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

<b>let </b><font color="Maroon" title="c1">x0</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c2">f2</font>, <font color="Maroon" title="c3">f1</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> , <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 &amp; <font color="Maroon" title="c3">f1</font> <a href="fdiff_1.html#R1" title="FDIFF_1:pred.1">is_differentiable_in</a> <font color="Maroon" title="c1">x0</font> &amp; <font color="Maroon" title="c2">f2</font> <a href="fdiff_1.html#R1" title="FDIFF_1:pred.1">is_differentiable_in</a> <font color="Maroon" title="c1">x0</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">N1</font> being    <a href="rcomp_1.html#M1" title="RCOMP_1:mode.1">Neighbourhood</a> of <font color="Maroon" title="c1">x0</font><b> such that </b><br/><a NAME="E3:18"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c4">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font>
 <b>by </b><i><a class="ref" href="fdiff_2.html#T11" target="_self" title="FDIFF_2:th.11">Th11</a></i>;<br/>
<a NAME="E4:18"/><i><font color="Green" title="E18">A3</font></i>: 
 ex <font color="Olive" title="b1">N2</font> being   <a href="rcomp_1.html#M1" title="RCOMP_1:mode.1">Neighbourhood</a> of <font color="Maroon" title="c1">x0</font> st <font color="Olive" title="b1">N2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="fdiff_2.html#T11" target="_self" title="FDIFF_2:th.11">Th11</a></i>;<br/>
<a NAME="E5:18"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c2">f2</font> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="fdiff_1.html#T32" title="FDIFF_1:th.32">FDIFF_1:32</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">N3</font> being    <a href="rcomp_1.html#M1" title="RCOMP_1:mode.1">Neighbourhood</a> of <font color="Maroon" title="c1">x0</font><b> such that </b><br/><a NAME="E7:18"/><i><font color="Green" title="E20">A5</font></i>: 
( <font color="Maroon" title="c5">N3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font> &amp; ( for <font color="Olive" title="b1">g</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N3</font> holds <br/><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 ) )
 <b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="fdiff_2.html#E4:18"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="fcont_3.html#T15" title="FCONT_3:th.15">FCONT_3:15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">N</font> being    <a href="rcomp_1.html#M1" title="RCOMP_1:mode.1">Neighbourhood</a> of <font color="Maroon" title="c1">x0</font><b> such that </b><br/><a NAME="E9:18"/><i><font color="Green" title="E21">A6</font></i>: 
( <font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">N1</font> &amp; <font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">N3</font> )
 <b>by </b><i><a class="ref" href="rcomp_1.html#T38" title="RCOMP_1:th.38">RCOMP_1:38</a></i>;<br/>
<a NAME="E10:18"/><i><font color="Green" title="E22">A7</font></i>: 
<font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E3:18"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="fdiff_2.html#E9:18"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E11:18"/>
<font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</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" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:18_1"/><i><font color="Green" title="E23">A8</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c8">x'</font> = <font color="Maroon" title="c7">x</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E3:18_1"/><i><font color="Green" title="E24">A9</font></i>: 
<font color="Maroon" title="c8">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">N3</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E9:18"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_1"><i><font color="Green" title="E23">A8</font></i></a></i>;<br/>
<a NAME="E4:18_1"/>
<font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c8">x'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E7:18"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="fdiff_2.html#E9:18"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_1"><i><font color="Green" title="E23">A8</font></i></a></i>;<br/>
<a NAME="E5:18_1"/><b>then </b>
not <font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c8">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E6:18_1"/><b>then </b>
not <font color="Maroon" title="c8">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E7:18_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E7:18"><i><font color="Green" title="E20">A5</font></i></a>, <a class="txt" href="fdiff_2.html#E3:18_1"><i><font color="Green" title="E24">A9</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:18"/><b>then </b><i><font color="Green" title="E23">A10</font></i>: 
<font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E13:18"/><b>then </b><i><font color="Green" title="E24">A11</font></i>: 
<font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#D4" title="RFUNCT_1:def.4">RFUNCT_1:def 4</a></i>;<br/>
<a NAME="E14:18"/>
for <font color="Olive" title="b1">h</font> being <a href="fdiff_1.html#V1" title="FDIFF_1:attr.1">convergent_to_0</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/> for <font color="Olive" title="b2">c</font> being <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>  st  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Olive" title="b2">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b1">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Olive" title="b2">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Olive" title="b2">c</font></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Olive" title="b2">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Olive" title="b2">c</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^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" title="c7">h</font> be  <a href="fdiff_1.html#V1" title="FDIFF_1:attr.1">convergent_to_0</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon" title="c8">c</font> be  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:18_2"/><i><font color="Green" title="E25">A12</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x0</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> )
 ;<br/>

<a NAME="E2:18_2"/><b>then </b><i><font color="Green" title="E26">A13</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#D4" title="RFUNCT_1:def.4">RFUNCT_1:def 4</a></i>;<br/>
<a NAME="E3:18_2"/>
( <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E4:18_2"/><b>then </b><i><font color="Green" title="E27">A14</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E2:18_2"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:18_2"/><i><font color="Green" title="E28">A15</font></i>: 
(  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font> &amp;  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font> )
 
;<br/>
<a NAME="E6:18_2"/>
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E7:18_2"/><b>then </b><i><font color="Green" title="E29">A16</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green" title="E27">A14</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:18_2"/>
( <font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green" title="E25">A12</font></i></a>, <a class="ref" href="fdiff_2.html#T4" target="_self" title="FDIFF_2:th.4">Th4</a></i>;<br/>
<a NAME="E9:18_2"/><b>then </b><i><font color="Green" title="E30">A17</font></i>: 
( <font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E5:18"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="fdiff_2.html#E7:18_2"><i><font color="Green" title="E29">A16</font></i></a>, <a class="ref" href="fcont_1.html#D1" title="FCONT_1:def.1">FCONT_1:def 1</a></i>;<br/>
<a NAME="E10:18_2"/><i><font color="Green" title="E31">A18</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green" title="E27">A14</font></i></a>, <a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">RFUNCT_1:def 8</a></i>;<br/>
<a NAME="E11:18_2"/><b>then </b><i><font color="Green" title="E32">A19</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green" title="E27">A14</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E12:18_2"/><i><font color="Green" title="E33">A20</font></i>: 
<font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#NR1" title="SEQ_1:NR.1">is_not_0</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18_2"><i><font color="Green" title="E31">A18</font></i></a>, <a class="ref" href="rfunct_2.html#T26" title="RFUNCT_2:th.26">RFUNCT_2:26</a></i>;<br/>
<a NAME="E13:18_2"/><i><font color="Green" title="E34">A21</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</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" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:18_2_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">c</font>
 ;<br/>

<a NAME="E2:18_2_1"/><b>then </b><i><font color="Green" title="E35">A22</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x0</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green" title="E25">A12</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:18_2_1"/>
<font color="Maroon" title="c1">x0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T37" title="RCOMP_1:th.37">RCOMP_1:37</a></i>;<br/>
