reserve i,j,k,n,m for Nat,
        b,b1,b2 for bag of n;

theorem Th6:
  for L being non empty ZeroStr, p being Series of n,L holds
    (p extended_by_0).(b bag_extend 0) = p.b
proof
  let L be non empty ZeroStr;
  let p be Series of n,L;
  (b bag_extend 0).n = 0 by HILBASIS:def 1;
  hence (p extended_by_0).(b bag_extend 0) = p.(0,n)-cut (b bag_extend 0)
    by Def3
    .= p.b by Th5;
end;
