<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">X</font> be   <a href="csspace.html#NM1">ComplexUnitarySpace</a>;<br/><b>let </b><font color="Maroon">seq</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">Cseq</font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>







<a NAME="E1:62"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p4">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:62"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T43">RLVECT_1:43</a></i>;<br/>
<a NAME="E3:62"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">X</font>)
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>;<br/>
<a NAME="E4:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T26">RLVECT_1:26</a></i>;<br/>
<a NAME="E5:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_1.html#K2">+</a> <span class="p5">(<span class="default"><a href="comseq_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_1.html#D10">COMSEQ_1:def 10</a></i>;<br/>
<a NAME="E6:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="comseq_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">Cseq</font></span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_1.html#T26">COMSEQ_1:26</a></i>;<br/>
<a NAME="E7:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="comseq_1.html#K4">(#)</a> <span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">Cseq</font></span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_1.html#T14">COMSEQ_1:14</a></i>;<br/>
<a NAME="E8:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="comseq_1.html#K4">(#)</a> <span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span></span>)</span> <a href="comseq_1.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="comseq_1.html#K4">(#)</a> <font color="Maroon">Cseq</font></span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_1.html#T14">COMSEQ_1:14</a></i>;<br/>
<a NAME="E9:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="comseq_1.html#K4">(#)</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span> <a href="comseq_1.html#K6">-</a> <font color="Maroon">Cseq</font></span>)</span></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="comseq_1.html#T21">COMSEQ_1:21</a></i>;<br/>
<a NAME="E10:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span> <a href="comseq_1.html#K6">-</a> <font color="Maroon">Cseq</font></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p5">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E11:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K9">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span> <a href="comseq_1.html#K6">-</a> <font color="Maroon">Cseq</font></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p5">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E12:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K10">-</a> <a href="complex1.html#K6">1r</a> </span>)</span> <a href="clvect_1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span> <a href="comseq_1.html#K6">-</a> <font color="Maroon">Cseq</font></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p5">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="clvect_1.html#D14">CLVECT_1:def 14</a></i>;<br/>
<a NAME="E13:62"/><b>then </b>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span> <a href="comseq_1.html#K6">-</a> <font color="Maroon">Cseq</font></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p5">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="clvect_1.html#T4">CLVECT_1:4</a></i>;<br/>
<b>hence </b><a NAME="E14:62"/>
<span class="p1">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">Cseq</font> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p3">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">Cseq</font> <a href="comseq_3.html#K6">^\</a> 1</span>)</span> <a href="comseq_1.html#K6">-</a> <font color="Maroon">Cseq</font></span>)</span> <a href="clvect_3.html#K7" target="_self">*</a> <span class="p4">(<span class="default"><a href="clvect_3.html#K1" target="_self">Partial_Sums</a> <font color="Maroon">seq</font></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>
 ;<br/>


</div>
