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

<b>let </b><font color="Maroon">f</font> be  non <a href="funct_1.html#V3">constant</a> <a href="goboard5.html#V2">standard</a> <a href="goboard5.html#NM1">special_circular_sequence</a>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">i2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:49"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">g</font> <a href="jordan4.html#R1" target="_self">is_a_part&gt;_of</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<font color="Maroon">i2</font> &amp; <font color="Maroon">i1</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">i2</font> )
 ;<br/>

<a NAME="E2:49"/><b>then </b><i><font color="Green">E33</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i2</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="jordan4.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E3:49"/><i><font color="Green">E34</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i1</font> &amp; <font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i2</font> &amp; <font color="Maroon">i2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> holds <br/><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="jordan4.html#K1" target="_self">S_Drop</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> <font color="Olive">i</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<font color="Maroon">f</font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="jordan4.html#T24" target="_self">Th24</a>, </i>;<br/>
<a NAME="E4:49"/><b>then </b><i><font color="Green">E35</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E5:49"/><b>then </b><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E6:49"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E7:49"/><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a></i>;<br/>
<a NAME="E8:49"/><i><font color="Green">E54</font></i>: 
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E9:49"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">i1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E10:49"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="jordan3.html#T7">JORDAN3:7</a></i>;<br/>
<a NAME="E11:49"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">i2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E12:49"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E13:49"/><b>then </b><i><font color="Green">E58</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="ref" href="jordan3.html#T1">JORDAN3:1</a></i>;<br/>
<a NAME="E14:49"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E15:49"/><b>then </b><i><font color="Green">E68</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E16:49"/><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>set </b><font color="Maroon">f1</font> =  <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>;<br/>
<a NAME="E17:49"/>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="ref" href="jordan4.html#T24" target="_self">Th24</a>, <a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E18:49"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 
<b>by </b><i><a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan4.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E19:49"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, </i>;<br/>
<a NAME="E20:49"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="jordan4.html#T28" target="_self">Th28</a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>;<br/>
<a NAME="E21:49"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E22:49"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_6.html#D1">FINSEQ_6:def 1</a></i>;<br/>
<a NAME="E23:49"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E24:49"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i>, <a class="txt" href="jordan4.html#E15:49"><i><font color="Green">E68</font></i></a>, <a class="ref" href="jordan4.html#T32" target="_self">Th32</a>, <a class="ref" href="finseq_6.html#D1">FINSEQ_6:def 1</a></i>;<br/>
<a NAME="E25:49"/><i><font color="Green">E85</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>;<br/>
<a NAME="E26:49"/><b>then </b><i><font color="Green">E86</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E27:49"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E28:49"/><b>then </b><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E29:49"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E30:49"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="ref" href="jordan3.html#T1">JORDAN3:1</a></i>;<br/>
<a NAME="E31:49"/><b>then </b><i><font color="Green">E88</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="jordan4.html#T34" target="_self">Th34</a>, <a class="ref" href="jordan4.html#D2" target="_self">Def2</a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<b>then </b><i><font color="Green">E89</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
;<br/>
<i><font color="Green">E90</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="ref" href="jordan4.html#T29" target="_self">Th29</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
<b>by </b><i><a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/>
<i><font color="Green">E91</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan4.html#T30" target="_self">Th30</a>, , , <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="ref" href="jordan4.html#T30" target="_self">Th30</a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>

;<br/>
<a NAME="E35:49"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan4.html#D4" target="_self">Def4</a>, <a class="ref" href="jordan4.html#T37" target="_self">Th37</a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/>
<a NAME="E36:49"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:49_4"/><i><font color="Green">E93</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> )
 ;<br/>

