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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E44">Th32</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: GROUP_24:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font>, <font color="Olive" title="b2">A</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b3">phi</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b2">A</font>,<span class="p1">(<span class="default"><a href="autgroup.html#K3" title="AUTGROUP:func.3">AutGroup</a> <font color="Olive" title="b1">G</font></span>)</span><br/>  for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="group_24.html#K1" title="GROUP_24:func.1">semidirect_product</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">phi</font>)</span>)</span>  ex <font color="Olive" title="b5">g</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font> ex <font color="Olive" title="b6">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">A</font> st <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_24.html#K2" title="GROUP_24:func.2">incl1</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">phi</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">g</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_24.html#K3" title="GROUP_24:func.3">incl2</a> (<font color="Olive" title="b1">G</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">phi</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font></div></div>
