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<b>let </b><font color="Maroon">G</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">G</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">G</font>, <font color="Maroon">C</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">G</font>, <font color="Maroon">D</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><a NAME="E1:123"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">A</font> <a href="connsp_1.html#R3">is_a_component_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">B</font> <a href="connsp_1.html#R3">is_a_component_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">C</font> <a href="connsp_1.html#R3">is_a_component_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">A</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> &amp; <font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="123_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:123_1"/>
<font color="Maroon">C</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:123_1"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</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="E3:123_1"/>
<font color="Maroon">C</font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/><a NAME="E4:123_1"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/><a NAME="E5:123_1"/>
<font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="connsp_1.html#T34">CONNSP_1:34</a></i>;<br/><b>hence </b><a NAME="E6:123_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="jordan2c.html#T27" target="_self">Th27</a>, <a class="ref" href="jordan2c.html#T28" target="_self">Th28</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:123"/>
<font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="connsp_1.html#T37">CONNSP_1:37</a></i>;<br/>


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