
theorem
  for a,b be non zero Real holds |.a|^2 - b|^2.| < |.a|^2 + b|^2.|
  proof
    let a,b be non zero Real;
    reconsider c = a|^(2*1) as positive Real;
    reconsider d = b|^(2*1) as positive Real;
    c*d > 0;
    hence thesis by MP;
  end;
