Documentation Verification Report

Defs

📁 Source: Mathlib/Order/ConditionallyCompletePartialOrder/Defs.lean

Statistics

MetricCount
DefinitionsConditionallyCompletePartialOrder, toConditionallyCompletePartialOrderInf, toConditionallyCompletePartialOrderSup, toInfSet, ConditionallyCompletePartialOrderInf, toInfSet, toPartialOrder, ConditionallyCompletePartialOrderSup, toPartialOrder, toSupSet
10
TheoremsisGLB_csInf_of_directed, isGLB_csInf_of_directed, isLUB_csSup_of_directed, ciInf_le, ciSup_le, le_ciInf, le_ciSup, csInf_le, csSup_le, isGLB_csInf, isLUB_csSup, le_csInf, le_csSup
13
Total23

ConditionallyCompletePartialOrder

Definitions

NameCategoryTheorems
toConditionallyCompletePartialOrderInf 📖CompOp
713 mathmath: continuousNeg_iInf, Nat.iInf_le_succ', ProbabilityTheory.bayesRisk_of_subsingleton, ENNReal.iInf_div_of_ne, MeasureTheory.OuterMeasure.map_iInf, OrderIso.map_radical, Set.Iic.coe_sInf, continuous_sInf_dom₂, PolynormableSpace.sInf, OrderIso.map_csInf, StarSubalgebra.coe_sInf, Filter.HasBasis.liminf_eq_ite, SetTheory.PGame.grundyValue_eq_sInf_moveLeft, GroupTopology.toTopologicalSpace_iInf, equicontinuousWithinAt_iInf_dom, le_mul_ciInf, isSaddlePointOn_value, iSupIndep.injOn_iInf, ContinuousMap.compactOpen_eq_iInf_induced, MeasureTheory.iInf_mul_le_lintegral, sInfHom.le_apply_bliminf, ENNReal.add_sInf, csSup_image2_eq_csInf_csInf, Algebra.mem_iInf, csInf_of_not_bddBelow, nhds_sInf, Ordinal.sInf_compl_lt_lift_ord_succ, MeasureTheory.hittingBtwn_apply_mono_right, IsMinOn.iInf_eq, continuousMul_sInf, TopologicalSpace.Closeds.iInf_def, MeasureTheory.hittingBtwn_mono_left, topologicalGroup_iInf, MeasureTheory.le_hitting_of_exists, eq_sInf_coatoms, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, DirectedOn.subset_Icc_csInf_csSup, FormalMultilinearSeries.radius_pi_eq_iInf, AntitoneOn.map_sSup_of_continuousWithinAt, Finset.inf'_univ_eq_ciInf, Set.Finite.lt_csInf_iff, RightOrdContinuous.map_sInf, ENat.iInf_mul_of_ne, ciInf_sub, le_csInf_iff, R1Space.iInf, MeasureTheory.hittingAfter_bot_le_iff, upperSemicontinuousAt_biInf, csInf_mem, nhds_iInf, Ordinal.log_def, Bornology.IsBounded.subset_Icc_sInf_sSup, add_ciInf, AffineSubspace.mem_sInf_iff, MeasureTheory.hittingBtwn_univ, ContinuousLinearMap.nnnorm_def, MeasureTheory.le_hitting, TopologicalSpace.eq_induced_by_maps_to_sierpinski, OrderIso.map_csInf', isLeast_csInf, le_ciInf_add_ciInf, Subalgebra.op_sInf, csInf_insert, continuousVAdd_sInf, le_ciInf_mul_ciInf, ENat.iInf_toNat, GaloisConnection.u_ciInf, Algebra.mem_sInf, ENNReal.ofReal_iInf, MeasureTheory.hittingBtwn_mem_Icc, generateFrom_sUnion, csInf_zero, Subalgebra.centralizer_coe_iSup, ProbabilityTheory.bayesRisk_of_subsingleton', Monotone.csInf_image_le, ENNReal.iInf_ennreal, Set.Nonempty.eq_Icc_iff_int, Set.Iic_ciInf, MeasureTheory.lowerCrossingTime_le, Submodule.spanRank_toENat_eq_iInf_encard, Sublocale.coe_iInf, NonUnitalAlgebra.sInf_toNonUnitalSubsemiring, MeasureTheory.hittingAfter_mono, ciInf_add, NonUnitalStarAlgebra.mem_sInf, AEMeasurable.iInf, Nat.iInf_lt_succ', IsCompact.isLeast_sInf, generateFrom_iUnion_isOpen, MeasureTheory.Measure.mkMetric_apply, ENNReal.mul_iInf, TopologicalSpace.Closeds.coe_iInf, MeasureTheory.Measure.iInf_IicSnd_gt, csInf_eq_of_forall_ge_of_forall_gt_exists_lt, Finite.ciInf_le, MeasureTheory.hitting_le_of_mem, MeasureTheory.lintegral_iInf_ae, ENNReal.inv_sSup, MeasurableSpace.measurableSet_iInf, IntermediateField.coe_iInf, MeasureTheory.OuterMeasure.comap_iInf, csInf_lt_iff, Filter.liminf_eq_iSup_iInf_of_nat', MeasureTheory.lintegral_iInf', Cardinal.lift_iInf, Filter.HasBasis.limsInf_eq_iSup_sInf, AddGroupTopology.toTopologicalSpace_sInf, Order.succ_eq_iInf, Filter.bliminf_eq_iSup_biInf_of_nat, upperSemicontinuous_biInf, IsClosed.sInf_mem, NonUnitalStarAlgebra.iInf_toNonUnitalSubalgebra, Ordinal.card_sInf_range_compl_le_lift, tendsto_atBot_ciInf, NonUnitalStarAlgebra.coe_sInf, ENNReal.le_iInf₂_add_iInf₂, NNReal.natCast_iInf, isGLB_ciInf, Filter.blimsup_eq, essInf_eq_ciInf, Pi.induced_restrict, Filter.HasBasis.limsup_eq_sInf_univ_of_empty, MeasureTheory.OuterMeasure.iInf_apply', MeasureTheory.hittingBtwn_mem_set, MeasureTheory.Measure.sInf_caratheodory, ProbabilityTheory.bayesRisk_eq_iInf_measure_of_subsingleton, Algebra.coe_iInf, MeasureTheory.OuterMeasure.restrict_iInf, MeasureTheory.OuterMeasure.le_sum_caratheodory, ENNReal.iInf_div, MeasureTheory.stoppedValue_hitting_mem, Filter.HasBasis.limsup_eq_ite, CompleteSublattice.coe_iInf, ENat.iInf_mul', IntermediateField.iInf_toSubfield, continuousNeg_sInf, MeasureTheory.OuterMeasure.map_iInf_comap, Pi.Lex.sInf_apply, csInf_div, Filter.HasBasis.limsup_eq_sInf_iUnion_iInter, ENNReal.iInf_sum, AffineSubspace.affineSpan_eq_sInf, MeasureTheory.hittingBtwn_mono, MeasureTheory.stoppedValue_hittingBtwn_mem, Ordinal.card_sInf_range_compl_le, MeasureTheory.hitting_le_iff_of_exists, regularSpace_sInf, Algebra.sInf_toSubsemiring, Algebra.sInf_toSubmodule, Monotone.rightLim_eq_sInf, topologicalAddGroup_sInf, ciInf_of_not_bddBelow, Nimber.add_def, MeasureTheory.upperCrossingTime_mono, continuous_iInf_rng, MeasureTheory.hittingBtwn_apply_anti, ciInf_mul, Set.Nonempty.ordConnected_iff_of_bdd', csInf_Ioc, MeasureTheory.hittingAfter_mem_set, MeasureTheory.hittingBtwn_bot_le_iff, MeasureTheory.Adapted.isStoppingTime_hittingBtwn, CompleteSublattice.coe_sInf', ENat.iInf_coe_lt_top, NonUnitalAlgebra.mem_iInf, ciInf_le_ciSup, csInf_mul, IsConnected.Ioo_csInf_csSup_subset, exists_eq_ciInf_of_finite, MeasureTheory.hitting_mem_Icc, ENat.iInf_mul, sInf_eq_argmin_on, AffineSubspace.mem_iInf_iff, PseudoMetricSpace.dist_ofPreNNDist, sInf_sub, MvPowerSeries.le_order_subst, ciInf_le', TopologicalSpace.Closeds.mem_sInf, MeasureTheory.lowerCrossingTime_le_upperCrossingTime_succ, ENNReal.iInf_add_iInf, AEMeasurable.biInf, MeasureTheory.OuterMeasure.trim_eq_iInf', CompleteSublattice.sInfClosed, SimpleGraph.chromaticNumber_eq_iInf, sInfHom.continuous, upperSemicontinuousOn_iInf, ciInf_eq_univ_of_not_bddBelow, Sublocale.sInf_mem, IsCompact.sInf_mem, Ordinal.succ_log_def, AlgebraicGeometry.IsLocalIso.eq_iInf, csSup_lowerBounds_eq_csInf, ContinuousOn.sInf_image_Icc_le, MeasureTheory.le_hittingBtwn, essSup_eq_sInf, MeasureTheory.upperCrossingTime_le_lowerCrossingTime, MeasureTheory.Content.outerMeasure_eq_iInf, essInf_count, MeasureTheory.hitting_eq_end_iff, Ordinal.enumOrd_zero, ciInf_mem, IntermediateField.sInf_toSubalgebra, ciInf_le_of_le, sSup_inv, ENNReal.iInf_mul_of_ne, MeasureTheory.hittingBtwn_le_of_mem, MonotoneOn.tendsto_nhdsGT, ENat.sInf_eq_zero, MeasureTheory.OuterMeasure.map_iInf_le, Monotone.map_csInf, WithTop.iInf_coe_eq_top, ENNReal.add_iInf, sInf_mul, induced_sInf, sInf_neg, csInf_le', SetTheory.PGame.grundyValue_eq_sInf_moveRight, PrimeSpectrum.iInf_localization_eq_bot, IsCoatom.sInf_le, ENNReal.inv_iSup, sInf_inv, TopCat.nonempty_isLimit_iff_eq_induced, MeasureTheory.OuterMeasure.iInf_apply, Filter.liminf_eq_sSup_sInf, iInf_eq_iInf_subseq_of_monotone, NonUnitalStarAlgebra.mem_iInf, CompleteSublattice.sInfClosed', MeasureTheory.isStoppingTime_hittingBtwn_isStoppingTime, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, CompletePseudometrizable.iInf, ContinuousOn.image_uIcc_eq_Icc, continuousInv_sInf, iInf_eq_of_tendsto, upperSemicontinuous_ciInf, Set.einfsep_insert, MeasureTheory.hitting_le, Filter.blimsup_eq_iInf_biSup, DirectedOn.csInf_le_csSup, ContinuousOn.image_Icc, TopologicalSpace.secondCountableTopology_iInf, cbiInf_eq_of_not_forall, LocallyConvexSpace.iInf, MeasureTheory.OuterMeasure.biInf_apply, Nat.iInf_le_succ, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp, ENNReal.iInf_add, ProbabilityTheory.bayesRisk_const_of_nonempty, AntitoneOn.map_csSup_of_continuousWithinAt, ENNReal.mul_iInf', MeasureTheory.hittingAfter_eq_top_iff, Order.radical_le_coatom, continuousSMul_sInf, MeasureTheory.measure_iInter_eq_iInf_measure_iInter_le, generateFrom_iUnion, csInf_Ioi, IsCompact.lt_sInf_iff_of_continuous, MeasureTheory.Filtration.rightCont_apply, EMetric.infEdist_biUnion, ENNReal.iInf_add_iInf_of_monotone, Set.einfsep_insert_le, LinearMap.mem_span_iff_continuous_of_finite, ENat.sub_iSup, ENat.iInf_eq_top_of_isEmpty, Function.support_iInf, Cardinal.ord_eq_Inf, MeasureTheory.hittingAfter_univ, le_ciInf_iff', ENat.iInf_coe_eq_top, untrop_sum, Set.Icc.coe_iInf, MeasureTheory.hittingBtwn_apply_mono_left, mul_ciInf, MeasureTheory.hittingBtwn_anti, MvPowerSeries.le_weightedOrder_subst, ENat.exists_eq_iInf, IsCompact.measure_eq_iInf_isOpen, UniformOnFun.topologicalSpace_eq, ENNReal.sub_eq_sInf, Finset.Nonempty.csInf_eq_min', MeasureTheory.OuterMeasure.ofFunction_eq_iInf_mem, MeasureTheory.Filtration.rightCont_def, Antitone.map_csSup_of_continuousAt, GroupTopology.toTopologicalSpace_sInf, AffineSubspace.direction_iInf_of_mem, GaloisConnection.u_csInf, dimH_eq_iInf, continuousAdd_iInf, MeasureTheory.Measure.sInf_apply, ENNReal.le_iInf_mul, regularSpace_iInf, Sublocale.coe_sInf, equicontinuous_iInf_dom, Monotone.measure_iInter, MeasureTheory.Measure.inf_apply, MeasureTheory.hittingAfter_apply_anti, sInf_one, InfClosed.biInf_mem_of_nonempty, IsIntegrallyClosed.iInf, ciInf_eq_of_forall_ge_of_forall_gt_exists_lt, InfClosed.iInf_mem_of_nonempty, Sublocale.sInf_mem', upperSemicontinuous_iInf, WithTop.iInf_coe_lt_top, ENat.coe_iInf, ENNReal.inv_iInf, ENat.mul_iInf_of_ne, eq_Icc_of_connected_compact, EMetric.infEdist_iUnion, continuous_sInf_dom, MonotoneOn.csInf_eq_of_subset_of_forall_exists_le, sInf_mem_closure, UniformSpace.toTopologicalSpace_sInf, ENNReal.toNNReal_iInf, csInf_upperBounds_range, Subalgebra.unop_iInf, MeasureTheory.inducedOuterMeasure_eq_iInf, MeasureTheory.lintegral_iInf, MeasureTheory.le_iInf_lintegral, NonUnitalAlgebra.coe_iInf, csInf_eq_bot_of_bot_mem, NNReal.le_iInf_mul_iInf, ENNReal.le_iInf_mul_iInf, Monotone.ciInf_comp_tendsto_atBot, Filter.HasBasis.liminf_eq_iSup_iInf, Algebra.iInf_toSubsemiring, Cardinal.sInf_eq_zero_iff, sInf_iUnion_Ici, PolynormableSpace.iInf, Set.Iic.coe_iInf, MeasureTheory.Filtration.rightCont_eq_of_not_isMax, topologicalGroup_sInf, ProbabilityTheory.bayesRisk_le_iInf, ContinuousOn.image_uIcc, Manifold.riemannianEDist_def, ciInf_div, RightOrdContinuous.map_sInf', Ordinal.cof_eq_sInf_lsub, MeasureTheory.hitting_bot_le_iff, Set.Iic.coe_biInf, csInf_le_csSup, AlgebraicGeometry.Scheme.IdealSheafData.support_iSup, Set.Icc.coe_sInf, MonotoneOn.map_csInf, StarSubalgebra.mem_iInf, SimpleGraph.edist_eq_sInf, MonotoneOn.tendsto_nhdsWithin_Ioo_right, Antitone.map_sSup_of_continuousAt, Filter.liminf_eq_iSup_iInf_of_nat, AntitoneOn.sInf_image_Icc, iInf_eq_of_forall_le_of_tendsto, csSup_inv, CompleteLattice.isCoatomistic_iff, MeasureTheory.hittingBtwn_mono_right, le_ciInf, isGLB_ciInf_set, AffineSubspace.direction_iInf, Pi.induced_precomp, Measurable.sInf, Set.indicator_iInter_apply, UniformSpace.toTopologicalSpace_iInf, csInf_image2_eq_csSup_csInf, Antitone.ciInf_comp_tendsto_atTop, Nat.iInf_lt_succ, Subalgebra.op_iInf, Filter.limsSup_eq_iInf_sSup, smul_iInf_le, trop_iInf, Set.Nonempty.ordConnected_iff_of_bdd, Algebra.iInf_toSubmodule, ciInf_add_ciInf_le_ciInf_add, Submodule.spanRank_toENat_eq_iInf_finset_card, IntermediateField.map_iInf, isSaddlePointOn_iff', sSup_div, ENNReal.mul_iInf_of_ne, le_csInf_iff', IsCompact.isGLB_sInf, Finset.untrop_sum, ENat.coe_sInf, eq_Icc_csInf_csSup_of_connected_bdd_closed, continuousAdd_sInf, MeasureTheory.hittingBtwn_isStoppingTime, ciInf_eq_bot_of_bot_mem, sInf_zero, LocallyConvexSpace.sInf, Set.einfsep_eq_iInf, NonUnitalAlgebra.map_iInf, MeasureTheory.hittingAfter_eq_sInf, Directed.ciInf_le_ciSup, WithTop.isGLB_sInf, ENNReal.iInf_mul_iInf, NNReal.le_mul_iInf, ExpGrowth.expGrowthInf_iInf, completelyRegularSpace_iInf, continuousSMul_iInf, csInf_Ioo, MeasureTheory.OuterMeasure.sInf_apply, IsTopologicalBasis.iInf, MeasureTheory.iInf_le_lintegral, upperSemicontinuousOn_ciInf, MeasureTheory.hitting_eq_hitting_of_exists, iSup₂_iInf₂_le_iInf₂_iSup₂, Cardinal.succ_def, NonUnitalStarAlgebra.coe_iInf, ENNReal.iInf_ne_top, MonotoneOn.sInf_image_Icc, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, StieltjesFunction.length_eq, ciInf_le, csInf_one, MeasureTheory.Filtration.rightCont_eq, csInf_eq_univ_of_not_bddBelow, MeasureTheory.measure_eq_iInf', le_csInf_iff'', ENNReal.iInf_mul', MeasureTheory.lintegral_iInf_directed_of_measurable, Pi.induced_restrict_sUnion, Set.mulIndicator_iInter_apply, MeasureTheory.hitting_mono, Cardinal.sInf_empty, Metric.infEDist_iUnion, sSup_neg, IsGLB.ciInf_set_eq, MeasureTheory.Measure.iInf_rat_gt_prod_Iic, MeasurableSpace.map_iInf, MeasureTheory.OuterMeasure.boundedBy_apply, equicontinuousAt_iInf_dom, AntitoneOn.tendsto_nhdsLT, csInf_neg, MeasureTheory.OuterMeasure.restrict_biInf, ENat.mul_iInf, sSup_sub, MeasureTheory.hittingAfter_mem_set_of_ne_top, Antitone.tendsto_nhdsLT, ProbabilityTheory.bayesRisk_le_iInf', Filter.liminf_eq_iSup_iInf, ExpGrowth.expGrowthInf_biInf, RightOrdContinuous.map_csInf, Ordinal.lift_card_sInf_compl_le, ENNReal.sub_iSup, Antitone.measure_iInter, AffineSubspace.direction_sInf, Function.mulSupport_iInf, WithBot.coe_biInf, InfClosed.biInf_mem, MeasurableSpace.measurableSet_sInf, IsCompact.continuous_sInf, ProbabilityTheory.bayesRisk_const_of_neZero, MeasureTheory.measure_eq_iInf, MeasureTheory.hitting_lt_iff, MeasureTheory.hittingBtwn_le, MeasureTheory.le_iInf₂_lintegral, upperSemicontinuousOn_biInf, disjointed_eq_inf_compl, ENNReal.le_iInf_add_iInf, induced_to_pi, iSupIndep.iInf, ENNReal.iInf_mul, MeasureTheory.hittingBtwn_eq_sInf, continuousMul_iInf, ENNReal.toReal_iInf, MeasureTheory.hittingAfter_isStoppingTime, IntermediateField.normal_iInf, AffineSubspace.direction_sInf_of_mem, MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict, ENNReal.sInf_add, tendsto_atTop_ciInf, Sublocale.iInf_mem, ENNReal.iInf_coe_lt_top, TopCat.induced_of_isLimit, Nimber.mul_def, ProbabilityTheory.bayesRisk_const, TopologicalSpace.Closeds.iInf_mk, NNReal.coe_iInf, OrderIso.map_ciInf, Antitone.map_iSup_of_continuousAt, MeasureTheory.hittingBtwn_le_iff_of_lt, SimpleGraph.chromaticNumber_eq_biInf, MeasureTheory.hittingBtwn_eq_end_iff, continuous_iInf_dom, Antitone.iInf_comp_tendsto_atTop, StarSubalgebra.sInf_toSubalgebra, MeasureTheory.upperCrossingTime_zero', MaximalSpectrum.iInf_localization_eq_bot, Filter.HasBasis.blimsup_eq_iInf_iSup, sInf_add, RightOrdContinuous.map_iInf, ENNReal.iInf₂_add, upperSemicontinuousWithinAt_biInf, csInf_upperBounds_eq_csSup, csInf_union, subset_Icc_csInf_csSup, Filter.limsup_eq_iInf_iSup, Cardinal.lift_sInf, MeasureTheory.OuterMeasure.top_apply', Monotone.iInf_comp_tendsto_atBot, Order.succ_eq_csInf, Measurable.iInf, MeasureTheory.Measure.hausdorffMeasure_apply, AffineSubspace.comap_supr, InfClosed.iInf_mem, inducing_iInf_to_pi, Filter.iInf_le_liminf, ProbabilityTheory.bayesRisk_discard, IntermediateField.sInf_toSubfield, essInf_count_eq_ciInf, isSaddlePointOn_iff, ENNReal.sub_iInf, MeasureTheory.lowerCrossingTime_mono, MeasureTheory.hitting_mem_set, NonUnitalAlgebra.mem_sInf, le_csInf_inter, csSup_div, MeasureTheory.hittingAfter_le_iff, ciInf_lt_iff, Set.measure_eq_iInf_isOpen, tendsto_atTop_iInf, csInf_lt_of_lt, Ordinal.sInf_compl_lt_ord_succ, equicontinuousOn_iInf_dom, ciInf_mul_ciInf_le_ciInf_mul, MeasureTheory.OuterMeasure.sInf_apply', BoundedContinuousFunction.nndist_eq, IsCompact.measure_eq_biInf_integral_hasCompactSupport, le_ciInf_mul, StarSubalgebra.coe_iInf, ciInf_set_le, StarSubalgebra.mem_sInf, Dense.ciInf', MeasureTheory.upperCrossingTime_le, Algebra.adjoin_eq_sInf, MeasureTheory.isStoppingTime_hitting_isStoppingTime, Filter.limsup_eq_iInf_iSup_of_nat', InfClosed.sInf_mem_of_nonempty, Finset.inf'_id_eq_csInf, MeasureTheory.hittingAfter_apply_mono, essInf_eq_iInf, WithTop.isGLB_sInf', csInf_sub, NNReal.sInf_empty, NNReal.mul_iInf, upperSemicontinuousAt_ciInf, MeasureTheory.StronglyAdapted.isStoppingTime_leastGE, MeasureTheory.le_hittingAfter, le_ciInf_set_iff, ciInf_le_of_le', GaloisConnection.u_ciInf_set, NNReal.iInf_mul, untrop_sum_eq_sInf_image, MeasureTheory.OuterMeasure.sInf_eq_boundedBy_sInfGen, Antitone.map_ciSup_of_continuousAt, NonUnitalAlgebra.coe_sInf, essInf_cond_count_eq_ciInf, MeasureTheory.hittingBtwn_of_lt, BooleanSubalgebra.sInf_mem, ciInf_mono, NNReal.iInf_empty, Filter.liminf_top_eq_iInf, IsClosed.csInf_mem, Finset.inf'_eq_csInf_image, MeasureTheory.hittingBtwn_lt_iff, BooleanSubalgebra.biInf_mem, MeasureTheory.OuterMeasure.sInfGen_def, Finset.Nonempty.csInf_mem, Directed.measure_iInter, Pi.induced_precomp', ENat.mul_iInf', RightOrdContinuous.map_ciInf, Filter.limsInf_principal_eq_sInf, continuousInv_iInf, csInf_image2_eq_csSup_csSup, Filter.liminf_top_eq_ciInf, NNReal.le_iInf_add_iInf, AffineSubspace.coe_iInf, BooleanSubalgebra.iInf_mem, MeasureTheory.hittingAfter_le_of_mem, Cardinal.iInf_eq_zero_iff, csInf_eq_csInf_of_forall_exists_le, exists_seq_tendsto_sInf, Filter.blimsup_eq_iInf_biSup_of_nat, Filter.limsup_eq_sInf_sSup, ENNReal.hasProd_iInf_prod, Pi.Colex.sInf_apply, csSup_image2_eq_csSup_csInf, Filter.HasBasis.limsSup_eq_iInf_sSup, Measurable.biInf, ENat.iInf_eq_zero, MeasureTheory.hitting_of_le, Filter.limsup_eq_iInf_iSup_of_nat, TopologicalSpace.Closeds.coe_sInf, csInf_image2_eq_csInf_csInf, IsCoatom.iInf_le, Measurable.iInf_Prop, MeasureTheory.hitting_of_lt, withSeminorms_iInf, ENNReal.add_iInf₂, le_add_ciInf, upperSemicontinuousAt_iInf, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, upperSemicontinuousWithinAt_iInf, Filter.limsup_eq, MeasureTheory.OuterMeasure.biInf_apply', IsCompact.exists_sInf_image_eq, OrderIso.map_ciInf_set, csInf_image2_eq_csInf_csSup, csInf_le_csInf', AddGroupTopology.toTopologicalSpace_iInf, NonUnitalStarAlgebra.sInf_toNonUnitalSubalgebra, csSup_sub, Algebra.map_iInf, NNReal.agm_eq_ciInf, IsGLB.ciInf_eq, ENNReal.iInf_gt_eq_self, Filter.limsInf_eq_iSup_sInf, MeasureTheory.Filtration.rightCont_eq_of_neBot_nhdsGT, IntermediateField.iInf_toSubalgebra, csInf_univ, MeasureTheory.hittingBtwn_of_le, Set.einfsep_iUnion_mem_option, ENNReal.toNNReal_sInf, Algebra.coe_sInf, MeasureTheory.OuterMeasure.trim_eq_iInf, ENNReal.inv_sInf, PolishSpace.iInf, ENNReal.coe_iInf, Monotone.le_csInf_image, Filter.bliminf_eq_iSup_biInf, induced_iInf, sInf_within_of_ordConnected, StarSubalgebra.map_iInf, TopologicalSpace.Closeds.mem_iInf, NonUnitalAlgebra.sInf_toSubmodule, MeasureTheory.hitting_eq_sInf, TopCat.limit_topology, iInf_eq_iInf_subseq_of_antitone, ENat.toENNReal_iInf, Filter.HasBasis.limsup_eq_iInf_iSup, MeasureTheory.OuterMeasure.map_biInf_comap, AlgebraicGeometry.Scheme.IdealSheafData.support_sSup, NNReal.le_iInf_mul, Filter.limsInf_principal_eq_csSup, upperSemicontinuousWithinAt_ciInf, IsPreconnected.mem_intervals, csSup_lowerBounds_range, csSup_image2_eq_csInf_csSup, le_ciInf_iff, IsClosed.isLeast_csInf, tendsto_atBot_iInf, Filter.HasBasis.limsup_eq_ciInf_ciSup, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSup, MeasureTheory.OuterMeasure.restrict_iInf_restrict, InfClosed.sInf_mem, ENNReal.tprod_eq_iInf_prod, csInf_add, csInf_mem_closure, MeasureTheory.OuterMeasure.ofFunction_apply, IntermediateField.coe_sInf, ProbabilityTheory.bayesRisk_const', R1Space.sInf, MeasureTheory.hittingBtwn_le_iff_of_exists, MeasureTheory.hittingAfter_anti, Monotone.tendsto_nhdsGT, MeasureTheory.hitting_le_iff_of_lt, StarSubalgebra.iInf_toSubalgebra, ENNReal.iInf_div', csInf_inv, MeasureTheory.hittingAfter_lt_iff, Filter.HasBasis.liminf_eq_ciSup_ciInf, csInf_pair, LinearMap.mem_span_iff_continuous, sInf_div, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSup, ENNReal.iInf_coe_eq_top, trop_sInf_image, topologicalAddGroup_iInf, Dense.ciInf, ENNReal.coe_sInf, Antitone.ciInf_comp_tendsto_atTop_of_linearOrder, MeasureTheory.iInf_mul_le_setLIntegral, Monotone.ciInf_comp_tendsto_atBot_of_linearOrder, continuous_sInf_rng, Metric.infEDist_biUnion, MeasureTheory.Adapted.isStoppingTime_hittingBtwn_isStoppingTime, le_ciInf_add, MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty, IsPreconnected.Ioi_csInf_subset, AntitoneOn.tendsto_nhdsWithin_Ioo_left, GaloisConnection.u_csInf', NonUnitalAlgebra.iInf_toSubmodule, NNReal.iInf_const_zero, WithTop.coe_sInf, SSet.Subcomplex.preimage_iInf, Order.succ_eq_sInf, MeasureTheory.le_hittingBtwn_of_exists, MeasureTheory.hitting_isStoppingTime, MeasureTheory.Adapted.isStoppingTime_hittingAfter, Set.Nonempty.csInf_mem, upperClosure_eq_Ici_csInf, AffineSubspace.coe_sInf, continuousVAdd_iInf, Ordinal.sInf_empty, MeasureTheory.Filtration.sInf_def, IsTopologicalBasis.iInf_induced, NonUnitalStarAlgebra.map_iInf, MeasureTheory.hittingBtwn_eq_hittingBtwn_of_exists, IsCompact.exists_sInf_image_eq_and_le, csSup_neg, SimpleGraph.radius_eq_iInf_iSup_edist, Subalgebra.unop_sInf, CompleteSublattice.coe_sInf, NNReal.coe_sInf, ENNReal.toReal_sInf
toConditionallyCompletePartialOrderSup 📖CompOp
