intros k l.
elim l; clear l.
intros a b forces_ab forces_a.
apply forces_ab with (k' := k); try assumption.
unfold Suc in |- *; apply successor_refl.
simpl in |- *; intros i l ih a b forces_ab forces_a.
apply ih with (a := Imp (Atom i) a); try assumption.
intros k' suc1 forces_ia.
unfold forces_t in |- *; unfold forces_t2 in |- *; simpl in |- *.
intros k'' suc2 suc3 forces_i.
change (forces_t2 k k'' b) in |- *.
apply forces_ab.
assumption.
apply (forces_ia k''); assumption.
Qed.

Lemma forces_vimp2 :
forall (k : kripke_tree) (l : list Int) (a b c : form),
(forall k' : kripke_tree,
Suc k' k -> forces_t2 k k' a -> forces_t2 k k' b -> forces_t2 k k' c) ->
forces_t k (vimp l a) -> forces_t k (vimp l b) -> forces_t k (vimp l c).