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<b>let </b><font color="Maroon">I</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">M</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="closure1.html#NM1">MSSetOp</a> of <font color="Maroon">M</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:33"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">P</font> is <a href="closure1.html#V3" target="_self">idempotent</a>
 <b>and </b><br/><a NAME="E2:33"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">R</font> is <a href="closure1.html#V3" target="_self">idempotent</a>
 <b>and </b><br/><a NAME="E3:33"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">P</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">R</font> <a href="pboole.html#R6">=</a> <font color="Maroon">R</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">P</font>
 ;<br/>

<b>let </b><font color="Maroon">X</font> be    <a href="pboole.html#M2">Element</a> of  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">M</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D4" target="_self">CLOSURE1:def 4</a><br/>

<a NAME="E4:33"/><i><font color="Green">E38</font></i>: 
 <a href="mssubfam.html#K1">doms</a> <font color="Maroon">R</font> <a href="pboole.html#R6">=</a>  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T17">MSSUBFAM:17</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K1">doms</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T12">MSSUBFAM:12</a></i>;<br/>
<a NAME="E6:33"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K1">doms</a> <font color="Maroon">R</font>
 
<b>by </b><i>, <a class="ref" href="mssubfam.html#T12">MSSUBFAM:12</a></i>;<br/>
<a NAME="E7:33"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">R</font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K1">doms</a> <font color="Maroon">R</font>
 
<b>by </b><i>, <a class="ref" href="mssubfam.html#T12">MSSUBFAM:12</a></i>;<br/>
<a NAME="E8:33"/>
 <a href="mssubfam.html#K1">doms</a> <font color="Maroon">P</font> <a href="pboole.html#R6">=</a>  <a href="mssubfam.html#K7">bool</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T17">MSSUBFAM:17</a></i>;<br/>
<a NAME="E9:33"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font> <a href="pboole.html#R1">in</a>  <a href="mssubfam.html#K1">doms</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="mssubfam.html#T12">MSSUBFAM:12</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">R</font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font> = 
<font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">P</font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">P</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="closure1.html#K3" target="_self">..</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">R</font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">R</font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="closure1.html#K4" target="_self">**</a> <font color="Maroon">R</font></span>)</span> <a href="closure1.html#K3" target="_self">..</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i>, </i>
;<br/>


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