<a NAME="E2:49_4"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jordan4.html#E16:49"><i><font color="Green">E78</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E3:49_4"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>;<br/>
<a NAME="E4:49_4"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E20:49"><i><font color="Green">E81</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="jordan4.html#D3" target="_self">Def3</a>, <a class="txt" href="jordan4.html#E18:49"><i><font color="Green">E79</font></i></a>, <a class="txt" href="jordan4.html#E19:49"><i><font color="Green">E80</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jordan4.html#E19:49"><i><font color="Green">E80</font></i></a>, <a class="txt" href="jordan4.html#E21:49"><i><font color="Green">E82</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
;<br/>
<b>hence </b><a NAME="E6:49_4"/>
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan4.html#T30" target="_self">Th30</a>, , , <a class="txt" href="jordan4.html#E19:49"><i><font color="Green">E80</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E37:49"/><b>then </b><i><font color="Green">E96</font></i>: 
 <a href="jordan3.html#K1">mid</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E18:49"><i><font color="Green">E79</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/>
<a NAME="E38:49"/><i><font color="Green">E97</font></i>: 
 <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="topreal1.html#D6">TOPREAL1:def 6</a></i>;<br/>
<a NAME="E39:49"/><i><font color="Green">E98</font></i>: 
 <a href="topreal1.html#K5">L~</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="topreal1.html#D6">TOPREAL1:def 6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_5"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_5_1"/>
( <font color="Maroon">i2</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 or <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_5_1_1"><b>case </b></a><a NAME="E1:49_5_1_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">i2</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:49_5_1_1"/>
<span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_5_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:49_5_1_1_1"/><i><font color="Green">E100</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="jordan3.html#T19">JORDAN3:19</a></i>;<br/>
<a NAME="E2:49_5_1_1_1"/>
<font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E3:49_5_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">i1</font></span>)</span> <a href="real_1.html#K3">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E4:49_5_1_1_1"/><b>then </b>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 
;<br/>
<a NAME="E5:49_5_1_1_1"/><b>then </b>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E6:49_5_1_1_1"/><b>then </b><i><font color="Green">E101</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="ref" href="jordan3.html#T1">JORDAN3:1</a></i>;<br/>
<a NAME="E7:49_5_1_1_1"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E8:49_5_1_1_1"/><b>then </b><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E9:49_5_1_1_1"/><b>then </b><i><font color="Green">E103</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="ref" href="jordan3.html#T1">JORDAN3:1</a></i>;<br/>
<i><font color="Green">E104</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="jordan4.html#E25:49"><i><font color="Green">E85</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>

;<br/>
<a NAME="E11:49_5_1_1_1"/><b>then </b><i><font color="Green">E105</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E26:49"><i><font color="Green">E86</font></i></a></i>;<br/>
<a NAME="E12:49_5_1_1_1"/><i><font color="Green">E106</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E28:49"><i><font color="Green">E87</font></i></a>, <a class="txt" href="jordan4.html#E31:49"><i><font color="Green">E88</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E13:49_5_1_1_1"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E14:49_5_1_1_1"/><b>then </b>
<font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E15:49_5_1_1_1"/><b>then </b><i><font color="Green">E108</font></i>: 
<font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E16:49_5_1_1_1"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E31:49"><i><font color="Green">E88</font></i></a>, </i>;<br/>
<a NAME="E17:49_5_1_1_1"/>
<font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E34:49"><i><font color="Green">E91</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E18:49_5_1_1_1"/><b>then </b><i><font color="Green">E110</font></i>: 
<font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E19:49_5_1_1_1"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/>
<a NAME="E20:49_5_1_1_1"/><i><font color="Green">E112</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E21:49_5_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> &amp;  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span>  )
 
<b>by </b><i><a class="txt" href="jordan4.html#E32:49"><i><font color="Green">E89</font></i></a>, <a class="txt" href="jordan4.html#E33:49"><i><font color="Green">E90</font></i></a>, , , <a class="ref" href="finseq_6.html#D1">FINSEQ_6:def 1</a></i>;<br/>
<a NAME="E22:49_5_1_1_1"/><b>then </b><i><font color="Green">E113</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E23:49_5_1_1_1"/><i><font color="Green">E114</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="txt" href="jordan4.html#E13:49"><i><font color="Green">E58</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 = 
2 <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="ref" href="jordan3.html#T1">JORDAN3:1</a></i>
<br/>.= 
1

