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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>



<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T32" target="_self" onmouseover="rs('rfunct_1/T32')" onmouseout="rh()">Th32</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">thus </span><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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T31" target="_self" onmouseover="rs('rfunct_1/T31')" onmouseout="rh()">Th31</a></span>
<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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="rfunct_1.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="rfunct_1.html#T28" target="_self" onmouseover="rs('rfunct_1/T28')" onmouseout="rh()">Th28</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T13" target="_self" onmouseover="rs('rfunct_1/T13')" onmouseout="rh()">Th13</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T31" target="_self" onmouseover="rs('rfunct_1/T31')" onmouseout="rh()">Th31</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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