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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">Th47</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: GROUP_22:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b3">H</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font> holds  <font color="Olive" title="b5">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Olive" title="b3">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a</font></span>)</span> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f</font> <a href="grsolv_1.html#K2" title="GRSOLV_1:func.2">.:</a> <font color="Olive" title="b3">H</font></span>)</span></div></div>
