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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</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="c1">G</font>,<font color="Maroon" title="c2">H</font>;<br/>



<b>assume </b><a NAME="E1:1"/>
<font color="Maroon" title="c3">h</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c2">H</font>
 ;<br/>

<a NAME="E2:1"/><b>then </b><i><font color="Green" title="E1">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</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">H</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T29" title="FUNCT_2:th.29">FUNCT_2:29</a></i>;<br/>
<b>assume </b><a NAME="E3:1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="tops_2.html#NK3" title="TOPS_2:NK.3">"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<a NAME="E4:1"/><b>then </b>
<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="ref" href="waybel_1.html#T25" title="WAYBEL_1:th.25">WAYBEL_1:25</a></i>;<br/>
<b>hence </b><a NAME="E5:1"/>
<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="txt" href="topalg_1.html#E2:1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="group_6.html#T70" title="GROUP_6:th.70">GROUP_6:70</a></i>;<br/>


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