intros i bs work ds ni ai ai' a k lookup forces_bs equiv_del k_forces_ngamma.
unfold forces_ngamma in |- *.
intros c in_ngamma.
elim (in_ngamma_del_ai_rev work ds ni i bs ai' ai a c); try assumption;
clear in_ngamma.
intros in_ngamma.
apply k_forces_ngamma; assumption.
intros in_bs; elim in_bs; clear in_bs.
intros b n nth eq_a.
rewrite eq_a.
apply forces_bs with n; assumption.
Qed.
(***********************************************************************)

Lemma forces_ngamma_eqv :
forall (ni1 ni2 : nested_imps) (work : nf_list) (ds : disjs)
(ai : atomic_imps) (a : atoms) (k : kripke_tree),
eqv_ni ni1 ni2 ->
forces_ngamma work ds ni2 ai a k -> forces_ngamma work ds ni1 ai a k.