
diff -r eacce1cd716a -r 05fc32a23b8b doc-src/TutorialI/Misc/document/AdvancedInd.tex
--- a/doc-src/TutorialI/Misc/document/AdvancedInd.tex	Tue Aug 16 13:42:21 2005 +0200
+++ b/doc-src/TutorialI/Misc/document/AdvancedInd.tex	Tue Aug 16 13:42:23 2005 +0200
@@ -1,7 +1,20 @@
 %
 \begin{isabellebody}%
 \def\isabellecontext{AdvancedInd}%
-\isamarkupfalse%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+\isamarkuptrue%
 %
 \begin{isamarkuptext}%
 \noindent
@@ -26,10 +39,16 @@
 Since \isa{hd} and \isa{last} return the first and last element of a
 non-empty list, this lemma looks easy to prove:%
 \end{isamarkuptext}%
-\isamarkuptrue%
+\isamarkupfalse%
 \isacommand{lemma}\ {\isachardoublequote}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ last\ xs{\isachardoublequote}\isanewline
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
 \isamarkupfalse%
-\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isamarkupfalse%
+\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ xs{\isacharparenright}\isamarkuptrue%
 %
 \begin{isamarkuptxt}%
 \noindent
@@ -62,10 +81,21 @@
 \attrdx{rule_format} (\S\ref{sec:forward}) convert the
 result to the usual \isa{{\isasymLongrightarrow}} form:%
 \end{isamarkuptxt}%
-\isamarkuptrue%
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
 \isamarkupfalse%
-\isacommand{lemma}\ hd{\isacharunderscore}rev\ {\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}{\isacharcolon}\ {\isachardoublequote}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ last\ xs{\isachardoublequote}\isamarkupfalse%
-\isamarkupfalse%
+\isacommand{lemma}\ hd{\isacharunderscore}rev\ {\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}{\isacharcolon}\ {\isachardoublequote}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongrightarrow}\ hd{\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ last\ xs{\isachardoublequote}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+\isamarkuptrue%
 %
 \begin{isamarkuptxt}%
 \noindent
@@ -122,8 +152,14 @@
 single theorem because it depends on the number of free variables in $t$ ---
 the notation $\overline{y}$ is merely an informal device.%
 \end{isamarkuptxt}%
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
 \isamarkuptrue%
-\isamarkupfalse%
 %
 \isamarkupsubsection{Beyond Structural and Recursion Induction%
 }
@@ -149,10 +185,10 @@
 As an application, we prove a property of the following
 function:%
 \end{isamarkuptext}%
-\isamarkuptrue%
+\isamarkupfalse%
 \isacommand{consts}\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}nat\ {\isasymRightarrow}\ nat{\isachardoublequote}\isanewline
 \isamarkupfalse%
-\isacommand{axioms}\ f{\isacharunderscore}ax{\isacharcolon}\ {\isachardoublequote}f{\isacharparenleft}f{\isacharparenleft}n{\isacharparenright}{\isacharparenright}\ {\isacharless}\ f{\isacharparenleft}Suc{\isacharparenleft}n{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
+\isacommand{axioms}\ f{\isacharunderscore}ax{\isacharcolon}\ {\isachardoublequote}f{\isacharparenleft}f{\isacharparenleft}n{\isacharparenright}{\isacharparenright}\ {\isacharless}\ f{\isacharparenleft}Suc{\isacharparenleft}n{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isamarkuptrue%
 %
 \begin{isamarkuptext}%
 \begin{warn}
@@ -168,8 +204,14 @@
 be proved by induction on \mbox{\isa{f\ n}}. Following the recipe outlined
 above, we have to phrase the proposition as follows to allow induction:%
 \end{isamarkuptext}%
+\isamarkupfalse%
