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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: OSAFREE:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="osalg_4.html#V2" title="OSALG_4:attr.2">locally_directed</a>  <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a><br/>  for <font color="Olive" title="b2">X</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="struct_0.html#NM8" title="STRUCT_0:NM.8">ManySortedSet</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">C</font> being   <a href="osalg_4.html#NM5" title="OSALG_4:NM.5">Component</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="osalg_4.html#K5" title="OSALG_4:func.5">CompClass</a> (<span class="p1">(<span class="default"><a href="osafree.html#K20" title="OSAFREE:func.20">PTCongruence</a> <font color="Olive" title="b2">X</font></span>)</span>,<font color="Olive" title="b3">C</font>) iff  ex <font color="Olive" title="b6">s1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font> st <br/>( <font color="Olive" title="b6">s1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">C</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b6">s1</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="osafree.html#K19" title="OSAFREE:func.19">PTClasses</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">y</font> ) )</div></div>
