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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E60">Th43</font></span>: <a NAME="T43"><span class="comment"><font color="firebrick">:: OSAFREE:43</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="osalg_1.html#V8" title="OSALG_1:attr.8">monotone</a>   <a href="osalg_1.html#V10" title="OSALG_1:attr.10">regular</a>   <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">t1</font> being    <a href="dtconstr.html#M1" title="DTCONSTR:mode.1">Element</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</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> holds  <span class="p1">(<span class="default"><a href="osafree.html#K29" title="OSAFREE:func.29">PTMin</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="osafree.html#K29" title="OSAFREE:func.29">PTMin</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="osafree.html#K29" title="OSAFREE:func.29">PTMin</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">t1</font></div></div>
