theorem
  for n holds Partial_Sums(||.seq.||).n >= 0
proof
  let n;
  ||.(seq.0).|| >= 0 by CSSPACE:44;
  then ||.seq.||.0 >= 0 by CLVECT_2:def 3;
  then Partial_Sums(||.seq.||).0 >= 0 by SERIES_1:def 1;
  hence thesis by Th35,SEQM_3:11;
end;
