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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green">E3</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green">E4</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E3:5"/><i><font color="Green">E5</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:5"/><i><font color="Green">E6</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = 1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>6</sub></font> = 1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E6:5"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E2:5"><i><font color="Green">E4</font></i></a></i>;<br/>
<a NAME="E7:5"/>
1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5"><i><font color="Green">E3</font></i></a>, <a class="ref" href="real_2.html#T142">REAL_2:142</a></i>;<br/>
<a NAME="E8:5"/><b>then </b>
1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
;<br/>
<a NAME="E9:5"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K2">"</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="holder_1.html#E6:5"><i><font color="Green">E7</font></i></a>, <a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/>
<a NAME="E10:5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K2">"</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T203">XCMPLX_1:203</a></i>;<br/>
<a NAME="E11:5"/><b>then </b><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5"><i><font color="Green">E3</font></i></a></i>;<br/>
<a NAME="E12:5"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="holder_1.html#E11:5"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<a NAME="E13:5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E2:5"><i><font color="Green">E4</font></i></a>, <a class="txt" href="holder_1.html#E11:5"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xcmplx_1.html#T117">XCMPLX_1:117</a></i>;<br/>
<a NAME="E14:5"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E12:5"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<i><font color="Green">E11</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
0
<b>by </b><i><a class="txt" href="holder_1.html#E14:5"><i><font color="Green">E10</font></i></a></i>
;<br/>
<i><font color="Green">E12</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="holder_1.html#E14:5"><i><font color="Green">E10</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>

;<br/>
<a NAME="E17:5"/><i><font color="Green">E13</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a>  st <br/>(  <a href="relat_1.html#K1">dom</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a>  &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Olive">b<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>3</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 ) ) ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="real_1.html#NM1">Real</a>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  = <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E2:5_3"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 <b>and </b><br/><a NAME="E3:5_3"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="partfun2.html#S2">PARTFUN2:sch 2</a>();<br/></i>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<a NAME="E4:5_3"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:5_3_1"/><i><font color="Green">E17</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E2:5_3_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E2:5_3"><i><font color="Green">E14</font></i></a></i>;<br/>
<a NAME="E3:5_3_1"/><b>then </b>
 <a href="numbers.html#K1">REAL</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:5_3_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_3_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:5_3"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  holds <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<a NAME="E1:5_3_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E3:5_3"><i><font color="Green">E15</font></i></a>, <a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:5_3_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:5_3"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a>  holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E1:5_3_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> 
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="holder_1.html#E5:5_3"><i><font color="Green">E17</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/>


</div><b>end;</b></div>
<a NAME="E7:5_3"/><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> is  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="ref" href="fcont_3.html#T4">FCONT_3:4</a>, <a class="ref" href="subset_1.html#D4">SUBSET_1:def 4</a></i>;<br/>
<a NAME="E8:5_3"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R2">is_differentiable_on</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="holder_1.html#E6:5_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="fdiff_1.html#T31">FDIFF_1:31</a></i>;<br/>
<a NAME="E9:5_3"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <br/>( <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>thus </b><a NAME="E1:5_3_4"/>
<font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="holder_1.html#E7:5_3"><i><font color="Green">E19</font></i></a>, <a class="txt" href="holder_1.html#E8:5_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="fdiff_1.html#T16">FDIFF_1:16</a></i>;<br/>

<b>thus </b> <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#K2">`|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="holder_1.html#E8:5_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="fdiff_1.html#D8">FDIFF_1:def 8</a></i>
<br/>.= 
 <a href="real_1.html#K1">-</a> 1
<b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="holder_1.html#E6:5_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="holder_1.html#E7:5_3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="fdiff_1.html#T31">FDIFF_1:31</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:5_3"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <br/>( <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Olive">b<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <br/>( <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 ) ) ) ) )
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="holder_1.html#E5:5_3"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E18:5"/><i><font color="Green">E14</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a>  st <br/>(  <a href="relat_1.html#K1">dom</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0 &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> ) ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_4"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p1">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<a NAME="E1:5_4"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5"><i><font color="Green">E3</font></i></a></i>;<br/>
<b>take </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p1">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
;<br/>

