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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="matrix_2.html#M3">Element</a> of  <a href="matrix_2.html#K11">Permutations</a> <font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E3:62"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="matrix_2.html#K12">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="matrix_2.html#D12">MATRIX_2:def 12</a></i>;<br/>
<a NAME="E4:62"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is   <a href="finseq_1.html#NM1">FinSequence</a>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E3:62"><i><font color="Green">E51</font></i></a></i>;<br/>
<a NAME="E5:62"/>
 <a href="matrix_2.html#K12">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="matrix_2.html#T22">MATRIX_2:22</a></i>;<br/>
<a NAME="E6:62"/><b>then </b><i><font color="Green">E53</font></i>: 
 <a href="setwop_2.html#K3">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E3:62"><i><font color="Green">E51</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E7:62"/>
<font color="Maroon">c<sub>3</sub></font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="matrix_2.html#D11">MATRIX_2:def 11</a></i>;<br/>
<a NAME="E8:62"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="matrix_9.html#E1:62"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:62"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E4:62"><i><font color="Green">E52</font></i></a>, <a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<b>thus </b><a NAME="E11:62"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="setwop_2.html#K2">Seg</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="matrix_9.html#E10:62"><i><font color="Green">E54</font></i></a>, <a class="txt" href="matrix_9.html#E6:62"><i><font color="Green">E53</font></i></a>, <a class="txt" href="matrix_9.html#E3:62"><i><font color="Green">E51</font></i></a></i>;<br/>


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