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_work_ai_weak : forall (i : Int) (bs work : nf_list) (ds : disjs) (ni : nested_imps) (ai ai' : atomic_imps) (a : atoms) (context : flist), LOOKUP nf_list i ai bs -> EQUIV_DEL nf_list i ai ai' -> nminimal work ds ni ai a context -> nminimal (bs ++ work) ds ni ai' a context.