Proposition lam_partial_setoid_eq_right (x : tm Γ X) (y : tm Γ Y) (q : Δ ⊢ ⟨ x , y ⟩ ∈ f) : Δ ⊢ φ [ ⟨ ⟨ x , z ⟩ , y ⟩ ]. Proof. use (iff_elim_right (lam_partial_setoid_eq_iff x y)). exact q. 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.