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<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> 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="E1:31"/><i><font color="Green">E29</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:31"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E3:31"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E4:31"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R1">//</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:31"><i><font color="Green">E30</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E5:31"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analoaf.html#R1">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E2:31"><i><font color="Green">E30</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E6:31"/><b>then </b><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="geomtrap.html#R1" target="_self">'||'</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="geomtrap.html#R1" target="_self">'||'</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E4:31"><i><font color="Green">E32</font></i></a>, <a class="ref" href="geomtrap.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:31"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="analoaf.html#R1">//</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E3:31"><i><font color="Green">E31</font></i></a>, <a class="txt" href="geomtrap.html#E4:31"><i><font color="Green">E32</font></i></a>, <a class="txt" href="geomtrap.html#E5:31"><i><font color="Green">E33</font></i></a>, <a class="ref" href="analoaf.html#T20">ANALOAF:20</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E8:31"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:31"><i><font color="Green">E29</font></i></a>, <a class="txt" href="geomtrap.html#E4:31"><i><font color="Green">E32</font></i></a>, <a class="txt" href="geomtrap.html#E5:31"><i><font color="Green">E33</font></i></a>, <a class="txt" href="geomtrap.html#E24"><i><font color="Green">Lemma21</font></i></a></i>;<br/>
<a NAME="E9:31"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="geomtrap.html#K1" target="_self">#</a> <font color="Maroon">c<sub>9</sub></font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="geomtrap.html#E1:31"><i><font color="Green">E29</font></i></a>, <a class="txt" href="geomtrap.html#E3:31"><i><font color="Green">E31</font></i></a>, <a class="txt" href="geomtrap.html#E6:31"><i><font color="Green">E34</font></i></a>, <a class="txt" href="geomtrap.html#E27"><i><font color="Green">Lemma24</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:31"/>
<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> <a href="geomtrap.html#R2" target="_self">are_DTr_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="geomtrap.html#E7:31"><i><font color="Green">E35</font></i></a>, <a class="ref" href="geomtrap.html#D3" target="_self">Def3</a></i>;<br/>


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