Definition memCP (cp : cartesianPower positive (S (S (S n)))) (s : SS.elt) := memCPAux (S n) cp s.

(* Specifications: *)
Lemma memMemCPOK : forall cp s, (forall e, InCP e cp -> S.mem e s = true) -> memCP cp s = true.
Lemma memCPConsHd : forall p s x, S.mem p s = true -> memCPAux n x s = true -> memCP (consHeadCP p x) s = true.