# HG changeset patch
# User paulson
# Date 976096823 -3600
# Node ID 894f845c3dbf9848f523de19e0ad751c0267400c
# Parent  322475c2cb758432a4243261171549a8fbadfc2d
auto update

diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Advanced/document/simp.tex
--- a/doc-src/TutorialI/Advanced/document/simp.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Advanced/document/simp.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -28,7 +28,7 @@
 controlled by so-called \bfindex{congruence rules}. This is the one for
 \isa{{\isasymlongrightarrow}}:
 \begin{isabelle}%
-\ \ \ \ \ P\ {\isacharequal}\ P{\isacharprime}\ {\isasymLongrightarrow}\ {\isacharparenleft}P{\isacharprime}\ {\isasymLongrightarrow}\ Q\ {\isacharequal}\ Q{\isacharprime}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymlongrightarrow}\ Q{\isacharprime}{\isacharparenright}%
+\ \ \ \ \ {\isasymlbrakk}P\ {\isacharequal}\ P{\isacharprime}{\isacharsemicolon}\ P{\isacharprime}\ {\isasymLongrightarrow}\ Q\ {\isacharequal}\ Q{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymlongrightarrow}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymlongrightarrow}\ Q{\isacharprime}{\isacharparenright}%
 \end{isabelle}
 It should be read as follows:
 In order to simplify \isa{P\ {\isasymlongrightarrow}\ Q} to \isa{P{\isacharprime}\ {\isasymlongrightarrow}\ Q{\isacharprime}},
@@ -38,15 +38,14 @@
 Here are some more examples.  The congruence rules for bounded
 quantifiers supply contextual information about the bound variable:
 \begin{isabelle}%
-\ \ \ \ \ A\ {\isacharequal}\ B\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ B\ {\isasymLongrightarrow}\ P\ x\ {\isacharequal}\ Q\ x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymforall}x{\isasymin}A{\isachardot}\ P\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymforall}x{\isasymin}B{\isachardot}\ Q\ x{\isacharparenright}%
+\ \ \ \ \ {\isasymlbrakk}A\ {\isacharequal}\ B{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ B\ {\isasymLongrightarrow}\ P\ x\ {\isacharequal}\ Q\ x{\isasymrbrakk}\isanewline
+\ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymforall}x{\isasymin}A{\isachardot}\ P\ x{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}{\isasymforall}x{\isasymin}B{\isachardot}\ Q\ x{\isacharparenright}%
 \end{isabelle}
 The congruence rule for conditional expressions supply contextual
 information for simplifying the arms:
 \begin{isabelle}%
-\ \ \ \ \ b\ {\isacharequal}\ c\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}c\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ u{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}{\isasymnot}\ c\ {\isasymLongrightarrow}\ y\ {\isacharequal}\ v{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}if\ b\ then\ x\ else\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ c\ then\ u\ else\ v{\isacharparenright}%
+\ \ \ \ \ {\isasymlbrakk}b\ {\isacharequal}\ c{\isacharsemicolon}\ c\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ u{\isacharsemicolon}\ {\isasymnot}\ c\ {\isasymLongrightarrow}\ y\ {\isacharequal}\ v{\isasymrbrakk}\isanewline
+\ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}if\ b\ then\ x\ else\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ c\ then\ u\ else\ v{\isacharparenright}%
 \end{isabelle}
 A congruence rule can also \emph{prevent} simplification of some arguments.
 Here is an alternative congruence rule for conditional expressions:
@@ -73,7 +72,7 @@
 \begin{warn}
 The congruence rule \isa{conj{\isacharunderscore}cong}
 \begin{isabelle}%
-\ \ \ \ \ P\ {\isacharequal}\ P{\isacharprime}\ {\isasymLongrightarrow}\ {\isacharparenleft}P{\isacharprime}\ {\isasymLongrightarrow}\ Q\ {\isacharequal}\ Q{\isacharprime}{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymand}\ Q{\isacharprime}{\isacharparenright}%
+\ \ \ \ \ {\isasymlbrakk}P\ {\isacharequal}\ P{\isacharprime}{\isacharsemicolon}\ P{\isacharprime}\ {\isasymLongrightarrow}\ Q\ {\isacharequal}\ Q{\isacharprime}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}P\ {\isasymand}\ Q{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}P{\isacharprime}\ {\isasymand}\ Q{\isacharprime}{\isacharparenright}%
 \end{isabelle}
 is occasionally useful but not a default rule; you have to use it explicitly.
