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 k st k >= 1 holds
    ex n st (n! <= k & k < (n+1)! &
      for m st m! <= k & k < (m+1)! holds m = n) by Lm52;
