Definition strict_and_monotone_PartialOrder_bottom : bottom_element strict_and_monotone_PartialOrder. Proof. refine ((_ ,, constant_is_strict_and_monotone PX PY) ,, _). abstract (intros f x ; cbn ; apply (pr2 PY)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.