theorem
  for z being Element of COMPLEX, p st z=euc2cpx(p) or p=cpx2euc(z)
  holds Arg(z)=Arg(p)
proof
  let z be Element of COMPLEX, p;
  assume
A1: z=euc2cpx(p) or p=cpx2euc(z);
  per cases by A1;
  suppose
    z=euc2cpx(p);
    hence thesis;
  end;
  suppose
    p=cpx2euc(z);
    hence thesis by Th1;
  end;
end;
