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 po_trans: forall a b c, Mem.perm_order'' a b -> Mem.perm_order'' b c -> Mem.perm_order'' a c.