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<div><span class="kw">theorem </span><a NAME="T34"><span class="comment"><font color="firebrick">:: MBOOLEAN:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</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">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Olive" title="b3">B</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() &amp; (  for <font color="Olive" title="b4">X</font>, <font color="Olive" title="b5">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="b4">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">Y</font> &amp; <font color="Olive" title="b4">X</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Olive" title="b2">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b5">Y</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Olive" title="b2">A</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Olive" title="b3">B</font> holds <br/><font color="Olive" title="b4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <font color="Olive" title="b5">Y</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">EmptyMS</a> <font color="Olive" title="b1">I</font> ) holds <br/> <a href="mboolean.html#K2" title="MBOOLEAN:func.2">union</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <font color="Olive" title="b3">B</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><a href="mboolean.html#K2" title="MBOOLEAN:func.2">union</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="pboole.html#K3" title="PBOOLE:func.3">(/\)</a> <span class="p1">(<span class="default"><a href="mboolean.html#K2" title="MBOOLEAN:func.2">union</a> <font color="Olive" title="b3">B</font></span>)</span></div></div>
