intros work ds ni1 ni2 ai a context eq12 sound.
unfold nsound in |- *.
intros c in_ngamma.
apply sound.
apply in_ngamma_eqv with ni2.
apply eqv_sym; assumption.
assumption.
Qed.

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