Definition nsound (work : nf_list) (ds : disjs) (ni : nested_imps)
  (ai : atomic_imps) (a : atoms) (context : flist) :=
  forall c : normal_form,
  in_ngamma work ds ni ai a c -> Derivable context (nf2form c).

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.