Zeckendorf's Theorem

This work formalizes Zeckendorf's theorem in Isabelle/HOL. The theorem states that every positive integer can be uniquely represented as a sum of one or more non-consecutive Fibonacci numbers. More precisely, if $N$ is a positive integer, there exist unique positive integers $c_i \ge 2$ with $c_i + 1 < c_{i+1}$, such that $$N = \sum_{i=0}^{k} F_{c_i}$$ where $F_n$ is the $n$-th Fibonacci number.