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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">J</font> be    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Maroon" title="c1">A</font>;<br/>



<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> ] <b>means </b>for <font color="Olive" title="b1">v</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> <font color="Maroon" title="c1">A</font> holds <br/> ( <font color="Maroon" title="c2">J</font>,<font color="Olive" title="b1">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a>  <a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> $1 iff <font color="Maroon" title="c2">J</font>,<font color="Olive" title="b1">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> <font color="Olive" title="b1">v</font>,$1</span>)</span> <a href="sublemma.html#R1" title="SUBLEMMA:pred.1">|=</a> $1 );<br/>
<a NAME="E1:109"/><i><font color="Green" title="E88">A1</font></i>: 
for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">S'</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <br/> for <font color="Olive" title="b3">x</font> being  <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a><br/> for <font color="Olive" title="b4">SQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span><br/> for <font color="Olive" title="b5">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="b6">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b5">k</font><br/> for <font color="Olive" title="b7">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b5">k</font><br/> for <font color="Olive" title="b8">e</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K1" title="SUBSTUT1:func.1">vSUB</a>  holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[ <a href="sublemma.html#K4" title="SUBLEMMA:func.4">Sub_P</a> <font color="Olive" title="b7">P</font>,<font color="Olive" title="b6">ll</font>,<font color="Olive" title="b8">e</font>] &amp; ( <font color="Olive" title="b1">S</font> is <a href="substut1.html#V2" title="SUBSTUT1:attr.2">Sub_VERUM</a> implies <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">S</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">S</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="sublemma.html#K6" title="SUBLEMMA:func.6">Sub_not</a> <font color="Olive" title="b1">S</font>] ) &amp; ( <font color="Olive" title="b1">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">S'</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">S</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">S'</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="sublemma.html#K7" title="SUBLEMMA:func.7">CQCSub_&amp;</a> <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">S'</font>] ) &amp; ( <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">S</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Olive" title="b4">SQ</font>] ) )
 
<b>by </b><i><a class="ref" href="sublemma.html#T4" target="_self" title="SUBLEMMA:th.4">Th4</a>, <a class="ref" href="sublemma.html#T16" target="_self" title="SUBLEMMA:th.16">Th16</a>, <a class="ref" href="sublemma.html#T20" target="_self" title="SUBLEMMA:th.20">Th20</a>, <a class="ref" href="sublemma.html#T26" target="_self" title="SUBLEMMA:th.26">Th26</a>, <a class="ref" href="sublemma.html#T92" target="_self" title="SUBLEMMA:th.92">Th92</a></i>;<br/>
<b>thus </b><a NAME="E2:109"/>
for <font color="Olive" title="b1">S</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">S</font>]
 <b>from </b><i><a class="ref" href="sublemma.html#S1" target="_self" title="SUBLEMMA:sch.1">SUBLEMMA:sch 1</a>(<a class="txt" href="sublemma.html#E1:109"><i><font color="Green" title="E88">A1</font></i></a>);</i><br/>


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