1606 mathmath: BooleanSubalgebra.map_iSup, CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSup, Ordinal.iSup_eq_iSup, Order.coheight_add_one_le, IsClosed.sSup_mem, upperBounds_supClosure, Filter.bliminf_sup_le_or_aux_right, Set.Finite.t2_separation, Ordinal.iSup_eq_bsup, TopCat.binaryCofan_isColimit_iff, dirSupClosed_iff_forall_sSup, tendsto_zero_iff_meromorphicOrderAt_pos, csSup_pair, Metric.ball_disjoint_ball, Ordinal.lift_card_iSup_le_sum_card, SimpleGraph.ediam_le_iff, OrderIso.map_radical, SimpleGraph.ediam_anti, Set.Iic.coe_sInf, Acc.rank_eq, homotopyEquivalences_le_quasiIso, Cardinal.mk_sUnion_le, Ordinal.iSup_pow_natCast, Filter.liminf_eq, Order.LTSeries.length_le_krullDim, ENat.floor_pos, AddSubmonoid.smul_iSup, Module.rank_def, isFullyInvariant_iff_sSup_isotypicComponents, Filter.HasBasis.liminf_eq_ite, Nat.iSup_lt_succ', MeasureTheory.lintegral_def, Continuous.strictMono_of_inj_boundedOrder', Ordinal.sup_eq_lsub_iff_lt_sup, FirstOrder.Language.Substructure.mem_sSup_of_directedOn, isSaddlePointOn_value, Order.krullDim_le_of_strictComono_and_surj, sInfHom.le_apply_bliminf, Measurable.biSup, EMetric.hausdorffEdist_iUnion_le, IntermediateField.sSup_toSubfield, ENat.sSup_eq_top_of_infinite, EisensteinSeries.hasSum_e2Summand_symmetricIcc, MulAction.IwasawaStructure.is_generator, AlgebraicGeometry.iSup_affineOpens_eq_top, Subalgebra.coe_iSup_of_directed, dimH_sUnion, MeasureTheory.hittingBtwn_apply_mono_right, Antitone.Icc, PartENat.ofENat_le, Subfield.mem_sSup_of_directedOn, MeasureTheory.hittingBtwn_mono_left, setOf_isOpen_iSup, RootPairing.Base.not_nonneg_iff_neg_of_sum_mem_range_root, isClosed_iSup_iff, lowerSemicontinuousOn_biSup, MeasureTheory.lintegral_iSup', Filter.bliminf_sup_le_and_aux_right, SeparatedNhds.disjoint, Cardinal.lift_iSup_le_lift_iSup, Order.krullDim_lt_coe_iff, eq_sInf_coatoms, TopologicalSpace.Opens.coe_iSup, TopCat.Presheaf.coveringOfPresieve.iSup_eq_of_mem_grothendieck, disjoint_or_subset_of_isClopen, FirstOrder.Language.Substructure.mem_iSup_of_directed, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, NNReal.iSup_of_not_bddAbove, Ordinal.sup_eq_lsub_iff_succ, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, NatOrdinal.instAddLeftReflectLE, SSet.modelCategoryQuillen.I_le_monomorphisms, supClosure_eq_self, MonotoneOn.Icc, Filter.blimsup_and_le_inf, Padic.withValUniformEquiv_norm_le_one_iff, tendsto_cobounded_iff_meromorphicOrderAt_neg, lowerSemicontinuousWithinAt_iSup, Set.Finite.lt_csInf_iff, NNReal.mul_iSup_le, NatOrdinal.lt_mul_iff, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, ENat.smul_sSup, Disjoint.of_span₀, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, MeasureTheory.setLIntegral_le_iSup_mul, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, Ordinal.iSup_typein_succ, LieSubmodule.iSup_toSubmodule, antitone_continuousOn, MeasureTheory.hittingAfter_bot_le_iff, isSublattice_latticeClosure, ProbabilityTheory.condIndep_iSup_of_antitone, IntermediateField.isPurelyInseparable_iSup, AlgebraicGeometry.IsAffineOpen.iSup_of_disjoint, strictMono_nhdsSet, Filter.bliminf_sup_le_and_aux_left, Metric.hausdorffEDist_def, SSet.iSup_subcomplexOfSimplex_prod_eq_top, continuous_sSup_dom, ConditionallyCompleteLinearOrder.toCompactIccSpace, Monotone.Ici, isPreconnected_iff_ordConnected, CategoryTheory.MorphismProperty.HasCardinalLT.iSup, AddMonoidHom.noncommPiCoprod_range, Subalgebra.op_sSup, isClosed_sSup_iff, Bornology.IsBounded.subset_Icc_sInf_sSup, iSupIndep.disjoint_biSup, Finset.ordConnected_range_coe, CompleteSublattice.isComplemented_iff, AntitoneOn.Ici, ciSup_partialSups_eq', Cardinal.iSup_of_empty, Order.krullDim_nonneg_iff, MeasureTheory.hittingBtwn_univ, SSet.finite_iSup_iff, Submodule.map₂_iSup_right, inf_mem_infClosure, sSup_Iio_eq_self_iff_isSuccPrelimit, IsOpen.measure_eq_iSup_isClosed, Cardinal.iSup_lt_of_isRegular, latticeClosure_univ, monotone_hausdorffEntourage, ENat.gc_toENNReal_floor, Ideal.mem_sSup_of_mem, Metric.hausdorffEDist_iUnion_le, IsCompactlyGenerated.BooleanGenerators.sSup_inter, ENNReal.iSup_pow_of_ne_zero, IsCompactlyGenerated.BooleanGenerators.isAtom, ENat.iSup_zero, NFA.pumping_lemma, ProbabilityTheory.Kernel.indep_iSup_directed_limsup, MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top, isPreconnected_Ici, NNReal.coe_sSup, Set.indicator_iUnion_apply, ProbabilityTheory.indep_iSup_of_monotone, MeasureTheory.lintegral_iSup_ae, isLeast_csInf, SeparatedNhds.disjoint_closure_left, ENat.ceil_le_ceil, IntermediateField.coe_iSup_of_directed, Order.length_le_coheight, Submodule.map_iSup, Int.padicValuation_lt_one_iff, Order.height_add_one_le, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, Submodule.mem_iSup_iff_exists_finsupp, Filter.Realizer.map_F, Ordinal.sup_succ_le_lsub, ClosedSubmodule.coe_sSup, IsUltrametricDist.ball_subset_trichotomy, Algebra.sSup_def, SimpleGraph.Walk.edist_le, Ordinal.iSup_le_lsub, Ordinal.card_iSup_Iio_le_sum_card, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, isGLB_infClosure, IsClosed.upperClosure, Monotone.Ioo, Order.krullDim_pos_iff, SimpleGraph.ComponentCompl.disjoint_right, Nimber.succ_def, Order.krullDim_le_one_iff, Filter.bliminf_sup_le_and, SimpleGraph.ediam_eq_top, MeasureTheory.OuterMeasure.coe_iSup, Cardinal.sum_le_mk_mul_iSup, MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone, EMetric.ball_disjoint, cbiSup_eq_of_not_forall, MeasureTheory.lintegral_iSup_directed, Subalgebra.centralizer_coe_iSup, Ideal.sup_primeHeight_eq_ringKrullDim, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, Function.sSup_div_semiconj, RootPairing.coe_chainBotCoeff_eq_sSup, ENNReal.iSup_add_iSup_le, setOf_liouvilleWith_subset_aux, WellFoundedGT.iSup_eq_monotonicSequenceLimit, Pi.Colex.le_sSup_apply, Set.Nonempty.eq_Icc_iff_int, IsCompact.separation_of_notMem, Directed.measure_iUnion, IsSublattice.latticeClosure_eq, MeasureTheory.lowerCrossingTime_le, DirectSum.isInternal_submodule_iff_iSupIndep_and_iSup_eq_top, CategoryTheory.GrothendieckTopology.monotone_close, SupClosed.biSup_mem_of_nonempty, ProbabilityTheory.condIndep_iSup_of_monotone, NatOrdinal.instIsOrderedMonoid, MeasureTheory.hittingAfter_mono, Submodule.iSup_map_single_le, NatOrdinal.instIsOrderedRing, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinal, Nimber.mul_le_of_forall_ne, IsCompact.sSup_mem, CompleteLattice.wellFoundedGT_iff_isSupFiniteCompact, LinearMap.iSup_range_single, ENat.le_floor, NNReal.coe_iSup, TopologicalSpace.Opens.iSup_mk, AddSubmonoid.iSup_map_single, iSupIndep.pairwiseDisjoint, LinearMap.eventually_iSup_ker_pow_eq, Subfield.coe_iSup_of_directed, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, BoxIntegral.Box.Ioo_subset_coe, IsCompact.isLeast_sInf, MeasureTheory.Measure.mkMetric_apply, RootPairing.setOf_root_add_zsmul_mem_eq_Icc, LinearOrderedField.lt_inducedMap_iff, Order.height_pos, MeasureTheory.biSup_measure_Iic, Filter.bliminf_antitone, Finite.ciInf_le, separated_by_continuous, ENNReal.toNNReal_sSup, Submodule.smul_iSup', Order.le_krullDim_iff, Antitone.pairwise_disjoint_on_Ioo_pred, ENNReal.inv_sSup, Filter.liminf_eq_iSup_iInf_of_nat', CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_transfiniteCompositions, SimpleGraph.ComponentCompl.pairwise_disjoint, iSup_partialSups_eq, Nimber.add_le_of_forall_ne, MeasurableSpace.measurableSet_sSup, Submodule.biSup_comap_subtype_eq_top, Filter.HasBasis.limsInf_eq_iSup_sInf, Subgroup.FG.biSup, disjoint_nested_nhds_of_not_inseparable, Order.succ_eq_iInf, Submodule.biSup_eq_range_dfinsupp_lsum, Algebra.adjoin_attach_biUnion, ContinuousLinearMap.sSup_sphere_eq_nnnorm, Set.mulIndicator_iUnion_apply, Filter.bliminf_eq_iSup_biInf_of_nat, MeasureTheory.SimpleFunc.iSup_coe_eapprox, LinearOrderedField.inducedOrderRingIso_self, exists_disjoint_vadd_of_isCompact, AntitoneOn.Icc, MeasurableSet.measure_eq_iSup_isCompact_of_ne_top, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, IsCompact.sSup_lt_iff_of_continuous, sSupIndep.pairwiseDisjoint, lowerSemicontinuousOn_iSup, Submodule.fg_biSup, generateFrom_iInter_of_generateFrom_eq_self, ENat.mul_iSup, ENat.sSup_eq_zero, Disjoint.of_span, RootPairing.Base.pos_or_neg_of_sum_smul_root_mem, sSup_atoms_le_eq, AddSubgroup.noncommPiCoprod_range, LinearMap.iInf_ker_proj_le_iSup_range_single, MeasureTheory.Measure.LebesgueDecomposition.iSup_succ_eq_sup, NNReal.iSup_eq_zero, Matroid.cRank_eq_iSup_cardinalMk_indep, TopologicalSpace.Closeds.gc, isEmbedding_sumElim, MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE, Ordinal.iSup_le, CompleteSublattice.sSupClosed', Pi.Colex.sSup_apply, IntermediateField.finiteDimensional_iSup_of_finset, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, MonotoneOn.Iio, AffineSubspace.span_iUnion, CategoryTheory.Sieve.overEquiv_le_overEquiv_iff, SSet.iSup_skeleton, disjoint_interior_frontier, PrimeSpectrum.iSup_basicOpen_eq_top_iff, IsNormalClosure.adjoin_rootSet, Submodule.annihilator_iSup, Subfield.closure_iUnion, Filter.Realizer.ne_bot_iff, ENNReal.iSup_ne_top, antitone_Ioi, TopCat.colimit_topology, Set.Finite.infClosure, ofDual_preimage_latticeClosure, Submodule.neg_iSup, Ordinal.iSup_succ, MeasureTheory.IsSetSemiring.disjointOfUnion_props, Ordinal.Principal.sSup, NatOrdinal.add_le_iff, egauge_univ_pi, ProbabilityTheory.indep_biSup_limsup, Order.coheight_le_krullDim, Ideal.Filtration.sSup_N, Monoid.CoprodI.mrange_eq_iSup, AlgebraicGeometry.Scheme.Hom.image_iSup₂, Order.krullDim_nonpos_iff_forall_isMax, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Finset.coe_wcovBy_coe, ExpGrowth.expGrowthSup_biSup, MeasureTheory.eLpNormEssSup_eq_iSup, isNoetherian_iSup, MeasureTheory.exists_isSigmaFiniteSet_measure_ge, Filter.HasBasis.limsup_eq_ite, ENat.biSup_add', Ideal.iSup_eq_span, Finset.sup_univ_eq_ciSup, Nimber.pos_iff_ne_zero, normalClosure_eq_iSup_adjoin', NatOrdinal.succ_def, ENNReal.biSup_add, MeasureTheory.measure_sigmaFiniteSetGE_le, sSup_isotypicComponents, Antitone.Ico, ENNReal.sSup_div, Monotone.pairwise_disjoint_on_Ioc_pred, continuous_sSup_rng, CategoryTheory.Pretopology.mem_toGrothendieck, Antitone.pairwise_disjoint_on_Ioo_succ, Measurable.iSup, MeasurableSpace.generateFrom_iUnion_measurableSet, ProbabilityTheory.Kernel.indep_iSup_limsup, Ordinal.iSup_pow, Submodule.submodule_eq_sSup_le_nonzero_spans, εNFA.pumping_lemma, EMetric.diam_insert, Cardinal.lift_iSup, Filter.HasBasis.limsup_eq_sInf_iUnion_iInter, Order.coheight_eq_coe_add_one_iff, ProbabilityTheory.indep_iSup_of_directed_le, latticeClosure_mono, Ordinal.deriv_limit, image_latticeClosure', Order.krullDim_nonpos_iff_forall_isMin, isConnected_Iio, Nimber.add_trichotomy, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types, ENNReal.coe_sSup, Measurable.iSup_Prop, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, AlgebraicGeometry.Scheme.Hom.preimage_iSup, MeasureTheory.hittingBtwn_mono, Pi.Lex.sInf_apply_le, MeasureTheory.Measure.LebesgueDecomposition.iSup_le_le, ENNReal.biSup_add_biSup_le, SupClosed.iSup_mem, Submodule.iSup_mul, NatOrdinal.lt_add_iff, Submodule.localized'_iSup, meromorphicOrderAt_add, LinearMap.isCompl_iSup_ker_pow_iInf_range_pow, HomogeneousIdeal.toIdeal_iSup₂, upperHemicontinuousWithinAt_iff_preimage_Iic, EisensteinSeries.G2_eq_tsum_symmetricIco, Ordinal.sSup_eq_bsup, Nimber.add_def, Cardinal.lift_sSup, MeasureTheory.Content.innerContent_iSup_nat, MeasureTheory.IsSetSemiring.isSetRing_supClosure, SimpleGraph.eccent_le_one_iff, Partition.pairwiseDisjoint, PartENat.toWithTop_lt, Filter.bliminf_sup_le_or_aux_left, MeasureTheory.upperCrossingTime_mono, Submodule.dualCoannihilator_iSup_eq, ENat.floor_le_ceil, isPreconnected_Iic, Ordinal.iSup_add_nat, Antitone.Ioc, MeasureTheory.hittingBtwn_apply_anti, Cardinal.mk_biUnion_le_lift, ENNReal.iSup_coe_lt_top, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le, IsCompact.isLUB_sSup, Submodule.span_attach_biUnion, NonarchimedeanGroup.exists_openSubgroup_separating, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top', MeasureTheory.lintegral_le_iSup_mul, RootPairing.setOf_root_sub_zsmul_mem_eq_Icc, Cardinal.lift_iSup_le, Int.cofinite_eq, Set.Nonempty.ordConnected_iff_of_bdd', MeasureTheory.AddContent.supClosure_apply_finpartition, CompleteAtomicBooleanAlgebra.instIsCoatomistic, Ordinal.iSup_sum, iSupIndep_pair, Submodule.comap_iSup_map_of_injective, Submodule.map₂_iSup_left, ENat.iInf_coe_lt_top, ProbabilityTheory.avgRisk_le_iSup_risk, LinearMap.iSup_range_single_eq_iInf_ker_proj, ENat.ceil_lt_top, Ctop.Realizer.nhds_F, Set.Finite.csSup_lt_iff, ENNReal.iSup_natCast, lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl, MeasureTheory.IsSetSemiring.mem_supClosure_iff, Order.height_le_krullDim, SupClosed.infClosure, Topology.IsUpper.isTopologicalSpace_basis, NatOrdinal.lt_one_iff_zero, tendsto_intCast_atBot_sup_atTop_cobounded, disjoint_nhdsSet_principal, BoxIntegral.Box.iUnion_Ioo_of_tendsto, t2_separation_nhds, sInf_eq_argmin_on, NatOrdinal.instIsOrderedCancelAddMonoid, sInf_sub, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_monotone, sSup_compact_eq_top, MonotoneOn.Ici, ENat.add_iSup, ciInf_le', NNReal.iSup_mul_iSup_le, Filter.bliminf_or_le_inf, MeasureTheory.lowerCrossingTime_le_upperCrossingTime_succ, IntermediateField.normal_iSup, Function.mulSupport_iSup, LieModule.coe_genWeightSpaceOf_zero, Ordinal.iSup_eq_lsub_or_succ_iSup_eq_lsub, CategoryTheory.GrothendieckTopology.closureOperator_isClosed, ENat.mul_sSup, infClosed_infClosure, SummationFilter.hasSum_symmetricIoc_int_iff, Submodule.isOrtho_sSup_right, Submodule.iSup_span, MeasurableSet.measure_eq_iSup_isCompact, Ordinal.sup_succ_eq_lsub, CategoryTheory.GrothendieckTopology.PreservesSheafification.le, Order.bot_lt_krullDim, SupClosed.sSup_mem_of_nonempty, isConnected_Ici, AnalyticAt.meromorphicOrderAt_nonneg, Ordinal.sSup_ord, topologicalKrullDim_subspace_le, AddSubmonoid.FG.iSup, Int.ball_eq_Ioo, essSup_eq_sInf, MeasureTheory.upperCrossingTime_le_lowerCrossingTime, TopCat.Presheaf.SheafConditionEqualizerProducts.w, csSup_one, CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSup, MeasureTheory.dense_of_generateFrom_isSetSemiring, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, topologicalKrullDim_zero_of_discreteTopology, Module.End.iSup_genEigenspace_eq, Set.isCoatom_iff, MeasureTheory.hitting_eq_end_iff, Monotone.Iio, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, AddSubmonoid.mul_iSup, ENNReal.smul_iSup, Order.krullDim_eq_iSup_coheight_of_nonempty, ENNReal.iSup_add, sSup_inv, Submodule.iSup_dualAnnihilator_le_iInf, Subgroup.FG.biSup_finset, ENat.coe_sSup, SummationFilter.hasSum_symmetricIcc_iff, MeasureTheory.measure_biUnion_eq_iSup, RootPairing.coe_chainTopCoeff_eq_sSup, supClosure_empty, Ordinal.iSup_mul_nat, ClosedSubmodule.toSubmodule_iSup, BooleanSubalgebra.sSup_mem, Submodule.sum_mem_iSup, sSup_mul, ENNReal.tsum_iSup_eq, isInducing_sumElim, BoxIntegral.Box.Ioo_ae_eq_Icc, Submodule.mem_iSup_iff_exists_dfinsupp, isOpen_sSup_iff, LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute, compl_image_latticeClosure, Submodule.span_range_eq_iSup, Order.krullDim_eq_iSup_length, Order.Ideal.PrimePair.isCompl_I_F, Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim, TopologicalSpace.Opens.gc, IntermediateField.sSup_def, Ideal.IsHomogeneous.iSup, PrimitiveSpectrum.gc_closureOperator, Finset.Nonempty.ciSup_mem_image, Order.coheight_pos_of_lt_top, egauge_pi, WithTop.iInf_coe_eq_top, AlgebraicGeometry.iSup_basicOpen_of_span_eq_top, upperHemicontinuousOn_iff_preimage_Iic, Submodule.iSup_eq_range_dfinsupp_lsum, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_W, Set.Nonempty.ciSup_lt_iff, Monoid.CoprodI.range_eq_iSup, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, sInf_neg, infClosure_singleton, Order.coheight_eq_coe_iff_maximal_le_coheight, ENat.ceil_le, csInf_le', MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, Partition.sSup_eq', NNReal.agm_eq_ciSup, DFinsupp.iSup_range_lsingle, RootPairing.setOf_root_add_zsmul_eq_Icc_of_linearIndependent, ENNReal.toNNReal_iSup, Partition.le_of_mem, Antitone.measure_iUnion, SetTheory.PGame.grundyValue_le_of_forall_moveLeft, Order.height_pos_of_bot_lt, Submonoid.iSup_map_mulSingle, HomogeneousIdeal.toIdeal_sSup, ENNReal.tsum_eq_iSup_nat', Set.isAtom_singleton, Metric.ediam_eq_sSup, NatOrdinal.not_lt_zero, ENNReal.inv_iSup, sInf_inv, ENat.ceil_lt, Filter.liminf_eq_sSup_sInf, Finset.sup'_eq_csSup_image, OrthogonalFamily.isInternal_iff, SimpleGraph.edist_pos_of_ne, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, Set.monotone_accumulate, tendsto_nhds_iff_meromorphicOrderAt_nonneg, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, Topology.IsInducing.disjoint_of_sumElim_aux, latticeClosure_prod, isPreconnected_Icc, ContinuousOn.image_uIcc_eq_Icc, SequentialSpace.iSup, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, Monotone.Ico, InfClosed.infClosure_eq, NumberField.isTotallyReal_iSup, Ordinal.sup_le_lsub, Ordinal.iSup_add_natCast, ENat.ceil_pos, EisensteinSeries.hasSum_e2Summand_symmetricIco, MeasureTheory.hitting_le, ENat.add_sSup, Filter.blimsup_eq_iInf_biSup, ENNReal.tsum_eq_iSup_sum, Sublattice.le_comap_iSup, Order.krullDim_nonpos_of_subsingleton, LinearOrderedField.inducedOrderRingHom_toFun, Ordinal.IsNormal.map_iSup, NNReal.sSup_of_not_bddAbove, iSupIndep_def'', Antitone.Iio, Padic.AddValuation.map_add, Order.coheight_eq_iSup_head_eq, Ordinal.card_iSup_Iio_le_card_mul_iSup, Algebra.iSup_toSubsemiring, upperHemicontinuousAt_iff_preimage_Iic, ENat.ceil_add_le, ENat.lt_ceil, TopCat.Sheaf.existsUnique_gluing, exists_nhds_disjoint_closure, LinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap, Submodule.isOrtho_iSup_left, ENat.coe_iSup, ENat.smul_iSup, iSup_le_iSup_of_partialSups_le_partialSups, PartENat.toWithTop_le, Finite.le_ciSup, Finset.Nonempty.csSup_mem, IsInducing.topologicalKrullDim_le, MeasureTheory.IsSetSemiring.diff_mem_supClosure, SupClosed.iSup_mem_of_nonempty, MeasureTheory.hittingAfter_eq_top_iff, LinearMap.ker_noncommProd_eq_of_supIndep_ker, infClosure_eq_self, ProbabilityTheory.indep_iSup_limsup, Cardinal.mul_ciSup, AddSubmonoid.mem_bsupr_iff_exists_dfinsupp, csInf_Ioi, IsCompact.lt_sInf_iff_of_continuous, CategoryTheory.PreZeroHypercover.presieve₀_restrictIndex_le, normalClosure_def, tsum_iSup_decode₂, meromorphicNFAt_iff_analyticAt_or, NNReal.iSup_pow_of_ne_zero, compl_image_latticeClosure_eq_of_compl_image_eq_self, Order.krullDim_eq_iSup_height_of_nonempty, MeasureTheory.iSup_lintegral_measurable_le_eq_lintegral, latticeClosure_singleton, Nimber.small_Ioo, Submodule.restrictScalars_sSup, Ordinal.sup_eq_bsup, Cardinal.ciSup_mul, setOf_isPreconnected_eq_of_ordered, coinduced_sSup, MeasurableSpace.measurableSpace_iSup_eq, Ordinal.Principal.iSup, ENat.sub_iSup, CompleteSublattice.codisjoint_iff, PrimeSpectrum.zeroLocus_iSup, Set.Nonempty.csSup_mem, MeasureTheory.hittingAfter_univ, ENNReal.biSup_add', ENat.floor_lt_ceil, iSupIndep_def', le_ciInf_iff', Submodule.toAddSubmonoid_sSup, csSup_empty, WithTop.iSup_coe_lt_top, ENNReal.iSup_add_iSup, Submodule.smul_iSup, lowerSemicontinuous_iSup, exists_open_nhds_disjoint_closure, untrop_sum, ENat.floor_lt_top, ENNReal.iSup_sub, ENNReal.tsum_eq_iSup_sum', disjoint_measurableAtom_of_notMem, AddSubgroup.ofAddUnits_sSup, MeasureTheory.disjoint_cylinder_iff, CompleteSublattice.isCompl_iff, MonotoneOn.Iic, isAtomic_of_complementedLattice, MeasureTheory.hittingBtwn_apply_mono_left, Subalgebra.unop_sSup, isPreconnected_Ioi, MeasureTheory.hittingBtwn_anti, CategoryTheory.MorphismProperty.retracts_transfiniteComposition_pushouts_coproducts_le_llp_rlp, ENat.gc_ceil_toENNReal, NFA.disjoint_evalFrom_reverse_iff, MeasureTheory.measure_sigmaFiniteSetWRT', Filter.bliminf_sup_le_inf_aux_left, Ordinal.opow_limit, infClosure_univ, Submodule.fg_iSup, SSet.skeleton_succ, Cardinal.preAleph_limit, sSup_atoms_eq_top, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, IsSemisimpleModule.finite_tfae, subset_latticeClosure, Filter.bliminf_sup_le_inf_aux_right, LinearPMap.domain_sSup, Order.height_eq_iSup_lt_height, Order.height_eq_coe_add_one_iff, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, subset_infClosure, Submodule.inf_iSup_genEigenspace, Ideal.iSup_mul, IsClosedEmbedding.topologicalKrullDim_le, continuous_iSup_dom, disjoint_frontier_iff_isOpen, NormedSpace.equicontinuous_TFAE, Order.krullDim_enat, isTotallyDisconnected_iff_lt, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, Order.height_le_coe_iff, IsGenericPoint.disjoint_iff, IsOpen.measure_eq_iSup_isCompact, PiLp.nnnorm_eq_ciSup, NatOrdinal.mul_le_iff, Cardinal.lift_iSup_le_sum, CompleteLattice.isSupClosedCompact_iff_wellFoundedGT, Order.height_eq_coe_iff, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', Algebra.sSup_toSubsemiring, MeasureTheory.hittingAfter_apply_anti, generateFrom_iInter, generateFrom_piiUnionInter_measurableSet, MeasureTheory.IsSetSemiring.diff_eq_sUnion', ENNReal.iSup_ennreal, AntitoneOn.Ioi, Antitone.pairwise_disjoint_on_Ioc_succ, SimpleGraph.edist_le_eccent, alexandrovDiscrete_iSup, partialSups_eq_biSup, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.exists_oneHypercover, isPreconnected_Ico, SimpleGraph.edist_triangle, NonUnitalSubalgebra.coe_iSup_of_directed, Filter.Realizer.mem_sets, AddSubmonoid.iSup_eq_mrange_dfinsuppSumAddHom, CompleteSublattice.coe_sSup', RootPairing.Base.not_nonpos_iff_pos_of_sum_mem_range_root, tprod_iSup_decode₂, WithTop.iInf_coe_lt_top, exists_seq_infinite_isOpen_pairwise_disjoint, ProbabilityTheory.condIndep_iSup_limsup, dimH_bUnion, Order.pred_eq_sSup, BooleanSubalgebra.latticeClosure_subset_closure, Antitone.Ioi, TopologicalSpace.Opens.mem_iSup, Cardinal.sum_le_lift_mk_mul_iSup, ConditionallyCompleteLinearOrderedField.to_archimedean, ENNReal.inv_iInf, Ordinal.bsup_eq_sup, Order.length_le_height, IsUltrametricDist.ball_eq_or_disjoint, eq_Icc_of_connected_compact, ProbabilityTheory.Kernel.indep_iSup_of_directed_le, Subfield.closure_sUnion, Multiset.iSup_mem_map_of_ne_zero, BooleanSubalgebra.closure_latticeClosure, essSup_eq_iSup, sSupHom.continuous, Order.height_le_height_apply_of_strictMono, upperHemicontinuous_iff_isOpen_preimage_Iic, upperHemicontinuous_iff_preimage_Iic, BoxIntegral.Prepartition.pairwiseDisjoint, Antitone.Ici, ciSup_or', trdeg_eq_iSup_cardinalMk_isTranscendenceBasis, ProbabilityTheory.Kernel.indep_iSup_of_monotone, NatOrdinal.instAddLeftStrictMono, Metric.ball_disjoint_closedBall, Order.krullDim_le_one_iff_of_boundedOrder, sSup_one, Ordinal.iSup_mul_natCast, Ordinal.mem_closure_iff_iSup, Filter.HasBasis.liminf_eq_iSup_iInf, AntitoneOn.Iic, sInf_iUnion_Ici, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.le, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, NNReal.iSup_div, Set.Finite.supClosure, Ideal.iSup_iInf_eq_top_iff_pairwise, Set.Iic.coe_iInf, MeasureTheory.measure_iUnion_of_tendsto_zero, Submodule.closure_coe_iSup_map_single, ENat.iSup_natCast, Ordinal.iSup_lt_ord_lift, TopCat.coinduced_of_isColimit, Filter.Realizer.ofEquiv_F, Pi.Colex.sInf_apply_le, ciSup_of_empty, CategoryTheory.ObjectProperty.HasCardinalLT.iSup, MeasureTheory.tendsto_ae_condExp, ProbabilityTheory.indep_iSup_directed_limsup, DividedPowers.SubDPIdeal.sSup_carrier_def, TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompact, ContinuousOn.image_uIcc, PiLp.edist_eq_iSup, CauchyFilter.monotone_gen, Set.isCoatom_singleton_compl, AddMonoidHom.noncommPiCoprod_mrange, Finset.Nonempty.csSup_eq_max', IsSemisimpleModule.sSup_simples_le, isOpen_iSup_iff, ENat.floor_mono, MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone', IsOpen.measure_eq_biSup_integral_continuous, CompleteLattice.IsSupClosedCompact.wellFoundedGT, Submodule.sInf_orthogonal, CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderComposition, Submonoid.inv_iSup, MeasureTheory.Measure.restrict_iUnion_apply_eq_iSup, LinearOrderedField.inducedMap_mono, SupClosed.biSup_mem, setOf_isPreconnected_subset_of_ordered, ProbabilityTheory.iSup_partitionFiltration_eq_generateFrom_range, connectedComponent_disjoint, ENat.le_ceil, Submodule.mul_iSup, Order.krullDim_eq_iSup_coheight, Set.Iic.coe_biInf, Set.Iic.coe_sSup, ENNReal.add_iSup, AlgebraicGeometry.Scheme.IdealSheafData.support_iSup, OrderIso.map_ciSup', TopCat.Presheaf.presieveOfCovering.indexOfHom_spec, ENNReal.iSup_coe_eq_top, Subfield.mem_iSup_of_directed, sup_mem_supClosure, ProbabilityTheory.condIndep_biSup_limsup, sSupIndep.disjoint_sSup, SimpleGraph.ediam_le_two_mul_radius, lowerBounds_infClosure, isPreconnected_Ioc, gc_nhdsKer_interior, Submodule.span_sSup, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, Filter.bliminf_eq, Submodule.iSup_eq_span, ENat.iSup_mul, Filter.liminf_eq_iSup_iInf_of_nat, Ordinal.mem_closure_tfae, Cardinal.iSup_lt_ord_lift_of_isRegular, isPreconnected_Ioo, SeparatedNhds.disjoint_closure_right, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, Submodule.span_iUnion, CompleteLattice.isCoatomistic_iff, SummationFilter.hasProd_symmetricIco_int_iff, MeasureTheory.hittingBtwn_mono_right, BoundedContinuousFunction.nndist_eq_iSup, monotone_Iio, SummationFilter.hasSum_symmetricIco_int_iff, SimpleGraph.eccent_le_ediam, supClosure_isClosed, LieSubmodule.sSup_toSubmodule, MeasureTheory.OuterMeasure.sSup_apply, NNReal.natCast_iSup, Order.pred_eq_iSup, Ideal.map_iSup_comap_of_surjective, AddSubmonoid.bsupr_eq_mrange_dfinsuppSumAddHom, SimpleGraph.ediam_eq_iSup_iSup_edist, Cardinal.iSup_lt_lift_of_isRegular, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsGenerating.le, CategoryTheory.Presieve.le_of_factorsThru_sieve, Ordinal.iSup'_eq_bsup, Set.isAtom_iff, Monotone.Ioc, Submodule.sum_mem_biSup, Matrix.ker_diagonal_toLin', Nimber.not_bddAbove_compl_of_small, Order.krullDim_eq_iSup_height, AddSubmonoid.FG.biSup, Finset.coe_covBy_coe, FirstOrder.Language.Substructure.iSup_eq_closure, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, UniformOnFun.edist_def', MeasureTheory.tendsto_measure_sigmaFiniteSetGE, CompleteSublattice.coe_iSup, MeasurableSpace.comap_iSup, SimpleGraph.eccent_pos_iff, ClosedSubmodule.mem_iSup, Topology.IsScott.instUnivSetOfIsUpper, Filter.HasBasis.liminf_eq_sSup_univ_of_empty, AddSubgroup.FG.iSup, Filter.limsSup_eq_iInf_sSup, smul_iInf_le, IsSemisimpleModule.sSup_simples_eq_top, hasCardinalLT_subtype_iSup, iSup_disjointed, ENat.sSup_add, Cardinal.beth_limit, supClosure_singleton, Function.support_iSup, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, trop_iInf, Order.coheight_le_coheight_apply_of_strictMono, AlgebraicGeometry.Scheme.Hom.image_iSup, image_latticeClosure, Alexandrov.lowerCone_π_app, ENNReal.biSup_add_biSup_le', Cardinal.mk_biUnion_le, MeasureTheory.lintegral_iSup_directed_of_measurable, MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part, Subfield.map_iSup, latticeClosure_eq_self, AddSubgroup.ofAddUnits_iSup₂, IntermediateField.map_iSup, iSup_eq_iSup_of_partialSups_eq_partialSups, CFilter.mem_toFilter_sets, isSaddlePointOn_iff', latticeClosure_empty, NatOrdinal.instAddLeftMono, Ordinal.iSup_sequence_lt_omega_one, ProbabilityTheory.Kernel.indep_biSup_limsup, BoxIntegral.Box.Ioo_subset_Icc, SimpleGraph.edist_anti, ENNReal.mul_sSup, ENNReal.iSup_add_iSup_of_monotone, Filter.mono_bliminf', sSup_div, le_csInf_iff', IsCompact.isGLB_sInf, BoxIntegral.Box.exists_seq_mono_tendsto, MonoidHom.noncommPiCoprod_mrange, MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE', SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, Finset.untrop_sum, supClosure_mono, Ideal.IsHomogeneous.sSup, Set.Iic.instIsCompactlyGenerated, ENNReal.sSup_mul, TopologicalSpace.Opens.map_iSup, ENNReal.iSup_zero, PartENat.ofENat_lt, t2_separation_compact_nhds, Order.one_le_krullDim_iff, Submonoid.FG.iSup, IndexedPartition.disjoint, Cardinal.sum_le_iSup_lift, IsWellFounded.rank_eq, SSet.horn_eq_iSup, Ordinal.iSup_typein_limit, lowerHemicontinuous_iff_isClosed_preimage_Iic, ENat.iSup_eq_zero, Nimber.not_lt_zero, Measurable.iSup', MeasureTheory.tendsto_eLpNorm_condExp, Ordinal.iSup_lt_lift, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, MeasureTheory.lintegral_eq_nnreal, UniformFun.edist_def, Cardinal.mk_iUnion_le_lift, Order.coheight_le_iff', Order.krullDim_le_of_strictMono, SSet.range_eq_iSup_sigma_ι, SupClosed.supClosure_eq, essInf_eq_sSup, WithTop.isGLB_sInf, Subspace.dualAnnihilator_iInf_eq, IntermediateField.isSplittingField_iSup, Submodule.iSup_map_single, MeasureTheory.SimpleFunc.lintegral_restrict_iUnion_of_directed, Submodule.mem_sSup_of_mem, FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion, ProbabilityTheory.iSup_countableFiltration, PrimitiveSpectrum.closedsGC_closureOperator, Monotone.pairwise_disjoint_on_Ico_pred, Order.pred_eq_csSup, ClosedSubmodule.toSubmodule_sSup, ProbabilityTheory.indep_iSup_of_antitone, FirstOrder.Language.Substructure.closure_iUnion, ConditionallyCompleteLinearOrder.isCompact_Icc, Ordinal.derivFamily_limit, BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm, Nimber.small_Ioc, coinduced_iSup, monotone_Iic, AntitoneOn.Ioo, Partition.iSup_eq, ZFSet.rank_range, IntermediateField.iSup_eq_adjoin, TopologicalSpace.Opens.mem_sSup, iSup₂_iInf₂_le_iInf₂_iSup₂, ENNReal.add_biSup', LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute, PartENat.withTopEquiv_le, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, Submodule.map_smul', Monotone.pairwise_disjoint_on_Ioo_succ, Ordinal.iSup_ord, inf_sSup_eq_iSup_inf_sup_finset, Metric.AreSeparated.disjoint, ENNReal.hasSum, BoxIntegral.Box.disjoint_coe, IntermediateField.iSup_toSubfield, ENat.iSup_add, Ordinal.sup_eq_sup, PartENat.withTopEquiv_lt, TopologicalSpace.Opens.leSupr_apply_mk, LinearMap.range_smul', DirectSum.IsInternal.addSubmonoid_iSup_eq_top, DFA.pumping_lemma, ENNReal.add_sSup, Submodule.small_iSup, Finsupp.disjoint_lsingle_lsingle, Ordinal.le_iSup, le_csInf_iff'', Nimber.small_Icc, Ordinal.iSup_eq_zero_iff, LinearOrderedField.inducedOrderRingIso_symm, AddSubgroup.FG.biSup_finset, FirstOrder.Language.Substructure.comap_iSup_map_of_injective, ProbabilityTheory.condIndep_biSup_compl, MeasureTheory.hitting_mono, CompleteSublattice.sSupClosed, Continuous.strictMono_of_inj, Finsupp.codisjoint_supported_supported_iff, IsCompactlyGenerated.exists_sSup_eq, Set.Iic.coe_iSup, iSupIndep_def, T2Space.t2, Module.End.genEigenspace_top, Monotone.Ioi, infClosure_min, ENNReal.iSup_div, Set.Nonempty.ciSup_mem_image, MonoidHom.noncommPiCoprod_range, Monoid.CoprodI.iSup_mrange_of, Submodule.iSup_torsionBy_eq_torsionBy_prod, sSup_neg, UniformOnFun.edist_def, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, IntermediateField.fg_iSup, IsCompactlyGenerated.BooleanGenerators.sSup_le_sSup_iff_of_atoms, MeasureTheory.OuterMeasure.boundedBy_apply, Metric.closedBall_disjoint_ball, ProbabilityTheory.iSup_bayesRisk_le_minimaxRisk, SSet.hasDimensionLT_iSup_iff, ENat.ceil_mono, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_llp_rlp, iSup_succ, Ordinal.sup_eq_bsup', Submodule.set_smul_eq_iSup, ProbabilityTheory.condIndep_iSup_directed_limsup, TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducible, IntermediateField.adjoin_iUnion, AntitoneOn.Iio, Ordinal.succ_iSup_eq_lsub_iff, LieSubmodule.sSup_toSubmodule_eq_iSup, CompleteSublattice.coe_sSup, isConnected_Iic, Filter.Realizer.le_iff, SimpleGraph.diam_def, Subgroup.FG.iSup, ENat.sSup_mul, Cardinal.sum_le_lift_mk_mul_iSup_lift, ENat.iSup_coe_eq_top, latticeClosure_idem, sSup_sub, ClosedSubmodule.mem_sSup, t2Space_iff_nhds, IntermediateField.normalClosure_def'', SSet.iSup_skeletonOfMono, DividedPowers.isSubDPIdeal_iSup, Nimber.small_Iic, Sublattice.map_iSup, MeasureTheory.hittingAfter_mem_set_of_ne_top, Monotone.pairwise_disjoint_on_Ioo_pred, CategoryTheory.MorphismProperty.retracts_transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, CompleteLattice.IsSupFiniteCompact.wellFoundedGT, BoundedContinuousFunction.edist_eq_iSup, RootPairing.Base.exists_root_eq_sum_int, Filter.liminf_eq_iSup_iInf, Filter.HasBasis.liminf_eq_sSup_iUnion_iInter, Ideal.homogeneousCore'_eq_sSup, TopologicalSpace.Opens.iSup_def, TopologicalSpace.Closeds.coe_sSup, Monotone.pairwise_disjoint_on_Ioc_succ, Ordinal.sup_eq_lsub, Nimber.one_le_iff_ne_zero, RootPairing.root_add_zsmul_mem_range_iff, sSupIndep_pair, SimpleGraph.edist_le_ediam, OrthogonalFamily.range_linearIsometry, iSup_Iio_eq_self_iff_isSuccPrelimit, Ordinal.iSup_eq_lsub_iff_lt_iSup, continuous_iSup_rng, ProbabilityTheory.Kernel.indep_iSup_of_antitone, ENNReal.toReal_sSup, sSup_compact_le_eq, isPreconnected_Iio, ENNReal.sub_iSup, Order.coheight_le_coe_iff, SSet.iSup_range_eq_top_of_isColimit, ContinuousMap.nnnorm_eq_iSup_nnnorm, Submodule.isOrtho_iSup_right, IsClosed.lowerClosure, partialSups_eq_ciSup_Iic, Algebra.isIntegral_iSup, Topology.IsScott.scott_eq_upper_of_completeLinearOrder, MeasureTheory.Measure.InnerRegularWRT.measure_eq_iSup, WithBot.coe_biInf, EisensteinSeries.tendsto_double_sum_S_act, Ordinal.IsNormal.map_iSup_of_bddAbove, SummationFilter.symmetricIcc_eq_symmetricIoo_int, AlgebraicGeometry.IsAffineOpen.biSup_of_disjoint, Cardinal.preBeth_limit, Submodule.iSup_smul, Submodule.mem_iSup_finset_iff_exists_sum, Submodule.iSup_eq_span', disjoint_principal_nhdsSet, Filter.Realizer.principal_F, infClosure_prod, MeasureTheory.hittingBtwn_le, Submodule.iInf_orthogonal, ProjectiveSpectrum.basicOpen_eq_union_of_projection, MeasureTheory.Measure.iSup_restrict_spanningSets, ContinuousMap.nndist_eq_iSup, FirstOrder.Language.Substructure.map_iSup_comap_of_surjective, NonUnitalStarSubalgebra.coe_iSup_of_directed, Subalgebra.op_iSup, AddSubmonoid.FG.biSup_finset, MeasureTheory.lintegral_iSup, Int.closedBall_eq_Icc, Ordinal.lt_iSup_iff, CategoryTheory.GrothendieckTopology.le_close, Set.antitone_dissipate, Ordinal.IsNormal.map_sSup_of_bddAbove, TopologicalSpace.Opens.coe_sSup, Order.krullDim_le_one_iff_forall_isMax, NatOrdinal.zero_le, RootedTree.subtrees_disjoint, EisensteinSeries.summable_e2Summand_symmetricIcc, ENNReal.iSup_eq_zero, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.top_mem_range, Ordinal.bsup'_eq_iSup, ENat.floor_lt, Submodule.span_sSup', Ordinal.IsNormal.apply_omega0, Filter.bliminf_or_le_inf_aux_left, MeasurableSet.measure_eq_iSup_isClosed_of_ne_top, Metric.eball_disjoint, Order.krullDim_pos_iff_of_orderTop, TopCat.Presheaf.presieveOfCovering.mem_grothendieckTopology, TopologicalSpace.IsOpenCover.iSup_eq_top, Nimber.mul_def, MeasureTheory.eLpNormEssSup_count, SimpleGraph.radius_le_ediam, Subfield.coe_sSup_of_directedOn, Ordinal.iSup_Iio_eq_bsup, WithTop.iSup_coe_eq_top, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_pt, MeasureTheory.OuterMeasure.iUnion_of_tendsto_zero, AEMeasurable.iSup, TopCat.Presheaf.SheafConditionEqualizerProducts.w_apply, WithTop.isLUB_sSup, ENNReal.smul_sSup, Submodule.map_iSup_comap_of_surjective, Submodule.coe_iSup_of_directed, IntermediateField.finiteDimensional_iSup_of_finite, Ordinal.iSup_eq_of_range_eq, MeasureTheory.hittingBtwn_eq_end_iff, Set.Finite.latticeClosure, Order.coheight_coe_enat, ZFSet.rank_iUnion, ENNReal.sSup_add, Ordinal.IsNormal.map_sSup, Topology.IsScott.isOpen_iff_Iic_compl_or_univ, CategoryTheory.MorphismProperty.transfiniteCompositions_le, TopologicalSpace.gc_generateFrom, BooleanSubalgebra.biSup_mem, TopologicalSpace.Closeds.isAtom_coe, SimpleGraph.eccent_le_iff, MeasureTheory.upperCrossingTime_zero', MeasureTheory.iSup₂_lintegral_le, Order.krullDim_eq_iSup_height_add_coheight_of_nonempty, Ordinal.iSup_sequence_lt_omega1, Filter.HasBasis.blimsup_eq_iInf_iSup, FiberBundle.exists_trivialization_Icc_subset, Alexandrov.projSup_obj, ENNReal.tsum_eq_iSup_nat, Ordinal.bsup_eq_iSup, Algebra.mem_iSup_of_mem, NFA.disjoint_stepSet_reverse, LinearOrderedField.inducedMap_nonneg, isAtomistic_of_complementedLattice, essSup_count, Order.krullDim_pos_iff_of_orderBot, Partition.disjoint, MeasureTheory.Filtration.sSup_def, SimpleGraph.ediam_def, IntermediateField.isAlgebraic_iSup, normalClosure_eq_iSup_adjoin, Ordinal.lsub_le_succ_iSup, Cardinal.ciSup_mul_ciSup, Submodule.mem_iSup_of_mem, Filter.limsup_eq_iInf_iSup, Nimber.small_Ico, AEMeasurable.biSup, Filter.limsup_le_iSup, Order.succ_eq_csInf, IsUltrametricDist.closedBall_subset_trichotomy, SupClosed.sSup_mem, MonotoneOn.Ico, Field.Emb.Cardinal.iSup_adjoin_eq_top, Filter.bliminf_antitone_filter, CliffordAlgebra.iSup_ι_range_eq_top, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, Finset.sup'_id_eq_csSup, NNReal.iSup_empty, Ideal.mul_iSup, IntermediateField.toSubalgebra_iSup_of_directed, IsUltrametricDist.nnnorm_tprod_le, MeasureTheory.Measure.hausdorffMeasure_apply, PartENat.withTopEquiv_symm_le, Alexandrov.lowerCone_pt, Submodule.span_biUnion, iSupIndep_map_orderIso_iff, ProbabilityTheory.indep_biSup_compl, IntermediateField.isSeparable_iSup, Filter.iInf_le_liminf, AddSubmonoid.mem_iSup_iff_exists_dfinsupp', supClosure_infClosure, ENNReal.iSup_pow, Ideal.sup_height_eq_ringKrullDim, isSaddlePointOn_iff, Set.instIsCoatomistic, Partition.bot_lt_of_mem, Ordinal.mem_iff_iSup_of_isClosed, infClosure_mono, NNReal.mul_iSup, EMetric.hausdorffEdist_def, ENNReal.sub_iInf, AddSubgroup.FG.biSup, isSeparatedMap_iff_nhds, LinearOrderedField.coe_inducedOrderRingIso, MeasureTheory.lowerCrossingTime_mono, Cardinal.add_ciSup, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, MonotoneOn.Ioc, Algebra.adjoin_iUnion, CompleteLattice.isSupFiniteCompact_iff_all_elements_compact, LieSubmodule.iSup_toSubmodule_eq_top, TopCat.nonempty_isColimit_iff_eq_coinduced, MeasureTheory.hittingAfter_le_iff, Submodule.isOrtho_sSup_left, ENNReal.iSup_lt_eq_self, Ideal.map_sSup, CompleteLattice.wellFoundedGT_characterisations, Order.coheight_eq_coe_iff, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, ENNReal.finsetSum_iSup_of_monotone, NatOrdinal.small_Ioc, MeasureTheory.AddContent.supClosure_apply_of_mem, monotone_nhdsSet, Finsupp.supported_iUnion, InfClosed.supClosure, exists_eq_ciSup_of_finite, SSet.modelCategoryQuillen.J_le_monomorphisms, antitone_Ici, MeasureTheory.SimpleFunc.iSup_eapprox_apply, CategoryTheory.MorphismProperty.isStableUnderTransfiniteCompositionOfShape_iff, SimpleGraph.radius_le_eccent, Submodule.restrictScalars_iSup, SSet.boundary_eq_iSup, ENat.toENNReal_iSup, AddSubmonoid.mem_iSup_iff_exists_dfinsupp, Ordinal.isClosed_iff_iSup, MeasureTheory.upperCrossingTime_le, Ordinal.bsup_eq_sup', Filter.limsup_eq_iInf_iSup_of_nat', ENat.lt_floor, NatOrdinal.small_Iio, Filter.limsSup_principal_eq_sSup, LinearOrderedField.coe_lt_inducedMap_iff, csSup_Iio, isConnected_Ioi, TopologicalSpace.Opens.coe_disjoint, MeasureTheory.hittingAfter_apply_mono, HomogeneousIdeal.irrelevant_eq_iSup, Set.Iic.coe_biSup, IsSemisimpleModule.exists_sSupIndep_sSup_simples_eq_top, Filter.blimsup_mono, CompleteAtomicBooleanAlgebra.instIsAtomistic, BoxIntegral.Box.measurableSet_Ioo, IsCompact.continuous_sSup, Subgroup.ofUnits_iSup₂, TopologicalSpace.Opens.isBasis_iff_cover, dimH_iUnion, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, Monotone.measure_iUnion, sSup_add, DirectSum.IsInternal.submodule_iSup_eq_top, MeasureTheory.le_hittingAfter, DoubleCoset.disjoint_out, Order.height_le_iff, Antitone.Iic, Submodule.mem_iSup_of_chain, OrderIso.apply_blimsup, MeasurableSpace.iSup_generateFrom, Submodule.mem_iSup_iff_exists_finset, Cardinal.lift_iSup_le_lift_iSup', FirstOrder.Language.DirectLimit.Equiv_isup_of_apply, MonotoneOn.Ioo, complementedLattice_iff_isAtomistic, infClosure_supClosure, CompleteLatticeHom.toOrderIsoRangeOfInjective_apply, Submodule.localized₀_iSup, untrop_sum_eq_sInf_image, Ordinal.sup_typein_limit, Filter.bliminf_or_le_inf_aux_right, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, Submodule.iSup_eq_toSubmodule_range, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, LinearMap.iSup_range_single_le_iInf_ker_proj, Filter.Realizer.bot_F, Order.KrullDimLE.krullDim_le, Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInf, ProbabilityTheory.condIndep_iSup_of_disjoint, Monotone.Iic, Submodule.mem_sSup_iff_exists_finset, NatOrdinal.small_Ico, supClosure_idem, LinearMap.disjoint_single_single, List.iSup_mem_map_of_ne_nil, ENNReal.iSup_mul_le, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, ENat.add_biSup, ciSup_false, Setoid.IsPartition.pairwiseDisjoint, Padic.norm_rat_le_one_iff_padicValuation_le_one, LieSubalgebra.span_iUnion, sSupIndep_iff_pairwiseDisjoint, ProbabilityTheory.iSup_partitionFiltration, Filter.Realizer.top_F, PrimitiveSpectrum.hull_sSup, EisensteinSeries.summable_e2Summand_symmetricIco, RootPairing.root_sub_zsmul_mem_range_iff, Partition.sSup_eq, Filter.blimsup_sup_le_or, Subgroup.ofUnits_sSup, NatOrdinal.small_Ioo, Order.coheight_anti, Cardinal.sum_le_iSup, infClosure_idem, EMetric.diam_eq_sSup, Module.End.iSup_maxGenEigenspace_eq_top, Nat.iSup_lt_succ, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, CompleteSublattice.disjoint_iff, Measurable.sSup, Order.height_mono, Ordinal.sup_eq_lsub_or_sup_succ_eq_lsub, ClosedSubmodule.coe_iSup, Submodule.finite_iSup, Order.height_le_iff', Order.krullDim_nonneg, upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl, Finsupp.lsingle_range_le_ker_lapply, Monotone.Icc, MeasureTheory.measure_iUnion_eq_iSup_accumulate, WCovBy.finset_coe, lowerSemicontinuousAt_iSup, FirstOrder.Language.DirectLimit.iSup_range_of_eq_top, MeasureTheory.SimpleFunc.iSup_approx_apply, BoxIntegral.Prepartition.disjoint_coe_of_mem, Cardinal.lift_iSup_le_iff, Filter.blimsup_eq_iInf_biSup_of_nat, SSet.Subcomplex.preimage_iSup, Filter.limsup_eq_sInf_sSup, Antitone.pairwise_disjoint_on_Ico_pred, Filter.HasBasis.limsSup_eq_iInf_sSup, Order.coheight_pos, CategoryTheory.MorphismProperty.transfiniteCompositions_pushouts_coproducts_le_llp_rlp, CompleteLattice.isAtomistic_iff, SummationFilter.symmetricIcc_eq_map_Icc_nat, sSup_simples_eq_top_iff_isSemisimpleModule, sSup_iUnion_Iic, Metric.ediam_iUnion_mem_option, Submodule.span_monotone, WithBot.coe_biSup, Matrix.range_diagonal, Filter.limsup_eq_iInf_iSup_of_nat, Submodule.mem_sSup_of_directed, Perfect.splitting, Order.index_le_height, CovBy.finset_coe, RestrictedProduct.topologicalSpace_eq_iSup, Order.coheight_eq, Metric.sphere_disjoint_ball, PrimitiveSpectrum.hull_iSup, infClosure_isClosed, Field.Emb.Cardinal.iSup_filtration, tendsto_intCast_atTop_cobounded, Cardinal.aleph_limit, Order.krullDim_le_one_iff_forall_isMin, SummationFilter.hasProd_symmetricIcc_iff, Topology.IsLower.isTopologicalSpace_basis, bsupr_limsup_dimH, Filter.blimsup_monotone_filter, subset_supClosure, ENat.floor_le_floor, MeasureTheory.iSup_lintegral_le, Pi.Lex.le_sSup_apply, Filter.limsup_eq, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top, ProjectiveSpectrum.zeroLocus_iSup_ideal, Finset.Nonempty.ciSup_eq_max'_image, AntitoneOn.Ioc, SimpleGraph.edist_le, setOf_isOpen_sSup, disjoint_nhdsWithin_of_mem_discrete, Ordinal.iSup_le_iff, Cardinal.iSup_lt_ord_of_isRegular, finsetInf'_mem_infClosure, iSupIndep.map_orderIso, Ordinal.iSup_eq_lsub, csInf_le_csInf', Dynamics.dynEntourage_antitone, Submodule.dualAnnihilator_iSup_eq, Order.rev_index_le_coheight, AntitoneOn.Ico, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, Int.padicValuation_le_one, MeasureTheory.OuterMeasure.iSup_apply, SSet.N.iSup_subcomplex_eq_top, ENNReal.iSup_mul, Ordinal.iSup_eq_lsub_iff, IsCompact.exists_sSup_image_eq, Topology.IsGeneratedBy.iSup, Submonoid.FG.biSup_finset, lowerSemicontinuousWithinAt_biSup, Submodule.mem_biSup_iff_exists_dfinsupp, Filter.mono_blimsup', nhdsKer_mono, ENat.sSup_eq_zero', latticeClosure_isClosed, Cardinal.ciSup_add_ciSup, SetTheory.PGame.grundyValue_le_of_forall_moveRight, isSemisimpleModule_biSup_of_isSemisimpleModule_submodule, sSupHom.apply_blimsup_le, isArtinian_iSup, ENNReal.finsetSum_iSup, MeasurableSpace.disjoint_countablePartition, TopCat.Sheaf.eq_of_locally_eq_iff, CompleteLattice.isCompactElement_iff_le_of_directed_sSup_le, Pi.Lex.sSup_apply, Ordinal.iSup_natCast, LinearMap.mapsTo_biSup_of_mapsTo, lowerSemicontinuousAt_biSup, Submodule.topologicalClosure_iSup_map_single, FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion_apply, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, Filter.limsInf_eq_iSup_sInf, Ordinal.iSup_iterate_eq_nfp, csInf_univ, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing, Int.instIsOrderBornology, ProbabilityTheory.condIndep_iSup_of_directed_le, DirectSum.isInternal_biSup_submodule_of_iSupIndep, NatOrdinal.small_Icc, Nimber.le_zero, Set.chainHeight_eq_iSup, MonotoneOn.Ioi, IsCompact.isGreatest_sSup, AddSubmonoid.neg_iSup, Subgroup.ofUnits_iSup, LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commute, Nimber.small_Iio, isLUB_supClosure, ZLattice.sum_piFinset_Icc_rpow_le, ContinuousMap.enorm_eq_iSup_enorm, ENNReal.inv_sInf, BooleanSubalgebra.iSup_mem, FirstOrder.Language.Substructure.map_iSup, Ordinal.apply_omega0_of_isNormal, IntermediateField.Lifts.carrier_union, Nat.iSup_le_succ', Filter.bliminf_eq_iSup_biInf, IntermediateField.normalClosure_def', Finsupp.disjoint_supported_supported_iff, PrimeSpectrum.iSup_basicOpen_eq_top_iff', Set.instIsAtomistic, Ideal.toIdeal_homogeneousHull_eq_iSup, Submodule.mem_iSup_iff_exists_dfinsupp', Order.height_eq_iSup_last_eq, BoundedContinuousFunction.enorm_eq_iSup_enorm, Filter.HasBasis.limsup_eq_iInf_iSup, ExpGrowth.expGrowthSup_iSup, Order.height_enat, ProbabilityTheory.Kernel.indep_biSup_compl, supClosure_prod, AlgebraicGeometry.Scheme.IdealSheafData.support_sSup, dimH_def, AddSubmonoid.iSup_mul, finsetSup'_mem_supClosure, Order.length_le_height_last, Finset.sup'_univ_eq_ciSup, Order.coheight_eq_iSup_gt_coheight, IsPreconnected.mem_intervals, tendsto_intCast_atBot_cobounded, NNReal.iSup_mul, infClosure_empty, Order.Ideal.PrimePair.disjoint, AddSubgroup.ofAddUnits_iSup, Submodule.mem_iSup_of_directed, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSup, Ordinal.lsub_le_sup_succ, MeasureTheory.AddContent.supClosure_apply, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_P, sSup_zero, iSupIndep_iff_pairwiseDisjoint, Ideal.mem_iSup_of_mem, AffineSubspace.map_iSup, MeasureTheory.AECover.iSup_lintegral_eq_of_countably_generated, Ideal.IsHomogeneous.iSup₂, Ideal.Filtration.iSup_N, Submodule.iSup_toAddSubmonoid, Pell.IsFundamental.y_strictMono, Dense.ciSup', NNReal.iSup_pow, Ordinal.succ_iSup_le_lsub_iff, supClosed_supClosure, MeasureTheory.hittingAfter_anti, Order.length_le_coheight_head, Nimber.lt_one_iff_zero, NatOrdinal.small_Iic, Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splits, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, MeasureTheory.setLIntegral_iUnion_of_directed, r1_separation, ENat.ceil_le_floor_add_one, Submodule.mem_sSup, MeasureTheory.lintegral_eq_iSup_eapprox_lintegral, ENNReal.coe_iSup, eq_sSup_atoms, PartENat.withTopEquiv_symm_lt, SummationFilter.hasProd_symmetricIoc_int_iff, Ordinal.IsNormal.apply_of_isSuccLimit, OnePoint.isCompl_range_coe_infty, ProbabilityTheory.indep_iSup_of_disjoint, Ordinal.iSup_lt_ord, FirstOrder.Language.DirectLimit.cod_partialEquivLimit, Ideal.map_iSup, FirstOrder.Language.DirectLimit.range_lift, MeasureTheory.hittingAfter_lt_iff, PrimitiveSpectrum.gc, Antitone.Ioo, HomogeneousIdeal.toIdeal_iSup, IntermediateField.finiteDimensional_iSup_of_finset', ENat.add_biSup', csSup_zero, ProbabilityTheory.Kernel.indep_iSup_of_disjoint, BooleanSubalgebra.le_comap_iSup, SSet.Subcomplex.image_iSup, sInf_div, Mathlib.Meta.Positivity.natCeil_pos, ENat.biSup_add, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSup, Order.bot_lt_krullDim_iff, ENNReal.iSup₂_pow_of_ne_zero, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, Cardinal.mk_iUnion_le, Order.height_eq_coe_iff_minimal_le_height, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, trop_sInf_image, supClosure_univ, Cardinal.iSup_le_sum, Projectivization.Subspace.span_iUnion, measurableSet_iSup_of_mem_piiUnionInter, Subgroup.noncommPiCoprod_range, le_iff_compact_le_imp, SimpleGraph.eccent_def, Cardinal.iSup_mk_le_mk_iUnion, iSup_limsup_dimH, t2_separation, DeltaGeneratedSpace.iSup, ZFSet.iSup_card_le_card_iUnion, Ordinal.card_iSup_le_sum_card, DirectSum.range_coeLinearMap, Alexandrov.projSup_map, Filter.Realizer.tendsto_iff, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, CategoryTheory.MorphismProperty.transfiniteCompositions_monotone, Cardinal.ciSup_add, WithTop.isLUB_sSup', latticeClosure_min, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, Ordinal.iSup_lt, Submodule.mem_iSup, Submodule.starProjection_tendsto_closure_iSup, Order.one_lt_height_iff, MeasureTheory.measure_sigmaFiniteSetGE_ge, ContinuousMap.edist_eq_iSup, Order.coheight_le_iff, ENat.iSup_coe_lt_top, Submodule.span_eq_iSup_of_singleton_spans, NNReal.iSup_mul_le, egauge_pi', CategoryTheory.MorphismProperty.transfiniteCompositions_le_llp_rlp, MeasureTheory.Filtration.stronglyMeasurable_limitProcess, MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty, ENNReal.toReal_iSup, IsCompact.exists_sSup_image_eq_and_ge, Submonoid.FG.biSup, IsUltrametricDist.closedBall_eq_or_disjoint, lowerSemicontinuous_biSup, SSet.range_eq_iSup_of_isColimit, Submodule.span_iUnion₂, FirstOrder.Language.DirectLimit.rangeLiftInclusion, ClassGroup.exists_mem_finset_approx', ENat.floor_le, sSup_mem_closure, Filter.limsup_top_eq_iSup, IsUltrametricDist.nnnorm_tsum_le, Nat.iSup_le_succ, Order.krullDimLE_iff, CategoryTheory.PreZeroHypercover.Hom.sieve₀_le_sieve₀, ENNReal.add_biSup, Metric.ediam_insert, SSet.skeletonOfMono_succ, Dynamics.dynEntourage_monotone, Ideal.span_iUnion, monotone_closure, Order.succ_eq_sInf, ClassGroup.exists_mem_finsetApprox, Rat.padicValuation_le_one_iff, PiLp.nndist_eq_iSup, Submodule.coe_iSup_of_chain, MeasurableSpace.measurableSet_iSup, FirstOrder.Language.DirectLimit.dom_partialEquivLimit, Finsupp.iSup_lsingle_range, Ordinal.sup_typein_succ, Antitone.pairwise_disjoint_on_Ico_succ, MeasureTheory.Measure.iSup_restrict_spanningSets_of_measurableSet, SimpleGraph.edist_le_one_iff_adj_or_eq, IntermediateField.biSup_adjoin_simple, OrderIso.apply_bliminf, MeasureTheory.lintegral_le_iSup, supClosure_min, Metric.closedBall_disjoint_closedBall, IsCompact.exists_sInf_image_eq_and_le, SimpleGraph.radius_eq_iInf_iSup_edist, ENNReal.mul_iSup, CategoryTheory.MorphismProperty.le_transfiniteCompositions, t2Space_iff, Subalgebra.unop_iSup, Submodule.finiteDimensional_iSup, dirSupInacc_iff_forall_sSup, EMetric.diam_iUnion_mem_option, Int.cobounded_eq, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, CategoryTheory.MorphismProperty.transfiniteCompositions_le_iff, HilbertBasis.finite_spans_dense, Monotone.pairwise_disjoint_on_Ico_succ
toInfSet 📖CompOp
1 mathmath: isGLB_csInf_of_directed

