toPartialOrder 📖 | CompOp | 751 mathmath: IsLocalization.AtPrime.coe_primeSpectrumOrderIso_symm_apply_asIdeal, Dynamics.netEntropyEntourage_monotone, Matroid.eRk_lt_top_iff, Dynamics.netMaxcard_monotone_subset, Set.ncard_mono, Matroid.exists_isBasis_disjoint_isBasis_of_subset, NonUnitalAlgebra.gc, Metric.disjoint_ball_infDist, convexIndependent_set_iff_inter_convexHull_subset, le_ωSup, SimpleGraph.vertexCoverNum_le_card_sub_one, Dynamics.coverEntropyInfEntourage_antitone, Ideal.height_le_spanFinrank, OrdinalApprox.lfpApprox_mono_mid, IsLinearMap.image_convexHull, LocalizedModule.subsingleton_iff_disjoint, ringKrullDim_succ_le_ringKrullDim_polynomial, FirstOrder.Language.Substructure.closure_eq_of_isRelational, AlgebraicGeometry.Scheme.isEmpty_pullback_iff, convexHull_insert, subset_closedConvexHull, Geometry.SimplicialComplex.vertex_mem_convexHull_iff, Matroid.eRk_lt_encard_iff_dep, SimpleGraph.isBipartiteWith_neighborSet_disjoint, closedConvexHull_min, PowerSeries.le_order_subst_left', PrimeSpectrum.localization_specComap_range, convexHull_multiset_sum, Geometry.SimplicialComplex.convexHull_subset_space, CategoryTheory.Retract.injectiveDimension_le, Ideal.height_le_iff_exists_minimalPrimes, BoxIntegral.Box.disjoint_splitCenterBox, SimpleGraph.le_chromaticNumber_iff_colorable, ContinuousHom.ωSup_apply, Matroid.isBase_compl_iff_maximal_disjoint_isBase, AlgebraicGeometry.Scheme.mem_grothendieckTopology_iff, SimpleGraph.le_chromaticNumber_iff_coloring, Geometry.SimplicialComplex.mem_space_iff, AlgebraicGeometry.HasAffineProperty.affineAnd_le_affineAnd, MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt, CategoryTheory.injectiveDimension_le_iff, OrderHom.le_map_sup_fixedPoints, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp, OrdinalApprox.gfp_mem_range_gfpApprox, Convex.convex_remove_iff_notMem_convexHull_remove, ProjectiveSpectrum.gc_homogeneousIdeal, SimpleGraph.chromaticNumber_pos, Matroid.eRk_singleton_le, Matroid.eRk_mono, convexHull_eq_iInter, Ring.krullDimLE_iff, FirstOrder.Language.Substructure.fg_closure_singleton, MeasureTheory.pairwise_disjoint_fundamentalInterior, Ideal.height_lt_top, MeasureTheory.monotone_spanningSets, LinearMap.polar_antitone, Dynamics.netMaxcard_le_coverMincard, HasCardinalLT.Set.functor_obj, PrimeSpectrum.gc, Complex.convexHull_reProdIm, Dynamics.coverMincard_finite_of_isCompact_invariant, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, Matroid.eRank_le_encard_add_eRk_compl, Matroid.IsBasis.contract_dep_iff, OrderHom.lfp_le_gfp, AddAction.orbit.pairwiseDisjoint, SimpleGraph.vertexCoverNum_le_iff, Topology.RelCWComplex.pairwiseDisjoint', convexJoin_segments, Matroid.contract_isCocircuit_iff, Dynamics.coverMincard_image_le, FirstOrder.Language.Substructure.small_closure, Set.chainHeight_le_encard, Topology.RelCWComplex.disjoint_openCell_of_ne, ContinuousHom.ωSup_apply_ωSup, OrderHom.ωSup_coe, FirstOrder.Language.Substructure.cg_def, Cardinal.mk_monotone, AddAction.IsBlock.disjoint_vadd_left, Matroid.le_eRk_iff, OrderIso.essSup_apply, OrderedFinpartition.disjoint, OrderHom.map_lfp, exists_partition_approximatesLinearOn_of_hasFDerivWithinAt, exists_dist_slope_lt_pairwiseDisjoint_hasSum, Ideal.primeHeight_mono, 