theorem Th32:
  StoneS(H) c= the carrier of Open_setLatt(HTopSpace H)
proof
  let x be object;
  set carrO = the carrier of Open_setLatt(HTopSpace H);
  assume x in StoneS(H);
  then reconsider z={x} as Subset of StoneS(H) by ZFMISC_1:31;
A1: union z = x by ZFMISC_1:25;
  carrO = the set of all union A where A is Subset of StoneS(H) by Def12;
  hence thesis by A1;
end;
