intros k mon a0 forces_a0 a1 b forces_a1_b.
unfold forces_t in |- *.
unfold forces_t2 in |- *.
apply forces_a1_imp_b__forces_a0_imp_a1_imp_b.
apply (kripke_tree_kripke_model k mon).
unfold Suc in |- *; apply succs_refl.
assumption.
assumption.
Qed.

Lemma forces_a0_imp_a1_imp_b__forces_a1_imp_b_t :
forall k : kripke_tree,
Is_Monotone_kripke_tree k ->
forall a0 : form,
forces_t k a0 ->
forall a1 b : form, forces_t k (Imp (Imp a0 a1) b) -> forces_t k (Imp a1 b).