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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:64"/><i><font color="Green">E60</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:64"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E3:64"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E4:64"/>
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E2:64"><i><font color="Green">E61</font></i></a>, <a class="txt" href="geomtrap.html#E3:64"><i><font color="Green">E62</font></i></a>, <a class="ref" href="geomtrap.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E5:64"/><b>then </b><i><font color="Green">E63</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="ref" href="geomtrap.html#T28" target="_self">Th28</a></i>;<br/>
<div><i><font color="Green">E64</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:64_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/><a NAME="E2:64_1"/>
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E3:64"><i><font color="Green">E62</font></i></a>, <a class="ref" href="geomtrap.html#T23" target="_self">Th23</a></i>;<br/><b>hence </b><a NAME="E3:64_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E5:64"><i><font color="Green">E63</font></i></a>, <a class="txt" href="geomtrap.html#E1:64_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="geomtrap.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E65</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="64_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:64_2"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:64_2"/>
<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E3:64"><i><font color="Green">E62</font></i></a>, <a class="ref" href="geomtrap.html#T23" target="_self">Th23</a></i>;<br/><b>hence </b><a NAME="E3:64_2"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E5:64"><i><font color="Green">E63</font></i></a>, <a class="txt" href="geomtrap.html#E1:64_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="geomtrap.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:64_3"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/><a NAME="E2:64_3"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R1">//</a> <font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="analoaf.html#T18">ANALOAF:18</a></i>;<br/><a NAME="E3:64_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="geomtrap.html#K1" target="_self">#</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E1:64_3"><i><font color="Green">E66</font></i></a>, <a class="txt" href="geomtrap.html#E23"><i><font color="Green">Lemma20</font></i></a></i>;<br/><a NAME="E4:64_3"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="geomtrap.html#K1" target="_self">#</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E22"><i><font color="Green">Lemma19</font></i></a></i>;<br/><a NAME="E5:64_3"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E1:64_3_1"/>
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>8</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E3:64"><i><font color="Green">E62</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E2:64_3_1"/><b>then </b><i><font color="Green">E69</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:64_3"><i><font color="Green">E66</font></i></a>, <a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/>
<a NAME="E3:64_3_1"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></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">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_3_1_1"><b>proof </b></a><div class="add">

<i><font color="Green">E71</font></i>: 2 <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="geomtrap.html#D2" target="_self">Def2</a></i>
;<br/>
<i><font color="Green">E72</font></i>:  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default">1 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></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"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E53"><i><font color="Green">Lemma48</font></i></a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> 2</span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default">2 <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E1:64_3_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="rlvect_1.html#T48">RLVECT_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="geomtrap.html#E2:64_3_1_1"><i><font color="Green">E72</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_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="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></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">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
;<br/>
<b>hence </b><a NAME="E4:64_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></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">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:64_3_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:64_3_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="analmetr.html#T11">ANALMETR:11</a></i>;<br/>
<a NAME="E5:64_3_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:64"><i><font color="Green">E60</font></i></a>, <a class="txt" href="geomtrap.html#E3:64_3_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="analmetr.html#T14">ANALMETR:14</a></i>;<br/>
<b>hence </b><a NAME="E6:64_3_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E6:64_3"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E1:64_3"><i><font color="Green">E66</font></i></a>, <a class="txt" href="geomtrap.html#E2:64_3"><i><font color="Green">E67</font></i></a>, <a class="txt" href="geomtrap.html#E4:64_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:64"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E6:64"><i><font color="Green">E64</font></i></a>, <a class="txt" href="geomtrap.html#E7:64"><i><font color="Green">E65</font></i></a></i>;<br/>


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