(****************)
simple induction n; auto.
intros. simpl in |- *. rewrite H. auto.
Qed. Hint Resolve BV_null_nat.

Lemma length_BV_null : forall n : nat, lengthbv (BV_null n) = n.
unfold lengthbv, BV_null in |- *. intro. apply length_list_const.