From eb0ac1c3704d7c4a5751a89ebc27387975abd269 Mon Sep 17 00:00:00 2001
From: Jacob Walchuk <jpw24@st-andrews.ac.uk>
Date: Mon, 7 Jul 2025 13:27:49 +0100
Subject: +1 graphic

---
 papers/3.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'papers/3.tex')

diff --git a/papers/3.tex b/papers/3.tex
index 6066649..84a52f1 100644
--- a/papers/3.tex
+++ b/papers/3.tex
@@ -205,7 +205,7 @@ $\forall x (Xx \ba x=y), Haec(X)(z) \wedge z \neq y \vdash Xy \ba y=y \\
 \end{quote}
 Then, from $\vdash Haec(X)(y) \ra Tra(X)(y)$, we can observe that: \\
 \begin{quote}
-\begin{tabulary}{\textwidth}{Lr}
+\begin{tabulary}{\textwidth}{LR}
 $\vdash \Box Haec(X)(y) \ra \Box Tra(X)(y)$ & (K)  \\
 $\vdash \Box \forall x (Xx \ba x=y) \ra \Box \Box \forall x (Xx \ba x=y)$ & (\textbf{4})\\
 $\vdash Haec(X)(y) \ra \Box Haec(X)(y)$ & (Chaining conditionals) \\
@@ -214,7 +214,7 @@ $\vdash Haec(X)(y) \ra \Box Tra(X)(y)$ &
 \end{quote}
 \subsection{The proof for (o-Tracking)} 
 \begin{quote}
-\begin{tabulary}{\textwidth}{Lr}
+\begin{tabulary}{\textwidth}{LR}
 $\vdash Haec(X)(o) \ra Tra(X)(o)$ & (Proved above) \\
 $\vdash \exists X Haec(X)(o) \ra \exists X Tra(X)(o)$ & (Derivable from $\forall$ rule) \\
 $\vdash \Box \exists X Haec(X)(o) \ra \Box \exists X Tra(X)(o)$ & (K)\\
-- 
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