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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</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"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><span class="p2">(<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">f2</font></span>)</span></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Olive" title="b1">f1</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">/</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Olive" title="b2">f2</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f2</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><span class="p2">(<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">f2</font></span>)</span></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c2">f1</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">/</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c3">f2</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></span><br/>





<span class="kw">thus </span><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><span class="p2">(<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">f2</font></span>)</span></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> = 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><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> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a></span>)</span></span>)</span></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cfunct_1.html#T39" target="_self" title="CFUNCT_1:th.39">Th51</a></span>
<br/>.= 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c2">f1</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f2</font> <a href="cfunct_1.html#K2" title="CFUNCT_1:func.2">^</a></span>)</span></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cfunct_1.html#T29" target="_self" title="CFUNCT_1:th.29">Th38</a></span>
<br/>.= 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c2">f1</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c3">f2</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="rfunct_1.html#K6" title="RFUNCT_1:func.6">^</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cfunct_1.html#T38" target="_self" title="CFUNCT_1:th.38">Th50</a></span>
<br/>.= 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c2">f1</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">/</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c3">f2</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T31" title="RFUNCT_1:th.31">RFUNCT_1:31</a></span>
; <a class="txt" 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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