Definition least_upper_bound_image {I} (f : I -> P) : least_upper_bound f <-> least_upper_bound (pr1carrier (image f)). Proof. split; intros x; apply (make_least_upper_bound x); apply is_least_upper_bound_image, least_upper_bound_property. 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.