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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <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> ] <span class="kw">means </span>for <font color="Olive" title="b1">Sub</font> being  <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>  ex <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>  st <br/>( <font color="Olive" title="b2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b2">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="b1">Sub</font> );<br/>
<a NAME="E1:13"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <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/> 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">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="b5">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b4">k</font><br/> for <font color="Olive" title="b6">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b4">k</font> holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> ] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b6">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b5">ll</font>] &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">p</font>] ) &amp; ( <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>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b2">q</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b1">p</font>] ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut2.html#T1" target="_self" title="SUBSTUT2:th.1">Th1</a>, <a class="ref" href="substut2.html#T2" target="_self" title="SUBSTUT2:th.2">Th2</a>, <a class="ref" href="substut2.html#T4" target="_self" title="SUBSTUT2:th.4">Th4</a>, <a class="ref" href="substut2.html#T5" target="_self" title="SUBSTUT2:th.5">Th5</a>, <a class="ref" href="substut2.html#T11" target="_self" title="SUBSTUT2:th.11">Th11</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:13"/>
for <font color="Olive" title="b1">p</font> being   <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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="cqc_lang.html#S1" title="CQC_LANG:sch.1">CQC_LANG:sch 1</a>(<a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E13">A1</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/>


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