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

<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>

<b>assume </b><a NAME="E1:97"/><i><font color="Green" title="E63">A1</font></i>: 
<font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">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="c2">H</font><b> such that </b><br/><a NAME="E3:97"/><i><font color="Green" title="E64">A2</font></i>: 
<font color="Maroon" title="c3">h</font> <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#D15" target="_self" title="GROUP_6:def.15">Def15</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">g1</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E5:97"/><i><font color="Green" title="E65">A3</font></i>: 
<font color="Maroon" title="c4">g1</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 <b>by </b><i><a class="txt" href="group_6.html#E1:97"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="group_6.html#D15" target="_self" title="GROUP_6:def.15">Def15</a></i>;<br/>
<a NAME="E6:97"/>
<font color="Maroon" title="c3">h</font> <a href="group_6.html#NR2" title="GROUP_6:NR.2">is_epimorphism</a> 
 
<b>by </b><i><a class="txt" href="group_6.html#E3:97"><i><font color="Green" title="E64">A2</font></i></a>, <a class="ref" href="group_6.html#D14" target="_self" title="GROUP_6:def.14">Def14</a></i>;<br/>
<a NAME="E7:97"/><b>then </b>
 <a href="group_6.html#K12" title="GROUP_6:func.12">Image</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T67" target="_self" title="GROUP_6:th.67">Th67</a></i>;<br/>
<a NAME="E8:97"/><b>then </b><i><font color="Green" title="E66">A4</font></i>: 
 <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c2">H</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T61" target="_self" title="GROUP_6:th.61">Th61</a></i>;<br/>
<a NAME="E9:97"/>
<font color="Maroon" title="c4">g1</font> <a href="group_6.html#NR2" title="GROUP_6:NR.2">is_epimorphism</a> 
 
<b>by </b><i><a class="txt" href="group_6.html#E5:97"><i><font color="Green" title="E65">A3</font></i></a>, <a class="ref" href="group_6.html#D14" target="_self" title="GROUP_6:def.14">Def14</a></i>;<br/>
<a NAME="E10:97"/><b>then </b>
 <a href="group_6.html#K12" title="GROUP_6:func.12">Image</a> <font color="Maroon" title="c4">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T67" target="_self" title="GROUP_6:th.67">Th67</a></i>;<br/>
<a NAME="E11:97"/><b>then </b>
 <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c1">G</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c2">H</font>
 
<b>by </b><i><a class="ref" href="group_6.html#T61" target="_self" title="GROUP_6:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E12:97"/>
 <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">Ord</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="group_6.html#E8:97"><i><font color="Green" title="E66">A4</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div>
