Cleanup style

1 files changed, 5 insertions, 5 deletions

diff --git a/mgr.tex b/mgr.tex
index dfbb56d..8ecbc83 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -223,8 +223,8 @@ The rest of our work is organized in the following way:
 
 We work with finite rooted trees whose vertices are labeled with letters from a
 finite alphabet. More formally, given a finite alphabet $\Sigma$, for each $a
-\in \Sigma$, $a$ is a tree, and if $t_1, \ldots, t_k$ are trees, then $a(t_1,
-\ldots, t_k)$ is also a tree. A tree $T$ can then also be seen as an acyclic
+\in \Sigma$, $a$ is a tree, and if $T_1, \ldots, T_k$ are trees, then $a(T_1,
+\ldots, T_k)$ is also a tree. A tree $T$ can then also be seen as an acyclic
 undirected graph with vertex set $V(T)$ and edge set $E(T)$, with a
 distinguished root vertex $r \in V(T)$.
 
@@ -240,7 +240,7 @@ Take a binary tree $T$. The \definedterm{post-order} of $V(T)$ is an ordering of
 $T$'s vertices produced by the following recursive procedure:
 
 \begin{enumerate}
-    \item First traverse the root's children's subtrees.
+    \item Traverse the root's children's subtrees.
     \item Visit the root.
 \end{enumerate}
 
@@ -248,14 +248,14 @@ Similarly, the \definedterm{pre-order} of $V(T)$ is produced by the following
 recursive procedure:
 
 \begin{enumerate}
-    \item First visit the root.
+    \item Visit the root.
     \item Traverse the root's children's subtrees.
 \end{enumerate}
 
 Finally, the following procedure produces the \definedterm{in-order} of $V(T)$:
 
 \begin{enumerate}
-    \item First traverse the left child's subtree.
+    \item Traverse the left child's subtree.
     \item Visit the root.
     \item Traverse the right child's subtree.
 \end{enumerate}