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_work_ai_strength : forall (i : Int) (bs work : nf_list) (ds : disjs) (ni : nested_imps) (ai ai' : atomic_imps) (a a' : atoms) (k : kripke_tree), Is_Monotone_kripke_tree k -> EQUIV_INS unit i (fun _ : unit => tt) tt a a' -> LOOKUP nf_list i ai bs -> EQUIV_DEL nf_list i ai ai' -> forces_ngamma work ds ni ai a' k -> forces_ngamma (bs ++ work) ds ni ai' a' k.