Fibonacci Number in terms of Larger Fibonacci Numbers

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

Then:
 * $\forall m, n \in \Z_{>0} : F_{m - n} = \paren {-1}^{n + 1} F_{m - 1} F_n + \paren {-1}^n F_m F_{n - 1}$