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26 lines
662 B
26 lines
662 B
This sequent is provable.
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\begin{logicproof}{1}
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(p \land q) \lor (p \land r) & \prem \\
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\begin{subproof}
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p \land q & \assum \\
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p & $\ande{1} 2$
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\end{subproof}
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\begin{subproof}
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p \land r & \assum \\
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p & $\ande{1} 4$
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\end{subproof}
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p & $\ore 1, 2-3, 4-5$ \\
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\begin{subproof}
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p \land q & \assum \\
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q & $\ande{2} 7$ \\
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q \lor r & $\ori 8$
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\end{subproof}
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\begin{subproof}
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p \land r & \assum \\
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r & $\ande{2} 10$ \\
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q \lor r & $\ori 11$
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\end{subproof}
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q \lor r & $\ore 1, 7-9, 10-12$ \\
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p \land (q \lor r) & $\andi 6, 13$
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\end{logicproof}
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