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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><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#NM3">bound_QC-variable</a>;<br/>





<b>assume </b><a NAME="E1:107"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:107"/>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <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="lukasi_1.html#T45">LUKASI_1:45</a></i>;<br/>
<a NAME="E3:107"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T98">CQC_THE1:98</a></i>;<br/>
<a NAME="E4:107"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E1:107"><i><font color="Green">E72</font></i></a>, <a class="ref" href="cqc_the1.html#T92">CQC_THE1:92</a></i>;<br/>
<a NAME="E5:107"/>
not <font color="Maroon">c<sub>3</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#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E6:107"/><b>then </b>
not <font color="Maroon">c<sub>3</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"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</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/>
<a NAME="E7:107"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E4:107"><i><font color="Green">E73</font></i></a>, <a class="ref" href="cqc_the1.html#T94">CQC_THE1:94</a></i>;<br/>
<a NAME="E8:107"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</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="lukasi_1.html#T44">LUKASI_1:44</a></i>;<br/>
<a NAME="E9:107"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T98">CQC_THE1:98</a></i>;<br/>
<b>hence </b><a NAME="E10:107"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the2.html#E7:107"><i><font color="Green">E74</font></i></a>, <a class="ref" href="cqc_the1.html#T92">CQC_THE1:92</a></i>;<br/>


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