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Theorems · Theorem · combinatorics

Set.Subsingleton.intersecting

∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {s : Set α},
  s.Subsingleton → (s.Intersecting ↔ s ≠ {⊥})
Defined in
Mathlib.Combinatorics.SetFamily.Intersecting
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemilatticeInfOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.intersecting_iff_eq_empty_of_subsingleton · cited by 0Set.intersecting_iff_eq_e…Set · cited by 53352SetBot.bot · cited by 4720Bot.botDisjoint · cited by 2201DisjointOrderBot · cited by 1055OrderBotSemilatticeInf · cited by 634SemilatticeInfSet.Subsingleton · cited by 276Set.SubsingletonSet.Intersecting · cited by 22Set.IntersectingSet.Subsingleton.pairwise · cited by 13Subsingleton.pairwiseSet.intersecting_iff_pairwise_not_disjoint · cited by 1Set.intersecting_iff_pair…Subsingleton.intersectingCITED BYCITES

Cites9

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Cited by1

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