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, N being Element of NAT, c being Real st f
  is convergent & lim f = c & for n st n >= N holds f.n = g.n holds g is
  convergent & lim g = c by Lm22;
