Definition least_upper_bound_is_upper_bound {I} {p : I -> P} (x : least_upper_bound p) : isupperbound p x := least_suchthat_satisfies x.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.