Proposition way_below_upper_scott_open_subset {x₁ x₂ y : X} (p : x₂ ≪ x₁) (H : way_below_upper_set x₁ y) : way_below_upper_set x₂ y. Proof. unfold way_below_upper_set in *. exact (trans_way_below p H). 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.