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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#NM3">bound_QC-variable</a>;<br/>





<a NAME="E1:56"/>
( <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>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="cqc_the1.html#V2">valid</a> &amp; <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>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="cqc_the2.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E2:56"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&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>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a>
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E8"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E3:56"/>
( 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#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; 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#K16">Ex</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#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:56"/><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#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</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#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E5:56"/>
<span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <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"><span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a>
 <b>by </b><i><a class="txt" href="cqc_the2.html#E2:56"><i><font color="Green">E44</font></i></a>, <a class="ref" href="cqc_the2.html#T22" target="_self">Th22</a></i>;<br/>

<a NAME="E6:56"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="cqc_the1.html#V2">valid</a> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</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="txt" href="cqc_the2.html#E10"><i><font color="Green">Lemma10</font></i></a></i>;<br/>
<a NAME="E7:56"/><b>then </b><i><font color="Green">E45</font></i>: 
(  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a> &amp;  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T26" target="_self">Th26</a></i>;<br/>
<a NAME="E8:56"/>
( <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&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>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a> &amp; <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&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>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#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T38" target="_self">Th38</a></i>;<br/>
<a NAME="E9:56"/><b>then </b>
( <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <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>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a> &amp; <span class="p1">(<span class="default"><a href="cqc_lang.html#K16">Ex</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#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i><a class="txt" href="cqc_the2.html#E7:56"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cqc_the1.html#T104">CQC_THE1:104</a></i>;<br/>
<b>hence </b><a NAME="E10:56"/>
<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>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="cqc_lang.html#K13">'or'</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K16">Ex</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#K16">Ex</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K13">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> is <a href="cqc_the1.html#V2">valid</a>
 <b>by </b><i><a class="txt" href="cqc_the2.html#E11"><i><font color="Green">Lemma11</font></i></a></i>;<br/>


</div>
