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

Lemma nthEqOK {T:Type} {m:nat} : forall (cp1 cp2 : cartesianPower T (S m)) (Default : T), (forall n, nthCP n cp1 Default = nthCP n cp2 Default) -> cp1 = cp2.