Theorems

NameKindAssumesProvesValidatesDepends On
isGLB_csInf_of_directed 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
toConditionallyCompletePartialOrderSup
Set.Nonempty
BddBelow
IsGLB
InfSet.sInf
toInfSet
——

ConditionallyCompletePartialOrderInf

Definitions

NameCategoryTheorems
toInfSet 📖CompOp
757 mathmath: continuousNeg_iInf, Nat.iInf_le_succ', ProbabilityTheory.bayesRisk_of_subsingleton, ENNReal.iInf_div_of_ne, MeasureTheory.OuterMeasure.map_iInf, OrderIso.map_radical, Set.Iic.coe_sInf, continuous_sInf_dom₂, PolynormableSpace.sInf, OrderIso.map_csInf, StarSubalgebra.coe_sInf, Filter.HasBasis.liminf_eq_ite, SetTheory.PGame.grundyValue_eq_sInf_moveLeft, GroupTopology.toTopologicalSpace_iInf, equicontinuousWithinAt_iInf_dom, le_mul_ciInf, isSaddlePointOn_value, iSupIndep.injOn_iInf, ContinuousMap.compactOpen_eq_iInf_induced, MeasureTheory.iInf_mul_le_lintegral, sInfHom.le_apply_bliminf, ENNReal.add_sInf, csSup_image2_eq_csInf_csInf, Algebra.mem_iInf, csInf_of_not_bddBelow, nhds_sInf, Ordinal.sInf_compl_lt_lift_ord_succ, MeasureTheory.hittingBtwn_apply_mono_right, IsMinOn.iInf_eq, continuousMul_sInf, TopologicalSpace.Closeds.iInf_def, MeasureTheory.hittingBtwn_mono_left, topologicalGroup_iInf, MeasureTheory.le_hitting_of_exists, eq_sInf_coatoms, inf_eq_bot_of_bot_mem, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, DirectedOn.subset_Icc_csInf_csSup, FormalMultilinearSeries.radius_pi_eq_iInf, AntitoneOn.map_sSup_of_continuousWithinAt, Finset.inf'_univ_eq_ciInf, Set.Finite.lt_csInf_iff, RightOrdContinuous.map_sInf, ENat.iInf_mul_of_ne, ciInf_sub, le_csInf_iff, R1Space.iInf, MeasureTheory.hittingAfter_bot_le_iff, upperSemicontinuousAt_biInf, csInf_mem, nhds_iInf, Ordinal.log_def, Bornology.IsBounded.subset_Icc_sInf_sSup, add_ciInf, AffineSubspace.mem_sInf_iff, MeasureTheory.hittingBtwn_univ, ContinuousLinearMap.nnnorm_def, MeasureTheory.le_hitting, TopologicalSpace.eq_induced_by_maps_to_sierpinski, OrderIso.map_csInf', isLeast_csInf, le_ciInf_add_ciInf, Subalgebra.op_sInf, csInf_insert, continuousVAdd_sInf, le_ciInf_mul_ciInf, ENat.iInf_toNat, GaloisConnection.u_ciInf, Algebra.mem_sInf, ENNReal.ofReal_iInf, csInf_singleton, MeasureTheory.hittingBtwn_mem_Icc, generateFrom_sUnion, csInf_zero, Subalgebra.centralizer_coe_iSup, Directed.ciInf_mono, ProbabilityTheory.bayesRisk_of_subsingleton', Monotone.csInf_image_le, ENNReal.iInf_ennreal, DirectedOn.le_ciInf_set_iff, Set.Nonempty.eq_Icc_iff_int, Set.Iic_ciInf, MeasureTheory.lowerCrossingTime_le, Submodule.spanRank_toENat_eq_iInf_encard, Sublocale.coe_iInf, NonUnitalAlgebra.sInf_toNonUnitalSubsemiring, MeasureTheory.hittingAfter_mono, ciInf_add, NonUnitalStarAlgebra.mem_sInf, AEMeasurable.iInf, Nat.iInf_lt_succ', IsCompact.isLeast_sInf, generateFrom_iUnion_isOpen, MeasureTheory.Measure.mkMetric_apply, ENNReal.mul_iInf, TopologicalSpace.Closeds.coe_iInf, MeasureTheory.Measure.iInf_IicSnd_gt, IsLeast.csInf_mem, csInf_eq_of_forall_ge_of_forall_gt_exists_lt, Finite.ciInf_le, MeasureTheory.hitting_le_of_mem, MeasureTheory.lintegral_iInf_ae, ENNReal.inv_sSup, MeasurableSpace.measurableSet_iInf, IntermediateField.coe_iInf, MeasureTheory.OuterMeasure.comap_iInf, csInf_lt_iff, Filter.liminf_eq_iSup_iInf_of_nat', MeasureTheory.lintegral_iInf', Cardinal.lift_iInf, Filter.HasBasis.limsInf_eq_iSup_sInf, AddGroupTopology.toTopologicalSpace_sInf, Order.succ_eq_iInf, Filter.bliminf_eq_iSup_biInf_of_nat, upperSemicontinuous_biInf, IsClosed.sInf_mem, NonUnitalStarAlgebra.iInf_toNonUnitalSubalgebra, Ordinal.card_sInf_range_compl_le_lift, tendsto_atBot_ciInf, NonUnitalStarAlgebra.coe_sInf, ENNReal.le_iInf₂_add_iInf₂, NNReal.natCast_iInf, isGLB_ciInf, Filter.blimsup_eq, essInf_eq_ciInf, Pi.induced_restrict, Filter.HasBasis.limsup_eq_sInf_univ_of_empty, MeasureTheory.OuterMeasure.iInf_apply', MeasureTheory.hittingBtwn_mem_set, MeasureTheory.Measure.sInf_caratheodory, ProbabilityTheory.bayesRisk_eq_iInf_measure_of_subsingleton, Algebra.coe_iInf, MeasureTheory.OuterMeasure.restrict_iInf, MeasureTheory.OuterMeasure.le_sum_caratheodory, ENNReal.iInf_div, MeasureTheory.stoppedValue_hitting_mem, Filter.HasBasis.limsup_eq_ite, CompleteSublattice.coe_iInf, ENat.iInf_mul', IntermediateField.iInf_toSubfield, continuousNeg_sInf, MeasureTheory.OuterMeasure.map_iInf_comap, Pi.Lex.sInf_apply, csInf_div, Filter.HasBasis.limsup_eq_sInf_iUnion_iInter, ENNReal.iInf_sum, AffineSubspace.affineSpan_eq_sInf, MeasureTheory.hittingBtwn_mono, MeasureTheory.stoppedValue_hittingBtwn_mem, OrderIso.map_ciInf_of_directed, Ordinal.card_sInf_range_compl_le, MeasureTheory.hitting_le_iff_of_exists, regularSpace_sInf, Algebra.sInf_toSubsemiring, Algebra.sInf_toSubmodule, Monotone.rightLim_eq_sInf, topologicalAddGroup_sInf, ciInf_of_not_bddBelow, Nimber.add_def, MeasureTheory.upperCrossingTime_mono, continuous_iInf_rng, MeasureTheory.hittingBtwn_apply_anti, ciInf_mul, Set.Nonempty.ordConnected_iff_of_bdd', csInf_Ioc, MeasureTheory.hittingAfter_mem_set, MeasureTheory.hittingBtwn_bot_le_iff, MeasureTheory.Adapted.isStoppingTime_hittingBtwn, CompleteSublattice.coe_sInf', ENat.iInf_coe_lt_top, NonUnitalAlgebra.mem_iInf, ciInf_le_ciSup, csInf_mul, IsConnected.Ioo_csInf_csSup_subset, exists_eq_ciInf_of_finite, MeasureTheory.hitting_mem_Icc, ENat.iInf_mul, sInf_eq_argmin_on, AffineSubspace.mem_iInf_iff, PseudoMetricSpace.dist_ofPreNNDist, sInf_sub, MvPowerSeries.le_order_subst, ciInf_le', TopologicalSpace.Closeds.mem_sInf, MeasureTheory.lowerCrossingTime_le_upperCrossingTime_succ, ENNReal.iInf_add_iInf, AEMeasurable.biInf, MeasureTheory.OuterMeasure.trim_eq_iInf', CompleteSublattice.sInfClosed, SimpleGraph.chromaticNumber_eq_iInf, sInfHom.continuous, IsLeast.csInf_eq, upperSemicontinuousOn_iInf, ciInf_eq_univ_of_not_bddBelow, Sublocale.sInf_mem, IsCompact.sInf_mem, Ordinal.succ_log_def, AlgebraicGeometry.IsLocalIso.eq_iInf, csSup_lowerBounds_eq_csInf, ContinuousOn.sInf_image_Icc_le, MeasureTheory.le_hittingBtwn, essSup_eq_sInf, MeasureTheory.upperCrossingTime_le_lowerCrossingTime, MeasureTheory.Content.outerMeasure_eq_iInf, essInf_count, MeasureTheory.hitting_eq_end_iff, Ordinal.enumOrd_zero, ciInf_mem, IntermediateField.sInf_toSubalgebra, ciInf_le_of_le, sSup_inv, ENNReal.iInf_mul_of_ne, MeasureTheory.hittingBtwn_le_of_mem, MonotoneOn.tendsto_nhdsGT, ENat.sInf_eq_zero, DirectedOn.isGLB_ciInf_set, MeasureTheory.OuterMeasure.map_iInf_le, Monotone.map_csInf, WithTop.iInf_coe_eq_top, ENNReal.add_iInf, ciInf_eq_ite, sInf_mul, induced_sInf, sInf_neg, csInf_le', SetTheory.PGame.grundyValue_eq_sInf_moveRight, PrimeSpectrum.iInf_localization_eq_bot, IsCoatom.sInf_le, ENNReal.inv_iSup, sInf_inv, TopCat.nonempty_isLimit_iff_eq_induced, MeasureTheory.OuterMeasure.iInf_apply, Filter.liminf_eq_sSup_sInf, iInf_eq_iInf_subseq_of_monotone, NonUnitalStarAlgebra.mem_iInf, CompleteSublattice.sInfClosed', MeasureTheory.isStoppingTime_hittingBtwn_isStoppingTime, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, CompletePseudometrizable.iInf, ContinuousOn.image_uIcc_eq_Icc, continuousInv_sInf, iInf_eq_of_tendsto, DirectedOn.csInf_le_iff, upperSemicontinuous_ciInf, Set.einfsep_insert, MeasureTheory.hitting_le, Filter.blimsup_eq_iInf_biSup, DirectedOn.csInf_le_csSup, ContinuousOn.image_Icc, TopologicalSpace.secondCountableTopology_iInf, cbiInf_eq_of_not_forall, LocallyConvexSpace.iInf, MeasureTheory.OuterMeasure.biInf_apply, Nat.iInf_le_succ, AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp, ENNReal.iInf_add, ProbabilityTheory.bayesRisk_const_of_nonempty, AntitoneOn.map_csSup_of_continuousWithinAt, ENNReal.mul_iInf', MeasureTheory.hittingAfter_eq_top_iff, Order.radical_le_coatom, continuousSMul_sInf, MeasureTheory.measure_iInter_eq_iInf_measure_iInter_le, ciInf_subsingleton, generateFrom_iUnion, csInf_Ioi, IsCompact.lt_sInf_iff_of_continuous, MeasureTheory.Filtration.rightCont_apply, EMetric.infEdist_biUnion, ENNReal.iInf_add_iInf_of_monotone, Set.einfsep_insert_le, LinearMap.mem_span_iff_continuous_of_finite, ENat.sub_iSup, ENat.iInf_eq_top_of_isEmpty, Function.support_iInf, Cardinal.ord_eq_Inf, MeasureTheory.hittingAfter_univ, le_ciInf_iff', ENat.iInf_coe_eq_top, Directed.ciInf_le, untrop_sum, Set.Icc.coe_iInf, MeasureTheory.hittingBtwn_apply_mono_left, mul_ciInf, MeasureTheory.hittingBtwn_anti, MvPowerSeries.le_weightedOrder_subst, ENat.exists_eq_iInf, IsCompact.measure_eq_iInf_isOpen, Directed.le_ciInf_iff, UniformOnFun.topologicalSpace_eq, ENNReal.sub_eq_sInf, Finset.Nonempty.csInf_eq_min', MeasureTheory.OuterMeasure.ofFunction_eq_iInf_mem, MeasureTheory.Filtration.rightCont_def, Antitone.map_csSup_of_continuousAt, GroupTopology.toTopologicalSpace_sInf, AffineSubspace.direction_iInf_of_mem, GaloisConnection.u_csInf, dimH_eq_iInf, continuousAdd_iInf, MeasureTheory.Measure.sInf_apply, ENNReal.le_iInf_mul, regularSpace_iInf, Sublocale.coe_sInf, equicontinuous_iInf_dom, DirectedOn.le_csInf_iff, Monotone.measure_iInter, MeasureTheory.Measure.inf_apply, MeasureTheory.hittingAfter_apply_anti, sInf_one, InfClosed.biInf_mem_of_nonempty, IsIntegrallyClosed.iInf, ciInf_eq_of_forall_ge_of_forall_gt_exists_lt, Directed.ciInf_le_of_le, InfClosed.iInf_mem_of_nonempty, Sublocale.sInf_mem', upperSemicontinuous_iInf, WithTop.iInf_coe_lt_top, ENat.coe_iInf, ENNReal.inv_iInf, ENat.mul_iInf_of_ne, eq_Icc_of_connected_compact, EMetric.infEdist_iUnion, continuous_sInf_dom, MonotoneOn.csInf_eq_of_subset_of_forall_exists_le, sInf_mem_closure, UniformSpace.toTopologicalSpace_sInf, ENNReal.toNNReal_iInf, csInf_upperBounds_range, Subalgebra.unop_iInf, MeasureTheory.inducedOuterMeasure_eq_iInf, MeasureTheory.lintegral_iInf, MeasureTheory.le_iInf_lintegral, NonUnitalAlgebra.coe_iInf, csInf_eq_bot_of_bot_mem, DirectedOn.csInf_eq_of_forall_ge_of_forall_gt_exists_lt, NNReal.le_iInf_mul_iInf, ENNReal.le_iInf_mul_iInf, Monotone.ciInf_comp_tendsto_atBot, Filter.HasBasis.liminf_eq_iSup_iInf, Algebra.iInf_toSubsemiring, Cardinal.sInf_eq_zero_iff, sInf_iUnion_Ici, PolynormableSpace.iInf, Set.Iic.coe_iInf, MeasureTheory.Filtration.rightCont_eq_of_not_isMax, topologicalGroup_sInf, ProbabilityTheory.bayesRisk_le_iInf, ContinuousOn.image_uIcc, Manifold.riemannianEDist_def, ciInf_div, OrderIso.map_csInf_of_directedOn, RightOrdContinuous.map_sInf', Ordinal.cof_eq_sInf_lsub, MeasureTheory.hitting_bot_le_iff, Set.Iic.coe_biInf, csInf_le_csSup, AlgebraicGeometry.Scheme.IdealSheafData.support_iSup, Set.Icc.coe_sInf, MonotoneOn.map_csInf, DirectedOn.le_csInf, StarSubalgebra.mem_iInf, SimpleGraph.edist_eq_sInf, MonotoneOn.tendsto_nhdsWithin_Ioo_right, Antitone.map_sSup_of_continuousAt, Filter.liminf_eq_iSup_iInf_of_nat, AntitoneOn.sInf_image_Icc, iInf_eq_of_forall_le_of_tendsto, csSup_inv, CompleteLattice.isCoatomistic_iff, MeasureTheory.hittingBtwn_mono_right, le_ciInf, isGLB_ciInf_set, DirectedOn.csInf_lt_of_lt, AffineSubspace.direction_iInf, Pi.induced_precomp, Measurable.sInf, Set.indicator_iInter_apply, UniformSpace.toTopologicalSpace_iInf, csInf_image2_eq_csSup_csInf, Antitone.ciInf_comp_tendsto_atTop, Nat.iInf_lt_succ, Subalgebra.op_iInf, Filter.limsSup_eq_iInf_sSup, smul_iInf_le, trop_iInf, Set.Nonempty.ordConnected_iff_of_bdd, Algebra.iInf_toSubmodule, ciInf_add_ciInf_le_ciInf_add, csInf_Ico, Submodule.spanRank_toENat_eq_iInf_finset_card, IntermediateField.map_iInf, isSaddlePointOn_iff', sSup_div, ENNReal.mul_iInf_of_ne, le_csInf_iff', IsCompact.isGLB_sInf, Finset.untrop_sum, ENat.coe_sInf, eq_Icc_csInf_csSup_of_connected_bdd_closed, continuousAdd_sInf, MeasureTheory.hittingBtwn_isStoppingTime, ciInf_eq_bot_of_bot_mem, sInf_zero, LocallyConvexSpace.sInf, Set.einfsep_eq_iInf, NonUnitalAlgebra.map_iInf, MeasureTheory.hittingAfter_eq_sInf, Directed.ciInf_le_ciSup, WithTop.isGLB_sInf, ENNReal.iInf_mul_iInf, NNReal.le_mul_iInf, ExpGrowth.expGrowthInf_iInf, completelyRegularSpace_iInf, continuousSMul_iInf, csInf_Ioo, MeasureTheory.OuterMeasure.sInf_apply, IsTopologicalBasis.iInf, MeasureTheory.iInf_le_lintegral, upperSemicontinuousOn_ciInf, MeasureTheory.hitting_eq_hitting_of_exists, iSup₂_iInf₂_le_iInf₂_iSup₂, Cardinal.succ_def, NonUnitalStarAlgebra.coe_iInf, DirectedOn.ciInf_set_le, ENNReal.iInf_ne_top, MonotoneOn.sInf_image_Icc, NNReal.iInf_real_pos_eq_iInf_nnreal_pos, GaloisConnection.u_csInf_of_directedOn, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iInf, StieltjesFunction.length_eq, ciInf_le, csInf_one, MeasureTheory.Filtration.rightCont_eq, csInf_eq_univ_of_not_bddBelow, MeasureTheory.measure_eq_iInf', le_csInf_iff'', ENNReal.iInf_mul', MeasureTheory.lintegral_iInf_directed_of_measurable, Directed.ciInf_eq_of_forall_ge_of_forall_gt_exists_lt, Pi.induced_restrict_sUnion, Set.mulIndicator_iInter_apply, MeasureTheory.hitting_mono, Cardinal.sInf_empty, Metric.infEDist_iUnion, sSup_neg, IsGLB.ciInf_set_eq, MeasureTheory.Measure.iInf_rat_gt_prod_Iic, MeasurableSpace.map_iInf, MeasureTheory.OuterMeasure.boundedBy_apply, equicontinuousAt_iInf_dom, AntitoneOn.tendsto_nhdsLT, csInf_neg, MeasureTheory.OuterMeasure.restrict_biInf, ENat.mul_iInf, sSup_sub, MeasureTheory.hittingAfter_mem_set_of_ne_top, Antitone.tendsto_nhdsLT, ProbabilityTheory.bayesRisk_le_iInf', Filter.liminf_eq_iSup_iInf, ExpGrowth.expGrowthInf_biInf, RightOrdContinuous.map_csInf, Ordinal.lift_card_sInf_compl_le, ENNReal.sub_iSup, Antitone.measure_iInter, AffineSubspace.direction_sInf, Function.mulSupport_iInf, WithBot.coe_biInf, InfClosed.biInf_mem, MeasurableSpace.measurableSet_sInf, IsCompact.continuous_sInf, ProbabilityTheory.bayesRisk_const_of_neZero, MeasureTheory.measure_eq_iInf, MeasureTheory.hitting_lt_iff, MeasureTheory.hittingBtwn_le, MeasureTheory.le_iInf₂_lintegral, upperSemicontinuousOn_biInf, csInf_Icc, disjointed_eq_inf_compl, ENNReal.le_iInf_add_iInf, induced_to_pi, iSupIndep.iInf, ENNReal.iInf_mul, MeasureTheory.hittingBtwn_eq_sInf, continuousMul_iInf, ENNReal.toReal_iInf, MeasureTheory.hittingAfter_isStoppingTime, IntermediateField.normal_iInf, AffineSubspace.direction_sInf_of_mem, MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict, ENNReal.sInf_add, tendsto_atTop_ciInf, Sublocale.iInf_mem, ENNReal.iInf_coe_lt_top, TopCat.induced_of_isLimit, Nimber.mul_def, ProbabilityTheory.bayesRisk_const, TopologicalSpace.Closeds.iInf_mk, NNReal.coe_iInf, DirectedOn.csInf_le_csInf, OrderIso.map_ciInf, Antitone.map_iSup_of_continuousAt, MeasureTheory.hittingBtwn_le_iff_of_lt, SimpleGraph.chromaticNumber_eq_biInf, MeasureTheory.hittingBtwn_eq_end_iff, DirectedOn.csInf_le, continuous_iInf_dom, Antitone.iInf_comp_tendsto_atTop, StarSubalgebra.sInf_toSubalgebra, ciInf_unique, MeasureTheory.upperCrossingTime_zero', MaximalSpectrum.iInf_localization_eq_bot, Filter.HasBasis.blimsup_eq_iInf_iSup, sInf_add, RightOrdContinuous.map_iInf, ENNReal.iInf₂_add, upperSemicontinuousWithinAt_biInf, csInf_upperBounds_eq_csSup, csInf_union, subset_Icc_csInf_csSup, Filter.limsup_eq_iInf_iSup, Cardinal.lift_sInf, cbiInf_eq_of_forall, MeasureTheory.OuterMeasure.top_apply', Monotone.iInf_comp_tendsto_atBot, Order.succ_eq_csInf, DirectedOn.csInf_le_of_le, Measurable.iInf, MeasureTheory.Measure.hausdorffMeasure_apply, AffineSubspace.comap_supr, ciInf_neg, InfClosed.iInf_mem, Directed.Iic_ciInf, inducing_iInf_to_pi, Filter.iInf_le_liminf, ProbabilityTheory.bayesRisk_discard, IntermediateField.sInf_toSubfield, essInf_count_eq_ciInf, isSaddlePointOn_iff, ENNReal.sub_iInf, MeasureTheory.lowerCrossingTime_mono, MeasureTheory.hitting_mem_set, NonUnitalAlgebra.mem_sInf, le_csInf_inter, csSup_div, MeasureTheory.hittingAfter_le_iff, ciInf_lt_iff, Set.measure_eq_iInf_isOpen, tendsto_atTop_iInf, csInf_lt_of_lt, Ordinal.sInf_compl_lt_ord_succ, equicontinuousOn_iInf_dom, ciInf_mul_ciInf_le_ciInf_mul, MeasureTheory.OuterMeasure.sInf_apply', BoundedContinuousFunction.nndist_eq, IsCompact.measure_eq_biInf_integral_hasCompactSupport, le_ciInf_mul, StarSubalgebra.coe_iInf, ciInf_set_le, StarSubalgebra.mem_sInf, Dense.ciInf', MeasureTheory.upperCrossingTime_le, Algebra.adjoin_eq_sInf, MeasureTheory.isStoppingTime_hitting_isStoppingTime, Filter.limsup_eq_iInf_iSup_of_nat', InfClosed.sInf_mem_of_nonempty, isGLB_csInf_of_directed, Finset.inf'_id_eq_csInf, MeasureTheory.hittingAfter_apply_mono, essInf_eq_iInf, WithTop.isGLB_sInf', csInf_sub, NNReal.sInf_empty, NNReal.mul_iInf, upperSemicontinuousAt_ciInf, MeasureTheory.StronglyAdapted.isStoppingTime_leastGE, MeasureTheory.le_hittingAfter, le_ciInf_set_iff, ciInf_le_of_le', GaloisConnection.u_ciInf_set, NNReal.iInf_mul, untrop_sum_eq_sInf_image, MeasureTheory.OuterMeasure.sInf_eq_boundedBy_sInfGen, Antitone.map_ciSup_of_continuousAt, NonUnitalAlgebra.coe_sInf, essInf_cond_count_eq_ciInf, MeasureTheory.hittingBtwn_of_lt, BooleanSubalgebra.sInf_mem, ciInf_mono, OrderIso.map_ciInf_set_of_directedOn, NNReal.iInf_empty, Filter.liminf_top_eq_iInf, IsClosed.csInf_mem, Finset.inf'_eq_csInf_image, MeasureTheory.hittingBtwn_lt_iff, BooleanSubalgebra.biInf_mem, MeasureTheory.OuterMeasure.sInfGen_def, Finset.Nonempty.csInf_mem, Directed.measure_iInter, Pi.induced_precomp', ENat.mul_iInf', RightOrdContinuous.map_ciInf, Filter.limsInf_principal_eq_sInf, continuousInv_iInf, csInf_image2_eq_csSup_csSup, Directed.isGLB_ciInf, Filter.liminf_top_eq_ciInf, NNReal.le_iInf_add_iInf, AffineSubspace.coe_iInf, BooleanSubalgebra.iInf_mem, MeasureTheory.hittingAfter_le_of_mem, Cardinal.iInf_eq_zero_iff, csInf_eq_csInf_of_forall_exists_le, exists_seq_tendsto_sInf, Filter.blimsup_eq_iInf_biSup_of_nat, Filter.limsup_eq_sInf_sSup, ENNReal.hasProd_iInf_prod, Pi.Colex.sInf_apply, csSup_image2_eq_csSup_csInf, Filter.HasBasis.limsSup_eq_iInf_sSup, Measurable.biInf, ENat.iInf_eq_zero, MeasureTheory.hitting_of_le, Filter.limsup_eq_iInf_iSup_of_nat, TopologicalSpace.Closeds.coe_sInf, csInf_image2_eq_csInf_csInf, IsCoatom.iInf_le, csInf_Ici, Measurable.iInf_Prop, MeasureTheory.hitting_of_lt, withSeminorms_iInf, ENNReal.add_iInf₂, le_add_ciInf, upperSemicontinuousAt_iInf, AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInf, upperSemicontinuousWithinAt_iInf, Filter.limsup_eq, MeasureTheory.OuterMeasure.biInf_apply', IsCompact.exists_sInf_image_eq, OrderIso.map_ciInf_set, csInf_image2_eq_csInf_csSup, csInf_le_csInf', AddGroupTopology.toTopologicalSpace_iInf, NonUnitalStarAlgebra.sInf_toNonUnitalSubalgebra, csSup_sub, Algebra.map_iInf, NNReal.agm_eq_ciInf, IsGLB.ciInf_eq, ENNReal.iInf_gt_eq_self, Filter.limsInf_eq_iSup_sInf, MeasureTheory.Filtration.rightCont_eq_of_neBot_nhdsGT, IntermediateField.iInf_toSubalgebra, csInf_univ, MeasureTheory.hittingBtwn_of_le, Set.einfsep_iUnion_mem_option, ENNReal.toNNReal_sInf, GaloisConnection.u_csInf_of_directedOn', Algebra.coe_sInf, MeasureTheory.OuterMeasure.trim_eq_iInf, ENNReal.inv_sInf, PolishSpace.iInf, ENNReal.coe_iInf, Monotone.le_csInf_image, Filter.bliminf_eq_iSup_biInf, induced_iInf, sInf_within_of_ordConnected, StarSubalgebra.map_iInf, TopologicalSpace.Closeds.mem_iInf, NonUnitalAlgebra.sInf_toSubmodule, MeasureTheory.hitting_eq_sInf, TopCat.limit_topology, iInf_eq_iInf_subseq_of_antitone, ENat.toENNReal_iInf, Filter.HasBasis.limsup_eq_iInf_iSup, MeasureTheory.OuterMeasure.map_biInf_comap, AlgebraicGeometry.Scheme.IdealSheafData.support_sSup, NNReal.le_iInf_mul, Filter.limsInf_principal_eq_csSup, upperSemicontinuousWithinAt_ciInf, IsPreconnected.mem_intervals, csSup_lowerBounds_range, csSup_image2_eq_csInf_csSup, le_ciInf_iff, IsClosed.isLeast_csInf, tendsto_atBot_iInf, Filter.HasBasis.limsup_eq_ciInf_ciSup, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSup, MeasureTheory.OuterMeasure.restrict_iInf_restrict, InfClosed.sInf_mem, ENNReal.tprod_eq_iInf_prod, csInf_add, csInf_mem_closure, MeasureTheory.OuterMeasure.ofFunction_apply, IntermediateField.coe_sInf, ciInf_Ici, ProbabilityTheory.bayesRisk_const', R1Space.sInf, MeasureTheory.hittingBtwn_le_iff_of_exists, MeasureTheory.hittingAfter_anti, GaloisConnection.u_ciInf_of_directed, Monotone.tendsto_nhdsGT, MeasureTheory.hitting_le_iff_of_lt, StarSubalgebra.iInf_toSubalgebra, ENNReal.iInf_div', csInf_inv, ciInf_pos, MeasureTheory.hittingAfter_lt_iff, Filter.HasBasis.liminf_eq_ciSup_ciInf, csInf_pair, Directed.le_ciInf, ciInf_const, LinearMap.mem_span_iff_continuous, sInf_div, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSup, ENNReal.iInf_coe_eq_top, trop_sInf_image, topologicalAddGroup_iInf, OrderIso.map_csInf_of_directedOn', Dense.ciInf, ENNReal.coe_sInf, Antitone.ciInf_comp_tendsto_atTop_of_linearOrder, MeasureTheory.iInf_mul_le_setLIntegral, Monotone.ciInf_comp_tendsto_atBot_of_linearOrder, continuous_sInf_rng, GaloisConnection.u_ciInf_set_of_directedOn, Metric.infEDist_biUnion, MeasureTheory.Adapted.isStoppingTime_hittingBtwn_isStoppingTime, le_ciInf_add, DirectedOn.isGLB_csInf, MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty, IsPreconnected.Ioi_csInf_subset, AntitoneOn.tendsto_nhdsWithin_Ioo_left, GaloisConnection.u_csInf', NonUnitalAlgebra.iInf_toSubmodule, NNReal.iInf_const_zero, WithTop.coe_sInf, SSet.Subcomplex.preimage_iInf, Order.succ_eq_sInf, MeasureTheory.le_hittingBtwn_of_exists, MeasureTheory.hitting_isStoppingTime, MeasureTheory.Adapted.isStoppingTime_hittingAfter, Set.Nonempty.csInf_mem, upperClosure_eq_Ici_csInf, AffineSubspace.coe_sInf, continuousVAdd_iInf, Ordinal.sInf_empty, MeasureTheory.Filtration.sInf_def, IsTopologicalBasis.iInf_induced, NonUnitalStarAlgebra.map_iInf, MeasureTheory.hittingBtwn_eq_hittingBtwn_of_exists, IsCompact.exists_sInf_image_eq_and_le, csSup_neg, SimpleGraph.radius_eq_iInf_iSup_edist, Subalgebra.unop_sInf, CompleteSublattice.coe_sInf, NNReal.coe_sInf, ENNReal.toReal_sInf
toPartialOrder 📖CompOp
1 mathmath: csInf_Ici

Theorems

NameKindAssumesProvesValidatesDepends On
isGLB_csInf_of_directed 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
toPartialOrder
Set.Nonempty
BddBelow
IsGLB
InfSet.sInf
toInfSet
——

