reserve X for ComplexUnitarySpace;
reserve g for Point of X;
reserve seq, seq1, seq2 for sequence of X;
reserve Rseq for Real_Sequence;
reserve Cseq,Cseq1,Cseq2 for Complex_Sequence;
reserve z,z1,z2 for Complex;
reserve r for Real;
reserve k,n,m for Nat;

theorem
  for n,m holds ||.Sum(seq,m,n).|| <= |.Sum(||.seq.||,m,n).|
proof
  let n,m;
  ||.Sum(seq,m) - Sum(seq,n).|| <= |.Sum(||.seq.||, m) - Sum(||.seq.||,
  n).| by Th40;
  hence thesis by SERIES_1:def 6;
end;
