Record memstep_preserve (P:mem -> mem -> Prop) :=
{
preserve_trans: forall m1 m2 m3, P m1 m2 -> P m2 m3 -> P m1 m3;
preserve_mem: forall m m', mem_step m m' -> P m m'
}.

Lemma mem_step_forward m m': mem_step m m' -> mem_forward m m'.
intros. apply preserve_mem; trivial.