simple induction v. intro. absurd (nil <> nilbv); unfold not in |- *; auto with arith.
intros. simpl in |- *. rewrite (trunc_O bool). trivial with arith.
Qed.

Lemma lowbit_is_abit :
forall v : BV, v <> nilbv -> consbv (lowbit v) nilbv = abit v 0.