Definition coproduct_dcpo_struct : dcpo_struct (setcoprod X Y). Proof. use make_dcpo_struct. - exact (coproduct_PartialOrder X Y). - intros I Df HDf. pose (D := make_directed_set _ I Df HDf). exact (coproduct_dcpo_lub D). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous.