Proposition exp_partial_setoid_eq_refl {Γ : ty H} {Δ : form Γ} (f : tm Γ (ℙ (X ×h Y))) : Δ ⊢ exp_partial_setoid_eq [ ⟨ f , f ⟩ ]. Proof. unfold exp_partial_setoid_eq. rewrite !forall_subst. do 2 use forall_intro. simplify. apply iff_refl. Qed.
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.