<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml package="xcolor"?>
<?latexml package="framed"?>
<?latexml package="ntheorem" options="thmmarks,thref,framed"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML">
  <resource src="LaTeXML.css" type="text/css"/>
  <resource src="ltx-article.css" type="text/css"/>
  <section inlist="toc" xml:id="S1">
    <tags>
      <tag>1</tag>
      <tag role="refnum">1</tag>
      <tag role="typerefnum">§1</tag>
    </tags>
    <title><tag close=" ">1</tag>Examples</title>
    <para xml:id="S1.p1">
      <p>Note, that parts of the setting are inherited. For instance, the
fonts are not reset before defining “Lemma”, so the font setting
of “Theorem” is used.</p>
    </para>
    <theorem class="ltx_theorem_Example" inlist="thm theorem:Example" xml:id="ThmExample1">
      <tags>
        <tag>1 Example</tag>
        <tag role="refnum">1</tag>
        <tag role="typerefnum">Example 1</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">1 Example</text></tag><text font="bold"> (Simple one)</text></title>
      <para xml:id="ThmExample1.p1">
        <p>The first example is just a text.</p>
      </para>
      <para xml:id="ThmExample1.p2">
        <p>In the next examples, it is shown how an endmark is put at a
displaymath, a single equation and both types of eqnarrays.
<text class="ltx_align_floatright"><Math mode="inline" tex="\ast" text="ast" xml:id="ThmExample1.p2.m1">
              <XMath>
                <XMTok name="ast" role="MULOP">∗</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_Theorem" inlist="thm theorem:Theorem" xml:id="ThmTheorem1">
      <tags>
        <tag>1 Theorem</tag>
        <tag role="refnum">1</tag>
        <tag role="typerefnum">Theorem 1</tag>
      </tags>
      <title class="ltx_outdent"><tag><text font="bold">1 Theorem</text></tag><text font="bold"> (Long Theorem):</text></title>
      <para xml:id="ThmTheorem1.p1">
        <p><text font="slanted">The examples are put into this theorem environment.</text></p>
      </para>
      <para xml:id="ThmTheorem1.p2">
        <p><text font="slanted">The next example will not appear in the list of examples</text></p>
      </para>
      <theorem class="ltx_theorem_Example" inlist="thm theorem:Example*" xml:id="ThmExample2">
        <tags>
          <tag>2 Example</tag>
          <tag role="refnum">2</tag>
          <tag role="typerefnum">Example 2</tag>
        </tags>
        <title class="ltx_runin"><tag><text font="bold">2 Example</text></tag><text font="bold"> (Ending with a displayed formula)</text></title>
        <para xml:id="ThmExample2.p1">
          <p>Look, the endmark is really at the bottom of the line:</p>
          <equation xml:id="S1.Ex1">
            <Math mode="display" tex="f^{(n)}(z)=\frac{n!}{2\pi i}\int\limits_{\partial D}\frac{f(\zeta)}{(\zeta-z)^%&#10;{n+1}}d\zeta" text="f ^ n * z = (nfactorial / (2 * pi * i)) * (integral _ (partial-differential@(D)))@(((f * zeta) / (zeta - z) ^ (n + 1)) * differential-d@(zeta))" xml:id="S1.Ex1.m1">
              <XMath>
                <XMApp>
                  <XMTok meaning="equals" role="RELOP">=</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok font="italic" role="UNKNOWN">f</XMTok>
                      <XMDual>
                        <XMRef idref="S1.Ex1.m1.1"/>
                        <XMWrap>
                          <XMTok fontsize="70%" role="OPEN" stretchy="false">(</XMTok>
                          <XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S1.Ex1.m1.1">n</XMTok>
                          <XMTok fontsize="70%" role="CLOSE" stretchy="false">)</XMTok>
                        </XMWrap>
                      </XMDual>
                    </XMApp>
                    <XMDual>
                      <XMRef idref="S1.Ex1.m1.4"/>
                      <XMWrap>
                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                        <XMTok font="italic" role="UNKNOWN" xml:id="S1.Ex1.m1.4">z</XMTok>
                        <XMTok role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMApp>
                      <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                      <XMApp>
                        <XMTok meaning="factorial" role="POSTFIX">!</XMTok>
                        <XMTok font="italic" role="UNKNOWN">n</XMTok>
                      </XMApp>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMTok meaning="2" role="NUMBER">2</XMTok>
                        <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                        <XMTok font="italic" role="UNKNOWN">i</XMTok>
                      </XMApp>
                    </XMApp>
                    <XMApp>
                      <XMApp scriptpos="mid">
                        <XMTok role="SUBSCRIPTOP" scriptpos="mid1"/>
                        <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                        <XMApp>
                          <XMTok fontsize="70%" meaning="partial-differential" name="partial" role="OPERATOR">∂</XMTok>
                          <XMTok font="italic" fontsize="70%" role="UNKNOWN">D</XMTok>
                        </XMApp>
                      </XMApp>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMApp>
                          <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok font="italic" role="UNKNOWN">f</XMTok>
                            <XMDual>
                              <XMRef idref="S1.Ex1.m1.2"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMTok font="italic" name="zeta" role="UNKNOWN" xml:id="S1.Ex1.m1.2">ζ</XMTok>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                          </XMApp>
                          <XMApp>
                            <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                            <XMDual>
                              <XMRef idref="S1.Ex1.m1.3"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMApp xml:id="S1.Ex1.m1.3">
                                  <XMTok meaning="minus" role="ADDOP">-</XMTok>
                                  <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                </XMApp>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                            <XMApp>
                              <XMTok fontsize="70%" meaning="plus" role="ADDOP">+</XMTok>
                              <XMTok font="italic" fontsize="70%" role="UNKNOWN">n</XMTok>
                              <XMTok fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
                            </XMApp>
                          </XMApp>
                        </XMApp>
                        <XMApp>
                          <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                          <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                        </XMApp>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math>
          </equation>
          <p><text class="ltx_align_floatright"><Math mode="inline" tex="\ast" text="ast" xml:id="ThmExample2.p1.m1">
                <XMath>
                  <XMTok name="ast" role="MULOP">∗</XMTok>
                </XMath>
              </Math></text></p>
        </para>
      </theorem>
      <theorem class="ltx_theorem_Lemma" inlist="thm theorem:Lemma" xml:id="ThmLemma1">
        <tags>
          <tag>α Lemma</tag>
          <tag role="refnum">α</tag>
          <tag role="typerefnum">Lemma α</tag>
        </tags>
        <title><tag><text font="bold">α Lemma</text></tag><text font="bold"> (Display with array):</text></title>
        <para xml:id="ThmLemma1.p1">
          <p><text font="slanted">Lemmata are indented and numbered with greek symbols.
