intros work i j ds ni ai a context sound.
unfold nsound in |- *.
intros c in_ngamma.
apply sound.
apply in_ngamma_cons_ds_tail; assumption.
Qed.
Remark nsound_del_ai :
forall (i : Int) (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai ai' : atomic_imps) (a : atoms) (context : flist),
EQUIV_DEL nf_list i ai ai' ->
nsound work ds ni ai a context -> nsound work ds ni ai' a context.
intros i work ds ni ai ai' a context equiv_del sound.
unfold nsound in |- *.
intros c in_ngamma.
apply sound.
apply in_ngamma_del_ai_tail with i ai'; assumption.
Qed.
(***********************************************************************)

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