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<b>let </b><font color="Maroon" title="c1">E</font> be  <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> non <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> non <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c1">E</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,2,2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Maroon" title="c1">E</font></span><br/>

<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E10">A1</font></i>: 
 <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c1">E</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,2,2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Maroon" title="c1">E</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:18"/>
<font color="Maroon" title="c1">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> <font color="Maroon" title="c1">E</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,2,2
 
<b>by </b><i><a class="ref" href="jordan1b.html#T18" target="_self" title="JORDAN1B:th.18">Th18</a></i>;<br/>
<a NAME="E3:18"/><b>then </b><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c1">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Maroon" title="c1">E</font>
 
<b>by </b><i><a class="txt" href="jordan1b.html#E1:18"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c2">e</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c1">E</font>;<br/>
<a NAME="E5:18"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">E</font>
 
;<br/>
<a NAME="E6:18"/>
 <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Maroon" title="c1">E</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c1">E</font>
 
<b>by </b><i><a class="ref" href="jordan1a.html#T15" title="JORDAN1A:th.15">JORDAN1A:15</a></i>;<br/>
<b>hence </b><a NAME="E7:18"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan1b.html#E3:18"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="jordan1b.html#E5:18"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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