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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>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<a NAME="E1:31"/><i><font color="Green">E25</font></i>: 
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T33">SPRECT_1:33</a></i>;<br/>
<b>assume </b><a NAME="E2:31"/>
<font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2
 ;<br/>

<a NAME="E3:31"/><b>then </b>
(  <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="jordan19.html#E1:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/>
<b>hence </b><a NAME="E4:31"/>
(  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan19.html#K3" target="_self">North_Arc</a> <font color="Maroon">c<sub>1</sub></font> or  not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="jordan19.html#K4" target="_self">South_Arc</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="jordan19.html#T27" target="_self">Th27</a></i>;<br/>


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