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<b>let </b><font color="Maroon">C</font> be  <a href="topreal2.html#V1">being_simple_closed_curve</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>



<b>assume </b><a NAME="E1:22"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">D</font>
 ;<br/>

<a NAME="E2:22"/>
<font color="Maroon">D</font> <a href="subset_1.html#R1">misses</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="jordan1a.html#T15">JORDAN1A:15</a></i>;<br/>
<a NAME="E3:22"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">C</font> <a href="subset_1.html#R1">misses</a> <font color="Maroon">D</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<b>assume </b><a NAME="E4:22"/>
not <font color="Maroon">D</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K2">UBD</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E5:22"/><b>then </b>
<font color="Maroon">D</font> <a href="tarski.html#R1">c=</a>  <a href="jordan2c.html#K1">BDD</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="jordan1k.html#T19">JORDAN1K:19</a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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