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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>





<b>thus </b><a NAME="E1:106"/>
( <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font> implies <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="106_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:106_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K7">}</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cqc_the1.html#D9">CQC_THE1:def 9</a><br/>

<a NAME="E2:106_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>;<br/>
<b>hence </b><a NAME="E3:106_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_the2.html#T92" target="_self">Th92</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cqc_the1.html#D9">CQC_THE1:def 9</a><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:106"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cqc_the1.html#D9">CQC_THE1:def 9</a><br/>

<a NAME="E3:106"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="cqc_the2.html#T92" target="_self">Th92</a></i>;<br/>
<b>hence </b><a NAME="E4:106"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="cqc_the1.html#K1">Cn</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cqc_the1.html#D9">CQC_THE1:def 9</a><br/>


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