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.

Lemma forces_ngamma_shift_ai_work_old : forall (i : Int) (b : normal_form) (work : nf_list) (ds : disjs) (ni : nested_imps) (bs : nf_list) (ai ai' : atomic_imps) (a : atoms) (k : kripke_tree), LOOKUP nf_list i ai bs -> EQUIV_INS nf_list i (cons b) nf_nil ai ai' -> forces_ngamma work ds ni ai' a k -> forces_ngamma (AImp i b :: work) ds ni ai a k.