Let $f_0 = 1$, and $f_1 = 1$, and $f_n = f_{n-1}+f_{n-2}$ when $n \gt 1$ (the Fibonacci sequence)
Prove using induction that $f_n\gt 2n$, when $n \geq 6$. (note the $f_6 = 13$, $f_7=21$)
I want to rewrite $f_n \gt 2n$ as $f_n\gt f_{2n}$ is this legal?