Also for displayed arrays of this form, it looks good:</text></p>
          <equation xml:id="S1.Ex2">
            <Math mode="display" tex="\begin{array}[]{l}a=\begin{array}[t]{l}first\ line\\&#10;second\ line\end{array}\mbox{try to put this text in the lowest line}\end{array}" text="Array[[a = Array[[f * i * r * s * t * l * i * n * e], [s * e * c * o * n * d * l * i * n * e]] * [try to put this text in the lowest line]]]" xml:id="S1.Ex2.m1">
              <XMath>
                <XMArray role="ARRAY" vattach="middle">
                  <XMRow>
                    <XMCell align="left">
                      <XMApp>
                        <XMTok meaning="equals" role="RELOP">=</XMTok>
                        <XMTok font="italic" role="UNKNOWN">a</XMTok>
                        <XMApp>
                          <XMTok meaning="times" role="MULOP">⁢</XMTok>
                          <XMArray role="ARRAY" vattach="top">
                            <XMRow>
                              <XMCell align="left">
                                <XMApp>
                                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">i</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">r</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">s</XMTok>
                                  <XMTok font="italic" role="UNKNOWN" rpadding="5.0pt">t</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">l</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">i</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">n</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                </XMApp>
                              </XMCell>
                            </XMRow>
                            <XMRow>
                              <XMCell align="left">
                                <XMApp>
                                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">s</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">c</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">o</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">n</XMTok>
                                  <XMTok font="italic" role="UNKNOWN" rpadding="5.0pt">d</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">l</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">i</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">n</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                </XMApp>
                              </XMCell>
                            </XMRow>
                          </XMArray>
                          <XMText><text font="slanted">try to put this text in the lowest line</text></XMText>
                        </XMApp>
                      </XMApp>
                    </XMCell>
                  </XMRow>
                </XMArray>
              </XMath>
            </Math>
          </equation>
          <p><text class="ltx_align_floatright" font="slanted"><Math mode="inline" tex="\heartsuit" text="heartsuit" xml:id="ThmLemma1.p1.m1">
                <XMath>
                  <XMTok font="upright" name="heartsuit" role="UNKNOWN">♡</XMTok>
                </XMath>
              </Math></text></p>
        </para>
      </theorem>
      <theorem class="ltx_theorem_Lemma" inlist="thm theorem:Lemma" xml:id="ThmLemma2">
        <tags>
          <tag>β Lemma</tag>
          <tag role="refnum">β</tag>
          <tag role="typerefnum">Lemma β</tag>
        </tags>
        <title><tag><text font="bold">β Lemma</text></tag><text font="bold"> (Equation):</text></title>
        <para xml:id="ThmLemma2.p1">
          <p><text font="slanted">For <verbatim font="typewriter upright">equation</verbatim>s, we decided to put the endmark after the equation
number, which is vertically centered.
Currently, we do not know, how to get the equation number centered and
the endmark at the bottom (one has to know the internal height of the
math material) … If anyone knows, please inform us.</text></p>
          <equation xml:id="S1.E1">
            <tags>
              <tag>(1)</tag>
              <tag role="refnum">1</tag>
            </tags>
            <Math mode="display" tex="\int_{\gamma}f(z)\,dz:=\int_{a}^{b}f(\gamma(t))\gamma^{\prime}(t)\,dt" text="(integral _ gamma)@(f * z * differential-d@(z)) assign ((integral _ a) ^ b)@(f * gamma * t * gamma ^ prime * t * differential-d@(t))" xml:id="S1.E1.m1">
              <XMath>
                <XMApp>
                  <XMTok meaning="assign" role="RELOP">:=</XMTok>
                  <XMApp>
                    <XMApp>
                      <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                      <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP">∫</XMTok>
                      <XMTok font="italic" fontsize="70%" name="gamma" role="UNKNOWN">γ</XMTok>
                    </XMApp>
                    <XMApp>
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok font="italic" role="UNKNOWN">f</XMTok>
                      <XMDual>
                        <XMRef idref="S1.E1.m1.1"/>
                        <XMWrap>
                          <XMTok role="OPEN" stretchy="false">(</XMTok>
                          <XMTok font="italic" role="UNKNOWN" xml:id="S1.E1.m1.1">z</XMTok>
                          <XMTok role="CLOSE" rpadding="1.7pt" stretchy="false">)</XMTok>
                        </XMWrap>
                      </XMDual>
                      <XMApp>
                        <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                        <XMTok font="italic" role="UNKNOWN">z</XMTok>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMApp>
                        <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                        <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP">∫</XMTok>
                        <XMTok font="italic" fontsize="70%" role="UNKNOWN">a</XMTok>
                      </XMApp>
                      <XMTok font="italic" fontsize="70%" role="UNKNOWN">b</XMTok>
                    </XMApp>
                    <XMApp>
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok font="italic" role="UNKNOWN">f</XMTok>
                      <XMDual>
                        <XMRef idref="S1.E1.m1.4"/>
                        <XMWrap>
                          <XMTok role="OPEN" stretchy="false">(</XMTok>
                          <XMApp xml:id="S1.E1.m1.4">
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok font="italic" name="gamma" role="UNKNOWN">γ</XMTok>
                            <XMDual>
                              <XMRef idref="S1.E1.m1.2"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMTok font="italic" role="UNKNOWN" xml:id="S1.E1.m1.2">t</XMTok>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                          </XMApp>
                          <XMTok role="CLOSE" stretchy="false">)</XMTok>
                        </XMWrap>
                      </XMDual>
                      <XMApp>
                        <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                        <XMTok font="italic" name="gamma" role="UNKNOWN">γ</XMTok>
                        <XMTok fontsize="70%" name="prime" role="SUPOP">′</XMTok>
                      </XMApp>
                      <XMDual>
                        <XMRef idref="S1.E1.m1.3"/>
                        <XMWrap>
                          <XMTok role="OPEN" stretchy="false">(</XMTok>
                          <XMTok font="italic" role="UNKNOWN" xml:id="S1.E1.m1.3">t</XMTok>
                          <XMTok role="CLOSE" rpadding="1.7pt" stretchy="false">)</XMTok>
                        </XMWrap>
                      </XMDual>
                      <XMApp>
                        <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                        <XMTok font="italic" role="UNKNOWN">t</XMTok>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math>
          </equation>
          <p><text class="ltx_align_floatright" font="slanted"><Math mode="inline" tex="\heartsuit" text="heartsuit" xml:id="ThmLemma2.p1.m1">
                <XMath>
                  <XMTok font="upright" name="heartsuit" role="UNKNOWN">♡</XMTok>
                </XMath>
              </Math></text></p>
        </para>
      </theorem>
      <para xml:id="ThmTheorem1.p3">
        <p><text font="slanted">With the —break—-theoremstyles, if the environment is labeled and
written as</text></p>
      </para>
      <theorem class="ltx_theorem_Lemma" inlist="thm theorem:Lemma" labels="LABEL:breakstyle" xml:id="ThmLemma3">
        <tags>
          <tag>γ Lemma</tag>
          <tag role="refnum">γ</tag>
          <tag role="typerefnum">Lemma γ</tag>
        </tags>
        <title><tag><text font="bold">γ Lemma</text></tag><text font="bold"> (Breakstyle):</text></title>
        <para xml:id="ThmLemma3.p1">
          <p><text font="slanted">From the predefined styles, this is exactly the case for the break-styles.
