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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</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">  for <font color="Olive" title="b1">g</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds <br/> (  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Olive" title="b1">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Olive" title="b1">g</font></span>)</span> &amp;  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">g</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Olive" title="b1">g</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</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> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</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="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">g</font></span>)</span> &amp;  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">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="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> )</span><br/>



<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"><font color="Maroon" title="c1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <font color="Maroon" title="c2">g</font></span>)</span> = 
 <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <span class="p3">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T39" target="_self" onmouseover="rs('rvsum_4/T39')" onmouseout="rh()">XFX</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T55" onmouseover="rs('afinsq_2/T55')" onmouseout="rh()">AFINSQ_2:55</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_4.html#T65" target="_self" onmouseover="rs('rvsum_4/T65')" onmouseout="rh()">FSS</a></span>
;<br/>
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c1">f</font></span>)</span> = 
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K9" title="AFINSQ_1:func.9">FS2XFS</a> <span class="p3">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</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#T40" target="_self" onmouseover="rs('rvsum_4/T40')" onmouseout="rh()">FXF</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">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="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p2">(<span class="default"><a href="rvsum_4.html#K11" title="RVSUM_4:func.11">XFS2FS</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_2.html#T32" onmouseover="rs('rvsum_2/T32')" onmouseout="rh()">RVSUM_2:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">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="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</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#T64" target="_self" onmouseover="rs('rvsum_4/T64')" onmouseout="rh()">XSS</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:125"/>
(  <a href="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="rvsum_4.html#K13" title="RVSUM_4:func.13">^</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="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">g</font></span>)</span> &amp;  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="rvsum_4.html#K12" title="RVSUM_4:func.12">^</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">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="afinsq_2.html#K7" title="AFINSQ_2:func.7">Sum</a> <font color="Maroon" title="c1">f</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:125"><span class="lab"><font color="Green" title="E47">A1</font></span></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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