<?xml version="1.0"?>
<div class="add">

<b>set </b><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="E1:82_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>
 
<b>by </b><i><a class="txt" href="mod_4.html#E79"><i><font color="Green" title="E48">Lm14</font></i></a></i>;<br/>
<b>then reconsider </b><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> <b>by </b><i><a class="ref" href="mod_4.html#D19" target="_self" title="MOD_4:def.19">Def19</a></i>;<br/>
<a NAME="E3:82_1_1"/><i><font color="Green" title="E49">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#E79"><i><font color="Green" title="E48">Lm14</font></i></a></i>;<br/>
<a NAME="E4:82_1_1"/><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="txt" href="mod_4.html#E79"><i><font color="Green" title="E48">Lm14</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a></span><br/>

<b>thus </b><a NAME="E5:82_1_1"/>
<font color="Maroon" title="c3">f</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 <b>by </b><i><a class="txt" href="#E3:82_1_1"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="#E4:82_1_1"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
