<?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>, <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>, <font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





















<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  )
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green">E45</font></i>: 
<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>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="anproj_2.html#R4" target="_self">lie_on_an_angle</a> 
 <b>and </b><br/><a NAME="E3:43"/><i><font color="Green">E46</font></i>: 
<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>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="anproj_2.html#R5" target="_self">are_half_mutually_not_Prop</a> 
 <b>and </b><br/><a NAME="E4:43"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <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="anproj_1.html#R2">are_LinDep</a>  )
 ;<br/>

<a NAME="E5:43"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>6</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>8</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>9</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>10</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E1:43"><i><font color="Green">E44</font></i></a>, <a class="ref" href="anproj_2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E6:43"/><i><font color="Green">E49</font></i>: 
( not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E2:43"><i><font color="Green">E45</font></i></a>, <a class="ref" href="anproj_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E7:43"/><i><font color="Green">E50</font></i>: 
( not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E3:43"><i><font color="Green">E46</font></i></a>, <a class="ref" href="anproj_2.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E8:43"/><i><font color="Green">E51</font></i>: 
( not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T17">ANPROJ_1:17</a></i>;<br/>
<a NAME="E9:43"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="anproj_2.html#R1" target="_self">are_Prop_Vect</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="ref" href="anproj_2.html#D1" target="_self">Def1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E11:43"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <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>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green">E51</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self">Th6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E13:43"/><i><font color="Green">E54</font></i>: 
( <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>2</sub></font> <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> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green">E51</font></i></a>, <a class="txt" href="anproj_2.html#E9:43"><i><font color="Green">E52</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self">Th6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E15:43"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green">E51</font></i></a>, <a class="txt" href="anproj_2.html#E9:43"><i><font color="Green">E52</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self">Th6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E17:43"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>19</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E8:43"><i><font color="Green">E51</font></i></a>, <a class="txt" href="anproj_2.html#E9:43"><i><font color="Green">E52</font></i></a>, <a class="ref" href="anproj_2.html#T6" target="_self">Th6</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>2</sub></font> <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>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>2</sub></font> <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>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E18:43"/><i><font color="Green">E57</font></i>: 
(  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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;  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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> &amp;  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp;  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E11:43"><i><font color="Green">E53</font></i></a>, <a class="txt" href="anproj_2.html#E13:43"><i><font color="Green">E54</font></i></a>, <a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E17:43"><i><font color="Green">E56</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<a NAME="E19:43"/><i><font color="Green">E58</font></i>: 
( not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <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> &amp; not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_1"/><i><font color="Green">E59</font></i>: 
(  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <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> or  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> )
 ;<br/>

<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:43_1_1"/>
 <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <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>
 ;<br/><a NAME="E2:43_1_1"/><b>then </b>
 <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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>by </b><i><a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T6">ANPROJ_1:6</a></i>;<br/><b>hence </b><a NAME="E3:43_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T6">ANPROJ_1:6</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:43_1_2"/>
 <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/><a NAME="E2:43_1_2"/><b>then </b>
 <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T6">ANPROJ_1:6</a></i>;<br/><b>hence </b><a NAME="E3:43_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T6">ANPROJ_1:6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:43_1"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E1:43_1"><i><font color="Green">E59</font></i></a>, <a class="txt" href="anproj_2.html#E2:43_1"><i><font color="Green">E60</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:43"/><i><font color="Green">E59</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_2"/>
 <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:43_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<b>hence </b><a NAME="E3:43_2"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:43"/><i><font color="Green">E60</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E22:43"/><i><font color="Green">E61</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_3"/>
 <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:43_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<b>hence </b><a NAME="E3:43_3"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E23:43"/><i><font color="Green">E62</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E24:43"/>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_4"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 ;<br/>

<a NAME="E2:43_4"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E3:43_4"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E4:43_4"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T16">ANPROJ_1:16</a></i>;<br/>
<b>hence </b><a NAME="E5:43_4"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E2:43_4"><i><font color="Green">E63</font></i></a>, <a class="txt" href="anproj_2.html#E3:43_4"><i><font color="Green">E64</font></i></a>, <a class="ref" href="anproj_1.html#T19">ANPROJ_1:19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E25:43"/><b>then </b><i><font color="Green">E63</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E26:43"/>
not <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_5"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 ;<br/>

