(****************)
simple induction v. simpl in |- *. unfold strip in |- *. simpl in |- *. trivial with arith.
simple induction i; simple induction j.
simpl in |- *. rewrite strip_O. rewrite trunc_O. trivial with arith.
rewrite trunc_O.
simpl in |- *. intros. unfold strip in |- *. simpl in |- *. rewrite trunc_O. trivial with arith.
rewrite strip_O. rewrite strip_O. elim minus_n_O. trivial with arith.
intros. rewrite strip_cons_S. simpl in |- *. rewrite strip_cons_S. apply H.
Qed.

Lemma trunc_strip :
forall (v : list A) (i j : nat),
trunc (strip v i) j = strip (trunc v (i + j)) i.