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<b>let </b><font color="Maroon">GX</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">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">GX</font>;<br/>





<b>assume </b><a NAME="E1:51"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="connsp_1.html#K1" target="_self">Component_of</a> <font color="Maroon">x</font>
 ;<br/>

<b>given </b><font color="Maroon">p</font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">GX</font><b> such that </b><a NAME="E2:51"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E3:51"/><i><font color="Green">E25</font></i>: 
 <a href="connsp_1.html#K1" target="_self">Component_of</a> <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E4:51"/>
(  <a href="connsp_1.html#K1" target="_self">Component_of</a> <font color="Maroon">p</font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">GX</font> &amp; <font color="Maroon">A</font> <a href="connsp_1.html#R3" target="_self">is_a_component_of</a> <font color="Maroon">GX</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:51"/><b>then </b>
 <a href="connsp_1.html#K1" target="_self">Component_of</a> <font color="Maroon">p</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T7" target="_self">Th7</a>, </i>;<br/>
<a NAME="E6:51"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><a href="connsp_1.html#K1" target="_self">Component_of</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">GX</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E7:51"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="connsp_1.html#K1" target="_self">Component_of</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:51"/>
contradiction
 <b>by </b><i>, <a class="ref" href="connsp_1.html#T8" target="_self">Th8</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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