.closure_univ, SimpleGraph.eccent_top, Filter.monotone_principal, LowerAdjoint.closure_union_closure_left, FirstOrder.Language.Substructure.closure_image, AbsConvex.absConvexHull_eq, SimpleGraph.chromaticNumber_bot, Antitone.pairwise_disjoint_on_Ico_succ, closedConvexHull_isClosed, edist_mulIndicator, Filter.mem_liminf_iff_eventually_mem, supClosure_min, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Metric.closedBall_disjoint_closedBall, Matroid.setOf_dep_eq, closedAbsConvexHull_closure_eq_closedAbsConvexHull, AlgebraicGeometry.Spec.map_app, upperClosure_anti, t2Space_iff, TopologicalSpace.Opens.mk_inf_mk, Complex.rectangle_eq_convexHull, LowerAdjoint.closure_iUnion_closure, FirstOrder.Language.Substructure.cg_closure_singleton, convexHull_subset_closedConvexHull, FirstOrder.Language.Structure.fg_iff, FirstOrder.Language.Substructure.cg_closure, SimpleGraph.Subgraph.coe_bot, Monotone.pairwise_disjoint_on_Ico_succ, Dynamics.coverMincard_monotone_subset, Finset.centerMass_mem_convexHull_of_nonpos
toCompletelyDistribLattice πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_iSup_eq πŸ“–mathematicalβ€”iInf
CompleteLattice.toInfSet
CompleteBooleanAlgebra.toCompleteLattice
toCompleteBooleanAlgebra
iSup
CompleteLattice.toSupSet
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CompleteBooleanAlgebra

