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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> 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="E1:26"/><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="E2:26"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="pboole.html#M2">Element</a> of  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Olive">b<sub>1</sub></font> <a href="pboole.html#R2">c=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</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#D4" target="_self">CLOSURE1:def 4</a><br/>

<b>thus </b><a NAME="E3:26"/>
<font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>4</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>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="closure1.html#E1:26"><i><font color="Green">E12</font></i></a>, <a class="ref" href="closure1.html#D2" target="_self">Def2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D13">PBOOLE:def 13</a><br/>

<b>thus </b><a NAME="E4:26"/>
<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>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#R2">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="closure1.html#E2:26"><i><font color="Green">E13</font></i></a></i>;<br/>


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