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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="substut1.html#NM1">CQC_Substitution</a>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p3"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="sublemma.html#K8">[</a><span class="default"><span class="p2"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p4"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span>;<br/>
<a NAME="E1:32"/><i><font color="Green">E19</font></i>: 
( <span class="p1"><a href="sublemma.html#K8">[</a><span class="default"><span class="p2"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p4"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="sublemma.html#K9">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p3"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span> &amp; <span class="p1"><a href="sublemma.html#K8">[</a><span class="default"><span class="p2"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p4"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="substut1.html#K23">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E2:32"/><b>then </b><i><font color="Green">E20</font></i>: 
( <span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K8">[</a><span class="default"><span class="p3"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p5"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="sublemma.html#K9">`1</a> </span>)</span> <a href="substut2.html#K5" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K8">[</a><span class="default"><span class="p3"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p5"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="sublemma.html#K9">`1</a> </span>)</span> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E3:32"/>
<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K38">CQC-Sub-WFF</a> 
 
;<br/>
<a NAME="E4:32"/><b>then </b>
<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="substut2.html#K6" target="_self">CFQ</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:32"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K8">[</a><span class="default"><span class="p3"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p5"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="sublemma.html#K9">`1</a> </span>)</span> <a href="substut2.html#K5" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <a href="substut1.html#K15">QSub</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <span class="p3">(<span class="default"><span class="p4"><a href="sublemma.html#K8">[</a><span class="default"><span class="p5"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p0">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="substut1.html#K23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="sublemma.html#K8">[</a><span class="default"><span class="p0"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p2"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> <a href="sublemma.html#K9">`1</a> </span>)</span> <a href="sublemma.html#K2">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span>
 
<b>by </b><i><a class="txt" href="substut2.html#E1:32"><i><font color="Green">E19</font></i></a>, <a class="txt" href="substut2.html#E2:32"><i><font color="Green">E20</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>;<br/>
<a NAME="E6:32"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="sublemma.html#K8">[</a><span class="default"><span class="p2"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="substut2.html#K6" target="_self">CFQ</a>  <a href="funct_2.html#K3">.</a> <span class="p4"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p5">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="sublemma.html#K8">]</a></span> is <a href="substut1.html#V3">quantifiable</a>
 
<b>by </b><i><a class="ref" href="substut1.html#D22">SUBSTUT1:def 22</a></i>;<br/>
<a NAME="E7:32"/>
 <a href="sublemma.html#K10">CQCSub_All</a> <span class="p1">(<span class="default"><a href="substut2.html#K7" target="_self">QScope</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="substut2.html#K8" target="_self">Qsc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24">Sub_All</a> <span class="p1">(<span class="default"><a href="substut2.html#K7" target="_self">QScope</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="substut2.html#K8" target="_self">Qsc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="substut2.html#E6:32"><i><font color="Green">E21</font></i></a>, <a class="ref" href="sublemma.html#D6">SUBLEMMA:def 6</a></i>;<br/>
<a NAME="E8:32"/><b>then </b>
<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="substut2.html#K8" target="_self">Qsc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="sublemma.html#K10">CQCSub_All</a> <span class="p1">(<span class="default"><a href="substut2.html#K7" target="_self">QScope</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="substut2.html#K8" target="_self">Qsc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="substut2.html#E1:32"><i><font color="Green">E19</font></i></a>, <a class="txt" href="substut2.html#E2:32"><i><font color="Green">E20</font></i></a>, <a class="txt" href="substut2.html#E6:32"><i><font color="Green">E21</font></i></a>, <a class="ref" href="substut1.html#D24">SUBSTUT1:def 24</a></i>;<br/>
<b>hence </b><a NAME="E9:32"/>
( <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="sublemma.html#K10">CQCSub_All</a> <span class="p1">(<span class="default"><a href="substut2.html#K7" target="_self">QScope</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="substut2.html#K8" target="_self">Qsc</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="substut2.html#K7" target="_self">QScope</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> is <a href="substut1.html#V3">quantifiable</a> )
 <b>by </b><i><a class="txt" href="substut2.html#E6:32"><i><font color="Green">E21</font></i></a></i>;<br/>


</div>