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, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app', AddMonoid.minOrder_le_addOrderOf, Localization.localRingHom_injective_of_primesOver_eq_singleton, SimpleGraph.two_le_chromaticNumber_of_adj, interior_convexHull_nonempty_iff_affineSpan_eq_top, OrderHom.gfp_const_inf_le, SimpleGraph.card_le_chromaticNumber_iff_forall_surjective, Matroid.IsBasis.contract_indep_iff, mem_absConvexHull_iff, SimpleGraph.three_le_egirth, Dynamics.IsDynNetIn.card_le_netMaxcard, Perfect.small_diam_splitting, Ideal.primeHeight_lt_top, SimpleGraph.chromaticNumber_le_sum_right, Geometry.SimplicialComplex.convexHull_inter_convexHull, HasCardinalLT.Set.cocone_pt, IsLocalization.AtPrime.coe_orderIsoOfPrime_symm_apply_coe, AffineBasis.convexHull_eq_nonneg_coord, FirstOrder.Language.Substructure.fg_closure, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app', segment_subset_convexHull, Metric.coveringNumber_two_mul_le_externalCoveringNumber, convexHull_toCone_eq_sInf, lowerSemicontinuous_iff_le_liminf, MulAction.IsBlock.disjoint_smul_of_ne, Balanced.convexHull, subset_absConvexHull, Ideal.height_strict_mono_of_is_prime, Matroid.IsMinor.exists_eq_contract_delete_disjoint, balancedHull_subset_convexHull_union_neg, SimpleGraph.chromaticNumber_mono_of_embedding, le_minSmoothness, ringKrullDim_succ_le_ringKrullDim_powerseries, Matroid.delete_eq_self_iff, CategoryTheory.IsGrothendieckAbelian.isomorphisms_le_pushouts_generatingMonomorphisms, Convex.convexHull_union, closedConvexHull_eq_closure_convexHull, Finset.mem_convexHull', subset_convexHull, Dynamics.one_le_coverMincard_iff, Dynamics.coverEntropy_monotone, MulAction.isBlock_iff_smul_eq_or_disjoint, Convex.convexHull_subset_iff, AffineBasis.interior_convexHull, Matroid.contract_eq_self_iff, Dynamics.coverMincard_monotone_time, AlgebraicIndependent.adjoin_iff_disjoint, OrdinalApprox.gfpApprox_le, Matroid.eRk_lt_encard_iff_dep_of_finite, IsContDiffImplicitAt.one_le, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, Geometry.SimplicialComplex.inter_subset_convexHull, convexJoin_segment_singleton, SimpleGraph.chromaticNumber_le_of_forall_imp, Matroid.isClosed_iff_isFlat, PowerSeries.le_order_subst_right', ωSup_le_iff, convexJoin_singleton_segment, convexHull_diam, Matroid.Coindep.delete_spanning_iff, ringKrullDim_nonneg_of_nontrivial, Prod.ωSup_zip, subset_closedAbsConvexHull, Dynamics.netEntropyEntourage_antitone, Fin.Embedding.exists_embedding_disjoint_range_of_add_le_Nat_card, instOrderHomClassContinuousHom, Finset.centerMass_id_mem_convexHull, Submodule.length_lt, Set.Finite.isCompact_convexHull, Finset.centerMass_id_mem_convexHull_of_nonpos, convexHull_add, 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, affineSpan_convexHull, AlgebraicGeometry.Scheme.Hom.app_appIso_inv_assoc, Cardinal.mk_strictMonoOn, MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier, Besicovitch.TauPackage.monotone_iUnionUpTo, Matroid.eRk_le_eRk_add_eRk_diff, Dynamics.coverMincard_closure_le, MeasureTheory.hittingBtwn_apply_anti, CategoryTheory.MorphismProperty.le_ind, Set.encard_strictMono, Submodule.height_strictMono, Subgroup.leftCoset_cover_filter_FiniteIndex_aux, Matroid.eRk_compl_insert_union_add_eRk_compl_insert_inter_le, convexHull_basis_eq_stdSimplex, Ideal.disjoint_powers_iff_notMem, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms_le_monomorphisms, Matroid.Indep.contract_dep_iff, Convex.radon_partition, IsOpen.exists_iUnion_isClosed, Metric.externalCoveringNumber_anti, Matroid.cRk_mono, ConvexOn.bddAbove_convexHull, FirstOrder.Language.Substructure.fg_def, Matroid.eRk_insert_le_add_one, Set.chainHeight_mono, Ideal.height_le_height_add