We need to make sure that the nesting gives appropriate behavior in the following cases:
\begin{problem}
\end{problem}
and nested with SAME environments
\begin{problem}
Here are some parts
\begin{problem}
part 1
\end{problem}
\begin{problem}
part 2
\end{problem}
\end{problem}
And nested with DIFFERENT environments
\begin{problem}
Parts where the headings are different than others
\begin{exercise}
here
\end{exercise}
\end{problem}
etc.
We need to make sure that the nesting gives appropriate behavior in the following cases:
and nested with SAME environments
And nested with DIFFERENT environments
etc.