<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:17"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="abcmiz_0.html#L1" target="_self">AdjectiveStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:17"/><i><font color="Green">E8</font></i>: 
the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K2">}</a></span>
 <b>and </b><br/><a NAME="E3:17"/><i><font color="Green">E9</font></i>: 
the <a href="abcmiz_0.html#U2" target="_self">non-op</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E4:17"/><i><font color="Green">E10</font></i>: 
the <a href="abcmiz_0.html#U2" target="_self">non-op</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>thus </b><a NAME="E5:17"/>
not the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E2:17"><i><font color="Green">E8</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D4" target="_self">ABCMIZ_0:def 4</a><br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D6" target="_self">ABCMIZ_0:def 6</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><a NAME="E1:17_1"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E2:17"><i><font color="Green">E8</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>thus </b> <a href="abcmiz_0.html#K1" target="_self">non-</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
the <a href="abcmiz_0.html#U2" target="_self">non-op</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="abcmiz_0.html#E3:17"><i><font color="Green">E9</font></i></a>, <a class="txt" href="abcmiz_0.html#E4:17"><i><font color="Green">E10</font></i></a>, <a class="txt" href="abcmiz_0.html#E1:17_1"><i><font color="Green">E11</font></i></a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">c<sub>3</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="abcmiz_0.html#D7" target="_self">ABCMIZ_0:def 7</a><br/>

<a NAME="E7:17"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E2:17"><i><font color="Green">E8</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>assume </b><a NAME="E8:17"/>
 <a href="abcmiz_0.html#K1" target="_self">non-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>hence </b><a NAME="E9:17"/>
contradiction
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E1:17"><i><font color="Green">E7</font></i></a>, <a class="txt" href="abcmiz_0.html#E3:17"><i><font color="Green">E9</font></i></a>, <a class="txt" href="abcmiz_0.html#E4:17"><i><font color="Green">E10</font></i></a>, <a class="txt" href="abcmiz_0.html#E7:17"><i><font color="Green">E11</font></i></a></i>;<br/>


</div>
