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<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="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ] <span class="kw">means </span> <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> $1 is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ;<br/>
<a NAME="E1:97_1_1"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">S9</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="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</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="substut1.html#K17" title="SUBSTUT1:func.17">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="substut1.html#K20" title="SUBSTUT1:func.20">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">S9</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">S9</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">S9</font>] ) &amp; ( <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</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="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Olive" title="b3">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Olive" title="b4">SQ</font>] ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T33" target="_self" title="SUBSTUT1:th.33">Th33</a>, <a class="ref" href="substut1.html#T35" target="_self" title="SUBSTUT1:th.35">Th35</a>, <a class="ref" href="substut1.html#T36" target="_self" title="SUBSTUT1:th.36">Th36</a>, <a class="ref" href="substut1.html#T37" target="_self" title="SUBSTUT1:th.37">Th37</a>, <a class="ref" href="substut1.html#T38" target="_self" title="SUBSTUT1:th.38">Th38</a></span>;<br/>
<a NAME="E2:97_1_1"/>
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>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="substut1.html#S5" target="_self" title="SUBSTUT1:sch.5">SUBSTUT1:sch 5</a>(<a class="txt" href="#E1:97_1_1"><span class="lab"><font color="Green" title="E57">A1</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E3:97_1_1"/>
 <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c1">S</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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