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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>assume </b><a NAME="E1:8"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">A</font> <a href="connsp_1.html#R3">is_a_component_of</a> <font color="Maroon">GX</font>
 ;<br/>

<a NAME="E2:8"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">A</font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i><a class="ref" href="connsp_1.html#D5">CONNSP_1:def 5</a></i>;<br/>
<a NAME="E3:8"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="connsp_3.html#K1" target="_self">Component_of</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:8"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">GX</font>
 
<b>by </b><i>, <a class="ref" href="connsp_1.html#T34">CONNSP_1:34</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
 <a href="connsp_3.html#K1" target="_self">Component_of</a> <font color="Maroon">A</font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:8"/>
 <a href="connsp_3.html#K1" target="_self">Component_of</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, , <a class="ref" href="connsp_1.html#D5">CONNSP_1:def 5</a></i>;<br/>


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