(**************)
simple induction v1. simpl in |- *. auto with arith.
intros. rewrite app_eq2.
rewrite length_eq2. elim i. simpl in |- *. rewrite trunc_O. trivial with arith.
intros. simpl in |- *. rewrite H. trivial with arith.
Qed. Hint Resolve trunc_app.

(* Specifications: *)
Lemma app_v_trunc :
forall (v1 v2 : list A) (i : nat),
v1 ++ trunc v2 i = trunc (v1 ++ v2) (length v1 + i).