Definition directed_set_top {X : hSet} {PX : PartialOrder X} (D : directed_set PX) (i j : D) : ∃ (k : D), PX (D i) (D k) × PX (D j) (D k) := is_directed_top (directed_set_is_directed D) i j.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.