Questionnaire-2024/natural_deduction_predicate_logic/0013_sol.tex

This sequent is not provable.

Model $\mathcal{M}$:\\
\begin{minipage}{0.2\textwidth}
  \begin{align*}
  \mathcal{A} =& \; \{ a,b \}\\
  P^\mathcal{M} =& \; \{ a \}\\
  Q^\mathcal{M} =& \; \{ a \} \\
  y \leftarrow \; b \\
\end{align*}
\end{minipage}\\

$\mathcal{M} \models \exists x \; (P(x) \imp Q(y)), \quad \exists x \; P(x)$\\
$\mathcal{M} \nmodels Q(y)$