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<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font>, <font color="Maroon" title="c4">Z</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/>







<b>thus </b><a NAME="E1:36"/>
( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c4">Z</font> implies ( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Z</font> &amp; ( for <font color="Olive" title="b1">V</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st <font color="Olive" title="b1">V</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Olive" title="b1">V</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Z</font> holds <br/><font color="Olive" title="b1">V</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font> ) ) )
 <b>by </b><i><a class="ref" href="pboole.html#T17" target="_self" title="PBOOLE:th.17">Th17</a>, <a class="ref" href="pboole.html#T19" target="_self" title="PBOOLE:th.19">Th19</a></i>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:36"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font>
 <b>and </b><br/><a NAME="E3:36"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Z</font>
 <b>and </b><br/><a NAME="E4:36"/><i><font color="Green" title="E29">A3</font></i>: 
for <font color="Olive" title="b1">V</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st <font color="Olive" title="b1">V</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Olive" title="b1">V</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Z</font> holds <br/><font color="Olive" title="b1">V</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font>
 ;<br/>

<b>thus </b><a NAME="E5:36"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c4">Z</font>
 <b>by </b><i><a class="txt" href="pboole.html#E2:36"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="pboole.html#E3:36"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="pboole.html#T19" target="_self" title="PBOOLE:th.19">Th19</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13" target="_self" title="PBOOLE:def.13">PBOOLE:def 13</a><br/>

<a NAME="E6:36"/>
( <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c4">Z</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c4">Z</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">Z</font> implies <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c4">Z</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font> )
 
<b>by </b><i><a class="txt" href="pboole.html#E4:36"><i><font color="Green" title="E29">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:36"/>
<font color="Maroon" title="c3">Y</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c4">Z</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="ref" href="pboole.html#T17" target="_self" title="PBOOLE:th.17">Th17</a></i>;<br/>


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