intros work ds x ni ai a k forces.
unfold forces_ngamma in |- *.
intros c in_ngamma.
apply forces.
apply in_ngamma_cons_ni_tail; assumption.
Qed.
Remark forces_ngamma_del_ai :
forall (i : Int) (work : nf_list) (ds : disjs) (ni : nested_imps)
(ai ai' : atomic_imps) (a : atoms) (k : kripke_tree),
EQUIV_DEL nf_list i ai ai' ->
forces_ngamma work ds ni ai a k -> forces_ngamma work ds ni ai' a k.
intros i work ds ni ai ai' a k equiv_del k_forces_ngamma.
unfold forces_ngamma in |- *.
intros c in_ngamma.
apply k_forces_ngamma.
apply in_ngamma_del_ai_tail with i ai'; assumption.
Qed.

Lemma forces_ngamma_del_ai_rev :
forall (i : Int) (bs work : nf_list) (ds : disjs)
(ni : nested_imps) (ai ai' : atomic_imps) (a : atoms)
(k : kripke_tree),
LOOKUP nf_list i ai bs ->
(forall (n : nat) (b : normal_form),
my_nth normal_form n bs b -> forces_t k (nf2form (AImp i b))) ->
EQUIV_DEL nf_list i ai ai' ->
forces_ngamma work ds ni ai' a k -> forces_ngamma work ds ni ai a k.