Definition val_inject_opt (j: meminj) (v1 v2: option val) :=
  match v1, v2 with Some v1', Some v2' => val_inject j v1' v2'
  | None, None => True
  | _, _ => False
  end.

Lemma inject_permorder: forall j m1 m2 (Inj : Mem.inject j m1 m2) (b b':block) ofs' (J: j b = Some (b', ofs')) ofs k, Mem.perm_order'' (PMap.get b' (Mem.mem_access m2) (ofs + ofs') k) (PMap.get b (Mem.mem_access m1) ofs k).