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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: MSUALG_8:16</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">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b4">e</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">i</font></span>)</span>  ex <font color="Olive" title="b5">E</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 <br/>( <font color="Olive" title="b5">E</font> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Olive" title="b3">i</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">e</font> &amp; (  for <font color="Olive" title="b6">j</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b6">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">i</font> holds <br/><font color="Olive" title="b5">E</font> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Olive" title="b6">j</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">j</font></span>)</span> ) )</div></div>
