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

Lemma nsound_shift_ni_x_ni_work :
forall (x : nested_imp) (work : nf_list) (ds : disjs)
(ni1 ni2 : nested_imps) (ai : atomic_imps) (a : atoms)
(context : flist),
nsound work ds (ni1 ++ x :: ni2) ai a context ->
nsound (NImp_NF (nested_imp2nimp x) :: work) ds (ni1 ++ ni2) ai a context.