;<br/>
<a NAME="E25:49_5_1_1_1"/><b>then </b><i><font color="Green">E115</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E39:49"><i><font color="Green">E98</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<i><font color="Green">E116</font></i>: <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 = 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1
<b>by </b><i><a class="txt" href="jordan4.html#E13:49"><i><font color="Green">E58</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<a NAME="E27:49_5_1_1_1"/><i><font color="Green">E117</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E39:49"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E28:49_5_1_1_1"/><i><font color="Green">E118</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>;<br/>
<a NAME="E29:49_5_1_1_1"/><i><font color="Green">E119</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>;<br/>
<a NAME="E30:49_5_1_1_1"/><i><font color="Green">E120</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 
<b>by </b><i><a class="ref" href="jordan4.html#T28" target="_self">Th28</a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/>
<a NAME="E31:49_5_1_1_1"/><b>then </b><i><font color="Green">E121</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E6:49_5_1_1_1"><i><font color="Green">E101</font></i></a>, <a class="txt" href="jordan4.html#E8:49_5_1_1_1"><i><font color="Green">E102</font></i></a>, <a class="txt" href="jordan4.html#E9:49_5_1_1_1"><i><font color="Green">E103</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E32:49_5_1_1_1"/><i><font color="Green">E122</font></i>: 
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E22:49"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan4.html#E10:49_5_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E33:49_5_1_1_1"/><i><font color="Green">E123</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>;<br/>
<a NAME="E34:49_5_1_1_1"/><i><font color="Green">E124</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E39:49"><i><font color="Green">E98</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E35:49_5_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E10:49_5_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan4.html#E12:49_5_1_1_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>;<br/>
<a NAME="E36:49_5_1_1_1"/><b>then </b><i><font color="Green">E126</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E12:49_5_1_1_1"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan4.html#E13:49_5_1_1_1"><i><font color="Green">E107</font></i></a>, <a class="txt" href="jordan4.html#E15:49_5_1_1_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E37:49_5_1_1_1"/><i><font color="Green">E127</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E12:49_5_1_1_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E38:49_5_1_1_1"/><i><font color="Green">E128</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E37:49"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jordan4.html#E1:49_5_1_1_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan4.html#E6:49_5_1_1_1"><i><font color="Green">E101</font></i></a>, <a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>;<br/>
<a NAME="E39:49_5_1_1_1"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E22:49"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan4.html#E10:49_5_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E40:49_5_1_1_1"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> &amp;  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 2</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span>  )
 
<b>by </b><i><a class="txt" href="jordan4.html#E37:49"><i><font color="Green">E96</font></i></a>, <a class="txt" href="jordan4.html#E1:49_5_1_1"><i><font color="Green">E99</font></i></a>, <a class="txt" href="jordan4.html#E1:49_5_1_1_1"><i><font color="Green">E100</font></i></a>, <a class="txt" href="jordan4.html#E11:49_5_1_1_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="jordan4.html#E16:49_5_1_1_1"><i><font color="Green">E109</font></i></a>, <a class="txt" href="jordan4.html#E18:49_5_1_1_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="jordan4.html#E19:49_5_1_1_1"><i><font color="Green">E111</font></i></a>, <a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/>
<a NAME="E41:49_5_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E42:49_5_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> </span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E38:49"><i><font color="Green">E97</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E43:49_5_1_1_1"/><b>then </b><i><font color="Green">E129</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> </span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E44:49_5_1_1_1"/>
<span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> </span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_5_1_1_1_4"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:49_5_1_1_1_4"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> </span>)</span>
 ;<br/>

