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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th39</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: GROUP_23:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="group_19.html#NM1" title="GROUP_19:NM.1">Group-Family</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b4">f</font> being    <a href="group_23.html#M1" title="GROUP_23:mode.1">Homomorphism-Family</a> of <font color="Olive" title="b3">G</font>,<font color="Olive" title="b2">F</font>  ex <font color="Olive" title="b5">phi</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b3">G</font>,<span class="p1">(<span class="default"><a href="group_7.html#K2" title="GROUP_7:func.2">product</a> <font color="Olive" title="b2">F</font></span>)</span> st <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="b3">G</font><br/>  for <font color="Olive" title="b7">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="group_23.html#K10" title="GROUP_23:func.10">.</a> <font color="Olive" title="b7">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_23.html#K12" title="GROUP_23:func.12">proj</a> (<font color="Olive" title="b2">F</font>,<font color="Olive" title="b7">j</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">phi</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">g</font></span>)</span></div></div>
