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<b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:90"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>let </b><font color="Maroon">n</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E2:90"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E3:90"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_3.html#T33" target="_self">Th33</a>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<b>hence </b><a NAME="E4:90"/>
for <font color="Olive">B</font> being <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>   holds <br/>(  not <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> ) </span>}</span>  or <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> or <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_3.html#K1" target="_self">-</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Olive">B</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T38" target="_self">Th38</a>, <a class="ref" href="finseq_1.html#T26">FINSEQ_1:26</a></i>;<br/>


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