Definition lift_PartialOrder {X : hSet} (PX : PartialOrder X) : PartialOrder (setcoprod X unitset). Proof. use make_PartialOrder. - exact (lift_hrel PX). - exact (lift_isPartialOrder PX). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. Require Import UniMath.OrderTheory.Posets.PointedPosets.