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

Lemma nsound_shift_work_ai :
forall (i : Int) (b : normal_form) (work : nf_list)
(ds : disjs) (ni : nested_imps) (ai ai' : atomic_imps)
(a : atoms) (context : flist),
EQUIV_INS nf_list i (cons b) nf_nil ai ai' ->
nsound (AImp i b :: work) ds ni ai a context ->
nsound work ds ni ai' a context.