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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: WAYBEL16:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>   <a href="waybel_8.html#V2" title="WAYBEL_8:attr.2">algebraic</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st  not <font color="Olive" title="b3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">x</font> holds <br/> ex <font color="Olive" title="b4">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font> st <br/>( <font color="Olive" title="b4">p</font> is  <a href="waybel16.html#V1" title="WAYBEL16:attr.1">completely-irreducible</a>  &amp; <font color="Olive" title="b2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">p</font> &amp;  not <font color="Olive" title="b3">y</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">p</font> )</div></div>
