 reserve a for non empty set;
 reserve b, x, o for object;

theorem Th15:
    for b be bag of 0 holds dom b = {} & b = EmptyBag {} & rng b = 0 &
    EmptyBag {} = {} --> 0  & Bags {} = {EmptyBag {}}
    proof
      let b be bag of 0;
      Bags {} = {EmptyBag {}}
      proof
        for o st o in Bags {} holds o in {EmptyBag {}}
        proof
          let o;
          assume o in Bags {}; then
          o = EmptyBag {};
          hence thesis by TARSKI:def 1;
        end; then
        Bags {} c= {EmptyBag {}};
        hence thesis;
      end;
      hence thesis;
    end;
