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<b>let </b><font color="Maroon">C</font> be   <a href="topreal2.html#NM1">Simple_closed_curve</a>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<a NAME="E1:5"/>
 <a href="jordan6.html#K8">Upper_Arc</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> is <a href="compts_1.html#V6">compact</a>
 
;<br/>
<b>hence </b><a NAME="E2:5"/>
<span class="p1">(<span class="default"><a href="jordan19.html#K1">Upper_Appr</a> <font color="Maroon">C</font></span>)</span> <a href="kurato_2.html#K7">.</a> <font color="Maroon">i</font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="ref" href="jordan19.html#D1">JORDAN19:def 1</a></i>;<br/>

<a NAME="E3:5"/>
 <a href="jordan6.html#K8">Upper_Arc</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> is <a href="connsp_1.html#V2">connected</a>
 
;<br/>
<b>hence </b><a NAME="E4:5"/>
<span class="p1">(<span class="default"><a href="jordan19.html#K1">Upper_Appr</a> <font color="Maroon">C</font></span>)</span> <a href="kurato_2.html#K7">.</a> <font color="Maroon">i</font> is <a href="connsp_1.html#V2">connected</a>
 <b>by </b><i><a class="ref" href="jordan19.html#D1">JORDAN19:def 1</a></i>;<br/>


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