Be more precise with relations

1 files changed, 5 insertions, 1 deletions

diff --git a/mgr.tex b/mgr.tex
index 257349b..9d9d0dc 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -158,10 +158,14 @@ over a signature with a single binary relation $E$ and unary relations $U_a$ for
 each $a \in \Sigma$. $E(v, w)$ represents a (directed from parent to child) edge
 from $v$ to $w$. $U_a(v)$ signifies that $v$'s label is $a$.
 
+In the case of binary trees, the relation $E$ is replaced with two binary
+relations $E_l$ and $E_r$, which represent an edge from parent to left child,
+and from parent to right child, respectively.
+
 For convenience, we will also make use of the binary relation $\leq$, with $v
 \leq w$ signifying that $v$ is an ancestor of $w$ (with every vertex being an
 ancestor of itself; $<$ can be used to signify a strict ancestor). Note that in
-the case of MSO on trees, $\leq$ could be defined using just the edge relation
+the case of MSO on trees, $\leq$ can be defined using just the edge relation
 $E$.
 
 We make use of a fundamental theorem tying MSO logic on trees and tree automata: