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Theorems · Theorem · combinatorics

Set.intersecting_iff_eq_empty_of_subsingleton

∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] [Subsingleton α] (s : Set α), s.Intersecting ↔ s = ∅
Defined in
Mathlib.Combinatorics.SetFamily.Intersecting
Cited by
0 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemilatticeInfOrderBotSubsingleton
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Around this declaration

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Set · cited by 53352SetBot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotSemilatticeInf · cited by 634SemilatticeInfSet.nonempty_iff_ne_empty · cited by 96Set.nonempty_iff_ne_emptySet.Nonempty.ne_empty · cited by 65Nonempty.ne_emptynot_imp_comm · cited by 56not_imp_commSet.singleton_nonempty · cited by 32Set.singleton_nonemptySet.Intersecting · cited by 22Set.IntersectingSet.Subsingleton.eq_singleton_of_mem · cited by 16Subsingleton.eq_singleton…Set.subsingleton_of_subsingleton · cited by 10Set.subsingleton_of_subsi…Set.Subsingleton.intersecting · cited by 1Subsingleton.intersectingSet.intersecting_iff_eq_empty…CITED BYCITES

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