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<b>set </b><font color="Maroon">c<sub>1</sub></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="nat_1.html#NM1">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">c<sub>2</sub></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>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <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> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:27_1_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></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> 
 <b>and </b><br/><a NAME="E3:27_1_2"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">b<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">b<sub>1</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 <b>and </b><br/><a NAME="E4:27_1_2"/><i><font color="Green">E21</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="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/>( <font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>6</sub></font>(<font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font>) &amp; <font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>7</sub></font>(<font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) &amp; <font color="Maroon">c<sub>3</sub></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">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>8</sub></font>(<font color="Olive">b<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font>) )
 <b>and </b><br/><a NAME="E5:27_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>4</sub></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> 
 <b>and </b><br/><a NAME="E6:27_1_2"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">b<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">b<sub>1</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 <b>and </b><br/><a NAME="E7:27_1_2"/><i><font color="Green">E24</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="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/>( <font color="Maroon">c<sub>4</sub></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">b<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>6</sub></font>(<font color="Maroon">c<sub>4</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font>) &amp; <font color="Maroon">c<sub>4</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>7</sub></font>(<font color="Maroon">c<sub>4</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) &amp; <font color="Maroon">c<sub>4</sub></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">b<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>8</sub></font>(<font color="Olive">b<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="cqc_sim1.html#K7" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font>) )
 ;<br/>

<a NAME="E8:27_1_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:27_1_2"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E9:27_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E5:27_1_2"><i><font color="Green">E22</font></i></a></i>;<br/>
<b>thus </b><a NAME="E10:27_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>from </b><i><a class="ref" href="cqc_sim1.html#S3" target="_self">CQC_SIM1:sch 3</a>(<a class="txt" href="cqc_sim1.html#E8:27_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="cqc_sim1.html#E3:27_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="cqc_sim1.html#E4:27_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="cqc_sim1.html#E9:27_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="cqc_sim1.html#E6:27_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="cqc_sim1.html#E7:27_1_2"><i><font color="Green">E24</font></i></a>);</i><br/>


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