intros k a0 b forces_a0_b a1.
unfold forces_t in |- *.
unfold forces_t2 in |- *.
apply forces_a0_imp_b__forces_a0_and_a1_imp_b.
assumption.
Qed.

(* Specifications: *)
Lemma forces_a1_imp_b__forces_a0_and_a1_imp_b_t :
forall (k : kripke_tree) (a1 b : form),
forces_t k (Imp a1 b) -> forall a0 : form, forces_t k (Imp (AndF a0 a1) b).