--- a/thys2/Journal/Paper.tex	Thu Nov 04 13:52:17 2021 +0000
+++ b/thys2/Journal/Paper.tex	Tue Dec 14 16:06:42 2021 +0000
@@ -191,7 +191,44 @@
 \isa{lexer\ r\ s\ {\isacharequal}{\kern0pt}\ blexer{\isacharunderscore}{\kern0pt}simp\ r\ s}
 \end{lemma}
 
-The nice thing about the aove%
+The nice thing about the above%
+\end{isamarkuptext}\isamarkuptrue%
+%
+\isadelimdocument
+%
+\endisadelimdocument
+%
+\isatagdocument
+%
+\isamarkupsection{Additional Simp Rules?%
+}
+\isamarkuptrue%
+%
+\endisatagdocument
+{\isafolddocument}%
+%
+\isadelimdocument
+%
+\endisadelimdocument
+%
+\begin{isamarkuptext}%
+One question someone would ask is:
+can we add more "atomic" simplification/rewriting rules,
+so the simplification is even more aggressive, making
+the intermediate results smaller, and therefore more space-efficient? 
+For example, one might want to do open up alternatives who is a child
+of a sequence:
+
+\begin{center}
+  \begin{tabular}{lcl}
+    \isa{ASEQ\ bs\ {\isacharparenleft}{\kern0pt}AALTs\ bs{\isadigit{1}}\ rs{\isacharparenright}{\kern0pt}\ r\ {\isasymleadsto}{\isacharquery}{\kern0pt}\ AALTs\ {\isacharparenleft}{\kern0pt}bs\ {\isacharat}{\kern0pt}\ bs{\isadigit{1}}{\isacharparenright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}map\ {\isacharparenleft}{\kern0pt}{\isasymlambda}r{\isacharprime}{\kern0pt}{\isachardot}{\kern0pt}\ ASEQ\ {\isacharbrackleft}{\kern0pt}{\isacharbrackright}{\kern0pt}\ r{\isacharprime}{\kern0pt}\ r{\isacharparenright}{\kern0pt}\ rs{\isacharparenright}{\kern0pt}}\\
+  \end{tabular}
+\end{center}
+
+
+This rule allows us to simplify \mbox{\isa{a\ {\isacharplus}{\kern0pt}\ b\ {\isasymcdot}\ c\ {\isacharplus}{\kern0pt}\ a\ {\isasymcdot}\ c}}
+ into  \mbox{\isa{a\ {\isasymcdot}\ c\ {\isacharplus}{\kern0pt}\ b\ {\isasymcdot}\ c}},
+which is not allowed under the  \<leadsto> rule%
 \end{isamarkuptext}\isamarkuptrue%
 %
 \isadelimdocument
@@ -1719,6 +1756,8 @@
 \isanewline
 %
 \endisadelimtheory
+\isanewline
+\isanewline
 %
 \end{isabellebody}%
 \endinput
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\ No newline at end of file
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\ No newline at end of file