<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml package="amsthm"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML" class="ltx_authors_1line">
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  <title>Newtheorem and theoremstyle test</title>
  <creator role="author">
    <personname>Michael Downes<break/>updated by Barbara Beeton</personname>
  </creator>
  <date role="creation">none</date>
  <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>Test of standard theorem styles</title>
    <para xml:id="S1.p1">
      <p>Ahlfors’ Lemma gives the principal criterion for obtaining lower bounds
on the Kobayashi metric.</p>
    </para>
    <theorem class="ltx_theorem_Ahlfors" inlist="thm theorem:Ahlfors" xml:id="ThmAhlforsx1">
      <tags>
        <tag>Ahlfors’ Lemma</tag>
        <tag role="typerefnum">Ahlfors’ Lemma</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">Ahlfors’ Lemma</text></tag><text font="bold">.</text></title>
      <para xml:id="ThmAhlforsx1.p1">
        <p><text font="italic">Let <Math mode="inline" tex="ds^{2}=h(z)|dz|^{2}" text="d * s ^ 2 = h * z * (absolute-value@(d * z)) ^ 2" xml:id="ThmAhlforsx1.p1.m1">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="equals" role="RELOP">=</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">d</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok role="UNKNOWN">s</XMTok>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">h</XMTok>
                    <XMDual>
                      <XMRef idref="ThmAhlforsx1.p1.m1.1"/>
                      <XMWrap>
                        <XMTok font="upright" role="OPEN" stretchy="false">(</XMTok>
                        <XMTok role="UNKNOWN" xml:id="ThmAhlforsx1.p1.m1.1">z</XMTok>
                        <XMTok font="upright" role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMDual>
                        <XMApp>
                          <XMTok meaning="absolute-value"/>
                          <XMRef idref="ThmAhlforsx1.p1.m1.2"/>
                        </XMApp>
                        <XMWrap>
                          <XMTok font="upright" role="VERTBAR" stretchy="false">|</XMTok>
                          <XMApp xml:id="ThmAhlforsx1.p1.m1.2">
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok role="UNKNOWN">d</XMTok>
                            <XMTok role="UNKNOWN">z</XMTok>
                          </XMApp>
                          <XMTok font="upright" role="VERTBAR" stretchy="false">|</XMTok>
                        </XMWrap>
                      </XMDual>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math> be a Hermitian pseudo-metric on
<Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="ThmAhlforsx1.p1.m2">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math>, <Math mode="inline" tex="h\in C^{2}(\mathbf{D}_{r})" text="h element-of C ^ 2 * D _ r" xml:id="ThmAhlforsx1.p1.m3">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="element-of" name="in" role="RELOP">∈</XMTok>
                  <XMTok role="UNKNOWN">h</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok role="UNKNOWN">C</XMTok>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                    <XMDual>
                      <XMRef idref="ThmAhlforsx1.p1.m3.1"/>
                      <XMWrap>
                        <XMTok font="upright" role="OPEN" stretchy="false">(</XMTok>
                        <XMApp xml:id="ThmAhlforsx1.p1.m3.1">
                          <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                          <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                          <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                        </XMApp>
                        <XMTok font="upright" role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math>, with <Math mode="inline" tex="\omega" text="omega" xml:id="ThmAhlforsx1.p1.m4">
              <XMath>
                <XMTok name="omega" role="UNKNOWN">ω</XMTok>
              </XMath>
            </Math> the associated
<Math mode="inline" tex="(1,1)" text="open-interval@(1, 1)" xml:id="ThmAhlforsx1.p1.m5">
              <XMath>
                <XMDual>
                  <XMApp>
                    <XMTok meaning="open-interval"/>
                    <XMRef idref="ThmAhlforsx1.p1.m5.1"/>
                    <XMRef idref="ThmAhlforsx1.p1.m5.2"/>
                  </XMApp>
                  <XMWrap>
                    <XMTok font="upright" role="OPEN" stretchy="false">(</XMTok>
                    <XMTok font="upright" meaning="1" role="NUMBER" xml:id="ThmAhlforsx1.p1.m5.1">1</XMTok>
                    <XMTok font="upright" role="PUNCT">,</XMTok>
                    <XMTok font="upright" meaning="1" role="NUMBER" xml:id="ThmAhlforsx1.p1.m5.2">1</XMTok>
                    <XMTok font="upright" role="CLOSE" stretchy="false">)</XMTok>
                  </XMWrap>
                </XMDual>
              </XMath>
            </Math>-form. If <Math mode="inline" tex="\mathop{\mathrm{Ric}}\nolimits\omega\geq\omega" text="Ric@(omega) &gt;= omega" xml:id="ThmAhlforsx1.p1.m6">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