Definitions

NameCategoryTheorems
toBooleanAlgebra πŸ“–CompOp
276 mathmath: SimpleGraph.locallyLinear_bot, SimpleGraph.cliqueSet_bot, SimplexCategoryGenRel.multiplicativeClosure_isGenerator_eq_top, Filter.sdiff_limsup, CategoryTheory.MorphismProperty.comp_eq_top_iff, SimpleGraph.killCopies_bot, SimpleGraph.TopEdgeLabeling.labelGraph_adj, SimpleGraph.cliqueFree_two, SimpleGraph.eccent_bot, CategoryTheory.MorphismProperty.DescendsAlong.top, CategoryTheory.MorphismProperty.Over.hasPullbacks, SimpleGraph.copyCount_bot, SimpleGraph.turanGraph_eq_top, CategoryTheory.MorphismProperty.Over.instHasTerminalTopOfContainsIdentities, SimpleGraph.bot_not_connected, SimpleGraph.isExtremal_top_free_iff_isTuranMaximal, compl_sInf, SimpleGraph.toTopEdgeLabeling_labelGraph_compl, SimpleGraph.edgeFinset_top, SimpleGraph.isClique_iff_induce_eq, CategoryTheory.MorphismProperty.Over.map_obj_left, CategoryTheory.MorphismProperty.Over.pullbackComp_hom_app_left, AlgebraicGeometry.Scheme.locallyCoverDense_of_le, CategoryTheory.MorphismProperty.Under.mk_hom, AlgebraicGeometry.instIsOpenImmersionLeftSchemeDiscretePUnitMapWalkingSpanOverTopMorphismPropertySpan, SimpleGraph.bot_not_preconnected, SimpleGraph.Copy.topEmbedding_apply, CategoryTheory.MorphismProperty.Over.mapCongr_inv_app_left, SimpleGraph.UnitDistEmbedding.bot_p, Filter.limsup_compl, CategoryTheory.MorphismProperty.IsMultiplicative.instTop, CategoryTheory.MorphismProperty.Over.pullbackMapHomPullback_app, SimpleGraph.cycleGraph_one_eq_bot, CategoryTheory.MorphismProperty.Over.mk_hom, CategoryTheory.MorphismProperty.Over.pullback_obj_left, CategoryTheory.MorphismProperty.Over.map_map_left, SimpleGraph.edgeDisjointTriangles_bot, SSet.Truncated.HomotopyCategory.multiplicativeClosure_morphismPropertyHomMk, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ΞΉ_transitionMap, SimpleGraph.emptyGraph_eq_bot, SimpleGraph.chromaticNumber_top, CategoryTheory.Localization.Construction.morphismProperty_eq_top', SimpleGraph.center_bot, biSup_symmDiff_biSup_le, CategoryTheory.MorphismProperty.Over.Hom.ext_iff, SimpleGraph.edgeSet_top, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_fst, SimpleGraph.deleteEdges_univ, compl_sSup', SimpleGraph.girth_bot, SimpleGraph.support_top_of_nontrivial, SimpleGraph.neighborFinset_completeEquipartiteGraph, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst, SimpleGraph.toTopEdgeLabeling_get, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_counit_app, SimpleGraph.cycleGraph_two_eq_top, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_f, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_pt, CategoryTheory.MorphismProperty.instRespectsIsoTop, CategoryTheory.MorphismProperty.instFaithfulOverTopOverForget, CategoryTheory.MorphismProperty.IsLocalAtSource.top, SimpleGraph.IsSRGWith.top, SimpleGraph.degree_completeEquipartiteGraph, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_id, CategoryTheory.MorphismProperty.Over.map_comp, CategoryTheory.MorphismProperty.Comma.instFullTopCommaForget, SimpleGraph.free_bot, compl_sSup, Digraph.default_def, Digraph.bot_adj, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopPullback, SimpleGraph.edist_top, SimpleGraph.cycleGraph_three_eq_top, SimpleGraph.edgeSet_bot, Language.IsRegular_compl, CategoryTheory.Cat.FreeRefl.multiplicativeClosure_morphismPropertyHomMk, CategoryTheory.MorphismProperty.Over.mapPullbackAdj_unit_app, SimpleGraph.edge_self_eq_bot, SimpleGraph.cliqueFree_bot, Digraph.toSimpleGraphStrict_top, SimpleGraph.Subgraph.spanningCoe_bot, CategoryTheory.MorphismProperty.Over.mapId_inv_app_left, SSet.Truncated.liftOfStrictSegal.naturalityProperty_eq_top, SimpleGraph.preconnected_top, AlgebraicGeometry.instHasOfPostcompPropertySchemeQuasiSeparatedTopMorphismProperty, CategoryTheory.MorphismProperty.Over.mapCongr_hom_app_left, CategoryTheory.MorphismProperty.IsLocalAtTarget.top, SimpleGraph.fromEdgeSet_not_isDiag, SimpleGraph.ConnectedComponent.top_supp_eq_univ, Filter.limsup_sdiff, SimpleGraph.preconnected_bot, SimpleGraph.chromaticNumber_eq_card_iff, SimpleGraph.egirth_bot, SimpleGraph.support_eq_bot_iff, CategoryTheory.MorphismProperty.instIsStableUnderCobaseChangeTop, CategoryTheory.MorphismProperty.Over.forget_comp_forget_map, CategoryTheory.MorphismProperty.Over.pullbackComp_inv_app_left, SimpleGraph.extremalNumber_top, SimpleGraph.isVertexCover_bot, SimpleGraph.dist_top_of_ne, CategoryTheory.MorphismProperty.instHasPullbackHomDiscretePUnitOfHasPullbacksAlong, SimpleGraph.top_adj, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionCocone_ΞΉ_app, SimpleGraph.maxDegree_bot_eq_zero, SimplexCategory.Truncated.morphismProperty_eq_top, SimpleGraph.card_edgeFinset_top_eq_card_choose_two, SimpleGraph.fromEdgeSet_univ, SimpleGraph.vertexCoverNum_eq_zero, SimpleGraph.isExtremal_top_free_turanGraph, SimpleGraph.ediam_top, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyTop, SimpleGraph.not_connected_bot, SimpleGraph.default_def, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_X, Digraph.toSimpleGraphInclusive_bot, SimpleGraph.top_isIndContained_iff_top_isContained, compl_iSup, SimpleGraph.ediam_eq_one, compl_iInf, SimpleGraph.diam_eq_one, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'_f, SimpleGraph.toTopEdgeLabeling_labelGraph, AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLE_eq_toGrothendieck_smallPretopology, CategoryTheory.MorphismProperty.instFullUnderTopUnderForget, CategoryTheory.Paths.morphismProperty_eq_top', Digraph.top_adj, Filter.liminf_compl, CategoryTheory.Localization.Construction.morphismProperty_is_top', CategoryTheory.MorphismProperty.instIsLeftAdjointOverTopMapOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, CategoryTheory.MorphismProperty.Over.mapComp_hom_app_left, SimpleGraph.IsContained.bot, SimpleGraph.edist_bot, Filter.liminf_sdiff, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ΞΉ_transitionMap_assoc, CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeTop, SimpleGraph.bot_isContained_iff_card_le, CategoryTheory.MorphismProperty.Over.w_assoc, SimpleGraph.dist_bot, CategoryTheory.Localization.Construction.morphismProperty_eq_top, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyTop, SimpleGraph.diam_bot, SimpleGraph.nonempty_dart_top, DFA.accepts_compl, SimpleGraph.turanGraph_zero, CategoryTheory.MorphismProperty.instFaithfulCostructuredArrowTopOverToOver, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_map, AlgebraicGeometry.instHasCoproductsOfShapeOverSchemeTopMorphismPropertyOfSmall, iSup_disjointed, SimpleGraph.support_bot, SimpleGraph.fromEdgeSet_empty, SimpleGraph.connected_bot_iff, CategoryTheory.MorphismProperty.CostructuredArrow.toOver_obj, CategoryTheory.MorphismProperty.Under.w, SimpleGraph.induce_singleton_eq_top, SimpleGraph.pathGraph_two_eq_top, CategoryTheory.MorphismProperty.Over.mk_left, SimpleGraph.cycleGraph_one_eq_top, CategoryTheory.MorphismProperty.CostructuredArrow.mk_left, SimpleGraph.lineGraph_bot, SimpleGraph.reachable_bot, CategoryTheory.MorphismProperty.Under.Hom.ext_iff, SimpleGraph.isNClique_map_copy_top, CategoryTheory.MorphismProperty.Under.mk_left, SimpleGraph.bot_preconnected_iff_subsingleton, SimpleGraph.bot_adj, SimpleGraph.isClique_bot_iff, SimpleGraph.diam_top, CategoryTheory.MorphismProperty.Over.instPreservesFiniteLimitsTopOverForget, SimpleGraph.isClique_range_copy_top, CategoryTheory.MorphismProperty.Under.forget_comp_forget_map, Language.IsRegular.compl, SimpleGraph.eq_bot_iff_forall_not_adj, AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp_X, CategoryTheory.MorphismProperty.instFullOverTopOverForget, SimpleGraph.edgeFinset_bot, CategoryTheory.MorphismProperty.Comma.hasColimitsOfShape_of_closedUnderColimitsOfShape, SimpleGraph.eq_top_iff_forall_eccent_eq_one, CategoryTheory.MorphismProperty.Over.w, DFA.acceptsFrom_compl, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans_app_left, Digraph.completeDigraph_eq_top, disjointed_eq_inf_compl, AlgebraicGeometry.Scheme.instLocallyCoverDenseOverTopMorphismPropertyOverForgetOverGrothendieckTopology, CategoryTheory.MorphismProperty.CodescendsAlong.top, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp, Language.compl_compl, SimpleGraph.TopEdgeLabeling.labelGraph_toTopEdgeLabeling, CategoryTheory.Cat.FreeRefl.morphismProperty_eq_top, CategoryTheory.Paths.morphismProperty_eq_top_of_isMultiplicative, SimpleGraph.completeGraph_eq_top, SimpleGraph.center_top, SimpleGraph.completeEquipartiteGraph_eq_bot_iff, AlgebraicGeometry.instHasOfPostcompPropertySchemeIsSeparatedTopMorphismProperty, CategoryTheory.MorphismProperty.Comma.hasColimit_of_closedUnderColimitsOfShape, SimpleGraph.not_isHamiltonian_bot_of_card_ne_one, CategoryTheory.MorphismProperty.CostructuredArrow.Hom.ext_iff, AlgebraicGeometry.IsImmersion.instHasOfPostcompPropertySchemeTopMorphismProperty, SimpleGraph.completeMultipartiteGraph.topEmbedding_apply_snd, AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopology, CategoryTheory.MorphismProperty.Over.pullback_map_left, SimpleGraph.chromaticNumber_top_eq_top_of_infinite, SimpleGraph.top_preconnected, SimpleGraph.card_commonNeighbors_top, AlgebraicGeometry.instIsLocallyDirectedCompSchemeOverOverTopMorphismPropertyForgetForgetForget, SimpleGraph.eq_top_iff_forall_ne_adj, SimpleGraph.edgeFinset_eq_empty, CategoryTheory.MorphismProperty.Over.pullback_obj_hom, Digraph.toSimpleGraphInclusive_top, CategoryTheory.FreeGroupoid.instIsLocalizationOfTopMorphismProperty, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyTop, Filter.sdiff_liminf, SimpleGraph.bot_degree, CategoryTheory.MorphismProperty.Over.mapComp_inv_app_left, SimpleGraph.bot_isCompleteMultipartite, CategoryTheory.Localization.morphismProperty_eq_top, SimpleGraph.radius_top, CategoryTheory.MorphismProperty.Under.w_assoc, CategoryTheory.MorphismProperty.instFullCostructuredArrowTopOverToOver, AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology, Digraph.toSimpleGraphStrict_bot, CategoryTheory.MorphismProperty.map_top_eq_top_of_essSurj_of_full, SimpleGraph.commonNeighbors_top_eq, CategoryTheory.MorphismProperty.instHasPullbackSndHomDiscretePUnitOfHasPullbacksAlongOfIsStableUnderBaseChangeAlong, SimpleGraph.minDegree_bot_eq_zero, SimpleGraph.preconnected_bot_iff_subsingleton, SimpleGraph.card_edgeFinset_completeEquipartiteGraph, SimpleGraph.radius_bot, iSup_symmDiff_iSup_le, SimpleGraph.eq_top_of_chromaticNumber_eq_card, essentiallySmall_of_le, SimpleGraph.edgeSet_eq_empty, AlgebraicGeometry.instMonoObjWalkingSpanCompOverSchemeTopMorphismPropertySpanOverForgetForgetForgetNoneWalkingPairSomeMapInitOfIsOpenImmersionLeftDiscretePUnit, compl_sInf', SimpleGraph.not_preconnected_bot, Digraph.emptyDigraph_eq_bot, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_map, SimpleGraph.killCopies_def, SimpleGraph.IsRegularOfDegree.top, SimpleGraph.isAcyclic_bot, SimpleGraph.Hom.injective_of_top_hom, SimpleGraph.isNClique_bot_iff, SimpleGraph.bot_preconnected, SimpleGraph.ediam_bot, SimpleGraph.card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph, SimpleGraph.edist_top_of_ne, AlgebraicGeometry.Scheme.Cover.ColimitGluingData.functor_obj, AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopology, CategoryTheory.MorphismProperty.Over.mapId_hom_app_left, CategoryTheory.MorphismProperty.Over.pullbackComp_left_fst_fst, SimpleGraph.cliqueFree_iff_top_free, SimpleGraph.cycleGraph_zero_eq_bot, SimpleGraph.chromaticNumber_eq_one_iff, CategoryTheory.MorphismProperty.Comma.hasLimitsOfShape_of_closedUnderLimitsOfShape, CategoryTheory.isGroupoid_iff_isomorphisms_eq_top, CategoryTheory.Localization.instIsGroupoidLocalizationTopMorphismProperty, CategoryTheory.MorphismProperty.top_apply, AlgebraicGeometry.instHasFiniteCoproductsOverSchemeTopMorphismProperty, CategoryTheory.Localization.Construction.morphismProperty_is_top, SimpleGraph.bot_strongly_regular, SimpleGraph.card_topEdgeLabeling, SimpleGraph.cycleGraph_zero_eq_top, SSet.Truncated.HomotopyCategory.morphismProperty_eq_top, CategoryTheory.MorphismProperty.top_eq, CategoryTheory.MorphismProperty.Over.pullbackCongr_hom_app_left_fst_assoc, SimpleGraph.isVertexCover_empty, CategoryTheory.MorphismProperty.CostructuredArrow.mk_hom, SimpleGraph.edist_bot_of_ne, CategoryTheory.Paths.morphismProperty_eq_top, SimpleGraph.dist_top, SimpleGraph.eccent_top, CategoryTheory.MorphismProperty.Comma.hasLimit_of_closedUnderLimitsOfShape, CategoryTheory.MorphismProperty.Over.map_obj_hom, SimpleGraph.chromaticNumber_bot, CategoryTheory.MorphismProperty.instFaithfulUnderTopUnderForget, SimpleGraph.Subgraph.coe_bot, SimplexCategory.morphismProperty_eq_top
toCompl πŸ“–CompOp
4 mathmath: himp_eq, sdiff_eq, top_le_sup_compl, inf_compl_le_bot
toCompleteDistribLattice πŸ“–CompOp
365 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Set.Finite.t2_separation, Matroid.exists_isBasis_disjoint_isBasis_of_subset, Metric.ball_disjoint_ball, Set.pairwiseDisjoint_pair_insert, Metric.disjoint_ball_infDist, Set.disjoint_ordT5Nhd, LocalizedModule.subsingleton_iff_disjoint, Finpartition.isPartition_parts, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, SimpleGraph.isBipartiteWith_neighborSet_disjoint, SeparatedNhds.disjoint, PrimeSpectrum.localization_specComap_range, disjoint_or_subset_of_isClopen, BoxIntegral.Box.disjoint_splitCenterBox, Matroid.isBase_compl_iff_maximal_disjoint_isBase, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, Disjoint.of_spanβ‚€, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, UpperSet.sdiff_eq_left, MeasureTheory.pairwise_disjoint_fundamentalInterior, SeparatedNhds.disjoint_closure_left, Set.Iio_disjoint_Ioi_of_not_lt, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, IsUltrametricDist.ball_subset_trichotomy, Matroid.IsBasis.contract_dep_iff, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, SimpleGraph.ComponentCompl.disjoint_right, LowerSet.disjoint_coe, AddAction.orbit.pairwiseDisjoint, EMetric.ball_disjoint, Topology.RelCWComplex.pairwiseDisjoint', Matroid.contract_isCocircuit_iff, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, Topology.RelCWComplex.disjoint_openCell_of_ne, IsCompact.separation_of_notMem, Finset.isWF_sup, AddAction.IsBlock.disjoint_vadd_left, OrderedFinpartition.disjoint, Set.Iio_disjoint_Ioi_iff, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, exists_dist_slope_lt_pairwiseDisjoint_hasSum, Besicovitch.exist_disjoint_covering_families, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.exists_null_pairwise_disjoint_diff, Matroid.IsBasis.contract_indep_iff, separated_by_continuous, Antitone.pairwise_disjoint_on_Ioo_pred, Perfect.small_diam_splitting, SimpleGraph.ComponentCompl.pairwise_disjoint, Set.Iic_disjoint_Ioi, Set.disjoint_pi_univ_Ioc_update_left_right, disjoint_nested_nhds_of_not_inseparable, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, exists_disjoint_vadd_of_isCompact, MulAction.IsBlock.disjoint_smul_of_ne, Disjoint.of_span, Matroid.IsMinor.exists_eq_contract_delete_disjoint, isEmbedding_sumElim, Prop.isCoatom_iff, Matroid.delete_eq_self_iff, MulAction.isBlock_iff_smul_eq_or_disjoint, disjoint_interior_frontier, Matroid.contract_eq_self_iff, Finset.sup_set_eq_biUnion, AlgebraicIndependent.adjoin_iff_disjoint, MeasureTheory.IsSetSemiring.disjointOfUnion_props, Set.Ioc_disjoint_Ioc, Matroid.Coindep.delete_spanning_iff, Monotone.pairwise_disjoint_on_Ioc_pred, Set.disjoint_right_ordSeparatingSet, LowerSet.sdiff_eq_left, Antitone.pairwise_disjoint_on_Ioo_succ, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Set.pairwise_disjoint_vadd_iff, Set.disjoint_iUnion_left, Set.definable_finset_sup, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Set.PairwiseDisjoint.exists_mem_filter, NonarchimedeanGroup.exists_openSubgroup_separating, Subgroup.leftCoset_cover_filter_FiniteIndex_aux, Ideal.disjoint_powers_iff_notMem, Matroid.Indep.contract_dep_iff, CompleteAtomicBooleanAlgebra.instIsCoatomistic, SimpleGraph.disjoint_edge, MeasureTheory.IsSetSemiring.mem_supClosure_iff, disjoint_nhdsSet_principal, Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, MulAction.disjoint_image_image_iff, t2_separation_nhds, SimpleGraph.disjoint_edgeFinset, Setoid.IsPartition.finpartition_parts, Set.disjoint_smul_set, AddAction.IsBlock.disjoint_vadd_vadd_set, Filter.disjoint_iff, Ideal.disjoint_map_primeCompl_iff_comap_le, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, not_disjoint_segment_convexHull_triple, Set.disjoint_sUnion_left, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, LowerSet.sdiff_lt_left, SimpleGraph.disjoint_edgeSet, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, Besicovitch.exist_finset_disjoint_balls_large_measure, isInducing_sumElim, Set.Ioi_disjoint_Iio_iff, Matroid.dual_indep_iff_exists', MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, AddAction.IsBlock.pairwiseDisjoint_range_vadd, Set.isAtom_singleton, Set.PairwiseDisjoint.exists_mem_filter_basis, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, MulAction.orbit.eq_or_disjoint, Topology.IsInducing.disjoint_of_sumElim_aux, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, IsLocalization.isPrime_iff_isPrime_disjoint, SubMulAction.disjoint_val_image, AddAction.IsBlock.disjoint_vadd_set_vadd, Metric.disjoint_closedEBall_of_lt_infEDist, exists_nhds_disjoint_closure, TopologicalSpace.Opens.coe_finset_sup, SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph, isNowhereDense_iff_disjoint, ConvexCone.disjoint_hull_left_of_convex, EisensteinSeries.pairwise_disjoint_gammaSet, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, MulAction.IsBlock.disjoint_smul_right, BoxIntegral.unitPartition.disjoint, MulAction.IsBlock.disjoint_smul_smul_set, Set.disjoint_iUnion_right, exists_open_nhds_disjoint_closure, disjoint_measurableAtom_of_notMem, MeasureTheory.disjoint_cylinder_iff, NFA.disjoint_evalFrom_reverse_iff, Matroid.contract_spanning_iff, Topology.CWComplex.pairwiseDisjoint', MulAction.IsBlock.disjoint_smul_set_smul, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, disjoint_frontier_iff_isOpen, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, IsGenericPoint.disjoint_iff, AddAction.IsBlock.disjoint_vadd_right, MeasureTheory.IsSetSemiring.diff_eq_sUnion', Antitone.pairwise_disjoint_on_Ioc_succ, exists_seq_infinite_isOpen_pairwise_disjoint, Set.disjoint_iUnionβ‚‚_right, IsUltrametricDist.ball_eq_or_disjoint, Filter.HasBasis.disjoint_iff, AddAction.isBlock_iff_vadd_eq_or_disjoint, Set.exists_union_disjoint_cardinal_eq_of_even, SimpleGraph.pairwise_disjoint_supp_connectedComponent, IsRetrocompact.finsetSup, Set.Ioi_disjoint_Iio_of_le, BoxIntegral.Prepartition.pairwiseDisjoint, Metric.ball_disjoint_closedBall, Matroid.IsCircuit.disjoint_coloops, UpperSet.lt_sdiff_left, Subgroup.IsComplement.pairwiseDisjoint_smul, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, Finset.intervalGapsWithin_pairwiseDisjoint_Ioc, SimpleGraph.EdgeLabeling.pairwiseDisjoint_univ_labelGraph, MulAction.IsBlock.smul_eq_smul_or_disjoint, ConvexCone.disjoint_coe, TopologicalSpace.Compacts.coe_finset_sup, Filter.disjoint_principal_principal, connectedComponent_disjoint, AddAction.IsBlock.disjoint_vadd_of_ne, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, Topology.RelCWComplex.disjoint_interior_base_closedCell, Set.Iic_disjoint_Ioc, SimpleGraph.IsBipartiteWith.disjoint, SeparatedNhds.disjoint_closure_right, Set.Ioc_disjoint_Ioi, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, Set.Iic_disjoint_Ici, Set.isAtom_iff, disjoint_ball_closedBall_iff, SimpleGraph.fromEdgeSet_disjoint, SimpleGraph.isBipartiteWith_neighborSet_disjoint', Interval.disjoint_coe, Set.Ioi_disjoint_Iio_of_not_lt, VitaliFamily.covering, Finset.isPWO_sup, Finset.partiallyWellOrderedOn_sup, exists_open_convex_of_notMem, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, AddAction.isBlock_iff_disjoint_vadd_of_ne, Vitali.exists_disjoint_subfamily_covering_enlargement, Matroid.coindep_contract_iff, t2_separation_compact_nhds, IndexedPartition.disjoint, Set.Ico_disjoint_Ico, AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, Topology.RelCWComplex.disjointBase, Monotone.pairwise_disjoint_on_Ico_pred, Metric.disjoint_closedBall_of_lt_infDist, Metric.frontier_thickening_disjoint, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, TopologicalSpace.Closeds.coe_finset_sup, Vitali.exists_disjoint_covering_ae, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, Monotone.pairwise_disjoint_on_Ioo_succ, Metric.AreSeparated.disjoint, Set.Ioi_disjoint_Iio_same, BoxIntegral.Box.disjoint_coe, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, IsLowerSet.disjoint_upperClosure_left, MulAction.isBlock_iff_disjoint_smul_of_ne, Besicovitch.exists_disjoint_closedBall_covering_ae, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, IsLocalization.orderIsoOfPrime_symm_apply_coe, Matroid.dual_indep_iff_exists, FreeGroup.startsWith.disjoint_iff_ne, Set.disjoint_vadd_set, disjoint_closedBall_closedBall_iff, Set.disjoint_sUnion_right, T2Space.t2, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, Metric.closedBall_disjoint_ball, IsLocalization.disjoint_comap_iff, AddAction.orbit.eq_or_disjoint, t2Space_iff_nhds, IsLowerSet.disjoint_upperClosure_right, Monotone.pairwise_disjoint_on_Ioo_pred, Set.ncard_union_eq_iff, Monotone.pairwise_disjoint_on_Ioc_succ, Matroid.delete_dep_iff, MeasureTheory.exists_subordinate_pairwise_disjoint, disjoint_principal_nhdsSet, Matroid.contract_spanning_iff', Set.exists_union_disjoint_cardinal_eq_iff, Matroid.Indep.contract_indep_iff, Metric.frontier_cthickening_disjoint, MulAction.orbit.pairwiseDisjoint, Set.Iio_disjoint_Ioi_same, Topology.RelCWComplex.disjoint_skeleton_openCell, RootedTree.subtrees_disjoint, Metric.eball_disjoint, MeasureTheory.AEDisjoint.exists_disjoint_diff, disjoint_ball_ball_iff, Topology.RelCWComplex.disjointBase', TopologicalSpace.Closeds.isAtom_coe, SimpleGraph.disjoint_left, disjoint_memPartition, Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one, NFA.disjoint_stepSet_reverse, PiNat.disjoint_cylinder_of_longestPrefix_lt, IsUpperSet.disjoint_lowerClosure_left, IsUltrametricDist.closedBall_subset_trichotomy, Set.disjoint_vadd_set_left, SimpleGraph.disjoint_image_val_universalVerts, ConvexCone.disjoint_hull_right_of_convex, Set.Ioc_disjoint_Ioc_of_le, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, EMetric.disjoint_closedBall_of_lt_infEdist, Set.pairwiseDisjoint_vadd_iff, Ideal.disjoint_primeCompl_of_liesOver, Composition.disjoint_range, MulAction.IsBlock.pairwiseDisjoint_range_smul, MulAction.isBlock_iff_pairwiseDisjoint_range_smul, isSeparatedMap_iff_nhds, Set.exists_union_disjoint_ncard_eq_of_even, Set.Ici_disjoint_Iic, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, Matroid.delete_isBasis_iff, Set.pairwiseDisjoint_iff, SimpleGraph.disjoint_fromEdgeSet, TopologicalSpace.Opens.coe_disjoint, CompleteAtomicBooleanAlgebra.instIsAtomistic, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, PMF.toOuterMeasure_apply_eq_zero_iff, AddAction.disjoint_image_image_iff, DoubleCoset.disjoint_out, Finset.wellFoundedOn_sup, AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux, Set.disjoint_vadd_set_right, Set.Iio_disjoint_Ici, Topology.RelCWComplex.disjoint_skeletonLT_openCell, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, Set.pairwise_disjoint_smul_iff, Setoid.IsPartition.pairwiseDisjoint, ModelWithCorners.disjoint_interior_boundary, Set.Ico_disjoint_Ico_same, Disjoint.edgeSet, SubAddAction.disjoint_val_image, BoxIntegral.Prepartition.disjoint_coe_of_mem, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, Antitone.pairwise_disjoint_on_Ico_pred, Matroid.Indep.contract_isBase_iff, Pairwise.exists_mem_filter_basis_of_disjoint, Set.pairwiseDisjoint_smul_iff, MulAction.IsBlock.smul_eq_or_disjoint, Set.Ioo_disjoint_Ioo, Perfect.splitting, Metric.sphere_disjoint_ball, RealRMK.range_cut_partition, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, Ideal.exists_disjoint_powers_of_span_eq_top, MeasureTheory.pairwise_disjoint_addFundamentalInterior, Topology.RelCWComplex.pairwiseDisjoint, Matroid.Coindep.delete_isBase_iff, Set.disjoint_smul_set_left, disjoint_nhdsWithin_of_mem_discrete, Filter.NeBot.not_disjoint, Set.disjoint_smul_set_right, Matroid.dualIndepMatroid_Indep, PrimeSpectrum.localization_comap_range, IsLocalization.orderIsoOfPrime_apply_coe, MeasurableSpace.disjoint_countablePartition, VitaliFamily.FineSubfamilyOn.covering_disjoint, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, Matroid.IsBasis'.contract_dep_iff, Matroid.delete_indep_iff, MeasureTheory.IsSetRing.finsetSup_mem, Pairwise.exists_mem_filter_of_disjoint, Set.disjoint_left_ordSeparatingSet, MeasureTheory.IsSetSemiring.exists_finpartition_diff, Matroid.Indep.disjoint_loops, Set.Iio_disjoint_Ioi_of_le, Finset.pairwiseDisjoint_pair_insert, Finsupp.disjoint_supported_supported_iff, Set.instIsAtomistic, Urysohns.CU.disjoint_C_support_lim, IsUpperSet.disjoint_lowerClosure_right, Order.Ideal.PrimePair.disjoint, Disjoint.exists_mem_filter_basis, IsLocalization.map_algebraMap_ne_top_iff_disjoint, SimpleGraph.deleteEdges_eq_self, Matroid.delete_isCircuit_iff, Set.disjoint_iUnionβ‚‚_left, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, r1_separation, Finset.sup_id_set_eq_sUnion, NumberField.InfinitePlace.disjoint_isReal_isComplex, Vitali.exists_disjoint_covering_ae', AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero, Matroid.IsBasis'.contract_indep_iff, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, disjoint_closedBall_ball_iff, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, PiNat.exists_disjoint_cylinder, t2_separation, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, Set.Ioc_disjoint_Ioi_same, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, Topology.RelCWComplex.disjoint_base_iUnion_openCell, AddAction.IsBlock.vadd_eq_or_disjoint, IsUltrametricDist.closedBall_eq_or_disjoint, Concept.disjoint_extent_intent, Antitone.pairwise_disjoint_on_Ico_succ, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Metric.closedBall_disjoint_closedBall, t2Space_iff, Monotone.pairwise_disjoint_on_Ico_succ
