<?xml version="1.0"?>
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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>





<a NAME="E1:47"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</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="procal_1.html#T40" target="_self">Th40</a></i>;<br/>
<a NAME="E2:47"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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#T34">LUKASI_1:34</a></i>;<br/>
<a NAME="E3:47"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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="procal_1.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E4:47"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="txt" href="procal_1.html#E2:47"><i><font color="Green">E32</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E5:47"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="qc_lang2.html#D3">QC_LANG2:def 3</a></i>;<br/>
<a NAME="E6:47"/>
<font color="Maroon">c<sub>3</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>3</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">LUKASI_1:27</a></i>;<br/>
<a NAME="E7:47"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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="txt" href="procal_1.html#E45"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<a NAME="E8:47"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="txt" href="procal_1.html#E5:47"><i><font color="Green">E33</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E9:47"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="procal_1.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E10:47"/><b>then </b><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="txt" href="procal_1.html#E8:47"><i><font color="Green">E34</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E11:47"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</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="procal_1.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E12:47"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</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#T31">LUKASI_1:31</a></i>;<br/>
<a NAME="E13:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</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="procal_1.html#E11:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="cqc_the1.html#T82">CQC_THE1:82</a></i>;<br/>
<a NAME="E14:47"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="txt" href="procal_1.html#E46"><i><font color="Green">Lemma30</font></i></a></i>;<br/>
<a NAME="E15:47"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></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="txt" href="procal_1.html#E10:47"><i><font color="Green">E35</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E16:47"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</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="procal_1.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E17:47"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</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#T31">LUKASI_1:31</a></i>;<br/>
<a NAME="E18:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</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="procal_1.html#E16:47"><i><font color="Green">E38</font></i></a>, <a class="ref" href="cqc_the1.html#T82">CQC_THE1:82</a></i>;<br/>
<a NAME="E19:47"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</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="txt" href="procal_1.html#E47"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E20:47"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</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="txt" href="procal_1.html#E15:47"><i><font color="Green">E37</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>


</div>
