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

Lemma consTailPerm {T:Type} {n:nat} : forall (cp : cartesianPower T (S (S n))), Permutation.Permutation (CPToList cp) (CPToList (consTailCP (tailCP cp) (headCP cp))).