Inductive plus: state -> state -> Prop :=
| plus_left: forall s1 s2 s3,
CCstep s1 s2 -> star s2 s3 -> plus s1 s3.

Lemma plus_star_trans: forall {s1 s2 s3},
plus s1 s2 -> star s2 s3 -> plus s1 s3.