ConditionallyCompletePartialOrderSup

Definitions

NameCategoryTheorems
toPartialOrder 📖CompOp
725 mathmath: Order.coheight_add_one_le, upperBounds_supClosure, Filter.bliminf_sup_le_or_aux_right, Set.Finite.t2_separation, TopCat.binaryCofan_isColimit_iff, dirSupClosed_iff_forall_sSup, tendsto_zero_iff_meromorphicOrderAt_pos, Metric.ball_disjoint_ball, SimpleGraph.ediam_le_iff, OrderIso.map_radical, SimpleGraph.ediam_anti, Set.Iic.coe_sInf, homotopyEquivalences_le_quasiIso, Filter.liminf_eq, Order.LTSeries.length_le_krullDim, ENat.floor_pos, Continuous.strictMono_of_inj_boundedOrder', Order.krullDim_le_of_strictComono_and_surj, sInfHom.le_apply_bliminf, EisensteinSeries.hasSum_e2Summand_symmetricIcc, MeasureTheory.hittingBtwn_apply_mono_right, Antitone.Icc, PartENat.ofENat_le, MeasureTheory.hittingBtwn_mono_left, RootPairing.Base.not_nonneg_iff_neg_of_sum_mem_range_root, Filter.bliminf_sup_le_and_aux_right, SeparatedNhds.disjoint, Order.krullDim_lt_coe_iff, eq_sInf_coatoms, disjoint_or_subset_of_isClopen, NatOrdinal.instAddLeftReflectLE, SSet.modelCategoryQuillen.I_le_monomorphisms, supClosure_eq_self, MonotoneOn.Icc, Filter.blimsup_and_le_inf, Padic.withValUniformEquiv_norm_le_one_iff, tendsto_cobounded_iff_meromorphicOrderAt_neg, Set.Finite.lt_csInf_iff, NatOrdinal.lt_mul_iff, Disjoint.of_span₀, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, antitone_continuousOn, MeasureTheory.hittingAfter_bot_le_iff, isSublattice_latticeClosure, strictMono_nhdsSet, Filter.bliminf_sup_le_and_aux_left, ConditionallyCompleteLinearOrder.toCompactIccSpace, Monotone.Ici, isPreconnected_iff_ordConnected, Bornology.IsBounded.subset_Icc_sInf_sSup, iSupIndep.disjoint_biSup, Finset.ordConnected_range_coe, CompleteSublattice.isComplemented_iff, AntitoneOn.Ici, Order.krullDim_nonneg_iff, MeasureTheory.hittingBtwn_univ, inf_mem_infClosure, sSup_Iio_eq_self_iff_isSuccPrelimit, latticeClosure_univ, monotone_hausdorffEntourage, ENat.gc_toENNReal_floor, IsCompactlyGenerated.BooleanGenerators.isAtom, NFA.pumping_lemma, isPreconnected_Ici, isLeast_csInf, SeparatedNhds.disjoint_closure_left, ENat.ceil_le_ceil, Order.length_le_coheight, Int.padicValuation_lt_one_iff, Order.height_add_one_le, MeromorphicNFAt.meromorphicOrderAt_nonneg_iff_analyticAt, Filter.Realizer.map_F, IsUltrametricDist.ball_subset_trichotomy, SimpleGraph.Walk.edist_le, BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff, isGLB_infClosure, IsClosed.upperClosure, Monotone.Ioo, Order.krullDim_pos_iff, SimpleGraph.ComponentCompl.disjoint_right, Nimber.succ_def, Order.krullDim_le_one_iff, Filter.bliminf_sup_le_and, SimpleGraph.ediam_eq_top, EMetric.ball_disjoint, BoxIntegral.Box.disjoint_withBotCoe, Antitone.pairwise_disjoint_on_Ioc_pred, Function.sSup_div_semiconj, setOf_liouvilleWith_subset_aux, WellFoundedGT.iSup_eq_monotonicSequenceLimit, Pi.Colex.le_sSup_apply, Set.Nonempty.eq_Icc_iff_int, IsCompact.separation_of_notMem, IsSublattice.latticeClosure_eq, MeasureTheory.lowerCrossingTime_le, CategoryTheory.GrothendieckTopology.monotone_close, NatOrdinal.instIsOrderedMonoid, MeasureTheory.hittingAfter_mono, NatOrdinal.instIsOrderedRing, Nimber.mul_le_of_forall_ne, CompleteLattice.wellFoundedGT_iff_isSupFiniteCompact, ENat.le_floor, iSupIndep.pairwiseDisjoint, BoxIntegral.Box.Ioo_subset_coe, IsCompact.isLeast_sInf, RootPairing.setOf_root_add_zsmul_mem_eq_Icc, LinearOrderedField.lt_inducedMap_iff, Order.height_pos, Filter.bliminf_antitone, Finite.ciInf_le, separated_by_continuous, Order.le_krullDim_iff, Antitone.pairwise_disjoint_on_Ioo_pred, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_transfiniteCompositions, SimpleGraph.ComponentCompl.pairwise_disjoint, Nimber.add_le_of_forall_ne, disjoint_nested_nhds_of_not_inseparable, Order.succ_eq_iInf, LinearOrderedField.inducedOrderRingIso_self, exists_disjoint_vadd_of_isCompact, AntitoneOn.Icc, IsCompact.sSup_lt_iff_of_continuous, sSupIndep.pairwiseDisjoint, Disjoint.of_span, RootPairing.Base.pos_or_neg_of_sum_smul_root_mem, sSup_atoms_le_eq, TopologicalSpace.Closeds.gc, isEmbedding_sumElim, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, MonotoneOn.Iio, CategoryTheory.Sieve.overEquiv_le_overEquiv_iff, disjoint_interior_frontier, Filter.Realizer.ne_bot_iff, antitone_Ioi, Set.Finite.infClosure, ofDual_preimage_latticeClosure, Ordinal.iSup_succ, MeasureTheory.IsSetSemiring.disjointOfUnion_props, NatOrdinal.add_le_iff, Order.coheight_le_krullDim, Order.krullDim_nonpos_iff_forall_isMax, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Finset.coe_wcovBy_coe, Nimber.pos_iff_ne_zero, NatOrdinal.succ_def, Antitone.Ico, Monotone.pairwise_disjoint_on_Ioc_pred, CategoryTheory.Pretopology.mem_toGrothendieck, Antitone.pairwise_disjoint_on_Ioo_succ, εNFA.pumping_lemma, Filter.HasBasis.limsup_eq_sInf_iUnion_iInter, Order.coheight_eq_coe_add_one_iff, latticeClosure_mono, image_latticeClosure', Order.krullDim_nonpos_iff_forall_isMin, isConnected_Iio, Nimber.add_trichotomy, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, MeasureTheory.hittingBtwn_mono, Pi.Lex.sInf_apply_le, NatOrdinal.lt_add_iff, meromorphicOrderAt_add, upperHemicontinuousWithinAt_iff_preimage_Iic, EisensteinSeries.G2_eq_tsum_symmetricIco, Nimber.add_def, MeasureTheory.IsSetSemiring.isSetRing_supClosure, SimpleGraph.eccent_le_one_iff, Partition.pairwiseDisjoint, PartENat.toWithTop_lt, Filter.bliminf_sup_le_or_aux_left, MeasureTheory.upperCrossingTime_mono, ENat.floor_le_ceil, isPreconnected_Iic, Antitone.Ioc, MeasureTheory.hittingBtwn_apply_anti, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le, IsCompact.isLUB_sSup, NonarchimedeanGroup.exists_openSubgroup_separating, RootPairing.setOf_root_sub_zsmul_mem_eq_Icc, Int.cofinite_eq, Set.Nonempty.ordConnected_iff_of_bdd', MeasureTheory.AddContent.supClosure_apply_finpartition, CompleteAtomicBooleanAlgebra.instIsCoatomistic, iSupIndep_pair, ENat.iInf_coe_lt_top, ENat.ceil_lt_top, Ctop.Realizer.nhds_F, Set.Finite.csSup_lt_iff, lowerHemicontinuous_iff_isOpen_compl_preimage_Iic_compl, MeasureTheory.IsSetSemiring.mem_supClosure_iff, Order.height_le_krullDim, SupClosed.infClosure, Topology.IsUpper.isTopologicalSpace_basis, NatOrdinal.lt_one_iff_zero, tendsto_intCast_atBot_sup_atTop_cobounded, disjoint_nhdsSet_principal, BoxIntegral.Box.iUnion_Ioo_of_tendsto, t2_separation_nhds, sInf_eq_argmin_on, NatOrdinal.instIsOrderedCancelAddMonoid, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_monotone, sSup_compact_eq_top, MonotoneOn.Ici, ciInf_le', Filter.bliminf_or_le_inf, MeasureTheory.lowerCrossingTime_le_upperCrossingTime_succ, CategoryTheory.GrothendieckTopology.closureOperator_isClosed, infClosed_infClosure, SummationFilter.hasSum_symmetricIoc_int_iff, CategoryTheory.GrothendieckTopology.PreservesSheafification.le, Order.bot_lt_krullDim, isConnected_Ici, AnalyticAt.meromorphicOrderAt_nonneg, topologicalKrullDim_subspace_le, Int.ball_eq_Ioo, essSup_eq_sInf, MeasureTheory.upperCrossingTime_le_lowerCrossingTime, CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSup, MeasureTheory.dense_of_generateFrom_isSetSemiring, NonarchimedeanAddGroup.exists_openAddSubgroup_separating, TopologicalSpace.Clopens.coe_disjoint, topologicalKrullDim_zero_of_discreteTopology, Set.isCoatom_iff, MeasureTheory.hitting_eq_end_iff, Monotone.Iio, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, SummationFilter.hasSum_symmetricIcc_iff, supClosure_empty, isInducing_sumElim, BoxIntegral.Box.Ioo_ae_eq_Icc, compl_image_latticeClosure, Order.Ideal.PrimePair.isCompl_I_F, TopologicalSpace.Opens.gc, PrimitiveSpectrum.gc_closureOperator, Order.coheight_pos_of_lt_top, WithTop.iInf_coe_eq_top, upperHemicontinuousOn_iff_preimage_Iic, Set.Nonempty.ciSup_lt_iff, infClosure_singleton, Order.coheight_eq_coe_iff_maximal_le_coheight, ENat.ceil_le, csInf_le', MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq, RootPairing.setOf_root_add_zsmul_eq_Icc_of_linearIndependent, Partition.le_of_mem, SetTheory.PGame.grundyValue_le_of_forall_moveLeft, Order.height_pos_of_bot_lt, Set.isAtom_singleton, NatOrdinal.not_lt_zero, ENat.ceil_lt, SimpleGraph.edist_pos_of_ne, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiffUnion, Set.monotone_accumulate, tendsto_nhds_iff_meromorphicOrderAt_nonneg, Topology.IsInducing.disjoint_of_sumElim_aux, latticeClosure_prod, isPreconnected_Icc, ContinuousOn.image_uIcc_eq_Icc, separated_by_isOpenEmbedding, Setoid.eqv_classes_disjoint, Monotone.Ico, InfClosed.infClosure_eq, ENat.ceil_pos, EisensteinSeries.hasSum_e2Summand_symmetricIco, MeasureTheory.hitting_le, Order.krullDim_nonpos_of_subsingleton, LinearOrderedField.inducedOrderRingHom_toFun, iSupIndep_def'', Antitone.Iio, Padic.AddValuation.map_add, upperHemicontinuousAt_iff_preimage_Iic, ENat.ceil_add_le, ENat.lt_ceil, exists_nhds_disjoint_closure, LinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap, iSup_le_iSup_of_partialSups_le_partialSups, PartENat.toWithTop_le, Finite.le_ciSup, IsInducing.topologicalKrullDim_le, MeasureTheory.IsSetSemiring.diff_mem_supClosure, MeasureTheory.hittingAfter_eq_top_iff, infClosure_eq_self, csInf_Ioi, IsCompact.lt_sInf_iff_of_continuous, CategoryTheory.PreZeroHypercover.presieve₀_restrictIndex_le, meromorphicNFAt_iff_analyticAt_or, compl_image_latticeClosure_eq_of_compl_image_eq_self, latticeClosure_singleton, Nimber.small_Ioo, setOf_isPreconnected_eq_of_ordered, CompleteSublattice.codisjoint_iff, MeasureTheory.hittingAfter_univ, ENat.floor_lt_ceil, iSupIndep_def', le_ciInf_iff', WithTop.iSup_coe_lt_top, exists_open_nhds_disjoint_closure, untrop_sum, ENat.floor_lt_top, disjoint_measurableAtom_of_notMem, MeasureTheory.disjoint_cylinder_iff, CompleteSublattice.isCompl_iff, MonotoneOn.Iic, isAtomic_of_complementedLattice, MeasureTheory.hittingBtwn_apply_mono_left, isPreconnected_Ioi, MeasureTheory.hittingBtwn_anti, CategoryTheory.MorphismProperty.retracts_transfiniteComposition_pushouts_coproducts_le_llp_rlp, ENat.gc_ceil_toENNReal, NFA.disjoint_evalFrom_reverse_iff, Filter.bliminf_sup_le_inf_aux_left, infClosure_univ, sSup_atoms_eq_top, subset_latticeClosure, Filter.bliminf_sup_le_inf_aux_right, Order.height_eq_coe_add_one_iff, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfUnion_of_mem, subset_infClosure, IsClosedEmbedding.topologicalKrullDim_le, disjoint_frontier_iff_isOpen, Order.krullDim_enat, isTotallyDisconnected_iff_lt, MeasureTheory.IsSetSemiring.pairwiseDisjoint_biUnion_disjointOfUnion, Order.height_le_coe_iff, IsGenericPoint.disjoint_iff, NatOrdinal.mul_le_iff, CompleteLattice.isSupClosedCompact_iff_wellFoundedGT, Order.height_eq_coe_iff, MeasureTheory.hittingAfter_apply_anti, MeasureTheory.IsSetSemiring.diff_eq_sUnion', AntitoneOn.Ioi, Antitone.pairwise_disjoint_on_Ioc_succ, SimpleGraph.edist_le_eccent, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.exists_oneHypercover, isPreconnected_Ico, SimpleGraph.edist_triangle, Filter.Realizer.mem_sets, RootPairing.Base.not_nonpos_iff_pos_of_sum_mem_range_root, WithTop.iInf_coe_lt_top, exists_seq_infinite_isOpen_pairwise_disjoint, Order.pred_eq_sSup, BooleanSubalgebra.latticeClosure_subset_closure, Antitone.Ioi, ConditionallyCompleteLinearOrderedField.to_archimedean, Order.length_le_height, IsUltrametricDist.ball_eq_or_disjoint, eq_Icc_of_connected_compact, BooleanSubalgebra.closure_latticeClosure, Order.height_le_height_apply_of_strictMono, upperHemicontinuous_iff_isOpen_preimage_Iic, upperHemicontinuous_iff_preimage_Iic, BoxIntegral.Prepartition.pairwiseDisjoint, Antitone.Ici, NatOrdinal.instAddLeftStrictMono, Metric.ball_disjoint_closedBall, Order.krullDim_le_one_iff_of_boundedOrder, AntitoneOn.Iic, sInf_iUnion_Ici, CategoryTheory.MorphismProperty.IsStableUnderTransfiniteCompositionOfShape.le, Set.Finite.supClosure, Set.Iic.coe_iInf, Filter.Realizer.ofEquiv_F, Pi.Colex.sInf_apply_le, CauchyFilter.monotone_gen, Set.isCoatom_singleton_compl, ENat.floor_mono, CompleteLattice.IsSupClosedCompact.wellFoundedGT, CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderComposition, LinearOrderedField.inducedMap_mono, setOf_isPreconnected_subset_of_ordered, connectedComponent_disjoint, ENat.le_ceil, Order.krullDim_eq_iSup_coheight, Set.Iic.coe_biInf, Set.Iic.coe_sSup, OrderIso.map_ciSup', sup_mem_supClosure, sSupIndep.disjoint_sSup, SimpleGraph.ediam_le_two_mul_radius, lowerBounds_infClosure, isPreconnected_Ioc, gc_nhdsKer_interior, ProperlyDiscontinuousSMul.exists_nhds_disjoint_image, isPreconnected_Ioo, SeparatedNhds.disjoint_closure_right, CompleteLattice.isCoatomistic_iff, SummationFilter.hasProd_symmetricIco_int_iff, MeasureTheory.hittingBtwn_mono_right, monotone_Iio, SummationFilter.hasSum_symmetricIco_int_iff, SimpleGraph.eccent_le_ediam, supClosure_isClosed, Order.pred_eq_iSup, CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsGenerating.le, CategoryTheory.Presieve.le_of_factorsThru_sieve, Set.isAtom_iff, Monotone.Ioc, Nimber.not_bddAbove_compl_of_small, Order.krullDim_eq_iSup_height, Finset.coe_covBy_coe, SimpleGraph.eccent_pos_iff, Topology.IsScott.instUnivSetOfIsUpper, smul_iInf_le, supClosure_singleton, trop_iInf, Order.coheight_le_coheight_apply_of_strictMono, image_latticeClosure, latticeClosure_eq_self, CFilter.mem_toFilter_sets, latticeClosure_empty, NatOrdinal.instAddLeftMono, BoxIntegral.Box.Ioo_subset_Icc, SimpleGraph.edist_anti, Filter.mono_bliminf', le_csInf_iff', IsCompact.isGLB_sInf, BoxIntegral.Box.exists_seq_mono_tendsto, SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint, Finset.untrop_sum, supClosure_mono, Set.Iic.instIsCompactlyGenerated, PartENat.ofENat_lt, t2_separation_compact_nhds, Order.one_le_krullDim_iff, IndexedPartition.disjoint, lowerHemicontinuous_iff_isClosed_preimage_Iic, Nimber.not_lt_zero, Order.coheight_le_iff', Order.krullDim_le_of_strictMono, SupClosed.supClosure_eq, essInf_eq_sSup, WithTop.isGLB_sInf, PrimitiveSpectrum.closedsGC_closureOperator, Monotone.pairwise_disjoint_on_Ico_pred, Order.pred_eq_csSup, ConditionallyCompleteLinearOrder.isCompact_Icc, Nimber.small_Ioc, monotone_Iic, AntitoneOn.Ioo, PartENat.withTopEquiv_le, ProperlyDiscontinuousVAdd.exists_nhds_disjoint_image, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, Monotone.pairwise_disjoint_on_Ioo_succ, Metric.AreSeparated.disjoint, BoxIntegral.Box.disjoint_coe, PartENat.withTopEquiv_lt, DFA.pumping_lemma, le_csInf_iff'', Nimber.small_Icc, LinearOrderedField.inducedOrderRingIso_symm, MeasureTheory.hitting_mono, Continuous.strictMono_of_inj, Finsupp.codisjoint_supported_supported_iff, IsCompactlyGenerated.exists_sSup_eq, Set.Iic.coe_iSup, iSupIndep_def, T2Space.t2, Monotone.Ioi, infClosure_min, IsCompactlyGenerated.BooleanGenerators.sSup_le_sSup_iff_of_atoms, Metric.closedBall_disjoint_ball, ENat.ceil_mono, CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_llp_rlp, iSup_succ, AntitoneOn.Iio, isConnected_Iic, Filter.Realizer.le_iff, latticeClosure_idem, t2Space_iff_nhds, Nimber.small_Iic, MeasureTheory.hittingAfter_mem_set_of_ne_top, Monotone.pairwise_disjoint_on_Ioo_pred, CategoryTheory.MorphismProperty.retracts_transfiniteCompositionsOfShape_pushouts_coproducts_le_llp_rlp, CompleteLattice.IsSupFiniteCompact.wellFoundedGT, RootPairing.Base.exists_root_eq_sum_int, Filter.HasBasis.liminf_eq_sSup_iUnion_iInter, Monotone.pairwise_disjoint_on_Ioc_succ, Nimber.one_le_iff_ne_zero, RootPairing.root_add_zsmul_mem_range_iff, sSupIndep_pair, SimpleGraph.edist_le_ediam, iSup_Iio_eq_self_iff_isSuccPrelimit, sSup_compact_le_eq, isPreconnected_Iio, Order.coheight_le_coe_iff, IsClosed.lowerClosure, Topology.IsScott.scott_eq_upper_of_completeLinearOrder, WithBot.coe_biInf, EisensteinSeries.tendsto_double_sum_S_act, SummationFilter.symmetricIcc_eq_symmetricIoo_int, disjoint_principal_nhdsSet, Filter.Realizer.principal_F, infClosure_prod, MeasureTheory.hittingBtwn_le, IsCompactlyGenerated.BooleanGenerators.isAtomistic_of_sSup_eq_top, Int.closedBall_eq_Icc, CategoryTheory.GrothendieckTopology.le_close, Set.antitone_dissipate, Order.krullDim_le_one_iff_forall_isMax, NatOrdinal.zero_le, RootedTree.subtrees_disjoint, EisensteinSeries.summable_e2Summand_symmetricIcc, ENat.floor_lt, Filter.bliminf_or_le_inf_aux_left, Metric.eball_disjoint, Order.krullDim_pos_iff_of_orderTop, Nimber.mul_def, SimpleGraph.radius_le_ediam, WithTop.iSup_coe_eq_top, WithTop.isLUB_sSup, MeasureTheory.hittingBtwn_eq_end_iff, Set.Finite.latticeClosure, Order.coheight_coe_enat, Topology.IsScott.isOpen_iff_Iic_compl_or_univ, CategoryTheory.MorphismProperty.transfiniteCompositions_le, TopologicalSpace.gc_generateFrom, TopologicalSpace.Closeds.isAtom_coe, SimpleGraph.eccent_le_iff, MeasureTheory.upperCrossingTime_zero', FiberBundle.exists_trivialization_Icc_subset, NFA.disjoint_stepSet_reverse, LinearOrderedField.inducedMap_nonneg, isAtomistic_of_complementedLattice, Order.krullDim_pos_iff_of_orderBot, Partition.disjoint, Nimber.small_Ico, Filter.limsup_le_iSup, Order.succ_eq_csInf, IsUltrametricDist.closedBall_subset_trichotomy, MonotoneOn.Ico, Filter.bliminf_antitone_filter, PartENat.withTopEquiv_symm_le, iSupIndep_map_orderIso_iff, Filter.iInf_le_liminf, supClosure_infClosure, Set.instIsCoatomistic, Partition.bot_lt_of_mem, infClosure_mono, isSeparatedMap_iff_nhds, LinearOrderedField.coe_inducedOrderRingIso, MeasureTheory.lowerCrossingTime_mono, MonotoneOn.Ioc, CompleteLattice.isSupFiniteCompact_iff_all_elements_compact, MeasureTheory.hittingAfter_le_iff, CompleteLattice.wellFoundedGT_characterisations, Order.coheight_eq_coe_iff, NatOrdinal.small_Ioc, MeasureTheory.AddContent.supClosure_apply_of_mem, monotone_nhdsSet, InfClosed.supClosure, SSet.modelCategoryQuillen.J_le_monomorphisms, antitone_Ici, CategoryTheory.MorphismProperty.isStableUnderTransfiniteCompositionOfShape_iff, SimpleGraph.radius_le_eccent, MeasureTheory.upperCrossingTime_le, ENat.lt_floor, NatOrdinal.small_Iio, LinearOrderedField.coe_lt_inducedMap_iff, csSup_Iio, isConnected_Ioi, TopologicalSpace.Opens.coe_disjoint, MeasureTheory.hittingAfter_apply_mono, Set.Iic.coe_biSup, Filter.blimsup_mono, CompleteAtomicBooleanAlgebra.instIsAtomistic, BoxIntegral.Box.measurableSet_Ioo, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, MeasureTheory.le_hittingAfter, DoubleCoset.disjoint_out, Order.height_le_iff, Antitone.Iic, OrderIso.apply_blimsup, MonotoneOn.Ioo, complementedLattice_iff_isAtomistic, infClosure_supClosure, CompleteLatticeHom.toOrderIsoRangeOfInjective_apply, untrop_sum_eq_sInf_image, Filter.bliminf_or_le_inf_aux_right, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, Filter.Realizer.bot_F, Order.KrullDimLE.krullDim_le, Monotone.Iic, NatOrdinal.small_Ico, supClosure_idem, Setoid.IsPartition.pairwiseDisjoint, Padic.norm_rat_le_one_iff_padicValuation_le_one, sSupIndep_iff_pairwiseDisjoint, Filter.Realizer.top_F, csSup_Iic, EisensteinSeries.summable_e2Summand_symmetricIco, RootPairing.root_sub_zsmul_mem_range_iff, Filter.blimsup_sup_le_or, NatOrdinal.small_Ioo, Order.coheight_anti, infClosure_idem, IsCompactlyGenerated.BooleanGenerators.eq_atoms_of_sSup_eq_top, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, CompleteSublattice.disjoint_iff, Order.height_mono, Order.height_le_iff', Order.krullDim_nonneg, upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl, Monotone.Icc, WCovBy.finset_coe, BoxIntegral.Prepartition.disjoint_coe_of_mem, Antitone.pairwise_disjoint_on_Ico_pred, Order.coheight_pos, CategoryTheory.MorphismProperty.transfiniteCompositions_pushouts_coproducts_le_llp_rlp, CompleteLattice.isAtomistic_iff, SummationFilter.symmetricIcc_eq_map_Icc_nat, sSup_iUnion_Iic, Submodule.span_monotone, WithBot.coe_biSup, Perfect.splitting, Order.index_le_height, CovBy