1.1 --- a/doc-src/TutorialI/Inductive/document/Star.tex Mon Dec 11 20:11:57 2000 +0100
1.2 +++ b/doc-src/TutorialI/Inductive/document/Star.tex Tue Dec 12 11:57:33 2000 +0100
1.3 @@ -51,9 +51,9 @@
1.4 To prove transitivity, we need rule induction, i.e.\ theorem
1.5 \isa{rtc{\isachardot}induct}:
1.6 \begin{isabelle}%
1.7 -\ \ \ \ \ {\isacharparenleft}{\isacharquery}xb{\isacharcomma}\ {\isacharquery}xa{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}\ {\isasymLongrightarrow}\isanewline
1.8 -\ \ \ \ \ {\isacharparenleft}{\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ x{\isacharparenright}\ {\isasymLongrightarrow}\isanewline
1.9 -\ \ \ \ \ {\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%
1.10 +\ \ \ \ \ {\isasymlbrakk}{\isacharparenleft}{\isacharquery}xb{\isacharcomma}\ {\isacharquery}xa{\isacharparenright}\ {\isasymin}\ {\isacharquery}r{\isacharasterisk}{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ {\isacharquery}P\ x\ x{\isacharsemicolon}\isanewline
1.11 +\ \ \ \ \ \ \ \ {\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
1.12 +\ \ \ \ \ {\isasymLongrightarrow}\ {\isacharquery}P\ {\isacharquery}xb\ {\isacharquery}xa%
1.13 \end{isabelle}
1.14 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,
1.15 i.e.\ if \isa{{\isacharquery}P} holds for the conclusion provided it holds for the
1.16 @@ -110,9 +110,8 @@
1.17 \begin{isabelle}%
1.18 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\isanewline
1.19 \ {\isadigit{2}}{\isachardot}\ {\isasymAnd}x\ y\ za{\isachardot}\isanewline
1.20 -\ \ \ \ \ \ \ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}\ {\isasymin}\ r\ {\isasymLongrightarrow}\isanewline
1.21 -\ \ \ \ \ \ \ {\isacharparenleft}y{\isacharcomma}\ za{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymLongrightarrow}\isanewline
1.22 -\ \ \ \ \ \ \ {\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}%
1.23 +\ \ \ \ \ \ \ {\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
1.24 +\ \ \ \ \ \ \ {\isasymLongrightarrow}\ {\isacharparenleft}za{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}\ {\isasymlongrightarrow}\ {\isacharparenleft}x{\isacharcomma}\ z{\isacharparenright}\ {\isasymin}\ r{\isacharasterisk}%
1.25 \end{isabelle}%
1.26 \end{isamarkuptxt}%
1.27 \ \isacommand{apply}{\isacharparenleft}blast{\isacharparenright}\isanewline
1.28 @@ -157,7 +156,7 @@
1.29 \begin{exercise}\label{ex:converse-rtc-step}
1.30 Show that the converse of \isa{rtc{\isacharunderscore}step} also holds:
1.31 \begin{isabelle}%
1.32 -\ \ \ \ \ {\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}%
1.33 +\ \ \ \ \ {\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}%
1.34 \end{isabelle}
1.35 \end{exercise}
1.36 \begin{exercise}