--- a/doc-src/TutorialI/Inductive/document/Advanced.tex Fri Jan 12 16:05:12 2001 +0100
+++ b/doc-src/TutorialI/Inductive/document/Advanced.tex Fri Jan 12 16:07:20 2001 +0100
@@ -17,24 +17,17 @@
\isanewline
\isacommand{lemma}\ gterms{\isacharunderscore}mono{\isacharcolon}\ {\isachardoublequote}F{\isasymsubseteq}G\ {\isasymLongrightarrow}\ gterms\ F\ {\isasymsubseteq}\ gterms\ G{\isachardoublequote}\isanewline
\isacommand{apply}\ clarify\isanewline
-\isacommand{apply}\ {\isacharparenleft}erule\ gterms{\isachardot}induct{\isacharparenright}\isanewline
+\isacommand{apply}\ {\isacharparenleft}erule\ gterms{\isachardot}induct{\isacharparenright}%
+\begin{isamarkuptxt}%
+\begin{isabelle}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
+\ \ \ \ \ \ \ {\isasymlbrakk}F\ {\isasymsubseteq}\ G{\isacharsemicolon}\ {\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F\ {\isasymand}\ t\ {\isasymin}\ gterms\ G{\isacharsemicolon}\ f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ G%
+\end{isabelle}%
+\end{isamarkuptxt}%
\isacommand{apply}\ blast\isanewline
\isacommand{done}%
\begin{isamarkuptext}%
-The situation after induction
-
-proof\ {\isacharparenleft}prove{\isacharparenright}{\isacharcolon}\ step\ {\isadigit{2}}\isanewline
-\isanewline
-goal\ {\isacharparenleft}lemma{\isacharparenright}{\isacharcolon}\isanewline
-F\ {\isasymsubseteq}\ G\ {\isasymLongrightarrow}\ gterms\ F\ {\isasymsubseteq}\ gterms\ G\isanewline
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
-\ \ \ \ \ \ \ {\isasymlbrakk}F\ {\isasymsubseteq}\ G{\isacharsemicolon}\ {\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F\ {\isasymand}\ t\ {\isasymin}\ gterms\ G{\isacharsemicolon}\ f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ G%
-\end{isamarkuptext}%
-%
-\begin{isamarkuptext}%
-We completely forgot about "rule inversion".
-
\begin{isabelle}%
\ \ \ \ \ {\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}
@@ -71,25 +64,20 @@
\end{isamarkuptext}%
\isacommand{lemma}\ gterms{\isacharunderscore}IntI\ {\isacharbrackleft}rule{\isacharunderscore}format{\isacharbrackright}{\isacharcolon}\isanewline
\ \ \ \ \ {\isachardoublequote}t\ {\isasymin}\ gterms\ F\ {\isasymLongrightarrow}\ t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F{\isasyminter}G{\isacharparenright}{\isachardoublequote}\isanewline
-\isacommand{apply}\ {\isacharparenleft}erule\ gterms{\isachardot}induct{\isacharparenright}\isanewline
+\isacommand{apply}\ {\isacharparenleft}erule\ gterms{\isachardot}induct{\isacharparenright}%
+\begin{isamarkuptxt}%
+\begin{isabelle}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}args\ f{\isachardot}\isanewline
+\ \ \ \ \ \ \ {\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ t\ {\isasymin}\ gterms\ F\ {\isasymand}\ {\isacharparenleft}t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ \ \ f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\isanewline
+\ \ \ \ \ \ \ \ \ \ Apply\ f\ args\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}%
+\end{isabelle}%
+\end{isamarkuptxt}%
\isacommand{apply}\ blast\isanewline
\isacommand{done}%
\begin{isamarkuptext}%
-Subgoal after induction. How would we cope without rule inversion?
-
-pr(latex xsymbols symbols)
-
-proof\ {\isacharparenleft}prove{\isacharparenright}{\isacharcolon}\ step\ {\isadigit{1}}\isanewline
-\isanewline
-goal\ {\isacharparenleft}lemma\ gterms{\isacharunderscore}IntI{\isacharparenright}{\isacharcolon}\isanewline
-t\ {\isasymin}\ gterms\ F\ {\isasymLongrightarrow}\ t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}\isanewline
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}args\ f{\isachardot}\isanewline
-\ \ \ \ \ \ \ {\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\ t\ {\isasymin}\ gterms\ F\ {\isasymand}\ {\isacharparenleft}t\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ t\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ f\ {\isasymin}\ F{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ G\ {\isasymlongrightarrow}\ Apply\ f\ args\ {\isasymin}\ gterms\ {\isacharparenleft}F\ {\isasyminter}\ G{\isacharparenright}%
-\end{isamarkuptext}%
-%
-\begin{isamarkuptext}%
\begin{isabelle}%
\ \ \ \ \ mono\ f\ {\isasymLongrightarrow}\ f\ {\isacharparenleft}A\ {\isasyminter}\ B{\isacharparenright}\ {\isasymsubseteq}\ f\ A\ {\isasyminter}\ f\ B%
\end{isabelle}
@@ -126,50 +114,59 @@
\isakeyword{monos}\ lists{\isacharunderscore}mono\isanewline
\isanewline
\isacommand{lemma}\ {\isachardoublequote}well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymsubseteq}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isachardoublequote}\isanewline
-\isacommand{apply}\ clarify\isanewline
-\isacommand{apply}\ {\isacharparenleft}erule\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isachardot}induct{\isacharparenright}\isanewline
-\isacommand{apply}\ auto\isanewline
-\isacommand{done}%
-\begin{isamarkuptext}%
-The situation after clarify (note the induction hypothesis!)
