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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="E2:57"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="closure2.html#V10" target="_self">topological</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_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="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#D15" target="_self">CLOSURE2:def 15</a><br/>

<a NAME="E1:57_1"/>
<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#M4">ManySortedSubset</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:57_1_1"/>
( <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="pboole.html#D23">PBOOLE:def 23</a></i>;<br/>
<b>hence </b><a NAME="E2:57_1_1"/>
<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>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D23">PBOOLE:def 23</a><br/>


</div><b>end;</b></div>
<a NAME="E2:57_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="hidden.html#R2">in</a>  <a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="closure2.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</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> = 
<font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
<br/>.= 
<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#K2">\/</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
<br/>.= 
<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#K2">\/</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>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
;<br/><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:57"/>
 <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#V10" target="_self">topological</a> <a href="closure2.html#NM3">SetOp</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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