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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-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="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>assume </b><a NAME="E1:78"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <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> st <font color="Olive">b<sub>1</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</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> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</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="E2:78"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>4</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"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</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"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E3:78"/><i><font color="Green">E64</font></i>: 
 <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T11">QC_LANG3:11</a></i>;<br/>
<a NAME="E4:78"/>
( not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> iff  not <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:78"><i><font color="Green">E62</font></i></a>, <a class="txt" href="sublemma.html#E2:78"><i><font color="Green">E63</font></i></a>, <a class="txt" href="sublemma.html#E3:78"><i><font color="Green">E64</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:78"/>
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="valuat_1.html#R1">|=</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="valuat_1.html#R1">|=</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="valuat_1.html#T28">VALUAT_1:28</a></i>;<br/>


</div>
