Documentation Verification Report

Nonempty

πŸ“ Source: Mathlib/Logic/Nonempty.lean

Statistics

MetricCount
Definitionsarbitrary, inhabited_of_nonempty', Nonempty, Nonempty, some, Nonempty, Nonempty, Nonempty
8
Theoremsnonempty_pi, nonempty, elim_to_inhabited, exists, forall, imp, map, map2, Nonempty, exists_const_iff, exists_true_iff_nonempty, nonempty_plift, nonempty_pprod, nonempty_prod, nonempty_psigma, nonempty_psum, nonempty_sigma, nonempty_subtype, nonempty_sum, nonempty_ulift, not_nonempty_iff_imp_false, subsingleton_of_not_nonempty
22
Total30

Classical

Definitions

NameCategoryTheorems
arbitrary πŸ“–CompOp
9 mathmath: OpenPartialHomeomorph.lift_openEmbedding_toFun, EuclideanGeometry.orthogonalProjection_apply', MeasureTheory.stoppedValue_stoppedProcess, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_pt, CategoryTheory.Limits.Trident.ofΞΉ_Ο€_app, CategoryTheory.CostructuredArrow.CreatesConnected.raiseCone_Ο€_app, CategoryTheory.Limits.Cotrident.ofΟ€_ΞΉ_app, EuclideanGeometry.orthogonalProjection_apply, EuclideanGeometry.reflection_apply
inhabited_of_nonempty' πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
nonempty_pi πŸ“–β€”β€”β€”β€”β€”

