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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="E1:65"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">g</font> is <a href="closure2.html#V8" target="_self">monotonic</a>
 <b>and </b><br/><a NAME="E2:65"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">h</font> is <a href="closure2.html#V8" target="_self">monotonic</a>
 ;<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>, <font color="Maroon">Y</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#D13" target="_self">CLOSURE2:def 13</a><br/>

<b>assume </b><a NAME="E3:65"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">X</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">Y</font>
 ;<br/>

<a NAME="E4:65"/><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="E5:65"/>
<font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">X</font> <a href="pboole.html#R2">c=</a> <font color="Maroon">h</font> <a href="closure2.html#K7" target="_self">.</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:65"/><b>then </b>
<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> <a href="pboole.html#R2">c=</a> <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">Y</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:65"/><b>then </b>
<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> <a href="pboole.html#R2">c=</a> <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">Y</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E8:65"/>
<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> <a href="pboole.html#R2">c=</a> <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">Y</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/>


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