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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>let </b><font color="Maroon">EqR3</font> be   <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">M</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green">E34</font></i>: 
<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">EqR3</font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">EqR</font> being  <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">M</font>  st <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="Olive">EqR</font> holds <br/><font color="Maroon">EqR3</font> <a href="pboole.html#R2">c=</a> <font color="Olive">EqR</font>
 ;<br/>

<a NAME="E3:14"/>
<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="E4:14"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">EqR3</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="E5:14"/>
<font color="Maroon">EqR1</font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">EqR2</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">EqR3</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon">EqR3</font> <a href="pboole.html#R6">=</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#D13">PBOOLE:def 13</a></i>;<br/>


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