intros. rewrite (length_app bool).
rewrite highs_is_strip. rewrite (length_strip bool). rewrite length_R1.
simpl in |- *. rewrite plus_comm. rewrite <- le_plus_minus. apply minus_le_lem2.
exact le_SO_size. exact H0. rewrite length_R1. exact le_SO_size. exact H0.
Qed.

Lemma BV_to_nat_lem0 :
forall v : BV,
lengthbv v <> 0 ->
BV_to_nat v =
BV_to_nat (consbv (lowbit v) nilbv) + power2 1 * BV_to_nat (highs v).