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

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">h</font> being   <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="c1">G</font> holds <br/> ( <font color="Olive" title="b1">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font> iff <font color="Olive" title="b1">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font> iff <font color="Maroon" title="c2">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</span><br/>



<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  implies <font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:6_1"/>
<font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/><a NAME="E2:6_1"/><span class="kw">then </span>
( <font color="Maroon" title="c2">h</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; <font color="Maroon" title="c2">h</font> 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="autgroup.html#D1" target="_self" title="AUTGROUP:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:6_1"/>
<font color="Maroon" title="c2">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:6"/>
( <font color="Maroon" title="c2">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  implies <font color="Maroon" title="c2">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="autgroup.html#K1" title="AUTGROUP:func.1">Aut</a> <font color="Maroon" title="c1">G</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="autgroup.html#D1" target="_self" title="AUTGROUP:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
