<?xml version="1.0" encoding="UTF-8"?>
<QEDEQ
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:noNamespaceSchemaLocation="http://www.qedeq.org/0_04_07/xml/qedeq.xsd">
  <HEADER email="mime@qedeq.org">
    <SPECIFICATION name="qedeq_sample2" ruleVersion="1.00.00">
      <LOCATIONS>
        <LOCATION value="http://www.qedeq.org/0_04_07/sample" />
      </LOCATIONS>
    </SPECIFICATION>
    <TITLE>
      <LATEX language="en">
        <![CDATA[
          Mathematical Example Module
        ]]>
      </LATEX>
      <LATEX language="de">
        <![CDATA[
          Mathematisches Beispielmodul
        ]]>
      </LATEX>
    </TITLE>
    <ABSTRACT>
      <LATEX language="en">
        <![CDATA[
          Just a sample.
        ]]>
      </LATEX>
      <LATEX language="de">
        <![CDATA[
          Nur ein Beispiel.
        ]]>
      </LATEX>
    </ABSTRACT>
    <AUTHORS>
      <AUTHOR email="michael@meyling.com">
        <NAME>
          <LATEX language="de">
            <![CDATA[
              Michael Meyling
            ]]>
          </LATEX>
        </NAME>
      </AUTHOR>
    </AUTHORS>
    <IMPORTS>
      <IMPORT label="l">
        <SPECIFICATION name="qedeq_logic_v1" ruleVersion="1.00.00">
          <LOCATIONS>
            <LOCATION value="../doc/math" />
            <LOCATION value="../math" />
            <LOCATION value="http://www.qedeq.org/0_04_07/doc/math" />
          </LOCATIONS>
        </SPECIFICATION>
      </IMPORT>
      <IMPORT label="s">
        <SPECIFICATION name="qedeq_set_theory_v1" ruleVersion="1.00.00">
          <LOCATIONS>
            <LOCATION value="../doc/math" />
            <LOCATION value="../math" />
            <LOCATION value="http://www.qedeq.org/0_04_07/doc/math" />
          </LOCATIONS>
        </SPECIFICATION>
      </IMPORT>
    </IMPORTS>
  </HEADER>
  <CHAPTER>
    <TITLE>
      <LATEX language="en">
        <![CDATA[
          Sample
        ]]>
      </LATEX>
      <LATEX language="de">
        <![CDATA[
          Beispiel
        ]]>
      </LATEX>
    </TITLE>
    <INTRODUCTION>
      <LATEX language="en">
        <![CDATA[
          We just use the two main QEDEQ modules and note a simple proposition.
        ]]>
      </LATEX>
      <LATEX language="de">
        <![CDATA[
          Wir verwenden die beiden QEDEQ-Hauptmodule und notieren eine einfache Proposition.
        ]]>
      </LATEX>
    </INTRODUCTION>
    <SECTION>
      <TITLE>
        <LATEX language="en">
          <![CDATA[
            First and only
          ]]>
        </LATEX>
        <LATEX language="de">
          <![CDATA[
            Erstes und einziges
          ]]>
        </LATEX>
      </TITLE>
      <INTRODUCTION>
        <LATEX language="en">
          <![CDATA[
            Here we start.
          ]]>
        </LATEX>
        <LATEX language="de">
          <![CDATA[
            Hier starten wir.
          ]]>
        </LATEX>
      </INTRODUCTION>
      <SUBSECTIONS>
       <NODE id="proposition:one" level="formal">
          <PRECEDING>
            <LATEX language="en">
              <![CDATA[
                We state our proposition which uses predicates that are defined in imported QEDEQ modules.
              ]]>
            </LATEX>
            <LATEX language="de">
                Wir schreiben unsere Proposition, welche Predicate benutzt, die in importierten QEDEQ-Modulen definiert sind.
              <![CDATA[
              ]]>
            </LATEX>
          </PRECEDING>
          <THEOREM>
            <FORMULA>
              <IMPL>
                <FORALL>
                  <VAR id="z"/>
                  <PREDCON ref="s.isSet">
                    <VAR id="z"/>
                  </PREDCON>
                  <EQUI>
                    <PREDCON ref="s.in">
                      <VAR id="z"/>
                      <VAR id="x"/>
                    </PREDCON>
                    <PREDCON ref="s.in">
                      <VAR id="z"/>
                      <VAR id="y"/>
                    </PREDCON>
                  </EQUI>
                </FORALL>
                <PREDCON ref="l.equal">
                  <VAR id="x"/>
                  <VAR id="y"/>
                </PREDCON>
              </IMPL>
            </FORMULA>
          </THEOREM>
        </NODE>
      </SUBSECTIONS>
    </SECTION>
  </CHAPTER>
</QEDEQ>
