Theorems · Theorem · order theory

ScottContinuousOn.prodMk

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ]
  {D : Set (Set α)} {f : α → β} {g : α → γ},
  (∀ (a b : α), a ≤ b → {a, b} ∈ D) →
    ScottContinuousOn D f → ScottContinuousOn D g → ScottContinuousOn D fun x => (f x, g x)

Defined in

Mathlib.Order.ScottContinuity

Cited by

2 results in Mathlib

Foundations

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

Assumes

PreorderPreorderPreorder