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

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:36_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:36_1_1"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="kurato_2.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E4:36_1_1"/><i><font color="Green">E24</font></i>: 
 <a href="kurato_2.html#K5" target="_self">lim_sup</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="kurato_2.html#E3:36_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="kurato_2.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E5:36_1_1"/><i><font color="Green">E25</font></i>: 
 <a href="kurato_2.html#K4" target="_self">lim_inf</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="kurato_2.html#E3:36_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="kurato_2.html#T18" target="_self">Th18</a></i>;<br/>
<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:36_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="kurato_2.html#E3:36_1_1"><i><font color="Green">E23</font></i></a></i>;<br/><b>hence </b><a NAME="E2:36_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:36_1_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="kurato_2.html#E3:36_1_1"><i><font color="Green">E23</font></i></a></i>;<br/><b>hence </b><a NAME="E2:36_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:36_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="kurato_2.html#V3" target="_self">convergent</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="kurato_2.html#V2" target="_self">ascending</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="kurato_2.html#V1" target="_self">descending</a> )
 <b>by </b><i><a class="txt" href="kurato_2.html#E4:36_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="kurato_2.html#E5:36_1_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="kurato_2.html#E6:36_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="kurato_2.html#D5" target="_self">Def5</a>, <a class="ref" href="kurato_2.html#D6" target="_self">Def6</a>, <a class="ref" href="kurato_2.html#D7" target="_self">Def7</a></i>;<br/>


</div>
