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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:48"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a> &amp; ex <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> ) ) )
 ;<br/>

<a NAME="E2:48"/><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> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 
<b>by </b><i><a class="ref" href="limfunc1.html#T41" target="_self">Th41</a></i>;<br/>
<a NAME="E3:48"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 
<b>by </b><i><a class="txt" href="limfunc1.html#E1:48"><i><font color="Green">E28</font></i></a>, <a class="ref" href="limfunc1.html#T49" target="_self">Th49</a></i>;<br/>
<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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<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"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K14">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T26">SEQ_1:26</a></i>
<br/>.= 
1 <a href="seq_1.html#K14">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="limfunc1.html#E1"><i><font color="Green">Lemma1</font></i></a>, <a class="ref" href="seq_1.html#T31">SEQ_1:31</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="seq_1.html#T35">SEQ_1:35</a></i>
;<br/>
<b>hence </b><a NAME="E5:48"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K11">(#)</a> <font color="Maroon">c<sub>3</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E3:48"><i><font color="Green">E29</font></i></a>, <a class="ref" href="limfunc1.html#T40" target="_self">Th40</a></i>;<br/>


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