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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="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:6"/><i><font color="Green">E5</font></i>: 
<span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="partit_2.html#R1" target="_self">c=</a>  <a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="partit_2.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E2:6"/>
<span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="eqrel_1.html#K3">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="partit_2.html#R1" target="_self">c=</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="partit_2.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
 <a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font> <a href="partit_2.html#R1" target="_self">c=</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T4">MSUALG_5:4</a></i>;<br/>
<b>hence </b><a NAME="E4:6"/>
<span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K7">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="partit_2.html#E1:6"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>

<a NAME="E5:6"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K7">*</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="partit_2.html#R1" target="_self">c=</a>  <a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="partit_2.html#T3" target="_self">Th3</a></i>;<br/>
<a NAME="E6:6"/>
<span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="eqrel_1.html#K3">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="partit_2.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K7">*</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="partit_2.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E7:6"/><b>then </b>
 <a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font> <a href="partit_2.html#R1" target="_self">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K7">*</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_5.html#T4">MSUALG_5:4</a></i>;<br/>
<b>hence </b><a NAME="E8:6"/>
<font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K7">*</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K1">nabla</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="partit_2.html#E5:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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