reserve a,b for Complex;

theorem Th4:
  (a - b)|^2 = a|^2 -2*a*b +b|^2
proof
  thus (a - b)|^2 = (a - b)*(a - b) by Th1
    .= a^2 - 2*a*b + b^2
    .= a|^2 -2*a*b +b*b by Th1
    .= a|^2 -2*a*b +b|^2 by Th1;
end;
