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<b>let </b><font color="Maroon">C</font> be  <a href="connsp_1.html#V2">connected</a> <a href="compts_1.html#V6">compact</a> non <a href="sppol_1.html#V1">horizontal</a> non <a href="sppol_1.html#V2">vertical</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>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">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#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:40"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">i</font> <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">n</font></span>)</span>
 <b>and </b><br/><a NAME="E2:40"/><i><font color="Green">E48</font></i>: 
 <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">i</font>,<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:40"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E4:40"/>
0 <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">n</font></span>)</span>
 
;<br/>
<a NAME="E5:40"/><b>then </b><i><font color="Green">E50</font></i>: 
not  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">i</font>,0 is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i>, <a class="ref" href="jordan1a.html#T45">JORDAN1A:45</a></i>;<br/>
<a NAME="E6:40"/>
 <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">C</font>,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">i</font>,0 <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2">UBD</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="jordan1a.html#T70">JORDAN1A:70</a></i>;<br/>
<a NAME="E7:40"/><b>then </b>
 <a href="jordan2c.html#K2">UBD</a> <font color="Maroon">C</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , <a class="ref" href="xboole_1.html#T68">XBOOLE_1:68</a></i>;<br/>
<b>hence </b><a NAME="E8:40"/>
contradiction
 <b>by </b><i><a class="ref" href="jordan2c.html#T28">JORDAN2C:28</a></i>;<br/>


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