reserve c, c1, c2, d, d1, d2, e, y for Real,
  k, n, m, N, n1, N0, N1, N2, N3, M for Element of NAT,
  x for set;

theorem
  for f,g being Real_Sequence holds for N holds (for n st n <= N holds f
  .n <= g.n) implies Sum(f,N) <= Sum (g,N) by Lm13;