That’s no bug, it’s LaTeX-immanent.</text></p>
        </para>
        <para xml:id="ThmLemma3.p2">
          <p><text font="slanted">The example goes on with an <verbatim font="typewriter upright">eqnarray</verbatim>:</text></p>
          <equationgroup class="ltx_eqn_eqnarray" xml:id="S1.EGx1">
            <equation xml:id="S1.E2">
              <tags>
                <tag>(2)</tag>
                <tag role="refnum">2</tag>
              </tags>
              <MathFork>
                <Math tex="\displaystyle f(z)=\frac{1}{2\pi i}\int\limits_{\partial D}\frac{f(\zeta)}{%&#10;\zeta-z}d\zeta" text="f * z = (1 / (2 * pi * i)) * (integral _ (partial-differential@(D)))@(((f * zeta) / (zeta - z)) * differential-d@(zeta))" xml:id="S1.E2.m4">
                  <XMath>
                    <XMApp>
                      <XMTok meaning="equals" role="RELOP">=</XMTok>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMTok font="italic" role="UNKNOWN">f</XMTok>
                        <XMDual>
                          <XMRef idref="S1.E2.m4.2"/>
                          <XMWrap>
                            <XMTok role="OPEN" stretchy="false">(</XMTok>
                            <XMTok font="italic" role="UNKNOWN" xml:id="S1.E2.m4.2">z</XMTok>
                            <XMTok role="CLOSE" stretchy="false">)</XMTok>
                          </XMWrap>
                        </XMDual>
                      </XMApp>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMApp>
                          <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                          <XMTok meaning="1" role="NUMBER">1</XMTok>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok meaning="2" role="NUMBER">2</XMTok>
                            <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                            <XMTok font="italic" role="UNKNOWN">i</XMTok>
                          </XMApp>
                        </XMApp>
                        <XMApp>
                          <XMApp scriptpos="mid">
                            <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                            <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                            <XMApp>
                              <XMTok fontsize="70%" meaning="partial-differential" name="partial" role="OPERATOR">∂</XMTok>
                              <XMTok font="italic" fontsize="70%" role="UNKNOWN">D</XMTok>
                            </XMApp>
                          </XMApp>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMApp>
                              <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                <XMDual>
                                  <XMRef idref="S1.E2.m4.1"/>
                                  <XMWrap>
                                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                                    <XMTok font="italic" name="zeta" role="UNKNOWN" xml:id="S1.E2.m4.1">ζ</XMTok>
                                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                                  </XMWrap>
                                </XMDual>
                              </XMApp>
                              <XMApp>
                                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                                <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                <XMTok font="italic" role="UNKNOWN">z</XMTok>
                              </XMApp>
                            </XMApp>
                            <XMApp>
                              <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                              <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                            </XMApp>
                          </XMApp>
                        </XMApp>
                      </XMApp>
                    </XMApp>
                  </XMath>
                </Math>
                <MathBranch>
                  <tr>
                    <td align="right"><Math mode="inline" tex="\displaystyle f(z)" text="f * z" xml:id="S1.E2.m1">
                        <XMath>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok font="italic" role="UNKNOWN">f</XMTok>
                            <XMDual>
                              <XMRef idref="S1.E2.m1.1"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMTok font="italic" role="UNKNOWN" xml:id="S1.E2.m1.1">z</XMTok>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                          </XMApp>
                        </XMath>
                      </Math></td>
                    <td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S1.E2.m2">
                        <XMath>
                          <XMTok meaning="equals" role="RELOP">=</XMTok>
                        </XMath>
                      </Math></td>
                    <td align="left"><Math mode="inline" tex="\displaystyle\frac{1}{2\pi i}\int\limits_{\partial D}\frac{f(\zeta)}{\zeta-z}d\zeta" text="(1 / (2 * pi * i)) * (integral _ (partial-differential@(D)))@(((f * zeta) / (zeta - z)) * differential-d@(zeta))" xml:id="S1.E2.m3">
                        <XMath>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMApp>
                              <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                              <XMTok meaning="1" role="NUMBER">1</XMTok>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok meaning="2" role="NUMBER">2</XMTok>
                                <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                                <XMTok font="italic" role="UNKNOWN">i</XMTok>
                              </XMApp>
                            </XMApp>
                            <XMApp>
                              <XMApp scriptpos="mid">
                                <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                                <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                                <XMApp>
                                  <XMTok fontsize="70%" meaning="partial-differential" name="partial" role="OPERATOR">∂</XMTok>
                                  <XMTok font="italic" fontsize="70%" role="UNKNOWN">D</XMTok>
                                </XMApp>
                              </XMApp>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMApp>
                                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                                  <XMApp>
                                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                    <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                    <XMDual>
                                      <XMRef idref="S1.E2.m3.1"/>
                                      <XMWrap>
                                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                                        <XMTok font="italic" name="zeta" role="UNKNOWN" xml:id="S1.E2.m3.1">ζ</XMTok>
                                        <XMTok role="CLOSE" stretchy="false">)</XMTok>
                                      </XMWrap>
                                    </XMDual>
                                  </XMApp>
                                  <XMApp>
                                    <XMTok meaning="minus" role="ADDOP">-</XMTok>
                                    <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                    <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                  </XMApp>
                                </XMApp>
                                <XMApp>
                                  <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                                  <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                </XMApp>
                              </XMApp>
                            </XMApp>
                          </XMApp>
                        </XMath>
                      </Math></td>
                  </tr>
                </MathBranch>
              </MathFork>
            </equation>
            <equation xml:id="S1.E3">
              <tags>
                <tag>(3)</tag>
                <tag role="refnum">3</tag>
              </tags>
              <MathFork>
                <Math tex="\displaystyle=\frac{1}{2\pi}\int\limits_{0}^{2\pi}f(z_{0}+re^{it})dt" text="absent = (1 / (2 * pi)) * ((integral _ 0) ^ (2 * pi))@(f * (z _ 0 + r * e ^ (i * t)) * differential-d@(t))" xml:id="S1.E3.m4">
                  <XMath>
                    <XMApp>
                      <XMTok meaning="equals" role="RELOP">=</XMTok>
                      <XMTok meaning="absent"/>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMApp>
                          <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                          <XMTok meaning="1" role="NUMBER">1</XMTok>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok meaning="2" role="NUMBER">2</XMTok>
                            <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                          </XMApp>
                        </XMApp>
                        <XMApp>
                          <XMApp scriptpos="mid">
                            <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                            <XMApp scriptpos="mid">
                              <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                              <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                              <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                            </XMApp>
                            <XMApp>
                              <XMTok meaning="times" role="MULOP">⁢</XMTok>
                              <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                              <XMTok font="italic" fontsize="70%" name="pi" role="UNKNOWN">π</XMTok>
                            </XMApp>
                          </XMApp>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok font="italic" role="UNKNOWN">f</XMTok>
                            <XMDual>
                              <XMRef idref="S1.E3.m4.1"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMApp xml:id="S1.E3.m4.1">
                                  <XMTok meaning="plus" role="ADDOP">+</XMTok>
                                  <XMApp>
                                    <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                                    <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                    <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                                  </XMApp>
                                  <XMApp>
                                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                    <XMTok font="italic" role="UNKNOWN">r</XMTok>
                                    <XMApp>
                                      <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                                      <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                      <XMApp>
