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.