 \end{warn}%
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/CTL/document/CTL.tex
--- a/doc-src/TutorialI/CTL/document/CTL.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/CTL/document/CTL.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -73,11 +73,12 @@
 \isacommand{apply}{\isacharparenleft}clarsimp\ simp\ add{\isacharcolon}\ af{\isacharunderscore}def\ Paths{\isacharunderscore}def{\isacharparenright}%
 \begin{isamarkuptxt}%
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ p\ {\isadigit{0}}\ {\isasymin}\ A\ {\isasymor}\isanewline
-\ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymforall}t{\isachardot}\ {\isacharparenleft}p\ {\isadigit{0}}{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymlongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymforall}p{\isachardot}\ t\ {\isacharequal}\ p\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharparenright}\ {\isasymlongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ {\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M\ {\isasymLongrightarrow}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isasymlbrakk}p\ {\isadigit{0}}\ {\isasymin}\ A\ {\isasymor}\isanewline
+\ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymforall}t{\isachardot}\ {\isacharparenleft}p\ {\isadigit{0}}{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymlongrightarrow}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymforall}p{\isachardot}\ t\ {\isacharequal}\ p\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharparenright}\ {\isasymlongrightarrow}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ {\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A%
 \end{isabelle}
 Now we eliminate the disjunction. The case \isa{p\ {\isadigit{0}}\ {\isasymin}\ A} is trivial:%
 \end{isamarkuptxt}%
@@ -91,10 +92,10 @@
 \isacommand{apply}{\isacharparenleft}clarsimp{\isacharparenright}%
 \begin{isamarkuptxt}%
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ {\isasymforall}pa{\isachardot}\ p\ {\isadigit{1}}\ {\isacharequal}\ pa\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}pa\ i{\isacharcomma}\ pa\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharparenright}\ {\isasymlongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymexists}i{\isachardot}\ pa\ i\ {\isasymin}\ A{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}p{\isachardot}\ {\isasymlbrakk}{\isasymforall}i{\isachardot}\ {\isacharparenleft}p\ i{\isacharcomma}\ p\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ {\isasymforall}pa{\isachardot}\ p\ {\isadigit{1}}\ {\isacharequal}\ pa\ {\isadigit{0}}\ {\isasymand}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ {\isacharparenleft}pa\ i{\isacharcomma}\ pa\ {\isacharparenleft}Suc\ i{\isacharparenright}{\isacharparenright}\ {\isasymin}\ M{\isacharparenright}\ {\isasymlongrightarrow}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}{\isasymexists}i{\isachardot}\ pa\ i\ {\isasymin}\ A{\isacharparenright}{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A%
 \end{isabelle}
 It merely remains to set \isa{pa} to \isa{{\isasymlambda}i{\isachardot}\ p\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}}, i.e.\ \isa{p} without its
 first element. The rest is practically automatic:%
@@ -170,10 +171,9 @@
 \noindent
 After simplification and clarification the subgoal has the following compact form
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ P\ s\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ {\isasymforall}s{\isachardot}\ P\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ \ {\isacharparenleft}path\ s\ P\ i{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}path\ s\ P\ i{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\isanewline
-\ \ \ \ \ \ \ \ P\ {\isacharparenleft}path\ s\ P\ i{\isacharparenright}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}i{\isachardot}\ {\isasymlbrakk}P\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ P\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}path\ s\ P\ i{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}path\ s\ P\ i{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\isanewline
+\ \ \ \ \ \ \ \ \ \ P\ {\isacharparenleft}path\ s\ P\ i{\isacharparenright}%
 \end{isabelle}
 and invites a proof by induction on \isa{i}:%
 \end{isamarkuptxt}%
@@ -183,15 +183,14 @@
 \noindent
 After simplification the base case boils down to
