(*****************)
simple induction v. simpl in |- *. trivial with arith.
simple induction i. repeat rewrite trunc_O. trivial with arith.
intros. simpl in |- *. rewrite H. trivial with arith.
Qed. Hint Resolve trunc_trunc1.

Lemma trunc_trunc2 :
forall (v : list A) (i j : nat),
i <= j -> trunc (trunc v i) j = trunc v i.