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 loadbytes_alloc_unchanged m1 lo hi m2 b : Mem.alloc m1 lo hi = (m2, b) -> forall n (b' : block) (ofs : Z), Mem.valid_block m1 b' -> Mem.loadbytes m2 b' ofs n = Mem.loadbytes m1 b' ofs n.