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

<span class="kw">let </span><font color="Maroon" title="c1">UA</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="autalg_1.html#K3" title="AUTALG_1:func.3">UAAutGroup</a> <font color="Maroon" title="c1">UA</font>, <a href="autalg_1.html#K6" title="AUTALG_1:func.6">MSAAutGroup</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>

<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> $1;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E2:55"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="autalg_1.html#K1" title="AUTALG_1:func.1">UAAut</a> <font color="Maroon" title="c1">UA</font> &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="autalg_1.html#K1" title="AUTALG_1:func.1">UAAut</a> <font color="Maroon" title="c1">UA</font> holds <br/><font color="Maroon" title="c2">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_1.html#S3" title="FUNCT_1:sch.3">FUNCT_1:sch 3</a>();<br/></span>
<span class="kw">reconsider </span><font color="Maroon" title="c3">h</font> = <font color="Maroon" title="c2">h</font> as   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="autalg_1.html#K3" title="AUTALG_1:func.3">UAAutGroup</a> <font color="Maroon" title="c1">UA</font></span>)</span>,<span class="p1">(<span class="default"><a href="autalg_1.html#K6" title="AUTALG_1:func.6">MSAAutGroup</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K10" title="MSUALG_1:func.10">MSAlg</a> <font color="Maroon" title="c1">UA</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="autalg_1.html#T40" target="_self" title="AUTALG_1:th.40">Th40</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">h</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="group_6.html#D15" title="GROUP_6:def.15">GROUP_6:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </span><br/>

<span class="kw">thus </span><a NAME="E4:55"/>
<font color="Maroon" title="c3">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="autalg_1.html#T41" target="_self" title="AUTALG_1:th.41">Th41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
