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<b>let </b><font color="Maroon">G</font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>, <font color="Maroon">H</font> be  <a href="group_1.html#V1">strict</a> <a href="group_1.html#NM1">Group</a>;<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/>



<a NAME="E1:14"/><i><font color="Green">E37</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E2:14"/><i><font color="Green">E38</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="group_2.html#D7">GROUP_2:def 7</a></i>;<br/>
<a NAME="E3:14"/><i><font color="Green">E39</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">H</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">H</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="group_2.html#D7">GROUP_2:def 7</a></i>;<br/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="grsolv_1.html#K2" target="_self">.:</a> <span class="p2">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">G</font></span>)</span></span>)</span> = 
<font color="Maroon">h</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T117">FUNCT_1:117</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">H</font></span>)</span>
<b>by </b><i>, <a class="ref" href="group_6.html#T40">GROUP_6:40</a></i>
;<br/>
<b>hence </b><a NAME="E5:14"/>
<font color="Maroon">h</font> <a href="grsolv_1.html#K2" target="_self">.:</a> <span class="p1">(<span class="default"><a href="group_2.html#K5">(1).</a> <font color="Maroon">G</font></span>)</span> <a href="group_2.html#R1">=</a>  <a href="group_2.html#K5">(1).</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="group_2.html#T68">GROUP_2:68</a></i>;<br/>

the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="grsolv_1.html#K2" target="_self">.:</a> <span class="p2">(<span class="default"><a href="group_2.html#K6">(Omega).</a> <font color="Maroon">G</font></span>)</span></span>)</span> = 
<font color="Maroon">h</font> <a href="relset_1.html#K10">.:</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>
<b>by </b><i/>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_2.html#K6">(Omega).</a> <span class="p2">(<span class="default"><a href="group_6.html#K12">Image</a> <font color="Maroon">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_6.html#D11">GROUP_6:def 11</a></i>
;<br/>
<b>hence </b><a NAME="E7:14"/>
<font color="Maroon">h</font> <a href="grsolv_1.html#K2" target="_self">.:</a> <span class="p1">(<span class="default"><a href="group_2.html#K6">(Omega).</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K6">(Omega).</a> <span class="p1">(<span class="default"><a href="group_6.html#K12">Image</a> <font color="Maroon">h</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_2.html#T68">GROUP_2:68</a></i>;<br/>


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