<?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="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>4</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>5</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>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><a NAME="E1:86"/><i><font color="Green">E68</font></i>: 
<span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>4</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>5</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>4</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>5</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</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>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>;<br/>
<a NAME="E2:86"/><i><font color="Green">E69</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E3:86"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a> 
 
<b>by </b><i><a class="ref" href="sublemma.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E4:86"/><b>then </b><i><font color="Green">E70</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="sublemma.html#T59" target="_self">Th59</a></i>;<br/>
<a NAME="E5:86"/><i><font color="Green">E71</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:86"><i><font color="Green">E69</font></i></a>, <a class="txt" href="sublemma.html#E4:86"><i><font color="Green">E70</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<div><i><font color="Green">E72</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_1"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E2:86_1"/><b>then </b><i><font color="Green">E73</font></i>: 
 <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>4</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>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:86"><i><font color="Green">E68</font></i></a>, <a class="ref" href="sublemma.html#T53" target="_self">Th53</a></i>;<br/><a NAME="E3:86_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:86_1_1"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<div><i><font color="Green">E75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_1_1_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <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>4</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>5</sub></font></span>)</span></span>)</span>
 ;<br/><div><i><font color="Green">E77</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_1_1_1_1"/><i><font color="Green">E78</font></i>: 
not <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E2:86_1_1_1_1"/>
not <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:86_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="sublemma.html#E1:86_1_1_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:86_1_1_1_1"/><b>then </b>
not <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="sublemma.html#T59" target="_self">Th59</a></i>;<br/><a NAME="E4:86_1_1_1_1"/><b>then </b>
not <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</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>6</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:86_1_1_1_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:86_1_1_1_1"/><b>then </b><i><font color="Green">E79</font></i>: 
not <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/><a NAME="E6:86_1_1_1_1"/><b>then </b><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="qc_lang1.html#NM3">bound_QC-variable</a> <b>by </b><i><a class="txt" href="sublemma.html#E1:86_1_1"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E8:86_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:86_1_1_1"><i><font color="Green">E76</font></i></a>, <a class="txt" href="sublemma.html#E6:86_1_1_1_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="sublemma.html#T49" target="_self">Th49</a></i>;<br/><b>hence </b><a NAME="E9:86_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:86_1_1_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_1_1_1_2"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E2:86_1_1_1_2"/>
 <a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</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>6</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/><a NAME="E3:86_1_1_1_2"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E4:86_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:86_1_1_1_2"><i><font color="Green">E78</font></i></a>, <a class="txt" href="sublemma.html#E3:86_1_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><b>hence </b><a NAME="E5:86_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:86_1_1_1_2"><i><font color="Green">E78</font></i></a>, <a class="txt" href="sublemma.html#E3:86_1_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:86_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:86_1_1_1"><i><font color="Green">E77</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_1_1_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <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>4</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>5</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:86_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:86_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:86_1_1_2"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="sublemma.html#T59" target="_self">Th59</a></i>;<br/><a NAME="E4:86_1_1_2"/>
 <a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</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>6</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/><a NAME="E5:86_1_1_2"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E6:86_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:86_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="txt" href="sublemma.html#E5:86_1_1_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><b>hence </b><a NAME="E7:86_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:86_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="txt" href="sublemma.html#E5:86_1_1_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:86_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:86_1_1"><i><font color="Green">E75</font></i></a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:86_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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#E5:86"><i><font color="Green">E71</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E2:86_2"/><i><font color="Green">E74</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:86"><i><font color="Green">E69</font></i></a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:86_2"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:86"><i><font color="Green">E71</font></i></a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E4:86_2"/><b>then </b><i><font color="Green">E75</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E5:86_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:86_2_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:86_2_1"/><i><font color="Green">E77</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>14</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>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:86_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="sublemma.html#E1:86_2_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:86_2_1"/>
 <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="sublemma.html#K2" target="_self">`1</a> </span>)</span> <a href="tarski.html#R1">c=</a>  <a href="substut1.html#K9">Bound_Vars</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="sublemma.html#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E4:86_2_1"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <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>4</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>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:86"><i><font color="Green">E68</font></i></a>, <a class="txt" href="sublemma.html#E1:86_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="sublemma.html#E2:86_2_1"><i><font color="Green">E77</font></i></a>, <a class="ref" href="sublemma.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E5:86_2_1"/><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p1">(<span class="default"><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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>;<br/>
<a NAME="E6:86_2_1"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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>3</sub></font> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p1">(<span class="default"><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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T75">FUNCT_4:75</a></i>;<br/>
<a NAME="E7:86_2_1"/><i><font color="Green">E81</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E5:86_2_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<div><i><font color="Green">E82</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_2_1_1"/><i><font color="Green">E83</font></i>: 
not <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:86_2_1_1"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:86_2_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E3:86_2_1_1"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:86_2_1"><i><font color="Green">E76</font></i></a>, <a class="txt" href="sublemma.html#E7:86_2_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="sublemma.html#E1:86_2_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E4:86_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:86_2_1_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/><a NAME="E5:86_2_1_1"/><b>then </b><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:86_2_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="sublemma.html#T49" target="_self">Th49</a></i>;<br/><a NAME="E6:86_2_1_1"/><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E6:86_2_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sublemma.html#E1:86_2_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E7:86_2_1_1"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:86_2_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E8:86_2_1_1"/><b>then </b>
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  &amp; <font color="Maroon">c<sub>14</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>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E9:86_2_1_1"/><b>then </b>
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>14</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>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="sublemma.html#T59" target="_self">Th59</a></i>;<br/><a NAME="E10:86_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E11:86_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:86_2_1_1"><i><font color="Green">E86</font></i></a>, <a class="txt" href="sublemma.html#E6:86_2_1_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="funct_1.html#T71">FUNCT_1:71</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:86_2_1_2"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:86_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</sub></font></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:86_2_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><b>hence </b><a NAME="E3:86_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E6:86_2_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="sublemma.html#E1:86_2_1_2"><i><font color="Green">E83</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:86_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p0">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K14" target="_self">NEx_Val</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K8">|</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E8:86_2_1"><i><font color="Green">E82</font></i></a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:86_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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#E4:86_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:86"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</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>4</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>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K13" target="_self">|</a> <font color="Maroon">c<sub>6</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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>3</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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</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>6</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>4</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#E6:86"><i><font color="Green">E72</font></i></a></i>;<br/>


</div>
