intros k mon a0 forces_a0 a1 b forces_a0a1_b.
unfold forces_t in |- *.
unfold forces_t2 in |- *.
apply forces_a0_imp_a1_imp_b__forces_a1_imp_b with a0.
apply (kripke_tree_kripke_model k mon).
unfold Suc in |- *; apply succs_refl.
assumption.
assumption.
Qed.

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).