Definition lift_pointed_PartialOrder {X : hSet} (PX : PartialOrder X) : pointed_PartialOrder (setcoprod X unitset). Proof. use make_pointed_PartialOrder. - exact (lift_PartialOrder PX). - exact (inr tt). - exact (λ _, tt). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.Posets.PointedPosets.