Definition isdirected_lub {P : Poset} (P_DC : is_directed_complete P) {I} (p : I -> P) (p_directed : isdirected p) : least_upper_bound p. Proof. exact (directed_lub P_DC (make_directed p_directed)). 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.