intros i b work ds ni ai ai' a context equiv_ins sound.
unfold nsound in |- *.
intros c in_ngamma.
apply sound.
apply in_ngamma_shift_ai_work with ai'; assumption.
Qed.

Lemma nsound_shift_work_a :
forall (i : Int) (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai : atomic_imps) (a a' : atoms) (context : flist),
EQUIV_INS unit i (fun _ : unit => tt) tt a a' ->
nsound (NAtom i :: work) ds ni ai a context ->
nsound work ds ni ai a' context.