intros i b work ds ni ai ai' a context lookup equiv_ins mon.
unfold nminimal in |- *.
intros c k k_is_mon k_forces_ngamma in_a.
apply mon; try assumption.
apply forces_ngamma_shift_ai_work_new with ai'; assumption.
Qed.

(* Specifications: *)
Lemma nminimal_shift_work_ai_old :
forall (i : Int) (b : normal_form) (work : nf_list)
(ds : disjs) (ni : nested_imps) (bs : nf_list) (ai ai' : atomic_imps)
(a : atoms) (context : flist),
LOOKUP nf_list i ai bs ->
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.