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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="msualg_3.html#K2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E2:24"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="closure1.html#V4" target="_self">topological</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="pboole.html#M2">Element</a> of  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D5" target="_self">CLOSURE1:def 5</a><br/>

<a NAME="E1:24_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="mssubfam.html#T12">MSSUBFAM:12</a></i>;<br/>
<a NAME="E2:24_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="mboolean.html#T1">MBOOLEAN:1</a></i>;<br/>
<a NAME="E3:24_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#T18">PBOOLE:18</a></i>;<br/>
<a NAME="E4:24_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="mboolean.html#T1">MBOOLEAN:1</a></i>;<br/>
<a NAME="E5:24_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font> is    <a href="pboole.html#M2">Element</a> of  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T11">MSSUBFAM:11</a></i>;<br/>
<b>hence </b><a NAME="E6:24_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K1" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="pboole.html#R6">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="closure1.html#T10" target="_self">Th10</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:24"/>
 <a href="msualg_3.html#K2">id</a> <span class="p1">(<span class="default"><a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is  <a href="closure1.html#V4" target="_self">topological</a> <a href="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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