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_LOOR_LOOB: forall m1 m2 j (Minj12 : Mem.inject j m1 m2) m3 m3', Mem.unchanged_on (loc_out_of_reach j m1) m3 m3' -> Mem.unchanged_on (loc_out_of_bounds m2) m3 m3'.