Fibonacci Number in terms of Larger Fibonacci Numbers

Theorem
Let $F_k$ be the $k$th Fibonacci number.

Then:
 * $\displaystyle \forall m, n \in \Z_{>0} : F_{m - n} = \left({-1}\right)^{n + 1} F_{m - 1} F_n + \left({-1}\right)^n F_m F_{n - 1}$