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ P\ s\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ {\isasymforall}s{\isachardot}\ P\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ {\isacharparenleft}s{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}\ {\isasymin}\ M%
+\ {\isadigit{1}}{\isachardot}\ {\isasymlbrakk}P\ s{\isacharsemicolon}\ {\isasymforall}s{\isachardot}\ P\ s\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymexists}t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}{\isasymrbrakk}\isanewline
+\ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}s{\isacharcomma}\ SOME\ t{\isachardot}\ {\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ t{\isacharparenright}\ {\isasymin}\ M%
 \end{isabelle}
 The conclusion looks exceedingly trivial: after all, \isa{t} is chosen such that \isa{{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M}
 holds. However, we first have to show that such a \isa{t} actually exists! This reasoning
 is embodied in the theorem \isa{someI{\isadigit{2}}{\isacharunderscore}ex}:
 \begin{isabelle}%
-\ \ \ \ \ {\isasymexists}a{\isachardot}\ {\isacharquery}P\ a\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ {\isasymLongrightarrow}\ {\isacharquery}Q\ x{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharquery}Q\ {\isacharparenleft}SOME\ x{\isachardot}\ {\isacharquery}P\ x{\isacharparenright}%
+\ \ \ \ \ {\isasymlbrakk}{\isasymexists}a{\isachardot}\ {\isacharquery}P\ a{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ {\isasymLongrightarrow}\ {\isacharquery}Q\ x{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}Q\ {\isacharparenleft}SOME\ x{\isachardot}\ {\isacharquery}P\ x{\isacharparenright}%
 \end{isabelle}
 When we apply this theorem as an introduction rule, \isa{{\isacharquery}P\ x} becomes
 \isa{{\isacharparenleft}s{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ M\ {\isasymand}\ P\ x} and \isa{{\isacharquery}Q\ x} becomes \isa{{\isacharparenleft}s{\isacharcomma}\ x{\isacharparenright}\ {\isasymin}\ M} and we have to prove
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/CTL/document/CTLind.tex
--- a/doc-src/TutorialI/CTL/document/CTLind.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/CTL/document/CTLind.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -121,7 +121,7 @@
 into a \isa{{\isasymAnd}p}, which would complicate matters below. As it is,
 \isa{Avoid{\isacharunderscore}in{\isacharunderscore}lfp} is now
 \begin{isabelle}%
-\ \ \ \ \ {\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ Avoid\ s\ A\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}%
+\ \ \ \ \ {\isasymlbrakk}{\isasymforall}p{\isasymin}Paths\ s{\isachardot}\ {\isasymexists}i{\isachardot}\ p\ i\ {\isasymin}\ A{\isacharsemicolon}\ t\ {\isasymin}\ Avoid\ s\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ t\ {\isasymin}\ lfp\ {\isacharparenleft}af\ A{\isacharparenright}%
 \end{isabelle}
 The main theorem is simply the corollary where \isa{t\ {\isacharequal}\ s},
 in which case the assumption \isa{t\ {\isasymin}\ Avoid\ s\ A} is trivially true
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/CTL/document/PDL.tex
--- a/doc-src/TutorialI/CTL/document/PDL.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/CTL/document/PDL.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -127,7 +127,7 @@
 \noindent
 After simplification and clarification we are left with
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}\ {\isasymLongrightarrow}\ t\ {\isasymin}\ A\ {\isasymLongrightarrow}\ x\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ t{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ t\ {\isasymin}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isasymin}\ lfp\ {\isacharparenleft}{\isasymlambda}T{\isachardot}\ A\ {\isasymunion}\ M{\isasyminverse}\ {\isacharcircum}{\isacharcircum}\ T{\isacharparenright}%
 \end{isabelle}
 This goal is proved by induction on \isa{{\isacharparenleft}s{\isacharcomma}\ t{\isacharparenright}\ {\isasymin}\ M\isactrlsup {\isacharasterisk}}. But since the model
 checker works backwards (from \isa{t} to \isa{s}), we cannot use the
@@ -135,9 +135,9 @@
 forward direction. Fortunately the converse induction theorem
 \isa{converse{\isacharunderscore}rtrancl{\isacharunderscore}induct} already exists:
 \begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ P\ b\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}y\ z{\isachardot}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r\ {\isasymLongrightarrow}\ {\isacharparenleft}z{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}\ {\isasymLongrightarrow}\ P\ z\ {\isasymLongrightarrow}\ P\ y{\isacharparenright}\ {\isasymLongrightarrow}\ P\ a%
+\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ P\ b{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ {\isasymAnd}y\ z{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}z{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}{\isacharsemicolon}\ P\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ y{\isasymrbrakk}\isanewline
+\ \ \ \ \ {\isasymLongrightarrow}\ P\ a%
 \end{isabelle}
 It says that if \isa{{\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isasymin}\ r\isactrlsup {\isacharasterisk}} and we know \isa{P\ b} then we can infer
 \isa{P\ a} provided each step backwards from a predecessor \isa{z} of
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Inductive/document/AB.tex
--- a/doc-src/TutorialI/Inductive/document/AB.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Inductive/document/AB.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -96,8 +96,8 @@
 1 on our way from 0 to 2. Formally, we appeal to the following discrete
 intermediate value theorem \isa{nat{\isadigit{0}}{\isacharunderscore}intermed{\isacharunderscore}int{\isacharunderscore}val}
 \begin{isabelle}%
-\ \ \ \ \ {\isasymforall}i{\isachardot}\ i\ {\isacharless}\ n\ {\isasymlongrightarrow}\ {\isasymbar}f\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharminus}\ f\ i{\isasymbar}\ {\isasymle}\ {\isacharhash}{\isadigit{1}}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ f\ {\isadigit{0}}\ {\isasymle}\ k\ {\isasymLongrightarrow}\ k\ {\isasymle}\ f\ n\ {\isasymLongrightarrow}\ {\isasymexists}i{\isachardot}\ i\ {\isasymle}\ n\ {\isasymand}\ f\ i\ {\isacharequal}\ k%
+\ \ \ \ \ {\isasymlbrakk}{\isasymforall}i{\isachardot}\ i\ {\isacharless}\ n\ {\isasymlongrightarrow}\ {\isasymbar}f\ {\isacharparenleft}i\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}\ {\isacharminus}\ f\ i{\isasymbar}\ {\isasymle}\ {\isacharhash}{\isadigit{1}}{\isacharsemicolon}\ f\ {\isadigit{0}}\ {\isasymle}\ k{\isacharsemicolon}\ k\ {\isasymle}\ f\ n{\isasymrbrakk}\isanewline
+\ \ \ \ \ {\isasymLongrightarrow}\ {\isasymexists}i{\isachardot}\ i\ {\isasymle}\ n\ {\isasymand}\ f\ i\ {\isacharequal}\ k%
 \end{isabelle}
 where \isa{f} is of type \isa{nat\ {\isasymRightarrow}\ int}, \isa{int} are the integers,
 \isa{abs} is the absolute value function, and \isa{{\isacharhash}{\isadigit{1}}} is the
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Inductive/document/Advanced.tex
--- a/doc-src/TutorialI/Inductive/document/Advanced.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Inductive/document/Advanced.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -36,7 +36,7 @@
 We completely forgot about "rule inversion". 
 
 \begin{isabelle}%
-\ \ \ \ \ a\ {\isasymin}\ even\ {\isasymLongrightarrow}\ {\isacharparenleft}a\ {\isacharequal}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}n{\isachardot}\ a\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymLongrightarrow}\ n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ P%
+\ \ \ \ \ {\isasymlbrakk}a\ {\isasymin}\ even{\isacharsemicolon}\ a\ {\isacharequal}\ {\isadigit{0}}\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}a\ {\isacharequal}\ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharsemicolon}\ n\ {\isasymin}\ even{\isasymrbrakk}\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P%
 \end{isabelle}
 \rulename{even.cases}
 
@@ -50,7 +50,7 @@
 \isacommand{thm}\ Suc{\isacharunderscore}Suc{\isacharunderscore}cases%
 \begin{isamarkuptext}%
 \begin{isabelle}%
-\ \ \ \ \ Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even\ {\isasymLongrightarrow}\ {\isacharparenleft}n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ P%
+\ \ \ \ \ {\isasymlbrakk}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isasymin}\ even{\isacharsemicolon}\ n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P%
 \end{isabelle}
 \rulename{Suc_Suc_cases}
 
@@ -65,7 +65,7 @@
 this is what we get:
 
 \begin{isabelle}%
-\ \ \ \ \ Apply\ f\ args\ {\isasymin}\ gterms\ F\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F\ {\isasymLongrightarrow}\ f\ {\isasymin}\ F\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ P%
+\ \ \ \ \ {\isasymlbrakk}Apply\ f\ args\ {\isasymin}\ gterms\ F{\isacharsemicolon}\ {\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F{\isacharsemicolon}\ f\ {\isasymin}\ F{\isasymrbrakk}\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P%
 \end{isabelle}
 \rulename{gterm_Apply_elim}%
 \end{isamarkuptext}%
