theorem Th6:
  for g be Real st 0 < g holds
  {y where y is Complex : |.y-z0.| < g} is Neighbourhood of z0
proof
  let g be Real such that
A1: g > 0;
  set N = {y where y is Complex : |.y-z0.| < g};
A2: N c= COMPLEX
  proof
    let z be object;
    assume z in {y where y is Complex : |.y-z0.| < g};
    then ex y be Complex st z = y & |.y-z0.| < g;
    hence thesis by XCMPLX_0:def 2;
  end;
  thus thesis by A1,A2,Def5;
end;
