Definition Poly (p : pol) : Cobham :=
  Plusl_e (fst p) (map (Poly_mon (fst p)) (snd p)).

(* Specifications: *)
Lemma arity_Poly : forall p, pWF p -> arity (Poly p) = ok_arity (parity p).
Lemma rec_bounded_Poly : forall p, rec_bounded (Poly p).
Lemma Poly_correct : forall p l, length (Sem (Poly p) l) = peval p (map (@length _) l).