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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E59">Def31</font></span>   defines <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> <a onclick="hs(this)" href="javascript:()">ABCMIZ_0:def 31 : <br/></a><span> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <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>   non  <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a>   <a href="abcmiz_0.html#L3" title="ABCMIZ_0:struct.3">TAS-structure</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="alg_1.html#NM1" title="ALG_1:NM.1">Relation</a> of <font color="Olive" title="b1">T</font> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  iff  for <font color="Olive" title="b3">t1</font>, <font color="Olive" title="b4">t2</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Olive" title="b1">T</font> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">t1</font>,<font color="Olive" title="b4">t2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> iff  ex <font color="Olive" title="b5">a</font> being   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Olive" title="b1">T</font> st <br/>(  not <font color="Olive" title="b5">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b4">t2</font> &amp; <font color="Olive" title="b5">a</font> <a href="abcmiz_0.html#R4" title="ABCMIZ_0:pred.4">is_properly_applicable_to</a> <font color="Olive" title="b4">t2</font> &amp; <font color="Olive" title="b5">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Olive" title="b4">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">t1</font> ) ) );<br/></span></div>
