unfold nilbv in |- *. simple induction v. trivial. intros.
rewrite BV_full_adder_sum_eq3. rewrite half_adder_carry_false.
rewrite half_adder_sum_false. rewrite H; auto.
Qed. Hint Resolve BV_full_adder_sum_v_nil_false.

(* Specifications: *)
Lemma BV_full_adder_carry_v_nil_false :
forall v : BV, BV_full_adder_carry v nilbv false = false.