toCompleteLattice πŸ“–CompOp
1204 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, upperBounds_supClosure, MeasureTheory.Measure.MeasureDense.approx, Dynamics.netEntropyEntourage_monotone, Dynamics.netMaxcard_monotone_subset, Set.Finite.t2_separation, TopCat.binaryCofan_isColimit_iff, Set.ncard_mono, Matroid.exists_isBasis_disjoint_isBasis_of_subset, AlgebraicGeometry.descendsAlong_isOpenImmersion_surjective_inf_flat_inf_quasicompact', Metric.ball_disjoint_ball, NonUnitalAlgebra.gc, Set.pairwiseDisjoint_pair_insert, homotopyEquivalences_le_quasiIso, fixingSubgroup_antitone, Metric.disjoint_ball_infDist, convexIndependent_set_iff_inter_convexHull_subset, Dynamics.coverEntropyInfEntourage_antitone, Set.disjoint_ordT5Nhd, LowerAdjoint.closure_iUnionβ‚‚_closure, Set.smul_set_symmDiff, AlgebraicGeometry.descendsAlong_universallyClosed_surjective_inf_flat_inf_quasicompact, Set.preimage_kernImage, Language.iSup_add, IsLinearMap.image_convexHull, ProbabilityTheory.measure_limsup_eq_one, Language.reverse_iInf, LocalizedModule.subsingleton_iff_disjoint, FirstOrder.Language.Substructure.closure_eq_of_isRelational, Finpartition.isPartition_parts, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, Filter.sdiff_limsup, convexHull_insert, Antitone.Icc, CategoryTheory.MorphismProperty.isomorphisms_le_of_containsIdentities, CategoryTheory.MorphismProperty.isStableUnderLimitsOfShape_iff_limitsOfShape_le, subset_closedConvexHull, Geometry.SimplicialComplex.vertex_mem_convexHull_iff, SimpleGraph.isBipartiteWith_neighborSet_disjoint, closedConvexHull_min, SeparatedNhds.disjoint, PrimeSpectrum.localization_specComap_range, Language.iSup_sub, convexHull_multiset_sum, Geometry.SimplicialComplex.convexHull_subset_space, MeasureTheory.liminf_ae_eq_of_forall_ae_eq, CategoryTheory.MorphismProperty.hasOfPostcompProperty_iff_le_diagonal, CategoryTheory.MorphismProperty.universally_inf, disjoint_or_subset_of_isClopen, BoxIntegral.Box.disjoint_splitCenterBox, Finset.inf_id_set_eq_sInter, Matroid.isBase_compl_iff_maximal_disjoint_isBase, LowerAdjoint.mem_iff, Set.iUnionLift_unary, SSet.modelCategoryQuillen.I_le_monomorphisms, supClosure_eq_self, MonotoneOn.Icc, Geometry.SimplicialComplex.mem_space_iff, MeasureTheory.measureReal_symmDiff_le, AlgebraicGeometry.HasAffineProperty.affineAnd_le_affineAnd, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt, Disjoint.of_spanβ‚€, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRing, antitone_continuousOn, isSublattice_latticeClosure, strictMono_nhdsSet, Descriptive.Tree.take_mem, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, lowerPolar_anti, himp_eq, Monotone.Ici, CategoryTheory.MorphismProperty.HasCardinalLT.iSup, Convex.convex_remove_iff_notMem_convexHull_remove, ProjectiveSpectrum.gc_homogeneousIdeal, LowerAdjoint.closure_union_closure, Finset.ordConnected_range_coe, AntitoneOn.Ici, AlgebraicGeometry.IsAffineOpen.isCompact_pullback_inf, Matroid.eRk_mono, inf_mem_infClosure, convexHull_eq_iInter, UpperSet.sdiff_eq_left, latticeClosure_univ, FirstOrder.Language.Substructure.fg_closure_singleton, monotone_hausdorffEntourage, NFA.pumping_lemma, MeasureTheory.pairwise_disjoint_fundamentalInterior, MeasureTheory.monotone_spanningSets, SeparatedNhds.disjoint_closure_left, Set.Iio_disjoint_Ioi_of_not_lt, LinearMap.polar_antitone, compl_sInf, HasCardinalLT.Set.functor_obj, Filter.Realizer.map_F, PrimeSpectrum.gc, Complex.convexHull_reProdIm, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, IsUltrametricDist.ball_subset_trichotomy, Matroid.IsBasis.contract_dep_iff, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, isGLB_infClosure, CategoryTheory.MorphismProperty.ContainsIdentities.inf, Monotone.Ioo, LowerAdjoint.le_iff_subset, SimpleGraph.ComponentCompl.disjoint_right, LowerSet.disjoint_coe, AddAction.orbit.pairwiseDisjoint, MeasureTheory.measure_symmDiff_eq_top, Language.instMulRightMono, EMetric.ball_disjoint, Topology.RelCWComplex.pairwiseDisjoint', convexJoin_segments, Matroid.contract_isCocircuit_iff, FirstOrder.Language.Substructure.small_closure, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, CategoryTheory.MorphismProperty.pushouts_le, Topology.RelCWComplex.disjoint_openCell_of_ne, CategoryTheory.Localization.LeftBousfield.galoisConnection, FirstOrder.Language.Substructure.cg_def, IsCompact.separation_of_notMem, Cardinal.mk_monotone, Finset.isWF_sup, CategoryTheory.ObjectProperty.isomorphisms_le_isoModSerre, IsSublattice.latticeClosure_eq, AddAction.IsBlock.disjoint_vadd_left, Language.mem_iSup, OrderedFinpartition.disjoint, biUnion_range_succ_disjointed, Set.Iio_disjoint_Ioi_iff, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, AlgebraicGeometry.isImmersion_eq_inf, exists_dist_slope_lt_pairwiseDisjoint_hasSum, LinearEquiv.dilatransvections_pow_mono, FirstOrder.Language.Substructure.mem_closure, CategoryTheory.MorphismProperty.colimitsOfShape_le_coproducts, Besicovitch.exist_disjoint_covering_families, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.exists_null_pairwise_disjoint_diff, convexHull_union_neg_eq_absConvexHull, PUnit.sSup_eq, BoxIntegral.Box.Ioo_subset_coe, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', Localization.localRingHom_injective_of_primesOver_eq_singleton, CategoryTheory.MorphismProperty.IsInvertedBy.iff_map_le_isomorphisms, MeasureTheory.measure_liminf_cofinite_eq_zero, interior_convexHull_nonempty_iff_affineSpan_eq_top, AlgebraicGeometry.descendsAlong_isomorphisms_surjective_inf_flat_inf_quasicompact, SummationFilter.support_eq_limsInf, Matroid.IsBasis.contract_indep_iff, Descriptive.Tree.mem_pullSub_long, separated_by_continuous, CategoryTheory.MorphismProperty.monotone_map, Antitone.pairwise_disjoint_on_Ioo_pred, mem_absConvexHull_iff, Language.reverse_iSup, Perfect.small_diam_splitting, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_transfiniteCompositions, AlgebraicGeometry.IsSeparated.eq_valuativeCriterion, SimpleGraph.ComponentCompl.pairwise_disjoint, Filter.limsup_compl, Set.Iic_disjoint_Ioi, AlgebraicGeometry.IsClosedImmersion.eq_proper_inf_monomorphisms, Geometry.SimplicialComplex.convexHull_inter_convexHull, HasCardinalLT.Set.cocone_pt, Set.disjoint_pi_univ_Ioc_update_left_right, disjoint_nested_nhds_of_not_inseparable, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, AffineBasis.convexHull_eq_nonneg_coord, CategoryTheory.MorphismProperty.IsMultiplicative.inf, FirstOrder.Language.Substructure.fg_closure, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', exists_disjoint_vadd_of_isCompact, AntitoneOn.Icc, segment_subset_convexHull, MeasureTheory.measureReal_symmDiff_eq, convexHull_toCone_eq_sInf, MulAction.IsBlock.disjoint_smul_of_ne, CategoryTheory.MorphismProperty.colimitsOfShape_le, Balanced.convexHull, Disjoint.of_span, subset_absConvexHull, CategoryTheory.MorphismProperty.IsLocalAtSource.inf, Matroid.IsMinor.exists_eq_contract_delete_disjoint, balancedHull_subset_convexHull_union_neg, SSet.Subcomplex.degenerate_eq_top_iff, TopologicalSpace.Closeds.gc, isEmbedding_sumElim, Matroid.delete_eq_self_iff, CategoryTheory.IsGrothendieckAbelian.isomorphisms_le_pushouts_generatingMonomorphisms, sdiff_eq, Convex.convexHull_union, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, closedConvexHull_eq_closure_convexHull, MonotoneOn.Iio, Finset.mem_convexHull', subset_convexHull, Dynamics.coverEntropy_monotone, MulAction.isBlock_iff_smul_eq_or_disjoint, disjoint_interior_frontier, blimsup_thickening_mul_ae_eq_aux, Convex.convexHull_subset_iff, AffineBasis.interior_convexHull, CategoryTheory.MorphismProperty.coproducts_monotone, Filter.Realizer.ne_bot_iff, Matroid.contract_eq_self_iff, antitone_Ioi, Finset.sup_set_eq_biUnion, AlgebraicIndependent.adjoin_iff_disjoint, Set.Finite.infClosure, ofDual_preimage_latticeClosure, MeasureTheory.IsSetSemiring.disjointOfUnion_props, PUnit.sInf_eq, biSup_symmDiff_biSup_le, MeasureTheory.Measure.QuasiMeasurePreserving.liminf_preimage_iterate_ae_eq, Finset.coe_wcovBy_coe, HomotopicalAlgebra.trivialCofibrations_sub_cofibrations, compl_sSup', Set.Ioc_disjoint_Ioc, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, UpperSet.codisjoint_coe, Geometry.SimplicialComplex.inter_subset_convexHull, convexJoin_segment_singleton, CategoryTheory.MorphismProperty.colimitsOfShape_discrete_le_llp_rlp, Matroid.isClosed_iff_isFlat, CategoryTheory.Limits.LimitPresentation.self_Ο€, beattySeq'_symmDiff_beattySeq_pos, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, gc_upperPolar_lowerPolar, Concept.isCompl_extent_intent, convexJoin_singleton_segment, convexHull_diam, TopologicalSpace.Opens.frameHom_toFun, Matroid.Coindep.delete_spanning_iff, Antitone.Ico, Monotone.pairwise_disjoint_on_Ioc_pred, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', Set.disjoint_right_ordSeparatingSet, CategoryTheory.MorphismProperty.isStableUnderRetracts_iff_retracts_le, LowerSet.sdiff_eq_left, Antitone.pairwise_disjoint_on_Ioo_succ, subset_closedAbsConvexHull, gc_upperBounds_lowerBounds, CategoryTheory.MorphismProperty.multiplicativeClosure_monotone, Dynamics.netEntropyEntourage_antitone, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Ξ΅NFA.pumping_lemma, CategoryTheory.Functor.relativelyRepresentable.isomorphisms_le, Finset.centerMass_id_mem_convexHull, CategoryTheory.MorphismProperty.DescendsAlong.inf, CategoryTheory.MorphismProperty.CodescendsAlong.inf, Set.pairwise_disjoint_vadd_iff, latticeClosure_mono, Set.Finite.isCompact_convexHull, image_latticeClosure', Finset.centerMass_id_mem_convexHull_of_nonpos, CompleteLatticeHom.setPreimage_apply, convexHull_add, CategoryTheory.MorphismProperty.retracts_le, IsFoelner.tendsto_meas_smul_symmDiff, Filter.cofinite.limsup_set_eq, Language.instMulLeftMono, CategoryTheory.MorphismProperty.IsStableUnderBaseChange.inf, Set.disjoint_iUnion_left, upperHemicontinuousWithinAt_iff_preimage_Iic, Set.definable_finset_sup, affineSpan_convexHull, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, MeasureTheory.IsSetSemiring.isSetRing_supClosure, Cardinal.mk_strictMonoOn, AlgebraicGeometry.instDescendsAlongSchemeMinMorphismPropertySurjectiveFlatLocallyOfFinitePresentationOfQuasiCompactOfIsZariskiLocalAtTarget, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Besicovitch.TauPackage.monotone_iUnionUpTo, HomotopicalAlgebra.trivialCofibrations_sub_weakEquivalences, AlgebraicGeometry.HasAffineProperty.affineAnd_eq_of_propertyIsLocal, Set.PairwiseDisjoint.exists_mem_filter, CategoryTheory.Localization.LeftBousfield.le_W_iff, Antitone.Ioc, MeasureTheory.hittingBtwn_apply_anti, CategoryTheory.MorphismProperty.le_ind, Set.encard_strictMono, AlgebraicGeometry.Etale.instHasOfPostcompPropertySchemeMinMorphismPropertyLocallyOfFiniteTypeFormallyUnramified, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le, MeasureTheory.Measure.MeasureDense.fin_meas_approx, compl_sSup, NonarchimedeanGroup.exists_openSubgroup_separating, HomotopicalAlgebra.trivialFibrations_sub_fibrations, Subgroup.leftCoset_cover_filter_FiniteIndex_aux, MeasureTheory.edist_indicatorConstLp_eq_enorm, AlgebraicGeometry.IsFinite.eq_proper_inf_locallyQuasiFinite, convexHull_basis_eq_stdSimplex, fixingAddSubmonoid_fixedPoints_gc, Ideal.disjoint_powers_iff_notMem, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_le_monomorphisms, Matroid.Indep.contract_dep_iff, Language.sub_iSup, blimsup_cthickening_ae_le_of_eventually_mul_le_aux, Convex.radon_partition, CompleteAtomicBooleanAlgebra.instIsCoatomistic, IsOpen.exists_iUnion_isClosed, Language.le_iff, Ctop.Realizer.nhds_F, lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl, Matroid.cRk_mono, ConvexOn.bddAbove_convexHull, MeasureTheory.IsSetSemiring.mem_supClosure_iff, FirstOrder.Language.Substructure.fg_def, SupClosed.infClosure, disjoint_nhdsSet_principal, BoxIntegral.Box.iUnion_Ioo_of_tendsto, CompleteAtomicBooleanAlgebra.iInf_iSup_eq, Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, MulAction.disjoint_image_image_iff, t2_separation_nhds, CompleteSublattice.mem_subtype, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_monotone, Setoid.IsPartition.finpartition_parts, MonotoneOn.Ici, CategoryTheory.MorphismProperty.isStableUnderCobaseChange_iff_pushouts_le, Set.disjoint_smul_set, AddAction.IsBlock.disjoint_vadd_vadd_set, Matroid.closure_eq_subtypeClosure, infClosed_infClosure, Filter.disjoint_iff, Ideal.disjoint_map_primeCompl_iff_comap_le, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, MeasureTheory.measure_symmDiff_le, ConvexIndependent.mem_convexHull_iff, CategoryTheory.MorphismProperty.universally_le, not_disjoint_segment_convexHull_triple, CategoryTheory.GrothendieckTopology.PreservesSheafification.le, AffineSubspace.inf_coe, AlgebraicGeometry.IsLocalIso.eq_iInf, Language.add_iSup, convexHull_vadd, Filter.monotone_mem, Matroid.closure_mono, FirstOrder.Language.Substructure.lift_card_closure_le_card_term, MeasureTheory.dense_of_generateFrom_isSetSemiring, Set.disjoint_sUnion_left, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, AlgebraicGeometry.topologically_iso_le, AffineSubspace.coe_inf, Set.isCoatom_iff, Monotone.Iio, exists_mem_interior_convexHull_affineBasis, LowerSet.sdiff_lt_left, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, MeasureTheory.measure_neg_vadd_symmDiff, supClosure_empty, FirstOrder.Language.Substructure.mem_closure_iff_exists_term, BooleanSubalgebra.sSup_mem, IsRetrocompact.finsetInf', Besicovitch.exist_finset_disjoint_balls_large_measure, blimsup_cthickening_ae_le_of_eventually_mul_le, isInducing_sumElim, BoxIntegral.Box.Ioo_ae_eq_Icc, QuotientAddGroup.strictMono_comap_prod_image, compl_image_latticeClosure, closedAbsConvexHull_min, Order.Ideal.PrimePair.isCompl_I_F, CategoryTheory.MorphismProperty.le_pushouts, TopologicalSpace.Opens.gc, Filter.cofinite.bliminf_set_eq, PrimitiveSpectrum.gc_closureOperator, beattySeq_symmDiff_beattySeq'_pos, Irrational.beattySeq_symmDiff_beattySeq_pos, upperHemicontinuousOn_iff_preimage_Iic, totallyBounded_absConvexHull, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_W, Set.Ioi_disjoint_Iio_iff, Matroid.dual_indep_iff_exists', infClosure_singleton, MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, absConvexHull_nonempty, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, Descriptive.Tree.take_coe, absConvexHull_empty, AddAction.IsBlock.pairwiseDisjoint_range_vadd, CategoryTheory.MorphismProperty.strictMap_multiplicativeClosure_le, Set.isAtom_singleton, Set.PairwiseDisjoint.exists_mem_filter_basis, absConvexHull_eq_self, Set.kernImage_mono, Filter.limsup_sdiff, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, Set.monotone_accumulate, MulAction.orbit.eq_or_disjoint, Topology.IsInducing.disjoint_of_sumElim_aux, Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, latticeClosure_prod, CategoryTheory.SmallObject.succStruct_prop_le_propArrow, CategoryTheory.Limits.ColimitPresentation.self_diag, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, IsLocalization.isPrime_iff_isPrime_disjoint, SubMulAction.disjoint_val_image, Monotone.Ico, InfClosed.infClosure_eq, MeasureTheory.measure_limsup_cofinite_eq_zero, Dynamics.coverMincard_antitone, NonUnitalStarAlgebra.gc, Dynamics.netMaxcard_antitone, AddAction.IsBlock.disjoint_vadd_set_vadd, AlgebraicGeometry.isCompl_range_inl_inr, CategoryTheory.MorphismProperty.isoClosure_le_iff, Antitone.Iio, Metric.disjoint_closedEBall_of_lt_infEDist, upperHemicontinuousAt_iff_preimage_Iic, exists_nhds_disjoint_closure, Seminorm.closedBall_finset_sup, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, ProjectiveSpectrum.gc_set, convexHull_add_subset, TopologicalSpace.Opens.coe_finset_sup, MeasureTheory.IsSetSemiring.diff_mem_supClosure, isNowhereDense_iff_disjoint, ConvexCone.disjoint_hull_left_of_convex, EisensteinSeries.pairwise_disjoint_gammaSet, Descriptive.Tree.pullSub_adjunction, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, Topology.IsLocallyConstructible.finsetInf, infClosure_eq_self, CategoryTheory.MorphismProperty.coproducts_le_iff, closedConvexHull_closure_eq_closedConvexHull, MulAction.IsBlock.disjoint_smul_right, compl_image_latticeClosure_eq_of_compl_image_eq_self, partialSups_eq_sUnion_image, Polynomial.rootSet_derivative_subset_convexHull_rootSet, BoxIntegral.unitPartition.disjoint, latticeClosure_singleton, closure_convexHull_extremePoints, CategoryTheory.ObjectProperty.galoisConnection_isColocal, CategoryTheory.MorphismProperty.map_inverseImage_le, MulAction.IsBlock.disjoint_smul_smul_set, MeasureTheory.le_measure_symmDiff, TopologicalSpace.Closeds.coe_finset_inf, CategoryTheory.MorphismProperty.le_isLocal_isLocal, CompleteSublattice.mem_sInf, MeasurableSet.bihimp, CategoryTheory.MorphismProperty.gc_llp_rlp, Dynamics.coverEntropyEntourage_monotone, Descriptive.coe_def, Set.Finite.isClosed_convexHull, Descriptive.Tree.pullSub_subAt, MeasureTheory.measure_symmDiff_inv_smul, convexHull_empty, Set.disjoint_iUnion_right, HomotopicalAlgebra.trivialFibrations_sub_weakEquivalences, Set.image_preimage, absConvexHull_add_subset, Finset.centerMass_mem_convexHull, exists_open_nhds_disjoint_closure, le_sup_inf, Sublattice.setLike_mem_inf, disjoint_measurableAtom_of_notMem, convexHull_pair, MeasureTheory.disjoint_cylinder_iff, MonotoneOn.Iic, CategoryTheory.MorphismProperty.HasCardinalLT.sup, Descriptive.Tree.take_eq_take, CategoryTheory.MorphismProperty.instIsStableUnderRetractsMin, preCantorSet_antitone, MeasureTheory.hittingBtwn_anti, CategoryTheory.MorphismProperty.retracts_transfiniteComposition_pushouts_coproducts_le_llp_rlp, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, NFA.disjoint_evalFrom_reverse_iff, Matroid.contract_spanning_iff, FirstOrder.Language.Substructure.mem_closed_of_isRelational, Topology.CWComplex.pairwiseDisjoint', Filter.antitone_seq_of_seq, infClosure_univ, Dynamics.coverEntropyInf_monotone, FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_family, Sublattice.ext_mem_iff, MulAction.IsBlock.disjoint_smul_set_smul, fixingSubmonoid_antitone, TopologicalSpace.Opens.coe_finset_inf, subset_latticeClosure, CategoryTheory.MorphismProperty.iSup_iff, convexJoin_subset_convexHull, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, subset_infClosure, SimpleGraph.Subgraph.verts_monotone, convexHull_eq_empty, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, FirstOrder.Language.ClosedUnder.inf, CategoryTheory.Limits.LimitPresentation.self_diag, FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, disjoint_frontier_iff_isOpen, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, MvPolynomial.supported_strictMono, IsGenericPoint.disjoint_iff, Sublattice.mem_subtype, AddAction.IsBlock.disjoint_vadd_right, convexHull_singleton, fixedPoints_addSubgroup_antitone, MeasureTheory.hittingAfter_apply_anti, compl_iSup, MeasureTheory.IsSetSemiring.diff_eq_sUnion', compl_iInf, AntitoneOn.Ioi, Antitone.pairwise_disjoint_on_Ioc_succ, dist_mulIndicator, CategoryTheory.MorphismProperty.map_le_iff, CompleteSublattice.mem_sup, Filter.Realizer.mem_sets, exists_seq_infinite_isOpen_pairwise_disjoint, LowerAdjoint.closure_union_closure_subset, BooleanSubalgebra.latticeClosure_subset_closure, Set.disjoint_iUnionβ‚‚_right, isFoelner_iff, Antitone.Ioi, convex_convexHull, CategoryTheory.ObjectProperty.le_isLocal_iff, convexHull_sum, Set.limsup_eq_tendsto_sum_indicator_atTop, Finset.inf_set_eq_iInter, IsUltrametricDist.ball_eq_or_disjoint, CategoryTheory.MorphismProperty.le_coproducts, Filter.HasBasis.disjoint_iff, IsFoelner.tendsto_meas_smul_symmDiff_smul, FirstOrder.Language.Substructure.closure_insert, isBounded_convexHull, CategoryTheory.MorphismProperty.RespectsLeft.inf, AddAction.isBlock_iff_vadd_eq_or_disjoint, Dynamics.netEntropyInfEntourage_monotone, Set.exists_union_disjoint_cardinal_eq_of_even, SimpleGraph.pairwise_disjoint_supp_connectedComponent, Language.instOrderedSub, Finset.mem_convexHull, Filter.liminf_compl, BooleanSubalgebra.closure_latticeClosure, convexHull_neg, upperHemicontinuous_iff_isOpen_preimage_Iic, convexIndependent_set_iff_notMem_convexHull_diff, IsRetrocompact.finsetSup, upperHemicontinuous_iff_preimage_Iic, Set.Ioi_disjoint_Iio_of_le, BoxIntegral.Prepartition.pairwiseDisjoint, Antitone.Ici, LinearEquiv.transvections_pow_mono, Concept.codisjoint_extent_intent, CategoryTheory.MorphismProperty.le_pullbacks, convexHull_sphere_eq_closedBall, CategoryTheory.ObjectProperty.epimorphisms_le_epiModSerre, Metric.ball_disjoint_closedBall, CategoryTheory.MorphismProperty.antitone_rlp, mem_add_wellApproximable_iff, CategoryTheory.MorphismProperty.bijective_eq_sup, LinearMap.polar_gc, AntitoneOn.Iic, LowerAdjoint.subset