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Inductive/document/Even.tex
--- a/doc-src/TutorialI/Inductive/document/Even.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Inductive/document/Even.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -31,7 +31,7 @@
 \rulename{even.step}
 
 \begin{isabelle}%
-\ \ \ \ \ xa\ {\isasymin}\ even\ {\isasymLongrightarrow}\ P\ {\isadigit{0}}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isasymAnd}n{\isachardot}\ n\ {\isasymin}\ even\ {\isasymLongrightarrow}\ P\ n\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isasymLongrightarrow}\ P\ xa%
+\ \ \ \ \ {\isasymlbrakk}xa\ {\isasymin}\ even{\isacharsemicolon}\ P\ {\isadigit{0}}{\isacharsemicolon}\ {\isasymAnd}n{\isachardot}\ {\isasymlbrakk}n\ {\isasymin}\ even{\isacharsemicolon}\ P\ n{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ n{\isacharparenright}{\isacharparenright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ xa%
 \end{isabelle}
 \rulename{even.induct}
 
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Inductive/document/Star.tex
--- a/doc-src/TutorialI/Inductive/document/Star.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Inductive/document/Star.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -51,9 +51,9 @@
 To prove transitivity, we need rule induction, i.e.\ theorem
 \isa{rtc{\isachardot}induct}:
 \begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}{\isacharquery}xb{\isacharcomma}\ {\isacharquery}xa{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ x{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}x\ y\ z{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ {\isacharquery}r\ {\isasymLongrightarrow}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ y\ z\ {\isasymLongrightarrow}\ {\isacharquery}P\ x\ z{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}xb\ {\isacharquery}xa%
+\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}{\isacharquery}xb{\isacharcomma}\ {\isacharquery}xa{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ x{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ {\isasymAnd}x\ y\ z{\isachardot}\ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}{\isacharsemicolon}\ {\isacharquery}P\ y\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}P\ x\ z{\isasymrbrakk}\isanewline
+\ \ \ \ \ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}xb\ {\isacharquery}xa%
 \end{isabelle}
 It says that \isa{{\isacharquery}P} holds for an arbitrary pair \isa{{\isacharparenleft}{\isacharquery}xb{\isacharcomma}{\isacharquery}xa{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}} if \isa{{\isacharquery}P} is preserved by all rules of the inductive definition,
 i.e.\ if \isa{{\isacharquery}P} holds for the conclusion provided it holds for the
@@ -110,9 +110,8 @@
 \begin{isabelle}%
 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\isanewline
 \ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y\ za{\isachardot}\isanewline
-\ \ \ \ \ \ \ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ {\isacharparenleft}y{\isacharcomma}\ za{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ \ \ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
+\ \ \ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}\ za{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isacharsemicolon}\ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
 \end{isabelle}%
 \end{isamarkuptxt}%
 \ \isacommand{apply}{\isacharparenleft}blast{\isacharparenright}\isanewline
@@ -157,7 +156,7 @@
 \begin{exercise}\label{ex:converse-rtc-step}
 Show that the converse of \isa{rtc{\isacharunderscore}step} also holds:
 \begin{isabelle}%
-\ \ \ \ \ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
+\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}{\isacharsemicolon}\ {\isacharparenleft}y{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
 \end{isabelle}
 \end{exercise}
 \begin{exercise}
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Misc/document/AdvancedInd.tex
--- a/doc-src/TutorialI/Misc/document/AdvancedInd.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Misc/document/AdvancedInd.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -95,7 +95,7 @@
 \isacommand{lemmas}\ myrule\ {\isacharequal}\ simple{\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}%
 \begin{isamarkuptext}%
 \noindent
-yielding \isa{A\ y\ {\isasymLongrightarrow}\ B\ y\ {\isasymLongrightarrow}\ B\ y\ {\isasymand}\ A\ y}.
+yielding \isa{{\isasymlbrakk}A\ y{\isacharsemicolon}\ B\ y{\isasymrbrakk}\ {\isasymLongrightarrow}\ B\ y\ {\isasymand}\ A\ y}.
