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<b>let </b><font color="Maroon" title="c2">n1</font>, <font color="Maroon" title="c3">n2</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>given </b><font color="Maroon" title="c4">s1</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><a NAME="E1:33_1_2"/><i><font color="Green" title="E11">A3</font></i>: 
( <font color="Maroon" title="c4">s1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> &amp; <font color="Maroon" title="c2">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s1</font> )
 ;<br/>

<b>given </b><font color="Maroon" title="c5">s2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><a NAME="E2:33_1_2"/><i><font color="Green" title="E12">A4</font></i>: 
( <font color="Maroon" title="c5">s2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> &amp; <font color="Maroon" title="c3">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">s2</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:33_1_2"/><i><font color="Green" title="E13">A5</font></i>: 
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font> holds <br/><font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="ref" href="matrix_2.html#D9" target="_self" title="MATRIX_2:def.9">Def9</a></i>;<br/>
<a NAME="E5:33_1_2"/><i><font color="Green" title="E14">A6</font></i>: 
<font color="Maroon" title="c6">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:33_1_2"/><i><font color="Green" title="E15">A7</font></i>: 
( <font color="Maroon" title="c4">s1</font> is   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font> &amp; <font color="Maroon" title="c5">s2</font> is   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font> )
 
<b>by </b><i><a class="txt" href="matrix_2.html#E1:33_1_2"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="matrix_2.html#E2:33_1_2"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="matrix_2.html#E4:33_1_2"><i><font color="Green" title="E13">A5</font></i></a></i>;<br/>
<a NAME="E7:33_1_2"/>
<font color="Maroon" title="c4">s1</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font>
 
<b>by </b><i><a class="txt" href="matrix_2.html#E1:33_1_2"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="matrix_2.html#E4:33_1_2"><i><font color="Green" title="E13">A5</font></i></a></i>;<br/>
<a NAME="E8:33_1_2"/><b>then </b><i><font color="Green" title="E16">A8</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T67" title="FUNCT_2:th.67">FUNCT_2:67</a></i>;<br/>
<a NAME="E9:33_1_2"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c6">n</font>
 
<b>by </b><i><a class="txt" href="matrix_2.html#E6:33_1_2"><i><font color="Green" title="E15">A7</font></i></a>, <a class="ref" href="funct_2.html#T67" title="FUNCT_2:th.67">FUNCT_2:67</a></i>;<br/>
<a NAME="E10:33_1_2"/><b>then </b>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">n</font> )
 
<b>by </b><i><a class="txt" href="matrix_2.html#E8:33_1_2"><i><font color="Green" title="E16">A8</font></i></a>, <a class="txt" href="matrix_2.html#E5:33_1_2"><i><font color="Green" title="E14">A6</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E11:33_1_2"/>
<font color="Maroon" title="c2">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n2</font>
 <b>by </b><i><a class="txt" href="matrix_2.html#E1:33_1_2"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="matrix_2.html#E2:33_1_2"><i><font color="Green" title="E12">A4</font></i></a></i>;<br/>


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