                  <XMApp>
                    <XMTok font="upright" role="BIGOP">Ric</XMTok>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  </XMApp>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                </XMApp>
              </XMath>
            </Math> on <Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="ThmAhlforsx1.p1.m7">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math>,
then <Math mode="inline" tex="\omega\leq\omega_{r}" text="omega &lt;= omega _ r" xml:id="ThmAhlforsx1.p1.m8">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  <XMApp>
                    <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                    <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math> on all of <Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="ThmAhlforsx1.p1.m9">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math> (or equivalently,
<Math mode="inline" tex="ds^{2}\leq ds_{r}^{2}" text="d * s ^ 2 &lt;= d * (s _ r) ^ 2" xml:id="ThmAhlforsx1.p1.m10">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">d</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok role="UNKNOWN">s</XMTok>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">d</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMApp>
                        <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                        <XMTok role="UNKNOWN">s</XMTok>
                        <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                      </XMApp>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math>).</text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_lem" inlist="thm theorem:lem" xml:id="S1.Thmthm1">
      <tags>
        <tag>Lemma 1.1</tag>
        <tag role="refnum">1.1</tag>
        <tag role="typerefnum">Lemma 1.1</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">Lemma 1.1</text></tag><text font="bold"> </text>(negatively curved families)<text font="bold">.</text></title>
      <para xml:id="S1.Thmthm1.p1">
        <p><text font="italic">Let <Math mode="inline" tex="\{ds_{1}^{2},\dots,ds_{k}^{2}\}" text="set@(d * (s _ 1) ^ 2, dots, d * (s _ k) ^ 2)" xml:id="S1.Thmthm1.p1.m1">
              <XMath>
                <XMDual>
                  <XMApp>
                    <XMTok meaning="set"/>
                    <XMRef idref="S1.Thmthm1.p1.m1.2"/>
                    <XMRef idref="S1.Thmthm1.p1.m1.1"/>
                    <XMRef idref="S1.Thmthm1.p1.m1.3"/>
                  </XMApp>
                  <XMWrap>
                    <XMTok font="upright" role="OPEN" stretchy="false">{</XMTok>
                    <XMApp xml:id="S1.Thmthm1.p1.m1.2">
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok role="UNKNOWN">d</XMTok>
                      <XMApp>
                        <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                        <XMApp>
                          <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                          <XMTok role="UNKNOWN">s</XMTok>
                          <XMTok font="upright" fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
                        </XMApp>
                        <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                      </XMApp>
                    </XMApp>
                    <XMTok font="upright" role="PUNCT">,</XMTok>
                    <XMTok font="upright" name="dots" role="ID" xml:id="S1.Thmthm1.p1.m1.1">…</XMTok>
                    <XMTok font="upright" role="PUNCT">,</XMTok>
                    <XMApp xml:id="S1.Thmthm1.p1.m1.3">
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok role="UNKNOWN">d</XMTok>
                      <XMApp>
                        <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                        <XMApp>
                          <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                          <XMTok role="UNKNOWN">s</XMTok>
                          <XMTok fontsize="70%" role="UNKNOWN">k</XMTok>
                        </XMApp>
                        <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                      </XMApp>
                    </XMApp>
                    <XMTok font="upright" role="CLOSE" stretchy="false">}</XMTok>
                  </XMWrap>
                </XMDual>
              </XMath>
            </Math> be a negatively curved family of metrics
on <Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="S1.Thmthm1.p1.m2">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math>, with associated forms <Math mode="inline" tex="\omega^{1}" text="omega ^ 1" xml:id="S1.Thmthm1.p1.m3">
              <XMath>
                <XMApp>
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  <XMTok font="upright" fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
                </XMApp>
              </XMath>
            </Math>, …, <Math mode="inline" tex="\omega^{k}" text="omega ^ k" xml:id="S1.Thmthm1.p1.m4">
              <XMath>
                <XMApp>
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">k</XMTok>
                </XMApp>
              </XMath>
            </Math>.
