
theorem
  for X being set, L being commutative non empty multLoopStr_0, p
  being Series of X,L, a being Element of L holds a * p = p * a
proof
  let n be set, L be commutative non empty multLoopStr_0, p be Series of n,L
  , a be Element of L;
  now
    let b be Element of Bags n;
    reconsider b9 = b as bag of n;
    thus (a * p).b = a * p.b9 by Def9
      .= (p * a).b by Def10;
  end;
  hence thesis;
end;
