intros j l; elim l; clear l.
intros; assumption.
intros i l ih a below_i below_a.
apply ih with (a := Imp (Atom i) a).
intros i0 in0.
apply below_i.
right; assumption.
split.
simpl in |- *.
apply below_i.
left; trivial.
assumption.
Qed.

(* Specifications: *)
Lemma below_vimp_tail :
forall (j : Int) (l : list Int) (a : form),
below_form (vimp l a) j -> forall i : Int, In i l -> Less i j.