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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E2">Th3</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: CLOSURE3:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">MA</font> being   <a href="msualg_1.html#V3" title="MSUALG_1:attr.3">strict</a>   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> over <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">F</font> being   <a href="closure2.html#NM1" title="CLOSURE2:NM.1">SubsetFamily</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">MA</font>  st <font color="Olive" title="b3">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="msualg_2.html#K6" title="MSUALG_2:func.6">SubSort</a> <font color="Olive" title="b2">MA</font> holds <br/> for <font color="Olive" title="b4">B</font> being   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Olive" title="b2">MA</font>  st <font color="Olive" title="b4">B</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="b3">F</font></span><a href="closure2.html#K5" title="CLOSURE2:func.5">:|</a></span> holds <br/><font color="Olive" title="b4">B</font> is  <a href="msualg_2.html#V3" title="MSUALG_2:attr.3">opers_closed</a> </div></div>
