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

<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font>, <font color="Maroon" title="c3">r</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> </span><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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="procal_1.html#T40" target="_self" title="PROCAL_1:th.40">Th40</a></i>;<br/>
<a NAME="E2:47"/><b>then </b><i><font color="Green" title="E32">A1</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T34" title="LUKASI_1:th.34">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#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="procal_1.html#T7" target="_self" title="PROCAL_1:th.7">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#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="#E2:47"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="lukasi_1.html#T3" title="LUKASI_1:th.3">LUKASI_1:3</a></i>;<br/>
<a NAME="E5:47"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D3" title="QC_LANG2:def.3">QC_LANG2:def 3</a></i>;<br/>
<a NAME="E6:47"/>
<font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T27" title="LUKASI_1:th.27">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" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="procal_1.html#E45"><i><font color="Green" title="E29">Lm5</font></i></a></i>;<br/>
<a NAME="E8:47"/><b>then </b><i><font color="Green" title="E34">A3</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="#E5:47"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="lukasi_1.html#T3" title="LUKASI_1:th.3">LUKASI_1:3</a></i>;<br/>
<a NAME="E9:47"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'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#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="procal_1.html#T17" target="_self" title="PROCAL_1:th.17">Th17</a></i>;<br/>
<a NAME="E10:47"/><b>then </b><i><font color="Green" title="E35">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="#E8:47"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="lukasi_1.html#T3" title="LUKASI_1:th.3">LUKASI_1:3</a></i>;<br/>
<a NAME="E11:47"/><i><font color="Green" title="E36">A5</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="procal_1.html#T17" target="_self" title="PROCAL_1:th.17">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#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T31" title="LUKASI_1:th.31">LUKASI_1:31</a></i>;<br/>
<a NAME="E13:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="#E11:47"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="cqc_the1.html#T82" title="CQC_THE1:th.82">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#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="procal_1.html#E46"><i><font color="Green" title="E30">Lm6</font></i></a></i>;<br/>
<a NAME="E15:47"/><b>then </b><i><font color="Green" title="E37">A6</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="#E10:47"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="lukasi_1.html#T3" title="LUKASI_1:th.3">LUKASI_1:3</a></i>;<br/>
<a NAME="E16:47"/><i><font color="Green" title="E38">A7</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="procal_1.html#T17" target="_self" title="PROCAL_1:th.17">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#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="ref" href="lukasi_1.html#T31" title="LUKASI_1:th.31">LUKASI_1:31</a></i>;<br/>
<a NAME="E18:47"/><b>then </b>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="#E16:47"><i><font color="Green" title="E38">A7</font></i></a>, <a class="ref" href="cqc_the1.html#T82" title="CQC_THE1:th.82">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" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 
<b>by </b><i><a class="txt" href="procal_1.html#E47"><i><font color="Green" title="E31">Lm7</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" title="c1">p</font> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'or'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> 
 <b>by </b><i><a class="txt" href="#E15:47"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="lukasi_1.html#T3" title="LUKASI_1:th.3">LUKASI_1:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
