fact: Definition prod_directed_set {X Y : hSet} {PX : PartialOrder X} {PY : PartialOrder Y} (D₁ : directed_set PX) (D₂ : directed_set PY) : directed_set (prod_PartialOrder PX PY).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions