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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:54"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:54"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:54"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E5:54"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="normform.html#T55" target="_self">Th55</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:54"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="normform.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E8:54"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="normform.html#K9" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="normform.html#E3:54"><i><font color="Green">E40</font></i></a>, <a class="ref" href="normform.html#T65" target="_self">Th65</a></i>;<br/>
<a NAME="E9:54"/>
<font color="Maroon">c<sub>7</sub></font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c<sub>6</sub></font> <a href="normform.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="normform.html#E5:54"><i><font color="Green">E42</font></i></a>, <a class="txt" href="normform.html#E7:54"><i><font color="Green">E43</font></i></a>, <a class="ref" href="normform.html#T28" target="_self">Th28</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="normform.html#K1" target="_self">\/</a> <font color="Maroon">c<sub>6</sub></font> as    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K7" target="_self">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="normform.html#T45" target="_self">Th45</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>8</sub></font>
;<br/>

<b>thus </b><a NAME="E11:54"/>
<font color="Maroon">c<sub>8</sub></font> <a href="normform.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="normform.html#E5:54"><i><font color="Green">E42</font></i></a>, <a class="txt" href="normform.html#E7:54"><i><font color="Green">E43</font></i></a>, <a class="ref" href="normform.html#T28" target="_self">Th28</a></i>;<br/>

<b>thus </b><a NAME="E12:54"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="normform.html#K9" target="_self">mi</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="normform.html#E4:54"><i><font color="Green">E41</font></i></a>, <a class="txt" href="normform.html#E8:54"><i><font color="Green">E44</font></i></a>, <a class="ref" href="normform.html#T56" target="_self">Th56</a></i>;<br/>


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