<a NAME="E2:49_5_1_1_1_4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">Y1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:49_5_1_1_1_4"/><i><font color="Green">E131</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y1</font> &amp; <font color="Maroon">Y1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">j1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:49_5_1_1_1_4"/><i><font color="Green">E132</font></i>: 
( <font color="Maroon">Y1</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">j1</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j1</font> &amp; <font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="jordan4.html#E23:49_5_1_1_1"><i><font color="Green">E114</font></i></a></i>;<br/>
<a NAME="E7:49_5_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="jordan4.html#E22:49_5_1_1_1"><i><font color="Green">E113</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">Y2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:49_5_1_1_1_4"/><i><font color="Green">E133</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y2</font> &amp; <font color="Maroon">Y2</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span>  )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">j2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E11:49_5_1_1_1_4"/><i><font color="Green">E134</font></i>: 
( <font color="Maroon">Y2</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Maroon">j2</font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j2</font> &amp; <font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> )
 <b>by </b><i><a class="txt" href="jordan4.html#E26:49_5_1_1_1"><i><font color="Green">E116</font></i></a></i>;<br/>
<a NAME="E12:49_5_1_1_1_4"/><i><font color="Green">E135</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">j1</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E13:49_5_1_1_1_4"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<a NAME="E14:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E136</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E15:49_5_1_1_1_4"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="jordan3.html#T19">JORDAN3:19</a></i>;<br/>
<a NAME="E16:49_5_1_1_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E17:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E138</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E35:49"><i><font color="Green">E92</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/>
<a NAME="E18:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E139</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E29:49_5_1_1_1"><i><font color="Green">E119</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E19:49_5_1_1_1_4"/>
<font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E20:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E140</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E21:49_5_1_1_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E22:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E141</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j1</font> &amp; <font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="txt" href="jordan4.html#E31:49_5_1_1_1"><i><font color="Green">E121</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E23:49_5_1_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan3.html#T23">JORDAN3:23</a></i>;<br/>
<a NAME="E24:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E142</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E29:49_5_1_1_1"><i><font color="Green">E119</font></i></a>, <a class="txt" href="jordan4.html#E33:49_5_1_1_1"><i><font color="Green">E123</font></i></a>, <a class="txt" href="jordan4.html#E34:49_5_1_1_1"><i><font color="Green">E124</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E25:49_5_1_1_1_4"/><i><font color="Green">E143</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E26:49_5_1_1_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E30:49_5_1_1_1"><i><font color="Green">E120</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E27:49_5_1_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E35:49"><i><font color="Green">E92</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/>
<a NAME="E28:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E36:49_5_1_1_1"><i><font color="Green">E126</font></i></a>, <a class="ref" href="jordan3.html#T23">JORDAN3:23</a></i>;<br/>
<a NAME="E29:49_5_1_1_1_4"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E30:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E147</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E31:49_5_1_1_1_4"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E32:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E148</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">j1</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E28:49_5_1_1_1"><i><font color="Green">E118</font></i></a>, <a class="txt" href="jordan4.html#E31:49_5_1_1_1"><i><font color="Green">E121</font></i></a>, <a class="txt" href="jordan4.html#E32:49_5_1_1_1"><i><font color="Green">E122</font></i></a>, <a class="ref" href="jordan4.html#T38" target="_self">Th38</a>, <a class="txt" href="jordan4.html#E37:49_5_1_1_1"><i><font color="Green">E127</font></i></a>, <a class="txt" href="jordan4.html#E38:49_5_1_1_1"><i><font color="Green">E128</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E33:49_5_1_1_1_4"/><i><font color="Green">E149</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E34:49_5_1_1_1_4"/><i><font color="Green">E150</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T18">FINSEQ_5:18</a></i>;<br/>
<a NAME="E35:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E151</font></i>: 
<font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E36:49_5_1_1_1_4"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">j2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E37:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E153</font></i>: 
<font color="Maroon">j2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E4:49_5_1_1_1_4"><i><font color="Green">E131</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<i><font color="Green">E154</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j2</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font>
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="txt" href="jordan4.html#E9:49_5_1_1_1_4"><i><font color="Green">E133</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font>
<b>by </b><i><a class="txt" href="jordan4.html#E10:49_5_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan4.html#E9:49_5_1_1_1_4"><i><font color="Green">E133</font></i></a>, <a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j2</font>
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="txt" href="jordan4.html#E11:49_5_1_1_1_4"><i><font color="Green">E134</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/>
<i><font color="Green">E155</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E1:49_5_1_1_1_4"><i><font color="Green">E130</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E10:49_5_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="finseq_3.html#T121">FINSEQ_3:121</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E1:49_5_1_1_1_4"><i><font color="Green">E130</font></i></a>, <a class="txt" href="jordan4.html#E6:49_5_1_1_1_4"><i><font color="Green">E132</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/>
<a NAME="E40:49_5_1_1_1_4"/><i><font color="Green">E156</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Maroon">j2</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<a NAME="E41:49_5_1_1_1_4"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j2</font> &amp; <font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="txt" href="jordan4.html#E4:49_5_1_1_1_4"><i><font color="Green">E131</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E42:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E157</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Maroon">j2</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">j2</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E12:49_5_1_1_1_4"><i><font color="Green">E135</font></i></a>, <a class="txt" href="jordan4.html#E14:49_5_1_1_1_4"><i><font color="Green">E136</font></i></a>, <a class="txt" href="jordan4.html#E15:49_5_1_1_1_4"><i><font color="Green">E137</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/>
<div><i><font color="Green">E158</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_5_1_1_1_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_5_1_1_1_4_3"/><i><font color="Green">E159</font></i>: 
(  not <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> 1 or  not <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 ;<br/><a NAME="E2:49_5_1_1_1_4_3"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="jordan4.html#T27" target="_self">Th27</a>, <a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E3:49_5_1_1_1_4_3"/><b>then </b><i><font color="Green">E160</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:49_5_1_1_1_4_3"/><b>then </b><i><font color="Green">E161</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E5:49_5_1_1_1_4_3"/><i><font color="Green">E162</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="jordan4.html#E22:49_5_1_1_1_4"><i><font color="Green">E141</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E6:49_5_1_1_1_4_3"/><i><font color="Green">E163</font></i>: 
<font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i2</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="jordan4.html#E10:49_5_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:49_5_1_1_1_4_3"/><i><font color="Green">E164</font></i>: 
<font color="Maroon">i2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="jordan4.html#T24" target="_self">Th24</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E8:49_5_1_1_1_4_3"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E9:49_5_1_1_1_4_3"/><b>then </b><i><font color="Green">E165</font></i>: 
<font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="jordan4.html#T39" target="_self">Th39</a>, <a class="ref" href="jordan4.html#T40" target="_self">Th40</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E10:49_5_1_1_1_4_3"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 <b>by </b><i><a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E11:49_5_1_1_1_4_3"/><b>then </b><i><font color="Green">E166</font></i>: 
( <font color="Maroon">j2</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 <b>by </b><i><a class="txt" href="jordan4.html#E24:49_5_1_1_1_4"><i><font color="Green">E142</font></i></a>, <a class="txt" href="jordan4.html#E28:49_5_1_1_1_4"><i><font color="Green">E146</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_5_1_1_1_4_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_5_1_1_1_4_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_5_1_1_1_4_3_1_1"/>
( <font color="Maroon">j2</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 or <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 )
 </span><b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="txt" href="jordan4.html#E20:49_5_1_1_1_4"><i><font color="Green">E140</font></i></a>, <a class="txt" href="jordan4.html#E25:49_5_1_1_1_4"><i><font color="Green">E143</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_5_1_1_1_4_3_1_1_1"><b>case </b></a><a NAME="E1:49_5_1_1_1_4_3_1_1_1"/>
<font color="Maroon">j2</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:49_5_1_1_1_4_3_1_1_1"/><b>then </b>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">j2</font>
 <b>by </b><i><a class="txt" href="jordan4.html#E30:49_5_1_1_1_4"><i><font color="Green">E147</font></i></a>, <a class="ref" href="goboard5.html#D4">GOBOARD5:def 4</a></i>;<br/><b>hence </b><a NAME="E3:49_5_1_1_1_4_3_1_1_1"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_5_1_1_1_4_3_1_1_2"><b>case </b></a><a NAME="E1:49_5_1_1_1_4_3_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1
 ;<br/><div class="add"><a NAME="E2:49_5_1_1_1_4_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:49_5_1_1_1_4_3_1_1_2"/><b>then </b>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span> <a href="xboole_0.html#R1">misses</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">j2</font>
 <b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E30:49_5_1_1_1_4"><i><font color="Green">E147</font></i></a>, <a class="ref" href="goboard5.html#D4">GOBOARD5:def 4</a></i>;<br/><b>hence </b><a NAME="E4:49_5_1_1_1_4_3_1_1_2"/>
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E13:49_5_1_1_1_4_3"/>
contradiction
 <b>by </b><i><a class="txt" href="jordan4.html#E23:49_5_1_1_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="txt" href="jordan4.html#E26:49_5_1_1_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="txt" href="jordan4.html#E43:49_5_1_1_1"><i><font color="Green">E129</font></i></a>, <a class="txt" href="jordan4.html#E17:49_5_1_1_1_4"><i><font color="Green">E138</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<b>then </b><i><font color="Green">E167</font></i>: <font color="Maroon">j1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/>
<a NAME="E45:49_5_1_1_1_4"/><i><font color="Green">E168</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, </i>;<br/>
<a NAME="E46:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E169</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E47:49_5_1_1_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E48:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E170</font></i>: 
<font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E49:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E171</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="real_1.html#K5">-</a> 1</span>)</span>
 
