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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Si</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">S3</font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Si</font>;<br/><b>let </b><font color="Maroon">S1</font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Si</font>;<br/><b>let </b><font color="Maroon">S2</font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Si</font>;<br/>









<b>assume </b><a NAME="E1:94"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S3</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">S2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>
 ;<br/>

<a NAME="E2:94"/>
for <font color="Olive">A3</font>, <font color="Olive">A1</font>, <font color="Olive">A2</font> being  <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>  st ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Olive">A3</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">A1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Olive">A2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span> ) holds <br/><span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K1" target="_self">inferior_setsequence</a> <font color="Olive">A1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K1" target="_self">inferior_setsequence</a> <font color="Olive">A2</font></span>)</span></span>)</span> <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="Olive">A3</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A3</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<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>let </b><font color="Maroon">A2</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:94_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">A3</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">n</font></span>)</span>
 ;<br/>

<a NAME="E2:94_1"/><i><font color="Green">E30</font></i>: 
 <a href="kurato_2.html#K4">lim_inf</a> <font color="Maroon">A1</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">A1</font></span>)</span>
 
;<br/>
<a NAME="E3:94_1"/><i><font color="Green">E38</font></i>: 
 <a href="kurato_2.html#K4">lim_inf</a> <font color="Maroon">A2</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">A2</font></span>)</span>
 
;<br/>
<a NAME="E4:94_1"/>
 <a href="kurato_2.html#K4">lim_inf</a> <font color="Maroon">A3</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">A3</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:94_1"/>
<span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K1" target="_self">inferior_setsequence</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <span class="p2">(<span class="default"><a href="setlim_1.html#K1" target="_self">inferior_setsequence</a> <font color="Maroon">A2</font></span>)</span></span>)</span> <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">A3</font></span>)</span>
 <b>by </b><i><a class="ref" href="setlim_1.html#T19" target="_self">Th19</a>, <a class="ref" href="setlim_1.html#T20" target="_self">Th20</a>, , <a class="ref" href="kurato_2.html#T13">KURATO_2:13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:94"/>
 <a href="setlim_1.html#K6" target="_self">lim_inf</a> <font color="Maroon">S3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K6" target="_self">lim_inf</a> <font color="Maroon">S1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K6" target="_self">lim_inf</a> <font color="Maroon">S2</font></span>)</span>
 <b>by </b><i><a class="ref" href="setlim_1.html#T18" target="_self">Th18</a></i>;<br/>


</div>
