Definition exp_partial_setoid_im_exists_law : form (ℙ (X ×h Y)) := let f := π₁ (tm_var (ℙ (X ×h Y) ×h X)) in let x := π₂ (tm_var (ℙ (X ×h Y) ×h X)) in let γ := π₁ (tm_var ((ℙ (X ×h Y) ×h X) ×h Y)) in (∀h (x ~ x ⇒ ∃h (⟨ x [ γ ]tm , π₂ (tm_var _) ⟩ ∈ (f [ γ ]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.