Proposition is_progressive_comp {X : dcpo} {f g : monotone_function X X} (Hf : is_progressive f) (Hg : is_progressive g) : is_progressive (comp_monotone_function f g). Proof. intros x ; cbn. exact (trans_dcpo (Hf x) (Hg (f x))). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Examples.Products. Require Import UniMath.OrderTheory.DCPOs.Examples.SubDCPO.