Definition directed_lub {P : Poset} (P_DC : is_directed_complete P) (p : Directed_family P) : least_upper_bound p. Proof. apply least_upper_bound_image. exact (P_DC (image_directed 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.