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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:53_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K20" target="_self">Sub_not</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K20" target="_self">Sub_not</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:53_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K12">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> )
 
;<br/>
<a NAME="E3:53_1_1"/><b>then </b>
 <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<b>then </b><i><font color="Green">E30</font></i>: <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2"><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="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span> = 
 <a href="qc_lang1.html#K12">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="qc_lang1.html#D14">QC_LANG1:def 14</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2"><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="p1">(<span class="default"><a href="qc_lang1.html#K10">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="qc_lang1.html#D14">QC_LANG1:def 14</a></i>
;<br/>
<i><font color="Green">E31</font></i>: <font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a>  = 
 <a href="qc_lang1.html#K10">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="qc_lang1.html#D12">QC_LANG1:def 12</a></i>
<br/>.= 
 <a href="qc_lang1.html#K10">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>
<b>by </b><i><a class="txt" href="substut1.html#E4:53_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#T46">FINSEQ_1:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> 
<b>by </b><i><a class="ref" href="qc_lang1.html#D12">QC_LANG1:def 12</a></i>
;<br/>
<a NAME="E6:53_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> &amp; <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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i><a class="ref" href="substut1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E7:53_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="substut1.html#E2:53_1_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="substut1.html#E5:53_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>


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