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