                                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                        <XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
                                        <XMTok font="italic" fontsize="70%" role="UNKNOWN">t</XMTok>
                                      </XMApp>
                                    </XMApp>
                                  </XMApp>
                                </XMApp>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                            <XMApp>
                              <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                              <XMTok font="italic" role="UNKNOWN">t</XMTok>
                            </XMApp>
                          </XMApp>
                        </XMApp>
                      </XMApp>
                    </XMApp>
                  </XMath>
                </Math>
                <MathBranch>
                  <tr>
                    <td align="right"/>
                    <td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S1.E3.m2">
                        <XMath>
                          <XMTok meaning="equals" role="RELOP">=</XMTok>
                        </XMath>
                      </Math></td>
                    <td align="left"><Math mode="inline" tex="\displaystyle\frac{1}{2\pi}\int\limits_{0}^{2\pi}f(z_{0}+re^{it})dt" text="(1 / (2 * pi)) * ((integral _ 0) ^ (2 * pi))@(f * (z _ 0 + r * e ^ (i * t)) * differential-d@(t))" xml:id="S1.E3.m3">
                        <XMath>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMApp>
                              <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                              <XMTok meaning="1" role="NUMBER">1</XMTok>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok meaning="2" role="NUMBER">2</XMTok>
                                <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                              </XMApp>
                            </XMApp>
                            <XMApp>
                              <XMApp scriptpos="mid">
                                <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                                <XMApp scriptpos="mid">
                                  <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                                  <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                                  <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                                </XMApp>
                                <XMApp>
                                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                  <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                                  <XMTok font="italic" fontsize="70%" name="pi" role="UNKNOWN">π</XMTok>
                                </XMApp>
                              </XMApp>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                <XMDual>
                                  <XMRef idref="S1.E3.m3.1"/>
                                  <XMWrap>
                                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                                    <XMApp xml:id="S1.E3.m3.1">
                                      <XMTok meaning="plus" role="ADDOP">+</XMTok>
                                      <XMApp>
                                        <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                                        <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                        <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                                      </XMApp>
                                      <XMApp>
                                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                        <XMTok font="italic" role="UNKNOWN">r</XMTok>
                                        <XMApp>
                                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                                          <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                          <XMApp>
                                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                            <XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
                                            <XMTok font="italic" fontsize="70%" role="UNKNOWN">t</XMTok>
                                          </XMApp>
                                        </XMApp>
                                      </XMApp>
                                    </XMApp>
                                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                                  </XMWrap>
                                </XMDual>
                                <XMApp>
                                  <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">t</XMTok>
                                </XMApp>
                              </XMApp>
                            </XMApp>
                          </XMApp>
                        </XMath>
                      </Math></td>
                  </tr>
                </MathBranch>
              </MathFork>
            </equation>
          </equationgroup>
          <p><text class="ltx_align_floatright" font="slanted"><Math mode="inline" tex="\heartsuit" text="heartsuit" xml:id="ThmLemma3.p2.m1">
                <XMath>
                  <XMTok font="upright" name="heartsuit" role="UNKNOWN">♡</XMTok>
                </XMath>
              </Math></text></p>
        </para>
      </theorem>
      <theorem class="ltx_theorem_Proof" inlist="thm theorem:Proof" xml:id="ThmProofx1">
        <tags>
          <tag>Proof</tag>
          <tag role="typerefnum">Proof</tag>
        </tags>
        <title class="ltx_runin"><tag><text font="bold">Proof</text></tag><text font="bold"> (of nothing)</text></title>
        <para xml:id="ThmProofx1.p1">
          <equationgroup class="ltx_eqn_eqnarray" xml:id="S1.EGx2">
            <equation xml:id="S1.Ex4">
              <MathFork>
                <Math tex="\displaystyle f(z)=\frac{1}{2\pi i}\int\limits_{\partial D}\frac{f(\zeta)}{%&#10;\zeta-z}d\zeta=\frac{1}{2\pi}\int\limits_{0}^{2\pi}f(z_{0}+re^{it})dt" text="f * z = (1 / (2 * pi * i)) * (integral _ (partial-differential@(D)))@(((f * zeta) / (zeta - z)) * differential-d@(zeta)) = (1 / (2 * pi)) * ((integral _ 0) ^ (2 * pi))@(f * (z _ 0 + r * e ^ (i * t)) * differential-d@(t))" xml:id="S1.Ex4.m4">
                  <XMath>
                    <XMApp>
                      <XMTok meaning="multirelation"/>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMTok font="italic" role="UNKNOWN">f</XMTok>
                        <XMDual>
                          <XMRef idref="S1.Ex4.m4.2"/>
                          <XMWrap>
                            <XMTok role="OPEN" stretchy="false">(</XMTok>
                            <XMTok font="italic" role="UNKNOWN" xml:id="S1.Ex4.m4.2">z</XMTok>
                            <XMTok role="CLOSE" stretchy="false">)</XMTok>
                          </XMWrap>
                        </XMDual>
                      </XMApp>
                      <XMTok meaning="equals" role="RELOP">=</XMTok>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMApp>
                          <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                          <XMTok meaning="1" role="NUMBER">1</XMTok>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok meaning="2" role="NUMBER">2</XMTok>
                            <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                            <XMTok font="italic" role="UNKNOWN">i</XMTok>
                          </XMApp>
                        </XMApp>
                        <XMApp>
                          <XMApp scriptpos="mid">
                            <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                            <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                            <XMApp>
                              <XMTok fontsize="70%" meaning="partial-differential" name="partial" role="OPERATOR">∂</XMTok>
                              <XMTok font="italic" fontsize="70%" role="UNKNOWN">D</XMTok>
                            </XMApp>
                          </XMApp>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMApp>
                              <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                <XMDual>
                                  <XMRef idref="S1.Ex4.m4.1"/>
                                  <XMWrap>
                                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                                    <XMTok font="italic" name="zeta" role="UNKNOWN" xml:id="S1.Ex4.m4.1">ζ</XMTok>
                                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                                  </XMWrap>
                                </XMDual>
                              </XMApp>
                              <XMApp>
                                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                                <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                <XMTok font="italic" role="UNKNOWN">z</XMTok>
                              </XMApp>
                            </XMApp>
                            <XMApp>
                              <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                              <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                            </XMApp>
                          </XMApp>
                        </XMApp>
                      </XMApp>
                      <XMTok meaning="equals" role="RELOP">=</XMTok>
                      <XMApp>
                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                        <XMApp>
                          <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                          <XMTok meaning="1" role="NUMBER">1</XMTok>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok meaning="2" role="NUMBER">2</XMTok>
                            <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                          </XMApp>
                        </XMApp>
                        <XMApp>
                          <XMApp scriptpos="mid">
                            <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                            <XMApp scriptpos="mid">
                              <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                              <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                              <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                            </XMApp>
                            <XMApp>
                              <XMTok meaning="times" role="MULOP">⁢</XMTok>
                              <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                              <XMTok font="italic" fontsize="70%" name="pi" role="UNKNOWN">π</XMTok>
                            </XMApp>
                          </XMApp>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok font="italic" role="UNKNOWN">f</XMTok>
