Suppression des slides superfules
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\maketitle
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\maketitle
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\end{frame}
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\end{frame}
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\section*{Table of contents}
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\begin{frame}{Plan of the presentation}
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\tableofcontents[hidesubsections]
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\end{frame}
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\section{GATs and 2-sortification}
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\section{GATs and 2-sortification}
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\begin{frame}{What is a GAT ?}
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\begin{frame}{What is a GAT ?}
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\begin{itemize}
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\begin{itemize}
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@ -404,7 +399,52 @@
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\end{remark}
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\end{remark}
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\end{frame}
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\end{frame}
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\section{The complete proof \& Discoveries}
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\section{Conclusion}
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\begin{frame}{Conclusion}
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\begin{center}
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\hspace{2ex}$\CC$ \hspace{3.5cm} $\BB$
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\vspace{.5cm}
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\includesvg[scale=.4]{graphs/diagrammeFG.svg}
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\end{center}
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\end{frame}
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\begin{frame}{Future work}
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\begin{itemize}
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\item Complete GAT (term constructors + equalities)
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\item Proof Assistant Formalization
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\item $S_i$ non-direct
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\end{itemize}
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\end{frame}
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\begin{frame}
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\begin{center}
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\Large Thank you for your attention
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\end{center}
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\end{frame}
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\appendix
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\begin{frame}
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\[\begin{array}{lcl}
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F_3G_3(Y)_\Con &=& G_3(Y)_p^{-1}(\{\Cstr^{G_3(Y)}_\Con\})\\
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&=& G_3(Y)_p^{-1}(\{\inj_1 \star\}) \\
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&=& Y_\Con
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\end{array}\]
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and
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\[\begin{array}{lcl}
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F_3G_3(Y)_\Ty(\Gamma) &=& G_3(Y)_p^{-1}(\{\Cstr^{G_3(Y)}_\Ty(\Gamma)\})\\
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&=& G_3(Y)_p^{-1}(\{\inj_2 \Gamma\}) \\
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&=& \operatorname{proj}_1^{-1}(\Gamma) \\
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&=& \left\{(\Gamma',A) \in \coprod_{\Gamma' \in Y_\Con}Y_\Ty(\Gamma') \middle| \Gamma' = \Gamma\right\}\\
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&\simeq& Y_\Ty(\Gamma)
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\end{array}\]
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and finally, with the same method, we get that
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\[
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F_3G_3(Y)_\Tm(\Delta,A) \simeq Y_\Tm(\Delta,A)
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\]
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\end{frame}
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\begin{frame}{Structure of the global proof}
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\begin{frame}{Structure of the global proof}
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\begin{itemize}
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\begin{itemize}
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@ -429,26 +469,6 @@
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\end{frame}
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\end{frame}
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\section{Conclusion}
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\begin{frame}{Conclusion}
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\end{frame}
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\begin{frame}{Future work}
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\begin{itemize}
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\item Complete GAT (term constructors + equalities)
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\item Proof Assistant Formalization
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\item $S_i$ non-direct
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\end{itemize}
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\end{frame}
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\begin{frame}
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\begin{center}
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\Large Thank you for your attention
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\end{center}
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\end{frame}
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\end{document}
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\end{document}
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@ -171,7 +171,7 @@
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\hypersetup{pdfpagemode=FullScreen}
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\hypersetup{pdfpagemode=FullScreen}
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% Transition en fade-in par défaut
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% Transition en fade-in par défaut
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\addtobeamertemplate{background canvas}{\transfade[duration=0.4]}{}
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%\addtobeamertemplate{background canvas}{\transfade[duration=0.4]}{}
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\addtobeamertemplate{frametitle}{
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\addtobeamertemplate{frametitle}{
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\let\insertframetitle\insertsubsectionhead}{}
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\let\insertframetitle\insertsubsectionhead}{}
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