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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E53">Th55</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: GROUP_24:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">H</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">N</font> being   <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font>  st <font color="Olive" title="b2">H</font>,<font color="Olive" title="b3">N</font> <a href="group_24.html#R1" title="GROUP_24:pred.1">are_complements_in</a> <font color="Olive" title="b1">G</font> holds <br/> ex <font color="Olive" title="b4">phi</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b2">H</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b3">N</font></span>)</span> st <br/>( (  for <font color="Olive" title="b5">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">H</font><br/>  for <font color="Olive" title="b6">g</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="b6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">h</font> holds <br/><font color="Olive" title="b4">phi</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">N</font> ) &amp; <font color="Olive" title="b4">phi</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  )</div></div>
