reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace;
reserve x,y for Point of X;
reserve A, B for Subset of X;
reserve P, Q for Subset of X;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace,
  Y0 for non empty SubSpace of X;

theorem
  for x, y being Point of Y holds the carrier of MaxADSspace(x) misses
  the carrier of MaxADSspace(y) or the TopStruct of MaxADSspace(x) = the
  TopStruct of MaxADSspace(y)
proof
  let x, y be Point of Y;
  assume
A1: the carrier of MaxADSspace(x) meets the carrier of MaxADSspace(y);
A2: the carrier of MaxADSspace(y) = MaxADSet(y) by Def17;
  the carrier of MaxADSspace(x) = MaxADSet(x) by Def17;
  hence thesis by A2,A1,Th22,TSEP_1:5;
end;
