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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">A0</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>, <font color="Maroon">A1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>, <font color="Maroon">A2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">GX</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">A0</font> is <a href="connsp_1.html#V2">connected</a> &amp; <font color="Maroon">A1</font> is <a href="connsp_1.html#V2">connected</a> &amp; <font color="Maroon">A2</font> is <a href="connsp_1.html#V2">connected</a> )
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">A0</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">A1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A2</font> )
 ;<br/>

<a NAME="E3:6"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">A0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E4:6"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">A0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A1</font> is <a href="connsp_1.html#V2">connected</a>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:6"/>
<span class="p1">(<span class="default"><font color="Maroon">A0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A0</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E6:6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">A0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T15">XBOOLE_1:15</a></i>;<br/>
<a NAME="E7:6"/><b>then </b>
<font color="Maroon">A0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A1</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E8:6"/>
<span class="p1">(<span class="default"><font color="Maroon">A0</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A1</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i>, , </i>;<br/>


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