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_sym : forall (v w : BV) (cin : bool), BV_full_adder_sum v w cin = BV_full_adder_sum w v cin.