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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">C</font> be  <a href="topreal2.html#V1">being_simple_closed_curve</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green">E44</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font>
 <b>and </b><br/><a NAME="E3:1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 <b>and </b><br/><a NAME="E4:1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font>
 <b>and </b><br/><a NAME="E5:1"/><i><font color="Green">E47</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E6:1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 <b>and </b><br/><a NAME="E7:1"/><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E8:1"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>set </b><font color="Maroon">p</font> = <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font>;<br/>
<b>set </b><font color="Maroon">q</font> = <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font>;<br/>
<b>set </b><font color="Maroon">S</font> =  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>;<br/>
<a NAME="E9:1"/>
 <a href="jordan1h.html#K3">X-SpanStart</a> <font color="Maroon">C</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="jordan1a.html#K1">Center</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan1b.html#T17">JORDAN1B:17</a></i>;<br/>
<a NAME="E10:1"/><b>then </b>
( 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="jordan1a.html#K1">Center</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> &amp;  <a href="jordan1a.html#K1">Center</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="jordan1h.html#T58">JORDAN1H:58</a></i>;<br/>
<a NAME="E11:1"/><b>then </b><i><font color="Green">E54</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="jordan1a.html#K1">Center</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> &amp;  <a href="jordan1a.html#K1">Center</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E12:1"/>
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E13:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K9">Lower_Arc</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E14:1"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K2">Lower_Seq</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="jordan1g.html#T64">JORDAN1G:64</a></i>;<br/>
<a NAME="E15:1"/>
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E16:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="jordan6.html#K8">Upper_Arc</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E17:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan1e.html#K1">Upper_Seq</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="jordan1g.html#T63">JORDAN1G:63</a></i>;<br/>
<a NAME="E18:1"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">k</font>
 
<b>by </b><i>, , , , <a class="ref" href="jordan1j.html#T57">JORDAN1J:57</a></i>;<br/>
<a NAME="E19:1"/><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="goboard7.html#T10">GOBOARD7:10</a></i>;<br/>
<a NAME="E20:1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="matrix_1.html#K2">Indices</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="goboard7.html#T10">GOBOARD7:10</a></i>;<br/>
<a NAME="E21:1"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font>
 
<b>by </b><i>, , <a class="ref" href="jordan1h.html#T32">JORDAN1H:32</a></i>;<br/>
<b>set </b><font color="Maroon">A</font> = <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span>;<br/>
<a NAME="E22:1"/><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="ref" href="jordan1.html#T52">JORDAN1:52</a></i>;<br/>
<a NAME="E23:1"/><i><font color="Green">E61</font></i>: 
 <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="connsp_1.html#R4">is_a_component_of</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="goboard9.html#D2">GOBOARD9:def 2</a></i>;<br/>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jordan6.html#T65">JORDAN6:65</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p5">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p5">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p5">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p4">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p5">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p4">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i>, , <a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
;<br/>
<a NAME="E25:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T90">XBOOLE_1:90</a></i>;<br/>
<a NAME="E26:1"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>
<a NAME="E27:1"/><i><font color="Green">E63</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#R2">meets</a>  <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , , , , , <a class="ref" href="jordan1j.html#T61">JORDAN1J:61</a></i>;<br/>
<a NAME="E28:1"/>
 <a href="jordan6.html#K8">Upper_Arc</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="jordan6.html#T76">JORDAN6:76</a></i>;<br/>
<a NAME="E29:1"/><b>then </b><i><font color="Green">E64</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span> <a href="subset_1.html#R2">meets</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E30:1"/><i><font color="Green">E65</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="jordan6.html#K8">Upper_Arc</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E31:1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="jordan6.html#K9">Lower_Arc</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E32:1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="jordan6.html#K8">Upper_Arc</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="jordan6.html#K9">Lower_Arc</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p3">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E33:1"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan6.html#T65">JORDAN6:65</a></i>;<br/>
<a NAME="E34:1"/><b>then </b><i><font color="Green">E66</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>;<br/>
<a NAME="E35:1"/>
 <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="subset_1.html#R1">misses</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="jordan10.html#T5">JORDAN10:5</a></i>;<br/>
<a NAME="E36:1"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="subset_1.html#R1">misses</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E37:1"/><b>then </b><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T84">XBOOLE_1:84</a></i>;<br/>
<a NAME="E38:1"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan10.html#T11">JORDAN10:11</a></i>;<br/>
<a NAME="E39:1"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p3">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p4">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="goboard9.html#K3">RightComp</a> <span class="p1">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span>
 
<b>by </b><i>, , , <a class="ref" href="goboard9.html#T6">GOBOARD9:6</a>, </i>;<br/>
<b>hence </b><a NAME="E40:1"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">j</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p2">(<span class="default"><a href="jordan1a.html#K1">Center</a> <span class="p3">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="jordan1h.html#T8">JORDAN1H:8</a></i>;<br/>


</div>
