Proof with auto.
induction v...
intros.
simpl.
apply sorted_cons'.
intros.
clear IHv.
rewrite list_round_trip in H2.
destruct (List.in_app_or v w y H2).
simpl in H.
apply (sorted_cons_inv' H).
rewrite list_round_trip...
apply H1...
left...
apply IHv...
simpl in H.
apply sorted_tail with a...
intros.
apply H1...
simpl...
Qed.

Lemma sorted_le_indices_le_values n (v: Vector.t X n): sorted v ->
forall (i j: natBelow n), i <= j -> Xle (nth v i) (nth v j).