reserve X for TopSpace;
reserve C for Subset of X;
reserve A, B for Subset of X;

theorem
  for Y being discrete TopStruct, A being Subset of Y holds (the
  carrier of Y) \ A in the topology of Y
proof
  let Y be discrete TopStruct, A be Subset of Y;
  the topology of Y = bool the carrier of Y by Def1;
  hence thesis;
end;
