reserve rseq, rseq1, rseq2 for Real_Sequence;
reserve seq, seq1, seq2 for Complex_Sequence;
reserve k, n, n1, n2, m for Nat;
reserve p, r for Real;
reserve z for Complex;
reserve Nseq,Nseq1 for increasing sequence of NAT;

theorem Th34:
  Partial_Sums |.seq.| is non-decreasing
proof
  for n holds 0 <= |.seq.|.n by Lm3;
  hence thesis by SERIES_1:16;
end;
