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<b>let </b><font color="Maroon" title="c1">GX</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">A0</font>, <font color="Maroon" title="c3">A1</font>, <font color="Maroon" title="c4">A2</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><b>that </b><br/><a NAME="E1:6"/><i><font color="Green" title="E7">A1</font></i>: 
( <font color="Maroon" title="c2">A0</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Maroon" title="c3">A1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Maroon" title="c4">A2</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green" title="E8">A2</font></i>: 
( <font color="Maroon" title="c2">A0</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A1</font> &amp; <font color="Maroon" title="c3">A1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">A2</font> )
 ;<br/>

<a NAME="E3:6"/><i><font color="Green" title="E9">A3</font></i>: 
( <font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c3">A1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="jordan1.html#E2:6"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E4:6"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">A1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 
<b>by </b><i><a class="txt" href="jordan1.html#E1:6"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="jordan1.html#E2:6"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="jordan1.html#T6" target="_self" title="JORDAN1:th.6">Th6</a></i>;<br/>
<a NAME="E5:6"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">A2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">A2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23" title="XBOOLE_1:th.23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E6:6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="jordan1.html#E3:6"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="xboole_1.html#T15" title="XBOOLE_1:th.15">XBOOLE_1:15</a></i>;<br/>
<a NAME="E7:6"/><b>then </b>
<font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">A1</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c4">A2</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E8:6"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A0</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">A1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">A2</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="txt" href="jordan1.html#E1:6"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="jordan1.html#E4:6"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="jordan1.html#T6" target="_self" title="JORDAN1:th.6">Th6</a></i>;<br/>


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