.finset_coe, Metric.sphere_disjoint_ball, infClosure_isClosed, tendsto_intCast_atTop_cobounded, Order.krullDim_le_one_iff_forall_isMin, SummationFilter.hasProd_symmetricIcc_iff, Topology.IsLower.isTopologicalSpace_basis, Filter.blimsup_monotone_filter, subset_supClosure, ENat.floor_le_floor, Pi.Lex.le_sSup_apply, Filter.limsup_eq, AntitoneOn.Ioc, SimpleGraph.edist_le, disjoint_nhdsWithin_of_mem_discrete, finsetInf'_mem_infClosure, iSupIndep.map_orderIso, csInf_le_csInf', Dynamics.dynEntourage_antitone, Order.rev_index_le_coheight, AntitoneOn.Ico, Int.padicValuation_le_one, Filter.mono_blimsup', nhdsKer_mono, latticeClosure_isClosed, SetTheory.PGame.grundyValue_le_of_forall_moveRight, sSupHom.apply_blimsup_le, MeasurableSpace.disjoint_countablePartition, CompleteLattice.isCompactElement_iff_le_of_directed_sSup_le, exists_disjoint_smul_of_isCompact, disjoint_nested_nhds, csInf_univ, Int.instIsOrderBornology, NatOrdinal.small_Icc, Nimber.le_zero, MonotoneOn.Ioi, IsCompact.isGreatest_sSup, Nimber.small_Iio, isLUB_supClosure, ZLattice.sum_piFinset_Icc_rpow_le, Finsupp.disjoint_supported_supported_iff, Set.instIsAtomistic, Order.height_enat, supClosure_prod, finsetSup'_mem_supClosure, Order.length_le_height_last, IsPreconnected.mem_intervals, tendsto_intCast_atBot_cobounded, infClosure_empty, Order.Ideal.PrimePair.disjoint, MeasureTheory.AddContent.supClosure_apply, iSupIndep_iff_pairwiseDisjoint, Pell.IsFundamental.y_strictMono, supClosed_supClosure, MeasureTheory.hittingAfter_anti, Order.length_le_coheight_head, Nimber.lt_one_iff_zero, NatOrdinal.small_Iic, r1_separation, ENat.ceil_le_floor_add_one, eq_sSup_atoms, PartENat.withTopEquiv_symm_lt, SummationFilter.hasProd_symmetricIoc_int_iff, OnePoint.isCompl_range_coe_infty, MeasureTheory.hittingAfter_lt_iff, PrimitiveSpectrum.gc, Antitone.Ioo, Mathlib.Meta.Positivity.natCeil_pos, Order.bot_lt_krullDim_iff, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, Order.height_eq_coe_iff_minimal_le_height, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, trop_sInf_image, supClosure_univ, le_iff_compact_le_imp, t2_separation, Filter.Realizer.tendsto_iff, CategoryTheory.MorphismProperty.transfiniteCompositions_monotone, WithTop.isLUB_sSup', latticeClosure_min, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiffUnion, Order.one_lt_height_iff, Order.coheight_le_iff, ENat.iSup_coe_lt_top, CategoryTheory.MorphismProperty.transfiniteCompositions_le_llp_rlp, IsCompact.exists_sSup_image_eq_and_ge, IsUltrametricDist.closedBall_eq_or_disjoint, ClassGroup.exists_mem_finset_approx', ENat.floor_le, Order.krullDimLE_iff, CategoryTheory.PreZeroHypercover.Hom.sieve₀_le_sieve₀, Dynamics.dynEntourage_monotone, monotone_closure, Order.succ_eq_sInf, ClassGroup.exists_mem_finsetApprox, Rat.padicValuation_le_one_iff, Antitone.pairwise_disjoint_on_Ico_succ, SimpleGraph.edist_le_one_iff_adj_or_eq, OrderIso.apply_bliminf, supClosure_min, Metric.closedBall_disjoint_closedBall, IsCompact.exists_sInf_image_eq_and_le, CategoryTheory.MorphismProperty.le_transfiniteCompositions, t2Space_iff, dirSupInacc_iff_forall_sSup, Int.cobounded_eq, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, CategoryTheory.MorphismProperty.transfiniteCompositions_le_iff, Monotone.pairwise_disjoint_on_Ico_succ
toSupSet 📖CompOp
1183 mathmath: BooleanSubalgebra.map_iSup, CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSup, Ordinal.iSup_eq_iSup, IsClosed.sSup_mem, Ordinal.iSup_eq_bsup, dirSupClosed_iff_forall_sSup, csSup_pair, Order.IsNormal.apply_of_isSuccLimit, Ordinal.lift_card_iSup_le_sum_card, Acc.rank_eq, Cardinal.mk_sUnion_le, Ordinal.iSup_pow_natCast, Filter.liminf_eq, AddSubmonoid.smul_iSup, Module.rank_def, isFullyInvariant_iff_sSup_isotypicComponents, Filter.HasBasis.liminf_eq_ite, Nat.iSup_lt_succ', MeasureTheory.lintegral_def, Function.csSup_div_semiconj, Ordinal.sup_eq_lsub_iff_lt_sup, ciSup_mul_le, FirstOrder.Language.Substructure.mem_sSup_of_directedOn, isSaddlePointOn_value, Measurable.biSup, EMetric.hausdorffEdist_iUnion_le, IntermediateField.sSup_toSubfield, csSup_image2_eq_csInf_csInf, ENat.sSup_eq_top_of_infinite, MulAction.IwasawaStructure.is_generator, iSup_eq_of_tendsto, AlgebraicGeometry.iSup_affineOpens_eq_top, Subalgebra.coe_iSup_of_directed, dimH_sUnion, lowerSemicontinuous_ciSup, Subfield.mem_sSup_of_directedOn, setOf_isOpen_iSup, isClosed_iSup_iff, lowerSemicontinuousOn_biSup, MeasureTheory.lintegral_iSup', Cardinal.lift_iSup_le_lift_iSup, Monotone.leftLim_eq_sSup, TopologicalSpace.Opens.coe_iSup, ciSup_unique, csSup_le_iff, DirectedOn.subset_Icc_csInf_csSup, TopCat.Presheaf.coveringOfPresieve.iSup_eq_of_mem_grothendieck, FirstOrder.Language.Substructure.mem_iSup_of_directed, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, ContinuousOn.le_sSup_image_Icc, csSup_le', NNReal.iSup_of_not_bddAbove, Ordinal.sup_eq_lsub_iff_succ, Matrix.iSup_eigenspace_toLin'_diagonal_eq_top, lowerSemicontinuousWithinAt_iSup, NNReal.mul_iSup_le, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, Set.Icc.coe_sSup, ENat.smul_sSup, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup, MeasureTheory.setLIntegral_le_iSup_mul, Ordinal.iSup_typein_succ, LieSubmodule.iSup_toSubmodule, ProbabilityTheory.condIndep_iSup_of_antitone, IntermediateField.isPurelyInseparable_iSup, AlgebraicGeometry.IsAffineOpen.iSup_of_disjoint, Metric.hausdorffEDist_def, SSet.iSup_subcomplexOfSimplex_prod_eq_top, Monotone.iSup_comp_tendsto_atTop, DirectedOn.csSup_eq_of_forall_le_of_forall_lt_exists_gt, continuous_sSup_dom, AntitoneOn.tendsto_nhdsGT, CategoryTheory.MorphismProperty.HasCardinalLT.iSup, AddMonoidHom.noncommPiCoprod_range, Subalgebra.op_sSup, isClosed_sSup_iff, Bornology.IsBounded.subset_Icc_sInf_sSup, iSupIndep.disjoint_biSup, ciSup_partialSups_eq', Cardinal.iSup_of_empty, SSet.finite_iSup_iff, Submodule.map₂_iSup_right, sSup_Iio_eq_self_iff_isSuccPrelimit, IsOpen.measure_eq_iSup_isClosed, Cardinal.iSup_lt_of_isRegular, Ideal.mem_sSup_of_mem, Metric.hausdorffEDist_iUnion_le, IsCompactlyGenerated.BooleanGenerators.sSup_inter, ENat.iSup_add_iSup_of_monotone, ENNReal.iSup_pow_of_ne_zero, ENat.iSup_zero, ProbabilityTheory.Kernel.indep_iSup_directed_limsup, MeasureTheory.OuterMeasure.iUnion_nat_of_monotone_of_tsum_ne_top, NNReal.coe_sSup, Set.indicator_iUnion_apply, ProbabilityTheory.indep_iSup_of_monotone, MeasureTheory.lintegral_iSup_ae, Directed.disjoint_iSup_right, IntermediateField.coe_iSup_of_directed, Submodule.map_iSup, Submodule.mem_iSup_iff_exists_finsupp, monotone_transfiniteIterate, Set.iSup_mulIndicator, Directed.Ici_ciSup, Ordinal.sup_succ_le_lsub, ClosedSubmodule.coe_sSup, Algebra.sSup_def, Ordinal.iSup_le_lsub, Ordinal.card_iSup_Iio_le_sum_card, sup_eq_top_of_top_mem, tendsto_atBot_ciSup, MeasureTheory.OuterMeasure.coe_iSup, Cardinal.sum_le_mk_mul_iSup, MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone, cbiSup_eq_of_not_forall, Dense.ciSup, MeasureTheory.lintegral_iSup_directed, Subalgebra.centralizer_coe_iSup, ciSup_add, Ideal.sup_primeHeight_eq_ringKrullDim, Function.sSup_div_semiconj, ciSup_sub, RootPairing.coe_chainBotCoeff_eq_sSup, ENNReal.iSup_add_iSup_le, WellFoundedGT.iSup_eq_monotonicSequenceLimit, Set.Nonempty.eq_Icc_iff_int, Directed.measure_iUnion, DirectSum.isInternal_submodule_iff_iSupIndep_and_iSup_eq_top, SupClosed.biSup_mem_of_nonempty, ProbabilityTheory.condIndep_iSup_of_monotone, Submodule.iSup_map_single_le, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinal, IsCompact.sSup_mem, LinearMap.iSup_range_single, NNReal.coe_iSup, TopologicalSpace.Opens.iSup_mk, AddSubmonoid.iSup_map_single, LinearMap.eventually_iSup_ker_pow_eq, Subfield.coe_iSup_of_directed, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one, MonotoneOn.tendsto_nhdsLT, MeasureTheory.Measure.mkMetric_apply, MeasureTheory.biSup_measure_Iic, ciSup_eq_of_forall_le_of_forall_lt_exists_gt, ENNReal.toNNReal_sSup, Submodule.smul_iSup', ENNReal.inv_sSup, Filter.liminf_eq_iSup_iInf_of_nat', le_ciSup_of_le, iSup_partialSups_eq, MeasurableSpace.measurableSet_sSup, Submodule.biSup_comap_subtype_eq_top, Filter.HasBasis.limsInf_eq_iSup_sInf, Subgroup.FG.biSup, lt_csSup_iff, Submodule.biSup_eq_range_dfinsupp_lsum, Algebra.adjoin_attach_biUnion, ContinuousLinearMap.sSup_sphere_eq_nnnorm, Set.mulIndicator_iUnion_apply, Filter.bliminf_eq_iSup_biInf_of_nat, MeasureTheory.SimpleFunc.iSup_coe_eapprox, GaloisConnection.l_csSup', DirectedOn.csSup_le, DirectedOn.disjoint_sSup_left, WithTop.coe_sSup, MeasurableSet.measure_eq_iSup_isCompact_of_ne_top, AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff, OrderIso.map_csSup_of_directedOn, IsCompact.sSup_lt_iff_of_continuous, lowerSemicontinuousOn_iSup, Submodule.fg_biSup, Order.IsSuccLimit.iSup_Iio, generateFrom_iInter_of_generateFrom_eq_self, ENat.mul_iSup, ENat.sSup_eq_zero, sSup_atoms_le_eq, AddSubgroup.noncommPiCoprod_range, csSup_eq_top_of_top_mem, LinearMap.iInf_ker_proj_le_iSup_range_single, MeasureTheory.Measure.LebesgueDecomposition.iSup_succ_eq_sup, ciSup_mul, NNReal.iSup_eq_zero, Matroid.cRank_eq_iSup_cardinalMk_indep, MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE, Ordinal.iSup_le, CompleteSublattice.sSupClosed', Pi.Colex.sSup_apply, IntermediateField.finiteDimensional_iSup_of_finset, Filter.limsup_top_eq_ciSup, AffineSubspace.span_iUnion, SSet.iSup_skeleton, csSup_Icc, ciSup_le_iff, PrimeSpectrum.iSup_basicOpen_eq_top_iff, IsNormalClosure.adjoin_rootSet, Submodule.annihilator_iSup, Subfield.closure_iUnion, ENNReal.iSup_ne_top, TopCat.colimit_topology, Submodule.neg_iSup, Ordinal.iSup_succ, Ordinal.Principal.sSup, egauge_univ_pi, tendsto_atTop_ciSup, ProbabilityTheory.indep_biSup_limsup, Ideal.Filtration.sSup_N, Monoid.CoprodI.mrange_eq_iSup, AlgebraicGeometry.Scheme.Hom.image_iSup₂, MeasureTheory.stoppedValue_hitting_mem, ExpGrowth.expGrowthSup_biSup, MeasureTheory.eLpNormEssSup_eq_iSup, isNoetherian_iSup, MeasureTheory.exists_isSigmaFiniteSet_measure_ge, Filter.HasBasis.limsup_eq_ite, ENat.biSup_add', Ideal.iSup_eq_span, Finset.sup_univ_eq_ciSup, ENat.sum_iSup, csSup_le_csSup', normalClosure_eq_iSup_adjoin', ENNReal.biSup_add, MeasureTheory.measure_sigmaFiniteSetGE_le, sSup_isotypicComponents, CompleteAtomicBooleanAlgebra.eq_setOf_le_sSup_and_isAtom, DirectedOn.le_csSup_of_le, ENNReal.sSup_div, continuous_sSup_rng, Measurable.iSup, MeasurableSpace.generateFrom_iUnion_measurableSet, ProbabilityTheory.Kernel.indep_iSup_limsup, Ordinal.iSup_pow, Submodule.submodule_eq_sSup_le_nonzero_spans, csInf_div, EMetric.diam_insert, Cardinal.lift_iSup, AntitoneOn.tendsto_nhdsWithin_Ioo_right, ProbabilityTheory.indep_iSup_of_directed_le, Ordinal.deriv_limit, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing_types, ENNReal.coe_sSup, Measurable.iSup_Prop, AlgebraicGeometry.Scheme.Hom.preimage_iSup, MeasureTheory.stoppedValue_hittingBtwn_mem, csSup_image2_eq_csSup_csSup, MeasureTheory.Measure.LebesgueDecomposition.iSup_le_le, ENNReal.biSup_add_biSup_le, SupClosed.iSup_mem, le_ciSup_iff', Submodule.iSup_mul, csSup_le_iff', GaloisConnection.l_ciSup_set_of_directedOn, Submodule.localized'_iSup, isLUB_ciSup, LinearMap.isCompl_iSup_ker_pow_iInf_range_pow, HomogeneousIdeal.toIdeal_iSup₂, Ordinal.sSup_eq_bsup, Cardinal.lift_sSup, MeasureTheory.Content.innerContent_iSup_nat, Monotone.tendsto_nhdsLT, Submodule.dualCoannihilator_iSup_eq, Ordinal.iSup_add_nat, Cardinal.mk_biUnion_le_lift, ENNReal.iSup_coe_lt_top, IsCompact.isLUB_sSup, Submodule.span_attach_biUnion, OrderIso.map_ciSup, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top', MeasureTheory.lintegral_le_iSup_mul, Cardinal.lift_iSup_le, Set.Nonempty.ordConnected_iff_of_bdd', Ordinal.iSup_sum, MeasureTheory.hittingAfter_mem_set, Submodule.comap_iSup_map_of_injective, le_ciSup_set, Submodule.map₂_iSup_left, ProbabilityTheory.avgRisk_le_iSup_risk, ciSup_add_le, LinearMap.iSup_range_single_eq_iInf_ker_proj, Set.Finite.csSup_lt_iff, ENNReal.iSup_natCast, ciInf_le_ciSup, IsConnected.Ioo_csInf_csSup_subset, DirectedOn.sSup_inf_eq, Antitone.iSup_comp_tendsto_atBot, IsGreatest.csSup_mem, sInf_sub, sSup_compact_eq_top, ENat.add_iSup, NNReal.iSup_mul_iSup_le, IntermediateField.normal_iSup, Function.mulSupport_iSup, LieModule.coe_genWeightSpaceOf_zero, Antitone.map_ciInf_of_continuousAt, ciSup_add_ciSup_le, Ordinal.iSup_eq_lsub_or_succ_iSup_eq_lsub, ENat.mul_sSup, csSup_mul, Submodule.isOrtho_sSup_right, Submodule.iSup_span, Antitone.tendsto_nhdsGT, MeasurableSet.measure_eq_iSup_isCompact, Ordinal.sup_succ_eq_lsub, SupClosed.sSup_mem_of_nonempty, csSup_lowerBounds_eq_csInf, Ordinal.sSup_ord, AddSubmonoid.FG.iSup, TopCat.Presheaf.SheafConditionEqualizerProducts.w, csSup_one, DirectedOn.ciSup_set_le_iff, Module.End.iSup_genEigenspace_eq, AddSubmonoid.mul_iSup, ENNReal.smul_iSup, Order.krullDim_eq_iSup_coheight_of_nonempty, ENNReal.iSup_add, sSup_inv, Submodule.iSup_dualAnnihilator_le_iInf, Subgroup.FG.biSup_finset, ENat.coe_sSup, MeasureTheory.measure_biUnion_eq_iSup, RootPairing.coe_chainTopCoeff_eq_sSup, Ordinal.iSup_mul_nat, ClosedSubmodule.toSubmodule_iSup, BooleanSubalgebra.sSup_mem, Submodule.sum_mem_iSup, sSup_mul, ENNReal.tsum_iSup_eq, Submodule.mem_iSup_iff_exists_dfinsupp, isOpen_sSup_iff, LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute, Submodule.span_range_eq_iSup, Order.krullDim_eq_iSup_length, Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim, Monotone.le_csSup_image, IntermediateField.sSup_def, Ideal.IsHomogeneous.iSup, Finset.Nonempty.ciSup_mem_image, egauge_pi, AlgebraicGeometry.iSup_basicOpen_of_span_eq_top, Submodule.iSup_eq_range_dfinsupp_lsum, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_W, Set.Nonempty.ciSup_lt_iff, Monoid.CoprodI.range_eq_iSup, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, sInf_neg, Partition.sSup_eq', NNReal.agm_eq_ciSup, DFinsupp.iSup_range_lsingle, ENNReal.toNNReal_iSup, Antitone.measure_iUnion, Submonoid.iSup_map_mulSingle, HomogeneousIdeal.toIdeal_sSup, ENNReal.tsum_eq_iSup_nat', Metric.ediam_eq_sSup, ENNReal.inv_iSup, sInf_inv, Filter.liminf_eq_sSup_sInf, Finset.sup'_eq_csSup_image, OrthogonalFamily.isInternal_iff, csSup_Ioo, AlgebraicGeometry.IsAffineOpen.self_le_basicOpen_union_iff, MeasureTheory.isStoppingTime_hittingBtwn_isStoppingTime, LeftOrdContinuous.map_sSup', lowerClosure_eq_Iic_csSup, ContinuousOn.image_uIcc_eq_Icc, IsMaxOn.iSup_eq, SequentialSpace.iSup, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, NumberField.isTotallyReal_iSup, Ordinal.sup_le_lsub, Ordinal.iSup_add_natCast, ENat.add_sSup, Filter.blimsup_eq_iInf_biSup, ENNReal.tsum_eq_iSup_sum, csSup_Ioc, DirectedOn.csInf_le_csSup, Sublattice.le_comap_iSup, Ordinal.IsNormal.map_iSup, NNReal.sSup_of_not_bddAbove, iSupIndep_def'', IsPreconnected.Iio_csSup_subset, iSup_eq_iSup_subseq_of_antitone, ciSup_le_iff', Order.coheight_eq_iSup_head_eq, Ordinal.card_iSup_Iio_le_card_mul_iSup, ContinuousOn.image_Icc, Algebra.iSup_toSubsemiring, GaloisConnection.l_csSup_of_directedOn, csSup_eq_of_is_forall_le_of_forall_le_imp_ge, TopCat.Sheaf.existsUnique_gluing, Submodule.isOrtho_iSup_left, ENat.coe_iSup, ENat.smul_iSup, iSup_le_iSup_of_partialSups_le_partialSups, Finite.le_ciSup, Finset.Nonempty.csSup_mem, SupClosed.iSup_mem_of_nonempty, LinearMap.ker_noncommProd_eq_of_supIndep_ker, ProbabilityTheory.indep_iSup_limsup, Cardinal.mul_ciSup, AddSubmonoid.mem_bsupr_iff_exists_dfinsupp, exists_seq_tendsto_sSup, ciSup_Iic, normalClosure_def, tsum_iSup_decode₂, NNReal.iSup_pow_of_ne_zero, Order.krullDim_eq_iSup_height_of_nonempty, MeasureTheory.iSup_lintegral_measurable_le_eq_lintegral, Submodule.restrictScalars_sSup, Ordinal.sup_eq_bsup, Cardinal.ciSup_mul, Antitone.map_csInf_of_continuousAt, coinduced_sSup, ciSup_le', MeasurableSpace.measurableSpace_iSup_eq, Ordinal.Principal.iSup, ENat.sub_iSup, IsLUB.ciSup_set_eq, PrimeSpectrum.zeroLocus_iSup, Set.Nonempty.csSup_mem, ENNReal.biSup_add', iSupIndep_def', Submodule.toAddSubmonoid_sSup, csSup_empty, WithTop.iSup_coe_lt_top, ENNReal.iSup_add_iSup, Submodule.smul_iSup, lowerSemicontinuous_iSup, OrderIso.map_csSup', ENNReal.iSup_sub, ENNReal.tsum_eq_iSup_sum', AddSubgroup.ofAddUnits_sSup, Subalgebra.unop_sSup, MeasureTheory.measure_sigmaFiniteSetWRT', ciSup_mem_iInter_Icc_of_antitone_Icc, Ordinal.opow_limit, mul_ciSup_le, Submodule.fg_iSup, SSet.skeleton_succ, Cardinal.preAleph_limit, sSup_atoms_eq_top, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, IsSemisimpleModule.finite_tfae, csSup_of_not_bddAbove, LinearPMap.domain_sSup, Order.height_eq_iSup_lt_height, DirectedOn.isLUB_ciSup_set, Submodule.inf_iSup_genEigenspace, le_csSup_iff', Ideal.iSup_mul, continuous_iSup_dom, NormedSpace.equicontinuous_TFAE, Monotone.ciSup_mem_iInter_Icc_of_antitone, IsOpen.measure_eq_iSup_isCompact, PiLp.nnnorm_eq_ciSup, Cardinal.lift_iSup_le_sum, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', Algebra.sSup_toSubsemiring, generateFrom_iInter, generateFrom_piiUnionInter_measurableSet, ENNReal.iSup_ennreal, alexandrovDiscrete_iSup, partialSups_eq_biSup, NonUnitalSubalgebra.coe_iSup_of_directed, AddSubmonoid.iSup_eq_mrange_dfinsuppSumAddHom, CompleteSublattice.coe_sSup', tprod_iSup_decode₂, ProbabilityTheory.condIndep_iSup_limsup, dimH_bUnion, Order.pred_eq_sSup, ciInf_eq_top_of_top_mem, TopologicalSpace.Opens.mem_iSup, Cardinal.sum_le_lift_mk_mul_iSup, ENNReal.inv_iInf, Ordinal.bsup_eq_sup, eq_Icc_of_connected_compact, ProbabilityTheory.Kernel.indep_iSup_of_directed_le, Subfield.closure_sUnion, Multiset.iSup_mem_map_of_ne_zero, essSup_eq_iSup, csInf_upperBounds_range, sSupHom.continuous, ciSup_or', trdeg_eq_iSup_cardinalMk_isTranscendenceBasis, lowerSemicontinuousWithinAt_ciSup, ProbabilityTheory.Kernel.indep_iSup_of_monotone, sSup_one, Ordinal.iSup_mul_natCast, Ordinal.mem_closure_iff_iSup, Filter.HasBasis.liminf_eq_iSup_iInf, ciSup_eq_univ_of_not_bddAbove, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iff, NNReal.iSup_div, Ideal.iSup_iInf_eq_top_iff_pairwise, MeasureTheory.measure_iUnion_of_tendsto_zero, Submodule.closure_coe_iSup_map_single, ENat.iSup_natCast, Ordinal.iSup_lt_ord_lift, TopCat.coinduced_of_isColimit, ciSup_of_empty, CategoryTheory.ObjectProperty.HasCardinalLT.iSup, MeasureTheory.tendsto_ae_condExp, ProbabilityTheory.indep_iSup_directed_limsup, DividedPowers.SubDPIdeal.sSup_carrier_def, TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompact, ContinuousOn.image_uIcc, iSup_eq_of_forall_le_of_tendsto, PiLp.edist_eq_iSup, AddMonoidHom.noncommPiCoprod_mrange, Finset.Nonempty.csSup_eq_max', IsSemisimpleModule.sSup_simples_le, isOpen_iSup_iff, MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone', IsOpen.measure_eq_biSup_integral_continuous, Submodule.sInf_orthogonal, Submonoid.inv_iSup, MeasureTheory.Measure.restrict_iUnion_apply_eq_iSup, AntitoneOn.map_sInf_of_continuousWithinAt, SupClosed.biSup_mem, ProbabilityTheory.iSup_partitionFiltration_eq_generateFrom_range, Submodule.mul_iSup, Order.krullDim_eq_iSup_coheight, Set.Iic.coe_sSup, ENNReal.add_iSup, csInf_le_csSup, AlgebraicGeometry.Scheme.IdealSheafData.support_iSup, OrderIso.map_ciSup', TopCat.Presheaf.presieveOfCovering.indexOfHom_spec, ENNReal.iSup_coe_eq_top, Subfield.mem_iSup_of_directed, ProbabilityTheory.condIndep_biSup_limsup, sSupIndep.disjoint_sSup, GaloisConnection.l_ciSup_of_directed, Submodule.span_sSup, Filter.bliminf_eq, Directed.ciSup_mono, Directed.iSup_inf_eq, Submodule.iSup_eq_span, ENat.iSup_mul, Filter.liminf_eq_iSup_iInf_of_nat, Ordinal.mem_closure_tfae, Cardinal.iSup_lt_ord_lift_of_isRegular, IsLUB.ciSup_eq, Set.Icc.coe_iSup, MonotoneOn.tendsto_nhdsWithin_Ioo_left, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