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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>thus </b><a NAME="E1:27"/>
 <a href="cqc_lang.html#K9">VERUM</a>  <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the1.html#T27" target="_self">Th27</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cqc_the1.html#D1" target="_self">CQC_THE1:def 1</a><br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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>5</sub></font> be   <a href="qc_lang1.html#NM8">QC-formula</a>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/>











<b>thus </b><a NAME="E2:27"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; <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"><a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>3</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#K10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="cqc_the1.html#T28" target="_self">Th28</a>, <a class="ref" href="cqc_the1.html#T29" target="_self">Th29</a>, <a class="ref" href="cqc_the1.html#T30" target="_self">Th30</a>, <a class="ref" href="cqc_the1.html#T31" target="_self">Th31</a>, <a class="ref" href="cqc_the1.html#T32" target="_self">Th32</a></i>;<br/>

<b>thus </b><a NAME="E3:27"/>
( <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> &amp; not <font color="Maroon">c<sub>6</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>2</sub></font> implies <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#K15">All</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> ) &amp; ( <font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_lang.html#K7">CQC-WFF</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_lang.html#K7">CQC-WFF</a>  &amp; not <font color="Maroon">c<sub>6</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>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>5</sub></font> <a href="cqc_lang.html#K17">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1" target="_self">Cn</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="cqc_the1.html#T33" target="_self">Th33</a>, <a class="ref" href="cqc_the1.html#T34" target="_self">Th34</a>, <a class="ref" href="cqc_the1.html#T35" target="_self">Th35</a></i>;<br/>


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