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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th23</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: ORDERS_2:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a><br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">a</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Olive" title="b3">c</font> iff <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="orders_2.html#K2" title="ORDERS_2:func.2">LowerCone</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b3">c</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</div></div>
