theorem Th26:
  Q is closed implies for P being Subset of A st P=Q holds P is closed
proof
  assume
A1: Q is closed;
  let P be Subset of A;
  assume P=Q;
  then Q /\ [#] A = P by XBOOLE_1:28;
  hence thesis by A1,PRE_TOPC:13;
end;
