reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;

theorem Th24:
  for G being Subset of Y, x being Point of Y st G is open & x in
  G holds MaxADSet(x) c= G
proof
  let G be Subset of Y, x be Point of Y;
  assume that
A1: G is open and
A2: x in G;
  {x} c= MaxADSet(x) by Th12;
  then
A3: x in MaxADSet(x) by ZFMISC_1:31;
  MaxADSet(x) is maximal_anti-discrete by Th20;
  then MaxADSet(x) is anti-discrete;
  hence thesis by A1,A2,A3;
end;
