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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/>



<b>set </b><font color="Maroon">A2</font> =  <a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font>;<br/>
<a NAME="E1:70"/>
 <a href="kurato_2.html#K1">Union</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K1" target="_self">inferior_setsequence</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E2:70"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="kurato_2.html#K4">lim_inf</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span>
 
;<br/>
<a NAME="E3:70"/>
 <a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:70"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="kurato_2.html#K5">lim_sup</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span>
 
;<br/>
<a NAME="E5:70"/><b>then </b>
 <a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font> is <a href="kurato_2.html#V3">convergent</a>
 
<b>by </b><i>, <a class="ref" href="kurato_2.html#D7">KURATO_2:def 7</a></i>;<br/>
<a NAME="E6:70"/><b>then </b>
 <a href="setlim_1.html#K3" target="_self">lim</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="setlim_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E7:70"/>
 <a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="setlim_1.html#K3" target="_self">lim</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span>
 ;<br/>


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