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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>3</sub></font> be   <a href="qc_lang1.html#NM8">QC-formula</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/>









<b>assume </b><a NAME="E1:38"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:38"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="cqc_the1.html#V2">valid</a>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T18" target="_self">Th18</a></i>;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_the2.html#T14" target="_self">Th14</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cqc_lang.html#T40">CQC_LANG:40</a></i>
;<br/>
<i><font color="Green">E35</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="cqc_the2.html#T14" target="_self">Th14</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cqc_lang.html#T40">CQC_LANG:40</a></i>
;<br/>
<a NAME="E5:38"/>
( not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:38"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cqc_the2.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E6:38"/><b>then </b>
not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K23">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="qc_lang2.html#K2">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E7:38"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="cqc_the1.html#V2">valid</a>
 <b>by </b><i><a class="txt" href="cqc_the2.html#E2:38"><i><font color="Green">E33</font></i></a>, <a class="txt" href="cqc_the2.html#E3:38"><i><font color="Green">E34</font></i></a>, <a class="txt" href="cqc_the2.html#E4:38"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cqc_the1.html#T107">CQC_THE1:107</a></i>;<br/>


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