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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <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>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="closure2.html#NM3">SetOp</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E2:56"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="closure2.html#V9" target="_self">idempotent</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure2.html#D14" target="_self">CLOSURE2:def 14</a><br/>

<b>thus </b><a NAME="E1:56_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:56"/>
 <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is  <a href="closure2.html#V9" target="_self">idempotent</a> <a href="closure2.html#NM3">SetOp</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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