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<b>let </b><font color="Maroon">Gc</font> be  <a href="gr_cy_1.html#V1">cyclic</a> <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H</font> be    <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">Gc</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Gc</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">Gc</font> <a href="hidden.html#R1">=</a>  <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">g</font></span><a href="domain_1.html#K6">}</a></span>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">g</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">g</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font> <b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E4:13"/>
 <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">g'</font></span><a href="domain_1.html#K6">}</a></span> is    <a href="group_6.html#M1">Subgroup</a> of <font color="Maroon">H</font>
 
;<br/>
<a NAME="E5:13"/><b>then </b>
 <a href="group_4.html#K5">gr</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">g</font></span><a href="domain_1.html#K6">}</a></span> is    <a href="group_6.html#M1">Subgroup</a> of <font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:13"/>
 <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Gc</font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">Gc</font> #) <a href="hidden.html#R1">=</a>  <a href="group_1.html#G1">HGrStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H</font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">H</font> #)
 <b>by </b><i>, <a class="ref" href="group_2.html#T64">GROUP_2:64</a></i>;<br/>


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