intros i j work ds ni ai a k k_forces_ngamma.
unfold forces_ngamma in |- *.
intros d in_gamma.
apply k_forces_ngamma.
apply in_ngamma_shift_work_ds; assumption.
Qed.

Lemma forces_ngamma_shift_work_ds :
forall (i j : Int) (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai : atomic_imps) (a : atoms) (k : kripke_tree),
forces_ngamma (NDisj i j :: work) ds ni ai a k ->
forces_ngamma work ((i, j) :: ds) ni ai a k.