
theorem COMPLEX155a:
  for a be Complex holds Im a >= -|.a.|
  proof
    let a be Complex;
    reconsider b = -a as Complex;
    Im b <= |.b.| by COMPLEX1:55; then
    -Im a <= -(-|.b.|) by COMPLEX1:17; then
    Im a >= -|.-a.| by XREAL_1:24;
    hence thesis by COMPLEX1:52;
  end;
