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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: OSAFREE:30</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">s</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font> holds   <a href="osafree.html#K23" title="OSAFREE:func.23">OSFreeGen</a> (<font color="Olive" title="b3">s</font>,<font color="Olive" title="b2">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="osalg_4.html#K18" title="OSALG_4:func.18">OSNat_Hom</a> (<span class="p5">(<span class="default"><a href="osafree.html#K8" title="OSAFREE:func.8">ParsedTermsOSA</a> <font color="Olive" title="b2">X</font></span>)</span>,<span class="p5">(<span class="default"><a href="osafree.html#K15" title="OSAFREE:func.15">LCongruence</a> <font color="Olive" title="b2">X</font></span>)</span>)</span>)</span> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Olive" title="b3">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="trees_4.html#K2" title="TREES_4:func.2">root-tree</a> <font color="Olive" title="b4">t</font></span>)</span></span>)</span> where <font color="Olive" title="b4">t</font> is   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <span class="p1">(<span class="default"><a href="osafree.html#K2" title="OSAFREE:func.2">DTConOSA</a> <font color="Olive" title="b2">X</font></span>)</span> : ( <font color="Olive" title="b4">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <span class="p1">(<span class="default"><a href="osafree.html#K2" title="OSAFREE:func.2">DTConOSA</a> <font color="Olive" title="b2">X</font></span>)</span> &amp; <font color="Olive" title="b4">t</font> <a href="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> ) </span> } </span> </div></div>
