lean_workbook_plus_82278

Let $f:\mathbb{N} \cup \{0\} \to \mathbb{N} \cup \{0\}$ be defined by $f(0)=0$ ,\n

for $n \ge 0$ and \n

for $n \ge 1$ \n\n If $g(n)=f(f(n))$ , prove that $g(n-g(n))=0$ for all $n \ge 0$ .