<?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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</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="E1:16"/><i><font color="Green">E16</font></i>: 
 <a href="analmetr.html#R1" target="_self">Gen</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:16"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E6:16"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E7:16"/><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="analmetr.html#E2:16"><i><font color="Green">E17</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E9:16"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E10:16"/><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="analmetr.html#E3:16"><i><font color="Green">E18</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E11:16"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:16"><i><font color="Green">E16</font></i></a>, <a class="txt" href="analmetr.html#E6:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="analmetr.html#E9:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="analmetr.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:16_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="analmetr.html#E4:16"><i><font color="Green">E19</font></i></a>, <a class="txt" href="analmetr.html#E6:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="analmetr.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/><a NAME="E3:16_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="analmetr.html#E10:16"><i><font color="Green">E23</font></i></a>, <a class="txt" href="analmetr.html#E11:16"><i><font color="Green">E24</font></i></a>, <a class="txt" href="analmetr.html#E1:16_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E4:16_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="analmetr.html#E7:16"><i><font color="Green">E21</font></i></a>, <a class="txt" href="analmetr.html#E1:16_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="analmetr.html#E2:16_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E5:16_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="analmetr.html#E9:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="analmetr.html#E3:16_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>;<br/><a NAME="E6:16_1"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>;<br/><i><font color="Green">E31</font></i>: <font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="analmetr.html#E5:16_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
<font color="Maroon">c<sub>9</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="analmetr.html#E6:16_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><b>then </b>1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> = 
0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="analmetr.html#E6:16_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="rlvect_1.html#D9">RLVECT_1:def 9</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
;<br/><b>hence </b><a NAME="E3:16_1_2"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:16_1"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:16_1"><i><font color="Green">E31</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><a NAME="E2:16_2"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:16"><i><font color="Green">E21</font></i></a>, <a class="txt" href="analmetr.html#E10:16"><i><font color="Green">E23</font></i></a>, <a class="txt" href="analmetr.html#E11:16"><i><font color="Green">E24</font></i></a></i>;<br/><i><font color="Green">E28</font></i>: <font color="Maroon">c<sub>9</sub></font> = 
1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="analmetr.html#E1:16_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="analmetr.html#E2:16_2"><i><font color="Green">E27</font></i></a></i>
;<br/><i><font color="Green">E29</font></i>: <font color="Maroon">c<sub>13</sub></font> = 
1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>13</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="analmetr.html#E1:16_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="analmetr.html#E2:16_2"><i><font color="Green">E27</font></i></a></i>
;<br/><a NAME="E5:16_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></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">c<sub>10</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="analmetr.html#E9:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="analmetr.html#E3"><i><font color="Green">Lemma3</font></i></a></i>;<br/><a NAME="E6:16_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span>
 ;<br/><div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_3"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 ;<br/><b>take </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>10</sub></font>;<br/><b>thus </b><a NAME="E2:16_2_3"/>
( <font color="Maroon">c<sub>15</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="analmetr.html#E3:16_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="analmetr.html#E5:16_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="analmetr.html#E6:16_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="analmetr.html#E1:16_2_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="analmetr.html#E3"><i><font color="Green">Lemma3</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2_4"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:16_2_4"/><b>then </b>
1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E6:16"><i><font color="Green">E20</font></i></a>, <a class="txt" href="analmetr.html#E9:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="analmetr.html#E3:16_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="analmetr.html#E4:16_2"><i><font color="Green">E29</font></i></a></i>;<br/><b>hence </b><a NAME="E3:16_2_4"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:16_2"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E7:16_2"><i><font color="Green">E32</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:16"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) )
 <b>by </b><i><a class="txt" href="analmetr.html#E12:16"><i><font color="Green">E25</font></i></a></i>;<br/>


</div>
