Proposition is_scott_open_upper_set {x y : X} (Py : P x) (p : x ⊑ y) : P y. Proof. exact (pr1 HP x y Py p). 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.Basis.Continuous.