_of_liesOver, Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, MvPowerSeries.le_order_subst, CategoryTheory.injectiveDimension_ge_iff, AddAction.IsBlock.disjoint_vadd_vadd_set, Matroid.closure_eq_subtypeClosure, Ideal.height_le_height_add_one_of_mem, Matroid.spanning_iff_eRk_le', Metric.packingNumber_two_mul_le_externalCoveringNumber, Ideal.disjoint_map_primeCompl_iff_comap_le, AddAction.IsBlock.vadd_eq_vadd_or_disjoint, ConvexIndependent.mem_convexHull_iff, not_disjoint_segment_convexHull_triple, convexHull_vadd, Matroid.closure_mono, FirstOrder.Language.Substructure.lift_card_closure_le_card_term, Dynamics.coverMincard_finite_of_isCompact_uniformContinuous, Ideal.height_le_card_of_mem_minimalPrimes_span, SimpleGraph.chromaticNumber_le_card, AlgebraicGeometry.topologically_iso_le, ringKrullDim_quotient_le, Matroid.eRk_inter_add_eRk_union_le, exists_mem_interior_convexHull_affineBasis, Ideal.disjoint_nonZeroDivisors_of_mem_minimalPrimes, essInf_antitone_measure, FirstOrder.Language.Substructure.mem_closure_iff_exists_term, ringKrullDim_succ_le_of_surjective, Besicovitch.exist_finset_disjoint_balls_large_measure, SimpleGraph.vertexCoverNum_mono, Ideal.primeHeight_le_ringKrullDim, closedAbsConvexHull_min, 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, totallyBounded_absConvexHull, Matroid.dual_indep_iff_exists', ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, SimpleGraph.chromaticNumber_le_iff_colorable, absConvexHull_nonempty, MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier, Ideal.primeHeight_strict_mono, absConvexHull_empty, AddAction.IsBlock.pairwiseDisjoint_range_vadd, upperSemicontinuousWithinAt_iff_limsup_le, absConvexHull_eq_self, OrderHom.isLeast_lfp, MulAction.orbit.eq_or_disjoint, Convex.mem_extremePoints_iff_mem_diff_convexHull_diff, CategoryTheory.SmallObject.succStruct_prop_le_propArrow, ringKrullDim_le_iff_height_le, IsLocalization.isPrime_iff_isPrime_disjoint, SubMulAction.disjoint_val_image, upperSemicontinuousOn_iff_limsup_le, natCast_le_analyticOrderAt, Dynamics.coverMincard_antitone, ωScottContinuous.map_ωSup, NonUnitalStarAlgebra.gc, Dynamics.netMaxcard_antitone, SimpleGraph.vertexCoverNum_le_encard_edgeSet, AddAction.IsBlock.disjoint_vadd_set_vadd, Matroid.IsRkFinite.eRk_lt_top, Matroid.Indep.encard_le_eRk_of_subset, AlgebraicGeometry.isCompl_range_inl_inr, Metric.disjoint_closedEBall_of_lt_infEDist, Matroid.eRank_le_encard_ground, SimpleGraph.vertexCoverNum_lt_card, OrdinalApprox.lfpApprox_ord_eq_lfp, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_inv_app'_assoc, ProjectiveSpectrum.gc_set, Matroid.eRank_lt_top_iff, convexHull_add_subset, ConvexCone.disjoint_hull_left_of_convex, Matroid.eRk_insert_inter_add_eRk_insert_union_le, ωScottContinuous_iff_map_ωSup_of_orderHom, Ideal.height_mono, EisensteinSeries.pairwise_disjoint_gammaSet, Submodule.spanFinrank_span_le_encard, ringKrullDim_le_ringKrullDim_quotient_add_card, closedConvexHull_closure_eq_closedConvexHull, ContinuousHom.coe_toOrderHom, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, Matroid.Indep.encard_le_eRank, MulAction.IsBlock.disjoint_smul_right, Polynomial.rootSet_derivative_subset_convexHull_rootSet, BoxIntegral.unitPartition.disjoint, Metric.IsCover.coveringNumber_le_encard, AlgebraicGeometry.Scheme.mem_overGrothendieckTopology, Ideal.height_le_ringKrullDim_quotient_add_one, closure_convexHull_extremePoints, MulAction.IsBlock.disjoint_smul_smul_set, ContinuousHom.forall_forall_merge, Dynamics.coverEntropyEntourage_monotone, Set.Finite.isClosed_convexHull, convexHull_empty, absConvexHull_add_subset, Ideal.height_le_iff, Finset.centerMass_mem_convexHull, SimpleGraph.chromaticNumber_le_two_iff_isBipartite, convexHull_pair, SimpleGraph.two_le_chromaticNumber_iff_ne_bot, preCantorSet_antitone, MeasureTheory.hittingBtwn_anti, MvPowerSeries.le_weightedOrder_subst, OrdinalApprox.lfpApprox_monotone, Dynamics.coverMincard_union_le, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_inv_app'_assoc, Matroid.contract_spanning_iff, MeasureTheory.stoppedProcess_eq, FirstOrder.Language.Substructure.mem_closed_of_isRelational, Topology.CWComplex.pairwiseDisjoint', Dynamics.coverEntropyInf_monotone, Module.length_le_of_surjective, OrdinalApprox.gfpApprox_antitone, FirstOrder.Language.Substructure.fg_iff_exists_fin_generating_family, MulAction.IsBlock.disjoint_smul_set_smul, convexJoin_subset_convexHull, Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull, convexHull_eq_empty, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp_assoc, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_invApp, Matroid.eRk_le_iff, SimpleGraph.le_chromaticNumber_iff_forall_surjective, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, MvPolynomial.supported_strictMono, AddAction.IsBlock.disjoint_vadd_right, convexHull_singleton, ωScottContinuous_iff_monotone_map_ωSup, MeasureTheory.hittingAfter_apply_anti, Pi.ωScottContinuous_uncurry, OrderHom.lfp_lfp, SimpleGraph.Colorable.chromaticNumber_le, convex_convexHull, convexHull_sum, OrdinalApprox.gfpApprox_ord_eq_gfp, FirstOrder.Language.Substructure.closure_insert, isBounded_convexHull, SimpleGraph.IsVertexCover.vertexCoverNum_le, AddAction.isBlock_iff_vadd_eq_or_disjoint, Dynamics.netEntropyInfEntourage_monotone, Set.exists_union_disjoint_cardinal_eq_of_even, Finset.mem_convexHull, OrderHom.isFixedPt_lfp, essSup_mono_measure, convexHull_neg, convexIndependent_set_iff_notMem_convexHull_diff, OrderHom.gfp_gfp, LinearEquiv.transvections_pow_mono, convexHull_sphere_eq_closedBall, ENat.LEInfty.out, LinearMap.polar_gc, Matroid.eRk_union_le_eRk_add_eRk, Matroid.IsCircuit.disjoint_coloops, Matroid.eRk_le_eRk_inter_add_eRk_diff, Subgroup.IsComplement.pairwiseDisjoint_smul, Convex.exists_subset_interior_convexHull_finset_of_isCompact, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp, convexHull_mono, VitaliFamily.FineSubfamilyOn.covering_disjoint_subtype, convex_absConvexHull, Cardinal.mk_strictMono, Metric.coveringNumber_pos_iff, convexHullAddMonoidHom_apply, absConvexHull_mono, Finset.convexHull_eq, Ideal.height_le_ringKrullDim_quotient_add_encard, MulAction.IsBlock.smul_eq_smul_or_disjoint, Ideal.primeHeight_add_one_le_of_lt, ConvexCone.disjoint_coe, totallyBounded_convexHull, Set.one_le_chainHeight_iff, Set.Nonempty.absConvexHull, tangentBundleCore.isContMDiff, SimpleGraph.cliqueNum_le_chromaticNumber, AddAction.IsBlock.disjoint_vadd_of_ne, TangentBundle.contMDiffVectorBundle, Topology.RelCWComplex.disjoint_interior_base_closedCell, absConvex_convexClosedHull, upperSemicontinuousAt_iff_limsup_le, isωSup_ωSup, convexHull_eq_singleton, convexHull_eq_zero, Set.encard_mono, OrdinalApprox.lfpApprox_mono_left, SimpleGraph.IsBipartiteWith.disjoint, FirstOrder.Language.Substructure.closure_empty, Dynamics.coverMincard_le_pow, Ideal.height_le_iff_covBy, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, isCompact_closedAbsConvexHull_of_totallyBounded, Dynamics.coverMincard_mul_le_pow, le_analyticOrderAt_sub, le_analyticOrderAt_add, VitaliFamily.FineSubfamilyOn.exists_disjoint_covering_ae, absConvexHull_subset_closedAbsConvexHull, ωScottContinuous.monotone_map_ωSup, Matroid.setOf_indep_eq, Dynamics.netMaxcard_monotone_time, toWeakSpace_closedConvexHull_eq, convexHull_pi, FirstOrder.Language.monotone_distinctConstantsTheory, FirstOrder.Language.Substructure.iSup_eq_closure, AddMonoid.le_minOrder_iff_forall_addSubgroup, disjoint_ball_closedBall_iff, ContinuousHom.toOrderHom_eq_coe, ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial, upperSemicontinuous_iff_limsup_le, SimpleGraph.isBipartiteWith_neighborSet_disjoint', doublyStochastic_eq_convexHull_permMatrix, Module.length_pos, absConvexHull_eq_iInter, isSaddlePointOn_iff', VitaliFamily.covering, exists_open_convex_of_notMem, Finset.centroid_mem_convexHull, AddAction.isBlock_iff_disjoint_vadd_of_ne, Vitali.exists_disjoint_subfamily_covering_enlargement, Matroid.coindep_contract_iff, AbsConvex.absConvexHull_subset_iff, AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eq, Metric.coveringNumber_subset_le, Topology.RelCWComplex.disjointBase, MeasureTheory.hittingAfter_eq_sInf, MeasureTheory.Egorov.notConvergentSeq_antitone, OrderHom.map_gfp, ringKrullDim_le_iff_isMaximal_height_le, Projectivization.Subspace.monotone_span, FirstOrder.Language.Substructure.subset_closure, AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff, ringKrullDim_le_ringKrullDim_add_card, FirstOrder.Language.Substructure.closure_iUnion, Metric.disjoint_closedBall_of_lt_infDist, absConvex_absConvexHull, Metric.frontier_thickening_disjoint, iSup₂_iInf₂_le_iInf₂_iSup₂, CategoryTheory.projectiveDimension_le_iff, MulAction.isBlock_iff_smul_eq_smul_or_disjoint, SimpleGraph.chromaticNumber_le_one_of_subsingleton, AddAction.isBlock_iff_pairwiseDisjoint_range_vadd, ProjectiveSpectrum.gc_ideal, lowerSemicontinuousWithinAt_iff_le_liminf, Metric.coveringNumber_le_packingNumber, Vitali.exists_disjoint_covering_ae, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, Monoid.le_minOrder_iff_forall_subgroup, Module.supportDim_le_ringKrullDim, MulAction.IsBlock.disjoint_smul_left, Set.Infinite.exists_union_disjoint_cardinal_eq_of_infinite, ωScottContinuous.isLUB, LinearMap.image_convexHull, Module.length_le_of_injective, FirstOrder.Language.Substructure.closure_union, MulAction.isBlock_iff_disjoint_smul_of_ne, ContinuousMap.ideal_gc, Module.supportDim_le_supportDim_quotSMulTop_succ, CategoryTheory.projectiveDimension_ge_iff, Dynamics.coverEntropyEntourage_antitone, Besicovitch.exists_disjoint_closedBall_covering_ae, AddSubgroup.IsComplement.pairwiseDisjoint_vadd, Matroid.eRk_le_eRank, PrimeSpectrum.gc_set, IsLocalization.orderIsoOfPrime_symm_apply_coe, StarAlgebra.gc, Matroid.dual_indep_iff_exists, convexHull_univ, convexHull_ediam, disjoint_closedBall_closedBall_iff, SimpleGraph.le_chromaticNumber_of_pairwise_adj, FirstOrder.Language.Structure.cg_iff, absConvexHull_min, ContinuousHom.monotone, PowerSeries.le_order_subst, ringKrullDim_lt_top, CategoryTheory.injectiveDimension_lt_iff, lowerSemicontinuousAt_iff_le_liminf, AddAction.isBlock_iff_vadd_eq_vadd_or_disjoint, OrderIso.essInf_apply, OrdinalApprox.gfpApprox_mono_mid, SimpleGraph.chromaticNumber_mono, HasCardinalLT.Set.cocone_ι_app, IsLocalization.disjoint_comap_iff, AffineIndependent.convexHull_inter', Polynomial.ringKrullDim_le, AddAction.orbit.eq_or_disjoint, convexHull_zero, Matroid.eRk_lt_encard_of_dep_of_finite, convexHull_eq_union_convexHull_finite_subsets, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.app_invApp_assoc, Set.ncard_union_eq_iff, ContinuousHom.ωSup_bind, OrderHom.isGreatest_gfp_le, ωScottContinuous.monotone, Matroid.delete_dep_iff, MeasureTheory.exists_subordinate_pairwise_disjoint, zero_mem_absConvexHull, Ideal.map_height_le_one_of_mem_minimalPrimes, Matroid.contract_spanning_iff', Set.exists_union_disjoint_cardinal_eq_iff, HasCardinalLT.Set.functor_map_coe, affineCombination_mem_convexHull, Matroid.Indep.contract_indep_iff, mem_convexHull_iff_exists_fintype, Metric.frontier_cthickening_disjoint, Dynamics.netMaxcard_finite_iff, MulAction.orbit.pairwiseDisjoint, absConvexHull_univ, MeasureTheory.hittingBtwn_eq_sInf, MeasureTheory.stoppedProcess_eq', Topology.RelCWComplex.disjoint_skeleton_openCell, convexHull_toCone_isLeast, posTangentConeAt_mono, Matroid.eRk_union_le_encard_add_eRk, Matroid.eRk_union_le_eRk_add_encard, MeasureTheory.AEDisjoint.exists_disjoint_diff, cauchy_davenport_minOrder_add, MeasurableSpace.generateMeasurableRec_mono, disjoint_ball_ball_iff, Dynamics.coverMincard_le_netMaxcard, extremePoints_convexHull_subset, MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection, Topology.RelCWComplex.disjointBase', Geometry.SimplicialComplex.face_subset_face_iff, OrdinalApprox.gfpApprox_mono_left, Convex.convexHull_eq, convexHull_convexHull_union_right, Subgroup.pairwiseDisjoint_leftCoset_cover_of_sum_inv_index_eq_one, SimpleGraph.egirth_le_length, PiNat.disjoint_cylinder_of_longestPrefix_lt, HasCardinalLT.Set.instIsCardinalFiltered, SimpleGraph.disjoint_image_val_universalVerts, ConvexCone.disjoint_hull_right_of_convex, MeasureTheory.Measure.exists_eq_disjoint_finiteSpanningSetsIn, EMetric.disjoint_closedBall_of_lt_infEdist, SimpleGraph.chromaticNumber_le_sum_left, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, FirstOrder.Language.Substructure.coe_closure_eq_range_term_realize, AlgebraicGeometry.targetAffineLocally_affineAnd_le, SimpleGraph.egirth_anti, Ideal.disjoint_primeCompl_of_liesOver, FirstOrder.Language.Substructure.closed, Prod.ωSup_snd, SimpleGraph.IsClique.card_le_chromaticNumber, essSup_comp_le_essSup_map_measure, MulAction.IsBlock.pairwiseDisjoint_range_smul, MulAction.isBlock_iff_pairwiseDisjoint_range_smul, isSaddlePointOn_iff, absConvexHull_isClosed, Set.encard_le_chainHeight_of_isChain, Set.exists_union_disjoint_ncard_eq_of_even, convexHull_convexHull_union_left, Ideal.finiteHeight_iff_lt, convexHull_min, Topology.RelCWComplex.Subcomplex.disjoint_openCell_subcomplex_of_not_mem, height_le_ringKrullDim_quotient_add_spanFinrank, convexHull_isClosed, Matroid.delete_isBasis_iff, AlgebraicGeometry.Scheme.exists_cover_of_mem_grothendieckTopology, ContinuousHom.forall_forall_merge', Ideal.height_le_height_add_encard_of_subset, closedAbsConvexHull_eq_closure_absConvexHull, Matroid.Dep.eRk_lt_encard, Metric.externalCoveringNumber_le_encard_self, Prod.