(********************)
simple induction v. simpl in |- *. auto with arith.
intros. case i. rewrite trunc_O. auto with arith.
intro. simpl in |- *. apply le_n_S. apply H.
Qed. Hint Resolve le_length_trunc.

Lemma trunc_app :
forall (v1 v2 : list A) (i : nat),
trunc (v1 ++ v2) i = trunc v1 i ++ trunc v2 (i - length v1).