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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>assume </b><a NAME="E1:59"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R7" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:59"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K14">&lt;=&gt;</a> <font color="Maroon">c<sub>2</sub></font> is <a href="cqc_the1.html#V2">valid</a>
 
<b>by </b><i><a class="ref" href="cqc_the3.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E3:59"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <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>1</sub></font></span>)</span> is <a href="cqc_the1.html#V2">valid</a>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#D4">QC_LANG2:def 4</a></i>;<br/>
<a NAME="E4:59"/><b>then </b>
 <a href="subset_1.html#K1">{}</a> <a href="cqc_lang.html#K7">CQC-WFF</a>  <a href="cqc_the1.html#R3">|-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <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>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D10">CQC_THE1:def 10</a></i>;<br/>
<a NAME="E5:59"/><b>then </b>
(  <a href="subset_1.html#K1">{}</a> <a href="cqc_lang.html#K7">CQC-WFF</a>  <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="subset_1.html#K1">{}</a> <a href="cqc_lang.html#K7">CQC-WFF</a>  <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>2</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="cqc_the3.html#E40"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<a NAME="E6:59"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K12">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> 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> <font color="Maroon">c<sub>1</sub></font> is <a href="cqc_the1.html#V2">valid</a> )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#D10">CQC_THE1:def 10</a></i>;<br/>
<b>hence </b><a NAME="E7:59"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="cqc_the3.html#T39" target="_self">Th39</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cqc_the3.html#D5" target="_self">CQC_THE3:def 5</a><br/>


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