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<a NAME="E1:7_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><a href="jordan19.html#K1">Upper_Appr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="kurato_2.html#K7">.</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="goboard9.html#K3">RightComp</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">c<sub>1</sub></font>,0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan22.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E2:7_1_1"/><b>then </b>
 <a href="kurato_2.html#K8">Lim_inf</a> <span class="p1">(<span class="default"><a href="jordan19.html#K1">Upper_Appr</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="compts_1.html#V6">compact</a>
 
<b>by </b><i><a class="ref" href="kurato_2.html#T63">KURATO_2:63</a></i>;<br/>
<b>hence </b><a NAME="E3:7_1_1"/>
 <a href="jordan19.html#K3">North_Arc</a> <font color="Maroon">c<sub>1</sub></font> is <a href="compts_1.html#V6">compact</a>
 <b>by </b><i><a class="ref" href="jordan19.html#D3">JORDAN19:def 3</a></i>;<br/>


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