intros i work ds ni ai a a' k equiv_ins k_forces_ngamma.
unfold forces_ngamma in |- *.
intros d in_gamma.
apply k_forces_ngamma.
apply in_ngamma_shift_a_work with a'; assumption.
Qed.

Lemma forces_ngamma_shift_work_ni_x_ni :
forall (x : nested_imp) (work : nf_list) (ds : disjs)
(ni1 ni2 : nested_imps) (ai : atomic_imps) (a : atoms)
(k : kripke_tree),
forces_ngamma (NImp_NF (nested_imp2nimp x) :: work) ds (ni1 ++ ni2) ai a k ->
forces_ngamma work ds (ni1 ++ x :: ni2) ai a k.