
theorem
  for x being Element of F_Complex st x <> 0.F_Complex holds x * 1_.(
  F_Complex) is Hurwitz
proof
  let x be Element of F_Complex;
  set p = x * 1_.(F_Complex);
  assume
A1: x <> 0.F_Complex;
  now
    let z be Element of F_Complex;
    assume z is_a_root_of p;
    then
A2: eval(p,z) = 0.F_Complex by POLYNOM5:def 7;
    eval(p,z) = x * eval(1_.(F_Complex),z) by POLYNOM5:30
      .= x * 1_F_Complex by POLYNOM4:18;
    hence Re(z) < 0 by A1,A2;
  end;
  hence thesis;
end;
