intros. apply le_n_S. auto with arith. Qed. Hint Resolve le_SO_size.

(* Specifications: *)
Lemma length_V1 : lengthbv V1 <> 0.
rewrite length_V1_size. auto with arith. Qed. Hint Resolve length_V1.
Lemma length_V2 : lengthbv V2 <> 0.
rewrite length_V2_size. auto with arith. Qed. Hint Resolve length_V2.
Lemma length_V2_V1 : lengthbv V2 = lengthbv V1.
transitivity size; auto with arith. Qed.
Lemma V1_not_nil : V1 <> nilbv.
apply (not_nil bool). auto with arith. Qed. Hint Resolve V1_not_nil.
Lemma V2_not_nil : V2 <> nilbv.
apply (not_nil bool). auto with arith. Qed. Hint Resolve V2_not_nil.
Lemma le_SO_length_V1 : 1 <= lengthbv V1.
apply (le_SO_length_v bool). auto with arith. Qed. Hint Resolve le_SO_length_V1.