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Theorems · Theorem · combinatorics

Set.Intersecting.ne_bot

∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {s : Set α} {a : α}, s.Intersecting → a ∈ s → a ≠ ⊥
Defined in
Mathlib.Combinatorics.SetFamily.Intersecting
Cited by
4 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
SemilatticeInfOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.Intersecting.isUpperSet' · cited by 2Intersecting.isUpperSet'Finset.card_biUnion_le_of_intersecting · cited by 0Finset.card_biUnion_le_of…Set.Intersecting.isUpperSet · cited by 0Intersecting.isUpperSetSet.intersecting_insert · cited by 0Set.intersecting_insertSet · cited by 53352SetBot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotSemilatticeInf · cited by 634SemilatticeInfSet.Intersecting · cited by 22Set.IntersectingSet.Intersecting.bot_notMem · cited by 1Intersecting.bot_notMemIntersecting.ne_botCITED BYCITES

Cites6

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

Cited by4

Results whose statement or proof uses this declaration.