(*****************)
unfold strip in |- *. simple induction i. simpl in |- *.
elim minus_n_O. intro. replace (length v) with (length (rev A v)).
rewrite trunc_all. rewrite trunc_app. rewrite trunc_all.
elim minus_n_n. rewrite trunc_O. rewrite app_v_nil. trivial with arith.
apply length_rev.
intros. apply rev_eq. simpl in |- *.
rewrite trunc_app. rewrite length_rev. rewrite minus_minus_lem1.
rewrite trunc_O. rewrite app_v_nil. trivial with arith.
Qed. Hint Resolve strip_cons_S.

Lemma length_strip :
forall (v : list A) (i : nat),
i <= length v -> length (strip v i) = length v - i.