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<b>let </b><font color="Maroon" title="c1">GX</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/>



<b>assume </b><a NAME="E1:42"/><i><font color="Green" title="E34">A1</font></i>: 
<font color="Maroon" title="c2">C</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/>

<b>assume </b><a NAME="E2:42"/><i><font color="Green" title="E35">A2</font></i>: 
<font color="Maroon" title="c3">S</font> <a href="connsp_1.html#R3" title="CONNSP_1:pred.3">is_a_component_of</a> <font color="Maroon" title="c1">GX</font>
 ;<br/>

<b>assume </b><a NAME="E3:42"/>
<font color="Maroon" title="c2">C</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">S</font>
 ;<br/>

<a NAME="E4:42"/><b>then </b><i><font color="Green" title="E36">A3</font></i>: 
not <font color="Maroon" title="c2">C</font>,<font color="Maroon" title="c3">S</font> <a href="connsp_1.html#R1" title="CONNSP_1:pred.1">are_separated</a> 
 
<b>by </b><i><a class="ref" href="connsp_1.html#T2" target="_self" title="CONNSP_1:th.2">Th2</a></i>;<br/>
<a NAME="E5:42"/>
<font color="Maroon" title="c3">S</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="connsp_1.html#E2:42"><i><font color="Green" title="E35">A2</font></i></a>, <a class="ref" href="connsp_1.html#D5" target="_self" title="CONNSP_1:def.5">Def5</a></i>;<br/>
<a NAME="E6:42"/><b>then </b><i><font color="Green" title="E37">A4</font></i>: 
<font color="Maroon" title="c2">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">S</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="connsp_1.html#E1:42"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="connsp_1.html#E4:42"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="connsp_1.html#T18" target="_self" title="CONNSP_1:th.18">Th18</a></i>;<br/>
<a NAME="E7:42"/>
<font color="Maroon" title="c3">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">S</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E8:42"/><b>then </b>
<font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">S</font>
 
<b>by </b><i><a class="txt" href="connsp_1.html#E2:42"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="connsp_1.html#E6:42"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="connsp_1.html#D5" target="_self" title="CONNSP_1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E9:42"/>
<font color="Maroon" title="c2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>


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