_closure, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.le, Matroid.IsCircuit.disjoint_coloops, UpperSet.lt_sdiff_left, MeasureTheory.tendsto_measure_symmDiff_preimage_nhds_zero, Set.Finite.supClosure, Subgroup.IsComplement.pairwiseDisjoint_smul, Filter.liminf_sdiff, Convex.exists_subset_interior_convexHull_finset_of_isCompact, Filter.Realizer.ofEquiv_F, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, MeasurableSet.measurableSet_bliminf, convexHull_mono, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, convex_absConvexHull, CauchyFilter.monotone_gen, Set.isCoatom_singleton_compl, Cardinal.mk_strictMono, convexHullAddMonoidHom_apply, Finset.intervalGapsWithin_pairwiseDisjoint_Ioc, absConvexHull_mono, biUnion_Iic_disjointed, Finset.convexHull_eq, MulAction.IsBlock.smul_eq_smul_or_disjoint, ConvexCone.disjoint_coe, totallyBounded_convexHull, CategoryTheory.MorphismProperty.le_llp_rlp, AlgebraicGeometry.HasRingHomProperty.inf, Set.Nonempty.absConvexHull, TopologicalSpace.Compacts.coe_finset_sup, CompleteSublattice.mem_inf, Filter.disjoint_principal_principal, connectedComponent_disjoint, AddAction.IsBlock.disjoint_vadd_of_ne, CategoryTheory.MorphismProperty.le_llp_iff_le_rlp, CategoryTheory.MorphismProperty.coproducts_le, MeasureTheory.IsSetRing.partialSups_mem, sup_mem_supClosure, lowerBounds_infClosure, gc_nhdsKer_interior, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, LowerAdjoint.closure_union_closure_right, Topology.RelCWComplex.disjoint_interior_base_closedCell, absConvex_convexClosedHull, Set.Iic_disjoint_Ioc, convexHull_eq_singleton, convexHull_eq_zero, Set.encard_mono, CategoryTheory.ObjectProperty.le_isColocal_iff, nndist_mulIndicator, SimpleGraph.IsBipartiteWith.disjoint, MeasureTheory.eLpNorm_indicator_sub_indicator, SeparatedNhds.disjoint_closure_right, Set.Ioc_disjoint_Ioi, FirstOrder.Language.Substructure.closure_empty, QuotientGroup.strictMono_comap_prod_image, monotone_Iio, isCompact_closedAbsConvexHull_of_totallyBounded, supClosure_isClosed, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, absConvexHull_subset_closedAbsConvexHull, Matroid.setOf_indep_eq, toWeakSpace_closedConvexHull_eq, Set.Iic_disjoint_Ici, convexHull_pi, FirstOrder.Language.monotone_distinctConstantsTheory, Set.isAtom_iff, Monotone.Ioc, Language.IsRegular.inf, MeasureTheory.measure_liminf_atTop_eq_zero, Finset.coe_covBy_coe, AlgebraicGeometry.isOpenImmersion_eq_inf, gc_upperClosure_coe, FirstOrder.Language.Substructure.iSup_eq_closure, disjoint_ball_closedBall_iff, MeasurableSet.symmDiff, Filter.EventuallyEq.symmDiff, iSup_disjointed, CategoryTheory.MorphismProperty.le_retracts, supClosure_singleton, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyMin, AlgebraicGeometry.IsClosedImmersion.eq_inf, SimpleGraph.isBipartiteWith_neighborSet_disjoint', image_latticeClosure, doublyStochastic_eq_convexHull_permMatrix, latticeClosure_eq_self, CategoryTheory.ObjectProperty.monomorphisms_le_monoModSerre, Interval.disjoint_coe, absConvexHull_eq_iInter, CFilter.mem_toFilter_sets, CategoryTheory.MorphismProperty.pretopology_inf, AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocally, Set.Ioi_disjoint_Iio_of_not_lt, latticeClosure_empty, VitaliFamily.covering, BoxIntegral.Box.Ioo_subset_Icc, Finset.isPWO_sup, Finset.partiallyWellOrderedOn_sup, MeasurableSet.measurableSet_liminf, exists_open_convex_of_notMem, Language.iSup_mul, CategoryTheory.MorphismProperty.inf, BoxIntegral.Box.exists_seq_mono_tendsto, Finset.centroid_mem_convexHull, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, supClosure_mono, CategoryTheory.MorphismProperty.RespectsRight.inf, CategoryTheory.MorphismProperty.coproducts_le_llp_rlp, AddAction.isBlock_iff_disjoint_vadd_of_ne, Vitali.exists_disjoint_subfamily_covering_enlargement, Matroid.coindep_contract_iff, t2_separation_compact_nhds, AbsConvex.absConvexHull_subset_iff, IndexedPartition.disjoint, lowerHemicontinuous_iff_isClosed_preimage_Iic, Set.Ico_disjoint_Ico, AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, Topology.RelCWComplex.disjointBase, SupClosed.supClosure_eq, MeasureTheory.Egorov.notConvergentSeq_antitone, ClosedSubmodule.coe_inf, Projectivization.Subspace.monotone_span, Locale.openOfElementHom_toFun, FirstOrder.Language.Substructure.subset_closure, PrimitiveSpectrum.closedsGC_closureOperator, Filter.cofinite.liminf_set_eq, Monotone.pairwise_disjoint_on_Ico_pred, AlgebraicGeometry.isPreimmersion_eq_inf, FirstOrder.Language.Substructure.closure_iUnion, Metric.disjoint_closedBall_of_lt_infDist, absConvex_absConvexHull, monotone_Iic, AntitoneOn.Ioo, mem_wellApproximable_iff, DFA.acceptsFrom_inter, Metric.frontier_thickening_disjoint, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, ProjectiveSpectrum.gc_ideal, TopologicalSpace.Closeds.coe_finset_sup, MeasureTheory.measure_inv_smul_symmDiff, Vitali.exists_disjoint_covering_ae, AlgebraicGeometry.isProper_eq, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, Monotone.pairwise_disjoint_on_Ioo_succ, Metric.AreSeparated.disjoint, Set.Ioi_disjoint_Iio_same, BoxIntegral.Box.disjoint_coe, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, LinearMap.image_convexHull, IsLowerSet.disjoint_upperClosure_left, FirstOrder.Language.Substructure.closure_union, MulAction.isBlock_iff_disjoint_smul_of_ne, ContinuousMap.ideal_gc, IsRetrocompact.finsetSup', Dynamics.coverEntropyEntourage_antitone, DFA.pumping_lemma, Besicovitch.exists_disjoint_closedBall_covering_ae, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, PrimeSpectrum.gc_set, IsLocalization.orderIsoOfPrime_symm_apply_coe, StarAlgebra.gc, Matroid.dual_indep_iff_exists, convexHull_univ, FreeGroup.startsWith.disjoint_iff_ne, Set.disjoint_vadd_set, convexHull_ediam, disjoint_closedBall_closedBall_iff, Finsupp.codisjoint_supported_supported_iff, Set.disjoint_sUnion_right, CategoryTheory.MorphismProperty.limitsOfShape_le, FirstOrder.Language.Structure.cg_iff, T2Space.t2, Monotone.Ioi, infClosure_min, absConvexHull_min, Filter.ker_mono, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, Descriptive.Tree.tree_eq_bot, Metric.closedBall_disjoint_ball, CategoryTheory.MorphismProperty.retracts_le_iff, HasCardinalLT.Set.cocone_ΞΉ_app, AlgebraicGeometry.universallyClosed_eq_universallySpecializing, IsLocalization.disjoint_comap_iff, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_llp_rlp, AffineIndependent.convexHull_inter', AntitoneOn.Iio, Filter.Realizer.le_iff, AddAction.orbit.eq_or_disjoint, latticeClosure_idem, convexHull_zero, t2Space_iff_nhds, IsLowerSet.disjoint_upperClosure_right, AlgebraicGeometry.Flat.surjective_descendsAlong_surjective_inf_flat_inf_quasicompact, convexHull_eq_union_convexHull_finite_subsets, Monotone.pairwise_disjoint_on_Ioo_pred, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, CategoryTheory.MorphismProperty.retracts_transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, Set.ncard_union_eq_iff, Concept.strictAnti_intent, AlgebraicGeometry.IsProper.eq_valuativeCriterion, Monotone.pairwise_disjoint_on_Ioc_succ, CategoryTheory.MorphismProperty.IsInvertedBy.iff_le_inverseImage_isomorphisms, MeasurableSet.measurableSet_limsup, AlgebraicGeometry.IsClosedImmersion.eq_isFinite_inf_mono, CategoryTheory.MorphismProperty.isomorphisms_le_pushouts, Matroid.delete_dep_iff, fixingSubmonoid_fixedPoints_gc, CompleteSublattice.mem_iSup, MeasureTheory.exists_subordinate_pairwise_disjoint, zero_mem_absConvexHull, MeasureTheory.MeasuredSets.dist_def, CategoryTheory.MorphismProperty.IsStableUnderComposition.inf, AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterion, Language.mem_inf, disjoint_principal_nhdsSet, Matroid.contract_spanning_iff', Filter.Realizer.principal_F, infClosure_prod, Set.exists_union_disjoint_cardinal_eq_iff, HasCardinalLT.Set.functor_map_coe, affineCombination_mem_convexHull, MeasureTheory.ae_mem_limsup_atTop_iff, CategoryTheory.MorphismProperty.le_leftBousfieldW_isLocal, disjointed_eq_inf_compl, Matroid.Indep.contract_indep_iff, mem_convexHull_iff_exists_fintype, Metric.frontier_cthickening_disjoint, dist_indicator, CategoryTheory.MorphismProperty.colimitsOfShape_le_of_final, MulAction.orbit.pairwiseDisjoint, Set.antitone_dissipate, absConvexHull_univ, Set.Iio_disjoint_Ioi_same, Topology.RelCWComplex.disjoint_skeleton_openCell, convexHull_toCone_isLeast, Set.partialSups_eq_accumulate, RootedTree.subtrees_disjoint, posTangentConeAt_mono, fixedPoints_subgroup_antitone, CategoryTheory.LocalizerMorphism.map, AlgebraicGeometry.isomorphisms_eq_isOpenImmersion_inf_surjective, Set.iUnionLift_binary, Metric.eball_disjoint, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyMin, CompleteSublattice.mem_top, Filter.mem_limsup_iff_frequently_mem, MeasureTheory.AEDisjoint.exists_disjoint_diff, fixingAddSubmonoid_antitone, MeasurableSpace.generateMeasurableRec_mono, disjoint_ball_ball_iff, Set.Finite.latticeClosure, extremePoints_convexHull_subset, MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection, Topology.RelCWComplex.disjointBase', MeasurableSet.measurableSet_blimsup, CategoryTheory.MorphismProperty.transfiniteCompositions_le, TopologicalSpace.gc_generateFrom, BooleanSubalgebra.biSup_mem, TopologicalSpace.Closeds.isAtom_coe, disjoint_memPartition, Geometry.SimplicialComplex.face_subset_face_iff, top_le_sup_compl, Convex.convexHull_eq, Descriptive.Tree.mem_subAt, Set.monotone_preimage, convexHull_convexHull_union_right, Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one, AlgebraicGeometry.geometrically_inf, NFA.disjoint_stepSet_reverse, MeasureTheory.measure_limsup_atTop_eq_zero, fixedPoints_antitone_addSubmonoid, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, CategoryTheory.MorphismProperty.retracts_le_llp_rlp, PiNat.disjoint_cylinder_of_longestPrefix_lt, IsUpperSet.disjoint_lowerClosure_left, HasCardinalLT.Set.instIsCardinalFiltered, IsUltrametricDist.closedBall_subset_trichotomy, Set.disjoint_vadd_set_left, MonotoneOn.Ico, SimpleGraph.disjoint_image_val_universalVerts, MeasureTheory.measure_symmDiff_eq, fixingAddSubgroup_fixedPoints_gc, ConvexCone.disjoint_hull_right_of_convex, Set.Ioc_disjoint_Ioc_of_le, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHom, CategoryTheory.MorphismProperty.antitone_llp, EMetric.disjoint_closedBall_of_lt_infEdist, FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize, AlgebraicGeometry.targetAffineLocally_affineAnd_le, Set.pairwiseDisjoint_vadd_iff, Ideal.disjoint_primeCompl_of_liesOver, MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative, FirstOrder.Language.Substructure.closed, blimsup_cthickening_ae_eq_blimsup_thickening, supClosure_infClosure, Composition.disjoint_range, MulAction.IsBlock.pairwiseDisjoint_range_smul, MulAction.isBlock_iff_pairwiseDisjoint_range_smul, absConvexHull_isClosed, Set.instIsCoatomistic, CategoryTheory.MorphismProperty.sSup_iff, infClosure_mono, isSeparatedMap_iff_nhds, Set.exists_union_disjoint_ncard_eq_of_even, convexHull_convexHull_union_left, MonotoneOn.Ioc, Set.mabs_mulIndicator_symmDiff, Set.Ici_disjoint_Iic, convexHull_min, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, fixingSubgroup_fixedPoints_gc, convexHull_isClosed, fixingAddSubgroup_antitone, Matroid.delete_isBasis_iff, MeasureTheory.AddContent.supClosure_apply_of_mem, monotone_nhdsSet, InfClosed.supClosure, SSet.modelCategoryQuillen.J_le_monomorphisms, antitone_Ici, CategoryTheory.MorphismProperty.isStableUnderTransfiniteCompositionOfShape_iff, Language.mul_iSup, MeasureTheory.measure_symmDiff_neg_vadd, MeasureTheory.limsup_ae_eq_of_forall_ae_eq, Filter.cofinite.blimsup_set_eq, Set.pairwiseDisjoint_iff, closedAbsConvexHull_eq_closure_absConvexHull, Seminorm.closedBall_finset_sup', TopologicalSpace.Opens.coe_disjoint, CategoryTheory.MorphismProperty.le_isColocal_isColocal, Filter.sdiff_liminf, Matroid.isFlat_iff_isClosed, CompleteAtomicBooleanAlgebra.instIsAtomistic, BoxIntegral.Box.measurableSet_Ioo, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, CompleteSublattice.mem_sSup, nndist_indicator, PMF.toOuterMeasure_apply_eq_zero_iff, ConvexCone.gc_hull_coe, AddAction.disjoint_image_image_iff, convexHull_prod, MeasureTheory.OuterMeasure.isCaratheodory_partialSups, DoubleCoset.disjoint_out, Antitone.Iic, FirstOrder.Language.Substructure.closure_withConstants_eq, blimsup_thickening_mul_ae_eq, Filter.IsAntitoneBasis.antitone, IsAddFoelner.tendsto_meas_vadd_symmDiff, Finset.wellFoundedOn_sup, CompleteSublattice.ext_iff, AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux, Set.disjoint_vadd_set_right, MonotoneOn.Ioo, infClosure_supClosure, convexHull_eq_union, Set.Iio_disjoint_Ici, Topology.RelCWComplex.disjoint_skeletonLT_openCell, convexHull_eq, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, Filter.Realizer.bot_F, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyMin, Monotone.Iic, supClosure_idem, BooleanSubalgebra.sInf_mem, Set.pairwise_disjoint_smul_iff, CompleteLatticeHom.coe_setPreimage, convexHull_smul, Setoid.IsPartition.pairwiseDisjoint, ModelWithCorners.disjoint_interior_boundary, CompleteLatticeHom.setPreimage_id, BooleanSubalgebra.biInf_mem, Filter.Realizer.top_F, Set.Nonempty.convexHull, absConvexHull_eq_convexHull_balancedHull, FirstOrder.Language.Substructure.map_closure, Set.Ico_disjoint_Ico_same, Set.Finite.convexHull_eq_image, Set.vadd_set_symmDiff, Filter.HasAntitoneBasis.antitone, CategoryTheory.MorphismProperty.precoverage_inf, AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHom, infClosure_idem, CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.inf, Disjoint.edgeSet, mem_convexHull_of_exists_fintype, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring, convexHull_rangle_single_eq_stdSimplex, FirstOrder.Language.Substructure.closure_le, CategoryTheory.MorphismProperty.monotone_isoClosure, AffineBasis.centroid_mem_interior_convexHull, AffineMap.image_convexHull, BooleanSubalgebra.iInf_mem, convexHull_union, convexHull_sub, FirstOrder.Language.Substructure.mem_closed_iff, upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl, SubAddAction.disjoint_val_image, Monotone.Icc, WCovBy.finset_coe, closure_subset_closedConvexHull, ConcaveOn.bddBelow_convexHull, BoxIntegral.Prepartition.disjoint_coe_of_mem, blimsup_cthickening_mul_ae_eq, Set.Countable.substructure_closure, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, AlgebraicGeometry.isomorphisms_eq_stalkwise, FirstOrder.Language.Substructure.subset_closure_withConstants, DFA.accepts_inter, Antitone.pairwise_disjoint_on_Ico_pred, convexHull_list_sum, Matroid.Indep.contract_isBase_iff, CategoryTheory.MorphismProperty.transfiniteCompositions_pushouts_coproducts_le_llp_rlp, Set.definable_finset_inf, Set.Finite.ncard_strictMonoOn, AlgebraicGeometry.IsOpenImmersion.le_monomorphisms, IntermediateField.gc, CategoryTheory.MorphismProperty.le_def, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', Submodule.span_monotone, partialSups_eq_biUnion_range, Filter.exists_antitone_seq, AlgebraicGeometry.IsFinite.eq_inf, CategoryTheory.MorphismProperty.pushouts_le_llp_rlp, Pairwise.exists_mem_filter_basis_of_disjoint, AlgebraicGeometry.affineLocally_le, Set.pairwiseDisjoint_smul_iff, MulAction.IsBlock.smul_eq_or_disjoint, CompleteSublattice.mem_iInf, Concept.strictMono_extent, Set.Ioo_disjoint_Ioo, Perfect.splitting, convexHull_nonempty_iff, CovBy.finset_coe, AlgebraicGeometry.GeometricallyIntegral.eq_geometricallyReduced_inf_geometricallyIrreducible, iSup_symmDiff_iSup_le, Metric.sphere_disjoint_ball, infClosure_isClosed, RealRMK.range_cut_partition, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃_W, CategoryTheory.MorphismProperty.isStableUnderColimitsOfShape_iff_colimitsOfShape_le, Topology.IsLocallyConstructible.finsetInf', Ideal.exists_disjoint_powers_of_span_eq_top, subset_supClosure, Dynamics.netEntropyInfEntourage_antitone, Descriptive.Tree.mem_pullSub_self, MeasureTheory.pairwise_disjoint_addFundamentalInterior, CategoryTheory.MorphismProperty.toSet_max, upperPolar_anti, Topology.RelCWComplex.pairwiseDisjoint, Matroid.Coindep.delete_isBase_iff, closedAbsConvexHull_isClosed, CategoryTheory.MorphismProperty.le_isoClosure, AntitoneOn.Ioc, HasCardinalLT.Set.instIsFilteredOfFactIsRegular, Set.disjoint_smul_set_left, disjoint_nhdsWithin_of_mem_discrete, finsetInf'_mem_infClosure, CategoryTheory.ObjectProperty.galoisConnection_isLocal, mem_convexHull_iff, Dynamics.dynEntourage_antitone, compl_sInf', AntitoneOn.Ico, Filter.NeBot.not_disjoint, Seminorm.ball_finset_sup, CategoryTheory.MorphismProperty.pullbacks_monotone, Set.disjoint_smul_set_right, Matroid.dualIndepMatroid_Indep, parallelepiped_eq_convexHull, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, nhdsKer_mono, PrimeSpectrum.localization_comap_range, latticeClosure_isClosed, IsLocalization.orderIsoOfPrime_apply_coe, MeasurableSpace.disjoint_countablePartition, CategoryTheory.MorphismProperty.universally_mono, CategoryTheory.MorphismProperty.presheaf_monomorphisms_le_monomorphisms, CategoryTheory.MorphismProperty.pushouts_le_iff, VitaliFamily.FineSubfamilyOn.covering_disjoint, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, MeasurableSet.exists_isOpen_symmDiff_lt, CategoryTheory.MorphismProperty.isStableUnderBaseChange_iff_pullbacks_le, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, absConvexHull_eq_empty, inf_compl_le_bot, Matroid.IsBasis'.contract_dep_iff, Matroid.delete_indep_iff, Submodule.sup_set_smul, Descriptive.Tree.mem_pullSub_short, MeasureTheory.IsSetRing.finsetSup_mem, MonotoneOn.Ioi, FirstOrder.Language.Substructure.cg_iff_empty_or_exists_nat_generating_family, Pairwise.exists_mem_filter_of_disjoint, Set.disjoint_left_ordSeparatingSet, fixedPoints_antitone, MeasureTheory.IsSetSemiring.exists_finpartition_diff, Set.abs_indicator_symmDiff, isLUB_supClosure, BooleanSubalgebra.iSup_mem, Matroid.Indep.disjoint_loops, Set.Iio_disjoint_Ioi_of_le, Finset.pairwiseDisjoint_pair_insert, gc_lowerClosure_coe, CompleteLatticeHom.setPreimage_comp, Finsupp.disjoint_supported_supported_iff, Set.instIsAtomistic, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, isClosed_closedAbsConvexHull, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Dβ‚„_W, MeasureTheory.MeasuredSets.edist_def, Sublattice.setLike_mem_coe, supClosure_prod, AffineIndependent.convexHull_inter, Set.sUnion_powerset_gc, MeasureTheory.measure_symmDiff_eq_zero_iff, finsetSup'_mem_supClosure, Urysohns.CU.disjoint_C_support_lim, Language.kstar_eq_iSup_pow, AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHom, CategoryTheory.MorphismProperty.pullbacks_le, IsUpperSet.disjoint_lowerClosure_right, infClosure_empty, Order.Ideal.PrimePair.disjoint, Disjoint.exists_mem_filter_basis, convex_closedConvexHull, IsRetrocompact.finsetInf, closure_subset_closedAbsConvexHull, IsLocalization.map_algebraMap_ne_top_iff_disjoint, AlgebraicGeometry.Scheme.codisjoint_zeroLocus, Descriptive.Tree.drop_coe, FirstOrder.Language.Hom.eqOn_closure, CategoryTheory.ConcreteCategory.injective_le_monomorphisms, SimpleGraph.deleteEdges_eq_self, HasCardinalLT.Set.isFiltered_of_aleph0_le, Submodule.coe_scott_continuous, Seminorm.ball_finset_sup', Matroid.delete_isCircuit_iff, Set.disjoint_iUnionβ‚‚_left, Set.Finite.convexHull_eq, CategoryTheory.MorphismProperty.pushouts_monotone, Sublattice.setLike_mem_sup, supClosed_supClosure, MeasureTheory.hittingAfter_anti, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, CategoryTheory.MorphismProperty.le_colimitsOfShape_punit, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, Set.ncard_strictMono, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Dβ‚‚_W, r1_separation, CategoryTheory.MorphismProperty.retracts_monotone, isClosed_closedConvexHull, edist_indicator, OnePoint.isCompl_range_coe_infty, CategoryTheory.ConcreteCategory.surjective_le_epimorphisms, Finset.sup_id_set_eq_sUnion, CategoryTheory.MorphismProperty.IsLocalAtTarget.inf, MeasureTheory.NullMeasurableSet.symmDiff, isAddFoelner_iff, NumberField.InfinitePlace.disjoint_isReal_isComplex, PrimitiveSpectrum.gc, Antitone.Ioo, Vitali.exists_disjoint_covering_ae', Set.Finite.encard_strictMonoOn, AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero, Matroid.IsBasis'.contract_indep_iff, CategoryTheory.MorphismProperty.le_multiplicativeClosure, Dynamics.coverEntropyInfEntourage_monotone, Set.smul_set_symmDiffβ‚€, balanced_absConvexHull, convexHull_subset_affineSpan, convexHull_eq_self, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, disjoint_closedBall_ball_iff, MeasureTheory.Measure.QuasiMeasurePreserving.limsup_preimage_iterate_ae_eq, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, CompleteSublattice.notMem_bot, supClosure_univ, AlgebraicGeometry.ValuativeCriterion.eq, MeasureTheory.dist_indicatorConstLp_eq_norm, lowerClosure_mono, balancedHull_convexHull_subseteq_absConvexHull, PiNat.exists_disjoint_cylinder, t2_separation, Algebra.gc, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, Filter.Realizer.tendsto_iff, CategoryTheory.MorphismProperty.transfiniteCompositions_monotone, Set.Ioc_disjoint_Ioi_same, latticeClosure_min, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, convexHull_range_eq_exists_affineCombination, convexIndependent_iff_notMem_convexHull_diff, Topology.RelCWComplex.disjoint_base_iUnion_openCell, AddAction.IsBlock.vadd_eq_or_disjoint, FirstOrder.Language.Substructure.lift_card_closure_le, FirstOrder.Language.Substructure.closure_eq, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_W, CategoryTheory.MorphismProperty.transfiniteCompositions_le_llp_rlp, AlgebraicGeometry.descendsAlong_universallyOpen_surjective_inf_flat_inf_quasicompact, FirstOrder.Language.Substructure.mem_closure_iff_of_isRelational, Descriptive.Tree.mem_pullSub_append, FirstOrder.Language.Substructure.closure_mono, IsUltrametricDist.closedBall_eq_or_disjoint, Concept.disjoint_extent_intent, Dynamics.dynEntourage_monotone, monotone_closure, FirstOrder.Language.Substructure.closure_univ, Filter.monotone_principal, LowerAdjoint.closure_union_closure_left, AlgebraicGeometry.sourceLocalClosure.le, FirstOrder.Language.Substructure.closure_image, AbsConvex.absConvexHull_eq, Antitone.pairwise_disjoint_on_Ico_succ, closedConvexHull_isClosed, edist_mulIndicator, Filter.mem_liminf_iff_eventually_mem, AlgebraicGeometry.descendsAlong_universallyInjective_surjective_inf_flat_inf_quasicompact, supClosure_min, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Metric.closedBall_disjoint_closedBall, Matroid.setOf_dep_eq, closedAbsConvexHull_closure_eq_closedAbsConvexHull, CategoryTheory.MorphismProperty.multiplicativeClosure_le_iff, CategoryTheory.MorphismProperty.le_transfiniteCompositions, AlgebraicGeometry.Spec.map_app, upperClosure_anti, t2Space_iff, TopologicalSpace.Opens.mk_inf_mk, CategoryTheory.MorphismProperty.toSet_iSup, Complex.rectangle_eq_convexHull, LowerAdjoint.closure_iUnion_closure, FirstOrder.Language.Substructure.cg_closure_singleton, convexHull_subset_closedConvexHull, CategoryTheory.Limits.ColimitPresentation.self_ΞΉ, CategoryTheory.MorphismProperty.transfiniteCompositions_le_iff, FirstOrder.Language.Structure.fg_iff, FirstOrder.Language.Substructure.cg_closure, Monotone.pairwise_disjoint_on_Ico_succ, Dynamics.coverMincard_monotone_subset, Finset.centerMass_mem_convexHull_of_nonpos
toHImp πŸ“–CompOp
1 mathmath: himp_eq
toSDiff πŸ“–CompOp
1 mathmath: sdiff_eq

