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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:135"/>
<font color="Maroon">c<sub>3</sub></font> <a href="jordan2c.html#R2" target="_self">is_outside_component_of</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:135"/><b>then </b><i><font color="Green">E115</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T27" target="_self">Th27</a></i>;<br/>
<b>assume </b><a NAME="E3:135"/>
<font color="Maroon">c<sub>2</sub></font> <a href="jordan2c.html#R1" target="_self">is_inside_component_of</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:135"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1" target="_self">BDD</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E5:135"/>
 <a href="jordan2c.html#K1" target="_self">BDD</a> <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="jordan2c.html#K2" target="_self">UBD</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="jordan2c.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E6:135"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="jordan2c.html#K1" target="_self">BDD</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E2:135"><i><font color="Green">E115</font></i></a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<b>hence </b><a NAME="E7:135"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="jordan2c.html#E4:135"><i><font color="Green">E116</font></i></a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>


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