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| author | Pierre-Marie Pédrot | 2015-07-27 14:28:15 +0200 |
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| committer | Pierre-Marie Pédrot | 2015-07-27 14:28:15 +0200 |
| commit | aff5a1aaeb9b50c60ff32b7d5336a44fd18428ee (patch) | |
| tree | 39d21c9798b9ce7fb59892414f71fb60be61bcde /doc/faq/FAQ.tex | |
| parent | 05f22a5d6d5b8e3e80f1a37321708ce401834430 (diff) | |
| parent | cb145fa37d463210832c437f013231c9f028e1aa (diff) | |
Merge branch 'v8.5'
Diffstat (limited to 'doc/faq/FAQ.tex')
| -rw-r--r-- | doc/faq/FAQ.tex | 35 |
1 files changed, 22 insertions, 13 deletions
diff --git a/doc/faq/FAQ.tex b/doc/faq/FAQ.tex index 589933578a..8495156ca1 100644 --- a/doc/faq/FAQ.tex +++ b/doc/faq/FAQ.tex @@ -503,19 +503,34 @@ $\forall A \forall x y:A \forall p_1 p_2:x=y, p_1=p_2$ \item Extensionality of functions: $\forall f g:A\rightarrow B, (\forall x, f(x)=g(x)) \rightarrow f=g$ \end{itemize} -Here is a summary of the relative strength of these axioms, most -proofs can be found in directory {\tt Logic} of the standard library. -The justification of their validity relies on the interpretability in -set theory. - +Figure~\ref{fig:axioms} is a summary of the relative strength of these +axioms, most proofs can be found in directory {\tt Logic} of the standard +library. (Statements in boldface are the most ``interesting'' ones for +Coq.) The justification of their validity relies on the interpretability +in set theory. + +% fig2dev -m 2 -L png axioms.fig axioms.png +% fig2dev -L pdftex axioms.fig axioms.pdf +% fig2dev -L pdftex_t -p axioms.pdf axioms.fig axioms.pdf_t +% fig2dev -L pstex axioms.fig axioms.eps +% fig2dev -L pstex_t -p axioms.eps axioms.fig axioms.eps_t + +\begin{figure}[htbp] %HEVEA\imgsrc{axioms.png} %BEGIN LATEX +\begin{center} \ifpdf % si on est en pdflatex -\includegraphics[width=1.0\textwidth]{axioms.png} +\scalebox{0.65}{\input{axioms.pdf_t}} +%\includegraphics[width=1.0\textwidth]{axioms.png} \else -\includegraphics[width=1.0\textwidth]{axioms.eps} +\scalebox{0.65}{\input{axioms.eps_t}} +%\includegraphics[width=1.0\textwidth]{axioms.eps} \fi +\end{center} %END LATEX +\caption{The dependency graph of axioms in the Calculus of Inductive Constructions} +\label{fig:axioms} +\end{figure} \Question{What standard axioms are inconsistent with {\Coq}?} @@ -2579,12 +2594,6 @@ Qed. You can help {\Coq} using the {\pattern} tactic. -\Question{Why does {\Coq} tell me that \texttt{\{x:A|(P x)\}} is not convertible with \texttt{(sig A P)}?} - - This is because \texttt{\{x:A|P x\}} is a notation for -\texttt{sig (fun x:A => P x)}. Since {\Coq} does not reason up to -$\eta$-conversion, this is different from \texttt{sig P}. - \Question{I copy-paste a term and {\Coq} says it is not convertible to the original term. Sometimes it even says the copied term is not |
