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<b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><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="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/>







<b>assume </b><a NAME="E1:1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font>
 ;<br/>

<b>then consider </b><font color="Maroon">q'</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>, <font color="Maroon">r</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E3:1"/><i><font color="Green">E35</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">r</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T26">FINSEQ_2:26</a></i>;<br/>
<b>consider </b><font color="Maroon">q</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>, <font color="Maroon">c</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E5:1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="finseq_2.html#T22">FINSEQ_2:22</a></i>;<br/>
<a NAME="E6:1"/><i><font color="Green">E37</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<b>take </b>
<font color="Maroon">q</font>
;<br/>

<b>take </b>
<font color="Maroon">r</font>
;<br/>

<b>take </b>
<font color="Maroon">c</font>
;<br/>

<b>thus </b><a NAME="E7:1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Maroon">r</font> )
 <b>by </b><i>, , </i>;<br/>


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