;<br/>
<a NAME="E50:49_5_1_1_1_4"/><i><font color="Green">E172</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E10:49"><i><font color="Green">E56</font></i></a>, <a class="ref" href="jordan3.html#T1">JORDAN3:1</a>, <a class="txt" href="jordan4.html#E25:49_5_1_1_1_4"><i><font color="Green">E143</font></i></a></i>;<br/>
<a NAME="E51:49_5_1_1_1_4"/><i><font color="Green">E173</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E10:49"><i><font color="Green">E56</font></i></a>, <a class="txt" href="jordan4.html#E22:49_5_1_1_1_4"><i><font color="Green">E141</font></i></a>, <a class="ref" href="jordan4.html#T39" target="_self">Th39</a>, <a class="ref" href="jordan3.html#T1">JORDAN3:1</a></i>;<br/>
<a NAME="E52:49_5_1_1_1_4"/><i><font color="Green">E174</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, , <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E53:49_5_1_1_1_4"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="jordan4.html#T27" target="_self">Th27</a>, <a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E54:49_5_1_1_1_4"/><b>then </b><i><font color="Green">E175</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i>, <a class="txt" href="jordan4.html#E30:49_5_1_1_1_4"><i><font color="Green">E147</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<b>then </b><i><font color="Green">E176</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jordan4.html#T40" target="_self">Th40</a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E24:49_5_1_1_1_4"><i><font color="Green">E142</font></i></a>, <a class="ref" href="jordan4.html#T40" target="_self">Th40</a>, <a class="ref" href="jordan3.html#T23">JORDAN3:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, , , <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/>
<i><font color="Green">E177</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>

