<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(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/>

<span class="kw">set </span><font color="Maroon" title="c2">g</font> =  <a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(1).</a> <font color="Maroon" title="c1">G</font></span>)</span>;<br/>
<a NAME="E1:86"/>
 <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <span class="p2">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(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#K6" title="GROUP_2:func.6">(1).</a> <font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T43" target="_self" onmouseover="rs('group_6/T43')" onmouseout="rh()">Th43</a></span>;<br/>
<a NAME="E2:86"/><span class="kw">then </span>
 <a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T56" target="_self" onmouseover="rs('group_6/T56')" onmouseout="rh()">Th56</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:86"/>
 <a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <span class="p1">(<span class="default"><a href="group_2.html#K6" title="GROUP_2:func.6">(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 class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T59" target="_self" onmouseover="rs('group_6/T59')" onmouseout="rh()">Th59</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