Theorems

NameKindAssumesProvesValidatesDepends On
himp_eq πŸ“–mathematicalβ€”HImp.himp
toHImp
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
Compl.compl
toCompl
β€”β€”
inf_compl_le_bot πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
SemilatticeInf.toMin
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
Compl.compl
toCompl
Bot.bot
OrderBot.toBot
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
β€”β€”
le_sup_inf πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
SemilatticeInf.toMin
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
SemilatticeSup.toMax
β€”β€”
sdiff_eq πŸ“–mathematicalβ€”toSDiff
SemilatticeInf.toMin
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
Compl.compl
toCompl
β€”β€”
top_le_sup_compl πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
Top.top
OrderTop.toTop
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
SemilatticeSup.toMax
Compl.compl
toCompl
β€”β€”

CompleteDistribLattice

Definitions

NameCategoryTheorems
ofMinimalAxioms πŸ“–CompOpβ€”
toBiheytingAlgebra πŸ“–CompOpβ€”
toCoframe πŸ“–CompOp
18 mathmath: Filter.bliminf_inf_not, Prop.isCoatom_iff, Filter.inf_limsup, liminf_eq_top, CompleteAtomicBooleanAlgebra.instIsCoatomistic, Filter.bliminf_or_eq_inf, Filter.limsup_sup_filter, Filter.liminf_sup_filter, Filter.blimsup_sup_not, Filter.sup_limsup, Filter.inf_liminf, Filter.bliminf_not_inf, Filter.limsup_piecewise, Filter.blimsup_not_sup, Filter.blimsup_or_eq_sup, UpperSet.codisjoint_prod, Filter.liminf_piecewise, Filter.sup_liminf
toFrame πŸ“–CompOp
369 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Set.Finite.t2_separation, Matroid.exists_isBasis_disjoint_isBasis_of_subset, Metric.ball_disjoint_ball, Set.pairwiseDisjoint_pair_insert, Metric.disjoint_ball_infDist, Set.disjoint_ordT5Nhd, LocalizedModule.subsingleton_iff_disjoint, Finpartition.isPartition_parts, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, SimpleGraph.isBipartiteWith_neighborSet_disjoint, SeparatedNhds.disjoint, PrimeSpectrum.localization_specComap_range, disjoint_or_subset_of_isClopen, BoxIntegral.Box.disjoint_splitCenterBox, Matroid.isBase_compl_iff_maximal_disjoint_isBase, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, Disjoint.of_spanβ‚€, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, UpperSet.sdiff_eq_left, MeasureTheory.pairwise_disjoint_fundamentalInterior, SeparatedNhds.disjoint_closure_left, Set.Iio_disjoint_Ioi_of_not_lt, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, IsUltrametricDist.ball_subset_trichotomy, Matroid.IsBasis.contract_dep_iff, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, SimpleGraph.ComponentCompl.disjoint_right, LowerSet.disjoint_coe, AddAction.orbit.pairwiseDisjoint, EMetric.ball_disjoint, Topology.RelCWComplex.pairwiseDisjoint', Matroid.contract_isCocircuit_iff, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, Topology.RelCWComplex.disjoint_openCell_of_ne, IsCompact.separation_of_notMem, Finset.isWF_sup, AddAction.IsBlock.disjoint_vadd_left, OrderedFinpartition.disjoint, Set.Iio_disjoint_Ioi_iff, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, exists_dist_slope_lt_pairwiseDisjoint_hasSum, Besicovitch.exist_disjoint_covering_families, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.exists_null_pairwise_disjoint_diff, Matroid.IsBasis.contract_indep_iff, separated_by_continuous, Antitone.pairwise_disjoint_on_Ioo_pred, Perfect.small_diam_splitting, SimpleGraph.ComponentCompl.pairwise_disjoint, Set.Iic_disjoint_Ioi, Set.disjoint_pi_univ_Ioc_update_left_right, disjoint_nested_nhds_of_not_inseparable, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, exists_disjoint_vadd_of_isCompact, MulAction.IsBlock.disjoint_smul_of_ne, Disjoint.of_span, Matroid.IsMinor.exists_eq_contract_delete_disjoint, isEmbedding_sumElim, Matroid.delete_eq_self_iff, MulAction.isBlock_iff_smul_eq_or_disjoint, disjoint_interior_frontier, Matroid.contract_eq_self_iff, Finset.sup_set_eq_biUnion, AlgebraicIndependent.adjoin_iff_disjoint, MeasureTheory.IsSetSemiring.disjointOfUnion_props, Set.Ioc_disjoint_Ioc, UpperSet.codisjoint_coe, Matroid.Coindep.delete_spanning_iff, Monotone.pairwise_disjoint_on_Ioc_pred, Set.disjoint_right_ordSeparatingSet, LowerSet.sdiff_eq_left, Antitone.pairwise_disjoint_on_Ioo_succ, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Set.pairwise_disjoint_vadd_iff, Set.disjoint_iUnion_left, Set.definable_finset_sup, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Set.PairwiseDisjoint.exists_mem_filter, NonarchimedeanGroup.exists_openSubgroup_separating, Subgroup.leftCoset_cover_filter_FiniteIndex_aux, Ideal.disjoint_powers_iff_notMem, Matroid.Indep.contract_dep_iff, SimpleGraph.disjoint_edge, MeasureTheory.IsSetSemiring.mem_supClosure_iff, disjoint_nhdsSet_principal, Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, MulAction.disjoint_image_image_iff, t2_separation_nhds, limsup_eq_bot, SimpleGraph.disjoint_edgeFinset, Setoid.IsPartition.finpartition_parts, Set.disjoint_smul_set, AddAction.IsBlock.disjoint_vadd_vadd_set, Filter.disjoint_iff, Ideal.disjoint_map_primeCompl_iff_comap_le, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, not_disjoint_segment_convexHull_triple, Set.disjoint_sUnion_left, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, LowerSet.sdiff_lt_left, SimpleGraph.disjoint_edgeSet, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, Besicovitch.exist_finset_disjoint_balls_large_measure, isInducing_sumElim, Set.Ioi_disjoint_Iio_iff, Matroid.dual_indep_iff_exists', MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, AddAction.IsBlock.pairwiseDisjoint_range_vadd, Set.isAtom_singleton, Set.PairwiseDisjoint.exists_mem_filter_basis, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, MulAction.orbit.eq_or_disjoint, Topology.IsInducing.disjoint_of_sumElim_aux, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, IsLocalization.isPrime_iff_isPrime_disjoint, SubMulAction.disjoint_val_image, AddAction.IsBlock.disjoint_vadd_set_vadd, Metric.disjoint_closedEBall_of_lt_infEDist, top_sdiff, exists_nhds_disjoint_closure, TopologicalSpace.Opens.coe_finset_sup, SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph, isNowhereDense_iff_disjoint, ConvexCone.disjoint_hull_left_of_convex, EisensteinSeries.pairwise_disjoint_gammaSet, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, MulAction.IsBlock.disjoint_smul_right, BoxIntegral.unitPartition.disjoint, MulAction.IsBlock.disjoint_smul_smul_set, Set.disjoint_iUnion_right, LowerSet.disjoint_prod, exists_open_nhds_disjoint_closure, disjoint_measurableAtom_of_notMem, MeasureTheory.disjoint_cylinder_iff, NFA.disjoint_evalFrom_reverse_iff, Matroid.contract_spanning_iff, Topology.CWComplex.pairwiseDisjoint', MulAction.IsBlock.disjoint_smul_set_smul, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, disjoint_frontier_iff_isOpen, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, IsGenericPoint.disjoint_iff, AddAction.IsBlock.disjoint_vadd_right, MeasureTheory.IsSetSemiring.diff_eq_sUnion', Antitone.pairwise_disjoint_on_Ioc_succ, exists_seq_infinite_isOpen_pairwise_disjoint, Set.disjoint_iUnionβ‚‚_right, IsUltrametricDist.ball_eq_or_disjoint, Filter.HasBasis.disjoint_iff, AddAction.isBlock_iff_vadd_eq_or_disjoint, Set.exists_union_disjoint_cardinal_eq_of_even, SimpleGraph.pairwise_disjoint_supp_connectedComponent, IsRetrocompact.finsetSup, Set.Ioi_disjoint_Iio_of_le, BoxIntegral.Prepartition.pairwiseDisjoint, Metric.ball_disjoint_closedBall, Matroid.IsCircuit.disjoint_coloops, UpperSet.lt_sdiff_left, Subgroup.IsComplement.pairwiseDisjoint_smul, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, Finset.intervalGapsWithin_pairwiseDisjoint_Ioc, SimpleGraph.EdgeLabeling.pairwiseDisjoint_univ_labelGraph, MulAction.IsBlock.smul_eq_smul_or_disjoint, ConvexCone.disjoint_coe, TopologicalSpace.Compacts.coe_finset_sup, Filter.disjoint_principal_principal, connectedComponent_disjoint, AddAction.IsBlock.disjoint_vadd_of_ne, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, Topology.RelCWComplex.disjoint_interior_base_closedCell, Set.Iic_disjoint_Ioc, SimpleGraph.IsBipartiteWith.disjoint, SeparatedNhds.disjoint_closure_right, Set.Ioc_disjoint_Ioi, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, Set.Iic_disjoint_Ici, Set.isAtom_iff, disjoint_ball_closedBall_iff, SimpleGraph.fromEdgeSet_disjoint, SimpleGraph.isBipartiteWith_neighborSet_disjoint', Interval.disjoint_coe, Set.Ioi_disjoint_Iio_of_not_lt, VitaliFamily.covering, Finset.isPWO_sup, Finset.partiallyWellOrderedOn_sup, exists_open_convex_of_notMem, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, AddAction.isBlock_iff_disjoint_vadd_of_ne, Vitali.exists_disjoint_subfamily_covering_enlargement, Matroid.coindep_contract_iff, t2_separation_compact_nhds, IndexedPartition.disjoint, Set.Ico_disjoint_Ico, AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, Topology.RelCWComplex.disjointBase, Monotone.pairwise_disjoint_on_Ico_pred, Metric.disjoint_closedBall_of_lt_infDist, Metric.frontier_thickening_disjoint, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, TopologicalSpace.Closeds.coe_finset_sup, Vitali.exists_disjoint_covering_ae, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, Monotone.pairwise_disjoint_on_Ioo_succ, Metric.AreSeparated.disjoint, Set.Ioi_disjoint_Iio_same, BoxIntegral.Box.disjoint_coe, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, IsLowerSet.disjoint_upperClosure_left, MulAction.isBlock_iff_disjoint_smul_of_ne, Besicovitch.exists_disjoint_closedBall_covering_ae, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, IsLocalization.orderIsoOfPrime_symm_apply_coe, Matroid.dual_indep_iff_exists, FreeGroup.startsWith.disjoint_iff_ne, Set.disjoint_vadd_set, disjoint_closedBall_closedBall_iff, Set.disjoint_sUnion_right, T2Space.t2, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, Metric.closedBall_disjoint_ball, IsLocalization.disjoint_comap_iff, sdiff_le_iff, AddAction.orbit.eq_or_disjoint, t2Space_iff_nhds, IsLowerSet.disjoint_upperClosure_right, Monotone.pairwise_disjoint_on_Ioo_pred, Set.ncard_union_eq_iff, Monotone.pairwise_disjoint_on_Ioc_succ, Matroid.delete_dep_iff, MeasureTheory.exists_subordinate_pairwise_disjoint, disjoint_principal_nhdsSet, Matroid.contract_spanning_iff', Set.exists_union_disjoint_cardinal_eq_iff, Matroid.Indep.contract_indep_iff, Metric.frontier_cthickening_disjoint, MulAction.orbit.pairwiseDisjoint, Set.Iio_disjoint_Ioi_same, Topology.RelCWComplex.disjoint_skeleton_openCell, RootedTree.subtrees_disjoint, Metric.eball_disjoint, MeasureTheory.AEDisjoint.exists_disjoint_diff, disjoint_ball_ball_iff, Topology.RelCWComplex.disjointBase', TopologicalSpace.Closeds.isAtom_coe, SimpleGraph.disjoint_left, disjoint_memPartition, Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one, NFA.disjoint_stepSet_reverse, PiNat.disjoint_cylinder_of_longestPrefix_lt, IsUpperSet.disjoint_lowerClosure_left, IsUltrametricDist.closedBall_subset_trichotomy, Set.disjoint_vadd_set_left, SimpleGraph.disjoint_image_val_universalVerts, ConvexCone.disjoint_hull_right_of_convex, Set.Ioc_disjoint_Ioc_of_le, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, EMetric.disjoint_closedBall_of_lt_infEdist, Set.pairwiseDisjoint_vadd_iff, Ideal.disjoint_primeCompl_of_liesOver, Composition.disjoint_range, MulAction.IsBlock.pairwiseDisjoint_range_smul, MulAction.isBlock_iff_pairwiseDisjoint_range_smul, isSeparatedMap_iff_nhds, Set.exists_union_disjoint_ncard_eq_of_even, Set.Ici_disjoint_Iic, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, Matroid.delete_isBasis_iff, SimpleGraph.Finsubgraph.coe_himp, Set.pairwiseDisjoint_iff, SimpleGraph.disjoint_fromEdgeSet, TopologicalSpace.Opens.coe_disjoint, CompleteAtomicBooleanAlgebra.instIsAtomistic, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, PMF.toOuterMeasure_apply_eq_zero_iff, AddAction.disjoint_image_image_iff, DoubleCoset.disjoint_out, Finset.wellFoundedOn_sup, AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux, Set.disjoint_vadd_set_right, Set.Iio_disjoint_Ici, Topology.RelCWComplex.disjoint_skeletonLT_openCell, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, Set.pairwise_disjoint_smul_iff, Setoid.IsPartition.pairwiseDisjoint, ModelWithCorners.disjoint_interior_boundary, Set.Ico_disjoint_Ico_same, SubAddAction.disjoint_val_image, BoxIntegral.Prepartition.disjoint_coe_of_mem, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, Antitone.pairwise_disjoint_on_Ico_pred, Matroid.Indep.contract_isBase_iff, Pairwise.exists_mem_filter_basis_of_disjoint, Set.pairwiseDisjoint_smul_iff, MulAction.IsBlock.smul_eq_or_disjoint, Set.Ioo_disjoint_Ioo, Perfect.splitting, Metric.sphere_disjoint_ball, RealRMK.range_cut_partition, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, Ideal.exists_disjoint_powers_of_span_eq_top, MeasureTheory.pairwise_disjoint_addFundamentalInterior, Topology.RelCWComplex.pairwiseDisjoint, Matroid.Coindep.delete_isBase_iff, Set.disjoint_smul_set_left, disjoint_nhdsWithin_of_mem_discrete, Filter.NeBot.not_disjoint, Set.disjoint_smul_set_right, Matroid.dualIndepMatroid_Indep, PrimeSpectrum.localization_comap_range, IsLocalization.orderIsoOfPrime_apply_coe, MeasurableSpace.disjoint_countablePartition, VitaliFamily.FineSubfamilyOn.covering_disjoint, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, Matroid.IsBasis'.contract_dep_iff, Matroid.delete_indep_iff, MeasureTheory.IsSetRing.finsetSup_mem, Pairwise.exists_mem_filter_of_disjoint, Set.disjoint_left_ordSeparatingSet, MeasureTheory.IsSetSemiring.exists_finpartition_diff, Matroid.Indep.disjoint_loops, Set.Iio_disjoint_Ioi_of_le, Finset.pairwiseDisjoint_pair_insert, Finsupp.disjoint_supported_supported_iff, Set.instIsAtomistic, SimpleGraph.Finsubgraph.coe_compl, Urysohns.CU.disjoint_C_support_lim, IsUpperSet.disjoint_lowerClosure_right, Order.Ideal.PrimePair.disjoint, Disjoint.exists_mem_filter_basis, IsLocalization.map_algebraMap_ne_top_iff_disjoint, SimpleGraph.deleteEdges_eq_self, Matroid.delete_isCircuit_iff, Set.disjoint_iUnionβ‚‚_left, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, r1_separation, Finset.sup_id_set_eq_sUnion, NumberField.InfinitePlace.disjoint_isReal_isComplex, Vitali.exists_disjoint_covering_ae', AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero, Matroid.IsBasis'.contract_indep_iff, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, disjoint_closedBall_ball_iff, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, PiNat.exists_disjoint_cylinder, t2_separation, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, Set.Ioc_disjoint_Ioi_same, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, Topology.RelCWComplex.disjoint_base_iUnion_openCell, AddAction.IsBlock.vadd_eq_or_disjoint, IsUltrametricDist.closedBall_eq_or_disjoint, Concept.disjoint_extent_intent, Antitone.pairwise_disjoint_on_Ico_succ, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Metric.closedBall_disjoint_closedBall, t2Space_iff, Monotone.pairwise_disjoint_on_Ico_succ
toHNot πŸ“–CompOp
1 mathmath: top_sdiff
toSDiff πŸ“–CompOp
2 mathmath: top_sdiff, sdiff_le_iff

Theorems

NameKindAssumesProvesValidatesDepends On
sdiff_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
toFrame
toSDiff
SemilatticeSup.toMax
β€”β€”
top_sdiff πŸ“–mathematicalβ€”toSDiff
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
toFrame
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
HNot.hnot
toHNot
β€”β€”

CompleteDistribLattice.MinimalAxioms

Definitions

NameCategoryTheorems
of πŸ“–CompOpβ€”
toCoframe πŸ“–CompOpβ€”
toCoframeMinimalAxioms πŸ“–CompOpβ€”
toCompleteLattice πŸ“–CompOp
2 mathmath: iInf_sup_le_sup_sInf, inf_sSup_le_iSup_inf
toFrame πŸ“–CompOpβ€”
toFrameMinimalAxioms πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_sup_le_sup_sInf πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
iInf
CompleteLattice.toInfSet
Set
Set.instMembership
SemilatticeSup.toMax
InfSet.sInf
β€”β€”
inf_sSup_le_iSup_inf πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
SemilatticeInf.toMin
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
SupSet.sSup
CompleteLattice.toSupSet
iSup
Set
Set.instMembership
β€”β€”

