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<b>let </b><font color="Maroon">n1</font> be   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">n2</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>given </b><font color="Maroon">s1</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E1:33_1_2"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">s1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">n1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s1</font> )
 ;<br/>

<b>given </b><font color="Maroon">s2</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E2:33_1_2"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">s2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s2</font> )
 ;<br/>

<b>consider </b><font color="Maroon">n</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:33_1_2"/><i><font color="Green">E61</font></i>: 
for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> holds <br/><font color="Olive">y</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:33_1_2"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E6:33_1_2"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">s1</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> &amp; <font color="Maroon">s2</font> is   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E7:33_1_2"/>
<font color="Maroon">s1</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>, <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">n</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:33_1_2"/><b>then </b><i><font color="Green">E64</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.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/>
<a NAME="E9:33_1_2"/>
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.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/>
<a NAME="E10:33_1_2"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E11:33_1_2"/>
<font color="Maroon">n1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n2</font>
 <b>by </b><i>, </i>;<br/>


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