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





<b>assume </b><a NAME="E1:67"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">G</font> is  <a href="group_1.html#V7">commutative</a> <a href="group_1.html#NM1">Group</a>
 ;<br/>

<b>let </b><font color="Maroon">h1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">g</font></span>)</span>, <font color="Maroon">h2</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">g</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D16">GROUP_1:def 16</a><br/>

<b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">h1</font>, <font color="Maroon">d</font> = <font color="Maroon">h2</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font> <b>by </b><i><a class="ref" href="group_2.html#T51">GROUP_2:51</a></i>;<br/>
<a NAME="E3:67"/>
<font color="Maroon">h1</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<b>then 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="E5:67"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="group_6.html#E1:67"><i><font color="Green">E45</font></i></a></i>;<br/>
<a NAME="E6:67"/>
<font color="Maroon">h2</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E8:67"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="group_6.html#E1:67"><i><font color="Green">E45</font></i></a></i>;<br/>
<b>thus </b><font color="Maroon">h1</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h2</font> = 
<font color="Maroon">c</font> <a href="group_1.html#K1">*</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="group_2.html#T52">GROUP_2:52</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="txt" href="group_6.html#E8:67"><i><font color="Green">E51</font></i></a>, , </i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">d</font> <a href="group_1.html#K1">*</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="group_6.html#E8:67"><i><font color="Green">E51</font></i></a>, , </i>
<br/>.= 
<font color="Maroon">h2</font> <a href="group_1.html#K1">*</a> <font color="Maroon">h1</font>
<b>by </b><i><a class="ref" href="group_2.html#T52">GROUP_2:52</a></i>
;<br/>


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