Definition CPToSS {m:nat} (cp : cartesianPower positive m) : SS.elt.

Lemma CoappDupAux {m : nat} : forall (cp : cartesianPower positive (S (S (S m)))), ~ List.NoDup (CPToList cp) -> exists e, exists (l : list positive), exists m', exists (cp' : cartesianPower positive (S (S (S m')))), Permutation.Permutation (CPToList cp') (CPToList cp) /\ headCP cp' = e /\ headCP (tailCP cp') = e.