Proposition is_least_upperbound_is_upperbound {x : X} (Hx : is_least_upperbound x) : is_upperbound x. Proof. exact (pr1 Hx). 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.