\begin{itemize}
    \item \textbf{Start a proof.} At the top of your page write the premises, at the bottom write the conclusion.
    \item \textbf{Work in both directions to fill the gap.} Work from the top to the bottom
by working with the premises, and simultaneously work upwards by using the conclusion.
    \item \textbf{Look at the conclusion first.} If the conclusion is of the form $\varphi \rightarrow \psi$, then immediately apply $\impi$.
    You still have to fill the gap in the box, but you have an extra assumption to work with and a simpler conclusion you try to reach. Similar, if your conclusion is of fhe form $\neg \varphi$, apply $\negi$ to make your life easier.
    \item \textbf{Assumption boxes.} At any time you can introduce a formula as assumption, by choosing a proof rule that opens the box.
The box defines the scope of the assumption. By opening a box you introduce an assumption.
But don't forget, you have to close the box precisely as
defined by the applied proof rule.
    \item \textbf{What rule should you apply?} The rules $\impi$ and $\negi$  make your life easier, apply them whenever you can.
    There is no easy recipe for when to use the other rules. The best way to get the hang of it is doing many proofs
    by yourself.
\end{itemize}
