
theorem Th2:
  for X being set, L being left_zeroed non empty addLoopStr, p
  being Series of X, L holds 0_(X,L) + p = p
proof
  let n be set, L be left_zeroed non empty addLoopStr, p be Series of n, L;
  reconsider ls = 0_(n,L) + p, p9 = p as Function of (Bags n), the carrier of
  L;
  now
    let b be Element of Bags n;
    thus ls.b = 0_(n,L).b + p.b by POLYNOM1:15
      .= 0.L + p9.b by POLYNOM1:22
      .= p9.b by ALGSTR_1:def 2;
  end;
  hence thesis by FUNCT_2:63;
end;
