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<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">M</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">EqR1</font> be   <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">EqR2</font> be   <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">M</font>;<br/>







<b>thus </b><a NAME="E1:17"/>
<font color="Maroon">EqR1</font> <a href="pboole.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">EqR1</font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">EqR2</font></span>)</span> <a href="pboole.html#R2">c=</a> <font color="Maroon">EqR1</font>
 <b>by </b><i><a class="ref" href="pboole.html#T17">PBOOLE:17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13">PBOOLE:def 13</a><br/>

<a NAME="E2:17"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">EqR1</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">EqR1</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">EqR2</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T16">PBOOLE:16</a></i>;<br/>
<a NAME="E3:17"/>
<font color="Maroon">EqR1</font> <a href="pboole.html#K2">\/</a> <font color="Maroon">EqR2</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">EqR1</font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">EqR2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:17"/><b>then </b>
<font color="Maroon">EqR1</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">EqR1</font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">EqR2</font>
 
<b>by </b><i>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
<font color="Maroon">EqR1</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">EqR1</font> <a href="pboole.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">EqR1</font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">EqR2</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#T19">PBOOLE:19</a></i>;<br/>


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