Theorems · Theorem · order theory

OrderIso.map_csSup_of_directedOn

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompletePartialOrderSup α]
  [inst_1 : ConditionallyCompletePartialOrderSup β] (e : α ≃o β) {s : Set α},
  DirectedOn (fun x1 x2 => x1 ≤ x2) s → s.Nonempty → BddAbove s → e (sSup s) = ⨆ x, e ↑x

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

ConditionallyCompletePartialOrderSupConditionallyCompletePartialOrderSup