+\isacommand{lemma}\ f{\isacharunderscore}incr{\isacharunderscore}lem{\isacharcolon}\ {\isachardoublequote}{\isasymforall}i{\isachardot}\ k\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isachardoublequote}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
 \isamarkuptrue%
-\isacommand{lemma}\ f{\isacharunderscore}incr{\isacharunderscore}lem{\isacharcolon}\ {\isachardoublequote}{\isasymforall}i{\isachardot}\ k\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isachardoublequote}\isamarkupfalse%
 %
 \begin{isamarkuptxt}%
 \noindent
@@ -177,8 +219,8 @@
 the same general induction method as for recursion induction (see
 \S\ref{sec:recdef-induction}):%
 \end{isamarkuptxt}%
-\isamarkuptrue%
-\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ k\ rule{\isacharcolon}\ nat{\isacharunderscore}less{\isacharunderscore}induct{\isacharparenright}\isamarkupfalse%
+\isamarkupfalse%
+\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ k\ rule{\isacharcolon}\ nat{\isacharunderscore}less{\isacharunderscore}induct{\isacharparenright}\isamarkuptrue%
 %
 \begin{isamarkuptxt}%
 \noindent
@@ -190,12 +232,12 @@
 distinction on \isa{i}. The case \isa{i\ {\isacharequal}\ {\isadigit{0}}} is trivial and we focus on
 the other case:%
 \end{isamarkuptxt}%
-\isamarkuptrue%
+\isamarkupfalse%
 \isacommand{apply}{\isacharparenleft}rule\ allI{\isacharparenright}\isanewline
 \isamarkupfalse%
 \isacommand{apply}{\isacharparenleft}case{\isacharunderscore}tac\ i{\isacharparenright}\isanewline
 \ \isamarkupfalse%
-\isacommand{apply}{\isacharparenleft}simp{\isacharparenright}\isamarkupfalse%
+\isacommand{apply}{\isacharparenleft}simp{\isacharparenright}\isamarkuptrue%
 %
 \begin{isamarkuptxt}%
 \begin{isabelle}%
@@ -203,8 +245,15 @@
 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}{\isasymforall}m{\isacharless}n{\isachardot}\ {\isasymforall}i{\isachardot}\ m\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isacharsemicolon}\ i\ {\isacharequal}\ Suc\ nat{\isasymrbrakk}\ {\isasymLongrightarrow}\ n\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i%
 \end{isabelle}%
 \end{isamarkuptxt}%
+\isamarkupfalse%
+\isacommand{by}{\isacharparenleft}blast\ intro{\isacharbang}{\isacharcolon}\ f{\isacharunderscore}ax\ Suc{\isacharunderscore}leI\ intro{\isacharcolon}\ le{\isacharunderscore}less{\isacharunderscore}trans{\isacharparenright}%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
 \isamarkuptrue%
-\isacommand{by}{\isacharparenleft}blast\ intro{\isacharbang}{\isacharcolon}\ f{\isacharunderscore}ax\ Suc{\isacharunderscore}leI\ intro{\isacharcolon}\ le{\isacharunderscore}less{\isacharunderscore}trans{\isacharparenright}\isamarkupfalse%
 %
 \begin{isamarkuptext}%
 \noindent
@@ -235,17 +284,29 @@
 
 The desired result, \isa{i\ {\isasymle}\ f\ i}, follows from \isa{f{\isacharunderscore}incr{\isacharunderscore}lem}:%
 \end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemmas}\ f{\isacharunderscore}incr\ {\isacharequal}\ f{\isacharunderscore}incr{\isacharunderscore}lem{\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ OF\ refl{\isacharbrackright}\isamarkupfalse%
+\isamarkupfalse%
+\isacommand{lemmas}\ f{\isacharunderscore}incr\ {\isacharequal}\ f{\isacharunderscore}incr{\isacharunderscore}lem{\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ OF\ refl{\isacharbrackright}\isamarkuptrue%
 %
 \begin{isamarkuptext}%
 \noindent
 The final \isa{refl} gets rid of the premise \isa{{\isacharquery}k\ {\isacharequal}\ f\ {\isacharquery}i}. 
