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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>

<b>thus </b><a NAME="E1:59"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  implies  <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:59_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 ;<br/>

<a NAME="E2:59_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:59_1"/>
 <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 <b>by </b><i><a class="txt" href="lukasi_1.html#E1:59_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="cqc_the1.html#T82">CQC_THE1:82</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:59"/><i><font color="Green">E53</font></i>: 
 <a href="cqc_lang.html#K10">'not'</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 ;<br/>

<a NAME="E3:59"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T25" target="_self">Th25</a></i>;<br/>
<b>hence </b><a NAME="E4:59"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 <b>by </b><i><a class="txt" href="lukasi_1.html#E2:59"><i><font color="Green">E53</font></i></a>, <a class="ref" href="cqc_the1.html#T82">CQC_THE1:82</a></i>;<br/>


</div>
