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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">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">w1</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="E1:22"/><i><font color="Green">E45</font></i>: 
 <a href="analmetr.html#R1">Gen</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">w1</font>,<font color="Maroon">v1</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">w1</font>,<font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 ;<br/>

<a NAME="E3:22"/>
( <font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>,<font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> &amp; <font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>,<font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 
<b>by </b><i>, <a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/>
<a NAME="E4:22"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font>,<span class="p1">(<span class="default"><font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font></span>)</span> <a href="analmetr.html#R2">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="analmetr.html#T14">ANALMETR:14</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font></span>)</span> = 
<font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">w1</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T41">RLVECT_1:41</a></i>
<br/>.= 
<font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">w1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">w1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T43">RLVECT_1:43</a></i>
<br/>.= 
<font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<font color="Maroon">v2</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">v1</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T26">RLVECT_1:26</a></i>
;<br/>
<b>hence </b><a NAME="E6:22"/>
<font color="Maroon">u</font>,<font color="Maroon">v</font>,<font color="Maroon">v1</font>,<font color="Maroon">v2</font> <a href="analmetr.html#R3">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="analmetr.html#D3">ANALMETR:def 3</a></i>;<br/>


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