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<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>assume </b><a NAME="E1:15"/>
<font color="Maroon">G</font> is <a href="group_1.html#V6">finite</a>
 ;<br/>

<a NAME="E2:15"/><b>then </b>
 <a href="group_1.html#K7">ord</a> <font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a>  <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">t</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:15"/><i><font color="Green">E42</font></i>: 
 <a href="group_1.html#K9">ord</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K7">ord</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_1.html#K9">ord</a> <font color="Maroon">G</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p2">(<span class="default"><a href="group_1.html#K7">ord</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font>
<b>by </b><i>, <a class="ref" href="group_1.html#T50">GROUP_1:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> <a href="group_1.html#K6">|^</a> <font color="Maroon">t</font>
<b>by </b><i><a class="ref" href="group_1.html#T82">GROUP_1:82</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
<b>by </b><i><a class="ref" href="group_1.html#T42">GROUP_1:42</a></i>
;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_1.html#K9">ord</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 ;<br/>


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