intros j l; elim l; clear l.
intros a below_la; assumption.
intros i l ih a below_la.
elim (ih (Imp (Atom i) a)); clear ih.
intros; assumption.
assumption.
Qed.

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