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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><a NAME="E1:58"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="euclid.html#K9">*</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:58"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E3:58"/><i><font color="Green">E54</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:58"><i><font color="Green">E52</font></i></a>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>
<a NAME="E4:58"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="rvsum_1.html#K2">multreal</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:58"><i><font color="Green">E52</font></i></a></i>;<br/>
<a NAME="E5:58"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a>  as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E7:58"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E5:58"><i><font color="Green">E55</font></i></a>, <a class="ref" href="funcop_1.html#D5">FUNCOP_1:def 5</a></i>;<br/>
<a NAME="E8:58"/><i><font color="Green">E57</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> &amp; ( 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="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> holds <br/><span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> ) )
 
<b>by </b><i><a class="ref" href="funct_3.html#D8">FUNCT_3:def 8</a></i>;<br/>
<a NAME="E9:58"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 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>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">c<sub>4</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">c<sub>5</sub></font> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:58_1"/><i><font color="Green">E58</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:58_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:58_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E2:58"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan2c.html#E3:58"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E4:58_1"/><b>then </b><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E7:58"><i><font color="Green">E56</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<a NAME="E5:58_1"/><i><font color="Green">E60</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>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E6:58_1"/><i><font color="Green">E61</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="txt" href="jordan2c.html#E8:58"><i><font color="Green">E57</font></i></a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E7:58_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:58_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<i><font color="Green">E63</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="numbers.html#K1">REAL</a> 
<b>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>
;<br/>
<a NAME="E9:58_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E6:58_1"><i><font color="Green">E61</font></i></a>, <a class="ref" href="funct_3.html#D8">FUNCT_3:def 8</a></i>;<br/>
<a NAME="E10:58_1"/><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E5:58_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E11:58_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>
<a NAME="E12:58_1"/>
<span class="p1">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K35">multreal</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K13">&lt;:</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><a href="partfun1.html#K6">id</a> <a href="numbers.html#K1">REAL</a> </span>)</span></span>)</span> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="funct_3.html#K13">:&gt;</a></span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E6:58_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="jordan2c.html#E8:58_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<a NAME="E13:58_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <a href="binop_2.html#K35">multreal</a>  <a href="metric_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E1:58"><i><font color="Green">E52</font></i></a>, <a class="txt" href="jordan2c.html#E4:58_1"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jordan2c.html#E9:58_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="jordan2c.html#E10:58_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="jordan2c.html#E11:58_1"><i><font color="Green">E66</font></i></a></i>;<br/>
<a NAME="E14:58_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan2c.html#E7:58_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="binop_2.html#D11">BINOP_2:def 11</a></i>;<br/>
<b>hence </b><a NAME="E15:58_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan2c.html#E2:58"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan2c.html#E3:58"><i><font color="Green">E54</font></i></a>, <a class="txt" href="jordan2c.html#E1:58_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E10:58"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 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>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">c<sub>4</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">c<sub>5</sub></font> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="jordan2c.html#E1:58"><i><font color="Green">E52</font></i></a>, <a class="txt" href="jordan2c.html#E2:58"><i><font color="Green">E53</font></i></a>, <a class="ref" href="finseq_2.html#T109">FINSEQ_2:109</a></i>;<br/>


</div>