<a NAME="E2:43_5"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E3:43_5"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E4:43_5"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#T16">ANPROJ_1:16</a></i>;<br/>
<b>hence </b><a NAME="E5:43_5"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E7:43"><i><font color="Green">E50</font></i></a>, <a class="txt" href="anproj_2.html#E2:43_5"><i><font color="Green">E64</font></i></a>, <a class="txt" href="anproj_2.html#E3:43_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="anproj_1.html#T19">ANPROJ_1:19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E27:43"/><b>then </b><i><font color="Green">E64</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E28:43"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>11</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green">E47</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E29:43"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>10</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green">E47</font></i></a>, <a class="ref" href="anproj_1.html#T10">ANPROJ_1:10</a></i>;<br/>
<a NAME="E30:43"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <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> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <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> <a href="anproj_1.html#NR1" target="_self">is_Prop_Vect</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E11:43"><i><font color="Green">E53</font></i></a>, <a class="txt" href="anproj_2.html#E13:43"><i><font color="Green">E54</font></i></a>, <a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E17:43"><i><font color="Green">E56</font></i></a>, <a class="txt" href="anproj_2.html#E33"><i><font color="Green">Lemma33</font></i></a></i>;<br/>
<a NAME="E31:43"/><i><font color="Green">E68</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E20:43"><i><font color="Green">E59</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green">Lemma30</font></i></a></i>;<br/>
<a NAME="E32:43"/><i><font color="Green">E69</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E11:43"><i><font color="Green">E53</font></i></a>, <a class="txt" href="anproj_2.html#E21:43"><i><font color="Green">E60</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green">Lemma30</font></i></a></i>;<br/>
<a NAME="E33:43"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green">E47</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E34:43"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>10</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="txt" href="anproj_2.html#E29:43"><i><font color="Green">E66</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<a NAME="E35:43"/><i><font color="Green">E72</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E17:43"><i><font color="Green">E56</font></i></a>, <a class="txt" href="anproj_2.html#E22:43"><i><font color="Green">E61</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green">Lemma30</font></i></a></i>;<br/>
<a NAME="E36:43"/><i><font color="Green">E73</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <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>by </b><i><a class="txt" href="anproj_2.html#E13:43"><i><font color="Green">E54</font></i></a>, <a class="txt" href="anproj_2.html#E23:43"><i><font color="Green">E62</font></i></a>, <a class="txt" href="anproj_2.html#E30"><i><font color="Green">Lemma30</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>25</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E38:43"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>24</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E28:43"><i><font color="Green">E65</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green">E67</font></i></a>, <a class="txt" href="anproj_2.html#E31:43"><i><font color="Green">E68</font></i></a>, <a class="ref" href="anproj_1.html#T11">ANPROJ_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>26</sub></font>, <font color="Maroon">c<sub>27</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E40:43"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>26</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<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></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E28:43"><i><font color="Green">E65</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green">E67</font></i></a>, <a class="txt" href="anproj_2.html#E32:43"><i><font color="Green">E69</font></i></a>, <a class="ref" href="anproj_1.html#T11">ANPROJ_1:11</a></i>;<br/>
<a NAME="E41:43"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>11</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>25</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="p2">(<span class="default"><font color="Maroon">c<sub>24</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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>25</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E38:43"><i><font color="Green">E74</font></i></a>, <a class="txt" href="anproj_2.html#E31"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<a NAME="E42:43"/>
<font color="Maroon">c<sub>11</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>27</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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>26</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E40:43"><i><font color="Green">E75</font></i></a>, <a class="txt" href="anproj_2.html#E32"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<a NAME="E43:43"/><b>then </b><i><font color="Green">E77</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>27</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>25</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>26</sub></font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E41:43"><i><font color="Green">E76</font></i></a>, <a class="ref" href="anproj_1.html#T13">ANPROJ_1:13</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>28</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E44:43"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_6"/>
not <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>then </b><font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="anproj_2.html#E38:43"><i><font color="Green">E74</font></i></a>, <a class="txt" href="anproj_2.html#E43:43"><i><font color="Green">E77</font></i></a>, <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</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="ref" href="rlvect_1.html#T23">RLVECT_1:23</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#T10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:43_6"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="ref" href="rlvect_1.html#D13">RLVECT_1:def 13</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E45:43"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E41:43"><i><font color="Green">E76</font></i></a>, <a class="txt" href="anproj_2.html#E43:43"><i><font color="Green">E77</font></i></a>, <a class="txt" href="anproj_2.html#E42"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<a NAME="E46:43"/><b>then </b><i><font color="Green">E79</font></i>: 
