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 e being positive Real, f being Real_Sequence st f.0 = 0 & (for n
st n > 0 holds f.n = log(2,n to_power e)) holds (f /" seq_n^(e)) is convergent
  & lim (f /" seq_n^(e)) = 0 by Lm10;
