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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">H</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">H</font>,<font color="Maroon">I</font>;<br/>









<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><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>thus </b><span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="group_6.html#K8" target="_self">*</a> <span class="p2">(<span class="default"><a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">G</font>,<font color="Maroon">H</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> = 
<font color="Maroon">h1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">G</font>,<font color="Maroon">H</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon">h1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">H</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">I</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2"><b>now </b></a><div class="add"><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>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">H</font>,<font color="Maroon">I</font></span>)</span> <a href="group_6.html#K8" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">H</font>,<font color="Maroon">I</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">I</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:52"/>
( <font color="Maroon">h1</font> <a href="group_6.html#K8" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">G</font>,<font color="Maroon">H</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">G</font>,<font color="Maroon">I</font> &amp; <span class="p1">(<span class="default"><a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">H</font>,<font color="Maroon">I</font></span>)</span> <a href="group_6.html#K8" target="_self">*</a> <font color="Maroon">h</font> <a href="funct_2.html#R2">=</a>  <a href="group_6.html#K9" target="_self">1:</a> <font color="Maroon">G</font>,<font color="Maroon">I</font> )
 <b>by </b><i>, </i>;<br/>


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