--- a/doc-src/TutorialI/Recdef/document/Nested2.tex Wed May 25 09:03:53 2005 +0200
+++ b/doc-src/TutorialI/Recdef/document/Nested2.tex Wed May 25 09:04:24 2005 +0200
@@ -5,8 +5,7 @@
\isamarkupfalse%
\isacommand{lemma}\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequote}t\ {\isasymin}\ set\ ts\ {\isasymlongrightarrow}\ size\ t\ {\isacharless}\ Suc{\isacharparenleft}term{\isacharunderscore}list{\isacharunderscore}size\ ts{\isacharparenright}{\isachardoublequote}\isanewline
\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
+\isacommand{by}{\isacharparenleft}induct{\isacharunderscore}tac\ ts{\isacharcomma}\ auto{\isacharparenright}\isamarkupfalse%
\isamarkupfalse%
%
\begin{isamarkuptext}%
@@ -21,9 +20,19 @@
\isamarkuptrue%
\isacommand{lemma}\ {\isachardoublequote}trev{\isacharparenleft}trev\ t{\isacharparenright}\ {\isacharequal}\ t{\isachardoublequote}\isanewline
\isamarkupfalse%
-\isamarkupfalse%
+\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ t\ rule{\isacharcolon}\ trev{\isachardot}induct{\isacharparenright}\isamarkupfalse%
+%
+\begin{isamarkuptxt}%
+\begin{isabelle}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ trev\ {\isacharparenleft}trev\ {\isacharparenleft}Var\ x{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ Var\ x\isanewline
+\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}f\ ts{\isachardot}\isanewline
+\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }{\isasymforall}x{\isachardot}\ x\ {\isasymin}\ set\ ts\ {\isasymlongrightarrow}\ trev\ {\isacharparenleft}trev\ x{\isacharparenright}\ {\isacharequal}\ x\ {\isasymLongrightarrow}\isanewline
+\isaindent{\ {\isadigit{2}}{\isachardot}\ \ \ \ }trev\ {\isacharparenleft}trev\ {\isacharparenleft}App\ f\ ts{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ App\ f\ ts%
+\end{isabelle}
+Both the base case and the induction step fall to simplification:%
+\end{isamarkuptxt}%
\isamarkuptrue%
-\isamarkupfalse%
+\isacommand{by}{\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ rev{\isacharunderscore}map\ sym{\isacharbrackleft}OF\ map{\isacharunderscore}compose{\isacharbrackright}\ cong{\isacharcolon}\ map{\isacharunderscore}cong{\isacharparenright}\isamarkupfalse%
%
\begin{isamarkuptext}%
\noindent