(** ** Sum of polynomials

  - [pplus p1 p2] is the sum of the polynomials [p1] and [p2].

  - [pplusl pl] is the sum of the polynomials in the list [pl].
*)

Definition pplus (p1 p2:pol) : pol :=
  (max (fst p1) (fst p2), snd p1 ++ snd p2).

Lemma parity_pplus : forall p1 p2, parity (pplus p1 p2) = max (parity p1) (parity p2).