fact: Definition greatest_suchthat_satisfies {A : P -> UU} (x : greatest_suchthat A) : A x := pr2 (greatest_of_family_index x).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.WellOrderedSets UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo