reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th54:
  for X being set, b being bag of X holds b-'b = EmptyBag X
proof
  let X be set, b be bag of X;
  now
    let x be object;
    assume x in X;
    thus (b-'b).x = b.x -' b.x by Def6
      .= 0 by XREAL_1:232
      .= (EmptyBag X).x;
  end;
  hence thesis;
end;
