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<b>let </b><font color="Maroon" title="c1">T</font> be  <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t</font> holds <br/>( <font color="Olive" title="b2">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Olive" title="b1">t</font> &amp; <font color="Olive" title="b2">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t</font> )</span><br/><b>let </b><font color="Maroon" title="c2">t</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c2">t</font> holds <br/>( <font color="Olive" title="b1">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c2">t</font> &amp; <font color="Olive" title="b1">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font> )</span><br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c2">t</font> implies ( <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c2">t</font> &amp; <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font> ) )</span><br/>





<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c2">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c2">t</font> &amp; <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font> )</span><br/>

<b>hence </b><a NAME="E2:55"/>
<font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#R1" title="ABCMIZ_0:pred.1">is_applicable_to</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="ref" href="abcmiz_0.html#T24" target="_self" title="ABCMIZ_0:th.24">Th24</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font></span><br/>

<a NAME="E3:55"/><b>then </b>
( <font color="Maroon" title="c2">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> &amp; <font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">t</font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E1:55"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="abcmiz_0.html#T21" target="_self" title="ABCMIZ_0:th.21">Th21</a>, <a class="ref" href="abcmiz_0.html#T24" target="_self" title="ABCMIZ_0:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
<font color="Maroon" title="c3">a</font> <a href="abcmiz_0.html#K5" title="ABCMIZ_0:func.5">ast</a> <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D3" title="YELLOW_0:def.3">YELLOW_0:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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