                            <XMDual>
                              <XMRef idref="S1.Ex4.m4.3"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMApp xml:id="S1.Ex4.m4.3">
                                  <XMTok meaning="plus" role="ADDOP">+</XMTok>
                                  <XMApp>
                                    <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                                    <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                    <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                                  </XMApp>
                                  <XMApp>
                                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                    <XMTok font="italic" role="UNKNOWN">r</XMTok>
                                    <XMApp>
                                      <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                                      <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                      <XMApp>
                                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                        <XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
                                        <XMTok font="italic" fontsize="70%" role="UNKNOWN">t</XMTok>
                                      </XMApp>
                                    </XMApp>
                                  </XMApp>
                                </XMApp>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                            <XMApp>
                              <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                              <XMTok font="italic" role="UNKNOWN">t</XMTok>
                            </XMApp>
                          </XMApp>
                        </XMApp>
                      </XMApp>
                    </XMApp>
                  </XMath>
                </Math>
                <MathBranch>
                  <tr>
                    <td align="right"><Math mode="inline" tex="\displaystyle f(z)" text="f * z" xml:id="S1.Ex3.m1">
                        <XMath>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok font="italic" role="UNKNOWN">f</XMTok>
                            <XMDual>
                              <XMRef idref="S1.Ex3.m1.1"/>
                              <XMWrap>
                                <XMTok role="OPEN" stretchy="false">(</XMTok>
                                <XMTok font="italic" role="UNKNOWN" xml:id="S1.Ex3.m1.1">z</XMTok>
                                <XMTok role="CLOSE" stretchy="false">)</XMTok>
                              </XMWrap>
                            </XMDual>
                          </XMApp>
                        </XMath>
                      </Math></td>
                    <td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S1.Ex3.m2">
                        <XMath>
                          <XMTok meaning="equals" role="RELOP">=</XMTok>
                        </XMath>
                      </Math></td>
                    <td align="left"><Math mode="inline" tex="\displaystyle\frac{1}{2\pi i}\int\limits_{\partial D}\frac{f(\zeta)}{\zeta-z}d\zeta" text="(1 / (2 * pi * i)) * (integral _ (partial-differential@(D)))@(((f * zeta) / (zeta - z)) * differential-d@(zeta))" xml:id="S1.Ex3.m3">
                        <XMath>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMApp>
                              <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                              <XMTok meaning="1" role="NUMBER">1</XMTok>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok meaning="2" role="NUMBER">2</XMTok>
                                <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                                <XMTok font="italic" role="UNKNOWN">i</XMTok>
                              </XMApp>
                            </XMApp>
                            <XMApp>
                              <XMApp scriptpos="mid">
                                <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                                <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                                <XMApp>
                                  <XMTok fontsize="70%" meaning="partial-differential" name="partial" role="OPERATOR">∂</XMTok>
                                  <XMTok font="italic" fontsize="70%" role="UNKNOWN">D</XMTok>
                                </XMApp>
                              </XMApp>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMApp>
                                  <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                                  <XMApp>
                                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                    <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                    <XMDual>
                                      <XMRef idref="S1.Ex3.m3.1"/>
                                      <XMWrap>
                                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                                        <XMTok font="italic" name="zeta" role="UNKNOWN" xml:id="S1.Ex3.m3.1">ζ</XMTok>
                                        <XMTok role="CLOSE" stretchy="false">)</XMTok>
                                      </XMWrap>
                                    </XMDual>
                                  </XMApp>
                                  <XMApp>
                                    <XMTok meaning="minus" role="ADDOP">-</XMTok>
                                    <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                    <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                  </XMApp>
                                </XMApp>
                                <XMApp>
                                  <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                                  <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                </XMApp>
                              </XMApp>
                            </XMApp>
                          </XMApp>
                        </XMath>
                      </Math></td>
                  </tr>
                  <tr>
                    <td align="right"/>
                    <td align="center"><Math mode="inline" tex="\displaystyle=" text="=" xml:id="S1.Ex4.m2">
                        <XMath>
                          <XMTok meaning="equals" role="RELOP">=</XMTok>
                        </XMath>
                      </Math></td>
                    <td align="left"><Math mode="inline" tex="\displaystyle\frac{1}{2\pi}\int\limits_{0}^{2\pi}f(z_{0}+re^{it})dt" text="(1 / (2 * pi)) * ((integral _ 0) ^ (2 * pi))@(f * (z _ 0 + r * e ^ (i * t)) * differential-d@(t))" xml:id="S1.Ex4.m3">
                        <XMath>
                          <XMApp>
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMApp>
                              <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                              <XMTok meaning="1" role="NUMBER">1</XMTok>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok meaning="2" role="NUMBER">2</XMTok>
                                <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                              </XMApp>
                            </XMApp>
                            <XMApp>
                              <XMApp scriptpos="mid">
                                <XMTok role="SUPERSCRIPTOP" scriptpos="mid2"/>
                                <XMApp scriptpos="mid">
                                  <XMTok role="SUBSCRIPTOP" scriptpos="mid2"/>
                                  <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                                  <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                                </XMApp>
                                <XMApp>
                                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                  <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                                  <XMTok font="italic" fontsize="70%" name="pi" role="UNKNOWN">π</XMTok>
                                </XMApp>
                              </XMApp>
                              <XMApp>
                                <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                <XMTok font="italic" role="UNKNOWN">f</XMTok>
                                <XMDual>
                                  <XMRef idref="S1.Ex4.m3.1"/>
                                  <XMWrap>
                                    <XMTok role="OPEN" stretchy="false">(</XMTok>
                                    <XMApp xml:id="S1.Ex4.m3.1">
                                      <XMTok meaning="plus" role="ADDOP">+</XMTok>
                                      <XMApp>
                                        <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                                        <XMTok font="italic" role="UNKNOWN">z</XMTok>
                                        <XMTok fontsize="70%" meaning="0" role="NUMBER">0</XMTok>
                                      </XMApp>
                                      <XMApp>
                                        <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                        <XMTok font="italic" role="UNKNOWN">r</XMTok>
                                        <XMApp>
                                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                                          <XMTok font="italic" role="UNKNOWN">e</XMTok>
                                          <XMApp>
                                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                                            <XMTok font="italic" fontsize="70%" role="UNKNOWN">i</XMTok>
                                            <XMTok font="italic" fontsize="70%" role="UNKNOWN">t</XMTok>
                                          </XMApp>
                                        </XMApp>
                                      </XMApp>
                                    </XMApp>
                                    <XMTok role="CLOSE" stretchy="false">)</XMTok>
                                  </XMWrap>
                                </XMDual>
                                <XMApp>
                                  <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                                  <XMTok font="italic" role="UNKNOWN">t</XMTok>
                                </XMApp>
                              </XMApp>
                            </XMApp>
                          </XMApp>
                        </XMath>
                      </Math></td>
                  </tr>
                </MathBranch>
              </MathFork>
            </equation>
          </equationgroup>
          <p><text class="ltx_align_floatright" font="italic"><rule height="4.3pt" width="4.3pt"/></text></p>
        </para>
      </theorem>
      <para xml:id="ThmTheorem1.p4">
        <p><text font="slanted">That’s it (the end of the Theorem).
