(********************* 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.
intros. apply preserve_mem; trivial.
eapply mem_forward_preserve; trivial.
Qed.

Lemma freelist_perm_inv: forall l m m' (L : Mem.free_list m l = Some m') b (B: Mem.valid_block m b)
ofs k p (P: Mem.perm m b ofs k p),
Mem.perm m b ofs Max Freeable \/ Mem.perm m' b ofs k p.