Proof star_step.

(* Specifications: *)
Lemma star_right:
forall ge s1 t1 s2 t2 s3 t,
star ge s1 t1 s2 -> step ge s2 t2 s3 -> t = t1 ** t2 ->
star ge s1 t s3.
Lemma star_E0_ind:
forall ge (P: state -> state -> Prop),
(forall s, P s s) ->
(forall s1 s2 s3, step ge s1 E0 s2 -> P s2 s3 -> P s1 s3) ->
forall s1 s2, star ge s1 E0 s2 -> P s1 s2.
Lemma star_right:
forall s1 t1 s2 t2 s3 t,
star s1 t1 s2 -> step s2 t2 s3 -> t = t1 ** t2 ->
star s1 t s3.
Lemma star_E0_ind:
forall (P: state -> state -> Prop),
(forall s, P s s) ->
(forall s1 s2 s3, step s1 E0 s2 -> P s2 s3 -> P s1 s3) ->
forall s1 s2, star s1 E0 s2 -> P s1 s2.