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<b>set </b><font color="Maroon">D</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ,  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">a<sub>1</sub></font>,  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">a<sub>1</sub></font>) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<a href="cqc_lang.html#K7">CQC-WFF</a>  =  <a href="cqc_sim1.html#K5" target="_self">ATOMIC</a> <font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>6</sub></font>(  <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="cqc_lang.html#K7">CQC-WFF</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<a href="cqc_lang.html#K7">CQC-WFF</a>  =  <a href="cqc_sim1.html#K1" target="_self">NEGATIVE</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>7</sub></font>(  <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="cqc_lang.html#K7">CQC-WFF</a> ,  <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="cqc_lang.html#K7">CQC-WFF</a> ,   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<a href="cqc_lang.html#K7">CQC-WFF</a>  =  <a href="cqc_sim1.html#K2" target="_self">CON</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K6" target="_self">QuantNbr</a> <font color="Maroon">a<sub>3</sub></font></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>8</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a> ,  <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="cqc_lang.html#K7">CQC-WFF</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<a href="cqc_lang.html#K7">CQC-WFF</a>  =  <a href="cqc_sim1.html#K3" target="_self">UNIVERSAL</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">V</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="funcop_1.html#K2">--&gt;</a> <a href="cqc_lang.html#K9">VERUM</a>  as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="cqc_lang.html#K7">CQC-WFF</a>  <b>by </b><i><a class="ref" href="funcop_1.html#T58">FUNCOP_1:58</a></i>;<br/>
<b>reconsider </b><font color="Maroon">V</font> = <font color="Maroon">V</font> as    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<a href="cqc_lang.html#K7">CQC-WFF</a>  <b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> , <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<a href="cqc_lang.html#K7">CQC-WFF</a> <b> such that </b><br/><a NAME="E4:27_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <a href="cqc_lang.html#K9">VERUM</a>  <a href="funct_2.html#R2">=</a> <font color="Maroon">V</font>
 <b>and </b><br/><a NAME="E5:27_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">l</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  <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">l</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">k</font>,<font color="Olive">P</font>,<font color="Olive">l</font>)
 <b>and </b><br/><a NAME="E6:27_1_1"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">r</font>, <font color="Olive">s</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="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/> ( <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Olive">r</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>6</sub></font>(<font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">r</font>,<font color="Olive">r</font>) &amp; <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">r</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">s</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>7</sub></font>(<font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">r</font>,<font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">s</font>,<font color="Olive">r</font>,<font color="Olive">s</font>) &amp; <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Olive">x</font>,<font color="Olive">r</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>8</sub></font>(<font color="Olive">x</font>,<font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">r</font>,<font color="Olive">r</font>) )
 <b>from </b><i><a class="ref" href="cqc_sim1.html#S2" target="_self">CQC_SIM1:sch 2</a>();<br/></i>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E7:27_1_1"/>
( <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <a href="cqc_lang.html#K9">VERUM</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="numbers.html#K5">NAT</a> ,<span class="p2">(<span class="default"><a href="fraenkel.html#K1">Funcs</a> <a href="qc_lang1.html#K2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="funcop_1.html#K2">--&gt;</a> <a href="cqc_lang.html#K9">VERUM</a>  &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">l</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  <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">P</font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">l</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="cqc_sim1.html#K5" target="_self">ATOMIC</a> <font color="Olive">P</font>,<font color="Olive">l</font> ) &amp; ( for <font color="Olive">r</font>, <font color="Olive">s</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="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/> ( <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Olive">r</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="cqc_sim1.html#K1" target="_self">NEGATIVE</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">r</font></span>)</span> &amp; <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">r</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">s</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="cqc_sim1.html#K2" target="_self">CON</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">r</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K6" target="_self">QuantNbr</a> <font color="Olive">r</font></span>)</span> &amp; <font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Olive">x</font>,<font color="Olive">r</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="cqc_sim1.html#K3" target="_self">UNIVERSAL</a> <font color="Olive">x</font>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">r</font></span>)</span> ) ) )
 <b>by </b><i>, , </i>;<br/>


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