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<b>let </b><font color="Maroon">S</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">zero</a> <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">S</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E3:16"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/>
<a NAME="E4:16"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E5:16"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<b>set </b><font color="Maroon">m</font> = <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="finseq_4.html#K5">..</a> <font color="Maroon">S</font>;<br/>
<a NAME="E6:16"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="finseq_4.html#K5">..</a> <font color="Maroon">S</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T30">FINSEQ_4:30</a></i>;<br/>
<a NAME="E7:16"/>
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="finseq_4.html#K5">..</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T29">FINSEQ_4:29</a></i>;<br/>
<b>hence </b><a NAME="E8:16"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="finseq_4.html#K5">..</a> <font color="Maroon">S</font>
 <b>by </b><i>, , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


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