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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:14"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:14"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E3:14"/>
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E4:14"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="msualg_5.html#E2:14"><i><font color="Green">E12</font></i></a></i>;<br/>
<a NAME="E5:14"/>
<font color="Maroon">c<sub>3</sub></font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="msualg_5.html#E1:14"><i><font color="Green">E11</font></i></a>, <a class="ref" href="msualg_5.html#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="msualg_5.html#K4" target="_self">"\/"</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="msualg_5.html#E4:14"><i><font color="Green">E13</font></i></a>, <a class="ref" href="pboole.html#D13">PBOOLE:def 13</a></i>;<br/>


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