diff --git a/tex/bounds-on-semistabilisers.tex b/tex/bounds-on-semistabilisers.tex
index 1451d05409b05b8c6a9281b995bd3e14cd766a90..372e1350f5ee34c56e922c95ec612c40a7b1b549 100644
--- a/tex/bounds-on-semistabilisers.tex
+++ b/tex/bounds-on-semistabilisers.tex
@@ -37,13 +37,13 @@ bounded above by:
 
 \begin{proof}
 The Bogomolov form applied to the twisted Chern character is the same as the
-untwisted one. So $0 \leq \Delta(E)$
+untwisted one. So $0 \leq \Delta(u)$
 (condition 2 from Corollary \ref{cor:num_test_prob2})
 yields:
 
 \begin{equation}
 	\label{eqn-bgmlv-on-E}
-	2\chern^\beta_0(E) \chern^\beta_2(E) \leq \chern^\beta_1(E)^2
+	2\chern^\beta_0(u) \chern^\beta_2(u) \leq \chern^\beta_1(u)^2
 \end{equation}
 
 \noindent
@@ -52,12 +52,12 @@ condition 5 from Corollary \ref{cor:num_test_prob2}
 gives:
 \begin{equation}
 	\label{eqn-tilt-cat-cond}
-	0 \leq \chern^\beta_1(E) \leq \chern^\beta_1(F)
+	0 < \chern^\beta_1(u) < \chern^\beta_1(v)
 \end{equation}
 % FUTURE maybe ref this back to some definition of first tilt
 
 \noindent
-The restrictions on $\chern^{\beta_-}_0(E)$ and $\chern^{\beta_-}_2(E)$
+The restrictions on $\chern^{\beta_-}_0(u)$ and $\chern^{\beta_-}_2(v)$
 is best seen with the following graph:
 
 % TODO: hyperbola restriction graph (shaded)