theorem
  for f being complex-valued FinSequence holds f is Element of COMPLEX len f
proof
  let f be complex-valued FinSequence;
  f is FinSequence of COMPLEX by Lm2; then
  f is Element of COMPLEX* by FINSEQ_1:def 11;
  then f in { s where s is Element of COMPLEX*: len s = len f };
  then f in ((len f)-tuples_on COMPLEX) by FINSEQ_2:def 4;
  hence thesis by SEQ_4:def 11;
end;
