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23 lines
935 B
23 lines
935 B
\setlength\subproofhorizspace{1.3em}
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\begin{logicproof}{2}
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\exists x \; P(x) \lor \exists x \; Q(x) & \prem\\
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\begin{subproof}
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\exists x \; P(x) & $\assum$\\
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\begin{subproof}
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P(x_0) & $\assum$ $\freshVar{$x_0$}$\\
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P(x_0) \lor Q(x_0) & $\ori3$\\
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\exists x \; (P(x) \lor Q(x)) & $\existi4$
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\end{subproof}
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\exists x \; (P(x) \lor Q(x)) & $\existe2,3-5$
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\end{subproof}
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\begin{subproof}
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\exists x \; Q(x) & $\assum$\\
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\begin{subproof}
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Q(x_0) & $\assum$ $\freshVar{$x_0$}$\\
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P(x_0) \lor Q(x_0) & $\ori8$\\
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\exists x \; (P(x) \lor Q(x)) & $\existi9$
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\end{subproof}
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\exists x \; (P(x)\lor Q(x)) & $\existe7,8-10$
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\end{subproof}
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\exists x \; (P(x)\lor Q(x)) & $\ore1,2-6,7-11$
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\end{logicproof}
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