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

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>thus </b><a NAME="E1:84"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_1"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:84_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D7" target="_self">Def7</a></i>;<br/><b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>thus </b><a NAME="E3:84_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>assume </b><a NAME="E1:84_1_2"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/><a NAME="E2:84_1_2"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/><a NAME="E3:84_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E4:84_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K14">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#T40" target="_self">Th40</a></i>;<br/><b>hence </b><a NAME="E5:84_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rfunct_2.html#T24">RFUNCT_2:24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:84_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="limfunc1.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:84"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 implies <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_2"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 ;<br/>

<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:84_2_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D7" target="_self">Def7</a></i>;<br/><b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>thus </b><a NAME="E3:84_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_2_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>assume </b><a NAME="E1:84_2_2"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/><a NAME="E2:84_2_2"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/><a NAME="E3:84_2_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E4:84_2_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K14">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#T40" target="_self">Th40</a></i>;<br/><b>hence </b><a NAME="E5:84_2_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_2_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rfunct_2.html#T24">RFUNCT_2:24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:84_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="limfunc1.html#D8" target="_self">Def8</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:84"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_3"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:84_3_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_3"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D8" target="_self">Def8</a></i>;<br/><b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>thus </b><a NAME="E3:84_3_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_3_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>assume </b><a NAME="E1:84_3_2"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/><a NAME="E2:84_3_2"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/><a NAME="E3:84_3_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_3"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:84_3_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K14">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E1:84_3"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#T41" target="_self">Th41</a></i>;<br/><b>hence </b><a NAME="E5:84_3_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_3_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rfunct_2.html#T24">RFUNCT_2:24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:84_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="limfunc1.html#D8" target="_self">Def8</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E4:84"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V5" target="_self">divergent_in+infty_to-infty</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 ;<br/>

<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:84_4"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E4:84"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D8" target="_self">Def8</a></i>;<br/><b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>thus </b><a NAME="E3:84_4"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_4"><i><font color="Green">E49</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>assume </b><a NAME="E1:84_5"/>
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/><a NAME="E2:84_5"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/><a NAME="E3:84_5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V2" target="_self">divergent_to-infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E4:84"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E4:84_5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K14">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E4:84"><i><font color="Green">E47</font></i></a>, <a class="ref" href="limfunc1.html#T41" target="_self">Th41</a></i>;<br/><b>hence </b><a NAME="E5:84_5"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is <a href="limfunc1.html#V1" target="_self">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E2:84_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rfunct_2.html#T24">RFUNCT_2:24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:84"/>
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> is <a href="limfunc1.html#V4" target="_self">divergent_in+infty_to+infty</a>
 <b>by </b><i><a class="txt" href="limfunc1.html#E5:84"><i><font color="Green">E48</font></i></a>, <a class="ref" href="limfunc1.html#D7" target="_self">Def7</a></i>;<br/>


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