reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;

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;