Then <Math mode="inline" tex="\omega^{i}\leq\omega_{r}" text="omega ^ i &lt;= omega _ r" xml:id="S1.Thmthm1.p1.m5">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMApp>
                    <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                    <XMTok fontsize="70%" role="UNKNOWN">i</XMTok>
                  </XMApp>
                  <XMApp>
                    <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                    <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math> for all <Math mode="inline" tex="i" text="i" xml:id="S1.Thmthm1.p1.m6">
              <XMath>
                <XMTok role="UNKNOWN">i</XMTok>
              </XMath>
            </Math>.</text></p>
      </para>
    </theorem>
    <para xml:id="S1.p2">
      <p>Then our main theorem:</p>
    </para>
    <theorem class="ltx_theorem_thm" inlist="thm theorem:thm" labels="LABEL:pigspan" xml:id="S1.Thmthm2">
      <tags>
        <tag>Theorem 1.2</tag>
        <tag role="refnum">1.2</tag>
        <tag role="typerefnum">Theorem 1.2</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">Theorem 1.2</text></tag><text font="bold">.</text></title>
      <para xml:id="S1.Thmthm2.p1">
        <p><text font="italic">Let <Math mode="inline" tex="d_{\max}" text="d _ maximum" xml:id="S1.Thmthm2.p1.m1">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok role="UNKNOWN">d</XMTok>
                  <XMTok font="upright" fontsize="70%" meaning="maximum" role="OPFUNCTION" scriptpos="post">max</XMTok>
                </XMApp>
              </XMath>
            </Math> and <Math mode="inline" tex="d_{\min}" text="d _ minimum" xml:id="S1.Thmthm2.p1.m2">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok role="UNKNOWN">d</XMTok>
                  <XMTok font="upright" fontsize="70%" meaning="minimum" role="OPFUNCTION" scriptpos="post">min</XMTok>
                </XMApp>
              </XMath>
            </Math> be the maximum, resp. minimum distance
between any two adjacent vertices of a quadrilateral <Math mode="inline" tex="Q" text="Q" xml:id="S1.Thmthm2.p1.m3">
              <XMath>
                <XMTok role="UNKNOWN">Q</XMTok>
              </XMath>
            </Math>. Let <Math mode="inline" tex="\sigma" text="sigma" xml:id="S1.Thmthm2.p1.m4">
              <XMath>
                <XMTok name="sigma" role="UNKNOWN">σ</XMTok>
              </XMath>
            </Math>
be the diagonal pigspan of a pig <Math mode="inline" tex="P" text="P" xml:id="S1.Thmthm2.p1.m5">
              <XMath>
                <XMTok role="UNKNOWN">P</XMTok>
              </XMath>
            </Math> with four legs.
Then <Math mode="inline" tex="P" text="P" xml:id="S1.Thmthm2.p1.m6">
              <XMath>
                <XMTok role="UNKNOWN">P</XMTok>
              </XMath>
            </Math> is capable of standing on the corners of <Math mode="inline" tex="Q" text="Q" xml:id="S1.Thmthm2.p1.m7">
              <XMath>
                <XMTok role="UNKNOWN">Q</XMTok>
              </XMath>
            </Math> iff</text></p>
        <equation labels="LABEL:sdq" xml:id="S1.E1">
          <tags>
            <tag>(1)</tag>
            <tag role="refnum">1</tag>
          </tags>
          <Math mode="display" tex="\sigma\geq\sqrt{d_{\max}^{2}+d_{\min}^{2}}." text="sigma &gt;= square-root@((d _ maximum) ^ 2 + (d _ minimum) ^ 2)" xml:id="S1.E1.m1">
            <XMath>
              <XMDual>
                <XMRef idref="S1.E1.m1.1"/>
                <XMWrap>
                  <XMApp xml:id="S1.E1.m1.1">
                    <XMTok meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
                    <XMTok font="italic" name="sigma" role="UNKNOWN">σ</XMTok>
                    <XMApp>
                      <XMTok meaning="square-root"/>
                      <XMApp>
                        <XMTok meaning="plus" role="ADDOP">+</XMTok>
                        <XMApp>
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMApp>
                            <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                            <XMTok font="italic" role="UNKNOWN">d</XMTok>
                            <XMTok fontsize="70%" meaning="maximum" role="OPFUNCTION" scriptpos="post">max</XMTok>
                          </XMApp>
                          <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                        </XMApp>
                        <XMApp>
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMApp>
                            <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                            <XMTok font="italic" role="UNKNOWN">d</XMTok>
                            <XMTok fontsize="70%" meaning="minimum" role="OPFUNCTION" scriptpos="post">min</XMTok>
                          </XMApp>
