
theorem Th2:
  for b being bag of {} holds decomp b = <* <* {}, {} *> *>
proof
  let b be bag of {};
A1: EmptyBag 0 = {} --> 0;
  then divisors b = <* {} *> by PRE_POLY:67;
  then
A2: len divisors b = 1 by FINSEQ_1:39;
A3: dom divisors b = dom decomp b by PRE_POLY:def 17;
  then 1 in dom decomp b by A2,FINSEQ_3:25;
  then
A4: (decomp b).1=(decomp b)/.1 by PARTFUN1:def 6
    .=<* {},{} *>by A1,PRE_POLY:71;
  len decomp b = 1 by A2,A3,FINSEQ_3:29;
  hence thesis by A4,FINSEQ_1:40;
end;
