Proposition is_directed_const {X : hSet} (PX : PartialOrder X) (x : X) (I : UU) (i : ∥ I ∥) : is_directed PX (λ _ : I, x). Proof. split. - exact i. - intros i₁ i₂. apply hinhpr. exists i₁. split ; apply refl_PartialOrder. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.