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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th44</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: GROUP_23:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b4">f1</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><br/>  for <font color="Olive" title="b5">f2</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</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">G1</font> holds <br/> ( <font color="Olive" title="b6">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f1</font></span>)</span> iff <font color="Olive" title="b4">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">g</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Olive" title="b5">f2</font> )</div></div>
