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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: WAYBEL_6:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/>  for <font color="Olive" title="b2">l</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b2">l</font> is  <a href="waybel_6.html#V5" title="WAYBEL_6:attr.5">prime</a>  iff  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">L</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"><font color="Olive" title="b3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>  st (  for <font color="Olive" title="b5">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  iff <font color="Olive" title="b5">p</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">l</font> ) ) holds <br/>( <font color="Olive" title="b4">f</font> is  <a href="waybel_0.html#V19" title="WAYBEL_0:attr.19">meet-preserving</a>  &amp; <font color="Olive" title="b4">f</font> is  <a href="waybel_0.html#V20" title="WAYBEL_0:attr.20">join-preserving</a>  ) )</div></div>
