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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">D</font>, <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="rearran1.html#NM1">RearrangmentGen</a> of <font color="Maroon">C</font>;<br/>







<b>assume </b><a NAME="E1:23"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">F</font> is <a href="partfun1.html#V1">total</a> &amp;  <a href="card_1.html#K4">card</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">D</font> )
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">F'</font> = <font color="Maroon">F</font> as  <a href="finset_1.html#V1">finite</a> <a href="funct_1.html#NM1">Function</a> <b>by </b><i><a class="ref" href="finset_1.html#T29">FINSET_1:29</a></i>;<br/>
<i><font color="Green">E42</font></i>: <font color="Maroon">D</font> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">D</font>
<b>by </b><i/>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="rfunct_3.html#K23">|</a> <font color="Maroon">D</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>
;<br/>
<a NAME="E5:23"/>
<font color="Maroon">F</font> <a href="rfunct_3.html#K23">|</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>
<a NAME="E6:23"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">F</font>, <a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i>, <a class="ref" href="rfunct_3.html#D14">RFUNCT_3:def 14</a></i>;<br/>
<b>set </b><font color="Maroon">a</font> =  <a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font>;<br/>
<a NAME="E7:23"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">a'</font> =  <a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font> as  <a href="finset_1.html#V1">finite</a> <a href="funct_1.html#NM1">Function</a> ;<br/>
<b>reconsider </b><font color="Maroon">da'</font> =  <a href="relat_1.html#K1">dom</a> <font color="Maroon">a'</font>, <font color="Maroon">dF'</font> =  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F'</font> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E10:23"/><i><font color="Green">E45</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">da'</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">dF'</font>
 
<b>by </b><i>, <a class="ref" href="rfinseq.html#T10">RFINSEQ:10</a></i>;<br/>
<b>thus </b> <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16">CHI</a> <font color="Maroon">A</font>,<font color="Maroon">C</font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">A</font>
<b>by </b><i><a class="ref" href="rfunct_3.html#D6">RFUNCT_3:def 6</a></i>
<br/>.= 
 <a href="card_1.html#K4">card</a> <font color="Maroon">C</font>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font></span>)</span>
<b>by </b><i>, , , , <a class="ref" href="finseq_1.html#T78">FINSEQ_1:78</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K22">FinS</a> <font color="Maroon">F</font>,<font color="Maroon">D</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfinseq.html#D3">RFINSEQ:def 3</a></i>
;<br/>


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