<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML" class="ltx_authors_1line">
  <resource src="LaTeXML.css" type="text/css"/>
  <resource src="ltx-article.css" type="text/css"/>
  <title>LaTeX’s Newtheorem</title>
  <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>
    <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"> (negatively curved families)</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.p1">
      <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></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></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>
  </section>
</document>
