Definition nat_directed_set_monotone {X : hSet} (PX : PartialOrder X) (D : ℕ → X) (HD : ∏ (i j : ℕ), i ≤ j → PX (D i) (D j)) : directed_set PX := ℕ ,, D ,, is_directed_nat PX D HD.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.