
theorem RI:
  for a be Complex holds |.Re a.| + |.Im a.| >= |.a.|
  proof
    let a be Complex;
    |.(Im a)*<i>.| = |.Im a.|*|.<i>.| by COMPLEX1:65
    .= |.Im a.| by COMPLEX1:49; then
    |.Re a + (Im a)*<i>.| <= |.Re a.| + |.Im a.| by COMPLEX1:56;
    hence thesis by COMPLEX1:13;
  end;
