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