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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:39"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>and </b><br/><a NAME="E2:39"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>and </b><br/><a NAME="E3:39"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 1
 <b>and </b><br/><a NAME="E4:39"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>1</sub></font>,<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>1</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</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">c<sub>2</sub></font>,1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="realset1.html#K5">}</a></span>
 ;<br/>

<a NAME="E5:39"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="graph_2.html#D2">GRAPH_2:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="topreal1.html#V2">unfolded</a> <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="topreal8.html#E2:39"><i><font color="Green">E38</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</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> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1;<br/>
<a NAME="E7:39"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</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> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#K1">/^</a> 1
 
<b>by </b><i><a class="ref" href="topreal8.html#T13" target="_self">Th13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 or ( not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 1 ) or ( not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> ) )
 </span><b>by </b><i><a class="ref" href="cqc_the1.html#T3">CQC_THE1:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_1"><b>suppose </b></a><a NAME="E1:39_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:39_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>by </b><i><a class="txt" href="topreal8.html#E5:39"><i><font color="Green">E41</font></i></a>, <a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_2"><b>suppose </b></a><a NAME="E1:39_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:39_1_2"/><b>then </b>
<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/><a NAME="E3:39_1_2"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</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> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_6.html#T86">FINSEQ_6:86</a></i>;<br/><b>hence </b><a NAME="E4:39_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>by </b><i><a class="txt" href="topreal8.html#E1:39"><i><font color="Green">E37</font></i></a>, <a class="txt" href="topreal8.html#E5:39"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_3"><b>suppose </b></a><a NAME="E1:39_1_3"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><a NAME="E2:39_1_3"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</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> <a href="graph_2.html#K2">-cut</a> <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="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="revrot_1.html#T2">REVROT_1:2</a></i>;<br/><b>hence </b><a NAME="E3:39_1_3"/>
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>by </b><i><a class="txt" href="topreal8.html#E1:39"><i><font color="Green">E37</font></i></a>, <a class="txt" href="topreal8.html#E5:39"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_1.html#T47">FINSEQ_1:47</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:39_1_4"/><i><font color="Green">E43</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>and </b><br/><a NAME="E2:39_1_4"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E3:39_1_4"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="topreal8.html#E1:39_1_4"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><a NAME="E4:39_1_4"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><a NAME="E5:39_1_4"/><b>then </b><i><font color="Green">E45</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>1</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>1</sub></font>
 <b>by </b><i><a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E6:39_1_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</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> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T79">FINSEQ_1:79</a></i>;<br/><a NAME="E7:39_1_4"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="topreal8.html#E2:39_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="jordan8.html#T1">JORDAN8:1</a></i>;<br/><a NAME="E8:39_1_4"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="topreal8.html#E5:39"><i><font color="Green">E41</font></i></a>, <a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_6.html#T50">FINSEQ_6:50</a></i>;<br/><a NAME="E9:39_1_4"/>
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">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="topreal8.html#E2:39_1_4"><i><font color="Green">E44</font></i></a></i>;<br/><a NAME="E10:39_1_4"/><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"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="topreal8.html#E2:39_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>;<br/><a NAME="E11:39_1_4"/><b>then </b><i><font color="Green">E47</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then </b><i><font color="Green">E48</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></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="topreal8.html#E2:39_1_4"><i><font color="Green">E44</font></i></a>, <a class="txt" href="topreal8.html#E11:39_1_4"><i><font color="Green">E47</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <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="topreal8.html#E2:39_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/><a NAME="E13:39_1_4"/><b>then </b>
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,1 <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="topreal8.html#E3:39"><i><font color="Green">E39</font></i></a>, <a class="txt" href="topreal8.html#E2:39_1_4"><i><font color="Green">E44</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/><b>hence </b><a NAME="E14:39_1_4"/>
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>by </b><i><a class="txt" href="topreal8.html#E1:39"><i><font color="Green">E37</font></i></a>, <a class="txt" href="topreal8.html#E4:39"><i><font color="Green">E40</font></i></a>, <a class="txt" href="topreal8.html#E5:39_1_4"><i><font color="Green">E45</font></i></a>, <a class="txt" href="topreal8.html#E8:39_1_4"><i><font color="Green">E46</font></i></a>, <a class="txt" href="topreal8.html#E12:39_1_4"><i><font color="Green">E48</font></i></a>, <a class="ref" href="sppol_2.html#T31">SPPOL_2:31</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_1_5"><b>suppose </b></a><b>that </b><a NAME="E1:39_1_5"/><i><font color="Green">E43</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>and </b><br/><a NAME="E2:39_1_5"/><i><font color="Green">E44</font></i>: 
2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E3:39_1_5"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="topreal8.html#E1:39_1_5"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><a NAME="E4:39_1_5"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><a NAME="E5:39_1_5"/><b>then </b><i><font color="Green">E45</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>1</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>1</sub></font>
 <b>by </b><i><a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E6:39_1_5"/><i><font color="Green">E46</font></i>: 
1 <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="topreal8.html#E2:39_1_5"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E7:39_1_5"/><i><font color="Green">E47</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">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="topreal8.html#E2:39_1_5"><i><font color="Green">E44</font></i></a></i>;<br/><a NAME="E8:39_1_5"/><i><font color="Green">E48</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="topreal8.html#E2:39_1_5"><i><font color="Green">E44</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E9:39_1_5"/>
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">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="topreal8.html#E7:39_1_5"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E10:39_1_5"/><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"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="topreal8.html#E8:39_1_5"><i><font color="Green">E48</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>;<br/><a NAME="E11:39_1_5"/><b>then </b><i><font color="Green">E49</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then </b><i><font color="Green">E50</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></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="topreal8.html#E8:39_1_5"><i><font color="Green">E48</font></i></a>, <a class="txt" href="topreal8.html#E11:39_1_5"><i><font color="Green">E49</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <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="topreal8.html#E2:39_1_5"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
;<br/><a NAME="E13:39_1_5"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,1 <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="topreal8.html#E3:39"><i><font color="Green">E39</font></i></a>, <a class="txt" href="topreal8.html#E2:39_1_5"><i><font color="Green">E44</font></i></a>, <a class="ref" href="topreal1.html#D5">TOPREAL1:def 5</a></i>;<br/><a NAME="E14:39_1_5"/>
 <a href="topreal1.html#K4">LSeg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,<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="topreal8.html#E8:39_1_5"><i><font color="Green">E48</font></i></a>, <a class="ref" href="sppol_2.html#T4">SPPOL_2:4</a></i>;<br/><a NAME="E15:39_1_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="topreal1.html#K4">LSeg</a> <font color="Maroon">c<sub>2</sub></font>,1</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"><span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>,<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="graph_2.html#K2">-cut</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="realset1.html#K5">}</a></span>
 <b>by </b><i><a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="txt" href="topreal8.html#E6:39_1_5"><i><font color="Green">E46</font></i></a>, <a class="txt" href="topreal8.html#E12:39_1_5"><i><font color="Green">E50</font></i></a>, <a class="ref" href="topreal1.html#D8">TOPREAL1:def 8</a></i>;<br/><b>hence </b><a NAME="E16:39_1_5"/>
<font color="Maroon">c<sub>1</sub></font> <a href="graph_2.html#K4">^'</a> <font color="Maroon">c<sub>2</sub></font> is <a href="topreal1.html#V2">unfolded</a>
 <b>by </b><i><a class="txt" href="topreal8.html#E1:39"><i><font color="Green">E37</font></i></a>, <a class="txt" href="topreal8.html#E4:39"><i><font color="Green">E40</font></i></a>, <a class="txt" href="topreal8.html#E5:39"><i><font color="Green">E41</font></i></a>, <a class="txt" href="topreal8.html#E7:39"><i><font color="Green">E42</font></i></a>, <a class="txt" href="topreal8.html#E5:39_1_5"><i><font color="Green">E45</font></i></a>, <a class="txt" href="topreal8.html#E13:39_1_5"><i><font color="Green">E51</font></i></a>, <a class="ref" href="sppol_2.html#T32">SPPOL_2:32</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
