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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">g</font> be   <a href="closure2.html#NM3">SetOp</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">h</font> be   <a href="closure2.html#NM3">SetOp</a> of <font color="Maroon">M</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:66"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">g</font> is <a href="closure2.html#V9" target="_self">idempotent</a>
 <b>and </b><br/><a NAME="E2:66"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">h</font> is <a href="closure2.html#V9" target="_self">idempotent</a>
 <b>and </b><br/><a NAME="E3:66"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">g</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">h</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">h</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">g</font>
 ;<br/>

<b>let </b><font color="Maroon">X</font> be    <a href="closure2.html#M1" target="_self">Element</a> of  <a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">M</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure2.html#D14" target="_self">CLOSURE2:def 14</a><br/>

<a NAME="E4:66"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:66"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="closure2.html#K6" target="_self">Bool</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font> = 
<font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p3">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="closure2.html#K8" target="_self">*</a> <font color="Maroon">h</font></span>)</span> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
;<br/>


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