CompleteLinearOrder

Definitions

NameCategoryTheorems
toCompletelyDistribLattice πŸ“–CompOp
240 mathmath: Matroid.eRk_lt_top_iff, Dynamics.netMaxcard_monotone_subset, SimpleGraph.vertexCoverNum_le_card_sub_one, Ideal.height_le_spanFinrank, ringKrullDim_succ_le_ringKrullDim_polynomial, Matroid.eRk_lt_encard_iff_dep, PowerSeries.le_order_subst_left', CategoryTheory.Retract.injectiveDimension_le, Ideal.height_le_iff_exists_minimalPrimes, SimpleGraph.le_chromaticNumber_iff_colorable, SimpleGraph.le_chromaticNumber_iff_coloring, CategoryTheory.injectiveDimension_le_iff, SimpleGraph.chromaticNumber_pos, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, Matroid.eRk_singleton_le, Matroid.eRk_mono, Ring.krullDimLE_iff, scottContinuous_inf_right, Ideal.height_lt_top, Dynamics.netMaxcard_le_coverMincard, Dynamics.coverMincard_finite_of_isCompact_invariant, Matroid.eRank_le_encard_add_eRk_compl, SimpleGraph.vertexCoverNum_le_iff, Dynamics.coverMincard_image_le, Set.chainHeight_le_encard, Matroid.le_eRk_iff, Ideal.primeHeight_mono, AddMonoid.minOrder_le_addOrderOf, SimpleGraph.two_le_chromaticNumber_of_adj, SimpleGraph.card_le_chromaticNumber_iff_forall_surjective, SimpleGraph.three_le_egirth, Dynamics.IsDynNetIn.card_le_netMaxcard, Ideal.primeHeight_lt_top, SimpleGraph.chromaticNumber_le_sum_right, Metric.coveringNumber_two_mul_le_externalCoveringNumber, lowerSemicontinuous_iff_le_liminf, Ideal.height_strict_mono_of_is_prime, SimpleGraph.chromaticNumber_mono_of_embedding, le_minSmoothness, ringKrullDim_succ_le_ringKrullDim_powerseries, Dynamics.one_le_coverMincard_iff, Dynamics.coverMincard_monotone_time, Matroid.eRk_lt_encard_iff_dep_of_finite, IsContDiffImplicitAt.one_le, ScottContinuous.infβ‚‚, SimpleGraph.chromaticNumber_le_of_forall_imp, PowerSeries.le_order_subst_right', ringKrullDim_nonneg_of_nontrivial, Submodule.length_lt, liminf_eq_top, Module.length_pos_iff, SimpleGraph.vertexCoverNum_le_vertexCoverNum_of_injective, Monoid.minOrder_le_natCard, AddMonoid.le_minOrder, Module.supportDim_le_of_injective, Metric.externalCoveringNumber_le_one_of_ediam_le, Matroid.eRk_le_eRk_add_eRk_diff, Dynamics.coverMincard_closure_le, Submodule.height_strictMono, Matroid.eRk_compl_insert_union_add_eRk_compl_insert_inter_le, Metric.externalCoveringNumber_anti, Matroid.eRk_insert_le_add_one, Set.chainHeight_mono, Ideal.height_le_height_add_of_liesOver, limsup_eq_bot, MvPowerSeries.le_order_subst, CategoryTheory.injectiveDimension_ge_iff, Ideal.height_le_height_add_one_of_mem, Matroid.spanning_iff_eRk_le', Metric.packingNumber_two_mul_le_externalCoveringNumber, Dynamics.coverMincard_finite_of_isCompact_uniformContinuous, Ideal.height_le_card_of_mem_minimalPrimes_span, SimpleGraph.chromaticNumber_le_card, ringKrullDim_quotient_le, Matroid.eRk_inter_add_eRk_union_le, ringKrullDim_succ_le_of_surjective, SimpleGraph.vertexCoverNum_mono, Ideal.primeHeight_le_ringKrullDim, Dynamics.IsDynCoverOf.coverMincard_le_card, Metric.externalCoveringNumber_mono_set, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, Metric.IsCover.externalCoveringNumber_le_encard, CategoryTheory.projectiveDimension_lt_iff, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, SimpleGraph.chromaticNumber_le_iff_colorable, Ideal.primeHeight_strict_mono, upperSemicontinuousWithinAt_iff_limsup_le, ringKrullDim_le_iff_height_le, upperSemicontinuousOn_iff_limsup_le, natCast_le_analyticOrderAt, Dynamics.coverMincard_antitone, Dynamics.netMaxcard_antitone, SimpleGraph.vertexCoverNum_le_encard_edgeSet, Matroid.IsRkFinite.eRk_lt_top, Matroid.Indep.encard_le_eRk_of_subset, Matroid.eRank_le_encard_ground, SimpleGraph.vertexCoverNum_lt_card, Matroid.eRank_lt_top_iff, Matroid.eRk_insert_inter_add_eRk_insert_union_le, Ideal.height_mono, Submodule.spanFinrank_span_le_encard, ringKrullDim_le_ringKrullDim_quotient_add_card, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, Matroid.Indep.encard_le_eRank, Metric.IsCover.coveringNumber_le_encard, Ideal.height_le_ringKrullDim_quotient_add_one, MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet, Ideal.height_le_iff, SimpleGraph.chromaticNumber_le_two_iff_isBipartite, SimpleGraph.two_le_chromaticNumber_iff_ne_bot, MvPowerSeries.le_weightedOrder_subst, Dynamics.coverMincard_union_le, MeasureTheory.stoppedProcess_eq, Module.length_le_of_surjective, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, Matroid.eRk_le_iff, SimpleGraph.le_chromaticNumber_iff_forall_surjective, SimpleGraph.Colorable.chromaticNumber_le, SimpleGraph.IsVertexCover.vertexCoverNum_le, ENat.LEInfty.out, Matroid.eRk_union_le_eRk_add_eRk, Matroid.eRk_le_eRk_inter_add_eRk_diff, EMetric.pair_reduction, Metric.coveringNumber_pos_iff, Ideal.height_le_ringKrullDim_quotient_add_encard, Ideal.primeHeight_add_one_le_of_lt, Set.one_le_chainHeight_iff, tangentBundleCore.isContMDiff, SimpleGraph.cliqueNum_le_chromaticNumber, TangentBundle.contMDiffVectorBundle, upperSemicontinuousAt_iff_limsup_le, Dynamics.coverMincard_le_pow, Ideal.height_le_iff_covBy, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, Dynamics.coverMincard_mul_le_pow, le_analyticOrderAt_sub, le_analyticOrderAt_add, Dynamics.netMaxcard_monotone_time, AddMonoid.le_minOrder_iff_forall_addSubgroup, ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial, upperSemicontinuous_iff_limsup_le, Module.length_pos, scottContinuous_inf_left, isSaddlePointOn_iff', Metric.coveringNumber_subset_le, ringKrullDim_le_iff_isMaximal_height_le, ringKrullDim_le_ringKrullDim_add_card, iSupβ‚‚_iInfβ‚‚_le_iInfβ‚‚_iSupβ‚‚, CategoryTheory.projectiveDimension_le_iff, SimpleGraph.chromaticNumber_le_one_of_subsingleton, lowerSemicontinuousWithinAt_iff_le_liminf, Metric.coveringNumber_le_packingNumber, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, Monoid.le_minOrder_iff_forall_subgroup, Module.supportDim_le_ringKrullDim, Module.length_le_of_injective, Module.supportDim_le_supportDim_quotSMulTop_succ, CategoryTheory.projectiveDimension_ge_iff, Matroid.eRk_le_eRank, SimpleGraph.le_chromaticNumber_of_pairwise_adj, PowerSeries.le_order_subst, ringKrullDim_lt_top, CategoryTheory.injectiveDimension_lt_iff, lowerSemicontinuousAt_iff_le_liminf, SimpleGraph.chromaticNumber_mono, Polynomial.ringKrullDim_le, Matroid.eRk_lt_encard_of_dep_of_finite, Ideal.map_height_le_one_of_mem_minimalPrimes, Dynamics.netMaxcard_finite_iff, MeasureTheory.stoppedProcess_eq', Matroid.eRk_union_le_encard_add_eRk, Matroid.eRk_union_le_eRk_add_encard, cauchy_davenport_minOrder_add, Dynamics.coverMincard_le_netMaxcard, SimpleGraph.egirth_le_length, SimpleGraph.chromaticNumber_le_sum_left, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, SimpleGraph.egirth_anti, SimpleGraph.IsClique.card_le_chromaticNumber, isSaddlePointOn_iff, Set.encard_le_chainHeight_of_isChain, Ideal.finiteHeight_iff_lt, height_le_ringKrullDim_quotient_add_spanFinrank, Ideal.height_le_height_add_encard_of_subset, Matroid.Dep.eRk_lt_encard, Metric.externalCoveringNumber_le_encard_self, ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomial, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing, PowerSeries.le_order_subst_right, Metric.IsSeparated.encard_le_packingNumber, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, Dynamics.coverMincard_finite_iff, Matroid.eRk_compl_union_add_eRk_compl_inter_le, ringKrullDim_le_ringKrullDim_add_spanFinrank, Metric.externalCoveringNumber_pos_iff, Matroid.eRk_le_one_iff, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes, Ideal.height_le_height_add_spanFinrank_of_le, Metric.packingNumber_pos_iff, Metric.externalCoveringNumber_le_coveringNumber, SimpleGraph.le_egirth, Metric.encard_le_of_isSeparated, Matroid.eRk_le_encard, Monoid.le_minOrder, Ideal.height_le_spanRank_toENat, cauchy_davenport_minOrder_mul, CategoryTheory.Retract.projectiveDimension_le, Matroid.one_le_eRank, Ideal.height_le_card_of_mem_minimalPrimes_span_finset, MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zero, Metric.coveringNumber_le_encard_self, Ideal.height_le_ringKrullDim_of_ne_top, SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNum, PairReduction.iSup_edist_pairSet, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, ringKrullDim_le_of_surjective, SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loop, Metric.packingNumber_le_encard_self, minSmoothness_monotone, Submodule.height_lt_top, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, Module.supportDim_le_of_surjective, SimpleGraph.chromaticNumber_mono_of_hom, Matroid.eRk_submod, Monoid.minOrder_le_orderOf, Dynamics.one_le_netMaxcard_iff, Metric.coveringNumber_anti, lowerSemicontinuousOn_iff_le_liminf, AddMonoid.minOrder_le_natCard, PowerSeries.le_weightedOrder_subst, Dynamics.le_coverMincard_image, Matroid.spanning_iff_eRk_le, natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zero, Polynomial.emultiplicity_le_one_of_separable, PowerSeries.le_order_subst_left, ringKrullDim_le_ringKrullDim_quotient_add_encard, Metric.coveringNumber_le_one_of_ediam_le, Dynamics.coverMincard_monotone_subset

CompletelyDistribLattice

Definitions

NameCategoryTheorems
ofMinimalAxioms πŸ“–CompOpβ€”
toBiheytingAlgebra πŸ“–CompOp
2 mathmath: SimpleGraph.Finsubgraph.coe_hnot, SimpleGraph.Finsubgraph.coe_sdiff
toCompl πŸ“–CompOp
1 mathmath: himp_bot
toCompleteDistribLattice πŸ“–CompOp
8 mathmath: LowerSet.disjoint_coe, UpperSet.codisjoint_coe, liminf_eq_top, limsup_eq_bot, LowerSet.disjoint_prod, SimpleGraph.Finsubgraph.coe_himp, UpperSet.codisjoint_prod, SimpleGraph.Finsubgraph.coe_compl
toCompleteLattice πŸ“–CompOp
245 mathmath: Matroid.eRk_lt_top_iff, Dynamics.netMaxcard_monotone_subset, SimpleGraph.vertexCoverNum_le_card_sub_one, Ideal.height_le_spanFinrank, ringKrullDim_succ_le_ringKrullDim_polynomial, Matroid.eRk_lt_encard_iff_dep, PowerSeries.le_order_subst_left', CategoryTheory.Retract.injectiveDimension_le, Ideal.height_le_iff_exists_minimalPrimes, SimpleGraph.le_chromaticNumber_iff_colorable, SimpleGraph.le_chromaticNumber_iff_coloring, CategoryTheory.injectiveDimension_le_iff, SimpleGraph.chromaticNumber_pos, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, Matroid.eRk_singleton_le, Matroid.eRk_mono, Ring.krullDimLE_iff, scottContinuous_inf_right, Ideal.height_lt_top, Dynamics.netMaxcard_le_coverMincard, Dynamics.coverMincard_finite_of_isCompact_invariant, Matroid.eRank_le_encard_add_eRk_compl, SimpleGraph.vertexCoverNum_le_iff, Dynamics.coverMincard_image_le, Set.chainHeight_le_encard, Matroid.le_eRk_iff, Ideal.primeHeight_mono, AddMonoid.minOrder_le_addOrderOf, SimpleGraph.two_le_chromaticNumber_of_adj, SimpleGraph.card_le_chromaticNumber_iff_forall_surjective, SimpleGraph.three_le_egirth, Dynamics.IsDynNetIn.card_le_netMaxcard, Ideal.primeHeight_lt_top, SimpleGraph.chromaticNumber_le_sum_right, Metric.coveringNumber_two_mul_le_externalCoveringNumber, lowerSemicontinuous_iff_le_liminf, Ideal.height_strict_mono_of_is_prime, SimpleGraph.chromaticNumber_mono_of_embedding, le_minSmoothness, ringKrullDim_succ_le_ringKrullDim_powerseries, Dynamics.one_le_coverMincard_iff, Dynamics.coverMincard_monotone_time, Matroid.eRk_lt_encard_iff_dep_of_finite, IsContDiffImplicitAt.one_le, ScottContinuous.infβ‚‚, sdiff_le_iff, SimpleGraph.chromaticNumber_le_of_forall_imp, PowerSeries.le_order_subst_right', ringKrullDim_nonneg_of_nontrivial, Submodule.length_lt, Module.length_pos_iff, SimpleGraph.vertexCoverNum_le_vertexCoverNum_of_injective, Monoid.minOrder_le_natCard, AddMonoid.le_minOrder, Module.supportDim_le_of_injective, Metric.externalCoveringNumber_le_one_of_ediam_le, Matroid.eRk_le_eRk_add_eRk_diff, Dynamics.coverMincard_closure_le, Submodule.height_strictMono, Matroid.eRk_compl_insert_union_add_eRk_compl_insert_inter_le, Metric.externalCoveringNumber_anti, Matroid.eRk_insert_le_add_one, Set.chainHeight_mono, Ideal.height_le_height_add_of_liesOver, MvPowerSeries.le_order_subst, CategoryTheory.injectiveDimension_ge_iff, Ideal.height_le_height_add_one_of_mem, Matroid.spanning_iff_eRk_le', Metric.packingNumber_two_mul_le_externalCoveringNumber, Dynamics.coverMincard_finite_of_isCompact_uniformContinuous, Ideal.height_le_card_of_mem_minimalPrimes_span, SimpleGraph.chromaticNumber_le_card, ringKrullDim_quotient_le, Matroid.eRk_inter_add_eRk_union_le, ringKrullDim_succ_le_of_surjective, SimpleGraph.vertexCoverNum_mono, Ideal.primeHeight_le_ringKrullDim, Dynamics.IsDynCoverOf.coverMincard_le_card, iInf_iSup_eq, Metric.externalCoveringNumber_mono_set, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, Metric.IsCover.externalCoveringNumber_le_encard, iInf_iSup_eq, CategoryTheory.projectiveDimension_lt_iff, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, SimpleGraph.chromaticNumber_le_iff_colorable, Ideal.primeHeight_strict_mono, upperSemicontinuousWithinAt_iff_limsup_le, ringKrullDim_le_iff_height_le, upperSemicontinuousOn_iff_limsup_le, natCast_le_analyticOrderAt, Dynamics.coverMincard_antitone, Dynamics.netMaxcard_antitone, SimpleGraph.vertexCoverNum_le_encard_edgeSet, Matroid.IsRkFinite.eRk_lt_top, Matroid.Indep.encard_le_eRk_of_subset, Matroid.eRank_le_encard_ground, SimpleGraph.vertexCoverNum_lt_card, Matroid.eRank_lt_top_iff, Matroid.eRk_insert_inter_add_eRk_insert_union_le, Ideal.height_mono, Submodule.spanFinrank_span_le_encard, ringKrullDim_le_ringKrullDim_quotient_add_card, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, Matroid.Indep.encard_le_eRank, Metric.IsCover.coveringNumber_le_encard, Ideal.height_le_ringKrullDim_quotient_add_one, MeasureTheory.tendsto_measure_norm_gt_of_isTightMeasureSet, Ideal.height_le_iff, SimpleGraph.chromaticNumber_le_two_iff_isBipartite, SimpleGraph.two_le_chromaticNumber_iff_ne_bot, MvPowerSeries.le_weightedOrder_subst, Dynamics.coverMincard_union_le, MeasureTheory.stoppedProcess_eq, Module.length_le_of_surjective, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, Matroid.eRk_le_iff, SimpleGraph.le_chromaticNumber_iff_forall_surjective, SimpleGraph.Colorable.chromaticNumber_le, SimpleGraph.IsVertexCover.vertexCoverNum_le, ENat.LEInfty.out, Matroid.eRk_union_le_eRk_add_eRk, Matroid.eRk_le_eRk_inter_add_eRk_diff, EMetric.pair_reduction, Metric.coveringNumber_pos_iff, Ideal.height_le_ringKrullDim_quotient_add_encard, Ideal.primeHeight_add_one_le_of_lt, Set.one_le_chainHeight_iff, tangentBundleCore.isContMDiff, SimpleGraph.cliqueNum_le_chromaticNumber, le_himp_iff, TangentBundle.contMDiffVectorBundle, upperSemicontinuousAt_iff_limsup_le, Dynamics.coverMincard_le_pow, Ideal.height_le_iff_covBy, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, Dynamics.coverMincard_mul_le_pow, le_analyticOrderAt_sub, le_analyticOrderAt_add, top_sdiff, Dynamics.netMaxcard_monotone_time, AddMonoid.le_minOrder_iff_forall_addSubgroup, ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial, upperSemicontinuous_iff_limsup_le, Module.length_pos, scottContinuous_inf_left, isSaddlePointOn_iff', Metric.coveringNumber_subset_le, ringKrullDim_le_iff_isMaximal_height_le, ringKrullDim_le_ringKrullDim_add_card, iSupβ‚‚_iInfβ‚‚_le_iInfβ‚‚_iSupβ‚‚, CategoryTheory.projectiveDimension_le_iff, SimpleGraph.chromaticNumber_le_one_of_subsingleton, lowerSemicontinuousWithinAt_iff_le_liminf, Metric.coveringNumber_le_packingNumber, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, Monoid.le_minOrder_iff_forall_subgroup, Module.supportDim_le_ringKrullDim, Module.length_le_of_injective, Module.supportDim_le_supportDim_quotSMulTop_succ, CategoryTheory.projectiveDimension_ge_iff, Matroid.eRk_le_eRank, SimpleGraph.le_chromaticNumber_of_pairwise_adj, PowerSeries.le_order_subst, ringKrullDim_lt_top, CategoryTheory.injectiveDimension_lt_iff, lowerSemicontinuousAt_iff_le_liminf, SimpleGraph.chromaticNumber_mono, Polynomial.ringKrullDim_le, Matroid.eRk_lt_encard_of_dep_of_finite, Ideal.map_height_le_one_of_mem_minimalPrimes, Dynamics.netMaxcard_finite_iff, MeasureTheory.stoppedProcess_eq', Matroid.eRk_union_le_encard_add_eRk, Matroid.eRk_union_le_eRk_add_encard, cauchy_davenport_minOrder_add, Dynamics.coverMincard_le_netMaxcard, SimpleGraph.egirth_le_length, SimpleGraph.chromaticNumber_le_sum_left, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, SimpleGraph.egirth_anti, SimpleGraph.IsClique.card_le_chromaticNumber, isSaddlePointOn_iff, Set.encard_le_chainHeight_of_isChain, Ideal.finiteHeight_iff_lt, height_le_ringKrullDim_quotient_add_spanFinrank, Ideal.height_le_height_add_encard_of_subset, Matroid.Dep.eRk_lt_encard, Metric.externalCoveringNumber_le_encard_self, himp_bot, ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomial, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing, PowerSeries.le_order_subst_right, Metric.IsSeparated.encard_le_packingNumber, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, Dynamics.coverMincard_finite_iff, Matroid.eRk_compl_union_add_eRk_compl_inter_le, ringKrullDim_le_ringKrullDim_add_spanFinrank, Metric.externalCoveringNumber_pos_iff, Matroid.eRk_le_one_iff, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes, Ideal.height_le_height_add_spanFinrank_of_le, Metric.packingNumber_pos_iff, Metric.externalCoveringNumber_le_coveringNumber, SimpleGraph.le_egirth, Metric.encard_le_of_isSeparated, Matroid.eRk_le_encard, Monoid.le_minOrder, Ideal.height_le_spanRank_toENat, cauchy_davenport_minOrder_mul, CategoryTheory.Retract.projectiveDimension_le, Matroid.one_le_eRank, Ideal.height_le_card_of_mem_minimalPrimes_span_finset, MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zero, Metric.coveringNumber_le_encard_self, Ideal.height_le_ringKrullDim_of_ne_top, SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNum, PairReduction.iSup_edist_pairSet, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, ringKrullDim_le_of_surjective, SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loop, Metric.packingNumber_le_encard_self, minSmoothness_monotone, Submodule.height_lt_top, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, Module.supportDim_le_of_surjective, SimpleGraph.chromaticNumber_mono_of_hom, Matroid.eRk_submod, Monoid.minOrder_le_orderOf, Dynamics.one_le_netMaxcard_iff, Metric.coveringNumber_anti, lowerSemicontinuousOn_iff_le_liminf, AddMonoid.minOrder_le_natCard, PowerSeries.le_weightedOrder_subst, Dynamics.le_coverMincard_image, Matroid.spanning_iff_eRk_le, natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zero, Polynomial.emultiplicity_le_one_of_separable, iSup_iInf_eq, PowerSeries.le_order_subst_left, ringKrullDim_le_ringKrullDim_quotient_add_encard, Metric.coveringNumber_le_one_of_ediam_le, Dynamics.coverMincard_monotone_subset
toHImp πŸ“–CompOp
2 mathmath: le_himp_iff, himp_bot
toHNot πŸ“–CompOp
1 mathmath: top_sdiff
toSDiff πŸ“–CompOp
2 mathmath: sdiff_le_iff, top_sdiff