Finset

Definitions

NameCategoryTheorems
Nonempty πŸ“–MathDef
175 mathmath: vadd_nonempty_iff, infs_nonempty, zero_nonempty, mem_image_const, sigma_nonempty, not_nonempty_empty, Equiv.Perm.IsCycle.nonempty_support, sdiff_nonempty, empty_ssubset, nonempty_Icc, CompositionAsSet.boundaries_nonempty, sdiff_nonempty_of_card_lt_card, attach_nonempty_iff, Colex.toColex_lt_toColex_iff_max'_mem, support_smulAntidiagonal_subset_smul, Caratheodory.minCardFinsetOfMemConvexHull_nonempty, isPWO_support_smulAntidiagonal, coe_nonempty, sym_nonempty, biUnion_nonempty, Equiv.Perm.support_cycleOf_nonempty, support_vaddAntidiagonal_subset_vadd, SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty', Aesop.nonempty_Iio_of_not_isMin, MvPolynomial.nonempty_support_finSuccEquiv, List.Aesop.toFinset_nonempty_of_ne, sumLexLift_nonempty, Geometry.SimplicialComplex.isRelLowerSet_faces, filter_nonempty_iff, compl_ne_univ_iff_nonempty, nonempty_range_add_one, MvPolynomial.support_finSuccEquiv_nonempty, Colex.toColex_le_toColex_iff_max'_mem, nonempty_range_iff, image_nonempty, compls_nonempty, div_nonempty, cons_nonempty, SimpleGraph.reachable_iff_exists_finsetWalkLength_nonempty, eq_singleton_iff_nonempty_unique_mem, Aesop.range_nonempty, SimpleGraph.edgeFinset_nonempty, mulEnergy_pos_iff, not_nonempty_iff_eq_empty, union_nonempty, dens_ne_zero, Ioi_nonempty, nonempty_coe_sort, fiber_nonempty_iff_mem_image, univ_nonempty, nonempty_def, nonempty_Ioo, singleton_nonempty, vadd_finset_nonempty, disjoint_or_nonempty_inter, Finpartition.mem_atomise, Polynomial.natDegree_eq_support_max', symmDiff_nonempty, Iio_nonempty, orderEmbOfFin_zero, Finpartition.parts_nonempty_iff, not_disjoint_iff_nonempty_inter, orderEmbOfFin_last, sorted_zero_eq_min', SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty, nonempty_iff_ne_empty, shatters_empty, mem_image_const_self, Set.toFinset_nonempty, smul_finset_nonempty, Finpartition.part_nonempty, map_nonempty, coe_infsep, inclusion_exclusion_card_biUnion, one_nonempty, MeasureTheory.integral_biUnion_eq_sum_powerset, nonempty_mk, powerset_nonempty, vsub_nonempty, sym2_nonempty, smul_nonempty_iff, Finsupp.support_nonempty_iff, add_nonempty, Nontrivial.erase_nonempty, nonempty_Iio, mulEnergy_self_pos_iff, Aesop.nonempty_Ioi_of_not_isMax, SimplexCategory.II.nonempty_finset, pi_nonempty, isPWO_support_vaddAntidiagonal, Polynomial.supNorm_def', min'_lt_max'_of_card, Colex.isInitSeg_iff_exists_initSeg, sups_nonempty, sub_nonempty, Aesop.nonempty_Ioc_of_lt, MvPolynomial.support_nonempty, erase_nonempty, Polynomial.natTrailingDegree_eq_support_min', sigmaLift_nonempty, isPWO_support_addAntidiagonal, MvPolynomial.nonempty_support_optionEquivLeft, Nat.nonempty_properDivisors, BoxIntegral.Prepartition.IsPartition.nonempty_boxes, diffs_nonempty, subsetSum_nonempty, Colex.initSeg_nonempty, Finpartition.card_filter_atomise_le_two_pow, RootPairing.Base.support_nonempty, Finpartition.nonempty_of_not_uniform, DFinsupp.nonempty_neLocus_iff, Colex.erase_le_erase_min', Shatters.nonempty, support_addAntidiagonal_subset_add, Aesop.nonempty_Icc_of_le, card_compl_lt_iff_nonempty, nonempty_Ici, Multiset.Aesop.toFinset_nonempty_of_ne, inclusion_exclusion_sum_biUnion, isPWO_support_mulAntidiagonal, nontrivial_prod_iff, mul_nonempty, nonempty_iff_eq_singleton_default, Polynomial.coeffs_nonempty_iff, Nat.nonempty_primeFactors, insert_nonempty, Nat.nonempty_divisors, ConvexOn.le_sup_of_mem_convexHull, powersetCard_nonempty, Polynomial.nonempty_support_iff, insertNone_nonempty, inter_nonempty_of_card_lt_card_add_card, card_pos, one_le_card, sumLiftβ‚‚_nonempty, Nontrivial.sdiff_singleton_nonempty, List.toFinset_nonempty_iff, nonempty_product, Finsupp.nonempty_neLocus_iff, nonempty_uIcc, nonempty_Ioi, inv_nonempty_iff, nonempty_range_succ, Nontrivial.nonempty, Geometry.SimplicialComplex.nonempty_of_mem_faces, addEnergy_self_pos_iff, nonempty_Ico, univ_nonempty_iff, imageβ‚‚_nonempty_iff, MeasureTheory.measureReal_biUnion_eq_sum_powerset, addEnergy_pos_iff, diag_nonempty, indicator_biUnion_eq_sum_powerset, ConvexOn.inf_le_of_mem_convexHull, Finpartition.biUnion_filter_atomise, neg_nonempty_iff, zero_mem_smul_iff, Set.Aesop.toFinset_nonempty_of_nonempty, Finpartition.parts_nonempty, Fintype.piFinset_nonempty, nonempty_Ioc, card_ne_zero, Polynomial.support_nonempty, nonempty_of_prod_ne_one, powersetCard_nonempty_of_le, Set.Finite.toFinset_nonempty, nonempty_of_sum_ne_zero, eq_empty_or_nonempty, Aesop.nonempty_Ico_of_lt, support_mulAntidiagonal_subset_mul, Finpartition.nonempty_of_mem_parts, nonempty_Iic, nonempty_of_ne_empty, dens_pos, Multiset.toFinset_nonempty

Function.Surjective

Theorems

NameKindAssumesProvesValidatesDepends On
nonempty πŸ“–β€”β€”β€”β€”β€”

