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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: YELLOW_2:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> holds <br/> (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> , <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <font color="Olive" title="b1">L</font></span>)</span> &amp;  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<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="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <font color="Olive" title="b1">L</font></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b1">L</font> )</div></div>
