Questionnaire-2024/natural_deduction_propositional_logic/0007_sol.tex

Translation: \\
$p:$ \quad I press the button. \\
$q:$ \quad The window is open.
\begin{tabbing}
    If I press the button, the window opens. \quad \= $p \imp q$ \\
    I pressed the button. \> $p$ \\
    The window is open. \> $q$
\end{tabbing}

\emph{Sequent:} \quad $p \imp q, p \vdash q$ \\

This sequent is provable.

\begin{logicproof}{1}
    p \imp q & \prem \\
    p & \prem \\
    q & $\impe 1,2$
\end{logicproof}