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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: CLOSURE3:13</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">M</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b3">AA</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st (  for <font color="Olive" title="b4">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">AA</font> holds <br/><font color="Olive" title="b4">x</font> is   <a href="closure2.html#NM1" title="CLOSURE2:NM.1">SubsetFamily</a> of <font color="Olive" title="b2">M</font> ) holds <br/> for <font color="Olive" title="b4">A</font>, <font color="Olive" title="b5">B</font> being   <a href="closure2.html#NM1" title="CLOSURE2:NM.1">SubsetFamily</a> of <font color="Olive" title="b2">M</font>  st <font color="Olive" title="b5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="closure3.html#K2" title="CLOSURE3:func.2">MSUnion</a> <font color="Olive" title="b6">X</font></span>)</span> where <font color="Olive" title="b6">X</font> is   <a href="closure2.html#NM1" title="CLOSURE2:NM.1">SubsetFamily</a> of <font color="Olive" title="b2">M</font> : <font color="Olive" title="b6">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">AA</font> </span> } </span>  &amp; <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b3">AA</font> holds <br/> <a href="closure3.html#K2" title="CLOSURE3:func.2">MSUnion</a> <font color="Olive" title="b5">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="closure3.html#K2" title="CLOSURE3:func.2">MSUnion</a> <font color="Olive" title="b4">A</font></div></div>
