fact: Definition smash_set_downward_closd : downward_closed (prod_pointed_PartialOrder RX RY) smash_set.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets