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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="filerec1.html#NM1" target="_self">File</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_8.html#R4">is_postposition_of</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:29"/><i><font color="Green">E18</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<a NAME="E3:29"/><i><font color="Green">E19</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<a NAME="E4:29"/>
0 <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">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="filerec1.html#E1:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="filerec1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E5:29"/><b>then </b><i><font color="Green">E20</font></i>: 
0 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E6:29"/><i><font color="Green">E21</font></i>: 
 <a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font> <a href="finseq_8.html#NR3" target="_self">is_preposition_of</a> 
 
<b>by </b><i><a class="txt" href="filerec1.html#E1:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_8.html#D9">FINSEQ_8:def 9</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1"><b>suppose </b></a><a NAME="E1:29_1_1"/><i><font color="Green">E22</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:29_1_1"/><i><font color="Green">E23</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>3</sub></font>,<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">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="filerec1.html#E1:29_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="filerec1.html#E1:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_8.html#T24">FINSEQ_8:24</a></i>;<br/><a NAME="E3:29_1_1"/><i><font color="Green">E24</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="filerec1.html#E1:29_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:29_1_1"/><i><font color="Green">E25</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></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> <span class="p3">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E5:29_1_1"/>
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,1,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="filerec1.html#E1:29_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_8.html#D8">FINSEQ_8:def 8</a>, <a class="txt" href="filerec1.html#E6:29"><i><font color="Green">E21</font></i></a>, <a class="txt" href="filerec1.html#E2:29"><i><font color="Green">E18</font></i></a></i>;<br/><b>then </b><i><font color="Green">E26</font></i>:  <a href="jordan3.html#K1">mid</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,1 = 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="jordan4.html#T30">JORDAN4:30</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_6.html#T29">FINSEQ_6:29</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_1_1_2_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_2_1_1"><b>case </b></a><a NAME="E1:29_1_1_2_1_1"/><i><font color="Green">E27</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:29_1_1_2_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a>, <a class="txt" href="filerec1.html#E1:29_1_1_2_1_1"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E3:29_1_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <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
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E4:29_1_1_2_1_1"/><b>then </b><i><font color="Green">E28</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">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</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">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="jordan3.html#T6">JORDAN3:6</a></i>;<br/><a NAME="E5:29_1_1_2_1_1"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="filerec1.html#E5:29"><i><font color="Green">E20</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a>, <a class="txt" href="filerec1.html#E3:29"><i><font color="Green">E19</font></i></a></i>;<br/> <a href="jordan3.html#K1">mid</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,1 = 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K17">|</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">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="filerec1.html#E1:29_1_1_2_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="jordan3.html#D1">JORDAN3:def 1</a></i>
<br/>.= 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rfinseq.html#K1">/^</a> 0</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="nat_2.html#T10">NAT_2:10</a>, <a class="txt" href="filerec1.html#E4:29_1_1_2_1_1"><i><font color="Green">E28</font></i></a></i>
<br/>.= 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#T31">FINSEQ_5:31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</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="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="filerec1.html#E4:29_1_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="filerec1.html#E5:29_1_1_2_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_6.html#T91">FINSEQ_6:91</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.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">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="filerec1.html#E3:29"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_6.html#T29">FINSEQ_6:29</a></i>
;<br/><b>then </b><i><font color="Green">E30</font></i>:  <a href="finseq_8.html#K3">ovlpart</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="finseq_8.html#K3">ovlpart</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="filerec1.html#E6:29_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="rfinseq.html#T21">RFINSEQ:21</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_8.html#T14">FINSEQ_8:14</a></i>
;<br/> <a href="finseq_8.html#K4">ovlcon</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_8.html#K1">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3">ovlpart</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_8.html#D3">FINSEQ_8:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="filerec1.html#E7:29_1_1_2_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="revrot_1.html#T2">REVROT_1:2</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/><b>hence </b><a NAME="E9:29_1_1_2_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_8.html#K8">addcr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_8.html#D11">FINSEQ_8:def 11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_1_2_1_2"><b>case </b></a><a NAME="E1:29_1_1_2_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 ;<br/><div class="add"><b>then </b><i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>2</sub></font> = 
 <a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>3</sub></font>,<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">c<sub>3</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="filerec1.html#E2:29_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="filerec1.html#E3:29_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>
<br/>.= 
 <a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.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">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="jordan3.html#T26">JORDAN3:26</a></i>
;<br/><a NAME="E3:29_1_1_2_1_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="revrot_1.html#T2">REVROT_1:2</a></i>;<br/><a NAME="E4:29_1_1_2_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_8.html#K1">^</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="filerec1.html#E2:29_1_1_2_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="rfinseq.html#T21">RFINSEQ:21</a></i>;<br/> <a href="finseq_8.html#K4">ovlcon</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_8.html#K1">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3">ovlpart</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_8.html#D3">FINSEQ_8:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_8.html#K1">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="filerec1.html#E4:29_1_1_2_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="finseq_8.html#T14">FINSEQ_8:14</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="filerec1.html#E3:29_1_1_2_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/><b>hence </b><a NAME="E6:29_1_1_2_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_8.html#K8">addcr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_8.html#D11">FINSEQ_8:def 11</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:29_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_8.html#K8">addcr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_1_2"><b>suppose </b></a><a NAME="E1:29_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:29_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E3:29_1_2"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><b>then </b><i><font color="Green">E23</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3">ovlpart</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K6">&lt;*&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="filerec1.html#T22" target="_self">Th22</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="finseq_1.html#T32">FINSEQ_1:32</a></i>
;<br/><b>thus </b> <a href="finseq_8.html#K8">addcr</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="finseq_8.html#K4">ovlcon</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_8.html#D11">FINSEQ_8:def 11</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_8.html#K1">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3">ovlpart</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_8.html#D3">FINSEQ_8:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_8.html#K1">^</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="filerec1.html#E4:29_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="finseq_5.html#T31">FINSEQ_5:31</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="filerec1.html#E3:29_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
