Definition pair_partial_setoid_morphism_form : form (W ×h prod_partial_setoid X Y) := let w := π₁ (tm_var (W ×h X ×h Y)) in let x := π₁ (π₂ (tm_var (W ×h X ×h Y))) in let y := π₂ (π₂ (tm_var (W ×h X ×h Y))) in φ [ ⟨ w , x ⟩ ] ∧ ψ [ ⟨ w , y ⟩ ].
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.