
theorem Th23:
  for n being set, L be right_zeroed non empty addLoopStr, p be
  Series of n, L holds p+0_(n,L) = p
proof
  let n be set, L be right_zeroed non empty addLoopStr, p be Series of n, L;
  reconsider ls = p+0_(n,L), p9 = p as Function of (Bags n), the carrier of L;
  now
    let b be Element of Bags n;
    thus ls.b = p.b + 0_(n,L).b by Th15
      .= p9.b+0.L
      .= p9.b by RLVECT_1:def 4;
  end;
  hence thesis;
end;
