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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/>

<div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E18</font></i>: 
 <a href="cqc_the3.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1"><b>now </b></a><div class="add"><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>assume </b><a NAME="E1:17_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:17_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is <a href="cqc_the1.html#V2">valid</a>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:17_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="cqc_the3.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E3:17_1_1"/>
 <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>
 <b>by </b><i><a class="ref" href="cqc_the1.html#D10">CQC_THE1:def 10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:17_1"/>
 <a href="subset_1.html#K1">{}</a> <a href="cqc_lang.html#K7">CQC-WFF</a>  <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_2"/><i><font color="Green">E18</font></i>: 
 <a href="subset_1.html#K1">{}</a> <a href="cqc_lang.html#K7">CQC-WFF</a>  <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1"><b>now </b></a><div class="add"><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>assume </b><a NAME="E1:17_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:17_2_1"/><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>2</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:17_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="cqc_the3.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E3:17_2_1"/>
<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_the1.html#D10">CQC_THE1:def 10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:17_2"/>
 <a href="cqc_the3.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:17"/>
(  <a href="cqc_the3.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font> iff  <a href="subset_1.html#K1">{}</a> <a href="cqc_lang.html#K7">CQC-WFF</a>  <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:17"><i><font color="Green">E17</font></i></a></i>;<br/>


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