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

<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g1</font>, <font color="Olive" title="b4">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Olive" title="b4">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b4">g</font></span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b2">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b4">g</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g1</font>, <font color="Maroon" title="c5">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span><br/>









<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <font color="Maroon" title="c5">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T52" target="_self" title="CFUNCT_1:th.52">Th52</a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c4">g1</font></span>)</span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T60" target="_self" title="CFUNCT_1:th.60">Th60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">g1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cfunct_1.html#K1" title="CFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cfunct_1.html#T26" target="_self" title="CFUNCT_1:th.26">Th26</a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
