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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:71_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#NR2" target="_self">is_of_order_0</a>  or <font color="Maroon">c<sub>2</sub></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="71_1_1"><b>suppose </b></a><a NAME="E1:71_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#NR2" target="_self">is_of_order_0</a> 
 ;<br/><div class="add"><a NAME="E2:71_1_1"/><b>then </b>
 <a href="group_1.html#K7" target="_self">ord</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="group_1.html#D12" target="_self">Def12</a></i>;<br/><b>hence </b><a NAME="E3:71_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <span class="p1">(<span class="default"><a href="group_1.html#K7" target="_self">ord</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="group_1.html#E50"><i><font color="Green">Lemma29</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="71_1_2"><b>suppose </b></a><a NAME="E1:71_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#NR1" target="_self">is_not_of_order_0</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:71_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K6" target="_self">|^</a> <span class="p1">(<span class="default"><a href="group_1.html#K7" target="_self">ord</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2" target="_self">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="group_1.html#D12" target="_self">Def12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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