Definition nminimal (work : nf_list) (ds : disjs) (ni : nested_imps)
  (ai : atomic_imps) (a : atoms) (context : flist) :=
  forall (c : form) (k : kripke_tree),
  Is_Monotone_kripke_tree k ->
  forces_ngamma work ds ni ai a k -> In c context -> forces_t k c.

Lemma nminimal_shift_ds_work_context : forall (work : nf_list) (c : normal_form) (i j : Int) (ds : disjs) (ni : nested_imps) (ai : atomic_imps) (a : atoms) (context : flist), (forall k : kripke_tree, Is_Monotone_kripke_tree k -> forces_t k (nf2form c) -> forces_t k (OrF (Atom i) (Atom j))) -> nminimal work ((i, j) :: ds) ni ai a context -> nminimal (c :: work) ds ni ai a (nf2form c :: context).