Definition chain_lub {P : Poset} (P_CC : is_chain_complete P) (p : Chain P) : least_upper_bound p. Proof. apply least_upper_bound_image. exact (P_CC (image_chain p)). Defined.
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.