reserve Y for TopStruct;

theorem
  for Y0, Y1 being TopStruct st the TopStruct of Y0 = the TopStruct of
  Y1 holds Y0 is almost_discrete implies Y1 is almost_discrete
proof
  let Y0, Y1 be TopStruct;
  assume
A1: the TopStruct of Y0 = the TopStruct of Y1;
  assume Y0 is almost_discrete;
  then for A being Subset of Y0 st A in the topology of Y0 holds (the carrier
  of Y0) \ A in the topology of Y0 by TDLAT_3:def 3;
  hence thesis by A1,TDLAT_3:def 3;
end;
