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<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green">E50</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<b>reconsider </b><font color="Maroon">v2</font> = <font color="Maroon">v1</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">k</font></span>)</span> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#T19">FINSEQ_1:19</a></i>;<br/>
<a NAME="E3:4"/>
<font color="Maroon">v2</font> <a href="tarski.html#R1">is_a_prefix_of</a> <font color="Maroon">v1</font>
 
<b>by </b><i><a class="ref" href="trees_1.html#D1">TREES_1:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">v</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E5:4"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">v</font>
 <b>by </b><i><a class="ref" href="trees_1.html#T8">TREES_1:8</a></i>;<br/>
<b>take </b>
<font color="Maroon">v2</font>
;<br/>

<b>take </b>
<font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> 1
;<br/>

<a NAME="E6:4"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</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="E7:4"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T21">FINSEQ_1:21</a></i>;<br/>
<a NAME="E8:4"/><b>then </b>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">v</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<a NAME="E9:4"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> 1
 
;<br/>
<b>hence </b><a NAME="E10:4"/>
( <font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 <b>by </b><i>, , , <a class="ref" href="finseq_1.html#T21">FINSEQ_1:21</a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>


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