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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> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:38"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E4:38"/><i><font color="Green">E34</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> is <a href="connsp_1.html#V2" target="_self">connected</a>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T29" target="_self">Th29</a></i>;<br/>
<a NAME="E5:38"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E6:38"/>
contradiction
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="txt" href="connsp_1.html#E2:38"><i><font color="Green">E33</font></i></a>, <a class="txt" href="connsp_1.html#E4:38"><i><font color="Green">E34</font></i></a>, <a class="ref" href="connsp_1.html#D5" target="_self">Def5</a></i>;<br/>


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