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 Th19:
  for D being Subset of Y, x being Point of Y st D is
  anti-discrete & x in D holds D c= MaxADSet(x)
proof
  let D be Subset of Y, x be Point of Y;
  assume
A1: D is anti-discrete;
  assume x in D;
  then D in {A where A is Subset of Y : A is anti-discrete & x in A} by A1;
  hence thesis by ZFMISC_1:74;
end;
