reserve Y for TopStruct;

theorem
  for Y0, Y1 being TopStruct st the TopStruct of Y0 = the TopStruct of
  Y1 holds Y0 is anti-discrete implies Y1 is anti-discrete
proof
  let Y0, Y1 be TopStruct;
  assume
A1: the TopStruct of Y0 = the TopStruct of Y1;
  assume Y0 is anti-discrete;
  then the topology of Y0 = {{},the carrier of Y0} by TDLAT_3:def 2;
  hence thesis by A1,TDLAT_3:def 2;
end;
