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









<b>assume </b><a NAME="E1:18"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">EqR</font> <a href="pboole.html#R6">=</a> <font color="Maroon">EqR1</font> <a href="pboole.html#K3">/\</a> <font color="Maroon">EqR2</font>
 ;<br/>

<a NAME="E2:18"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">EqR1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">EqR1</font> <a href="pboole.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">EqR1</font> <a href="pboole.html#K3">/\</a> <font color="Maroon">EqR2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T37">PBOOLE:37</a></i>;<br/>
<a NAME="E3:18"/>
for <font color="Olive">EqR4</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> <span class="p1">(<span class="default"><font color="Maroon">EqR1</font> <a href="pboole.html#K3">/\</a> <font color="Maroon">EqR2</font></span>)</span> <a href="pboole.html#R2">c=</a> <font color="Olive">EqR4</font> holds <br/><font color="Maroon">EqR1</font> <a href="pboole.html#R2">c=</a> <font color="Olive">EqR4</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T37">PBOOLE:37</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
<font color="Maroon">EqR1</font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">EqR</font> <a href="pboole.html#R6">=</a> <font color="Maroon">EqR1</font>
 <b>by </b><i>, , </i>;<br/>


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