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19 lines
445 B
19 lines
445 B
This sequent is provable.
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\begin{logicproof}{1}
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(p \land q) \imp (r \lor s) & \prem\\
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r \land p \land q & \prem\\
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p \land q & $\ande{2} 1$\\
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r \lor s & $\impe 1,3$ \\
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\begin{subproof}
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q & \assum\\
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r & $\ande{1} 2$
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\end{subproof}
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q \imp r & $\impi 5-6$ \\
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\begin{subproof}
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s & \assum\\
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q & $\ande{2} 3$
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\end{subproof}
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s \imp q & $\impi 8-9$ \\
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(q \imp r) \land (s \imp q) & $\andi 7, 10$
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\end{logicproof}
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