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<b>let </b><font color="Maroon">f1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">B</font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:2_2_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K3">pr2</a> <font color="Maroon">h1</font>
 ;<br/><a NAME="E2:2_2_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">h1</font>
 <b>by </b><i><a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/><b>hence </b><a NAME="E3:2_2_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h1</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>thus </b><a NAME="E4:2_2_1_1"/>
( <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f1</font> implies <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  )
 <b>by </b><i>, , <a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><b>that </b><br/><a NAME="E2:2_2_1"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h1</font>
 <b>and </b><br/><a NAME="E3:2_2_1"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">n</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f1</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font></span>)</span> <a href="mcart_1.html#K2">`2</a> 
 ;<br/>

<a NAME="E4:2_2_1"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f1</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font></span>)</span> <a href="mcart_1.html#K2">`2</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E5:2_2_1"/><b>then </b>
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">h1</font> &amp; ( for <font color="Olive">n</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f1</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  ) )
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/>
<b>hence </b><a NAME="E6:2_2_1"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="mcart_1.html#K16">pr2</a> <font color="Maroon">h1</font>
 <b>by </b><i><a class="ref" href="mcart_1.html#D13">MCART_1:def 13</a></i>;<br/>


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