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_a : forall (i : Int) (work : nf_list) (ds : disjs) (ni : nested_imps) (ai : atomic_imps) (a a' : atoms) (context : flist), EQUIV_INS unit i (fun _ : unit => tt) tt a a' -> nminimal (NAtom i :: work) ds ni ai a context -> nminimal work ds ni ai a' context.