cut (star (star b a) (inv a) = inv a).
rewrite <- (G1 b a (inv a)); auto.
rewrite (G3b a); auto.
rewrite (G2c b); auto.
rewrite H'1.
rewrite (G2b (inv a)); auto.
Qed.

(* Specifications: *)
Theorem self_inv : e = inv e.
apply resolve; auto.