<a NAME="E4:18_2_1"/><b>then </b>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E12:18"><i><font color="Green" title="E23">A10</font></i></a>, <a class="txt" href="fdiff_2.html#E2:18_2_1"><i><font color="Green" title="E35">A22</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:18_2_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">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" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E15:18_2"/><b>then </b><i><font color="Green" title="E35">A23</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E13:18_2"><i><font color="Green" title="E34">A21</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E16:18_2"/><b>then </b><i><font color="Green" title="E36">A24</font></i>: 
<font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font> <a href="seq_1.html#NR1" title="SEQ_1:NR.1">is_not_0</a> 
 
<b>by </b><i><a class="ref" href="rfunct_2.html#T26" title="RFUNCT_2:th.26">RFUNCT_2:26</a></i>;<br/>
<a NAME="E17:18_2"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#D8" title="RFUNCT_1:def.8">RFUNCT_1:def 8</a></i>;<br/>
<a NAME="E18:18_2"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E19:18_2"/><b>then </b><i><font color="Green" title="E37">A25</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c8">c</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E15:18_2"><i><font color="Green" title="E35">A23</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green" title="E38">A26</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" title="RFUNCT_1:th.47">RFUNCT_1:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" title="RFUNCT_1:th.47">RFUNCT_1:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E11:18_2"><i><font color="Green" title="E32">A19</font></i></a>, <a class="ref" href="rfunct_2.html#T23" title="RFUNCT_2:th.23">RFUNCT_2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18_2"><i><font color="Green" title="E31">A18</font></i></a>, <a class="ref" href="rfunct_2.html#T27" title="RFUNCT_2:th.27">RFUNCT_2:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D9" title="SEQ_1:def.9">SEQ_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</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" title="E34">A21</font></i></a>, <a class="ref" href="rfunct_2.html#T23" title="RFUNCT_2:th.23">RFUNCT_2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</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" title="E35">A23</font></i></a>, <a class="ref" href="rfunct_2.html#T27" title="RFUNCT_2:th.27">RFUNCT_2:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D9" title="SEQ_1:def.9">SEQ_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</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" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</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" title="E33">A20</font></i></a>, <a class="txt" href="fdiff_2.html#E16:18_2"><i><font color="Green" title="E36">A24</font></i></a>, <a class="ref" href="seq_1.html#T58" title="SEQ_1:th.58">SEQ_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K19" title="SEQ_1:func.19">/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T49" title="SEQ_1:th.49">SEQ_1:49</a></i>
;<br/>
<b>set </b><font color="Maroon" title="c9">w1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span>;<br/>
<a NAME="E21:18_2"/><i><font color="Green" title="E39">A27</font></i>: 
( <font color="Maroon" title="c8">c</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green" title="E25">A12</font></i></a>, <a class="ref" href="fdiff_2.html#T4" target="_self" title="FDIFF_2:th.4">Th4</a></i>;<br/>
<a NAME="E22:18_2"/><b>then </b><i><font color="Green" title="E40">A28</font></i>: 
( <font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E5:18"><i><font color="Green" title="E19">A4</font></i></a>, <a class="txt" href="fdiff_2.html#E19:18_2"><i><font color="Green" title="E37">A25</font></i></a>, <a class="ref" href="fcont_1.html#D1" title="FCONT_1:def.1">FCONT_1:def 1</a></i>;<br/>
<a NAME="E23:18_2"/><b>then </b><i><font color="Green" title="E41">A29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E9:18_2"><i><font color="Green" title="E30">A17</font></i></a>, <a class="ref" href="seq_2.html#T28" title="SEQ_2:th.28">SEQ_2:28</a></i>;<br/>
<a NAME="E24:18_2"/><i><font color="Green" title="E42">A30</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E9:18_2"><i><font color="Green" title="E30">A17</font></i></a>, <a class="txt" href="fdiff_2.html#E22:18_2"><i><font color="Green" title="E40">A28</font></i></a>, <a class="ref" href="seq_2.html#T29" title="SEQ_2:th.29">SEQ_2:29</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">v1</font> = <font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">v2</font> = <font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c12">u1</font> = <font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font>;<br/>
