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

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:46"/><i><font color="Green">E27</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="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E2:46"/>
 <a href="funct_3.html#K6">incl</a> <a href="numbers.html#K5">NAT</a>  is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 
<b>by </b><i><a class="txt" href="limfunc1.html#E58"><i><font color="Green">Lemma25</font></i></a>, <a class="ref" href="limfunc1.html#T47" target="_self">Th47</a></i>;<br/>
<a NAME="E3:46"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K14">(#)</a> <span class="p1">(<span class="default"><a href="funct_3.html#K6">incl</a> <a href="numbers.html#K5">NAT</a> </span>)</span> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 
<b>by </b><i><a class="ref" href="limfunc1.html#T40" target="_self">Th40</a></i>;<br/>
<a NAME="E4:46"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="seq_1.html#K17">-</a> <span class="p1">(<span class="default"><a href="funct_3.html#K6">incl</a> <a href="numbers.html#K5">NAT</a> </span>)</span> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 
<b>by </b><i><a class="ref" href="seq_1.html#T25">SEQ_1:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="seq_1.html#K17">-</a> <span class="p2">(<span class="default"><a href="funct_3.html#K6">incl</a> <a href="numbers.html#K5">NAT</a> </span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_3.html#K6">incl</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T14">SEQ_1:14</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="limfunc1.html#E58"><i><font color="Green">Lemma25</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="limfunc1.html#E1:46"><i><font color="Green">E27</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:46"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E4:46"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div>
