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author | David A. Madore <david+git@madore.org> | 2023-11-27 23:44:20 +0100 |
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committer | David A. Madore <david+git@madore.org> | 2023-11-27 23:44:20 +0100 |
commit | f41200967e489fb7e1fe14e189080a48903a0674 (patch) | |
tree | dd8266880dd42b6fb488e5447b1773f523303503 | |
parent | 8d9b259203eac848f2e9092abeba9d5b3f358bbf (diff) | |
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Rules of inuitionistic propositional calculus in natural deduction style.
-rw-r--r-- | transp-inf110-02-typage.tex | 39 |
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diff --git a/transp-inf110-02-typage.tex b/transp-inf110-02-typage.tex index 45d1ca2..7df864b 100644 --- a/transp-inf110-02-typage.tex +++ b/transp-inf110-02-typage.tex @@ -1335,4 +1335,43 @@ hypothèses $P_1,\ldots,P_r$, on a $Q$ ». \end{frame} % +\begin{frame} +\frametitle{Le calcul propositionnel intuitionniste : survol des règles} + +Axiomes : si $Q \in \{P_1,\ldots,P_r\}$ alors $P_1,\ldots,P_r \vdash Q$. + +\bigskip + +Introduction et élimination des connecteurs (style « déduction naturelle ») : + +\smallskip + +\begin{tabular}{c|c|c} +&Intro&Élim\\\hline +$\Rightarrow$ +&$\inferrule{\Gamma,P\vdash Q}{\Gamma\vdash P\Rightarrow Q}$ +&$\inferrule{\Gamma\vdash P\Rightarrow Q\\\Gamma\vdash P}{\Gamma\vdash Q}$ +\\\hline +$\land$ +&$\inferrule{\Gamma\vdash Q_1\\\Gamma\vdash Q_2}{\Gamma\vdash Q_1\land Q_2}$ +&$\inferrule{\Gamma\vdash Q_1\land Q_2}{\Gamma\vdash Q_1}$ +\quad$\inferrule{\Gamma\vdash Q_1\land Q_2}{\Gamma\vdash Q_2}$ +\\\hline +$\lor$ +&$\inferrule{\Gamma\vdash Q_1}{\Gamma\vdash Q_1\lor Q_2}$ +\quad$\inferrule{\Gamma\vdash Q_2}{\Gamma\vdash Q_1\lor Q_2}$ +&$\inferrule{\Gamma\vdash P_1\lor P_2\\\Gamma,P_1\vdash Q\\\Gamma,P_2\vdash Q}{\Gamma\vdash Q}$ +\\\hline +$\top$ +&$\inferrule{\strut}{\Gamma\vdash \top}$ +&(néant) +\\\hline +$\bot$ +&(néant) +&$\inferrule{\Gamma\vdash \bot}{\Gamma\vdash Q}$ +\\ +\end{tabular} + +\end{frame} +% \end{document} |