Reduce the following lambda term:$((\backslash$m$.$

$.$ m n$)(\backslash$f$.\backslash$x$.$ f $($f x$)))(\backslash$f$.\backslash$x$.$ f $($f $($f x$)))$ This part $($the harder part$)$ of the homework only requires the definition of capture avoiding substitution. It can be solved by a sequence of $($if I counted correctly$)7$ beta reductions$\mathrm{.}2)$ Explain what function on natural numbers $(\backslash$m$.$

$.$ m n$)$ implements.This part $($the easier part$)$ requires to know about Church numerals