reserve x for Complex;

theorem Th1:
  x + 0 = x
proof
  0 in NAT;
  then reconsider Z =0 as Element of REAL by NUMBERS:19;
  x in COMPLEX by XCMPLX_0:def 2;
  then consider x1,x2 being Element of REAL such that
A1: x = [*x1,x2*] by ARYTM_0:9;
  0 = [*Z,Z*] by ARYTM_0:def 5;
  then x + 0 = [*+(x1,Z),+(x2,Z)*] by A1,XCMPLX_0:def 4
    .= [* x1,+(x2,Z)*] by ARYTM_0:11
    .= x by A1,ARYTM_0:11;
  hence thesis;
end;
