(********************* Lemmas and definitions related to mem_step ********)
apply (mem_step_freelist _ _ nil); trivial.
Qed.
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'
}.
subst; trivial. Qed.

Theorem loc_not_writable_preserve:
memstep_preserve (fun m m' => mem_forward m m' /\ Mem.unchanged_on (loc_not_writable m) m m').