<a NAME="E2:5_4"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 
<b>by </b><i><a class="ref" href="taylor_1.html#D3">TAYLOR_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:5_4"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>;<br/>

<div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:5_4_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E2:5_4_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_4_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:5_4_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_4_1"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:5_4_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E3:5_4"><i><font color="Green">E16</font></i></a>, <a class="ref" href="seq_1.html#D6">SEQ_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E2:5_4_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="taylor_1.html#D3">TAYLOR_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>
;<br/><br/><a NAME="E4:5_4_1"/><i><font color="Green">E20</font></i>: 
 <a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_4_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="taylor_1.html#T21">TAYLOR_1:21</a></i>;<br/><b>hence </b><a NAME="E5:5_4_1"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p1">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="fdiff_1.html#T23">FDIFF_1:23</a></i>;<br/><b>thus </b> <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E4:5_4_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="fdiff_1.html#T23">FDIFF_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_4_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="taylor_1.html#T21">TAYLOR_1:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>

<br/>.= 
1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_4"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>

;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E5:5_4"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p1">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K13">(#)</a> <span class="p2">(<span class="default"><a href="taylor_1.html#K3">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_4"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E20:5"/><i><font color="Green">E15</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 <b>and </b><br/><a NAME="E21:5"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E22:5"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> holds <br/>( <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 <b>by </b><i><a class="txt" href="holder_1.html#E17:5"><i><font color="Green">E13</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E24:5"/><i><font color="Green">E18</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>and </b><br/><a NAME="E25:5"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>( <font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="holder_1.html#E18:5"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font>;<br/>
<i><font color="Green">E20</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="limfunc1.html#K4">right_open_halfline</a> 0</span>)</span> <a href="subset_1.html#K8">/\</a> <a href="numbers.html#K1">REAL</a> 
<b>by </b><i><a class="txt" href="holder_1.html#E20:5"><i><font color="Green">E15</font></i></a>, <a class="txt" href="holder_1.html#E24:5"><i><font color="Green">E18</font></i></a></i>
<br/>.= 
 <a href="limfunc1.html#K4">right_open_halfline</a> 0
<b>by </b><i><a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E27:5"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0 holds <br/>( <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E1:5_6"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 ;<br/>

<a NAME="E2:5_6"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_6"><i><font color="Green">E22</font></i></a>, <a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/>
<a NAME="E3:5_6"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> )
 
;<br/>
<a NAME="E4:5_6"/><b>then </b><i><font color="Green">E23</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font>
 
;<br/>
<a NAME="E5:5_6"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E22:5"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E6:5_6"/><i><font color="Green">E25</font></i>: 
 <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 
<b>by </b><i><a class="txt" href="holder_1.html#E22:5"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E7:5_6"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E25:5"><i><font color="Green">E19</font></i></a>, <a class="txt" href="holder_1.html#E4:5_6"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E8:5_6"/><i><font color="Green">E27</font></i>: 
 <a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E25:5"><i><font color="Green">E19</font></i></a>, <a class="txt" href="holder_1.html#E4:5_6"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E26:5"><i><font color="Green">E20</font></i></a>, <a class="txt" href="holder_1.html#E1:5_6"><i><font color="Green">E22</font></i></a>, <a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E25:5"><i><font color="Green">E19</font></i></a>, <a class="txt" href="holder_1.html#E4:5_6"><i><font color="Green">E23</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E21:5"><i><font color="Green">E16</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>

;<br/>

<b>thus </b><a NAME="E10:5_6"/>
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E5:5_6"><i><font color="Green">E24</font></i></a>, <a class="txt" href="holder_1.html#E7:5_6"><i><font color="Green">E26</font></i></a>, <a class="ref" href="fdiff_1.html#T21">FDIFF_1:21</a></i>;<br/>

<b>thus </b> <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E5:5_6"><i><font color="Green">E24</font></i></a>, <a class="txt" href="holder_1.html#E7:5_6"><i><font color="Green">E26</font></i></a>, <a class="ref" href="fdiff_1.html#T21">FDIFF_1:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="txt" href="holder_1.html#E6:5_6"><i><font color="Green">E25</font></i></a>, <a class="txt" href="holder_1.html#E8:5_6"><i><font color="Green">E27</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E28:5"/><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="holder_1.html#E2:5"><i><font color="Green">E4</font></i></a>, <a class="ref" href="prepower.html#T87">PREPOWER:87</a></i>;<br/>
<a NAME="E29:5"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 holds <br/><font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E1:5_7"/><i><font color="Green">E24</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 ;<br/>

