doc-src/TutorialI/Recdef/document/Nested2.tex
changeset 9924 3370f6aa3200
parent 9834 109b11c4e77e
child 9933 9feb1e0c4cb3
     1.1 --- a/doc-src/TutorialI/Recdef/document/Nested2.tex	Mon Sep 11 17:59:53 2000 +0200
     1.2 +++ b/doc-src/TutorialI/Recdef/document/Nested2.tex	Mon Sep 11 18:00:47 2000 +0200
     1.3 @@ -1,5 +1,6 @@
     1.4  %
     1.5  \begin{isabellebody}%
     1.6 +\def\isabellecontext{Nested2}%
     1.7  %
     1.8  \begin{isamarkuptext}%
     1.9  \noindent
    1.10 @@ -22,12 +23,10 @@
    1.11  \begin{isamarkuptxt}%
    1.12  \noindent
    1.13  This leaves us with a trivial base case \isa{trev\ {\isacharparenleft}trev\ {\isacharparenleft}Var\ x{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ Var\ x} and the step case
    1.14 -%
    1.15  \begin{isabelle}%
    1.16  \ \ \ \ \ {\isasymforall}t{\isachardot}\ t\ {\isasymin}\ set\ ts\ {\isasymlongrightarrow}\ trev\ {\isacharparenleft}trev\ t{\isacharparenright}\ {\isacharequal}\ t\ {\isasymLongrightarrow}\isanewline
    1.17  \ \ \ \ \ trev\ {\isacharparenleft}trev\ {\isacharparenleft}App\ f\ ts{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ App\ f\ ts%
    1.18 -\end{isabelle}%
    1.19 -
    1.20 +\end{isabelle}
    1.21  both of which are solved by simplification:%
    1.22  \end{isamarkuptxt}%
    1.23  \isacommand{by}{\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}rev{\isacharunderscore}map\ sym{\isacharbrackleft}OF\ map{\isacharunderscore}compose{\isacharbrackright}{\isacharparenright}%
    1.24 @@ -62,12 +61,10 @@
    1.25  \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
    1.26  \isacommand{recdef} has been supplied with the congruence theorem
    1.27  \isa{map{\isacharunderscore}cong}:
    1.28 -%
    1.29  \begin{isabelle}%
    1.30  \ \ \ \ \ {\isasymlbrakk}xs\ {\isacharequal}\ ys{\isacharsemicolon}\ {\isasymAnd}x{\isachardot}\ x\ {\isasymin}\ set\ ys\ {\isasymLongrightarrow}\ f\ x\ {\isacharequal}\ g\ x{\isasymrbrakk}\isanewline
    1.31  \ \ \ \ \ {\isasymLongrightarrow}\ map\ f\ xs\ {\isacharequal}\ map\ g\ ys%
    1.32 -\end{isabelle}%
    1.33 -
    1.34 +\end{isabelle}
    1.35  Its second premise expresses (indirectly) that the second argument of
    1.36  \isa{map} is only applied to elements of its third argument. Congruence
    1.37  rules for other higher-order functions on lists would look very similar but