Definition nthCP {T:Type} {m:nat} (n : nat) (cp : cartesianPower T m) (Default : T) := nth (n-1) (CPToList cp) Default.

Lemma CPToListOK {T:Type} {n:nat} : forall (cp : cartesianPower T (S (S n))), CPToList cp = cons (headCP cp) (CPToList (tailCP cp)).