Proposition comp_is_strict_scott_continuous {X Y Z : hSet} {DX : dcppo_struct X} {DY : dcppo_struct Y} {DZ : dcppo_struct Z} {f : X → Y} {g : Y → Z} (Df : is_strict_scott_continuous DX DY f) (Dg : is_strict_scott_continuous DY DZ g) : is_strict_scott_continuous DX DZ (λ x, g(f x)). Proof. split. - exact (comp_is_scott_continuous Df Dg). - rewrite (is_strict_scott_continuous_on_bot Df). exact (is_strict_scott_continuous_on_bot Dg). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Core.IntrinsicApartness.