Theorems

NameKindAssumesProvesValidatesDepends On
himp_bot πŸ“–mathematicalβ€”HImp.himp
toHImp
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
Compl.compl
toCompl
β€”β€”
iInf_iSup_eq πŸ“–mathematicalβ€”iInf
CompleteLattice.toInfSet
toCompleteLattice
iSup
CompleteLattice.toSupSet
β€”β€”
le_himp_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
HImp.himp
toHImp
SemilatticeInf.toMin
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
β€”β€”
sdiff_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
toSDiff
SemilatticeSup.toMax
β€”β€”
top_sdiff πŸ“–mathematicalβ€”toSDiff
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
HNot.hnot
toHNot
β€”β€”

CompletelyDistribLattice.MinimalAxioms

Definitions

NameCategoryTheorems
of πŸ“–CompOpβ€”
toCompleteDistribLattice πŸ“–CompOpβ€”
toCompleteLattice πŸ“–CompOp
3 mathmath: iSup_iInf_eq, iInf_iSup_eq', iInf_iSup_eq

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_iSup_eq πŸ“–mathematicalβ€”iInf
CompleteLattice.toInfSet
toCompleteLattice
iSup
CompleteLattice.toSupSet
β€”β€”
iInf_iSup_eq' πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
iInf_subtype
iInf_congr_Prop
iInf_range
iSup_subtype
iSup_congr_Prop
iSup_range
iInf_iSup_eq
iSup_le
le_trans
le_iInf
iInf_le
le_refl
le_iSup
le_iInf_iSup
iSup_iInf_eq πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”le_antisymm
iSup_iInf_le
iInf_iSup_eq'
iSup_le
Mathlib.Tactic.Push.not_forall_eq
le_trans
le_iInf
iInf_le
le_iSup

Frame

Definitions

NameCategoryTheorems
toDistribLattice πŸ“–CompOpβ€”

Function.Injective

Definitions

NameCategoryTheorems
coframe πŸ“–CompOpβ€”
coframeMinimalAxioms πŸ“–CompOpβ€”
completeAtomicBooleanAlgebra πŸ“–CompOpβ€”
completeBooleanAlgebra πŸ“–CompOpβ€”
completeDistribLattice πŸ“–CompOpβ€”
completeDistribLatticeMinimalAxioms πŸ“–CompOpβ€”
completelyDistribLattice πŸ“–CompOpβ€”
completelyDistribLatticeMinimalAxioms πŸ“–CompOpβ€”
frame πŸ“–CompOpβ€”
frameMinimalAxioms πŸ“–CompOpβ€”

Order

Definitions

NameCategoryTheorems
Coframe πŸ“–CompDataβ€”
Frame πŸ“–CompDataβ€”

Order.Coframe

Definitions

NameCategoryTheorems
ofMinimalAxioms πŸ“–CompOpβ€”
toCoheytingAlgebra πŸ“–CompOp
14 mathmath: AlgebraicGeometry.Scheme.support_nilradical, Prop.isCoatom_iff, liminf_eq_top, CompleteAtomicBooleanAlgebra.instIsCoatomistic, iSup_sdiff_eq, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff, hnot_eq_sInf_codisjoint, sdiff_eq_sInf, le_sdiff_iff, RestrictedProduct.isEmbedding_inclusion_top, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_top, AlgebraicGeometry.Scheme.IdealSheafData.support_bot, UpperSet.codisjoint_prod, sdiff_iSup_eq
toCompleteLattice πŸ“–CompOp
30 mathmath: Filter.bliminf_inf_not, iInf_sup_iInf, Filter.inf_limsup, Filter.bliminf_or_eq_inf, Filter.limsup_sup_filter, iSup_sdiff_eq, Filter.liminf_sup_filter, Filter.blimsup_sup_not, Filter.sup_limsup, hnot_eq_sInf_codisjoint, sInf_sup_eq, top_sdiff, sdiff_eq_sInf, le_sdiff_iff, sdiff_le_iff, iInfβ‚‚_sup_eq, Filter.inf_liminf, biInf_sup_biInf, iInf_sup_eq, Filter.bliminf_not_inf, sup_sInf_eq, Filter.limsup_piecewise, Filter.blimsup_not_sup, sup_iInfβ‚‚_eq, Filter.blimsup_or_eq_sup, sup_iInf_eq, Filter.liminf_piecewise, Filter.sup_liminf, sdiff_iSup_eq, sInf_sup_sInf
toHNot πŸ“–CompOp
1 mathmath: top_sdiff
toSDiff πŸ“–CompOp
2 mathmath: top_sdiff, sdiff_le_iff

Theorems

NameKindAssumesProvesValidatesDepends On
sdiff_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
toSDiff
SemilatticeSup.toMax
β€”β€”
top_sdiff πŸ“–mathematicalβ€”toSDiff
Top.top
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
HNot.hnot
toHNot
β€”β€”

Order.Coframe.MinimalAxioms

Definitions

NameCategoryTheorems
of πŸ“–CompOpβ€”
toCompleteLattice πŸ“–CompOp
6 mathmath: iInf_sup_eq, sup_iInf_eq, sup_iInfβ‚‚_eq, sup_sInf_eq, iInf_sup_le_sup_sInf, sInf_sup_eq

Theorems

NameKindAssumesProvesValidatesDepends On
iInf_sup_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iInf.eq_1
sInf_sup_eq
iInf_range
iInf_sup_le_sup_sInf πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
iInf
CompleteLattice.toInfSet
Set
Set.instMembership
SemilatticeSup.toMax
InfSet.sInf
β€”β€”
sInf_sup_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
iInf
Set
Set.instMembership
β€”sup_comm
iInf_congr_Prop
sup_sInf_eq
sup_iInf_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”sup_comm
iInf_sup_eq
sup_iInfβ‚‚_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”sup_iInf_eq
sup_sInf_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
iInf
Set
Set.instMembership
β€”LE.le.antisymm
sup_sInf_le_iInf_sup
iInf_sup_le_sup_sInf

Order.Frame

Definitions

NameCategoryTheorems
ofMinimalAxioms πŸ“–CompOpβ€”
toCompl πŸ“–CompOp
1 mathmath: himp_bot
toCompleteLattice πŸ“–CompOp
68 mathmath: Nucleus.himp_apply, Frm.coe_comp, Nucleus.map_himp_apply, sSup_inf_sSup, Frm.Iso.mk_hom, Sublocale.coe_iInf, sSup_disjoint_iff, iSupβ‚‚_inf_eq, Nucleus.restrict_toFun, Nucleus.map_himp_le, Sublocale.top_mem, biSup_inf_biSup, Frm.ext_iff, Nucleus.mem_toSublocale, inf_iSupβ‚‚_eq, Sublocale.sInf_mem, compl_eq_sSup_disjoint, Sublocale.coe_inf, disjoint_iSup_iff, Nucleus.comp_eq_right_iff_le, inf_sSup_eq, Frm.Iso.mk_inv, CompleteDistribLattice.top_sdiff, Nucleus.coe_toSublocale, Set.pairwiseDisjoint_prod_left, Nucleus.toSublocale_le_toSublocale, iSup_inf_eq, Frm.hom_comp, le_himp_iff, Sublocale.coe_sInf, iSup_disjoint_iff, Frm.id_apply, Nucleus.range_subset_range, Sublocale.sInf_mem', Frm.coe_id, inf_iSup_eq, iSupβ‚‚_disjoint_iff, Frm.inv_hom_apply, Frm.hom_inv_apply, Sublocale.inf_mem, disjoint_sSup_iff, CompleteDistribLattice.sdiff_le_iff, Frm.ofHom_comp, Nucleus.mem_range, Frm.ofHom_id, Frm.hom_id, himp_bot, himp_iInf_eq, Sublocale.toNucleus_le_toNucleus, Sublocale.iInf_mem, himp_le_iff, iSup_himp_eq, nucleusIsoSublocale.eq_toSublocale, nucleusIsoSublocale.symm_eq_toNucleus, Frm.ofHom_apply, Nucleus.restrict_toSublocale, Sublocale.infClosed, Frm.comp_apply, sSupIndep_iff_pairwiseDisjoint, Frm.forget_map, Sublocale.range_toNucleus, Sublocale.restrict_of_mem, Sublocale.toNucleus_apply, sSup_inf_eq, iSupIndep_iff_pairwiseDisjoint, disjoint_iSupβ‚‚_iff, iSup_inf_iSup, himp_eq_sSup
toHImp πŸ“–CompOp
2 mathmath: le_himp_iff, himp_bot
toHeytingAlgebra πŸ“–CompOp
409 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Set.Finite.t2_separation, Matroid.exists_isBasis_disjoint_isBasis_of_subset, Metric.ball_disjoint_ball, Set.pairwiseDisjoint_pair_insert, Metric.disjoint_ball_infDist, Set.disjoint_ordT5Nhd, LocalizedModule.subsingleton_iff_disjoint, Finpartition.isPartition_parts, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, SimpleGraph.isBipartiteWith_neighborSet_disjoint, SeparatedNhds.disjoint, PrimeSpectrum.localization_specComap_range, Nucleus.himp_apply, disjoint_or_subset_of_isClopen, BoxIntegral.Box.disjoint_splitCenterBox, Matroid.isBase_compl_iff_maximal_disjoint_isBase, Nucleus.map_himp_apply, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, Disjoint.of_spanβ‚€, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.Scheme.Hom.preimage_bot, UpperSet.sdiff_eq_left, MeasureTheory.pairwise_disjoint_fundamentalInterior, SeparatedNhds.disjoint_closure_left, Set.Iio_disjoint_Ioi_of_not_lt, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, IsUltrametricDist.ball_subset_trichotomy, Matroid.IsBasis.contract_dep_iff, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, SimpleGraph.ComponentCompl.disjoint_right, LowerSet.disjoint_coe, AddAction.orbit.pairwiseDisjoint, EMetric.ball_disjoint, Topology.RelCWComplex.pairwiseDisjoint', Matroid.contract_isCocircuit_iff, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, Topology.RelCWComplex.disjoint_openCell_of_ne, IsCompact.separation_of_notMem, Finset.isWF_sup, AddAction.IsBlock.disjoint_vadd_left, OrderedFinpartition.disjoint, sSup_disjoint_iff, Set.Iio_disjoint_Ioi_iff, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, exists_dist_slope_lt_pairwiseDisjoint_hasSum, Besicovitch.exist_disjoint_covering_families, IsLocalization.coe_primeSpectrumOrderIso_symm_apply_asIdeal, MeasureTheory.exists_null_pairwise_disjoint_diff, Matroid.IsBasis.contract_indep_iff, separated_by_continuous, Antitone.pairwise_disjoint_on_Ioo_pred, Perfect.small_diam_splitting, SimpleGraph.ComponentCompl.pairwise_disjoint, Set.Iic_disjoint_Ioi, Nucleus.map_himp_le, Set.disjoint_pi_univ_Ioc_update_left_right, disjoint_nested_nhds_of_not_inseparable, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, exists_disjoint_vadd_of_isCompact, MulAction.IsBlock.disjoint_smul_of_ne, Disjoint.of_span, Matroid.IsMinor.exists_eq_contract_delete_disjoint, isEmbedding_sumElim, Matroid.delete_eq_self_iff, MulAction.isBlock_iff_smul_eq_or_disjoint, disjoint_interior_frontier, Matroid.contract_eq_self_iff, Finset.sup_set_eq_biUnion, AlgebraicIndependent.adjoin_iff_disjoint, MeasureTheory.IsSetSemiring.disjointOfUnion_props, Set.Ioc_disjoint_Ioc, UpperSet.codisjoint_coe, Matroid.Coindep.delete_spanning_iff, Monotone.pairwise_disjoint_on_Ioc_pred, Set.disjoint_right_ordSeparatingSet, LowerSet.sdiff_eq_left, Antitone.pairwise_disjoint_on_Ioo_succ, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, Set.pairwise_disjoint_vadd_iff, Set.disjoint_iUnion_left, Set.definable_finset_sup, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Set.PairwiseDisjoint.exists_mem_filter, NonarchimedeanGroup.exists_openSubgroup_separating, Subgroup.leftCoset_cover_filter_FiniteIndex_aux, Ideal.disjoint_powers_iff_notMem, Matroid.Indep.contract_dep_iff, SimpleGraph.disjoint_edge, MeasureTheory.IsSetSemiring.mem_supClosure_iff, disjoint_nhdsSet_principal, Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, MulAction.disjoint_image_image_iff, t2_separation_nhds, limsup_eq_bot, SimpleGraph.disjoint_edgeFinset, Setoid.IsPartition.finpartition_parts, Set.disjoint_smul_set, AddAction.IsBlock.disjoint_vadd_vadd_set, Filter.disjoint_iff, Ideal.disjoint_map_primeCompl_iff_comap_le, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, not_disjoint_segment_convexHull_triple, compl_eq_sSup_disjoint, Set.disjoint_sUnion_left, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, LowerSet.sdiff_lt_left, SimpleGraph.disjoint_edgeSet, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, Besicovitch.exist_finset_disjoint_balls_large_measure, isInducing_sumElim, PrimeSpectrum.basicOpen_zero, disjoint_iSup_iff, Set.Ioi_disjoint_Iio_iff, Matroid.dual_indep_iff_exists', MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, AddAction.IsBlock.pairwiseDisjoint_range_vadd, Set.isAtom_singleton, Set.PairwiseDisjoint.exists_mem_filter_basis, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, MulAction.orbit.eq_or_disjoint, Topology.IsInducing.disjoint_of_sumElim_aux, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, IsLocalization.isPrime_iff_isPrime_disjoint, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, SubMulAction.disjoint_val_image, AddAction.IsBlock.disjoint_vadd_set_vadd, Metric.disjoint_closedEBall_of_lt_infEDist, exists_nhds_disjoint_closure, TopologicalSpace.Opens.coe_finset_sup, SimpleGraph.EdgeLabeling.pairwise_disjoint_labelGraph, isNowhereDense_iff_disjoint, ConvexCone.disjoint_hull_left_of_convex, EisensteinSeries.pairwise_disjoint_gammaSet, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_ENat_card, MulAction.IsBlock.disjoint_smul_right, BoxIntegral.unitPartition.disjoint, MeasureTheory.Content.innerContent_bot, MulAction.IsBlock.disjoint_smul_smul_set, AlgebraicGeometry.disjoint_opensRange_sigmaΞΉ, Set.pairwiseDisjoint_prod_left, Set.disjoint_iUnion_right, LowerSet.disjoint_prod, exists_open_nhds_disjoint_closure, disjoint_measurableAtom_of_notMem, MeasureTheory.disjoint_cylinder_iff, NFA.disjoint_evalFrom_reverse_iff, Matroid.contract_spanning_iff, Topology.CWComplex.pairwiseDisjoint', MulAction.IsBlock.disjoint_smul_set_smul, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, disjoint_frontier_iff_isOpen, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, Sublocale.himp_mem', IsGenericPoint.disjoint_iff, AddAction.IsBlock.disjoint_vadd_right, iSup_disjoint_iff, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, MeasureTheory.IsSetSemiring.diff_eq_sUnion', Antitone.pairwise_disjoint_on_Ioc_succ, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, exists_seq_infinite_isOpen_pairwise_disjoint, Set.disjoint_iUnionβ‚‚_right, IsUltrametricDist.ball_eq_or_disjoint, Filter.HasBasis.disjoint_iff, AddAction.isBlock_iff_vadd_eq_or_disjoint, Set.exists_union_disjoint_cardinal_eq_of_even, SimpleGraph.pairwise_disjoint_supp_connectedComponent, IsRetrocompact.finsetSup, Set.Ioi_disjoint_Iio_of_le, BoxIntegral.Prepartition.pairwiseDisjoint, Metric.ball_disjoint_closedBall, Matroid.IsCircuit.disjoint_coloops, UpperSet.lt_sdiff_left, Subgroup.IsComplement.pairwiseDisjoint_smul, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, Finset.intervalGapsWithin_pairwiseDisjoint_Ioc, SimpleGraph.EdgeLabeling.pairwiseDisjoint_univ_labelGraph, MulAction.IsBlock.smul_eq_smul_or_disjoint, ConvexCone.disjoint_coe, TopologicalSpace.Compacts.coe_finset_sup, Filter.disjoint_principal_principal, iSupβ‚‚_disjoint_iff, connectedComponent_disjoint, AddAction.IsBlock.disjoint_vadd_of_ne, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, Topology.RelCWComplex.disjoint_interior_base_closedCell, Set.Iic_disjoint_Ioc, SimpleGraph.IsBipartiteWith.disjoint, SeparatedNhds.disjoint_closure_right, Set.Ioc_disjoint_Ioi, Sublocale.coe_himp, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, Set.Iic_disjoint_Ici, Set.isAtom_iff, disjoint_ball_closedBall_iff, SimpleGraph.fromEdgeSet_disjoint, SimpleGraph.isBipartiteWith_neighborSet_disjoint', Interval.disjoint_coe, Set.Ioi_disjoint_Iio_of_not_lt, VitaliFamily.covering, Finset.isPWO_sup, Sublocale.himp_mem, Finset.partiallyWellOrderedOn_sup, exists_open_convex_of_notMem, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, AddAction.isBlock_iff_disjoint_vadd_of_ne, Vitali.exists_disjoint_subfamily_covering_enlargement, Matroid.coindep_contract_iff, t2_separation_compact_nhds, IndexedPartition.disjoint, TopologicalSpace.Opens.eq_bot_or_top, Set.Ico_disjoint_Ico, AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, Topology.RelCWComplex.disjointBase, Monotone.pairwise_disjoint_on_Ico_pred, Metric.disjoint_closedBall_of_lt_infDist, Metric.frontier_thickening_disjoint, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, TopologicalSpace.Closeds.coe_finset_sup, Vitali.exists_disjoint_covering_ae, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, Monotone.pairwise_disjoint_on_Ioo_succ, disjoint_sSup_iff, Metric.AreSeparated.disjoint, Set.Ioi_disjoint_Iio_same, BoxIntegral.Box.disjoint_coe, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, IsLowerSet.disjoint_upperClosure_left, MulAction.isBlock_iff_disjoint_smul_of_ne, Besicovitch.exists_disjoint_closedBall_covering_ae, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, IsLocalization.orderIsoOfPrime_symm_apply_coe, Matroid.dual_indep_iff_exists, FreeGroup.startsWith.disjoint_iff_ne, Set.disjoint_vadd_set, disjoint_closedBall_closedBall_iff, Set.disjoint_sUnion_right, T2Space.t2, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, Metric.closedBall_disjoint_ball, IsLocalization.disjoint_comap_iff, ProjectiveSpectrum.basicOpen_zero, AddAction.orbit.eq_or_disjoint, t2Space_iff_nhds, IsLowerSet.disjoint_upperClosure_right, Monotone.pairwise_disjoint_on_Ioo_pred, Set.ncard_union_eq_iff, Monotone.pairwise_disjoint_on_Ioc_succ, Matroid.delete_dep_iff, MeasureTheory.exists_subordinate_pairwise_disjoint, TopCat.Presheaf.isSheaf_on_punit_iff_isTerminal, disjoint_principal_nhdsSet, Matroid.contract_spanning_iff', Set.exists_union_disjoint_cardinal_eq_iff, himp_iInf_eq, Matroid.Indep.contract_indep_iff, Metric.frontier_cthickening_disjoint, MulAction.orbit.pairwiseDisjoint, Set.Iio_disjoint_Ioi_same, Topology.RelCWComplex.disjoint_skeleton_openCell, RootedTree.subtrees_disjoint, himp_le_iff, Metric.eball_disjoint, iSup_himp_eq, MeasureTheory.AEDisjoint.exists_disjoint_diff, disjoint_ball_ball_iff, Topology.RelCWComplex.disjointBase', TopologicalSpace.Closeds.isAtom_coe, SimpleGraph.disjoint_left, disjoint_memPartition, Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one, NFA.disjoint_stepSet_reverse, PiNat.disjoint_cylinder_of_longestPrefix_lt, IsUpperSet.disjoint_lowerClosure_left, IsUltrametricDist.closedBall_subset_trichotomy, Set.disjoint_vadd_set_left, SimpleGraph.disjoint_image_val_universalVerts, ConvexCone.disjoint_hull_right_of_convex, Set.Ioc_disjoint_Ioc_of_le, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, EMetric.disjoint_closedBall_of_lt_infEdist, Set.pairwiseDisjoint_vadd_iff, Ideal.disjoint_primeCompl_of_liesOver, AlgebraicGeometry.Proj.basicOpen_zero, Composition.disjoint_range, MulAction.IsBlock.pairwiseDisjoint_range_smul, MulAction.isBlock_iff_pairwiseDisjoint_range_smul, isSeparatedMap_iff_nhds, Set.exists_union_disjoint_ncard_eq_of_even, Set.Ici_disjoint_Iic, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, Matroid.delete_isBasis_iff, SimpleGraph.Finsubgraph.coe_himp, Set.pairwiseDisjoint_iff, SimpleGraph.disjoint_fromEdgeSet, TopologicalSpace.Opens.coe_disjoint, CompleteAtomicBooleanAlgebra.instIsAtomistic, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, PMF.toOuterMeasure_apply_eq_zero_iff, AddAction.disjoint_image_image_iff, DoubleCoset.disjoint_out, AlgebraicGeometry.Scheme.basicOpen_zero, Finset.wellFoundedOn_sup, AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux, Set.disjoint_vadd_set_right, Set.Iio_disjoint_Ici, Topology.RelCWComplex.disjoint_skeletonLT_openCell, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, AlgebraicGeometry.isAffineOpen_bot, Set.pairwise_disjoint_smul_iff, Setoid.IsPartition.pairwiseDisjoint, ModelWithCorners.disjoint_interior_boundary, sSupIndep_iff_pairwiseDisjoint, Set.Ico_disjoint_Ico_same, SubAddAction.disjoint_val_image, BoxIntegral.Prepartition.disjoint_coe_of_mem, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, Antitone.pairwise_disjoint_on_Ico_pred, Matroid.Indep.contract_isBase_iff, Pairwise.exists_mem_filter_basis_of_disjoint, Set.pairwiseDisjoint_smul_iff, MulAction.IsBlock.smul_eq_or_disjoint, Set.Ioo_disjoint_Ioo, Perfect.splitting, Metric.sphere_disjoint_ball, AlgebraicGeometry.basicOpen_eq_bot_iff, RealRMK.range_cut_partition, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, Ideal.exists_disjoint_powers_of_span_eq_top, MeasureTheory.pairwise_disjoint_addFundamentalInterior, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_of_isNilpotent, Topology.RelCWComplex.pairwiseDisjoint, Matroid.Coindep.delete_isBase_iff, Set.disjoint_smul_set_left, disjoint_nhdsWithin_of_mem_discrete, Filter.NeBot.not_disjoint, Set.disjoint_smul_set_right, Matroid.dualIndepMatroid_Indep, PrimeSpectrum.localization_comap_range, IsLocalization.orderIsoOfPrime_apply_coe, MeasurableSpace.disjoint_countablePartition, VitaliFamily.FineSubfamilyOn.covering_disjoint, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, Matroid.IsBasis'.contract_dep_iff, Matroid.delete_indep_iff, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, MeasureTheory.IsSetRing.finsetSup_mem, Pairwise.exists_mem_filter_of_disjoint, Set.disjoint_left_ordSeparatingSet, MeasureTheory.IsSetSemiring.exists_finpartition_diff, Matroid.Indep.disjoint_loops, Set.Iio_disjoint_Ioi_of_le, Finset.pairwiseDisjoint_pair_insert, Finsupp.disjoint_supported_supported_iff, Set.instIsAtomistic, SimpleGraph.Finsubgraph.coe_compl, Urysohns.CU.disjoint_C_support_lim, IsUpperSet.disjoint_lowerClosure_right, TopologicalSpace.Opens.not_nonempty_iff_eq_bot, Order.Ideal.PrimePair.disjoint, Disjoint.exists_mem_filter_basis, IsLocalization.map_algebraMap_ne_top_iff_disjoint, iSupIndep_iff_pairwiseDisjoint, SimpleGraph.deleteEdges_eq_self, Matroid.delete_isCircuit_iff, Set.disjoint_iUnionβ‚‚_left, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, r1_separation, Finset.sup_id_set_eq_sUnion, NumberField.InfinitePlace.disjoint_isReal_isComplex, Vitali.exists_disjoint_covering_ae', AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero, Matroid.IsBasis'.contract_indep_iff, disjoint_iSupβ‚‚_iff, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, disjoint_closedBall_ball_iff, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, PiNat.exists_disjoint_cylinder, t2_separation, TopCat.Presheaf.isSheaf_iff_isTerminal_of_indiscrete, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, Set.Ioc_disjoint_Ioi_same, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, Topology.RelCWComplex.disjoint_base_iUnion_openCell, AddAction.IsBlock.vadd_eq_or_disjoint, IsUltrametricDist.closedBall_eq_or_disjoint, Concept.disjoint_extent_intent, PrimeSpectrum.basicOpen_eq_bot_iff, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, Antitone.pairwise_disjoint_on_Ico_succ, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Metric.closedBall_disjoint_closedBall, t2Space_iff, Monotone.pairwise_disjoint_on_Ico_succ, himp_eq_sSup

