(*****************)
intros. rewrite (trunc_max (trunc v i) j). trivial with arith.
apply le_trans with i. apply le_length_trunc. exact H.
Qed.

(* Specifications: *)
Lemma trunc_trunc3 :
forall (v : list A) (i j : nat),
j <= i -> trunc (trunc v i) j = trunc v j.