Matroid

Definitions

NameCategoryTheorems
Nonempty πŸ“–CompData
8 mathmath: instNonemptyMapEmbedding, rankPos_nonempty, eq_emptyOn_or_nonempty, instNonemptyMap, instNonemptyMapEquiv, ground_nonempty_iff, dual_nonempty, instNonemptyElemERestrictSubtype

Nonempty

Definitions

NameCategoryTheorems
some πŸ“–CompOp
15 mathmath: CochainComplex.IsKProjective.homotopyZero_def, CategoryTheory.ThinSkeleton.fromThinSkeleton_map, CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_def, LinearMap.det_def, CategoryTheory.skeletonEquivalence_unitIso, IsFreeGroup.mulEquiv_def, CochainComplex.IsKInjective.homotopyZero_def, CategoryTheory.HasClassifier.comm, NormedSpace.exp_def, Metric.Sum.dist_eq_glueDist, CategoryTheory.HasClassifier.isPullback_Ο‡, LinearMap.coe_det, CategoryTheory.HasClassifier.comm_assoc, SimpleGraph.coe_recolorOfCardLE, Metric.Sigma.dist_ne

Theorems

NameKindAssumesProvesValidatesDepends On
elim_to_inhabited πŸ“–β€”β€”β€”β€”β€”
exists πŸ“–β€”β€”β€”β€”β€”
forall πŸ“–β€”β€”β€”β€”β€”
imp πŸ“–β€”β€”β€”β€”forall
map πŸ“–β€”β€”β€”β€”β€”
map2 πŸ“–β€”β€”β€”β€”β€”

Order.IsIdeal

Theorems

NameKindAssumesProvesValidatesDepends On
Nonempty πŸ“–mathematicalOrder.IsIdealSet.Nonemptyβ€”β€”

PSet

Definitions

NameCategoryTheorems
Nonempty πŸ“–MathDef
7 mathmath: nonempty_of_mem, ZFSet.nonempty_mk_iff, nonempty_def, nonempty_of_nonempty_type, not_nonempty_empty, nonempty_type_iff_nonempty, nonempty_toSet_iff

