reserve o1,o2 for Ordinal;

theorem Th3:
  for a be Element of Bags o1,b be Element of Bags o2 st o2 = {}
  holds a +^ b = a
proof
  let a be Element of Bags o1,b be Element of Bags o2;
  assume o2={};
  then reconsider ab = a +^ b as Element of Bags o1 by ORDINAL2:27;
  for i being object st i in o1 holds ab.i = a.i by Def1;
  hence thesis by PBOOLE:3;
end;
