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

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