
diff -r d48cfc286cb1 -r f702fd716bd8 slides02.tex
--- a/slides02.tex	Thu Oct 04 09:07:33 2012 +0100
+++ b/slides02.tex	Thu Oct 04 09:07:43 2012 +0100
@@ -311,7 +311,7 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
+\frametitle{\begin{tabular}{c}The Derivative of a Rexp (2)\end{tabular}}
 
 \begin{center}
 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
@@ -319,8 +319,9 @@
   \bl{der c ($\epsilon$)}           & \bl{$\dn$} & \bl{$\varnothing$} & \\
   \bl{der c (d)}           & \bl{$\dn$} & \bl{if c $=$ d then [] else $\varnothing$} & \\
   \bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\
-  \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{((der c r$_1$) $\cdot$ r$_2$) + } & \\
-       &          & \bl{\hspace{3mm}(if nullable r$_1$ then der c r$_2$ else $\varnothing$)}\\
+  \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$}  & \bl{if nullable r$_1$}\\
+  & & \bl{then ((der c r$_1$) $\cdot$ r$_2$) + (der c r$_2$)}\\ 
+  & & \bl{else (der c r$_1$) $\cdot$ r$_2$}\\
   \bl{der c (r$^*$)}          & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)} &\smallskip\\\pause
 
   \bl{ders [] r}     & \bl{$\dn$} & \bl{r} & \\
@@ -430,6 +431,26 @@
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Proofs about Strings (2)\end{tabular}}
+
+Let \bl{Der c A} be the set defined as
+
+\begin{center}
+\bl{Der c A $\dn$ $\{$ s $|$  c::s $\in$ A$\}$ } 
+\end{center}
+
+Assume that \bl{$L$(der c r) = Der c ($L$(r))}. Prove that
+
+\begin{center}
+\bl{matcher(r, s)  if and only if  s $\in$ $L$(r)} 
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{




