Definition BV_full_adder (v w : BV) (cin : bool) : BV :=
  appbv (BV_full_adder_sum v w cin)
    (consbv (BV_full_adder_carry v w cin) nilbv).

Lemma BV_full_adder_sum_v_nil_false : forall v : BV, BV_full_adder_sum v nilbv false = v.