From 41b5e6d6b1e10092b99d0bdfef33a260e229bffe Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Mon, 13 Dec 2021 16:49:15 +0100
Subject: Let w = u_0

---
 mgr.tex | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/mgr.tex b/mgr.tex
index ec250b6..56502cb 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -1052,8 +1052,8 @@ Consider the subtree of $v$ with hole $w$. It can be divided into the following
 components:
 
 \begin{itemize}
-    \item A path from $w$ up to $v$, notate it as $u_0 = w, u_1, \ldots, u_p =
-        v$.
+    \item A path from the parent of $w$ up to $v$, notate it as $u_1, u_2,
+        \ldots, u_p = v$.
     \item For each $i$ from 1 to $p$, the subtree of $u_i$'s child that doesn't
         lie on the path from $w$ to $v$. Let $u_i'$ be the child of $u_i$ that
         doesn't lie on the $w$ to $v$ path.
@@ -1070,6 +1070,10 @@ components:
     }\label{subtree-with-hole-figure}
 \end{figure}
 
+$w$ is not a part of the subtree with hole, but we will need to consider it
+during the following computation, so for ease of notation we will let $u_0 =
+w$, extending the path of $u_i$'s.
+
 Figure \ref{subtree-with-hole-figure} depicts a subtree with hole labeled
 according to this nomenclature.
 
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