diff -r fe13743ffc8b -r 3370f6aa3200 doc-src/TutorialI/Recdef/document/Nested2.tex --- a/doc-src/TutorialI/Recdef/document/Nested2.tex Mon Sep 11 17:59:53 2000 +0200 +++ b/doc-src/TutorialI/Recdef/document/Nested2.tex Mon Sep 11 18:00:47 2000 +0200 @@ -1,5 +1,6 @@ % \begin{isabellebody}% +\def\isabellecontext{Nested2}% % \begin{isamarkuptext}% \noindent @@ -22,12 +23,10 @@ \begin{isamarkuptxt}% \noindent This leaves us with a trivial base case \isa{trev\ {\isacharparenleft}trev\ {\isacharparenleft}Var\ x{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ Var\ x} and the step case -% \begin{isabelle}% \ \ \ \ \ {\isasymforall}t{\isachardot}\ t\ {\isasymin}\ set\ ts\ {\isasymlongrightarrow}\ trev\ {\isacharparenleft}trev\ t{\isacharparenright}\ {\isacharequal}\ t\ {\isasymLongrightarrow}\isanewline \ \ \ \ \ trev\ {\isacharparenleft}trev\ {\isacharparenleft}App\ f\ ts{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ App\ f\ ts% -\end{isabelle}% - +\end{isabelle} both of which are solved by simplification:% \end{isamarkuptxt}% \isacommand{by}{\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}rev{\isacharunderscore}map\ sym{\isacharbrackleft}OF\ map{\isacharunderscore}compose{\isacharbrackright}{\isacharparenright}% @@ -62,12 +61,10 @@ \isacommand{recdef} would try to prove the unprovable \isa{size\ t\ {\isacharless}\ Suc\ {\isacharparenleft}term{\isacharunderscore}list{\isacharunderscore}size\ ts{\isacharparenright}}, without any assumption about \isa{t}. Therefore \isacommand{recdef} has been supplied with the congruence theorem \isa{map{\isacharunderscore}cong}: -% \begin{isabelle}% \ \ \ \ \ {\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}% - +\end{isabelle} Its second premise expresses (indirectly) that the second argument of \isa{map} is only applied to elements of its third argument. Congruence rules for other higher-order functions on lists would look very similar but