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<b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be  <a href="prob_2.html#V1">disjoint_valued</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">D</font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">F1</font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">X</font>,<font color="Maroon">D</font>, <font color="Maroon">F2</font> be    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">X</font>,<font color="Maroon">D</font>;<br/>







<b>assume </b><a NAME="E1:11"/><i><font color="Green">E24</font></i>: 
 <a href="msafree1.html#K1" target="_self">Flatten</a> <font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a>  <a href="msafree1.html#K1" target="_self">Flatten</a> <font color="Maroon">F2</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:11_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/><b>then reconsider </b><font color="Maroon">Di</font> = <font color="Maroon">D</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  <b>by </b><i><a class="ref" href="pboole.html#D16">PBOOLE:def 16</a></i>;<br/><b>reconsider </b><font color="Maroon">f1</font> = <font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>, <font color="Maroon">f2</font> = <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">Di</font> <b>by </b><i>, <a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:11_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/><b>hence </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="msafree1.html#K1" target="_self">Flatten</a> <font color="Maroon">F1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, , , </i>
;<br/><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:11_1"/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:11"/>
<font color="Maroon">F1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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