Definition sub_dcpo_struct : dcpo_struct S. Proof. use make_dcpo_struct. - exact (sub_PartialOrder X P). - intros I D HD. exact (sub_dcpo_lub (make_directed_set _ I D HD)). Defined.
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.ScottContinuous.