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).
Hint Unfold BV_full_adder.
(****************************************************************)

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