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<b>let </b><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c1">H</font>;<br/><b>let </b><font color="Maroon" title="c4">g1</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c2">G</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:84"/><i><font color="Green" title="E63">A1</font></i>: 
<font color="Maroon" title="c3">h</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green" title="E64">A2</font></i>: 
<font color="Maroon" title="c4">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 ;<br/>

<a NAME="E3:84"/><i><font color="Green" title="E65">A3</font></i>: 
<font color="Maroon" title="c3">h</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="group_6.html#E1:84"><i><font color="Green" title="E63">A1</font></i></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></i>;<br/>
<a NAME="E4:84"/><b>then </b><i><font color="Green" title="E66">A4</font></i>: 
<font color="Maroon" title="c4">g1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="group_6.html#E2:84"><i><font color="Green" title="E64">A2</font></i></a>, <a class="ref" href="funct_1.html#T62" title="FUNCT_1:th.62">FUNCT_1:62</a></i>;<br/>
<a NAME="E5:84"/><i><font color="Green" title="E67">A5</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">G</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:84"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 
<b>by </b><i><a class="txt" href="group_6.html#E2:84"><i><font color="Green" title="E64">A2</font></i></a>, <a class="txt" href="group_6.html#E3:84"><i><font color="Green" title="E65">A3</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E7:84"/>
<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#E4:84"><i><font color="Green" title="E66">A4</font></i></a>, <a class="txt" href="group_6.html#E5:84"><i><font color="Green" title="E67">A5</font></i></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></i>;<br/>


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