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<b>let </b><font color="Maroon">T</font> be  <a href="abcmiz_0.html#V8" target="_self">consistent</a>  <a href="abcmiz_0.html#L2" target="_self">TA-structure</a> ;<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="E1:44"/>
 <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">a</font> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:44"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E4:44"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon">t1</font> being   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E6:44"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t1</font> &amp; <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">t1</font> )
 <b>by </b><i>, </i>;<br/>
<a NAME="E7:44"/>
 ex <font color="Olive">t2</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">t2</font> &amp;  <a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Olive">t2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:44"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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