theorem
  for n holds Partial_Sums(||.seq.||).n >= 0
proof
  let n;
  ||.(seq.0).|| >= 0 by BHSP_1:28;
  then
A1: ||.seq.||.0 >= 0 by BHSP_2:def 3;
  Partial_Sums(||.seq.||).0 <= Partial_Sums(||.seq.||).n by Th35,SEQM_3:11;
  hence thesis by A1,SERIES_1:def 1;
end;
