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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</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="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="valuat_1.html#M1">interpretation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Maroon">c<sub>2</sub></font>;<br/>













<b>assume </b><a NAME="E1:77"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K8">|</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:77"/><i><font color="Green">E62</font></i>: 
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K22">still_not-bound_in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T9">QC_LANG3:9</a></i>;<br/>
<a NAME="E3:77"/><i><font color="Green">E63</font></i>: 
( <span class="p1">(<span class="default"><a href="valuat_1.html#K12">Valid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="valuat_1.html#T16">VALUAT_1:16</a></i>;<br/>
<a NAME="E4:77"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K7">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K22">still_not-bound_in</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> iff <font color="Maroon">c<sub>7</sub></font> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="sublemma.html#T60" target="_self">Th60</a></i>;<br/>
<a NAME="E5:77"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> iff <span class="p1">(<span class="default"><a href="valuat_1.html#K12">Valid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 
<b>by </b><i><a class="ref" href="valuat_1.html#T16">VALUAT_1:16</a></i>;<br/>
<b>hence </b><a NAME="E6:77"/>
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font> iff <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>4</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:77"><i><font color="Green">E61</font></i></a>, <a class="txt" href="sublemma.html#E2:77"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sublemma.html#E3:77"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sublemma.html#E4:77"><i><font color="Green">E64</font></i></a>, <a class="ref" href="sublemma.html#T60" target="_self">Th60</a>, <a class="ref" href="valuat_1.html#D12">VALUAT_1:def 12</a></i>;<br/>


</div>
