Definition exp_partial_setoid_cod_defined_law : form (ℙ (X ×h Y)) := let f := π₁ (π₁ (tm_var ((ℙ (X ×h Y) ×h X) ×h Y))) in let x := π₂ (π₁ (tm_var ((ℙ (X ×h Y) ×h X) ×h Y))) in let y := π₂ (tm_var ((ℙ (X ×h Y) ×h X) ×h Y)) in (∀h ∀h (⟨ x , y ⟩ ∈ f ⇒ y ~ y)).
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.