<text class="ltx_align_floatright"><Math mode="inline" tex="\diamondsuit" text="diamondsuit" xml:id="ThmTheorem1.p4.m1">
                <XMath>
                  <XMTok font="upright" name="diamondsuit" role="UNKNOWN">♢</XMTok>
                </XMath>
              </Math></text></text></p>
      </para>
    </theorem>
    <para xml:id="S1.p2">
      <p>If there are some environments in the same thm-environment,
the last one gets the endmark:</p>
    </para>
    <para xml:id="S1.p3">
      <p><rule height="1px" width="100%"/></p>
    </para>
    <theorem class="ltx_theorem_Definition" inlist="thm theorem:Definition" xml:id="ThmDefinition1">
      <tags>
        <tag>Definition 1</tag>
        <tag role="refnum">1</tag>
        <tag role="typerefnum">Definition 1</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">Definition 1</text></tag><text font="bold"> (With a list).</text></title>
      <para xml:id="ThmDefinition1.p1">
        <equation xml:id="S1.E4">
          <tags>
            <tag>(4)</tag>
            <tag role="refnum">4</tag>
          </tags>
          <Math mode="display" tex="\int_{\gamma}f(z)\,dz:=\int_{a}^{b}f(\gamma(t))\gamma^{\prime}(t)\,dt" text="(integral _ gamma)@(f * z * differential-d@(z)) assign ((integral _ a) ^ b)@(f * gamma * t * gamma ^ prime * t * differential-d@(t))" xml:id="S1.E4.m1">
            <XMath>
              <XMApp>
                <XMTok meaning="assign" role="RELOP">:=</XMTok>
                <XMApp>
                  <XMApp>
                    <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                    <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP">∫</XMTok>
                    <XMTok font="italic" fontsize="70%" name="gamma" role="UNKNOWN">γ</XMTok>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok font="italic" role="UNKNOWN">f</XMTok>
                    <XMDual>
                      <XMRef idref="S1.E4.m1.1"/>
                      <XMWrap>
                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                        <XMTok font="italic" role="UNKNOWN" xml:id="S1.E4.m1.1">z</XMTok>
                        <XMTok role="CLOSE" rpadding="1.7pt" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                    <XMApp>
                      <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                      <XMTok font="italic" role="UNKNOWN">z</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
                <XMApp>
                  <XMApp>
                    <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                    <XMApp>
                      <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                      <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP">∫</XMTok>
                      <XMTok font="italic" fontsize="70%" role="UNKNOWN">a</XMTok>
                    </XMApp>
                    <XMTok font="italic" fontsize="70%" role="UNKNOWN">b</XMTok>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok font="italic" role="UNKNOWN">f</XMTok>
                    <XMDual>
                      <XMRef idref="S1.E4.m1.4"/>
                      <XMWrap>
                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                        <XMApp xml:id="S1.E4.m1.4">
                          <XMTok meaning="times" role="MULOP">⁢</XMTok>
                          <XMTok font="italic" name="gamma" role="UNKNOWN">γ</XMTok>
                          <XMDual>
                            <XMRef idref="S1.E4.m1.2"/>
                            <XMWrap>
                              <XMTok role="OPEN" stretchy="false">(</XMTok>
                              <XMTok font="italic" role="UNKNOWN" xml:id="S1.E4.m1.2">t</XMTok>
                              <XMTok role="CLOSE" stretchy="false">)</XMTok>
                            </XMWrap>
                          </XMDual>
                        </XMApp>
                        <XMTok role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok font="italic" name="gamma" role="UNKNOWN">γ</XMTok>
                      <XMTok fontsize="70%" name="prime" role="SUPOP">′</XMTok>
                    </XMApp>
                    <XMDual>
                      <XMRef idref="S1.E4.m1.3"/>
                      <XMWrap>
                        <XMTok role="OPEN" stretchy="false">(</XMTok>
                        <XMTok font="italic" role="UNKNOWN" xml:id="S1.E4.m1.3">t</XMTok>
                        <XMTok role="CLOSE" rpadding="1.7pt" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                    <XMApp>
                      <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                      <XMTok font="italic" role="UNKNOWN">t</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMApp>
            </XMath>
          </Math>
        </equation>
        <itemize xml:id="S1.I1">
          <item xml:id="S1.I1.i1">
            <tags>
              <tag>•</tag>
              <tag role="typerefnum">1st item</tag>
            </tags>
            <para xml:id="S1.I1.i1.p1">
              <p><text font="italic">you’ve seen, how it works for text and</text></p>
            </para>
          </item>
          <item xml:id="S1.I1.i2">
            <tags>
              <tag>•</tag>
              <tag role="typerefnum">2nd item</tag>
            </tags>
            <para xml:id="S1.I1.i2.p1">
              <p><text font="italic">math environments,</text></p>
            </para>
          </item>
          <item xml:id="S1.I1.i3">
            <tags>
              <tag>•</tag>
              <tag role="typerefnum">3rd item</tag>
            </tags>
            <para xml:id="S1.I1.i3.p1">
              <p><text font="italic">and it works for lists.</text></p>
            </para>
          </item>
        </itemize>
        <p><text class="ltx_align_floatright" font="italic"><Math mode="inline" tex="\clubsuit" text="clubsuit" xml:id="ThmDefinition1.p1.m1">
              <XMath>
                <XMTok font="upright" name="clubsuit" role="UNKNOWN">♣</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_Corollary" inlist="thm theorem:Corollary" xml:id="ThmTheorem2">
      <tags>
        <tag>2 Corollary</tag>
        <tag role="refnum">2</tag>
        <tag role="typerefnum">Corollary 2</tag>
      </tags>
      <title><tag><text font="bold">2 Corollary</text></tag><text font="bold"> (Q.E.D.):</text></title>
      <para xml:id="ThmTheorem2.p1">
        <p><text font="slanted">And here is a trivial corollary, which is ended by
<text class="ltx_align_floatright">q.e.d</text><text class="ltx_align_floatright"><Math mode="inline" tex="\spadesuit" text="spadesuit" xml:id="ThmTheorem2.p1.m1">
                <XMath>
                  <XMTok font="upright" name="spadesuit" role="UNKNOWN">♠</XMTok>
                </XMath>
              </Math></text></text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_Example" inlist="thm theorem:Example" xml:id="ThmExample3">
      <tags>
        <tag>3 Example</tag>
        <tag role="refnum">3</tag>
        <tag role="typerefnum">Example 3</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">3 Example</text></tag></title>
      <para xml:id="ThmExample3.p1">
        <equation xml:id="S1.Ex5">
          <Math mode="display" tex="f^{(n)}(z)=\frac{n!}{2\pi i}\int\limits_{\partial D}\frac{f(\zeta)}{(\zeta-z)^%&#10;{n+1}}d\zeta" text="f ^ n * z = (nfactorial / (2 * pi * i)) * (integral _ (partial-differential@(D)))@(((f * zeta) / (zeta - z) ^ (n + 1)) * differential-d@(zeta))" xml:id="S1.Ex5.m1">
            <XMath>
              <XMApp>
                <XMTok meaning="equals" role="RELOP">=</XMTok>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMApp>
                    <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                    <XMTok font="italic" role="UNKNOWN">f</XMTok>
                    <XMDual>
                      <XMRef idref="S1.Ex5.m1.1"/>
                      <XMWrap>
                        <XMTok fontsize="70%" role="OPEN" stretchy="false">(</XMTok>
                        <XMTok font="italic" fontsize="70%" role="UNKNOWN" xml:id="S1.Ex5.m1.1">n</XMTok>
                        <XMTok fontsize="70%" role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                  </XMApp>
                  <XMDual>
                    <XMRef idref="S1.Ex5.m1.4"/>
                    <XMWrap>
                      <XMTok role="OPEN" stretchy="false">(</XMTok>
                      <XMTok font="italic" role="UNKNOWN" xml:id="S1.Ex5.m1.4">z</XMTok>
                      <XMTok role="CLOSE" stretchy="false">)</XMTok>
                    </XMWrap>
                  </XMDual>
                </XMApp>
                <XMApp>
                  <XMTok meaning="times" role="MULOP">⁢</XMTok>
                  <XMApp>
                    <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                    <XMApp>
                      <XMTok meaning="factorial" role="POSTFIX">!</XMTok>
                      <XMTok font="italic" role="UNKNOWN">n</XMTok>
                    </XMApp>
                    <XMApp>
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok meaning="2" role="NUMBER">2</XMTok>
                      <XMTok font="italic" name="pi" role="UNKNOWN">π</XMTok>
                      <XMTok font="italic" role="UNKNOWN">i</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMApp scriptpos="mid">
                      <XMTok role="SUBSCRIPTOP" scriptpos="mid1"/>
                      <XMTok mathstyle="display" meaning="integral" name="int" role="INTOP" scriptpos="mid">∫</XMTok>
                      <XMApp>
                        <XMTok fontsize="70%" meaning="partial-differential" name="partial" role="OPERATOR">∂</XMTok>
                        <XMTok font="italic" fontsize="70%" role="UNKNOWN">D</XMTok>
                      </XMApp>
                    </XMApp>
                    <XMApp>
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMApp>
                        <XMTok mathstyle="display" meaning="divide" role="FRACOP"/>
                        <XMApp>
                          <XMTok meaning="times" role="MULOP">⁢</XMTok>
                          <XMTok font="italic" role="UNKNOWN">f</XMTok>
                          <XMDual>
                            <XMRef idref="S1.Ex5.m1.2"/>
                            <XMWrap>
                              <XMTok role="OPEN" stretchy="false">(</XMTok>
                              <XMTok font="italic" name="zeta" role="UNKNOWN" xml:id="S1.Ex5.m1.2">ζ</XMTok>
                              <XMTok role="CLOSE" stretchy="false">)</XMTok>
                            </XMWrap>
                          </XMDual>
                        </XMApp>
                        <XMApp>
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMDual>
                            <XMRef idref="S1.Ex5.m1.3"/>
                            <XMWrap>
                              <XMTok role="OPEN" stretchy="false">(</XMTok>
                              <XMApp xml:id="S1.Ex5.m1.3">
                                <XMTok meaning="minus" role="ADDOP">-</XMTok>
                                <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                                <XMTok font="italic" role="UNKNOWN">z</XMTok>
                              </XMApp>
                              <XMTok role="CLOSE" stretchy="false">)</XMTok>
                            </XMWrap>
                          </XMDual>
                          <XMApp>
                            <XMTok fontsize="70%" meaning="plus" role="ADDOP">+</XMTok>
                            <XMTok font="italic" fontsize="70%" role="UNKNOWN">n</XMTok>
                            <XMTok fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
                          </XMApp>
                        </XMApp>
                      </XMApp>
                      <XMApp>
                        <XMTok font="italic" meaning="differential-d" role="DIFFOP">d</XMTok>
                        <XMTok font="italic" name="zeta" role="UNKNOWN">ζ</XMTok>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMApp>
            </XMath>
          </Math>
        </equation>
        <p>If there is some text after an environment, the endmark is put
after the text.