 We could have included this derivation in the original statement of the lemma:%
 \end{isamarkuptext}%
+\isamarkupfalse%
+\isacommand{lemma}\ f{\isacharunderscore}incr{\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ OF\ refl{\isacharbrackright}{\isacharcolon}\ {\isachardoublequote}{\isasymforall}i{\isachardot}\ k\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isachardoublequote}%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
+%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
 \isamarkuptrue%
-\isacommand{lemma}\ f{\isacharunderscore}incr{\isacharbrackleft}rule{\isacharunderscore}format{\isacharcomma}\ OF\ refl{\isacharbrackright}{\isacharcolon}\ {\isachardoublequote}{\isasymforall}i{\isachardot}\ k\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isachardoublequote}\isamarkupfalse%
-\isamarkupfalse%
 %
 \begin{isamarkuptext}%
 \begin{exercise}
@@ -292,10 +353,16 @@
 available for \isa{nat} and want to derive complete induction.  We
 must generalize the statement as shown:%
 \end{isamarkuptext}%
-\isamarkuptrue%
+\isamarkupfalse%
 \isacommand{lemma}\ induct{\isacharunderscore}lem{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isasymAnd}n{\isacharcolon}{\isacharcolon}nat{\isachardot}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m\ {\isasymLongrightarrow}\ P\ n{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m{\isachardoublequote}\isanewline
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
 \isamarkupfalse%
-\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ n{\isacharparenright}\isamarkupfalse%
+\isacommand{apply}{\isacharparenleft}induct{\isacharunderscore}tac\ n{\isacharparenright}\isamarkuptrue%
 %
 \begin{isamarkuptxt}%
 \noindent
@@ -303,10 +370,17 @@
 hypothesis and case \isa{m\ {\isacharequal}\ n} follows from the assumption, again using
 the induction hypothesis:%
 \end{isamarkuptxt}%
-\ \isamarkuptrue%
+\ \isamarkupfalse%
 \isacommand{apply}{\isacharparenleft}blast{\isacharparenright}\isanewline
 \isamarkupfalse%
-\isacommand{by}{\isacharparenleft}blast\ elim{\isacharcolon}\ less{\isacharunderscore}SucE{\isacharparenright}\isamarkupfalse%
+\isacommand{by}{\isacharparenleft}blast\ elim{\isacharcolon}\ less{\isacharunderscore}SucE{\isacharparenright}%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+\isamarkuptrue%
 %
 \begin{isamarkuptext}%
 \noindent
@@ -322,10 +396,23 @@
 happens automatically when we add the lemma as a new premise to the
 desired goal:%
 \end{isamarkuptext}%
-\isamarkuptrue%
+\isamarkupfalse%
 \isacommand{theorem}\ nat{\isacharunderscore}less{\isacharunderscore}induct{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isasymAnd}n{\isacharcolon}{\isacharcolon}nat{\isachardot}\ {\isasymforall}m{\isacharless}n{\isachardot}\ P\ m\ {\isasymLongrightarrow}\ P\ n{\isacharparenright}\ {\isasymLongrightarrow}\ P\ n{\isachardoublequote}\isanewline
+%
+\isadelimproof
+%
+\endisadelimproof
+%
+\isatagproof
 \isamarkupfalse%
-\isacommand{by}{\isacharparenleft}insert\ induct{\isacharunderscore}lem{\isacharcomma}\ blast{\isacharparenright}\isamarkupfalse%
+\isacommand{by}{\isacharparenleft}insert\ induct{\isacharunderscore}lem{\isacharcomma}\ blast{\isacharparenright}%
+\endisatagproof
+{\isafoldproof}%
+%
+\isadelimproof
+%
+\endisadelimproof
+\isamarkuptrue%
 %
 \begin{isamarkuptext}%
 HOL already provides the mother of
@@ -334,8 +421,19 @@
 a special case of \isa{wf{\isacharunderscore}induct} where \isa{r} is \isa{{\isacharless}} on
 \isa{nat}. The details can be found in theory \isa{Wellfounded_Recursion}.%
 \end{isamarkuptext}%
-\isamarkuptrue%
-\isamarkupfalse%
+%
+\isadelimtheory
+%
+\endisadelimtheory
+%
+\isatagtheory
+%
+\endisatagtheory
+{\isafoldtheory}%
+%
+\isadelimtheory
+%
+\endisadelimtheory
 \end{isabellebody}%
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