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 A being non empty Subset of Y holds the TopStruct of MaxADSspace(A
  ) = the TopStruct of MaxADSspace(MaxADSet(A))
proof
  let A be non empty Subset of Y;
A1: the carrier of MaxADSspace(MaxADSet(A)) = MaxADSet(MaxADSet(A)) by Def18;
  the carrier of MaxADSspace(A) = MaxADSet(A) by Def18;
  hence thesis by A1,Th33,TSEP_1:5;
end;
