fact: Definition directed_set {X : hSet} (PX : PartialOrder X) : UU := ∑ (I : UU) (D : I → X), is_directed PX D.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions