diff --git a/pdf/grandpa.tex b/pdf/grandpa.tex index 776d58f..7732ed9 100644 --- a/pdf/grandpa.tex +++ b/pdf/grandpa.tex @@ -358,7 +358,7 @@ Let's define $V_{r,v,t}$ be the set $V_{r,v}$ at time $t$ and similarly for $C_{ \begin{lemma} \label{lem:message-monotonicity-completed-estimate} Let $v,v'$ be (possibly identical) honest participants, $t,t'$ be times with $t \leq t'$, and $r$ be a round. -Then if $V_{r,v,t} \subseteq V_{r,v',r'}$ and $C_{r,v,t} \subseteq C_{r,v',r'}$, all these sets are tolerant, and $v$ sees that $r$ is completable at time $t$, then $E_{r,v,t} \leq E_{r,v',t'}$ and $v'$ sees that $r$ is completable at time $t'$. +Then if $V_{r,v,t} \subseteq V_{r,v',t'}$ and $C_{r,v,t} \subseteq C_{r,v',t'}$, all these sets are tolerant, and $v$ sees that $r$ is completable at time $t$, then $E_{r,v,t} \leq E_{r,v',t'}$ and $v'$ sees that $r$ is completable at time $t'$. \end{lemma} \begin{proof} Since $v$ sees that $r$ is completable at time $t$, $V_{r,v,t}$, $C_{r,v,t}$ each contain votes from $n-f$ voters and so the same holds for $V_{r,v',t'}$ and $C_{r,v',t'}$.