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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E61">Th67</font></span>: <a NAME="T67"><span class="comment"><font color="firebrick">:: ABCMIZ_0:67</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a>   <a href="abcmiz_0.html#V1" title="ABCMIZ_0:attr.1">Noetherian</a>   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#L3" title="ABCMIZ_0:struct.3">TAS-structure</a> <br/>  for <font color="Olive" title="b2">t1</font>, <font color="Olive" title="b3">t2</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b2">t1</font>,<font color="Olive" title="b3">t2</font> holds <br/><font color="Olive" title="b2">t1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b3">t2</font></div></div>
