relations 13 fini

[cours-maths-dis.git] / main13.aux

diff --git a/main13.aux b/main13.aux
index 2be045cff556137e55260ff3ae62ed9e359042b3..44666a45e32b4003924c76c13d42281d080c9073 100644 (file)
--- a/main13.aux
+++ b/main13.aux
@@ -245,53 +245,45 @@
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{1}}{Relation binaire}}{30}{Def.1}}
 \@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{1}}{}}{30}{Exo.1}}
 \@writefile{thm}{\contentsline {Rem}{{Remarque}{4.{1}}{}}{30}{Rem.1}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{1}}{Relation binaire}}{30}{Def.1}}
 \@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{1}}{}}{30}{Exo.1}}
 \@writefile{thm}{\contentsline {Rem}{{Remarque}{4.{1}}{}}{30}{Rem.1}}

-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{2}}{}}{30}{Exo.2}}

 \@writefile{toc}{\contentsline {section}{\numberline {II}Relations d'ordre}{30}{section.4.2}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {II.1}R\IeC {\'e}flexivit\IeC {\'e}, antisym\IeC {\'e}trie, transitivit\IeC {\'e}}{30}{subsection.4.2.1}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{2}}{Réflexivité}}{30}{Def.2}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{3}}{Antisymétrie}}{30}{Def.3}}
 \@writefile{toc}{\contentsline {section}{\numberline {II}Relations d'ordre}{30}{section.4.2}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {II.1}R\IeC {\'e}flexivit\IeC {\'e}, antisym\IeC {\'e}trie, transitivit\IeC {\'e}}{30}{subsection.4.2.1}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{2}}{Réflexivité}}{30}{Def.2}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{3}}{Antisymétrie}}{30}{Def.3}}

-\@writefile{thm}{\contentsline {Def}{{Définition}{4.{4}}{Transitivité}}{31}{Def.4}}
+\@writefile{thm}{\contentsline {Def}{{Définition}{4.{4}}{Transitivité}}{30}{Def.4}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{2}}{}}{30}{Exo.2}}

 \@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{3}}{}}{31}{Exo.3}}
 \@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{3}}{}}{31}{Exo.3}}

-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{4}}{}}{31}{Exo.4}}
-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{5}}{}}{31}{Exo.5}}

 \@writefile{toc}{\contentsline {subsection}{\numberline {II.2}Relation d'ordre}{31}{subsection.4.2.2}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{5}}{Relation d'ordre}}{31}{Def.5}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {II.2}Relation d'ordre}{31}{subsection.4.2.2}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{5}}{Relation d'ordre}}{31}{Def.5}}

-\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{6}}{}}{31}{Exo.6}}
-\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{7}}{Relation de divisibilité}}{31}{Exo.7}}
+\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{4}}{}}{31}{Exo.4}}
+\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{5}}{Relation de divisibilité}}{31}{Exo.5}}

 \global\def\markxxExi{\ensuremath {}}
 \global\def\markxxExi{\ensuremath {}}

-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{8}}{}}{31}{Exo.8}}
-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{9}}{Diagrammes de transitivité}}{31}{Exo.9}}
-\@writefile{toc}{\contentsline {section}{\numberline {III}Relations d'\IeC {\'e}quivalence}{32}{section.4.3}}
-\@writefile{thm}{\contentsline {Def}{{Définition}{4.{6}}{Relation symétrique}}{32}{Def.6}}
-\@writefile{thm}{\contentsline {Def}{{Définition}{4.{7}}{Relation d'équivalence}}{32}{Def.7}}
-\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{10}}{}}{32}{Exo.10}}
-\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{11}}{Relation de congruence modulo $n$ dans $\Z $}}{32}{Exo.11}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{6}}{}}{31}{Exo.6}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{7}}{Diagrammes de transitivité}}{31}{Exo.7}}
+\@writefile{toc}{\contentsline {section}{\numberline {III}Relations d'\IeC {\'e}quivalence}{31}{section.4.3}}
+\@writefile{thm}{\contentsline {Def}{{Définition}{4.{6}}{Relation symétrique}}{31}{Def.6}}
+\@writefile{thm}{\contentsline {Def}{{Définition}{4.{7}}{Relation d'équivalence}}{31}{Def.7}}
+\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{8}}{}}{31}{Exo.8}}
+\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{9}}{Relation de congruence modulo $n$ dans $\Z $}}{32}{Exo.9}}

 \global\def\markxxiiExi{\ensuremath {}}
 \global\def\markxxiiExi{\ensuremath {}}

-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{12}}{}}{32}{Exo.12}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{10}}{}}{32}{Exo.10}}

 \@writefile{toc}{\contentsline {subsection}{\numberline {III.1}Classes d'\IeC {\'e}quivalence}{32}{subsection.4.3.1}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{8}}{Classe d'équivalence}}{32}{Def.8}}
 \@writefile{thm}{\contentsline {Notation}{{Notation}{4.{1}}{}}{32}{Notation.1}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {III.1}Classes d'\IeC {\'e}quivalence}{32}{subsection.4.3.1}}
 \@writefile{thm}{\contentsline {Def}{{Définition}{4.{8}}{Classe d'équivalence}}{32}{Def.8}}
 \@writefile{thm}{\contentsline {Notation}{{Notation}{4.{1}}{}}{32}{Notation.1}}

-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{13}}{}}{32}{Exo.13}}
-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{14}}{}}{32}{Exo.14}}
-\@writefile{thm}{\contentsline {Th}{{Propriété}{4.{1}}{}}{33}{Th.1}}
-\@writefile{thm}{\contentsline {Rem}{{Remarque}{4.{2}}{}}{33}{Rem.2}}
-\@writefile{thm}{\contentsline {Pre}{{Preuve}{1}{}}{33}{Pre.1}}
-\@writefile{thm}{\contentsline {Def}{{Définition}{4.{9}}{Partition d'un ensemble}}{33}{Def.9}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{11}}{}}{32}{Exo.11}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{12}}{}}{32}{Exo.12}}
+\@writefile{thm}{\contentsline {Th}{{Propriété}{4.{1}}{}}{32}{Th.1}}
+\@writefile{thm}{\contentsline {Pre}{{Preuve}{1}{}}{32}{Pre.1}}
+\@writefile{thm}{\contentsline {Def}{{Définition}{4.{9}}{Partition d'un ensemble}}{32}{Def.9}}

 \@writefile{thm}{\contentsline {Th}{{Propriété}{4.{2}}{}}{33}{Th.2}}
 \@writefile{thm}{\contentsline {Pre}{{Preuve}{2}{}}{33}{Pre.2}}
 \@writefile{thm}{\contentsline {Th}{{Propriété}{4.{2}}{}}{33}{Th.2}}
 \@writefile{thm}{\contentsline {Pre}{{Preuve}{2}{}}{33}{Pre.2}}

-\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{15}}{}}{33}{Exo.15}}
+\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{13}}{}}{33}{Exo.13}}

 \global\def\markxxiiiEx{\ensuremath {}}
 \global\def\markxxiiiEx{\ensuremath {}}

-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{16}}{}}{33}{Exo.16}}
-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{17}}{Une relation d'équivalence}}{33}{Exo.17}}
-\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{18}}{}}{33}{Exo.18}}
-\@writefile{toc}{\contentsline {subsection}{\numberline {III.2}Ensemble-quotient}{34}{subsection.4.3.2}}
-\@writefile{thm}{\contentsline {Def}{{Définition}{4.{10}}{Ensemble-quotient}}{34}{Def.10}}
-\@writefile{thm}{\contentsline {Notation}{{Notation}{4.{2}}{}}{34}{Notation.2}}
-\@writefile{thm}{\contentsline {Ex}{{Exemple}{4.{19}}{Congruence modulo 4}}{34}{Exo.19}}
-\@writefile{toc}{\contentsline {part}{III\hspace  {1em}Annexes}{35}{part.3}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{14}}{}}{33}{Exo.14}}
+\@writefile{thm}{\contentsline {Exo}{{Exercice}{4.{15}}{}}{33}{Exo.15}}
+\@writefile{toc}{\contentsline {part}{III\hspace  {1em}Annexes}{34}{part.3}}

 \@input{PPN.aux}
 \bibstyle{alpha}
 \bibdata{biblio}
 \bibcite{Dowek07}{Dow07}
 \@input{PPN.aux}
 \bibstyle{alpha}
 \bibdata{biblio}
 \bibcite{Dowek07}{Dow07}

-\@writefile{toc}{\contentsline {chapter}{Index}{37}{chapter.5}}
+\@writefile{toc}{\contentsline {chapter}{Index}{36}{chapter.5}}

 \@input{Bibliographie.aux}
 \@input{Bibliographie.aux}