Definition forces_t (k : kripke_tree) := forces_t2 k k.

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).