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<div><span class="kw">theorem </span><a NAME="T49"><span class="comment"><font color="firebrick">:: GROUP_23:49</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> holds   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <span class="p2">(<span class="default"><a href="group_23.html#K13" title="GROUP_23:func.13">product</a> <font color="Olive" title="b4">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K1" title="SETFAM_1:func.1">meet</a> <span class="p1"> { <span class="default">  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="group_6.html#K9" title="GROUP_6:func.9">Ker</a> <span class="p3">(<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="b5">i</font></span>)</span></span>)</span> where <font color="Olive" title="b5">i</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> : verum </span> } </span> </div></div>
