intros work c i j ds ni ai a context forces_ij mon.
unfold nminimal in |- *.
intros c0 k k_is_mon k_forces_ngamma in_context.
inversion_clear in_context.
rewrite <- H; clear H c0.
apply k_forces_ngamma.
apply in_ngamma_cons_work_head.
apply mon; try assumption.
apply forces_ngamma_shift_work_ds.
apply forces_ngamma_cons_work_weak with c; try assumption.
intro forces_c.
apply forces_ij; assumption.
Qed.

Lemma nminimal_cons_work_cons_context :
forall (c : normal_form) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(context : flist),
nminimal work ds ni ai a context ->
nminimal (c :: work) ds ni ai a (nf2form c :: context).