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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</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">p</font> be    <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K12">Permutations</a> <font color="Maroon">n</font>;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">n</font>
 ;<br/>

<a NAME="E2:63"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/>
<a NAME="E3:63"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T67">FUNCT_2:67</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">s</font> = <font color="Maroon">p</font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E5:63"/>
<font color="Maroon">i</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_2.html#D3">FUNCT_2:def 3</a>, </i>;<br/>
<b>then consider </b><font color="Maroon">k</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="E7:63"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K3">dom</a> <font color="Maroon">s</font> &amp; <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<b>thus </b><a NAME="E8:63"/>
 ex <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">n</font> &amp; <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> )
 <b>by </b><i>, <a class="txt" href="matrix_9.html#E6"><i><font color="Green">Lemma53</font></i></a></i>;<br/>


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