Definition preserves_binproduct_functor_to_partial_setoids_inv : partial_setoid_morphism (prod_partial_setoid (eq_partial_setoid X) (eq_partial_setoid Y)) (eq_partial_setoid (X ×h Y)). Proof. use make_partial_setoid_morphism. - exact preserves_binproduct_functor_to_partial_setoids_inv_form. - exact preserves_binproduct_functor_to_partial_setoids_inv_laws. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERs. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERMorphisms. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERCategory. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERConstantObjects.