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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th42</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: MSUALG_6:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</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">A</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">R</font> being   <a href="msualg_4.html#NM2" title="MSUALG_4:NM.2">ManySortedRelation</a> of <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b4">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">s</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="msualg_5.html#K3" title="MSUALG_5:func.3">EqCl</a> <font color="Olive" title="b3">R</font></span>)</span> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Olive" title="b4">s</font> iff <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Olive" title="b3">R</font> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Olive" title="b4">s</font> )</div></div>
