fact: Definition downward_closed_to_hrel : hrel X := λ x₁ x₂, eqset x₁ x₂ ∨ I x₁ ∧ I x₂.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.Posets.PointedPosets