<text class="ltx_align_floatright"><Math mode="inline" tex="\ast" text="ast" xml:id="ThmExample3.p1.m1">
              <XMath>
                <XMTok name="ast" role="MULOP">∗</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_Example" inlist="thm theorem:Example" xml:id="ThmExample4">
      <tags>
        <tag>4 Example</tag>
        <tag role="refnum">4</tag>
        <tag role="typerefnum">Example 4</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">4 Example</text></tag><text font="bold"> (Using —verbatim—)</text></title>
      <para xml:id="ThmExample4.p1">
        <verbatim font="typewriter">
And, it also works for verbatim
... when the end{verbatim} is in the
same line as the text ends. 
</verbatim>
        <p><text class="ltx_align_floatright"><Math mode="inline" tex="\ast" text="ast" xml:id="ThmExample4.p1.m1">
              <XMath>
                <XMTok name="ast" role="MULOP">∗</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <para xml:id="S1.p4">
      <p>There must be no empty line in the input before the end
(since then, the end mark is ignored) <break/></p>
    </para>
    <theorem class="ltx_theorem_Theorem" inlist="thm theorem:Theorem" labels="LABEL:ex-empty-line" xml:id="ThmTheorem3">
      <tags>
        <tag>3 Theorem</tag>
        <tag role="refnum">3</tag>
        <tag role="typerefnum">Theorem 3</tag>
      </tags>
      <title class="ltx_outdent"><tag><text font="bold">3 Theorem</text></tag><text font="bold">:</text></title>
      <para xml:id="ThmTheorem3.p1">
        <p><text font="slanted">some text … but no end mark</text></p>
      </para>
      <para xml:id="ThmTheorem3.p2">
        <p><text class="ltx_align_floatright" font="slanted"><Math mode="inline" tex="\diamondsuit" text="diamondsuit" xml:id="ThmTheorem3.p2.m1">
              <XMath>
                <XMTok font="upright" name="diamondsuit" role="UNKNOWN">♢</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <para xml:id="S1.p5">
      <p>Now, there is a corollary which should appear with a different
name in the list of corollaries:</p>
    </para>
    <theorem class="ltx_theorem_Corollary" inlist="thm theorem:Corollary*" labels="LABEL:otherlabel" xml:id="ThmTheorem4">
      <tags>
        <tag>4 Corollary</tag>
        <tag role="refnum">4</tag>
        <tag role="typerefnum">Corollary 4</tag>
      </tags>
      <title><tag><text font="bold">4 Corollary</text></tag><text font="bold"> (title in text):</text></title>
      <para xml:id="ThmTheorem4.p1">
        <p><text font="slanted">let’s do something weird:</text></p>
        <p align="center"><text font="slanted">It also works in the</text></p>
        <p align="center"><text font="slanted">center</text></p>
        <p align="center"><text font="slanted">environment.</text></p>
        <p><text class="ltx_align_floatright" font="slanted"><Math mode="inline" tex="\spadesuit" text="spadesuit" xml:id="ThmTheorem4.p1.m1">
              <XMath>
                <XMTok font="upright" name="spadesuit" role="UNKNOWN">♠</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_Theorem" inlist="thm theorem:Theorem" xml:id="ThmTheorem5">
      <tags>
        <tag>5 Theorem</tag>
        <tag role="refnum">5</tag>
        <tag role="typerefnum">Theorem 5</tag>
      </tags>
      <title class="ltx_outdent"><tag><text font="bold">5 Theorem</text></tag><text font="bold"> (Quote):</text></title>
      <para xml:id="ThmTheorem5.p1">
        <quote>
          <p><text font="slanted">In quote environments, the text is normally indented from left
and right by the same space. The endmark is not indented from the
right margin, i.e., it is typeset to the right margin of the
surrounding text.</text></p>
        </quote>
        <p><text class="ltx_align_floatright" font="slanted"><Math mode="inline" tex="\diamondsuit" text="diamondsuit" xml:id="ThmTheorem5.p1.m1">
              <XMath>
                <XMTok font="upright" name="diamondsuit" role="UNKNOWN">♢</XMTok>
              </XMath>
            </Math></text></p>
      </para>
    </theorem>
    <para xml:id="S1.p6">
      <p>Here is an example for turning off the endmark automatics and
manual handling:</p>
    </para>
    <theorem class="ltx_theorem_Theorem" inlist="thm theorem:Theorem" labels="LABEL:somelabel" xml:id="ThmTheorem6">
      <tags>
        <tag>6 Theorem</tag>
        <tag role="refnum">6</tag>
        <tag role="typerefnum">Theorem 6</tag>
      </tags>
      <title class="ltx_outdent"><tag><text font="bold">6 Theorem</text></tag><text font="bold"> (Manual End Mark):</text></title>
      <para xml:id="ThmTheorem6.p1">
        <p><text font="slanted">a line of text with a manually set endmark  <text class="ltx_align_floatright"><Math mode="inline" tex="\diamondsuit" text="diamondsuit" xml:id="ThmTheorem6.p1.m1">
                <XMath>
                  <XMTok font="upright" name="diamondsuit" role="UNKNOWN">♢</XMTok>
                </XMath>
              </Math></text><break/>some more text, but no automatic endmark set.</text></p>
      </para>
    </theorem>
    <para xml:id="S1.p7">
      <p>Also, one should note, that — — is inserted to set
the endmark at the right margin.</p>
    </para>
    <theorem class="ltx_theorem_Example" inlist="thm theorem:Example" xml:id="ThmExample5">
      <tags>
        <tag>5 Example</tag>
        <tag role="refnum">5</tag>
        <tag role="typerefnum">Example 5</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">5 Example</text></tag><text font="bold"> (Quickie)</text></title>
      <para xml:id="ThmExample5.p1">
        <p>It also works for short one’s.</p>
      </para>
    </theorem>
    <para xml:id="S1.p8">
      <p>If you are tired of the greek numbers and the indentation for lemmata …
you can redefine it:</p>
    </para>
    <theorem class="ltx_theorem_Lemma" inlist="thm theorem:Lemma" xml:id="ThmLemma4">
      <tags>
        <tag>4 Lemma</tag>
        <tag role="refnum">4</tag>
        <tag role="typerefnum">Lemma 4</tag>
      </tags>
      <title><tag><text font="bold">4 Lemma</text></tag><text font="bold">:</text></title>
      <para xml:id="ThmLemma4.p1">
        <p><text font="slanted">another lemma, with arabic numbering … note that the numbering
continues.</text></p>
      </para>
    </theorem>
    <para xml:id="S1.p9">
      <p>the optional argument (i.e. the ‘theorem’-name) can be accessed by
eg. <verbatim font="typewriter">\Theoremname</verbatim></p>
    </para>
    <theorem class="ltx_theorem_Theorem" inlist="thm theorem:Theorem" xml:id="ThmTheorem7">
      <tags>
        <tag>7 Theorem</tag>
        <tag role="refnum">7</tag>
        <tag role="typerefnum">Theorem 7</tag>
      </tags>
      <title class="ltx_outdent"><tag><text font="bold">7 Theorem</text></tag><text font="bold"> (somename):</text></title>
      <para xml:id="ThmTheorem7.p1">
        <p><text font="slanted">Obviously, we are in Theorem somename.</text></p>
      </para>
    </theorem>
    <para xml:id="S1.p10">
      <p>Now, we define an environment —KappaTheorem— which uses the same
style parameters as Theorems and is numbered together with
Corollaries (Theorems are also numbered with Corollaries).
