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
  (for n holds 0 <= |.seq1.|.n & |.seq1.|.n <= |.seq2.|.n) & seq2 is
  absolutely_summable implies seq1 is absolutely_summable & Sum |.seq1.| <= Sum
  |.seq2.|
by SERIES_1:20;
