reserve X for set,
  Y for non empty set;
reserve n for Nat;
reserve r for Real,
  M for non empty MetrSpace;

theorem
  BDD [#]TOP-REAL n = {}TOP-REAL n
proof
  BDD [#]TOP-REAL n c= ([#]TOP-REAL n)` by JORDAN2C:25;
  then BDD [#]TOP-REAL n c= {}TOP-REAL n by XBOOLE_1:37;
  hence thesis by XBOOLE_1:3;
end;
