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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>let </b><font color="Maroon">R</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>let </b><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>let </b><font color="Maroon">Q</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><a NAME="E1:134"/>
<font color="Maroon">P</font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">Q</font>
 ;<br/>

<a NAME="E2:134"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">Q</font>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E3:134"/>
<font color="Maroon">R</font> <a href="jordan2c.html#R1" target="_self">is_inside_component_of</a> <font color="Maroon">Q</font>
 ;<br/>

<a NAME="E4:134"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">R</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1" target="_self">BDD</a> <font color="Maroon">Q</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:134"/>
 <a href="jordan2c.html#K1" target="_self">BDD</a> <font color="Maroon">Q</font> <a href="xboole_0.html#R1">misses</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">Q</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:134"/><b>then </b>
<font color="Maroon">P</font> <a href="xboole_0.html#R1">misses</a>  <a href="jordan2c.html#K1" target="_self">BDD</a> <font color="Maroon">Q</font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T28" target="_self">Th28</a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<b>hence </b><a NAME="E7:134"/>
<font color="Maroon">P</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="jordan2c.html#T29" target="_self">Th29</a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>


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