(** ** 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).

(* Specifications: *)
Lemma parity_pplus : forall p1 p2, parity (pplus p1 p2) = max (parity p1) (parity p2).
Lemma pWF_pplus : forall p1 p2, pWF p1 -> pWF p2 -> pWF (pplus p1 p2).
Lemma pplus_correct : forall p1 p2 l, peval (pplus p1 p2) l = peval p1 l + peval p2 l.