Definition prod_pointed_PartialOrder {X Y : hSet} (RX : pointed_PartialOrder X) (RY : pointed_PartialOrder Y) : pointed_PartialOrder (X × Y)%set. Proof. use make_pointed_PartialOrder. - exact (prod_PartialOrder RX RY). - exact (⊥_{RX} ,, ⊥_{RY}). - intro y. refine (_ ,, _). + apply pointed_PartialOrder_min_point. + apply pointed_PartialOrder_min_point. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.