reserve X for TopSpace;

theorem Th2:
  for X being TopStruct holds X is SubSpace of X
proof
  let X be TopStruct;
  thus [#]X c= [#]X;
  thus for P being Subset of X holds P in the topology of X iff ex Q being
  Subset of X st Q in the topology of X & P = Q /\ [#]X
  proof
    let P be Subset of X;
    thus P in the topology of X implies ex Q being Subset of X st Q in the
    topology of X & P = Q /\ [#]X
    proof
      assume
A1:   P in the topology of X;
      take P;
      thus thesis by A1,XBOOLE_1:28;
    end;
    thus thesis by XBOOLE_1:28;
  end;
end;
