Theorems · Theorem · order theory

Directed.inf_iSup_eq

∀ {ι : Sort u_1} {α : Type u_2} [inst : CompleteLattice α] {f : ι → α} [IsCompactlyGenerated α] {a : α},
  Directed (fun x1 x2 => x1 ≤ x2) f → a ⊓ ⨆ i, f i = ⨆ i, a ⊓ f i

Defined in

Mathlib.Order.CompactlyGenerated.Basic

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompleteLatticeIsCompactlyGenerated