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<b>let </b><font color="Maroon" title="c1">I</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">M</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c3">EqR1</font>, <font color="Maroon" title="c4">EqR2</font> be   <a href="msualg_5.html#NM1" title="MSUALG_5:NM.1">Equivalence_Relation</a> of <font color="Maroon" title="c2">M</font>;<br/>







<b>thus </b><a NAME="E1:15"/>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font>
 <b>by </b><i><a class="ref" href="pboole.html#T17" title="PBOOLE:th.17">PBOOLE:17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</a><br/>

<a NAME="E2:15"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T16" title="PBOOLE:th.16">PBOOLE:16</a></i>;<br/>
<a NAME="E3:15"/>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">EqR2</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T6" target="_self" title="MSUALG_5:th.6">Th6</a></i>;<br/>
<a NAME="E4:15"/><b>then </b>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font>
 
<b>by </b><i><a class="txt" href="msualg_5.html#E2:15"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">EqR1</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">EqR1</font> <a href="msualg_5.html#K4" title="MSUALG_5:func.4">"\/"</a> <font color="Maroon" title="c4">EqR2</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#T19" title="PBOOLE:th.19">PBOOLE:19</a></i>;<br/>


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