Theorems · Theorem · order theory

DirectedOn.disjoint_sSup_left

∀ {α : Type u_2} [inst : CompleteLattice α] [IsCompactlyGenerated α] {a : α} {s : Set α},
  DirectedOn (fun x1 x2 => x1 ≤ x2) s → (Disjoint (sSup s) a ↔ ∀ ⦃b : α⦄, b ∈ s → Disjoint b a)

Defined in

Mathlib.Order.CompactlyGenerated.Basic

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompleteLatticeIsCompactlyGenerated