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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>3</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>4</sub></font> be    <a href="valuat_1.html#M1">interpretation</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:94"/><i><font color="Green">E77</font></i>: 
( ( for <font color="Olive">b<sub>1</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>3</sub></font><br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="sublemma.html#NM1">Val_Sub</a> of <font color="Maroon">c<sub>3</sub></font> st ( for <font color="Olive">b<sub>5</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>3</sub></font> holds <br/> not <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>5</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>4</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>5</sub></font> ) &amp;  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>4</sub></font> holds <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> ) ) &amp; ( for <font color="Olive">b<sub>1</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>3</sub></font><br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="sublemma.html#NM1">Val_Sub</a> of <font color="Maroon">c<sub>3</sub></font> st ( for <font color="Olive">b<sub>5</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>3</sub></font> holds <br/> not <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>5</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>4</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>5</sub></font> ) &amp;  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relset_1.html#K4">dom</a> <font color="Olive">b<sub>4</sub></font> holds <br/>( <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> ) ) )
 ;<br/>

<b>let </b><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>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="sublemma.html#NM1">Val_Sub</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E2:94"/><i><font color="Green">E78</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/> not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E3:94"/><i><font color="Green">E79</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/>( not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/>

<b>assume </b><a NAME="E1:94_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:94_1"/><b>then </b>
not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:94"><i><font color="Green">E78</font></i></a></i>;<br/>
<a NAME="E3:94_1"/><b>then </b>
not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</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="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang3.html#T14">QC_LANG3:14</a></i>;<br/>
<b>hence </b><a NAME="E4:94_1"/>
( not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:94"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> iff ( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:94_2"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> implies ( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:94_2_1"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:94_2_1"/><i><font color="Green">E81</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/> not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</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="txt" href="sublemma.html#E3:94"><i><font color="Green">E79</font></i></a></i>;<br/>
<a NAME="E3:94_2_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/> not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E3:94"><i><font color="Green">E79</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:94_2_1"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:94"><i><font color="Green">E77</font></i></a>, <a class="txt" href="sublemma.html#E2:94"><i><font color="Green">E78</font></i></a>, <a class="txt" href="sublemma.html#E1:94_2_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sublemma.html#E2:94_2_1"><i><font color="Green">E81</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E2:94_2"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> implies ( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:94_2_2"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:94_2_2"/><i><font color="Green">E81</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/> not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</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="txt" href="sublemma.html#E3:94"><i><font color="Green">E79</font></i></a></i>;<br/>
<a NAME="E3:94_2_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/> not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E3:94"><i><font color="Green">E79</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:94_2_2"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:94"><i><font color="Green">E77</font></i></a>, <a class="txt" href="sublemma.html#E2:94"><i><font color="Green">E78</font></i></a>, <a class="txt" href="sublemma.html#E1:94_2_2"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sublemma.html#E2:94_2_2"><i><font color="Green">E81</font></i></a></i>;<br/>


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


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:94"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="valuat_1.html#T29">VALUAT_1:29</a></i>;<br/>


</div>
