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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: MSUALG_7:7</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">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">X</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="msualg_5.html#K5" title="MSUALG_5:func.5">EqRelLatt</a> <font color="Olive" title="b2">M</font></span>)</span><br/>  for <font color="Olive" title="b4">X1</font> being   <a href="closure2.html#NM1" title="CLOSURE2:NM.1">SubsetFamily</a> of <span class="p1"><a href="pboole.html#K6" title="PBOOLE:func.6">[|</a><span class="default"><font color="Olive" title="b2">M</font>,<font color="Olive" title="b2">M</font></span><a href="pboole.html#K6" title="PBOOLE:func.6">|]</a></span>  st <font color="Olive" title="b4">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">X</font> holds <br/> for <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font> being   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Olive" title="b2">M</font>  st <font color="Olive" title="b5">a</font> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</a>  <a href="mssubfam.html#K4" title="MSSUBFAM:func.4">meet</a> <span class="p1"><a href="closure2.html#K5" title="CLOSURE2:func.5">|:</a><span class="default"><font color="Olive" title="b4">X1</font></span><a href="closure2.html#K5" title="CLOSURE2:func.5">:|</a></span> &amp; <font color="Olive" title="b6">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X</font> holds <br/><font color="Olive" title="b5">a</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b6">b</font></div></div>
