
theorem
  for n being Ordinal, T being connected TermOrder of n, L being non
  empty ZeroStr, p being Series of n,L holds (EmptyBag n) *' p = p
proof
  let n be Ordinal, T be connected TermOrder of n, L be non empty ZeroStr, p
  be Series of n,L;
  set e = EmptyBag n;
A1: now
    let u be object;
    assume u in dom p;
    then reconsider u9 = u as Element of Bags n;
    EmptyBag n divides u9 by PRE_POLY:59;
    then (e*'p).u9 = p.(u9-'e) by Def1
      .= p.u9 by PRE_POLY:54;
    hence (e*'p).u = p.u;
  end;
  dom(e*'p) = Bags n by FUNCT_2:def 1
    .= dom p by FUNCT_2:def 1;
  hence thesis by A1,FUNCT_1:2;
end;
