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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>, <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>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R6" target="_self">is_an_universal_closure_of</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="cqc_the3.html#R6" target="_self">is_an_universal_closure_of</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:55_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:55_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:55_1"/><b>then </b><i><font color="Green">E47</font></i>: 
 <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:55"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cqc_the3.html#E2:55"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cqc_the3.html#T48" target="_self">Th48</a></i>;<br/><a NAME="E4:55_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:55_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="cqc_the3.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E5:55_1"/><b>then </b>
 <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:55"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cqc_the3.html#E2:55"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cqc_the3.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E6:55_1"/>
 <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E3:55_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="cqc_the3.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:55"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a> <font color="Maroon">c<sub>4</sub></font> implies  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:55_2"/><i><font color="Green">E46</font></i>: 
 <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:55_2"/><b>then </b>
 <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="cqc_the3.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:55_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:55"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cqc_the3.html#E2:55"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cqc_the3.html#T48" target="_self">Th48</a></i>;<br/><a NAME="E4:55_2"/>
 <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:55_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="cqc_the3.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E5:55_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R1" target="_self">|-</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E1:55"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cqc_the3.html#E2:55"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cqc_the3.html#T48" target="_self">Th48</a></i>;<br/><b>hence </b><a NAME="E6:55_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="cqc_the3.html#E3:55_2"><i><font color="Green">E47</font></i></a>, <a class="ref" href="cqc_the3.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:55"/>
(  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>1</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a>  <a href="cqc_lang.html#K10">'not'</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="cqc_the3.html#R5" target="_self">|-|</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>


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