reserve T for TopStruct;
reserve GX for TopSpace;

theorem
  for T being 1-sorted, P,Q being Subset of T st [#]T = P \/ Q & P
  misses Q holds Q = [#]T \ P
proof
  let T be 1-sorted, P,Q be Subset of T;
  assume that
A1: [#]T = P \/ Q and
A2: P misses Q;
  [#]T \ P = Q \ P by A1,XBOOLE_1:40
    .= Q by A2,XBOOLE_1:83;
  hence thesis;
end;
