intros t context a der_t k mon forces_context.
unfold forces_t in |- *.
unfold forces_t2 in |- *.
apply soundness with t context.
assumption.
apply (kripke_tree_kripke_model k mon).
unfold Suc in |- *; apply succs_refl.
exact forces_context.
Qed.

Lemma forces_b__forces_a_imp_b_t :
forall k : kripke_tree,
Is_Monotone_kripke_tree k ->
forall b : form, forces_t k b -> forall a : form, forces_t k (Imp a b).