Theorems · Theorem · order theory

BddAbove.bddAbove_image2_of_bddBelow

∀ {α : Type u} {β : Type v} {γ : Type w} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ] {f : α → β → γ}
  {s : Set α} {t : Set β},
  (∀ (b : β), Monotone (Function.swap f b)) →
    (∀ (a : α), Antitone (f a)) → BddAbove s → BddBelow t → BddAbove (Set.image2 f s t)

Defined in

Mathlib.Order.Bounds.Image

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorderPreorder