If one searches online, one will find many different methods to do “proof by cases” in LaTeX. The most simple and convenient method in my opinion is to use the description environment.
Something like this:
\begin{proof} Proceed by cases.
\begin{description}
\item[Case 1: This.] And so on.
\item[Case 2: That.] And more.
\end{proof}Source: Reddit
No additional package is needed. One drawback is there is no auto-numbering, but I am sure that is still ok, unless your proof has many many cases.
Mathtuition88 