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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font> &amp; <font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font></span>)</span> )</span><br/>



<b>thus </b><a NAME="E1:45"/>
 <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font>
 <b>by </b><i><a class="ref" href="rfunct_1.html#T48" target="_self" title="RFUNCT_1:th.48">Th48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font></span>)</span></span><br/>

<b>thus </b><font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c2">g</font></span>)</span> = 
<font color="Maroon" title="c1">f</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
<br/>.= 
<font color="Maroon" title="c1">f</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="valued_1.html#K24" title="VALUED_1:func.24">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="rfunct_1.html#T44" target="_self" title="RFUNCT_1:th.44">Th44</a></i>
<br/>.= 
 <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T25" target="_self" title="RFUNCT_1:th.25">Th25</a></i>
<br/>.= 
 <a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rfunct_1.html#K1" title="RFUNCT_1:func.1">/</a> <font color="Maroon" title="c2">g</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T47" target="_self" title="RFUNCT_1:th.47">Th47</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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