Proposition is_least_upperbound_is_least {x : X} (Hx : is_least_upperbound x) {y : X} (Hy : is_upperbound y) : PX x y. Proof. exact (pr2 Hx y Hy). Qed.
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.