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

Lemma trunc_plus_petit :
forall (v1 v2 : list A) (i j : nat),
j <= i -> trunc v1 i = v2 -> trunc v1 j = trunc v2 j.