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<b>let </b><font color="Maroon">f</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E1:11_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<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">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="jordan23.html#D1" target="_self">JORDAN23:def 1</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:11_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E3:11_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E4:11_1_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 or <font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 <b>and </b><br/><a NAME="E5:11_1_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> or <font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>and </b><br/><a NAME="E6:11_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 ;<br/>

<b>thus </b><a NAME="E7:11_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


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