X-Git-Url: http://plrg.eecs.uci.edu/git/?p=iotcloud.git;a=blobdiff_plain;f=doc%2Fiotcloud.tex;fp=doc%2Fiotcloud.tex;h=4d0c9f491dbc12085ed551a060fe60188663992b;hp=de40d0e2727577f8615dea19305aa22730de9b1f;hb=f498aec54ac8672e6b7c5d813f6487b4a57ed5a6;hpb=eebed07efef8749eed766cbc3682a0038265aa44

diff --git a/doc/iotcloud.tex b/doc/iotcloud.tex
index de40d0e..4d0c9f4 100644
--- a/doc/iotcloud.tex
+++ b/doc/iotcloud.tex
@@ -587,7 +587,7 @@ $\tuple{ck,\tuple{k, v}} \in KV_s \wedge
 
 \begin{algorithmic}[1]
 \Function{Put}{$KV_s,\tuple{k_s,v_s}$}  \Comment{Interface function to update a key-value pair}
-\State $\tuple{ck_s,\tuple{k_s,v_t}} \gets GetKVPair(KV,k_s)$
+\State $\tuple{ck_s,\tuple{k_s,v_t}} \gets GetKVPair(KV_s,k_s)$
 \If{$\tuple{ck_s,\tuple{k_s,v_t}} = \emptyset$}
 	\State $KV_s \gets KV_s \cup \{\tuple{ck_p, \tuple{k_s,v_s}}\}$
 	\State $ck_p \gets ck_p + 1$
@@ -956,9 +956,10 @@ call them $\mathsf{t}$ and $\mathsf{u}$ such that $\mathsf{s_t \le s_u}$.
 Then $\mathsf{t}$ is in the path of $\mathsf{u}$. 
 \end{lem}
 \begin{proof}
-Assume otherwise. Then there are some pairs $\mathsf{(t,u)}$ that violate this lemma. 
-Take a specific $\mathsf{(t,u)}$ such that $\mathsf{s_u}$ is minimized and 
-$\mathsf{s_t}$ is maximized for this choice of $\mathsf{s_u}$.
+Assume that there are some pairs of messages $\mathsf{(t,u)}$ that violate this lemma. 
+Take a specific $\mathsf{(t,u)}$ such that $\mathsf{s_u}$ is minimized, and 
+$\mathsf{s_t}$ is maximized for this choice of $\mathsf{s_u}$. We will show that $\mathsf{C}$
+cannot receive both $\mathsf{t}$ and $\mathsf{u}$ without throwing an error.
 
 Clearly $\mathsf{C}$ will throw an error if $\mathsf{s_t = s_u}$. So 
 $\mathsf{s_t < s_u}$. Additionally, if $\mathsf{C}$ receives $\mathsf{u}$ before