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