Definition downward_closed_to_eqrel : eqrel X. Proof. use make_eqrel. - exact downward_closed_to_hrel. - exact iseqrel_downward_closed_to_hrel. Defined.
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.