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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#NM2">Subset</a> of <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/>



<div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R4" target="_self">|-|</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>let </b><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>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:20_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:20_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:20_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="cqc_the3.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:20_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D2" target="_self">Def2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_2"><b>now </b></a><div class="add"><b>let </b><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>assume </b><a NAME="E1:20_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:20_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:20_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:20_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="cqc_the3.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:20_1"/>
<font color="Maroon">c<sub>2</sub></font> <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="20_2"><b>now </b></a><div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:20_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R2" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:20_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <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="20_2_1"><b>now </b></a><div class="add"><b>let </b><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/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:20_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:20_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E2:20_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="cqc_the3.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E4:20_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:20_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:20_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R2" target="_self">|-</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:20_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="cqc_the3.html#T9" target="_self">Th9</a></i>;<br/><b>hence </b><a NAME="E4:20_2_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#T10" target="_self">Th10</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:20_2_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">c<sub>2</sub></font> <a href="cqc_the1.html#R3">|-</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:20_2_1"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:20_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R4" target="_self">|-|</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R4" target="_self">|-|</a> <font color="Maroon">c<sub>2</sub></font> iff ( <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R2" 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#R2" target="_self">|-</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:20"><i><font color="Green">E19</font></i></a></i>;<br/>


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