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<b>let </b><font color="Maroon">T</font> be  <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1">with_suprema</a> <a href="abcmiz_0.html#V1" target="_self">Noetherian</a> <a href="abcmiz_0.html#V9" target="_self">adj-structured</a>  <a href="abcmiz_0.html#L2" target="_self">TA-structure</a> ;<br/><b>let </b><font color="Maroon">t</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:55"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t</font>
 ;<br/>

<b>hence </b><a NAME="E2:55"/>
<font color="Maroon">a</font> <a href="abcmiz_0.html#R1" target="_self">is_applicable_to</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>

<a NAME="E3:55"/><b>then </b>
( <font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font> &amp; <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E4:55"/>
<font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D3">YELLOW_0:def 3</a></i>;<br/>


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