Theorems

NameKindAssumesProvesValidatesDepends On
himp_bot πŸ“–mathematicalβ€”HImp.himp
toHImp
Bot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
BoundedOrder.toOrderBot
CompleteLattice.toBoundedOrder
Compl.compl
toCompl
β€”β€”
le_himp_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
HImp.himp
toHImp
SemilatticeInf.toMin
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
β€”β€”

Order.Frame.MinimalAxioms

Definitions

NameCategoryTheorems
of πŸ“–CompOpβ€”
toCompleteLattice πŸ“–CompOp
6 mathmath: iSup_inf_eq, sSup_inf_eq, inf_iSupβ‚‚_eq, inf_iSup_eq, inf_sSup_eq, inf_sSup_le_iSup_inf

Theorems

NameKindAssumesProvesValidatesDepends On
iSup_inf_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup.eq_1
sSup_inf_eq
iSup_range
inf_iSup_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”inf_comm
iSup_inf_eq
inf_iSupβ‚‚_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”inf_iSup_eq
inf_sSup_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
toCompleteLattice
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
β€”LE.le.antisymm
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
inf_sSup_le_iSup_inf
iSup_inf_le_inf_sSup
inf_sSup_le_iSup_inf πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
toCompleteLattice
SemilatticeInf.toMin
Lattice.inf
Lattice.inf_le_left
Lattice.inf_le_right
Lattice.le_inf
SupSet.sSup
CompleteLattice.toSupSet
iSup
Set
Set.instMembership
β€”β€”
sSup_inf_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
toCompleteLattice
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
β€”inf_comm
iSup_congr_Prop
inf_sSup_eq

OrderDual

Definitions

NameCategoryTheorems
instCoframe πŸ“–CompOpβ€”
instCompleteAtomicBooleanAlgebra πŸ“–CompOpβ€”
instCompleteBooleanAlgebra πŸ“–CompOpβ€”
instCompleteDistribLattice πŸ“–CompOpβ€”
instCompletelyDistribLattice πŸ“–CompOpβ€”
instFrame πŸ“–CompOpβ€”

PUnit

Definitions

NameCategoryTheorems
instCompleteAtomicBooleanAlgebra πŸ“–CompOpβ€”
instCompleteBooleanAlgebra πŸ“–CompOp
6 mathmath: sSup_eq, sInf_eq, CategoryTheory.Limits.LimitPresentation.self_Ο€, CategoryTheory.Limits.ColimitPresentation.self_diag, CategoryTheory.Limits.LimitPresentation.self_diag, CategoryTheory.Limits.ColimitPresentation.self_ΞΉ

Theorems

NameKindAssumesProvesValidatesDepends On
sInf_eq πŸ“–mathematicalβ€”InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
instCompleteBooleanAlgebra
β€”β€”
sSup_eq πŸ“–mathematicalβ€”SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompleteBooleanAlgebra.toCompleteLattice
instCompleteBooleanAlgebra
β€”β€”

Pi

Definitions

NameCategoryTheorems
instCoframe πŸ“–CompOpβ€”
instCompleteAtomicBooleanAlgebra πŸ“–CompOpβ€”
instCompleteBooleanAlgebra πŸ“–CompOpβ€”
instCompleteDistribLattice πŸ“–CompOpβ€”
instCompletelyDistribLattice πŸ“–CompOpβ€”
instFrame πŸ“–CompOpβ€”

Prod

Definitions

NameCategoryTheorems
instCoframe πŸ“–CompOpβ€”
instCompleteAtomicBooleanAlgebra πŸ“–CompOpβ€”
instCompleteBooleanAlgebra πŸ“–CompOpβ€”
instCompleteDistribLattice πŸ“–CompOpβ€”
instCompletelyDistribLattice πŸ“–CompOpβ€”
instFrame πŸ“–CompOpβ€”

Prop

Definitions

NameCategoryTheorems
instCompleteAtomicBooleanAlgebra πŸ“–CompOpβ€”
instCompleteBooleanAlgebra πŸ“–CompOp
1 mathmath: isCoatom_iff

(root)

Definitions

NameCategoryTheorems
CompleteAtomicBooleanAlgebra πŸ“–CompDataβ€”
CompleteBooleanAlgebra πŸ“–CompDataβ€”
CompleteDistribLattice πŸ“–CompDataβ€”
CompletelyDistribLattice πŸ“–CompDataβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
biInf_sup_biInf πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”biSup_inf_biSup
biSup_iInter_of_pairwise_disjoint πŸ“–mathematicalPairwise
Function.onFun
Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompletelyDistribLattice.toCompleteLattice
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
CompletelyDistribLattice.toBiheytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.iInter
iInf
CompleteSemilatticeInf.toInfSet
β€”iInf_iSup_eq
iSup_congr_Prop
le_antisymm
iSupβ‚‚_le
le_iSupβ‚‚_of_le
le_iInf
le_rfl
iInf_le
Mathlib.Tactic.Push.not_forall_eq
le_inf
Disjoint.eq_bot
bot_le
biSup_inf_biSup πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”iSup_subtype'
iSup_inf_iSup
Function.Surjective.iSup_congr
Equiv.surjective
biSup_inter_of_pairwise_disjoint πŸ“–mathematicalPairwise
Function.onFun
Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
Set.instInter
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”biSup_inf_biSup
le_antisymm
iSupβ‚‚_le
le_iSupβ‚‚_of_le
le_inf
le_rfl
inf_le_left
Disjoint.eq_bot
iSup_congr_Prop
biSup_symmDiff_biSup_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
symmDiff
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BooleanAlgebra.toSDiff
CompleteBooleanAlgebra.toBooleanAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_trans
iSup_symmDiff_iSup_le
iSup_mono
compl_eq_sSup_disjoint πŸ“–mathematicalβ€”Compl.compl
HeytingAlgebra.toCompl
Order.Frame.toHeytingAlgebra
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Order.Frame.toCompleteLattice
setOf
Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
HeytingAlgebra.toOrderBot
β€”IsLUB.sSup_eq
IsGreatest.isLUB
isGreatest_compl
compl_iInf πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
CompleteBooleanAlgebra.toBooleanAlgebra
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”le_antisymm
compl_le_of_compl_le
le_iInf
le_iSup
iSup_le
compl_le_compl
iInf_le
compl_iSup πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
CompleteBooleanAlgebra.toBooleanAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompleteBooleanAlgebra.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”compl_injective
compl_compl
compl_iInf
compl_sInf πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
CompleteBooleanAlgebra.toBooleanAlgebra
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set
Set.instMembership
β€”sInf_eq_iInf
compl_iInf
compl_sInf' πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
CompleteBooleanAlgebra.toBooleanAlgebra
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Set.image
β€”compl_sInf
sSup_image
compl_sSup πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
CompleteBooleanAlgebra.toBooleanAlgebra
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompleteBooleanAlgebra.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set
Set.instMembership
β€”sSup_eq_iSup
compl_iSup
compl_sSup' πŸ“–mathematicalβ€”Compl.compl
BooleanAlgebra.toCompl
CompleteBooleanAlgebra.toBooleanAlgebra
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompleteBooleanAlgebra.toCompleteLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Set.image
β€”compl_sSup
sInf_image
disjoint_iSup_iff πŸ“–mathematicalβ€”Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_disjoint_iff
disjoint_iSupβ‚‚_iff πŸ“–mathematicalβ€”Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”β€”
disjoint_sSup_iff πŸ“–mathematicalβ€”Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup_disjoint_iff
himp_eq_sSup πŸ“–mathematicalβ€”HImp.himp
GeneralizedHeytingAlgebra.toHImp
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Order.Frame.toCompleteLattice
setOf
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”IsLUB.sSup_eq
IsGreatest.isLUB
isGreatest_himp
himp_iInf_eq πŸ“–mathematicalβ€”HImp.himp
GeneralizedHeytingAlgebra.toHImp
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
β€”eq_of_forall_le_iff
himp_le_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HImp.himp
GeneralizedHeytingAlgebra.toHImp
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
β€”himp_eq_sSup
hnot_eq_sInf_codisjoint πŸ“–mathematicalβ€”HNot.hnot
CoheytingAlgebra.toHNot
Order.Coframe.toCoheytingAlgebra
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Order.Coframe.toCompleteLattice
setOf
Codisjoint
CompleteSemilatticeInf.toPartialOrder
CoheytingAlgebra.toOrderTop
β€”IsGLB.sInf_eq
IsLeast.isGLB
isLeast_hnot
iInf_iSup_eq πŸ“–mathematicalβ€”iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
CompletelyDistribLattice.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”CompletelyDistribLattice.MinimalAxioms.iInf_iSup_eq'
iInf_sup_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_inf_eq
iInf_sup_iInf πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSup_inf_iSup
iInf_sup_of_antitone πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_inf_of_monotone
Antitone.dual_right
iInf_sup_of_monotone πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”iSup_inf_of_antitone
Monotone.dual_right
iInfβ‚‚_sup_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”iSupβ‚‚_inf_eq
iSup_disjoint_iff πŸ“–mathematicalβ€”Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_inf_eq
iSup_himp_eq πŸ“–mathematicalβ€”HImp.himp
GeneralizedHeytingAlgebra.toHImp
HeytingAlgebra.toGeneralizedHeytingAlgebra
Order.Frame.toHeytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Order.Frame.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”eq_of_forall_le_iff
inf_iSup_eq
iSup_iInf_eq πŸ“–mathematicalβ€”iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
CompletelyDistribLattice.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”CompletelyDistribLattice.MinimalAxioms.iSup_iInf_eq
iSup_iInf_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”le_iInf_iSup
iSup_inf_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup.eq_1
sSup_inf_eq
iSup_range
iSup_inf_iSup πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_inf_eq
inf_iSup_eq
iSup_prod
iSup_inf_of_antitone πŸ“–mathematicalAntitone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”iSup_inf_of_monotone
OrderDual.isDirected_le
Antitone.dual_left
iSup_inf_of_monotone πŸ“–mathematicalMonotone
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
β€”LE.le.antisymm
le_iSup_inf_iSup
iSup_inf_iSup
iSup_mono'
directed_of
inf_le_inf
iSup_sdiff_eq πŸ“–mathematicalβ€”GeneralizedCoheytingAlgebra.toSDiff
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
Order.Coframe.toCompleteLattice
β€”eq_of_forall_ge_iff
iSup_symmDiff_iSup_le πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
CompleteBooleanAlgebra.toCompleteLattice
symmDiff
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
BooleanAlgebra.toSDiff
CompleteBooleanAlgebra.toBooleanAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_mono
le_symmDiff_sup_right
sup_comm
symmDiff_comm
iSupβ‚‚_disjoint_iff πŸ“–mathematicalβ€”Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”β€”
iSupβ‚‚_inf_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”iSup_inf_eq
inf_iSup_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”inf_comm
iSup_inf_eq
inf_iSupβ‚‚_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”inf_iSup_eq
inf_sSup_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
β€”GaloisConnection.l_sSup
gc_inf_himp
le_iInf_iSup πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iInf
CompleteSemilatticeInf.toInfSet
β€”iSup_le
le_iInf
le_trans
iInf_le
le_iSup
le_sdiff_iff πŸ“–mathematicalβ€”Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Coframe.toCompleteLattice
GeneralizedCoheytingAlgebra.toSDiff
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
β€”sdiff_eq_sInf
sInf_sup_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
iInf
Set
Set.instMembership
β€”sSup_inf_eq
sInf_sup_sInf πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
iInf
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”sSup_inf_sSup
sSup_disjoint_iff πŸ“–mathematicalβ€”Disjoint
CompleteSemilatticeInf.toPartialOrder
CompleteLattice.toCompleteSemilatticeInf
Order.Frame.toCompleteLattice
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”sSup_inf_eq
sSup_inf_eq πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
β€”inf_comm
iSup_congr_Prop
inf_sSup_eq
sSup_inf_sSup πŸ“–mathematicalβ€”SemilatticeInf.toMin
Lattice.toSemilatticeInf
CompleteLattice.toLattice
Order.Frame.toCompleteLattice
SupSet.sSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
iSup
Set
Set.instMembership
SProd.sprod
Set.instSProd
β€”sSup_eq_iSup
biSup_inf_biSup
sdiff_eq_sInf πŸ“–mathematicalβ€”GeneralizedCoheytingAlgebra.toSDiff
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Order.Coframe.toCompleteLattice
setOf
Preorder.toLE
PartialOrder.toPreorder
CompleteSemilatticeInf.toPartialOrder
SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
β€”IsGLB.sInf_eq
IsLeast.isGLB
isLeast_sdiff
sdiff_iSup_eq πŸ“–mathematicalβ€”GeneralizedCoheytingAlgebra.toSDiff
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
Order.Coframe.toCoheytingAlgebra
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
Order.Coframe.toCompleteLattice
iSup
CompleteSemilatticeSup.toSupSet
CompleteLattice.toCompleteSemilatticeSup
β€”eq_of_forall_ge_iff
iInf_sup_eq
sup_iInf_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”inf_iSup_eq
sup_iInfβ‚‚_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
iInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
β€”inf_iSupβ‚‚_eq
sup_sInf_eq πŸ“–mathematicalβ€”SemilatticeSup.toMax
Lattice.toSemilatticeSup
CompleteLattice.toLattice
Order.Coframe.toCompleteLattice
InfSet.sInf
CompleteSemilatticeInf.toInfSet
CompleteLattice.toCompleteSemilatticeInf
iInf
Set
Set.instMembership
β€”GaloisConnection.u_sInf
gc_sdiff_sup

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