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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<br/>

<a NAME="E1:5"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="group_6.html#T47">GROUP_6:47</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:5"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>
<a NAME="E4:5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<a NAME="E1:5_1"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="autgroup.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<b>hence </b><a NAME="E2:5_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 <b>by </b><i><a class="ref" href="group_6.html#D13">GROUP_6:def 13</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:5"/>
 <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is    <a href="fraenkel.html#M2">Element</a> of  <a href="autgroup.html#K1" target="_self">Aut</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="autgroup.html#E3:5"><i><font color="Green">E5</font></i></a>, <a class="ref" href="autgroup.html#D1" target="_self">Def1</a></i>;<br/>


</div>
