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





<a NAME="E1:27"/><i><font color="Green">E18</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</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#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E2:27"/>
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</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">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:27"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</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> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</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#E16"><i><font color="Green">Lemma21</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E4:27"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</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> <font color="Maroon">r</font></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">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E5:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">r</font></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">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</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">p</font></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">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</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#T8">LUKASI_1:8</a></i>;<br/>
<a NAME="E6:27"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</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> <font color="Maroon">p</font></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">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</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#E17"><i><font color="Green">Lemma22</font></i></a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E7:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</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> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</font></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="E8:27"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></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">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></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">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</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#T13">LUKASI_1:13</a></i>;<br/>
<a NAME="E9:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</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">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</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">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</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">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</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="lukasi_1.html#T11">LUKASI_1:11</a></i>;<br/>
<a NAME="E10:27"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">p</font></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">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">q</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">p</font></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">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</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#E6:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="cqc_the1.html#T82">CQC_THE1:82</a></i>;<br/>
<a NAME="E11:27"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</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> <font color="Maroon">p</font></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">q</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">r</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#T15" target="_self">Th15</a>, <a class="ref" href="lukasi_1.html#T3">LUKASI_1:3</a></i>;<br/>
<a NAME="E12:27"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</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> <font color="Maroon">p</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E13:27"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">q</font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K4">TAUT</a> 
 <b>by </b><i/>;<br/>


</div>
