Definition const_directed_set {X : hSet} (PX : PartialOrder X) (x : X) (I : UU) (i : ∥ I ∥) : directed_set PX. Proof. use (make_directed_set _ I). - exact (λ _, x). - exact (is_directed_const PX x I i). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.