Definition forces_t (k : kripke_tree) := forces_t2 k k.

Lemma soundness_t : forall (t : proof_term) (context : flist) (a : form), derives context t a -> forall k : kripke_tree, Is_Monotone_kripke_tree k -> (forall c : form, In c context -> forces_t k c) -> forces_t k a.