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

Lemma forces_a_imp_b0_a_imp_b1__forces_a_imp_a0_and_a1 : forall (a b0 b1 : form) (k : kripke_tree), forces_t k (Imp a b0) -> forces_t k (Imp a b1) -> forces_t k (Imp a (AndF b0 b1)).