                          <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                        </XMApp>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                  <XMTok role="PERIOD">.</XMTok>
                </XMWrap>
              </XMDual>
            </XMath>
          </Math>
        </equation>
      </para>
    </theorem>
    <theorem class="ltx_theorem_cor" inlist="thm theorem:cor" xml:id="S1.Thmthm3">
      <tags>
        <tag>Corollary 1.3</tag>
        <tag role="refnum">1.3</tag>
        <tag role="typerefnum">Corollary 1.3</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">Corollary 1.3</text></tag><text font="bold">.</text></title>
      <para xml:id="S1.Thmthm3.p1">
        <p><text font="italic">Admitting reflection and rotation, a three-legged pig <Math mode="inline" tex="P" text="P" xml:id="S1.Thmthm3.p1.m1">
              <XMath>
                <XMTok role="UNKNOWN">P</XMTok>
              </XMath>
            </Math> is capable of
standing on the corners of a triangle <Math mode="inline" tex="T" text="T" xml:id="S1.Thmthm3.p1.m2">
              <XMath>
                <XMTok role="UNKNOWN">T</XMTok>
              </XMath>
            </Math> iff (<ref labelref="LABEL:sdq"/>) holds.</text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_rmk" inlist="thm theorem:rmk" xml:id="Thmrmkx1">
      <tags>
        <tag>Remark</tag>
        <tag role="typerefnum">Remark</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="italic">Remark</text></tag><text font="italic">.</text></title>
      <para xml:id="Thmrmkx1.p1">
        <p>As two-legged pigs generally fall over, the case of a polygon of order
<Math mode="inline" tex="2" text="2" xml:id="Thmrmkx1.p1.m1">
            <XMath>
              <XMTok meaning="2" role="NUMBER">2</XMTok>
            </XMath>
          </Math> is uninteresting.</p>
      </para>
    </theorem>
  </section>
  <section inlist="toc" xml:id="S2">
    <tags>
      <tag>2</tag>
      <tag role="refnum">2</tag>
      <tag role="typerefnum">§2</tag>
    </tags>
    <title><tag close=" ">2</tag>Custom theorem styles</title>
    <theorem class="ltx_theorem_exer" inlist="thm theorem:exer" xml:id="Thmexer1">
      <tags>
        <tag>Exercise 1</tag>
        <tag role="refnum">1</tag>
        <tag role="typerefnum">Exercise 1</tag>
      </tags>
      <title><tag><text font="bold">Exercise 1</text></tag><text font="bold">.</text></title>
      <para xml:id="Thmexer1.p1">
        <p><text font="italic">Generalize Theorem <ref labelref="LABEL:pigspan"/> to three and four dimensions.</text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_note" inlist="thm theorem:note" xml:id="Thmnote1">
      <tags>
        <tag>Note 1</tag>
        <tag role="refnum">1</tag>
        <tag role="typerefnum">Note 1</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="italic">Note 1</text></tag><text font="italic">:</text></title>
      <para xml:id="Thmnote1.p1">
        <p>This is a test of the custom theorem style ‘note’. It is supposed to have
variant fonts and other differences.</p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_bthm" inlist="thm theorem:bthm" xml:id="Thmbthm1">
      <tags>
        <tag>B-Theorem 1</tag>
        <tag role="refnum">1</tag>
        <tag role="typerefnum">B-Theorem 1</tag>
      </tags>
      <title><tag><text font="bold">B-Theorem 1</text></tag><text font="bold">.</text></title>
      <para xml:id="Thmbthm1.p1">
        <p><text font="italic">Test of the ‘linebreak’ style of theorem heading.</text></p>
      </para>
    </theorem>
    <para xml:id="S2.p1">
      <p>This is a test of a citing theorem to cite a theorem from some other source.</p>
    </para>
    <theorem class="ltx_theorem_varthm" inlist="thm theorem:varthm" xml:id="Thmvarthmx1">
      <title class="ltx_runin" font="bold">Theorem 3.6 in <cite class="ltx_citemacro_cite">[<bibref bibrefs="thatone" separator="," yyseparator=","/>]</cite>.</title>
      <para xml:id="Thmvarthmx1.p1">
        <p><text font="italic">No hyperlinking available here yet … but that’s not a
bad idea for the future.</text></p>
      </para>
    </theorem>
  </section>
  <section inlist="toc" xml:id="S3">
    <tags>
      <tag>3</tag>
      <tag role="refnum">3</tag>
      <tag role="typerefnum">§3</tag>
    </tags>
    <title><tag close=" ">3</tag>The proof environment</title>
    <proof>
      <title class="ltx_runin" font="italic">Proof.</title>
      <para xml:id="S3.p1">
        <p>Here is a test of the proof environment.
∎</p>
      </para>
    </proof>
    <proof>
      <title class="ltx_runin" font="italic">Proof of Theorem <ref labelref="LABEL:pigspan"/>.</title>
      <para xml:id="S3.p2">
        <p>And another test.
∎</p>
      </para>
    </proof>
    <proof>
      <title class="ltx_runin" font="italic">Proof <text font="upright">(</text>necessity<text font="upright">)</text>.</title>
      <para xml:id="S3.p3">
        <p>And another.
