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

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>





<b>assume </b><a NAME="E1:52"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">x1</font> <a href="euclidlp.html#R2" target="_self">//</a> <font color="Maroon">x2</font>
 ;<br/>

<b>then consider </b><font color="Maroon">r</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:52"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font>
 <b>by </b><i/>;<br/>
<a NAME="E4:52"/><i><font color="Green">E88</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="euclidlp.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E5:52"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="euclidlp.html#T2" target="_self">Th2</a>, <a class="ref" href="euclid_4.html#T3">EUCLID_4:3</a></i>;<br/>
<a NAME="E6:52"/><i><font color="Green">E90</font></i>: 
<span class="p1"><a href="euclid_4.html#K5">|(</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="euclid_4.html#K5">)|</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="euclid_4.html#K5">|(</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">x2</font></span><a href="euclid_4.html#K5">)|</a></span>
 
<b>by </b><i><a class="ref" href="euclid_4.html#T26">EUCLID_4:26</a>, <a class="ref" href="euclidlp.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E7:52"/>
<span class="p1"><a href="euclid_4.html#K5">|(</a><span class="default"><font color="Maroon">x2</font>,<font color="Maroon">x2</font></span><a href="euclid_4.html#K5">)|</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="euclidlp.html#T3" target="_self">Th3</a>, <a class="ref" href="euclid_4.html#T22">EUCLID_4:22</a></i>;<br/>
<a NAME="E8:52"/><b>then </b>
<span class="p1"><a href="euclid_4.html#K5">|(</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="euclid_4.html#K5">)|</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="euclidlp.html#T4" target="_self">Th4</a>, <a class="ref" href="euclidlp.html#T5" target="_self">Th5</a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<a NAME="E9:52"/><b>then </b>
not <font color="Maroon">x1</font>,<font color="Maroon">x2</font> <a href="euclid_4.html#R1">are_orthogonal</a> 
 
<b>by </b><i><a class="ref" href="euclid_4.html#D6">EUCLID_4:def 6</a></i>;<br/>
<b>hence </b><a NAME="E10:52"/>
not <font color="Maroon">x1</font> <a href="euclidlp.html#R4" target="_self">_|_</a> <font color="Maroon">x2</font>
 <b>by </b><i/>;<br/>


</div>