 You can go one step further and include these derivations already in the
 statement of your original lemma, thus avoiding the intermediate step:%
 \end{isamarkuptext}%
@@ -182,7 +182,8 @@
 \begin{isamarkuptxt}%
 \begin{isabelle}%
 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}n\ i\ nat{\isachardot}\isanewline
-\ \ \ \ \ \ \ {\isasymforall}m{\isachardot}\ m\ {\isacharless}\ n\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ m\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isacharparenright}\ {\isasymLongrightarrow}\ i\ {\isacharequal}\ Suc\ nat\ {\isasymLongrightarrow}\ n\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i%
+\ \ \ \ \ \ \ {\isasymlbrakk}{\isasymforall}m{\isachardot}\ m\ {\isacharless}\ n\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymforall}i{\isachardot}\ m\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i{\isacharparenright}{\isacharsemicolon}\ i\ {\isacharequal}\ Suc\ nat{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ {\isasymLongrightarrow}\ n\ {\isacharequal}\ f\ i\ {\isasymlongrightarrow}\ i\ {\isasymle}\ f\ i%
 \end{isabelle}%
 \end{isamarkuptxt}%
 \isacommand{by}{\isacharparenleft}blast\ intro{\isacharbang}{\isacharcolon}\ f{\isacharunderscore}ax\ Suc{\isacharunderscore}leI\ intro{\isacharcolon}\ le{\isacharunderscore}less{\isacharunderscore}trans{\isacharparenright}%
@@ -195,7 +196,7 @@
 proved as follows. From \isa{f{\isacharunderscore}ax} we have \isa{f\ {\isacharparenleft}f\ j{\isacharparenright}\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}}
 (1) which implies \isa{f\ j\ {\isasymle}\ f\ {\isacharparenleft}f\ j{\isacharparenright}} (by the induction hypothesis).
 Using (1) once more we obtain \isa{f\ j\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}} (2) by transitivity
-(\isa{le{\isacharunderscore}less{\isacharunderscore}trans}: \isa{i\ {\isasymle}\ j\ {\isasymLongrightarrow}\ j\ {\isacharless}\ k\ {\isasymLongrightarrow}\ i\ {\isacharless}\ k}).
+(\isa{le{\isacharunderscore}less{\isacharunderscore}trans}: \isa{{\isasymlbrakk}i\ {\isasymle}\ j{\isacharsemicolon}\ j\ {\isacharless}\ k{\isasymrbrakk}\ {\isasymLongrightarrow}\ i\ {\isacharless}\ k}).
 Using the induction hypothesis once more we obtain \isa{j\ {\isasymle}\ f\ j}
 which, together with (2) yields \isa{j\ {\isacharless}\ f\ {\isacharparenleft}Suc\ j{\isacharparenright}} (again by
 \isa{le{\isacharunderscore}less{\isacharunderscore}trans}).
@@ -267,7 +268,7 @@
 \noindent
 The elimination rule \isa{less{\isacharunderscore}SucE} expresses the case distinction:
 \begin{isabelle}%
-\ \ \ \ \ m\ {\isacharless}\ Suc\ n\ {\isasymLongrightarrow}\ {\isacharparenleft}m\ {\isacharless}\ n\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}m\ {\isacharequal}\ n\ {\isasymLongrightarrow}\ P{\isacharparenright}\ {\isasymLongrightarrow}\ P%
+\ \ \ \ \ {\isasymlbrakk}m\ {\isacharless}\ Suc\ n{\isacharsemicolon}\ m\ {\isacharless}\ n\ {\isasymLongrightarrow}\ P{\isacharsemicolon}\ m\ {\isacharequal}\ n\ {\isasymLongrightarrow}\ P{\isasymrbrakk}\ {\isasymLongrightarrow}\ P%
 \end{isabelle}
 
 Now it is straightforward to derive the original version of
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Misc/document/simp.tex
--- a/doc-src/TutorialI/Misc/document/simp.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Misc/document/simp.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -299,8 +299,8 @@
 In contrast to splitting the conclusion, this actually creates two
 separate subgoals (which are solved by \isa{simp{\isacharunderscore}all}):
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ ys\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymLongrightarrow}\ xs\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymlbrakk}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharat}\ ys\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}\isanewline
+\ {\isadigit{2}}{\isachardot}\ {\isasymlbrakk}xs\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}{\isacharsemicolon}\ ys\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isasymrbrakk}\ {\isasymLongrightarrow}\ xs\ {\isacharat}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymnoteq}\ {\isacharbrackleft}{\isacharbrackright}%
 \end{isabelle}
 If you need to split both in the assumptions and the conclusion,
 use $t$\isa{{\isachardot}splits} which subsumes $t$\isa{{\isachardot}split} and
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Recdef/document/Nested2.tex
--- a/doc-src/TutorialI/Recdef/document/Nested2.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Recdef/document/Nested2.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -61,9 +61,8 @@
 \isacommand{recdef} has been supplied with the congruence theorem
 \isa{map{\isacharunderscore}cong}:
 \begin{isabelle}%
-\ \ \ \ \ xs\ {\isacharequal}\ ys\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ set\ ys\ {\isasymLongrightarrow}\ f\ x\ {\isacharequal}\ g\ x{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
-\ \ \ \ \ map\ f\ xs\ {\isacharequal}\ map\ g\ ys%
+\ \ \ \ \ {\isasymlbrakk}xs\ {\isacharequal}\ ys{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ set\ ys\ {\isasymLongrightarrow}\ f\ x\ {\isacharequal}\ g\ x{\isasymrbrakk}\isanewline
+\ \ \ \ \ {\isasymLongrightarrow}\ map\ f\ xs\ {\isacharequal}\ map\ g\ ys%
 \end{isabelle}
 Its second premise expresses (indirectly) that the second argument of
 \isa{map} is only applied to elements of its third argument. Congruence
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Types/document/Axioms.tex
--- a/doc-src/TutorialI/Types/document/Axioms.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Types/document/Axioms.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -68,8 +68,8 @@
 specialized to type \isa{bool}, as subgoals:
 \begin{isabelle}%
 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isasymColon}bool{\isachardot}\ x\ {\isacharless}{\isacharless}{\isacharequal}\ x\isanewline
-\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}{\isacharparenleft}x{\isasymColon}bool{\isacharparenright}\ {\isacharparenleft}y{\isasymColon}bool{\isacharparenright}\ z{\isasymColon}bool{\isachardot}\ x\ {\isacharless}{\isacharless}{\isacharequal}\ y\ {\isasymLongrightarrow}\ y\ {\isacharless}{\isacharless}{\isacharequal}\ z\ {\isasymLongrightarrow}\ x\ {\isacharless}{\isacharless}{\isacharequal}\ z\isanewline
-\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}{\isacharparenleft}x{\isasymColon}bool{\isacharparenright}\ y{\isasymColon}bool{\isachardot}\ x\ {\isacharless}{\isacharless}{\isacharequal}\ y\ {\isasymLongrightarrow}\ y\ {\isacharless}{\isacharless}{\isacharequal}\ x\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ y\isanewline
+\ {\isadigit{2}}{\isachardot}\ {\isasymAnd}{\isacharparenleft}x{\isasymColon}bool{\isacharparenright}\ {\isacharparenleft}y{\isasymColon}bool{\isacharparenright}\ z{\isasymColon}bool{\isachardot}\ {\isasymlbrakk}x\ {\isacharless}{\isacharless}{\isacharequal}\ y{\isacharsemicolon}\ y\ {\isacharless}{\isacharless}{\isacharequal}\ z{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isacharless}{\isacharless}{\isacharequal}\ z\isanewline
+\ {\isadigit{3}}{\isachardot}\ {\isasymAnd}{\isacharparenleft}x{\isasymColon}bool{\isacharparenright}\ y{\isasymColon}bool{\isachardot}\ {\isasymlbrakk}x\ {\isacharless}{\isacharless}{\isacharequal}\ y{\isacharsemicolon}\ y\ {\isacharless}{\isacharless}{\isacharequal}\ x{\isasymrbrakk}\ {\isasymLongrightarrow}\ x\ {\isacharequal}\ y\isanewline
