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<b>set </b><font color="Maroon" title="c2">f</font> =  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font>;<br/>
<a NAME="E1:81_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="mod_4.html#E87"><i><font color="Green" title="E58">Lm20</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">f</font> =  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font> as    <a href="mod_4.html#M1" title="MOD_4:mode.1">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="mod_4.html#D18" target="_self" title="MOD_4:def.18">Def18</a></i>;<br/>
<a NAME="E3:81_1_1"/><i><font color="Green" title="E59">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="mod_4.html#E87"><i><font color="Green" title="E58">Lm20</font></i></a></i>;<br/>
<a NAME="E4:81_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="mod_4.html#E87"><i><font color="Green" title="E58">Lm20</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:81_1_1"/>
 <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font> is   <a href="mod_4.html#NM3" title="MOD_4:NM.3">Automorphism</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="mod_4.html#E3:81_1_1"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="mod_4.html#D21" target="_self" title="MOD_4:def.21">Def21</a></i>;<br/>


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