<b>set </b><font color="Maroon" title="c13">u2</font> = <font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font>;<br/>
<a NAME="E25:18_2"/><i><font color="Green" title="E43">A31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c14">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</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" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</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" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6" title="RFUNCT_2:th.6">RFUNCT_2:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</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" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">SEQ_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</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" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6" title="RFUNCT_2:th.6">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6" title="RFUNCT_2:th.6">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T12" title="SEQ_1:th.12">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" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c14">n</font>
<b>by </b><i><a class="ref" href="rfunct_2.html#T6" title="RFUNCT_2:th.6">RFUNCT_2:6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:18_2_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon" title="c14">h1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c15">h2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span>;<br/>
<a NAME="E26:18_2"/><i><font color="Green" title="E44">A32</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green" title="E25">A12</font></i></a>, <a class="txt" href="fdiff_2.html#E4:18_2"><i><font color="Green" title="E27">A14</font></i></a>, <a class="txt" href="fdiff_2.html#E5:18_2"><i><font color="Green" title="E28">A15</font></i></a>, <a class="ref" href="fdiff_2.html#T12" target="_self" title="FDIFF_2:th.12">Th12</a></i>;<br/>
<a NAME="E27:18_2"/><b>then </b><i><font color="Green" title="E45">A33</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E22:18_2"><i><font color="Green" title="E40">A28</font></i></a>, <a class="ref" href="seq_2.html#T28" title="SEQ_2:th.28">SEQ_2:28</a></i>;<br/>
<a NAME="E28:18_2"/><i><font color="Green" title="E46">A34</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E22:18_2"><i><font color="Green" title="E40">A28</font></i></a>, <a class="txt" href="fdiff_2.html#E26:18_2"><i><font color="Green" title="E44">A32</font></i></a>, <a class="ref" href="seq_2.html#T29" title="SEQ_2:th.29">SEQ_2:29</a></i>;<br/>
<a NAME="E29:18_2"/><i><font color="Green" title="E47">A35</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="fdiff_2.html#E1:18_2"><i><font color="Green" title="E25">A12</font></i></a>, <a class="txt" href="fdiff_2.html#E5:18_2"><i><font color="Green" title="E28">A15</font></i></a>, <a class="txt" href="fdiff_2.html#E7:18_2"><i><font color="Green" title="E29">A16</font></i></a>, <a class="ref" href="fdiff_2.html#T12" target="_self" title="FDIFF_2:th.12">Th12</a></i>;<br/>
<a NAME="E30:18_2"/>
<font color="Maroon" title="c3">f1</font> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="fdiff_1.html#T32" title="FDIFF_1:th.32">FDIFF_1:32</a></i>;<br/>
<a NAME="E31:18_2"/><b>then </b><i><font color="Green" title="E48">A36</font></i>: 
( <font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E15:18_2"><i><font color="Green" title="E35">A23</font></i></a>, <a class="txt" href="fdiff_2.html#E21:18_2"><i><font color="Green" title="E39">A27</font></i></a>, <a class="ref" href="fcont_1.html#D1" title="FCONT_1:def.1">FCONT_1:def 1</a></i>;<br/>
<a NAME="E32:18_2"/><b>then </b><i><font color="Green" title="E49">A37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E29:18_2"><i><font color="Green" title="E47">A35</font></i></a>, <a class="ref" href="seq_2.html#T28" title="SEQ_2:th.28">SEQ_2:28</a></i>;<br/>
<a NAME="E33:18_2"/><i><font color="Green" title="E50">A38</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E29:18_2"><i><font color="Green" title="E47">A35</font></i></a>, <a class="txt" href="fdiff_2.html#E31:18_2"><i><font color="Green" title="E48">A36</font></i></a>, <a class="ref" href="seq_2.html#T29" title="SEQ_2:th.29">SEQ_2:29</a></i>;<br/>
