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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} |