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Usual definitions on binary relations.
The booleanChristophe Raffalli, Paul RoziereParis VII, Paris XII university
Christophe Raffalli 2005-03-02
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm transitive}\hspace{0.2...
...Verb{Verb}transitive D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img59.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm reflexive}\hspace{0.2e...
...eVerb{Verb}reflexive D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img60.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm anti}.\text{\rm reflex...
...{Verb}anti.reflexive D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img61.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm symmetric}\hspace{0.2e...
...eVerb{Verb}symmetric D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img62.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm anti}.\text{\rm symmet...
...{Verb}anti.symmetric D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img63.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm preorder}\hspace{0.2em...
...veVerb{Verb}preorder D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img64.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm strict}.\text{\rm orde...
...rb{Verb}strict.order D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img65.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm order}\hspace{0.2em} \...
...\SaveVerb{Verb}order D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img66.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm equivalence}\hspace{0....
...erb{Verb}equivalence D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img67.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm total}\hspace{0.2em} \...
...\SaveVerb{Verb}total D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img68.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm strict}.\text{\rm tota...
...rb{Verb}strict.total D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img69.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm well}.\text{\rm founde...
...rb{Verb}well.founded D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img70.png)
![\begin{definition}[]~
\begin{center}%
\afdmath{}\text{\rm well}.\text{\rm order}...
...Verb{Verb}well.order D R\marginpar{\UseVerb{Verb}}\end{center}\end{definition}](img71.png)
![\begin{fact}[ Some properties of well founded relations. ]\hspace{1cm}
\begin{it...
...endprettybox{}\right)\endprettybox{}\endafdmmath{}}
\par
\end{itemize}\end{fact}](img72.png)