<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/>



<b>reconsider </b><font color="Maroon">a</font> =  <a href="msualg_3.html#K2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7">bool</a> <font color="Maroon">A</font></span>)</span> as   <a href="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">A</font> ;<br/>
<a NAME="E2:23"/>
<font color="Maroon">a</font> is <a href="closure1.html#V3" target="_self">idempotent</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="pboole.html#M2">Element</a> of  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D4" target="_self">CLOSURE1:def 4</a><br/>

<b>thus </b><a NAME="E1:23_1"/>
<font color="Maroon">a</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font> <a href="pboole.html#R6">=</a> <font color="Maroon">a</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:23"/>
 <a href="msualg_3.html#K2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7">bool</a> <font color="Maroon">A</font></span>)</span> is  <a href="closure1.html#V3" target="_self">idempotent</a> <a href="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">A</font>
 ;<br/>


</div>
