Notation parity := (@fst nat (list mon)).
(** * Well-formedness of polynomials *)
Definition pWF_pow (ar:nat)(xn:pow) : Prop :=
fst xn < ar.
Definition pWF_mon (ar:nat)(m:mon) : Prop :=
andl (pWF_pow ar) (snd m).
Definition pWF' (ar:nat)(ml:list mon) : Prop :=
andl (pWF_mon ar) ml.
Definition pWF (p:pol) : Prop :=
pWF' (fst p) (snd p).

Lemma parity_mon_correct : forall ar m l l1 l2,
pWF_mon ar m -> length l = ar -> peval_mon m (l++l1) = peval_mon m (l++l2).