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

<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#K8" title="QC_LANG1:func.8">QC-WFF</a> ] <span class="kw">means </span>( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a>  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="E1:54"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K11" title="QC_LANG1:func.11">VERUM</a> ]
 
;<br/>
<a NAME="E2:54"/><span class="lab"><font color="Green" title="E19">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#K8" title="QC_LANG1:func.8">QC-WFF</a>   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#K12" title="QC_LANG1:func.12">'not'</a> <font color="Olive" title="b1">p</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D18" target="_self" title="QC_LANG1:def.18">Def18</a></span>;<br/>
<a NAME="E3:54"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
for <font color="Olive" title="b1">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a><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#K8" title="QC_LANG1:func.8">QC-WFF</a>   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#K14" title="QC_LANG1:func.14">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#D20" target="_self" title="QC_LANG1:def.20">Def20</a></span>;<br/>
<a NAME="E4:54"/><span class="lab"><font color="Green" title="E21">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#K8" title="QC_LANG1:func.8">QC-WFF</a>   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#K13" title="QC_LANG1:func.13">'&amp;'</a> <font color="Olive" title="b2">q</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D19" target="_self" title="QC_LANG1:def.19">Def19</a></span>;<br/>
<a NAME="E5:54"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">p</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">ll</font> being  <a href="qc_lang1.html#NM7" title="QC_LANG1:NM.7">QC-variable_list</a> of <font color="Olive" title="b1">k</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">p</font> <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">!</a> <font color="Olive" title="b3">ll</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D17" target="_self" title="QC_LANG1:def.17">Def17</a></span>;<br/>
<span class="kw">thus </span><a NAME="E6:54"/>
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#K8" title="QC_LANG1:func.8">QC-WFF</a>  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" title="QC_LANG1:sch.1">QC_LANG1:sch 1</a>(<a class="txt" href="#E5:54"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="txt" href="#E4:54"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E20">A3</font></span></a>);</span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