Set

Definitions

NameCategoryTheorems
Nonempty πŸ“–MathDef
469 mathmath: sups_nonempty, VitaliFamily.nonempty_interior, closure_nonempty_iff, MeasureTheory.Measure.haar.nonempty_iInter_clAddPrehaar, mem_closure_iff, upperHemicontinuousWithinAt_iff_frequently, HahnSeries.untop_orderTop_of_ne_zero, Convex.nontrivial_iff_nonempty_interior, image_nonempty, sub_nonempty, singleton_nonempty, Cardinal.compl_nonempty_of_mk_lt_mk, Complex.reProdIm_nonempty, not_nonempty_empty, range_nonempty_iff_nonempty, MulAction.nonempty_orbit, disjoint_or_nonempty_inter, encard_ne_zero, SimpleGraph.reachable_iff_nonempty_univ, insert_nonempty, ConvexCone.canLift, clusterPt_principal_iff, iUnion_nonempty_index, MeasureTheory.Measure.eventually_nonempty_inter_smul_of_density_one, AddAction.nonempty_orbit, union_nonempty, locallyFinite_iff_smallSets, offDiag_nonempty, nonempty_image_addRight_neg_inter_iff, diff_nonempty_of_ncard_lt_ncard, nonempty_uIoc, sigma_nonempty_iff, nonempty_iUnion, nonempty_of_ssubset, Flow.nonempty_orbit, AddAction.isTopologicallyTransitive_iff, MeasureTheory.exists_nonempty_inter_of_measureReal_univ_lt_sum_measureReal, EMetric.dense_iff, FirstOrder.Language.IsFraisse.is_nonempty, tangentConeAt_nonempty_of_properSpace, TopologicalSpace.Compacts.isClosed_inter_nonempty_of_isClosed, powerset_nonempty, Ordinal.isAcc_iff, Nat.nonempty_of_sInf_eq_succ, surjOn_univ_of_subsingleton_nonempty, TopologicalSpace.Opens.ne_bot_iff_nonempty, IsLowerSet.bot_mem, AffineSubspace.WSameSide.nonempty, mem_closure_iff_nhds, graphOn_nonempty, MeasureTheory.Measure.nonempty_support_iff, MeasureTheory.nonempty_of_measure_ne_zero, Nonempty.of_subtype, upperHemicontinuousOn_iff_frequently, nonempty_Ioc, diagonal_nonempty, vsub_nonempty, bot_lt_affineSpan, nonempty_iInter_Iic_iff, nonempty_star, spectrum.nonempty_of_isAlgClosed_of_finiteDimensional, inter_nonempty_iff_exists_right, Finset.coe_nonempty, MeasureTheory.Measure.mkMetric_apply, interior_convexHull_nonempty_iff_affineSpan_eq_top, MeasureTheory.measure_pos_iff_nonempty_of_isAddLeftInvariant, balancedCore_nonempty_iff, Nontrivial.offDiag_nonempty, Subtype.preimage_coe_nonempty, Matroid.IsBase.nonempty, Filter.HasBasis.inf_basis_neBot_iff, SetRel.isCover_univ, Filter.principal_neBot_iff, NNReal.spectrum_nonempty, countable_setOf_nonempty_of_disjoint, infinite_add, preimage_singleton_nonempty, quasispectrum.nonempty, Perfect.closure_nhds_inter, nonempty_image_addLeft_neg_inter_iff, Absorbent.gauge_set_nonempty, inter_nonempty, Metric.empty_or_nonempty_of_hausdorffEDist_ne_top, AffineSubspace.SOppSide.nonempty, Filter.forall_mem_nonempty_iff_neBot, Dynamics.one_le_coverMincard_iff, Filter.Realizer.ne_bot_iff, nonempty_coe_sort, IsMaxAntichain.nonempty_iff, Matroid.IsCircuit.nonempty, Filter.HasBasis.neBot_iff, EuclideanGeometry.Sphere.nonempty_iff, vadd_nonempty, MeasureTheory.nonempty_inter_of_measureReal_lt_add', AffineSubspace.perpBisector_nonempty, not_nonempty_iff_eq_empty, ProperCone.nonempty, infinite_prod, EMetric.empty_or_nonempty_of_hausdorffEdist_ne_top, AffineSubspace.sSameSide_self_iff, Order.PFilter.nonempty, FirstOrder.Language.age.nonempty, zero_nonempty, nonempty_biUnion, nonempty_sections_of_finite_cofiltered_system, rieszContentAux_image_nonempty, Dynamics.nonempty_inter_of_coverMincard, nonempty_of_finprod_mem_ne_one, PMF.support_nonempty, TopologicalSpace.vietoris.isClosed_inter_nonempty_of_isClosed, infinite_sub, MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_sum_measure, Order.Ideal.nonempty', Matroid.dual_dep_iff_forall, nonempty_compl_of_nontrivial, Subsingleton.mem_iff_nonempty, LocallyFinite.exists_mem_basis, isIrreducible_iff_sInter, MeasureTheory.Measure.nonempty_inter_support_of_pos