<?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>assume </b><a NAME="E1:4"/><i><font color="Green">E5</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="substut1.html#NM1">CQC_Substitution</a>ex <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="substut1.html#NM1">CQC_Substitution</a>;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> <b> such that </b><br/><a NAME="E3:4"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="substut2.html#E1:4"><i><font color="Green">E5</font></i></a></i>;<br/>
<a NAME="E4:4"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="substut2.html#E3:4"><i><font color="Green">E6</font></i></a>, <a class="ref" href="substut1.html#T10">SUBSTUT1:10</a></i>;<br/>
<a NAME="E5:4"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K16">QC-Sub-WFF</a> 
 
<b>by </b><i><a class="txt" href="substut2.html#E4:4"><i><font color="Green">E7</font></i></a></i>;<br/>
<a NAME="E6:4"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K10">@</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K16">QC-Sub-WFF</a> 
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D12">QC_LANG1:def 12</a></i>;<br/>
<a NAME="E7:4"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4"><a href="domain_1.html#K1">[</a><span class="default">1,0</span><a href="domain_1.html#K1">]</a></span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K10">@</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K16">QC-Sub-WFF</a> 
 
<b>by </b><i><a class="ref" href="substut1.html#D16">SUBSTUT1:def 16</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> as    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16">QC-Sub-WFF</a>  <b>by </b><i><a class="ref" href="qc_lang1.html#D14">QC_LANG1:def 14</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<a NAME="E9:4"/>
<font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K18">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</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="E10:4"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="substut1.html#K38">CQC-Sub-WFF</a> 
 
<b>by </b><i><a class="ref" href="substut1.html#D39">SUBSTUT1:def 39</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  ;<br/>
<a NAME="E12:4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K19">`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/>
<b>hence </b><a NAME="E13:4"/>
( <font color="Maroon">c<sub>4</sub></font> is    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K19">`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/>


</div>
