Proof
fun X A a p E _ _ e =>
e p (eq_refl (sum X (X -> Prop)) (inr X (X -> Prop) p))
(eq_refl (sum X (X -> Prop)) (out X (X -> Prop))).
(** We now prove that the left injection (inl X X->Prop) is a delocation from (X, A) to ((sum X X->Prop), (POWER X A a)), and deduce the expected property of bisimilarity. *)

(* Specifications: *)
Lemma POWER_deloc :
forall (X : Typ1) (A : Rel X) (a : X),
deloc X A (sum X (X -> Prop)) (POWER X A a) (inl X (X -> Prop)).
Lemma POWER_eqv :
forall (X : Typ1) (A : Rel X) (a x : X),
EQV X A x (sum X (X -> Prop)) (POWER X A a) (inl X (X -> Prop) x).