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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th33</font></span>: <a NAME="T33"><span class="comment"><font color="firebrick">:: WAYBEL27:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>  ex <font color="Olive" title="b2">F</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="waybel27.html#K2" title="WAYBEL27:func.2">UPS</a> (<font color="Olive" title="b1">S</font>,<span class="p2">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Olive" title="b1">S</font></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b2">F</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>  &amp; (  for <font color="Olive" title="b3">f</font> being   <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">S</font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> holds  <font color="Olive" title="b2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )</div></div>
