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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> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E12</font></i>: 
 <a href="analmetr.html#R1" target="_self">Gen</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

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



<b>consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:12"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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="analmetr.html#E1:12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:12"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</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="analmetr.html#E1:12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="analmetr.html#D1" target="_self">Def1</a></i>;<br/>
<i><font color="Green">E15</font></i>:  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</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"><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#T10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default">0 <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>
;<br/>
<a NAME="E7:12"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K4">*</a> 0</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="real_1.html#K4">*</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon">c<sub>4</sub></font>, <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E3:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="analmetr.html#E6:12"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self">Def2</a></i>;<br/>

<a NAME="E9:12"/>
<span class="p1">(<span class="default">0 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default">0 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<b>hence </b><a NAME="E10:12"/>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="analmetr.html#E5:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="analmetr.html#E6:12"><i><font color="Green">E15</font></i></a>, <a class="ref" href="analmetr.html#D2" target="_self">Def2</a></i>;<br/>


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