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 alloc_forward: forall m lo hi m' b (A: Mem.alloc m lo hi = (m',b)), mem_forward m m'.