
theorem
  for f be complex-valued FinSequence holds Sum f = f.1 + Sum (f/^1)
  proof
    let f be complex-valued FinSequence;
    reconsider f as FinSequence of COMPLEX by RVSUM_1:146;
    Sum f = Sum ((f|1)^(f/^1))
    .= Sum (f|1) + Sum (f/^1) by RVSUM_2:32;
    hence thesis by NEWTON04:33;
  end;
