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<div><span class="kw">theorem </span><a NAME="T40"><span class="comment"><font color="firebrick">:: GROUP_11:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b2">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">N</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G</font> holds  <font color="Olive" title="b3">N</font> <a href="group_11.html#K2" title="GROUP_11:func.2">~</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">N</font> <a href="group_11.html#K1" title="GROUP_11:func.1">`</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">N</font> <a href="group_11.html#K2" title="GROUP_11:func.2">~</a> <font color="Olive" title="b2">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">N</font> <a href="group_11.html#K2" title="GROUP_11:func.2">~</a> <font color="Olive" title="b2">A</font></div></div>