<a NAME="E2:5_7"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 or <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_7"><i><font color="Green">E24</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<a NAME="E3:5_7"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_7"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E4:5_7"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 
<b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/>
<a NAME="E5:5_7"/><i><font color="Green">E27</font></i>: 
 <a href="limfunc1.html#K4">right_open_halfline</a> 0 is  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="fcont_3.html#T7">FCONT_3:7</a></i>;<br/>
<a NAME="E6:5_7"/><i><font color="Green">E28</font></i>: 
 <a href="limfunc1.html#K4">right_open_halfline</a> 0 <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E26:5"><i><font color="Green">E20</font></i></a></i>;<br/>
<a NAME="E7:5_7"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0 holds <br/><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R1">is_differentiable_in</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E27:5"><i><font color="Green">E21</font></i></a></i>;<br/>
<a NAME="E8:5_7"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R2">is_differentiable_on</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 
<b>by </b><i><a class="txt" href="holder_1.html#E5:5_7"><i><font color="Green">E27</font></i></a>, <a class="txt" href="holder_1.html#E6:5_7"><i><font color="Green">E28</font></i></a>, <a class="txt" href="holder_1.html#E7:5_7"><i><font color="Green">E29</font></i></a>, <a class="ref" href="fdiff_1.html#T16">FDIFF_1:16</a></i>;<br/>
<a NAME="E9:5_7"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fcont_1.html#R2">is_continuous_on</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 
<b>by </b><i><a class="ref" href="fdiff_1.html#T33">FDIFF_1:33</a></i>;<br/>
<a NAME="E10:5_7"/>
1 <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
;<br/>
<a NAME="E11:5_7"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 
<b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/>
<b>then </b><i><font color="Green">E32</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="txt" href="holder_1.html#E27:5"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="ref" href="prepower.html#T87">PREPOWER:87</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="holder_1.html#E2:5"><i><font color="Green">E4</font></i></a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_7_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_7_2_1"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 or <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="holder_1.html#E2:5_7"><i><font color="Green">E25</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_7_2_1_1"><b>case </b></a><a NAME="E1:5_7_2_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>11</sub></font> = 1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>;<br/><a NAME="E2:5_7_2_1_1"/>
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_7_2_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E3:5_7_2_1_1"/><b>then </b><i><font color="Green">E34</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><a NAME="E4:5_7_2_1_1"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2_1_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:5_7_2_1_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/><a NAME="E2:5_7_2_1_1_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_7_2_1_1_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:5_7_2_1_1_1_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> )
 ;<br/><a NAME="E5:5_7_2_1_1_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="holder_1.html#E4:5_7_2_1_1_1_1"><i><font color="Green">E37</font></i></a></i>;<br/><a NAME="E6:5_7_2_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_7_2_1_1_1_1"><i><font color="Green">E37</font></i></a></i>;<br/><b>hence </b><a NAME="E7:5_7_2_1_1_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:5_7_2_1_1_1"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:5_7_2_1_1"/>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/><a NAME="E6:5_7_2_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_7_2_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:5_7_2_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="txt" href="holder_1.html#E9:5_7"><i><font color="Green">E31</font></i></a>, <a class="txt" href="holder_1.html#E4:5_7_2_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="fcont_1.html#T17">FCONT_1:17</a></i>;<br/><a NAME="E8:5_7_2_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="txt" href="holder_1.html#E8:5_7"><i><font color="Green">E30</font></i></a>, <a class="txt" href="holder_1.html#E6:5_7_2_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="fdiff_1.html#T34">FDIFF_1:34</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E10:5_7_2_1_1"/><i><font color="Green">E39</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E11:5_7_2_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1
 <b>and </b><br/><a NAME="E12:5_7_2_1_1"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E7:5_7_2_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="holder_1.html#E8:5_7_2_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="rolle.html#T4">ROLLE:4</a></i>;<br/><a NAME="E13:5_7_2_1_1"/>
0 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E10:5_7_2_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E14:5_7_2_1_1"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_7"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E15:5_7_2_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E16:5_7_2_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E11:5_7_2_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E17:5_7_2_1_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E18:5_7_2_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:5_7_2_1_1_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="holder_1.html#E15:5_7_2_1_1"><i><font color="Green">E42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:5_7_2_1_1_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:5_7_2_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E17:5_7_2_1_1"><i><font color="Green">E43</font></i></a></i>;<br/><a NAME="E20:5_7_2_1_1"/><i><font color="Green">E46</font></i>: 