∎</p>
      </para>
    </proof>
    <proof>
      <title class="ltx_runin" font="italic">Proof <text font="upright">(</text>sufficiency<text font="upright">)</text>.</title>
      <para xml:id="S3.p4">
        <p>And another, ending with a display:</p>
        <equation xml:id="S3.Ex1">
          <Math mode="display" tex="1+1=2\,.\qed" text="1 + 1 = 2" xml:id="S3.Ex1.m1">
            <XMath>
              <XMDual>
                <XMRef idref="S3.Ex1.m1.1"/>
                <XMWrap>
                  <XMApp xml:id="S3.Ex1.m1.1">
                    <XMTok meaning="equals" role="RELOP">=</XMTok>
                    <XMApp>
                      <XMTok meaning="plus" role="ADDOP">+</XMTok>
                      <XMTok meaning="1" role="NUMBER">1</XMTok>
                      <XMTok meaning="1" role="NUMBER">1</XMTok>
                    </XMApp>
                    <XMTok meaning="2" role="NUMBER" rpadding="1.7pt">2</XMTok>
                  </XMApp>
                  <XMTok role="PERIOD">.</XMTok>
                  <XMTok font="italic" role="PUNCT">∎</XMTok>
                </XMWrap>
              </XMDual>
            </XMath>
          </Math>
        </equation>
      </para>
    </proof>
  </section>
  <section inlist="toc" xml:id="S4">
    <tags>
      <tag>4</tag>
      <tag role="refnum">4</tag>
      <tag role="typerefnum">§4</tag>
    </tags>
    <title><tag close=" ">4</tag>Test of number-swapping</title>
    <para xml:id="S4.p1">
      <p>This is a repeat of the first section but with numbers in theorem heads
swapped to the left.</p>
    </para>
    <para xml:id="S4.p2">
      <p>Ahlfors’ Lemma gives the principal criterion for obtaining lower bounds
on the Kobayashi metric.</p>
    </para>
    <theorem class="ltx_theorem_Ahlfors" inlist="thm theorem:Ahlfors" xml:id="ThmAhlforsx2">
      <tags>
        <tag>Ahlfors’ Lemma</tag>
        <tag role="typerefnum">Ahlfors’ Lemma</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">Ahlfors’ Lemma</text></tag><text font="bold">.</text></title>
      <para xml:id="ThmAhlforsx2.p1">
        <p><text font="italic">Let <Math mode="inline" tex="ds^{2}=h(z)|dz|^{2}" text="d * s ^ 2 = h * z * (absolute-value@(d * z)) ^ 2" xml:id="ThmAhlforsx2.p1.m1">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="equals" role="RELOP">=</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">d</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok role="UNKNOWN">s</XMTok>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">h</XMTok>
                    <XMDual>
                      <XMRef idref="ThmAhlforsx2.p1.m1.1"/>
                      <XMWrap>
                        <XMTok font="upright" role="OPEN" stretchy="false">(</XMTok>
                        <XMTok role="UNKNOWN" xml:id="ThmAhlforsx2.p1.m1.1">z</XMTok>
                        <XMTok font="upright" role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMDual>
                        <XMApp>
                          <XMTok meaning="absolute-value"/>
                          <XMRef idref="ThmAhlforsx2.p1.m1.2"/>
                        </XMApp>
                        <XMWrap>
                          <XMTok font="upright" role="VERTBAR" stretchy="false">|</XMTok>
                          <XMApp xml:id="ThmAhlforsx2.p1.m1.2">
                            <XMTok meaning="times" role="MULOP">⁢</XMTok>
                            <XMTok role="UNKNOWN">d</XMTok>
                            <XMTok role="UNKNOWN">z</XMTok>
                          </XMApp>
                          <XMTok font="upright" role="VERTBAR" stretchy="false">|</XMTok>
                        </XMWrap>
                      </XMDual>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math> be a Hermitian pseudo-metric on
<Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="ThmAhlforsx2.p1.m2">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math>, <Math mode="inline" tex="h\in C^{2}(\mathbf{D}_{r})" text="h element-of C ^ 2 * D _ r" xml:id="ThmAhlforsx2.p1.m3">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="element-of" name="in" role="RELOP">∈</XMTok>
                  <XMTok role="UNKNOWN">h</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok role="UNKNOWN">C</XMTok>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                    <XMDual>
                      <XMRef idref="ThmAhlforsx2.p1.m3.1"/>
                      <XMWrap>
                        <XMTok font="upright" role="OPEN" stretchy="false">(</XMTok>
                        <XMApp xml:id="ThmAhlforsx2.p1.m3.1">
                          <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                          <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                          <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                        </XMApp>
                        <XMTok font="upright" role="CLOSE" stretchy="false">)</XMTok>
                      </XMWrap>
                    </XMDual>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math>, with <Math mode="inline" tex="\omega" text="omega" xml:id="ThmAhlforsx2.p1.m4">
