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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E52">UniversalPropertyQuotientGroups</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: GROUP_24:53</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">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">G1</font><br/>  for <font color="Olive" title="b4">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>  st <font color="Olive" title="b3">N</font> is    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of  <a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <font color="Olive" title="b4">f</font> holds <br/> ex <font color="Olive" title="b5">fBar</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">G1</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Olive" title="b3">N</font></span>)</span>,<font color="Olive" title="b2">G2</font> st <font color="Olive" title="b4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b5">fBar</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K8" title="GROUP_6:func.8">nat_hom</a> <font color="Olive" title="b3">N</font></span>)</span></div></div>
