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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> be   <a href="msualg_5.html#NM1">Equivalence_Relation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="eqrel_1.html#NM2">Equivalence_Relation</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="ref" href="msualg_4.html#D3">MSUALG_4:def 3</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
 <a href="msualg_5.html#K1" target="_self">EqCl</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="msualg_5.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="msualg_5.html#K1" target="_self">EqCl</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="msualg_4.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:10"/>
 <a href="msualg_5.html#K3" target="_self">EqCl</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="msualg_5.html#D3" target="_self">Def3</a></i>;<br/>


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