What is the proof of the equation for the aliased frequency fa = |R*n - fs|?
This is incomplete but should point you in the right direction. Assume $k$ is an integer and $f_s=1/T_s$ is the sampling frequency. The signal being sampled is $$\cos(2\pi f_0t).$$ The sampled signal is $\cos(2\pi f_0kT_s)$. This signal has an alias at frequency $f_1=(f_s/2-f_0)+f_s/2=f_s-f_0$. To prove it:
\begin{align*}
\cos(2\pi(f_s-f_0)kT_s) &amp;= \cos(2\pi f_skT_s-2\pi f_0kT_s) \\
&amp;= \cos(2\pi k - 2\pi f_0kTs)\\
&amp;= \cos(2\pi f_0kT_s).
\end{align*}
A similar argument can be made for all other aliases.