π, csSup_inv, Submodule.span_iUnion, BoundedContinuousFunction.nndist_eq_iSup, ciSup_partialSups_eq, DirectedOn.le_ciSup_set, LieSubmodule.sSup_toSubmodule, MeasureTheory.OuterMeasure.sSup_apply, NNReal.natCast_iSup, Order.pred_eq_iSup, Ideal.map_iSup_comap_of_surjective, AddSubmonoid.bsupr_eq_mrange_dfinsuppSumAddHom, SimpleGraph.ediam_eq_iSup_iSup_edist, Cardinal.iSup_lt_lift_of_isRegular, Ordinal.iSup'_eq_bsup, Submodule.sum_mem_biSup, Matrix.ker_diagonal_toLin', IsAtom.le_iSup, Order.krullDim_eq_iSup_height, AddSubmonoid.FG.biSup, FirstOrder.Language.Substructure.iSup_eq_closure, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, UniformOnFun.edist_def', csInf_image2_eq_csSup_csInf, MeasureTheory.tendsto_measure_sigmaFiniteSetGE, CompleteSublattice.coe_iSup, IsClosed.csSup_mem, MeasurableSpace.comap_iSup, ClosedSubmodule.mem_iSup, Filter.HasBasis.liminf_eq_sSup_univ_of_empty, AddSubgroup.FG.iSup, Filter.limsSup_eq_iInf_sSup, IsSemisimpleModule.sSup_simples_eq_top, hasCardinalLT_subtype_iSup, iSup_disjointed, ENat.sSup_add, Cardinal.beth_limit, Function.support_iSup, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, AlgebraicGeometry.Scheme.Hom.image_iSup, Alexandrov.lowerCone_π_app, ENNReal.biSup_add_biSup_le', Cardinal.mk_biUnion_le, MeasureTheory.lintegral_iSup_directed_of_measurable, Set.Nonempty.ordConnected_iff_of_bdd, MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_part, Subfield.map_iSup, AddSubgroup.ofAddUnits_iSup₂, IntermediateField.map_iSup, iSup_eq_iSup_of_partialSups_eq_partialSups, csSup_insert, isSaddlePointOn_iff', Ordinal.iSup_sequence_lt_omega_one, ProbabilityTheory.Kernel.indep_biSup_limsup, ENNReal.mul_sSup, ENNReal.iSup_add_iSup_of_monotone, sSup_div, le_ciSup, MonoidHom.noncommPiCoprod_mrange, essSup_uniformOn_eq_ciSup, MeasureTheory.Measure.LebesgueDecomposition.iSup_mem_measurableLE', Ideal.IsHomogeneous.sSup, ENNReal.sSup_mul, iSup_eq_iSup_subseq_of_monotone, TopologicalSpace.Opens.map_iSup, eq_Icc_csInf_csSup_of_connected_bdd_closed, ENNReal.iSup_zero, Submonoid.FG.iSup, Cardinal.sum_le_iSup_lift, IsWellFounded.rank_eq, SSet.horn_eq_iSup, Ordinal.iSup_typein_limit, ENat.iSup_eq_zero, Measurable.iSup', MeasureTheory.tendsto_eLpNorm_condExp, Ordinal.iSup_lt_lift, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, MeasureTheory.lintegral_eq_nnreal, UniformFun.edist_def, Cardinal.mk_iUnion_le_lift, Directed.ciInf_le_ciSup, SSet.range_eq_iSup_sigma_ι, essInf_eq_sSup, Subspace.dualAnnihilator_iInf_eq, IntermediateField.isSplittingField_iSup, Submodule.iSup_map_single, Filter.limsSup_principal_eq_csSup, MeasureTheory.SimpleFunc.lintegral_restrict_iUnion_of_directed, Submodule.mem_sSup_of_mem, ENat.biSup_add_biSup_le', FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion, ProbabilityTheory.iSup_countableFiltration, Order.pred_eq_csSup, ClosedSubmodule.toSubmodule_sSup, ProbabilityTheory.indep_iSup_of_antitone, FirstOrder.Language.Substructure.closure_iUnion, Ordinal.derivFamily_limit, mul_ciSup, BoundedContinuousFunction.nnnorm_eq_iSup_nnnorm, coinduced_iSup, AntitoneOn.map_csInf_of_continuousWithinAt, ciSup_pos, Partition.iSup_eq, ZFSet.rank_range, IntermediateField.iSup_eq_adjoin, TopologicalSpace.Opens.mem_sSup, iSup₂_iInf₂_le_iInf₂_iSup₂, ENNReal.add_biSup', LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute, DirectedOn.le_csSup_iff, Submodule.map_smul', Ordinal.iSup_ord, inf_sSup_eq_iSup_inf_sup_finset, ENNReal.hasSum, IntermediateField.iSup_toSubfield, ENat.iSup_add_iSup, tendsto_atTop_iSup, GaloisConnection.l_csSup, ENat.iSup_add, Ordinal.sup_eq_sup, TopologicalSpace.Opens.leSupr_apply_mk, LinearMap.range_smul', DirectSum.IsInternal.addSubmonoid_iSup_eq_top, ENNReal.add_sSup, Submodule.small_iSup, Finsupp.disjoint_lsingle_lsingle, Ordinal.le_iSup, Directed.ciSup_eq_of_forall_le_of_forall_lt_exists_gt, essSup_count_eq_ciSup, Ordinal.iSup_eq_zero_iff, AddSubgroup.FG.biSup_finset, FirstOrder.Language.Substructure.comap_iSup_map_of_injective, ProbabilityTheory.condIndep_biSup_compl, CompleteSublattice.sSupClosed, isLUB_ciSup_set, ciSup_mul_ciSup_le, IsCompactlyGenerated.exists_sSup_eq, Order.IsNormal.map_iSup, Set.Iic.coe_iSup, iSupIndep_def, Module.End.genEigenspace_top, ENNReal.iSup_div, Directed.ciSup_le, tendsto_atBot_iSup, Set.Nonempty.ciSup_mem_image, MonoidHom.noncommPiCoprod_range, Monoid.CoprodI.iSup_mrange_of, Submodule.iSup_torsionBy_eq_torsionBy_prod, sSup_neg, UniformOnFun.edist_def, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, IntermediateField.fg_iSup, IsClosed.isGreatest_csSup, IsCompactlyGenerated.BooleanGenerators.sSup_le_sSup_iff_of_atoms, MeasureTheory.OuterMeasure.boundedBy_apply, ProbabilityTheory.iSup_bayesRisk_le_minimaxRisk, SSet.hasDimensionLT_iSup_iff, iSup_succ, Ordinal.sup_eq_bsup', csInf_neg, Submodule.set_smul_eq_iSup, ProbabilityTheory.condIndep_iSup_directed_limsup, TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducible, IntermediateField.adjoin_iUnion, Ordinal.succ_iSup_eq_lsub_iff, LieSubmodule.sSup_toSubmodule_eq_iSup, CompleteSublattice.coe_sSup, SimpleGraph.diam_def, ciSup_div, Subgroup.FG.iSup, ENat.sSup_mul, Cardinal.sum_le_lift_mk_mul_iSup_lift, ENat.iSup_coe_eq_top, sSup_sub, ClosedSubmodule.mem_sSup, IntermediateField.normalClosure_def'', SSet.iSup_skeletonOfMono, DividedPowers.isSubDPIdeal_iSup, Sublattice.map_iSup, MeasureTheory.hittingAfter_mem_set_of_ne_top, BoundedContinuousFunction.edist_eq_iSup, Filter.liminf_eq_iSup_iInf, Filter.HasBasis.liminf_eq_sSup_iUnion_iInter, Ideal.homogeneousCore'_eq_sSup, TopologicalSpace.Opens.iSup_def, TopologicalSpace.Closeds.coe_sSup, Ordinal.sup_eq_lsub, isLUB_csSup_of_directed, Set.iSup_indicator, OrthogonalFamily.range_linearIsometry, DirectedOn.lt_csSup_of_lt, iSup_Iio_eq_self_iff_isSuccPrelimit, Order.IsSuccLimit.sSup_Iio, Ordinal.iSup_eq_lsub_iff_lt_iSup, continuous_iSup_rng, ProbabilityTheory.Kernel.indep_iSup_of_antitone, ENNReal.toReal_sSup, sSup_compact_le_eq, ENNReal.sub_iSup, SSet.iSup_range_eq_top_of_isColimit, ContinuousMap.nnnorm_eq_iSup_nnnorm, Submodule.isOrtho_iSup_right, partialSups_eq_ciSup_Iic, Algebra.isIntegral_iSup, LeftOrdContinuous.map_csSup, MeasureTheory.Measure.InnerRegularWRT.measure_eq_iSup, DirectedOn.le_csSup, Ordinal.IsNormal.map_iSup_of_bddAbove, AlgebraicGeometry.IsAffineOpen.biSup_of_disjoint, Cardinal.preBeth_limit, Submodule.iSup_smul, Submodule.mem_iSup_finset_iff_exists_sum, Submodule.iSup_eq_span', csSup_singleton, DirectedOn.csSup_le_iff, Submodule.iInf_orthogonal, ProjectiveSpectrum.basicOpen_eq_union_of_projection, MeasureTheory.Measure.iSup_restrict_spanningSets, ContinuousMap.nndist_eq_iSup, FirstOrder.Language.Substructure.map_iSup_comap_of_surjective, NonUnitalStarSubalgebra.coe_iSup_of_directed, Subalgebra.op_iSup, AddSubmonoid.FG.biSup_finset, MeasureTheory.lintegral_iSup, Ordinal.lt_iSup_iff, csSup_eq_of_forall_le_of_forall_lt_exists_gt, Ordinal.IsNormal.map_sSup_of_bddAbove, Order.IsNormal.preimage_Iic, TopologicalSpace.Opens.coe_sSup, OrderIso.map_ciSup_set, ENNReal.iSup_eq_zero, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.top_mem_range, Ordinal.bsup'_eq_iSup, Submodule.span_sSup', Ordinal.IsNormal.apply_omega0, MeasurableSet.measure_eq_iSup_isClosed_of_ne_top, TopCat.Presheaf.presieveOfCovering.mem_grothendieckTopology, TopologicalSpace.IsOpenCover.iSup_eq_top, DirectedOn.csSup_le_csSup, MeasureTheory.eLpNormEssSup_count, Subfield.coe_sSup_of_directedOn, GaloisConnection.l_ciSup, Ordinal.iSup_Iio_eq_bsup, WithTop.iSup_coe_eq_top, TopCat.Presheaf.SheafConditionEqualizerProducts.fork_pt, MeasureTheory.OuterMeasure.iUnion_of_tendsto_zero, AEMeasurable.iSup, TopCat.Presheaf.SheafConditionEqualizerProducts.w_apply, WithTop.isLUB_sSup, ENNReal.smul_sSup, Submodule.map_iSup_comap_of_surjective, Antitone.map_iInf_of_continuousAt, isOrderRightAdjoint_csSup, Submodule.coe_iSup_of_directed, IntermediateField.finiteDimensional_iSup_of_finite, Ordinal.iSup_eq_of_range_eq, ZFSet.rank_iUnion, ciSup_of_not_bddAbove, ENNReal.sSup_add, Ordinal.IsNormal.map_sSup, BooleanSubalgebra.biSup_mem, MeasureTheory.iSup₂_lintegral_le, Order.krullDim_eq_iSup_height_add_coheight_of_nonempty, Ordinal.iSup_sequence_lt_omega1, Filter.HasBasis.blimsup_eq_iInf_iSup, Alexandrov.projSup_obj, ENNReal.tsum_eq_iSup_nat, Ordinal.bsup_eq_iSup, Algebra.mem_iSup_of_mem, essSup_count, MeasureTheory.Filtration.sSup_def, SimpleGraph.ediam_def, IntermediateField.isAlgebraic_iSup, MonotoneOn.csSup_eq_of_subset_of_forall_exists_le, normalClosure_eq_iSup_adjoin, Ordinal.lsub_le_succ_iSup, csInf_upperBounds_eq_csSup, subset_Icc_csInf_csSup, Cardinal.ciSup_mul_ciSup, ciSup_eq_ite, Submodule.mem_iSup_of_mem, DirectedOn.inf_sSup_eq, Filter.limsup_eq_iInf_iSup, AEMeasurable.biSup, Filter.limsup_le_iSup, SupClosed.sSup_mem, Field.Emb.Cardinal.iSup_adjoin_eq_top, lt_csSup_of_lt, CliffordAlgebra.iSup_ι_range_eq_top, AlgebraicGeometry.Scheme.IdealSheafData.ideal_iSup, Finset.sup'_id_eq_csSup, NNReal.iSup_empty, cbiSup_eq_of_forall, Ideal.mul_iSup, Set.Ici_ciSup, IntermediateField.toSubalgebra_iSup_of_directed, IsUltrametricDist.nnnorm_tprod_le, MeasureTheory.Measure.hausdorffMeasure_apply, Alexandrov.lowerCone_pt, Submodule.span_biUnion, ProbabilityTheory.indep_biSup_compl, IntermediateField.isSeparable_iSup, AddSubmonoid.mem_iSup_iff_exists_dfinsupp', Directed.inf_iSup_eq, ENNReal.iSup_pow, Ideal.sup_height_eq_ringKrullDim, isSaddlePointOn_iff, Ordinal.mem_iff_iSup_of_isClosed, NNReal.mul_iSup, EMetric.hausdorffEdist_def, csSup_inter_le, ENNReal.sub_iInf, AddSubgroup.FG.biSup, Cardinal.add_ciSup, OrderIso.map_csSup, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, Algebra.adjoin_iUnion, LieSubmodule.iSup_toSubmodule_eq_top, csSup_div, TopCat.nonempty_isColimit_iff_eq_coinduced, Submodule.isOrtho_sSup_left, ENNReal.iSup_lt_eq_self, Ideal.map_sSup, AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpens, ENNReal.finsetSum_iSup_of_monotone, Finsupp.supported_iUnion, exists_eq_ciSup_of_finite, Antitone.ciSup_comp_tendsto_atBot, MeasureTheory.SimpleFunc.iSup_eapprox_apply, Submodule.restrictScalars_iSup, SSet.boundary_eq_iSup, ENat.toENNReal_iSup, AddSubmonoid.mem_iSup_iff_exists_dfinsupp, Ordinal.isClosed_iff_iSup, MeasureTheory.isStoppingTime_hitting_isStoppingTime, Ordinal.bsup_eq_sup', Filter.limsup_eq_iInf_iSup_of_nat', csSup_add, Filter.limsSup_principal_eq_sSup, csSup_Iio, ciSup_subsingleton, HomogeneousIdeal.irrelevant_eq_iSup, Set.Iic.coe_biSup, IsSemisimpleModule.exists_sSupIndep_sSup_simples_eq_top, ciSup_mul_le_ciSup_mul_ciSup, csInf_sub, OrderIso.map_ciSup_of_directed, IsCompact.continuous_sSup, Subgroup.ofUnits_iSup₂, TopologicalSpace.Opens.isBasis_iff_cover, WellFoundedGT.ciSup_eq_monotonicSequenceLimit, dimH_iUnion, Monotone.measure_iUnion, Directed.disjoint_iSup_left, sSup_add, DirectSum.IsInternal.submodule_iSup_eq_top, CompleteLattice.IsCompactElement.directed_sSup_lt_of_lt, Submodule.mem_iSup_of_chain, MeasurableSpace.iSup_generateFrom, Submodule.mem_iSup_iff_exists_finset, Cardinal.lift_iSup_le_lift_iSup', FirstOrder.Language.DirectLimit.Equiv_isup_of_apply, OrderIso.map_ciSup_set_of_directedOn, Submodule.localized₀_iSup, Ordinal.sup_typein_limit, AlgebraicGeometry.IsAffineOpen.basicOpen_union_eq_self_iff, Submodule.iSup_eq_toSubmodule_range, Order.IsSuccPrelimit.sSup_Iio, LinearMap.iSup_range_single_le_iInf_ker_proj, Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInf, ProbabilityTheory.condIndep_iSup_of_disjoint, Submodule.mem_sSup_iff_exists_finset, LinearMap.disjoint_single_single, List.iSup_mem_map_of_ne_nil, ENNReal.iSup_mul_le, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, ENat.add_biSup, ciSup_false, LieSubalgebra.span_iUnion, ProbabilityTheory.iSup_partitionFiltration, PrimitiveSpectrum.hull_sSup, csSup_Iic, GaloisConnection.l_ciSup_set, Monotone.csSup_image_le, ciSup_set_le_iff, Partition.sSup_eq, Subgroup.ofUnits_sSup, GaloisConnection.l_csSup_of_directedOn', Cardinal.sum_le_iSup, EMetric.diam_eq_sSup, ENat.sum_iSup_of_monotone, Module.End.iSup_maxGenEigenspace_eq_top, csInf_image2_eq_csSup_csSup, Nat.iSup_lt_succ, Measurable.sSup, Ordinal.sup_eq_lsub_or_sup_succ_eq_lsub, ClosedSubmodule.coe_iSup, Submodule.finite_iSup, Finsupp.lsingle_range_le_ker_lapply, MeasureTheory.measure_iUnion_eq_iSup_accumulate, lowerSemicontinuousAt_iSup, FirstOrder.Language.DirectLimit.iSup_range_of_eq_top, MeasureTheory.SimpleFunc.iSup_approx_apply, Cardinal.lift_iSup_le_iff, Filter.blimsup_eq_iInf_biSup_of_nat, csSup_mem_closure, SSet.Subcomplex.preimage_iSup, csSup_eq_univ_of_not_bddAbove, Filter.limsup_eq_sInf_sSup, csSup_image2_eq_csSup_csInf, Filter.HasBasis.limsSup_eq_iInf_sSup, CompleteLattice.isAtomistic_iff, lt_ciSup_iff, sSup_simples_eq_top_iff_isSemisimpleModule, sSup_iUnion_Iic, Metric.ediam_iUnion_mem_option, WithBot.coe_biSup, Monotone.ciSup_comp_tendsto_atTop, Matrix.range_diagonal, Filter.limsup_eq_iInf_iSup_of_nat, Submodule.mem_sSup_of_directed, RestrictedProduct.topologicalSpace_eq_iSup, Order.coheight_eq, PrimitiveSpectrum.hull_iSup, Field.Emb.Cardinal.iSup_filtration, Cardinal.aleph_limit, bsupr_limsup_dimH, ciSup_const, lowerSemicontinuousOn_ciSup, MeasureTheory.iSup_lintegral_le, add_ciSup, Directed.ciSup_le_iff, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top, ProjectiveSpectrum.zeroLocus_iSup_ideal, Finset.Nonempty.ciSup_eq_max'_image, setOf_isOpen_sSup, Ordinal.iSup_le_iff, Cardinal.iSup_lt_ord_of_isRegular, csInf_image2_eq_csInf_csSup, Ordinal.iSup_eq_lsub, Submodule.dualAnnihilator_iSup_eq, Matrix.iSup_eigenspace_toLin_diagonal_eq_top, MeasureTheory.OuterMeasure.iSup_apply, SSet.N.iSup_subcomplex_eq_top, ENNReal.iSup_mul, Ordinal.iSup_eq_lsub_iff, IsCompact.exists_sSup_image_eq, Topology.IsGeneratedBy.iSup, Submonoid.FG.biSup_finset, lowerSemicontinuousWithinAt_biSup, Submodule.mem_biSup_iff_exists_dfinsupp, IsGreatest.csSup_eq, ENat.sSup_eq_zero', Cardinal.ciSup_add_ciSup, csSup_sub, isSemisimpleModule_biSup_of_isSemisimpleModule_submodule, sSupHom.apply_blimsup_le, isArtinian_iSup, ENNReal.finsetSum_iSup, TopCat.Sheaf.eq_of_locally_eq_iff, Pi.Lex.sSup_apply, Ordinal.iSup_natCast, LinearMap.mapsTo_biSup_of_mapsTo, lowerSemicontinuousAt_biSup, Submodule.topologicalClosure_iSup_map_single, FirstOrder.Language.DirectLimit.Equiv_isup_symm_inclusion_apply, Filter.limsInf_eq_iSup_sInf, Directed.le_ciSup_of_le, Ordinal.iSup_iterate_eq_nfp, ENat.biSup_add_biSup_le, TopCat.Presheaf.IsSheaf.isSheafUniqueGluing, lt_csSup_iff', ProbabilityTheory.condIndep_iSup_of_directed_le, ciSup_add_le_ciSup_add_ciSup, DirectSum.isInternal_biSup_submodule_of_iSupIndep, LeftOrdContinuous.map_ciSup, Set.chainHeight_eq_iSup, IsCompact.isGreatest_sSup, AddSubmonoid.neg_iSup, Subgroup.ofUnits_iSup, LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commute, ContinuousMap.enorm_eq_iSup_enorm, ENNReal.inv_sInf, BooleanSubalgebra.iSup_mem, FirstOrder.Language.Substructure.map_iSup, Ordinal.apply_omega0_of_isNormal, IntermediateField.Lifts.carrier_union, Nat.iSup_le_succ', Filter.bliminf_eq_iSup_biInf, IntermediateField.normalClosure_def', PrimeSpectrum.iSup_basicOpen_eq_top_iff', ENat.iSup_add_iSup_le, Ideal.toIdeal_homogeneousHull_eq_iSup, Submodule.mem_iSup_iff_exists_dfinsupp', Order.height_eq_iSup_last_eq, BoundedContinuousFunction.enorm_eq_iSup_enorm, Filter.HasBasis.limsup_eq_iInf_iSup, ExpGrowth.expGrowthSup_iSup, ProbabilityTheory.Kernel.indep_biSup_compl, AlgebraicGeometry.Scheme.IdealSheafData.support_sSup, dimH_def, AddSubmonoid.iSup_mul, ciSup_mono', Finset.sup'_univ_eq_ciSup, Order.coheight_eq_iSup_gt_coheight, IsPreconnected.mem_intervals, ciSup_le, csSup_lowerBounds_range, csSup_image2_eq_csInf_csSup, NNReal.iSup_mul, AddSubgroup.ofAddUnits_iSup, Filter.HasBasis.limsup_eq_ciInf_ciSup, Submodule.mem_iSup_of_directed, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSup, Ordinal.lsub_le_sup_succ, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.iSup_P, sSup_zero, Ideal.mem_iSup_of_mem, AffineSubspace.map_iSup, OrderIso.map_csSup_of_directedOn', Antitone.map_sInf_of_continuousAt, MeasureTheory.AECover.iSup_lintegral_eq_of_countably_generated, Ideal.IsHomogeneous.iSup₂, Ideal.Filtration.iSup_N, Submodule.iSup_toAddSubmonoid, Order.IsSuccPrelimit.iSup_Iio, DirectedOn.isLUB_csSup, Dense.ciSup', NNReal.iSup_pow, Ordinal.succ_iSup_le_lsub_iff, MonotoneOn.sSup_image_Icc, essSup_eq_ciSup, Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splits, LeftOrdContinuous.map_sSup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, MeasureTheory.setLIntegral_iUnion_of_directed, DirectedOn.disjoint_sSup_right, Submodule.mem_sSup, MeasureTheory.lintegral_eq_iSup_eapprox_lintegral, ENNReal.coe_iSup, eq_sSup_atoms, lt_ciSup_iff', isLUB_csSup', Ordinal.IsNormal.apply_of_isSuccLimit, csInf_inv, ProbabilityTheory.indep_iSup_of_disjoint, Ordinal.iSup_lt_ord, FirstOrder.Language.DirectLimit.cod_partialEquivLimit, Ideal.map_iSup, Directed.le_ciSup, Order.IsNormal.map_sSup, FirstOrder.Language.DirectLimit.range_lift, HomogeneousIdeal.toIdeal_iSup, IntermediateField.finiteDimensional_iSup_of_finset', ENat.add_biSup', lowerSemicontinuousAt_ciSup, Filter.HasBasis.liminf_eq_ciSup_ciInf, csSup_zero, ProbabilityTheory.Kernel.indep_iSup_of_disjoint, BooleanSubalgebra.le_comap_iSup, SSet.Subcomplex.image_iSup, sInf_div, ENat.biSup_add, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSup, ENNReal.iSup₂_pow_of_ne_zero, csSup_union, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, Cardinal.mk_iUnion_le, add_ciSup_le, Cardinal.iSup_le_sum, Projectivization.Subspace.span_iUnion, measurableSet_iSup_of_mem_piiUnionInter, Subgroup.noncommPiCoprod_range, SimpleGraph.eccent_def, Cardinal.iSup_mk_le_mk_iUnion, iSup_limsup_dimH, DeltaGeneratedSpace.iSup, ZFSet.iSup_card_le_card_iUnion, Ordinal.card_iSup_le_sum_card, DirectSum.range_coeLinearMap, Alexandrov.projSup_map, TopCat.Presheaf.SheafConditionEqualizerProducts.res_π_apply, Cardinal.ciSup_add, WithTop.isLUB_sSup', Ordinal.iSup_lt, Submodule.mem_iSup, Submodule.starProjection_tendsto_closure_iSup, MeasureTheory.measure_sigmaFiniteSetGE_ge, ContinuousMap.edist_eq_iSup, ENat.iSup_coe_lt_top, Submodule.span_eq_iSup_of_singleton_spans, MeasureTheory.Adapted.isStoppingTime_hittingBtwn_isStoppingTime, NNReal.iSup_mul_le, egauge_pi', MeasureTheory.Filtration.stronglyMeasurable_limitProcess, AntitoneOn.sSup_image_Icc, MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty, ENNReal.toReal_iSup, IsCompact.exists_sSup_image_eq_and_ge, IsAtom.le_sSup, Submonoid.FG.biSup, lowerSemicontinuous_biSup, Monotone.ciSup_comp_tendsto_atTop_of_linearOrder, SSet.range_eq_iSup_of_isColimit, Submodule.span_iUnion₂, FirstOrder.Language.DirectLimit.rangeLiftInclusion, sSup_mem_closure, Filter.limsup_top_eq_iSup, IsUltrametricDist.nnnorm_tsum_le, Antitone.ciSup_comp_tendsto_atBot_of_linearOrder, Nat.iSup_le_succ, ENNReal.add_biSup, Metric.ediam_insert, SSet.skeletonOfMono_succ, Ideal.span_iUnion, PiLp.nndist_eq_iSup, Submodule.coe_iSup_of_chain, MeasurableSpace.measurableSet_iSup, FirstOrder.Language.DirectLimit.dom_partialEquivLimit, Finsupp.iSup_lsingle_range, sSup_within_of_ordConnected, Ordinal.sup_typein_succ, MeasureTheory.Measure.iSup_restrict_spanningSets_of_measurableSet, IntermediateField.biSup_adjoin_simple, MeasureTheory.lintegral_le_iSup, csSup_neg, SimpleGraph.radius_eq_iInf_iSup_edist, ENNReal.mul_iSup, LeftOrdContinuous.map_iSup, Subalgebra.unop_iSup, Directed.isLUB_ciSup, Submodule.finiteDimensional_iSup, EMetric.diam_iUnion_mem_option, csSup_Ico, csSup_eq_csSup_of_forall_exists_le, ciSup_neg, ciSup_mono, HilbertBasis.finite_spans_dense

