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_ds : forall (i j : Int) (work : nf_list) (ds : disjs) (ni : nested_imps) (ai : atomic_imps) (a : atoms) (context : flist), nsound (NDisj i j :: work) ds ni ai a context -> nsound work ((i, j) :: ds) ni ai a context.