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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">H</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>;<br/>





<b>assume </b><a NAME="E1:77"/>
<font color="Maroon" title="c3">h</font> <a href="group_6.html#NR2" title="GROUP_6:NR.2">is_epimorphism</a> 
 ;<br/>

<a NAME="E2:77"/><b>then </b><i><font color="Green" title="E58">A1</font></i>: 
 <a href="group_6.html#K12" title="GROUP_6:func.12">Image</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T67" target="_self" title="GROUP_6:th.67">Th67</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" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">H</font>;<br/><a NAME="E1:77_1"/>
<font color="Maroon" title="c4">c</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a>  <a href="group_6.html#K12" title="GROUP_6:func.12">Image</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="group_6.html#E2:77"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="rlvect_1.html#D1" title="RLVECT_1:def.1">RLVECT_1:def 1</a></i>;<br/><b>hence </b><a NAME="E2:77_1"/>
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="group_6.html#T54" target="_self" title="GROUP_6:th.54">Th54</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:77"/>
for <font color="Olive" title="b1">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">H</font>  ex <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font>
 ;<br/>


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