              <XMath>
                <XMTok name="omega" role="UNKNOWN">ω</XMTok>
              </XMath>
            </Math> the associated
<Math mode="inline" tex="(1,1)" text="open-interval@(1, 1)" xml:id="ThmAhlforsx2.p1.m5">
              <XMath>
                <XMDual>
                  <XMApp>
                    <XMTok meaning="open-interval"/>
                    <XMRef idref="ThmAhlforsx2.p1.m5.1"/>
                    <XMRef idref="ThmAhlforsx2.p1.m5.2"/>
                  </XMApp>
                  <XMWrap>
                    <XMTok font="upright" role="OPEN" stretchy="false">(</XMTok>
                    <XMTok font="upright" meaning="1" role="NUMBER" xml:id="ThmAhlforsx2.p1.m5.1">1</XMTok>
                    <XMTok font="upright" role="PUNCT">,</XMTok>
                    <XMTok font="upright" meaning="1" role="NUMBER" xml:id="ThmAhlforsx2.p1.m5.2">1</XMTok>
                    <XMTok font="upright" role="CLOSE" stretchy="false">)</XMTok>
                  </XMWrap>
                </XMDual>
              </XMath>
            </Math>-form. If <Math mode="inline" tex="\mathop{\mathrm{Ric}}\nolimits\omega\geq\omega" text="Ric@(omega) &gt;= omega" xml:id="ThmAhlforsx2.p1.m6">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
                  <XMApp>
                    <XMTok font="upright" role="BIGOP">Ric</XMTok>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  </XMApp>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                </XMApp>
              </XMath>
            </Math> on <Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="ThmAhlforsx2.p1.m7">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math>,
then <Math mode="inline" tex="\omega\leq\omega_{r}" text="omega &lt;= omega _ r" xml:id="ThmAhlforsx2.p1.m8">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  <XMApp>
                    <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                    <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math> on all of <Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="ThmAhlforsx2.p1.m9">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math> (or equivalently,
<Math mode="inline" tex="ds^{2}\leq ds_{r}^{2}" text="d * s ^ 2 &lt;= d * (s _ r) ^ 2" xml:id="ThmAhlforsx2.p1.m10">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">d</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMTok role="UNKNOWN">s</XMTok>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                  <XMApp>
                    <XMTok meaning="times" role="MULOP">⁢</XMTok>
                    <XMTok role="UNKNOWN">d</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                      <XMApp>
                        <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                        <XMTok role="UNKNOWN">s</XMTok>
                        <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                      </XMApp>
                      <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math>).</text></p>
      </para>
    </theorem>
    <theorem class="ltx_theorem_lemsw" inlist="thm theorem:lemsw" xml:id="S4.Thmthmsw1">
      <tags>
        <tag>4.1 Lemma</tag>
        <tag role="refnum">4.1</tag>
        <tag role="typerefnum">Lemma 4.1</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">4.1 Lemma</text></tag><text font="bold"> </text>(negatively curved families)<text font="bold">.</text></title>
      <para xml:id="S4.Thmthmsw1.p1">
        <p><text font="italic">Let <Math mode="inline" tex="\{ds_{1}^{2},\dots,ds_{k}^{2}\}" text="set@(d * (s _ 1) ^ 2, dots, d * (s _ k) ^ 2)" xml:id="S4.Thmthmsw1.p1.m1">
              <XMath>
                <XMDual>
                  <XMApp>
                    <XMTok meaning="set"/>
                    <XMRef idref="S4.Thmthmsw1.p1.m1.2"/>
                    <XMRef idref="S4.Thmthmsw1.p1.m1.1"/>
                    <XMRef idref="S4.Thmthmsw1.p1.m1.3"/>
                  </XMApp>
                  <XMWrap>
                    <XMTok font="upright" role="OPEN" stretchy="false">{</XMTok>
                    <XMApp xml:id="S4.Thmthmsw1.p1.m1.2">
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok role="UNKNOWN">d</XMTok>
                      <XMApp>
                        <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                        <XMApp>
                          <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                          <XMTok role="UNKNOWN">s</XMTok>
                          <XMTok font="upright" fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
                        </XMApp>
                        <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                      </XMApp>
                    </XMApp>
                    <XMTok font="upright" role="PUNCT">,</XMTok>
                    <XMTok font="upright" name="dots" role="ID" xml:id="S4.Thmthmsw1.p1.m1.1">…</XMTok>
                    <XMTok font="upright" role="PUNCT">,</XMTok>
