intros i j work ds ni ai a context sound.
unfold nsound in |- *.
intros c in_ngamma.
apply sound.
apply in_ngamma_shift_ds_work; assumption.
Qed.

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