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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ] <b>means </b>for <font color="Olive">Sub</font> being  <a href="substut1.html#NM1">CQC_Substitution</a>  ex <font color="Olive">S</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  st <br/>( <font color="Olive">S</font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">S</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Olive">Sub</font> );<br/>
<a NAME="E1:13"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <br/> for <font color="Olive">x</font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a><br/> for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">ll</font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">k</font><br/> for <font color="Olive">P</font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">k</font> holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K9">VERUM</a> ] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">ll</font>] &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K10">'not'</a> <font color="Olive">p</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">q</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">q</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K15">All</a> <font color="Olive">x</font>,<font color="Olive">p</font>] ) )
 
<b>by </b><i>, , , , </i>;<br/>
<b>thus </b><a NAME="E2:13"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>]
 <b>from </b><i><a class="ref" href="cqc_lang.html#S1">CQC_LANG:sch 1</a>();</i><br/>


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