                    <XMApp xml:id="S4.Thmthmsw1.p1.m1.3">
                      <XMTok meaning="times" role="MULOP">⁢</XMTok>
                      <XMTok role="UNKNOWN">d</XMTok>
                      <XMApp>
                        <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                        <XMApp>
                          <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                          <XMTok role="UNKNOWN">s</XMTok>
                          <XMTok fontsize="70%" role="UNKNOWN">k</XMTok>
                        </XMApp>
                        <XMTok font="upright" fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                      </XMApp>
                    </XMApp>
                    <XMTok font="upright" role="CLOSE" stretchy="false">}</XMTok>
                  </XMWrap>
                </XMDual>
              </XMath>
            </Math> be a negatively curved family of metrics
on <Math mode="inline" tex="\mathbf{D}_{r}" text="D _ r" xml:id="S4.Thmthmsw1.p1.m2">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok font="bold upright" role="UNKNOWN">D</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                </XMApp>
              </XMath>
            </Math>, with associated forms <Math mode="inline" tex="\omega^{1}" text="omega ^ 1" xml:id="S4.Thmthmsw1.p1.m3">
              <XMath>
                <XMApp>
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  <XMTok font="upright" fontsize="70%" meaning="1" role="NUMBER">1</XMTok>
                </XMApp>
              </XMath>
            </Math>, …, <Math mode="inline" tex="\omega^{k}" text="omega ^ k" xml:id="S4.Thmthmsw1.p1.m4">
              <XMath>
                <XMApp>
                  <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                  <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                  <XMTok fontsize="70%" role="UNKNOWN">k</XMTok>
                </XMApp>
              </XMath>
            </Math>.
Then <Math mode="inline" tex="\omega^{i}\leq\omega_{r}" text="omega ^ i &lt;= omega _ r" xml:id="S4.Thmthmsw1.p1.m5">
              <XMath>
                <XMApp>
                  <XMTok font="upright" meaning="less-than-or-equals" name="leq" role="RELOP">≤</XMTok>
                  <XMApp>
                    <XMTok role="SUPERSCRIPTOP" scriptpos="post1"/>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                    <XMTok fontsize="70%" role="UNKNOWN">i</XMTok>
                  </XMApp>
                  <XMApp>
                    <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                    <XMTok name="omega" role="UNKNOWN">ω</XMTok>
                    <XMTok fontsize="70%" role="UNKNOWN">r</XMTok>
                  </XMApp>
                </XMApp>
              </XMath>
            </Math> for all <Math mode="inline" tex="i" text="i" xml:id="S4.Thmthmsw1.p1.m6">
              <XMath>
                <XMTok role="UNKNOWN">i</XMTok>
              </XMath>
            </Math>.</text></p>
      </para>
    </theorem>
    <para xml:id="S4.p3">
      <p>Then our main theorem:</p>
    </para>
    <theorem class="ltx_theorem_thmsw" inlist="thm theorem:thmsw" xml:id="S4.Thmthmsw2">
      <tags>
        <tag>4.2 Theorem</tag>
        <tag role="refnum">4.2</tag>
        <tag role="typerefnum">Theorem 4.2</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">4.2 Theorem</text></tag><text font="bold">.</text></title>
      <para xml:id="S4.Thmthmsw2.p1">
        <p><text font="italic">Let <Math mode="inline" tex="d_{\max}" text="d _ maximum" xml:id="S4.Thmthmsw2.p1.m1">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok role="UNKNOWN">d</XMTok>
                  <XMTok font="upright" fontsize="70%" meaning="maximum" role="OPFUNCTION" scriptpos="post">max</XMTok>
                </XMApp>
              </XMath>
            </Math> and <Math mode="inline" tex="d_{\min}" text="d _ minimum" xml:id="S4.Thmthmsw2.p1.m2">
              <XMath>
                <XMApp>
                  <XMTok role="SUBSCRIPTOP" scriptpos="post1"/>
                  <XMTok role="UNKNOWN">d</XMTok>
                  <XMTok font="upright" fontsize="70%" meaning="minimum" role="OPFUNCTION" scriptpos="post">min</XMTok>
                </XMApp>
              </XMath>
            </Math> be the maximum, resp. minimum distance
between any two adjacent vertices of a quadrilateral <Math mode="inline" tex="Q" text="Q" xml:id="S4.Thmthmsw2.p1.m3">
              <XMath>
                <XMTok role="UNKNOWN">Q</XMTok>
              </XMath>
            </Math>. Let <Math mode="inline" tex="\sigma" text="sigma" xml:id="S4.Thmthmsw2.p1.m4">
              <XMath>
                <XMTok name="sigma" role="UNKNOWN">σ</XMTok>
              </XMath>
            </Math>
be the diagonal pigspan of a pig <Math mode="inline" tex="P" text="P" xml:id="S4.Thmthmsw2.p1.m5">
              <XMath>
                <XMTok role="UNKNOWN">P</XMTok>
              </XMath>
            </Math> with four legs.
Then <Math mode="inline" tex="P" text="P" xml:id="S4.Thmthmsw2.p1.m6">
              <XMath>
                <XMTok role="UNKNOWN">P</XMTok>
              </XMath>
            </Math> is capable of standing on the corners of <Math mode="inline" tex="Q" text="Q" xml:id="S4.Thmthmsw2.p1.m7">
              <XMath>
                <XMTok role="UNKNOWN">Q</XMTok>
              </XMath>
            </Math> iff</text></p>
        <equation labels="LABEL:sdqsw" xml:id="S4.E2">
          <tags>
            <tag>(2)</tag>
            <tag role="refnum">2</tag>
          </tags>
          <Math mode="display" tex="\sigma\geq\sqrt{d_{\max}^{2}+d_{\min}^{2}}." text="sigma &gt;= square-root@((d _ maximum) ^ 2 + (d _ minimum) ^ 2)" xml:id="S4.E2.m1">
            <XMath>
              <XMDual>
                <XMRef idref="S4.E2.m1.1"/>
                <XMWrap>
                  <XMApp xml:id="S4.E2.m1.1">
                    <XMTok meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
                    <XMTok font="italic" name="sigma" role="UNKNOWN">σ</XMTok>
                    <XMApp>
                      <XMTok meaning="square-root"/>
                      <XMApp>
                        <XMTok meaning="plus" role="ADDOP">+</XMTok>
                        <XMApp>
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMApp>
                            <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                            <XMTok font="italic" role="UNKNOWN">d</XMTok>
                            <XMTok fontsize="70%" meaning="maximum" role="OPFUNCTION" scriptpos="post">max</XMTok>
                          </XMApp>
                          <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                        </XMApp>
                        <XMApp>
                          <XMTok role="SUPERSCRIPTOP" scriptpos="post2"/>
                          <XMApp>
                            <XMTok role="SUBSCRIPTOP" scriptpos="post2"/>
                            <XMTok font="italic" role="UNKNOWN">d</XMTok>
                            <XMTok fontsize="70%" meaning="minimum" role="OPFUNCTION" scriptpos="post">min</XMTok>
                          </XMApp>
                          <XMTok fontsize="70%" meaning="2" role="NUMBER">2</XMTok>
                        </XMApp>
                      </XMApp>
                    </XMApp>
                  </XMApp>
                  <XMTok role="PERIOD">.</XMTok>
                </XMWrap>
              </XMDual>
            </XMath>
          </Math>
        </equation>
      </para>
    </theorem>
    <theorem class="ltx_theorem_corsw" inlist="thm theorem:corsw" xml:id="S4.Thmthmsw3">
      <tags>
        <tag>4.3 Corollary</tag>
        <tag role="refnum">4.3</tag>
        <tag role="typerefnum">Corollary 4.3</tag>
      </tags>
      <title class="ltx_runin"><tag><text font="bold">4.3 Corollary</text></tag><text font="bold">.</text></title>
      <para xml:id="S4.Thmthmsw3.p1">
        <p><text font="italic">Admitting reflection and rotation, a three-legged pig <Math mode="inline" tex="P" text="P" xml:id="S4.Thmthmsw3.p1.m1">
              <XMath>
                <XMTok role="UNKNOWN">P</XMTok>
              </XMath>
            </Math> is capable of
standing on the corners of a triangle <Math mode="inline" tex="T" text="T" xml:id="S4.Thmthmsw3.p1.m2">
              <XMath>
                <XMTok role="UNKNOWN">T</XMTok>
              </XMath>
            </Math> iff (<ref labelref="LABEL:sdqsw"/>) holds.</text></p>
      </para>
    </theorem>
  </section>
  <bibliography xml:id="bib">
    <title>References</title>
    <biblist>
      <bibitem key="thatone" xml:id="bib.bib1">
        <tags>
          <tag>[1]</tag>
          <tag role="refnum">1</tag>
        </tags>
        <bibblock> Dummy entry.
</bibblock>
      </bibitem>
    </biblist>
  </bibliography>
</document>
