reserve q,th,r for Real,
  a,b,p for Real,
  w,z for Complex,
  k,l,m,n,n1,n2 for Nat,
  seq,seq1,seq2,cq1 for Complex_Sequence,
  rseq,rseq1,rseq2 for Real_Sequence,
  rr for set,
  hy1 for 0-convergent non-zero Real_Sequence;

theorem Th17:
  1 <= Sum(|.z.| rExpSeq)
proof
 |. Partial_Sums(z ExpSeq).0 .|=|. (z ExpSeq).0 .| by SERIES_1:def 1
    .=1 by Th3,COMPLEX1:48;
  hence thesis by Th16;
end;
