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_ds_work; assumption.
Qed.

Lemma forces_ngamma_shift_ni_work :
forall (x : nested_imp) (work : nf_list) (ds : disjs)
(ni : nested_imps) (ai : atomic_imps) (a : atoms)
(k : kripke_tree),
forces_ngamma work ds (x :: ni) ai a k ->
forces_ngamma (NImp_NF (nested_imp2nimp x) :: work) ds ni ai a k.