Definition is_directed_top (H : is_directed) (i j : I) : ∃ (k : I), PX (D i) (D k) × PX (D j) (D k) := pr2 H i j.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.