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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>let </b><font color="Maroon">H</font> be    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G</font>;<br/>





<a NAME="E1:100"/>
(  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">H</font> &amp; <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <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#K1">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:100"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> <a href="group_2.html#K12" target="_self">*</a> <font color="Maroon">H</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H</font> <a href="group_2.html#K13" target="_self">*</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="txt" href="group_2.html#E32"><i><font color="Green">Lemma64</font></i></a>, <a class="ref" href="group_2.html#T29" target="_self">Th29</a></i>;<br/>


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