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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> non <a href="abcmiz_0.html#V4" target="_self">void</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">v</font> be    <a href="finseq_1.html#M2">FinSequence</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="E1:81"/>
<font color="Maroon">v</font> <a href="abcmiz_0.html#R3" target="_self">is_applicable_to</a> <font color="Maroon">t</font>
 ;<br/>

<a NAME="E2:81"/><b>then </b>
( <font color="Maroon">v</font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">v</font> <a href="tarski.html#R1">c=</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="abcmiz_0.html#K8" target="_self">ast</a> <font color="Maroon">t</font></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:81"/>
for <font color="Olive">A</font> being  <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>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">v</font> holds <br/><font color="Olive">A</font> <a href="abcmiz_0.html#R2" target="_self">is_applicable_to</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>


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