Theorems · Theorem · order theory

AntitoneOn.sSup_image_Icc

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : ConditionallyCompleteLattice β] {f : α → β} {a b : α},
  b ≤ a → AntitoneOn f (Set.Icc b a) → sSup (f '' Set.Icc b a) = f b

Defined in

Mathlib.Order.ConditionallyCompleteLattice.Basic

Cited by

0 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderConditionallyCompleteLattice