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<b>set </b><font color="Maroon">c<sub>1</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> ] means <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>;<br/>
<a NAME="E1:16"/>
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <a href="complfld.html#K1">F_Complex</a> 
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D2">RLVECT_1:def 2</a></i>;<br/>
<a NAME="E2:16"/><b>then </b><i><font color="Green">E14</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="finseq_1.html#K6">&lt;*&gt;</a> the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> ]
 
<b>by </b><i><a class="ref" href="polynom5.html#T9" target="_self">Th9</a>, <a class="ref" href="complfld.html#T93">COMPLFLD:93</a>, <a class="ref" href="rlvect_1.html#T60">RLVECT_1:60</a>, <a class="ref" href="rvsum_1.html#T102">RVSUM_1:102</a></i>;<br/>
<div><i><font color="Green">E15</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/><b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>]
 ;<br/><a NAME="E2:16_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:16_1"/>
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="fvsum_1.html#T87">FVSUM_1:87</a></i>;<br/><a NAME="E4:16_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T100">COMPLFLD:100</a></i>;<br/><span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="complfld.html#K3">.|</a></span> = 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="complfld.html#K3">|.</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="complfld.html#K3">.|</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finsop_1.html#T12">FINSOP_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T10" target="_self">Th10</a></i>
<br/>.= 
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T105">RVSUM_1:105</a></i>
<br/>.= 
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span>
<b>by </b><i><a class="ref" href="polynom5.html#T13" target="_self">Th13</a></i>
;<br/><b>hence </b><a NAME="E6:16_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span>]
 <b>by </b><i><a class="txt" href="polynom5.html#E2:16_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="polynom5.html#E4:16_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div>
<b>thus </b><a NAME="E4:16"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a>  holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="finseq_2.html#S2">FINSEQ_2:sch 2</a>(<a class="txt" href="polynom5.html#E2:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="polynom5.html#E3:16"><i><font color="Green">E15</font></i></a>);</i><br/>


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