
theorem COMPLEX154a:
  for a be Complex holds Re a >= -|.a.|
  proof
    let a be Complex;
    reconsider b = -a as Complex;
    Re b <= |.b.| by COMPLEX1:54; then
    -Re a <= -(-|.b.|) by COMPLEX1:17; then
    Re a >= -|.-a.| by XREAL_1:24;
    hence thesis by COMPLEX1:52;
  end;
