intros a i j.
elim a; clear a.
intros; trivial.
simpl in |- *.
intros i0 less_i0 less_i.
apply less_trans with i; assumption.
intros a ih_a b ih_b below_ab less_ij.
elim below_ab; clear below_ab.
intros below_a below_b.
split.
apply ih_a; assumption.
apply ih_b; assumption.
intros a ih_a b ih_b below_ab less_ij.
elim below_ab; clear below_ab.
intros below_a below_b.
split.
apply ih_a; assumption.
apply ih_b; assumption.
intros a ih_a b ih_b below_ab less_ij.
elim below_ab; clear below_ab.
intros below_a below_b.
split.
apply ih_a; assumption.
apply ih_b; assumption.
Qed.

(* Specifications: *)
Lemma below_list_less_below_list :
forall (l : flist) (i j : Int), below_list l i -> Less i j -> below_list l j.