Proposition le_largest_progressive_map {X : dcpo} (f : progressive_map X) (x : X) : f x ⊑ largest_progressive_map X x. Proof. exact (less_than_dcpo_lub (directed_set_progressive_maps X) (pr1 f) f (refl_dcpo _) 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.