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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/>

<b>assume </b><a NAME="E1:46"/><i><font color="Green">E34</font></i>: 
 <a href="jordan21.html#K1" target="_self">UMP</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="jordan21.html#K2" target="_self">LMP</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:46"/>
<span class="p1">(<span class="default"><a href="jordan21.html#K2" target="_self">LMP</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="jordan21.html#K1" target="_self">UMP</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="euclid.html#K22">`2</a> 
 
<b>by </b><i><a class="ref" href="jordan21.html#T49" target="_self">Th49</a></i>;<br/>
<b>hence </b><a NAME="E3:46"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan21.html#E1:46"><i><font color="Green">E34</font></i></a></i>;<br/>


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