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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>













<b>assume </b><a NAME="E1:29"/><i><font color="Green">E39</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>

<b>assume </b><a NAME="E2:29"/>
<font color="Maroon">u</font>,<font color="Maroon">u1</font>,<font color="Maroon">v</font>,<font color="Maroon">v1</font> <a href="analort.html#R1" target="_self">are_COrte_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>

<a NAME="E3:29"/><b>then </b>
 <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">v</font>,<font color="Maroon">v1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:29"/><b>then </b>
<font color="Maroon">v</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a>  <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21">ANALOAF:21</a></i>;<br/>
<a NAME="E5:29"/><b>then </b>
 <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a>  <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u</font></span>)</span>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:29"/><b>then </b>
 <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<span class="p1">(<span class="default"><a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">u1</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:29"/><b>then </b>
 <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font>, <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:29"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font>, <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font> <a href="analoaf.html#R1">//</a>  <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v1</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21">ANALOAF:21</a></i>;<br/>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font></span>)</span> = 
<font color="Maroon">u</font> <a href="analort.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<font color="Maroon">u</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font>

;<br/>
<a NAME="E10:29"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font>, <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u1</font>,<font color="Maroon">u</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T24">ANALOAF:24</a></i>;<br/>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:29_2"/>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font>
 ;<br/><a NAME="E2:29_2"/><b>then </b>
 <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u1</font>,<font color="Maroon">u</font>
 <b>by </b><i>, , <a class="ref" href="analoaf.html#T20">ANALOAF:20</a></i>;<br/><b>hence </b><a NAME="E3:29_2"/>
<font color="Maroon">v</font>,<font color="Maroon">v1</font>,<font color="Maroon">u1</font>,<font color="Maroon">u</font> <a href="analort.html#R1" target="_self">are_COrte_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:29_3"/>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font>
 ;<br/><b>then </b><font color="Maroon">u</font> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">u1</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<font color="Maroon">u1</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
;<br/><a NAME="E3:29_3"/><b>then </b>
 <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v</font>, <a href="analort.html#K3" target="_self">Orte</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">v1</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u1</font>,<font color="Maroon">u</font>
 <b>by </b><i><a class="ref" href="analoaf.html#T18">ANALOAF:18</a></i>;<br/><b>hence </b><a NAME="E4:29_3"/>
<font color="Maroon">v</font>,<font color="Maroon">v1</font>,<font color="Maroon">u1</font>,<font color="Maroon">u</font> <a href="analort.html#R1" target="_self">are_COrte_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:29"/>
<font color="Maroon">v</font>,<font color="Maroon">v1</font>,<font color="Maroon">u1</font>,<font color="Maroon">u</font> <a href="analort.html#R1" target="_self">are_COrte_wrt</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/>


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