Theorems · Theorem · order theory

mem_lowerBounds_image2

∀ {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} {a : α} {b : β},
  (∀ (b : β), Monotone (Function.swap f b)) →
    (∀ (a : α), Monotone (f a)) → a ∈ lowerBounds s → b ∈ lowerBounds t → f a b ∈ lowerBounds (Set.image2 f s t)

Defined in

Mathlib.Order.Bounds.Image

Cited by

3 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorderPreorder