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<b>set </b><font color="Maroon">f</font> =  <a href="grcat_1.html#K7">id</a> <font color="Maroon">G</font>;<br/>
<a NAME="E1:81_1_1"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Olive">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">G</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="mod_4.html#T9" target="_self">Th9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> =  <a href="grcat_1.html#K7">id</a> <font color="Maroon">G</font> as    <a href="mod_4.html#M1" target="_self">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">G</font> <b>by </b><i/>;<br/>
<a NAME="E3:81_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="mod_4.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E4:81_1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="mod_4.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E5:81_1_1"/>
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">G</font> is   <a href="mod_4.html#NM3">Automorphism</a> of <font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/>


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