;<br/>
<a NAME="E57:49_5_1_1_1_4"/><i><font color="Green">E178</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="jordan4.html#T40" target="_self">Th40</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E58:49_5_1_1_1_4"/><i><font color="Green">E179</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E32:49_5_1_1_1_4"><i><font color="Green">E148</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>then </b><i><font color="Green">E180</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E35:49_5_1_1_1_4"><i><font color="Green">E151</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E34:49_5_1_1_1_4"><i><font color="Green">E150</font></i></a>, <a class="txt" href="jordan4.html#E35:49_5_1_1_1_4"><i><font color="Green">E151</font></i></a>, <a class="ref" href="jordan3.html#T23">JORDAN3:23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E8:49"><i><font color="Green">E54</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/>
<i><font color="Green">E181</font></i>:  <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">j1</font> = 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E20:49_5_1_1_1_4"><i><font color="Green">E140</font></i></a>, <a class="txt" href="jordan4.html#E28:49_5_1_1_1_4"><i><font color="Green">E146</font></i></a>, <a class="txt" href="jordan4.html#E36:49_5_1_1_1_4"><i><font color="Green">E152</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>
<br/>.= 
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="jordan4.html#E11:49"><i><font color="Green">E57</font></i></a>, , <a class="txt" href="jordan4.html#E33:49_5_1_1_1_4"><i><font color="Green">E149</font></i></a>, <a class="txt" href="jordan4.html#E37:49_5_1_1_1_4"><i><font color="Green">E153</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>
;<br/>
<a NAME="E61:49_5_1_1_1_4"/>
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Maroon">j2</font> <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">f</font>,1
 
