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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:91"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></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/>
<a NAME="E3:91"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rfunct_3.html#E1:91"><i><font color="Green">E58</font></i></a></i>;<br/>
<a NAME="E4:91"/><i><font color="Green">E60</font></i>: 
 <a href="rfunct_3.html#K22" target="_self">FinS</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">c<sub>3</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="txt" href="rfunct_3.html#E1:91"><i><font color="Green">E58</font></i></a>, <a class="ref" href="rfunct_3.html#D14" target="_self">Def14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" target="_self">FinS</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E6:91"/><i><font color="Green">E61</font></i>: 
 <a href="setwop_2.html#K3">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" target="_self">FinS</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="setwop_2.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" target="_self">FinS</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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>thus </b> <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font> = 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="rfunct_3.html#E3:91"><i><font color="Green">E59</font></i></a>, <a class="txt" href="rfunct_3.html#E4:91"><i><font color="Green">E60</font></i></a>, <a class="ref" href="rfinseq.html#T10">RFINSEQ:10</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K22" target="_self">FinS</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_3.html#E6:91"><i><font color="Green">E61</font></i></a>, <a class="ref" href="finseq_1.html#T78">FINSEQ_1:78</a></i>
;<br/>


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