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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</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>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:91"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:91"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E3:91"/><i><font color="Green">E85</font></i>: 
<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>4</sub></font>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E1:91"><i><font color="Green">E83</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E4:91"/>
<font color="Maroon">c<sub>1</sub></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="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_6.html#E2:91"><i><font color="Green">E84</font></i></a>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<b>then </b><i><font color="Green">E86</font></i>:  <a href="finseq_1.html#K3">len</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>4</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:91"><i><font color="Green">E83</font></i></a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E3:91"><i><font color="Green">E85</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:91_2"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</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>4</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><a NAME="E2:91_2"/><i><font color="Green">E88</font></i>: 
 <a href="finseq_1.html#K4">dom</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>4</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_5.html#T20">FINSEQ_5:20</a></i>;<br/><a NAME="E3:91_2"/><i><font color="Green">E89</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</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> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseq_6.html#E3:91"><i><font color="Green">E85</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>;<br/><a NAME="E4:91_2"/>
<font color="Maroon">c<sub>5</sub></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">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E5:91"><i><font color="Green">E86</font></i></a>, <a class="txt" href="finseq_6.html#E1:91_2"><i><font color="Green">E87</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/><a NAME="E6:91_2"/><i><font color="Green">E90</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <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="E7:91_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="finseq_6.html#E1:91_2"><i><font color="Green">E87</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E8:91_2"/><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">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font> <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">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/><a NAME="E9:91_2"/><b>then </b>
<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">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</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">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E10:91_2"/><b>then </b><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 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>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_6.html#E6:91_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>thus </b><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>4</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<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>4</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:91_2"><i><font color="Green">E87</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:91_2"><i><font color="Green">E87</font></i></a>, <a class="ref" href="finseq_4.html#T85">FINSEQ_4:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:91_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="finseq_6.html#E2:91_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></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> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E1:91_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="finseq_6.html#E2:91_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="finseq_6.html#E3:91_2"><i><font color="Green">E89</font></i></a>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></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> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_6.html#E3:91"><i><font color="Green">E85</font></i></a>, <a class="txt" href="finseq_6.html#E10:91_2"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:91"/>
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rfinseq.html#K1">/^</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_5.html#K4">Rev</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="finseq_6.html#E5:91"><i><font color="Green">E86</font></i></a>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>


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