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

Lemma nthCircPerm2 {T:Type} {n:nat} : forall (cp : cartesianPower T (S (S n))) (t Default : T) id, t = nthCP (S (S id)) cp Default -> id <= n -> t = nthCP (S id) (consTailCP (tailCP cp) (headCP cp)) Default.