reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;

theorem
  for A,B being Subset of TOP-REAL n holds A is not bounded & B is
  bounded implies A \ B is not bounded
proof
  let A,B be Subset of TOP-REAL n;
  assume that
A1: A is not bounded and
A2: B is bounded;
A3: (A \ B) \/ A /\ B = A \ (B \ B) by XBOOLE_1:52
    .= A \ {} by XBOOLE_1:37
    .= A;
  A /\ B is bounded by A2,Th82;
  hence thesis by A1,A3,Th65;
end;
