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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="group_6.html#K9" title="GROUP_6:func.9">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> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a></span><br/>

<b>set </b><font color="Maroon" title="c2">g</font> =  <a href="group_6.html#K9" title="GROUP_6:func.9">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="E1:83"/>
 <a href="group_6.html#K10" title="GROUP_6:func.10">Ker</a> <span class="p1">(<span class="default"><a href="group_6.html#K9" title="GROUP_6:func.9">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="E2:83"/><b>then </b>
(  <a href="group_6.html#K9" title="GROUP_6:func.9">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> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="group_6.html#K9" title="GROUP_6:func.9">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> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</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="E3:83"/>
 <a href="group_6.html#K9" title="GROUP_6:func.9">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> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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