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

Lemma InNth {T:Type} {n:nat} : forall (cp : cartesianPower T n) (t Default : T), InCP t cp -> (exists id, id >= 1 /\ id <= n /\ t = nthCP id cp Default).