 <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E27:5"><i><font color="Green">E21</font></i></a>, <a class="txt" href="holder_1.html#E18:5_7_2_1_1"><i><font color="Green">E44</font></i></a></i>;<br/><a NAME="E21:5_7_2_1_1"/>
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5"><i><font color="Green">E3</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E22:5_7_2_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1
 ;<br/><a NAME="E23:5_7_2_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> 0
 <b>by </b><i><a class="txt" href="holder_1.html#E15:5_7_2_1_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="holder_1.html#E19:5_7_2_1_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="holder_1.html#E22:5_7_2_1_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="power.html#T45">POWER:45</a></i>;<br/><a NAME="E24:5_7_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> 0
 <b>by </b><i><a class="txt" href="holder_1.html#E15:5_7_2_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="power.html#D2">POWER:def 2</a></i>;<br/><a NAME="E25:5_7_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> 0
 <b>by </b><i><a class="txt" href="holder_1.html#E15:5_7_2_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="power.html#D2">POWER:def 2</a></i>;<br/><a NAME="E26:5_7_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E15:5_7_2_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="prepower.html#T85">PREPOWER:85</a></i>;<br/><a NAME="E27:5_7_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E28:5_7_2_1_1"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K4">*</a> 0
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E20:5_7_2_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E29:5_7_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E30:5_7_2_1_1"/><b>then </b><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E12:5_7_2_1_1"><i><font color="Green">E41</font></i></a></i>;<br/><a NAME="E31:5_7_2_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E12:5_7"><i><font color="Green">E32</font></i></a>, <a class="txt" href="holder_1.html#E30:5_7_2_1_1"><i><font color="Green">E48</font></i></a></i>;<br/><a NAME="E32:5_7_2_1_1"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E27:5"><i><font color="Green">E21</font></i></a>, <a class="txt" href="holder_1.html#E4:5_7"><i><font color="Green">E26</font></i></a></i>;<br/><a NAME="E33:5_7_2_1_1"/><b>then </b>
0 <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E34:5_7_2_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_7_2_1_2"><b>case </b></a><a NAME="E1:5_7_2_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1;<br/><a NAME="E2:5_7_2_1_2"/>
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_7_2_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E3:5_7_2_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1
 ;<br/><a NAME="E4:5_7_2_1_2"/><i><font color="Green">E35</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2_1_2_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2_1_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:5_7_2_1_2_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/><a NAME="E2:5_7_2_1_2_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_7_2_1_2_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:5_7_2_1_2_1_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> )
 ;<br/><a NAME="E5:5_7_2_1_2_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_7_2_1_2_1_1"><i><font color="Green">E37</font></i></a></i>;<br/><b>hence </b><a NAME="E6:5_7_2_1_2_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:5_7_2_1_2_1"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:5_7_2_1_2"/>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/><a NAME="E6:5_7_2_1_2"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5_7_2_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E7:5_7_2_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fcont_1.html#R2">is_continuous_on</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="txt" href="holder_1.html#E9:5_7"><i><font color="Green">E31</font></i></a>, <a class="txt" href="holder_1.html#E4:5_7_2_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="fcont_1.html#T17">FCONT_1:17</a></i>;<br/><a NAME="E8:5_7_2_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font> <a href="fdiff_1.html#R2">is_differentiable_on</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default">1,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="txt" href="holder_1.html#E8:5_7"><i><font color="Green">E30</font></i></a>, <a class="txt" href="holder_1.html#E6:5_7_2_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="fdiff_1.html#T34">FDIFF_1:34</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E10:5_7_2_1_2"/><i><font color="Green">E39</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E11:5_7_2_1_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1
 <b>and </b><br/><a NAME="E12:5_7_2_1_2"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E7:5_7_2_1_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="holder_1.html#E8:5_7_2_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="rolle.html#T4">ROLLE:4</a></i>;<br/><a NAME="E13:5_7_2_1_2"/><i><font color="Green">E41</font></i>: 
