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 pWF_mon_app : forall ar a1 xl1 a2 xl2,
pWF_mon ar (a1, xl1) -> pWF_mon ar (a2, xl2) ->
pWF_mon ar (a1*a2, xl1++xl2).