(*********************)
simple induction v. intro. absurd (nil <> nil :>list A). unfold not in |- *. auto with arith.
exact H.
intros. simpl in |- *. apply le_n_S. auto with arith.
Qed.

Lemma le_SO_length_v :
forall v : list A,
length v <> 0 -> 1 <= length v.