apply mem_step_refl.
destruct H0 as [m'' [CS CSN]]. eapply mem_step_trans.
eapply corestep_mem; eassumption.
eapply IHn; eassumption.
Qed.

Lemma memsem_preservesN P (HP: memstep_preserve P)
n c m c' m' (H: corestepN M n c m c' m'): P m m'.