Fixpoint multpf (p : list (Term A n)) : list (Term A n) -> list (Term A n) :=
  fun q : list (Term A n) =>
  match p with
  | nil => pO A n
  | a :: p' =>
      pluspf (A:=A) A0 (eqA:=eqA) plusA eqA_dec (n:=n) (ltM:=ltM) ltM_dec
        (mults (A:=A) multA (n:=n) a q) (multpf p' q)
  end.

Theorem multpf_comp : forall p r : list (Term A n), eqP A eqA n p r -> forall q s : list (Term A n), canonical A0 eqA ltM p -> canonical A0 eqA ltM q -> canonical A0 eqA ltM r -> canonical A0 eqA ltM s -> eqP A eqA n q s -> eqP A eqA n (multpf p q) (multpf r s).