(** Moreover, any subset of (X, A, a) is bisimilar to a pointed graph of the form ((sum X X->Prop), (POWER X A a), (inr X X->Prop) p) for a suitable predicate p : X->Prop. *)

Lemma POWER_subset_eqv :
forall (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) (B : Rel Y) (b : Y),
SUB Y B b X A a ->
EQV Y B b (sum X (X -> Prop)) (POWER X A a)
(inr X (X -> Prop) (fun x' => and (A x' a) (ELT X A x' Y B b))).