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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">p</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">r1</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/><b>let </b><font color="Maroon">r2</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K2" target="_self">AMSpace</a> <font color="Maroon">V</font>,<font color="Maroon">w</font>,<font color="Maroon">y</font></span>)</span>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:44"/><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="E2:44"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">r</font>,<font color="Maroon">r1</font>
 <b>and </b><br/><a NAME="E3:44"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">r</font>,<font color="Maroon">r2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">u</font> = <font color="Maroon">p</font>, <font color="Maroon">v</font> = <font color="Maroon">q</font>, <font color="Maroon">w1</font> = <font color="Maroon">r</font>, <font color="Maroon">v1</font> = <font color="Maroon">r1</font>, <font color="Maroon">v2</font> = <font color="Maroon">r2</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> ;<br/>
<a NAME="E5:44"/>
( <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" target="_self">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" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 
<b>by </b><i><a class="txt" href="analmetr.html#E1:44"><i><font color="Green">E38</font></i></a>, <a class="txt" href="analmetr.html#E2:44"><i><font color="Green">E39</font></i></a>, </i>;<br/>
<a NAME="E6:44"/><b>then </b>
( <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" target="_self">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" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E7:44"/><b>then </b><i><font color="Green">E51</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" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E1"><i><font color="Green">Lemma37</font></i></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"><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> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">w1</font></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/>
<a NAME="E9:44"/><b>then </b>
<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" target="_self">are_Ort_wrt</a> <font color="Maroon">w</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="txt" href="analmetr.html#E2"><i><font color="Green">Lemma40</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E10:44"/>
<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="analmetr.html#R4" target="_self">_|_</a> <font color="Maroon">r1</font>,<font color="Maroon">r2</font>
 <b>by </b><i/>;<br/>


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