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<b>let </b><font color="Maroon">H</font> be   <a href="group_1.html#NM1">Group</a>;<br/><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_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/>





<b>assume </b><a NAME="E1:91"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">h</font> is <a href="funct_1.html#V2">one-to-one</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D12" target="_self">GROUP_6:def 12</a><br/>

<b>reconsider </b><font color="Maroon">ih</font> = <font color="Maroon">h</font> as   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font></span>)</span> <b>by </b><i><a class="ref" href="group_6.html#T2" target="_self">Th2</a></i>;<br/>
<b>take </b>
<font color="Maroon">ih</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15" target="_self">GROUP_6:def 15</a><br/>

<a NAME="E3:91"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">ih</font> <a href="group_6.html#NR1" target="_self">is_monomorphism</a> 
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>now </b></a><div class="add"><a NAME="E1:91_1"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">ih</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:91_1"/>
<font color="Maroon">ih</font> <a href="group_6.html#NR2" target="_self">is_epimorphism</a> 
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:91"/>
<font color="Maroon">ih</font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i><a class="ref" href="group_6.html#D1" target="_self">Def1</a>, <a class="ref" href="group_6.html#T8" target="_self">Th8</a></i>;<br/>


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