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_new : forall (i : Int) (b : normal_form) (work : nf_list) (ds : disjs) (ni : nested_imps) (ai ai' : atomic_imps) (a : atoms) (context : flist), (forall bs : nf_list, LOOKUP nf_list i ai bs -> False) -> EQUIV_INS nf_list i (cons b) nf_nil ai ai' -> nminimal (AImp i b :: work) ds ni ai a context -> nminimal work ds ni ai' a context.