From 015e6d74a6a51d742c03977bd62a42157706ad43 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 13 Sep 2023 21:58:32 +0100
Subject: [PATCH] Extend main lemma to rank 0

---
 main.tex | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/main.tex b/main.tex
index 3749d16..8550862 100644
--- a/main.tex
+++ b/main.tex
@@ -505,7 +505,7 @@ semistabilizing sequence.
 \begin{lemma}[Numerical tests for left-wall pseudo-semistabilizers]
 \label{lem:pseudo_wall_numerical_tests}
 Let $v$ and $u$ be Chern characters with $\Delta(v),
-\Delta(u)\geq 0$, and $v$ has positive rank. Let $P$ be a point on $\Theta_v^-$.
+\Delta(u)\geq 0$, and $v$ has non-negative rank. Let $P$ be a point on $\Theta_v^-$.
 
 \noindent
 The following conditions:
@@ -613,6 +613,8 @@ Therefore, it's also a pseudo-semistabilizer further along the circle at $Q$
 Finally, consequence 4 along with $P$ being to the left of $V_u$ implies
 $\nu_P(u) > 0$ giving supposition b.
 
+The case with rank 0 can be handled the same way.
+
 \end{proof}
 
 \section{The Problem: Finding Pseudo-walls}
-- 
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