, Convex.radon_partition, AlgebraicGeometry.Scheme.Opens.nonempty_iff, infinite_mul, exists_nonempty_countable_separating, Dynamics.IsDynCoverOf.nonempty_inter, nonempty_uIoo, Order.IsIdeal.Nonempty, TopologicalSpace.PositiveCompacts.interior_nonempty, MeasureTheory.measure_pos_iff_nonempty_of_vaddInvariant, AffineSubspace.WOppSide.nonempty, Ordinal.IsAcc.inter_Ioo_nonempty, Order.IsPredLimit.nonempty_Ioi, diff_ssubset_left_iff, Convex.interior_nonempty_iff_affineSpan_eq_top, univ_nonempty, UniformSpace.hausdorff.isOpen_inter_nonempty_of_isOpen, Function.Injective.nonempty_apply_iff, TopologicalSpace.NonemptyCompacts.isOpen_inter_nonempty_of_isOpen, TopologicalSpace.NonemptyCompacts.nonempty', IsUpperSet.top_mem, TopologicalSpace.Compacts.isOpen_inter_nonempty_of_isOpen, nonempty_Icc, Ultrafilter.nonempty_of_mem, infinite_image2, absConvexHull_nonempty, Dense.nonempty, jacobsonSpace_iff_locallyClosed, Metric.nonempty_ball, univ_pi_nonempty_iff, IsLeast.nonempty, NonemptyInterval.coe_nonempty, zero_mem_smul_iff, not_disjoint_iff_nonempty_inter, TopologicalSpace.Opens.nonempty_coe, nonempty_of_encard_ne_zero, HahnSeries.orderTop_of_ne, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, MeasureTheory.Measure.nonempty_support, nonempty_Ioo, Semiquot.nonempty, IsSelfAdjoint.spectrum_nonempty, associatedPrimes.nonempty, Nat.nonempty_of_pos_sInf, BoxIntegral.Box.nonempty_coe, SimpleGraph.degree_pos_iff_nonempty, Function.mulSupport_nonempty_iff, DiscreteTiling.PlacedTile.coe_nonempty_iff, LinearOrderedField.cutMap_nonempty, FirstOrder.Language.exists_countable_is_age_of_iff, nonempty_inter_of_lt_ncard_add_ncard, vadd_inter_nonempty_iff', TopologicalSpace.PositiveCompacts.interior_nonempty', nonempty_iInter, natCard_pos, mem_closure_iff_nhds_basis', Filter.nonempty_of_mem, isPathConnected_iff, Nontrivial.nonempty, SimpleGraph.center_nonempty, prod_nonempty_iff, nonempty_def, SimpleGraph.edgeSet_nonempty, notMem_nonZeroDivisors_iff, one_nonempty, spanPoints_nonempty, zero_mem_asymptoticCone, toFinset_nonempty, IsLUB.nonempty, pathComponent.nonempty, MeasurableSpace.nonempty_countableGeneratingSet, exists_perfect_nonempty_of_isClosed_of_not_countable, Metric.dense_iff, op_smul_inter_nonempty_iff, BoxIntegral.Box.isSome_iff, ModelWithCorners.nonempty_interior, eq_singleton_iff_nonempty_unique_mem, Matroid.ground_nonempty, Infinite.nonempty, nonempty_iInter_Ici_iff, nonempty_of_not_isMeagre, BoxIntegral.Box.not_disjoint_coe_iff_nonempty_inter, nonempty_inter_compl_of_ncard_add_ncard_lt, TopologicalSpace.NonemptyCompacts.isClosed_inter_nonempty_of_isClosed, TopologicalSpace.IsTopologicalBasis.mem_closure_iff, upperHemicontinuous_iff_frequently, IsSimplyConnected.nonempty, TopologicalSpace.Closeds.coe_nonempty, SimpleGraph.Preconnected.set_univ_walk_nonempty, Delone.DeloneSet.nonempty, SimpleGraph.Subgraph.connected_iff_forall_exists_walk_subgraph, Submodule.annihilator_top_inter_nonZeroDivisors, Ordinal.cof_lsub_def_nonempty, powersetCard.coe_nonempty_iff, TopologicalSpace.Opens.nonempty_coeSort, MultilinearMap.map_nonempty, IsApproximateSubgroup.nonempty, IsIrreducible.nonempty, IsPathConnected.nonempty, MeasureTheory.measure_ne_zero_iff_nonempty_of_isMulLeftInvariant, iUnion_nonempty_self, nonempty_of_union_eq_top_of_nonempty, SimpleGraph.nonempty_of_pos_dist, SeminormFamily.basisSets_nonempty, MeasureTheory.Measure.MeasureDense.nonempty, comap_coe_nhdsLT_eq_atTop_iff, spectrum.nonempty, lowerHemicontinuousAt_iff, nonempty_Ico, MeasureTheory.nonempty_of_measureReal_ne_zero, Iio_nonempty, Metric.coveringNumber_pos_iff, HahnSeries.support_nonempty_iff, nonempty_image_mulLeft_inv_inter_iff, one_le_chainHeight_iff, Cardinal.diff_nonempty_of_mk_lt_mk, Dense.nonempty_iff, eq_empty_or_nonempty, AffineSubspace.wSameSide_self_iff, AddSubgroup.IsComplement.nonempty_right, MeasureTheory.upperCrossingTime_lt_nonempty, AffineSubspace.mk'_nonempty, SimpleGraph.Subgraph.ne_bot_iff_nonempty_verts, SimpleGraph.Subgraph.Connected.nonempty, Ordinal.mem_closure_tfae, Metric.nonempty_closedBall, Metric.thickening_nonempty_iff_of_pos, nonempty_iff_univ_nonempty, nonempty_Ioi, ProperlyDiscontinuousVAdd.finite_disjoint_inter_image, HahnSeries.orderTop_of_ne_zero, TopologicalSpace.NonemptyCompacts.nonempty, HahnSeries.order_of_ne, diff_nonempty, Order.IsSuccLimit.nonempty_Iio, MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant, eval_image_pi_of_notMem, MeasureTheory.measure_ne_zero_iff_nonempty_of_isAddLeftInvariant, IsConnected.nonempty, IsGLB.nonempty, nonempty_sInter, add_nonempty, Dense.inter_nhds_nonempty, nhdsSet_neBot_iff, nonempty_of_ncard_ne_zero, nonempty_frontier_iff, Archimedean.ratLt'_nonempty, Subgroup.IsComplement.nonempty_left, exists_eq_singleton_iff_nonempty_subsingleton, Bornology.nonempty_of_not_isBounded, SimpleGraph.Walk.support_nonempty, op_vadd_inter_nonempty_iff, range_nonempty, TopologicalSpace.vietoris.isOpen_inter_nonempty_of_isOpen, Submodule.nonempty, Module.nonempty_support_of_nontrivial, mem_omegaLimit_iff_frequently, ConvexBody.nonempty, smul_nonempty, nonempty_interior_of_iUnion_of_closed, nonempty_iff_empty_ne, Nonempty.nhdsSet_neBot, nonempty_sUnion, MeasureTheory.OuterMeasure.boundedBy_apply, MeasureTheory.Measure.haar.nonempty_iInter_clPrehaar, Order.Ideal.inter_nonempty, clusterPt_iff_nonempty, MeasureTheory.nonempty_inter_of_measure_lt_add, nonempty_of_not_bddBelow, subset_sSup_def, UniformSpace.mem_comp_comp, Nonempty.of_sUnion_eq_univ, seqLeft_def, Cardinal.mk_set_ne_zero_iff, asymptoticCone_nonempty, ZFSet.nonempty_coe, connectedComponentIn_nonempty_iff, UpperSet.coe_nonempty, UniformSpace.mem_closure_iff_ball, Matroid.Nonempty.ground_nonempty, Order.isIdeal_iff, Submodule.range_map_nonempty, MeasureTheory.Measure.count_ne_zero_iff, SimpleGraph.ComponentCompl.nonempty, AffineSubspace.nonempty_of_affineSpan_eq_top, Ordinal.nonempty_compl_range, smul_set_nonempty, Order.Ideal.nonempty, affineSpan_nonempty, intrinsicInterior_nonempty, smul_inter_nonempty_iff, dense_iff_inter_open, ZFSet.nonempty_toSet_iff, notMem_singleton_empty, Setoid.nonempty_of_mem_partition, ProperlyDiscontinuousSMul.finite_disjoint_inter_image, UpperHemicontinuous.isClosed_domain, Matroid.Dep.nonempty, ncard_pos, DiscreteTiling.PlacedTile.coe_mk_nonempty_iff, encard_pos, nonempty_iff_ne_empty, Filter.HasBasis.inf_neBot_iff, ConvexOn.le_sup_of_mem_convexHull, mul_nonempty, UniformSpace.mem_closure_iff_symm_ball, vadd_set_nonempty, Filter.generate_neBot_iff, Ordinal.IsAcc.forall_lt, IsApproximateAddSubgroup.nonempty, connectedComponent_nonempty, infinite_div, Ideal.nonempty_inter_nonZeroDivisors_of_faithfulSMul, PairwiseDisjoint.finite_biUnion_iff, interior_extChartAt_target_nonempty, MeasureTheory.Measure.hausdorffMeasure_apply, Module.nonempty_support_iff, nonempty_of_not_subset, smul_inter_nonempty_iff', nonempty_uIcc, Real.sSup_def, NormedSpace.sphere_nonempty, MeasureTheory.measure_pos_iff_nonempty_of_isMulLeftInvariant, nonempty_inv, MulAction.orbitRel.Quotient.orbit_nonempty, nonempty_Iic, MeasureTheory.Measure.MeasureDense.nonempty', mem_omegaLimit_iff_frequentlyβ‚‚, Filter.lift'_neBot_iff, nonempty_of_mem, Filter.NeBot.nonempty_of_mem, FilterBasis.nonempty, Metric.thickening_nonempty_iff, MulAction.orbit_nonempty, inter_nonempty_iff_exists_left, MulAction.orbitRel.Quotient.nonempty_orbit, IsGreatest.nonempty, LinearMap.polar_nonempty, seqRight_def, intrinsicClosure_nonempty, LowerSet.coe_nonempty, Matroid