Note that we define a complex header text and a complex end mark.</p>
    </para>
    <theorem class="ltx_theorem_KappaTheorem" inlist="thm theorem:KappaTheorem" labels="LABEL:kappatheorem1" xml:id="ThmTheorem8">
      <tags>
        <tag>8 <Math mode="inline" tex="\kappa" text="kappa" xml:id="ThmTheorem8.m1">
            <XMath>
              <XMTok font="italic" name="kappa" role="UNKNOWN">κ</XMTok>
            </XMath>
          </Math>-Theorem</tag>
        <tag role="refnum">8</tag>
        <tag role="typerefnum"><Math mode="inline" tex="\kappa" text="kappa" xml:id="ThmTheorem8.m2">
            <XMath>
              <XMTok font="italic" name="kappa" role="UNKNOWN">κ</XMTok>
            </XMath>
          </Math>-Theorem 8</tag>
      </tags>
      <title><tag><text font="bold">8 </text><Math mode="inline" tex="\kappa" text="kappa" xml:id="ThmTheorem8.m3">
            <XMath>
              <XMTok font="italic" name="kappa" role="UNKNOWN">κ</XMTok>
            </XMath>
          </Math><text font="bold">-Theorem</text></tag><text font="bold"> (1st <Math mode="inline" tex="\kappa" text="kappa" xml:id="ThmTheorem8.m4">
            <XMath>
              <XMTok font="medium italic" name="kappa" role="UNKNOWN">κ</XMTok>
            </XMath>
          </Math>-Theorem):</text></title>
      <para xml:id="ThmTheorem8.p1">
        <p><text font="slanted">That’s the first Kappa-Theorem.</text></p>
      </para>
    </theorem>
    <subsection inlist="toc" labels="LABEL:sec-ExtRef" xml:id="S1.SS1">
      <tags>
        <tag>1.1</tag>
        <tag role="refnum">1.1</tag>
        <tag role="typerefnum">§1.1</tag>
      </tags>
      <title><tag close=" ">1.1</tag>Extended Referencing Features</title>
      <para xml:id="S1.SS1.p1">
        <p>This is <ref labelref="LABEL:sec-ExtRef" show="typerefnum"/>.
A theorem end mark has been set manually in <ref labelref="LABEL:somelabel" show="typerefnum"/>.
A center environment has been shown in <ref labelref="LABEL:otherlabel" show="typerefnum"/>.
The first Kappa-Theorem has been given in <ref labelref="LABEL:kappatheorem1" show="typerefnum"/>.</p>
      </para>
    </subsection>
    <subsection inlist="toc" xml:id="S1.SS2">
      <tags>
        <tag>1.2</tag>
        <tag role="refnum">1.2</tag>
        <tag role="typerefnum">§1.2</tag>
      </tags>
      <title><tag close=" ">1.2</tag>Framed and Shaded Theorems</title>
      <theorem class="ltx_framed ltx_theorem_importantTheorem" inlist="thm theorem:importantTheorem" xml:id="ThmTheorem9">
        <tags>
          <tag>Theorem 9</tag>
          <tag role="refnum">9</tag>
          <tag role="typerefnum">Theorem 9</tag>
        </tags>
        <title><tag><text font="bold">Theorem 9</text></tag><text font="bold"> (Important Theorem):</text></title>
        <para xml:id="ThmTheorem9.p1">
          <p><text font="slanted">This is an important theorem.</text></p>
        </para>
      </theorem>
      <theorem backgroundcolor="#FFE6E6" class="ltx_theorem_moreImportantTheorem" inlist="thm theorem:moreImportantTheorem" xml:id="ThmTheorem10">
        <tags>
          <tag>Theorem 10</tag>
          <tag role="refnum">10</tag>
          <tag role="typerefnum">Theorem 10</tag>
        </tags>
        <title><tag><text font="bold">Theorem 10</text></tag><text font="bold"> (More Important Theorem):</text></title>
        <para xml:id="ThmTheorem10.p1">
          <p><text font="slanted">This is a more important theorem.</text></p>
        </para>
      </theorem>
      <theorem backgroundcolor="#FF8080" class="ltx_theorem_evenMoreImportantTheorem" inlist="thm theorem:evenMoreImportantTheorem" xml:id="ThmTheorem11">
        <tags>
          <tag>Theorem 11</tag>
          <tag role="refnum">11</tag>
          <tag role="typerefnum">Theorem 11</tag>
        </tags>
        <title><tag><text font="bold">Theorem 11</text></tag><text font="bold"> (Even More Important Theorem):</text></title>
        <para xml:id="ThmTheorem11.p1">
          <p><text font="slanted">This is an even more important theorem.</text></p>
        </para>
      </theorem>
    </subsection>
    <subsection inlist="toc" xml:id="S1.SS3">
      <tags>
        <tag>1.3</tag>
        <tag role="refnum">1.3</tag>
        <tag role="typerefnum">§1.3</tag>
      </tags>
      <title><tag close=" ">1.3</tag>Lists of Theorems and Friends</title>
      <TOC lists="theorem:Lemma"/>
      <TOC lists="theorem:Example"/>
      <TOC lists="theorem:Theorem theorem:importantTheorem theorem:moreImportantTheorem theorem:evenMoreImportantTheorem theorem:MostImportantTheorem theorem:Lemma"/>
    </subsection>
  </section>
</document>
