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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">F</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/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> or <font color="Olive" title="b1">F</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  or <font color="Olive" title="b1">F</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  or <font color="Olive" title="b1">F</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  or <font color="Olive" title="b1">F</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  )</span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <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>] <span class="kw">means </span>( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font> or $1 is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  or $1 is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  or $1 is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  or $1 is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  );<br/>
<a NAME="E1:39"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Maroon" title="c1">A</font>]
 
;<br/>
<a NAME="E2:39"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
 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>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'not'</a> <font color="Olive" title="b1">p</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D19" target="_self" onmouseover="rs('qc_lang1/D19')" onmouseout="rh()">Def19</a></span>;<br/>
<a NAME="E3:39"/><span class="lab"><font color="Green" title="E22">A3</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">A</font><br/>  for <font color="Olive" title="b2">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>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">p</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">All</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">p</font>)]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D21" target="_self" onmouseover="rs('qc_lang1/D21')" onmouseout="rh()">Def21</a></span>;<br/>
<a NAME="E4:39"/><span class="lab"><font color="Green" title="E23">A4</font></span>: 
 for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">q</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font> <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">'&amp;'</a> <font color="Olive" title="b2">q</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D20" target="_self" onmouseover="rs('qc_lang1/D20')" onmouseout="rh()">Def20</a></span>;<br/>
<a NAME="E5:39"/><span class="lab"><font color="Green" title="E24">A5</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">p</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">A</font><br/>  for <font color="Olive" title="b3">ll</font> being   <a href="qc_lang1.html#NM9" title="QC_LANG1:NM.9">QC-variable_list</a> of <font color="Olive" title="b1">k</font>,<font color="Maroon" title="c1">A</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">p</font> <a href="qc_lang1.html#K10" title="QC_LANG1:func.10">!</a> <font color="Olive" title="b3">ll</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D18" target="_self" onmouseover="rs('qc_lang1/D18')" onmouseout="rh()">Def18</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:39"/>
 for <font color="Olive" title="b1">F</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  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">F</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="qc_lang1.html#S1" target="_self" onmouseover="rs('qc_lang1/S1')" onmouseout="rh()">QC_LANG1:sch 1</a>(<a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="txt" href="#E4:39"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E22">A3</font></span></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/>


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