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

<b>let </b><font color="Maroon" title="c1">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon" title="c3">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>;<br/><b>let </b><font color="Maroon" title="c4">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> ;<br/>







<b>set </b><font color="Maroon" title="c5">Sub1</font> = <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">Sub</font> = <font color="Maroon" title="c3">Sub</font> as   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> ;<br/>
<b>assume </b><a NAME="E2:11"/><i><font color="Green" title="E11">A1</font></i>: 
( <font color="Maroon" title="c4">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c4">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )
 ;<br/>

<a NAME="E3:11"/><i><font color="Green" title="E12">A2</font></i>: 
<span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c6">Sub</font></span>)</span>
 
<b>by </b><i><a class="ref" href="substut2.html#T9" target="_self" title="SUBSTUT2:th.9">Th9</a></i>;<br/>
<a NAME="E4:11"/><i><font color="Green" title="E13">A3</font></i>: 
(  <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T8" title="QC_LANG2:th.8">QC_LANG2:8</a></i>;<br/>
<a NAME="E5:11"/>
 <a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font> is <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D20" title="QC_LANG1:def.20">QC_LANG1:def 20</a></i>;<br/>
<a NAME="E6:11"/><b>then </b>
 <a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c6">Sub</font> <a href="substut1.html#R1" title="SUBSTUT1:pred.1">PQSub</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="substut2.html#E3:11"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="substut2.html#E4:11"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="substut1.html#D14" title="SUBSTUT1:def.14">SUBSTUT1:def 14</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E8:11"/><i><font color="Green" title="E14">A4</font></i>: 
( <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c6">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p4">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p5">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p4">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p5"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p0">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp;  <a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c6">Sub</font> <a href="substut1.html#R1" title="SUBSTUT1:pred.1">PQSub</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span> )
 ;<br/>
<a NAME="E9:11"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a> 
 
<b>by </b><i><a class="txt" href="substut2.html#E8:11"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="substut1.html#D15" title="SUBSTUT1:def.15">SUBSTUT1:def 15</a></i>;<br/>
<a NAME="E10:11"/><b>then </b><i><font color="Green" title="E15">A5</font></i>: 
<a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c6">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="substut2.html#E8:11"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></i>;<br/>
<a NAME="E11:11"/><i><font color="Green" title="E16">A6</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span></span>)</span> <a href="sublemma.html#K15" title="SUBLEMMA:func.15">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="sublemma.html#K13" title="SUBLEMMA:func.13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="substut2.html#E2:11"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E12:11"/><i><font color="Green" title="E17">A7</font></i>: 
<span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E13:11"/><i><font color="Green" title="E18">A8</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 
<b>by </b><i><a class="txt" href="substut2.html#E2:11"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E14:11"/><b>then </b><i><font color="Green" title="E19">A9</font></i>: 
<span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>
 
<b>by </b><i><a class="txt" href="substut2.html#E10:11"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="substut2.html#E11:11"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="substut2.html#E12:11"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="substut1.html#D22" title="SUBSTUT1:def.22">SUBSTUT1:def 22</a></i>;<br/>
<b>thus </b><a NAME="E15:11"/>
<span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>
 <b>by </b><i><a class="txt" href="substut2.html#E10:11"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="substut2.html#E11:11"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="substut2.html#E12:11"><i><font color="Green" title="E17">A7</font></i></a>, <a class="txt" href="substut2.html#E13:11"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="substut1.html#D22" title="SUBSTUT1:def.22">SUBSTUT1:def 22</a></i>;<br/>

<b>reconsider </b><font color="Maroon" title="c8">Sub</font> = <font color="Maroon" title="c6">Sub</font> as    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <b>by </b><i><a class="txt" href="substut2.html#E10:11"><i><font color="Green" title="E15">A5</font></i></a>, <a class="txt" href="substut2.html#E11:11"><i><font color="Green" title="E16">A6</font></i></a>, <a class="txt" href="substut2.html#E12:11"><i><font color="Green" title="E17">A7</font></i></a>, <a class="txt" href="substut2.html#E13:11"><i><font color="Green" title="E18">A8</font></i></a>, <a class="txt" href="substut2.html#E14:11"><i><font color="Green" title="E19">A9</font></i></a>, <a class="ref" href="substut1.html#D23" title="SUBSTUT1:def.23">SUBSTUT1:def 23</a></i>;<br/>
<b>take </b><font color="Maroon" title="c9">S1</font> =  <a href="sublemma.html#K10" title="SUBLEMMA:func.10">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c8">Sub</font>;<br/>

<a NAME="E17:11"/>
<font color="Maroon" title="c9">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c4">S</font>,<font color="Maroon" title="c2">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>,<font color="Maroon" title="c8">Sub</font>
 
<b>by </b><i><a class="txt" href="substut2.html#E14:11"><i><font color="Green" title="E19">A9</font></i></a>, <a class="ref" href="sublemma.html#D6" title="SUBLEMMA:def.6">SUBLEMMA:def 6</a></i>;<br/>
<b>hence </b><a NAME="E18:11"/>
<font color="Maroon" title="c9">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15" title="CQC_LANG:func.15">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span>
 <b>by </b><i><a class="txt" href="substut2.html#E12:11"><i><font color="Green" title="E17">A7</font></i></a>, <a class="txt" href="substut2.html#E13:11"><i><font color="Green" title="E18">A8</font></i></a>, <a class="txt" href="substut2.html#E14:11"><i><font color="Green" title="E19">A9</font></i></a>, <a class="ref" href="substut1.html#D24" title="SUBSTUT1:def.24">SUBSTUT1:def 24</a></i>;<br/>


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