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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>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K2" target="_self">Bool</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="closure2.html#NM3">SetOp</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</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>;<br/>











<b>assume </b><a NAME="E1:62"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:62"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="closure2.html#V10" target="_self">topological</a>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="closure2.html#D15" target="_self">Def15</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K4">\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#K2">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#T73">PBOOLE:73</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="pboole.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="closure2.html#E1:62"><i><font color="Green">E29</font></i></a>, <a class="txt" href="closure2.html#E2:62"><i><font color="Green">E30</font></i></a>, <a class="ref" href="closure2.html#D15" target="_self">Def15</a></i>
;<br/>
<a NAME="E4:62"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R2">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="pboole.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T16">PBOOLE:16</a></i>;<br/>
<a NAME="E5:62"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#R2">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="pboole.html#K2">\/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="pboole.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T59">PBOOLE:59</a></i>;<br/>
<a NAME="E6:62"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#R2">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T81">PBOOLE:81</a></i>;<br/>
<a NAME="E7:62"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#T62">PBOOLE:62</a></i>;<br/>
<b>hence </b><a NAME="E8:62"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="pboole.html#K4">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="closure2.html#E6:62"><i><font color="Green">E31</font></i></a>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>


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