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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="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:31"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="closure1.html#V1" target="_self">reflexive</a>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="closure1.html#V1" target="_self">reflexive</a>
 ;<br/>

<b>let </b><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#D2" target="_self">CLOSURE1:def 2</a><br/>

<a NAME="E3:31"/>
 <a href="mssubfam.html#K1">doms</a> <font color="Maroon">c<sub>4</sub></font> <a href="pboole.html#R6">=</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#T17">MSSUBFAM:17</a></i>;<br/>
<a NAME="E4:31"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K1">doms</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T12">MSSUBFAM:12</a></i>;<br/>
<a NAME="E5:31"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="closure1.html#E2:31"><i><font color="Green">E13</font></i></a>, <a class="ref" href="closure1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E6:31"/>
<font color="Maroon">c<sub>4</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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="txt" href="closure1.html#E1:31"><i><font color="Green">E12</font></i></a>, <a class="ref" href="closure1.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E7:31"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</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="txt" href="closure1.html#E5:31"><i><font color="Green">E15</font></i></a>, <a class="ref" href="pboole.html#T15">PBOOLE:15</a></i>;<br/>
<b>hence </b><a NAME="E8:31"/>
<font color="Maroon">c<sub>5</sub></font> <a href="pboole.html#R2">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="closure1.html#E4:31"><i><font color="Green">E14</font></i></a>, <a class="ref" href="closure1.html#T4" target="_self">Th4</a></i>;<br/>


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