intro. rewrite BV_increment_adder. rewrite BV_full_adder_ok.
simpl in |- *. elim plus_n_O. elim plus_n_Sm. auto.
Qed.

Lemma BV_decr_incr : forall v : BV, BV_decrement (BV_increment v) = v.
simple induction v. simpl in |- *. trivial.