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<b>let </b><font color="Maroon">p</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">q</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="E1:5"/><i><font color="Green">E43</font></i>: 
( ( for <font color="Olive">Sub</font> being  <a href="substut1.html#NM1">CQC_Substitution</a>  ex <font color="Olive">S</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">S</font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Olive">S</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Olive">Sub</font> ) ) &amp; ( for <font color="Olive">Sub</font> being  <a href="substut1.html#NM1">CQC_Substitution</a>  ex <font color="Olive">S</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">S</font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp; <font color="Olive">S</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Olive">Sub</font> ) ) )
 ;<br/>

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

<b>consider </b><font color="Maroon">S1</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="E3:5"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">S1</font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <font color="Maroon">S1</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">Sub</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">S2</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="E5:5"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">S2</font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp; <font color="Maroon">S2</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">Sub</font> )
 <b>by </b><i/>;<br/>
<a NAME="E6:5"/>
( <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i>, , <a class="ref" href="substut1.html#T10">SUBSTUT1:10</a></i>;<br/>
<a NAME="E7:5"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">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>  &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">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>  )
 
;<br/>
<a NAME="E8:5"/><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">p</font></span>)</span>,<font color="Maroon">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>  &amp; <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">q</font></span>)</span>,<font color="Maroon">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="E9:5"/><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">(<span class="default"><span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p5"><a href="domain_1.html#K1">[</a><span class="default">2,0</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="p4">(<span class="default"><a href="qc_lang1.html#K10">@</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K10">@</a> <font color="Maroon">q</font></span>)</span></span>)</span>,<font color="Maroon">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">S</font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">q</font></span>)</span>,<font color="Maroon">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#D15">QC_LANG1:def 15</a></i>;<br/>
<b>take </b>
<font color="Maroon">S</font>
;<br/>

<a NAME="E11:5"/>
<font color="Maroon">S</font> <a href="substut1.html#K18">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">q</font>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E12:5"/><b>then </b>
<font color="Maroon">S</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">S</font> = <font color="Maroon">S</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  ;<br/>
<a NAME="E14:5"/>
<font color="Maroon">S</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">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="E15:5"/>
( <font color="Maroon">S</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  &amp; <font color="Maroon">S</font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">q</font> &amp; <font color="Maroon">S</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">Sub</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>


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