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
  for X be set, b being bag of X holds (EmptyBag X) -' b = EmptyBag X
proof
  let X be set, b be bag of X;
  now
    let x be object;
    assume x in X;
    thus ((EmptyBag X)-'b).x = (EmptyBag X).x-'b.x by Def6
      .= (EmptyBag X).x by NAT_2:8;
  end;
  hence thesis;
end;
