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26 lines
669 B
26 lines
669 B
This sequent is provable.
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\begin{logicproof}{3}
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\begin{subproof}
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\neg ((p \imp q) \lor \neg q) & \assum\\
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\begin{subproof}
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p \imp q & \assum \\
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(p \imp q) \lor \neg q & $\ori{1} 3$ \\
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\bot & $\nege 3, 1 $
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\end{subproof}
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\neg (p \imp q) & $\negi 2-4 $ \\
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\begin{subproof}
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q & \assum \\
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\begin{subproof}
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p & \assum \\
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q & $\copying 6$
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\end{subproof}
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p \imp q & $\impi 7-8$ \\
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\bot & $\nege 9, 5$
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\end{subproof}
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\neg q & $\negi 6-10$ \\
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(p \imp q) \lor \neg q & $\ori 11$ \\
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\bot & $\nege 12, 1$
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\end{subproof}
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(p \imp q) \lor \neg q & $\PBC 1-13$
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\end{logicproof}
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