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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>set </b><font color="Maroon" title="c2">g</font> =  <a href="group_6.html#K10" title="GROUP_6:func.10">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span>;<br/>
<a NAME="E1:86"/>
 <a href="group_6.html#K11" title="GROUP_6:func.11">Ker</a> <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">nat_hom</a> <span class="p2">(<span class="default"><a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T52" target="_self" title="GROUP_6:th.52">Th52</a></i>;<br/>
<a NAME="E2:86"/><b>then </b>
(  <a href="group_6.html#K10" title="GROUP_6:func.10">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_6.html#NR1" title="GROUP_6:NR.1">is_monomorphism</a>  &amp;  <a href="group_6.html#K10" title="GROUP_6:func.10">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_6.html#NR2" title="GROUP_6:NR.2">is_epimorphism</a>  )
 
<b>by </b><i><a class="ref" href="group_6.html#T66" target="_self" title="GROUP_6:th.66">Th66</a>, <a class="ref" href="group_6.html#T69" target="_self" title="GROUP_6:th.69">Th69</a></i>;<br/>
<b>hence </b><a NAME="E3:86"/>
 <a href="group_6.html#K10" title="GROUP_6:func.10">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 <b>by </b><i><a class="ref" href="group_6.html#D14" target="_self" title="GROUP_6:def.14">Def14</a></i>;<br/>


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