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

Lemma app_2_n_app_eq {T:Type} {n:nat} :
forall (pred : arity T (S (S (S n)))) (x1 x2 : T)
(cpp : cartesianPower T (S n)) (cpt : cartesianPower T (S (S (S n)))),
headCP cpt = x1 -> headCP (tailCP cpt) = x2 -> tailCP (tailCP cpt) = cpp ->
(app pred cpt <-> app_2_n pred x1 x2 cpp).