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<b>let </b><font color="Maroon">D</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">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>





<b>assume </b><a NAME="E1:93"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">f</font> <a href="finseq_4.html#R2">just_once_values</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E2:93"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T7">FINSEQ_4:7</a></i>;<br/>
<a NAME="E3:93"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>;<br/>
<a NAME="E4:93"/><b>then </b>
<font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">n</font> = <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 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#T18">INT_1:18</a></i>;<br/>
<a NAME="E6:93"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></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">f</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="finseq_6.html#T28" target="_self">Th28</a>, </i>;<br/>
<a NAME="E7:93"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <span class="p3">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
;<br/>
<a NAME="E8:93"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 
;<br/>
 <a href="finseq_5.html#K3">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K7">|--</a> <font color="Maroon">p</font></span>)</span> = 
 <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_6.html#T29" target="_self">Th29</a>, <a class="ref" href="finseq_5.html#T38">FINSEQ_5:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_1.html#K17">|</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="finseq_6.html#T31" target="_self">Th31</a>, <a class="ref" href="finseq_6.html#T25" target="_self">Th25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D15">FINSEQ_1:def 15</a></i>
;<br/>
<b>hence </b><a NAME="E10:93"/>
 <a href="finseq_5.html#K3">Rev</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K7">|--</a> <font color="Maroon">p</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">f</font></span>)</span> <a href="finseq_4.html#K6">-|</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="finseq_6.html#T30" target="_self">Th30</a>, <a class="ref" href="finseq_4.html#D6">FINSEQ_4:def 6</a></i>;<br/>


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