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<b>let </b><font color="Maroon" title="c1">D</font>, <font color="Maroon" title="c2">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c4">B</font> be   <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>;<br/>







<b>set </b><font color="Maroon" title="c5">p</font> =  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>;<br/>
<b>assume </b><a NAME="E1:48"/>
( <font color="Maroon" title="c3">F</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> )
 ;<br/>

<a NAME="E2:48"/><b>then </b><i><font color="Green" title="E36">A1</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font>
 
<b>by </b><i><a class="ref" href="rearran1.html#T21" target="_self" title="REARRAN1:th.21">Th21</a></i>;<br/>
<a NAME="E3:48"/><b>then </b><i><font color="Green" title="E37">A2</font></i>: 
<span class="p1">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">|</a> <font color="Maroon" title="c2">C</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></i>;<br/>
<b>hence </b><a NAME="E4:48"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:48"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="rfunct_3.html#T70" title="RFUNCT_3:th.70">RFUNCT_3:70</a></i>;<br/>

<a NAME="E5:48"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>
<a NAME="E6:48"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font>
 
;<br/>
<a NAME="E7:48"/><b>then </b>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>hence </b><a NAME="E8:48"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <span class="p2">(<span class="default"><a href="rearran1.html#K4" title="REARRAN1:func.4">Rlor</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>,<font color="Maroon" title="c2">C</font></span>)</span>
 <b>by </b><i><a class="txt" href="rearran1.html#E2:48"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="rearran1.html#E3:48"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="rfunct_3.html#T70" title="RFUNCT_3:th.70">RFUNCT_3:70</a></i>;<br/>


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