Definition family_lub {P:Poset} (P_complete : is_complete P) {I:UU} (f : I -> P) : least_upper_bound f. Proof. apply least_upper_bound_image, P_complete. 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.