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<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> = <font color="Maroon">F<sub>2</sub></font>() as  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="txt" href="cqc_sim1.html#E1:37"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means (  not <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> or ( <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>] ) );<br/>
<a NAME="E2:37_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E1:37"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E3:37_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] or <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>] )
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E1:37"><i><font color="Green">E23</font></i></a>, <a class="txt" href="cqc_sim1.html#E2:37"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E4:37_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>]
 
<b>by </b><i><a class="txt" href="cqc_sim1.html#E1:37"><i><font color="Green">E23</font></i></a>, <a class="txt" href="cqc_sim1.html#E3:37"><i><font color="Green">E25</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:37_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E7:37_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="card_3.html#S3">CARD_3:sch 3</a>(<a class="txt" href="cqc_sim1.html#E2:37_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="cqc_sim1.html#E3:37_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="cqc_sim1.html#E4:37_1"><i><font color="Green">E28</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i><a class="txt" href="cqc_sim1.html#E1:37"><i><font color="Green">E23</font></i></a>, <a class="txt" href="cqc_sim1.html#E6:37_1"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E9:37_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i><a class="txt" href="cqc_sim1.html#E6:37_1"><i><font color="Green">E29</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<b>assume </b><a NAME="E10:37_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/>

<b>hence </b><a NAME="E11:37_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>]
 <b>by </b><i><a class="txt" href="cqc_sim1.html#E6:37_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="cqc_sim1.html#E7:37_1"><i><font color="Green">E30</font></i></a></i>;<br/>


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