Definition largest_progressive_map (X : dcpo) : progressive_map X. Proof. use make_progressive_map. - exact (largest_progressive_map_monotone X). - abstract (apply is_progressive_lub ; intro d ; apply progressive_map_is_progressive). Defined.
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.