intros work ds ni1 ni2 ai a context le sound.
unfold nsound in |- *.
intros c in_ngamma.
apply sound.
apply in_ngamma_ge with ni2; assumption.
Qed.

Lemma nsound_ge :
forall (work : nf_list) (ds : disjs) (ni1 ni2 : nested_imps)
(ai : atomic_imps) (a : atoms) (context : flist),
le_ni ni2 ni1 ->
nsound work ds ni1 ai a context -> nsound work ds ni2 ai a context.