Theorems

NameKindAssumesProvesValidatesDepends On
isLUB_csSup_of_directed 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
toPartialOrder
Set.Nonempty
BddAbove
IsLUB
SupSet.sSup
toSupSet
——

Directed

Theorems

NameKindAssumesProvesValidatesDepends On
ciInf_le 📖mathematicalDirected
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderInf.toPartialOrder
BddBelow
Set.range
iInf
ConditionallyCompletePartialOrderInf.toInfSet
—DirectedOn.csInf_le
directedOn_range
Set.mem_range_self
ciSup_le 📖mathematicalDirected
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
—DirectedOn.csSup_le
directedOn_range
Set.range_nonempty
Set.forall_mem_range
le_ciInf 📖mathematicalDirected
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderInf.toPartialOrder
iInf
ConditionallyCompletePartialOrderInf.toInfSet
—DirectedOn.le_csInf
directedOn_range
Set.range_nonempty
Set.forall_mem_range
le_ciSup 📖mathematicalDirected
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
BddAbove
Set.range
iSup
ConditionallyCompletePartialOrderSup.toSupSet
—DirectedOn.le_csSup
directedOn_range
Set.mem_range_self

DirectedOn

Theorems

NameKindAssumesProvesValidatesDepends On
csInf_le 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderInf.toPartialOrder
BddBelow
Set
Set.instMembership
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
—isGLB_csInf
csSup_le 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Set.Nonempty
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
—isLUB_csSup
isGLB_csInf 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderInf.toPartialOrder
Set.Nonempty
BddBelow
IsGLB
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
—ConditionallyCompletePartialOrderInf.isGLB_csInf_of_directed
isLUB_csSup 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
Set.Nonempty
BddAbove
IsLUB
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
—ConditionallyCompletePartialOrderSup.isLUB_csSup_of_directed
le_csInf 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderInf.toPartialOrder
Set.Nonempty
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
—isGLB_csInf
le_csSup 📖mathematicalDirectedOn
Preorder.toLE
PartialOrder.toPreorder
ConditionallyCompletePartialOrderSup.toPartialOrder
BddAbove
Set
Set.instMembership
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
—isLUB_csSup

(root)

Definitions

NameCategoryTheorems
ConditionallyCompletePartialOrder 📖CompData—
ConditionallyCompletePartialOrderInf 📖CompData—
ConditionallyCompletePartialOrderSup 📖CompData—

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