
theorem Th48:
  for f being Polynomial of F_Complex st f is Hurwitz for x being
  Element of F_Complex st Re(x) >= 0 holds 0 < |.eval(f,x).|
proof
  let f be Polynomial of F_Complex;
  assume
A1: f is Hurwitz;
  let x be Element of F_Complex;
  assume
A2: Re(x) >= 0;
    eval(f,x) <> 0.F_Complex by A1,A2,POLYNOM5:def 7;
  hence thesis by COMPLEX1:47,COMPLFLD:7;
end;
