theorem
  seq1 = -seq2 iff for n holds seq1.n= -seq2.n
proof
  thus seq1 = -seq2 implies for n holds seq1.n=-seq2.n by VALUED_1:8;
  assume for n holds seq1.n= -seq2.n;
  then
A1: for n being object st n in dom seq1 holds seq1.n = - seq2.n;
  dom seq1 = NAT by FUNCT_2:def 1
    .= dom seq2 by FUNCT_2:def 1;
  hence thesis by A1,VALUED_1:9;
end;
