(** The following lemma states that the bisimilarity relation can be shifted one vertex down by following the edges of both local membership relations. *)

Lemma EQV_shift :
forall (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) (B : Rel Y) (b : Y),
EQV X A a Y B b ->
forall a' : X,
A a' a -> ex2 Y (fun b' => B b' b) (fun b' => EQV X A a' Y B b').