theorem
  Sum((a,b) In_Power (m+n)) = Sum((a,b) In_Power m)*Sum((a,b) In_Power n)
  proof
    Sum((a,b) In_Power (m+n)) = (a+b)|^(m+n) by NEWTON:30
    .=(a+b)|^m*(a+b)|^n by NEWTON:8
    .= Sum((a,b) In_Power m)*(a+b)|^n by NEWTON:30
    .= Sum((a,b) In_Power m)*Sum((a,b) In_Power n) by NEWTON:30;
    hence thesis;
  end;
