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

<b>set </b><font color="Maroon">V</font> =  <a href="qc_lang1.html#K2">bound_QC-variables</a> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ) <b>-&gt; </b>  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>  =  <a href="substut1.html#K8" target="_self">Bound_Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16">the_arguments_of</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a> ) <b>-&gt; </b>  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>  = <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a> ,  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ,  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  = <font color="Maroon">a<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>thus </b><a NAME="E1:14_1_1"/>
(  ex <font color="Olive">d</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>  ex <font color="Olive">F</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> , <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  st <br/>( <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <br/> for <font color="Olive">d1</font>, <font color="Olive">d2</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/> ( ( <font color="Olive">p</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K1">{}</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V2">atomic</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">p</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V3">negative</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">d1</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V4">conjunctive</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K18">the_left_argument_of</a> <font color="Olive">p</font></span>)</span> &amp; <font color="Olive">d2</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K19">the_right_argument_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">d1</font>,<font color="Olive">d2</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V5">universal</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">p</font>,<font color="Olive">d1</font>) ) ) ) ) &amp; ( for <font color="Olive">x1</font>, <font color="Olive">x2</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>   st  ex <font color="Olive">F</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> , <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  st <br/>( <font color="Olive">x1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <br/> for <font color="Olive">d1</font>, <font color="Olive">d2</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/> ( ( <font color="Olive">p</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K1">{}</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V2">atomic</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">p</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V3">negative</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">d1</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V4">conjunctive</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K18">the_left_argument_of</a> <font color="Olive">p</font></span>)</span> &amp; <font color="Olive">d2</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K19">the_right_argument_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">d1</font>,<font color="Olive">d2</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V5">universal</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">p</font>,<font color="Olive">d1</font>) ) ) ) ) &amp;  ex <font color="Olive">F</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> , <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  st <br/>( <font color="Olive">x2</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> &amp; ( for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <br/> for <font color="Olive">d1</font>, <font color="Olive">d2</font> being  <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2">bound_QC-variables</a>  holds <br/> ( ( <font color="Olive">p</font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K9">VERUM</a>  implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K1">{}</a> <a href="qc_lang1.html#K2">bound_QC-variables</a>  ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V2">atomic</a> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">p</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V3">negative</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">d1</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V4">conjunctive</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K18">the_left_argument_of</a> <font color="Olive">p</font></span>)</span> &amp; <font color="Olive">d2</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K19">the_right_argument_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">d1</font>,<font color="Olive">d2</font>) ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V5">universal</a> &amp; <font color="Olive">d1</font> <a href="hidden.html#R1">=</a> <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <font color="Olive">p</font></span>)</span> implies <font color="Olive">F</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">p</font>,<font color="Olive">d1</font>) ) ) ) ) holds <br/><font color="Olive">x1</font> <a href="hidden.html#R1">=</a> <font color="Olive">x2</font> ) )
 <b>from </b><i><a class="ref" href="qc_lang3.html#S2">QC_LANG3:sch 2</a>();</i><br/>


</div>
