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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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>assume </b><a NAME="E1:18"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>3</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:18"/><i><font color="Green">E17</font></i>: 
<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>3</sub></font>
 <b>by </b><i><a class="ref" href="fdiff_2.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E4:18"/><i><font color="Green">E18</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</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="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="ref" href="fdiff_2.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E5:18"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="fcont_1.html#R1">is_continuous_in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="ref" href="fdiff_1.html#T32">FDIFF_1:32</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:18"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>5</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> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> holds <br/><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#NR2" target="_self">&lt;&gt;</a> 0 ) )
 <b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fdiff_2.html#E4:18"><i><font color="Green">E18</font></i></a>, <a class="ref" href="fcont_3.html#T15">FCONT_3:15</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="rcomp_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:18"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="rcomp_1.html#T38">RCOMP_1:38</a></i>;<br/>
<a NAME="E10:18"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E3:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="fdiff_2.html#E9:18"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E11:18"/>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E3:18_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E9:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_1"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E4:18_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E7:18"><i><font color="Green">E20</font></i></a>, <a class="txt" href="fdiff_2.html#E9:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_1"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E5:18_1"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:18_1"/><b>then </b>
not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E7:18_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E7:18"><i><font color="Green">E20</font></i></a>, <a class="txt" href="fdiff_2.html#E3:18_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:18"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E13:18"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>6</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="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#D4">RFUNCT_1:def 4</a></i>;<br/>
<a NAME="E14:18"/>
for <font color="Olive">b<sub>1</sub></font> being <a href="fdiff_1.html#V1">convergent_to_0</a> <a href="seq_1.html#NM1">Real_Sequence</a><br/>for <font color="Olive">b<sub>2</sub></font> being <a href="funct_1.html#V3">constant</a> <a href="seq_1.html#NM1">Real_Sequence</a> st  <a href="relset_1.html#K5">rng</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K9">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <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="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K9">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K9">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be  <a href="fdiff_1.html#V1">convergent_to_0</a> <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be  <a href="funct_1.html#V3">constant</a> <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:18_2"/><i><font color="Green">E25</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/>

<a NAME="E2:18_2"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#D4">RFUNCT_1:def 4</a></i>;<br/>
<a NAME="E3:18_2"/>
( <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E4:18_2"/><b>then </b><i><font color="Green">E27</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E2:18_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:18_2"/><i><font color="Green">E28</font></i>: 
(  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
;<br/>
<a NAME="E6:18_2"/>
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span> <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="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E7:18_2"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:18_2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="fdiff_2.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E9:18_2"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E5:18"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fdiff_2.html#E7:18_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="fcont_1.html#D1">FCONT_1:def 1</a></i>;<br/>
<a NAME="E10:18_2"/><i><font color="Green">E31</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="rfunct_1.html#D8">RFUNCT_1:def 8</a></i>;<br/>
<a NAME="E11:18_2"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E12:18_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#NR1" target="_self">is_not_0</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="rfunct_2.html#T26">RFUNCT_2:26</a></i>;<br/>
<a NAME="E13:18_2"/><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:18_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:18_2_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:18_2_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T37">RCOMP_1:37</a></i>;<br/>
<a NAME="E4:18_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E12:18"><i><font color="Green">E23</font></i></a>, <a class="txt" href="fdiff_2.html#E2:18_2_1"><i><font color="Green">E35</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:18_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rfunct_1.html#D8">RFUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E14:18_2"/>
( <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <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>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E15:18_2"/><b>then </b><i><font color="Green">E35</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</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>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E13:18_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E16:18_2"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#NR1" target="_self">is_not_0</a> 
 
<b>by </b><i><a class="ref" href="rfunct_2.html#T26">RFUNCT_2:26</a></i>;<br/>
<a NAME="E17:18_2"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#D8">RFUNCT_1:def 8</a></i>;<br/>
<a NAME="E18:18_2"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span> <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="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E19:18_2"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>8</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="txt" href="fdiff_2.html#E15:18_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green">E38</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47">RFUNCT_1:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47">RFUNCT_1:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E11:18_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rfunct_2.html#T23">RFUNCT_2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K18">"</a> </span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="rfunct_2.html#T27">RFUNCT_2:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D9">SEQ_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#K4">^</a> </span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E13:18_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="rfunct_2.html#T23">RFUNCT_2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K18">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E15:18_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="rfunct_2.html#T27">RFUNCT_2:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D9">SEQ_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E12:18_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="fdiff_2.html#E16:18_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="seq_1.html#T58">SEQ_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K19">/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T49">SEQ_1:49</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</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>8</sub></font></span>)</span>;<br/>
<a NAME="E21:18_2"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="fdiff_2.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E22:18_2"/><b>then </b><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</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>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E5:18"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fdiff_2.html#E19:18_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="fcont_1.html#D1">FCONT_1:def 1</a></i>;<br/>
<a NAME="E23:18_2"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</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>8</sub></font></span>)</span> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E9:18_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="seq_2.html#T28">SEQ_2:28</a></i>;<br/>
<i><font color="Green">E42</font></i>:  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E9:18_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="fdiff_2.html#E22:18_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="seq_2.html#T29">SEQ_2:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> 

