diff --git a/main.tex b/main.tex
index f124e7726a645d9953a769a31f103ede0a741d53..52e23349d353ce49ed0aefffe7f43accbf02a758 100644
--- a/main.tex
+++ b/main.tex
@@ -1058,6 +1058,11 @@ amounts to:
 		Δ(u) ≥ 0
 	}
 }
+This condition refers to condition
+\ref{item:bgmlvu:lem:num_test_prob1}
+from lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2}).
+
 
 \begin{sagesilent}
 # First Bogomolov-Gieseker form expression that must be non-negative:
@@ -1148,6 +1153,11 @@ for the bound found for $d$ in subsubsection \ref{subsect-d-bound-radiuscond}.
 }
 \label{subsect-d-bound-bgmlv3}
 
+This condition refers to condition
+\ref{item:bgmlvv-u:lem:num_test_prob1}
+from lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2}).
+
 Expressing $\Delta(v-u)\geq 0$ in term of $q$ and rearranging as a bound on
 $d$ yields: