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\newtheorem{abr}{Abbreviation}[section]
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\begin{document}

\title{Substitution of Proof Lines}
\author{Michael Meyling}
\email{principa@meyling.com}
\date{2002-07-27T20:51:18}

\begin{abstract}
This module declares the general rule for substituting variables.
\end{abstract}

\makeatletter
\long\def\hyper@section@backref#1#2#3{%
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\section*{module specification}

Author of this module: 
\begin{longtable}[h!]{l@{\extracolsep{\fill}}l}
Michael Meyling & michael@meyling.com \\
\end{longtable}


\medskip
This module has the following specification:

\mbox{}
\begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}}
Name: & subst \\
Version: & 1.00.00 \\
Rule version: & 1.01.00 \\
Orgin: & \url{http://www.meyling.com/principia/0_00_51/subst_1.00.00_1.01.00.qedeq} \\
\end{longtable}


\medskip
The following modules were used:

\mbox{}
\begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}}
Name: & propaxiom \\
Version: & 1.00.00 \\
Rule version: & 1.00.00 \\
Orgin: & \url{propaxiom_1.00.00_1.00.00.qedeq}  \\
pdf: & \url{propaxiom_1.00.00_1.00.00.pdf}  \\
Name: & predaxiom \\
Version: & 1.00.00 \\
Rule version: & 1.00.00 \\
Orgin: & \url{predaxiom_1.00.00_1.00.00.qedeq}  \\
pdf: & \url{predaxiom_1.00.00_1.00.00.pdf}  \\
\end{longtable}

\medskip
Is used by the following modules:

\mbox{}
\begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}}
Name: & prophilbert1 \\
Version: & 1.00.00 \\
Rule version: & 1.02.00 \\
Orgin: & \url{prophilbert1_1.00.00_1.02.00.qedeq}  \\
pdf: & \url{prophilbert1_1.00.00_1.02.00.pdf}  \\
\end{longtable}



If a proof line could be derived by using <a href="propaxiom_1.00.00_1.00.00.html#rule4">rename proposition variable</a>, <a href="predaxiom_1.00.00_1.00.00.html#predrule1">rename bound subject variable</a> and <a href="predaxiom_1.00.00_1.00.00.html#predrule2">rename free subject variable</a> multiple times, we declare a new rule to shorten that derivation:




\begin{dec}
Substitute Variables
\hypertarget{rule8}{}
\label{rule8}
\end{dec}



The use of this rule could always be replaced by proof lines that make only use of the referenced rules.



\bigskip


\section*{}
This module used by the following modules:

\mbox{}
\begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}}
Name: & prophilbert1 \\
Version: & 1.00.00 \\
Rule version: & 1.02.00 \\
Orgin: & \url{prophilbert1_1.00.00_1.02.00.qedeq}  \\
pdf: & \url{prophilbert1_1.00.00_1.02.00.pdf}  \\
\end{longtable}

\end{document}