reserve Y for TopStruct;

theorem Th12:
  for Y0, Y1 being TopStruct st the TopStruct of Y0 = the
  TopStruct of Y1 holds Y0 is discrete implies Y1 is discrete
proof
  let Y0, Y1 be TopStruct;
  assume
A1: the TopStruct of Y0 = the TopStruct of Y1;
  assume Y0 is discrete;
  then the topology of Y0 = bool the carrier of Y0 by TDLAT_3:def 1;
  hence thesis by A1,TDLAT_3:def 1;
end;
