(******************)
simple induction v. intros. rewrite strip_nil. rewrite strip_nil. trivial with arith.
simple induction i. intros. rewrite strip_O.
do 2 rewrite strip_cons_S. rewrite strip_O. trivial with arith.
simple induction j. rewrite strip_O.
repeat rewrite strip_cons_S. elim n. rewrite strip_O. trivial with arith.
intros. rewrite <- H. rewrite strip_O. trivial with arith.
intros. do 2 rewrite strip_cons_S. apply H.
Qed.

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