apply corestepN_mem in H. apply HP; trivial. Qed.

(* Specifications: *)
Lemma memsem_preserves_plus P (HP:memstep_preserve P)
c m c' m' (H: corestep_plus M c m c' m'): P m m'.
Lemma memsem_preserves_plus P (HP:memstep_preserve P)
c m c' m' (H: corestep_plus M c m c' m'): P m m'.