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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:135"/><i><font color="Green">E47</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>, <font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> <font color="Maroon">n</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:135"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">P</font> is <a href="jordan2c.html#V1" target="_self">Bounded</a>
 <b>and </b><br/><a NAME="E3:135"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">A</font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">P</font> &amp; <font color="Maroon">B</font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">P</font> )
 ;<br/>

<a NAME="E4:135"/><i><font color="Green">E58</font></i>: 
 <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T28" target="_self">Th28</a>, <a class="ref" href="jordan2c.html#T29" target="_self">Th29</a>, </i>;<br/>
<a NAME="E5:135"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">A</font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a>  &amp; <font color="Maroon">B</font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a>  )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E6:135"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T28" target="_self">Th28</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E7:135"/><b>then </b>
not <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a>  is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T29" target="_self">Th29</a>, </i>;<br/>
<a NAME="E8:135"/><b>then </b><i><font color="Green">E60</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">B</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="sprect_1.html#T6">SPRECT_1:6</a></i>;<br/>
<a NAME="E9:135"/><i><font color="Green">E61</font></i>: 
 <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> <a href="connsp_1.html#R4">is_a_component_of</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="jordan2c.html#T31" target="_self">Th31</a>, </i>;<br/>
<a NAME="E10:135"/>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> &amp; <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T30" target="_self">Th30</a>, </i>;<br/>
<a NAME="E11:135"/><b>then </b>
( <font color="Maroon">A</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> &amp; <font color="Maroon">B</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> )
 
<b>by </b><i><a class="ref" href="jordan2c.html#T33" target="_self">Th33</a>, <a class="ref" href="xboole_1.html#T69">XBOOLE_1:69</a></i>;<br/>
<a NAME="E12:135"/><b>then </b>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">P</font> )
 
<b>by </b><i>, <a class="ref" href="jordan2c.html#T35" target="_self">Th35</a>, <a class="ref" href="goboard9.html#T3">GOBOARD9:3</a></i>;<br/>
<b>hence </b><a NAME="E13:135"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/>


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