Definition partial_setoid_pr1_form : form ((prod_partial_setoid X Y) ×h X) := let x := π₁ (π₁ (tm_var _)) : tm ((X ×h Y) ×h X) X in let y := π₂ (π₁ (tm_var _)) : tm ((X ×h Y) ×h X) Y in let x' := π₂ (tm_var _) : tm ((X ×h Y) ×h X) X in x ~ x' ∧ y ~ 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.