Definition prod_partial_setoid : partial_setoid H. Proof. use make_partial_setoid. - exact (X ×h Y). - exact prod_per. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine.