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<span class="kw">deffunc </span><font color="Maroon">H<sub>5</sub></font>(   <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> ,  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of $1,  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of $1) <span class="kw">-&gt; </span>   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  =  <a href="cqc_sim1.html#K5" title="CQC_SIM1:func.5">ATOMIC</a> $2,$3;<br/>
<span class="kw">set </span><font color="Maroon" title="c1">D</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>6</sub></font>(  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  =  <a href="cqc_sim1.html#K1" title="CQC_SIM1:func.1">NEGATIVE</a> $1;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>7</sub></font>(  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,   <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 href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  =  <a href="cqc_sim1.html#K2" title="CQC_SIM1:func.2">CON</a> $1,$2,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K6" title="CQC_SIM1:func.6">QuantNbr</a> $3</span>)</span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>8</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <span class="kw">-&gt; </span>   <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  =  <a href="cqc_sim1.html#K3" title="CQC_SIM1:func.3">UNIVERSAL</a> $1,$2;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">V</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  ;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">F</font>, <font color="Maroon" title="c4">G</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ,<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p3">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  &amp; ( for <font color="Olive" title="b1">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="b2">l</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> holds  <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">l</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K5" title="CQC_SIM1:func.5">ATOMIC</a> <font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">l</font> ) &amp; ( for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  holds <br/> ( <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K1" title="CQC_SIM1:func.1">NEGATIVE</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font></span>)</span> &amp; <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K2" title="CQC_SIM1:func.2">CON</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b2">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K6" title="CQC_SIM1:func.6">QuantNbr</a> <font color="Olive" title="b1">r</font></span>)</span> &amp; <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><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">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K3" title="CQC_SIM1:func.3">UNIVERSAL</a> <font color="Olive" title="b3">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font></span>)</span> ) ) &amp; <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  &amp; ( for <font color="Olive" title="b1">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="b2">l</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> holds  <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">l</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K5" title="CQC_SIM1:func.5">ATOMIC</a> <font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">l</font> ) &amp; ( for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  holds <br/> ( <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K1" title="CQC_SIM1:func.1">NEGATIVE</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font></span>)</span> &amp; <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K2" title="CQC_SIM1:func.2">CON</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b2">s</font></span>)</span>,<span class="p1">(<span class="default"><a href="cqc_sim1.html#K6" title="CQC_SIM1:func.6">QuantNbr</a> <font color="Olive" title="b1">r</font></span>)</span> &amp; <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><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">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="cqc_sim1.html#K3" title="CQC_SIM1:func.3">UNIVERSAL</a> <font color="Olive" title="b3">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font></span>)</span> ) ) implies <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:26_1_2"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> 
 <span class="kw">and </span><br/><a NAME="E3:26_1_2"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
for <font color="Olive" title="b1">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="b2">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> holds  <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">ll</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b1">k</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">ll</font>)
 <span class="kw">and </span><br/><a NAME="E4:26_1_2"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  holds <br/> ( <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>6</sub></font>(<font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font>,<font color="Olive" title="b1">r</font>) &amp; <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>7</sub></font>(<font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font>,<font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b2">s</font>,<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">s</font>) &amp; <font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><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">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>8</sub></font>(<font color="Olive" title="b3">x</font>,<font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font>,<font color="Olive" title="b1">r</font>) )
 <span class="kw">and </span><br/><a NAME="E5:26_1_2"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> ,<a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a> 
 <span class="kw">and </span><br/><a NAME="E6:26_1_2"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
for <font color="Olive" title="b1">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="b2">ll</font> being  <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Olive" title="b1">k</font><br/> for <font color="Olive" title="b3">P</font> being  <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Olive" title="b1">k</font> holds  <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K5" title="CQC_LANG:func.5">!</a> <font color="Olive" title="b2">ll</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive" title="b1">k</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">ll</font>)
 <span class="kw">and </span><br/><a NAME="E7:26_1_2"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K2" title="QC_LANG1:func.2">bound_QC-variables</a>  holds <br/> ( <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'not'</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>6</sub></font>(<font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font>,<font color="Olive" title="b1">r</font>) &amp; <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">r</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">'&amp;'</a> <font color="Olive" title="b2">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>7</sub></font>(<font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font>,<font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b2">s</font>,<font color="Olive" title="b1">r</font>,<font color="Olive" title="b2">s</font>) &amp; <font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <span class="p1">(<span class="default"><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">r</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">H<sub>8</sub></font>(<font color="Olive" title="b3">x</font>,<font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <font color="Olive" title="b1">r</font>,<font color="Olive" title="b1">r</font>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">G</font></span><br/>

<a NAME="E8:26_1_2"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c4">G</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_2"><span class="lab"><font color="Green" title="E21">A7</font></span></a></span>;<br/>
<a NAME="E9:26_1_2"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<font color="Maroon" title="c3">F</font> <a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">.</a> <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">VERUM</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1_2"><span class="lab"><font color="Green" title="E18">A4</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E10:26_1_2"/>
<font color="Maroon" title="c3">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">G</font>
 <span class="kw">from</span> <span class="lab"><a class="ref" href="cqc_sim1.html#S3" target="_self" title="CQC_SIM1:sch.3">CQC_SIM1:sch 3</a>(<a class="txt" href="#E9:26_1_2"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E3:26_1_2"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E4:26_1_2"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:26_1_2"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E6:26_1_2"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E7:26_1_2"><span class="lab"><font color="Green" title="E23">A9</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/>


</div>
