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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: ABCMIZ_0:51</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>   <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a>   <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> <br/>  for <font color="Olive" title="b2">t</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b3">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of  the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Olive" title="b1">T</font>  st <font color="Olive" title="b3">A</font> <a href="abcmiz_0.html#R2" title="ABCMIZ_0:pred.2">is_applicable_to</a> <font color="Olive" title="b2">t</font> holds <br/><font color="Olive" title="b3">A</font> <a href="abcmiz_0.html#K6" title="ABCMIZ_0:func.6">ast</a> <font color="Olive" title="b2">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K4" title="ABCMIZ_0:func.4">types</a> <font color="Olive" title="b3">A</font></div></div>
