
theorem
  for X be ComplexNormSpace, seq1,seq2 be sequence of X holds (for n be
  Nat holds 0 <= ||.seq1.||.n & ||.seq1.||.n <= ||.seq2.||.n) & seq2
is norm_summable implies seq1 is norm_summable & Sum ||.seq1.|| <= Sum ||.seq2
  .||
by SERIES_1:20;
