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

Lemma forces_ngamma_shift_a_work :
forall (i : Int) (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai : atomic_imps) (a a' : atoms) (k : kripke_tree),
EQUIV_INS unit i (fun _ : unit => tt) tt a a' ->
forces_ngamma work ds ni ai a' k ->
forces_ngamma (NAtom i :: work) ds ni ai a k.