Theorems · Theorem · order theory

ScottContinuousOn.comp

∀ {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 : β → γ} {D' : Set (Set β)},
  (∀ (a b : α), a ≤ b → {a, b} ∈ D) →
    Set.MapsTo (fun x => f '' x) D D' → ScottContinuousOn D' g → ScottContinuousOn D f → ScottContinuousOn D (g ∘ f)

Defined in

Mathlib.Order.ScottContinuity

Cited by

3 results in Mathlib

Foundations

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

Assumes

PreorderPreorderPreorder