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<span class="kw">let </span><font color="Maroon" title="c1">c</font> be   <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds   <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="rvsum_2.html#K9" title="RVSUM_2:func.9">*</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <font color="Olive" title="b1">F</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="rvsum_2.html#K9" title="RVSUM_2:func.9">*</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <font color="Maroon" title="c2">F</font></span>)</span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">F1</font> = <font color="Maroon" title="c2">F</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="rvsum_2.html#E5"><span class="lab"><font color="Green" title="E3">Lm4</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">s</font> = <font color="Maroon" title="c1">c</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">cM</font> = <a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> <font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span>;<br/>
<span class="kw">thus </span> <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">c</font> <a href="rvsum_2.html#K9" title="RVSUM_2:func.9">*</a> <font color="Maroon" title="c2">F</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> <font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c3">F1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T71" title="SEQ_4:th.71">SEQ_4:71</a>, <a class="ref" href="seq_4.html#T68" title="SEQ_4:th.68">SEQ_4:68</a>, <a class="ref" href="setwop_2.html#T41" title="SETWOP_2:th.41">SETWOP_2:41</a></span>
<br/>.= 
<font color="Maroon" title="c1">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c3">F1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="rvsum_2.html#E3"><span class="lab"><font color="Green" title="E2">Lm3</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c1">c</font> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <font color="Maroon" title="c2">F</font></span>)</span>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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