 <a href="anproj_1.html#R1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E44:43"><i><font color="Green">E78</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>29</sub></font>, <font color="Maroon">c<sub>30</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E48:43"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green">E67</font></i></a>, <a class="txt" href="anproj_2.html#E33:43"><i><font color="Green">E70</font></i></a>, <a class="txt" href="anproj_2.html#E35:43"><i><font color="Green">E72</font></i></a>, <a class="ref" href="anproj_1.html#T11">ANPROJ_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>31</sub></font>, <font color="Maroon">c<sub>32</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E50:43"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<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></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="txt" href="anproj_2.html#E30:43"><i><font color="Green">E67</font></i></a>, <a class="txt" href="anproj_2.html#E34:43"><i><font color="Green">E71</font></i></a>, <a class="txt" href="anproj_2.html#E36:43"><i><font color="Green">E73</font></i></a>, <a class="ref" href="anproj_1.html#T11">ANPROJ_1:11</a></i>;<br/>
<a NAME="E51:43"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>10</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>30</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="p2">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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>30</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E48:43"><i><font color="Green">E80</font></i></a>, <a class="txt" href="anproj_2.html#E31"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<a NAME="E52:43"/>
<font color="Maroon">c<sub>10</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>32</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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>32</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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E50:43"><i><font color="Green">E81</font></i></a>, <a class="txt" href="anproj_2.html#E32"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<a NAME="E53:43"/><b>then </b><i><font color="Green">E83</font></i>: 
( <font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font> &amp; <font color="Maroon">c<sub>29</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>32</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>30</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>31</sub></font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E51:43"><i><font color="Green">E82</font></i></a>, <a class="ref" href="anproj_1.html#T13">ANPROJ_1:13</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>33</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E54:43"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_7"/>
not <font color="Maroon">c<sub>30</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>then </b><font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="anproj_2.html#E48:43"><i><font color="Green">E80</font></i></a>, <a class="txt" href="anproj_2.html#E53:43"><i><font color="Green">E83</font></i></a>, <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</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="ref" href="rlvect_1.html#T23">RLVECT_1:23</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#T10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:43_7"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="ref" href="rlvect_1.html#D13">RLVECT_1:def 13</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E55:43"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>30</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E51:43"><i><font color="Green">E82</font></i></a>, <a class="txt" href="anproj_2.html#E53:43"><i><font color="Green">E83</font></i></a>, <a class="txt" href="anproj_2.html#E42"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<a NAME="E56:43"/><b>then </b><i><font color="Green">E85</font></i>: 
 <a href="anproj_1.html#R1">are_Prop</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E54:43"><i><font color="Green">E84</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<a NAME="E57:43"/><i><font color="Green">E86</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E11:43"><i><font color="Green">E53</font></i></a>, <a class="txt" href="anproj_2.html#E17:43"><i><font color="Green">E56</font></i></a>, <a class="txt" href="anproj_2.html#E25:43"><i><font color="Green">E63</font></i></a>, <a class="txt" href="anproj_2.html#E34"><i><font color="Green">Lemma34</font></i></a></i>;<br/>
<a NAME="E58:43"/><i><font color="Green">E87</font></i>: 
not  <a href="anproj_1.html#R1">are_Prop</a> <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E13:43"><i><font color="Green">E54</font></i></a>, <a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E27:43"><i><font color="Green">E64</font></i></a>, <a class="txt" href="anproj_2.html#E34"><i><font color="Green">Lemma34</font></i></a></i>;<br/>
<a NAME="E59:43"/><i><font color="Green">E88</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <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>,<font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font> <a href="anproj_1.html#R2">are_LinDep</a>  )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E4:43"><i><font color="Green">E47</font></i></a>, <a class="txt" href="anproj_2.html#E18:43"><i><font color="Green">E57</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>34</sub></font>, <font color="Maroon">c<sub>35</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E61:43"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<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></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E30:43"><i><font color="Green">E67</font></i></a>, <a class="txt" href="anproj_2.html#E57:43"><i><font color="Green">E86</font></i></a>, <a class="ref" href="anproj_1.html#T11">ANPROJ_1:11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>36</sub></font>, <font color="Maroon">c<sub>37</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E63:43"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>36</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<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></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>37</sub></font> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="anproj_2.html#E30:43"><i><font color="Green">E67</font></i></a>, <a class="txt" href="anproj_2.html#E58:43"><i><font color="Green">E87</font></i></a>, <a class="txt" href="anproj_2.html#E59:43"><i><font color="Green">E88</font></i></a>, <a class="ref" href="anproj_1.html#T11">ANPROJ_1:11</a></i>;<br/>
<a NAME="E64:43"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>35</sub></font></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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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>35</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E61:43"><i><font color="Green">E89</font></i></a>, <a class="txt" href="anproj_2.html#E35"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<a NAME="E65:43"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>36</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>37</sub></font></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="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>36</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></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>37</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E63:43"><i><font color="Green">E90</font></i></a>, <a class="txt" href="anproj_2.html#E35"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<a NAME="E66:43"/><b>then </b>
( <font color="Maroon">c<sub>34</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>36</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>37</sub></font> &amp; <font color="Maroon">c<sub>34</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>36</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>35</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>37</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font> )
 