.ground_nonempty_iff, Metric.externalCoveringNumber_pos_iff, symmDiff_nonempty, Filter.HasBasis.clusterPt_iff, empty_ssubset, nonempty_image_mulRight_inv_inter_iff, HahnSeries.min_le_min_add, ConvexBody.nonempty', AddAction.orbitRel.Quotient.nonempty_orbit, Metric.packingNumber_pos_iff, Function.Surjective.nonempty_preimage, TopologicalSpace.NoetherianSpace.exists_isOpen_nonempty_subset_irreducibleComponent, isPreconnected_Icc_aux, mem_diff_singleton_empty, convexHull_nonempty_iff, nonempty_sections_of_finite_inverse_system, Matroid.IsCocircuit.nonempty, pathComponentIn_nonempty_iff, Ioi_nonempty, Filter.HasBasis.inf_principal_neBot_iff, SimpleGraph.Subgraph.connected_iff, SimpleGraph.nonempty_ends_of_infinite, nonempty_Ici, CFC.spectrum_nonempty, nonempty_neg, IsMaxChain.nonempty_iff, one_le_encard_iff_nonempty, Function.support_nonempty_iff, Besicovitch.TauPackage.lastStep_nonempty, vadd_inter_nonempty_iff, MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_tsum_measure, Finset.Nonempty.to_set, NonemptyChain.Nonempty', Function.Fiber.fiber_nonempty, SimpleGraph.IsIndepSet.nonempty_mem_compl_mem_edge, ConvexOn.inf_le_of_mem_convexHull, LocallyFinite.finite_nonempty_inter_compact, Filter.inf_neBot_iff, infs_nonempty, PSet.nonempty_toSet_iff, TopologicalSpace.Compacts.coe_nonempty, nonempty_of_finsum_mem_ne_zero, AffineSubspace.eq_bot_or_nonempty, subset_sInf_def, TopologicalSpace.NoetherianSpace.exists_open_ne_empty_le_irreducibleComponent, ContinuousFunctionalCalculus.spectrum_nonempty, Subgroup.coe_nonempty, isPreconnected_closed_iff, ModelWithCorners.nonempty_interior', TopologicalSpace.Opens.not_nonempty_iff_eq_bot, comap_coe_nhdsGT_eq_atBot_iff, nonempty_sections_of_finite_cofiltered_system.init, Partition.parts_nonempty, MulAction.isTopologicallyTransitive_iff, inter_compl_nonempty_iff, TopologicalSpace.nonempty_of_mem_countableBasis, image2_nonempty_iff, notMem_nonZeroDivisorsLeft_iff, singleton_inter_nonempty, notMem_nonZeroDivisors_iff_right, SimpleGraph.colorable_set_nonempty_of_colorable, nonempty_compl, IsGenericPoint.mem_open_set_iff, pi_nonempty_iff, finite_iUnion_iff, AffineSubspace.nonempty_iff_ne_bot, Dynamics.one_le_netMaxcard_iff, AffineSubspace.SSameSide.nonempty, LocallyFinite.eventually_smallSets, nonempty_inter_of_le_ncard_add_ncard, TopologicalSpace.IsTopologicalBasis.dense_iff, TopologicalSpace.PositiveCompacts.nonempty, nonempty_ordConnectedComponent, upperHemicontinuousAt_iff_frequently, Archimedean.ratLt_nonempty, AddSubgroup.coe_nonempty, nonempty_Iio, compl_ne_univ, SimpleGraph.Connected.set_univ_walk_nonempty, AddSubgroup.IsComplement.nonempty_left, notMem_nonZeroDivisorsRight_iff, Finite.toFinset_nonempty, nonempty_of_ssubset', nonempty_iInterβ‚‚, SmoothBumpFunction.nonempty_support, LocallyFinite.finite_nonempty_of_compact, nhdsWithin_neBot, StrongDual.polar_nonempty, TopCat.partialSections.nonempty, closure_inter_open_nonempty_iff, PiTensorProduct.nonempty_lifts, lowerHemicontinuousWithinAt_iff, nonempty_of_not_bddAbove, Subgroup.IsComplement.nonempty_right, IsOpen.measure_pos_iff, image_inter_nonempty_iff, inter_singleton_nonempty, SimpleGraph.ConnectedComponent.nonempty_supp, MeasureTheory.Filtration.sInf_def, IsPGroup.nonempty_fixed_point_of_prime_not_dvd_card, Filter.inf_principal_neBot_iff, affineSpan_eq_top_iff_nonempty_of_subsingleton, MeasureTheory.nonempty_inter_of_measureReal_lt_add, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, div_nonempty, dirSupInacc_iff_forall_sSup, MeasureTheory.nonempty_inter_of_measure_lt_add', ChainCompletePartialOrder.nonempty_fixedPoints_of_inflationary, TopologicalSpace.Closeds.isOpen_inter_nonempty_of_isOpen, AlgebraicGeometry.IsAffineOpen.primeIdealOf_genericPoint

ZFSet

Definitions

NameCategoryTheorems
Nonempty πŸ“–MathDef
9 mathmath: singleton_nonempty, nonempty_mk_iff, nonempty_def, eq_empty_or_nonempty, insert_nonempty, nonempty_coe, nonempty_of_mem, nonempty_toSet_iff, not_nonempty_empty

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
exists_const_iff πŸ“–β€”β€”β€”β€”β€”
exists_true_iff_nonempty πŸ“–β€”β€”β€”β€”β€”
nonempty_plift πŸ“–β€”β€”β€”β€”β€”
nonempty_pprod πŸ“–β€”β€”β€”β€”β€”
nonempty_prod πŸ“–β€”β€”β€”β€”β€”
nonempty_psigma πŸ“–β€”β€”β€”β€”β€”
nonempty_psum πŸ“–β€”β€”β€”β€”β€”
nonempty_sigma πŸ“–β€”β€”β€”β€”β€”
nonempty_subtype πŸ“–β€”β€”β€”β€”β€”
nonempty_sum πŸ“–β€”β€”β€”β€”β€”
nonempty_ulift πŸ“–β€”β€”β€”β€”β€”
not_nonempty_iff_imp_false πŸ“–β€”β€”β€”β€”Nonempty.imp
subsingleton_of_not_nonempty πŸ“–β€”β€”β€”β€”not_nonempty_iff_imp_false

---

← Back to Index