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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K1">QC-variables</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="qc_lang1.html#K17">the_argument_of</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="qc_lang1.html#K20">bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:57"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="qc_lang2.html#V4">existential</a>
 ;<br/>

<a NAME="E2:57"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang2.html#K5">Ex</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T56">QC_LANG2:56</a></i>;<br/>
<a NAME="E3:57"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p5">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D5">QC_LANG2:def 5</a></i>;<br/>
<b>then </b> <a href="qc_lang3.html#K4" target="_self">Vars</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="qc_lang3.html#K4" target="_self">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p5">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="qc_lang3.html#T50" target="_self">Th50</a></i>
<br/>.= 
 <a href="qc_lang3.html#K4" target="_self">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p4">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="qc_lang3.html#T55" target="_self">Th55</a></i>
<br/>.= 
 <a href="qc_lang3.html#K4" target="_self">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="qc_lang3.html#T50" target="_self">Th50</a></i>
;<br/>
<b>hence </b><a NAME="E5:57"/>
 <a href="qc_lang3.html#K4" target="_self">Vars</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang3.html#K4" target="_self">Vars</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K17">the_argument_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div>
