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 Th61:
  Partial_Sums |.seq.| is bounded_above iff seq is absolutely_summable
proof
  Partial_Sums(|.seq.|) is bounded_above iff |.seq.| is summable;
  hence thesis;
end;
