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

Lemma forces_a0_imp_b__forces_a0_and_a1_imp_b_t : forall (k : kripke_tree) (a0 b : form), forces_t k (Imp a0 b) -> forall a1 : form, forces_t k (Imp (AndF a0 a1) b).