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<b>let </b><font color="Maroon">C</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">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/>



<a NAME="E1:35"/><i><font color="Green">E35</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/><b>assume </b><a NAME="E1:35_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span>
 ;<br/><a NAME="E2:35_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:35_1"/><b>then </b><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span> <a href="complex1.html#K12">"</a> 
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span> <a href="complex1.html#K12">"</a> 
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font>
<b>by </b><i>, , <a class="ref" href="partfun2.html#T32">PARTFUN2:32</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:35"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="partfun2.html#T3">PARTFUN2:3</a></i>;<br/>


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