Definition forces_ngamma (work : nf_list) (ds : disjs) 
  (ni : nested_imps) (ai : atomic_imps) (a : atoms) 
  (k : kripke_tree) :=
  forall c : normal_form,
  in_ngamma work ds ni ai a c -> forces_t k (nf2form c).

(* Specifications: *)
Lemma forces_ngamma_cons_work : forall (c : normal_form) (work : nf_list) (ds : disjs) (ni : nested_imps) (ai : atomic_imps) (a : atoms) (k : kripke_tree), forces_t k (nf2form c) -> forces_ngamma work ds ni ai a k -> forces_ngamma (c :: work) ds ni ai a k.
Lemma forces_ngamma_cons_work_tail : forall (c : normal_form) (work : nf_list) (ds : disjs) (ni : nested_imps) (ai : atomic_imps) (a : atoms) (k : kripke_tree), forces_ngamma (c :: work) ds ni ai a k -> forces_ngamma work ds ni ai a k.