Definition corestep_plus c m c' m' :=
    exists n, corestepN (S n) c m c' m'.Definition corestep_star c m c' m' :=
    exists n, corestepN n c m c' m'.

Lemma corestep_star_plus_trans : forall c1 c2 c3 m1 m2 m3, corestep_star c1 m1 c2 m2 -> corestep_plus c2 m2 c3 m3 -> corestep_plus c1 m1 c3 m3.