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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/>

<a NAME="E3:7"/><i><font color="Green" title="E9">A3</font></i>: 
<font color="Maroon" title="c1">G</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 
<b>by </b><i><a class="txt" href="gr_cy_2.html#E2:7"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="gr_cy_1.html#D9" title="GR_CY_1:def.9">GR_CY_1:def 9</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">G1</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>

<a NAME="E4:7"/>
<font color="Maroon" title="c3">G1</font> is  <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 
<b>by </b><i><a class="txt" href="gr_cy_2.html#E1:7"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="gr_cy_2.html#E3:7"><i><font color="Green" title="E9">A3</font></i></a>, <a class="ref" href="gr_cy_1.html#T44" title="GR_CY_1:th.44">GR_CY_1:44</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">G1</font><b> such that </b><br/><a NAME="E6:7"/><i><font color="Green" title="E10">A4</font></i>: 
<font color="Maroon" title="c3">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="gr_cy_1.html#D9" title="GR_CY_1:def.9">GR_CY_1:def 9</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">b1</font> = <font color="Maroon" title="c4">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="group_2.html#T51" title="GROUP_2:th.51">GROUP_2:51</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E9:7"/><i><font color="Green" title="E11">A5</font></i>: 
<font color="Maroon" title="c5">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c6">p</font>
 <b>by </b><i><a class="txt" href="gr_cy_2.html#E1:7"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="gr_cy_2.html#E2:7"><i><font color="Green" title="E8">A2</font></i></a>, <a class="ref" href="gr_cy_2.html#T12" target="_self" title="GR_CY_2:th.12">Th12</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">p</font>
;<br/>

<b>thus </b><a NAME="E10:7"/>
<font color="Maroon" title="c3">G1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c6">p</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="gr_cy_2.html#E6:7"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="gr_cy_2.html#E9:7"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="gr_cy_2.html#T9" target="_self" title="GR_CY_2:th.9">Th9</a></i>;<br/>


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