Proof
fun X A a Y B b E H1 H2 H3 H4 =>
H4 (eq_refl (sum X Y) (inr X Y b)) (eq_refl (sum X Y) (out X Y)).
(** We first check that the left injection (inl X Y) : X -> (sum X Y) is a delocation, and deduce that the pointed graphs (X, A, a) and ((sum X Y), (PAIR X A a Y B b), (inl X Y a)) are bisimilar. *)

(* Specifications: *)
Lemma PAIR_deloc1 :
forall (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) (B : Rel Y) (b : Y),
deloc X A (sum X Y) (PAIR X A a Y B b) (inl X Y).
Lemma PAIR_eqv1 :
forall (X : Typ1) (A : Rel X) (a : X) (Y : Typ1) (B : Rel Y) (b : Y),
EQV X A a (sum X Y) (PAIR X A a Y B b) (inl X Y a).