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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H</font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/>





<b>assume </b><a NAME="E1:77"/>
<font color="Maroon">h</font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 ;<br/>

<a NAME="E2:77"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T4" target="_self">Th4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/><a NAME="E1:77_1"/>
<font color="Maroon">c</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font>
 <b>by </b><i><a class="ref" href="group_6.html#T7" target="_self">Th7</a>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/><b>hence </b><a NAME="E2:77_1"/>
 ex <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="group_6.html#E2:77"><i><font color="Green">E45</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:77"/>
for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>  ex <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font>
 ;<br/>


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