<b>by </b><i><a class="txt" href="jordan4.html#E12:49_5_1_1_1"><i><font color="Green">E106</font></i></a>, <a class="txt" href="jordan4.html#E18:49_5_1_1_1_4"><i><font color="Green">E139</font></i></a>, <a class="ref" href="sppol_2.html#T3">SPPOL_2:3</a></i>;<br/>
<a NAME="E62:49_5_1_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Maroon">j1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Maroon">j2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E38:49_5_1_1_1_4"><i><font color="Green">E154</font></i></a>, <a class="ref" href="jordan4.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E63:49_5_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="jordan4.html#E23:49_5_1_1_1"><i><font color="Green">E114</font></i></a>, <a class="txt" href="jordan4.html#E25:49_5_1_1_1"><i><font color="Green">E115</font></i></a>, <a class="txt" href="jordan4.html#E26:49_5_1_1_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="jordan4.html#E27:49_5_1_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E45:49_5_1_1_1"/>
<span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>,<font color="Olive">i</font></span>)</span> where <font color="Olive">i</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> ) </span>}</span> </span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span>,<font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">i2</font></span>)</span> ) </span>}</span> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="jordan4.html#E20:49_5_1_1_1"><i><font color="Green">E112</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="E3:49_5_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E20:49"><i><font color="Green">E81</font></i></a>, <a class="txt" href="jordan4.html#E21:49"><i><font color="Green">E82</font></i></a>, <a class="ref" href="jordan3.html#T25">JORDAN3:25</a></i>;<br/><a NAME="E4:49_5_1_1"/><b>then </b><i><font color="Green">E182</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="txt" href="jordan4.html#E15:49"><i><font color="Green">E68</font></i></a>, <a class="ref" href="jordan3.html#T26">JORDAN3:26</a></i>;<br/><a NAME="E5:49_5_1_1"/>
 <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 <b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E22:49"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan4.html#E6:49"><i><font color="Green">E44</font></i></a></i>;<br/><b>hence </b><a NAME="E6:49_5_1_1"/>
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 <b>by </b><i><a class="ref" href="jordan4.html#T31" target="_self">Th31</a>, <a class="ref" href="jordan4.html#T33" target="_self">Th33</a>, <a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="ref" href="jordan3.html#T80">JORDAN3:80</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_5_1_2"><b>case </b></a><a NAME="E1:49_5_1_2"/>
<font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then </b><i><font color="Green">E183</font></i>:  <a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font> = 
<font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> 1
<b>by </b><i><a class="ref" href="jordan3.html#T25">JORDAN3:25</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_5.html#T23">FINSEQ_5:23</a></i>
;<br/><a NAME="E3:49_5_1_2"/><i><font color="Green">E184</font></i>: 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="jordan4.html#T32" target="_self">Th32</a>, <a class="ref" href="jordan4.html#D1" target="_self">Def1</a>, <a class="ref" href="jordan4.html#T35" target="_self">Th35</a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/><a NAME="E4:49_5_1_2"/><i><font color="Green">E185</font></i>: 
 <a href="jordan3.html#K1">mid</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="jordan4.html#D3" target="_self">Def3</a>, <a class="ref" href="jordan3.html#T25">JORDAN3:25</a></i>;<br/><a NAME="E5:49_5_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="jordan4.html#T34" target="_self">Th34</a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><b>hence </b><a NAME="E6:49_5_1_2"/>
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,1,<font color="Maroon">i2</font></span>)</span> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 <b>by </b><i><a class="ref" href="jordan4.html#T31" target="_self">Th31</a>, <a class="txt" href="jordan4.html#E22:49"><i><font color="Green">E83</font></i></a>, <a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="txt" href="jordan4.html#E25:49"><i><font color="Green">E85</font></i></a>, <a class="ref" href="finseq_5.html#T24">FINSEQ_5:24</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E41:49"/><b>then </b><i><font color="Green">E186</font></i>: 
<font color="Maroon">g</font> <a href="topreal1.html#NR2" target="_self">is_S-Seq</a> 
 
<b>by </b><i><a class="ref" href="jordan4.html#T24" target="_self">Th24</a>, <a class="txt" href="jordan4.html#E19:49"><i><font color="Green">E80</font></i></a>, <a class="ref" href="jordan4.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E42:49"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">i1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E43:49"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, <a class="ref" href="jordan4.html#T30" target="_self">Th30</a>, , , <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>;<br/>
<a NAME="E44:49"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E45:49"/><b>then </b>
1 <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> <span class="p2">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E46:49"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E47:49"/><b>then </b>
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">f</font>,<font color="Maroon">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> 1
 
<b>by </b><i><a class="ref" href="jordan4.html#T25" target="_self">Th25</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/>
<a NAME="E48:49"/><b>then </b><i><font color="Green">E188</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E9:49"><i><font color="Green">E55</font></i></a>, <a class="txt" href="jordan4.html#E14:49"><i><font color="Green">E59</font></i></a>, , , <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>;<br/>
<a NAME="E49:49"/><i><font color="Green">E189</font></i>: 
<font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E50:49"/>
<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="txt" href="jordan4.html#E24:49"><i><font color="Green">E84</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E51:49"/><b>then </b>
( <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> 1 &amp; <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="jordan4.html#E7:49"><i><font color="Green">E53</font></i></a>, <a class="ref" href="jordan4.html#T28" target="_self">Th28</a>, <a class="txt" href="jordan4.html#E25:49"><i><font color="Green">E85</font></i></a>, <a class="txt" href="jordan4.html#E26:49"><i><font color="Green">E86</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<b>hence </b><a NAME="E52:49"/>
 <a href="topreal1.html#K5">L~</a> <font color="Maroon">g</font> <a href="topreal4.html#R1">is_S-P_arc_joining</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i1</font>,<font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i2</font>
 <b>by </b><i><a class="txt" href="jordan4.html#E22:49"><i><font color="Green">E83</font></i></a>, <a class="ref" href="topreal4.html#D1">TOPREAL4:def 1</a></i>;<br/>


</div>
