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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</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="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <font color="Maroon" title="c1">f</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">g</font> =  <a href="rvsum_4.html#K15" title="RVSUM_4:func.15">Re</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <font color="Maroon" title="c1">f</font></span>)</span> as   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">h</font> =  <a href="rvsum_4.html#K16" title="RVSUM_4:func.16">Im</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <font color="Maroon" title="c1">f</font></span>)</span> as   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a> ;<br/>
<a NAME="E3:124"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
(  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" title="COMSEQ_3:func.3">Re</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K3" title="COMSEQ_3:func.3">Re</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> &amp;  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" title="COMSEQ_3:func.4">Im</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K4" title="COMSEQ_3:func.4">Im</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T66" target="_self" onmouseover="rs('rvsum_4/T66')" onmouseout="rh()">SSF</a></span>;<br/>
<a NAME="E4:124"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
(  <a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K3" title="COMSEQ_3:func.3">Re</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rvsum_4.html#K15" title="RVSUM_4:func.15">Re</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp;  <a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K4" title="COMSEQ_3:func.4">Im</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="rvsum_4.html#K16" title="RVSUM_4:func.16">Im</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <font color="Maroon" title="c1">f</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T24" target="_self" onmouseover="rs('rvsum_4/T24')" onmouseout="rh()">RSF</a>, <a class="ref" href="rvsum_4.html#T25" target="_self" onmouseover="rs('rvsum_4/T25')" onmouseout="rh()">ISF</a></span>;<br/>
 <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font> = 
<span class="p1">(<span class="default"><a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <span class="p3">(<span class="default"><a href="comseq_3.html#K3" title="COMSEQ_3:func.3">Re</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p3">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <span class="p4">(<span class="default"><a href="comseq_3.html#K4" title="COMSEQ_3:func.4">Im</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:124"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="rvsum_4.html#T61" target="_self" onmouseover="rs('rvsum_4/T61')" onmouseout="rh()">RSI</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c3">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:124"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="comseq_3.html#T56" onmouseover="rs('comseq_3/T56')" onmouseout="rh()">COMSEQ_3:56</a></span>
<br/>.= 
 <a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p2">(<span class="default"><a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c3">h</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="comseq_3.html#T54" onmouseover="rs('comseq_3/T54')" onmouseout="rh()">COMSEQ_3:54</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:124"/>
 <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p1">(<span class="default"><a href="rvsum_4.html#K7" title="RVSUM_4:func.7">Sequel</a> <font color="Maroon" title="c1">f</font></span>)</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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