<?xml version="1.0" encoding="UTF-8"?>
<?latexml class="article"?>
<?latexml RelaxNGSchema="LaTeXML"?>
<document xmlns="http://dlmf.nist.gov/LaTeXML">
  <title>LaTeX's Newtheorem</title>
  <date role="creation">none</date>
  <section refnum="1" xml:id="S1">
    <title>Test of standard theorem styles</title>
    <theorem refnum="1.1" xml:id="S1.Thmthm1">
      <title>
        <text font="bold">Lemma 1.1 (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}\}" xml:id="S1.Thmthm1.p1.m1" text="set@(d * (s _ 1) ^ 2, dots, d * (s _ k) ^ 2)"><XMath><XMApp><XMTok meaning="set" role="FENCED" argclose="}" argopen="{" separators=",,"/><XMApp><XMTok meaning="times" role="MULOP">⁢</XMTok><XMTok role="UNKNOWN">d</XMTok><XMApp><XMTok role="SUPERSCRIPTOP" scriptpos="post3"/><XMApp><XMTok role="SUBSCRIPTOP" scriptpos="post3"/><XMTok role="UNKNOWN">s</XMTok><XMTok meaning="1" role="NUMBER" font="upright">1</XMTok></XMApp><XMTok meaning="2" role="NUMBER" font="upright">2</XMTok></XMApp></XMApp><XMTok name="dots" role="ID" font="upright">…</XMTok><XMApp><XMTok meaning="times" role="MULOP">⁢</XMTok><XMTok role="UNKNOWN">d</XMTok><XMApp><XMTok role="SUPERSCRIPTOP" scriptpos="post3"/><XMApp><XMTok role="SUBSCRIPTOP" scriptpos="post3"/><XMTok role="UNKNOWN">s</XMTok><XMTok role="UNKNOWN">k</XMTok></XMApp><XMTok meaning="2" role="NUMBER" font="upright">2</XMTok></XMApp></XMApp></XMApp></XMath></Math> be a negatively curved family of metrics
on <Math mode="inline" tex="\mathbf{D}_{r}" xml:id="S1.Thmthm1.p1.m2" text="D _ r"><XMath><XMApp><XMTok role="SUBSCRIPTOP" scriptpos="post3"/><XMTok role="UNKNOWN" font="bold upright">D</XMTok><XMTok role="UNKNOWN">r</XMTok></XMApp></XMath></Math>, with associated forms <Math mode="inline" tex="\omega^{1}" xml:id="S1.Thmthm1.p1.m3" text="omega ^ 1"><XMath><XMApp><XMTok role="SUPERSCRIPTOP" scriptpos="post3"/><XMTok name="omega" role="UNKNOWN">ω</XMTok><XMTok meaning="1" role="NUMBER" font="upright">1</XMTok></XMApp></XMath></Math>, …, <Math mode="inline" tex="\omega^{k}" xml:id="S1.Thmthm1.p1.m4" text="omega ^ k"><XMath><XMApp><XMTok role="SUPERSCRIPTOP" scriptpos="post3"/><XMTok name="omega" role="UNKNOWN">ω</XMTok><XMTok role="UNKNOWN">k</XMTok></XMApp></XMath></Math>.
