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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">w</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v2</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green">E38</font></i>: 
 <a href="analmetr.html#R1" target="_self">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E3:17"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">u</font>,<font color="Maroon">v2</font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 ;<br/>

<b>consider </b><font color="Maroon">a1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a2</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:17"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> &amp; <font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:17"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">b2</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">a1'</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a2'</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">c1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">c2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E8:17"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a1'</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2'</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> &amp; <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c1</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">c2</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span> )
 <b>and </b><br/><a NAME="E9:17"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2'</font> <a href="real_1.html#K4">*</a> <font color="Maroon">c2</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, </i>;<br/>
<a NAME="E10:17"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1'</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2'</font> )
 
<b>by </b><i>, , , </i>;<br/>
<a NAME="E11:17"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">c1</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K3">+</a> <font color="Maroon">c2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E12:17"/>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">c1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K3">+</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E13:17"/>
<font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i>, , </i>;<br/>

<a NAME="E14:17"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">c1</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">c2</font></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E15:17"/>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">c1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">b2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">c2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E16:17"/>
<font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v2</font> <a href="analmetr.html#R2" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i>, , </i>;<br/>


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