Proposition trans_dcpo_specialization {x y z : X} (p : x ⊑s y) (q : y ⊑s z) : x ⊑s z. Proof. intros P HP Px. apply (q P HP). apply (p P HP Px). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Core.ScottTopology. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous.