Definition is_directed : hProp := ∥ I ∥ ∧ ∀ (i j : I), ∃ (k : I), PX (D i) (D k) × PX (D j) (D k).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.