fact: Definition downward_closed {X : hSet} (RX : PartialOrder X) (I : X → hProp) : UU := ∏ (x₁ x₂ : X), RX x₁ x₂ → I x₂ → I x₁.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets