Definition app_2_n {T:Type} {n:nat} (pred : arity T (S (S n))) (x1 x2 : T) (cp : cartesianPower T n) : Prop.

Lemma PermOKAux {T : Type} {m : nat} :
forall (appPred : (cartesianPower T (S (S m))) -> Prop) n,
(forall (A : T) (X : cartesianPower T (S m)), appPred (consHeadCP A X) -> appPred (consTailCP X A)) ->
(forall (X : cartesianPower T (S (S m))),
appPred X -> appPred (circPermNCP n X)).