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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:72"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">h</font> <a href="group_6.html#NR1" target="_self">is_monomorphism</a> 
 <b>and </b><br/><a NAME="E2:72"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">h'</font> = <font color="Maroon">h</font> as   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G</font>,<span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font></span>)</span> <b>by </b><i><a class="ref" href="group_6.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E4:72"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">h'</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i>, <a class="txt" href="group_6.html#E4:72"><i><font color="Green">E51</font></i></a></i>;<br/>
<a NAME="E5:72"/>
<font color="Maroon">h'</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h'</font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>proof </b></a><div class="add">

<a NAME="E1:72_1"/><i><font color="Green">E52</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">h'</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:72_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K12" target="_self">Image</a> <font color="Maroon">h</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:72_1"/>
<font color="Maroon">h'</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h'</font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="group_6.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_1.html#T57">FUNCT_1:57</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:72"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/>


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