Definition exp_comm_partial_setoid_1 : form (((X ×h Z) ×h Y) ×h X ×h ℙ (X ×h Y)) := let x := π₁ (π₂ (tm_var (((X ×h Z) ×h Y) ×h X ×h ℙ (X ×h Y)))) in let x' := π₁ (π₁ (π₁ (tm_var (((X ×h Z) ×h Y) ×h X ×h ℙ (X ×h Y))))) in let y := π₂ (π₁ (tm_var (((X ×h Z) ×h Y) ×h X ×h ℙ (X ×h Y)))) in let z := π₂ (π₁ (π₁ (tm_var (((X ×h Z) ×h Y) ×h X ×h ℙ (X ×h Y))))) in let f := π₂ (π₂ (tm_var (((X ×h Z) ×h Y) ×h X ×h ℙ (X ×h Y)))) in exp_partial_setoid_is_function [ f ] ∧ ⟨ x , y ⟩ ∈ f.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.Tripos. Require Import UniMath.CategoryTheory.Hyperdoctrines.GenericPredicate. 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.PERBinProducts. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.ExponentialPER. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.ExponentialEval. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.ExponentialLam.