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

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">C</font> be  <a href="connsp_1.html#V2">connected</a> <a href="compts_1.html#V6">compact</a> non <a href="sppol_1.html#V1">horizontal</a> non <a href="sppol_1.html#V2">vertical</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>





<b>assume </b><a NAME="E1:85"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">j</font>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">a<sub>1</sub></font> implies  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> );<br/>
<a NAME="E2:85"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<a NAME="E3:85"/><i><font color="Green">E71</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>proof </b></a><div class="add">

<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/>

<b>assume </b><a NAME="E1:85_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">n</font>]
 ;<br/>

<b>assume </b><a NAME="E2:85_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<a NAME="E3:85_1"/><b>then </b><i><font color="Green">E76</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>set </b><font color="Maroon">j</font> = <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1;<br/>
<b>set </b><font color="Maroon">a</font> =  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font>;<br/>
<b>set </b><font color="Maroon">s</font> =  <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font>;<br/>
<a NAME="E4:85_1"/><i><font color="Green">E78</font></i>: 
(  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span></span>)</span> &amp;  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<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="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="wsierp_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="jordan1a.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E5:85_1"/>
2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="newton.html#T102">NEWTON:102</a></i>;<br/>
<a NAME="E6:85_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="nat_1.html#K2">*</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E7:85_1"/>
 <a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T33">SPRECT_1:33</a></i>;<br/>
<a NAME="E8:85_1"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p0">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p0">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T92">XCMPLX_1:92</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span>

;<br/>
<a NAME="E10:85_1"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p4">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pscomp_1.html#K17">E-bound</a> <font color="Maroon">C</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="pscomp_1.html#K15">W-bound</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="jordan1a.html#T13" target="_self">Th13</a>, <a class="ref" href="jordan1a.html#T14" target="_self">Th14</a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a></i>;<br/>
<a NAME="E11:85_1"/><b>then </b>
 <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">n</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<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="jordan1a.html#T12" target="_self">Th12</a>, <a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/>
<b>hence </b><a NAME="E12:85_1"/>
 <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<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="txt" href="jordan1a.html#E2:85"><i><font color="Green">E65</font></i></a>, <a class="ref" href="jordan1a.html#T11" target="_self">Th11</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:85"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, <a class="txt" href="jordan1a.html#E1:85"><i><font color="Green">E64</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:85"/>
 <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">i</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K15">W-bound</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5">L~</a> <span class="p2">(<span class="default"><a href="jordan9.html#K1">Cage</a> <font color="Maroon">C</font>,<font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/>


</div>
