Theorems · Theorem · order theory

Monotone.upperBounds_image_of_directedOn_prod

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {γ : Type u_3} [inst_2 : Preorder γ]
  {g : α × β → γ},
  Monotone g →
    ∀ {d : Set (α × β)},
      DirectedOn (fun x1 x2 => x1 ≤ x2) d → upperBounds (g '' d) = upperBounds (g '' (Prod.fst '' d) ×ˢ (Prod.snd '' d))

Defined in

Mathlib.Order.Bounds.Image

Cited by

1 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorderPreorder