reserve k,m,n,p for Nat;
reserve x, a, b, c for Real;

theorem
  for n being Nat holds |.Fib(n) - (tau to_power n)/(sqrt 5 ).| < 1
proof
  let n;
  set k = Fib(n), x = (tau to_power n), y = (tau_bar to_power n), z = sqrt 5;
  k = (x - y)/z by Th7
    .= x/z - y/z;
  then |.-(k - x/z).| < 1 by Lm16;
  hence thesis by COMPLEX1:52;
end;
