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

<b>let </b><font color="Maroon">G</font> be  <a href="group_1.html#V1">strict</a> <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">m</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_1"/>
( <font color="Maroon">a</font> <a href="group_1.html#NR2" target="_self">is_of_order_0</a>  or <font color="Maroon">a</font> <a href="group_1.html#NR1" target="_self">is_not_of_order_0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_1"><b>suppose </b></a><a NAME="E1:9_1_1"/>
<font color="Maroon">a</font> <a href="group_1.html#NR2" target="_self">is_of_order_0</a> 
 ;<br/><div class="add"><a NAME="E2:9_1_1"/><b>then </b>
 <a href="group_1.html#K7">ord</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="group_1.html#D12">GROUP_1:def 12</a></i>;<br/><b>hence </b><a NAME="E3:9_1_1"/>
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</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="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="group_1.html#T43">GROUP_1:43</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_1_2"><b>suppose </b></a><a NAME="E1:9_1_2"/>
<font color="Maroon">a</font> <a href="group_1.html#NR1" target="_self">is_not_of_order_0</a> 
 ;<br/><div class="add"><a NAME="E2:9_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_1.html#K7">ord</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="group_1.html#D12">GROUP_1:def 12</a></i>;<br/><a NAME="E3:9_1_2"/>
<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">m</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:9_1_2"/>
<font color="Maroon">a</font> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</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="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i>, <a class="ref" href="group_1.html#T67">GROUP_1:67</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
