\subsection{Workflow}
{\scriptsize the notes in this section may seem a bit over the top,
    but in the exercise sessions it was mentioned repeatedly that they will heavily deduct points for not following the scheme.
    One example that was named is that in some exams out of 36 points for a proof, 9 were awarded for simply following the expected structure}
\begin{enumerate}
    \item Determine the exact expression to proof (possibly generalizing it, and if so, state something like ``Consider the generalized statement'')
    \item Then, start the proof by stating something along the lines of ``We prove $\forall n \in \N P$ by weak mathematical induction on $n$''.
    \item Depending on the proof type, proceed with base cases, or case analysis. \hl{Important}: State ``Let $m$ be arbitrary'' for free variables,
          and if there are extra variables introduced by the application (e.g. a \texttt{Leaf} type has value $x$ in it), state ``Fix $x$ and we show $P[t \mapsto \texttt{Leaf} x]$''
    \item Then, do the step case (if applicable). \hl{Important}: State ``Let $n$ be arbitrary'', or in the case of structural induction, there may be arguments for the type,
          such as for \texttt{Tree}, then state ``Let \texttt{l::Tree} and \texttt{r::Tree} be arbitrary''.
\end{enumerate}
