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<b>let </b><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font> holds   <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Olive" title="b1">A</font></span>)</span> is  <a href="closure1.html#V3" title="CLOSURE1:attr.3">idempotent</a> <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Maroon" title="c2">A</font></span>)</span> is  <a href="closure1.html#V3" title="CLOSURE1:attr.3">idempotent</a> <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Maroon" title="c2">A</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c3">a</font> =  <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Maroon" title="c2">A</font></span>)</span> as   <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Maroon" title="c2">A</font> ;<br/>
<a NAME="E2:23"/>
<font color="Maroon" title="c3">a</font> is <a href="closure1.html#V3" title="CLOSURE1:attr.3">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" title="c4">X</font> be    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of  <a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Maroon" title="c2">A</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D4" target="_self" title="CLOSURE1:def.4">CLOSURE1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">a</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font></span>)</span></span><br/>

<b>thus </b><a NAME="E1:23_1"/>
<font color="Maroon" title="c3">a</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c3">a</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="closure1.html#T8" target="_self" title="CLOSURE1:th.8">Th8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:23"/>
 <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Maroon" title="c2">A</font></span>)</span> is  <a href="closure1.html#V3" title="CLOSURE1:attr.3">idempotent</a> <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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