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Pi-Clarzach
Pi-Cla
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Fix TRules getting swapped
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content/normal-modal-logic/tableaux/rules-for-K.tex

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@@ -108,20 +108,20 @@
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prefix~$\sigma$ is $\sigma.n$. However, which $n$ is allowed depends
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on whether the sign is~$\True$ or~$\False$.
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\iftag{prvBox}{The $\TRule{\Box}{\True}$ rule extends a branch
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\iftag{prvBox}{The $\TRule{\True}{\Box}$ rule extends a branch
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containing $\sFmla{\True}{\Box !A}[\sigma]$ by
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$\sFmla{\True}{!A}[\sigma.n]$.\iftag{prvDiamond}{ Similarly,
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t}{}}{T}\iftag{prvDiamond}{he $\TRule{\Diamond}{\False}$ rule
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t}{}}{T}\iftag{prvDiamond}{he $\TRule{\False}{\Diamond}$ rule
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extends a branch containing $\sFmla{\False}{\Diamond !A}[\sigma]$ by
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$\sFmla{\False}{!A}[\sigma.n]$.}{}
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\iftag{notprvBox,notprvDiamond}{It}{They} can only be applied for a
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prefix~$\sigma.n$ which \emph{already} occurs on the branch in which
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it is applied. Let's call such a prefix ``used'' (on the branch).
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\iftag{prvBox}{The $\TRule{\Box}{\False}$ rule extends a branch
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\iftag{prvBox}{The $\TRule{\False}{\Box}$ rule extends a branch
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containing $\sFmla{\False}{\Box !A}[\sigma]$ by
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$\sFmla{\False}{!A}[\sigma.n]$.\iftag{prvDiamond}{ Similarly,
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t}{}}{T}\iftag{prvDiamond}{he $\TRule{\Diamond}{\True}$ rule extends
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t}{}}{T}\iftag{prvDiamond}{he $\TRule{\True}{\Diamond}$ rule extends
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a branch containing $\sFmla{\True}{\Diamond !A}[\sigma]$ by
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$\sFmla{\True}{!A}[\sigma.n]$.}{}
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\iftag{notprvBox,notprvDiamond}{This rule}{These rules}, however, can

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