Definition greatest_suchthat_property {A : P -> hProp} (x : greatest_suchthat A) : is_greatest_suchthat A x. Proof. split. - apply @greatest_suchthat_satisfies. - apply greatest_is_greatest. 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.