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%%% Project Hilbert II - http://www.qedeq.org
%%% Copyright 2001, 2002, 2003, 2004 Michael Meyling (mime@qedeq.org)
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\documentclass[a4paper]{article}

\usepackage{amsmath,amsthm,amsfonts}
\usepackage[]{color}
\usepackage{xr}
\usepackage{epsfig,longtable}
\usepackage{varioref}
\usepackage[bookmarksnumbered,colorlinks,breaklinks,plainpages,backref,bookmarksopen=true,pdfpagemode=None]{hyperref}

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\textheight          220mm


\newtheorem{axm}{Axiom}[section]
\newtheorem{abr}{Abbreviation}[section]
\newtheorem{thm}{Theorem}[section]
\newtheorem{dec}{Rule Declaration}[section]
\newtheorem{cor}[thm]{Corollary}
\newtheorem{prop}{Proposition}
\newtheorem{lem}[thm]{Lemma}
\theoremstyle{remark}
\newtheorem*{rmk}{Remark}

\makeindex
\makeatletter
\externaldocument{subst_1.00.00_1.01.00.qedeq}
\hyperbaseurl{subst_1.00.00_1.01.00.qedeq}
\makeatother

\setlength{\LTleft}{0pt}
\setlength{\LTright}{0pt}

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\frenchspacing \sloppy
\pagestyle{headings}

\title{Substitution of Proof Lines}
\author{Michael Meyling}
\date{\tt <module@qedeq.org>}


\begin{document}

\maketitle

\setlongtables



{\small
This document is part of the project ``Hilbert II''.
To get more information about this project look at:\\
\mbox{\url{http://www.qedeq.org}}.


Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no
Back-Cover Texts. See also under \url{http://www.gnu.org/copyleft/}
}


\section*{Abstract}

This module declares the general rule for substituting variables.


\section*{Specification}

This document has the following specification:

\begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}}
Name: & subst \\
Version: & 1.00.00 \\
Rule version: & 1.01.00 \\
Orgin: & \url{http://www.qedeq.org/0_00_53/subst_1.00.00_1.01.00.qedeq} \\
\end{longtable}

\medskip

Author of this module: 
\begin{longtable}[h!]{l@{\extracolsep{\fill}}l}
Michael Meyling & mime@qedeq.org \\
\end{longtable}




\section*{References}

This document uses the results of the following documents:

\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}


\section*{Content}




If a proof line could be derived by using rule4 (rename proposition variable), predrule1 (rename bound subject variable) and predrule2 (rename free subject variable) multiple times, we declare a new rule to shorten that derivation:




\begin{dec}[rule8]
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{Cross Reference}

This module is used by the following modules:

\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}
