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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> ] means for <font color="Olive">b<sub>1</sub></font> being  <a href="substut1.html#NM1">CQC_Substitution</a>ex <font color="Olive">b<sub>2</sub></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">b<sub>2</sub></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">b<sub>2</sub></font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> );<br/>
<a NAME="E1:13"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></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">b<sub>3</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a><br/>for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">b<sub>4</sub></font><br/>for <font color="Olive">b<sub>6</sub></font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">b<sub>4</sub></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">b<sub>6</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">b<sub>5</sub></font>] &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K10">'not'</a> <font color="Olive">b<sub>1</sub></font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">b<sub>2</sub></font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <font color="Maroon">S<sub>1</sub></font>[ <a href="cqc_lang.html#K15">All</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font>] ) )
 
<b>by </b><i><a class="ref" href="substut2.html#T1" target="_self">Th1</a>, <a class="ref" href="substut2.html#T2" target="_self">Th2</a>, <a class="ref" href="substut2.html#T4" target="_self">Th4</a>, <a class="ref" href="substut2.html#T5" target="_self">Th5</a>, <a class="ref" href="substut2.html#T11" target="_self">Th11</a></i>;<br/>
<b>thus </b><a NAME="E2:13"/>
for <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="cqc_lang.html#S1">CQC_LANG:sch 1</a>(<a class="txt" href="substut2.html#E1:13"><i><font color="Green">E13</font></i></a>);</i><br/>


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