<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:91"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font> holds  <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> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <span class="p3">(<span class="default"><a href="prob_1.html#K3">Complement</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:91_1"/><i><font color="Green">E64</font></i>: 
 <a href="kurato_2.html#K4">lim_inf</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <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> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
;<br/>
<a NAME="E2:91_1"/>
<span class="p1">(<span class="default"><a href="kurato_2.html#K5">lim_sup</a> <span class="p2">(<span class="default"><a href="prob_1.html#K3">Complement</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <span class="p3">(<span class="default"><a href="prob_1.html#K3">Complement</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 
;<br/>
<b>hence </b><a NAME="E3:91_1"/>
 <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> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prob_1.html#K4">Intersection</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <span class="p3">(<span class="default"><a href="prob_1.html#K3">Complement</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>by </b><i><a class="txt" href="setlim_1.html#E1:91_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="kurato_2.html#T12">KURATO_2:12</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:91"/>
 <a href="setlim_1.html#K6" target="_self">lim_inf</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K7" target="_self">lim_sup</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K9" target="_self">@Complement</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K3">`</a> 
 ;<br/>


</div>
