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13 lines
646 B
13 lines
646 B
\item
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The soundness of natural deduction for propositional logic can be proven via a \emph{mathematical course-of-values induction on the length of the Natural Deduction proof}. Let $M(k)$ be the following assertion:
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$M(k)\coloneqq$ „For all sequents $\phi_1,\phi_2,\dots,\phi_n\vdash \psi$ which have a proof of length $k$,
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it is the case that $\phi_1,\phi_2,\dots,\phi_n\models \psi$ holds.”
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Your tasks:
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\begin{enumerate}
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\setlength{\itemsep}{-0.1em}
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\item Proof the induction base-case, i.e., $M(1)$ holds.
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\item Explain the proof idea of the induction step:
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$M(1)\wedge M(2) \land \dots \land M(k-1) \rightarrow M(k)$.
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\end{enumerate}
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