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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th14</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: GROUP_24:27</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>, <font color="Olive" title="b5">y</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><br/>  for <font color="Olive" title="b6">a1</font>, <font color="Olive" title="b7">a2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b8">g1</font>, <font color="Olive" title="b9">g2</font>, <font color="Olive" title="b10">g3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K5" title="GROUP_7:func.5">&lt;*</a><span class="default"><font color="Olive" title="b8">g1</font>,<font color="Olive" title="b6">a1</font></span><a href="group_7.html#K5" title="GROUP_7:func.5">*&gt;</a></span> &amp; <font color="Olive" title="b5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K5" title="GROUP_7:func.5">&lt;*</a><span class="default"><font color="Olive" title="b9">g2</font>,<font color="Olive" title="b7">a2</font></span><a href="group_7.html#K5" title="GROUP_7:func.5">*&gt;</a></span> &amp; <font color="Olive" title="b10">g3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">phi</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">a1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b9">g2</font> holds <br/><font color="Olive" title="b4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="group_7.html#K5" title="GROUP_7:func.5">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b8">g1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b10">g3</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b6">a1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b7">a2</font></span>)</span></span><a href="group_7.html#K5" title="GROUP_7:func.5">*&gt;</a></span></div></div>
