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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#L2" target="_self">TA-structure</a> ;<br/>

<b>assume </b><a NAME="E1:32"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">t1</font>, <font color="Olive">t2</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> holds   <a href="abcmiz_0.html#K2" target="_self">adjs</a> <span class="p1">(<span class="default"><font color="Olive">t1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">t2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Olive">t1</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Olive">t2</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D11" target="_self">ABCMIZ_0:def 11</a><br/>

<b>let </b><font color="Maroon">t1</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>, <font color="Maroon">t2</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><a NAME="E2:32"/>
<font color="Maroon">t1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t2</font>
 ;<br/>

<a NAME="E3:32"/><b>then </b>
<font color="Maroon">t1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">t2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t2</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>;<br/>
<a NAME="E4:32"/><b>then </b>
 <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t1</font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:32"/>
 <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t2</font> <a href="tarski.html#R1">c=</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">t1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>


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