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

<b>let </b><font color="Maroon">f</font> be   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">g</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 ;<br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 ;<br/>

<b>assume </b><a NAME="E3:15"/><i><font color="Green">E59</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">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> <font color="Maroon">m</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 ;<br/>

<b>assume </b><a NAME="E4:15"/><i><font color="Green">E60</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&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">f</font> holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 ;<br/>

<b>assume </b><a NAME="E5:15"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 ;<br/>

<a NAME="E6:15"/>
<font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">m2</font> = <font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<a NAME="E8:15"/>
<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">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">m3</font> = <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">n</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<a NAME="E10:15"/><i><font color="Green">E62</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m3</font>
 
;<br/>
<a NAME="E11:15"/><i><font color="Green">E63</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m3</font>
 
<b>by </b><i>, <a class="ref" href="rfinseq.html#T16">RFINSEQ:16</a></i>;<br/>
<b>consider </b><font color="Maroon">s1</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">r1</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E13:15"/><i><font color="Green">E64</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m3</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">r1</font> )
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T25">FINSEQ_2:25</a></i>;<br/>
<b>consider </b><font color="Maroon">s2</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">r2</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E15:15"/><i><font color="Green">E65</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m3</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">r2</font> )
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T25">FINSEQ_2:25</a></i>;<br/>
<a NAME="E16:15"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m2</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">p1</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">q1</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E18:15"/><i><font color="Green">E66</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> &amp; <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">q1</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T25">FINSEQ_2:25</a></i>;<br/>
<a NAME="E19:15"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m2</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">p2</font> being   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">q2</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E21:15"/><i><font color="Green">E67</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> &amp; <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">q2</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T25">FINSEQ_2:25</a></i>;<br/>
<a NAME="E22:15"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">r1</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E23:15"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">q2</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">r2</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E24:15"/><i><font color="Green">E73</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p1</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E25:15"/><i><font color="Green">E74</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p2</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">m3</font>
 ;<br/><a NAME="E2:15_1"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">r1</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:15_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">r2</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E4:15_1"/><i><font color="Green">E80</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m3</font> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E5:15_1"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E6:15_1"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E7:15_1"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:15_1"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">s1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <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="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b><font color="Maroon">r1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">s1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E1"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">s2</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , , , </i>
<br/>.= 
<font color="Maroon">r2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E27:15"/><b>then </b>
<font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font>
 
<b>by </b><i>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>
<a NAME="E28:15"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">s1</font>,<font color="Maroon">s2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i>, , , <a class="ref" href="rfinseq.html#T14">RFINSEQ:14</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:15_2"/><i><font color="Green">E102</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">m</font>
 ;<br/><a NAME="E2:15_2"/><b>then </b><i><font color="Green">E135</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><b>thus </b><font color="Maroon">p1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="txt" href="scpqsort.html#E1"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">p2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="txt" href="scpqsort.html#E1"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E30:15"/><b>then </b>
<font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font>
 
<b>by </b><i>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>
<a NAME="E31:15"/><b>then </b><i><font color="Green">E136</font></i>: 
<font color="Maroon">q1</font>,<font color="Maroon">q2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E32:15"/><i><font color="Green">E137</font></i>: 
<font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, , <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<a NAME="E34:15"/><i><font color="Green">E138</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q1</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E35:15"/><i><font color="Green">E139</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">m2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q2</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E36:15"/><i><font color="Green">E140</font></i>: 
1 <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/>
<a NAME="E37:15"/><i><font color="Green">E141</font></i>: 
<font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E38:15"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q2</font>
 
<b>by </b><i>, , , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E40:15"/><i><font color="Green">E142</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q2</font> &amp; <font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="txt" href="scpqsort.html#E1"><i><font color="Green">Lemma31</font></i></a>, </i>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i/>;<br/>
<a NAME="E42:15"/><i><font color="Green">E143</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m2</font> )
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<b>take </b><font color="Maroon">k</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">y</font>;<br/>

<a NAME="E43:15"/><i><font color="Green">E144</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font></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="E44:15"/>
<font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/>
<b>hence </b><a NAME="E45:15"/>
<font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font>
 <b>by </b><i>, , <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>

<a NAME="E46:15"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m2</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>hence </b><a NAME="E47:15"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>

<a NAME="E48:15"/><i><font color="Green">E145</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q1</font>
 
<b>by </b><i>, , , , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E49:15"/><b>then </b><i><font color="Green">E146</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">s1</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/>
<a NAME="E50:15"/><i><font color="Green">E147</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">s2</font>
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T41">FINSEQ_1:41</a></i>;<br/>
<b>thus </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<font color="Maroon">s1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">q2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
<b>by </b><i>, , <a class="ref" href="scpqsort.html#T1" target="_self">Th1</a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p2</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="txt" href="scpqsort.html#E1:15"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
;<br/>


</div>
