Definition quotient_lower_set_order : hrel (setquotinset downward_closed_to_eqrel). Proof. use quotrel. - exact quotient_lower_set_order_on_el. - exact quotient_lower_set_order_on_el_comprel. 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.