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<b>let </b><font color="Maroon">E</font> be  <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>assume </b><a NAME="E1:19"/><i><font color="Green">E47</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">E</font>,0</span>)</span>,2,2 <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">E</font>
 ;<br/>

<a NAME="E2:19"/>
<font color="Maroon">E</font> <a href="tarski.html#R1">c=</a>  <a href="goboard5.html#K3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1">Gauge</a> <font color="Maroon">E</font>,0</span>)</span>,2,2
 
<b>by </b><i/>;<br/>
<a NAME="E3:19"/><b>then </b><i><font color="Green">E48</font></i>: 
<font color="Maroon">E</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">E</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>consider </b><font color="Maroon">e</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">E</font>;<br/>
<a NAME="E5:19"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font>
 
;<br/>
<a NAME="E6:19"/>
 <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">E</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="jordan1a.html#T15">JORDAN1A:15</a></i>;<br/>
<b>hence </b><a NAME="E7:19"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>


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