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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">N</font> be  <a href="group_3.html#V1">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">G</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">S</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">N</font></span>)</span>;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E2:64_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">N</font> &amp; <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N</font> <a href="group_2.html#K13">*</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="group_6.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:64_1"/>
<span class="p1">(<span class="default"><a href="group_6.html#K10" target="_self">nat_hom</a> <font color="Maroon">N</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_2.html#K12">*</a> <font color="Maroon">N</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:64_1"/>
<font color="Maroon">S</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_6.html#K12" target="_self">Image</a> <span class="p1">(<span class="default"><a href="group_6.html#K10" target="_self">nat_hom</a> <font color="Maroon">N</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_6.html#T2" target="_self">Th2</a>, <a class="txt" href="group_6.html#E2:64_1"><i><font color="Green">E45</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:64"/>
 <a href="group_6.html#K12" target="_self">Image</a> <span class="p1">(<span class="default"><a href="group_6.html#K10" target="_self">nat_hom</a> <font color="Maroon">N</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">N</font>
 <b>by </b><i><a class="ref" href="group_2.html#T71">GROUP_2:71</a></i>;<br/>


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