End corestepN.
Section memstepN.
Context {C:Type} (M:@MemSem C).

(* Specifications: *)
Lemma corestepN_mem n: forall c m c' m', corestepN M n c m c' m' -> mem_step m m'.
induction n; intros; inv H.
Lemma corestepN_mem n: forall c m c' m', corestepN M n c m c' m' -> mem_step m m'.
induction n; intros; inv H.