
diff -r ff6787d730d5 -r 260090b54ef9 doc-src/Exercises/0304/a3/generated/a3.tex
--- a/doc-src/Exercises/0304/a3/generated/a3.tex	Fri Apr 29 18:13:28 2005 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,83 +0,0 @@
-%
-\begin{isabellebody}%
-\def\isabellecontext{a{\isadigit{3}}}%
-\isamarkupfalse%
-%
-\isamarkupsubsection{Natural deduction -- Propositional Logic \label{psv0304a3}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-In this exercise, we will prove some lemmas of propositional
-logic with the aid of a calculus of natural deduction.
-
-For the proofs, you may only use
-
-\begin{itemize}
-\item the following lemmas: \\
-\isa{notI{\isacharcolon}}~\isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ False{\isacharparenright}\ {\isasymLongrightarrow}\ {\isasymnot}\ A},\\
-\isa{notE{\isacharcolon}}~\isa{{\isasymlbrakk}{\isasymnot}\ A{\isacharsemicolon}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ B},\\
-\isa{conjI{\isacharcolon}}~\isa{{\isasymlbrakk}A{\isacharsemicolon}\ B{\isasymrbrakk}\ {\isasymLongrightarrow}\ A\ {\isasymand}\ B},\\ 
-\isa{conjE{\isacharcolon}}~\isa{{\isasymlbrakk}A\ {\isasymand}\ B{\isacharsemicolon}\ {\isasymlbrakk}A{\isacharsemicolon}\ B{\isasymrbrakk}\ {\isasymLongrightarrow}\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ C},\\
-\isa{disjI{\isadigit{1}}{\isacharcolon}}~\isa{A\ {\isasymLongrightarrow}\ A\ {\isasymor}\ B},\\
-\isa{disjI{\isadigit{2}}{\isacharcolon}}~\isa{A\ {\isasymLongrightarrow}\ B\ {\isasymor}\ A},\\
-\isa{disjE{\isacharcolon}}~\isa{{\isasymlbrakk}A\ {\isasymor}\ B{\isacharsemicolon}\ A\ {\isasymLongrightarrow}\ C{\isacharsemicolon}\ B\ {\isasymLongrightarrow}\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ C},\\
-\isa{impI{\isacharcolon}}~\isa{{\isacharparenleft}A\ {\isasymLongrightarrow}\ B{\isacharparenright}\ {\isasymLongrightarrow}\ A\ {\isasymlongrightarrow}\ B},\\
-\isa{impE{\isacharcolon}}~\isa{{\isasymlbrakk}A\ {\isasymlongrightarrow}\ B{\isacharsemicolon}\ A{\isacharsemicolon}\ B\ {\isasymLongrightarrow}\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ C},\\
-\isa{mp{\isacharcolon}}~\isa{{\isasymlbrakk}A\ {\isasymlongrightarrow}\ B{\isacharsemicolon}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ B}\\
-\isa{iffI{\isacharcolon}}~\isa{{\isasymlbrakk}A\ {\isasymLongrightarrow}\ B{\isacharsemicolon}\ B\ {\isasymLongrightarrow}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ A\ {\isacharequal}\ B}, \\
-\isa{iffE{\isacharcolon}}~\isa{{\isasymlbrakk}A\ {\isacharequal}\ B{\isacharsemicolon}\ {\isasymlbrakk}A\ {\isasymlongrightarrow}\ B{\isacharsemicolon}\ B\ {\isasymlongrightarrow}\ A{\isasymrbrakk}\ {\isasymLongrightarrow}\ C{\isasymrbrakk}\ {\isasymLongrightarrow}\ C}\\
-\isa{classical{\isacharcolon}}~\isa{{\isacharparenleft}{\isasymnot}\ A\ {\isasymLongrightarrow}\ A{\isacharparenright}\ {\isasymLongrightarrow}\ A}
-
-\item the proof methods \isa{rule}, \isa{erule} and \isa{assumption}
-\end{itemize}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\ I{\isacharcolon}\ {\isachardoublequote}A\ {\isasymlongrightarrow}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}A\ {\isasymand}\ B\ {\isasymlongrightarrow}\ B\ {\isasymand}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}A\ {\isasymand}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}A\ {\isasymor}\ B{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}{\isacharparenleft}A\ {\isasymor}\ B{\isacharparenright}\ {\isasymor}\ C{\isacharparenright}\ {\isasymlongrightarrow}\ A\ {\isasymor}\ {\isacharparenleft}B\ {\isasymor}\ C{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ K{\isacharcolon}\ {\isachardoublequote}A\ {\isasymlongrightarrow}\ B\ {\isasymlongrightarrow}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}A\ {\isasymor}\ A{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}A\ {\isasymand}\ A{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ S{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B\ {\isasymlongrightarrow}\ C{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ A\ {\isasymlongrightarrow}\ C{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}B\ {\isasymlongrightarrow}\ C{\isacharparenright}\ {\isasymlongrightarrow}\ A\ {\isasymlongrightarrow}\ C{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isasymnot}\ {\isasymnot}\ A\ {\isasymlongrightarrow}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}A\ {\isasymlongrightarrow}\ {\isasymnot}\ {\isasymnot}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}{\isasymnot}\ A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}{\isasymnot}\ B\ {\isasymlongrightarrow}\ A{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}{\isacharparenleft}A\ {\isasymlongrightarrow}\ B{\isacharparenright}\ {\isasymlongrightarrow}\ A{\isacharparenright}\ {\isasymlongrightarrow}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}A\ {\isasymor}\ {\isasymnot}\ A{\isachardoublequote}\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\isacommand{lemma}\ {\isachardoublequote}{\isacharparenleft}{\isasymnot}\ {\isacharparenleft}A\ {\isasymand}\ B{\isacharparenright}{\isacharparenright}\ {\isacharequal} {\isacharparenleft}{\isasymnot}\ A\ {\isasymor}\ {\isasymnot}\ B{\isacharparenright}{\isachardoublequote}\isamarkupfalse%
-\isamarkupfalse%
-\isanewline
-\isamarkupfalse%
-\end{isabellebody}%
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "root"
-%%% End:




