Proposition lub_is_least (x : lub) (y : X) (Hy : is_upperbound y) : PX x y. Proof. exact (is_least_upperbound_is_least (pr2 x) 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.