(**************)
simple induction v1. simpl in |- *. intros. elim minus_n_O. trivial with arith.
simple induction v2. intro. simpl in |- *.
rewrite strip_nil. rewrite app_v_nil. rewrite app_v_nil. trivial with arith.
simple induction i.
rewrite strip_O. simpl in |- *. rewrite strip_O. rewrite strip_O. auto with arith.
intros. rewrite app_eq2. rewrite strip_cons_S.
rewrite strip_cons_S. rewrite length_eq2. simpl in |- *. apply H.
Qed.

Lemma strip_strip_S :
forall (v : list A) (i j : nat),
strip (strip v (S i)) j = strip (strip v i) (S j).