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<b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:13_1_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> )
 <b>and </b><br/><a NAME="E3:13_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="goboard1.html#D2">GOBOARD1:def 2</a></i>;<br/>
<a NAME="E4:13_1_1"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">k1</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i</font>, <font color="Maroon">l1</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font> 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/>
<b>take </b><font color="Maroon">k</font> = <font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> 1; <i><font color="Red">:: according to </font></i><a class="ref" href="goboard1.html#D2">GOBOARD1:def 2</a><br/>

<b>take </b><font color="Maroon">l</font> = <font color="Maroon">l1</font> <a href="nat_1.html#K1">+</a> 1;<br/>

<a NAME="E6:13_1_1"/>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <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
 
;<br/>
<b>hence </b><a NAME="E7:13_1_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T62">FINSEQ_5:62</a></i>;<br/>

<b>then </b><i><font color="Green">E57</font></i>: <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<font color="Maroon">f</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">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">k</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span>

;<br/>
<a NAME="E9:13_1_1"/>
<font color="Maroon">l</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <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
 
;<br/>
<b>hence </b><a NAME="E10:13_1_1"/>
<font color="Maroon">l</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T62">FINSEQ_5:62</a></i>;<br/>

<b>then </b><span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font> = 
<font color="Maroon">f</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">f</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">l</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font></span>)</span>

;<br/>
<b>hence </b><a NAME="E12:13_1_1"/>
not <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">l</font>
 <b>by </b><i>, </i>;<br/>


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