Move `OrderedPair` and `Relation` to Enderton.

These modules probably won't be very useful in general; there exist
better representations in Lean when dealing with ordered pairs or
relations already.

Bookshelf/Enderton/Set.lean

@@ -1,3 +1,5 @@
 import Bookshelf.Enderton.Set.Chapter_1
 import Bookshelf.Enderton.Set.Chapter_2
-import Bookshelf.Enderton.Set.Chapter_3
+import Bookshelf.Enderton.Set.Chapter_3
+import Bookshelf.Enderton.Set.OrderedPair
+import Bookshelf.Enderton.Set.Relation

Bookshelf/Enderton/Set.tex

@@ -73,6 +73,12 @@ There is a set having no members:
 
 \end{axiom}
 
+\section{\partial{Equivalence Relation}}%
+\label{ref:equivalence-relation}
+
+Relation $R$ is an \textbf{equivalence relation} if and only if $R$ is a binary
+  relation that is reflexive, symmetric, and transitive.
+
 \section{\defined{Extensionality Axiom}}%
 \label{ref:extensionality-axiom}
 
@@ -236,6 +242,12 @@ Given \nameref{ref:relation} $R$, the \textbf{range} of $R$, denoted $\ran{R}$,
 
 \end{definition}
 
+\section{\partial{Reflexive Relation}}%
+\label{ref:reflexive-relation}
+
+A binary relation $R$ is \textbf{reflexive} on $A$ if and only if $xRx$ for all
+  $x \in A$.
+
 \section{\defined{Relation}}%
 \label{ref:relation}
 
@@ -272,6 +284,12 @@ For each formula $\phi$ not containing $B$, the following is an axiom:
 
 \end{axiom}
 
+\section{\partial{Symmetric Relation}}%
+\label{ref:symmetric-relation}
+
+A binary relation $R$ is \textbf{symmetric} on $A$ if and only if whenever
+  $xRy$ then $yRx$.
+
 \section{\defined{Symmetric Difference}}%
 \label{ref:symmetric-difference}
 
@@ -284,6 +302,12 @@ The \textbf{symmetric difference} $A + B$ of sets $A$ and $B$ is the set
 
 \end{definition}
 
+\section{\partial{Transitive Relation}}%
+\label{ref:transitive-relation}
+
+A binary relation $R$ is \textbf{transitive} on $A$ if and only if whenever
+  $xRy$ and $yRz$, then $xRz$.
+
 \section{\defined{Union Axiom}}%
 \label{ref:union-axiom}
 
@@ -3148,6 +3172,25 @@ For any one-to-one function $F$, $F^{-1}$ is also one-to-one.
 
 \end{proof}
 
+\section{Equivalence Relations}%
+\label{sec:equivalence-relations}
+
+\subsection{\unverified{Theorem 3M}}%
+\label{sub:theorem-3m}
+
+\begin{theorem}[3M]
+
+  If $R$ is a symmetric and transitive relation, then $R$ is an equivalence
+    relation on $\fld{R}$.
+
+\end{theorem}
+
+\begin{proof}
+
+  TODO
+
+\end{proof}
+
 \section{Exercises 3}%
 \label{sec:exercises-3}
 

Bookshelf/Enderton/Set/Chapter_2.lean

@@ -1,9 +1,6 @@
-import Mathlib.Data.Set.Basic
-import Mathlib.Data.Set.Lattice
-
 import Bookshelf.Enderton.Set.Chapter_1
-import Common.Logic.Basic
 import Common.Set.Basic
+import Mathlib.Data.Set.Lattice
 
 /-! # Enderton.Chapter_2
 

Bookshelf/Enderton/Set/Chapter_3.lean

@@ -1,6 +1,6 @@
 import Bookshelf.Enderton.Set.Chapter_2
-import Common.Set.OrderedPair
+import Bookshelf.Enderton.Set.OrderedPair
-import Common.Set.Relation
+import Bookshelf.Enderton.Set.Relation
 
 /-! # Enderton.Chapter_3
 

Bookshelf/Enderton/Set/Relation.lean

@@ -1,6 +1,4 @@
-import Common.Set.OrderedPair
+import Bookshelf.Enderton.Set.OrderedPair
-import Mathlib.Data.Set.Basic
-import Mathlib.Data.Set.Prod
 
 /-! # Relations
 

Common/Set.lean

@@ -1,5 +1,3 @@
 import Common.Set.Basic
 import Common.Set.Interval
-import Common.Set.OrderedPair
+import Common.Set.Partition
-import Common.Set.Partition
-import Common.Set.Relation