Upper and Lower Bound of Fibonacci Number

Theorem
For all $n \in \N_{> 0}$:
 * $\phi^{n - 2} \le F_n \le \phi^{n - 1}$

where:
 * $F_n$ is the $n$th Fibonacci number
 * $\phi$ is the golden section: $\phi = \dfrac {1 + \sqrt 5} 2$

Proof
From Fibonacci Number greater than Golden Section to Power less Two:
 * $F_n \ge \phi^{n - 2}$

From Fibonacci Number less than Golden Section to Power less One:
 * $F_n \le \phi^{n - 1}$