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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Olive" title="b2">q</font></span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> is  <a href="cqc_the1.html#V2" title="CQC_THE1:attr.2">valid</a> </span><br/>





<a NAME="E1:6"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lukasi_1.html#T25" onmouseover="rs('lukasi_1/T25')" onmouseout="rh()">LUKASI_1:25</a></span>;<br/>
<a NAME="E2:6"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> <font color="Maroon" title="c1">A</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> <font color="Maroon" title="c1">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="procal_1.html#T14" onmouseover="rs('procal_1/T14')" onmouseout="rh()">PROCAL_1:14</a>, <a class="ref" href="procal_1.html#T48" onmouseover="rs('procal_1/T48')" onmouseout="rh()">PROCAL_1:48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_the1.html#K4" title="CQC_THE1:func.4">TAUT</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lukasi_1.html#T3" onmouseover="rs('lukasi_1/T3')" onmouseout="rh()">LUKASI_1:3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cqc_the1.html#D10" onmouseover="rs('cqc_the1/D10')" onmouseout="rh()">CQC_THE1:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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