Theorems · Theorem · combinatorics

Finset.truncatedInf_of_isAntichain

∀ {α : Type u_1} [inst : SemilatticeInf α] {s : Finset α} {a : α} [inst_1 : DecidableLE α] [inst_2 : BoundedOrder α],
  IsAntichain (fun x1 x2 => x1 ≤ x2) ↑s → a ∈ s → s.truncatedInf a = a

Defined in

Mathlib.Combinatorics.SetFamily.AhlswedeZhang

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeInfDecidableLEBoundedOrder