proof of alternative merge formulation

diff --git a/article.tex b/article.tex
index e6cc12aca29c8002485a2f6f5f8c486bac9abb47..1dd625fb915d87f34687753e19ec98647e753ebe 100644 (file)
--- a/article.tex
+++ b/article.tex
@@ -218,10 +218,25 @@ We maintain these each time we construct a new commit. \\
     \text{as above with L and R exchanged}
   \end{cases}
 }\]
-\proof{
-  Truth table xxx
-
-  Original definition is symmetrical in $L$ and $R$.
+\proof{ ~ Truth table (ordered by original definition): \\
+  \begin{tabular}{cccc|c|cc}
+     $D = C$ &
+          $\isin L$ &
+               $\isin M$ &
+                    $\isin R$ & $\isin C$ &
+                                      $L$ vs. $R$ & $L$ vs. $M$
+  \\\hline
+     y &  ? &  ? &  ?      &      y   & ?         & ?            \\
+     n &  y &  y &  y      &      y   & $\equiv$  & $\equiv$     \\
+     n &  y &  n &  y      &      y   & $\equiv$  & $\nequiv$    \\
+     n &  n &  y &  n      &      n   & $\equiv$  & $\nequiv$    \\
+     n &  n &  n &  n      &      n   & $\equiv$  & $\equiv$     \\
+     n &  y &  y &  n      &      n   & $\nequiv$ & $\equiv$     \\
+     n &  n &  y &  y      &      n   & $\nequiv$ & $\nequiv$    \\
+     n &  y &  n &  n      &      y   & $\nequiv$ & $\nequiv$    \\
+     n &  n &  n &  y      &      y   & $\nequiv$ & $\equiv$     \\
+  \end{tabular} \\
+  And original definition is symmetrical in $L$ and $R$.
 }
 
 \[ \eqn{Exclusive Tip Contents:}{