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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="subset_1.html#NM2">Subset</a> of the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E1:87"/>
<font color="Maroon">a</font> <a href="abcmiz_0.html#R2" target="_self">is_applicable_to</a> <font color="Maroon">t</font>
 ;<br/>

<a NAME="E2:87"/><b>then </b>
<span class="p1">(<span class="default"><a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">a</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">t</font></span>)</span> is   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">T</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:87"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">a</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">a</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">t</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:87"/><b>then </b>
<font color="Maroon">a</font> <a href="abcmiz_0.html#K6" target="_self">ast</a> <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">a</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">t</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:87"/>
<font color="Maroon">a</font> <a href="abcmiz_0.html#K6" target="_self">ast</a> <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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