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13 lines
345 B
13 lines
345 B
This sequent is not provable.
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Model $\mathcal{M}$:\\
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\begin{minipage}{0.2\textwidth}
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\begin{align*}
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\mathcal{A} =& \; \{ a,b \}\\
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P^\mathcal{M} =& \; \{ a \}\\
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Q^\mathcal{M} =& \; \{ a \}\\
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\end{align*}
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\end{minipage}\\
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$\mathcal{M} \models \forall x \; (P(x)\imp Q(x)), \quad \exists x \; P(x)$\\
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$\mathcal{M} \nmodels \forall x Q(x)$
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