Proposition to_lam_partial_setoid_eq {Γ : ty H} (z : tm Γ Z) (f : tm Γ (exp_partial_setoid X Y)) {Δ : form Γ} (p₁ : Δ ⊢ z ~ z) (p₂ : Δ ⊢ exp_partial_setoid_is_function [ f ]) (p₃ : Δ ⊢ lam_partial_setoid_eq [⟨ z , f ⟩]) : Δ ⊢ lam_partial_setoid_form [ ⟨ z , f ⟩ ]. Proof. unfold lam_partial_setoid_form, lam_partial_setoid_is_def. cbn. simplify_form. rewrite partial_setoid_subst. simplify. repeat use conj_intro. - exact p₁. - exact p₂. - exact p₃. 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. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERCategory. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERBinProducts. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.ExponentialPER.