reserve z,z1,z2 for Complex;
reserve r,x1,x2 for Real;
reserve p0,p,p1,p2,p3,q for Point of TOP-REAL 2;

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;
