intros k a b c forces_abc.
unfold forces_t in |- *; unfold forces_t2 in |- *; simpl in |- *.
intros k' suc_k' suc_k''.
change (forces_t2 k k' (Imp a Falsum) -> forces_t2 k k' c) in |- *.
intros forces1.
apply (forces_abc k'); try assumption.
intros k'' suc3 suc4 forces_a.
elimtype False.
apply (forces1 k''); assumption.
Qed.

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