<a NAME="E34:18_2"/><i><font color="Green" title="E51">A39</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E25:18_2"><i><font color="Green" title="E43">A31</font></i></a>, <a class="txt" href="fdiff_2.html#E27:18_2"><i><font color="Green" title="E45">A33</font></i></a>, <a class="txt" href="fdiff_2.html#E32:18_2"><i><font color="Green" title="E49">A37</font></i></a>, <a class="ref" href="seq_2.html#T25" title="SEQ_2:th.25">SEQ_2:25</a></i>;<br/>
<a NAME="E35:18_2"/><i><font color="Green" title="E52">A40</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E25:18_2"><i><font color="Green" title="E43">A31</font></i></a>, <a class="txt" href="fdiff_2.html#E27:18_2"><i><font color="Green" title="E45">A33</font></i></a>, <a class="txt" href="fdiff_2.html#E28:18_2"><i><font color="Green" title="E46">A34</font></i></a>, <a class="txt" href="fdiff_2.html#E32:18_2"><i><font color="Green" title="E49">A37</font></i></a>, <a class="txt" href="fdiff_2.html#E33:18_2"><i><font color="Green" title="E50">A38</font></i></a>, <a class="ref" href="seq_2.html#T26" title="SEQ_2:th.26">SEQ_2:26</a></i>;<br/>
<a NAME="E36:18_2"/>
<font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#NR1" title="SEQ_1:NR.1">is_not_0</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E10:18_2"><i><font color="Green" title="E31">A18</font></i></a>, <a class="ref" href="rfunct_2.html#T26" title="RFUNCT_2:th.26">RFUNCT_2:26</a></i>;<br/>
<a NAME="E37:18_2"/><b>then </b><i><font color="Green" title="E53">A41</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="seq_1.html#NR1" title="SEQ_1:NR.1">is_not_0</a> 
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E16:18_2"><i><font color="Green" title="E36">A24</font></i></a>, <a class="ref" href="seq_1.html#T43" title="SEQ_1:th.43">SEQ_1:43</a></i>;<br/>
<a NAME="E38:18_2"/><i><font color="Green" title="E54">A42</font></i>: 
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:18"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="fdiff_2.html#E24:18_2"><i><font color="Green" title="E42">A30</font></i></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></i>;<br/>
<b>hence </b><a NAME="E39:18_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E20:18_2"><i><font color="Green" title="E38">A26</font></i></a>, <a class="txt" href="fdiff_2.html#E23:18_2"><i><font color="Green" title="E41">A29</font></i></a>, <a class="txt" href="fdiff_2.html#E34:18_2"><i><font color="Green" title="E51">A39</font></i></a>, <a class="txt" href="fdiff_2.html#E37:18_2"><i><font color="Green" title="E53">A41</font></i></a>, <a class="ref" href="seq_2.html#T37" title="SEQ_2:th.37">SEQ_2:37</a></i>;<br/>

<b>thus </b><a NAME="E40:18_2"/>
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K18" title="SEQ_1:func.18">"</a> </span>)</span> <a href="seq_1.html#K11" title="SEQ_1:func.11">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="seq_1.html#K9" title="SEQ_1:func.9">+</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span> <a href="seq_1.html#K10" title="SEQ_1:func.10">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="rfunct_2.html#K1" title="RFUNCT_2:func.1">*</a> <font color="Maroon" title="c8">c</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E20:18_2"><i><font color="Green" title="E38">A26</font></i></a>, <a class="txt" href="fdiff_2.html#E23:18_2"><i><font color="Green" title="E41">A29</font></i></a>, <a class="txt" href="fdiff_2.html#E24:18_2"><i><font color="Green" title="E42">A30</font></i></a>, <a class="txt" href="fdiff_2.html#E34:18_2"><i><font color="Green" title="E51">A39</font></i></a>, <a class="txt" href="fdiff_2.html#E35:18_2"><i><font color="Green" title="E52">A40</font></i></a>, <a class="txt" href="fdiff_2.html#E37:18_2"><i><font color="Green" title="E53">A41</font></i></a>, <a class="txt" href="fdiff_2.html#E38:18_2"><i><font color="Green" title="E54">A42</font></i></a>, <a class="ref" href="seq_2.html#T38" title="SEQ_2:th.38">SEQ_2:38</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E15:18"/>
( <font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font> <a href="fdiff_1.html#R1" title="FDIFF_1:pred.1">is_differentiable_in</a> <font color="Maroon" title="c1">x0</font> &amp;  <a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f2</font></span>)</span>,<font color="Maroon" title="c1">x0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="fdiff_1.html#K1" title="FDIFF_1:func.1">diff</a> <font color="Maroon" title="c2">f2</font>,<font color="Maroon" title="c1">x0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="fdiff_2.html#E13:18"><i><font color="Green" title="E24">A11</font></i></a>, <a class="ref" href="fdiff_2.html#T12" target="_self" title="FDIFF_2:th.12">Th12</a></i>;<br/>


</div>
