intros k a b forces_a forces_ab.
apply (forces_ab k).
unfold Suc in |- *; apply successor_refl.
unfold Suc in |- *; apply successor_refl.
assumption.
Qed.

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)).