0 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E10:5_7_2_1_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E14:5_7_2_1_2"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E15:5_7_2_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E16:5_7_2_1_2"/><i><font color="Green">E43</font></i>: 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7_2_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:5_7_2_1_2_2"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="real_1.html#NM1">Real</a> : 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="holder_1.html#E15:5_7_2_1_2"><i><font color="Green">E42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:5_7_2_1_2_2"/>
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 <b>by </b><i><a class="ref" href="limfunc1.html#D3">LIMFUNC1:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E17:5_7_2_1_2"/>
1 <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E13:5_7_2_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E18:5_7_2_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E19:5_7_2_1_2"/><i><font color="Green">E45</font></i>: 
 <a href="fdiff_1.html#K1">diff</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E27:5"><i><font color="Green">E21</font></i></a>, <a class="txt" href="holder_1.html#E16:5_7_2_1_2"><i><font color="Green">E43</font></i></a></i>;<br/><a NAME="E20:5_7_2_1_2"/>
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5"><i><font color="Green">E3</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E21:5_7_2_1_2"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E18:5_7_2_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="prepower.html#T100">PREPOWER:100</a></i>;<br/><a NAME="E22:5_7_2_1_2"/><b>then </b>
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E23:5_7_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> 0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5_7_2_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="holder_1.html#E19:5_7_2_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/><a NAME="E24:5_7_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="fdiff_1.html#K1">diff</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p3">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E25:5_7_2_1_2"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E12:5_7_2_1_2"><i><font color="Green">E40</font></i></a></i>;<br/><a NAME="E26:5_7_2_1_2"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="seq_1.html#K6">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E12:5_7"><i><font color="Green">E32</font></i></a>, <a class="txt" href="holder_1.html#E25:5_7_2_1_2"><i><font color="Green">E46</font></i></a></i>;<br/><a NAME="E27:5_7_2_1_2"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E27:5"><i><font color="Green">E21</font></i></a>, <a class="txt" href="holder_1.html#E4:5_7"><i><font color="Green">E26</font></i></a></i>;<br/><a NAME="E28:5_7_2_1_2"/><b>then </b>
0 <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E29:5_7_2_1_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E14:5_7"/>
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E30:5"/><i><font color="Green">E24</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T95">PREPOWER:95</a></i>;<br/>
<a NAME="E31:5"/><b>then </b><i><font color="Green">E25</font></i>: 
0 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E32:5"/><i><font color="Green">E26</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T95">PREPOWER:95</a></i>;<br/>
<a NAME="E33:5"/>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_8"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_8_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_8_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_8_1_1_1"><b>case </b></a><a NAME="E1:5_8_1_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E28:5"><i><font color="Green">E22</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_8_1_1_1"><i><font color="Green">E27</font></i></a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_8_1_1_2"><b>case </b></a><a NAME="E1:5_8_1_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><div class="add"><b>thus </b><a NAME="E2:5_8_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E29:5"><i><font color="Green">E23</font></i></a>, <a class="txt" href="holder_1.html#E31:5"><i><font color="Green">E25</font></i></a>, <a class="txt" href="holder_1.html#E1:5_8_1_1_2"><i><font color="Green">E27</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:5_8"/>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E34:5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E32:5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E35:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
;<br/>
<a NAME="E36:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>;<br/>
<a NAME="E37:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T86">PREPOWER:86</a></i>;<br/>
<a NAME="E38:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="txt" href="holder_1.html#E30:5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="prepower.html#T92">PREPOWER:92</a></i>;<br/>
<a NAME="E39:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T105">PREPOWER:105</a></i>;<br/>
<a NAME="E40:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E41:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>;<br/>
<a NAME="E42:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E43:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>;<br/>
<a NAME="E44:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>;<br/>
<a NAME="E45:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="holder_1.html#E15:5"><i><font color="Green">E11</font></i></a>, <a class="ref" href="prepower.html#T85">PREPOWER:85</a></i>;<br/>
<a NAME="E46:5"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>;<br/>
<a NAME="E47:5"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>;<br/>
<a NAME="E48:5"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> iff <font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_9"><b>proof </b></a><div class="add">

