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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"> (  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp;  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp;  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  &amp; (  for <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Maroon" title="c1">A</font> holds <br/> (  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) ) ) )</span><br/>

<a NAME="E1:57"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E2:57"/>
(  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp;  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp;  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp;  not  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T18" target="_self" onmouseover="rs('qc_lang1/T18')" onmouseout="rh()">Th18</a>, <a class="ref" href="qc_lang1.html#T19" target="_self" onmouseover="rs('qc_lang1/T19')" onmouseout="rh()">Th19</a></span>; <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> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Maroon" title="c1">A</font> holds <br/> (  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp; <font color="Olive" title="b1">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-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"> (  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) )</span><br/>

<a NAME="E3:57"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T18" target="_self" onmouseover="rs('qc_lang1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E4:57"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T18" target="_self" onmouseover="rs('qc_lang1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E5:57"/>
( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T18" target="_self" onmouseover="rs('qc_lang1/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:57"/>
(  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp;  not <!--HUMANRECFAILED-->( <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  &amp; <font color="Maroon" title="c2">p</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:57"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:57"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="qc_lang1.html#T19" target="_self" onmouseover="rs('qc_lang1/T19')" onmouseout="rh()">Th19</a></span>; <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/>


</div>
