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<span class="kw">set </span><font color="Maroon" title="c2">f</font> =  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">G</font>;<br/>
<a NAME="E1:89_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="struct_0.html#K3" title="STRUCT_0:func.3">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="algstr_0.html#K1" title="ALGSTR_0:func.1">+</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="struct_0.html#K3" title="STRUCT_0:func.3">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="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="mod_4.html#E79"><span class="lab"><font color="Green" title="E48">Lm14</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">f</font> =  <a href="struct_0.html#K3" title="STRUCT_0:func.3">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#D19" target="_self" title="MOD_4:def.19">Def19</a></span>;<br/>
<a NAME="E3:89_1_1"/>
( <font color="Maroon" title="c3">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Maroon" title="c3">f</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="mod_4.html#E79"><span class="lab"><font color="Green" title="E48">Lm14</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:89_1_1"/>
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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