diff --git a/main.tex b/main.tex
index e3bf6ab87c82d79d9eda37b9353c94b96509f573..ba80f4110c85fec348a1c5ba1a9af422b145504e 100644
--- a/main.tex
+++ b/main.tex
@@ -711,6 +711,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
 		\item $0\leq\chern_1^{\beta(P)}(u)\leq\chern_1^{\beta(P)}(v)$
 			\label{item:chern1bound:lem:num_test_prob1}
 		\item $\chern_2^{P}(u)>0$
+			\label{item:radiuscond:lem:num_test_prob1}
 	\end{enumerate}
 \end{lemma}
 
@@ -1026,11 +1027,14 @@ lemma \ref{lem:num_test_prob1}
 \subsubsection{Size of pseudo-wall: $\chern_2^P(u)>0$ }
 \label{subsect-d-bound-radiuscond}
 
-This condition refers to consequence 4 from
-lemma \ref{lem:pseudo_wall_numerical_tests}.
+This condition refers to condition
+\ref{item:radiuscond:lem:num_test_prob1}
+from lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2}).
 
-In the case where $P$ was chosen to be the base of $\Theta_v^-$: $P=(\beta_{-},0)$.
-This condition amounts to:
+In the case where we are tackling problem \ref{problem:problem-statement-2}
+(with $\beta = \beta_{-}$), this condition, when expressed as a bound on $d$,
+amounts to:
 
 \begin{align}
 \label{eqn:radius-cond-betamin}