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