(** No transitions: stuck state *)

Definition nostep (s: state) : Prop :=
  forall t s', ~(step s t s').

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.