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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:2"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="connsp_1.html#V2">connected</a>
 <b>and </b><br/><a NAME="E2:2"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E3:2"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:2"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:2"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E6:2"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E7:2"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:2"><i><font color="Green">E3</font></i></a>, <a class="txt" href="jordan9.html#E2:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="jordan9.html#E4:2"><i><font color="Green">E6</font></i></a>, <a class="txt" href="jordan9.html#E6:2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="goboard9.html#T6">GOBOARD9:6</a></i>;<br/>
<a NAME="E8:2"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan9.html#E1:2"><i><font color="Green">E3</font></i></a>, <a class="txt" href="jordan9.html#E3:2"><i><font color="Green">E5</font></i></a>, <a class="txt" href="jordan9.html#E5:2"><i><font color="Green">E7</font></i></a>, <a class="txt" href="jordan9.html#E6:2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="goboard9.html#T6">GOBOARD9:6</a></i>;<br/>
<a NAME="E9:2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="jordan9.html#E4:2"><i><font color="Green">E6</font></i></a>, <a class="ref" href="xboole_1.html#T65">XBOOLE_1:65</a></i>;<br/>
<a NAME="E10:2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan9.html#E7:2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="jordan9.html#E8:2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="xboole_1.html#T68">XBOOLE_1:68</a></i>;<br/>
<b>hence </b><a NAME="E11:2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="jordan9.html#E2:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="jordan9.html#E3:2"><i><font color="Green">E5</font></i></a>, <a class="ref" href="goboard9.html#T3">GOBOARD9:3</a></i>;<br/>


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