<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><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/>





<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"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<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#K8">/\</a> <font color="Maroon">X</font>
<b>by </b><i/>
<br/>.= 
 <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> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_2"><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="E1:55_2"/><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"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span>
 ;<br/><a NAME="E2:55_2"/><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> <span class="p2">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:55_2"/><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> <span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:55_2"/><b>then </b>
<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>
 <b>by </b><i/>;<br/><a NAME="E5:55_2"/><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#K8">/\</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T7" target="_self">Th7</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:55_2"/><b>then </b><i><font color="Green">E41</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"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E7:55_2"/><b>then </b><i><font color="Green">E42</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"><a href="comseq_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self">Th5</a>, <a class="ref" href="partfun2.html#T32">PARTFUN2:32</a></i>
<br/>.= 
 <a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
 <a href="complex1.html#K10">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, <a class="ref" href="partfun2.html#T32">PARTFUN2:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="cfunct_1.html#E12"><i><font color="Green">Lemma46</font></i></a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:55"/>
<span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="comseq_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="partfun2.html#T3">PARTFUN2:3</a></i>;<br/>

<a NAME="E4:55"/><i><font color="Green">E50</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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="tarski.html#R1">c=</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> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i/>;<br/>
<i><font color="Green">E51</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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> = 
<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> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="complex1.html#K5">0c</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="complex1.html#K5">0c</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T50">XBOOLE_1:50</a></i>
<br/>.= 
<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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="complex1.html#K5">0c</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="complex1.html#K5">0c</a> </span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T139">FUNCT_1:139</a></i>
<br/>.= 
 <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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span>
<b>by </b><i/>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_4"><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="E1:55_4"/><i><font color="Green">E80</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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span>
 ;<br/><a NAME="E2:55_4"/><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> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:55_4"/><b>then </b><i><font color="Green">E81</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"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <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="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> = 
<span class="p1">(<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>
<b>by </b><i><a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, <a class="ref" href="partfun2.html#T32">PARTFUN2:32</a></i>
<br/>.= 
<span class="p1">(<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> 
<b>by </b><i><a class="txt" href="cfunct_1.html#E12"><i><font color="Green">Lemma46</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></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><a class="ref" href="cfunct_1.html#T5" target="_self">Th5</a>, <a class="ref" href="cfunct_1.html#T7" target="_self">Th7</a>, <a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, <a class="ref" href="partfun2.html#T32">PARTFUN2:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></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>
<b>by </b><i><a class="ref" href="cfunct_1.html#T7" target="_self">Th7</a>, <a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:55"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cfunct_1.html#K2" target="_self">^</a> </span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="cfunct_1.html#K2" target="_self">^</a> 
 <b>by </b><i><a class="ref" href="cfunct_1.html#T7" target="_self">Th7</a>, <a class="ref" href="partfun2.html#T3">PARTFUN2:3</a></i>;<br/>

<i><font color="Green">E82</font></i>:  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<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#K8">/\</a> <font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="comseq_1.html#D13">COMSEQ_1:def 13</a></i>
<br/>.= 
 <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> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span>
<b>by </b><i><a class="ref" href="comseq_1.html#D13">COMSEQ_1:def 13</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_6"><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="E1:55_6"/><i><font color="Green">E83</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"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span>
 ;<br/><a NAME="E2:55_6"/><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> <span class="p2"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:55_6"/><b>then </b><i><font color="Green">E84</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"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:55_6"/><i><font color="Green">E86</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"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, <a class="txt" href="cfunct_1.html#E12"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="comseq_1.html#D13">COMSEQ_1:def 13</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> = 
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="txt" href="cfunct_1.html#E12"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><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></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T15" target="_self">Th15</a>, <a class="ref" href="comseq_1.html#D13">COMSEQ_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T16" target="_self">Th16</a>, <a class="ref" href="partfun2.html#T32">PARTFUN2:32</a></i>
<br/>.= 
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, <a class="txt" href="cfunct_1.html#E12"><i><font color="Green">Lemma46</font></i></a>, <a class="ref" href="comseq_1.html#D13">COMSEQ_1:def 13</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:55"/>
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">f</font></span><a href="comseq_1.html#K9">.|</a></span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span></span><a href="comseq_1.html#K9">.|</a></span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T9" target="_self">Th9</a>, <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>


</div>
