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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</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="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>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="substut1.html#M1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>;<br/>











<b>assume </b><a NAME="E1:87"/><i><font color="Green">E69</font></i>: 
<span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span> is <a href="substut1.html#V3">quantifiable</a>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="substut1.html#K35">S_Bound</a> <span class="p1">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>thus </b><a NAME="E2:87"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font> ) implies for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:87_1"/><i><font color="Green">E70</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>;<br/>
<a NAME="E2:87_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p5">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p0">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <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>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <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>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:87"><i><font color="Green">E69</font></i></a>, <a class="ref" href="sublemma.html#T71" target="_self">Th71</a></i>;<br/>
<a NAME="E3:87_1"/><b>then </b><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a>  iff <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a>  )
 
<b>by </b><i><a class="ref" href="sublemma.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E4:87_1"/>
<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:87_1"><i><font color="Green">E70</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:87_1"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:87_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="sublemma.html#D3" target="_self">Def3</a></i>;<br/>


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

<b>thus </b><a NAME="E3:87"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font> ) implies for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:87_2"/><i><font color="Green">E70</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>;<br/>
<a NAME="E2:87_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p5">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p0">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <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>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span></span>)</span> <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>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:87"><i><font color="Green">E69</font></i></a>, <a class="ref" href="sublemma.html#T71" target="_self">Th71</a></i>;<br/>
<a NAME="E3:87_2"/><b>then </b><i><font color="Green">E71</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a>  iff <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#R1">|=</a> <font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K2" target="_self">`1</a>  )
 
<b>by </b><i><a class="ref" href="sublemma.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E4:87_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:87_2"><i><font color="Green">E70</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:87_2"/>
<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p4">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="sublemma.html#R1" target="_self">|=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:87_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="sublemma.html#D3" target="_self">Def3</a></i>;<br/>


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


</div>
