Theorems · Theorem · order theory

OrderIso.map_ciInf_set_of_directedOn

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : ConditionallyCompletePartialOrderInf α]
  [inst_1 : ConditionallyCompletePartialOrderInf β] (e : α ≃o β) {s : Set γ} {f : γ → α},
  DirectedOn (fun x1 x2 => x2 ≤ x1) (f '' s) → BddBelow (f '' s) → s.Nonempty → e (⨅ i, f ↑i) = ⨅ i, e (f ↑i)

Defined in

Mathlib.Order.ConditionallyCompletePartialOrder.Indexed

Cited by

0 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompletePartialOrderInfConditionallyCompletePartialOrderInf