 \ {\isadigit{4}}{\isachardot}\ {\isasymAnd}{\isacharparenleft}x{\isasymColon}bool{\isacharparenright}\ y{\isasymColon}bool{\isachardot}\ {\isacharparenleft}x\ {\isacharless}{\isacharless}\ y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}{\isacharless}{\isacharequal}\ y\ {\isasymand}\ x\ {\isasymnoteq}\ y{\isacharparenright}%
 \end{isabelle}
 Fortunately, the proof is easy for blast, once we have unfolded the definitions
diff -r 322475c2cb75 -r 894f845c3dbf doc-src/TutorialI/Types/document/Typedef.tex
--- a/doc-src/TutorialI/Types/document/Typedef.tex	Wed Dec 06 10:24:44 2000 +0100
+++ b/doc-src/TutorialI/Types/document/Typedef.tex	Wed Dec 06 11:00:23 2000 +0100
@@ -204,7 +204,7 @@
 Expanding \isa{three{\isacharunderscore}def} yields the premise \isa{n\ {\isasymle}\ {\isadigit{2}}}. Repeated
 elimination with \isa{le{\isacharunderscore}SucE}
 \begin{isabelle}%
-\ \ \ \ \ {\isacharquery}m\ {\isasymle}\ Suc\ {\isacharquery}n\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isacharquery}m\ {\isasymle}\ {\isacharquery}n\ {\isasymLongrightarrow}\ {\isacharquery}R{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharparenleft}{\isacharquery}m\ {\isacharequal}\ Suc\ {\isacharquery}n\ {\isasymLongrightarrow}\ {\isacharquery}R{\isacharparenright}\ {\isasymLongrightarrow}\ {\isacharquery}R%
+\ \ \ \ \ {\isasymlbrakk}{\isacharquery}m\ {\isasymle}\ Suc\ {\isacharquery}n{\isacharsemicolon}\ {\isacharquery}m\ {\isasymle}\ {\isacharquery}n\ {\isasymLongrightarrow}\ {\isacharquery}R{\isacharsemicolon}\ {\isacharquery}m\ {\isacharequal}\ Suc\ {\isacharquery}n\ {\isasymLongrightarrow}\ {\isacharquery}R{\isasymrbrakk}\ {\isasymLongrightarrow}\ {\isacharquery}R%
 \end{isabelle}
 reduces \isa{n\ {\isasymle}\ {\isadigit{2}}} to the three cases \isa{n\ {\isasymle}\ {\isadigit{0}}}, \isa{n\ {\isacharequal}\ {\isadigit{1}}} and
 \isa{n\ {\isacharequal}\ {\isadigit{2}}} which are trivial for simplification:%
@@ -231,10 +231,10 @@
 \isacommand{apply}{\isacharparenleft}rule\ cases{\isacharunderscore}lemma{\isacharparenright}%
 \begin{isamarkuptxt}%
 \begin{isabelle}%
-\ {\isadigit{1}}{\isachardot}\ P\ A\ {\isasymLongrightarrow}\ P\ B\ {\isasymLongrightarrow}\ P\ C\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ {\isadigit{0}}{\isacharparenright}\isanewline
-\ {\isadigit{2}}{\isachardot}\ P\ A\ {\isasymLongrightarrow}\ P\ B\ {\isasymLongrightarrow}\ P\ C\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ {\isadigit{1}}{\isacharparenright}\isanewline
-\ {\isadigit{3}}{\isachardot}\ P\ A\ {\isasymLongrightarrow}\ P\ B\ {\isasymLongrightarrow}\ P\ C\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ {\isadigit{2}}{\isacharparenright}\isanewline
-\ {\isadigit{4}}{\isachardot}\ P\ A\ {\isasymLongrightarrow}\ P\ B\ {\isasymLongrightarrow}\ P\ C\ {\isasymLongrightarrow}\ Rep{\isacharunderscore}three\ x\ {\isasymin}\ three%
+\ {\isadigit{1}}{\isachardot}\ {\isasymlbrakk}P\ A{\isacharsemicolon}\ P\ B{\isacharsemicolon}\ P\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ {\isadigit{0}}{\isacharparenright}\isanewline
+\ {\isadigit{2}}{\isachardot}\ {\isasymlbrakk}P\ A{\isacharsemicolon}\ P\ B{\isacharsemicolon}\ P\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ {\isadigit{1}}{\isacharparenright}\isanewline
+\ {\isadigit{3}}{\isachardot}\ {\isasymlbrakk}P\ A{\isacharsemicolon}\ P\ B{\isacharsemicolon}\ P\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ P\ {\isacharparenleft}Abs{\isacharunderscore}three\ {\isadigit{2}}{\isacharparenright}\isanewline
+\ {\isadigit{4}}{\isachardot}\ {\isasymlbrakk}P\ A{\isacharsemicolon}\ P\ B{\isacharsemicolon}\ P\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ Rep{\isacharunderscore}three\ x\ {\isasymin}\ three%
 \end{isabelle}
 The resulting subgoals are easily solved by simplification:%
 \end{isamarkuptxt}%