Then <Math mode="inline" tex="\omega^{i}\leq\omega _{r}" xml:id="S1.Thmthm1.p1.m5" text="omega ^ i less= omega _ r"><XMath><XMApp><XMTok meaning="less-than-or-equals" name="leq" role="RELOP" font="upright">≤</XMTok><XMApp><XMTok role="SUPERSCRIPTOP" scriptpos="post3"/><XMTok name="omega" role="UNKNOWN">ω</XMTok><XMTok role="UNKNOWN">i</XMTok></XMApp><XMApp><XMTok role="SUBSCRIPTOP" scriptpos="post3"/><XMTok name="omega" role="UNKNOWN">ω</XMTok><XMTok role="UNKNOWN">r</XMTok></XMApp></XMApp></XMath></Math> for all <Math mode="inline" tex="i" xml:id="S1.Thmthm1.p1.m6" text="i"><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 refnum="1.2" xml:id="S1.Thmthm2" labels="LABEL:pigspan">
      <title>
        <text font="bold">Theorem 1.2.</text>
      </title>
      <para xml:id="S1.Thmthm2.p1">
        <p>
          <text font="italic">Let <Math mode="inline" tex="d_{{\max}}" xml:id="S1.Thmthm2.p1.m1" text="d _ maximum"><XMath><XMApp><XMTok role="SUBSCRIPTOP" scriptpos="post3"/><XMTok role="UNKNOWN">d</XMTok><XMTok meaning="maximum" role="LIMITOP" scriptpos="post" font="upright">max</XMTok></XMApp></XMath></Math> and <Math mode="inline" tex="d_{{\min}}" xml:id="S1.Thmthm2.p1.m2" text="d _ minimum"><XMath><XMApp><XMTok role="SUBSCRIPTOP" scriptpos="post3"/><XMTok role="UNKNOWN">d</XMTok><XMTok meaning="minimum" role="LIMITOP" scriptpos="post" font="upright">min</XMTok></XMApp></XMath></Math> be the maximum, resp. minimum distance
between any two adjacent vertices of a quadrilateral <Math mode="inline" tex="Q" xml:id="S1.Thmthm2.p1.m3" text="Q"><XMath><XMTok role="UNKNOWN">Q</XMTok></XMath></Math>. Let <Math mode="inline" tex="\sigma" xml:id="S1.Thmthm2.p1.m4" text="sigma"><XMath><XMTok name="sigma" role="UNKNOWN">σ</XMTok></XMath></Math>
be the diagonal pigspan of a pig <Math mode="inline" tex="P" xml:id="S1.Thmthm2.p1.m5" text="P"><XMath><XMTok role="UNKNOWN">P</XMTok></XMath></Math> with four legs.
Then <Math mode="inline" tex="P" xml:id="S1.Thmthm2.p1.m6" text="P"><XMath><XMTok role="UNKNOWN">P</XMTok></XMath></Math> is capable of standing on the corners of <Math mode="inline" tex="Q" xml:id="S1.Thmthm2.p1.m7" text="Q"><XMath><XMTok role="UNKNOWN">Q</XMTok></XMath></Math> iff</text>
        </p>
        <equation refnum="1" xml:id="S1.E1" labels="LABEL:sdq">
          <Math mode="display" tex="\sigma\geq\sqrt{d_{{\max}}^{2}+d_{{\min}}^{2}}." xml:id="S1.E1.m1" text="sigma &gt;= square-root@((d _ maximum) ^ 2 + (d _ minimum) ^ 2)">
            <XMath>
              <XMApp punctuation=".">
                <XMTok meaning="greater-than-or-equals" name="geq" role="RELOP">≥</XMTok>
                <XMTok name="sigma" role="UNKNOWN" font="italic">σ</XMTok>
                <XMApp>
                  <XMTok meaning="square-root"/>
                  <XMApp>
                    <XMTok meaning="plus" role="ADDOP">+</XMTok>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
                      <XMApp>
                        <XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
                        <XMTok role="UNKNOWN" font="italic">d</XMTok>
                        <XMTok meaning="maximum" role="LIMITOP" scriptpos="post">max</XMTok>
                      </XMApp>
                      <XMTok meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                    <XMApp>
                      <XMTok role="SUPERSCRIPTOP" scriptpos="post4"/>
                      <XMApp>
                        <XMTok role="SUBSCRIPTOP" scriptpos="post4"/>
                        <XMTok role="UNKNOWN" font="italic">d</XMTok>
                        <XMTok meaning="minimum" role="LIMITOP" scriptpos="post">min</XMTok>
                      </XMApp>
                      <XMTok meaning="2" role="NUMBER">2</XMTok>
                    </XMApp>
                  </XMApp>
                </XMApp>
              </XMApp>
            </XMath>
          </Math>
        </equation>
      </para>
    </theorem>
    <theorem refnum="1.3" xml:id="S1.Thmthm3">
      <title>
        <text font="bold">Corollary 1.3.</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" xml:id="S1.Thmthm3.p1.m1" text="P"><XMath><XMTok role="UNKNOWN">P</XMTok></XMath></Math> is capable of
standing on the corners of a triangle <Math mode="inline" tex="T" xml:id="S1.Thmthm3.p1.m2" text="T"><XMath><XMTok role="UNKNOWN">T</XMTok></XMath></Math> iff (<ref labelref="LABEL:sdq"/>) holds.</text>
        </p>
      </para>
    </theorem>
  </section>
</document>
