(*****************)
simple induction v. simpl in |- *. auto with arith.
intros b b0 H. simple induction i. simpl in |- *. trivial with arith.
simpl in |- *. intros. apply eq_S. apply H. apply le_S_n. exact H1.
Qed.

Lemma trunc_inv :
forall (v : list A) (i : nat) (b : A),
b :: trunc v i = trunc (b :: v) (S i).