Theorems · Theorem · order theory

Order.IsNormal.map_iSup

∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : ConditionallyCompleteLinearOrder α]
  [inst_1 : ConditionallyCompleteLinearOrder β] {ι : Sort u_4} [Nonempty ι] {g : ι → α},
  Order.IsNormal f → BddAbove (Set.range g) → f (⨆ i, g i) = ⨆ i, f (g i)

Defined in

Mathlib.Order.IsNormal

Cited by

8 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompleteLinearOrderConditionallyCompleteLinearOrderNonempty