Proposition partial_setoid_refl_r {H : first_order_hyperdoctrine} {X : partial_setoid H} {Γ : ty H} {Δ : form Γ} {x y : tm Γ X} (p : Δ ⊢ x ~ y) : Δ ⊢ y ~ y. Proof. use (partial_setoid_trans x _ p). use partial_setoid_sym. exact p. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine.