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 Th27:
  for x being complex-valued FinSequence holds x + 0c (len x) = x
proof
  let x be complex-valued FinSequence;
A1:x is FinSequence of COMPLEX by Lm2; then
  reconsider x9=x as Element of (len x)-tuples_on COMPLEX by FINSEQ_2:92;
  x + 0c (len x) = x+(len x) |-> 0c by SEQ_4:def 12
    .= addcomplex.:(x,(len x) |-> 0c) by A1,SEQ_4:def 6
    .= x9 by BINOP_2:1,FINSEQOP:56;
  hence thesis;
end;