<b>by </b><i><a class="txt" href="anproj_2.html#E6:43"><i><font color="Green">E49</font></i></a>, <a class="txt" href="anproj_2.html#E64:43"><i><font color="Green">E91</font></i></a>, <a class="ref" href="anproj_1.html#T13">ANPROJ_1:13</a></i>;<br/>
<a NAME="E67:43"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>35</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E19:43"><i><font color="Green">E58</font></i></a>, <a class="txt" href="anproj_2.html#E37"><i><font color="Green">Lemma37</font></i></a></i>;<br/>
<a NAME="E68:43"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></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"><span class="p5">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></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="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="real_1.html#K4">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E19:43"><i><font color="Green">E58</font></i></a>, <a class="txt" href="anproj_2.html#E64:43"><i><font color="Green">E91</font></i></a>, <a class="txt" href="anproj_2.html#E39"><i><font color="Green">Lemma39</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>38</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>;<br/>
<a NAME="E69:43"/>
<font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_8"/>
not <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>then </b><font color="Maroon">c<sub>9</sub></font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="anproj_2.html#E61:43"><i><font color="Green">E89</font></i></a>, <a class="txt" href="anproj_2.html#E67:43"><i><font color="Green">E92</font></i></a>, <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</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="ref" href="rlvect_1.html#T23">RLVECT_1:23</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#T10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E3:43_8"/>
contradiction
 <b>by </b><i><a class="txt" href="anproj_2.html#E5:43"><i><font color="Green">E48</font></i></a>, <a class="ref" href="rlvect_1.html#D13">RLVECT_1:def 13</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E70:43"/><b>then </b>
<font color="Maroon">c<sub>35</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"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="anproj_2.html#E15:43"><i><font color="Green">E55</font></i></a>, <a class="txt" href="anproj_2.html#E19:43"><i><font color="Green">E58</font></i></a>, <a class="txt" href="anproj_2.html#E38"><i><font color="Green">Lemma38</font></i></a></i>;<br/>
<a NAME="E71:43"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="anproj_1.html#R1">are_Prop</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"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E68:43"><i><font color="Green">E93</font></i></a>, <a class="txt" href="anproj_2.html#E29"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>39</sub></font> = <font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>40</sub></font> =  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>;<br/>
<a NAME="E72:43"/>
( <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>16</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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>16</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</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#K3">+</a> <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"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="hidden.html#R1">=</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="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <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"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> )
 
;<br/>
<a NAME="E73:43"/><b>then </b>
<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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K5">-</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>16</sub></font></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="p5">(<span class="default"><span class="p0">(<span class="default"><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="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p5">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></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"><a href="real_1.html#K1">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p4">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="anproj_2.html#E41"><i><font color="Green">Lemma41</font></i></a></i>;<br/>
<a NAME="E74:43"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>16</sub></font></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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="real_1.html#K4">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<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></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="anproj_1.html#R2">are_LinDep</a> 
 
<b>by </b><i><a class="ref" href="anproj_1.html#D3">ANPROJ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E75:43"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="anproj_1.html#R2">are_LinDep</a> 
 <b>by </b><i><a class="txt" href="anproj_2.html#E46:43"><i><font color="Green">E79</font></i></a>, <a class="txt" href="anproj_2.html#E56:43"><i><font color="Green">E85</font></i></a>, <a class="txt" href="anproj_2.html#E71:43"><i><font color="Green">E94</font></i></a>, <a class="ref" href="anproj_1.html#T9">ANPROJ_1:9</a></i>;<br/>


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