
theorem Th14:
  for a be Element of F_Complex st 0 <= Re a & Im a = 0 holds |.a .| = Re a
proof
  let z be Element of F_Complex;
  assume that
A1: 0 <= Re z and
A2: Im z = 0;
  reconsider a = z as Element of COMPLEX by COMPLFLD:def 1;
  |. a .| = |.Re a.| by A2,COMPLEX1:50;
  hence thesis by A1,ABSVALUE:def 1;
end;
