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

Lemma forces_a1_imp_b__forces_a0_imp_a1_imp_b_t : forall k : kripke_tree, Is_Monotone_kripke_tree k -> forall a0 : form, forces_t k a0 -> forall a1 b : form, forces_t k (Imp a1 b) -> forces_t k (Imp (Imp a0 a1) b).