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 Th28:
  for x being complex-valued FinSequence holds x + -x = 0c (len x)
proof
  let x be complex-valued FinSequence;
A1:x is FinSequence of COMPLEX & -x is FinSequence of COMPLEX by Lm2; then
  reconsider x9=x as Element of (len x)-tuples_on COMPLEX by FINSEQ_2:92;
  x + -x = addcomplex.:(x,-x) by A1,SEQ_4:def 6
    .= addcomplex.:(x,compcomplex*x) by A1,SEQ_4:def 8
    .= (len x9) |-> 0c by BINOP_2:1,FINSEQOP:73,SEQ_4:51,52
    .= 0c (len x9) by SEQ_4:def 12;
  hence thesis;
end;
