diff --git a/pdf/grandpa.tex b/pdf/grandpa.tex
index 7732ed9..269fee9 100644
--- a/pdf/grandpa.tex
+++ b/pdf/grandpa.tex
@@ -353,7 +353,7 @@ If there at most $f$ Byzantine voters in any vote, $B$ was finalised in round $r
 
 We show the protocol is deadlock free and also that it finalises new blocks quickly in a weakly synchronous model.
 
-Let's define $V_{r,v,t}$ be the set $V_{r,v}$ at time $t$ and similarly for $C_{r,v,t}$ and the block $E_{r,v,t}$ .
+We define $V_{r,v,t}$ be the set $V_{r,v}$ at time $t$ and similarly for $C_{r,v,t}$ and the block $E_{r,v,t}$ .
 
 
 \begin{lemma} \label{lem:message-monotonicity-completed-estimate}