diff --git a/tex/setting-and-problems.tex b/tex/setting-and-problems.tex
index 17a01fc2707c8966b689b85245002d365a828501..073d46796b6ae373e97a333a127bb07c3336a5c7 100644
--- a/tex/setting-and-problems.tex
+++ b/tex/setting-and-problems.tex
@@ -395,10 +395,10 @@ with the choice $P=(\beta_{-},0)$, the point where $\Theta_v^-$ meets the
 $\beta$-axis.
 This is because all circular walls left of $V_v$ intersect $\Theta_v^-$ (once).
 The $\beta_{-}(v) \in \QQ$ condition is to ensure that there are finitely many
-solutions. As mentioned in the introduction (\ref{sec:intro}), this is known,
-however this will also be proved again implicitly in section
-\ref{sect:prob2-algorithm}, where an algorithm is produced to find all
-solutions.
+solutions. As mentioned in the introduction to this Part, this is known,
+however this will also be proved again implicitly in Chapter
+\ref{chapt:computing-semistabilisers},
+where an algorithm is produced to find all solutions.
 
 This description still holds for the case of rank 0 case if we consider $V_v$ to
 be infinitely far to the right
@@ -411,7 +411,7 @@ The problems introduced in this section are phrased in the context of stability
 conditions. However, these can be reduced down completely to purely numerical
 problem using Lemma \ref{lem:pseudo_wall_numerical_tests}.
 
-\begin{lemma}[Numerical Tests for Sufficiently Large `left' Pseudo-walls]
+\begin{theorem}[Numerical Tests for Sufficiently Large `left' Pseudo-walls]
 	\label{lem:num_test_prob1}
 	Given a Chern character $v$ with non-negative rank
 	(and $\chern_1(v)>0$ if rank 0),
@@ -436,7 +436,7 @@ problem using Lemma \ref{lem:pseudo_wall_numerical_tests}.
 			\label{item:radiuscond:lem:num_test_prob1}
 		\end{multicols}
 	\end{enumerate}
-\end{lemma}
+\end{theorem}
 
 \begin{proof}
 	Consider the context of $v$ being a Chern character with non-negative rank
@@ -452,7 +452,7 @@ problem using Lemma \ref{lem:pseudo_wall_numerical_tests}.
 
 \end{proof}
 
-\begin{corollary}[Numerical Tests for All `left' Pseudo-walls]
+\begin{theorem}[Numerical Tests for All `left' Pseudo-walls]
 \label{cor:num_test_prob2}
 	Given a Chern character $v$ with non-negative rank
 	(and $\chern_1(v)>0$ if rank 0),
@@ -478,7 +478,7 @@ problem using Lemma \ref{lem:pseudo_wall_numerical_tests}.
 			\label{item:radiuscond:lem:num_test_prob2}
 		\end{multicols}
 	\end{enumerate}
-\end{corollary}
+\end{theorem}
 
 \begin{proof}
 	This is a specialization of the previous Lemma, using $P=(\beta_{-},0)$.