theorem Th29:
  StoneH(H).(Bottom H) = {}
proof
  set x = the Element of StoneH(H).(Bottom H);
  assume StoneH(H).(Bottom H) <> {};
  then
  ex F being Filter of H st F=x & F <> the carrier of H & F is prime &
  Bottom H in F by Th12;
  hence contradiction by FILTER_0:26;
end;
