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

Lemma trunc_trunc1 :
forall (v : list A) (i : nat),
trunc (trunc v i) i = trunc v i.