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





<b>thus </b><a NAME="E1:40"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>2</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> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="40_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:40_1"/>
<font color="Maroon">c<sub>2</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> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#T17" target="_self">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13" target="_self">PBOOLE:def 13</a><br/>

<a NAME="E2:40_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</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>2</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E3:40_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R2" target="_self">c=</a> <font color="Maroon">c<sub>2</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="ref" href="pboole.html#T19" target="_self">Th19</a></i>;<br/>


</div><b>end;</b></div>

<b>hence </b><a NAME="E2:40"/>
<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> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E3:40"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K3" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2" target="_self">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K3" target="_self">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="pboole.html#E1:40"><i><font color="Green">E30</font></i></a></i>;<br/>


</div>
