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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>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="pboole.html#M1" target="_self">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:119"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:119"/><b>then </b><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T16" target="_self">Th16</a></i>;<br/>
<b>assume </b><a NAME="E3:119"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R5" target="_self">misses</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R5" target="_self">misses</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E4:119"/><b>then </b><i><font color="Green">E69</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6" target="_self">=</a>  <a href="pboole.html#K1" target="_self">[0]</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T121" target="_self">Th121</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pboole.html#E2:119"><i><font color="Green">E68</font></i></a>, <a class="ref" href="pboole.html#T25" target="_self">Th25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K2" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T38" target="_self">Th38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="pboole.html#E4:119"><i><font color="Green">E69</font></i></a>, <a class="ref" href="pboole.html#T38" target="_self">Th38</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="pboole.html#E2:119"><i><font color="Green">E68</font></i></a>, <a class="ref" href="pboole.html#T25" target="_self">Th25</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="pboole.html#E2:119"><i><font color="Green">E68</font></i></a>, <a class="ref" href="pboole.html#T25" target="_self">Th25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K2" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T38" target="_self">Th38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="pboole.html#E4:119"><i><font color="Green">E69</font></i></a>, <a class="ref" href="pboole.html#T38" target="_self">Th38</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="pboole.html#E2:119"><i><font color="Green">E68</font></i></a>, <a class="ref" href="pboole.html#T25" target="_self">Th25</a></i>
;<br/>


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