Mathlib Map

Theorems · Theorem · combinatorics

Set.intersecting_singleton

∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {a : α}, {a}.Intersecting ↔ a ≠ ⊥
Defined in
Mathlib.Combinatorics.SetFamily.Intersecting
Cited by
2 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext, Quot.sound
Assumes
SemilatticeInfOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.Intersecting.is_max_iff_card_eq · cited by 2Intersecting.is_max_iff_c…Set.intersecting_iff_pairwise_not_disjoint · cited by 1Set.intersecting_iff_pair…Set · cited by 53352SetBot.bot · cited by 4720Bot.botDisjoint · cited by 2201DisjointOrderBot · cited by 1055OrderBotSemilatticeInf · cited by 634SemilatticeInfSet.Intersecting · cited by 22Set.IntersectingSet.intersecting_singletonCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.