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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/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:79_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">c<sub>2</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>
 ;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K4" target="_self">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</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#T76" target="_self">Th76</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="pboole.html#E1:79_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="pboole.html#T65" target="_self">Th65</a></i>
;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:79"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K4" target="_self">\</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6" target="_self">=</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>2</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#T69" target="_self">Th69</a></i>;<br/>


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