reserve c, c1, d for Real,
  k for Nat,
  n, m, N, n1, N1, N2, N3, N4, N5, M for Element of NAT,
  x for set;

theorem Th10: :: Reflexivity of Big_Oh (page 83; Problem 3.9)
  for f being eventually-nonnegative Real_Sequence holds f in Big_Oh(f)
proof
  let f be eventually-nonnegative Real_Sequence;
  consider N being Nat such that
A1: for n being Nat st n >= N holds f.n >= 0 by Def2;
  reconsider N as Element of NAT by ORDINAL1:def 12;
  f is Element of Funcs(NAT, REAL) & for n st n >= N holds f.n <= 1*f.n &
  f.n >= 0 by A1,FUNCT_2:8;
  hence thesis;
end;
