Definition Rtheory:ring_theory ring0 ring1 add mul sub opp _==_.

(* Specifications: *)
Lemma PolZadd_correct : forall P' P l, PhiR l (PolZadd P P') == ((PhiR l P) + (PhiR l P')).
Lemma PolZmul_correct : forall P P' l, PhiR l (PolZmul P P') == ((PhiR l P) * (PhiR l P')).
Lemma R_power_theory : Ring_theory.power_theory ring1 mul _==_ N.to_nat pow.
Lemma norm_correct : forall (l : list R) (pe : PEZ), PEevalR l pe == PhiR l (norm pe).
Lemma PolZeq_correct : forall P P' l, PolZeq P P' = true -> PhiR l P == PhiR l P'.