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 Th22:
  for x, y being Point of Y holds MaxADSet(x) misses MaxADSet(y)
  or MaxADSet(x) = MaxADSet(y)
proof
  let x, y be Point of Y;
  assume MaxADSet(x) /\ MaxADSet(y) <> {};
  then consider a being object such that
A1: a in MaxADSet(x) /\ MaxADSet(y) by XBOOLE_0:def 1;
  reconsider a as Point of Y by A1;
  a in MaxADSet(x) by A1,XBOOLE_0:def 4;
  then
A2: MaxADSet(a) = MaxADSet(x) by Th21;
  a in MaxADSet(y) by A1,XBOOLE_0:def 4;
  hence thesis by A2,Th21;
end;
