Definition forces_gamma (gamma : flist) (work : nf_list) 
  (k : kripke_tree) := forall a : form, in_gamma gamma work a -> forces_t k a.

Lemma forces_gamma_cons_gamma_weak : forall (gamma : flist) (work : nf_list) (k : kripke_tree) (a b : form), (forces_t k a -> forces_t k b) -> forces_gamma (a :: gamma) work k -> forces_gamma (b :: gamma) work k.