fact: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions