
theorem
  for a,b be non zero Real holds (a/b + b/a)|^2 >= 4
  proof
    let a,b be non zero Real;
    ((a/b + b/a)/2)|^(2*1) >= 1 by TA1; then
    ((a/b + b/a)/2)|^2*4 >= 1*4 by XREAL_1:64; then
    (a/b + b/a)|^2/2|^2*(2*2) >= 4 by PREPOWER:8; then
    (a/b + b/a)|^2/(2|^2)*(2|^2) >= 4 by NEWTON:81;
    hence thesis by XCMPLX_1:87;
  end;
