theorem
  a1|^m - b1|^m = (a1-b1)*k implies
  a1|^(m+2) - b1|^(m+2) = (a1|^(m+1)+b1|^(m+1) + a1*b1*k)*(a1-b1)
  proof
    assume a1|^m - b1|^m = (a1-b1)*k;
    hence a1|^(m+2) - b1|^(m+2) =
    (a1|^(m+1)+b1|^(m+1))*(a1-b1) + a1*b1*((a1-b1)*k) by Th21
    .= (a1|^(m+1)+b1|^(m+1) + a1*b1*k)*(a1-b1);
  end;