<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_9_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_9_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E2:5_9_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_9_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>;<br/><a NAME="E3:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>;<br/><a NAME="E4:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> 0</span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T85">PREPOWER:85</a></i>;<br/><a NAME="E5:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E15:5"><i><font color="Green">E11</font></i></a></i>;<br/><a NAME="E6:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>;<br/><a NAME="E7:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>;<br/><a NAME="E8:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E9:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>;<br/><a NAME="E10:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E11:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T105">PREPOWER:105</a></i>;<br/><a NAME="E12:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="txt" href="holder_1.html#E30:5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="prepower.html#T92">PREPOWER:92</a></i>;<br/><a NAME="E13:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T86">PREPOWER:86</a></i>;<br/><a NAME="E14:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>;<br/><a NAME="E15:5_9_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E16:5_9_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E32:5"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/><a NAME="E17:5_9_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E29:5"><i><font color="Green">E23</font></i></a>, <a class="txt" href="holder_1.html#E31:5"><i><font color="Green">E25</font></i></a>, <a class="txt" href="holder_1.html#E16:5_9_1"><i><font color="Green">E31</font></i></a></i>;<br/><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>

<br/>.= 
1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E17:5_9_1"><i><font color="Green">E32</font></i></a></i>
;<br/><a NAME="E19:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>;<br/><a NAME="E20:5_9_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T85">PREPOWER:85</a></i>;<br/><b>hence </b><a NAME="E21:5_9_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="holder_1.html#E16:5"><i><font color="Green">E12</font></i></a>, <a class="ref" href="prepower.html#T105">PREPOWER:105</a></i>;<br/></div><b>end;</b></div>
<a NAME="E2:5_9"/><i><font color="Green">E30</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T95">PREPOWER:95</a></i>;<br/>
<a NAME="E3:5_9"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:5"><i><font color="Green">E3</font></i></a></i>;<br/>
<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_9_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_9_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:5_9_2"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="holder_1.html#E16:5"><i><font color="Green">E12</font></i></a>, <a class="ref" href="prepower.html#T105">PREPOWER:105</a></i>;<br/><font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> 1
<b>by </b><i><a class="txt" href="holder_1.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="ref" href="prepower.html#T86">PREPOWER:86</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E3:5_9"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="ref" href="prepower.html#T105">PREPOWER:105</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E2:5_9"><i><font color="Green">E30</font></i></a>, <a class="txt" href="holder_1.html#E2:5_9_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="prepower.html#T105">PREPOWER:105</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="prepower.html#K13">#R</a> 1
<b>by </b><i><a class="txt" href="holder_1.html#E3:5_9"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xcmplx_1.html#T107">XCMPLX_1:107</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E2:5_9"><i><font color="Green">E30</font></i></a>, <a class="ref" href="prepower.html#T86">PREPOWER:86</a></i>
;<br/><a NAME="E4:5_9_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 ;<br/><a NAME="E5:5_9_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T85">PREPOWER:85</a></i>;<br/><a NAME="E6:5_9_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>;<br/><a NAME="E7:5_9_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E8:5_9_2"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="holder_1.html#E2:5_9"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E1:5_9_2"><i><font color="Green">E33</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> 1
<b>by </b><i><a class="txt" href="holder_1.html#E2:5"><i><font color="Green">E4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E8:5_9_2"><i><font color="Green">E35</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T89">PREPOWER:89</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="holder_1.html#E4:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="prepower.html#T86">PREPOWER:86</a></i>
;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E5:5_9"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> iff <font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="holder_1.html#E1:5_9"><i><font color="Green">E29</font></i></a>, <a class="txt" href="holder_1.html#E4:5_9"><i><font color="Green">E32</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E49:5"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; ( <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> implies <font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font> ) &amp; ( <font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K13">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="holder_1.html#E47:5"><i><font color="Green">E27</font></i></a>, <a class="txt" href="holder_1.html#E48:5"><i><font color="Green">E28</font></i></a></i>;<br/>


</div>
