<?xml version="1.0" encoding="ISO-8859-1"?>
<?xml-stylesheet type="text/xsl" href="qedeq.xsl"?>
<QEDEQ 
		xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
		xsi:noNamespaceSchemaLocation="http://www.qedeq.org/0_03_04/xml/qedeq.xsd">
	<HEADER email="mime@qedeq.org">
		<SPECIFICATION name="module1" ruleVersion="1.00.00">
			<LOCATIONS>
				<LOCATION value="http://qedeq.org/0_03_04"/>
			</LOCATIONS>
		</SPECIFICATION>
		<TITLE>
			<LATEX language="en">
			   examplemodule
			</LATEX>
			<LATEX language="de">
			   Beispielmodul
			</LATEX>
		</TITLE>
		<ABSTRACT>
			<LATEX language="en">
			   In this very first qedeq module the specification is demonstrated.
			</LATEX>
			<LATEX language="de">
			   In diesem allerersten Qedeq-Modul wird die Spezifikation demonstriert.
			</LATEX>
		</ABSTRACT>
		<AUTHORS>
			<AUTHOR email="michael@meyling.com">
				<NAME>
					<LATEX language="de">
						Michael Meyling
					</LATEX>
				</NAME>
			</AUTHOR>
		</AUTHORS>
		<IMPORTS>
			<IMPORT label="predlogic">
				<SPECIFICATION name="predlogic" ruleVersion="1.00.00">
					<LOCATIONS>
						<LOCATION value="http://qedeq.org/0_03_04"/>
					</LOCATIONS>
				</SPECIFICATION>
			</IMPORT>
			<IMPORT label="proplogic">
				<SPECIFICATION name="proplogic" ruleVersion="1.00.00">
					<LOCATIONS>
						<LOCATION value="http://qedeq.org/0_03_04"/>
					</LOCATIONS>
				</SPECIFICATION>
			</IMPORT>
		</IMPORTS>
		<USEDBY>
			<SPECIFICATION name="module2" ruleVersion="1.00.00">
				<LOCATIONS>
					<LOCATION value="."/>
				</LOCATIONS>
			</SPECIFICATION>
		</USEDBY>
	</HEADER>
	<CHAPTER>
		<TITLE>
			<LATEX language="en">
				Basics
			</LATEX>
			<LATEX language="de">
				Anfangsgründe
			</LATEX>
		</TITLE>
		<INTRODUCTION>
			<LATEX language="en">
				In this chapter we start with the very basic axioms and definitions of set theory.
			</LATEX>
			<LATEX language="de">
				In diesem Kapitel beginnen wir mit den ganz elementaren Axiomen und Definitionen der Mengenlehre.
			</LATEX>
		</INTRODUCTION>
		<SECTION>
			<TITLE>
				<LATEX language="en">
					Axioms
				</LATEX>
				<LATEX language="de">
					Axiome
				</LATEX>
			</TITLE>
			<SUBSECTIONS>
				<NODE id="module1:def1">
					<NAME>
						<LATEX language="en">contains</LATEX>
						<LATEX language="de">enthält</LATEX>
					</NAME>
					<PRECEDING>
						<LATEX language="en">
							At first we define the contains operator.
						</LATEX>
						<LATEX language="de">
							Zunächst einmal wird der Enthaltensseinoperator festgelegt.
						</LATEX>
					</PRECEDING>
					<!-- es gibt eine Umsetzung zwischen Praedikatennummer unnd Label ??? -->
					<DEFINITION_PREDICATE arguments="2" name="in">
						<LATEXPATTERN>#1 \in #2</LATEXPATTERN>
						<VARLIST>
							<VAR id="1"/>
							<VAR id="2"/>
						</VARLIST>
					</DEFINITION_PREDICATE>
					<SUCCEEDING>
						<LATEX language="en">
							This is the only predicate we start with. All other will be defined.
						</LATEX>
						<LATEX language="de">
							Dies ist das einzige Prädikat welches wir zu Begin haben. Alle anderen werden definiert. 
						</LATEX>
					</SUCCEEDING>
				</NODE>
				<NODE id="isSet">
					<NAME>
						<LATEX language="en">is set</LATEX>
						<LATEX language="de">ist Menge</LATEX>
					</NAME>
					<PRECEDING>
						<LATEX language="en">
							Now we introduce sets.
						</LATEX>
						<LATEX language="de">
							Jetzt legen wir fest, was eine Menge ist.
						</LATEX>
					</PRECEDING>
					<DEFINITION_PREDICATE arguments="1" name="isSet">
						<LATEXPATTERN>\mathfrak{M}(#1)</LATEXPATTERN>
						<VARLIST>
							<VAR id="1"/>
						</VARLIST>
						<FORMULA>
							<EXISTS>
								<VAR id="2"/>
								<PREDCON ref="in">
									<VAR id="1"/>
									<VAR id="2"/>
								</PREDCON>
							</EXISTS>
						</FORMULA>
					</DEFINITION_PREDICATE>
					<SUCCEEDING>
						<LATEX language="en">
							So sets are nothing else than special classes.
						</LATEX>
						<LATEX language="de">
							Mengen sind also nichts anderes, als Klassen mit einer besonderen Eigenschaft.
						</LATEX>
					</SUCCEEDING>
				</NODE>
				<NODE id="module1:theorem" level="formal">
					<NAME>
						<LATEX language="en">is set</LATEX>
						<LATEX language="de">ist Menge</LATEX>
					</NAME>
					<PRECEDING>
						<LATEX language="en">
							 The first conclusion bla bla bla
						</LATEX>
						<LATEX language="de">
							 Als erste Folgerung bla bla bla
						</LATEX>
					</PRECEDING>
					<THEOREM>
						<FORMULA>
							<EXISTS>
								<VAR id="1"/>
								<PREDCON ref="isSet">
									<VAR id="1"/>
								</PREDCON>
							</EXISTS>
						</FORMULA>
					</THEOREM>
				</NODE>
				<NODE id="module1:axiom" level="formal">
					<!-- vielleicht auch eine Kurzbezeichnung hier?? -->
					<NAME>
						<LATEX language="en">comprehension</LATEX>
						<LATEX language="de">Komprehensionsaxiom</LATEX>
					</NAME>
					<PRECEDING>
						<LATEX language="en">
							 Our first axiom is the comprehensive axiom.
						</LATEX>
						<LATEX language="de">
							 Unser erstes Axiom ist das Komprehensionsaxiom.
						</LATEX>
					</PRECEDING>
					<AXIOM>
						<FORMULA>
							<FORALL>
								<VAR id="1"/>
								<AND>
									<PREDCON ref="isSet">
										<VAR id="1"/>
									</PREDCON>
									<PREDCON ref="isSet">
										<VAR id="1"/>
									</PREDCON>
								</AND>
							</FORALL>
						</FORMULA>
					</AXIOM>
				</NODE>
			</SUBSECTIONS>
		</SECTION>
	</CHAPTER>
</QEDEQ>