-
-pr(latex xsymbols symbols)
-
-proof\ {\isacharparenleft}prove{\isacharparenright}{\isacharcolon}\ step\ {\isadigit{2}}\isanewline
-\isanewline
-goal\ {\isacharparenleft}lemma{\isacharparenright}{\isacharcolon}\isanewline
-well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymsubseteq}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\isanewline
+\isacommand{apply}\ clarify%
+\begin{isamarkuptxt}%
+The situation after clarify
+\begin{isabelle}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymLongrightarrow}\isanewline
+\ \ \ \ \ \ \ \ x\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity%
+\end{isabelle}%
+\end{isamarkuptxt}%
+\isacommand{apply}\ {\isacharparenleft}erule\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isachardot}induct{\isacharparenright}%
+\begin{isamarkuptxt}%
+note the induction hypothesis!
+\begin{isabelle}%
\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
\ \ \ \ \ \ \ {\isasymlbrakk}{\isasymforall}t{\isasymin}set\ args{\isachardot}\isanewline
-\ \ \ \ \ \ \ \ \ \ \ t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymand}\ t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\ {\isasymand}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ t\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity{\isacharsemicolon}\isanewline
\ \ \ \ \ \ \ \ \ \ length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity%
-\end{isamarkuptext}%
+\end{isabelle}%
+\end{isamarkuptxt}%
+\isacommand{apply}\ auto\isanewline
+\isacommand{done}\isanewline
+\isanewline
+\isanewline
+\isanewline
\isacommand{lemma}\ {\isachardoublequote}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasymsubseteq}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isachardoublequote}\isanewline
-\isacommand{apply}\ clarify\isanewline
-\isacommand{apply}\ {\isacharparenleft}erule\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}{\isachardot}induct{\isacharparenright}\isanewline
+\isacommand{apply}\ clarify%
+\begin{isamarkuptxt}%
+The situation after clarify
+\begin{isabelle}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasymLongrightarrow}\isanewline
+\ \ \ \ \ \ \ \ x\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity%
+\end{isabelle}%
+\end{isamarkuptxt}%
+\isacommand{apply}\ {\isacharparenleft}erule\ well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}{\isachardot}induct{\isacharparenright}%
+\begin{isamarkuptxt}%
+note the induction hypothesis!
+\begin{isabelle}%
+\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
+\ \ \ \ \ \ \ {\isasymlbrakk}args\isanewline
+\ \ \ \ \ \ \ \ {\isasymin}\ lists\isanewline
+\ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasyminter}\isanewline
+\ \ \ \ \ \ \ \ \ \ \ \ {\isacharbraceleft}x{\isachardot}\ x\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isacharbraceright}{\isacharparenright}{\isacharsemicolon}\isanewline
+\ \ \ \ \ \ \ \ \ \ length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
+\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity%
+\end{isabelle}%
+\end{isamarkuptxt}%
\isacommand{apply}\ auto\isanewline
\isacommand{done}%
\begin{isamarkuptext}%
\begin{isabelle}%
\ \ \ \ \ lists\ {\isacharparenleft}A\ {\isasyminter}\ B{\isacharparenright}\ {\isacharequal}\ lists\ A\ {\isasyminter}\ lists\ B%
-\end{isabelle}
-\rulename{lists_Int_eq}
-
-The situation after clarify (note the strange induction hypothesis!)
-
-pr(latex xsymbols symbols)
-
-proof\ {\isacharparenleft}prove{\isacharparenright}{\isacharcolon}\ step\ {\isadigit{2}}\isanewline
-\isanewline
-goal\ {\isacharparenleft}lemma{\isacharparenright}{\isacharcolon}\isanewline
-well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasymsubseteq}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity\isanewline
-\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}x\ args\ f{\isachardot}\isanewline
-\ \ \ \ \ \ \ {\isasymlbrakk}args\isanewline
-\ \ \ \ \ \ \ \ {\isasymin}\ lists\isanewline
-\ \ \ \ \ \ \ \ \ \ \ {\isacharparenleft}well{\isacharunderscore}formed{\isacharunderscore}gterm{\isacharprime}\ arity\ {\isasyminter}\ {\isacharbraceleft}u{\isachardot}\ u\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity{\isacharbraceright}{\isacharparenright}{\isacharsemicolon}\isanewline
-\ \ \ \ \ \ \ \ \ \ length\ args\ {\isacharequal}\ arity\ f{\isasymrbrakk}\isanewline
-\ \ \ \ \ \ \ {\isasymLongrightarrow}\ Apply\ f\ args\ {\isasymin}\ well{\isacharunderscore}formed{\isacharunderscore}gterm\ arity%
+\end{isabelle}%
\end{isamarkuptext}%
%
\begin{isamarkuptext}%