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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:76_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> or  not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1"><b>suppose </b></a><a NAME="E1:76_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:76_1_1"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3" target="_self">Rev</a> <font color="Maroon">c<sub>1</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="finseq_5.html#T60" target="_self">Th60</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1 = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="finseq_5.html#E1:76_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K3" target="_self">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</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>
<b>by </b><i><a class="txt" href="finseq_5.html#E2:76_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="finseq_5.html#E1:76_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K3" target="_self">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="finseq_5.html#E2:76_1_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_2"><b>suppose </b></a><a NAME="E1:76_1_2"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><a NAME="E2:76_1_2"/><b>then </b><i><font color="Green">E40</font></i>: 
 <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="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><a NAME="E3:76_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <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> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T5">FINSEQ_1:5</a></i>;<br/><a NAME="E4:76_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="finseq_5.html#K3" target="_self">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</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> = 
<font color="Maroon">c<sub>1</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</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> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#T61" target="_self">Th61</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1

;<br/><br/><a NAME="E6:76_1_2"/>
( 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 <b>by </b><i><a class="txt" href="finseq_5.html#E2:76_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><a NAME="E7:76_1_2"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="finseq_5.html#K3" target="_self">Rev</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<font color="Maroon">c<sub>1</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"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#T61" target="_self">Th61</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></font></span>)</span>

;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

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