Definition least_suchthat_is_least {A : P -> UU} (x : least_suchthat A) : ∏ y, A y -> x ≤ y. Proof. intros y A_y. exact (least_is_least _ x (_,,A_y)). 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.