ωSupImpl_fst, Matroid.isFlat_iff_isClosed, Matroid.IsCircuit.isCocircuit_disjoint_or_nontrivial_inter, PMF.toOuterMeasure_apply_eq_zero_iff, ConvexCone.gc_hull_coe, convexHull_prod, ringKrullDim_add_enatCard_le_ringKrullDim_mvPolynomial, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing, ContinuousHom.continuous, FirstOrder.Language.Substructure.closure_withConstants_eq, PowerSeries.le_order_subst_right, Metric.IsSeparated.encard_le_packingNumber, Dynamics.coverMincard_finite_iff, AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux, AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology, convexHull_eq_union, Topology.RelCWComplex.disjoint_skeletonLT_openCell, Matroid.eRk_compl_union_add_eRk_compl_inter_le, convexHull_eq, OrderHom.isGreatest_gfp, convexHull_smul, ModelWithCorners.disjoint_interior_boundary, ringKrullDim_le_ringKrullDim_add_spanFinrank, Set.Nonempty.convexHull, absConvexHull_eq_convexHull_balancedHull, FirstOrder.Language.Substructure.map_closure, Pi.ωScottContinuous_curry, Set.Finite.convexHull_eq_image, Metric.externalCoveringNumber_pos_iff, ContinuousHom.coe_apply, OrdinalApprox.lfp_mem_range_lfpApprox, AlgebraicGeometry.HasAffineProperty.affineAnd_le_isAffineHom, mem_convexHull_of_exists_fintype, ContinuousHom.toMono_coe, convexHull_rangle_single_eq_stdSimplex, FirstOrder.Language.Substructure.closure_le, Matroid.eRk_le_one_iff, AffineBasis.centroid_mem_interior_convexHull, AffineMap.image_convexHull, convexHull_union, convexHull_sub, FirstOrder.Language.Substructure.mem_closed_iff, SubAddAction.disjoint_val_image, Pi.uncurry_curry_ωScottContinuous, closure_subset_closedConvexHull, MeasureTheory.SimpleFunc.iSup_approx_apply, ConcaveOn.bddBelow_convexHull, Set.Countable.substructure_closure, MeasureTheory.exists_pair_mem_lattice_not_disjoint_vadd, FirstOrder.Language.Substructure.subset_closure_withConstants, convexHull_list_sum, Matroid.Indep.contract_isBase_iff, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes, Set.Finite.ncard_strictMonoOn, AlgebraicGeometry.IsOpenImmersion.le_monomorphisms, IntermediateField.gc, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app', Ideal.height_le_height_add_spanFinrank_of_le, Metric.packingNumber_pos_iff, AlgebraicGeometry.affineLocally_le, MulAction.IsBlock.smul_eq_or_disjoint, Metric.externalCoveringNumber_le_coveringNumber, convexHull_nonempty_iff, SimpleGraph.le_egirth, Prod.ωSup_fst, RealRMK.range_cut_partition, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, Metric.encard_le_of_isSeparated, Ideal.exists_disjoint_powers_of_span_eq_top, Matroid.eRk_le_encard, Dynamics.netEntropyInfEntourage_antitone, MeasureTheory.pairwise_disjoint_addFundamentalInterior, Topology.RelCWComplex.pairwiseDisjoint, Matroid.Coindep.delete_isBase_iff, closedAbsConvexHull_isClosed, HasCardinalLT.Set.instIsFilteredOfFactIsRegular, Monoid.le_minOrder, mem_convexHull_iff, Ideal.height_le_spanRank_toENat, Matroid.dualIndepMatroid_Indep, parallelepiped_eq_convexHull, cauchy_davenport_minOrder_mul, AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.app_invApp_assoc, OrdinalApprox.le_lfpApprox, PrimeSpectrum.localization_comap_range, CategoryTheory.Retract.projectiveDimension_le, IsLocalization.orderIsoOfPrime_apply_coe, VitaliFamily.FineSubfamilyOn.covering_disjoint, Matroid.one_le_eRank, Ideal.height_le_card_of_mem_minimalPrimes_span_finset, absConvexHull_eq_empty, Matroid.IsBasis'.contract_dep_iff, MvPowerSeries.le_weightedOrder_subst_of_forall_ne_zero, Metric.coveringNumber_le_encard_self, Matroid.delete_indep_iff, FirstOrder.Language.Substructure.cg_iff_empty_or_exists_nat_generating_family, Ideal.height_le_ringKrullDim_of_ne_top, Matroid.Indep.disjoint_loops, SimpleGraph.IsContained.vertexCoverNum_le_vertexCoverNum, MeasureTheory.hitting_eq_sInf, AlgebraicGeometry.Scheme.Hom.app_appIso_inv, OrderHom.map_inf_fixedPoints_le, isClosed_closedAbsConvexHull, OrderHom.omegaCompletePartialOrder_ωSup_coe, essSup_mono_measure', AffineIndependent.convexHull_inter, Urysohns.CU.disjoint_C_support_lim, ringKrullDim_le_of_surjective, convex_closedConvexHull, SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loop, closure_subset_closedAbsConvexHull, Metric.packingNumber_le_encard_self, IsLocalization.map_algebraMap_ne_top_iff_disjoint, AlgebraicGeometry.Scheme.codisjoint_zeroLocus, minSmoothness_monotone, Submodule.height_lt_top, FirstOrder.Language.Hom.eqOn_closure, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Prod.ωSupImpl_snd, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, HasCardinalLT.Set.isFiltered_of_aleph0_le, OrderHom.isFixedPt_gfp, Matroid.delete_isCircuit_iff, Set.Finite.convexHull_eq, OrderHom.isLeast_lfp_le, Module.supportDim_le_of_surjective, MeasureTheory.hittingAfter_anti, SimpleGraph.ConnectedComponent.Represents.disjoint_supp_of_notMem, AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.app_inv_app'_assoc, Set.ncard_strictMono, SimpleGraph.chromaticNumber_mono_of_hom, isClosed_closedConvexHull, Matroid.eRk_submod, OrderHom.map_lfp_comp, Monoid.minOrder_le_orderOf, Dynamics.one_le_netMaxcard_iff, NumberField.InfinitePlace.disjoint_isReal_isComplex, Metric.coveringNumber_anti, Vitali.exists_disjoint_covering_ae', Set.Finite.encard_strictMonoOn, AddSubgroup.pairwiseDisjoint_leftCoset_cover_of_sum_neg_index_eq_zero, Matroid.IsBasis'.contract_indep_iff, lowerSemicontinuousOn_iff_le_liminf, Dynamics.coverEntropyInfEntourage_monotone, balanced_absConvexHull, convexHull_subset_affineSpan, AddMonoid.minOrder_le_natCard, convexHull_eq_self, PowerSeries.le_weightedOrder_subst, disjoint_closedBall_ball_iff, IsLocalization.coe_primeSpectrumOrderIso_apply_coe_asIdeal, Scott.IsOpen.isUpperSet, Dynamics.le_coverMincard_image, balancedHull_convexHull_subseteq_absConvexHull, Matroid.spanning_iff_eRk_le, PiNat.exists_disjoint_cylinder, Algebra.gc, NumberField.mixedEmbedding.disjoint_negAt_plusPart, PMF.toMeasure_apply_eq_zero_iff, convexHull_range_eq_exists_affineCombination, convexIndependent_iff_notMem_convexHull_diff, OrderHom.map_gfp_comp, Topology.RelCWComplex.disjoint_base_iUnion_openCell, ContinuousHom.map_ωSup', AddAction.IsBlock.vadd_eq_or_disjoint, FirstOrder.Language.Substructure.lift_card_closure_le, natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zero, Polynomial.emultiplicity_le_one_of_separable, FirstOrder.Language.Substructure.closure_eq, PowerSeries.le_order_subst_left, FirstOrder.Language.Substructure.mem_closure_iff_of_isRelational, FirstOrder.Language.Substructure.closure_mono, ringKrullDim_le_ringKrullDim_quotient_add_encard, FirstOrder.Language.Substructure.closure_univ, AlgebraicGeometry.sourceLocalClosure.le, FirstOrder.Language.Substructure.closure_image, AbsConvex.absConvexHull_eq, isLUB_range_ωSup, closedConvexHull_isClosed, Topology.RelCWComplex.disjoint_interior_base_iUnion_closedCell, Matroid.setOf_dep_eq, closedAbsConvexHull_closure_eq_closedAbsConvexHull, AlgebraicGeometry.Spec.map_app, Complex.rectangle_eq_convexHull, FirstOrder.Language.Substructure.cg_closure_singleton, Metric.coveringNumber_le_one_of_ediam_le, convexHull_subset_closedConvexHull, FirstOrder.Language.Structure.fg_iff, FirstOrder.Language.Substructure.cg_closure, Dynamics.coverMincard_monotone_subset, Finset.centerMass_mem_convexHull_of_nonpos
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