<?xml version="1.0"?>
<div class="add">

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() = <font color="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> $1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> $1</span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> $1</span>)</span>);<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() = <font color="Maroon">F<sub>5</sub></font>($1,<span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> $2</span>)</span>);<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() = <font color="Maroon">F<sub>6</sub></font>($1,$2,<span class="p1">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> $3</span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> $3</span>)</span>);<br/>
<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() = <font color="Maroon">F<sub>7</sub></font>(<span class="p1">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> $2</span>)</span>,$1,<span class="p1">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> $2</span>)</span>);<br/>
<b>consider </b><font color="Maroon" title="c1">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()<b> such that </b><br/><a NAME="E2:11_1"/><i><font color="Green" title="E7">A1</font></i>: 
( <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; ( for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  holds <br/> ( ( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a> implies <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">p</font>) ) &amp; ( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a> implies <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Olive" title="b1">p</font>) ) &amp; ( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a> implies <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Olive" title="b1">p</font>) ) &amp; ( <font color="Olive" title="b1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> implies <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Olive" title="b1">p</font></span>)</span>,<font color="Olive" title="b1">p</font>) ) ) ) )
 <b>from </b><i><a class="ref" href="cqc_sim1.html#S1" target="_self" title="CQC_SIM1:sch.1">CQC_SIM1:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon" title="c2">G</font> = <font color="Maroon" title="c1">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() <b>by </b><i><a class="ref" href="funct_2.html#T38" title="FUNCT_2:th.38">FUNCT_2:38</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">G</font>
;<br/>

<b>thus </b><a NAME="E4:11_1"/>
<font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>()
 <b>by </b><i><a class="txt" href="cqc_sim1.html#E2:11_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>

<b>thus </b><a NAME="E5:11_1"/>
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Olive" title="b2">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b1">k</font>,<font color="Olive" title="b3">P</font>,<font color="Olive" title="b2">l</font>)
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c4">l</font> be   <a href="cqc_lang.html#NM2" title="CQC_LANG:NM.2">CQC-variable_list</a> of <font color="Maroon" title="c3">k</font>;<br/><b>let </b><font color="Maroon" title="c5">P</font> be   <a href="qc_lang1.html#NM6" title="QC_LANG1:NM.6">QC-pred_symbol</a> of <font color="Maroon" title="c3">k</font>;<br/>





<a NAME="E1:11_1_1"/><i><font color="Green" title="E8">A2</font></i>: 
<font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c4">l</font> is <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D17" title="QC_LANG1:def.17">QC_LANG1:def 17</a></i>;<br/>
<a NAME="E2:11_1_1"/><b>then </b><i><font color="Green" title="E9">A3</font></i>: 
(  <a href="qc_lang1.html#K16" title="QC_LANG1:func.16">the_arguments_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c4">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">l</font> &amp;  <a href="qc_lang1.html#K15" title="QC_LANG1:func.15">the_pred_symbol_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c4">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> &amp;  <a href="qc_lang1.html#K6" title="QC_LANG1:func.6">the_arity_of</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T35" title="QC_LANG1:th.35">QC_LANG1:35</a>, <a class="ref" href="qc_lang1.html#D21" title="QC_LANG1:def.21">QC_LANG1:def 21</a>, <a class="ref" href="qc_lang1.html#D22" title="QC_LANG1:def.22">QC_LANG1:def 22</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c4">l</font></span>)</span> = 
<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="cqc_lang.html#K8" title="CQC_LANG:func.8">!</a> <font color="Maroon" title="c4">l</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">l</font>)
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:11_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="cqc_sim1.html#E1:11_1_1"><i><font color="Green" title="E8">A2</font></i></a>, <a class="txt" href="cqc_sim1.html#E2:11_1_1"><i><font color="Green" title="E9">A3</font></i></a></i>
;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c5">x</font> be    <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> ;<br/>





<b>set </b><font color="Maroon" title="c6">r'</font> = <font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">r</font>;<br/>
<b>set </b><font color="Maroon" title="c7">s'</font> = <font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font>;<br/>
<a NAME="E6:11_1"/><i><font color="Green" title="E8">A4</font></i>: 
( <font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">r</font> &amp; <font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<a NAME="E7:11_1"/><i><font color="Green" title="E9">A5</font></i>: 
 <a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c3">r</font> is <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D18" title="QC_LANG1:def.18">QC_LANG1:def 18</a></i>;<br/>
<a NAME="E8:11_1"/><b>then </b><i><font color="Green" title="E10">A6</font></i>: 
 <a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_argument_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D23" title="QC_LANG1:def.23">QC_LANG1:def 23</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span> = 
<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10" title="CQC_LANG:func.10">'not'</a> <font color="Maroon" title="c3">r</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">F<sub>5</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font>)
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:11_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="cqc_sim1.html#E6:11_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="cqc_sim1.html#E7:11_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="cqc_sim1.html#E8:11_1"><i><font color="Green" title="E10">A6</font></i></a></i>
;<br/>

<a NAME="E10:11_1"/><i><font color="Green" title="E11">A7</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">s</font> is <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D19" title="QC_LANG1:def.19">QC_LANG1:def 19</a></i>;<br/>
<a NAME="E11:11_1"/><b>then </b><i><font color="Green" title="E12">A8</font></i>: 
(  <a href="qc_lang1.html#K18" title="QC_LANG1:func.18">the_left_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_right_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D24" title="QC_LANG1:def.24">QC_LANG1:def 24</a>, <a class="ref" href="qc_lang1.html#D25" title="QC_LANG1:def.25">QC_LANG1:def 25</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span> = 
<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">'&amp;'</a> <font color="Maroon" title="c4">s</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">F<sub>6</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">r</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font>)
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:11_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="cqc_sim1.html#E6:11_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="cqc_sim1.html#E10:11_1"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="cqc_sim1.html#E11:11_1"><i><font color="Green" title="E12">A8</font></i></a></i>
;<br/>

<a NAME="E13:11_1"/><i><font color="Green" title="E13">A9</font></i>: 
 <a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">r</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D20" title="QC_LANG1:def.20">QC_LANG1:def 20</a></i>;<br/>
<a NAME="E14:11_1"/><b>then </b><i><font color="Green" title="E14">A10</font></i>: 
(  <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> &amp;  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D26" title="QC_LANG1:def.26">QC_LANG1:def 26</a>, <a class="ref" href="qc_lang1.html#D27" title="QC_LANG1:def.27">QC_LANG1:def 27</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">r</font></span>)</span> = 
<font color="Maroon" title="c1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">r</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">F<sub>7</sub></font>(<font color="Maroon" title="c5">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font>)
<b>by </b><i><a class="txt" href="cqc_sim1.html#E2:11_1"><i><font color="Green" title="E7">A1</font></i></a>, <a class="txt" href="cqc_sim1.html#E6:11_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="cqc_sim1.html#E13:11_1"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="cqc_sim1.html#E14:11_1"><i><font color="Green" title="E14">A10</font></i></a></i>
;<br/>


</div>
