Definition least_suchthat_property {A : P -> hProp} (x : least_suchthat A) : is_least_suchthat A x. Proof. split. - apply @least_suchthat_satisfies. - apply least_is_least. 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.