<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">s</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:10"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 <b>and </b><br/><a NAME="E2:10"/><i><font color="Green">E49</font></i>: 
 <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="group_4.html#K5">gr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="group_4.html#K5">gr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">k</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 <b>and </b><br/><a NAME="E3:10"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">k</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E4:10"/><i><font color="Green">E54</font></i>: 
 <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> is <a href="group_1.html#V6">finite</a>
 
<b>by </b><i>, <a class="ref" href="group_2.html#T48">GROUP_2:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">h</font> = <font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">k</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="group_4.html#K5">gr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E6:10"/>
 <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="group_4.html#K5">gr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">h</font></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="group_4.html#K5">gr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b> <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">s</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> = 
 <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">h</font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i>, <a class="ref" href="group_2.html#T85">GROUP_2:85</a></i>
<br/>.= 
 <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">k</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i/>
;<br/><br/>


</div>
