Added simple diagram for lemma in proof

diff --git a/doc/iotcloud.tex b/doc/iotcloud.tex
index 143791dfe6362e3fd3149d2fe464d382687b6f5f..250ddcf165b0c7eb011febd3268f9f88d5126b41 100644 (file)
--- a/doc/iotcloud.tex
+++ b/doc/iotcloud.tex
@@ -6,6 +6,7 @@
 \usepackage{graphicx}\r
 \usepackage{mathrsfs}\r
 \usepackage{algpseudocode}% http://ctan.org/pkg/algorithmicx\r
+\usepackage[all]{xy}\r
 \newtheorem{theorem}{Theorem}\r
 \newtheorem{prop}{Proposition}\r
 \newtheorem{lem}{Lemma}\r
@@ -685,6 +686,14 @@ $\tuple{ck,\tuple{k, v}} \in KV_s \wedge
 \r
 \end{lem}\r
 \r
+\begin{figure}[h]\r
+  \centering\r
+      \xymatrix{\r
+\dots \ar[r] & q \ar[dr]_{J} \ar[r]^{K} & S_1 \ar[r] & S_2 \ar[rr] & & \dots \ar[r] & S_n = u \\\r
+& & R_1 \ar[r] & R_2 \ar[r] & \dots \ar[r] & R_m = t}\r
+\caption{By Lemma 2, receiving $t$ before $u$ is impossible.}\r
+\end{figure}\r
+\r
 \begin{lem} If two packets $t$ and $u$, with $i(t) \le i(u)$, are received without errors by a client $C$, then $t$ is in the path of $u$. \end{lem}\r
 \begin{proof}\r
 Assume that $t$ is not in the path of $u$. Take $u$ to be the packet of smallest index for which this occurs, and $t$ be the packet with largest index for this $u$. We will prove that an error occurs upon receipt of $u$.\r