;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font>;<br/>
<a NAME="E25:18_2"/><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2_4"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6">RFUNCT_2:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6">RFUNCT_2:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6">RFUNCT_2:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>14</sub></font>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6">RFUNCT_2:6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:18_2_4"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E26:18_2"/><i><font color="Green">E44</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fdiff_2.html#E5:18_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="fdiff_2.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E27:18_2"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</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>8</sub></font></span>)</span> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E22:18_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="seq_2.html#T28">SEQ_2:28</a></i>;<br/>
<a NAME="E28:18_2"/><i><font color="Green">E46</font></i>: 
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E22:18_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fdiff_2.html#E26:18_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="seq_2.html#T29">SEQ_2:29</a></i>;<br/>
<a NAME="E29:18_2"/><i><font color="Green">E47</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="fdiff_2.html#E5:18_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="fdiff_2.html#E7:18_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="fdiff_2.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E30:18_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="fcont_1.html#R1">is_continuous_in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="ref" href="fdiff_1.html#T32">FDIFF_1:32</a></i>;<br/>
<a NAME="E31:18_2"/><b>then </b><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E15:18_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="fdiff_2.html#E21:18_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="fcont_1.html#D1">FCONT_1:def 1</a></i>;<br/>
<a NAME="E32:18_2"/><b>then </b><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E29:18_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="seq_2.html#T28">SEQ_2:28</a></i>;<br/>
<a NAME="E33:18_2"/><i><font color="Green">E50</font></i>: 
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E29:18_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fdiff_2.html#E31:18_2"><i><font color="Green">E48</font></i></a>, <a class="ref" href="seq_2.html#T29">SEQ_2:29</a></i>;<br/>
<a NAME="E34:18_2"/><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E25:18_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="fdiff_2.html#E27:18_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fdiff_2.html#E32:18_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="seq_2.html#T25">SEQ_2:25</a></i>;<br/>
<a NAME="E35:18_2"/><i><font color="Green">E52</font></i>: 
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E25:18_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="fdiff_2.html#E27:18_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fdiff_2.html#E28:18_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fdiff_2.html#E32:18_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fdiff_2.html#E33:18_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="seq_2.html#T26">SEQ_2:26</a></i>;<br/>
<a NAME="E36:18_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="seq_1.html#NR1" target="_self">is_not_0</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="rfunct_2.html#T26">RFUNCT_2:26</a></i>;<br/>
<a NAME="E37:18_2"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</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>8</sub></font></span>)</span> <a href="seq_1.html#NR1" target="_self">is_not_0</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E16:18_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="seq_1.html#T43">SEQ_1:43</a></i>;<br/>
<a NAME="E38:18_2"/><i><font color="Green">E54</font></i>: 
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fdiff_2.html#E24:18_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<b>hence </b><a NAME="E39:18_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> is <a href="seq_2.html#V4">convergent</a>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E20:18_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fdiff_2.html#E23:18_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="fdiff_2.html#E34:18_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fdiff_2.html#E37:18_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="seq_2.html#T37">SEQ_2:37</a></i>;<br/>

<b>thus </b><a NAME="E40:18_2"/>
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K18">"</a> </span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K9">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rfunct_2.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E20:18_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fdiff_2.html#E23:18_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="fdiff_2.html#E24:18_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="fdiff_2.html#E34:18_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fdiff_2.html#E35:18_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="fdiff_2.html#E37:18_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="fdiff_2.html#E38:18_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="seq_2.html#T38">SEQ_2:38</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E15:18"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rfunct_1.html#K2">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="fdiff_2.html#E13:18"><i><font color="Green">E24</font></i></a>, <a class="ref" href="fdiff_2.html#T12" target="_self">Th12</a></i>;<br/>


</div>
