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<div><span class="kw">theorem </span><a NAME="T125"><span class="comment"><font color="firebrick">:: PBOOLE:125</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">x</font>, <font color="Olive" title="b3">X</font>, <font color="Olive" title="b4">Y</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b2">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Olive" title="b3">X</font> &amp; <font color="Olive" title="b2">x</font> <a href="pboole.html#R3" title="PBOOLE:pred.3">in</a> <font color="Olive" title="b4">Y</font> holds <br/><font color="Olive" title="b3">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <font color="Olive" title="b4">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">EmptyMS</a> <font color="Olive" title="b1">I</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T8" target="_self" onmouseover="rs('pboole/T8')" onmouseout="rh()">Th8</a>, <a class="ref" href="pboole.html#T124" target="_self" onmouseover="rs('pboole/T124')" onmouseout="rh()">Th124</a></span>;<br/></div></div>
