Definition lam_partial_setoid_comm_form (x := π₁ (π₁ (π₂ (tm_var ((X ×h Y) ×h (X ×h Z) ×h Y))))) (y := π₂ (π₂ (tm_var ((X ×h Y) ×h (X ×h Z) ×h Y)))) (z := π₂ (π₁ (π₂ (tm_var ((X ×h Y) ×h (X ×h Z) ×h Y))))) : tm ((X ×h Z) ×h Y) (ℙ (X ×h Y)) := {{ lam_image_form φ }} [ ⟨ !! , π₂ (π₁ (tm_var _)) ⟩ ]tm.
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.