intros k a1 b forces_a1_b a0.
unfold forces_t in |- *.
unfold forces_t2 in |- *.
apply forces_a1_imp_b__forces_a0_and_a1_imp_b.
assumption.
Qed.
(*****************************************************************)

Lemma forces_a_a_imp_b__forces_b_t :
forall (k : kripke_tree) (a b : form),
forces_t k a -> forces_t k (Imp a b) -> forces_t k b.