--- a/doc-src/Exercises/2001/a1/generated/Aufgabe1.tex Fri Apr 29 18:13:28 2005 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,84 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{Aufgabe{\isadigit{1}}}%
-\isamarkupfalse%
-%
-\isamarkupsubsection{Lists%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Define a function \isa{replace}, such that \isa{replace\ x\ y\ zs}
-yields \isa{zs} with every occurrence of \isa{x} replaced by \isa{y}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{consts}\ replace\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isamarkupfalse%
-%
-\begin{isamarkuptext}%
-Prove or disprove (by counter example) the following theorems.
-You may have to prove some lemmas first.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{theorem}\ {\isachardoublequote}rev{\isacharparenleft}replace\ x\ y\ zs{\isacharparenright}\ {\isacharequal}\ replace\ x\ y\ {\isacharparenleft}rev\ zs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}replace\ x\ y\ {\isacharparenleft}replace\ u\ v\ zs{\isacharparenright}\ {\isacharequal}\ replace\ u\ v\ {\isacharparenleft}replace\ x\ y\ zs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}replace\ y\ z\ {\isacharparenleft}replace\ x\ y\ zs{\isacharparenright}\ {\isacharequal}\ replace\ x\ z\ zs{\isachardoublequote}\isamarkupfalse%
-\isamarkupfalse%
-%
-\begin{isamarkuptext}%
-Define two functions for removing elements from a list:
-\isa{del{\isadigit{1}}\ x\ xs} deletes the first occurrence (from the left) of
-\isa{x} in \isa{xs}, \isa{delall\ x\ xs} all of them.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{consts}\ del{\isadigit{1}}\ \ \ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isanewline
-\ \ \ \ \ \ \ delall\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequote}\isamarkupfalse%
-%
-\begin{isamarkuptext}%
-Prove or disprove (by counter example) the following theorems.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{theorem}\ {\isachardoublequote}del{\isadigit{1}}\ x\ {\isacharparenleft}delall\ x\ xs{\isacharparenright}\ {\isacharequal}\ delall\ x\ xs{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}delall\ x\ {\isacharparenleft}delall\ x\ xs{\isacharparenright}\ {\isacharequal}\ delall\ x\ xs{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}delall\ x\ {\isacharparenleft}del{\isadigit{1}}\ x\ xs{\isacharparenright}\ {\isacharequal}\ delall\ x\ xs{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}del{\isadigit{1}}\ x\ {\isacharparenleft}del{\isadigit{1}}\ y\ zs{\isacharparenright}\ {\isacharequal}\ del{\isadigit{1}}\ y\ {\isacharparenleft}del{\isadigit{1}}\ x\ zs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}delall\ x\ {\isacharparenleft}del{\isadigit{1}}\ y\ zs{\isacharparenright}\ {\isacharequal}\ del{\isadigit{1}}\ y\ {\isacharparenleft}delall\ x\ zs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}delall\ x\ {\isacharparenleft}delall\ y\ zs{\isacharparenright}\ {\isacharequal}\ delall\ y\ {\isacharparenleft}delall\ x\ zs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}del{\isadigit{1}}\ y\ {\isacharparenleft}replace\ x\ y\ xs{\isacharparenright}\ {\isacharequal}\ del{\isadigit{1}}\ x\ xs{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}delall\ y\ {\isacharparenleft}replace\ x\ y\ xs{\isacharparenright}\ {\isacharequal}\ delall\ x\ xs{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}replace\ x\ y\ {\isacharparenleft}delall\ x\ zs{\isacharparenright}\ {\isacharequal}\ delall\ x\ zs{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}replace\ x\ y\ {\isacharparenleft}delall\ z\ zs{\isacharparenright}\ {\isacharequal}\ delall\ z\ {\isacharparenleft}replace\ x\ y\ zs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}rev{\isacharparenleft}del{\isadigit{1}}\ x\ xs{\isacharparenright}\ {\isacharequal}\ del{\isadigit{1}}\ x\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{theorem}\ {\isachardoublequote}rev{\isacharparenleft}delall\ x\ xs{\isacharparenright}\ {\isacharequal}\ delall\ x\ {\isacharparenleft}rev\ xs{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isamarkupfalse%
-\isamarkupfalse%
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End: