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 length_BV_full_adder_sum : forall (v w : BV) (cin : bool), lengthbv v = lengthbv w -> lengthbv (BV_full_adder_sum v w cin) = lengthbv v.