fact: Definition lift_PartialOrder {X : hSet} (PX : PartialOrder X) : PartialOrder (setcoprod X unitset).
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets